text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
{"url":"http:\/\/www.chegg.com\/homework-help\/questions-and-answers\/a-normal-population-has-a-mean-of-60-and-a-standard-deviation-of-12-you-select-a-random-sa-q3273098","text":"## Stats\n\nA normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Use Appendix A.1 for the z-values. Compute the probability the sample mean is: (Round your answers to 4 decimal places.) a. Greater than 63. Probability b. Less than 56. Probability c. Between 56 and 63. Probability","date":"2013-05-18 20:47:00","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\": 0.8858281373977661, \"perplexity\": 396.35638965194397}, \"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-2013-20\/segments\/1368696382851\/warc\/CC-MAIN-20130516092622-00014-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/ggobi.github.io\/ggally\/index.html","text":"ggplot2 is a plotting system for R based on the grammar of graphics. GGally extends ggplot2 by adding several functions to reduce the complexity of combining geoms with transformed data. Some of these functions include a pairwise plot matrix, a scatterplot plot matrix, a parallel coordinates plot, a survival plot, and several functions to plot networks.\n\n## Installation\n\nTo install this package from GitHub or CRAN, do the following from the R console:\n\n# Github\nlibrary(devtools)\ninstall_github(\"ggobi\/ggally\")\n# CRAN\ninstall.packages(\"GGally\")","date":"2021-04-14 16:00:20","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\": 0.2924966514110565, \"perplexity\": 5331.482984362457}, \"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-2021-17\/segments\/1618038077843.17\/warc\/CC-MAIN-20210414155517-20210414185517-00183.warc.gz\"}"} | null | null |
package org.plantuml.idea.grammar;
import com.intellij.lexer.Lexer;
import com.intellij.psi.impl.cache.impl.BaseFilterLexer;
import com.intellij.psi.impl.cache.impl.OccurrenceConsumer;
import com.intellij.psi.search.UsageSearchContext;
import com.intellij.psi.tree.IElementType;
import org.plantuml.idea.lang.PlantUmlParserDefinition;
final class PumlFilterLexer extends BaseFilterLexer {
PumlFilterLexer(final Lexer originalLexer, final OccurrenceConsumer table) {
super(originalLexer, table);
}
@Override
public void advance() {
final IElementType tokenType = getDelegate().getTokenType();
if (PlantUmlParserDefinition.COMMENTS.contains(tokenType)) {
scanWordsInToken(UsageSearchContext.IN_COMMENTS | UsageSearchContext.IN_PLAIN_TEXT, false, false);
advanceTodoItemCountsInToken();
} else {
scanWordsInToken(UsageSearchContext.IN_CODE | UsageSearchContext.IN_FOREIGN_LANGUAGES | UsageSearchContext.IN_PLAIN_TEXT, false, false);
}
getDelegate().advance();
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,277 |
Clearwater Beach Condos for Sale – Find your own personal paradise.
How to buy successfully in the current market.
What is your condo (or home) worth?
How to sell successfully in the current market.
List of all condo communities with info on Amenities, Fees, Pet Rules, & Rental Rules. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,148 |
La 63ª edición de la París-Roubaix tuvo lugar el 11 de abril de 1965 y fue ganada por el belga Rik Van Looy, consiguiendo así su tercera victoria en esta prueba.
Clasificación final
Enlaces externos
Clasificación completa
Resultados a les-sports.info
Resultados a cyclebase.nl
París-Roubaix
Ciclismo en 1965
Francia en 1965 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,485 |
\section{Acknowledgments}
\label{sec:acknowledgments}
The first two authors were supported by the National Science Foundation under
Grant Nos. 1703835 and 1521539. The second author was supported by the National Science Foundation under Grant No. 2104535.
\section{Conclusion} \label{conclusion}
We started with the aim of designing a dependent calculus that can analyze dependencies in general, and run-time and compile-time irrelevance in particular. Towards this end, we designed a simple dependency calculus, SDC, and then extended it to two dependent calculi, $\textsc{DDC}^{\top}$ and DDC. $\textsc{DDC}^{\top}$ can track run-time irrelevance while DDC can track both run-time and compile-time irrelevance along with other dependencies.
\iffalse
Our approach of using a general dependency framework to track irrelevance enables us to work with strong irrelevant $\Sigma$-types, something that prior work on irrelevance found difficult to handle. This approach also benefits from the fact that soundness of irrelevance follows immediately from a general non-interference theorem. Additionally, our style of analyzing dependencies through graded typing judgments makes the proof of non-interference particularly easy.
\fi
In future, we would like to explore how irrelevance interacts with other dependencies. We also want to explore whether our systems can be integrated with existing graded type systems, especially quantitative type systems. Yet another interesting direction for research is that how they compare with graded effect systems.
Our work lies in the intersection of dependency analysis and irrelevance tracking in dependent type systems. Both these areas have rich literature of their own. We hope that the connections established in this paper will be mutually beneficial and help in the future exploration of dependencies and irrelevance in dependent type systems.
\iffalse
Graded type theories have been used for many purposes: from tracking
variable usage to enforcing security constraints. We can
divide such theories into two broad categories: quantitative or coeffect-based and
qualitative or effect-based. The former are good at counting while the latter
are good at dependency tracking. Our Dependent Dependency Calculus (DDC)
is a member of the latter category and is a general-purpose system for
analysing dependency in dependent type theories.
In this paper, we use DDC for one specific application: tracking
compile-time and run-time irrelevance. The generality of the language
gives us a novel way of handling irrelevance. A benefit of using this approach is
that DDC can analyse strong irrelevant $\Sigma$-types, a feature that often
causes difficulty in the setting of compile-time irrelevance. The modular
structure of DDC also gives us the flexibility to choose between several
points in the design space (\DDC$^{\top}${}, EPTS-like, or full \textsc{DDC}{}) trading
type-system complexity for expressiveness.
Another novelty of our calculus lies in its graded design, which enables
syntactic reasoning about security properties. We provide a straightforward
syntactic proof of non-interference. The syntactic methods are valuable
because sometimes semantic models are hard to construct. For example, it is
difficult to give a denotational model for a Curry-style dependently typed language tracking irrelevance,
or a type-in-type type system tracking irrelevance.
There are many topics worth exploring in future, some of which have already
been mentioned: combining irrelevance and information flow in dependent
systems, combining quantitative type systems with our calculus, finding the
relation between our calculus and graded effect systems in dependent type
theories, etc. Because our work is based on a general approach to
dependency tracking, and is connected to existing work such as DCC, we believe
that it is an appropriate framework for future exploration of dependencies in
dependent type systems.
\fi
\section{A Dependent Dependency Analyzing Calculus} \label{DDCT}
\iffalse
\subsection{Lattice Structure for Tracking Irrelevance}
We want our dependent type system to track dependency, especially irrelevance. We saw two kinds of irrelevance: compile-time irrelevance and run-time irrelevance. Which lattice structure is best suited to represent both these kinds of irrelevance? Here, we investigate this question.
Let us start with just two levels: $\{\top,\bot\}$ with $ { \color{black}{\bot} } \leq { \color{black}{\top} } $ and see what we can do with them. The idea is to use $\top$ for a compile-time observer and $\bot$ for a runtime observer. Can we, then, distinguish the erasable parts of programs (to be marked by $\top$) from the parts necessary at run time (to be marked by $\bot$)? Let's look at an example: consider the polymorphic identity function and its type.
\begin{lstlisting}
id : Π x:$^{ { \color{black}{\top} } }$Type. x -> x
id = $\lambda^{ { \color{black}{\top} } }$x. λy. y
\end{lstlisting}
In this section, we treat runtime observer to be the default. If the label on a variable or term is left off, it is understood to be $ { \color{black}{\bot} } $. Coming back to the example, the first parameter of the identity
function is only needed during type checking; it can be erased before execution. The $ { \color{black}{\top} } $ on the parameter signifies this fact. While we apply this function, as in
\lstinline{id Bool$^{ { \color{black}{\top} } }$ True}, we can erase the first argument,
\lstinline{Bool}, but the second one, \lstinline{True}, is
needed at runtime.
Note that though the argument \cd{x} is
irrelevant in the body of the function (i.e. in \lstinline{λy.y}), it is relevant in
the body of the type (i.e. in \cd{x -> x}). Can a variable be irrelevant in a term but be relevant in its type? This question has no one answer. Some authors \citep{pfenning:2001,abel}
do not allow this form of irrelevant quantification while others
\citep{mishra,barras:icc-star} do. We discuss this design choice further in
Section~\ref{sec:irrelevance-related}.
The above example may lead one to think that though irrelevant variables may appear in types, they never appear in terms. But that is not the full story: irrelevant variables can appear in terms, as long as they do in irrelevant contexts. Let us understand this through an example.
Consider the \cd{Vec} datatype for length-indexed
vectors and an associated mapping operation, as they might look in a core
language inspired by GHC~\cite{systemfc,weirich:systemd}. Below, the syntax
notates that the \cd{Vec} datatype has two parameters, \cd{n} and \cd{a}, that
appear in the types of the data constructors. Such parameters are relevant to
the type \cd{Vec}, but irrelevant to the constructors \cd{Nil} and
\cd{Cons}. (In the types of the data constructors, the equality constraints
\cd{(n ~ Zero)} and \cd{(n ~ Succ m)} force \cd{n} to be equal to the length
of the vector. We won't show these constraints explicitly in the rest of this
paper, but they are explicit in GHC's internal language.)
\begin{lstlisting}
Vec : Nat -> Type -> Type
Vec = λ n a.
Nil : (n ~ Zero) => Vec n a
Cons : Π m:$^{ { \color{black}{\top} } }$ Nat. (n ~ Succ m) => a -> Vec m a -> Vec n a
\end{lstlisting}
Since \cd{m} is irrelevant to \cd{cons}, we label \cd{m} with $ { \color{black}{\top} } $. We would like this value to
be erasable and not stored with the vector at run time.
Now consider a mapping function \cd{vmap} on vectors which maps a given function over a given vector. The length of the vector and the type arguments are not really necessary while running \cd{vmap}: they are all erasable. So we assign them $ { \color{black}{\top} } $.
\noindent
\begin{minipage}{\linewidth}
\begin{lstlisting}
vmap : Πn:$^{ { \color{black}{\top} } }$Nat.Πa b:$^{ { \color{black}{\top} } }$Type. (a -> b) -> Vec n a -> Vec n b
vmap = λ$^{ { \color{black}{\top} } }$ n a b. λ f xs.
case xs of
Nil -> Nil
Cons m$^{ { \color{black}{\top} } }$ x xs -> Cons m$^{ { \color{black}{\top} } }$ (f x) (vmap m$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ b$^{ { \color{black}{\top} } }$ f xs)
\end{lstlisting}
\end{minipage}
Note that all of the variables \cd{m}, \cd{a} and \cd{b} appear in the definition of \cd{vmap}, but since they appear in $ { \color{black}{\top} } $ contexts, we are fine. So a two element lattice gives us the ability to distinguish between erasable and relevant terms.
We can use this analysis to produce leaner code and run programs faster. But there are at least two other things we can do with irrelevance analysis: type-check faster and track erasable but compile-time relevant programs, as in \cd{Complex} example. We shall consider faster type-checking later; for now, let's look at erasable but compile-time relevant programs.
Till now, we were just differentiating between erasable and relevant programs and a two level lattice served us good. With erasable but compile-time relevant programs joining the game, we would need another level. Let's call the level $ { \color{black}{C} } $; it's between $ { \color{black}{\top} } $ and $ { \color{black}{\bot} } $. We now consider an example that puts our lattice to test: the \cd{filter} function
for length-indexed vectors.
The \cd{filter} function filters a vector based on a predicate. The
difficulty with this function is that we cannot statically predict the length
of the vector that will be returned, so we package the result in a
$\Sigma$-type.
\noindent
\begin{minipage}{\linewidth}
\begin{lstlisting}
filter : Πn:$^{ { \color{black}{\top} } }$Nat.Πa:$^{ { \color{black}{\top} } }$Type. (a -> Bool) -> Vec n a -> $\Sigma$m:$^{ { \color{black}{C} } }$Nat. Vec m a
filter = λ$^{ { \color{black}{\top} } }$ n a. λ f vec.
case vec of
Nil -> (Zero$^{ { \color{black}{C} } }$, Nil)
Cons n1$^{ { \color{black}{\top} } }$ x xs
| f x -> let ys : $\Sigma$m:$^{ { \color{black}{C} } }$Nat. Vec m a
ys = filter n1$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ f xs
in ((Succ ($\pi_1$ ys))$^{ { \color{black}{C} } }$, Cons ($\pi_1$ ys)$^{ { \color{black}{\top} } }$ x ($\pi_2$ ys))
| _ -> filter n1$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ f xs
\end{lstlisting}
\end{minipage}
Since \cd{n} and \cd{a} are not required at runtime, we assign them $ { \color{black}{\top} } $. But what do we assign to \cd{m}? We would like to also erase this component
at runtime; but, it is required for type-checking, if we want to get the output vector using projection. So we don't want to use $ { \color{black}{\bot} } $, but it cannot not be assigned $ { \color{black}{\top} } $ either; therefore we assign it $ { \color{black}{C} } $.
\citet{eisenberg:existentials} observe that in Haskell it is important to use
projection functions to access the components of the $\Sigma$ type that
results from the recursive call (as in \cd{$\pi_1$ ys}, \cd{$\pi_2$ ys}) to ensure that this function is not excessively strict. If \cd{filter} had been written with pattern matching to eliminate
the $\Sigma$-type instead, it would then have to filter the entire vector
before returning the first successful value.
So with three levels, we can track run-time relevant, run-time irrelevant but compile-time relevant and compile-time irrelevant programs. But can we also make type checking faster? Short answer: yes. How? Our story shall follow this question as we go along. Let us now move on to the language basics.
\subsection{The Basics}
\fi
\begin{figure}
\centering
\[
\begin{array}{lcll}
\ottnt{a}, \ottnt{A}, \ottnt{b}, \ottnt{B}
& ::= & \ottnt{s} \mid \ottkw{unit} \mid \ottkw{Unit} & \mbox{\it sorts and unit }\\
& \mid & \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} \mid \ottmv{x} \mid
\lambda \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{a} \mid \ottnt{a} \; \ottnt{b} ^{ \ell } & \mbox{\it dependent functions} \\
& \mid & \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \ottnt{A} . \ottnt{B} \mid
( \ottnt{a} ^{ \ell }, \ottnt{b} ) \mid \ottkw{let} \; ( \ottmv{x} ^{ \ell } , \ottmv{y} )\ =\ \ottnt{a} \ \ottkw{in} \ \ottnt{b} & \mbox{\it dependent pairs} \\
& \mid & \ottnt{A} + \ottnt{B} \mid \ottkw{inj}_1\, \ottnt{a} \mid \ottkw{inj}_2\, \ottnt{a} \mid
\ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} & \mbox{\it disjoint unions} \\
\\
\end{array}
\]
\caption{Dependent Dependency Calculus Grammar (Types and Terms)}
\label{fig:ddc-grammar}
\end{figure}
Here and in the next section, we present dependently-typed languages, with dependency analysis in the style of SDC.
The first extension, called $\textsc{DDC}^{\top}$ is a straightforward integration of labels and dependent types. This
system subsumes SDC, and so can be used for the same purposes. Here, we show how it can be used to analyze \emph{run-time irrelevance}.
Then, in Section \ref{sec:compile-time-irrelevance}, we generalize this system to \textsc{DDC}{}, which allows definitional equality to ignore unnecessary sub-terms, thus also enabling \emph{compile-time irrelevance}. We present the system in this way both to simplify the
presentation and to show that $\textsc{DDC}^{\top}$ is an intermediate point in the design space.
Both $\textsc{DDC}^{\top}$ and \textsc{DDC}{} are pure type systems~\citep{pts}.
They share the same syntax, shown in Figure~\ref{fig:ddc-grammar}, combining
terms and types into the same grammar.
They are parameterized by a set of sorts $\ottnt{s}$, a set of axioms $ \mathcal{A}( \ottnt{s_{{\mathrm{1}}}} , \ottnt{s_{{\mathrm{2}}}} ) $ which is a binary relation on sorts, and a set of rules $ \mathcal{R}( \ottnt{s_{{\mathrm{1}}}} , \ottnt{s_{{\mathrm{2}}}} , \ottnt{s_{{\mathrm{3}}}} ) $ which is a ternary relation on sorts. For simplicity, we assume, without loss of generality, that for every sort $\ottnt{s_{{\mathrm{1}}}}$, there is some sort $\ottnt{s_{{\mathrm{2}}}}$, such that $ \mathcal{A}( \ottnt{s_{{\mathrm{1}}}} , \ottnt{s_{{\mathrm{2}}}} ) $.\footnote{This assumption does not lead to any loss in generality because given a pure type system $(\mathit{S'},\mathit{A'},\mathit{R'})$ that does not meet the above condition, we can provide another pure type system $(\mathit{S''}, \mathit{A''}, \mathit{R''})$, where $\mathit{S''} = S' \cup \{ \pentagon \}$ (given $\pentagon \notin S'$) and $\mathit{A''} = A' \cup \{ (s, \pentagon) | s \in S'' \}$ and $\mathit{R''} = \mathit{R'}$, such that there exists a straightforward bisimulation between the two systems.}
We annotate several syntactic forms with grades for dependency analysis.
The dependent function type, written $ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} $, includes the grade of the
argument to a function having this type. Similarly, the dependent pair type, written
$ \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \ottnt{A} . \ottnt{B} $, includes the grade of the first component of a pair having this type. \footnote{We use standard abbreviations when $\ottmv{x}$ is not free in $\ottnt{B}$: we write $ {}^{ \ell } \! \ottnt{A} \to \ottnt{B} $
for $ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} $ and $ {}^{ \ell } \! \ottnt{A} \times \ottnt{B} $ for $ \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \ottnt{A} . \ottnt{B} $.} We can interpret these types as a fusion of the usual, ungraded dependent types and the graded modality $ T^{ \ell }\; \ottnt{A} $ we saw earlier. In other words, $ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} $ acts like the type
$ \Pi \ottmv{y} \!:\! \ottsym{(} T^{ \ell }\; \ottnt{A} \ottsym{)} . \ottkw{bind} \, \ottmv{x} = \ottmv{y} \, \ottkw{in} \, \ottnt{B} $ and $ \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \ottnt{A} . \ottnt{B} $ acts like the type
$ \Sigma \ottmv{y} \!:\! \ottsym{(} T^{ \ell }\; \ottnt{A} \ottsym{)} . \ottkw{bind} \, \ottmv{x} = \ottmv{y} \, \ottkw{in} \, \ottnt{B} $. Because of this fusion, we do not need
to add the graded modality type as a separate form---we can define $ T^{ \ell }\; \ottnt{A} $ as $ \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \ottnt{A} . \ottkw{Unit} $. Using $ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} $ instead of $ \Pi \ottmv{y} \!:\! \ottsym{(} T^{ \ell }\; \ottnt{A} \ottsym{)} . \ottkw{bind} \, \ottmv{x} = \ottmv{y} \, \ottkw{in} \, \ottnt{B} $ has an advantage:
the former allows $\ottmv{x}$ to be held at differing grades while type checking $\ottnt{B}$ and the body of a function having this $\Pi$-type while the latter requires $\ottmv{x}$ to be held at the same grade in both the cases. We utilize this flexibility in Section \ref{sec:compile-time-irrelevance}.
\subsection{$\textsc{DDC}^{\top}$ : $\Pi$-types}
\label{sec:erasure}
\begin{figure}
\begin{drulepar*}[]{$ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $}{Typing}
\drule{DCT-Var}
\drule{DCT-Type}
\drule[width=2.5in]{DCT-Pi}
\drule{DCT-Abs}
\drule{DCT-App}
\drule{DCT-Conv}
\end{drulepar*}
\caption{$\textsc{DDC}^{\top}$ type system (core rules)}
\label{fig:sdc-typing}
\end{figure}
The core typing rules for $\textsc{DDC}^{\top}$ appear in
Figure~\ref{fig:sdc-typing}. As in the simple type system, the variables in
the context are labelled and the judgement itself includes a label $\ell$.
\Rref{DCT-Var} is similar to its counterpart in the simply-typed language: the variable being observed must be graded less than or equal to the level of the observer.
\Rref{DCT-Pi} propagates the level of the expression to the sub-terms of the
$\Pi$-type. Note that this type is annotated with an arbitrary label
$\ell_{{\mathrm{0}}}$: the purpose of this label $\ell_{{\mathrm{0}}}$ is to denote the level at
which the argument to a function having this type may be used.
In \rref{DCT-Abs}, the parameter of the function is introduced into the context
at level $ \ell_{{\mathrm{0}}} \vee \ell $ (akin to \rref{SDC-Bind}). In \rref{DCT-App}, the
argument to the function is checked at level $ \ell_{{\mathrm{0}}} \vee \ell $ (akin to \rref{SDC-Return}).
Note that the $\Pi$-type is checked at $ { \color{black}{\top} } $ in \rref{DCT-Abs}. In
$\textsc{DDC}^{\top}$, level $ { \color{black}{\top} } $ corresponds to `compile time' observers
and motivates the superscript $ { \color{black}{\top} } $ in the language name.
\Rref{DCT-Conv} converts the type of an expression to an equivalent type. The
judgment $ | \Omega | \vdash \ottnt{A} \equiv_{ { \color{black}{\top} } } \ottnt{B} $ is a label-indexed definitional
equality relation instantiated to $ { \color{black}{\top} } $. This relation is the closure of the indexed indistinguishability relation (Section \ref{sec:geq}) under small-step call-by-name evaluation. When instantiated to $ { \color{black}{\top} } $, the relation degenerates to $\beta$-equivalence. So the \rref{DCT-Conv} is essentially casting a term to a $\beta$-equivalent type; however, in the next section, we utilize the flexibility of label-indexing to cast a term to a type that may not be $\beta$-equivalent. Also, note that the equality relation itself is untyped. As such, we need the third premise to guarantee that the new type is well-formed.
\iffalse
It is important that this include $\ell$, consider this example, based
on length-indexed vectors. Here, we would
like to avoid storing the natural number index in the data structure. Therefore, in the type
of \cd{Cons}, we would like to mark this argument with $ { \color{black}{\top} } $, so that it is erasable.
But what does that mean for the application \cd{Succ n}, that appears in the type of \cd{Cons}?
The argument to Succ must not be erasable so, it must be $ { \color{black}{\bot} } $ (recall that we elide all $ { \color{black}{\bot} } $ annotations). If we had to type check the application \cd{Vec (Succ n)} at level $ { \color{black}{\bot} } $, we would not be able to use \cd{n}. This type system checks all types at $ { \color{black}{\top} } $,
so the join ensures that we can accesss \cd{n} in this context.
\begin{lstlisting}
Succ : Nat -> Nat -- increments the natural number
Vec : Nat -> Type -> Type -- length indexed vector
Cons : Π n:$^{ { \color{black}{\top} } }$Nat. Π a:$^{ { \color{black}{\top} } }$ Type. a -> Vec n a -> Vec (Succ n) a
\end{lstlisting}
The fact that this join incorporates $\ell_{{\mathrm{0}}}$ is not so important in this
context (we could use the modality explicitly) but will be more important in
the full version of DDC.
This shows up in conversion
(\rref{SDT-Conv}) in two ways: the level of the definitional equality relation
is $ { \color{black}{\top} } $ (this version does not support compile-time irrelevance) and the
new type of the expression $\ottnt{B}$, is checked at level $ { \color{black}{\top} } $. (Because
definitional equality is untyped, the type system must separately verify that
$\ottnt{B}$ is a well-formed type.)
As long as all runtime levels are \textbf{strictly less than} $ { \color{black}{\top} } $, this
system distinguishes between code needed for execution and code needed only
for type checking. In other words, by tracking this dependency, we support
{\emph{erasure}} for compile-time data. The compiler is free to trivialize any
data marked by $ { \color{black}{\top} } $ during compilation.
What this means in \rref{SDT-Pi}, is that it doesn't really matter (in this
first version) whether the bound variable is introduced at level $\ell$, as
opposed to $\ell_{{\mathrm{0}}}$ or $ \ell_{{\mathrm{0}}} \vee \ell $ as in \rref{SDT-Abs}). The level
of this variable will almost always be $ { \color{black}{\top} } $ and may be used relevantly in
the body of the type (which is also checked at the same level).
\fi
\subsection{$\textsc{DDC}^{\top}$ : $\Sigma$-types}
The language $\textsc{DDC}^{\top}$ includes $\Sigma$ types, as specified by the rules below.
\[ \drule[width=3in]{DCT-WSigma} \ \drule[width=3in]{DCT-WPair} \]
Like $\Pi$-types, $\Sigma$-types include a grade that is not related to how the bound variable is used in the body of the type. The grade indicates the level at which the first component of a pair having the $\Sigma$-type may be used.
In \rref{DCT-WPair}, we check the first component $\ottnt{a}$ of the
pair at a level raised by $\ell_{{\mathrm{0}}}$, the level annotating the
type, akin to \rref{SDC-Return}. The second component $\ottnt{b}$ is checked at the current level.
\[ \drule[width=5in]{DCT-LetPair} \]
The \rref{DCT-LetPair} eliminates pairs using dependently-typed
pattern matching. The pattern variables $\ottmv{x}$ and $\ottmv{y}$
are introduced into the context while checking the body $\ottnt{c}$. Akin to \rref{SDC-Bind},
the level of the first pattern variable, $\ottmv{x}$, is raised by $\ell_{{\mathrm{0}}}$.
The result type $\ottnt{C}$ is refined by the
pattern match, informing the type system that the pattern $ ( \ottmv{x} ^{ \ell_{{\mathrm{0}}} }, \ottmv{y} ) $ is equal
to the scrutinee $\ottnt{a}$.
Because of this refinement in the result type, we can define
the projection operations through pattern matching. In particular, the first projection, $ \pi_1^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} := \ottkw{let} \; ( \ottmv{x} ^{ \ell_{{\mathrm{0}}} } , \ottmv{y} )\ =\ \ottnt{a} \ \ottkw{in} \ \ottmv{x} $ while the second projection, $ \pi_2^{ \ell_{{\mathrm{0}}} } \ottnt{a} := \ottkw{let} \; ( \ottmv{x} ^{ \ell_{{\mathrm{0}}} } , \ottmv{y} )\ =\ \ottnt{a} \ \ottkw{in} \ \ottmv{y} $. These projections can be type checked
according to the following derived rules:
\[ \drule[width=3in]{DCT-ProjOne} \qquad \drule{DCT-ProjTwo} \]
Note that the derived \rref{DCT-Proj1} limits access to the first
component through the premise $\ell_{{\mathrm{0}}} \leq \ell$, akin to \rref{Sealing-Unseal}. This condition makes sense
because it aligns the observability of the first
component of the pair with the label on the $\Sigma$-type.
\subsection{Embedding SDC into $\textsc{DDC}^{\top}$}
Here, we show how to embed SDC into $\textsc{DDC}^{\top}$.
We define a translation function, $\overline{\overline{\cdot}}$, that takes the types and terms in SDC to terms in $\textsc{DDC}^{\top}$. For types, the translation is defined as: $ \overline{\overline{ \ottnt{A} \to \ottnt{B} } } := {}^{ { \color{black}{\bot} } } \! \overline{\overline{ \ottnt{A} } } \to \overline{\overline{ \ottnt{B} } } $, $ \overline{\overline{ \ottnt{A} \times \ottnt{B} } } := {}^{ { \color{black}{\bot} } } \! \overline{\overline{ \ottnt{A} } } \times \overline{\overline{ \ottnt{B} } } $ and $ \overline{\overline{ T^{ \ell }\; \ottnt{A} } } := \Sigma \ottmv{x} \!\!:^{ \ell }\!\! \overline{\overline{ \ottnt{A} } } . \ottkw{Unit} $. For terms, the translation is straightforward except for the following cases: $ \overline{\overline{ \eta^{ \ell }\; \ottnt{a} } } := ( \overline{\overline{ \ottnt{a} } } ^{ \ell }, \ottkw{unit} ) $ and $ \overline{\overline{ \ottkw{bind} ^{ \ell } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} } } := \ottkw{let} \; ( \ottmv{x} ^{ \ell } , \ottmv{y} )\ =\ \overline{\overline{ \ottnt{a} } } \ \ottkw{in} \ \overline{\overline{ \ottnt{b} } } $, where $\ottmv{y}$ is a fresh variable.
By lifting the translation to contexts, we show that translation preserves typing.
\begin{theorem}[Trans. Preserves Typing]
If $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then $ \overline{\overline{ \Omega } } \vdash \overline{\overline{ \ottnt{a} } } :^{ \ell } \overline{\overline{ \ottnt{A} } } $.
\end{theorem}
Next, assuming a standard call-by-name small-step semantics for both the languages, we can provide a bisimulation.
\begin{theorem}[Forward Simulation]
If $ \ottnt{a} \leadsto \ottnt{a'} $ in SDC, then $ \overline{\overline{ \ottnt{a} } } \leadsto \overline{\overline{ \ottnt{a'} } } $ in $\textsc{DDC}^{\top}$.
\end{theorem}
\begin{theorem}[Backward Simulation]
For any term $a$ in SDC, if $ \overline{\overline{ \ottnt{a} } } \leadsto \ottnt{b} $ in $\textsc{DDC}^{\top}$, then there exists $\ottnt{a'}$ in SDC such that $\ottnt{b} \ottsym{=} \overline{\overline{ \ottnt{a'} } } $ and $ \ottnt{a} \leadsto \ottnt{a'} $.
\end{theorem}
Hence, SDC can be embedded into $\textsc{DDC}^{\top}$, preserving meaning. As such, $\textsc{DDC}^{\top}$ can analyze dependencies in general.
\subsection{Run-time Irrelevance}
Next, we show how to track run-time irrelevance using $\textsc{DDC}^{\top}$. We use the two element lattice $\{ { \color{black}{\bot} } , { \color{black}{\top} } \}$ with $ { \color{black}{\bot} } < { \color{black}{\top} } $ such that $ { \color{black}{\bot} } $ and $ { \color{black}{\top} } $ correspond to run-time relevant and run-time irrelevant terms respectively. So, we need to erase terms marked with $ { \color{black}{\top} } $. However, we first define a general indexed erasure function, $\lfloor \cdot \rfloor_{\ell}$, on $\textsc{DDC}^{\top}$ terms, that erases everything an $\ell$-user should not be able to see. The function is defined by straightforward recursion in most cases. For example, \\ $ \lfloor \ottmv{x} \rfloor_ \ell := \ottmv{x}$ and $ \lfloor \Pi \ottmv{x} \!:^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} . \ottnt{B} \rfloor_ \ell := \Pi \ottmv{x} \!:^{ \ell_{{\mathrm{0}}} }\! \lfloor \ottnt{A} \rfloor_ \ell . \lfloor \ottnt{B} \rfloor_ \ell $ and $ \lfloor \lambda^{ \ell_{{\mathrm{0}}} } \ottmv{x} . \ottnt{b} \rfloor_ \ell := \lambda^{ \ell_{{\mathrm{0}}} } \ottmv{x} . \lfloor \ottnt{b} \rfloor_ \ell $. \\ The interesting cases are: \\ $\qquad \lfloor \ottnt{b} \; \ottnt{a} ^{ \ell_{{\mathrm{0}}} } \rfloor_ \ell := \ottsym{(} \lfloor \ottnt{b} \rfloor_ \ell \; \lfloor \ottnt{a} \rfloor_ \ell ^{ \ell_{{\mathrm{0}}} } \ottsym{)}$ if $\ell_{{\mathrm{0}}} \leq \ell$ and $\ottsym{(} \lfloor \ottnt{b} \rfloor_ \ell \; \ottkw{unit} ^{ \ell_{{\mathrm{0}}} } \ottsym{)}$ otherwise, \\ $\qquad \lfloor ( \ottnt{a} ^{ \ell_{{\mathrm{0}}} }, \ottnt{b} ) \rfloor_ \ell := ( \lfloor \ottnt{a} \rfloor_ \ell ^{ \ell_{{\mathrm{0}}} }, \lfloor \ottnt{b} \rfloor_ \ell ) $ if $\ell_{{\mathrm{0}}} \leq \ell$ and $ ( \ottkw{unit} ^{ \ell_{{\mathrm{0}}} }, \lfloor \ottnt{b} \rfloor_ \ell ) $ otherwise. \\ They are so defined because if $ \neg \ottsym{(} \ell_{{\mathrm{0}}} \leq \ell \ottsym{)} $, an $\ell$-user should not be able to see $\ottnt{a}$, so we replace it with $\ottkw{unit}$.
This erasure function is closely related to the indistinguishability relation, we saw in Section \ref{sec:geq}, extended to a dependent setting. (This definition appears in \auxref{dep-indist}.) The erasure function maps the equivalence classes formed by the indistinguishability relation to their respective canonical elements. We have verified the following lemmas using the Coq proof assistant. Footnotes mark the file and lemma name of the corresponding mechanized results.
\begin{lemma}[Canonical Element\footnote{\texttt{erasure.v:Canonical\_element}.}]
If $ \Phi \vdash \ottnt{a_{{\mathrm{1}}}} \sim_{ \ell } \ottnt{a_{{\mathrm{2}}}} $, then $ \lfloor \ottnt{a_{{\mathrm{1}}}} \rfloor_ \ell = \lfloor \ottnt{a_{{\mathrm{2}}}} \rfloor_ \ell $.
\end{lemma}
Further, a well-graded term and its erasure are indistinguishable.
\begin{lemma}[Erasure Indistinguishability\footnote{\texttt{erasure.v:Erasure\_Indistinguishability}}] \label{erasure_ind}
If $ \Phi \vdash \ottnt{a} : \ell $, then $ \Phi \vdash \ottnt{a} \sim_{ \ell } \lfloor \ottnt{a} \rfloor_ \ell $.
\end{lemma}
Next, we can show that erased terms simulate the reduction behavior of their unerased counterparts.
\begin{lemma}[Erasure Simulation\footnote{\texttt{erasure.v:Step\_erasure,Value\_erasure}}]
If $ \Phi \vdash \ottnt{a} : \ell $ and $ \ottnt{a} \leadsto \ottnt{b} $, then $ \lfloor \ottnt{a} \rfloor_ \ell \leadsto \lfloor \ottnt{b} \rfloor_ \ell $. Otherwise, if $\ottnt{a}$ is a value, then so is $ \lfloor \ottnt{a} \rfloor_ \ell $.
\end{lemma}
This lemma follows from Lemma \ref{erasure_ind} and the non-interference theorem (Theorem \ref{lemma:GEq_respects_Step}). Therefore, it is safe to erase, before run time, all sub-terms marked with $ { \color{black}{\top} } $.
This shows that we can correctly analyze run-time irrelevance using $\textsc{DDC}^{\top}$. However, supporting compile-time irrelevance requires some changes to the system. We take them up in the next section.
\section{\textsc{DDC}{}: Run-time and Compile-time Irrelevance}
\label{sec:compile-time-irrelevance}
\subsection{Towards Compile-time Irrelevance}
Recall that terms which may be safely ignored while checking for type equality are said to be compile-time irrelevant. In $\textsc{DDC}^{\top}$, the conversion \rref{DCT-Conv} checks for type equality at $ { \color{black}{\top} } $.
\[ \drule[width=3in]{DCT-Conv} \]
The equality judgment used in this rule $ \Phi \vdash \ottnt{a} \equiv_{ { \color{black}{\top} } } \ottnt{b} $ is an instantiation of the general judgment $ \Phi \vdash \ottnt{a} \equiv_{ \ell } \ottnt{b} $, which is the closure of the indistinguishability relation at $\ell$ under $\beta$-equivalence. When $\ell$ is $ { \color{black}{\top} } $, indistinguishability is just identity. As such, the equality relation at $ { \color{black}{\top} } $ degenerates to standard $\beta$-equivalence. So, \rref{DCT-Conv} does not ignore any part of the terms when checking for type equality.
To support compile-time irrelevance then, we need the conversion rule to use equality at some grade strictly less than $ { \color{black}{\top} } $ so that $ { \color{black}{\top} } $-marked terms may be ignored. For the irrelevance lattice $\mathcal{L}_I$, the level $ { \color{black}{C} } $ can be used for this purpose. For any other lattice $\mathcal{L}$, we can add two new elements, $ { \color{black}{C} } $ and $ { \color{black}{\top} } $, above every other existing element, such that $\mathcal{L} < { \color{black}{C} } < { \color{black}{\top} } $, and thereafter use level $ { \color{black}{C} } $ for this purpose. So, for any lattice, we can support compile-time irrelevance by equating types at $ { \color{black}{C} } $.
Referring back to the examples in Section \ref{comp-irr}, note that for \cd{phantom : Nat$\!^{ { \color{black}{\top} } }$ -> Type}, we have \cd{phantom 0$^{ { \color{black}{\top} } }$ $\equiv_{ { \color{black}{C} } }$ phantom 1$^{ { \color{black}{\top} } }$}. With this equality, we can type-check \cd{idp : phantom 0$^{ { \color{black}{\top} } }$ -> phantom 1$^{ { \color{black}{\top} } }$ = λ x. x}, even without knowing the definition of \cd{phantom}.
Now, observe that in \rref{DCT-Conv}, the new type $\ottnt{B}$ is also checked at $ { \color{black}{\top} } $. If we want to check for type equality at $ { \color{black}{C} } $, we need to make sure that the types themselves are checked at $ { \color{black}{C} } $. However, checking types at $ { \color{black}{C} } $ would rule out variables marked at $ { \color{black}{\top} } $ from appearing in them. This would restrict us from expressing many examples, including the polymorphic identity function.
To move out of this impasse, we take inspiration from EPTS~\citep{mishra,mishra-linger:phd}. The key idea, adapted from \citet{mishra}, is to use a judgment of the form $ { \color{black}{C} } \wedge \Omega \vdash \ottnt{a} :^{ { \color{black}{C} } } \ottnt{A} $ instead of a judgment of the form $ \Omega \vdash \ottnt{a} :^{ { \color{black}{\top} } } \ottnt{A} $. The operation $ { \color{black}{C} } \wedge \Omega$ takes the point-wise meet of the labels in the context $\Omega$ with $ { \color{black}{C} } $, essentially reducing any label marked as $ { \color{black}{\top} } $ to $ { \color{black}{C} } $, making it available for use in a $ { \color{black}{C} } $-expression. This operation, called \emph{truncation}, makes $ { \color{black}{\top} } $ marked variables available at $ { \color{black}{C} } $. Other systems also use similar mechanisms for tracking irrelevance --- for example, we can see a relation between this idea and analogous ones in \cite{pfenning:2001} and \cite{abel}. In these systems, ``context resurrection'' operation makes proof variables and irrelevant variables in the context available for use, similar to
how $C \wedge \Omega$ makes $\top$-marked variables in the context available for use.
\subsection{DDC: Basics}
Next, we design a general dependency analyzing calculus, \textsc{DDC}{},
that takes advantage of compile-time irrelevance in its type system.
\textsc{DDC}{} is a generalization of $\textsc{DDC}^{\top}$ and
$\text{EPTS}^{\bullet}$ \citep{mishra}. When $ { \color{black}{C} } $ equals $ { \color{black}{\top} } $, DDC
degenerates to $\textsc{DDC}^{\top}$, that does not use compile-time
irrelevance. When $ { \color{black}{C} } $ equals $ { \color{black}{\bot} } $,
DDC degenerates to $\text{EPTS}^{\bullet}$, that identifies compile-time and run-time
irrelevance. A crucial distinction between $\text{EPTS}^{\bullet}$ and DDC is that
while the former is tied to a two element lattice, the latter can use any lattice.
Thus, not only can \textsc{DDC}{} distinguish between run-time and compile-time irrelevance,
but also it can simultaneously track other dependencies.
\iffalse
We now extend our dependently typed language to also support compile-time
irrelevance: we want to ignore compile-time irrelevant terms when checking for type equality in the language. Coarsening the equality used
in the conversion rule can have significant practical benefits during type
checking, as we saw in \cd{phantom} example.
Of course, we should not overcoarsen our definition of equivalence. Going to an extreme
we could equate all types, but such a type system would not
be sound. Therefore, we need to make sure that the type system correctly identifies which parts of an expression are \emph{safe}
to ignore during type checking.
As discussed earlier, we need to work with a lattice with at least three elements:
$ { \color{black}{\bot} } < ... < { \color{black}{C} } < { \color{black}{\top} } $. Here, the label $ { \color{black}{\bot} } $ (and any
other label less than $ { \color{black}{C} } $) marks run-time terms. $ { \color{black}{C} } $
indicates that a sub-term is erasable at run time, but relevant at compile time,
and $ { \color{black}{\top} } $ is reserved for the parts of a program that are
irrelevant in both contexts.
To see why these are different, consider both \cd{x} and \cd{y} below, which
have types that are equal to \cd{Int}. In the first example, we apply the polymorphic identity function to \cd{Int}; its first argument (\cd{Type}) is not relevant at compile
time. So it is safe to mark this argument with $ { \color{black}{\top} } $ (and allow the
compiler to ignore it when reducing this expression to $\ottkw{Int}$). In the
second example, we also compute \cd{Int} by projecting from a dependent
pair. Note that the first component of this pair must be marked as $ { \color{black}{C} } $, not
$ { \color{black}{\top} } $, because it is used to compute the type of \cd{y}.
\begin{lstlisting}
x : id Type$^{ { \color{black}{\top} } }$ Int
x = 5
y : $\pi_1$ (Int$^{ { \color{black}{C} } }$, unit)
y = 4
\end{lstlisting}
With this intuition, there are two problems that we need to solve in tracking
and using compile-time irrelevance. First, we need a version of definitional
equality for the conversion rule that ignores subterms marked as
$ { \color{black}{\top} } $. Second, we must safely employ this definition of equality in the
type system.
\subsection{Graded definitional equality}
\label{sec:defeq}
Creating a level-aware version of definitional equality is not so difficult.
Our definition of Guarded Equality, from Section~\ref{sec:geq}, is a
good inspiration.
For example, we can show that \cd{phantom a$^{ { \color{black}{\top} } }$\ $\equiv_{ { \color{black}{C} } }$ phantom b$^{ { \color{black}{\top} } }$}, as long as we know that the argument to \cd{phantom} is irrelevant at compile time.
These rules are similar in spirit to the extended
equality relation (Section \ref{sec:geq}), used to sometimes ignore the contents of $ \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} $. Furthermore, there is an analogue to guarded equality definable for \textsc{DDC}{} and that relation is contained in definitional equality. (The key difference between the two is that definitional equality
also contains $\beta$-reductions, so equates many more terms.)
\begin{lemma}[Contains guarded equivalence\footnote{\texttt{defeq.v:CEq\_DefEq}}]
If $ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $ then $ \Phi \vdash \ottnt{a} \equiv_{ \ell } \ottnt{b} $
\end{lemma}
Like guarded equality, definitional equality includes a label-context $\Phi$ that
specifies the labels of all variables that occur in the visible parts of the
terms. This label context tells us what sort of substitutions are valid for
this equality. If the variable is visible, then it must be substituted by
related terms at the same level of equivalence. Otherwise, if the variable
is not visible, then any pair of terms can be used for
substitution.
\begin{lemma}[Relevant substitution\footnote{\texttt{defeq.v:DefEq\_equality\_substitution}}]
If $ \Phi , \ottmv{x} \! : k \vdash \ottnt{b_{{\mathrm{1}}}} \equiv_{ \ell } \ottnt{b_{{\mathrm{2}}}} $ and $k \leq \ell$
and $ \Phi \vdash \ottnt{a_{{\mathrm{1}}}} \equiv_{ \ell } \ottnt{a_{{\mathrm{2}}}} $, then
$ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \equiv_{ \ell } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $.
\end{lemma}
\begin{lemma}[Irrelevant substitution\footnote{\texttt{defeq.v:DefEq\_substitution\_irrel2}}]
If $ \Phi , \ottmv{x} \! : k \vdash \ottnt{b_{{\mathrm{1}}}} \equiv_{ \ell } \ottnt{b_{{\mathrm{2}}}} $ and $ \neg \ottsym{(} k \leq \ell \ottsym{)} $, then
$ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \equiv_{ \ell } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $.
\end{lemma}
\subsection{When compile-time isn't $ { \color{black}{\top} } $}
Guarded equality in hand, we now must allow the language to make use of it.
This is more challenging than it first seems. We cannot just replace the
definitional equality in \rref{SDT-Conv} with $ | \Omega | \vdash \ottnt{A} \equiv_{ { \color{black}{C} } } \ottnt{B} $ without
making other changes to the type system.
For example, when types are compared for equality, the type system must ensure that there are no dependencies on $ { \color{black}{\top} } $-marked subterms . Can this condition fail to hold?
In $\textsc{DDC}^{\top}$, types are checked at $ { \color{black}{\top} } $. So the first
projection from a pair of type $ \Sigma \ottmv{x} \!\!:^{ { \color{black}{\top} } }\!\! \ottnt{A} . \ottnt{B} $ can be used in
types. However, in this language, that would be unsound, as it would allow the
following program to type check.
This example would unfortunately type check because we have an equality between
the two pairs---both the first components are marked as compile-time irrelevant, so
definitional equality at level $ { \color{black}{C} } $ is free to ignore them.
\begin{center}
\begin{lstlisting}
$\vdash$ $\pi_1$ (Int$^{ { \color{black}{\top} } }$, unit) $\equiv_{ { \color{black}{C} } }$ $\pi_1$ (Bool$^{ { \color{black}{\top} } }$, unit)
\end{lstlisting}
\end{center}
So we cannot check types at $ { \color{black}{\top} } $ and then check type equality at $ { \color{black}{C} } $. If we want to
use $ { \color{black}{C} } $ for checking type equality, we must check all types at level
$ { \color{black}{C} } $ as well. But this modification poses its own
difficulties---sometimes variables marked as $ { \color{black}{\top} } $ are valid in type
expressions, and we don't want to rule them out. For example, when type checking
the polymorphic identity function, the type system must show that the
inner function is well-formed, i.e. $ \ottmv{x} \! :^{ { \color{black}{\top} } }\! \ottnt{s} \vdash \lambda \ottmv{y} . \ottmv{y} :^{ { \color{black}{\bot} } } \ottmv{x} \to \ottmv{x} $. But then, we cannot show $ \ottmv{x} \! :^{ { \color{black}{\top} } }\! \ottnt{s} \vdash \ottmv{x} \to \ottmv{x} :^{ { \color{black}{C} } } \ottnt{s} $. A problem!
To move out of this impasse, we look to EPTS~\cite{mishra,mishra-linger:phd}.
We cannot use EPTS directly, as it is hard-wired to only two levels and we want to support
at least three. But ETPS does provide a clue about how to safely work with
multiple levels of dependency.
The key idea, adapted from \citet{mishra}, is to use a
judgement of the form $ { \color{black}{C} } \wedge \Omega \vdash \ottnt{a} :^{ { \color{black}{C} } } \ottnt{A} $ instead of a judgement
of the form $ \Omega \vdash \ottnt{a} :^{ { \color{black}{\top} } } \ottnt{A} $, whenever the type system needs to check types at
`compile time'. The operation $ { \color{black}{C} } \wedge \Omega$ takes the point-wise meet of the
labels in the context $\Omega$ with $ { \color{black}{C} } $, essentially reducing any label marked as $ { \color{black}{\top} } $ to
$ { \color{black}{C} } $ and making it available for use in a $ { \color{black}{C} } $-expression. We call this operation \emph{truncation} and it is related to the \textsc{Reset} rule from EPTS. Due to the use of truncation, even though the judgment is checked at $ { \color{black}{C} } $, all $ { \color{black}{\top} } $ marked variables are still
available.
\textsc{DDC}{} is a generalization of EPTS. Under the assumption that
$ { \color{black}{C} } = { \color{black}{\bot} } $, i.e. where the lattice has only two levels, it
degenerates to a form equivalent to EPTS. However, in that setting, the type
system cannot distinguish between run-time and compile-time irrelevance.
\fi
\begin{figure}[h]
\drules[T]
{$ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $}{\textsc{DDC}{} core typing rules}{Var,Type,Pi,AbsC,AppC,ConvC}
\begin{drulepar*}[]{$ \Omega \Vdash \ottnt{a} :^{ \ell } \ottnt{A} $}{Truncate at $ { \color{black}{\top} } $}
\drule{CT-Leq}
\drule[width=3in]{CT-Top}
\end{drulepar*}
\caption{Dependent type system with compile-time irrelevance (core rules)}
\label{fig:ddc}
\label{fig:truncation}
\end{figure}
The core typing rules of DDC appear in Figure~\ref{fig:ddc}. Compared to
$\textsc{DDC}^{\top}$, this type system maintains the invariant that for any
$ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $, we have $\ell \leq { \color{black}{C} } $. To ensure that this is
the case, \rref{T-Type} and \rref{T-Var} include this precondition. This restriction means that we cannot
really derive any term at $ { \color{black}{\top} } $ in DDC. We can get around this restriction by deriving $ { \color{black}{C} } \wedge \Omega \vdash \ottnt{a} :^{ { \color{black}{C} } } \ottnt{A} $ in place of $ \Omega \vdash \ottnt{a} :^{ { \color{black}{\top} } } \ottnt{A} $.
Wherever $\textsc{DDC}^{\top}$ uses $ { \color{black}{\top} } $ as the observer level on a typing judgment, DDC uses truncation and level $ { \color{black}{C} } $ instead. If $\textsc{DDC}^{\top}$ uses some grade other than $ { \color{black}{\top} } $ as the observer level, DDC leaves the derivation as such. So a $\textsc{DDC}^{\top}$ judgment $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ is replaced with a \emph{truncated-at-top judgment}, $ \Omega \Vdash \ottnt{a} :^{ \ell } \ottnt{A} $ which can be read as: if $\ell = { \color{black}{\top} } $, use the truncated version $ { \color{black}{C} } \wedge \Omega \vdash \ottnt{a} :^{ { \color{black}{C} } } \ottnt{A} $; otherwise use the normal version $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $, as we see in Figure \ref{fig:truncation}. In the typing rules, uses of this new judgment have been highlighted in gray to emphasize the modification with respect to \DDC$^{\top}${}.
\subsection{$\Pi$-types}
\Rref{T-Pi} is unchanged. The lambda \rref{T-AbsC} now checks the type at $ { \color{black}{C} } $ after truncating the variables in the context to $ { \color{black}{C} } $. The application \rref{T-AppC} checks the argument using the truncated-at-top judgment. Note that if $\ell_{{\mathrm{0}}} = { \color{black}{\top} } $, the term $\ottnt{a}$ can depend upon any variable in $\Omega$. Such a dependence is allowed since information can always flow from relevant to irrelevant contexts.
To see how irrelevance works in this system, let's consider the
definition and use of the polymorphic identity function.
\begin{lstlisting}
id : Π x:$^{ { \color{black}{\top} } }$Type. x -> x
id = λ$^{ { \color{black}{\top} } }$x. λ y. y
\end{lstlisting}
In \DDC$^{\top}${}, the type \lstinline{Π x:$^{ { \color{black}{\top} } }$Type. x -> x} is checked at $ { \color{black}{\top} } $.
However, here it must be checked at level $ { \color{black}{C} } $, which requires the premise \hspace{2pt}\lstinline{x:$^{ { \color{black}{C} } }$Type $\vdash$ x -> x :$^{ { \color{black}{C} } }$ Type}. Note that if we used the same grade for the bound variable $\ottmv{x}$ in \rref{T-Pi} and \rref{T-AbsC}, we would have been in trouble because variable \cd{x} is compile-time relevant while we check the type, even though it is irrelevant in the term.\footnote{This is why we fuse the graded modality with the dependent types. If they
were separated, and we had to bind here, it would be a problem since a dependent function and its type have different restrictions vis-\`{a}-vis the bound variable. }
Finally, observe that \rref{T-ConvC} uses the definitional equality at
$ { \color{black}{C} } $ instead of $ { \color{black}{\top} } $ and that the new type is checked after truncation.
\subsection{$\Sigma$-types}
\[ \drule{T-WPairC} \qquad \drule{T-LetPairC} \]
We also need to modify the typing rules for $\Sigma$ types accordingly. In particular, when we create a pair, we check the first component using the truncated-at-top judgment. This is akin to how we check the argument in \rref{T-AppC}. Note that if $\ell_{{\mathrm{0}}} = { \color{black}{\top} } $, the first component $\ottnt{a}$ is compile-time irrelevant. In such a situation, we cannot type-check the second projection since it requires the first projection, as we see in the derived\footnote{\texttt{strong\_exists.v:T\_wproj1,T\_wproj2}} projection rules below. So pairs having type $ \Sigma \ottmv{x} \!\!:^{ { \color{black}{\top} } }\!\! \ottnt{A} . \ottnt{B} $ can only be eliminated via pattern matching if $B$ mentions $x$. However, pairs having type $ \Sigma \ottmv{x} \!\!:^{ { \color{black}{C} } }\!\! \ottnt{A} . \ottnt{B} $ can be eliminated via projections.
For example, for an output of the \cd{filter} function, \cd{ys : $\Sigma$m:$\!^{ { \color{black}{C} } }$Nat. Vec m Bool}, we have \cd{$\pi_1$ ys} $:^{ { \color{black}{C} } }$ \cd{Nat} and \cd{$\pi_2$ ys : Vec ($\pi_1$ ys) Bool}. Note that (\cd{$\pi_1$ ys}) is visible at $ { \color{black}{C} } $ and is used in the type of (\cd{$\pi_2$ ys}). We can substitute (\cd{$\pi_1$ ys}) for \cd{m} in (\cd{Vec m Bool}) because \cd{m :$^{ { \color{black}{C} } }$Nat $\ \vdash$ Vec m Bool $\ :^{ { \color{black}{C} } }$ Type}. However, (\cd{$\pi_1$ ys}) cannot be used at $ { \color{black}{\bot} } $, so it will be erasable then.
\[ \drule[width=3in]{T-ProjOne} \qquad \drule[width=3in]{T-ProjTwoC} \]
\subsection{Non-interference}
\label{sec:ddc-geq}
DDC satisfies an analogous noninterference theorem to the one presented for
SDC, using suitable definitions for the \emph{grading} relation, written $ \Phi \vdash \ottnt{a} : \ell $, and \emph{indexed
indistiguishability}, written $ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \sim_{ \ell } \ottnt{b_{{\mathrm{2}}}} $. The complete definition of these judgements appears in the extended version of this paper~\citep{DDC-arXiv}.
\begin{lemma}[Typing implies grading\footnote{\texttt{typing.v:Typing\_Grade}}] \label{DDC:typing_grading}
If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ then $ | \Omega | \vdash \ottnt{a} : \ell $.
\end{lemma}
\begin{lemma}[Equivalence\footnote{\texttt{geq.v:GEq\_refl,GEq\_symmetry,GEq\_trans}}] \label{DDC:ind_equivalence}
Indexed indistinguishability at $\ell$ is an equivalence relation on well-graded terms at $\ell$.
\end{lemma}
\begin{lemma}[Indistinguishability under substitution\footnote{\texttt{subst.v:CEq\_GEq\_equality\_substitution}}]
If $ \Phi , \ottmv{x} \! : \ell \vdash \ottnt{b_{{\mathrm{1}}}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} $ and $ \Phi \vdash^{ \ell }_{ k } \ottnt{a_{{\mathrm{1}}}} \sim \ottnt{a_{{\mathrm{2}}}} $ then $ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $.
\end{lemma}
\begin{theorem}[Non-interference for DDC\footnote{\texttt{geq.v:CEq\_GEq\_respects\_Step}}]
\label{lemma:DDC:GEq_respects_Step}
If $ \Phi \vdash \ottnt{a_{{\mathrm{1}}}} \sim_{ k } \ottnt{a'_{{\mathrm{1}}}} $ and $ \ottnt{a_{{\mathrm{1}}}} \leadsto \ottnt{a_{{\mathrm{2}}}} $ then there exists some $\ottnt{a'_{{\mathrm{2}}}}$ such that $ \ottnt{a'_{{\mathrm{1}}}} \leadsto \ottnt{a'_{{\mathrm{2}}}} $ and $ \Phi \vdash \ottnt{a_{{\mathrm{2}}}} \sim_{ k } \ottnt{a'_{{\mathrm{2}}}} $.
\end{theorem}
\subsection{Consistency of Equality}
\label{consisteq}
The equality relation of DDC incorporates compile-time irrelevance. To show that the
type system is sound, we need to show that the equality relation is consistent. Consistency of definitional equality means that there is no derivation that equates two
types having different head forms. For example, it should not equate $ \mathbf{Nat} $ with $\ottkw{Unit}$.
Note that if $ { \color{black}{\top} } $ inputs can interfere with $ { \color{black}{C} } $ outputs, the equality relation cannot
be consistent. To see why, let $ \ottmv{x} \! :^{ { \color{black}{\top} } }\! \ottnt{A} \vdash \, \ottnt{b} \, :^{ { \color{black}{C} } } \, \ottkw{Bool} $ and for $\ottnt{a_{{\mathrm{1}}}} , \ottnt{a_{{\mathrm{2}}}} : A$, let
the terms $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ and $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ reduce to $\ottkw{True}$ and $\ottkw{False}$
respectively. Now, $ \ottsym{(} \lambda^{ { \color{black}{\top} } } \ottmv{x} . \ottkw{if} \, \ottnt{b} \, \ottkw{then} \, \mathbf{Nat} \, \ottkw{else} \, \ottkw{Unit} \ottsym{)} \; \ottnt{a_{{\mathrm{1}}}} ^{ { \color{black}{\top} } } \equiv_{ { \color{black}{C} } } \ottsym{(} \lambda^{ { \color{black}{\top} } } \ottmv{x} . \ottkw{if} \, \ottnt{b} \, \ottkw{then} \, \mathbf{Nat} \, \ottkw{else} \, \ottkw{Unit} \ottsym{)} \; \ottnt{a_{{\mathrm{2}}}} ^{ { \color{black}{\top} } } $. But then, by $\beta$-equivalence $ \mathbf{Nat} \equiv_{ { \color{black}{C} } } \ottkw{Unit} $.
To prove consistency, we construct a standard parallel
reduction relation and show that this relation is confluent. Thereafter, we prove
that if two terms are definitionally equal at $\ell$, then they are joinable at $\ell$, meaning they reduce, through parallel reduction, to two terms that are indistinguishable at $\ell$. Next, we show that joinability at $\ell$ implies consistency. Therefore, we conclude that for any $\ell$, the equality relation at $\ell$ is consistent. This implies that the equality relation at $ { \color{black}{C} } $, that ignores sub-terms marked with $ { \color{black}{\top} } $, is sound. Hence, DDC tracks compile-time irrelevance correctly. Note that DDC can track run-time irrelevance the same way as $\textsc{DDC}^{ { \color{black}{\top} } }$.
We formally state consistency in terms of \emph{head forms}, i.e. syntactic
forms that correspond to types such as sorts $\ottnt{s}$, $\ottkw{Unit}$, $ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} $, etc.
\begin{theorem}[Consistency\footnote{\texttt{consist.v:DefEq\_Consistent}}]
If $ \Phi \vdash \ottnt{a} \equiv_{ \ell } \ottnt{b} $, and $\ottnt{a}$ and $\ottnt{b}$ both are head forms, then they have the same head form.
\end{theorem}
\subsection{Soundness theorem}
DDC is type sound and we have checked this and other results using the
Coq proof assistant. Below, we give an overview of the important lemmas in this
development.
The properties below are stated for \textsc{DDC}{}, but they also apply to $\textsc{DDC}^{\top}$ since \textsc{DDC}{} degenerates to \DDC$^{\top}${} whenever $ { \color{black}{C} } = { \color{black}{\top} } $.
First, we list the properties related to grading that hold for all judgments:
indexed indistinguishability, definitional equality, and typing. (We only state
the lemmas for typing, their counterparts are analogous.) These lemmas are similar to
their simply-typed counterparts in Section~\ref{sec:sdc-metatheory}.
\begin{lemma}[Narrowing\footnote{\texttt{narrowing.v:Typing\_narrowing}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ and $\Omega' \leq \Omega$, then $ \Omega' \vdash \ottnt{a} :^{ \ell } \ottnt{A} $
\end{lemma}
\begin{lemma}[Weakening\footnote{\texttt{weakening.v:Typing\_weakening}}]
If $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ then $ \Omega_{{\mathrm{1}}} , \Omega , \Omega_{{\mathrm{2}}} \vdash \ottnt{a} :^{ \ell } \ottnt{A} $.
\end{lemma}
\begin{lemma}[Restricted upgrading\footnote{\texttt{pumping.v:Typing\_pumping}}]
If $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash \ottnt{b} :^{ \ell } \ottnt{B} $ and $\ell_{{\mathrm{1}}} \leq \ell$ then
$ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} \vee \ell_{{\mathrm{1}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash \ottnt{b} :^{ \ell } \ottnt{B} $.
\end{lemma}
Next, we list some properties that are specific to the typing judgment. For any typing judgment in DDC,
the observer grade $\ell$ is at most $ { \color{black}{C} } $. Further, the observer grade of any judgment can be
raised up to $ { \color{black}{C} } $.
\begin{lemma}[Bounded by $ { \color{black}{C} } $\footnote{\texttt{pumping.v:Typing\_leq\_C}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ then $\ell \leq { \color{black}{C} } $.
\end{lemma}
\begin{lemma}[Subsumption\footnote{\texttt{typing.v:Typing\_subsumption}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ and $\ell \leq k$ and $k \leq { \color{black}{C} } $ then $ \Omega \vdash \ottnt{a} :^{ k } \ottnt{A} $
\end{lemma}
\iffalse
As before, the proof of the subsumption lemma requires pumping in order to
raise the level of variables up to the level of the term.
Through narrowing and subsumption, we can transform a well-typed expression at any grade
to be suitable to be used in at `compile time'.
\begin{corollary}[Lift\footnote{\texttt{typing.v:Typing\_lift}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ then $ \Omega \Vdash \ottnt{a} :^{ { \color{black}{\top} } } \ottnt{A} $.
\end{corollary}
\fi
Note that we don't require contexts to be well-formed in the typing judgment; we add context
well-formedness constraints, as required, to our lemmas. The following lemmas are true for well-formed contexts. A context $\Omega$ is well-formed, expressed as $\vdash \Omega$, iff for any assumption
$\ottmv{x}:^\ell\ottnt{A}$ in $\Omega$, we have $ \Omega' \Vdash \ottnt{A} :^{ { \color{black}{\top} } } \ottnt{s} $, where
$\Omega'$ is the prefix of $\Omega$ that appears before the assumption.
\begin{lemma}[Substitution\footnote{\texttt{typing.v:Typing\_substitution\_CTyping}}]
If $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash \ottnt{b} :^{ \ell } \ottnt{B} $ and $\vdash \Omega_{{\mathrm{1}}}$ and $ \Omega_{{\mathrm{1}}} \Vdash \ottnt{a} :^{ \ell_{{\mathrm{0}}} } \ottnt{A} $
then $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} \vdash \ottnt{b} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} :^{ \ell } \ottnt{B} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} $
\end{lemma}
Next, if a term is well-typed in our system, the type itself is also well-typed.
\begin{lemma}[Regularity\footnote{\texttt{typing.v:Typing\_regularity}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ and $\vdash \Omega$ then $ \Omega \Vdash \ottnt{A} :^{ { \color{black}{\top} } } \ottnt{s} $.
\end{lemma}
\noindent Finally, we have the two main lemmas proving type soundness.
\begin{lemma}[Preservation\footnote{\texttt{typing.v:Typing\_preservation}}]
If $ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ and $\vdash \Omega$ and $ \ottnt{a} \leadsto \ottnt{a'} $, then $ \Omega \vdash \ottnt{a'} :^{ \ell } \ottnt{A} $.
\end{lemma}
\begin{lemma}[Progress\footnote{\texttt{progress.v:Typing\_progress}}]
If $ \varnothing \vdash \ottnt{a} :^{ \ell } \ottnt{A} $ then either $\ottnt{a}$ is a value or there exists some
$\ottnt{a'}$ such that $ \ottnt{a} \leadsto \ottnt{a'} $.
\end{lemma}
\iffalse
The proof of the progress lemma requires showing that definitional equality is
consistent. Consistency of definitional equality means that there is no derivation that equates two
types having different head forms. We prove this property by constructing a parallel
reduction relation and showing that this relation is confluent. We show
that if two terms are definitionally equal, then they reduce, through parallel
reduction, to two terms that are related by the guarded equality relation. The
proof of consistency holds regardless of the level used for definitional equality.
\fi
Hence, DDC is type sound. We have seen earlier that it tracks run-time and compile-time irrelevance correctly.
DDC is parameterized by a generic pure type system and a generic lattice. When the parameterizing pure type system is strongly normalizing, such as the Calculus of Constructions, type-checking is decidable. In the next section, we provide a demonstration.
\iffalse
\subsection{Extensions and Variations}
The current section presents \textsc{DDC} and its application to tracking run-time and
compile-time irrelevance. However, there are several variations and extensions
that we would like to consider in future work.
\paragraph{Decidable type checking}
We have presented DDC in a quasi-Curry-style manner, where the syntax of the language
lacks type annotations. Furthermore, because the language is nonterminating,
the definitional equality judgement used in conversion is undecidable.
As a result, type checking for \textsc{DDC} is undecidable.
However, it would not be difficult to modify this type system to support
decidable type checking. The missing ingredients are annotations on
$\lambda$-bound variables and explicit coercions at uses of definitional
equality, similar to the design of FC~\cite{systemfc} and
DC~\cite{weirich:systemd} languages. Additionally, the mechanisms presented
here can be used to ensure that these new components remain erasable and
irrelevant.
\paragraph{Type and dependency inference}
We make no attempt in this work to \emph{infer} dependencies; the syntax of
this language requires label annotations throughout. As a result, this type
system is appropriate for verifying the output of such an inference, perhaps
similar to those proposed by \citet{brady:inductive-types,matus}, once it has
been embedded into the syntax of the programming language.
\paragraph{Propositional guarded equality}
Because guarded equality is already a component of the design of \textsc{DDC}, it may
be possible to internalize the judgement $ \Phi \vdash \ottnt{a} \equiv_{ \ell } \ottnt{b} $ as a
proposition/type $ \ottnt{a} =_{ \ell } \ottnt{b} $. This form of propositional equality would
allow reasoning about non-interference directly inside the language,
permitting internal verification of security properties. We hope to explore
this idea in future work.
\paragraph{Roles}
In Haskell, users sometimes distinguish between nominal types and their
underlying representations (using type-indexed types) while at other times, treat them as the same type
(using zero-cost coercions). The type system feature of
\emph{roles}~\cite{breitner2016,weirich:dep-roles} determines whether
representational coercions are safe by tracking the dependencies in
parameterized types. In future work, we hope to use or adapt the general
mechanisms for dependency tracking, presented here, for implementing roles.
\fi
\iffalse
\subsection{Examples}
\paragraph{Matus}
Matus argues that C's argument should be erasable but not irrelevant.
\begin{lstlisting}
data T : Type where
C : (𝑏 : Bool) → T
data U : T → Type where
UT : U (C True)
UF : U (C False)
𝑓 : U (C True) → Bool
𝑓 UT = True
\end{lstlisting}
What do we say? DDC will require C's argument to be $ { \color{black}{C} } $ or less. Whether it is erasable depends on
how it it used elsewhere in the program.
\begin{lstlisting}
C : Pi (𝑏 $:^{ { \color{black}{C} } }$ Bool) → T
data U : T → Type where
UT : U (C True$^{ { \color{black}{C} } $})
UF : U (C False$^{ { \color{black}{C} } $)
𝑓 : U (C True$^{ { \color{black}{C} } $) → Bool
𝑓 UT = True
\end{lstlisting}
\paragraph{Scherer and Abel}
This is example 2.8 from Abel and Scherer and requires $\eta$-equivalence in
definitional equality. It observes that with an untyped equality, identity
functions with different types must be equated under computational
irrelevance. But if the types are ignored by the type checker, how can
$\eta$-equality be implemented?
\begin{lstlisting}
T : Bool -> Type
T True = (Bool -> Bool)
T False = Bool
s : $\Pi$ f :$^{ { \color{black}{\top} } }$ ($\Pi$ b:Bool). (T b -> T b) -> Type
((f false (\x. x)) -> Bool) ->
((f true (\x. x)) ->
Bool
s = \ f$^{ { \color{black}{\top} } }$. \g . \a. g a
t : $\Pi$ f :$^{ { \color{black}{\top} } }$ ($\Pi$ b:Bool). (T b -> T b) -> Type
((f false (\x. x)) -> Bool) ->
((f true (\x. \y. x y)) ->
Bool
t = \ f$^{ { \color{black}{\top} } }$. \g . \a. g a
\end{lstlisting}
In checking the application \cd{g a}, Agda's type inference algorithm would ask
\paragraph{Run-tme irrelevance}
Assuming that we have extended DDC with datatype definitions and pattern
matching, we might express them with the following form, inspired by the GHC's
core language. Below, the syntax notates that the |Vec| datatype has two
parameters that are uniform over the data constructor definitions. The GADT
indices are also replaced by equality constraints on the data
constructors. (We won't show these constraints explicitly in the rest of this
section, but they are explicit in GHC's internal language.)
\begin{lstlisting}
Vec :: Nat -> Type -> Type
Vec = \ a n.
Nil : (n ~ Zero) => Vec n a
(:>) : Π n1:Nat. (n ~ Succ n1) => a -> Vec n1 a -> Vec n a
\end{lstlisting}
Elaborated, the internal language term looks something like this, where all of
the inferred type arguments have been made explicit. The \emph{cons}
constructor now binds three variables in pattern matching and must be supplied with
this length argument explicitly.
\begin{lstlisting}
vmap :: Π a: Type. Π b: Type. Π n: Nat. (a -> b) -> Vec n a -> Vec n b
vmap = \ a b n f xs .
case xs of
Nil -> Nil
(:>) n1 x xs -> (:>) n1 (f x) (vmap a b n1 f xs)
\end{lstlisting}
Now let's add labels for compile-time irrelevant ($ { \color{black}{\top} } $) and eraseable
($ { \color{black}{C} } $) parameters and arguments. (In the examples below, assume that
all unmarked parameters and arguments are marked with $ { \color{black}{R} } $ --- needed
both for runtime and for definitional equality). In this data definition, we
choose to use the label $ { \color{black}{\top} } $ \cd{n1} in the \cd{(:>)} data constructor.
In the mapping function, we can see that the type arguments |a| and |b| and
the length argument |n| can be given the highest label in the definition of
|vmap|.
\begin{lstlisting}
Vec :: Nat -> Type -> Type
Vec = \ a n.
Nil : (n ~ Zero) => Vec n a
(:>) : Π n1:$^{ { \color{black}{\top} } }$ Nat. (n ~ Succ n1) => a -> Vec n1 a -> Vec n a
vmap :: Π a:$^{ { \color{black}{\top} } }$ Type. Π b:$^{ { \color{black}{\top} } }$ Type. Π n:$^{ { \color{black}{\top} } }$ Nat. (a -> b) -> (Vec n a) -> (Vec n b)
vmap = \ a$^{ { \color{black}{\top} } }$ b$^{ { \color{black}{\top} } }$ n$^{ { \color{black}{\top} } }$ f xs .
case xs of
Nil -> Nil
(:>) n1$^{ { \color{black}{\top} } }$ x xs -> (:>) n1$^{ { \color{black}{\top} } }$ (f x) (vmap a$^{ { \color{black}{\top} } }$ b$^{ { \color{black}{\top} } }$ n1$^{ { \color{black}{\top} } }$ f xs)
\end{lstlisting}
With these annotations, that can be verified by the internal language type
system, the compiler can be sure which parts of the term may be safely erased.
\paragraph{Compile-time irrelevance}
In DDC, every subterm that is marked with runtime irrelevance is also ignored
by the compiler during equivalence checking. Compiletime is particularly
important for coercion evidence, like (n ~ Succ m) above.
\paragraph{Strong-existentials}
Eisenberg et al.~\cite{eisenberg:existentials} shows how to extend the Haskell language
with strong, inferred, existential types. In particular, they present an
extension of GHC's type inference algorithm with mechanisms to support
automatic introduction and elimination of existential types.
For example, consider the following Haskell function that selects elements from
a length-indexed vector.
\begin{lstlisting}
filter :: (a -> Bool) -> Vec n a -> exists m. Vec m a
filter _ Nil = Nil
filter p (x :> xs) | p x = x :> filter p xs
| otherwise = filter p xs
\end{lstlisting}
Because we do not know how many elements at the beginning of the vector will satisfy
the predicate, this function must existentially quantify the results.
We can elaborate this program into a dependently typed core language, as
below, where the arguments to polymorphic functions and first components of
the existential types have been made explicit. It is important that this
example uses a \emph{strong existential} so that the laziness of the original
Haskell program is preserved. Note the let expression below is a lazy let --
the recursive call does not need to be evaluated until after the \texttt{(:>)}
has been forced. If this program had used pattern matching instead, to access
the length of the list that is the result of the function call, then the
recursive call would need to be executed before the \texttt{(:>)} evaluates.
We can annotate the levels of this function using DDC and observe that the
first component of the strong existential needs to be relevant at
compiletime. If we had annotated this component with $ { \color{black}{\top} } $ instead, then
we would be unable to acces the first projection, even in subterms marked
$ { \color{black}{\top} } $.
\begin{lstlisting}
filter :: Π (n:$^{ { \color{black}{\top} } }$Nat). Π (a:$^{ { \color{black}{\top} } }$Type). (a -> Bool) -> Vec n a -> $\Sigma$ (m:$^{ { \color{black}{C} } }$Nat) . Vec m a
filter = \ n$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ f vec ->
case vec of
Nil -> (Zero$^{ { \color{black}{C} } }$, Nil)
(:>) n1$^{ { \color{black}{\top} } }$ x xs
| f x -> let ys : $\Sigma$ (m:$^{ { \color{black}{C} } }$Nat) . Vec m a
ys = filter n1$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ f xs
in ( (Succ ($\pi_1$ ys))$^{ { \color{black}{C} } }$, (:>) ($\pi_1$ ys)$^{ { \color{black}{\top} } }$ x ($\pi_2$ ys) )
| otherwise -> filter n1$^{ { \color{black}{\top} } }$ a$^{ { \color{black}{\top} } }$ f xs
\end{lstlisting}
Note also, that even though the resulting length is marked as $ { \color{black}{C} } $, it does not come from the
$ { \color{black}{\top} } $ marked argument $\ottmv{n}$.
Compare this treatment to the |dropWhile| function.
\begin{lstlisting}
dropWhile :: (a -> Bool) -> Vec n a -> exists m. Vec m a
dropWhile _ Nil = Nil
dropWhile p (x :> xs) | p x = dropWhile p xs
| otherwise = (x :> xs)
\end{lstlisting}
Then DDC will force the length parameter of this function to be compile-time relevent (but still erasable) because it is
returned in the strong existential in the last case of the expression.
\begin{lstlisting}
dropWhile :: Π (n:$^{ { \color{black}{C} } }$Nat). Π (a:$^{ { \color{black}{\top} } }$Type). (a -> Bool) -> Vec n a -> $\Sigma$ (m:$^{ { \color{black}{C} } }$Nat). Vec m a
dropWhile = \ n a f vec ->
case vec of
Nil -> (Zero$^{ { \color{black}{C} } }$ , Nil)
(:>) n1$^{ { \color{black}{\top} } }$ x xs
| f x -> dropWhile n1$^{ { \color{black}{C} } }$ a$^{ { \color{black}{\top} } }$ xs
| otherwise -> ( n$^{ { \color{black}{C} } }$, vec )
\end{lstlisting}
\fi
\section{Irrelevance and Dependent Types}
\iffalse
In this section, we briefly sketch out the background. We first motivate the generic lattice structure of dependency. Thereafter, we delve into run-time and compile-time irrelevance in dependently-typed languages.
\subsection{Lattice Structure of Dependency} \label{dependencies}
Let us consider a world of objects sharing information with one another. For any given ordered pair $(O_1,O_2)$ of objects, we may either allow or block information flow from $O_1$ to $O_2$. For example, if $O_1$ is general public and $O_2$ is secret services agent, we allow information flow from $O_1$ to $O_2$ but we block flow along the other way. Such flow constraints induce an ordering ($ \leq $) on the objects sharing information, with $O_1 \leq O_2$ meaning information can flow from $O_1$ to $O_2$.
The ordering is generally reflexive and transitive. We expect information to flow from object $O$ to itself. We also expect that, if information can flow from $O_1$ to $O_2$ and also from $O_2$ to $O_3$, then it can flow from $O_1$ to $O_3$. These properties give us a pre-order. Now, if information can flow from $O_1$ to $O_2$ and also from $O_2$ to $O_1$, it makes sense to merge the two objects together into a single level. A set of objects between which information may freely flow is called a level. With this grouping, we arrive at a partial ordering of levels, reflecting an ordering on the nature of information itself. There are many examples of partially-ordered information: a) An order with two levels: Public or low security, $ { \color{black}{L} } $ and Private or high security, $ { \color{black}{H} } $ with $ { \color{black}{L} } \leq { \color{black}{H} } $. b) An order with four levels: General Staff, Marketing Director, Sales Manager and CEO with General Staff at the Bottom and CEO at the top while Marketing Director and Sales Manager are in between and incomparable to one another.
Now, given any finite partial ordering of information, we can convert it into a unique lattice by adding the missing `joins' and `meets'. This idea of a lattice model of information flow, introduced in \citet{denning1}, has been used extensively in the design of secure information flow systems. Many programming languages \citep[][etc.]{denning2,smith-volpano,slam,binding-time} use the lattice model to statically enforce information flow constraints in programs. \citet{dcc} unified some of these languages through the Dependency Core Calculus (DCC). Over the years, DCC has served as a foundational framework for static analysis of information flow in programming languages. In this paper, we extend the Dependency Core Calculus to dependent types and use operational methods to reason about information flow properties. To the best of our knowledge, our paper is the first of its kind in this respect. Further, we use dependency to track irrelevance in dependent type systems.
\iffalse
\subsection{Modules with Projections}
Let us consider the definition of complex numbers, \verb|Complex| again. A complex number is represented as a pair of real numbers with addition and modulus functions defined on this representation. We want programs to use this definition to perform computations on complex numbers. This means that a module should hide its internal representation. In other words, such information should never flow to the world at large. Put differently, user programs should not depend on the internal representation of a module.
We see that we should not be able to run (\verb|π₁ Complex|). But we do need (\verb|π₁ Complex|) to type-check programs: \verb|ℂ (3 , 4) : π₁ Complex|. And, for this, we need to allow the typing judgement: $\emptyset \vdash$ \verb|π₁ Complex : Set|. Together, this implies that we should divide programs into ones that are executable and others that are compile-time only. For example, \verb|ℂ (3 , 4)| is an executable program whereas (\verb|π₁ Complex|) is a compile-time-only program. Programs that are compile-time-only can `see' the internal representation of modules but executable ones can not. This gives us two levels of viewing the world of programs: level $ { \color{black}{R} } $ of executable programs and level $\ottnt{C}$ of compile-time programs. Some programs at level $\ottnt{C}$ can `peek inside' modules but such programs should not pass on that information to any program at level $ { \color{black}{R} } $. In other words, we can enforce modularity by requiring that information never flows from $\ottnt{C}$ to $ { \color{black}{R} } $.
Thus, we can implement modules with projections by controlling the flow of information.
\scw{Same comment as above. Our lack of type case muddies the issue. Should we add a runtime type equality operation? Or change the example to have an erasable nat? }
\subsection{Irrelevance}
\scw{This section is unclear. I'm eot getting the distinction between runtime irrelevance (erasability) and compiletime irrelevance from your description or example. }
We can also use information flow control to track irrelevance. The key idea is that information should never flow from irrelevant variables to relevant contexts. So, we divide the world of programs into two levels: ones that are relevant and others that are not and require that information never flows from the latter to the former. Since relevant programs are executable and vice versa, we use the same level $ { \color{black}{R} } $ for relevant programs.
But irrelevant programs are different from compile-time ones. In fact, irrelevant programs are not strictly required even during compile-time. For example, \verb|duplicate m v| uses \verb|m| in an irrelevant way. This argument does not play any role in evaluation and can be erased before compile-time. We can rewrite \verb|duplicate| as:
\begin{verbatim}
duplicate : ∀ (m : Nat) → Vec Nat m → Vec Nat (m * 2) =
λ m . λ v . case v of
[] => []
| n :: ns => n :: n :: duplicate _ ns
\end{verbatim}
Note that while calling \verb|duplicate|, we leave out the irrelevant argument. Now then, \verb|duplicate m₁| and \verb|duplicate m₂| for programs \verb|m₁, m₂ : Nat| are syntactically the same (after each takes a $\beta$-step). So, we can just write \verb|duplicate _| in lieu of \verb|duplicate m₁| or \verb|duplicate m₂|. We use level $I$ to denote irrelevant programs. We ensure irrelevance by requiring that information never flows from $I$ to $ { \color{black}{R} } $.
The discussion above brings forth another important point. Note that, \verb|duplicate m₁| and \verb|duplicate m₂|, though syntactically the same, have different types, viz. \verb|Vec Nat m₁ → Vec Nat (m₁ * 2)| and \verb|Vec Nat m₂ → Vec Nat (m₂ * 2)| respectively. This means that the same term inhabits two unequal types. Thus, if we ignore irrelevant applications, our equality relation becomes heterogeneous. Generally, dependent type systems use a homogeneous equality in the Conversion rule but we use a heterogeneous relation, equating terms modulo irrelevant application. \scw{Need to introduce definitional equality much earlier in this explanation.}
The equality being discussed, \verb|duplicate m₁ = duplicate m₂|, can also be seen as non-interference in action: irrelevant arguments don't interfere in the computation of relevant results. Therefore, a function, on any two irrelevant inputs, will produce the same relevant output. In some sense, our equality relation internalizes the non-interference property.
\scw{Need to point out that even though m is irrelevant as an argument to duplicate, it is (compile-time) relevant in the Vec type.}
We see that both irrelevance and erasability can be implemented through information flow control.
\subsection{Information Flow Control}
\fi
\iffalse
While the aim of quantitative type theory is counting of resources, the aim of qualitative type theory is comparison of qualities. The question `how many' in quantitative type theory is replaced with `how much' in qualitative type theory. To answer `how many', a semiring structure is required; to answer `how much', a partial order suffices. Hence, we parametrize our qualitative type theory over an abstract partially-ordered set of qualities, with increasing order denoting higher quality.
The set is treated abstractly so that it may be interpreted according to need. Let $\Psi$ denote the set of qualities and $ \leq $ be the partial order. We may instantiate $\Psi$ to $\Psi_{RC} := \{ { \color{black}{R} } , { \color{black}{C} } \}$ with $ { \color{black}{R} } \leq { \color{black}{C} } $, where $ { \color{black}{R} } $ and $ { \color{black}{C} } $ denote run-time and compile-time views respectively. The idea behind the ordering is that any program visible at run time is also visible at compile time; but some programs, visible at compile time but not necessary from a computational perspective, may be erased and become unavailable at run time. We may also instantiate $(\Psi, \leq )$ to a security lattice with increasing order denoting higher security. For $\ell_{{\mathrm{1}}} \leq \ell_{{\mathrm{2}}}$ in such a lattice, data visible at $\ell_{{\mathrm{1}}}$ is also visible at $\ell_{{\mathrm{2}}}$ but not necessarily the other way around. For example, in a two point lattice $\Psi_{LH} := (\{ { \color{black}{H} } , { \color{black}{L} } \}, { \color{black}{L} } \leq { \color{black}{H} } )$, data visible at $ { \color{black}{L} } $ is also visible at $ { \color{black}{H} } $ but some sensitive data may only be visible at $ { \color{black}{H} } $.
With this introduction on qualities, let us look at the type system.
\fi
\subsection{Run-time and Compile-time irrelevance}
\fi
\label{sec:irrelevance}
\textit{Run-time irrelevance} (sometimes called \emph{erasure}) and
\textit{compile-time irrelevance} are two forms of \textit{dependency} analyses that
arise in dependent type theories. Tracking these dependencies helps compilers produce faster
executables and makes type checking more flexible. \citep{pfenning:2001,miquel,barras:icc-star,mishra,abel,McBride:2016,atkey,Nuyts18,matus,Moon:2021}.
\subsection{Run-time irrelevance}
Parts of a program that are not required during run time are said to be
run-time irrelevant. Our goal is to identify such parts. Let's consider some examples. We shall mark variables and arguments
with $\top$ if they can be erased prior to execution and leave them unmarked if
they should be preserved.
For example, the polymorphic identity function can be marked as:
\begin{lstlisting}
id : Π x:$\!^{ { \color{black}{\top} } }$Type. x -> x
id = $\lambda\!^{ { \color{black}{\top} } }$x. λy. y
\end{lstlisting}
The first parameter, $\ottmv{x}$, of the identity function is only needed during
type checking; it can be erased before execution. The second
parameter, $\ottmv{y}$, though, is required during runtime.
When we apply this function to arguments, as in \lstinline{(id Bool$\!^{ { \color{black}{\top} } }$ True)}, we
can erase the first argument, \lstinline{Bool}, but the second one,
\lstinline{True}, must be retained.
Indexed data structures provide another example of run-time irrelevance.
Consider the \cd{Vec} datatype for length-indexed
vectors, as it might look in a core
language inspired by GHC~\citep{systemfc,weirich:systemd}. The \cd{Vec} datatype has two parameters, \cd{n} and \cd{a}, that also appear in the types of the data constructors \cd{Nil} and \cd{Cons}.
These parameters are relevant to \cd{Vec}, but irrelevant to the data constructors. (In the types of the constructors, the equality constraints
\cd{(n $\ \sim$ Zero)} and \cd{(n $\ \sim$ Succ m)} force \cd{n} to be equal to the length
of the vector.)
\begin{lstlisting}
Vec : Nat -> Type -> Type
Nil : Π n:$\!^{ { \color{black}{\top} } }$Nat. Π a:$\!^{ { \color{black}{\top} } }$Type. (n $\sim$ Zero) => Vec n a
Cons : Π n:$\!^{ { \color{black}{\top} } }$Nat. Π a:$\!^{ { \color{black}{\top} } }$Type. Π m:$\!^{ { \color{black}{\top} } }$Nat. (n $\sim$ Succ m) => a -> Vec m a -> Vec n a
\end{lstlisting}
Now consider a function \cd{vmap} that maps a given function over a given vector. The length of the vector and the type arguments are not necessary for running \cd{vmap}; they are all erasable. So we assign them $ { \color{black}{\top} } $.
\noindent
\begin{minipage}{\linewidth}
\begin{lstlisting}
vmap : Π n:$\!^{ { \color{black}{\top} } }$Nat.Π a b:$\!^{ { \color{black}{\top} } }$Type. (a -> b) -> Vec n a -> Vec n b
vmap = λ$\!^{ { \color{black}{\top} } }$ n a b. λ f xs.
case xs of
Nil -> Nil
Cons m$\!^{ { \color{black}{\top} } }$ x xs -> Cons m$\!^{ { \color{black}{\top} } }$ (f x) (vmap m$\!^{ { \color{black}{\top} } }$ a$\!^{ { \color{black}{\top} } }$ b$\!^{ { \color{black}{\top} } }$ f xs)
\end{lstlisting}
\end{minipage}
Note that the $ { \color{black}{\top} } $-marked variables \cd{m}, \cd{a} and \cd{b} appear in the definition of \cd{vmap}, but only in $ { \color{black}{\top} } $ contexts. By requiring that `unmarked' terms \textit{don't depend} on terms marked with $ { \color{black}{\top} } $, we can track run-time irrelevance and guarantee safe erasure. Observe that even though
these arguments are marked with $ { \color{black}{\top} } $ to describe their use in the \emph{definition} of \cd{vmap}, this marking does not reflect their usage in the \emph{type} of \cd{vmap}. In particular, we are free to use these variables with \cd{Vec} in a relevant manner.
\subsection{Compile-time Irrelevance} \label{comp-irr}
Some type constructors may have arguments which can be ignored during type checking.
Such arguments are said to be \emph{compile-time irrelevant}. For example, suppose we have a constant function that ignores its argument and returns a type.
\begin{lstlisting}
phantom : Nat$\!^{ { \color{black}{\top} } }$ -> Type
phantom = λ$\!^{ { \color{black}{\top} } }$ x. Bool
\end{lstlisting}
To type check \cd{idp} below, we must show that
\cd{phantom 0} equals \cd{phantom 1}. Without compile-time irrelevance,
we need to $\beta$-reduce both sides to show that the input and output types are equal.
\begin{lstlisting}
idp : phantom 0$\!^{ { \color{black}{\top} } }$ -> phantom 1$\!^{ { \color{black}{\top} } }$
idp = λ x. x
\end{lstlisting}
However, in the presence of compile-time irrelevance, we can use the dependency
information contained in the type of a function to reason about it abstractly.
Because the function \cd{f} below ignores its argument, it is sound to equate the input and output types.
\begin{lstlisting}
ida : Π f $:\!^{ { \color{black}{\top} } }$(Nat$\!^{ { \color{black}{\top} } }$ -> Type). f 0$\!^{ { \color{black}{\top} } }$ -> f 1$\!^{ { \color{black}{\top} } }$
ida = λ$\!^{ { \color{black}{\top} } }$ f. λ x. x
\end{lstlisting}
In the absence of compile-time irrelevance, we cannot type-check \cd{ida}. So compile-time irrelevance makes type checking more flexible.
Compile-time irrelevance can also make type checking faster when the types contain
expensive computation that can be safely ignored. For example, consider the
following program that type checks without compile-time irrelevance.
However, in that case, the type checker must show that \cd{fib 28} reduces to
\cd{317811}, where \cd{fib} represents the Fibonacci function.
\begin{lstlisting}
idn : Π f $:\!^{ { \color{black}{\top} } }$(Nat$\!^{ { \color{black}{\top} } }$ -> Type). f (fib 28)$\!^{ { \color{black}{\top} } }$ -> f 317811$\!^{ { \color{black}{\top} } }$
idn = λ$\!^{ { \color{black}{\top} } }$ f. λ x. x
\end{lstlisting}
So far, we have used two annotations on variables and terms: $ { \color{black}{\top} } $ for irrelevant ones
and `unmarked' for relevant ones. We used $ { \color{black}{\top} } $ to mark both arguments that can be erased at runtime
and arguments that can be safely ignored by the type checker. However, sometimes we need a finer distinction.
\subsection{Strong Irrelevant $\Sigma$-types}
Consider the type \cd{$\Sigma$m:$\!^{ { \color{black}{\top} } }$Nat. Vec m a}, which contains pairs whose
first component is marked as irrelevant. This type might be useful, say, for the output
of a \cd{filter} function for vectors, where the length of the output vector
cannot be calculated statically. If we never need to use this length at
runtime, then it would be good to mark it with $ { \color{black}{\top} } $ so that
it need not be stored.\footnote{It is, however, safe for \cd{m} to be used in a relevant position in the
body of the $\Sigma$-type even when it is marked with $ { \color{black}{\top} } $. This marking indicates
how the first component of a pair having this type is used, not how the bound variable \cd{m}
is used in the body of the type.}
However, marking \cd{m} with $ { \color{black}{\top} } $ means that the first component of the pair of this type must also be
\emph{compile-time} irrelevant. This results in a significant
limitation for strong $\Sigma$ types: we cannot project the second component from the pair.
Say we have \cd{ys: $\Sigma$m:$\!^{ { \color{black}{\top} } }$Nat. Vec m a}. The type of (\cd{$\pi_1$ ys}) is
a \cd{Nat} that can only be used in irrelevant positions. However, note that the argument \cd{n} in \cd{Vec n a} must be compile-time relevant; otherwise the type checker would equate \cd{Vec 0 a} with \cd{Vec 1 a}, making the length index meaningless. The
type of (\cd{$\pi_2$ ys}) would then be \cd{Vec ($\pi_1$ ys) a},
which is ill-formed because an irrelevant term ($\pi_1$ ys) appears in a relevant position.
Therefore, we don't want to mark the first component of the output of \cd{filter} with $ { \color{black}{\top} } $.
However, if we leave it unmarked, we cannot erase it at runtime, something that we might want to.
A way out of this quandry comes by considering terms that are run-time irrelevant but not compile-time irrelevant. Such terms exist between completely irrelevant and completely relevant terms. They should not depend upon irrelevant terms and relevant terms should not depend upon them. We mark such terms with a new annotation, $ { \color{black}{C} } $, with the constraints that `unmarked' terms do not depend on $ { \color{black}{C} } $ and $ { \color{black}{C} } $ terms do not depend on $ { \color{black}{\top} } $ terms. The three annotations, then, correspond to the three levels of a lattice modelling secure information flow, with $ { \color{black}{\bot} } < { \color{black}{C} } < { \color{black}{\top} } $, using $ { \color{black}{\bot} } $ in lieu of `unmarked'. We call the lattice $\mathcal{L}_I$, for irrelevance lattice.
Using this lattice, we can type check the following \cd{filter} function.
\noindent
\begin{minipage}{\linewidth}
\noindent
\begin{lstlisting}
filter : Πn:$\!^{ { \color{black}{\top} } }$Nat.Πa:$\!^{ { \color{black}{\top} } }$Type.(a -> Bool) -> Vec n a -> $\Sigma$m:$^{ { \color{black}{C} } }$Nat. Vec m a
filter = λ$\!^{ { \color{black}{\top} } }$ n a. λ f vec.
case vec of
Nil -> (Zero$^{ { \color{black}{C} } }$, Nil)
Cons n1$\!^{ { \color{black}{\top} } }$ x xs
| f x -> ((Succ ($\pi_1$ ys))$^{ { \color{black}{C} } }$, Cons ($\pi_1$ ys)$\!^{ { \color{black}{\top} } }$ x ($\pi_2$ ys))
where
ys = filter n1$\!^{ { \color{black}{\top} } }$ a$\!^{ { \color{black}{\top} } }$ f xs
| _ -> filter n1$\!^{ { \color{black}{\top} } }$ a$\!^{ { \color{black}{\top} } }$ f xs
\end{lstlisting}
\end{minipage}
\citet{eisenberg:existentials} observe that, in Haskell, it is important to use
projection functions to access the components of the pair that
results from the recursive call (as in \cd{$\pi_1$ ys} and \cd{$\pi_2$ ys}) to
ensure that \cd{filter} is not excessively strict. If \cd{filter} instead used pattern matching to eliminate the pair returned by the recursive call, it would
have needed to filter the entire vector before returning the first successful
value. This \cd{filter} function demonstrates the practical utility of strong irrelevant $\Sigma$-types because it supports the same run-time behavior of the usual list \cd{filter} function but with a more richly-typed data structure.
\iffalse
For example, consider the following function, written in a hypothetical dependently-typed language augmented with dependency-tracking, which adopts Agda syntax.
This function takes a bounded number and returns the same number
but with a larger bound~\citep{finagda}. (The \cd{Fin n} type contains exactly the natural numbers less than \cd{n}.)
\begin{lstlisting}
inject+ : ∀ (n m : Nat)$^\top$ → (fin : Fin n) → Fin (n + m)
inject+ _ _ zero = zero
inject+ _ _ (suc fin) = suc (inject+ _ _ fin)
\end{lstlisting}
The first two arguments to this function, \verb|n| and \verb|n| are not
required during runtime, so we mark them with $\top$ to indicate that they are
\textit{run-time irrelevant}. (Unmarked arguments are assumed to be relevant
at runtime.)
So \cd{inject+ 5 9 2 = 2} and \cd{inject+ 10 42 2 = 2}. The first two arguments to this function, \verb|n| and \verb|m|, are only used to specify its type. The output value \textit{does not depend} on either of them. Therefore, to save time and space, we can erase these programs to (\cd{inject+ _ _ 2}) before running them. Since \verb|n| and \verb|m| are not required during run time, we say that they are \textit{run-time irrelevant}. Erasing sub-terms irrelevant to run-time computation makes programs run faster.
However, with dependently typed languages, type-checking also requires us to compute.
\begin{comment}
For example, \verb|inject+| with all parameters explicit, looks like:
\begin{lstlisting}
inject+ : ∀ (n m : Nat) → (fin : Fin n) → Fin (n + m)
inject+ (suc n) m (zero {n}) = zero {n + m}
inject+ (suc n) m (suc {n} fin) = suc {n + m} (inject+ n m fin)
\end{lstlisting}
Note that in the above definition, the result should have type (\verb|Fin (suc n + m)|) but both the outputs have type (\verb|Fin (suc (n + m))|). We need to reduce (\verb|suc n + m|) to (\verb|suc (n + m)|) to know that the types are equal. Here, we need just a single step to check type equality but type reductions may get quite complex at times. Below, we show an example that demonstrates how analysing dependency helps us reduce complexity and makes type-checking faster.
\end{comment}
Consider the following contrived but illustrative example:
\begin{lstlisting}
phantom : Set → Set
phantom a = if (fib 28 == 317810) then Nat else Bool
\end{lstlisting}
The function \verb|phantom| \textit{does not depend} on its argument \verb|a|. It just returns either \verb|Nat| or \verb|Bool| based on a conditional. The conditional checks whether the Fibonacci number $F_{28}$ equals $317810$.
Next, we use this function to specify a type:
\begin{lstlisting}
conv : ∀ (a b : Set) → phantom a -> phantom b
conv _ _ x = x
\end{lstlisting}
The function \verb|conv| is essentially an identity. We can immediately see that \verb|conv| should type-check. Since \verb|phantom| ignores its argument, \verb|phantom a = phantom b|. But, if we have no way of communicating this information to the type-checker, it must reduce \verb|phantom a| and \verb|phantom b| to find out whether they are equal. With a computationally-intensive conditional, such a reduction may take a really long time.
\scw{This example is also slow in Agda due to the compilers reliance on full normalization.
If the compiler could notice after a single step that the two types are actually equal, it would not need to compute any further. While compile-time irrelevance could help here, this isn't the best example.}
In fact, on a modern laptop, Agda takes about a minute and a half to type-check \verb|conv|. But we could do this in no time just by informing the compiler that it can ignore the argument to \verb|phantom| while checking for equality between types. Ignoring such arguments makes type-checking faster. Arguments that can be ignored while checking for type equality at compile time are called \textit{compile-time irrelevant}.
Note that the argument to \verb|phantom| is also run-time irrelevant because we can ignore \verb|a| while reducing \verb|phantom a|. Further, note that the first two arguments to \verb|inject+| are not only run-time irrelevant but also compile-time irrelevant because \verb|inject+ n₁ m₁ = inject+ n₂ m₂ = λ x. x|. To summarize, a sub-term is said to be run-time irrelevant if it can be erased without affecting reduction whereas a sub-term is said to be compile-time irrelevant if it can be ignored while checking for type equality.
If a sub-term can be ignored while checking for type equality, it can also be erased without affecting computation. In other words, compile-time irrelevance implies run-time irrelevance. To see why, let $\mathit{C}[\_]$ be a program with a hole and $\mathit{C}[a]$ be a program such that sub-term $a$ can be ignored while checking for type equality. Hence, for any term $b$, if $\textit{C}[b]$ is a well-formed program, then $\textit{C}[a] = \textit{C}[b]$. Therefore, to reduce $\textit{C}[a]$, we don't need $a$. As such, $a$ can be erased without affecting computation.
But run-time irrelevance does not imply compile-time irrelevance. A sub-term may not be required for computation but it may be needed during equality checking. Next, we take up an example that illustrates this point.
Consider the \cd{filter} function that filters a vector based on a predicate. The
difficulty with this function is that we cannot statically predict the length
of the output vector. So we need to package the result in a $\Sigma$-type.
\noindent
\begin{minipage}{\linewidth}
\noindent
\begin{lstlisting}
filter : ∀ (a : Set)$^\top$ (n : Nat)$^\top$ → (a → Bool) → Vec a n → Σ[ m ∈ Nat ]$^{Ctime}$ Vec a m
filter _ _ pred [] = (zero$^{ { \color{black}{C} } }$ , [])
filter _ _ pred (x :: xs) =
if pred x then ( suc($\pi_1$ ys)^$\top$ , x :: $\pi_2$ ys) else ys
where ys = filter _ _ pred xs
\end{lstlisting}
\end{minipage}
In the above example, we package the output vector in a $\Sigma$-type because we don't know its
length statically. However, we still don't want to carry around the length of this vector at run time.
In other words, we don't want the first component of the output to have run-time computational significance. So we make the first component run-time irrelevant. However, we cannot make it compile-time irrelevant. To see why, note that the first component of the output is required in type-checking its second component. Further, we can never ignore the first component of a pair while deriving type equalities because otherwise \verb|(Int , a) = (Bool , a)| which results in type unsoundness. Thus, in the above example, we can make the first component of the output run-time irrelevant but not compile-time irrelevant.
In this section, we have seen two kinds of irrelevance: run-time irrelevance and compile-time irrelevance. While compile-time irrelevance implies run-time irrelevance, the converse is not true. This means that we have three classes of sub-terms based on relevance: ones that are both compile-time and run-time irrelevant, others that are only run-time irrelevant but not compile-time irrelevant and the remaining ones that are both compile-time and run-time relevant. Let us denote these classes by $ { \color{black}{\top} } $, $ { \color{black}{C} } $ and $ { \color{black}{\bot} } $ respectively; the reason behind this naming will become clear as we go along.
Now, looking at these classes from the perspective of information flow control, we would want that information \textit{does not} flow along any of these directions: $ { \color{black}{\top} } \to { \color{black}{\bot} } $, $ { \color{black}{\top} } \to { \color{black}{C} } $ and $ { \color{black}{C} } \to { \color{black}{\bot} } $. Put in other words, a compile-time irrelevant sub-term should not interfere in a compile-time relevant program and a run-time irrelevant sub-term should not interfere in a run-time relevant program. These are the non-interference assertions \citep{goguen} we want to enforce.
A general dependency calculus can enforce such non-interference assertions. So, we first design a general dependent dependency calculus and thereafter show how to instantiate it to analyse irrelevance. We start with a simple dependency calculus to help us understand the dependent calculus better.
\fi
\iffalse
Consider the following definition of complex numbers:
\begin{lstlisting}
Complex : Σ[ α ∈ Set ]
((ℂ : Real × Real → α) × (_+_ : α × α → α) × (|_| : α → Real))
Complex = ( Real × Real , (id , sum , mod)) where
sum : (Real × Real) → (Real × Real) → (Real × Real)
sum (m , n) (p , q) = ((m + n) , (p + q))
mod : Real × Real → Real
mod (m , n) = sqrt (m^2 + n^2)
\end{lstlisting}
\verb|Complex| has a $\Sigma$-type. Its first component gives the underlying representation while the second component defines some functions on complex numbers: we can construct (\verb|ℂ|) a complex number from a pair of real numbers, we can add (\verb|_+_|) two complex numbers and we can find the absolute value (|\_|) of a complex number. Here, a complex number is represented in cartesian form as a pair of real numbers. But we don't want any user program to depend on this information. This \textit{non-dependence} gives the implementer the flexibility to unnoticeably change the representation to a different, for example, polar form. In other words, changing the representation to a polar form would not change the run-time behavior of any user program. So we may say that the first component of \verb|Complex| is run-time irrelevant. It is not compile-time irrelevant though: we cannot ignore it while deriving type equality.
\iffalse
Now, since user programs \textit{don't depend} on the representation type, the type itself should have no runtime significance. \scw{But without typecase, type components like this one have to be erasable. Is there
an example that we can give where the erasable value is a nat instead? }
In other words, the first component of \verb|Complex| is runtime \textit{erasable}. In general, the representation types in modules, viewed as $\Sigma$-types, are runtime erasable. We can construct a complex number from a pair of real numbers with addition \verb|sum| and modulus \verb|mod| defined in the usual way.
If a sub-term is compiletime irrelevant, it must be runtime irrelevant as well. But can a sub-term be runtime irrelevant but not compiletime irrelevant? In other words,
But there are functions whose output do not depend on one or more of their arguments. For example, consider the following function that copies at-place the elements of a vector:
\vspace*{5pt}
\begin{lstlisting}
duplicate : ∀ (n : Nat) → Vec Nat n → Vec Nat (n * 2)
duplicate 0 [] = []
duplicate (S m) (k :: ks) = k :: (k :: duplicate m ks)
\end{lstlisting}
The output of \verb|duplicate| can be computed from its second argument alone; the first argument need not be present at runtime. So, though the first argument is necessary for a correct specification of the type; the runtime behaviour of the function \verb|duplicate| \textit{does not depend} on it. Such an argument is \textit{runtime irrelevant}. Let us now consider whether the argument is compiletime relevant. In a Curry-style calculus, we can write \verb|duplicate| as:
\begin{lstlisting}
duplicate = λ n . λ v . case v of [] => [] | k :: ks => k :: k :: duplicate _ ks
\end{lstlisting}
Note that with this definition, after a $\beta$-step, \verb|duplicate n₁| and \verb|duplicate n₂| are syntactically the same. So with a Curry-style calculus, the first argument of \verb|duplicate| is \textit{not relevant} during compiletime as well
. Such arguments are necessary for specification but don't play a role in evaluation. \scw{irrelevant by itself is ambiguous. We need to be very careful to distinguish between compile-time and runtime irrelevance from the beginning of the paper.}
Universally-quantified variables can be categorized as relevant or irrelevant. Let us see what happens with existentially-quantified variables.
\scw{More explanation for people who aren't so familiar with
Agda syntax, or don't know what C, sum and mod should be.}
\scw{And, is this a strong $\Sigma$ or a weak $\Sigma$ in this example?}
The first component of terms having $\Sigma$-types may not be always erasable, though. At times, it can be used computationally. For example, consider the following definition of even and odd numbers:
\begin{lstlisting}
even : Nat → Set
even n = Σ[ m ∈ Nat ] (m * 2 ≡ n)
odd : Nat → Set
odd n = Σ[ m ∈ Nat ] (1 + (m * 2) ≡ n)
\end{lstlisting}
We can use this definition to build a divide-by-2 function:
\begin{lstlisting}
div-by-2 : ∀ (n : Nat) → Nat
div-by-2 n with (even-or-odd n)
... | inl (k , _) = k
... | inr (k , _) = k
\end{lstlisting}
\scw{What is even-or-odd?}
The output is essentially the number that witnesses the evenness or oddness of the given number. In this case, we cannot erase the first components of the $\Sigma$-typed terms since computation \textit{depends} upon them. \scw{But in this example, the second component is eraseable. Should we bring that up?}
\fi
We use our dependency calculus to analyse irrelevance. The constraint we must abide by is that information should never flow from irrelevant to relevant contexts. Our calculus ensures that this flow constraint is satisfied. This means, once we show our calculus is correct, we know that a) erasing any irrelevant term at run time is safe and b) ignoring compile-time irrelevant terms while checking for type equality is sound.
With the background set up, let us move to the calculi.
\fi
\section{Flow-aware Semantics for DDC} \label{DDC-heap}
hhh
\section{Dependency Analysis}
Consider this judgment from a type system that has been augmented with
\emph{dependency analysis}.
\[
\ottmv{x} \! :^{ { \color{black}{L} } }\! \ottkw{Int} , \ottmv{y} \! :^{ { \color{black}{H} } }\! \ottkw{Bool} , \ottmv{z} \! :^{ { \color{black}{M} } }\! \ottkw{Bool} \vdash \, \ottkw{if} \, \ottmv{z} \, \ottkw{then} \, \ottmv{x} \, \ottkw{else} \, \ottsym{3} \, :^{ { \color{black}{M} } } \, \ottkw{Int}
\]
In this judgment, $ { \color{black}{L} } $, $ { \color{black}{M} } $ and $ { \color{black}{H} } $ stand for low, medium and
high security levels respectively. The computed value of the expression is meant to be a medium-security result. The inputs, $\ottmv{x}$, $\ottmv{y}$ and $\ottmv{z}$ have
been marked with their respective security levels. This expression type-checks
because it is permissible for medium-security results to \emph{depend} on both
low and medium-security inputs. Note that the high-security boolean variable $\ottmv{y}$ is
not used in the expression. However, if we replace $\ottmv{z}$ with $\ottmv{y}$ in the
conditional, then the type checker would reject that expression. Even though the
high-security input would not be returned directly, the medium-security result would still
depend on it.
Dependency analysis, as we see above, is an \emph{expressive} addition to
programming languages. Such analyses allow languages to protect
sensitive information~\citep{smith-volpano,slam}, support run-time code generation~\citep{binding-time}, slice programs while preserving behavior~\citep{slicing}, etc. Several existing dependency analyses were unified by \citet{dcc} in their Dependency Core Calculus (DCC). This calculus has served as a foundation
for static analysis of dependencies in programming languages.
What makes DCC powerful is the parameterization of the type system
by a \emph{generic} lattice of dependency levels. Dependency
analysis, in essence, is about ensuring secure information flow---that information never flows from more secure to less secure levels. \citet{denning1} showed that a lattice model, where increasing order corresponds to higher security, can be used to enforce secure flow of information. DCC integrates this lattice model with the computational $\lambda$-calculus \citep{moggi} by grading the monad operator of the latter with elements of the former. This integration enables DCC to analyze dependencies in its type system.
\iffalse
At the same time, dependency tracking is \emph{simple}. In essence, the type system need only
ensure that a variable is used at a level at least as secure as its own assigned one. In
the above example, $\ottmv{z}$, a medium-security boolean, may be used either in a medium-security computation or in a high-security computation, but never in a low-security one.
\fi
However, even though many typed languages have included dependency analysis in
some form, this feature has seen relatively little attention in the context of
\emph{dependently-typed} languages. This is unfortunate because, as we show in
this paper, dependency analysis can provide an elegant foundation for
compile-time and run-time irrelevance, two important concerns in the design of dependently-typed
languages. Compile-time irrelevance identifies sub-expressions that are not needed for type checking while run-time irrelevance identifies sub-expressions that do not affect the result of evaluation.
By ignoring or erasing such sub-expressions, compilers for dependently-typed languages increase the expressiveness of the type system,
improve on compilation time and produce more efficient executables.
Therefore, in this work, we augment a dependently-typed language with a
\emph{primitive} notion of dependency analysis and use it to track compile-time and
run-time irrelevance. We call this language DDC, for Dependent Dependency Calculus, in homage to
DCC. Although our dependency analyses are structured differently,
we show that DDC can faithfully embed the terminating fragment of DCC and
support its many well-known applications, in addition to our
novel application of tracking compile-time and run-time irrelevance.
More specifically, our work makes the following contributions:
\begin{itemize}
\item We design a language SDC, for Simple Dependency Calculus, that can analyze
dependencies in a simply-typed language. We show that SDC is no less expressive
than the terminating fragment of DCC. The structure of dependency analysis in SDC
enables a relatively straightforward syntactic proof of non-interference. (Section~\ref{SDC})
\item We extend SDC to a dependent calculus, $\textsc{DDC}^{\top}$. Using this calculus, we analyze
run-time irrelevance and show the analysis is correct using a non-interference theorem.
$\textsc{DDC}^{\top}$ contains SDC as a sub-language. As such, it can be used to track other forms of dependencies as
well. (Section~\ref{DDCT})
\item We generalize $\textsc{DDC}^{\top}$ to DDC. Using this calculus, we analyze both run-time and
compile-time irrelevance and show that the analyses are correct. To the best of our knowledge, DDC
is the only system that can distinguish run-time and compile-time irrelevance as separate modalities, necessary for the proper treatment
of projection from irrelevant $\Sigma$-types. (Section~\ref{sec:compile-time-irrelevance})
\iffalse
\item We show that SDC can be considered as a graded effect system by
showing that its categorical model in classified sets has the
structure of a category of graded algebras. The latter category can be
abstracted into a new multicategory that captures the base structure
of fully graded type systems, and is called a grade-indexed multicategory. (Section~\ref{subsec:graded_types})
\fi
\iffalse
\item We provide a detailed comparison of DDC against existing mechanisms for
analysing compile-time and run-time irrelevance. To the best of our
knowledge, DDC is the only system that combines separate quantifiers for
compile-time and run-time irrelevance in the same framework. \scw{Check this
sentence in relation to Orchard, Eades work} In particular, we observe
that the distinctions made by DDC are necessary for a proper treatment of
erasable projections from strong $\Sigma$ types. (Section~\ref{related})
\fi
\item We have used the Coq proof assistant to mechanically verify the most
important and delicate part of our designs, the non-interference and type
soundness theorems for DDC. \ifanonymous Our proof scripts are available to
reviewers as anonymized supplementary material and we plan to make this
development publicly available. \else This mechanization is available online\footnote{
\url{https://github.com/sweirich/graded-haskell}} and as a self-contained
artifact~\citep{esop22:artifact}. \fi
\end{itemize}
\iffalse
We design a general Dependent Dependency Calculus (DDC) that can analyse any graded dependency that obeys a lattice structure. We use this general calculus to analyse irrelevance, viewed as a lattice. Our calculus can also be used to analyse other notions of dependency. In fact, our calculus is a generalization of the Dependency Core Calculus (DCC) of \citet{dcc} to dependent types. As such, our calculus can be used for analysing the various dependencies discussed in \citet{dcc}, including secure information flow.
But unlike \citet{dcc}, we analyse dependency using more syntactic methods. The Dependency Core Calculus uses a denotational model to prove soundness of the type system. On the other hand, we use an operational model to prove soundness. The advantage of using an operational model is that it carries over smoothly to dependent types. Further, our syntactic treatment of equality opens up the possibility of internalizing non-interference in the type system. \scw{Rephrase: it it easy to internalize as a
judgement. It doesn't require the addition of an axiom (like internalized parametricity).}
\fi
\iffalse
Here, we sketch the idea behind qualitative type theory. We designed a qualitative type theory to address some issues rising in quantitative type theory. Quantitative type theories are quite useful, especially in tracking variable usage. Such theories are generally parametrized over semiring-like structures whereby the semiring operations are used to count resource usage. Counting invariably requires a baseline, a unit. This is provided by the multiplicative identity of the semiring. Taking the unit as reference, quantitative type systems can count the resources used by programs. This feature is a strength and a weakness at the same time. Its strength lies in enabling counting; its weakness lies in its hard-wired reference. Once a reference is selected, programs can be seen from that reference alone.
But there are instances when we might want to see programs from several different angles. We may learn about different aspects by viewing from different angles; such knowledge may be useful for different applications. For example, we are familiar with the compile time and run time views of programs; each with its own use. Another example: in security applications, users get to see data according to their privilege levels. In order to view programs from multiple angles, we need to abandon the fixed reference of quantitative systems. Giving up a fixed reference would mean we can no longer count. But such an approach would provide the flexibility to view programs from different levels.
This idea motivates a qualitative type theory. We replace the fixed reference and quantities in quantitative type theory with flexible reference and qualities in qualitative type theory. We replace the semiring and counting over it in quantitative type theory with partial order and comparing over it in qualitative type theory. While quantitative type theory is useful in tracking resource usage, qualitative type theory is useful in information flow control.
With this informal introduction, let us now look at the formal description of qualitative type theory.
\fi
\section{Discussions and Related Work} \label{related}
\subsection{Irrelevance in Dependent Type Theories}
\label{sec:irrelevance-related}
Overall, compile-time and run-time irrelevance is a well-studied topic in
the design of dependent type systems. In some systems, the focus is only
on support for run-time irrelevance: see~\cite{McBride:2016,atkey,brady:idris2,miquel,mishra,matus}. In other systems, the focus is on compile-time irrelevance: see~\cite{pfenning:2001,abel}. Some systems support both, but require them to overlap, such as ~\cite{barras:icc-star,mishra-linger:phd,weirich:systemd,Nuyts18}. The system of \citet{Moon:2021} does not require them to overlap but their type system does not make use of compile-time irrelevance in the conversion rule.
To compare, system $\textsc{DDC}^{\top}$, presented here, can support run-time irrelevance only and is similar to the core language of \citet{matus}. However, note that $\textsc{DDC}^{\top}$ can track dependencies in general while the system in \citet{matus} tracks run-time irrelevance alone. \textsc{DDC}, on the other hand, is the only system that we are aware of that tracks run-time and compile-time irrelevance separately and makes use of the latter in the conversion rule. Further, \textsc{DDC} tracks these irrelevances in the presence of strong $\Sigma$-types with erasable first components, something which, to the best of our knowledge, no prior work has been able to.
Prior work has identified the difficulty in handling strong $\Sigma$-types with erasable first
components in a setting that tracks compile-time irrelevance. \citet{abel} point out that strong irrelevant $\Sigma$-types make their theory inconsistent. Similarly, EPTS$^{\bullet}$~\citep{mishra-linger:phd} cannot define the projections for pairs having such $\Sigma$-types. The reason behind this is that EPTS$^{\bullet}$ is hard-wired to work with a two-element lattice which identifies compile-time and run-time irrelevance. As such, projections from such pairs lead to type unsoundness. For example, considering the first components to be run-time irrelevant, the pairs $ ( \ottkw{Int} , \ottkw{unit} ) $ and $ ( \ottkw{Bool} , \ottkw{unit} ) $ are run-time equivalent. Since EPTS$^{\bullet}$ identifies run-time and compile-time irrelevance, these pairs are also compile-time equivalent. Then, taking the first projections of these pairs, one ends up with $\ottkw{Int}$ and $\ottkw{Bool}$ being compile-time equivalent. We resolve this problem by distinguishing between run-time and compile-time irrelevance, thus requiring a lattice with three elements.
Next, we compare our work with existing literature with respect to the equality relation. We analyze compile-time irrelevance to enable the equality relation to ignore unnecessary sub-terms. However, since our equality relation is untyped, we cannot include type-dependent
rules in our system, such as $\eta$-equivalence for the \cd{Unit} type.
Several prior works on irrelevance~\citep{miquel,barras:icc-star,mishra-linger:phd,matus} use an untyped equality relation. However, some prior work, such as~\cite{pfenning:2001,abel}, do consider compile-time irrelevance in the context of typed-directed equality. But such systems require irrelevant arguments to functions appear only irrelevantly in the codomain type of the function, thus ruling out several examples including the polymorphic identity function.
\iffalse
These two versions of equality are not equivalent, even for terms that have
the same type. Consider the examples below, all of which depend on \cd{Proxy}
declared as follows:
\begin{lstlisting}
type Proxy : Π x:$^{ { \color{black}{\top} } }$Type. x -> Type
\end{lstlisting}
\noindent Now, which of the following types should be equal?
\begin{lstlisting}
t1 : Type
t1 = Proxy (Unit -> Unit)$^{ { \color{black}{\top} } }$ (λ x:Unit.x)
t2 : Type
t2 = Proxy (Bool -> Bool)$^{ { \color{black}{\top} } }$ (λ x:Bool.x)
t3 : Type
t3 = Proxy (Unit -> Unit)$^{ { \color{black}{\top} } }$ (λ x:Unit.unit)
\end{lstlisting}
Under an untyped definitional equivalence, types \cd{t1} and \cd{t2} can be
equated as long as the first argument to \cd{Proxy} is irrelevant. However, an
untyped equivalence does not include $\eta$-equiavalence for the \cd{Unit}
type, so the third type \cd{t3} is not the same.
In contrast, type-directed equivalence can equate \cd{t1} and \cd{t3}. However,
because type information is used as part of this equivalence, systems such as
\citet{abel} do not allow \cd{x}, the first argument of \cd{Proxy}, to be
irrelevant at compile time. As a result, typed equivalence must distinguish
between \cd{t1} and \cd{t2}.
A typed equivalence relates more terms, because it may include type-dependent
rules such as $\eta$-equiavalence for the \cd{Unit} type. But this expressiveness comes at a cost.
In such systems, a compile-time irrelevant variable must appear
irrelevantly \emph{both} in the term and the type. As a result, in that setting
runtime irrelevance does not imply compiletime irrelevance, limiting opportunities for its
application.
\fi
\subsection{Quantitative Type Systems}
Our work is closely related to quantitative type systems \citep{petricek,Ghica:2014,Brunel:2014,McBride:2016,atkey,orchard,abel20,grad,Moon:2021}. Such systems provide a fine-grained accounting of coeffects, viewed as resources, for example, variable usage, linearity, liveness, etc. A typical judgment from a quantitative type system \citep{grad} may look like: \[ \ottmv{x} \! :^{ 1 }\! \ottkw{Bool} , \ottmv{y} \! :^{ 1 }\! \ottkw{Int} , \ottmv{z} \! :^{ 0 }\! \ottkw{Bool} \vdash \ottkw{if}\, x \, \ottkw{then}\, y + 1\, \ottkw{else}\, y - 1\, :^1\, \ottkw{Int} \] The variable $\ottmv{x}$ is used once in the condition, the variable $\ottmv{y}$ is used once in each of the branches while the variable $\ottmv{z}$ is not used at all. As such, they are marked with these quantities in the context.
This form of judgment is very similar to our typing judgments with quantities appearing in place of levels. However, there is a crucial difference: to the right of the turnstile, while any level may appear in our judgments, only the quantity $ 1 $ can appear in typing judgments of quantitative systems. A quantitative system that allows an arbitrary quantity to the right of the turnstile is not closed under
substitution \citep{McBride:2016,atkey}. As such, quantitative systems are tied to a fixed reference while our systems can view programs from different reference levels. This difference in form results from the difference in the purposes the two kinds of systems serve: quantitative systems count while our systems compare. Counting requires a fixed standard or reference whereas comparison does not. Applications that require counting, like linearity tracking, are handled well by quantitative systems while applications that require comparison, like ensuring secure information flow, are handled well by systems of our kind.
From a type-theoretic standpoint, in general, quantitative systems cannot eliminate pairs through projections. This is so because there is no general way to split the resources of the context that type-checks a pair. Eliminating pairs through projections is straightforward in our systems because the grade on the typing judgment can control where the projections are visible.
\iffalse
A quantitative typing judgement has a semi-graded nature: meaning, the
contexts are graded by quantities $q \in Q$, but the term is always derived at
a fixed grade, $1$. This restriction is necessary: a quantitative system that
allows an arbitrary grade on the RHS of a typing judgement is not closed under
substitution \citep{McBride:2016,atkey}. Our type system is not quantitative
in nature: as such, we are not bound by this restriction.
One way to read a quantitative typing judgement
$x_1 :^{q_1} A_1 , x_2 :^{q_2} A_2, \ldots , x_n :^{q_n} A_n \vdash a : A$ is
that, to produce one copy of resource $a$, we need $q_i$ copies of resource
$x_i$, where $1 \leq i \leq n$. We can compare this to our typing judgement:
$x_1 :^{\ell_1} A_1 , x_2 :^{\ell_2} A_2, \ldots , x_n :^{\ell_n} A_n \vdash a
:^{\ell} A$ which can be read as, observer $\ell$ can see $a$, assuming $x_i$
is $\ell_i$-secure for $1 \leq i \leq n$. Dependency tracking is more
\emph{qualitative} in nature than quantitative: it cannot count, but it can
compare. Quantitative type systems are good at counting: for example, tracking
linear variables or run-time irrelevant variables. But they are not that good at
modelling sharing. For example, say, we want to take the projections of a term
having a strong $\Sigma$-type; how do we split the context between the two
projections? We may say that we don't care about the quantities when dealing
with terms having strong $\Sigma$-types; in which case, we also don't care
about the quantities for the projections. But this is not very
satisfactory. On the other hand, in our system, we don't need to split. We can get the first
projection at some level and the second one at some other level. We have this
flexibility since we are not restricted to a fixed grade on the RHS of the
typing judgement.
Many dependency analyses, including information flow control, require a system
that can compare levels to one another and decide on the flow between the
levels. The grade on the RHS comes in handy during such
comparison. Quantitative type theories can also control information flow by
instantiating the partially-ordered semiring $(+,\times,0,1,\leq)$ to a
lattice $(\wedge,\vee,\top,\bot,\leq)$; but all the analysis has to be carried
out relative to level $1$. This makes qualitative type theories like ours a
better mechanism for tracking information flow and analysing
dependency. On the flip side, we can not track linearity and other properties
related to counting.
However, on a two-point lattice, correspondingly a two element semiring,
qualitative and quantitative type theories come quite close.
Let $S$ be a partially-ordered semiring with two elements $\{0,1\}$ such that
$1 + 1 = 1$ and $1 \leq 0$. Quantitative type systems over such a semiring can
track whether a variable is definitely irrelevant ($0$) or potentially
irrelevant ($1$). The semiring $S$ can also be seen as a two-point lattice
with $\bot = 1$ and $\top = 0$ and $\vee = \times$ and $\wedge = +$.
Using this structure with just two grades, we compare our
\textsc{DDC}{} with two quantitative dependent type theories: \textsc{GraD} of
\citet{grad} and QTT of \citep{atkey}.
With this semiring, a \textsc{GraD} typing judgement $\Gamma \vdash a : A$ can
be derived in \textsc{DDC}{} as $\Gamma \vdash a :^{\bot} A$. The \textsc{GraD} type
system axiomatizes an untyped definition of equivalence and can be
instantiated with one that includes compile-time irrelevance. However, with
only two points, \textsc{GraD} cannot distinguish between run-time irrelevance
and compile-time irrelevance, so cannot support an erasable $\Sigma$ type
eliminated via projections.
Now we compare DDC with QTT. In QTT, there are two fragments, one where
resources are tracked (the $1$ fragment), and the other where resources are
ignored (the $0$ fragment). For both resource-aware and resource-agnostic
derivations $\Gamma \vdash a :^1 A$ and $\Gamma \vdash a :^0 A$ respectively
in QTT, we have corresponding derivations $\Gamma \vdash a :^{\bot} A$ and
$\Gamma \vdash a :^{\top} A$ in \DDC$^{\top}${}. Going the other way is problematic
here too, since QTT allows projections from $\Sigma$-types only in the
resource-agnostic fragment, whereas DDC allows projections both at $ { \color{black}{C} } $ and
$\bot$.
Over just two grades, these three type systems are quite close to each
other. But, in general, DDC and quantitative type theories are unique in their
own ways. The former provides a more precise account of irrelevance and
information flow control, while the latter enables counting and tracking
of resource usage.
\fi
\iffalse
\subsection{QTT and GraD}
\scw{I don't know if we have the space or inclination to go into this
much detail in the paper. But we should do this analysis first before
writing our real related work section.}
A recent trend is to use quantitative type systems to track irrelevance in
dependently typed languages. Example systems include QTT~\cite{atkey},
Granule~\cite{granule} and GraD~\cite{choudhury}. These methods have been
adopted in Agda and Idris.
In these type systems, as in this work, every variable in the context is
annotated with a label drawn from an abstract semiring. These labels are used
to (abstractly) count the uses of variables within functions. For example, by
choosing the semi-ring that includes three elements (0, 1 and $\omega$), these
type systems can distinguish linear, unrestricted, and irrelevant uses of
variables.
What happens if we instantiate QTT or GraD with a semiring with only two
elements, called 0 and $\omega$? The type system then tracks only whether a
variable is definitely irrelevant (0) or potentially irrelevant ($\omega$) in
the expression. This instance then makes a good point of comparison with DDC.
The 0 and $\omega$ labels of that semiring correspond directly to the $\top$
and $\bot$ labels respectively in DDC. Furthermore, the semiring
multiplication operation corresponds to the join operation and the semiring
addition operation corresponds to meet.
\iffalse
\[
\begin{array}{lclclcl}
k \vee \ell & & & & k \wedge \ell \\
0 * 0 &=& 0 & \hspace{5ex} & 0 + 0 &=& 0 \\
0 * \omega &=& 0 & & 0 + \omega &=& \omega \\
\omega * 0 &=& 0 & & \omega + 0 &=& \omega \\
\omega * \omega &=& \omega & & \omega + \omega &=& \omega\\
\end{array}
\]
\fi
\paragraph{GraD}
For the purposes of comparison, we present the GraD typing rules using the
same syntax as DDC and make other small changes to aid comparison.
For example, the typing judgement in the GraD type system does not include a
label because that system only checks terms at a single level. This level
would be 1 (or $\bot$ in this semi-ring), so we mark all GraD judgements with
$ { \color{black}{\bot} } $.
Confusingly, GraD has an ordering relation on labels, but the ordering
relation is reversed when compared to DDC. (In other words, GraD would say
that $\top\leq\bot$.) Therefore, we present the rules with GraD's ordering
relation reversed to keep matters simple and easier to compare with this
paper. This matters in the rule that explicitly adds narrowing to the type
system. If a variable is marked as definitely irrelevant, the judgement will
still hold if we mark it as (potentially) relevant.
The variable rule only allows relevant variables to be used. However, as we
will see below, this system works like the Mishra-Linger-Sheard system and
uses ``reset'' operation ($bot /\ W$) to bring variables in the context down to
$\bot$ when checking subterms that occur in irrelevant contexts.
\[ \drule{GraD-Sub} \qquad \drule{GraD-Var} \]
In GraD, the $\Pi$ formation rule does not constrain the use of the variable
in the body of the function type. In practice, this means that this variable
might as well be tagged with $\bot$ because that provides the most flexibility.
Furthermore, due to narrowing, the version of the rule shown on the right below
is equivalent.
\[ \drule{GraD-Pi} \qquad \drule{Grad-PiS} \]
The abstraction rule uses the label directly. Because the label on the
judgement is hardwired to $ { \color{black}{\bot} } $, this is equivalent to the DDC rule, which
uses $ \ell \vee { \color{black}{\bot} } $. The application rule looks likes the rule on the right
below and, like \rref{GraD-Pi}, includes computation on the context in the
conclusion.
\[ \drule{GraD-Abs} \qquad \drule{GraD-App} \]
However, in this setting, we can understand this rule better if we consider
the two cases individually.
\[ \drule{GraD-AppRel} \qquad \drule{GraD-AppIrrel} \]
If we consider the two labels individually, when the argument is relevant,
i.e. $ { \color{black}{\bot} } $, then we have $\Omega_{{\mathrm{1}}} \wedge \ottsym{(} { \color{black}{\bot} } \vee \Omega_{{\mathrm{2}}} \ottsym{)}$. But $ { \color{black}{\bot} } \vee \Omega_{{\mathrm{2}}}$ is
$\Omega_{{\mathrm{2}}}$. That means that the context in the conclusion must be the meet of
the two contexts that are used to check $\ottnt{a}$ and $\ottnt{b}$. However, due to
\rref{Grad-Sub}, we can just use the same context for both.
In the case of an irrelevant argument, the context in the conclusion should be
$\Omega_{{\mathrm{1}}} \wedge \ottsym{(} { \color{black}{\top} } \vee \Omega_{{\mathrm{2}}} \ottsym{)}$. In this case, $ { \color{black}{\top} } \vee \Omega_{{\mathrm{2}}}$ is the context where
everything is marked as $ { \color{black}{\top} } $ and $\Omega_{{\mathrm{1}}} \wedge \ottsym{(} { \color{black}{\top} } \vee \Omega_{{\mathrm{2}}} \ottsym{)}$ is $\Omega_{{\mathrm{1}}}$. As
a result, in this rule, we can type check the argument using any set of labels
in the context. Equivalent, we can mark all labels in this context as
$ { \color{black}{\bot} } $.
The definitional equality relation used by conversion in GraD is axiomatized,
not specified. It is conjectured that this relation could incorporate
irrelevance.
The GraD type system does not allow strong Sigma types where the component has
been annotated with $ { \color{black}{\top} } $. The reason is that the judgement is restricted
to $ { \color{black}{\bot} } $ --- the first projection rule requires that the component be less
than the level of the judgement, but there is no judgement form labeled with
$ { \color{black}{\top} } $ in this system.
The GraD type system includes weak Sigmas, eliminated through pattern
matching. However, we also cannot use them to define $ { \color{black}{\top} } $-annotated
strong sigmas in this system because the $ { \color{black}{\top} } $ marked variable cannot be
used in the body of the pattern match. The type system must stay at level
$ { \color{black}{\bot} } $.
In summary, this instantiation of the GraD type system supports both erasure
and (probably) compile-time irrelevance using mechanisms similar to the
Mishra-Linger-Sheard type system. However, there does not appear to be a way
to extend this system to include strong Sigma types with an erasable
component.
\paragraph{QTT}
The QTT type system is similar to GraD in many ways, but it differs in its
treatment of 0. GraD uses an unlabeled judgement, where the missing label should be interpreted as 1. QTT uses a labeled judgement, but restricts that label to
only be 1 (as in GraD) or 0.
The QTT type system does not support sub-usaging--so we are not allowed to use
context narrowing in this system. Every variable that we use must match the
current level of the judgement. However, when we check that a type is
well-formed, we use the join rule to convert all variables in the context to
$ { \color{black}{\top} } $ and check the term at level $ { \color{black}{\top} } $. This is similar to the Mishra-Linger-Sheard case except that it compresses everything about the judgement to $ { \color{black}{\top} } $ instead of $ { \color{black}{\bot} } $. (i.e. instead of $ { \color{black}{\bot} } \wedge \Omega \vdash \ottnt{a} :^{ { \color{black}{\bot} } } \ottnt{A} $, this
system uses $ { \color{black}{\top} } \vee \Omega \vdash \ottnt{a} :^{ { \color{black}{\top} } } \ottnt{A} $). We can think of the former translation as
changing our point of view --- we can use runtime reasoning about compiletime computation by pretending that all compiletime variables are available at runtime. In contrast, the latter degenerates the type system and completely removes any reasoning about quantities.
\[ \drule{QTT-Var} \qquad \drule{QTT-Pi} \qquad \drule{QTT-Abs} \]
The abstraction rule can be presented as a single rule in QTT, but for clarity in this context, we separate it into two cases: one for when the argument is relevant and one when the argument is irrelevant.
\[ \drule{QTT-AppRel} \qquad \drule{QTT-AppIrrel} \]
The rule for relevant arguments is similar to the DDC application rule. We've added the (useless) join operation for the argument for comparison.
\scw{Say more about what is going on with the context manipulation here}
The conversion rule in QTT does not support compile-time irrelevance.
However, this type system allows projections from Sigma types, but only at label $ { \color{black}{\top} } $. Because QTT generalizes linear type systems, projections are not available in general, as they throw away resources. Instead, in this setting, they are only available where resource tracking is disabled.
\begin{enumerate}
\item Both Quantitative and Qualitative systems support labeled assumptions in the context that can be internalized via a graded modal type.
\item Qualitative systems can index the judgment with an arbitrary label, but quantitative systems require the judgement to be labeled by 1.
(Exception: we can design a quantitative type system, but it requires so many restrictions on the algebra that it is useless.)
(Exception: Atkey's QTT has a 0-fragment, but that part of the system trivializes the labels, forgetting all of their information content.)
\item Is the join and meet operation the same as the plus and times in quantitative systems?
\item Qualitative systems are better for applications that require this different view of the judgement: we discuss two examples in depth --- information flow and dependent types with both irrelevance and erasure. Perhaps there are more (roles?)
\item It is possible to combine these systems together. But can we identify the two sorts of zeros?
\item Weak and Strong Sigmas are different and one is not
\end{enumerate}
\fi
\subsection{Dependency Analysis and Dependent Type Theory}
Dependency analysis and dependent type theories have come together in some existing work.
Like our system, \cite{prost:lambda-cube} extends the $\lambda$-cube so that it may track
dependencies. However, unlike our system, this work uses sorts to track dependencies.
It is inspired by the distinction between sorts in the Calculus of Constructions
where computationally relevant and irrelevant terms live in sorts \cd{Set} and \cd{Prop} respectively.
As \citet{mishra-linger:phd} points out, such an approach ties up two distinct language features,
sorts and dependency analysis, which can be treated in a more orthogonal manner.
\iffalse
Somewhat tangential to our work, \citet{algehed} give an embedding of the Dependency Core Calculus in the Calculus of Constructions (CoC) and derives the non-interference theorem as a corollary of the general parametricity theorem of CoC. This work follows the arc of a long line of research initiated by \citet{tse-zdancewic} and carried forward by \citet{igarashi,ahmed}. The goal of this direction of research has been to derive non-interference from parametricity. Our paper takes a different route: we use dependency to track irrelevance in dependent type theory.
\fi
\citet{color} is very related to our work. They use colors to erase terms while we use grades. Colors and grades both form a lattice structure and their usage in the respective type systems are quite similar. However, \citet{color} use internalized parametricity to reason about erasure; so it is important that their type theory is logically consistent. Our work does not rely on the normalizing nature of the theory; we take a direct route to analyzing erasure.
Like our work, \citet{caires} track information flow in a dependent type system. But \citet{caires} focus on more imperative features, like modeling of state while we focus on irrelevance. A distinguishing feature of their system is that they allow security labels to depend upon terms, something that we don't attempt here.
\iffalse
\subsection{Graded Type systems and effects}
Graded types have roots as far back as nearly thirty years ago with
\citet{Girard:1992}'s introduction of bounded linear logic. This
system introduced the modality $!_pA$ which can be seen as an
annotated version of the of-course modality $!A$ with a polynomial $p$
that captures the usage of programs with type $A$. They use this
bounded exponential in complexity analysis. Fast forward six years
when \citet{Wadler:1998} introduces what one could consider to be the
first graded effect type system which has a new notion of labelled monad
$T^\sigma A$ annotated with an effect delimiter $\sigma$ that
describes the kinds of effects the monad $T$ has access to.
Moving forward, \citet{Ghica:2014} show how to generalize bounded
linear logic to be parameterized by a general semiring; the bounded
exponential $!_rA$ is now labelled by an element of the
semiring. Similar to the previous system, this system is the first
graded coeffect system to be introduced. In the same year, \citet{Brunel:2014} propose a graded coeffect type system that is perhaps the closest in presentation to modern day graded type
systems, and is highly related to \citet{Ghica:2014}'s system; but they
provide several interesting meta-theoretical results for their system
including a sound operational model.
At this point, the study of
graded type systems begins to pick up with new results in the area
continuing every year \citep{Katsumata:2014,petricek,Gaboardi:2016,Eades:2019,McBride:2016,atkey,grad,Moon:2021,Fujii:2016b}. The calculi presented in this paper can be seen as fully graded effect systems.
Perhaps the system that is most closely related to our system SDC is
SDCC of \citet{algehed:security}. They simplify DCC into a system that
exposes an equivalent formalization of DCC as essentially a graded
monadic system. However, our system is a fully graded type system. In
addition, we are not aware of any dependent graded effect systems
other than the Granule language of \citet{orchard}, but Granule
has a restricted notion of type dependency called index types where
DDC has full dependent types.
\fi
\section{A Simple Dependency Analyzing Calculus} \label{SDC}
Our ultimate goal is a dependent dependency calculus. However, we first start with a simply-typed version
so that we can explain our approach to dependency analysis and non-interference in a simplified setting.
We call the calculus of this section SDC, for Simple Dependency Calculus. This calculus is parameterized by a lattice of \emph{labels} or \emph{grades}, which can also be thought of as security \emph{levels}.\footnote{We use the terms label, level and grade interchangeably.}
An excerpt of this calculus appears in Figure~\ref{fig:min}; it
is an extension of the simply-typed $\lambda$-calculus with a grade-indexed
modal type $ T^{ \ell }\; \ottnt{A} $. The modal type $ T^{ \ell }\; \ottnt{A} $ can be thought of as putting a security barrier of grade $\ell$ around the values of $\ottnt{A}$. The calculus itself is also \emph{graded}, which means that in a typing judgment, the
derived term and every variable in the context carries a label or grade.
(The specification of the full system, which includes unit, products and sums, appears in \auxref{app:sdc-rules}.)
\begin{figure}
\centering
\begin{flushright}
\textit{(Grammar)}
\end{flushright}
\vspace{-3ex}
\[
\begin{array}{llcll}
\textit{labels} & \ell, k & ::= & { \color{black}{\bot} } \mid { \color{black}{\top} } \mid k \wedge \ell \mid k \vee \ell \mid \ldots \\
\textit{types} & \ottnt{A},\ottnt{B} & ::=& \ottkw{Unit} \mid \ottnt{A} \to \ottnt{B} \mid T^{ \ell }\; \ottnt{A} \\
\textit{terms} & \ottnt{a}, \ottnt{b} & ::=& \ottmv{x} \mid \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{a} \mid \ottnt{a} \; \ottnt{b} & \mbox{\it variables and functions} \\
&& \mid & \eta^{ \ell }\; \ottnt{a} \mid \ottkw{bind} ^{ \ell } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} & \mbox{\it graded modality}
\\
\textit{contexts} & \Omega & ::= & \varnothing \mid \Omega , \ottmv{x} \! :^{ \ell }\! \ottnt{A} \\
\\
\end{array}
\]
\vspace{-6ex}
\drules[SDC]{$ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $}{Typing rules}
{Var,Abs,App,Return,Bind}
\vspace{-6ex}
\drules[SDCStep]{$ \ottnt{a} \leadsto \ottnt{a'} $}{Small step}
{Beta,BindBeta}
\vspace{-3ex}
\caption{Simple Dependency Calculus (Excerpt)}
\label{fig:min}
\label{fig:typing}
\end{figure}
\subsection{Type System}
The typing judgment has the form $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ which means that ``$\ell$ is allowed to
observe $\ottnt{a}$'' or that ``$\ottnt{a}$ is visible at $\ell$''. Selected typing rules for SDC appear in Figure \ref{fig:typing}. Most rules are straightforward and propagate the level of the sub-terms to the expression.
The \rref{SDC-Var} requires that the grade of the variable in the
context must be less than or equal to the grade of the observer. In other
words, an observer at level $\ell$ is allowed to use a variable from level
$k$ if and only if $k \leq \ell$. If the variable's level is too high, then
this rule does not apply, ensuring that information can always flow to more
secure levels but never to less secure ones. Abstraction
\rref{SDC-Abs} uses the current level of the expression for the newly
introduced variable in the context. This makes sense because the argument to
the function is checked at the same level in \rref{SDC-App}.
The modal type, introduced and eliminated with \rref{SDC-Return} and
\rref{SDC-Bind} respectively, manipulates the levels. The former says that, if a
term is $( \ell \vee \ell_{{\mathrm{0}}} )$-secure, then we can put it in an
$\ell_{{\mathrm{0}}}$-secure box and release it at level $\ell$. An $\ell_{{\mathrm{0}}}$-secure
boxed term can be unboxed only by someone who has security clearance for
$\ell_{{\mathrm{0}}}$, as we see in the latter rule. The join operation in \rref{SDC-Bind}
ensures that $\ottnt{b}$ can depend on $\ottnt{a}$ only if $\ottnt{b}$ itself is
$\ell_{{\mathrm{0}}}$-secure or $\ell_{{\mathrm{0}}} \leq \ell$.
\subsection{Meta-theoretic Properties} \label{sec:sdc-metatheory}
This type system satisfies the following properties related to levels.
First, we can always weaken our assumptions about the variables in the
context. If a term is derivable with an assumption held at some grade, then
that term is also derivable with that assumption held at any lower
grade. Below, for any two contexts $\Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}}$, we say that
$\Omega_{{\mathrm{1}}} \leq \Omega_{{\mathrm{2}}}$ iff they are the same modulo the grades and further, for
any $\ottmv{x}$, if $ \ottmv{x} \! :^{ \ell_{{\mathrm{1}}} }\! \ottnt{A} \in \Omega_{{\mathrm{1}}} $ and $ \ottmv{x} \! :^{ \ell_{{\mathrm{2}}} }\! \ottnt{A} \in \Omega_{{\mathrm{2}}} $, then
$\ell_{{\mathrm{1}}} \leq \ell_{{\mathrm{2}}}$.
\begin{lemma}[Narrowing]
If $ \Omega' \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ and $\Omega \leq \Omega'$, then $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $.
\end{lemma}
\iffalse
\begin{proof}
By induction on $ \Omega' \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $. For \rref{SDC-Var}, we use the transitivity of $ \leq $. The other cases follow from the inductive hypothesis.
\end{proof}
\fi
Narrowing says that we can always downgrade any variable in the
context. Conversely, we cannot upgrade context variables in general, but we
can upgrade them to the level of the judgment.
\begin{lemma}[Restricted Upgrading] \label{pumping}
If $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ and $\ell_{{\mathrm{1}}} \leq \ell$, then $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} \vee \ell_{{\mathrm{1}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $.
\end{lemma}
The restricted upgrading lemma is needed to show subsumption. Subsumption states that, if a term is visible at some grade, then it is also visible at all higher grades.
\begin{lemma}[Subsumption] \label{subusage}
If $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ and $\ell \leq k$, then $ \Omega \vdash \, \ottnt{a} \, :^{ k } \, \ottnt{A} $.
\end{lemma}
\iffalse
\begin{proof}
By induction on $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $. For \rref{SDC-Var}, we use the transitivity of $ \leq $. For \rref{SDC-Return}, we use the fact that if $\ell \leq \ell_{{\mathrm{1}}}$, then for any $\ell_{{\mathrm{0}}}$, we have, $ \ell \vee \ell_{{\mathrm{0}}} \leq \ell_{{\mathrm{1}}} \vee \ell_{{\mathrm{0}}} $. For \rref{SDC-Abs}, we use lemma \ref{pumping}. The other cases follow from the inductive hypothesis.
\end{proof}
\fi
Subsumption is necessary (along with a standard weakening lemma) to show that substitution holds for this language. For substitution, we need to ensure that the level of the variable matches up with that of the substituted expression.
\begin{lemma}[Substitution] \label{substitution}
If $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ and $ \Omega_{{\mathrm{1}}} \vdash \, \ottnt{a} \, :^{ \ell_{{\mathrm{0}}} } \, \ottnt{A} $, then $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \vdash \, \ottnt{b} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} \, :^{ \ell } \, \ottnt{B} $.
\end{lemma}
\iffalse
\begin{proof}
By induction on $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $.
For \rref{SDC-Var}, if $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $, we know that $\ell_{{\mathrm{0}}} \leq \ell$. Then, by weakening and subsumption, we get $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $. The other cases follow from the inductive hypothesis.
\end{proof}
\fi
SDC terms are reduced using a call-by-name strategy. An excerpt of the small-step semantics appears in Figure \ref{fig:typing}. Note how the labels on the introduction form and the corresponding elimination form match up in \rref{SDCStep-Beta,SDCStep-BindBeta}. Further, note that we could have also used a call-by-value strategy to reduce SDC terms; we chose a call-by-name strategy because our development is motivated by potential applications in Haskell.
For a call-by-name operational semantics, the above lemmas allow us to prove, a standard progress and preservation based type soundness result, which we omit here.
Next, we show that our type system is secure by proving non-interference.
\iffalse
\subsection{Standard Type Soundness}
We use a standard small-step call-by-value semantics. The values of our language are:
\begin{center}
Values, $\ottnt{u} , \ottnt{v} ::= \ottkw{unit} \mid \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{b} \mid ( \ottnt{u} , \ottnt{v} ) \mid \ottkw{inj}_1\, \ottnt{v} \mid \ottkw{inj}_2\, \ottnt{v} \mid \eta^{ \ell }\; \ottnt{v} $
\end{center}
The step relation is mostly standard. We present an excerpt: the rules for reducing bind expressions.
\begin{figure}[h]
\centering
\drules[SDCStep]{$ \ottnt{a} \leadsto \ottnt{a'} $}{Step relation (excerpt)}
{BindCong, BindBeta}
\end{figure}
Our type system is sound with respect to this semantics, as we show through preservation and progress.
\begin{lemma}[Weakening] \label{weakening}
If $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $, then $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $.
\end{lemma}
\begin{proof}
By induction on $ \Omega_{{\mathrm{1}}} , \Omega_{{\mathrm{2}}} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. All the cases follow from inductive hypothesis.
\end{proof}
\begin{theorem}[Preservation] \label{preservation}
If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ and $ \ottnt{a} \leadsto \ottnt{a'} $, then $ \Omega \vdash\, \ottnt{a'} \, :^{ \ell } \, \ottnt{A} $.
\end{theorem}
\begin{proof}
By induction on $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $.
For \rref{SDC-App}, let $ \Omega \vdash\, \ottnt{c} \; \ottnt{b} \, :^{ \ell } \, \ottnt{C} $ such that $ \Omega \vdash\, \ottnt{c} \, :^{ \ell } \, \ottnt{B} \to \ottnt{C} $ and $ \Omega \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. Now, if $ \ottnt{c} \leadsto \ottnt{c'} $, then $ \Omega \vdash\, \ottnt{c'} \, :^{ \ell } \, \ottnt{B} \to \ottnt{C} $, and as such $ \Omega \vdash\, \ottnt{c'} \; \ottnt{b} \, :^{ \ell } \, \ottnt{C} $. On the other hand, if $\ottnt{c}$ is a value, then there are two cases to consider: first, $ \ottnt{b} \leadsto \ottnt{b'} $ in which case, using the induction hypothesis, we get $ \Omega \vdash\, \ottnt{c} \; \ottnt{b'} \, :^{ \ell } \, \ottnt{C} $; second, $\ottnt{b}$ is a value. In this case, $\ottnt{c} \ottsym{=} \lambda \ottmv{x} \!:\! \ottnt{B} . \ottnt{c'} $ and $ \Omega , \ottmv{x} \! :^{ \ell }\! \ottnt{B} \vdash\, \ottnt{c'} \, :^{ \ell } \, \ottnt{C} $. By substitution, $ \Omega \vdash\, \ottnt{c'} \ottsym{\{} \ottnt{b} \ottsym{/} \ottmv{x} \ottsym{\}} \, :^{ \ell } \, \ottnt{C} $.
For \rref{SDC-ProjF}, let $ \Omega \vdash\, \pi_1\ \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} $ such that $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} \times \ottnt{A_{{\mathrm{2}}}} $. Now, if $ \ottnt{a} \leadsto \ottnt{a'} $, then $ \Omega \vdash\, \ottnt{a'} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} \times \ottnt{A_{{\mathrm{2}}}} $, and as such $ \Omega \vdash\, \pi_1\ \ottnt{a'} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} $. On the other hand, if $\ottnt{a}$ is a value, then $\ottnt{a} \ottsym{=} ( \ottnt{v_{{\mathrm{1}}}} , \ottnt{v_{{\mathrm{2}}}} ) $ and $ \Omega \vdash\, \ottnt{v_{{\mathrm{1}}}} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} $.
For \rref{SDC-Case}, let $ \Omega \vdash\, \ottkw{case} \, \ottnt{a} \, \ottkw{of} \, \ottmv{x} \hookrightarrow \ottnt{b_{{\mathrm{1}}}} \mid \ottmv{y} \hookrightarrow \ottnt{b_{{\mathrm{2}}}} \, :^{ \ell } \, \ottnt{B} $ such that $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} + \ottnt{A_{{\mathrm{2}}}} $ and $ \Omega , \ottmv{x} \! :^{ \ell }\! \ottnt{A_{{\mathrm{1}}}} \vdash\, \ottnt{b_{{\mathrm{1}}}} \, :^{ \ell } \, \ottnt{B} $ and $ \Omega , \ottmv{y} \! :^{ \ell }\! \ottnt{A_{{\mathrm{2}}}} \vdash\, \ottnt{b_{{\mathrm{2}}}} \, :^{ \ell } \, \ottnt{B} $. Now, if $ \ottnt{a} \leadsto \ottnt{a'} $, then $ \Omega \vdash\, \ottnt{a'} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} + \ottnt{A_{{\mathrm{2}}}} $, and as such $ \Omega \vdash\, \ottkw{case} \, \ottnt{a'} \, \ottkw{of} \, \ottmv{x} \hookrightarrow \ottnt{b_{{\mathrm{1}}}} \mid \ottmv{y} \hookrightarrow \ottnt{b_{{\mathrm{2}}}} \, :^{ \ell } \, \ottnt{B} $. On the other hand, if $\ottnt{a}$ is a value, then $\ottnt{a} \ottsym{=} \ottkw{inj}_1\, \ottnt{v_{{\mathrm{1}}}} $ or $\ottnt{a} \ottsym{=} \ottkw{inj}_2\, \ottnt{v_{{\mathrm{2}}}} $. Say, $\ottnt{a} \ottsym{=} \ottkw{inj}_1\, \ottnt{v_{{\mathrm{1}}}} $. By inversion, $ \Omega \vdash\, \ottnt{v_{{\mathrm{1}}}} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} $. By substitution lemma, we get $ \Omega \vdash\, \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{v_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \, :^{ \ell } \, \ottnt{B} $.
For \rref{SDC-Bind}, let $ \Omega \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ such that $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ and $ \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! \ottnt{A} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. Now, if $ \ottnt{a} \leadsto \ottnt{a'} $, then $ \Omega \vdash\, \ottnt{a'} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ , and as such $ \Omega \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a'} \, \ottkw{in} \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. On the other hand, if $\ottnt{a}$ is a value, then $\ottnt{a} \ottsym{=} \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{v} $. By inversion, $ \Omega \vdash\, \ottnt{v} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} $. By substitution, $ \Omega \vdash\, \ottnt{b} \ottsym{\{} \ottnt{v} \ottsym{/} \ottmv{x} \ottsym{\}} \, :^{ \ell } \, \ottnt{B} $.
The other cases follow from inductive hypothesis.
\end{proof}
\begin{theorem}[Progress] \label{progress}
If $ \varnothing \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then either $\ottnt{a}$ is a value or there exists $\ottnt{a'}$ such that $ \ottnt{a} \leadsto \ottnt{a'} $.
\end{theorem}
\begin{proof}
By induction on $ \varnothing \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $.
\end{proof}
Therefore SDC is sound with respect to standard operational semantics. But this soundness theorem is not strong enough to show that programs derived in the calculus are secure by design. We address this issue next by presenting a syntactic proof of non-interference for SDC.
\fi
\subsection{A Syntactic Proof of Non-interference}
\label{sec:geq}
When users with low-security clearance are oblivious to high-security data, we say that the system enjoys \emph{non-interference}. Non-interference results from level-specific views of the world. The values $ \eta^{ { \color{black}{H} } }\; \ottkw{True} $ and $ \eta^{ { \color{black}{H} } }\; \ottkw{False} $ appear the same to an $ { \color{black}{L} } $-user while an $ { \color{black}{H} } $-user can differentiate between them. To capture this notion of a level-specific view, we design an indexed equivalence relation on open terms, $\sim_{\ell}$, called \textit{indexed indistinguishability}, and shown in Figure \ref{fig:guarded-equality}. To define this relation, we need the labels of the variables in the context but not their types. So, we use grade-only contexts $\Phi$, defined as $\Phi ::= \varnothing \mid \Phi , \ottmv{x} \! : \ell $. These contexts are like graded contexts $\Omega$ without the type information on variables, also denoted by $ | \Omega | $.
\begin{figure}
\centering
\drules[SGEq]{$ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $}{Indexed Indistinguishability}
{Var,Abs,App,Return,Bind}
\boxed{ \Phi \vdash^{ \ell_{{\mathrm{0}}} }_{ \ell } \ottnt{a_{{\mathrm{1}}}} \sim \ottnt{a_{{\mathrm{2}}}} }
\[ \drule{SEq-Leq} \qquad \drule{SEq-Nleq} \]
\caption{Indexed indistiguishability for SDC (Excerpt)}
\label{fig:guarded-equality}
\end{figure}
Informally, $\Phi \vdash \ottnt{a} \sim_{\ell} \ottnt{b}$ means that $\ottnt{a}$ and $\ottnt{b}$ appear the same to an $\ell$-user. For example, $ \eta^{ { \color{black}{H} } }\; \ottkw{True} \sim_{ { \color{black}{L} } } \eta^{ { \color{black}{H} } }\; \ottkw{False} $ but $\neg( \eta^{ { \color{black}{H} } }\; \ottkw{True} \sim_{ { \color{black}{H} } } \eta^{ { \color{black}{H} } }\; \ottkw{False} )$. We define this relation $\sim_{\ell}$ by structural induction on terms. We think of terms as ASTs annotated at various nodes with labels, say $\ell_{{\mathrm{0}}}$, that determine whether an observer $\ell$ is allowed to look at the corresponding sub-tree. If $\ell_{{\mathrm{0}}} \leq \ell$, then observer $\ell$ can start exploring the sub-tree; otherwise the entire sub-tree appears as a blob. So we can also read $\Phi \vdash \ottnt{a} \sim_{\ell} \ottnt{b}$ as: ``$\ottnt{a}$ is syntactically equal to $\ottnt{b}$ at all parts of the terms marked with any label $\ell_{{\mathrm{0}}}$, where $\ell_{{\mathrm{0}}} \leq \ell$, but may be
arbitrarily different elsewhere.''
Note the \rref{SGEq-Return} in Figure \ref{fig:guarded-equality}. It uses an auxiliary relation, $ \Phi \vdash^{ \ell_{{\mathrm{0}}} }_{ \ell } \ottnt{a_{{\mathrm{1}}}} \sim \ottnt{a_{{\mathrm{2}}}} $. This auxiliary \textit{extended equivalence} relation $ \Phi \vdash^{ \ell_{{\mathrm{0}}} }_{ \ell } \ottnt{a_{{\mathrm{1}}}} \sim \ottnt{a_{{\mathrm{2}}}} $ formalizes the idea discussed above: if $\ell_{{\mathrm{0}}} \leq \ell$, then $\ottnt{a_{{\mathrm{1}}}}$ and $\ottnt{a_{{\mathrm{2}}}}$ must be indistinguishable at $\ell$; otherwise, they may be arbitrary terms.
Now, we explore some properties of the indistinguishability relation.\footnote{Because this relation is untyped, its analogue for DDC is similar. For each lemma below, we include a reference to the location in the Coq development where it may be found for the dependent system.} \\ If we remove the second component from an indistinguishability relation, $ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $, we get a new judgment, $ \Phi \vdash \ottnt{a} : \ell $, called grading judgment. Now, corresponding to every indistinguishability rule, we define a grading rule where the indistinguishability judgments have been replaced with their grading counterparts. Terms derived using these grading rules are called well-graded. We can show that well-typed terms are well-graded.
\begin{lemma}[Typing implies grading] \label{typing_grading}
If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ then $ | \Omega | \vdash \ottnt{a} : \ell $.
\end{lemma}
\begin{lemma}[Equivalence] \label{ind_equivalence}
Indexed indistinguishability at $\ell$ is an equivalence relation on well-graded terms at $\ell$.
\end{lemma}
\iffalse
The guarded equality at level $\ell$ shows us the terms that are equal at $\ell$. Now, terms that are guarded equal at some level may not be guarded equal at a higher level. For example, $ \eta^{ { \color{black}{H} } }\; \ottkw{True} \sim_{ { \color{black}{L} } } \eta^{ { \color{black}{H} } }\; \ottkw{False} $ but $\neg( \eta^{ { \color{black}{H} } }\; \ottkw{True} \sim_{ { \color{black}{H} } } \eta^{ { \color{black}{H} } }\; \ottkw{False} )$. But terms that are guarded equal at some level are also guarded equal at any lower level.
\begin{lemma}[Downgrading Guarded Equality]
For $\ell_{{\mathrm{0}}} \leq \ell$, if $ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $ and $ \Phi \vdash \ottnt{a} : \ell_{{\mathrm{0}}} $ and $ \Phi \vdash \ottnt{b} : \ell_{{\mathrm{0}}} $, then $ \Phi \vdash \ottnt{a} \sim_{ \ell_{{\mathrm{0}}} } \ottnt{b} $.
\end{lemma}
\fi
\iffalse
The guarded equality relation is closed under substitution.
\begin{lemma}[Guarded equality substitution]
If $ \Phi , \ottmv{x} \! : \ell \vdash \ottnt{b_{{\mathrm{1}}}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} $ and $ \Phi \vdash \ottnt{a} \sim_{ k } \ottnt{a} $ then $ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} $.
\end{lemma}
\fi
The above lemma shows that indistinguishability is an equivalence relation. Observe that at the highest element of the lattice, $ { \color{black}{\top} } $, this equivalence degenerates to the identity relation.\\
Indistinguishability is closed under extended equivalence. The following is like a substitution lemma for the relation.
\begin{lemma}[Indistinguishability under substitution]
If $ \Phi , \ottmv{x} \! : \ell \vdash \ottnt{b_{{\mathrm{1}}}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} $ and $ \Phi \vdash^{ \ell }_{ k } \ottnt{a_{{\mathrm{1}}}} \sim \ottnt{a_{{\mathrm{2}}}} $ then $ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $.
\end{lemma}
With regard to the above lemma, consider the situation when $ \neg \ottsym{(} \ell \leq k \ottsym{)} $, for example, when $\ell = { \color{black}{H} } $ and $k = { \color{black}{L} } $. In such a situation, for any two terms $\ottnt{a_{{\mathrm{1}}}}$ and $\ottnt{a_{{\mathrm{2}}}}$, if $ \Phi , \ottmv{x} \! : \ell \vdash \ottnt{b_{{\mathrm{1}}}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} $, then $ \Phi \vdash \ottnt{b_{{\mathrm{1}}}} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \sim_{ k } \ottnt{b_{{\mathrm{2}}}} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $. Let us work out a concrete example. For a typing derivation $ \ottmv{x} \! :^{ { \color{black}{H} } }\! \ottnt{A} \vdash\, \ottnt{b} \, :^{ { \color{black}{L} } } \, \ottkw{Bool} $, we have, by lemmas \ref{typing_grading} and \ref{ind_equivalence}, $ \ottmv{x} \! : { \color{black}{H} } \vdash \ottnt{b} \sim_{ { \color{black}{L} } } \ottnt{b} $. Then, $ \varnothing \vdash \ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}} \sim_{ { \color{black}{L} } } \ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}} $. This is almost non-interference in action. What's left to show is that the indistinguishability relation respects the small step semantics, written $ \ottnt{a_{{\mathrm{1}}}} \leadsto \ottnt{a_{{\mathrm{2}}}} $. The small-step relation is standard call-by-name reduction.
\begin{theorem}[Non-interference]
\label{lemma:GEq_respects_Step}
If $ \Phi \vdash \ottnt{a_{{\mathrm{1}}}} \sim_{ k } \ottnt{a'_{{\mathrm{1}}}} $ and $ \ottnt{a_{{\mathrm{1}}}} \leadsto \ottnt{a_{{\mathrm{2}}}} $ then there exists some $\ottnt{a'_{{\mathrm{2}}}}$ such that $ \ottnt{a'_{{\mathrm{1}}}} \leadsto \ottnt{a'_{{\mathrm{2}}}} $ and $ \Phi \vdash \ottnt{a_{{\mathrm{2}}}} \sim_{ k } \ottnt{a'_{{\mathrm{2}}}} $.
\end{theorem}
Since the step relation is deterministic, in the above lemma, there is exactly one such $\ottnt{a'_{{\mathrm{2}}}}$ that $\ottnt{a'_{{\mathrm{1}}}}$ steps to. Now, going back to our last example, we see that $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ and $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ take steps in tandem and they are $ { \color{black}{L} } $-indistinguishable after each and every step. Since the language itself is terminating, both the terms reduce to boolean values, values that are themselves $ { \color{black}{L} } $-indistinguishable as well. But the indistinguishability for boolean values is just the identity relation. This means that $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{1}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ and $\ottnt{b} \ottsym{\{} \ottnt{a_{{\mathrm{2}}}} \ottsym{/} \ottmv{x} \ottsym{\}}$ reduce to the same value.
The indistinguishability relation gives us a syntactic method of proving non-interference for programs derived in SDC. Essentially, we show that a user with low-security clearance cannot distinguish between high security values just by observing program behavior.\\ Next, we show that SDC is no less expressive than the terminating fragment of DCC.
\iffalse
when all high security values are erased, program behavior does not change for a low-security user. We shall use this idea to implement irrelevance in dependent types.
\subsection{Erasure} \label{erasure}
We define an indexed erasure function $\lfloor \cdot \rfloor_{\ell}$ on SDC terms that erases everything an $\ell$-user should not be able to see. The definition is given by straightforward recursion on terms in most cases. For example: $ \lfloor \ottmv{x} \rfloor_ \ell = \ottmv{x}$ and $ \lfloor \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{a} \rfloor_ \ell = \lambda \ottmv{x} \!:\! \ottnt{A} . \lfloor \ottnt{a} \rfloor_ \ell $. The interesting case is: $ \lfloor \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} \rfloor_ \ell = \eta^{ \ell_{{\mathrm{0}}} }\; \lfloor \ottnt{a} \rfloor_ \ell $ if $\ell_{{\mathrm{0}}} \leq \ell$ and $ \eta^{ \ell_{{\mathrm{0}}} }\; \blacksquare $ otherwise. This is so because if $ \neg \ottsym{(} \ell_{{\mathrm{0}}} \leq \ell \ottsym{)} $, an $\ell$-user should not be able to see $\ottnt{a}$. We extend the language with $ \blacksquare $ (which stands for erased terms) and update all the definitions accordingly.
The erasure function maps the equivalence classes formed by the indistinguishability relation to their respective canonical elements, as we see in the lemma below.
\begin{lemma}[Canonical Element]
If $ \Phi \vdash \ottnt{a_{{\mathrm{1}}}} \sim_{ \ell } \ottnt{a_{{\mathrm{2}}}} $, then $ \lfloor \ottnt{a_{{\mathrm{1}}}} \rfloor_ \ell = \lfloor \ottnt{a_{{\mathrm{2}}}} \rfloor_ \ell $.
\end{lemma}
Further, a well-graded term and its erasure are indistinguishable.
\begin{lemma}[Erasure Indistinguishability]
If $ \Phi \vdash \ottnt{a} : \ell $, then $ \Phi \vdash \ottnt{a} \sim_{ \ell } \lfloor \ottnt{a} \rfloor_ \ell $.
\end{lemma}
Now that we have seen the correspondence between the erasure function and the indistinguishability relation, let us look at the semantics of erased terms. Erased terms simulate the reduction behavior of their unerased counterparts.
\begin{lemma}[Erasure Simulation]
If $ \Phi \vdash \ottnt{a} : \ell $ and $ \ottnt{a} \leadsto \ottnt{b} $, then $ \lfloor \ottnt{a} \rfloor_ \ell \leadsto \lfloor \ottnt{b} \rfloor_ \ell $. Otherwise, if $\ottnt{a}$ is a value, then so is $ \lfloor \ottnt{a} \rfloor_ \ell $.
\end{lemma}
Further, the observable behavior of a program remains the same after erasure.
\begin{theorem}[Erasure Observability]
If $ \varnothing \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ and $ \varnothing \vdash \, \ottmv{f} \, :^{ \ell } \, \ottnt{A} \to \ottkw{Bool} $, then $\ottsym{(} \ottmv{f} \; \ottnt{a} \ottsym{)}$ and $\ottsym{(} \ottmv{f} \; \lfloor \ottnt{a} \rfloor_ \ell \ottsym{)}$ reduce to the same value.
\end{theorem}
}
The above theorem can be seen as a non-interference theorem as well. In fact, the term non-interference was originally introduced by \citet{goguen} to refer to a similar property: a set of users $G$ is non-interfering with another set of users $G'$ if and only if for all possible programs $w$, the observable behavior of $w$ for $G'$ remains the same even after erasing all the commands in $w$ that are initiated by users in $G$. The above theorem also shows that the erasure operation on terms is safe. We shall use this property to implement run-time and compile-time irrelevance in the dependent calculus.
\fi
\subsection{Relation with Sealing Calculus and Dependency Core Calculus}
SDC is extremely similar to the sealing calculus $\lambda^{[]}$ of
\citet{igarashi}. Like SDC, $\lambda^{[]}$ has a label on the typing
judgment.\footnote{Note that our labels correspond to observer levels of
\citet{igarashi}, which can be viewed as a lattice.} But unlike SDC, $\lambda^{[]}$ uses
standard ungraded typing contexts $\Gamma$. Both the calculi have the same types. As far as terms are concerned, there is only one difference. The sealing calculus has an $\ottkw{unseal}$ term whereas SDC uses
$\ottkw{bind}$. We present the rules for sealing and unsealing terms in $\lambda^{[]}$ below.\footnote{We take the liberty of making small cosmetic changes in the presentation.}
\[ \drule{Sealing-Seal}\drule{Sealing-Unseal} \]
\citet{igarashi} have shown that $\lambda^{[]}$ is equivalent to
$\text{DCC}_{\text{pc}}$, an extension of the terminating fragment of
DCC. Therefore, we compare SDC to DCC by simulating $\lambda^{[]}$ in SDC.
For this, we define a translation $\bar{\cdot}$, from $\lambda^{[]}$ to SDC. Most of the cases are handled inductively in a straightforward manner. For $\ottkw{unseal}$, we have, $ \overline{ \ottkw{unseal}^{ \ell } \ottnt{a} } := \ottkw{bind} ^{ \ell } \, \ottmv{x} = \overline{ \ottnt{a} } \, \ottkw{in} \, \ottmv{x} $.
With this translation, we can give a forward and a backward simulation
connecting the two languages. The reduction relation $\leadsto$ below is
full reduction for both the languages, the reduction strategy used by \citet{igarashi} for $\lambda^{[]}$. Full reduction is a non-deterministic reduction strategy whereby a $\beta$-redex in any sub-term may be reduced.
\begin{theorem}[Forward Simulation]
If $ \ottnt{a} \leadsto \ottnt{a'} $ in $\lambda^{[]}$, then $ \overline{ \ottnt{a} } \leadsto \overline{ \ottnt{a'} } $ in SDC.
\end{theorem}
\begin{theorem}[Backward Simulation]
For any term $a$ in $\lambda^{[]}$, if $ \overline{ \ottnt{a} } \leadsto \ottnt{b} $ in SDC, then there exists $\ottnt{a'}$ in $\lambda^{[]}$ such that $\ottnt{b} \ottsym{=} \overline{ \ottnt{a'} } $ and $ \ottnt{a} \leadsto \ottnt{a'} $.
\end{theorem}
The translation also preserves typing. In fact, a source term and its target have the same type. Below, for an ordinary context $\Gamma$, the graded context $ \Gamma ^{ \ell } $ denotes $\Gamma$ with the labels
for all the variables set to $\ell$.
\begin{theorem}[Translation Preserves Typing]
If $ \Gamma \vdash \ottnt{a} :^{ \ell } \ottnt{A} $, then $ \Gamma ^{ \ell } \vdash\, \overline{ \ottnt{a} } \, :^{ \ell } \, \ottnt{A} $.
\end{theorem}
\iffalse
\begin{proof}
By induction on $ \Gamma \vdash \ottnt{a} :^{ \ell } \ottnt{A} $.
For \rref{Sealing-Seal}, we have $ \Gamma \vdash \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} :^{ \ell } T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ where $ \Gamma \vdash \ottnt{a} :^{ \ell \vee \ell_{{\mathrm{0}}} } \ottnt{A} $. By inductive hypothesis, $ \Gamma ^{ \ell \vee \ell_{{\mathrm{0}}} } \vdash \, \overline{ \ottnt{a} } \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} $. By \rref{SDC-Return}, we have, $ \Gamma ^{ \ell \vee \ell_{{\mathrm{0}}} } \vdash\, \eta^{ \ell_{{\mathrm{0}}} }\; \overline{ \ottnt{a} } \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $. By dereliction, $ \Gamma ^{ \ell } \vdash\, \eta^{ \ell_{{\mathrm{0}}} }\; \overline{ \ottnt{a} } \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $.
For \rref{Sealing-Unseal}, we have $ \Gamma \vdash \ottkw{unseal}^{ \ell_{{\mathrm{0}}} } \ottnt{a} :^{ \ell } \ottnt{A} $ where $ \Gamma \vdash \ottnt{a} :^{ \ell } T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ and $\ell_{{\mathrm{0}}} \leq \ell$. By inductive hypothesis, $ \Gamma ^{ \ell } \vdash\, \overline{ \ottnt{a} } \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $. By \rref{SDC-Var}, we have, $ \Gamma ^{ \ell } , \ottmv{x} \! :^{ \ell }\! \ottnt{A} \vdash\, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $. Note $ \ell \vee \ell_{{\mathrm{0}}} = \ell$. So, by \rref{SDC-Bind}, we get, $ \Gamma ^{ \ell } \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \overline{ \ottnt{a} } \, \ottkw{in} \, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $.
\end{proof}
\fi
The above translation shows that the terminating fragment of DCC can be embedded into SDC. Therefore SDC is at least as expressive as the terminating fragment of DCC. Further, SDC lends itself nicely to syntactic proof techniques for non-interference. This approach generalizes to more expressive systems, as we shall see in the next section, where we extend SDC to a general dependent dependency calculus.
\iffalse
The flow-aware operational semantics is modelled through heaps. A heap is an ordered list of tuples: variable, assigned term, type and associated security level. Formally, a heap is:\\
\begin{center}
Heap , $ \ottnt{H} ::= \varnothing \mid \ottnt{H} , \ottmv{x} \overset{ \ell }{\mapsto} \ottnt{a} : \ottnt{A} $
\end{center}
The flow-aware step relation takes, at a given security level, one heap term pair to another heap term pair. While stepping, it checks that the information asked for can be accessed at the given security level. We present an excerpt of the flow-aware step relation in Figure \ref{fig:heap}.
\begin{figure}
\centering
\drules[HeapStep]{$ [ \ottnt{H} ] \ottnt{a} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{a'} $}{Heap Semantics (excerpt)}
{Var,AppCong,AppBeta,BindCong,BindBeta}
\caption{Flow-aware step relation}
\label{fig:heap}
\end{figure}
The \rref{HeapStep-Var} is interesting. It allows $\ell$ to see $\ottmv{x}$ which is at security level $\ell_{{\mathrm{0}}}$ if and only if $\ell_{{\mathrm{0}}} \leq \ell$. This rule ensures that one cannot access data without the appropriate permissions. The other rule that is essential for ensuring security is \rref{HeapStep-BindBeta}. Through this rule, we ensure that a term wrapped in a $\ell_{{\mathrm{0}}}$-secure box is assigned a level at least as secure as $\ell_{{\mathrm{0}}}$. With this stepping relation, we can prove an indistinguishability lemma:
\begin{lemma}[Indistinguishability] \label{indistinguishable}
If $ \neg \ottsym{(} \ell_{{\mathrm{0}}} \leq \ell \ottsym{)} $ and $ [ \ottnt{H_{{\mathrm{1}}}} , \ottmv{x} \overset{ \ell_{{\mathrm{0}}} }{\mapsto} \ottnt{a_{{\mathrm{1}}}} : \ottnt{A} , \ottnt{H_{{\mathrm{2}}}} ] \ottnt{b} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{b'} $, then $ [ \ottnt{H_{{\mathrm{1}}}} , \ottmv{x} \overset{ \ell_{{\mathrm{0}}} }{\mapsto} \ottnt{a_{{\mathrm{2}}}} : \ottnt{A} , \ottnt{H_{{\mathrm{2}}}} ] \ottnt{b} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{b'} $.
\end{lemma}
\begin{proof}
By induction on $ [ \ottnt{H_{{\mathrm{1}}}} , \ottmv{x} \overset{ \ell_{{\mathrm{0}}} }{\mapsto} \ottnt{a_{{\mathrm{1}}}} : \ottnt{A} , \ottnt{H_{{\mathrm{2}}}} ] \ottnt{b} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{b'} $.
\end{proof}
This lemma shall help us prove non-interference. But for that, we need a soundness lemma. Since we prove soundness on open terms, we need a compatibility relation to make sure that the levels on the assignments in the heap are correct. This relation is presented below:
\begin{figure}[h]
\centering
\drules[Compat]{$ \ottnt{H} \vdash \Omega $}{Compatibility relation}
{Empty,Cons}
\end{figure}
Now we state and prove the soundness theorem:
\begin{theorem}[Soundness] \label{soundness}
If $ \ottnt{H} \vdash \Omega $ and $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then either $\ottnt{a}$ is a value or there exists $\ottnt{a'}$, $\ottnt{H'}$ and $\Omega'$ such that $ [ \ottnt{H} ] \ottnt{a} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{a'} $ and $ \Omega' \vdash \, \ottnt{a'} \, :^{ \ell } \, \ottnt{A} $ and $ \ottnt{H'} \vdash \Omega' $ and $\Omega$ is a prefix list of $\Omega'$.
\end{theorem}
\begin{proof}
By induction on $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $.
For \rref{SDC-Var}, we have, $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $ where $\ell_{{\mathrm{0}}} \leq \ell$. Further, $ \ottnt{H} \vdash \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} $. So $\ottnt{H} = \ottnt{H_{{\mathrm{1}}}} , \ottmv{x} \overset{ \ell_{{\mathrm{0}}} }{\mapsto} \ottnt{a} : \ottnt{A} , \ottnt{H_{{\mathrm{2}}}} $ where $ \Omega_{{\mathrm{1}}} \vdash\, \ottnt{a} \, :^{ \ell_{{\mathrm{0}}} } \, \ottnt{A} $. Now, $ [ \ottnt{H} ] \ottmv{x} \Rightarrow^{ \ell } [ \ottnt{H} ] \ottnt{a} $ and by weakening and subsumption, $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $.
For \rref{SDC-App}, we have, $ \Omega \vdash\, \ottnt{b} \; \ottnt{a} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{A} \to \ottnt{B} $ and $ \Omega \vdash\, \ottnt{a} \, :^{ { \color{black}{\bot} } } \, \ottnt{A} $. Now, either $\ottnt{b}$ steps or it's a value. In the former case, using the induction hypothesis, we get $ [ \ottnt{H} ] \ottnt{b} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{b'} $ and $ \Omega' \vdash\, \ottnt{b'} \, :^{ \ell } \, \ottnt{A} \to \ottnt{B} $ where $ \ottnt{H'} \vdash \Omega' $. By weakening and \rref{SDC-App}, we have $ \Omega' \vdash\, \ottnt{b'} \; \ottnt{a} \, :^{ \ell } \, \ottnt{B} $. In the latter case, $\ottnt{b} = \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{b_{{\mathrm{1}}}} $ and by inversion, $ \Omega , \ottmv{x} \! :^{ { \color{black}{\bot} } }\! \ottnt{A} \vdash\, \ottnt{b_{{\mathrm{1}}}} \, :^{ { \color{black}{\bot} } } \, \ottnt{B} $. But, $ \ottnt{H} , \ottmv{x} \overset{ { \color{black}{\bot} } }{\mapsto} \ottnt{a} : \ottnt{A} \vdash \Omega , \ottmv{x} \! :^{ { \color{black}{\bot} } }\! \ottnt{A} $.
For \rref{SDC-Bind}, we have, $ \Omega \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ and $ \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! \ottnt{A} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. Now, either $\ottnt{a}$ takes a step or it's a value. In the former case, we get $ [ \ottnt{H} ] \ottnt{a} \Rightarrow^{ \ell } [ \ottnt{H'} ] \ottnt{a'} $ and $ \Omega' \vdash\, \ottnt{a'} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ where $ \ottnt{H'} \vdash \Omega' $. By weakening and \rref{SDC-Bind}, we have $ \Omega' \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a'} \, \ottkw{in} \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. In the latter case, $\ottnt{a} = \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a_{{\mathrm{1}}}} $ and by inversion, $ \Omega \vdash\, \ottnt{a_{{\mathrm{1}}}} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} $. But, $ \ottnt{H} , \ottmv{x} \overset{ \ell \vee \ell_{{\mathrm{0}}} }{\mapsto} \ottnt{a_{{\mathrm{1}}}} : \ottnt{A} \vdash \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! \ottnt{A} $.
The other cases are similar.
\end{proof}
The soundness theorem, along with the indistinguishability lemma, implies that programs derived in SDC are secure by design. In the next section, we shall use this theorem to give an operational proof of non-interference for DCC.
\fi
\iffalse
\paragraph{Variables}\
\centerline{\drule{ST-Var}\drule{ST-Weak}}
\vspace{1ex}
If $\ell_{{\mathrm{0}}} = { \color{black}{R} } $ meaning $\ottmv{x}$ is available at run-time, $\ell$ may be instantiated to $ { \color{black}{C} } $ meaning $\ottmv{x}$ may be used at compile-time as well. If $\ell_{{\mathrm{0}}} = { \color{black}{L} } $ meaning $\ottmv{x}$ stands for low-security data, $\ell$ may be instantiated to $ { \color{black}{H} } $ meaning $\ottmv{x}$ may be treated as high-security data. But if $\ell_{{\mathrm{0}}} = { \color{black}{C} } $, then $\ell$ cannot be $ { \color{black}{R} } $. Similarly, if $\ell_{{\mathrm{0}}} = { \color{black}{H} } $, we cannot have $\ell$ equal to $ { \color{black}{L} } $. The \rref{ST-Weak} says that we can add additional assumptions having arbitrary qualities.
\paragraph{Unit}\
\centerline{\drule{ST-Unit}\drule{ST-UnitE}}
\vspace{1ex}
Since $\ottkw{unit}$ is a constant, we can observe it at any quality. For eliminating a value of type $\ottkw{Unit}$, we just match it with $\ottkw{unit}$ and return whatever follows in the let-expression. The let-expression itself and the term that is returned are checked at the same quality.
\paragraph{Functions}\
\centerline{\drule{ST-Lam}\drule{ST-App}}\
\vspace{1ex}
We annotate the arrow type with the quality of the argument to the function. The \rref{ST-Lam} then reads, for $\ell$ to be able to observe a function whose argument has quality $\ell_{{\mathrm{0}}}$, we need to observe the body at $\ell$ while assuming quality $\ell_{{\mathrm{0}}}$ for the argument. Example: say $\ell = { \color{black}{L} } $ is qualified to observe a function taking $\ell_{{\mathrm{0}}} = { \color{black}{H} } $ quality argument. Since $ { \color{black}{L} } $ is not allowed to see $ { \color{black}{H} } $ values, such a function can only be constant. The type system ensures this by checking the body at $ { \color{black}{L} } $ while maintaining the argument variable at $ { \color{black}{H} } $, thus making it unavailable.
Now, we look at \rref{ST-App}. The argument $\ottnt{a}$ is checked at $ \ell_{{\mathrm{0}}} \vee \ell $, the modified join of $\ell_{{\mathrm{0}}}$ and $\ell$. Note that since we are working with a partial order, some $\ell_{{\mathrm{1}}}$ and $\ell_{{\mathrm{2}}}$ may not have a join. We define $ \ell_{{\mathrm{0}}} \vee \ell $ to be the join of $\ell_{{\mathrm{0}}}$ and $\ell$, in case $\ell_{{\mathrm{0}}}$ and $\ell$ are comparable; otherwise it equals $\ell_{{\mathrm{0}}}$. We could have used just $\ell_{{\mathrm{0}}}$ instead of $ \ell_{{\mathrm{0}}} \vee \ell $ to check the argument. But checking at the modified join provides more flexibility. Say, $\ell_{{\mathrm{0}}} = { \color{black}{L} } $ and $\ell = { \color{black}{H} } $. This means that an $ { \color{black}{H} } $ function expects an $ { \color{black}{L} } $ argument. In such a scenario, we can provide an $ { \color{black}{H} } $ argument to the function since it is qualified to observe $ { \color{black}{H} } $ values.
\paragraph{Products}\
\centerline{\drule{ST-WPair}\drule{ST-WUnpair}}\
\vspace{1ex}
Similar to the arrow type, we annotate the product type with the quality of the first component. The \rref{ST-WPair} then reads, for $\ell$ to observe a pair whose first component has quality $\ell_{{\mathrm{0}}}$, we should be able to observe the first component at $ \ell_{{\mathrm{0}}} \vee \ell $ and the second component at $\ell$. As in the \rref{ST-App}, checking at the modified join provides more flexibility.
The \rref{ST-WUnpair} eliminates the pair through pattern matching. The pattern variables $\ottmv{x}$ and $\ottmv{y}$ are assumed to have the corresponding qualities, here $\ell_{{\mathrm{0}}}$ and $\ell$ respectively.
There is another way by which we can eliminate a pair: through projections. We introduce another product type below, called strong product, as opposed to the weak product type above. Terms of the strong product type are eliminated via projections.\\
\centerline{\drule{ST-SPair}\drule{ST-ProjF}\drule{ST-ProjS}}\
\vspace{1ex}
The \rref{ST-SPair} is essentially the same as \rref{ST-WPair}. The \rref{ST-ProjF} says that, if $\ell$ can observe a pair whose first component has quality $\ell_{{\mathrm{0}}}$, then the first component may be observed at the modified join of $\ell_{{\mathrm{0}}}$ and $\ell$. The \rref{ST-ProjS} says that the second component of a pair may be observed wherever the pair itself can be. Example: for a pair with $\ell = { \color{black}{H} } $ quality with a $\ell_{{\mathrm{0}}} = { \color{black}{L} } $ quality first component, we can only view the first component at $ { \color{black}{H} } $.
\paragraph{Sums}\
\centerline{\drule{ST-InjF}\drule{ST-InjS}\drule{ST-Case}}\
\vspace{1ex}
Now we look at sums. Unlike the arrow and the product types, we don't annotate the sum type with a quality. This does not lead to loss in expressiveness since an annotated sum type can be derived using the unannotated sum type and an annotated product type along with the Unit type. The introduction rules use the same quality for the premise and the conclusion. The elimination \rref{ST-Case} is interesting. The sum and the branches are observed at the same quality $\ell$. A question arises, could we observe the sum at a different quality? Say, if the branches are observed at $ { \color{black}{L} } $, could we observe the sum at $ { \color{black}{H} } $? The second and the third premises could make sure that such a sum does not influence the output of either branch. But even then, the choice of the branch would still depend on the $ { \color{black}{H} } $ sum value. This would lead to an implicit flow of information from $ { \color{black}{H} } $ to $ { \color{black}{L} } $, something we want to avoid. So we use the same quality to check the sum and the branches. But why do we have $\ell_{{\mathrm{0}}}$ as the quality of the pattern in the branches? We could have used $\ell$ but using $\ell_{{\mathrm{0}}}$ provides more flexibility. The case-expression behaves like an if-expression whenever $\ell$ cannot observe $\ell_{{\mathrm{0}}}$.
\fi
\section{Equivalence of SDC and DCC} \label{SDCC}
In this section, we show that SDC and the terminating fragment of DCC are equivalent. To this end, we first present a meaning-preserving translation from the terminating fragment of DCC to SDC. DCC programs are assigned meaning using a categorical model \textit{DC}. We shall also interpret SDC in the same model. But before that, we want to bring out an issue with the categorical model of DCC.
\subsection{An Issue with the Categorical Model of DCC}
The interpretation of DCC in category \textit{DC}, as presented in \citet{dcc}, is unsound. We explain the reason behind the unsoundness below. If we restrict ourselves to the terminating fragment of DCC, the objects of category \textbf{DC} are sets with label-indexed binary relations on them while the morphisms are functions that respect the relations. An object $C$ of category \textit{DC} is a set $| C |$ together with a family $R_{|C|,\ell}$ of binary relations on $| C |$ indexed by labels $\ell$. A morphism from $C$ to $D$ is a function $f$ from $| C |$ to $ D |$ such that for any $\ell$, if $ (c_1 , c_2) \in R_{| C |, \ell}$, then $( f c_1 , f c_2 ) \in R_{| D |, \ell}$.
The category is cartesian. The terminal object $\bd{1}$ is the singleton set with identity relation. Now, for objects $C, D$, the product $C \mathbf{\times} D$ is defined as:
\begin{align*}
| C \bd{\times} D | & = | C | \times | D | \\
R_{|C \bd{\times} D|, \ell} & = \{ ((c_1, d_1) , (c_2 , d_2)) \, | \, (c_1 , c_2) \in R_{|C|,\ell} \wedge (d_1 , d_2) \in R_{|D|,\ell} \}
\end{align*}
But contrary to what is mentioned in \citet{dcc}, the category is not cartesian closed. In \citet{dcc}, the exponential object $D^C$, for objects $C, D$, has the set of morphisms from $C$ to $D$ as its underlying set. But this definition does not give us the required universal property for exponentials. We demonstrate this below.
Consider a two-point lattice $ { \color{black}{L} } \leq { \color{black}{H} } $. Consider objects $C , D, E$ such that
\begin{align*}
| C | & = \{ c_1 , c_2 \} \\
| D | & = \{ d_1 , d_2 \} \\
| E | & = \{ e_1 , e_2 \} \\
R_{|C|, { \color{black}{L} } } & = | C | \times | C | \\
R_{|C|, { \color{black}{H} } } & = I_{|C|} \\
R_{|D|, { \color{black}{L} } } & = R_{|D|, { \color{black}{H} } } = I_{|D|} \\
R_{|E|, { \color{black}{L} } } & = R_{|E|, { \color{black}{H} } } = \{ (e_1 , e_1) \}
\end{align*}
Here, $I_X$ represents the identity relation on $X$.
We can count that there are $8$ morphisms from $E \mathbf{\times} C$ to $D$ whereas there are only $2$ morphisms from $C$ to $D$. So $| D^C |$ has $2$ elements and thus, there can be at most $4$ morphisms from $E$ to $D^C$. Hence, $\textsf{Hom}(E \mathbf{\times} C , D)$ can not be isomorphic to $\textsf{Hom} (E , D^C)$. Therefore, the universal property of exponentials fails to hold. So the interpretation is unsound.
If we analyse the problem, we find it stems from the fact that $(e_2 , e_2) \notin R_{| E |, \ell}$. Owing to this, a morphism can map $(e_2 , c_1)$ and $(e_2 , c_2)$ to unrelated values even though $c_1$ and $c_2$ are related. Generalizing this observation, we see that for any object $C$, the relation $R_{|C|,\ell}$ should be \textit{reflexive} for the interpretation to be sound. In fact, with this restriction, category \textit{DC} is a sound model of DCC. Henceforth, we refer to this restricted category as \textit{DC}.
Next, we interpret SDC in \textit{DC}.
\subsection{Categorical Model of SDC}
Category \textit{DC} is a bicartesian closed category with a label-indexed monad $(\bd{T}^{\ell} , \bd{\eta}^{\ell} , \bd{\mu}^{\ell})$. The monad is defined as:
\begin{align*}
| \bd{T}^{\ell} (C) | & = | C | \\
R_{|\bd{T}^{\ell} (C)|, \ell_{{\mathrm{0}}}} & = R_{|C|, \ell} \text{ if } \ell \leq \ell_{{\mathrm{0}}} \text{ and } | C | \bd{\times} | C | \text{ otherwise} \\
\bd{T}^\ell (f : C \bd{\to} D) & = f \\
\bd{\eta}^{\ell}_C : C \bd{\to} \bd{T}^{\ell} (C) & = \bd{\lambda} x . x \\
\bd{\mu}^{\ell}_C : \bd{T}^\ell (\bd{T}^{\ell} (C)) \bd{\to} \bd{T}^{\ell} (C) & = \bd{\lambda} x . x
\end{align*}
The cartesian product is described above. The coproduct $C \bd{+} D$ for objects $C, D$ is defined as:
\begin{align*}
| C \bd{+} D | & = | C | + | D | \\
R_{|C \bd{+} D|, \ell} & = \{ (\mathsf{inl } \, c_1 , \mathsf{inl } \, c_2) \, | \, (c_1 , c_2 ) \in R_{|C|,\ell} \} \cup \{ (\mathsf{inr } \, d_1 , \mathsf{inr } \, d_2) \, | \, (d_1 , d_2 ) \in R_{|D|,\ell} \}
\end{align*}
Lastly, the exponential $D^C$ for objects $C, D$ is given by:
\begin{align*}
| D^C | & = \mathsf{Hom} (C , D) \\
R_{| D^C |, \ell} & = \{ (f , g) \, | \, \forall (c_1 , c_2) \in R_{|C|,\ell} \Rightarrow (f c_1 , g c_2) \in R_{|D|,\ell} \}
\end{align*}
The following propositions hold in category \textit{DC}:
\begin{proposition}
\begin{enumerate}
\item $\bd{T}^{\ell} (C \bd{\times} D) = \bd{T}^{\ell} C \bd{\times} \bd{T}^{\ell} D$
\item $(\bd{T}^{\ell} D)^C = (\bd{T}^{\ell} D)^{\bd{T}^{\ell} C}$
\item $\bd{T}^{ \ell \vee \ell_{{\mathrm{0}}} } C = \bd{T}^{\ell} (\bd{T}^{\ell_{{\mathrm{0}}}} C)$
\item $\bd{T}^{ { \color{black}{\bot} } } C = C$
\item For $\ell_{{\mathrm{0}}} \leq \ell$, there exists a natural transformation $\tau^{\ell_{{\mathrm{0}}} \leq \ell}$ from $\bd{T}^{\ell_{{\mathrm{0}}}}$ to $\bd{T}^{\ell}$ such that for any object $C$, we have $\tau^{\ell_{{\mathrm{0}}} \leq \ell}_C = \bd{\lambda} x . x$.
\end{enumerate}
\end{proposition}
But the following are \textbf{not} true in general: $\bd{T}^{\ell} (C \bd{+} D) = \bd{T}^{\ell} C \bd{+} \bd{T}^{\ell} D$ and $\bd{T}^{\ell} (D^C) = (\bd{T}^{\ell} D)^{\bd{T}^{\ell} C}$. With this understanding of the category, let us now look at the interpretation of SDC.
The types are interpreted as objects of the category:
\begin{align*}
\llbracket \ottkw{Unit} \rrbracket & = \bd{1} \\
\llbracket \ottnt{A} \times \ottnt{B} \rrbracket & = \llbracket \ottnt{A} \rrbracket \bd{\times} \llbracket \ottnt{B} \rrbracket \\
\llbracket \ottnt{A} + \ottnt{B} \rrbracket & = \llbracket \ottnt{A} \rrbracket \bd{+} \llbracket \ottnt{B} \rrbracket \\
\llbracket \ottnt{A} \to \ottnt{B} \rrbracket & = \llbracket \ottnt{B} \rrbracket ^{ \llbracket \ottnt{A} \rrbracket } \\
\llbracket T^{ \ell }\; \ottnt{A} \rrbracket & = \bd{T}^{\ell} \llbracket \ottnt{A} \rrbracket
\end{align*}
An open term $ \Omega \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega = x_1 :^{\ell_{{\mathrm{1}}}} A_1 , x_2 :^{\ell_{{\mathrm{2}}}} A_2 , \ldots, x_n :^{\ell_{n}} A_n $ is interpreted as a morphism $ \llbracket \ottnt{b} \rrbracket : \llbracket \Omega \rrbracket \bd{\to} \bd{T}^{\ell} \llbracket \ottnt{B} \rrbracket $ where $ \llbracket \Omega \rrbracket = \bd{T}^{\ell_{{\mathrm{1}}}} \llbracket \ottnt{A_{{\mathrm{1}}}} \rrbracket \bd{\times} \bd{T}^{\ell_{{\mathrm{2}}}} \llbracket \ottnt{A_{{\mathrm{2}}}} \rrbracket \bd{\times} \ldots \bd{\times} \bd{T}^{\ell_n} \llbracket A_n \rrbracket$. With this interpretation, we show that category \textit{DC} is a sound model of SDC.
\begin{theorem}[Soundness] \label{soundness}
If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{A} \rrbracket )$.
\end{theorem}
\begin{proof}
By induction on $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $.
\begin{itemize}
\item
For \rref{SDC-Var}, we have $ \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \vdash\, \ottmv{x} \, :^{ \ell } \, \ottnt{A} $ where $\ell_{{\mathrm{0}}} \leq \ell$. \\ Let $\Omega_{{\mathrm{1}}}$ be a list of length $k$. \\ Then $ \llbracket \ottmv{x} \rrbracket \in \mathsf{Hom}( \llbracket \Omega_{{\mathrm{1}}} \rrbracket \bd{\times} \bd{T}^{\ell_{{\mathrm{0}}}} \llbracket \ottnt{A} \rrbracket \bd{\times} \llbracket \Omega_{{\mathrm{2}}} \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{A} \rrbracket )$ is interpreted as: $ \llbracket \ottmv{x} \rrbracket = \tau^{\ell_{{\mathrm{0}}} \leq \ell}_{ \llbracket \ottnt{A} \rrbracket } \circ \bd{\pi}_{k + 1}$.
\item
For \rref{SDC-Unit}, we have $ \Omega \vdash\, \ottkw{unit} \, :^{ \ell } \, \ottkw{Unit} $. \\ Then $ \llbracket \ottkw{unit} \rrbracket $ is the unique morphism from $ \llbracket \Omega \rrbracket $ to $\bd{1}$.
\item
For \rref{SDC-Abs}, we have $ \Omega \vdash\, \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{b} \, :^{ \ell } \, \ottnt{A} \to \ottnt{B} $ where $ \Omega , \ottmv{x} \! :^{ { \color{black}{\bot} } }\! \ottnt{A} \vdash\, \ottnt{b} \, :^{ { \color{black}{\bot} } } \, \ottnt{B} $. \\ Using the inductive hypothesis, we get $ \llbracket \ottnt{b} \rrbracket \in \textsf{Hom} ( \llbracket \Omega \rrbracket \bd{\times} \llbracket \ottnt{A} \rrbracket , \llbracket \ottnt{B} \rrbracket )$. \\ Then, $ \llbracket \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{b} \rrbracket = \tau^{ { \color{black}{\bot} } \leq \ell}_{ \llbracket \ottnt{A} \to \ottnt{B} \rrbracket } \circ \textsf{curry} \llbracket \ottnt{b} \rrbracket $.
\item
For \rref{SDC-App}, we have $ \Omega \vdash\, \ottnt{b} \; \ottnt{a} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{A} \to \ottnt{B} $ and $ \Omega \vdash\, \ottnt{a} \, :^{ { \color{black}{\bot} } } \, \ottnt{A} $. \\ Using the inductive hypothesis, we get, $ \llbracket \ottnt{b} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} ( \llbracket \ottnt{B} \rrbracket ^{ \llbracket \ottnt{A} \rrbracket }))$ and $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \llbracket \ottnt{A} \rrbracket )$. \\ Then, $ \llbracket \ottnt{b} \; \ottnt{a} \rrbracket = \mathsf{app} \circ \langle \llbracket \ottnt{b} \rrbracket , \tau^{ { \color{black}{\bot} } \leq \ell}_{ \llbracket \ottnt{A} \rrbracket } \circ \llbracket \ottnt{a} \rrbracket \rangle$.
\item
For \rref{SDC-Pair}, we have $ \Omega \vdash\, ( \ottnt{a} , \ottnt{b} ) \, :^{ \ell } \, \ottnt{A} \times \ottnt{B} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $ and $ \Omega \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{A} \rrbracket )$ and $ \llbracket \ottnt{b} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{B} \rrbracket )$. \\ Then, $ \llbracket ( \ottnt{a} , \ottnt{b} ) \rrbracket = \langle \llbracket \ottnt{a} \rrbracket , \llbracket \ottnt{b} \rrbracket \rangle$.
\item
For \rref{SDC-ProjF}, we have $ \Omega \vdash\, \pi_1\ \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} \times \ottnt{A_{{\mathrm{2}}}} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{A_{{\mathrm{1}}}} \times \ottnt{A_{{\mathrm{2}}}} \rrbracket )$. \\ Then $ \llbracket \pi_1\ \ottnt{a} \rrbracket = \bd{\pi_1} \circ \llbracket \ottnt{a} \rrbracket $. The \rref{SDC-ProjS} follows similarly.
\item
For \rref{SDC-InjF}, we have $ \Omega \vdash\, \ottkw{inj}_1\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} + \ottnt{B} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \llbracket \ottnt{A} \rrbracket )$. \\ Then $ \llbracket \ottkw{inj}_1\, \ottnt{a} \rrbracket = \tau^{ { \color{black}{\bot} } \leq \ell}_{ \llbracket \ottnt{A} + \ottnt{B} \rrbracket } \circ \bd{i_1} \llbracket \ottnt{a} \rrbracket $. The \rref{SDC-InjS} follows similarly.
\item
For \rref{SDC-Case}, we have $ \Omega \vdash\, \ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} + \ottnt{A_{{\mathrm{2}}}} $ and $ \Omega \vdash\, \ottnt{b_{{\mathrm{1}}}} \, :^{ \ell } \, \ottnt{A_{{\mathrm{1}}}} \to \ottnt{B} $ and $ \Omega \vdash\, \ottnt{b_{{\mathrm{2}}}} \, :^{ \ell } \, \ottnt{A_{{\mathrm{2}}}} \to \ottnt{B} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{A_{{\mathrm{1}}}} + \ottnt{A_{{\mathrm{2}}}} \rrbracket )$ and $ \llbracket \ottnt{b_{{\mathrm{1}}}} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} ( \llbracket \ottnt{B} \rrbracket ^{ \llbracket \ottnt{A_{{\mathrm{1}}}} \rrbracket }))$ and $ \llbracket \ottnt{b_{{\mathrm{2}}}} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket , \bd{T}^{\ell} ( \llbracket \ottnt{B} \rrbracket ^{ \llbracket \ottnt{A_{{\mathrm{2}}}} \rrbracket }))$. \\ Then $ \llbracket \ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} \rrbracket = \bd{T}^{\ell} (\mathsf{app}) \circ \langle \langle \llbracket \ottnt{b_{{\mathrm{1}}}} \rrbracket , \llbracket \ottnt{b_{{\mathrm{2}}}} \rrbracket \rangle , \llbracket \ottnt{a} \rrbracket \rangle$.
\item
For \rref{SDC-Return}, we have $ \Omega \vdash\, \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom}( \llbracket \Omega \rrbracket , \bd{T}^{ \ell \vee \ell_{{\mathrm{0}}} } \llbracket \ottnt{A} \rrbracket )$. \\ Then, $ \llbracket \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} \rrbracket = \llbracket \ottnt{a} \rrbracket $.
\item
For \rref{SDC-Bind}, we have $ \Omega \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $ where $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ and $ \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! \ottnt{A} \vdash\, \ottnt{b} \, :^{ \ell } \, \ottnt{B} $. \\ By inductive hypothesis, $ \llbracket \ottnt{a} \rrbracket \in \mathsf{Hom}( \llbracket \Omega \rrbracket , \bd{T}^{\ell} (\bd{T}^{\ell_{{\mathrm{0}}}} \llbracket \ottnt{A} \rrbracket ))$ and $ \llbracket \ottnt{b} \rrbracket \in \mathsf{Hom} ( \llbracket \Omega \rrbracket \bd{\times} \bd{T}^{ \ell \vee \ell_{{\mathrm{0}}} } \llbracket \ottnt{A} \rrbracket , \bd{T}^{\ell} \llbracket \ottnt{B} \rrbracket )$. \\ Then $ \llbracket \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} \rrbracket = \llbracket \ottnt{b} \rrbracket \circ \langle \bd{id} , \llbracket \ottnt{a} \rrbracket \rangle$.
\end{itemize}
\end{proof}
With this interpretation of SDC, we can relate it to DCC through category \textit{DC}.
\subsection{Meaning-preserving Translation of DCC into SDC}
In this section, we translate programs derived in the terminating fragment of DCC to programs in SDC such that the meaning of programs in category \textit{DC} is preserved. For this, we first translate DCC types to SDC types. We use $s , t$ for DCC types and $A, B$ for SDC types. Now, we define a function $\lceil \_ \rceil $ from DCC types to labels which gives us the maximum security clearance of a type.
\begin{align*}
\lceil \ottkw{Unit} \rceil & = { \color{black}{\top} } \\
\lceil \texttt{\textcolor{red}{<<no parses (char 7): s -> t*** >>}} \rceil & = \lceil \ottnt{t} \rceil \\
\lceil \texttt{\textcolor{red}{<<no parses (char 10): s times t*** >>}} \rceil & = \lceil \ottnt{s} \rceil \wedge \lceil \ottnt{t} \rceil \\
\lceil \texttt{\textcolor{red}{<<no parses (char 6): s + t*** >>}} \rceil & = { \color{black}{\bot} } \\
\lceil \texttt{\textcolor{red}{<<no parses (char 8): T psi s*** >>}} \rceil & = \ell \vee \lceil \ottnt{s} \rceil
\end{align*}
The maximum clearance function is closely related to the `protected at' judgement of \citet{dcc}. We recap this judgement in Figure \ref{fig:protected}. A type $\ottnt{s}$ is protected at a level $\ell$, written $\texttt{\textcolor{red}{<<no parses (char 10): psi <<= s*** >>}}$, if $\ottnt{s}$ is allowed to see terms observable at $\ell$. We have the following relation between the protection judgement and the maximum clearance function.
\begin{figure}
\centering
\drules[Protect]{$\texttt{\textcolor{red}{<<no parses (char 10): psi <<= s*** >>}}$}{}
{Unit,Fun,Prod,Sum,MonadE,MonadI}
\caption{Protection Judgement of DCC}
\label{fig:protected}
\end{figure}
\begin{lemma}
If $\texttt{\textcolor{red}{<<no parses (char 10): psi <<= s*** >>}}$, then $\ell \leq \lceil \ottnt{s} \rceil$.
\end{lemma}
\begin{proof}
By induction on $\texttt{\textcolor{red}{<<no parses (char 10): psi <<= s*** >>}}$.
\end{proof}
Now, we define the translation function ${}^{\overline{}}$ from DCC types to SDC types.
\begin{align*}
\texttt{\textcolor{red}{<<no parses (char 7): D Unit*** >>}} & = T^{ { \color{black}{\top} } }\; \ottkw{Unit} \\
\texttt{\textcolor{red}{<<no parses (char 15): D (\# s -> t \#)*** >>}} & = \texttt{\textcolor{red}{<<no parses (char 38): T (\# M (\# s -> t \#) \#) ( D s -> D t )*** >>}} \\
\texttt{\textcolor{red}{<<no parses (char 18): D (\# s times t \#)*** >>}} & = \texttt{\textcolor{red}{<<no parses (char 42): T (\# M (\# s times t \#) \#) (D s times D t)*** >>}} \\
\texttt{\textcolor{red}{<<no parses (char 14): D (\# s + t \#)*** >>}} & = \texttt{\textcolor{red}{<<no parses (char 34): T (\# M (\# s + t \#) \#) (D s + D t)*** >>}} \\
\texttt{\textcolor{red}{<<no parses (char 16): D (\# T psi s \#)*** >>}} & = \texttt{\textcolor{red}{<<no parses (char 46): T (\# M (\# T psi s \#) \#) (\# T psi (\# D s \#) \#)*** >>}}
\end{align*}
Note that the translation changes the type to one guarded by its maximum clearance. Since the initial type already had that clearance, the change is of a purely syntactic nature. In fact, we can show that both the types have the same meaning in category \textit{DC}.
\begin{lemma}
$ \llbracket \overline{ \ottnt{s} } \rrbracket = \texttt{\textcolor{red}{<<no parses (char 8): [\mbox{$\mid$} s \mbox{$\mid$}]*** >>}}$.
\end{lemma}
\begin{proof}
By induction on $s$.
\end{proof}
\begin{figure}
\centering
\drules[DCC]{$\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$}{}
{Var,Unit,Lam,App,Pair,ProjF,ProjS,InjF,InjS,Case,Return,Bind}
\caption{DCC Type System}
\label{fig:dccType}
\end{figure}
Now, we translate open DCC terms to SDC terms. The DCC type system is presented in Figure \ref{fig:dccType}. Formally, given a DCC derivation $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$, we translate it to $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$, where for $\Gamma = \ottmv{x_{{\mathrm{1}}}} : \ottnt{s_{{\mathrm{1}}}} , \ottmv{x_{{\mathrm{2}}}} : \ottnt{s_{{\mathrm{2}}}} , \ldots, x_n : s_n$, we define $ \overline{ \Gamma }^{ \ell } $ as $ \ottmv{x_{{\mathrm{1}}}} \! :^{ \ell }\! \overline{ \ottnt{s_{{\mathrm{1}}}} } , \ottmv{x_{{\mathrm{2}}}} \! :^{ \ell }\! \overline{ \ottnt{s_{{\mathrm{2}}}} } , \ldots, x_n \! :^{\ell} \! \overline{s_n}$. For translating, we need some lemmas.
\begin{lemma}[Join] \label{join}
If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottsym{(} T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} \ottsym{)} $, then there exists a term $ \ottkw{join}\, \ottnt{a} $ such that $ \Omega \vdash\, \ottkw{join}\, \ottnt{a} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} $ and if $ \ottnt{a} \leadsto \ottnt{b} $, then $ \ottkw{join}\, \ottnt{a} \leadsto \ottkw{join}\, \ottnt{b} $.
\end{lemma}
\begin{proof}
We have:
\begin{align*}
& \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} \vdash\, \ottmv{x} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} & \text{[By \rref{SDC-Var}]} \\
& \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} , \ottmv{y} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! \ottnt{A} \vdash\, \ottmv{y} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} & \text{[By \rref{SDC-Var}]} \\
& \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{y} = \ottmv{x} \, \ottkw{in} \, \ottmv{y} \, :^{ \ell \vee \ell_{{\mathrm{0}}} } \, \ottnt{A} & \text{[By \rref{SDC-Bind}]} \\
& \Omega , \ottmv{x} \! :^{ \ell \vee \ell_{{\mathrm{0}}} }\! T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} \vdash\, \eta^{ \ell_{{\mathrm{0}}} }\; \ottsym{(} \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{y} = \ottmv{x} \, \ottkw{in} \, \ottmv{y} \ottsym{)} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} & \text{[By \rref{SDC-Return}]} \\
& \Omega \vdash\, \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \eta^{ \ell_{{\mathrm{0}}} }\; \ottsym{(} \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{y} = \ottmv{x} \, \ottkw{in} \, \ottmv{y} \ottsym{)} \, :^{ \ell } \, T^{ \ell_{{\mathrm{0}}} }\; \ottnt{A} & \text{[By \rref{SDC-Bind}]}
\end{align*}
Then, $ \ottkw{join}\, \ottnt{a} = \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \eta^{ \ell_{{\mathrm{0}}} }\; \ottsym{(} \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{y} = \ottmv{x} \, \ottkw{in} \, \ottmv{y} \ottsym{)} $. Note that if $ \ottnt{a} \leadsto \ottnt{b} $, then $ \ottkw{join}\, \ottnt{a} \leadsto \ottkw{join}\, \ottnt{b} $.
\end{proof}
\begin{theorem}[Forward Translation]
If $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$, then there exists $\texttt{\textcolor{red}{<<no parses (char 4): D a*** >>}}$ such that $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$ and if $ \ottnt{a} \leadsto \ottnt{a_{{\mathrm{1}}}} $, then $\texttt{\textcolor{red}{<<no parses (char 16): \mbox{$\mid$}- D a ~>> D a1*** >>}}$; otherwise if $\ottnt{a}$ is a value, then so is $\texttt{\textcolor{red}{<<no parses (char 4): D a*** >>}}$.
\end{theorem}
\begin{proof}
By induction on $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$.
\begin{itemize}
\item
For \rref{DCC-Var}, we have $\texttt{\textcolor{red}{<<no parses (char 29): (G1 ++ x : s) ++ G2 \mbox{$\mid$}- x : s*** >>}}$. \\ We translate it to $ \overline{ \Gamma_{{\mathrm{1}}} }^{ { \color{black}{\bot} } } , \ottmv{x} \! :^{ { \color{black}{\bot} } }\! \overline{ \ottnt{s} } , \overline{ \Gamma_{{\mathrm{2}}} }^{ { \color{black}{\bot} } } \vdash\, \ottmv{x} \, :^{ { \color{black}{\bot} } } \, \overline{ \ottnt{s} } $.
\item
For \rref{DCC-Unit}, we have $ \Gamma \vdash \, \ottkw{unit} \, : \, \ottkw{Unit} $. \\ We translate it to $\texttt{\textcolor{red}{<<no parses (char 36): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N top unit : D Unit*** >>}}$.
\item
For \rref{DCC-Lam}, we have $\texttt{\textcolor{red}{<<no parses (char 25): G \mbox{$\mid$}- \mbox{$\backslash{}$} x : s. b : s -> t*** >>}}$ where $ \Gamma , \ottmv{x} : \ottnt{s} \vdash \, \ottnt{b} \, : \, \ottnt{t} $. \\ By the inductive hypothesis, we get $\texttt{\textcolor{red}{<<no parses (char 41): D bot G ++ x : bot D s \mbox{$\mid$}\mbox{$\mid$}- bot D b : D t*** >>}}$. \\ Now, using \rref{SDC-Lam}, we have, $\texttt{\textcolor{red}{<<no parses (char 45): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot \mbox{$\backslash{}$} x : D s . D b : D s -> D t*** >>}}$. \\ By promotion and \rref{SDC-Return}, we get, $\texttt{\textcolor{red}{<<no parses (char 95): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N (\# M (\# s -> t \#) \#) (\mbox{$\backslash{}$} x : D s . D b) : T (\# M (\# s -> t \#) \#) (D s -> D t)*** >>}}$.
\item
For \rref{DCC-App}, we have $ \Gamma \vdash \, \ottnt{b} \; \ottnt{a} \, : \, \ottnt{t} $ where $\texttt{\textcolor{red}{<<no parses (char 16): G \mbox{$\mid$}- b : s -> t*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$. \\ By the inductive hypothesis, we get $\texttt{\textcolor{red}{<<no parses (char 59): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D b : T (\# M (\# s -> t \#) \#) (D s -> D t)*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$. \\ Let $\ell = \texttt{\textcolor{red}{<<no parses (char 21): (\# M (\# s -> t \#) \#)*** >>}}$. Using \rref{SDC-Bind}, we get $\texttt{\textcolor{red}{<<no parses (char 51): D bot G \mbox{$\mid$}\mbox{$\mid$}- psi bind psi x = D b in x : D s -> D t*** >>}}$. \\ Using \rref{SDC-App}, we have, $\texttt{\textcolor{red}{<<no parses (char 50): D bot G \mbox{$\mid$}\mbox{$\mid$}- psi (bind psi x = D b in x) D a : D t*** >>}}$. \\ Again, using \rref{SDC-Return}, $ \texttt{\textcolor{red}{<<no parses (char 65): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N psi ((bind psi x = D b in x) D a) : T psi D t*** >>}}$. \\ Now, $\texttt{\textcolor{red}{<<no parses (char 10): T psi D t*** >>}} = T^{ \ell }\; T^{ \ell }\; \ottnt{t'} $. Then, $\texttt{\textcolor{red}{<<no parses (char 65): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot join (N psi ((bind psi x = D b in x) D a)) : D t*** >>}}$. \\ So $\texttt{\textcolor{red}{<<no parses (char 12): D (\# b a \#)*** >>}} = \texttt{\textcolor{red}{<<no parses (char 43): join (N psi ((bind psi x = D b in x) D a))*** >>}}$. \\ Now, $ \ottnt{b} \; \ottnt{a} $ can step in three ways:
\begin{itemize}
\item $ \ottnt{b} \leadsto \ottnt{b_{{\mathrm{1}}}} $. Then, $\texttt{\textcolor{red}{<<no parses (char 16): \mbox{$\mid$}- D b ~>> D b1*** >>}}$. So $\texttt{\textcolor{red}{<<no parses (char 32): \mbox{$\mid$}- D (\# b a \#) ~>> D (\# b1 a \#)*** >>}}$.
\item $\ottnt{b}$ is a value and $ \ottnt{a} \leadsto \ottnt{a_{{\mathrm{1}}}} $. Then, $\texttt{\textcolor{red}{<<no parses (char 4): D b*** >>}}$ is a value and $\texttt{\textcolor{red}{<<no parses (char 16): \mbox{$\mid$}- D a ~>> D a1*** >>}}$. So $\texttt{\textcolor{red}{<<no parses (char 32): \mbox{$\mid$}- D (\# b a \#) ~>> D (\# b a1 \#)*** >>}}$.
\item $\ottnt{b}$ and $\ottnt{a}$ are values. In this case, $\ottnt{b} = \texttt{\textcolor{red}{<<no parses (char 13): \mbox{$\backslash{}$} x : s . b1*** >>}}$. And $\texttt{\textcolor{red}{<<no parses (char 4): D b*** >>}} = \texttt{\textcolor{red}{<<no parses (char 25): N psi (\mbox{$\backslash{}$} x : D s . D b1)*** >>}}$.
\end{itemize}
\item
For \rref{DCC-Pair}, we have $\texttt{\textcolor{red}{<<no parses (char 25): G \mbox{$\mid$}- (a , b) : s times t*** >>}}$ where $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$ and $ \Gamma \vdash \, \ottnt{b} \, : \, \ottnt{t} $. \\ By the inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D b : D t*** >>}}$. \\ By \rref{SDC-Pair}, we get $\texttt{\textcolor{red}{<<no parses (char 44): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot (D a , D b) : D s times D t*** >>}}$. \\ By promotion and \rref{SDC-Return}, $\texttt{\textcolor{red}{<<no parses (char 98): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N (\# M (\# s times t \#) \#) (D a , D b) : T (\# M (\# s times t \#) \#) (D s times D t)*** >>}}$. \\ Since $\texttt{\textcolor{red}{<<no parses (char 10): [\mbox{$\mid$} D a \mbox{$\mid$}]*** >>}} = \llbracket \ottnt{a} \rrbracket $ and $\texttt{\textcolor{red}{<<no parses (char 10): [\mbox{$\mid$} D b \mbox{$\mid$}]*** >>}} = \llbracket \ottnt{b} \rrbracket $, so $ \texttt{\textcolor{red}{<<no parses (char 44): [\mbox{$\mid$} N (\# M (\# s times t \#) \#) (D a , D b) \mbox{$\mid$}]*** >>}} = \llbracket ( \ottnt{a} , \ottnt{b} ) \rrbracket $.
\item
For \rref{DCC-ProjF}, we have $\texttt{\textcolor{red}{<<no parses (char 15): G \mbox{$\mid$}- fst a : s*** >>}}$ where $\texttt{\textcolor{red}{<<no parses (char 19): G \mbox{$\mid$}- a : s times t*** >>}}$. \\ By the inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 64): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : T (\# M (\# s times t \#) \#) (D s times D t)*** >>}}$. \\ Let $\ell = \texttt{\textcolor{red}{<<no parses (char 24): (\# M (\# s times t \#) \#)*** >>}}$. Then, using \rref{SDC-Bind}, we get $\texttt{\textcolor{red}{<<no parses (char 54): D bot G \mbox{$\mid$}\mbox{$\mid$}- psi bind psi x = D a in x : D s times D t*** >>}}$. \\ By \rref{SDC-ProjF}, $\texttt{\textcolor{red}{<<no parses (char 50): D bot G \mbox{$\mid$}\mbox{$\mid$}- psi fst (bind psi x = D a in x) : D s*** >>}}$. \\ Now, since $\ell \leq \lceil \ottnt{s} \rceil $, by promotion $\texttt{\textcolor{red}{<<no parses (char 56): D bot G \mbox{$\mid$}\mbox{$\mid$}- (\# M s \#) fst (bind psi x = D a in x) : D s*** >>}}$. \\ By \rref{SDC-Return}, $\texttt{\textcolor{red}{<<no parses (char 76): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N (\# M s \#) (fst (bind psi x = D a in x)) : T (\# M s \#) D s*** >>}}$. \\ But $ \overline{ \ottnt{s} } = \texttt{\textcolor{red}{<<no parses (char 15): T (\# M s \#) s'*** >>}}$. So $\texttt{\textcolor{red}{<<no parses (char 71): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot join (N (\# M s \#) (fst (bind psi x = D a in x))) : D s*** >>}}$. \\ Then, $\texttt{\textcolor{red}{<<no parses (char 14): D (\# fst a \#)*** >>}} = \texttt{\textcolor{red}{<<no parses (char 49): join (N (\# M s \#) (fst (bind psi x = D a in x)))*** >>}}$. \\ Using the inductive hypothesis and lemma \ref{join}, we see that $ \pi_1\ \ottnt{a} $ and $\texttt{\textcolor{red}{<<no parses (char 14): D (\# fst a \#)*** >>}}$ have the same meaning. \\ The \rref{DCC-ProjS} follows similarly.
\item
For \rref{DCC-InjF}, we have $\texttt{\textcolor{red}{<<no parses (char 20): G \mbox{$\mid$}- inj1 a : s + t*** >>}}$ where $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$. \\
By the inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$.\\
By \rref{SDC-InjF}, we have, $\texttt{\textcolor{red}{<<no parses (char 37): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot inj1 D a : D s + D t*** >>}}$.\\
By \rref{SDC-Return}, we get, $\texttt{\textcolor{red}{<<no parses (char 69): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N bot (inj1 D a) : T (\# M (\# s + t \#) \#) (D s + D t)*** >>}}$. \\
Then, $\texttt{\textcolor{red}{<<no parses (char 15): D (\# inj1 a \#)*** >>}} = \texttt{\textcolor{red}{<<no parses (char 17): N bot (inj1 D a)*** >>}}$. By inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 21): [\mbox{$\mid$} D (\# inj1 a \#) \mbox{$\mid$}]*** >>}} = \llbracket \ottkw{inj}_1\, \ottnt{a} \rrbracket $.\\
The \rref{DCC-InjS} follows similarly.
\item
For \rref{DCC-Case}, we have $ \Gamma \vdash \, \ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} \, : \, \ottnt{t} $ where $\texttt{\textcolor{red}{<<no parses (char 17): G \mbox{$\mid$}- a : s1 + s2*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 18): G \mbox{$\mid$}- b1 : s1 -> t*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 18): G \mbox{$\mid$}- b2 : s2 -> t*** >>}}$. \\
By the inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 42): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : T bot (D s1 + D s2)*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 49): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D b1 : T (\# M t \#) (D s1 -> D t)*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 49): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D b2 : T (\# M t \#) (D s2 -> D t)*** >>}}$. \\
By \rref{SDC-Bind}, we get, $\texttt{\textcolor{red}{<<no parses (char 19): D bot G \mbox{$\mid$}\mbox{$\mid$}- (\# M t*** \#) bind x = D b1 in x : D s1 -> D t >>}}$. \\
By \rref{SDC-Bind}, we get, $\texttt{\textcolor{red}{<<no parses (char 19): D bot G \mbox{$\mid$}\mbox{$\mid$}- (\# M t*** \#) bind y = D b2 in x : D s2 -> D t >>}}$. \\
By \rref{SDC-Case}, we get, $\texttt{\textcolor{red}{<<no parses (char 19): D bot G \mbox{$\mid$}\mbox{$\mid$}- (\# M t*** \#) case D a of (bind x = D b1 in x); (bind y = D b2 in y) : D t >>}}$. \\
By \rref{SDC-Return}, we get, $\texttt{\textcolor{red}{<<no parses (char 91): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N (\# M t \#) (case D a of (bind x = D b1 in x); (bind y = D b2 in y)) : D t*** >>}}$. \\
By lemma \ref{join}, we have, $\texttt{\textcolor{red}{<<no parses (char 98): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot join (N (\# M t \#) (case D a of (bind x = D b1 in x); (bind y = D b2 in y))) : D t*** >>}}$. \\
Then, $\texttt{\textcolor{red}{<<no parses (char 25): D (\# case a of b1; b2 \#)*** >>}} = \texttt{\textcolor{red}{<<no parses (char 76): join (N (\# M t \#) (case D a of (bind x = D b1 in x); (bind y = D b2 in y)))*** >>}}$. \\
By inductive hypothesis and lemma \ref{join}, $\texttt{\textcolor{red}{<<no parses (char 31): [\mbox{$\mid$} D (\# case a of b1; b2 \#) \mbox{$\mid$}]*** >>}} = \llbracket \ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} \rrbracket $.
\item
For \rref{DCC-Return}, we have $\texttt{\textcolor{red}{<<no parses (char 23): G \mbox{$\mid$}- N psi a : T psi s*** >>}}$ where $\texttt{\textcolor{red}{<<no parses (char 11): G \mbox{$\mid$}- a : s*** >>}}$. \\
By inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 26): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : D s*** >>}}$. \\
By promotion and \rref{SDC-Return}, we get, $\texttt{\textcolor{red}{<<no parses (char 76): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot N (\# psi \mbox{$\backslash{}$}/ M s \#) N psi D a : T (\# psi \mbox{$\backslash{}$}/ M s \#) T psi D s*** >>}}$. \\
Then, $\texttt{\textcolor{red}{<<no parses (char 16): D (\# N psi a \#)*** >>}} = \texttt{\textcolor{red}{<<no parses (char 29): N (\# psi \mbox{$\backslash{}$}/ M s \#) N psi D a*** >>}}$. \\
By inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 22): [\mbox{$\mid$} D (\# N psi a \#) \mbox{$\mid$}]*** >>}} = \llbracket \eta^{ \ell }\; \ottnt{a} \rrbracket $.
\item
For \rref{DCC-Bind}, we have $ \Gamma \vdash \, \ottkw{bind} \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} \, : \, \ottnt{t} $ where $\texttt{\textcolor{red}{<<no parses (char 17): G \mbox{$\mid$}- a : T psi s*** >>}}$ and $ \Gamma , \ottmv{x} : \ottnt{s} \vdash \, \ottnt{b} \, : \, \ottnt{t} $ and $ \ell \leq \ottnt{t} $.\\
By inductive hypothesis, $\texttt{\textcolor{red}{<<no parses (char 51): D bot G \mbox{$\mid$}\mbox{$\mid$}- bot D a : T (\# psi \mbox{$\backslash{}$}/ M s \#) T psi D s*** >>}}$ and $\texttt{\textcolor{red}{<<no parses (char 41): D bot G ++ x : bot D s \mbox{$\mid$}\mbox{$\mid$}- bot D b : D t*** >>}}$.
\end{itemize}
\end{proof}
\section{A Dependent Qualitiative Type System}
In this section we extend the simple system to include dependent types.
First, some notation. We write $\phi < \ell$ when we have
$ \neg \ottsym{(} \ell \leq \phi \ottsym{)} $ and $\phi \leq \ell$.
Dependent types provide both opportunities and difficulties. On one hand,
having a builtin notion of dependence is important in order to support
compile-time irrelevance: we would like to use the guarded version of
definitional equality in the conversion rule so that compile-time equivalence
can ignore parts of the term (as long as it is sound to do so).
\[ \drule{T-Conv} \]
Which parts of terms should be ignored during conversion? As much as
possible. Because I don't yet know what that level should be, I'm going to
mark it as $\texttt{\textcolor{red}{<<no parses (char 8): type psi*** >>}}$ for now.
If this level is $ \top $, then we do not have any compile-time irrelevance.
If this level is $ \bot $, then we have as much compile-time irrelevance as possible.
\begin{itemize}
\item Type annotations in the term should be equated with a grade that is
higher than all runtime grades. We do not annotate the argument types of
lambda, but if we did, those argument types should allow both runtime and
compile-time irrelevance.
\item If a variable \emph{only} appears in a type then it should be graded
with a higher grade.
For example, consider a derivation for the polymorphic identity function.
\[
\varnothing \vdash_{ \phi } \lambda^{ \ell } \ottmv{x} . \lambda^{ \phi } \ottmv{y} . \ottmv{y} : \ottsym{(} \Pi \ottmv{x} \!:^{ \ell }\! \textbf{Type} . \Pi \ottmv{y} \!:^{ \phi }\! \ottmv{x} . \ottmv{x} \ottsym{)}
\]
This means that we want to allow uses of this expression to mark arguments as
ignorable.
\[
\varnothing \vdash_{ \phi } \ottsym{(} \lambda^{ \ell } \ottmv{x} . \lambda^{ \phi } \ottmv{y} . \ottmv{y} \ottsym{)} \; \ottkw{Unit} ^{ \ell } : {}^{ \phi } \! \ottkw{Unit} \to \ottkw{Unit}
\]
If we have $ \neg \ottsym{(} \ell \leq \phi \ottsym{)} $, then definitional equality gives us:
\[
\varnothing \vdash_{ \phi } \ottsym{(} \lambda^{ \ell } \ottmv{x} . \lambda^{ \phi } \ottmv{y} . \ottmv{y} \ottsym{)} \; \ottkw{Unit} ^{ \ell } \equiv \ottsym{(} \lambda^{ \ell } \ottmv{x} . \lambda^{ \phi } \ottmv{y} . \ottmv{y} \ottsym{)} \; \ottkw{Bool} ^{ \ell }
\]
(Definitional equality is untyped, so these two expressions can be equated even though they have different types. There are longer examples that demonstrate the same idea, but equate terms with the same types.)
\item In functions, the use of the argument in the term (can be) different from its use in a type.
Going back to the previous example of the polymorphic identity function,
notice that in the derivation, the variable $\ottmv{x}$ does not appear in the
term but does appear in the type. This means that our typing rule for $\Pi$
types needs to allow this different usage if we are to admit this example.
\[ \drule{T-Pi} \]
In otherwords, we cannot use $\ell_{{\mathrm{1}}}$ when we check $\ottnt{B}$, we need to use some other label $\ell_{{\mathrm{0}}}$, that is potentially $\ell_{{\mathrm{0}}} \leq \ell_{{\mathrm{1}}}$.
It does not seem likely that we will need to have $\ell_{{\mathrm{0}}}$ that is not $ \leq $ $\ell_{{\mathrm{1}}}$.
\item We want to keep the formation rule for $\Pi$ types general and not fix it at a certain level. That will allow us to compare types at different levels. i.e. it might be the case that two types are equal at level $ { \color{red}{C} } < \top $
$ \varnothing \vdash_{ { \color{red}{C} } } \Pi \ottmv{x} \!:^{ \phi }\! \ottnt{A_{{\mathrm{1}}}} . \ottnt{B_{{\mathrm{1}}}} \equiv \Pi \ottmv{x} \!:^{ \phi }\! \ottnt{A_{{\mathrm{2}}}} . \ottnt{B_{{\mathrm{2}}}} $
where $ \top $-marked subterms inside the types can be ignored, but not equal at $ \top $.
\item Our ``regularity'' lemma for the type system must check types with
a ``higher'' grade.
$ \Omega \vdash_{ \phi } \ottnt{a} : \ottnt{A} $ implies $ \Omega \vdash_{ \ell } \ottnt{A} : \textbf{Type} $
where $ \neg \ottsym{(} \ell \leq \phi \ottsym{)} $. Furthermore, we'd also like to allow term variables to appear in types (this is the heart of dependent types) so we also need $\phi \leq \ell$.
If we are going to allow runtime irrelevance, we need to make sure that the $\ell$ we use to check types describes arguments that are not needed at runtime and allows them to be used in types.
\item But now consider the application rule: we need to use the argument in two places, in the term and in in the type.
We substitute in the type when type checking and in the body of the function during evaluation. Both of these substitutions must be good.
\[ \drule{T-App} \]
For the reasons described in the previous section, we need to check the argument using $ \ell_{{\mathrm{0}}} \vee \ell $.
But if we are going to show that $ \Omega \vdash_{ \phi } \ottnt{B} \ottsym{\{} \ottnt{a} \ottsym{/} \ottmv{x} \ottsym{\}} : \textbf{Type} $ then we need to know that this argument is valid for the body of the $\Pi$ type.
\item Making the grade in the body of the pi the same as the grade on the lambda does NOT solve the issue with preservation.
Going this route requires adding an assumption that the $\Pi$ is well formed in the abs rule because the level
influences how types are checked.
\[
\frac{
\Omega , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} \vee \ell }\! \ottnt{A} \vdash_{ \ell } \ottnt{b} : \ottnt{B} \qquad
\texttt{\textcolor{red}{<<no parses (char 8): W \mbox{$\mid$}-- ty***pe psi (Pi x:psi0 A. B) : type >>}}
}{
\Omega \vdash_{ \ell } \lambda^{ \ell_{{\mathrm{0}}} } \ottmv{x} . \ottnt{b} : \Pi \ottmv{x} \!:^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} . \ottnt{B}
}
\]
This modification is enough for regularity. But not for preservation.
The problem is that if definitional equality is at some fixed level $ { \color{red}{C} } $, we have the argument
graded at $\texttt{\textcolor{red}{<<no parses (char 6): psi0 **** psi >>}}$. But we need it to be graded at $\texttt{\textcolor{red}{<<no parses (char 6): psi0 **** CTime >>}}$. As in the prior version,
we don't know whether $\ell \leq { \color{red}{C} } $>
\end{itemize}
\section{Type Checking}
\label{sec:typechecking}
\newcommand{$\text{ICC}^{\ast}$}{$\text{ICC}^{\ast}$}
As a pure type system, not all instances of DDC admit decidable type
checking. For example, in the presence of the \textsf{type}:\textsf{type}
axiom, the system includes non-terminating computations via Girard's
paradox. As as a result, we cannot decide equality in that system, so type
checking will be undecidable. However, if the sorts, axioms and rules are
chosen such that the language is strongly normalizing, then we can define a
decidable type checking algorithm. This algorithm is standard, but relies on a
decision procedure for the equality judgement.
Our consistency proof, described in Section~\ref{consisteq}, gives us a
start. This proof uses an auxiliary binary relation called \emph{joinability},
which holds when two terms can use multiple steps of parallel reduction to
reach two simpler terms that differ only in their unobservable components. Joinability
and definitional equality induce the same relation on DDC terms. We can show
that two DDC terms are definitionally equal if and only if they
are joinable\footnote{\texttt{consist.v:DefEq\_Joins,Joins\_DefEq}}, which
means that a decision procedure based on joinability will be sound and
complete for DDC's labeled definition of equivalence.
Therefore, the decidability of type checking reduces to showing strong
normalization. If we select the sorts, axioms and rules of DDC to match those
of the Calculus of Constructions~\citep{pts},
we believe that this result holds, but leave a direct proof for future
work. However, by translating this instance of DDC to $\text{ICC}^{\ast}${}, we can show that
a sublanguage of this instance is strongly
normalizing. $\text{ICC}^{\ast}${}~\citep{barras:icc-star}, is a version of the Implicit
Calculus of Constructions with annotations that support decidable type
checking, but because it includes only (relevant and irrelevant) $\Pi$-types, so we must
restrict our attention to the corresponding fragment of DDC.
We define the following translation, written $\widetilde{\cdot}$,
that converts DDC terms to $\text{ICC}^{\ast}${} terms. The key parts of this translation map
arguments labeled $ { \color{black}{C} } $ and below to relevant arguments, and those
labeled greater than $ { \color{black}{C} } $, such as $ { \color{black}{\top} } $, to irrelevant
arguments.\footnote{The syntax of $\text{ICC}^{\ast}${} uses parentheses to indicate usual
(relevant) arguments and square brackets to indicate arguments that are
irrelevant at both run time and compile time.}
\begin{align*}
\widetilde{ \ottmv{x} } = \ottmv{x} & \hspace*{20pt} \widetilde{ \ottnt{s} } = \ottnt{s} &
\widetilde{ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} } & = \begin{cases}
\Pi ( \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ). \widetilde{ \ottnt{B} } \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\Pi [ \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ] . \widetilde{ \ottnt{B} } \;\; \text{otherwise}
\end{cases} \\
\widetilde{ \lambda \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{b} } & = \begin{cases}
\lambda ( \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ) . \widetilde{ \ottnt{b} } \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\lambda [ \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ] . \widetilde{ \ottnt{b} } \;\; \text{otherwise}
\end{cases} &
\widetilde{ \ottnt{b} \; \ottnt{a} ^{ \ell } } & = \begin{cases}
\widetilde{ \ottnt{b} } \; ( \widetilde{ \ottnt{a} } ) \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\widetilde{ \ottnt{b} } \; [ \widetilde{ \ottnt{a} } ] \;\; \text{otherwise}
\end{cases}
\end{align*}
Note that $\text{ICC}^{\ast}${} compares terms for equality after an erasure
operation, written $\cdot^{\ast}$, that removes all irrelevant arguments.
Now, we can show that the above translation preserves definitional equality and typing.
Here, $ \widetilde{ \Omega } $ denotes $\Omega$ with the labels at
the variable bindings omitted.
\begin{lemma}[Translation preservation] \label{DDCToICCStar}
If $ \Phi \vdash \ottnt{A} \equiv_{ { \color{black}{C} } } \ottnt{B} $, then $ \widetilde{ \ottnt{A} } ^{\ast} \cong_{\beta\eta} \widetilde{ \ottnt{B} } ^{\ast} $. \\
If $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then $ \widetilde{ \Omega } \vdash\, \widetilde{ \ottnt{a} } \, : \, \widetilde{ \ottnt{A} } $.
\end{lemma}
Next, observe that because $\beta$-reductions are preserved by the
translation, any parallel reduction in DDC between terms $\ottnt{a}$ and $\ottnt{b}$ at level
$ { \color{black}{C} } $, where $\ottnt{a} \neq \ottnt{b}$, would correspond to a sequence of reduction steps
$ \widetilde{ \ottnt{a} } \rightarrow^{+}_{\beta_{ie}} \widetilde{ \ottnt{b} } $ in $\text{ICC}^{\ast}${}. That means that an infinite sequence of parallel reductions $\ottnt{a_{{\mathrm{0}}}}$, $\ottnt{a_{{\mathrm{1}}}}$, \ldots, where
each term differs from the previous, corresponds to an infinite sequence of
reductions $ \widetilde{ \ottnt{a_{{\mathrm{0}}}} } $, $ \widetilde{ \ottnt{a_{{\mathrm{1}}}} } $ \ldots in $\text{ICC}^{\ast}${}. Therefore, as all
well-typed $\text{ICC}^{\ast}${} terms are strongly normalizing, we can conclude that this
is so for this instance of DDC.
\paragraph{Non-terminating instances of DDC.}
For pure type systems that are not strongly normalizing, such as the
\textsf{type}:\textsf{type} language, there is an alternative approach to
developing a calculus with decidable type checking, following
\citet{weirich:systemd}. The key idea is to develop an annotated version of
DDC that book-keeps additional information from typing and equality derivations.
In such an annotated version, the conversion rule would include an explicit coercion
annotation that witnesses the equality between the concerned types, thus avoiding the need for
normalization.
\iffalse
Showing that
such a normalize-and-compare decision procedure works requires
showing that reduction is strongly normalizing for the given selection of
sorts, axioms and rules. We can show this by translating our system to the desired
strongly normalizing system. Next, we take up an example that demonstrates this method.
We fix a PTS: the Calculus of Constructions (CoC). With CoC as the underlying PTS,
we want to show that type-checking is decidable for DDC . The key step is showing that
the equality relation is decidable. To decide equality between types, we use
a normalize-and-compare method. Such a method, however, rests on a proof of strong
normalization. A strong normalization proof for DDC, from first principles, while
possible, demands considerable extra machinery. To avoid the extra machinery, we
prove strong normalization for DDC by translating it to a language that is an extension
of CoC and is known to be strongly normalizing. The language we chose is $\text{ICC}^{\ast}$ of
\citet{barras:icc-star} because it aids in a simple translation. Next, we review the
calculus $\text{ICC}^{\ast}$ and thereafter, present our translation from DDC to $\text{ICC}^{\ast}$.
\subsection{Implicit Calculus of Constructions}
\citet{miquel} designed the Implicit Calculus of Constructions (ICC) by extending the Calculus of Constructions with an implicit $\Pi$-type, the type of functions that use their arguments implicitly.
The implicit $\Pi$-type of ICC is akin to $\Pi$-type of DDC where the label is set to $ { \color{black}{\top} } $.
Later, \citet{barras:icc-star} designed $\text{ICC}^{\ast}$. $\text{ICC}^{\ast}$, a restriction of ICC, enjoys several desirable properties: decidable type-checking, strong normalization, etc. We show that DDC with CoC as the underlying PTS is strongly normalizing by
translating it to $\text{ICC}^{\ast}$.
$\text{ICC}^{\ast}$, like ICC, is standard CoC extended with an implicit $\Pi$-type. Implicit functions and implicit applications introduce and eliminate the implicit $\Pi$-type. The terms of $\text{ICC}^{\ast}$ are given below. The implicit forms appear below their explicit counterparts.
\begin{align*}
& \text{Sorts}, & s & ::= \mathbf{Prop} \: | \: \mathbf{Type}_i \: (i \in \mathbb{N}) \\
& \text{Terms}, & A , B , a , b & ::= x \: | \: s \\
& & & | \: \Pi ( \ottmv{x} \!:\! \ottnt{A} ). \ottnt{B} \: | \: \lambda ( \ottmv{x} \!:\! \ottnt{A} ) . \ottnt{b} \: | \: \ottnt{b} \; ( \ottnt{a} ) \\
& & & | \: \Pi [ \ottmv{x} \!:\! \ottnt{A} ] . \ottnt{B} \: | \: \lambda [ \ottmv{x} \!:\! \ottnt{A} ] . \ottnt{b} \: | \: \ottnt{b} \; [ \ottnt{a} ]
\end{align*}
The type system of $\text{ICC}^{\ast}$ uses an extraction function to ensure that implicit arguments do not get used in the body of their functions. The extraction function is essentially an erasure function that strips off implicit lambdas and implicit arguments (of applications). Though extraction function of \citet{barras:icc-star} erases $\text{ICC}^{\ast}$ terms to ICC terms, for our purposes, we can just erase to CoC terms. The interesting cases of the function definition are given below.
Next, we look at the type system of $\text{ICC}^{\ast}$. Some of the interesting typing rules appear in Figure \ref{icctyping}. Note the restriction on free-variables of $\ottnt{b}$ in \rref{IS-ILam}. Further, note the use of $\beta\eta$ equality on erased CoC terms in \rref{IS-Conv}.
\begin{figure}
\drules[IS]{$ \Gamma \vdash\, \ottnt{a} \, : \, \ottnt{A} $}{Excerpt}{ELam,ILam,EApp,IApp,Conv}
\caption{Selected Typing Rules of $\text{ICC}^{\ast}$}
\label{icctyping}
\end{figure}
With this review of $\text{ICC}^{\ast}$, we now present our translation from DDC to $\text{ICC}^{\ast}$.
\subsection{Translation from DDC to $\text{ICC}^{\ast}$}
The translation function is presented below.
\begin{align*}
\widetilde{ \ottmv{x} } = \ottmv{x} & \hspace*{20pt} \widetilde{ \ottnt{s} } = \ottnt{s} &
\widetilde{ \Pi \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{B} } & = \begin{cases}
\Pi ( \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ). \widetilde{ \ottnt{B} } \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\Pi [ \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ] . \widetilde{ \ottnt{B} } \;\; \text{otherwise}
\end{cases} \\
\widetilde{ \lambda \ottmv{x} \!:^{ \ell }\! \ottnt{A} . \ottnt{b} } & = \begin{cases}
\lambda ( \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ) . \widetilde{ \ottnt{b} } \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\lambda [ \ottmv{x} \!:\! \widetilde{ \ottnt{A} } ] . \widetilde{ \ottnt{b} } \;\; \text{otherwise}
\end{cases} &
\widetilde{ \ottnt{b} \; \ottnt{a} ^{ \ell } } & = \begin{cases}
\widetilde{ \ottnt{b} } \; ( \widetilde{ \ottnt{a} } ) \;\; \text{if}\: \ell \leq { \color{black}{C} } \\
\widetilde{ \ottnt{b} } \; [ \widetilde{ \ottnt{a} } ] \;\; \text{otherwise}
\end{cases}
\end{align*}
Since $\text{ICC}^{\ast}$ is strongly normalizing, by Theorem \ref{DDCToICCStar}, DDC is also strongly normalizing.
Therefore, given types $\ottnt{A}$ and $\ottnt{B}$,
we can decide whether they are equal at $ { \color{black}{C} } $ by normalizing and comparing them.
With the equality relation being decidable, type-checking can proceed via standard techniques.
Here we have shown that type-checking is decidable in DDC with CoC as the underlying PTS.
A future work would be to extend this construction to an arbitrary strongly normalizing PTS.
\fi
\iffalse
Such a decision procedure is already included in the joinability relation, shown in Appendix
\ref{parconsist}. To see why this decision procedure is correct, note that two terms
are joinable if and only if they are definitionally equal. Our consistency proof (described
briefly in \ref{consisteq}) already includes the difficult part of this correctness argument:
it shows that terms that are definitionally equal are joinable. The remainder of the correctness
argument (that joinability implies definitional equality) is via a simple
induction\footnote{\texttt{consist.v:Joins\_DefEq}}.
Showing that such a normalize-and-compare decision procedure is decidable also requires
showing that reduction is strongly normalizing for the given selection of
sorts, axioms and rules. We can show this by translating our system to the desired
strongly normalizing system. For example, for the appropriate
sorts, axioms and rules, we can translate DDC to the strongly normalizing
Calculus of Constructions (CoC) by forgetting all the level annotations and thereafter, show that DDC normalizes in lock-step with CoC.
\pc{Such a translation is not straightforward. To see why, note the following judgment: $ \ottmv{x} \! :^{ { \color{black}{C} } }\! {}^{ { \color{black}{\top} } } \! \ottkw{Int} \to Type , \ottmv{y} \! :^{ { \color{black}{C} } }\! \ottmv{x} \; \ottsym{3} ^{ { \color{black}{\top} } } \vdash \, \ottmv{y} \, :^{ { \color{black}{C} } } \, \ottmv{x} \; \ottsym{4} ^{ { \color{black}{\top} } } $ which is derivable in DDC. However, $ \ottmv{x} : \ottkw{Int} \to Type , \ottmv{y} : \ottmv{x} \; \ottsym{3} \vdash \, \ottmv{y} \, : \, \ottmv{x} \; \ottsym{4} $ is not derivable in CoC. The reason behind this difference is that while DDC can equate $ \ottmv{x} \; \ottsym{3} ^{ { \color{black}{\top} } } $ and $ \ottmv{x} \; \ottsym{4} ^{ { \color{black}{\top} } } $ of type $ {}^{ { \color{black}{\top} } } \! \ottkw{Int} \to Type $ at $ { \color{black}{C} } $, it would be unsound for CoC to equate $ \ottmv{x} \; \ottsym{3} $ and $ \ottmv{x} \; \ottsym{4} $ of type $ \ottkw{Int} \to Type $. So, a level agnostic translation from DDC to CoC would not work. Can this problem be avoided by translating domain types marked with top as $\ottkw{Unit}$? With respect to the above example, it works since $ \ottmv{x} : \ottkw{Unit} \to Type , \ottmv{y} : \ottmv{x} \; \ottkw{unit} \vdash \, \ottmv{y} \, : \, \ottmv{x} \; \ottkw{unit} $. However, then the polymorphic identity type $ \Pi \ottmv{x} \!:^{ { \color{black}{\top} } }\! Type . \ottmv{x} \to \ottmv{x} $ gets translated to $ \Pi \ottmv{x} \!:\! \ottkw{Unit} . \ottmv{x} \to \ottmv{x} $, something that's undesirable. \\\\ So, we should retain the domain type of a $\Pi$-type, even when marked with $ { \color{black}{\top} } $, as such since it is used in the body of the $\Pi$. But we need to replace arguments to a function having such type with some fixed `element of choice' of the domain type. With respect to the above example, assuming $0$ to be our `element of choice' for $\ottkw{Int}$, we can write $ \ottmv{x} : \ottkw{Int} \to Type , \ottmv{y} : \ottmv{x} \; \ottsym{0} \vdash \, \ottmv{y} \, : \, \ottmv{x} \; \ottsym{0} $, which is indeed a valid derivation in CoC. Such a translation, however, requires that CoC satisfies Axiom of Choice. I don't know how Axiom of Choice interacts with CoC. There is existing literature on this topic: \citep{werner} (see Definition 14). At this point, it seems to me that a translation from DDC to CoC requires a careful construction and could be a topic of independent investigation in its own right.}
In fact, given a strongly normalizing pure type system, we can check for type equality by first erasing
sub-parts of the types marked with $\top$ and then normalizing-and-comparing them. Such a procedure
is correct because by Erasure Simulation (Lemma 10), if an unerased term
normalizes, then the corresponding erased term also normalizes and their normal forms are indistinguishable.
The reason that projection rules such as \textsc{Eq-PiSnd} do not interfere
with decidability is that they are ``admissible'' rules, similar to
\textsc{Eq-Trans} and \textsc{Eq-SubstIrrel}, and they should not be interpreted
algorithmically. These rules are properties of the relation, so it is
convenient to include them in the definition of the system. However, there is
no free lunch: we eventually must prove them sound and our consistency proof
does that.
Our ultimate goal is to incorporate the ideas of DDC into Dependent
Haskell, adopting the \textsf{type}:\textsf{type} axiom. Even though such a
system has an undecidable type checking, all is not lost. We plan to follow the
approach laid out by \cite{weirich:systemd}. That paper starts with a similar
undecidable type system (called System D) and derives an equivalent annotated
version of the type system (called System DC) that supports decidable type
checking. (Like DDC, System D also includes rules similar to \textsc{Eq-PiSnd},
which are appropriately annotated in System DC). The process of defining an
equivalent annotated version is rather mechanical and is based on the use of explicit
proofs of conversion in terms such that the proofs include all information needed to check the type equalities. We are confident that we can construct a similar annotated system for the type
system DDC, presented in our paper.
\fi
\iffalse
\newcommand{\mathsf{act}}{\mathsf{act}}
\newcommand{\cat}[1]{\mathcal{#1}}
\newcommand{\mathsf{RRel}}{\mathsf{RRel}}
\newcommand{\mathsf{CSet}}{\mathsf{CSet}}
\newcommand{\mathsf{Set}}{\mathsf{Set}}
\newcommand{\mathsf{id}}{\mathsf{id}}
\newcommand{\mathsf{curry}}{\mathsf{curry}}
\newcommand{\func}[1]{\mathsf{#1}}
\newcommand{\mathsf{Id}}{\mathsf{Id}}
A type system can be explicitly monadic by having an explicit type for
the monad. In such a system a typing judgment of a type with side
effects has the form $\Gamma \vdash t : \mathsf{m}A$. We can program
in the world with all the side effects given to us by the monad by
applying the monad to all of our types; e.g., judgments of the form
$x_1:\mathsf{m}A_1,\ldots,x_i:\mathsf{m}A_i \vdash t :
\mathsf{m}A$. In fact, this offers up an alternative design where we
leave off the explicit application of the monad, but with every type
being endowed with the side effects of the monad.
Moving over to categorical models of type systems a system with an
explicit monad can be modeled by a category and a monad over the
category; e.g., a tuple $(\cat{C}, \mathsf{m}, \eta, \mu)$ where the
$\mathsf{m} : \cat{C} \mto \cat{C}$ is a functor, $\delta : A \mto
\mathsf{m}A$ is the return of the monad, $\mu : \mathsf{m}^2A \mto
\mathsf{m}A$ is the join of the monad, and this structure is subject
to several coherence laws called the monad laws\footnote{We omit the
various coherence laws from our discussion.}. Every monad is related
to its category of algebras (often called the Eilenberg-Moore
Category) $\cat{C}^{\mathsf{m}}$ which consists of objects pairs $(A,
h)$ called an algebra where $A$ is an object of $\cat{C}$ and $h :
\mathsf{m}A \mto A$ is an action on $A$. The model of implicitly
monadic systems is the category of algebras for the monad. Finally,
these two systems are related through an adjunction
$\cat{C}^{\mathsf{m}} : \func{U} \dashv \func{F} : \cat{C}$ where the
functor $\func{U} : \cat{C}^{\mathsf{m}} \mto \cat{C}$ forgets the
action of an algebra and the functor $\func{F} : \cat{C} \mto
\cat{C}^{\mathsf{m}}$ sends an object $A$ to the free algebra
$(\mathsf{m}A,\mu_A)$. This implies that each design--explicitly or
implicitly monadic--result in expressively equivalent systems, but
with alternative perspectives.
In this section, we look at our work from this perspective and begin
to understand how the systems we present here are related to graded
types. We can already divide the work on graded type systems up into
explicitly graded and implicitly graded systems. The first contains
all of the type systems with an explicit graded (co)monad such as the
systems from \citet{orchard,Gaboardi:2016,petricek,Ghica:2014}. These
systems only label variables that were introduced through the
(co)monad with a grade. Implicitly graded type systems label every
type with a grade such as the systems from
\citet{McBride:2016,atkey,grad,Moon:2021}. We might call these
implicitly graded type systems \emph{fully graded type systems}.
Now are these two perspectives related in the similar way that they
are for monads? We conjecture that the answer is positive, but we are
not currently able to answer this conjecture in full generality.
Instead we show that the categories of algebras for graded monads can
be abstracted into a new category that captures the semantic notion of
being fully graded. This result also shows that SDC should have an
equivalent (up to a translation) formalization in terms of a graded
monadic effect system. Furthermore, this implies that there should be
an embedding of SDC into existing graded effect type systems such as
Granule.
We show that SDC~(Fig.~\ref{fig:typing}) is a fully graded effect type
system by showing that its categorical model has the structure of a
category of graded algebras. We do this by first abstracting the
category of graded algebras into a new category called a
\emph{grade-indexed multicategory}, that captures the basic structure
of fully graded type systems.
\begin{definition}
\label{def:grade-indexed-multicategory}
Suppose $(\cat{R},\leq)$ is a preorder and $\cat{M}$ is a class of
objects. Then a \emph{grade-indexed multicategory}
$\mathsf{Gr}(\cat{R},\cat{M})$ consists of objects, pairs $(X,r)$
where $X \in \cat{M}$ and $r \in \cat{R}$, and morphisms
%
$f : \langle (X^1,{r_1}),\ldots,(X^n,{r_n}) \rangle \mto (Y, r)$
%
with $\langle (X^1, r_1),\ldots,(X^n, r_n) \rangle$ being a vector of objects.
A notion of approximation must exist. That is, for any
$s \leq s'$, $r'_1 \leq r_1,\ldots,r'_n$ $\leq r_n$, and morphism $f :
\langle (X^1,r_1),\ldots,(X^n,r_n) \rangle \mto (Z,s)$ there must be
an approximated morphism $\mathsf{approx}(f) : \langle
(X^1,r'_1),\ldots,(X^n,r'_n) \rangle \mto (Z,s')$\footnote{There are
a number of coherence axioms necessary that we omit here, but can be
found in Appendix~\ref{sec:relating_graded_types_with_qualities}.}.
\end{definition}
The category of graded algebras due to \cite{Fujii:2016b} can be
generalized into a category of lax monoidal functors of the shape $X :
\cat{R} \mto \cat{M}$ and grades $r \in \cat{R}$. This generalization
is indeed a grade-indexed multicategory where the multimorphisms are
induced by the monoidal structure of $\cat{M}$. An example of such a
category can be found in the model of classified sets.
\begin{definition}
\label{def:classified-sets}
Suppose $\cat{L}$ is a set of labels. The category of classified
sets $\mathsf{CSet}(\cat{L})$ has the following data. Objects are classified
sets $S$ (functors $S : \cat{L} \mto \mathsf{RRel}$ from the discrete
category $\cat{L}$ to the category of reflexive relations). A
morphism between classified sets $S$ and $S'$ is a natural
transformation $h : S \mto S'$.
\end{definition}
\noindent
Let's unpack the previous definition. Here we define $\mathsf{RRel}$ to be the
category of binary relations that respect reflexivity. That is, given
a relation $R_X \subseteq X \times X$ over some set $X$ then $x\,R\,x$
holds for all $x \in X$. Now, a morphism from relation $R_X$ to
relation $R_Y$ in $\mathsf{RRel}$ is a function $X \mto^f Y$ such that
$f(x_1)\,R_Y\,f(x_2)$ holds when $x_1\,R_X\,x_2$ holds for any
$x_1,x_2 \in X$. This implies that the components of a natural
transformation $S \mto^h S'$ between classified sets are morphisms
$S(l) \mto^{h_l} S'(l)$ in $\mathsf{RRel}$, and thus, have the previous
property.
The definition of classified sets given above is different from the
standard definition~\cite{10.1145/3290333}, but the definition given
here makes it quite easy to show that classified sets define a
grade-indexed multicategory.
\newcommand{\mathsf{Gr}}{\mathsf{Gr}}
\begin{lemma}[Grade-Indexed Multicategory of Relations]
\label{lemma:graded-indexed_multicategory_of_relations}
Suppose $(L,\leq,\top,\perp,\sqcup,\sqcap)$ is a lattice. Then
there is a grade-indexed multicategory $\mathsf{Gr}(L,\mathsf{CSet}(L))$.
\end{lemma}
The most interesting aspect of the proof of previous fact is the
definition of multimorphisms. A multimoirphism
$f : \langle (S_1,l_1),\ldots,(S_n,l_n) \rangle \mto (S,l)$
is the natural transformation:
\[
(S_1(l_1) \times \cdots \times S_n(l_n)) \mto^{S_1(a_1) \times \cdots \times S_n(a_n)} (S_1 \times \cdots \times S_n)(l_1 \sqcup \cdots \sqcup l_n) \mto^f S(l)
\]
where
$f : (S_1 \times \cdots \times S_n)(l_1 \sqcup \cdots \sqcup l_n) \mto S(l)$ is a morphism in $\mathsf{RRel}$ that is natural in each label,
$a_i : l_i \leq (l_1 \sqcup \cdots \sqcup l_i \sqcup \cdots \sqcup l_n)$
for $1 \leq i \leq n$, and
$S_1 \times S_2 = \lambda l'.S_1(l') \times S_2(l')$.
The graded-indexed multicategory $\mathsf{Gr}(L,\mathsf{CSet}(L))$ has lots of
structure. We can define the graded cartesian product and internal hom.
In fact, we get all of the necessary structure to soundly interpret
SDC in classified sets.
\newcommand{\interp}[1]{[\negthinspace[#1]\negthinspace]}
\begin{lemma}[Sound Typing]
\label{lemma:sound_typing}
Suppose
%
$(L,\leq,\top,\perp,\sqcup,\sqcap)$
%
is the lattice parameterizing SDC. If $ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then
there is a multimorphism
%
$\interp{\ottnt{a}} : \langle \interp{\Omega} \rangle \mto \interp{\ottnt{A}}_{\ell}$
%
in $\mathsf{Gr}(L,\mathsf{CSet}(L))$. Furthermore, if $ \ottnt{a} \leadsto \ottnt{b} $, then $\interp{\ottnt{a}} = \interp{\ottnt{b}}$.
\end{lemma}
\noindent
The latter holds by the fact that $\mathsf{Gr}(L,\mathsf{CSet}(L))$ is cartesian
closed and the proof of the former is a fairly straightforward proof
by induction on the assumed typing derivation.
What we have shown here is that SDC has a model in classified sets and
this model can be phrased as a grade-indexed multicategory. This result reveals
that the structure of the model is the same kind of structure we find
in the categories of algebras of graded monads.
\fi
\section{Relating Graded Types with Qualities}
\label{sec:relating_graded_types_with_qualities}
At the base of the categorical models for graded types either
coeffectful or effectful is the notion of a \emph{grade-indexed
multicategory}.
\begin{definition}
\label{def:grade-indexed-multicategory}
Suppose $(\cat{R},\leq)$ is a preorder and $\cat{M}$ is a class of
objects. Then a \emph{grade-indexed multicategory}
$\mathsf{Gr}(\cat{R},\cat{M})$ consists of the following
data:
\begin{enumerate}
\item (Objects) pairs $X_r$ where $X \in \cat{M}$ and $r \in \cat{R}$.
\item (Morphisms) Morphisms are of the form
%
$\langle X^1_{r_1},\ldots,X^n_{r_n} \rangle \mto^{f} Y_{r}$
%
where $\langle X^1_{r_1},\ldots,X^n_{r_n} \rangle$ is a vector of objects.
\begin{enumerate}
\item Identity morphisms $\langle X_{r} \rangle \mto^{\mathsf{id}} X_{r}$.
\item The composition of morphisms:
%
\[
\begin{array}{lll}
\langle X^{11}_{r_{11}},\ldots, X^{1n_1}_{r_{1n_1}} \rangle \mto^{f_1} Y^1_{s_1}
,\ldots,
\langle X^{m1}_{r_{m1}}, \ldots, X^{mn_m}_{r_{mn_m}} \rangle \mto^{f_m} Y^m_{s_m}\\
\langle Y^1_{s_1},\ldots,Y^m_{s_m} \rangle \mto^{g} Z_{r}
\end{array}
\]
%
is a morphism:
\[
\langle X^{11}_{r_{11}},\ldots,X^{1n_1}_{r_{1n_1}},X^{m1}_{r_{m1}}, \ldots, X^{mn_m}_{r_{mn_m}} \rangle \mto^{g(f_1,\ldots,f_m)} Z_{r}
\]
\item (Approximation) There is a natural transformation:
\[
\inferrule* [flushleft,right=] {
s \leq s',r'_1 \leq r_1,\ldots,r'_n \leq r_n \\
\langle X^1_{r_1},\ldots,X^n_{r_n} \rangle \mto^{f} Z_{s}
}{\langle X^1_{r'_1},\ldots,X^n_{r'_n} \rangle \mto^{\mathsf{approx}(r'_1,\ldots,r'_n,f)} Z_{s'}}
\]
\end{enumerate}
\end{enumerate}
\end{definition}
\begin{definition}
\label{def:classified-sets}
Suppose $\cat{L}$ is a set of labels. The category of classified
sets $\mathsf{CSet}(L)$ has the following data. Objects are classified sets
$S$ which are functors $S_X : \cat{L} \mto \mathsf{RRel}$ from the discrete
category $\mathsf{L}$ to the category of reflexive relations. A
morphism between classified sets $S$ and $S'$ is a natural
transformation $h : S \mto S'$.
\end{definition}
\noindent
Let's unpack the previous definition. Here we define $\mathsf{RRel}$ to be the
category of binary relations that respect reflexivity. That is, given
a relation $R_X \subseteq X \times X$ over some set $X$ then $x\,R\,x$
holds for all $x \in X$. Now a morphism from relation $R_X$ to
relation $R_Y$ in $\mathsf{RRel}$ is a function $X \mto^f Y$ such that
$f(x_1)\,R_Y\,f(x_2)$ holds when $x_1\,R_X\,x_2$ holds for any
$x_1,x_2 \in X$. This implies that the components of a natural
transformation $S \mto^h S'$ between classified sets are morphisms
$S(l) \mto^{h_1} S'(l)$ in $\mathsf{RRel}$, and thus, have the previous
property.
\begin{lemma}[Graded-Indexed Multicategory of Relations]
\label{lemma:graded-indexed_multicategory_of_relations}
Suppose $(L,\leq,\top,\perp,\sqcup,\sqcap)$ is a lattice. Then
there is a grade-indexed multicategory $\mathsf{Gr}(L,\mathsf{CSet}(L))$.
\end{lemma}
\begin{proof}
Define an object to be a pair $(S,l)$ for every object $S$ in $\mathsf{CSet}(L)$
and label $l \in L$. Given two relations $R_X$ and $R_Y$ we can
define the relation $R_X \times R_Y$ as
\[
(x,y) (R_X \times R_Y) (x',y') = x\,R_X\,x' \land y\,R_Y,y'
\]
and there are morphisms:
\[
\begin{array}{lll}
\pi_1 : R_X \times R_Y \mto R_X\\
\pi_2 : R_X \times R_Y \mto R_Y\\
(f,g) : R_Z \mto R_X \times R_Y\\
\end{array}
\]
making the standard diagram commute. The previous morphisms are
inherited from the structure of $\mathsf{Set}$ which is the bases of the
morphisms in $\mathsf{RRel}$. We now use this cartesian product on relations
to define multimorphisms. A multimorphism
%
$\langle (S_1,l_1),\ldots,(S_n,l_n) \rangle \mto^f (S,l)$
%
is the natural transformation:
\[
(S_1(l_1) \times \cdots \times S_n(l_n)) \mto^{S_1(a_1) \times \cdots \times S_n(a_n)} (S_1 \times \cdots \times S_n)(l_1 \sqcup \cdots \sqcup l_n) \mto^f S(l_1 \sqcup \cdots \sqcup l_n) \mto^{S(a)} S(l)
\]
where
%
$(S_1 \times \cdots \times S_n) \mto^f S$ is a morphism in $\mathsf{CSet}(L)$,
%
$a : (l_1 \sqcup \cdots \sqcup l_n) \leq l$,
%
$a_i : l_i \leq (l_1 \sqcup \cdots \sqcup l_i \sqcup \cdots \sqcup l_n)$
%
for $1 \leq i \leq n$, and
%
$S_1 \times S_2 = \lambda l'.S_1(l') \times S_2(l')$.
Notice that we do not have a morphism $\mathsf{id}_{S_1(l_1) \times
S_2(l_2)} : \langle (S_1,l_1),(S_2,l_2) \rangle \mto S_1(l_1)
\times S_2(l_2)$ making this a non-representable multicategory.
Approximation comes from the fact that we have a morphism $S(l_1)
\mto^{S(a)} S(l_2)$ when $a : l_1 \leq l_2$ due to the fact that $S : L \mto
\mathsf{RRel}$ is a functor.
\end{proof}
Lets take a look at the structure of $\mathsf{Gr}(L,\mathsf{CSet}(L))$. First, we
can define the graded cartesian product:
\[
(S_1,l) \times (S_2,l) = (S_1 \times S_2,l)
\]
This definition implies the following:
\[
\inferrule* [flushleft,right=] {
\langle (S_1,l_1),\ldots,(S_i,l_i),(S_{i+1},l_i),\ldots,(S_n,l_n) \rangle \mto^f (S,l)
}{\langle (S_1,l_1),\ldots,(S_i,l_i) \times (S_{i+1},l_i),\ldots,(S_n,l_n) \rangle \mto^{\mathsf{prodl}(f)} (S,l)}
\]
where $\mathsf{prod}(f) = f$ because $\mathsf{Gr}(L,\mathsf{CSet}(L))$. In addition, we have the following:
\[
\inferrule* [flushleft,right=] {
\langle (S_1,l_1),\ldots,(S_n,l_n) \rangle \mto^{f_1} (S,l)\\
\langle (S'_1,l'_1),\ldots,(S'_n,l'_n) \rangle \mto^{f_2} (S',l)
}{\langle (S_1,l_1),\ldots,(S_n,l_n),(S'_1,l'_1),\ldots,(S'_n,l'_n) \rangle \mto^{\mathsf{prodr}(f_1,f_2)} (S,l) \times (S',l)}
\]
where $\mathsf{prodr}(f_1,f_2) = f_1 \times f_2$.
The internal-hom is defined as follows:
\[
S_1 \Rightarrow S_2 := \lambda l.\lambda f.\lambda g.a\,S_1(l)\,b \implies f(a)\,S_2(l)\,g(b)
\]
This implies the following bijection:
\[
\inferrule* [flushleft,right=] {
\langle (S_1,l_1),\ldots,(S_{n-1},l_{n-1}),(S_n,l_n) \rangle \mto^f (S,l)
}{\langle (S_1,l_1),\ldots,(S_{n-1},l_{n-1}) \rangle \mto^{\mathsf{curry}(f)} (S_n,l_n) \Rightarrow (S,l)}
\]
Since $\mathsf{Gr}(L,\mathsf{CSet}(L))$ is indeed cartesian closed we have the following structural rules:
\[
\begin{array}{lll}
\langle (S,l) \rangle \mto^{\mathsf{contract}} (S,l) \times (S,l)\\
\langle (S,l) \rangle \mto^{\mathsf{weak}} \top\\
\end{array}
\]
where $\top := \lambda l.\mathsf{true}$ is the singleton classified
set, and hence, is terminal.
The final element of the model is a grade actor which we define to be the join of the lattice.
Using this we define an action:
\[
(S,l') \odot l = (S,l' \sqcup l)
\]
Furthermore, we can define an adjunction. First, we have the following forgetful functor:
\[
\begin{array}{lll}
\mathsf{Forget} : \mathsf{Gr}(L,\mathsf{CSet}(L)) \mto \mathsf{CSet}(L)\\
\mathsf{Forget}(S,l) = S(- \sqcup l)\\
\mathsf{Forget}(f : \langle (S_1,l_1),\ldots,(S_n,l_n)\rangle \mto (S,l)) = f : S_1(- \sqcup l_1) \times \ldots \times S_n(- \sqcup l_n) \mto S(- \sqcup l)
\end{array}
\]
and we have the following free functor:
\[
\begin{array}{lll}
\mathsf{Free} : \mathsf{CSet}(L) \mto \mathsf{Gr}(L,\mathsf{CSet}(L))\\
\mathsf{Free}(S) = (S, \perp)\\
\mathsf{Free}(f : S_1 \mto S_2) = f : \langle (S_1,\perp) \rangle \mto (S_2,\perp)
\end{array}
\]
We can now prove that there is an adjunction
$\mathsf{CSet}(L) : \mathsf{Free} \dashv \mathsf{Forget} : \mathsf{Gr}(L,\mathsf{CSet}(L))$.
We have:
\newcommand{\Hom}[0]{\mathsf{Hom}}
\newcommand{\Free}[0]{\mathsf{Free}}
\newcommand{\free}[0]{\mathsf{free}}
\newcommand{\Forget}[0]{\mathsf{Forget}}
\begin{align}
\Forget(\Free(S))
& = \Forget(S, \perp)\\
& = S(- \sqcup \perp)
\end{align}
Then we have:
\begin{align}
\Free(\Forget(S,l))
& = \Free(S(- \sqcup l))\\
& = (S(- \sqcup l),\perp)
\end{align}
\begin{theorem}[Free Forgetful Adjunction]
\label{theorem:free_forgetful_adjunction}
There is an adjunction:
\[
\mathsf{CSet}(L) : \mathsf{Free} \dashv \mathsf{Forget} : \mathsf{Gr}(L,\mathsf{CSet}(L))
\]
\end{theorem}
\begin{proof}
To have a morphism $\eta_S : S \mto \Forget(\Free(S))$ is to have a natural transformation
$\eta_S : S \mto S(- \sqcup \perp)$ which we can define as the coordinate
$\hat{\eta}_{S(l)} = \mathsf{id}_{S(l)} : S(l) \mto S(l)$
because we know $l = l \sqcup \perp$ for any $l$.
\ \\\noindent To have a morphism $\varepsilon_{(S,l)} : \langle
\Free(\Forget(S,l)) \rangle \mto (S,l)$ means we must have a
morphism $\varepsilon_{(S,l)} : \langle (S(- \sqcup l),\perp)
\rangle \mto (S,l)$, but this is equivalent to $\hat{\varepsilon}_{(S,l)}
: S(\perp \sqcup l) \mto S(l)$. And, again $\perp \sqcup l = l$, and
thus, set $\hat{\varepsilon}_{(S,l)} = \mathsf{id}_{S(l)}$.
\ \\ \noindent
Finally, we have:
\begin{align}
& \Free(S) \mto^{\Free(\eta_S)} \Free(\Forget(\Free(S)))\\
= & \Free(S) \mto^{\mathsf{id}_{\Free(S)}} \Free(S)\\
= & \langle \Free(\Forget(\Free(S))) \rangle \mto^{\varepsilon_{\Free(S)}} \Free(S)
\end{align}
and
\begin{align}
& \Forget(S,l) \mto^{\eta_{\Forget(S,l)}} \Forget(\Free(\Forget(S,l)))\\
= & \Forget(S,l) \mto^{\mathsf{id}_{\Forget(S,l)}} \Forget(S,l)\\
= & \langle \Forget(\Free(\Forget(S,l))) \rangle \mto^{\Forget(\varepsilon_{(S,l)})} \Forget(S,l)
\end{align}
Since both $\eta$ and $\varepsilon$ are both identities it is clear
they are natural transformations. Therefore,
%
$\mathsf{CSet}(L) : \mathsf{Free} \dashv \mathsf{Forget} : \mathsf{Gr}(L,\mathsf{CSet}(L))$
%
is indeed an adjunction.
\end{proof}
Now the previous adjunction along with the previously defined action implies there is a graded monad:
\begin{align}
T & : L \times \mathsf{CSet}(L) \mto \mathsf{CSet}(L)\\
T_l(S) & = \Forget(\Free(S) \odot l) \\
& = \Forget((S,\perp) \odot l)\\
& = \Forget(S, \perp \sqcup l) \\
& = \Forget(S,l)\\
& = S(- \sqcup l)
\end{align}
This comes with the following data:
\[
\begin{array}{lll}
\eta = \mathsf{id}_S : S \mto T_\perp S\\
\mu = \mathsf{id}_{S(- \sqcup l_1 \sqcup l_2)} : T_{l_1}T_{l_2}S \mto T_{l_1 \sqcup l_2}S
\end{array}
\]
Clearly, the standard diagrams will hold. In fact, this graded monad
is indeed just a renaming of the action $T_l = - \odot l : \mathsf{CSet}(L)
\mto \mathsf{CSet}(L)$, and the adjunction is an equivalence of categories
because the unit and counit are identities. Thus, the latter has all
the necessary structure to model the system presented here, and makes
the interpretation of the system quite simple.
The interpretation terms and types is as follows:
\begin{lemma}[Sound Typing]
\label{lemma:sound_typing}
Suppose
%
$(L,\leq,\top,\perp,\sqcup,\sqcap)$
%
is the lattice parameterizing SDC. If $ \Omega \vdash \, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $, then
there is a multimorphism
%
$\interp{\ottnt{a}} : \langle \interp{\Omega} \rangle \mto \interp{\ottnt{A}}_{\ell}$
%
in $\mathsf{Gr}(L,\mathsf{CSet}(L))$.
\end{lemma}
\begin{proof}
This is a proof by induction on the form of the assumed typing
derivation.
\ \\\noindent
First, consider the variable rule:
\[
\drule{SDC-Var}
\]
We know that $ \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} \in \Omega $, and hence,
%
$\interp{\Omega} = \ottsym{(} \Omega_{{\mathrm{1}}} , \ottmv{x} \! :^{ \ell_{{\mathrm{0}}} }\! \ottnt{A} , \Omega_{{\mathrm{2}}} \ottsym{)}$
%
for some $\Omega_{{\mathrm{1}}}$ and $\Omega_{{\mathrm{2}}}$. Hence, it suffices to find a multimorphism:
\[
\interp{\ottmv{x}} : \langle \interp{\Omega_{{\mathrm{1}}}},\interp{\ottnt{A}}_{\ell_{{\mathrm{0}}}},\interp{\Omega_{{\mathrm{2}}}} \rangle \mto \interp{\ottnt{A}}_{\ell}
\]
We know by definition that
%
$\interp{\ottnt{A}}_{\ell_{{\mathrm{0}}}} = (\interp{\ottnt{A}}, \ell_{{\mathrm{0}}})$,
%
and
%
$\interp{\ottnt{A}}_{\ell} = (\interp{\ottnt{A}}, \ell)$.
%
By assumption we know $\ell_{{\mathrm{0}}} \leq \ell$ which implies that there is a unique multimorphism $f : \ell_{{\mathrm{0}}} \leq \ell$.
Thus, we have the following multimorphism:
\[
\langle \interp{\Omega_{{\mathrm{1}}}},(\interp{\ottnt{A}} , \ell_{{\mathrm{0}}}),\interp{\Omega_{{\mathrm{2}}}} \rangle \mto^{\pi} (\interp{\ottnt{A}}, \ell_{{\mathrm{0}}}) \mto^{\interp{\ottnt{A}}(f)} (\interp{\ottnt{A}}, \ell)
\]
Furthermore, this is natural in $\interp{\Omega_{{\mathrm{1}}}}$, $\interp{\Omega_{{\mathrm{2}}}}$, $\ottnt{A}$, $\ell_{{\mathrm{0}}}$, and $\ell$.
\ \\\noindent
Next consider the abstraction rule:
\[
\drule{SDC-Abs}
\]
By the induction hypothesis we have a multimorphism:
\[
\langle \interp{\Omega},(\interp{\ottnt{A}} , \ell) \rangle \mto^{\interp{\ottnt{b}}} (\interp{\ottnt{B}}, \ell)
\]
Finally, define
%
$\interp{ \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{b} } = \mathsf{curry}(\interp{\ottnt{b}})$.
%
\ \\\noindent
Now consider the application rule:
\[
\drule{SDC-App}
\]
By the induction hypothesis we have the following multimorphisms:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{b}}} (\interp{\ottnt{A}}, \ell) \Rightarrow (\interp{\ottnt{B}},\ell)\\
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a}}} (\interp{\ottnt{A}}, \ell)
\end{align}
and then our final interpretation is as follows:
\[
\langle \interp{\Omega} \rangle
\mto^{\mathsf{prod}(\interp{\ottnt{b}},\interp{\ottnt{a}})} ((\interp{\ottnt{A}}, \ell) \Rightarrow (\interp{\ottnt{B}},\ell)) \times (\interp{\ottnt{A}}, \ell) \mto^{\mathsf{eval}} (\interp{\ottnt{B}},\ell)
\]
\ \\\noindent
Consider the pair rule:
\[
\drule{SDC-Pair}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a_{{\mathrm{1}}}}}} (\interp{\ottnt{A_{{\mathrm{1}}}}},\ell)\\
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a_{{\mathrm{2}}}}}} (\interp{\ottnt{A_{{\mathrm{2}}}}},\ell)\\
\end{align}
Then out final interpretation is $\interp{ ( \ottnt{a_{{\mathrm{1}}}} , \ottnt{a_{{\mathrm{2}}}} ) } = \mathsf{prod}(\ottnt{a_{{\mathrm{1}}}},\ottnt{a_{{\mathrm{2}}}})$.
\ \\\noindent
Consider the first projection rule:
\[
\drule{SDC-ProjOne}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a}}} (\interp{\ottnt{A_{{\mathrm{1}}}}},\ell) \times (\interp{\ottnt{A_{{\mathrm{2}}}}},\ell)\\
\end{align}
Then our final interpretation is $\interp{ \pi_1\ \ottnt{a} } =
\pi_1(\interp{\ottnt{a}})$. The case for the second projection is
similar.
\ \\\noindent
Consider the first injection rule:
\[
\drule{SDC-InjOne}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a_{{\mathrm{1}}}}}} (\interp{\ottnt{A_{{\mathrm{1}}}}},\ell)
\end{align}
Then our final interpretation is $\interp{ \ottkw{inj}_1\, \ottnt{a_{{\mathrm{1}}}} } = \iota_1(\interp{\ottnt{a_{{\mathrm{1}}}}})$. The second injection is similar.
\ \\\noindent
Consider the case rule:
\[
\drule{SDC-Case}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a}}} (\interp{\ottnt{A_{{\mathrm{1}}}}},\ell) + (\interp{\ottnt{A_{{\mathrm{2}}}}},\ell)\\
\langle \interp{\Omega}, (\interp{\ottnt{A_{{\mathrm{1}}}}},\ell) \rangle & \mto^{\interp{\ottnt{b_{{\mathrm{1}}}}}} (\interp{\ottnt{B}},\ell)\\
\langle \interp{\Omega}, (\interp{\ottnt{A_{{\mathrm{2}}}}},\ell) \rangle & \mto^{\interp{\ottnt{b_{{\mathrm{2}}}}}} (\interp{\ottnt{B}},\ell)\\
\end{align}
Then our final interpretation is:
\[
\interp{ \ottkw{case} \, \ottnt{a} \, \ottkw{of} \, \ottmv{x} \hookrightarrow \ottnt{b_{{\mathrm{1}}}} \mid \ottmv{y} \hookrightarrow \ottnt{b_{{\mathrm{2}}}} } = \mathsf{contract}_{\interp{\Omega}}(\mathsf{coprod}(\interp{\ottnt{b_{{\mathrm{1}}}}},\interp{\ottnt{b_{{\mathrm{2}}}}})(\mathsf{id}_{\interp{\Omega}},\interp{\ottnt{a}}))
\]
\ \\\noindent
Consider the case rule:
\[
\drule{SDC-Return}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a}}} (\interp{\ottnt{A}}, \ell \vee \ell_{{\mathrm{0}}} )
\end{align}
Furthermore, define $\interp{ T^{ \ell }\; \ottnt{A} } = \interp{\ottnt{A}}(- \lor \ell)$.
Then we have the following final interpretation
%
$\interp{ \eta^{ \ell_{{\mathrm{0}}} }\; \ottnt{a} } = \interp{\ottnt{a}}$.
%
This is because for a morphism $(\interp{\ottnt{A}}, \ell \vee \ell_{{\mathrm{0}}} ) \mto (\interp{\ottnt{A}}(\ell_{{\mathrm{0}}} \lor -) ,\ell)$
to exist there must be a morphism $\interp{\ottnt{A}}( \ell \vee \ell_{{\mathrm{0}}} ) \mto^f \interp{\ottnt{A}}( \ell \vee \ell_{{\mathrm{0}}} )$, but this implies
that we can define $f = \mathsf{id}$. Thus, we can freely internalize labels in the model using least-upper bound.
\ \\\noindent
Consider the case rule:
\[
\drule{SDC-Bind}
\]
By the induction hypothesis we have:
\begin{align}
\langle \interp{\Omega} \rangle & \mto^{\interp{\ottnt{a}}} (\interp{\ottnt{A}}(- \lor \ell_{{\mathrm{0}}}),\ell)\\
\langle \interp{\Omega},(\interp{\ottnt{A}}, \ell \vee \ell_{{\mathrm{0}}} ) \rangle & \mto^{\interp{\ottnt{b}}} (\interp{\ottnt{B}},\ell)\\
\end{align}
Then we have the following final interpretation $\interp{ \ottkw{bind} ^{ \ell_{{\mathrm{0}}} } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} } = \interp{\ottnt{b}}(\mathsf{id}_{\Omega},\interp{\ottnt{a}})$.
That is, bind is simply composition in the model.
\end{proof}
\fi
\section{System Specification for SDC }
\label{app:sdc-rules}
\[
\begin{array}{llcll}
\textit{labels} & \ell, k & ::= & { \color{black}{\bot} } \mid { \color{black}{\top} } \mid k \wedge \ell \mid k \vee \ell \mid \ldots \\
\textit{types} & \ottnt{A},\ottnt{B} & ::=& \ottkw{Unit} \mid \ottnt{A} \to \ottnt{B} \mid \ottnt{A} \times \ottnt{B} \mid \ottnt{A} + \ottnt{B} \mid T^{ \ell }\; \ottnt{A} \\
\textit{terms} & \ottnt{a}, \ottnt{b} & ::=& \ottmv{x} \mid \lambda \ottmv{x} \!:\! \ottnt{A} . \ottnt{a} \mid \ottnt{a} \; \ottnt{b} & \mbox{\it variables and functions} \\
&& \mid & \ottkw{unit} \mid ( \ottnt{a} , \ottnt{b} ) \mid \pi_1\ \ottnt{a} \mid \pi_2\ \ottnt{a} & \mbox{\it unit and products} \\
&& \mid & \ottkw{inj}_1\, \ottnt{a} \mid \ottkw{inj}_2\, \ottnt{a} \mid \ottkw{case} \, \ottnt{a} \, \ottkw{of}\, \ottnt{b_{{\mathrm{1}}}} ; \ottnt{b_{{\mathrm{2}}}} & \mbox{\it sums} \\
&& \mid & \eta^{ \ell }\; \ottnt{a} \mid \ottkw{bind} ^{ \ell } \, \ottmv{x} = \ottnt{a} \, \ottkw{in} \, \ottnt{b} & \mbox{\it graded modality}
\\
\textit{contexts} & \Omega & ::= & \varnothing \mid \Omega , \ottmv{x} \! :^{ \ell }\! \ottnt{A} \\
\\
\end{array}
\]
\subsection{Typing and Operational Semantics}
\drules[SDC]{$ \Omega \vdash\, \ottnt{a} \, :^{ \ell } \, \ottnt{A} $}{Typing rules for SDC}{Var,Unit,Abs,App,Pair,ProjOne,ProjTwo,InjOne,InjTwo,Case,Return,Bind}
\drules[SDCStep]{$ \ottnt{a} \leadsto \ottnt{a'} $}{CBN small step operational semantics for SDC}{AppCong,Beta,ProjOneCong,ProjTwoCong,ProjOneBeta,ProjTwoBeta,CaseCong,CaseOneBeta,CaseTwoBeta,BindCong,BindBeta}
\subsection{Indexed Indistinguishability}
\drules[SGEq]{$ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $}{Indexed Syntactic Equality}{Var,Unit,Abs,App,Return,Bind,Pair,ProjOne,ProjTwo,InjOne,InjTwo,Case}
\drules[SEq]{$ \Phi \vdash^{ \ell_{{\mathrm{0}}} }_{ \ell } \ottnt{a} \sim \ottnt{b} $}{Conditional Syntactic Equality}{Leq,Nleq}
\section{System Specification for DDC }
\label{app:ddc-rules}
This is the complete system that we have formalized using the Coq proof
assistant. The type setting of all of these rules is generated from the same Ott
source that also generates the Coq definitions. Some of the following rules may appear different from
their presentation in the paper. The reason behind this is that Ott is not very good at handling multiple
variable bindings. So, when necessary, we replace expressions involving multiple bound variables with equivalent expressions that have only single bound variable.
\subsection{Operational semantics}
\drules[ValueType]{}{Values that are types}{Type,Pi,WSigma,Sum,Unit}
\drules[V]{}{Values}{ValueType,TmUnit,WPair,InjOne,InjTwo}
\drules[S]{$ \ottnt{a} \leadsto \ottnt{a'} $}{CBN small-step operational semantics}{AppCong,Beta,CaseCong,CaseOneBeta,CaseTwoBeta,
LetPairCong,LetPairBeta}
\subsection{Definitional equality}
\drules[Eq]{$ \Phi \vdash \ottnt{a} \equiv_{ \ell } \ottnt{b} $}{Definitional Equality}{Refl,Sym,Trans,SubstIrrel,Beta,Pi,Abs,App,PiFst,PiSnd,
WSigma,WSigmaFst,WSigmaSnd,WPair,LetPair,
Sum,SumFst,SumSnd,InjOne,InjTwo,Case,TyUnit,TmUnit}
\drules[CEq]{$ \Phi \vdash^{ k } \ottnt{a} \equiv_{ \ell } \ottnt{b} $}{Conditional Definitional Equality}{Leq,Nleq}
\drules[G]{$ \Phi \vdash \ottnt{a} : k $}{Grading}{Type,Var,Pi,Abs,App,WSigma,WPair,LetPair,
Sum,InjOne,InjTwo,Case,TyUnit,TmUnit}
\drules[CG]{$ \Phi \vdash_{ k }^{ \ell } \ottnt{a} $}{Conditional Grading}{Leq,Nleq}
\subsection{Type System}
\drules[T]{$ \Omega \vdash \ottnt{a} :^{ \ell } \ottnt{A} $}{Typing}{Type,Conv,Var,Pi,Abs,App,AppIrrel,WSigma,WPair,WPairIrrel,LetPairCA,
Sum,InjOne,InjTwo,CaseC,TmUnit,TyUnit}
\subsection{Indexed Indistinguishability} \label{dep-indist}
\drules[GEq]{$ \Phi \vdash \ottnt{a} \sim_{ \ell } \ottnt{b} $}{Indexed Indistinguishability}{Type,Var,Pi,Abs,App,WSigma,WPair,LetPair,Sum,InjOne,InjTwo,Case,TyUnit,TmUnit}
\drules[CEq]{$ \Phi \vdash^{ \ell_{{\mathrm{0}}} }_{ \ell } \ottnt{a} \sim \ottnt{b} $}{Conditional Indistinguishability}{Leq,Nleq}
\subsection{Auxiliary Judgments}
\label{parconsist}
\drules[Par]{$ \Phi \vdash \ottnt{a} \Rightarrow_{ \ell } \ottnt{b} $}{Parallel reduction}{Refl,Pi,AppBeta,App,Abs,WSigma,WPair,WPairBeta,LetPair,
Sum,InjOne,InjTwo,CaseBetaOne,CaseBetaTwo,Case}
\drules[CPar]{$ \Phi \vdash^{ k }_{ \ell } \ottnt{a} \Rightarrow \ottnt{b} $}{Conditional Parallel reduction}{Leq,Nleq}
\drules[MP]{$ \Phi \vdash \ottnt{a} \Rightarrow^{\ast} _{ \ell } \ottnt{b} $}{Parallel reduction, reflexive transitive closure}
{Refl,Step}
\drules[]{$ \Phi \vdash \ottnt{a} \Leftrightarrow _{ \ell } \ottnt{b} $}{Joinability}
{join}
\drules[ConsistentXXa]{$ \mathsf{Consistent}\ \ottnt{a} \ \ottnt{b} $}{Consistent Head Forms}{Type,Unit,Pi,WSigma,Sum,StepXXR,StepXXL}
\f
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,129 |
var mongoose = require('mongoose');
var generatedDeltaModels = {};
var Meerkat = {
deltaModel: function(schemaDefinition, name) {
if (!generatedDeltaModels[name]) {
var deltaSchema = this.generateDeltaSchema(schemaDefinition, name);
generatedDeltaModels[name] = mongoose.model(name + 'Delta', deltaSchema);
}
return generatedDeltaModels[name]
},
Schema: function(schemaDefinition, name) {
var privateSchema = this.generatePrivateSchema(schemaDefinition);
privateSchema.versionNumber = {
type: Number,
default: 1
}
privateSchema.currentVersionNumber = {
type: Number,
default: 1
}
privateSchema.delta = {
type: mongoose.Schema.ObjectId,
ref: name + "Delta"
}
var mongooseSchema = mongoose.Schema(privateSchema);
var DeltaModel = this.deltaModel(schemaDefinition, name);
this.generateVirtualMethods(mongooseSchema, schemaDefinition, DeltaModel);
// Add in the difference function
mongooseSchema.pre('save', function(next) {
var hasChanged = false;
if (this._delta && this._id) {
var oldDelta = this.delta;
if (this.currentVersionNumber == this.versionNumber) {
this.currentVersionNumber++;
}
this.versionNumber++;
this._delta.previousDelta = oldDelta;
this._delta.linkedDocument = this;
this.delta = this._delta;
this._delta.save(function(error, results) {
next();
});
this._delta = null;
} else {
next();
}
});
var recallVersion = function(target, current, model, delta, callback) {
if (target == current) {
callback(null, model);
} else {
DeltaModel.findOne({_id: delta}, function(error, results) {
current--;
for (var key in results) {
if (results[key] instanceof Buffer) {
model[key] = module.exports.applyDelta(model[key], results[key])
}
}
recallVersion(target, current, model, results.previousDelta, callback);
})
}
}
mongooseSchema.set('toObject', {getters: true});
mongooseSchema.set('toJSON', {getters: true});
mongooseSchema.methods.getVersion = function(versionNumber, callback) {
if (versionNumber < this.versionNumber && versionNumber > 0) {
recallVersion(versionNumber, this.versionNumber, this, this.delta, callback);
} else {
callback(null, this);
}
}
mongooseSchema.methods.setCurrentVersionNumber = function(versionNumber, callback) {
this.currentVersionNumber = versionNumber;
this.save(callback);
}
mongooseSchema.methods.getCurrentVersionNumber = function() {
return this.currentVersionNumber;
}
return mongooseSchema;
},
model: function(name, schema) {
var mongooseModel = mongoose.model(name, schema);
var insertUnderscores = function(params) {
var alteredParams = {};
for (var key in params) {
alteredParams['_' + key] = params[key];
}
return alteredParams
}
var legacyFind = mongooseModel.find;
mongooseModel.find = function() {
arguments[0] = insertUnderscores(arguments[0])
legacyFind.apply(mongooseModel, arguments);
}
var legacyFindOne = mongooseModel.findOne;
mongooseModel.findOne = function() {
arguments[0] = insertUnderscores(arguments[0])
legacyFindOne.apply(mongooseModel, arguments);
}
return mongooseModel;
},
generateDeltaSchema: function(schemaDefinition, name) {
var deltaSchema = {};
for (var key in schemaDefinition) {
deltaSchema[key] = Buffer;
}
deltaSchema.linkedDocument = {
type: mongoose.Schema.ObjectId,
ref: name
}
deltaSchema.previousDelta = {
type: mongoose.Schema.ObjectId,
ref: name + "Delta"
}
return deltaSchema;
},
generatePrivateSchema: function(schemaDefinition) {
var privateSchema = {};
for (var key in schemaDefinition) {
privateSchema["_" + key] = schemaDefinition[key]
}
return privateSchema;
},
generateVirtualMethods: function(schema, schemaDefinition, DeltaModel) {
var self = this;
var setupSchema = function(key) {
schema.virtual(key)
.get(function() {
return this["_" + key];
})
.set(function(value) {
if (this['_' + key] != null &&
this['_' + key] != undefined &&
value != this['_' + key]) {
if (!this._delta) {
this._delta = new DeltaModel();
}
this._delta[key] = self.calculateDelta(value, this['_' + key])
}
this.set("_" + key, value);
})
}
for (var key in schemaDefinition) {
setupSchema(key);
}
},
calculateDelta: function(moreRecent, lessRecent) {
moreRecent = moreRecent.toString();
lessRecent = lessRecent.toString();
var moreRecent = new Buffer(moreRecent);
var lessRecent = new Buffer(lessRecent);
// var diff = new Buffer(Math.max(lessRecent.length, moreRecent.length));
var diff = new Buffer(lessRecent.length);
var index = 0;
var results = [];
for (var i = 0; i < diff.length; i++) {
diff[i] = moreRecent[i] ^ lessRecent[i];
}
return diff;
},
applyDelta: function(moreRecent, diff) {
var moreRecent = moreRecent.toString();
var moreRecent = new Buffer(moreRecent);
var lessRecent = new Buffer(diff.length);
for (var i = 0; i < lessRecent.length; i++) {
lessRecent[i] = moreRecent[i] ^ diff[i];
}
return lessRecent.toString();
}
}
module.exports = Meerkat; | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,055 |
Last summer, Heat president Pat Riley stated his desire to land a "whale," seemingly meaning Kevin Durant.
This year, Riley is taking a more modest approach to Miami's offseason.
The Heat emerged as a feel-good story with their incredible second-half turnaround. Role players like Dion Waiters and James Johnson clearly bought into Miami's culture, and Waiters has already said he wants to re-sign.
And, yes, the new Collective Bargaining Agreement's designated-veteran-player rule will make it more difficult for the Heat to land star free agents.
But if the Heat win their eventual case that Chris Bosh can no longer safely play basketball, they'll be guaranteed to have his salary removed from the cap only this offseason. This is their opportunity to upgrade the roster.
I'd caution against assuming this group of overachievers will overachieve again. Hassan Whiteside is a foundational piece, and Goran Dragic found his groove later in the season. Justise Winslow will return, too. But that's not close to a championship core, and locking up Waiters and Johnson isn't the ticket, either.
If the Heat are content being merely good right now, sure, keep this core together. They compete hard, and chemistry matters. This could be a fine team next year if it returns mostly intact.
But Miami is a market – with championship pedigree, no state income tax, warm weather and quality nightlife – that can dream bigger. This is a place that attracted LeBron James, Dwyane and Chris Bosh and, before that, Shaquille O'Neal (who approved his trade from the Lakers). Will Riley really shift his strategy so significantly? | {
"redpajama_set_name": "RedPajamaC4"
} | 6,481 |
Rockblot #011: Rorschach Inkblot Test with Exes For Eyes Vocalist Big James Arsenian
In Alternative/Rock Interviews Music
Rockblot #010: Rorschach Inkblot Test with Eagles of Death Metal Vocalist and Guitarist Jesse "Boots Electric" Hughes
This 10th episode of Rockblot is dedicated to Eagles of Death Metal's Merch Manager, Nick Alexander, as well as all of the others who needlessly lost their lives during the heinous Paris attacks.
Rockblot #009: Rorschach Inkblot Test with InAeona Drummer James Dunham
By Christopher Gonda 11/13/2015 1 Min Read
Prosthetic Records post-rock outfit InAeona rolled through Toronto, Canada and we spent some time chatting with the band. Check out this Rockblot episode with drummer James Dunham!
In Interviews Metal Music
Rockblot #008: Rorschach Inkblot Test with The Black Dahlia Murder Lead Vocalist Trevor Strnad
We peered into the mind of Trevor Strnad, lead vocalist of Metal Blade Records' melodic death metal maestros The Black Dahlia Murder, via a short Rorschach inkblot test. What do manta rays, ovaries, and microwaves have in common? Find out here!
Rockblot #007: Rorschach Inkblot Test with Against Me! Vocalist/Guitarist Laura Jane Grace and Drummer Atom Willard
At this year's Toronto edition of Riot Fest, where Against Me! were supporting their new live collection 23 Live Sex Acts, we gave vocalist/guitarist Laura Jane Grace and drummer Atom Willard our Rockblot test!
Rockblot #006: Rorschach Inkblot Test with Slipknot percussionist Shawn "Clown" Crahan
At Heavy MTL 2015 we sat down with the talented and ever-intriguing Slipknot co-founder, Mr. Shawn Crahan (aka #6, aka Clown), and, in order to get further into the depths of his curious mind, took him through Rockblot.
Rockblot #005: Rorschach Inkblot Test with Andrew W.K.
While at the Toronto, Canada edition of Riot Fest 2015, we caught up with infamous party rocker Andrew W.K. an gave Andrew the Rorschach inkblot test!
Rockblot #004: Rorschach Inkblot Test with Wilson Lead Vocalist Chad Nicefield
While at Heavy MTL, Chad Nicefield, lead vocalist for the Razor & Tie Detroit rock rebels Wilson, allowed us to use him as a guinea pig for our new psychology-based series, Rockblot. He took the Rorschach inkblot test to a level we weren't expecting!
Rockblot #003: Rorschach Inkblot Test with Blessthefall Lead Vocalist Beau Bokan
Ever wanted to know what makes Beau Bokan, lead singer of the Fearless Records rockers Blessthefall, tick? Well, here's your chance! Bokan recently took our Rockblot Rorschach test and gave us some awesome responses!
Rockblot #002: Rorschach Inkblot Test with Bullet For My Valentine Drummer Michael "Moose" Thomas
While at Heavy MTL we sat down with Michael "Moose" Thomas, drummer for UK metal band Bullet For My Valentine, and did some Rorschach Inkblot testing. This is Rockblot!
Rockblot #001: Rorschach Inkblot Test with Devin Townsend
While at Heavy MTL 2015 we caught up with legendary Canadian metaller, Devin Townsend, to see how he'd respond to the Rorschach Inkblot test… #Rockblot | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,448 |
[](https://gitter.im/bjackson/fixter?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
Fixter is a Node.js library to interact with the FIX protocol.
Pull requests and new tests are greatly welcomed.
Fixter is licensed under a BSD license. Do what you want with it.
## Example usage
When messages are received, they are emitted as events on the Initiator object. For example:
```
let initiator = new Initiator(options);
initiator.on('IOI', function(message) {
console.log('New IOI for ${message.Symbol}. Price: ${message.Price}');
});
```
## SSL support
To use SSL, set `SSL` to true in your Initiator's options.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,044 |
Q: How to force a TextInput with security entry in expo react native to open an azerty keyboard? I have this code:
<View className="mx-9">
<TextInput
placeholder="Email"
value={value.email}
onChangeText={(text) => setValue({ ...value, email: text })}
/>
<TextInput
placeholder="Password"
value={value.password}
secureTextEntry={true}
onChangeText={(text) => setValue({ ...value, password: text })}
/>
*
*I don't understand why on the email input, I see an azerty keyboard (which is my local) and on the password input, I see a qwerty keyboard.
Is there a way to force the local keyboard on password input?
For information, when I remove the secureTextEntry={true} I can see an azerty keyboard on the password input.
*More over, when I add keyboardType="email-address" on the email input, I see again a qwerty keyboard instead of azerty. And when I remove keyboardType="email-address" I see an azerty keyboard.
EDIT :
I've fixed the second point by writing this in my app.config.js :
export default {
expo: {
name: "myapp",
slug: "myapp",
version: "1.0.0",
// ...
ios: {
// ...
infoPlist: {
CFBundleLocalizations: ["fr"],
CFBundleDevelopmentRegion: "fr",
},
},
Now my email input with keyboardType="email-address" open an azerty keyboard. But I don't think it's a good solution to force local. It should take the local of the hardware event on a `keyboardType="email-address"``
Moreover, the password input still opening a qwerty keyboard.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 637 |
<?php
namespace Barryvdh\Debugbar\DataFormatter;
use DebugBar\DataFormatter\DataFormatter;
/**
* Simple DataFormatter based on the deprecated Symfony ValueExporter
*
* @see https://github.com/symfony/symfony/blob/v3.4.4/src/Symfony/Component/HttpKernel/DataCollector/Util/ValueExporter.php
*/
class SimpleFormatter extends DataFormatter
{
/**
* @param $data
* @return string
*/
public function formatVar($data)
{
return $this->exportValue($data);
}
/**
* Converts a PHP value to a string.
*
* @param mixed $value The PHP value
* @param int $depth Only for internal usage
* @param bool $deep Only for internal usage
*
* @return string The string representation of the given value
* @author Bernhard Schussek <bschussek@gmail.com>
*/
private function exportValue($value, $depth = 1, $deep = false)
{
if ($value instanceof \__PHP_Incomplete_Class) {
return sprintf('__PHP_Incomplete_Class(%s)', $this->getClassNameFromIncomplete($value));
}
if (is_object($value)) {
if ($value instanceof \DateTimeInterface) {
return sprintf('Object(%s) - %s', get_class($value), $value->format(\DateTime::ATOM));
}
return sprintf('Object(%s)', get_class($value));
}
if (is_array($value)) {
if (empty($value)) {
return '[]';
}
$indent = str_repeat(' ', $depth);
$a = array();
foreach ($value as $k => $v) {
if (is_array($v)) {
$deep = true;
}
$a[] = sprintf('%s => %s', $k, $this->exportValue($v, $depth + 1, $deep));
}
if ($deep) {
$args = [$indent, implode(sprintf(", \n%s", $indent), $a), str_repeat(' ', $depth - 1)];
return sprintf("[\n%s%s\n%s]", ...$args);
}
$s = sprintf('[%s]', implode(', ', $a));
if (80 > strlen($s)) {
return $s;
}
return sprintf("[\n%s%s\n]", $indent, implode(sprintf(",\n%s", $indent), $a));
}
if (is_resource($value)) {
return sprintf('Resource(%s#%d)', get_resource_type($value), $value);
}
if (null === $value) {
return 'null';
}
if (false === $value) {
return 'false';
}
if (true === $value) {
return 'true';
}
return (string) $value;
}
/**
* @param \__PHP_Incomplete_Class $value
* @return mixed
* @author Bernhard Schussek <bschussek@gmail.com>
*/
private function getClassNameFromIncomplete(\__PHP_Incomplete_Class $value)
{
$array = new \ArrayObject($value);
return $array['__PHP_Incomplete_Class_Name'];
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,481 |
\section{}
\begin{abstract}
Recently, simple conditions for well-behaved-ness of anisotropic Voronoi diagrams have been proposed.
While these conditions ensure well-behaved-ness of two types of practical anisotropic Voronoi diagrams, as well as the geodesic-distance one,
in any dimension,
they are both prohibitively expensive to evaluate, and not well-suited for typical problems in approximation or optimization.
We propose simple conditions that can be efficiently evaluated, and are better suited to practical problems of approximation and optimization.
The practical utility of this analysis is enhanced by the fact that orphan-free anisotropic Voronoi diagrams have embedded triangulations as duals.
\end{abstract}
\section{Introduction and Previous Work}
The Voronoi diagram, or Dirichlet tesselation, is a fundamental mathematical construct, with extensive practical application in diverse fields~\cite{Aurenhammer91}.
Given a discrete set of sites, its definition requires a choice of distance function, which determines how the input domain is broken up into tiles of points closest to a unique site.
The distance typically used is the natural distance in a Euclidean space, but generalizations based on other choices of distance can be defined~\cite{Power,DW,Power2,LS,LL2000}.
The use of a particular distance can be motivated by the intended application.
In particular, Voronoi diagrams with respect to the geodesic distance on a Riemannian manifold can be useful in defining approximations of the manifold that satisfy certain properties,
such as asymptotic optimality~\cite{enets,LL2000}.
When considering applications in which specifying a Riemannian metric to induce a distance is appropriate,
the cost of computing geodesic paths for any pair of points may be very high for practical applications (see for instance~\cite{MMP}).
For this reason, fast approximations to the geodesic distance have been proposed~\cite{DW,LS}, which take constant time to evaluate, provided that the metric can be evaluated at any point in constant time.
However, while the geodesic-distance diagrams are guaranteed to be composed of cells, each of which contains its generating site (the diagram is orphan-free),
this is, in general, not the case for the approximations of~\cite{DW,LS}.
Since the definition of the dual of diagram with orphans is problematic (i.e.\ it may require detecting orphans and placing new sites inside each, a process that could potentially become recursive),
and since certain approximation or optimization guarantees may be lost in the presence of orphans,
it is natural to consider orphan-freedom as a basic well-behave-ness condition for these anisotropic Voronoi diagrams.
For instance, duals of two-dimensional diagrams of the type of~\cite{DW} can be shown to be embedded triangulations~\cite{adt}, if they are orphan-free.
While the work of~\cite{DW} does not provide guarantees on orphan-freedom, that of~\cite{LS} provides an algorithm that is guaranteed to output an orphan-free diagram, in two dimensions.
More recently, the work of~\cite{avd} provides general conditions for orphan-freedom of anisotropic Voronoi diagrams of both types,
which hold in any number of dimensions. The condition is that the sites form an (asymmetric) $\epsilon$-net, for a suitable value of $\epsilon$, which depends on the underlying metric.
This condition is natural for problems in optimal covering, and $\mathcal{L}^\infty$ approximation~\cite{GruberMenets,enets}.
However, while quite general, the above results have some drawbacks, which make them difficult to be applied in practice. In particular, for problems of average-case ($\mathcal{L}^2$) optimization or approximation, an optimal set of sites has been shown to satisfy a Delone property~\cite{enets,OQ,GruberOQ}, which is generally weaker than the net property.
Additionally, the work of~\cite{avd} uses a Lipschitz-type constant on the underlying metric to obtain conditions for orphan-freedom.
In practice, however, computing this constant could potentially entail visiting all pairs of points in the domain, making it prohibitively expensive to compute.
This work addresses the above drawbacks, by providing conditions for orphan-freedom of anisotropic Voronoi diagrams that apply to more general sets of sites,
including those typically used for $\mathcal{L}^2$ optimization and approximation,
and use information from the metric that can be computed efficiently.
\section{Formal Setup}
Given a continuous metric $Q\in\mathcal{C}^0$ (a symmetric positive-definite matrix field) over a domain $\O\in\mathbb{R}^n$ of $n$-dimensional Euclidean space,
we begin by defining the functions
\[ D_Q^{{ }^{DW}}(a,b) = \left[ (a-b)^t Q_b (a-b) \right]^{1/2} \text{ , } a,b\in\O\]
and
\[ D_Q^{{ }^{LS}}(a,b) = \left[ (a-b)^t Q_a (a-b) \right]^{1/2} \text{ , } a,b\in\O \]
which are not symmetric, but are understood as distances for the purposes of constructing Voronoi diagrams, and where, because of their asymmetry, special attention must be given to the order of their arguments.
Given a discrete set $V$, the Labelle-Shewchuk diagram of $V$~\cite{LS} is composed of regions
\[ R(v) = \{ p\in\O : D_Q^{{ }^{LS}}(p,v) \le D_Q^{{ }^{LS}}(q,v), \forall q\in\O \} \text{ , } v\in V\]
and an analogous definition of a Du/Wang diagram~\cite{DW} uses the distance $D_Q^{{ }^{DW}}$ instead.
In the sequel, we will make extensive use of the square-root matrix field $M$, which, at each point, is the unique symmetric positive-definite matrix satisfying $M^t M=Q$.
As shown in~\cite{avd}, $M$ must be of the same differentiability class as $Q$.
Following~\cite{avd}, we denote the spectral matrix norm as $\rho(\cdot)$, which, when applied to positive-definite matrices, returns the maximum eigenvalue, and
define the function $\rho_m(\cdot)$, which returns the smallest eigenvalue of a positive-definite matrix.
Finally, the (worst-case) metric variation constant $\sigma_0$ is defined as
\[ \sigma_0 := \displaystyle{\max_{a,b\in\O} \frac{ \rho(M_b M_a^{-1} - I) }{ \|M_a(a-b)\| } } \]
where the maximum is assumed to exist (for instance, if $\O$ is compact).
\section{Orphan-Free Anisotropic Voronoi Diagrams of Delone Sets}
We begin by extending the results of~\cite{avd} to sets of sites that satisfy a $(C,P)$-Delone property ($C$-cover, asymmetric $P$-packing%
\footnote{$V$ is an asymmetric $P$-packing w.r.t.\ $D$ if, for all $v,w\in V$, it is either $D(v,w)\ge P$ \emph{or} $D(w,v)\ge P$.}),
which is a strict generalization of an asymmetric $\epsilon$-net ($\epsilon$-cover, asymmetric $\epsilon$ packing).
The result is a simple extension of~\cite{avd}, in which the proof structure is kept exactly as is,
but some of the lemmas are slightly modified to account for the unequal relation between $C$ and $P$.
We proceed by replacing $\epsilon$ by the cover constant $C$ in all the technical lemmas of~\cite{avd},
except in those in which the packing property is used: Lemmas 8 and 10, which become:
\begin{lemma}[From Lemma 8,~\cite{avd}]
Let $V$ be an asymmetric $\varepsilon$-net w.r.t. $D_Q^{{ }^{DW}}$, and $v,w\in V$ be Voronoi neighbors of the resulting DW-diagram.
If $c\in\O$ is in the Voronoi regions of $v,w$ then
\[ \|M_c (v-w)\| > P / (1+C\sigma_0) \]
\end{lemma}
\begin{lemma}[From Lemma 10,~\cite{avd}]
Let $V$ be an asymmetric $\varepsilon$-net w.r.t. $D_Q^{{ }^{LS}}$, and $v,w\in V$ be Voronoi neighbors of the resulting LS diagram.
If $k=(1+C\sigma_0) / (1-C\sigma_0)$, then
\[ P/k \le \|M_v (v-w)\| \le C(1+k) \]
\end{lemma}
It is a somewhat tedious, but simple exercise to verify that, assuming a Delone property for the set of sites, results in the following conditions for orphan-freedom of anisotropic Voronoi diagrams.
\begin{theorem}[Adapted from Theorem 1,~\cite{avd}]\label{th1}
Given $Q\in\mathcal{C}^0$ of worst-case variation $\sigma_0$,
the Du/Wang diagram of a $(C,P)$-Delone set (with respect to $D_Q^{{ }^{DW}}$) is orphan free if
$(P/C)^2 / \left( 2 (1 + C\sigma_0)^2 \right) - 2(C\sigma_0)^2 - 4C\sigma_0 > 0$.
\end{theorem}
\begin{theorem}[Adapted from Theorem 2,~\cite{avd}]\label{th2}
Given $Q\in\mathcal{C}^0$ of worst-case variation $\sigma_0$,
the Labelle/Shewchuk diagram of a $(C,P)$-Delone set (with respect to $D_Q^{{ }^{LS}}$) is orphan free if
$\left((P/C)^2 k^{-2} - \gamma^2 - 2\gamma\right)/2 - \gamma^2 - 2\gamma > 0$, where $\gamma=C\sigma_0(1+k)$ and $k=(1+C\sigma_0) / (1-C\sigma_0)$.
\end{theorem}
The above are similar to the analogous theorems in~\cite{avd}, but make explicit the relation between metric variation $\sigma_0$, and the cover and packing constants ($C,P$).
This generalization enables the application of these results not just to $\mathcal{L}^\infty$ optimization or approximation,
but also to problems in average-case ($\mathcal{L}^2$) optimization or approximation~\cite{OQ,GruberOQ}.
Typically, a lower metric variation means that a lower cover, and higher packing constants may be used while preserving orphan-freedom.
If we fix $\sigma_0$, then a lower relation $P/C$ requires a lower (stricter) cover constant to meet the well-behave-ness condition.
For instance, for a Delone set in which $P/C < 1$ (less strict than a $C$-net, and similar to the one used in~\cite{GruberOQ}), in order to satisfy the conditions of the above theorems,
the cover constant must be set lower than for the net condition ($P/C=1$).
Finally, note that these conditions reduce to the ones in~\cite{avd} for the net case, as expected.
\section{Differentiable and Piecewise Linear Metrics}\label{C1}
The main drawback of the above results, and those of~\cite{avd}, from a practical standpoint, is that the evaluation of the metric variation $\sigma_0$ may be prohibitively expensive in practice since,
in the worst case, it requires visiting all pair of points in the domain. We address this problem here.
Since $\sigma_0$ is a Lipschitz-type constant controlling the rate of change of $Q$, we may hope to find a simpler expression for differentiable metrics ($Q\in\mathcal{C}^1$) by simply taking the limit
in the definition of $\sigma_0$ as the pair of points becomes increasingly close, from every direction. In this way, we can define the differentiable-metric variation:
\[
\sigma_1 := \displaystyle{\sup_{r\ne 0} \lim_{\lambda\rightarrow 0}\frac{ \rho\left( M_{p+\lambda r} M_p^{-1} - I \right) }{ \|M_p \lambda r\| } }
= \displaystyle{\sup_{r\ne 0} \lim_{\lambda\rightarrow 0}\frac{ \rho\left( \frac{M_{p+\lambda r} - M_p}{\lambda} M_p^{-1}\right) }{ \|M_p r\| } }
= \displaystyle{\sup_{r\ne 0} \frac{\rho(D_r M_p M_p^{-1})}{ \|M_p r\| }}
\]
Clearly, the above expression can be evaluated by visiting each point in the domain only once.
Note that, from the definitions of $\sigma_0$ and $\sigma_1$, it is
\begin{eqnarray*}
\sigma_1 = \displaystyle{\sup_{r\ne 0} \lim_{\lambda\rightarrow 0}\frac{ \rho\left( M_{p+\lambda r} M_p^{-1} - I \right) }{ \|M_p \lambda r\| } } \le \displaystyle{\sup_{r\ne 0} \lim_{\lambda\rightarrow 0} \sigma_0} = \sigma_0
\end{eqnarray*}
In order to apply the results of Theorems~\ref{th1} and~\ref{th2} to the case in which we only have knowledge of $\sigma_1$, we can simply try to obtain an upper bound of $\sigma_0$ using $\sigma_1$.
However, while
a differentiable function $f$ over a compact domain in $\mathbb{R}$ has a Lipschitz constant $L=\max_{p\in\O} f'_p$~\cite{rudin-analysis},
there is no such simple relation of $\sigma_1$ bounding $\sigma_0$ from above.
The reason for this is the denominator $\|M_p r\|$ in the definition of $\sigma_1$, which prevents a simple analysis using integration and the Mean Value Theorem.
It is, however, possible to prove similar results to those of Theorems~\ref{th1} and~\ref{th2} by using only the differentiable-metric variation $\sigma_1$, without resorting to $\sigma_0$.
We begin by proving the following technical lemma, whose statement is the same as Lemma 2 of~\cite{avd}, but replacing $\sigma_0$ by $\sigma_1$,
but whose proof requires a new analysis using different techniques, and is relegated to Appendix A in the interest of conciseness.
\begin{lemma}\label{lem2}
If $\sigma_1$ is the differentiable-metric variation of $Q\in\mathcal{C}^1$, then for all $a,b\in\O$ and every constant $\varepsilon$, $\|M_a(a-b)\|\le \varepsilon$ implies
\[ 1-\varepsilon\sigma_1 \le \rho_m(M_b M_a^{-1}) \le {\|M_b (a-b)\|}/{\|M_a (a-b)\|} \le \rho(M_b M_a^{-1}) \le 1+\varepsilon\sigma_1 \]
\end{lemma}
Since this is the key technical lemma from which all results in~\cite{avd} stem, it can easily be verified that the above implies well-behave-ness results using the differentiable-metric constant.
In particular:
\begin{corollary} \label{cor1}
Given $Q\in\mathcal{C}^1$ of differentiable-metric variation $\sigma_1$,
the Du/Wang diagram of a $(C,P)$-Delone set (with respect to $D_Q^{{ }^{DW}}$) is orphan free if
$(P/C)^2 / \left( 2 (1 + C\sigma_1)^2 \right) - 2(C\sigma_1)^2 - 4C\sigma_1 > 0$.
\end{corollary}
\begin{corollary} \label{cor2}
Given $Q\in\mathcal{C}^1$ of differentiable-metric variation $\sigma_1$,
the Labelle/Shewchuk diagram of a $(C,P)$-Delone set (with respect to $D_Q^{{ }^{LS}}$) is orphan free if
$\left((P/C)^2 k^{-2} - \gamma^2 - 2\gamma\right)/2 - \gamma^2 - 2\gamma > 0$, where $\gamma=C\sigma_1(1+k)$ and $k=(1+C\sigma_1) / (1-C\sigma_1)$.
\end{corollary}
In particular, if the sites form an $\varepsilon$-net, then the above results imply that a $DW$ diagram is orphan-free whenever $\sigma_1\varepsilon \le 0.09868$, and a $LS$ diagram is orphan-free
if $\sigma_1\varepsilon \le 0.0584$. \\
\noindent{\bf Relation between metric variations $\sigma_0$ and $\sigma_1$}.
Interestingly, it is also possible to use Lemma~\ref{lem2} above to find some form of upper bound on $\sigma_0$, using only knowledge of $\sigma_1$.
To this end we first need to introduce the metric variation $\sigma_0(C)$, over neighborhoods of size $C$ as:
\[
\sigma_0(C) := \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \frac{ \rho(M_b M_a^{-1} - I) }{ \|M_a(a-b)\| } }
\]
which is identical to the definition of $\sigma_0$, but only considers pairs of points, vaguely speaking, within range $C$ of each other.
Given Eq.~\ref{tech2} from the proof of Lemma~\ref{lem2}, the definition of $\sigma_1$, and the (constant velocity) parametrized straight line connecting $a,b$ ($q:[0,1]\rightarrow \overline{ab}$), it is
\begin{equation}\label{eq01}
\begin{split}
\sigma_0(C) &= \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \frac{ \rho\left( (M_b - M_a)M_a^{-1} \right) }{ \|M_a(a-b)\| } } \\
&= \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \frac{ \rho\left( \int_0^1 D_{b-a}M_{q(\lambda)} M_{q(\lambda)}^{-1} M_{q(\lambda)} M_a^{-1} d\lambda \right) }{ \|M_a(a-b)\| } } \\
&\le \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \int_0^1 \frac{ \rho(D_{b-a} M_{q(\lambda)} M_{q(\lambda)}^{-1} ) }{ \|M_{q(\lambda)}(b-a)\| } \rho( M_{q(\lambda)}M_a^{-1})^2 d\lambda }\\
&\le \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \sigma_1 \int_0^1 \rho( M_{q(\lambda)}M_a^{-1})^2 d\lambda }\\
&\le \displaystyle{ \sup_{a,b\in\O, \text{ } \|M_a(a-b)\|\le C} \sigma_1 \int_0^1 (1+\lambda C \sigma_1)^2 d\lambda } \\
& \le \sigma_1 ( 1 + C\sigma_1 + (C\sigma_1)^2/3)
\end{split}
\end{equation}
where, typically, the value of $C$ used in the above expression will be the cover constant of the sites.
We finally note that, given $\sigma_1$, it is possible to use Eq.~\ref{eq01} to upper bound $\sigma_0$, and plug this in Theorems~\ref{th1} and~\ref{th2}.
However, because it is always $1 + C\sigma_1 + (C\sigma_1)^2/3 > 1$, we can always obtain better (less restrictive) conditions for well-behave-ness of anisotropic Voronoi diagrams
by using instead Corollaries~\ref{cor1} and~\ref{cor2} directly.
\subsection{Piecewise-Linear Metrics}\label{sec:PL}
So far we have considered conditions for well-behave-ness of anisotropic Voronoi diagrams only for metrics of class $\mathcal{C}^0$ and $\mathcal{C}^1$.
In practice, however, it may be the case that the input metric is given as a PL function over a simplicial complex.
This is typically the case in approximation problems in which the metric itself is derived from a previous estimate of the solution.
In this case, the metric is almost everywhere differentiable, and therefore the integrals in Eq.~\ref{eq01},
and those in the proof of Lemma~\ref{lem2} can be suitably broken into pieces in which the derivative of $M$ is defined.
This implies that the results from Sec.~\ref{C1} apply to the PL metric case, without change.
The definition of $\sigma_1$, however, becomes a supremum over all points where the metric is differentiable, which always exists in the case of PL metrics in which $M$ is
interpolated inside simplicies, using values given at the vertices.
In a slight abuse of notation, we replace supremums over the interior of simplicies with maximums, where it is understood that the supremum exists.
In the piecewise-linear metric case, it is possible to make use of the simple structure of the metric to efficiently compute an upper bound of $\sigma_1$.
Let $M^k_i = \partial_k M$ be the derivative of $M$ in the $k$-th coordinate direction (which is constant inside each $i$-th simplex),
$\mathcal{T}=\{\tau_i : i=1,\dots,m\}$ the set of simplicies over which $Q$ is linearly interpolated,
and $\{v_j : j\in I_i\}$ the set of vertices incident to the $i$-th simplex $\tau_i$.
Noticing, from its definition, that $\sigma_1$ is invariant to a scaling of $r$, and from the convexity of $\rho$, it follows that:
\begin{equation}\label{eqPL}
\begin{split}
\sigma_1 &= \displaystyle{ \max_{i=1,\dots,m} \max_{p\in{\tau_i}} \max_{\|r\|=1} \frac{\rho(D_r M_p M_p^{-1})}{ \|M_p r\| } } \\
&\overset{Lem. 7.1}{= } \displaystyle{ \max_{i=1,\dots,m} \max_{p\in{\tau_i}} \max_{\|r\|=1} \left[ \|M_p r\| \rho_m(M_p (D_r M)^{-1}) \right]^{-1} } \\
&{= } \displaystyle{ \max_{i=1,\dots,m} \max_{\|r\|=1} \left[ \min_{p\in{\tau_i}} \|M_p r\| \rho_m(M_p (D_r M)^{-1}) \right]^{-1} } \\
&\le \displaystyle{ \max_{i=1,\dots,m} \max_{\|r\|=1} \left[ \min_{j\in I_i} \lambda_1(v_j)^2 \rho_m( (D_r M)^{-1} ) \right]^{-1} } \\
&\overset{Lem. 7.1}{=} \displaystyle{ \max_{i=1,\dots,m} \max_{\|r\|=1} \frac{ \rho(D_r M) }{ \min_{j\in I_i} \lambda_1(v_j)^2 } } \\
&\le \displaystyle{ \max_{i=1,\dots,m} \max_{\|r\|=1} \frac{ \sum_{k=1}^n \rho( M_i^k ) r_k }{ \min_{j\in I_i} \lambda_1(v_j)^2 } } \\
&\le \displaystyle{ \max_{i=1,\dots,m} \frac{ \left[ \sum_{k=1}^n \rho( M_i^k )^2 \right]^{1/2} }{ \min_{j\in I_i} \lambda_1(v_j)^2 } }
\end{split}
\end{equation}
where $\lambda_1(p)$ is the smallest eigenvalue of $M_p$, and the numerator in the sixth line has been maximized by setting
$ r^k = \rho\left( M_i^k \right) / \left[ \sum_l \rho\left( M_i^l \right)^2 \right]^{1/2}$, which is clearly a unit vector.
The bound of Eq.~\ref{eqPL} is clearly conservative, however, crucially, it can be computed in time linear in the size of $\mathcal{T}$, since it is a maximum over terms, one per simplex,
which (for fixed dimension $n$) can be computed in constant time.
\section{Practical Considerations}
Consider the following practical scenario.
A metric $Q$ is given, which is PL over a simplicial complex $\mathcal{T}$, in $n$ dimensions (as in Sec.~\ref{sec:PL}, by linearly interpolating the square-root $M$ inside simplicies).
We are also provided a finite set $V$ of sites.
We consider the problem of determining whether the anisotropic Voronoi diagram of $V$ is orphan-free (whether of the Du/Wang, or Labelle/Shewchuk type), and if so, computing it efficiently.
To answer this question, we can make use of Corollaries~\ref{cor1} and~\ref{cor2}.
To this end, we first use Eq.~\ref{eqPL} to evaluate the differential-metric variation $\sigma_1$ of $Q$ (in time proportional to the size of $\mathcal{T}$).
Next, we may compute the packing and cover constants of $V$ (with respect to either $D_Q^{{ }^{DW}}$ or $D_Q^{{ }^{LS}}$), and check whether the conditions of Corollaries~\ref{cor1} and~\ref{cor2} are met,
in which case we are ensured that the anisotropic Voronoi diagram of $V$ is orphan-free.
In certain cases, such as when using the simple front-propagation algorithm of~\cite{adt}, it is the case that computing the Voronoi diagram can be done efficiently (in time proportional to the size of $\mathcal{T}$), and the output is correct if there is a priori knowledge that the diagram is orphan-free.
The missing step in the above reasoning is computing the covering and packing constants of $V$.
The packing constant can be simply computed from $V$, and by evaluating the metric at points in $V$ only, since it involves only distances between sites.
Computing, or finding an upper bound of the cover constant, however, may require computing a full anisotropic Voronoi diagram, and measuring distances from all points in each Voronoi region to their generating site. In the case of Labelle/Shewchuk diagrams, computing the diagram, as in~\cite{LS}, may itself already provide an answer to whether the diagram is orphan-free.
As for Du/Wang diagrams, an efficient solution is to use the optimistic algorithm of~\cite{adt}. This algorithm runs efficiently (in time proportional to the size of $\mathcal{T}$),
and produces a correct diagram only if the correct diagram of $V$ is orphan-free. If it isn't, then the algorithm returns a diagram that differs from the true one only at the orphans.
If the diagram of $V$ isn't orphan-free, then the algorithm of~\cite{adt} provides an upper bound of the cover constant $C$, which cannot satisfy Corollary~\ref{cor1}, since the true diagram isn't orphan-free. If, on the other hand, the true diagram of $V$ is orphan-free, then the algorithm provides the exact cover constant, which can be used to verify the conditions of Corollary~\ref{cor1}.
In conclusion, the use of the algorithm of~\cite{adt}, along with Corollary~\ref{cor1}, to check for orphan-freedom, never produces a false-positive,
and only produces false-negatives in cases in which it computes the exact cover constant, and therefore the false-negative cases can all be explained only by how loose the bounds of Corollary~\ref{cor1} are, and not by the fact that the algorithm of~\cite{adt} is optimistic. We believe this point to be of practical importance.
\section{Conclusion}
Given the problem of determining whether the anisotropic Voronoi diagram of a set of sites is orphan-free,
we have provided an analysis that results in new conditions that can be efficiently evaluated in the case of smooth or piecewise-linear metrics and,
perhaps more importantly, which can be applied to typical sets of sites resulting from problems in $\mathcal{L}^2$ optimization and approximation.
While the analysis is somewhat complex and technical, the results are simple to formulate and verify.
The emphasis throughout has been on the analysis, while the algorithmic aspects are only superficially discussed.
We hope that this work may provide a useful piece of analysis in the ongoing progress in practical algorithms for the computation of anisotropic Voronoi diagrams and anisotropic Delaunay triangulations.
\newpage
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,357 |
package edu.cornell.pserc.jpower.pf;
import cern.colt.matrix.AbstractMatrix;
import cern.colt.matrix.tdouble.DoubleFactory1D;
import cern.colt.matrix.tdouble.DoubleFactory2D;
import cern.colt.matrix.tdouble.DoubleMatrix1D;
import cern.colt.matrix.tdouble.DoubleMatrix2D;
import cern.colt.matrix.tdouble.impl.SparseRCDoubleMatrix2D;
import cern.colt.matrix.tint.IntFactory1D;
import cern.colt.matrix.tint.IntMatrix1D;
import edu.cornell.pserc.jpower.jpc.Branch;
import edu.cornell.pserc.jpower.jpc.Bus;
import static edu.emory.mathcs.utils.Utils.ifunc;
import static edu.emory.mathcs.utils.Utils.dfunc;
import static edu.emory.mathcs.utils.Utils.irange;
import static edu.emory.mathcs.utils.Utils.any;
import static edu.emory.mathcs.utils.Utils.dblm;
import static edu.emory.mathcs.utils.Utils.nonzero;
import static edu.emory.mathcs.utils.Utils.icat;
/**
* Builds the B matrices and phase shift injections for DC power flow.
*/
@SuppressWarnings("static-access")
public class Djp_makeBdc {
/**
* Builds the B matrices and phase shift injections for DC power flow.
* Returns the
* B matrices and phase shift injection vectors needed for a DC power flow.
* The bus real power injections are related to bus voltage angles by
* P = BBUS * Va + PBUSINJ
* The real power flows at the from end the lines are related to the bus
* voltage angles by
* Pf = BF * Va + PFINJ
* Does appropriate conversions to p.u.
*
* @param baseMVA
* @param bus
* @param branch
* @return
*/
public static AbstractMatrix[] makeBdc(double baseMVA, Bus bus, Branch branch) {
int nb, nl;
int[] xfmr, ft, il;
double[] v;
DoubleMatrix1D stat, b, tap, Pfinj, Pbusinj;
SparseRCDoubleMatrix2D Cft;
DoubleMatrix2D Bf, Bbus;
/* constants */
nb = bus.size(); // number of buses
nl = branch.size(); // number of lines
/* check that bus numbers are equal to indices to bus (one set of bus numbers) */
if ( any( bus.bus_i.copy().assign(IntFactory1D.dense.make(irange(nb)),
ifunc.equals).assign(ifunc.equals(0))) )
System.err.println("makeBdc: buses must be numbered consecutively in bus matrix");
// TODO: throw non consecutive bus numbers exception.
/* for each branch, compute the elements of the branch B matrix and the
* phase shift "quiescent" injections, where
*
* | Pf | | Bff Bft | | Vaf | | Pfinj |
* | | = | | * | | + | |
* | Pt | | Btf Btt | | Vat | | Ptinj |
*/
// ones at in-service branches
stat = dblm(branch.br_status);
// series susceptance
b = stat.assign(branch.br_x, dfunc.div);
// default tap ratio = 1
tap = DoubleFactory1D.dense.make(nl, 1);
// indices of non-zero tap ratios
xfmr = nonzero(branch.tap);
// assign non-zero tap ratios
tap.viewSelection(xfmr).assign(branch.tap.viewSelection(xfmr));
b.assign(tap, dfunc.div);
/* build connection matrix Cft = Cf - Ct for line and from - to buses */
ft = IntFactory1D.dense.make(new IntMatrix1D[] {branch.f_bus, branch.t_bus}).toArray();
il = icat(irange(nl), irange(nl));
v = DoubleFactory1D.dense.make(new DoubleMatrix1D[] {
DoubleFactory1D.dense.make(nl, 1),
DoubleFactory1D.dense.make(nl, -1)
}).toArray();
Cft = new SparseRCDoubleMatrix2D(nl, nb, il, ft, v, false, false, false);
/* build Bf such that Bf * Va is the vector of real branch powers
* injected at each branch's "from" bus
*/
Bf = DoubleFactory2D.sparse.diagonal(b).zMult(Cft, null);
/* build Bbus */
Bbus = Cft.viewDice().zMult(Bf, null);
/* build phase shift injection vectors */
Pfinj = branch.shift.copy();
Pfinj.assign(dfunc.chain(dfunc.mult(Math.PI), dfunc.div(180)));
Pfinj.assign(dfunc.neg);
Pfinj.assign(b, dfunc.mult); // injected at the from bus
// DoubleMatrix1D Ptinj = Pfinj.assign(dfunc.neg); // and extracted at the to bus
Pbusinj = Cft.viewDice().zMult(Pfinj, null);
return new AbstractMatrix[] {Bbus, Bf, Pbusinj, Pfinj};
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,914 |
import os
from conan.tools.build import build_jobs
from conan.tools.cmake.presets import load_cmake_presets, get_configure_preset
from conan.tools.cmake.utils import is_multi_configuration
from conan.tools.files import chdir, mkdir
from conan.tools.microsoft.msbuild import msbuild_verbosity_cmd_line_arg
from conans.client.tools.oss import args_to_string
from conans.errors import ConanException
def _validate_recipe(conanfile):
forbidden_generators = ["cmake", "cmake_multi"]
if any(it in conanfile.generators for it in forbidden_generators):
raise ConanException("Usage of toolchain is only supported with 'cmake_find_package'"
" or 'cmake_find_package_multi' generators")
def _cmake_cmd_line_args(conanfile, generator):
args = []
if not generator:
return args
# Arguments related to parallel
njobs = build_jobs(conanfile)
if njobs and ("Makefiles" in generator or "Ninja" in generator) and "NMake" not in generator:
args.append("-j{}".format(njobs))
maxcpucount = conanfile.conf.get("tools.microsoft.msbuild:max_cpu_count", check_type=int)
if maxcpucount and "Visual Studio" in generator:
args.append("/m:{}".format(njobs))
# Arguments for verbosity
if "Visual Studio" in generator:
verbosity = msbuild_verbosity_cmd_line_arg(conanfile)
if verbosity:
args.append(verbosity)
return args
class CMake(object):
""" CMake helper to use together with the toolchain feature. It implements a very simple
wrapper to call the cmake executable, but without passing compile flags, preprocessor
definitions... all that is set by the toolchain. Only the generator and the CMAKE_TOOLCHAIN_FILE
are passed to the command line, plus the ``--config Release`` for builds in multi-config
"""
def __init__(self, conanfile):
_validate_recipe(conanfile)
# Store a reference to useful data
self._conanfile = conanfile
cmake_presets = load_cmake_presets(conanfile.generators_folder)
configure_preset = get_configure_preset(cmake_presets, conanfile)
self._generator = configure_preset["generator"]
self._toolchain_file = configure_preset.get("toolchainFile")
self._cache_variables = configure_preset["cacheVariables"]
self._cmake_program = "cmake" # Path to CMake should be handled by environment
def configure(self, variables=None, build_script_folder=None, cli_args=None):
cmakelist_folder = self._conanfile.source_folder
if build_script_folder:
cmakelist_folder = os.path.join(self._conanfile.source_folder, build_script_folder)
build_folder = self._conanfile.build_folder
generator_folder = self._conanfile.generators_folder
mkdir(self._conanfile, build_folder)
arg_list = [self._cmake_program]
if self._generator:
arg_list.append('-G "{}"'.format(self._generator))
if self._toolchain_file:
if os.path.isabs(self._toolchain_file):
toolpath = self._toolchain_file
else:
toolpath = os.path.join(generator_folder, self._toolchain_file)
arg_list.append('-DCMAKE_TOOLCHAIN_FILE="{}"'.format(toolpath.replace("\\", "/")))
if self._conanfile.package_folder:
pkg_folder = self._conanfile.package_folder.replace("\\", "/")
arg_list.append('-DCMAKE_INSTALL_PREFIX="{}"'.format(pkg_folder))
if not variables:
variables = {}
self._cache_variables.update(variables)
arg_list.extend(['-D{}="{}"'.format(k, v) for k, v in self._cache_variables.items()])
arg_list.append('"{}"'.format(cmakelist_folder))
if cli_args:
arg_list.extend(cli_args)
command = " ".join(arg_list)
self._conanfile.output.info("CMake command: %s" % command)
with chdir(self, build_folder):
self._conanfile.run(command)
def _build(self, build_type=None, target=None, cli_args=None, build_tool_args=None, env=""):
bf = self._conanfile.build_folder
is_multi = is_multi_configuration(self._generator)
if build_type and not is_multi:
self._conanfile.output.error("Don't specify 'build_type' at build time for "
"single-config build systems")
bt = build_type or self._conanfile.settings.get_safe("build_type")
if not bt:
raise ConanException("build_type setting should be defined.")
build_config = "--config {}".format(bt) if bt and is_multi else ""
args = []
if target is not None:
args = ["--target", target]
if cli_args:
args.extend(cli_args)
cmd_line_args = _cmake_cmd_line_args(self._conanfile, self._generator)
if build_tool_args:
cmd_line_args.extend(build_tool_args)
if cmd_line_args:
args += ['--'] + cmd_line_args
arg_list = ['"{}"'.format(bf), build_config, args_to_string(args)]
arg_list = " ".join(filter(None, arg_list))
command = "%s --build %s" % (self._cmake_program, arg_list)
self._conanfile.output.info("CMake command: %s" % command)
self._conanfile.run(command, env=env)
def build(self, build_type=None, target=None, cli_args=None, build_tool_args=None):
self._build(build_type, target, cli_args, build_tool_args)
def install(self, build_type=None):
mkdir(self._conanfile, self._conanfile.package_folder)
bt = build_type or self._conanfile.settings.get_safe("build_type")
if not bt:
raise ConanException("build_type setting should be defined.")
is_multi = is_multi_configuration(self._generator)
build_config = "--config {}".format(bt) if bt and is_multi else ""
pkg_folder = '"{}"'.format(self._conanfile.package_folder.replace("\\", "/"))
build_folder = '"{}"'.format(self._conanfile.build_folder)
arg_list = ["--install", build_folder, build_config, "--prefix", pkg_folder]
arg_list = " ".join(filter(None, arg_list))
command = "%s %s" % (self._cmake_program, arg_list)
self._conanfile.output.info("CMake command: %s" % command)
self._conanfile.run(command)
def test(self, build_type=None, target=None, cli_args=None, build_tool_args=None, env=""):
if self._conanfile.conf.get("tools.build:skip_test", check_type=bool):
return
if not target:
is_multi = is_multi_configuration(self._generator)
is_ninja = "Ninja" in self._generator
target = "RUN_TESTS" if is_multi and not is_ninja else "test"
# The default for ``test()`` is both the buildenv and the runenv
env = ["conanbuild", "conanrun"] if env == "" else env
self._build(build_type=build_type, target=target, cli_args=cli_args,
build_tool_args=build_tool_args, env=env)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 592 |
Q: HTA Document.Body.OffsetHeight with doctype Please consider this HTA:
<html>
<head>
<title>My HTML application</title>
<HTA:APPLICATION
APPLICATIONNAME="My HTML application"
ID="MyHTMLapplication"
SCROLL="No"
VERSION="1.0"/>
</head>
<script language="VBScript">
Sub Window_OnLoad
ResizeTo 100, 100
msgbox Document.Body.OffsetWidth & "x" & Document.Body.OffsetHeight
End Sub
</script>
<body style="border:0;margin:0"></body>
</html>
On my PC it reports: 111x66 and that's actual size of window without window frame.
Now if I add <!DOCTYPE html> to this HTA, I get: 107x19 where width is actually correct, but not the height.
If I even want to use <meta http-equiv="X-UA-Compatible" content="IE=EDGE"> I get: 107x0
My HTA depends on doctype, and I can't remove it. OTOH I want to be able to detect actual window size and act upon it.
Can someone explain why Document.Body.OffsetHeight behaves like this, or maybe provide other solution for detecting correct window size (body element size)?
A: By default HTA is in backward-compatibility mode where document.body.offsetWidth and document.body.offsetHeight return expected result.
With doctype declaration HTA turns in standards mode (CSS1Compat) in which case this should be used instead: document.documentElement.offsetWidth and document.documentElement.offsetHeight
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,891 |
@interface NSOrderedSetBlocksKitTest : XCTestCase
@end
@implementation NSOrderedSetBlocksKitTest {
id _subject;
NSInteger _total;
BOOL _hasClassAvailable;
}
- (void)setUp {
Class BKOrderedSet = NSClassFromString(@"NSOrderedSet");
if (BKOrderedSet) {
_hasClassAvailable = YES;
_subject = [NSOrderedSet orderedSetWithArray:@[ @"1", @"22", @"333" ]];
} else {
_hasClassAvailable = NO;
}
_total = 0;
}
- (void)tearDown {
_subject = nil;
}
- (void)testEach {
if (!_hasClassAvailable)
return;
void(^senderBlock)(id) = ^(NSString *sender) {
_total += [sender length];
};
[(NSOrderedSet *)_subject bk_each:senderBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
}
- (void)testMatch {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] == 22) ? YES : NO;
return match;
};
id found = [(NSOrderedSet *)_subject bk_match:validationBlock];
XCTAssertEqual(_total, (NSInteger)3, @"total length of \"122\" is %ld", (long)_total);
XCTAssertEqual(found, @"22", @"matched object is %@", found);
}
- (void)testNotMatch {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] == 4444) ? YES : NO;
return match;
};
id found = [(NSOrderedSet *)_subject bk_match:validationBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
XCTAssertNil(found, @"no matched object");
}
- (void)testSelect {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] < 300) ? YES : NO;
return match;
};
NSOrderedSet *subject = _subject;
NSOrderedSet *found = [subject bk_select:validationBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
NSOrderedSet *target = [NSOrderedSet orderedSetWithArray:@[ @"1", @"22" ]];
XCTAssertEqualObjects(found, target, @"selected items are %@", found);
}
- (void)testSelectedNone {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] > 400) ? YES : NO;
return match;
};
NSOrderedSet *subject = _subject;
NSOrderedSet *found = [subject bk_select:validationBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
XCTAssertTrue(found.count == 0, @"no item is selected");
}
- (void)testReject {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] > 300) ? YES : NO;
return match;
};
NSOrderedSet *subject = _subject;
NSOrderedSet *left = [subject bk_reject:validationBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
NSOrderedSet *target = [NSOrderedSet orderedSetWithArray:@[ @"1", @"22" ]];
XCTAssertEqualObjects(left, target, @"not rejected items are %@", left);
}
- (void)testRejectedAll {
if (!_hasClassAvailable)
return;
BOOL(^validationBlock)(id) = ^(NSString *obj) {
_total += [obj length];
BOOL match = ([obj intValue] < 400) ? YES : NO;
return match;
};
NSOrderedSet *subject = _subject;
NSOrderedSet *left = [subject bk_reject:validationBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
XCTAssertTrue(left.count == 0, @"all items are rejected");
}
- (void)testMap {
if (!_hasClassAvailable)
return;
id(^transformBlock)(id) = ^(NSString *obj) {
_total += [obj length];
return [obj substringToIndex:1];
};
NSOrderedSet *subject = _subject;
NSOrderedSet *transformed = [subject bk_map:transformBlock];
XCTAssertEqual(_total, (NSInteger)6, @"total length of \"122333\" is %ld", (long)_total);
NSOrderedSet *target = [NSOrderedSet orderedSetWithArray:@[ @"1", @"2", @"3" ]];
XCTAssertEqualObjects(transformed, target, @"transformed items are %@", transformed);
}
- (void)testReduceWithBlock {
if (!_hasClassAvailable)
return;
id(^accumlationBlock)(id, id) = ^(id sum,id obj) {
return [sum stringByAppendingString:obj];
};
NSString *concatenated = [_subject bk_reduce:@"" withBlock:accumlationBlock];
XCTAssertTrue([concatenated isEqualToString:@"122333"], @"concatenated string is %@", concatenated);
}
- (void)testAny {
if (!_hasClassAvailable)
return;
BOOL(^existsBlockTrue)(id) = ^BOOL(id obj) {
return [obj hasPrefix:@"1"];
};
BOOL(^existsBlockFalse)(id) = ^BOOL(id obj) {
return [obj hasPrefix:@"4"];
};
BOOL letterExists = [(NSOrderedSet *)_subject bk_any:existsBlockTrue];
XCTAssertTrue(letterExists, @"letter is not in array");
BOOL letterDoesNotExist = [(NSOrderedSet *)_subject bk_any:existsBlockFalse];
XCTAssertFalse(letterDoesNotExist, @"letter is in array");
}
- (void)testAll {
if (!_hasClassAvailable)
return;
NSOrderedSet *names = [NSOrderedSet orderedSetWithArray:@[ @"John", @"Joe", @"Jon", @"Jester" ]];
NSOrderedSet *names2 = [NSOrderedSet orderedSetWithArray:@[ @"John", @"Joe", @"Jon", @"Mary" ]];
// Check if array has element with prefix 1
BOOL(^nameStartsWithJ)(id) = ^BOOL(id obj) {
return [obj hasPrefix:@"J"];
};
BOOL allNamesStartWithJ = [names bk_all:nameStartsWithJ];
XCTAssertTrue(allNamesStartWithJ, @"all names do not start with J in array");
BOOL allNamesDoNotStartWithJ = [names2 bk_all:nameStartsWithJ];
XCTAssertFalse(allNamesDoNotStartWithJ, @"all names do start with J in array");
}
- (void)testNone {
if (!_hasClassAvailable)
return;
NSOrderedSet *names = [NSOrderedSet orderedSetWithArray:@[ @"John", @"Joe", @"Jon", @"Jester" ]];
NSOrderedSet *names2 = [NSOrderedSet orderedSetWithArray:@[ @"John", @"Joe", @"Jon", @"Mary" ]];
// Check if array has element with prefix 1
BOOL(^nameStartsWithM)(id) = ^BOOL(id obj) {
return [obj hasPrefix:@"M"];
};
BOOL noNamesStartWithM = [names bk_none:nameStartsWithM];
XCTAssertTrue(noNamesStartWithM, @"some names start with M in array");
BOOL someNamesStartWithM = [names2 bk_none:nameStartsWithM];
XCTAssertFalse(someNamesStartWithM, @"no names start with M in array");
}
- (void)testCorresponds {
if (!_hasClassAvailable)
return;
NSOrderedSet *numbers = [NSOrderedSet orderedSetWithArray:@[ @(1), @(2), @(3) ]];
NSOrderedSet *letters = [NSOrderedSet orderedSetWithArray:@[ @"1", @"2", @"3" ]];
BOOL doesCorrespond = [numbers bk_corresponds:letters withBlock:^(id number, id letter) {
return [[number stringValue] isEqualToString:letter];
}];
XCTAssertTrue(doesCorrespond, @"1,2,3 does not correspond to \"1\",\"2\",\"3\"");
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,657 |
{"url":"https:\/\/zbmath.org\/?format=complete&q=an:0653.10001","text":"# zbMATH \u2014 the first resource for mathematics\n\nDivisors. (English) Zbl\u00a00653.10001\nCambridge Tracts in Mathematics, 90. Cambridge (UK) etc.: Cambridge University Press. xvi, 167 p. \u00a325.00; \\$ 39.50 (1988).\nThe aim of these authors is to present a cohesive study, with a logical structure, of questions concerning the divisors of an integer, the main focus being on divisors in short intervals and the propinquity of divisors, and this goal has been successfully achieved. The modern theory has its roots in work of Hardy and Ramanujan and owes a great deal to the perceptiveness of Paul Erd\u0151s, whose continuing influence on the subject is very evident here and elsewhere. In the last decade, much progress had been made in developing our understanding of the behaviour of divisors, and the present authors have been in the forefront of this sphere of activity. Many of the results established in this book have been available previously only in the research journals, and some proofs are given here in detail for the first time.\nThis volume is likely to be an important reference book in an active research field for a considerable time. It is intended for graduate students in analytic number theory and others interested in gaining an insight into this rich area either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style.\nFor the reader new to the field (and for others!), this book is demanding and the proofs (inevitably) are very technical, but the authors take care to give sufficient explanation and motivation to help those prepared to persevere to follow the arguments and to gain a familiarity with the methods used. These incorporate well known techniques from Analysis and Number Theory, but a probabilistic train of thought is also apparent. The diligent reader should be proficient in the use of H\u00f6lder\u2019s inequality by the time he reaches the end of the book!\nEach chapter concentrates on one main theme, which is clearly set in context, and ends with some useful background notes and a wealth of challenging exercises. A collection of results required subsequently are given in chapter 0, whilst the objective of chapter 1 is to obtain optimal results concerning the size, for almost all positive integers $$n$$, of $$|\\omega(n,t)-\\log\\log t|$$, where $$\\omega(n,t) = \\text{card}\\, \\{p: p \\mid n,\\;p \\leq t\\}$$ ($$p$$ prime). Chapters 2 and 3 are devoted, respectively, to estimating the function $$H(x,y,z)$$, the number of positive integers $$n \\leq x$$ with a divisor $$d$$ satisfying $$y < d \\leq z$$, and to examining the function $$\\tau(n,\\theta) = \\sum _{d\\mid n} d^{i\\theta}$$ ($$\\theta$$ real); this latter function was first systematically studied in this way by the first author [J. Lond. Math. Soc., II. Ser. 9, 571\u2013580 (1975; Zbl 0308.10037)].\nIn the next chapter, functions measuring in some way the propinquity of the divisors of $$n$$ are investigated, examples being the function $T(n,\\alpha) = \\text{card}\\, \\{d,d': d\\mid n,\\;d'\\mid n,\\;| \\log d \/ d'| \\leq \\log^\\alpha n\\} \\text{ for } \\alpha \\leq 1$ and Erd\u0151s\u2019 function $\\tau^+(n) = \\text{card}\\, \\{k \\in Z : \\exists d\\mid n: 2^ k < d \\leq 2^{k + 1}\\}.$\n\nThe motivation for chapter 5 is Erd\u0151s\u2019 conjecture, made nearly half a century ago, that almost all integers have two divisors $$d,d'$$ satisfying $$d<d'\\leq 2d$$; this was finally proved, in a stronger form, by H. Maier and the second author [Invent. Math. 76, 121\u2013128 (1984; Zbl 0536.10039)]. The function $\\Delta_ r(n) = \\max _{u_ 1,...,u_{r- 1}}\\text{card}\\,\\{d_ 1...d_{r-1}\\mid n: u_ i < \\log d_ i \\leq u_ i + 1\\quad (1 \\leq i < r)\\}$ was first introduced by C. Hooley [Proc. Lond. Math. Soc., III. Ser. 38, 115\u2013151 (1979; Zbl 0394.10027)] in a wide ranging paper that highlights the potential in applications for results of the type described in this volume; the main task of chapters 6 and 7 is to establish good bounds for the sum $\\sum_{n\\leq x} \\Delta_ r(n) y^{\\omega(n)}\\quad (y > 0)$ when $$y$$ lies outside and within a certain critical interval.\nAt the end of the book, there is a comprehensive and useful list of references. A combination of the notation section at the beginning and the index at the end will assist in the task of locating key definitions and results. It might perhaps have been helpful to the reader from another area of mathematics if the authors had included in the notation section an explanation of the few symbols that might be unfamiliar to someone from outside number theory, but this is a very minor point.\nAltogether, this volume is a very valuable addition to the stock of current, research level books and makes a major and worthwhile contribution to the literature.\n\n##### MSC:\n 11-02 Research exposition (monographs, survey articles) pertaining to number theory 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11N05 Distribution of primes 11N37 Asymptotic results on arithmetic functions 11K65 Arithmetic functions in probabilistic number theory 11B83 Special sequences and polynomials","date":"2021-01-15 23:26:09","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\": 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\": 0.6178424954414368, \"perplexity\": 390.9727398425341}, \"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\/1610703497681.4\/warc\/CC-MAIN-20210115224908-20210116014908-00252.warc.gz\"}"} | null | null |
Q: Value does not fall within the expected range using nlog with entity frameWork I use nlog dll(version 3.1.0.0) to write to database - oracle with entity frameWork in the line :
logger.Log(logLevel, "try");
I get in the logs of nlog the following error:
Error Error when writing to database System.ArgumentException: Value
does not fall within the expected range. at
Oracle.ManagedDataAccess.Client.OracleCommand.set_CommandType(CommandType
value) at
NLog.Targets.DatabaseTarget.WriteEventToDatabase(LogEventInfo
logEvent) at NLog.Targets.DatabaseTarget.Write(LogEventInfo
logEvent)
the code is:
SetPropGDC(LogEntity);
NLog.LogLevel logLevel = SetLogLevel(Level.Debug);
logger.Log(logLevel, "try");
ClearGDC();
private static LogLevel SetLogLevel(Level level)
{
switch (level)
{
case Level.Debug: return LogLevel.Debug;
case Level.Error: return LogLevel.Error;
case Level.Fatal: return LogLevel.Fatal;
case Level.Info: return LogLevel.Info;
default: return LogLevel.Error;
}
}
private void SetPropGDC(LogEntity LogEntity)
{
GlobalDiagnosticsContext.Set("connectionString", _unitOfWork.getConnectionString());
GlobalDiagnosticsContext.Set(processId, LogEntity.PROCESS_ID.ToString());
GlobalDiagnosticsContext.Set("TIME_STAMP", LogEntity.TIME_STAMP.ToString());
GlobalDiagnosticsContext.Set(customerId, LogEntity.CUSTOMER_ID.ToString());
GlobalDiagnosticsContext.Set("REQUEST", LogEntity.REQUEST.ToString());
GlobalDiagnosticsContext.Set("RESPONSE", LogEntity.RESPONSE.ToString());
GlobalDiagnosticsContext.Set("EXCEPTION", LogEntity.EXCEPTION.ToString());
GlobalDiagnosticsContext.Set("STACK_TRACE", LogEntity.STACK_TRACE.ToString());
GlobalDiagnosticsContext.Set("DETAILS", LogEntity.DETAILS.ToString());
}
<targets>
<target name="TRACEDatabase" type="DataBase" keepConnection="false"
dbProvider="Oracle.ManagedDataAccess.Client" connectionString="${gdc:connectionString}"
commandText="insert into TLOG_SITE_GENERAL_TRACE( PROCESS_ID,TIME_STAMP,CUSTOMER_ID,LOG_LEVEL,REQUEST,RESPONSE,EXCEPTION,STACK_TRACE,MESSAGE)
values(:PROCESS_ID,:TIME_STAMP,:CUSTOMER_ID,:LOG_LEVEL,:REQUEST,:RESPONSE,:EXCEPTION,:STACK_TRACE,:MESSAGE)">
<parameter name="PROCESS_ID" layout="${gdc:PROCESS_ID}" />
<parameter name="TIME_STAMP" layout="${gdc:TIME_STAMP}" />
<parameter name="CUSTOMER_ID" layout="${gdc:CUSTOMER_ID}" />
<parameter name="LOG_LEVEL" layout="${level:uppercase=true}" />
<parameter name="REQUEST" layout="${gdc:REQUEST}" />
<parameter name="RESPONSE" layout="${gdc:RESPONSE}" />
<parameter name="EXCEPTION" layout="${gdc:EXCEPTION}" />
<parameter name="STACK_TRACE" layout="${gdc:STACK_TRACE}" />
<parameter name="MESSAGE" layout="${message}" />
</target>
Can anyone help?
A: I think you're looking for type support for database parameters, that's introduced in NLog 4.6.
PS: Please note that event properties (on LogEventInfo) are a more robust than the GlobalDiagnosticsContext in your example
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<?php
use yii\helpers\Html;
use yii\grid\GridView;
use common\vendor\AppLabels;
use backend\models\Sector;
/* @var $this yii\web\View */
/* @var $searchModel backend\models\Smk3Search */
/* @var $dataProvider yii\data\ActiveDataProvider */
$this->title = sprintf("%s %s", "AHENG", AppLabels::SMK3);
$this->params['breadcrumbs'][] = $this->title;
?>
<div class="smk3-index">
<div class="page-header">
<h1><?= Html::encode($this->title) ?></h1>
</div>
<div class="clearfix">
<div class="pull-right">
<?= Html::a(AppLabels::BTN_ADD, ['create'], ['class' => 'btn btn-sm btn-success']); ?>
</div>
</div>
<hr/>
<div class="table-responsive">
<?= GridView::widget([
'dataProvider' => $dataProvider,
'filterModel' => $searchModel,
'columns' => [
['class' => 'yii\grid\SerialColumn'],
[
'attribute' => 'sector_id',
'value' => 'sector.sector_name',
'filter' => Html::activeDropDownList($searchModel, 'sector_id', Sector::map(new Sector(), 'sector_name'), ['class' => 'chosen-select form-control'])
],
[
'attribute' => 'power_plant_id',
'value' => 'powerPlant.pp_name'
],
'smk3_year',
'smk3_auditor',
['class' => 'yii\grid\ActionColumn'],
],
]); ?>
</div>
</div>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,955 |
Fiesta Shows Set to Open on March 21
by Sue Woodcock • March 1, 2019 • 0 Comments
Get ready for a good snow storm in March or April because the Licensing Commission has approved a permit for Fiesta Shows to come to town once again.
Traditionally it snows at least once when Fiesta open its first show of the season in the Showcase Cinema parking lot off Squire Road on March 21 and close on April 15 operating every day from 3-11 p.m.
This year the License Commission reminded show owner John Flynn of years past when there were incidences but they noted that last year was a good year with no problems. This is credited to beefed up security and the installation of cameras around the cinema.
"In the past sometimes I voted for this sometimes against," said Commissioner Linda Guinasso. "I've looked at other cities and towns and I wonder why they allow the show, and it all comes down to the money. It's hard to turn this money down for the kids."
The funds do go to the McCarthy-Trifone fund, which is used to support sports in the city.
Ward 5 Councillor John Powers said Flynn has stepped up over the years.
Jane D'Angelo, president of the McCarthy-Trifone fund said without the carnival there would be no other means of money for the fund.
"He has been very generous even in the years it snowed and rained," she said.
← Officials Happy with Federal Wetlands Protection
News Briefs → | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,047 |
{"url":"https:\/\/cseducators.stackexchange.com\/questions\/860\/how-do-i-convince-my-students-that-visual-programming-is-real-programming","text":"# How do I convince my students that visual programming is real programming?\n\nI have been considering taking a visual programming language, such as Snap!, to my high school students as a way to make some of the concepts we delve into a little more fun. The kids themselves already have a pretty substantial background in Java, Python, C and 6502 assembly, and many of them are also familiar with the JS\/PHP\/SQL stack for web dev.\n\nI have a very strong feeling that they won't consider a block-based language to be a real language, even though it contains typing, parameters, lambdas, etc. How do I get past the initial hump and persuade them that this is worth their time?\n\n\u2022 I'm curious why you think it'll make things more fun or what you plan to do to make things more fun. One of the downsides of DnD languages is that to do something substantial you need some serious screen real estate and in my experience, experienced students have found repeated dragging and dropping tedious over using text editor functionality. This is not to say that DnD won't be great in your case but I'm looking for more info on how you want to use them Jun 20, 2017 at 12:12\n\u2022 If these kids already have that extensive a programming background, what you're proposing isn't likely to be fun. Jun 20, 2017 at 17:17\n\u2022 Put your money where your mouth is. Build something useful\/cool in the language and demo it for them while introducing it. Jun 20, 2017 at 18:27\n\u2022 From the sound of it, your students use programming languages to do things. Snap! is going to have to earn its keep in the minds of students like that. I'm a developer, not a teacher, but my first thought when I looked at the examples on the Snap! page was \"this is actually just a text based programming language given goofy colors.\" Contrast that with something like LabView which is a serious language used in serious contexts (and with a serious price tag, of course). You're going to have to convince them that it's not different for the sake of being different. Jun 20, 2017 at 20:06\n\u2022 What kind of high school students are you lucky enough to work with?! I don't know many high school students with that substantial a background in programming. Jun 20, 2017 at 23:25\n\nTwo thoughts:\n\n1. I'd start with telling them why you think it's worth their time. Whatever I or anyone else says on here, you're the one who thought it would be fun and worthwhile, and you must have reasons for that. Your reasons are more authentic and probably more applicable to your students than our reasons will be. Just be straight with the kids about what they are.\n\n2. You mentioned assembly, C, Java, and Python, which means that the kids not only have experience with \"real\" languages, but they have experiences with languages with a wide range of abstraction. You can present DnD\/block programming languages as yet another level of abstraction, in which common language structures (blocks and certain bits of syntax) are abstracted visually rather than textually. This is not so radically different from what Python does when it visually presents code blocks as indented regions rather than as text sandwiched between curly brackets. You can point out the similarities between the block interpreter and the Python interpreter. You can compare the power, efficiency, learning curve, and programmer time requirements for each language and maybe even make a nice chart on the board. This will reinforce the idea that when comparing Snap! to Python to C, they really are comparing apples to apples.\n\n\u2022 so after comparison it turns out that visual blocks are worse in all aspects. then the students won't really understand why the teacher did bring it up at all. Jun 21, 2017 at 5:06\n\u2022 \"This is not so radically different from what Python does when it visually presents code blocks as indented regions rather than as text sandwiched between curly brackets.\" Actually, yes, it is quite different. Python is enforcing an arrangement of text; it isn't abandoning text. The rest of your answer might still fly. Jun 21, 2017 at 5:26\n\u2022 @jpmc26 Python is still text, but you don't get to pick the keyword you want to use, e.g., for a while loop. Snap! effectively just replaces the fixed scaffolding you would type with a graphical element. Python still gives you more flexibility in what you can do within the fixed elements, but the similarity is still there. (Full disclosure: I've only used Scratch, and that years ago, but Snap! looks fundamentally the same.) Jun 21, 2017 at 17:40\n\u2022 @chepner What I see as \"radically\" different is the departure from typing simple words using standard characters to using custom non-text, graphical\/binary items that are more difficult manage because we don't have dedicated tooling for them (like keyboards and find\/replace). I do understand that there might be similarities in terms of structure, especially after the text is parsed, but I see abandoning text as quite different. I understand that, in some ways, this analysis supports the rest of the answer. Jun 21, 2017 at 18:13\n\u2022 @jpmc26 considering that assembly is a \"radical\" departure from the underlying machine code (\"you can read it now!\"), and C is a \"radical\" departure from the ~1:1 of assembly to machine code, and Haskell is a \"radical\" departure... etc. I would say this supports Neal's arguments more not less. \"...are more difficult to manage because we don't have dedicated tooling for them...\" is generally what managers say to resist switching to new paradigms. The real question to potentially bring up is \"Is this abstraction of programming particularly useful? If so, for what classes of tasks?\" Jun 21, 2017 at 20:54\n\nEveryone uses high-level languages these days, and we let compilers do the grunt work. Block-based programming is just a kind of IDE with a slightly different autocomplete mechanism. Block-based code can be trivially transpiled to textual form. After they complete an exercise, you can have them perform that conversion to textual code or pseudocode.\n\nTo debunk the \"Real programmers don't use _____\" fallacy, you could discuss what happens when you take that mentality to its logical extreme.\n\n\u2022 Some of the commenters at the top should make note of this answer.\n\u2013\u00a0Ben I.\nJun 21, 2017 at 17:44\n\u2022 Don't believe it, it is not true. We use sed. Jul 10, 2017 at 17:41\n\u2022 Snap has a facility to allow you to write a translator, to convert snap code to any other language. And another to make snap look like another language. Jul 10, 2017 at 17:43\n\nYou could use some environment that lets you switch between blocks and text and work in both. That way, students can see firsthand that the code in the blocks converts to textual \"real\" code. This can help them understand the leap.\n\nHere's one example of blocks switching with text on a Karel program on CodeHS (Note: I'm one of the founders of CodeHS)\n\nHere's how I explained it to my students after teaching with App Inventor during a pre-college summer program:\n\nWith textual programming languages, your program won't work if you have a semicolon or even a space character (in Python) out of place. This can be frustrating, especially for beginners. They might conclude that programming is about punctuation, when it isn't; it's about logic, design, teamwork, and problem-solving. The argument for starting with visual programming languages is to expose beginners to the essence of computer science, rather than the superficial issue of placement of curly braces, colons, etc. If they enjoy it, they can go on to learn those things.\n\nTo use an analogy, programming with blocks is like writing stories with word magnets. On the positive side, you don't need to worry about spelling or punctuation; on the negative side, your vocabulary is limited.\n\nProgrammers disagree about whether using languages like App Inventor (or Scratch or Alice) is really programming\/coding. To me, it is, since the logic is there. I don't see a fundamental difference between using a mouse and using a keyboard. That would be like saying that Jean-Dominique Bauby wasn't a real author because he used blinks instead of a keyboard or pen. (See also these Dilbert and xkcd cartoons.) To be fair, not everyone agrees with me.\n\nNonetheless, I can understand the frustration of students who wanted to learn \"real coding\" and why visual programming languages tend to be used just by beginners. One of the most common questions about App Inventor is: Why can't I see and modify the Java code created by App Inventor? The answer is that App Inventor doesn't create Java code; it creates something called byte code that is not human readable. Learning textual programming languages is incredibly useful and fulfilling; it's like moving from Lite Brite to an unlimited set of paints and brushes. I hope that some of you go on to do so.\n\nDisclaimer: I am one of the creators of App Inventor.\n\n\u2022 My personal definition (or test) of a \"real\" programming language is if you can use it to directly call the host system's platform API or not - so C and C++ are, as is C# and Java (through P\/Invoke and JNI respectively) but not Flash ActionScript or LOGO. Would you agree with my definition?\n\u2013\u00a0Dai\nJun 21, 2017 at 6:43\n\u2022 @Dai That should be a separate question, not a discussion within comments. Jun 21, 2017 at 17:53\n\nI was at this camp one summer, and it was a programming camp for building models of different systems. I was super excited - I'd already been programming on Khan Academy and Codecademy. So I walk in, and they say that we'll be using this language called StarLogo Nova. We open our chromebooks, go to the site - and I begin questioning things, because I figure out pretty quickly that it's a drag and drop language.\n\nI had (have?) a dislike for drag and drop languages - I had tried Scratch after doing what I considered \"real\" programming, and I didn't like it. However, that class changed my mind. We created a model of an epidemic, a model of an ecosystem - and I was hooked. I literally still occasionally take a look at those programs when I'm in the mood and add new features.\n\nThe about-face was because, I think, it felt useful. I felt more able to create something cool in StarLogo Nova than Scratch. So I guess, I'd say to first, pick a good, fun DnD language, and second, build something cool in it and show it to them.\n\nYou might also go into the idea of higher vs lower level programming languages, with DnD languages just another step higher than something like Python. Assembly is no more \"real\" a coding language than Python is. (If anything, it's the other way round =P)\n\nAll this being said, don't stuff beans up your nose - your students may not even be thinking any less of DnD languages and may have quite a bit of fun without you saying anything at all.\n\n\u2022 I haven't used StarLogo Nova but have extensively used NetLogo (and years ago StarLogo). The things you liked - were they because they were drag and drop or were they due to the modelling environment which NetLogo provides with a text based language. Just curious. Jun 20, 2017 at 23:43\n\u2022 @MikeZamansky StarLogo Nova does provide a nice modelling environment with a wide array of things you can do with it, which I enjoyed - I didn't like it for being drag and drop, I liked it for its usefulness. That it was drag and drop didn't seem like such a bad thing because of how much I liked everything else. Jun 20, 2017 at 23:47\n\u2022 Yes, build something useful. Something fun if you can. That would probably work with Scratch as well. Sep 21, 2017 at 11:48\n\nHere I would go to Microsoft's Project Spark (even though it is discontinued, I think it is still downloadable. I have a local copy, so I'm not sure. But it's worth a shot)\n\nProject spark is Microsoft's \"experiment\" as a game for making games. It is visual. And you can say block based. It's not like Scratch or Snap!, but it is visual.\n\nIt makes game creation quite easy, (there are limitations on the game models that can be used and other stuff, but that's not too relevant for this answer) and is very good to teach programming. Types, Objects, Methods and many other things can be taught with it.\n\nI have used it for a while, and it is a real language. I suggest you try it, and maybe search videos in youtube that show aspects of Project Spark.\n\nA sneak peak to the block programming (or \"Kode\") of Project spark:\n\nThe kode (not a typo) is fairly straight forward and self-explanatory.\n\nEDIT: It is discontinued, but can still be used. It is free, and a very good way to learn programming concepts (as well as a good way to have fun)\n\nIt isn't very \"fun\", but there are visual languages widely used in the industry. For example the FBD language.\n\nFrom Wikipedia:\n\nThe Function Block Diagram (FBD) is a graphical language for programmable logic controller design, that can describe the function between input variables and output variables. A function is described as a set of elementary blocks. Input and output variables are connected to blocks by connection lines.\n\nEDIT: here my try at a real example:\n\nHere in Germany Siemens-hardware and -software is widely used in a wide variety of factories, power plants and most other aspects of automation. The programming languages the PLCs of Siemens are programmed with are based on the IEC 61131 and the EN 61131 (German). They are called FUP (function plan, looks like Flipflops, I had those in my electrical engineering studies), KOP (contact-plan, looks like a circuit diagram), GRAPH (flowchart-style), AWL (really basic Statements) and SCL (a high language based on another language... i think pascal).\n\nThe first three of those are all graphical and most people simply use whatever fits them the most. You can translate those languages into each other with a simple click, within some borders.\n\nThere are several IDEs used, but the most common is TIA-Portal (that's kinda new for newer PLCs of the S7-series), Simatic Manager (older S7-series) and an even older one I don't know the exact Name of for the S5-series. The naming process of Siemens is extremely weird and a world of itself.\n\nSiemens is used in other countries too, but of course I don't exactly know how much in detail.\n\n\u2022 Welcome! Could you please add details on why FBD would be a good idea? Jun 20, 2017 at 13:52\n\u2022 That's a good example - I'm also entirely unfamiliar with FBD. Can you flesh this answer out a little bit (so that I can use your answer better in the classroom)?\n\u2013\u00a0Ben I.\nJun 20, 2017 at 14:26\n\u2022 @BenI. he's not saying to consider it for use in the classroom, but rather consider it as an example of real world usage of a visual programming language. That is, visual programming need not be necessarily \"for kids\". Jun 20, 2017 at 19:11\n\u2022 @DavidLiu I understood that. But if I will even use it as a passing example in class, I would need to give at least some more detail about the language, which could totally fit into the answer here to make it more useful.\n\u2013\u00a0Ben I.\nJun 20, 2017 at 19:20\n\u2022 In real industry, there's a reality that not everyone who uses our software can be versed in C++ and have 4 years of practice with the software. They need a powerful language to interact with our software which doesn't pack such a training price tag. FBDs are really popular for solving that problem. They show that there are many levels with which one can interact with a piece of software. The C++\/Java code at the bottom is only one of those ways. Jun 20, 2017 at 20:08\n\nYou used two key words here: \"persuade\" and \"convince.\" Let's approach this issue from the perspective of the three Aristotelian rhetorical appeals: logos, ethos, and pathos.\n\n\u2022 Logos: Appeal to their reason as programmers. Have them create a program in Scratch or Snap!, and as they add each block, have them write the corresponding line(s) of code in a language of their choice. DnD is merely an interface for \"real code\" that is in fact being executed underneath the hood. Have them use their proficiency to attempt to reconstruct what might actually be happening. For example, how does one of these programs handle event-listening? How can something that looks so simple on the surface actually be running a number of more complex processes that are abstracted away? You could even start by having them focus on just the logic of their program without the implementation of the graphical implementation of the language (i.e. treating a graphic as part of a pre-constructed whose logic they don't need to worry about). Then, have them consider the sprites themselves. If they're still not convinced, give them the assignment of designing their own DnD language\/interface\/block and color system based on Java, Python, or C (or even assembly (!)).\n\n\u2022 Ethos: Appeal to two big names in computer science: Harvard and UC Berkeley. Harvard begins their famed and incredibly well-designed CS50 course with Scratch. They introduce computer science at the university (viz. Ivy League) level with a couple weeks of DnD programming. It clearly plays an important pedagogical role in the course. Similarly, Berkeley's CS10 utilizes Snap!. They build almost an entire course around this environment because it is important to emphasize the thinking behind and the logic of programming languages, not the interface or the syntax. (This is a nice time to remind students that \"computer science != coding\".)\n\n\u2022 Pathos: Appeal to the incredible complexity of some DnD programs, and let them simply feel amazed. Here is one program I just found called \"Landscape Generation\" in Scratch. Here's quite a bit going on here that is far beyond dragging some simple blocks around. If something like that doesn't impress them, send them to the Games tab and have them explore those and encourage them to \"See inside\" to examine what went into designing the game. Snap! doesn't have as easy a database of sample programs to explore (at least none that I can find). However, the same logic should apply to Scratch and Snap!. There is incredibly impressive work being done in both environments, work that clearly demands a level of skill that goes far beyond what beginners are capable of. If you really want to blow the away, show them Pokemon Go in Scratch (Harvard used this in Week 0 last fall).\n\n\u2022 Landscape Generation => define (Create Perspective Hack) Yep, it's real programming when it's all built on a hack :P Jul 26, 2017 at 18:02\n\nFull disclosure: I'm generally not a fan of DnD programming languages in high school (maybe even late middle school) and I think DnD languages are frequently used by stem oil salesmen and used incorrectly so I'm frequently down on them.\n\nMore disclosure: DnD languages can be real languages and can be properly and soundly used in educational settings.\n\nOk, now to answer the question.\n\nI think the easiest way is to head over to code.org and show them their DnD language which has a convenient \"show code\" button which will show the Javascript (a real language!!! :-)) equivalent to the blocks. You now have a platform to talk about how the block based language visually described the same code but visually (as opposed to textually with indentation).\n\ncodesters.com also has a pseudo DnD environment and while I like codesters very much, their DnD doesn't really feel like block based programming since it's really text chunk based - I'm a fan but I don't know if it would help in your situation.\n\nA lot of people are talking about how visual scripting is a higher abstraction, and that's all the difference, and the debate has moved more to a question of \"is visual scripting 'real' programming?\" The general consensus appears to be that yes, DnD languages are still real languages, and sure, it's a higher abstraction, but what does that mean?\n\nThere's a value to higher abstraction that no one seems to be mentioning, and that's the speed of it. When you remove details, you can write more, in the same amount of time. It's why we compare Python to C as 1 line for every 6. The value of visual scripting for people who are experienced programmers is the speed at which you can develop. This is an incredibly important factor in development, especially when smaller teams try to produce large, complex software.\n\nA good example of a visual scripting system is the Playmaker extension for the Unity game engine. Every Unity developer and their grandmother uses it, and for good reason. It allows them to rapidly prototype ideas and build complex systems in hours instead of weeks. And once the prototyping phase is done? The system they built is production-ready in most cases. Time is a very expensive resource in the software industry. If the cost of time needed to perfectly optimize your game in C is more expensive than the slight loss in efficiency you'll have for a fraction of the development time, it's a foolish business decision to ignore the option which enables you to make more money.\n\n\u2022 Welcome to CSE? This is an excellent answer, and I hope we hear more from you in the future.\n\u2013\u00a0Ben I.\nJun 21, 2017 at 22:43\n\nFirst and foremost, don't let your feeling about their feelings affect your judgement. It seems to me that most kids want to learn new things, they want to be 'beta testers' and on the cutting edge. Visual programming is something relatively new, let them be an early adopter as this new form of programming matures.\n\nMore importantly though, programming isn't about the process of programming. Programming is about accomplishing a goal. We can use different programming 'tools' to accomplish our goals.\n\nDifferent languages make the process easier just like having a screw driver gets a screw in the wood easier than using an awl. And planing is easier with a planer than with a claw hammer.\n\nPerhaps instead of convincing them what is better, have them do various exercises and let them choose their own tool set. Of course the exercises should do something interesting and in some or most cases allow the visual tool to save time. The grade should be given on the finished product - not which tool was used to accomplish the goal. If you have short exercises, have them do them in class and when the visual tool is faster, those students will be done sooner. Let them decide how they want to spend their time.\n\nRemember the goal - it isn't just to learn a language, it is to teach students how to make good decisions and (hopefully) those lessons carry over into everyday life.\n\n\u2022 Very nice answer. Welcome to CSE!\n\u2013\u00a0Ben I.\nJun 22, 2017 at 20:31\n\n# Have your students write a visual programming editor.\n\nIt sounds like your students are pretty savvy, so what better way to show them how awesome a visual editor can be than to have them build their own! There are many benefits to this approach.\n\n## Relevancy\n\nThey're creating software to make them more efficient at what they already do and love.\n\n## Flexibility\n\nThe students can choose their preferred language.\nThis could also be a solo or a group project.\n\n## Pay-Off\n\nThis is an assignment with some legs. It's not something that will go into a folder and be forgotten. They can use it on their next assignment or in their own personal projects!\n\n# Real-world motivation\n\nI have a neutral opinion on visual programming. I have dabbled in it and decided that I am not interested. But. It is simply a tool.\n\nTools are complicated to motivate. Just enter any room of programmers and give them the exercise to, once and for all, decide on whether vi or Emacs is better. You might as well ask them to choose the new Pope...\n\nOn the other hand, in my opinion, an intelligent person (which your pupils certainly are!) does not need to actually be fond of or deeply knowledgeable of a tool to appreciate its merits. In the same vein as being able to learn about war and famine (which are decidedly not fun), they should be able to learn about Visual Programming even if you do not find a \"fun\" exercise for it.\n\nSo, you can easily teach them that there is a place for almost every tool. Visual Programming has its place in certain niches (depending on viewpoint, obviously) where you just do not need the expressive power of a general programming language. For example, if you are into Business Process Management, you can achieve a lot with visual programming. If you are using one of the game engines which focus on higher level creation, the same is true. A program like Blender can go far with a very domain-specific visual \"programming\" for what it does (physics simulation and so on). CAD\/CAM systems are largely \"programmed\" with very, very domain specific visual tools.\n\nPick a few nice examples, and maybe you find some open source \/ free visual programming environments where they just play around, as a bonus. Even if they never touch them again, they will at least know that such things exist, and they may appreciate that somebody out there (who, likely, would never \"program\" anything at all, if they couldn't do it visually) puts them to good use.\n\n# \"Convince\"?\n\nTry not to convince them. Show them what is real, what exists, and that in itself should be convincing enough.\n\nThis might sound like nitpicking, but in the business world, if people start to try to \"convince\" someone of something, then it's usually a red flag. I prefer if they show me that something so I can understand and appreciate (or deny) it myself.\n\nJust because you are using abstraction does not mean it is no longer programming.\n\nAnything above actually flipping the bits by hand is us just being lazy.\n\nMy only objection to using an obscure language just for fun is. Why learn it if I would not use it in real life later?\n\nEssentially I\u2019d say. As long as the problem to be solved is fun. I.e. Not how to implement a solution using a recurs7function, I\u2019d say you are grand. 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tv [untitled] May 23, 2011 9:30pm-10:00pm EDT
all of them are all. you know sometimes you see a story and it seems so bleak you think you understand it and then you glimpse something else and you hear see some of the part of it and realize everything you saw you don't know i'm sorry welcome as a big. fat .
bag the big picture on tom hartman coming up in this half hour one nation under sex plus the woman who was apparently victimized by i.m.f. chief strauss had a secret weapon at her disposal player when i was just a few months and the sixty day grace period is over for the so-called war in libya so will president obama finally get the congressional stamp of approval he needs to continue that war.
as we all learned of the high profile such scandal broke regarding i.m.f. chief dominique strauss kahn a guy who was likely to become the next president of france if he didn't try to rape a hotel maid in new york city a week ago allegedly. just today new york police confirmed that semen found on the maid's dress does indeed belong to dominic strauss kahn but the case of strauss kahn highlights another more important issue that of women of no power being able to fight back against men of enormous power too often a who would you believe more frame determines the killed or innocence of powerful men accused of rape which then discourages future women from reporting incidents and given the dominic strauss kahn is one of the most powerful men bankers in the world and his alleged victim is just a hotel maid from africa it's likely that this crime would have been swept under the rug too had it not been for a secret weapon that the hotel maid had she belonged to
a union and she knew that she could take that brave step forward against strauss kahn because her union would protect her and her job wouldn't be put at risk and that's just what she did and now strauss kahn is headed for prison. so isn't this just another example unions check of the power of wealthy elites for more on this i'm joined by democratic strategist. erica welcome to ivy here great to have you with us other women have come forward since this revolution revolution saying that they had been. stayed silent in the face of similar activities including one who was a french journalist a woman who was a french journalist does this show. an immigrant made in new york. with a union behind her has more power than a fairly high profile french journalist i think it i think it does i think actually one of the very interesting things here is that new york city has one of the strongest. the most unionized hotel workers that's about thirty five percent of
hotel workers are unionized and so you pick the wrong city it's a massive a union worker it's a tough union and it's very straightforward very strong that anybody who is experiencing abuse or inappropriate behavior has the right and has the ability to report that's their superior and absolutely as their top protected and that's part of their contract they have spent years fighting for this the i think the new york hotel workers union first formed in the one nine hundred thirty s. so you know this fighting for rights of you know a particular type of worker which is in a service industry that basically makes its money off of being able to provide every convenience possible to its customers and you know you think about the typical customer is always right environment i can't think of anything more so than a three thousand dollar a night hotel room and particularly a man who is in charge of the world's economy is really feeling that he has the
ultimate ability to do whatever he wants here is a woman who is you know for lack of a better word cleaning up after him and that you know she was in a position where he had all the power and she had none. and often people report you know fail to report not just you know there if there's one issue you don't want to go through the process of having to face here accuser but it's also having the resource that mean power is really about resource allocation and this is the perfect example of somebody who had all the money quit all the power and all the position in the world versus somebody who our paper didn't except she had a union with collective bargaining rights that are gay and went to work for you know the hotel workers and made it so that they have the right to protect themselves and to fight against it was it was because women in the past had confronted this exact same situation had not had that power and had been fired for raising things like you know that they didn't put the customer first is the customer have to be replaced and there's a lot of there's
a lot of time social sexual mores and and kind of roles there where you have the maid and the master of the house and so there's a lot of kind of an odd dynamic there that often unfortunately you know puts women in this position which are often alone when they're made they're coming to service a room and to flip mattresses or change sheets so they are in particularly vulnerable position and another interesting thing is that a lot of the hotel workers are undocumented immigrants and so there's you know particularly you know a feeling that there's a lot of underreporting of you know similar behavior because you know people are afraid to kind of ruffle feathers and i think that this goes this is a great example of how you know one person with not only just the support or you know the guarantee of keeping her job but the support of a union to back her up to help her through the grievance process to help her know her rights and to educate her on her rights that's incredibly important knowledge
is so powerful and to have a group that educates you on what the pursuit for the proper procedure is what you can do and how to protect yourself i mean that's that's. if the power balance back in her favor former nixon speechwriter brown's right wing gadfly columnist i should have. gone to him. so. you know why should we believe this woman's that because he's a rich and powerful white man and because she is a hotel why isn't this kind of a typical perspective from the from the wealthy elites basically yeah and sexual assault is is often out and mostly just about power and control and domination and the fact that her employment status or her job would somehow speak to her credibility or is some sort of evidence i'm not even hearing the story but that oh she's amazing she's not credible is really so much like saying that as human right
it harkens back to the days of slavery oh it's exactly same not as human not as worthy not as valid not as you know ethical not as trust but some of that shouldn't be believed and i think that that's you know ben stein should and it's disgusting quite frankly and it's weak minded and i think that you know the other interesting thing here is that another pattern that we often see in these situations is that once one woman is brave enough or one person stands up others often come out here and so in this instance i think this is also a prime example of how the union protection not just union members but all workers and all people and that the broader culture of what is appropriate at work and a safe work environment and you know the weekend and the five ten work week that we all benefit from came from unions the fact that there's a journalist in france who didn't feel that she had enough power and support who then suddenly felt the courage to come out because of the hotel workers union in new york speaks to turn this around about what unions to level the playing field
for everybody plus their democracy in the workplace which is this little island of democracy and what normally or kingdoms are going to be thanks so much for being with us absolutely very great to hear your perspective and see. sex scandals aren't anything new in american politics either heck it's about the only thing more common in american politics than partisan bickering and negative campaign ads a list of prominent politicians have been caught with their pants down is growing after the recent news of arnold schwarzenegger's secret love child he joins the likes of former arizona senator john ensign former south carolina governor mark sanford john edwards former new york governor eliot spitzer cambridge the list goes on and on and that is politicians cheating on their wives something new in america it's just something that has garnered more attention now that there are twenty four seven cable news outlets that feed on scandal and his new book one nation under sex larry flynt argues that american presidents of actually been behaving badly since
the birth of our nation and he joins me now from our studio in los angeles he's the publisher of hustler magazine and a life long on average advocate for free speech larry welcome. larry. can you hear me. apparently larry can hear me. ok we're going to take a very quick break here we'll be back. let's not forget that we had an apartheid regime. i think. even one well.
we never got the says for the keep you safe get ready because of their freedom. you know sometimes you see a story and it seems so bleak you think you understand it and then you glimpse something else and you hear or see some of the part of it and realize that everything you saw. i'm sorry is a big. larry
flynt joins me now from our studios in los angeles he is the publisher of hustler magazine and a lifelong advocate for free speech larry welcome glad to be worth your time thank you your book your new book details the numerous american presidents who behaved badly but i do think this happened so often. i'll always wondered if the founding fathers had their sights count.
and ironically they did. play their stuff out for you whether it was how much you have a son in law or alexander and want to know why there were a lot of good lead that. five. years. it's how i am going. to manage p. mammie a. they had to be confirmed by d.n.a. and in fact he did so. for a great story like i'm curious were nixon in carter both guys who kept their pants on and and what about reagan. reagan as far as we know were true blue carded after. the bell at the end of the.
no evidence annex and. what does this say about america. may extend there as you know. more than china that it a chinese fish. which here goober maintained a file on. never really became public but we do cover it in the book well that's interesting richard nixon. summaries i always figured he was probably the last guy what does this say about americans that we feign outrage by what publishes a pornography like you do but we love politicians who are supposed to be the embodiment of morality and get away with much worse. many many americans speak with . the europeans are much more laid back than the.
thought of creation album fair that's why they take those three hour lunches but america has theirs need. me. about sex but when you consider that other than those are thirty five all the strongest single desire we have is that of which sacks so you examine something we use to communicate with more than any other medium you know make that effort and . we don't need saying they aren't saying right and they're right and wanted to be creative. and well david vitter after he came out with for being with prostitutes actually got a standing ovation from the republicans in the senate but i'm curious if french president francois mitterrand funeral his wife his mistress and his illegitimate teenage daughter all stood at his graveside did queen. victoria made out in rule
and the us crazy are we the only two countries that are crazy interview or sex. allowed to go about it till the end when i thought i was a mild guy that wrote the story on better he would stand by stupid from what he said and then beat up all and a while and the reason why oh why wrath running up was he was worse or absence in the senate he was going around there trying to please promote their absolute program you need girls i mean here. and you possibly me and i guess the only reason why we are late into the center you know is if you are . i don't. care i walk around planet by all appearances so. you came to be somebody who would know what i mean why are there and are real and i guess he somehow he got forgiven i just don't get it larry flynt thanks so much for being with us tonight. graduating great check out larry flynt's new book one nation
under sex it's definitely an interesting read. after my break idealy take on why the war in libya war on terror and war in afghanistan may never come to an end. you know sometimes you see a story and it seems so you think you understand it and then you glimpse something
else and you hear see some other part of it and realize that everything you saw you don't. work because of the. crazy alert aren't going to hungary this weekend exotic weaponry was a theme of two different fast food restaurants in america in kentucky a woman threaten employees at a pizza hut with a sword and in arizona another one woman threatened workers at a dairy queen with a slightly more modern piece of weaponry a grenade both women were arrested so managers of mcdonald's and burger king are taking notice something about fast food that provokes violence the next person demanding a big mac be carrying a bazooka. last
friday marked sixty days two months since the war in libya began and there's still no formal declaration of war from congress according to our constitution congress is the only branch of government with the power to declare war and not a president turned right article one section eight of the constitution the congress shall have the power to declare war and to raise and support armies but no appropriation of money to that use shall be for a longer term than two years. the framers of the constitution added that little last bit about the two year time limit on appropriations for war just to prevent things like and with this war and for most of american history that separation
of power between the president and the congress remained intact but then after u.s. presidents ignored congress to launch the korean war in the one nine hundred fifty s. and the vietnam war shortly thereafter congress asserted its constitutional authority to rein in richard nixon with the war powers resolution this is a new law that lets the president commit the nation to war progress but only for sixty days it's still a pretty generous handover of power of the executive branch one that in my personal opinion is clearly unconstitutional and should be rolled back by the supreme court but that's another whole nother rant it was an affront to nixon however who vetoed the war powers resolution basically saying he was going to play ball with any of these new restrictions on the power he and his recent predecessors had claimed in the oval office the congress overturned a nixon's veto and passed into law these new checks on presidential power that our
founders never intended the president to al from that point on after sixty days a president must ask congress for permission to continue a war. so now the sixty days are up in libya is president obama going to congress. know. the white house wrote a letter to the congressional leadership last week arguing that the limited nature of u.s. military involvement does not require approval from congress exactly what the white house is definition of limited is a war that's cost american taxpayers over seven hundred fifty million dollars so far and involves our military machine killing a lot of people. you've got me. but what is know is that president obama is the fifth us president in a row in a row to start his own war overseas centrex
a broad with the orders to kill and not think twice about asking congress of that's ok in fact congress hasn't stamp approval on a war since world war two the reasons for these unapproved wars over the last few decades have had numerous but most of them at least have had endgames reagan invaded greneda briefly likely taking a page from his good friend prime minister maggie thatcher in the u.k. who invaded the falkland islands for political capital that little war made her instantly pocket reagan saw that said hey we can do that and grenada helped reagan in the same way bush sr went to war in kuwait to kick out the iraqis it was mostly over oil and even set it up by having the u.s. envoy to iraq april glaspie tell saddam hussein that if he invaded kuwait the u.s. would consider it an internal affair and i'd get involved so much for april's
assurances the same to bush senior's q. and gave bush the excuse he needed to have his own war although it was short only a few days long clinton went to war in kosovo a war that was very popular but is still being debated and then george w. bush came to power thanks to the supreme court in two thousand and like reagan bush had plans to start a war for political capital but he told his biographer mickey herskowitz back in one thousand nine hundred ninety. before you even started running for president if he became president he was going to invade iraq to earn enough political capital that privatized social security. but then nine eleven happened and cetera and instead of a one time war as bush had intended he and his handlers like donald rumsfeld dick cheney opted for a perpetual war a war on terror it would last as long as this presidency was. so afghanistan happened iraq happened and countless other covert military actions in places like
yemen happen with the war on terror the george w. bush dreamed up the as they so america was for the first time involved in a war without any clear ending. a recipe for a perpetual war or well in perpetual war listen to how bush justified his endless war. we can't really count on that. he might as well have ripped his words straight from the text of orwell's one thousand nine hundred four and big brother told everyone that war is peace but last week it went on steroids to really commit america to a war ravaged dystopia last week congress took a step toward shrine in perpetual war into law with the defense authorization act it reads congress affirms that the united states is engaged in an armed conflict flicked with al qaeda the taliban and associated forces and that those entities
continue to pose a threat to the united states and its citizens the president has the authority to use all necessary and appropriate force during the current armed conflict pursuant to the authorization for use of military force until the termination of hostilities . in other words war of terror war on terror which has me until all the terrorists on planet earth are killed something that will never happen. this is the worst nightmare for james madison the father of our constitution the fourth president of the united states madison wrote so eloquently that all the enemies of true liberty war is perhaps the most to be dreaded because it comprises and develops the germ of every other in war madison continued the discretionary power of the president is extended its influence in dealing out offices honors and of all humans is multiplied and all the means of seducing the mines are added to those of
subduing the force of the people war is in fact the true nurse of executive of a grand eyes bent in war a physical force is to be created and it is the executive that would be the president when he starts what exactly is time in the executive branch the president and it is the executives will which is to direct it in war the public treasuries are to be unlocked and it is the executive the president's hand which is to dispense them ultimately madison said no nation no nation can preserve its freedom in the midst of continual work for good here we are in the midst of perpetual warfare against terrorism with our current president telling congress that he doesn't need their approval for a billion dollar war in libya and puts american soldiers in harm's way and really has nothing to do with terrorism but as psychologist abraham as low famously noted
when your only tool is a hammer every problem out there looks like nails and even though some progress is made trust obama with perpetual war powers to defeat terrorism with the next president will he or she be trusted with the wheel to america's were machine in an interview last year with journalist bob woodward president obama perhaps without realizing its application to himself so. war is hell and once the dogs of war on leashed you don't know where it's going to lead. and tragically right now our congress in a republican led effort but with very little resistance from democrats is doing everything it can to prevent the dogs of war from ever coming back home that's a big picture first and i for more information on the stories we covered you can visit our web sites at tom harkin dot com and r t dot com also check out our youtube pages of youtube dot com slash the big picture i'd see that you tube dot
com slash tom parker and this entire show is available as a free podcast on i tunes and don't forget democracy begins with you when you show up when you participate tag you're it.
May 23, 2011 9:30pm-10:00pm EDT
Captioning provided by Automated Speech Recognition, not the broadcaster
Congress 16, America 7, American 6, Libya 5, Reagan 5, New York 4, Larry Flynt 4, Bush 4, Nixon 4, Larry 4, U.s. 4, Obama 3, Iraq 3, Strauss Kahn 3, French 3, France 2, Senate 2, Richard Nixon 2, Madison 2, George W. Bush 2
Channel 89 (615 MHz)
Uploaded by TV Archive on May 24, 2011 | {
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{"url":"https:\/\/brilliant.org\/problems\/charged-pendulum-3\/","text":"# Charged pendulum\n\nLet the period of an uncharged pendulum be $t$. This pendulum is now charged with a charge of $+q$ and placed in a uniform electric field pointing vertically upward. If the new period of the pendulum is denoted by $T,$ which of the following is correct?\n\n\u00d7","date":"2019-08-21 19:24:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 10, \"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\": 0.9852443337440491, \"perplexity\": 259.163633282987}, \"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-2019-35\/segments\/1566027316150.53\/warc\/CC-MAIN-20190821174152-20190821200152-00297.warc.gz\"}"} | null | null |
Q: Change the Font Style - (Set Lable text in All-Caps format ) in Objective C I want to set the UILable text font style in Small-Caps format like below image.
Please give me the solution for this if anyone know,
Thanks.
:)
A: Fonts available in iOS don't have "capitalic style". You should add own font or try to create font using function CTFontDescriptorCreateCopyWithFeature.
I think that the simplest way will be to build attributed string (NSAttributedString) with mixed font sizes.
A: For iOS 7 custom fonts, the method is described by Anthony Mattox. For system font I do not know a way.
Typesetting a font in small caps on iOS
A: If I didn't get you wrong, is this what you want?
NSString *uppercaseString = [yourString uppercaseString];
A: you can try with this
NSString* str=@"mudit";
label.text=[str uppercaseString];
it will give you the output like this:MUDIT
A: To make the UILabel render as an upper-case string, where the first letter of each word is larger, you can do something like this:
@implementation CapitalicTextLabel
- (void)drawRect:(CGRect)rect
{
// Drawing code
NSArray* words = [self.text componentsSeparatedByCharactersInSet:[NSCharacterSet whitespaceAndNewlineCharacterSet]];
CGContextRef context = UIGraphicsGetCurrentContext();
CGContextSetCharacterSpacing(context, 1);
CGContextSetFillColorWithColor(context, [self.textColor CGColor]);
CGAffineTransform myTextTransform = CGAffineTransformScale(CGAffineTransformIdentity, 1.f, -1.f );
CGContextSetTextMatrix (context, myTextTransform);
CGFloat x = 0;
float centeredY = (self.font.pointSize + (self.frame.size.height - self.font.pointSize) / 2) - 2;
CGFloat firstLetterSize = self.font.pointSize * 1.4;
for (NSString* word in words)
{
NSString* letter = [[word substringToIndex:1] uppercaseString];
CGContextSelectFont(context, [self.font.fontName cStringUsingEncoding:NSASCIIStringEncoding], firstLetterSize, kCGEncodingMacRoman);
CGContextShowTextAtPoint(context, x, centeredY, [letter cStringUsingEncoding:NSASCIIStringEncoding], [letter length]);
x = CGContextGetTextPosition(context).x;
NSString* restOfWord = [[[word substringFromIndex:1] uppercaseString] stringByAppendingString:@" "];
CGContextSelectFont(context, [self.font.fontName cStringUsingEncoding:NSASCIIStringEncoding], self.font.pointSize,
kCGEncodingMacRoman);
CGContextShowTextAtPoint(context, x, centeredY, [restOfWord cStringUsingEncoding:NSASCIIStringEncoding], [restOfWord length]);
CGPoint v = CGContextGetTextPosition(context);
x = CGContextGetTextPosition(context).x;
}
}
@end
This implementation doesn't handle splitting across multiple-lines or honor the TextAlignment setting, This would be should be simple enough to add afterwards.
Example:
A: try with this one
NSString *string = @"askdfjgjksdfgh";
NSString *upString = [string uppercaseString];
NSLog(@"U %@", upString);
A: It is not possible to change the font size or type of a individual letter within a UILabel.
What you want to do is to have 2 labels, one in the begging for the first bigger letter and one right after that for the remaining word.
In order to access the first letter and the rest of the word you may use:
NSString * word = @"COMPLETED";
NSString * firstLetter = [word substringToIndex:1];
NSString * remainingWord = [word substringFromIndex:1];
What you see in the picture are probably pictures of words and not UILabels.
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Rooted In Revenue
Susan Finch
Revenue and sales driven by marketing, sales skills and events.
Transactional vs. Lifetime Customers - which do you cultivate?
If you are in sales, you'd better know if you are transactional-focused or lifetime-focused when it comes to how you approach prospects and customers. There is no wrong version, but you need to know which you are. Your sales manager needs to know which you are too. That deep honesty will allow you to play to your strengths. The theme of this episode is two-fold - being in awe of the fantastic things people you encounter do and who they are, and knowing yourself to the core. If you don't like it, change it. There is also homework at the end from both of us. A favorite quote from The Big Kahuna is, "It doesn't matter whether you're selling Jesus or Buddha or civil rights or 'How to Make Money in Real Estate With No Money Down'. That doesn't make you a human being; it makes you a marketing rep. If you want to talk to somebody honestly, as a human being, ask him about his kids. Find out what his dreams are - just to find out, for no other..." Jason Beck, this list of movies for sales professionals is for you. You can listen to our commentary in this episode. Check them out - some are not available on Amazon or Netflix at this time - but check back. The more extensive commentary is on Salesman.org - sign up for their newsletter, too. Used Cars with Kurt Russell Jerry Maguire The Wolf of Wall Street (duh) Death of a Salesman 1985 - or see it on stage - so powerful Moneyball Seize the Day - Robin Williams In Pursuit of Happyness Tin Men Glengarry Glen Ross Tommy Boy Diamond Men Lord of War Love and Other drugs The Big Kahuna - a sleeper and feel-good movie about sales The Goods: Live Hard, Sell Hard Jason Beck is Vice President of Sales at Enerex, retail energy's trusted data platform, providing secure connectivity to the entire value chain — brokers, suppliers, agents, customers, and utilities — to drive efficient transactions. Their flagship service, Sparkplug, is the #1 retail energy sales platform in the world, powering over 10% of US commercial and industrial (C&I) transactions. He's also been a wonderful guest on Market Dominance Guys. Connect with Jason on LinkedIn.
Kindness in Your Culture for Reputation, Recruitment, and Retention
It's been proven that kindness in the workplace has a stunning ROI. Kindness decreases stress, reduces employee burnout, and builds increasing levels of happiness and satisfaction in the workplace. Susan's guest is author Linda Cohen. They visit about the simplicity of transforming your business to incorporate kindness as a method of recruitment, retention, reputation without spending a lot of money. Her ideas are so simple you can start them today. Imagine a company culture where employees feel valued, recognized, and empowered enough to go the extra mile for customers and colleagues; where the leadership is able to be authentic, transparent, and connected to their team. The Economy of Kindness: How Kindness Transforms Your Bottom Line provides real-life examples of companies that have employed kindness as their secret weapon to build and maintain their organizations. Join Susan and Linda for this 20-minute discussion about The Economy of Kindness: How Kindness Transforms Your Bottom Line .
The Role of the Conductor in B2B Leadership
Christopher Lochhead wrote a book called Play Bigger. He was the CMO of Mercury Interactive and a couple of other real high-flying Silicon Valley startups and just an awesome guy. But he has a saying. He likes to say, "Thinking about thinking is the most important thinking you do. A lot of what we're talking about is stepping back because it's so easy to default to, Hey, I just raised my Series A; I'm in MarTech, let's go get somebody out of drift or let's go get a sale. Let's go find someone in Salesforce marketing. Let's go get a director from Salesforce to run our marketing. Oh, they'll crush it for us. And it's a natural default, right? And then a person comes in and because they weren't clear... And usually that person, they don't know how to vet. So, they're told this and they're super excited. Oh, wow. This is my chance. Put a stamp on it, but they forget that I'm not going to be in Salesforce anymore. Meaning, I'm not going to have, first of all, the Salesforce brand and just all the power of that. I'm not going to have all the resources. ----more---- And so anyway, the questions are just so important. Our guest, Mark Donnigan spends a lot of time just going through with the CEOs and the founders he works with and just really talking it through. Listen to the rest of the interview with Mark. Part one of this interview is here: The Two-Way Interview with Mark Donnigan About Susan's Guest: Mark Donnigan designs and executes marketing programs and go-to-market strategies that build markets and establish disruptive innovation companies as a category king. With 20 years of experience as a transformative and strategic B2B marketing and business leader Mark understands what's required to succeed in today's winner takes all market. Leveraging marketing and growth tactics that work, Mark produces real business results for early and growth-stage technology and disruptive innovation startup companies. Being well versed in SaaS, software licensing, wholesale, and retail distribution models, he helps companies build nimble, highly efficient marketing teams that routinely outperform larger marketing groups. Mark is passionate about extracting the most value from every marketing dollar invested. He provides startup founders in the early stages of building their sales engine with high-impact marketing playbooks so that they can reach their revenue goals and scale sustainably.
The Two-Way Interview with Mark Donnigan
Mark Donnigan from Growth Stage Marketing says, "It's important that a professional team work together and all the executives should be rowing in the same direction and all these kind of truisms, which are all true but there are some very profound implications to how we market and how we sell, which gets wrapped up in go to market as a result of the fragmented buyer's journey that we are in today." He also reminds us, "think about how you talk about yourself, how you talk about what you do. And even as a full-time employee, in fact, I could argue that as a full-time employee, it matters as much or even more because it's so amazing when you hear one person who just describes themselves in kind of the HR job description. What do you do?" Listen to the first half of this interview to walk away walking a little bit taller, and able to go into interviews with more confidence. ----more---- About Susan's Guest: Mark Donnigan designs and executes marketing programs and go-to-market strategies that build markets and establish disruptive innovation companies as a category king. With 20 years of experience as a transformative and strategic B2B marketing and business leader Mark understands what's required to succeed in today's winner takes all market. Leveraging marketing and growth tactics that work, Mark produces real business results for early and growth-stage technology and disruptive innovation startup companies. Being well versed in SaaS, software licensing, wholesale, and retail distribution models, he helps companies build nimble, highly efficient marketing teams that routinely outperform larger marketing groups. Mark is passionate about extracting the most value from every marketing dollar invested. He provides startup founders in the early stages of building their sales engine with high-impact marketing playbooks so that they can reach their revenue goals and scale sustainably.
Correcting the Disconnect in Your Customer Service
If someone is completing a form, you never want your customer to take any action that they don't know what's next for them. They need to know what's next and how long it will take. This is just one tip from Sonia Portwood and Virginia Robbins from PCBB. Customer service can make or break your business. Look at everything that you do from the point of view of your customers and you can't go wrong. Virginia reminds us to be brave when a customer leaves. Pick up the phone and ask what happened and how you could improve. It will only make you more successful. We made so many sudden changes last year and now it's time to review, adjust and make sure we are truly listening to our customers and incorporating their problems, hiccups, and complaints to be better at serving them to hopefully avoid repeating the mistakes. ----more---- About our guests: Virginia Robbins, Chief Platform Product Manager | PCBB Virginia Robbins has more than 40 years of experience in product development, technology, and operational excellence for financial institutions. Virginia is the Chief Platform Product Manager and oversees product development for the advisory solutions division of PCBB. Sonia Portwood, EVP, Business Development and Strategic Execution | PCBB Sonia Portwood has over 25 years of sales and marketing experience in banking, finance and capital markets. At PCBB, Ms. Portwood is responsible for all business development and the execution of strategic initiatives. Prior to joining PCBB, Ms. Portwood served as Vice President at Kensington Investment Group where she was involved in sales and served as its lead account manager for national clients. Earlier in her career, Ms. Portwood worked for Financial Oxygen, BISYS Professional Services, SunTrust Securities, Bank of America, and Deposit Guaranty National Bank. Ms. Portwood earned a Bachelor of Science degree in Business Administration from Belhaven University.
Vetting Your Network Security Vendor and Locking It Down.
What are the questions you should ask before you select a network security advisor? What should you ask yourself? What are your accessibility needs? Be sure to include the factor of your team's cell phones. How secure are they? The simple requirement for facial recognition to login can save headaches and disasters. Listen to this short episode walking through the logic and some actionable tips.
Time for Security Review to Continue #WFH or Hybrid
When we all were sent home suddenly, not everything was ready for this transition, including the security of the workspace we were cobbling together at home, in closets, on kitchen tables, our cars, coffee shops. Many companies have continued to evolve policies, purchase equipment for those working remotely. But many haven't been able to. This episode will help those companies start that thought process and catch up. Michael says, "Treat your remote and home network the same way you would your corporate environment. Having policies in place that you review regularly helps you stay on top of this." Michael tells the story of someone who was able to work from home, but what the company didn't realize, she was sharing the computer with her student daughter. This left a lot of vulnerability because the company didn't send her home with a dedicated computer, or cite the requirements to protect company information and that of their clients. This episode helps us pick up where we left off when we started working from home. Many aren't going back. It's working out well. Follow these tips to ensure it continues to work better and improve constantly. ----more---- About Michael Blood, President, Matraex, Inc. App Visionary & Strategist | Project Consultant | Remove Project Constraints & Risks and Guide Development Teams to Realize Those Breakthrough Moments | Always on The Lookout For That Next Big Opportunity Throughout his career, he's led project idea development, design, architecture, and road-mapping. At times, he's consulted on and taken over projects that were stalled and needed an innovative breakthrough or alternative solution. What he finds exciting about application/software development is its expansion with near-endless possibilities. He's very passionate about taking an idea and making it come to fruition. This is true whether it's a business, project in development, or guiding his teams.
What you need to know before going after an International or Global Market
Today, I am interviewing Craig Ostbo. I met Craig because Nina Hambleton, who was on our team, everybody loves Nina. She said, "You need to interview my professor because he's the real deal. And he knows everything about international marketing and has so much passion and joy for this." From a touring musician to the perfect timing getting into the natural, the organic, and sustainable world of products, and taking clients brands global is the story he's telling us today. He's also shared some free resources and advice. ----more---- From Craig: Here's a site where you can do a tremendous amount of research on market opportunities for different products in most countries of the world: https://www.trade.gov/export-solutions Here's a site that gives you even more data/country reports if your product is made from an agricultural commodity. This is the Foreign Agriculture Service or FAS: https://www.fas.usda.gov/ It helps to know the Harmonized System Code for your product. This number identifies your product category down to the nth degree in almost every country on earth. This system creates standards for global import/export: https://www.trade.gov/harmonized-system-hs-codes The HS code system is a great way to do research on your product category. The HS Code will allow you to determine if there are tariffs, duties, or any other barriers in that foreign country aimed at your imported product. Often, without understanding the tariff structure, you may think you can easily compete on price against the domestic or even other foreign competitors until you discover the 35% tariff leveled at JUST USA BRANDS . . . there goes your margin :)
What if the old audience is still enjoyable, but not as profitable?
"I understand that your clients are your gold, and I'm not going to do anything to tarnish that." Doug C. Who is your ideal client? do not be afraid to truthfully state it. Everyone is not our client. Dream it! You are not being ungrateful grabbing all the crumbs. Free up your time, free up your effort. What do you want your income level to be? Is that enough? It may be fine, everyone has their own level of gratification. ----more---- Some of us base it on time, not money. Why not have it accomplish both? Doug tells us his one thing, with a City Slickers' reference. His one thing was building an agency within the company. Listen in to hear how he did this and increased his revenue by nearly 850%! He also helps us recover when we need to identify a new 'best audience' without abandoning the old audience. Do not cannibalize your base overnight just to go after a new market. It's easier to keep going with your existing clients and more profitable. Include your existing clients in your ideas. You will be pleasantly surprised that they catch your excitement and are willing to consider your new offerings. Check out his new book: Win-Win Selling - special price for two weeks: $0.99 for the ebook version.
No lead should be ignored, but not all leads should be sold to.
Continuing our discussions with Ledge on ways to quickly jump start your sales team, and ultimately your company's revenue and joy he tackles good vs bad leads and why they all need to be addressed. He says, "From the funnel standpoint, you can use some automation for that, but ultimately make sure you have sales and marketing work together on a human look at the discernment in your funnel. Is this a fit? Why is it not a fit? If it's not a fit are there any flags that I can indicate ahead of time from an automation standpoint?" He continues, "It's unethical to even try to take somebody's money for that when down the street there could be a provider that could help them out." Tune in for tips, insights, and your inspiration. ----more---- A bit about Add1Zero.co Lead-to-close sales execution for B2B tech companies ready to leap from 6 to 7 digits of revenue. Their team joins your team - under your brand - to pick up your leads as soon as they hit your CRM, engage and close them, and hand a signed client over to your onboarding and CS teams. Using a proven process for 6- to 7-digit annual growth, they provide sales strategy, execution, and ops -- the real work that needs to get done to close deals.
Keeping Your Event Attendees Engaged and Wanting More
Ever the optimist, Award-winning Magician, Scott Tokar, is looking forward to the irreplaceable trade shows he is a part of regularly. His corral of other performers know they can adjust and do online appearances, but nothing replaces the barker at a trade show driving people you never reached before to hear your message through entertainment. This episode of Rooted in Revenue first appeared on SLMA Radio. Susan Finch interviews Scott to talk about adjusting, the value of performers to help carry the "hosting" load at virtual and in-person events, as well as how you can plan for when in-person events return or how to stand out with your hybrid or virtual event. ----more---- About Susan's guest: Scott Tokar, CEO Corporate-Fx Trade Show Magic Group Scott Tokar is unique among magicians, having focused solely on corporate entertainment (Infotainment) and visual communication, he is known today as a "specialist" in tradeshow magic and sales meeting motivation. Unlike his magical colleagues, Scott does not perform in nightclubs, at kids' birthday parties, or picnics.
Tucking Away Emotion to Build Your Invincible Brand
Until you address the emotion in a volatile situation with compassion and respect, you will not diffuse a situation and may do more damage raising the intensity to a blistering crescendo. This is the continuing conversation that started a couple of weeks ago with Melissa Agnes. In this episode, we deep dive into one aspect of our response to a crisis, confrontation, and conflict as our brands and key people are bombarded with heavy emotion. ----more---- Some of what is covered is how to get ahead of high emotional relatability when you can never overcome emotion with pure logic. 1. Validate the emotion. 2. Relate to them on that basis. 3. Proof and logic to support your position and facts. The tips Melissa gives us will help us protect our brands, but also have more success diffusing situations in our everyday lives. You will want to take notes here. If you missed the first episode with Melissa, Crisis Readiness Equals Freedom, you can listen here > About Susan's guest: Author of Crisis Ready: Building an Invincible Brand in an Uncertain World, Melissa Agnes is a leading authority on crisis preparedness, reputation management, and brand protection. Agnes is a coveted speaker, commentator, and advisor to some of today's leading organizations faced with the greatest risks. In Crisis Ready, Melissa Agnes draws from her remarkable experience in helping global brands, government organizations, and world leaders prevent and overcome a range of real-world, high-impact crises. She uses this experience to provide your organization with a clear roadmap to implementing a crisis ready culture–and thus building an INVINCIBLE brand. Order Crisis Ready on Amazon Crisis Ready is not about crisis management. Management is what happens after the negative event has occurred. Readiness is what is done to build an INVINCIBLE brand, where negative situations don't occur—and even if they do, they're instantly overcome in a way that leads to increased organizational trust, credibility, and goodwill. No matter the size, type, or industry of your business, Crisis Ready will provide your team with the insight into how to be perfectly prepared for anything life throws at you. Organizations that are crisis ready are more than just resilient. They're invincible. Crisis Ready is your roadmap to business invincibility.
Crisis Readiness Equals Freedom - 3 Steps
When I think of peace of mind in business, it comes from being prepared for the expected, as well as the unexpected. It's not all sparkle ponies, unicorns and laughter. Bad stuff happens. What we do to respond in those moments as leaders and team members can change the course of a company and set into motion a chain reaction of positive outcomes or a Coyote/Roadrunner death spiral into dust. A bit dramatic I know, but I wanted you to have a visual as I introduce you to an expert in crisis readiness, Melissa Agnes. You don't have to put this off. You and your company can immediately take steps to build your crisis readiness. You may have more in place than you think you do. Learn from Melissa Agnes who is the author of Crisis Readiness on Amazon. ----more---- About Susan's guest: Author of Crisis Ready: Building an Invincible Brand in an Uncertain World, Melissa Agnes is a leading authority on crisis preparedness, reputation management, and brand protection. Agnes is a coveted speaker, commentator, and advisor to some of today's leading organizations faced with the greatest risks. In Crisis Ready, Melissa Agnes draws from her remarkable experience in helping global brands, government organizations, and world leaders prevent and overcome a range of real-world, high-impact crises. She uses this experience to provide your organization with a clear roadmap to implementing a crisis ready culture–and thus building an INVINCIBLE brand. Order Crisis Ready on Amazon Crisis Ready is not about crisis management. Management is what happens after the negative event has occurred. Readiness is what is done to build an INVINCIBLE brand, where negative situations don't occur—and even if they do, they're instantly overcome in a way that leads to increased organizational trust, credibility, and goodwill. No matter the size, type, or industry of your business, Crisis Ready will provide your team with the insight into how to be perfectly prepared for anything life throws at you. Organizations that are crisis ready are more than just resilient. They're invincible. Crisis Ready is your roadmap to business invincibility.
Generate Revenue From All of Your Passions
Susan's guest is Richard Moore. Not only is he a successful architect, but he's a graphic artist and product designer. Richard talks about the unexpected lessons learned when he started mass producing products. With over 100 SKUs, he's been able to successfully refine the process. The first step, hiring someone specifically to manage the production process. They met through a Kickstarter program several years ago launching their Chimeras through Walrus Toys. ----more---- When Susan asked Richard how he balances his love of being an architect with product development, he tells her that it's not always balanced and that people need to get over insisting everything is always balanced, including the balance between partners in an endeavor. Just keep doing what you love. A quote he used to explain how fortunate he is was taken from architectural school, "Graphic artists always want to be product designers. Product Designers always want to be architects, and architects always want to be graphic artists." He and his partner are able to be all three. Listen to this 24-minute episode about what that looks like, his advice, tips and insights. There will also be a new Kickstarter soon to launch four new toys completely separate from the successful and popular, Chimeras line. He would give us NO hints, you'll just have to get on his mailing list to find out. You don't want to miss the Kickstarter opportunity! Now, I need to go to find my next gifts on ilovehandles.com - they are always inventing SOMETHING I want. Learn more about Walrus Toys, ILoveHandles and Zero One Ten.
Get out of your way and create a successful business.
My guest today is Corinne McCormack for part two of the interview we did a couple of weeks ago about how to build a multimillion-dollar business. Yes, you can, and she has some final tips, advice, and strategies for you in this episode you don't want to miss. Here we go. I'm here with Corinne McCormack, and we have had some great interviews recently and there were a couple of topics though that I wanted to cover with her. Corinne, are you open, let's tackle those last two topics that we didn't get to do in our earlier shows. In your book, From Living Room to Boardroom: How I Launched and Sold a Multimillion-Dollar Business, you tell your whole journey. What I noticed in it is you were very upfront and open to talking about how you were able to borrow against your home to finance the start of your business. You're in New York. You had some equity, you were good. But what do you recommend for people with less than that type of option? Is that a deal-breaker if they can't get that initial funding? ----more---- Corinne: Let me just start by saying when I write about the apartment in my book, the reality is you're right. It is New York real estate. And after five or 10 years, our apartment value went up to the point that we were able to take out a second and third mortgage, which we used to finance the business. But what people need to understand is that I took a risk. So that when I lost my business, my husband and I were in the process of buying an apartment. And we knew we were on the line for a larger mortgage. I hadn't lost my job, but the president of our company, our parent company went Chapter 11. The president of the company lost his job. I called my accountant because it was four more weeks until our apartment closed. "Oh, my God, Larry. What do I do? We're going to be closing on this apartment in four weeks, the company is in Chapter 11. what am I going to do? Should we be taking on all of this mortgage?" Because it was a big mortgage, and my accountant said something to the effect, "Well, you have to live somewhere." My husband and I just looked at each other and said, "We're taking the risk. We're going to go into this mortgage, we're going to figure it out. We'll figure out how to make it get paid." So for the first year of my business, we now had this very large mortgage to pay. I didn't have the benefit of substantial real estate when I first launched my business because we were still paying off a mortgage. And at that point, the apartment hadn't increased in value. We were just looking to make mortgage payments. So the first thing I have to say is people who want to make things happen in their life, sometimes you have to take a risk, but you have to take it or you live with regrets. I talk about risk in my book. You have to take a knowledgeable risk. Back to earning money for people or creating money when they want to launch their own business and they don't come from a lot of money, there are a lot more ways to fund startup businesses today than there were back in 1993. There's the internet, there are Kickstart campaigns. So there are opportunities. If you have a great idea for a company and you know how to position yourself online and develop a website, and develop an Instagram account and get a following, and go on Kickstarter and start selling your idea to people, people will gravitate towards you. I was just mentoring a couple of young women who started a business. And they did a Kickstart campaign and they launched enough money that they were able to finance their first round of inventory. A substantial amount of money, so there's a lot of opportunities. It's not what are the troubles or what are the problems to make what I want. It's like, "What do I want and how do I make it happen?" And I remember when I first financed my business, I became part of a women's organization. It was called American Economic Development Corporation. It doesn't exist anymore, but there are a lot of women's organizations out there that you can partner with. And this organization had an event where they invited a senior vice president from Chase Bank to talk to women about financing their business. 200 women attended, I was one of them. He went through this whole presentation about how they wanted to finance startup businesses. And at the end when he had the question and answer session and I said, "Oh, I have a question. I have a really important question. I want to launch this business. I've gone to three different banks looking for money, and all the banks say you need to be in business for two to three years before we'll loan you. But I won't be in business in two to three years unless I get a loan. So it's a catch 22. What am I supposed to do?" So this gentleman said, "Here's my phone number." Yeah, we didn't have emails. There was no internet. "Here's my phone number. Call me tomorrow." So I got on the phone at nine o'clock in the morning. I wanted to be the first one in line to get through because we used to get busy signals. Millennials, yes, you used to use your phone and there was something known a busy signal. If more than one person was talking on the phone, you couldn't talk to the other person. So I wanted to be first in line. I got through, I spoke with him, and then I started on the process to get my loan. And a couple of weeks later I said, "By the way, how many other people reached out after that meeting?" The answer was none. So lots of times people tell themselves that they want something, but then they think of all the reasons why it won't work, and they stop themselves from moving forward to make it happen. So my motto is if you want something, figure out how to get it and go for it. And yes, you're going to need you to take a risk. Nothing comes easy. Susan: I like, too, that you covered through more traditional financing. Sometimes it's a credit union. Sometimes it's the small banks, it's a local bank. I know Chase had launched a new program right at the exact same time. You had perfect timing with them. That's what they were investing in, small businesses because that was the new wave. Corinne: That was the new wave. Right. The internet was up and coming. All of these things were starting to happen and people were starting to understand the value of small businesses. It was just perfect timing, and yet it wasn't perfect timing because there was also a bad recession going on at the same time. So again, had I told myself the story, you know that, oh, it's a recession. People aren't spending money. Things are bad. I better get another job. I never would have launched my own company. You really need to believe in yourself. I had asked a lot of people prior to launching my own business because I knew someday I wanted to do it. "What do you need to have when you launch your own business?" And people said to me, among other things, you need enough money in the bank that you got two years worth of salary. So in case you don't make any money, you could draw on that. I didn't have any money in the bank. We had nothing. We had a new mortgage and no job, and my husband was working, but my salary wasn't coming in. So I had a severance package that would last for six months. That's what I had. Susan: I think the nos are all fear-driven, and they are also those that don't have enough drive. It is their excuse. It is their show stopper. When they hit that fork in the road, it's the path easily taken that's smooth and paved. And you can see the end of the path. I think what people need to remember too is okay if it doesn't work, what's the worst that it can be? Can you survive that? And if you think that all the way through rather than just I can't do it because I'm afraid of that, how bad really is that? And how much does that stink? Can you dig yourself out of that? And I think once you have those, to me those are safety net thoughts. It takes the fear out of the risk, out of the leap, out of the trust. Corinne: You have to want it more than you fear it. There's a lot of things out there that are scary and you know, what if. But if what you want is stronger and your drive to succeed is stronger, and your belief that you're going to figure out a way no matter what. And that's what I believed. I kept saying to myself, "I'm going to figure out how to find the money for this company no matter what." And that's what I did. And when the bank said to us, "You need to put your property up as collateral against your loan," meaning if the business goes under, you lose your home. My husband and I said, "Well, go for it." Because what are our other options, not to go for our dream? We'd rather roll the dice and risk at all, than sit back and say, "No. That's too risky. I don't want to do it." No regrets. No regrets. Right. And you're right, you do have to move forward and you have to have ... You know, what's the worst that can happen? And something bad happens, I'll figure out a way to get out of that too. So you really do need to believe in yourself. And the nice thing about the world today is that there is the internet, there are opportunities to reach out to like-minded people. I have an Instagram page called Corinne Consults. People can come on there and ask me questions. I'm happy to, to talk to people. I have a website, corinnemccormackconsulting. Come on my website. I'm happy to talk to you. And there's different, and it's not just me. There's a world out there of people that if you Google something, you can get the answer very quickly. And you just need to to make it happen. But check the credibility of whose advice you're following. You need to be smart enough to be able to judge the crap from the good. On the web, there can be a lot of hucksters, shall we say. Susan: Any ding-dong can have a microphone and can type. The last thing on the financing I want to remind you, most of your communities have community grants. And especially if you are creating an opportunity that could hire another person in your community. Remember, grants don't have to be repaid. Grants are a, "Hey. Make it happen, guys. Let me see what you can do with it." Look deeper. It isn't always just about the Kickstarters, as we know. It isn't always about the banks. Be creative. How bad do you want it? Go get it. Believe in yourself. Corinne McCormack, this has been a wonderful wrap up to these conversations. And I want to send everybody to Amazon. Go on Kindle, go anywhere you get books to find From Living Room to Boardroom: How I Launched and Sold a Multimillion-Dollar Business by Corinne McCormack. And go find her. Go to corinnemccormackconsulting.Com. Find her as she said on Instagram, Corinne Consults. Go find her. Connect, learn from her.
Corinne McCormack - How to launch a multi-million dollar business.
This is the first part of an interview with author, entrepreneur, inventor, speaker - Corinne McCormack. My guest today is author, consultant, seasoned executive, and entrepreneur, Corinne McCormack. We are here today to talk about her new book, From Living Room to Boardroom: How I Launched and Sold a Multi-million Dollar Business. I have it and I love this book. Before I wanted to interview her I said, "Hey, I need your book so that I can read through, get a few chapters under my belt." I couldn't put it down Corinne, I loved it. ----more---- Corinne McCormack: Thank you. I'm so glad to be here. It's great. Susan Finch: So many of you who have listened to my show before, you heard the show with Susan Finch, Susan E. Finch in New York, the voice and dialect coach extraordinaire, and Corinne is one of her friends. Corinne accidentally emailed me instead of Susan, and here we are. Corinne McCormack: I was emailing her about my new book, and then you replied, and I said, "Well, maybe you'd be interested in my new book anyway." And then here we are. Susan Finch: Here we are because I was very interested. Your story is very near and dear to my heart, and the essence of the book, folks, is to take you on a step-by-step outline. Let's say, if you want to be a business owner, these are the steps. It includes some of my favorite pages are these black pages, the Seeds of Success pages, and they are dog-eared throughout this book. This whole book is highlighted and dog-eared, and I keep rereading the Seeds of Success. They're so succinct, so evergreen. This is relevant. It was relevant to you back in '93 when you started your business. The tips in there, of course, include new technology, but this is all about her journey. Corinne McCormack: I wanted to tell the story for other people to understand what it is to launch your business because I always find when people say, like, if you speak to a very well-known designer, like a Tory Burch, how did you start your business? "Oh, you know, oh, a few friends looked at my shoes and they loved them, and the next thing you know I have a multi-million dollar business." They always make it sound very effortless and they don't really give you all the behind-the-scenes machinations of what goes into making something happen. And there's also a lot of people who have a lot of background funding that they don't share with you. I remember reading stories about one shoe designer who would talk about how they went from zero to $5 million. Well, you don't go to $5 million without having really five to $10 million in backing. And so here I was somebody who had recently lost my job. I had less than six months for a severance package to run out, and that was my big opportunity to launch my business. I wanted to tell the story of what I did in that first year that made things happen really fast and really well so that other people could do it too. Susan Finch: Well, you did that. So quickly, folks, I want to give you a bit of background. Corinne started her company in 1993. That's actually about the same time I started to get into one of my companies, one of my iterations. She launched a brand of designer eyewear and developed this brand. I'm wearing them, aren't they gorgeous? These are not from her original line, but this is the result of this journey, and it developed into a leader in premium reading glasses. Some of you pups won't remember reading glasses used to be super ugly and you had no options. Corinne McCormack: When I started my business, it was so funny. I was 40-years-old, and I didn't need reading glasses, and so I was designing jewelry, and I was designing eyeglass chains, and cases. I hired a stylist, and I said, "Go out and find fabulous sunglasses and reading glasses, and great colors, and here's my colors," blah, blah, blah, blah. She came back in a couple of days, and she had beautiful sunglasses and nothing in reading glasses. And I'm like, "You know, you brought me one pair of antique brass reading glasses. This is not what I want. I want color, I want fashion." She said they don't exist. And I said, "Oh my God." Because when I needed reading glasses, or I know all the other women that were right behind me turning 40 in referent numbers we're not going to want to wear those old lady grandma looking glasses. That's how I started my road to creating designer reading glasses. And so that was just a necessity, a future necessity. Susan Finch: And you saw a hole. That's the biggest thing. And you leaped on it. But you know, just saying that "Oh, I want to design designer eyeglasses." Like you were saying, that is not the journey. It isn't, "Oh, one day I woke up and decided to do that and here I am." You had a lot of experiences that led to that. So, I want to jump into that part of it because too often I feel, especially women more than men, typically we think differently. We apply our experiences differently. I think that women especially discount the learning journey including networking and all the relationships along the way. In your book From Living Room to Boardroom you talk about the acquisition of the skills from each position you held and how you pushed to gain more knowledge that was then was presented to you, and here's the job description. You constantly pushed yourself and all of that culminated into the first business that you launched. Corinne McCormack: When I launched my book I talk about the eight entrepreneurial essentials. Number one is a passion, and number two is drive. What I did after my journey, as I was writing this book, I said, "What is the essence? What made me an entrepreneur? What makes other people entrepreneurs?" And if you look at my story, I spent 15 years in Corporate America before I launched my own business, I knew I wanted to have my own business, but I didn't have the resources. I didn't have the money. I didn't have the time to do it until I did. But at each part of my career, I assumed a position that I owned the company I was working for, so I never was just an employee. I always treated it as if it was my own business and did things to the best of my ability in the way an owner would want me to. I really believe that that's important because a lot of younger people today come out of college or business school and they think, "I need to launch your business tomorrow." They don't necessarily get under their belt all the skills and the life's learnings to make them successful, and then they're going to jump around from company to company to company and maybe not really get that knowledge that they need to understand what it is that makes a good business. Susan Finch: I agree, and I think I'm very grateful for knowing enough to pay attention to watching CEOs and CMOs that I've worked for forge relationships, solve problems, please clients, make nice with a client when it didn't go well, nurture vendor relationships. Corinne McCormack: What it all boils down to, relationships and relating to people. Whether it's your employees - because as I hired employees they were not just employees who were to be dismissed or treated differently than I would treat my family. Actually, I treat my family quite nicely. So I know in some families, it's not quite like that. But I treated my employees with respect, and also treated them as though they were partners in my company. When I worked with my buyers, and the department stores, and wanted them to carry my products, again, it was developing a one-on-one relationship that set us apart from every other company. And then back to the networking idea, right from the beginning of my career and through my launching my own business, I was constantly building a network of people and individuals that could ultimately not just support me, but also I could give back to them so that I made it when somebody called and needed something answered or had a question whether they were a customer, or a friend, or an employee, I would stop, take the time, and be with them to find out what it was they needed and how I could support them, who I could introduce them to. And then the same happened for me if I needed something, you know, when I started my eyewear collection I had developed such a great relationship with one of my buyers that I was able to go to her and say, "What are the best factories in the world that I need to talk to so that I can launch a new glass collection?" And she gave me three or four wonderful companies, one of which I continue to use for over 20 years. So it's those sort of special relationships that really make business wonderful. Susan Finch: I find that I had an interesting call yesterday, and I had a client start up with me recently too, that I had met 25 years ago when I worked for an ad agency. He was a photographer at that time and just starting with this 360 kind of photo thing, and it was so new then just like little desktop computers were too. But he came back to me because he enjoyed working with me at that agency all that time ago and said, "Hey, I've been following you and I think I need your help." And these are old relationships that I've followed him and stayed in touch with him throughout just to check-in on him and share out anything positive that he shared out. Don't burn your bridges, folks. Corinne McCormack: In the optical industry, I belong to the Optical Women's Association. And that was an organization that's very near and dear to my heart and I started attending their seminars. I didn't realize they had only started maybe two years before I joined them. But in that organization, I met so many other women from all different aspects of the optical industry and forged relationships that really helped me to become a better member of the industry, and also to become part of this really great network. And then there's also something called The Vision Council and I devoted a lot of my time, my volunteer time to be in The Vision Council. The Vision Council, again, this was not just women, this was women, and men, and large companies, and small companies altogether, banded together to support consumers, and eyewear, and getting the eyewear message, good eye care out to consumers. But it also was great for networking and meeting people and I just started [crosstalk 00:11:23]. Susan Finch: Let me chime in for a second. You're hitting on something really important, and what I was talking about was just people that go to work and leave work. You're talking about, this is super important, you're diving into helping others in something related to your industry. This invites you to meet quality people with good hearts, integrity, and a bigger vision and less ego. Corinne McCormack: That's very true because the organizations that I was really volunteering my time for other people were volunteering their time for, so you do find other like-minded individuals who are working together for the greater good. For the optical women, it was to build leadership opportunities for women in the optical industry and to raise the visibility of women, and we supported one another. Vision Council is all about getting out there and talking to consumers because people don't really understand until something goes wrong. You're so used to having your eyesight and your vision, although we're both wearing glasses, so we know how important glasses are. But otherwise, people who have good vision they don't even think about their eyes. And then voila, God forbid, one day you wake up, and you've got a problem. So it's getting out there and conveying a message, but by doing that you start working with and learning about a lot of other people and companies, and it opens up your world. So people really should network. People really should invest their time and find out what they're passionate about, and then go out there, and volunteer, and pursue relationships. I wouldn't say it's a two-way street, I think it's a one-way street. You need to pick up the phone, you need to contact people, you need to talk to them, you need to be open to meeting people. That was something that I developed along the way that I probably did not have before I started my own company. I was more of those, I had a two-year-old son, I went to work, I came home, I took care of my son. But then as I grew into my company and grew into owning a business I began to look for other opportunities and the importance of these relationships. Susan Finch: From the start, you were very sure of your own talents, at least everything I read in here you were not a self-doubter. You were passionate, driven, right from the beginning. So I'm wondering what kind of discernment process do you recommend to people wanting to identify their unique talent, or skill, or product they can bring to market? I hear too many stories of self-doubters that they nip it in the bud right then and there. It's like, "I want to have a business, but I can't." And they sabotage themselves. Corinne McCormack: Well, I think what I love about the world today is with computers and with the internet whatever your skill set is you can find an opportunity should you want to have your own business to create a business. So what I would say to someone, like for myself based on my background I was in retail, I was in wholesale, and I was product development. So I knew that I loved developing products, I loved finding needs and wants of consumers, and developing something that they didn't have. That was my passion. And I also loved making money. So loved figuring out how much something costs, trying to get it for as little as possible, creating value so that when I sold it to my customers they were satisfied. They felt that they got great value and a good product. That was me. So that's why I knew that I needed to develop something in that world. But there are people out there that are terribly creative when it comes to art or graphic artists. So could you create your own graphic art company? Of course. But you could also become a freelancer, and there are ways to position yourself and go out there and network, and go online, and use Instagram, and so many other wonderful platforms to get your name out there. I'm actually working with a couple of teachers right now. These are people who by day they teach math and one of my friends is also a sign language interpreter and works in a school, but they're both terribly creative and we're working now on developing the businesses for them because one of them makes handbags and sells them to friends, and the other one embroiders jeans and sells that to friends, and then she also is an artist. I'm working with them about developing "a business" because they didn't realize with these skills, it could become a business. Now, and I distinguish the difference between a hobby and a business. A hobby is something you do because you enjoy it. Yes, you might sell it to your friends, but you're not really serious about making it into something bigger than it is. But there are other people who will really enjoy turning it into something that could become bigger and broader. So people just really need to know what their skills are. I mean if somebody is great at accounting they can go off on their own and become an accountant. Computer skills. So many people I know are great with computers. Now you could go in and become a great employee in a company, or you could become a freelancer and find out where the voids are because there are a lot of small companies that need people to come in and develop systems or support them in their computers if they can't afford to hire a full-time computer person. So there are lots of little niche businesses that can be created and developed that people can take advantage of. Susan Finch: I agree. It gets back though to our earlier topic of gaining that experience, and I know a lot, I know enough younger entrepreneurs even in my own family, and they've never worked for anybody else. "Oh, I don't want to do that. I'm just going to do my own thing." But where I see them faltering or slowing down is because they didn't take the time or appreciate, or they weren't willing to pay a few dues to gain some valuable experience that somebody's paying you to gain. This is an education you're getting paid for folks when you work for somebody else for even a while. Corinne McCormack: That's true because in your own career if you have the idea that you want to have your business, I recommend in your career you develop a career so that in each position you take you're taking on positions with more authority, more responsibility, but also creating a well-rounded experience for yourself. And as long as when you're doing that, you're also taking good care of the company you work for they're happy to continue to give you that experience and to have you grow, or you launch from one company in one industry into another company in another industry to learn something else. I think people don't realize the value of working for companies and how great that can be when it comes time should they want to go in and launch their own business. There's a lot that you can learn. Susan Finch: You can take it to different industries and that comes back to that discerning process. It's not only finding out what you want to do, but what's your core? And for me, my core is teaching, inspiring, and advocating, so it doesn't matter whether I'm doing that with podcasting, doing it with graphic design, doing it with web, doing it with copywriting, it's the same core and if I take that with me everywhere and stay true to it, it usually works out pretty well. Corinne McCormack: That goes back to the eight entrepreneurial essentials. It's back to passion, and drive, and also inquisitiveness. I said that's one of the important elements of being an entrepreneur is you don't ... As an entrepreneur, I, to this day I'm still learning new things and want to continue to learn new things. It's not as if I created a business, and sold a business, and now I'm sitting back and saying, "Done it all. I'm finished." It's like, "No, there's so much more to learn and do, and the world is changing more rapidly than ever." So it's really imperative that people stay on top of what's going on, and see, and learn as much as they possibly can. And then the other thing that I say to be a good entrepreneur is you need to have a vision, and vision is this, it's having a vision of if I want to own my own company someday and I'm working for other companies back to that, what are my core skills? What is it that I do that I love? Because there is that old saying, "Do what you love and the money will follow." It' really true. If you do what you love you will be successful. And so many times, I think this is where people get caught is when you have a natural talent you tend to think everybody has the same skill. Even just seeing and developing product or design I kind of believed that it wasn't that unusual like anybody could do that, but anybody can't do what we can do. So there are certain innate skills that we've got or ways of looking at the world that we have that other people don't. And if you really start to understand and appreciate what makes you that special person, then what really gets you going, and then find those positions, if you will, or ways to earn money to support that I think you're on the path to success. You need to know what your skills are and what your talents are, and then find somebody who's got that, if you will, those other talents that round out your talents so that together you can be a great pair. Susan Finch: I think that's a wonderful idea. That's the advice I think so many people when they're starting a business they think they have to do it all. Or they're afraid to let go of certain pieces. Corinne McCormack: You hit on another one of my entrepreneurial essentials, which is self-sufficiency. So you do need to believe you can do it all because especially when my company was first starting, and we had like three employees if an order needed to go out the door and somebody called in sick, well guess what? It had to get out the door. So we had to figure out how to do it. So I really needed to believe, and I think any owner of a company needs to understand exactly what's going on so that everything happens smoothly regardless of what's going on out there. But self-sufficiency doesn't mean you don't need people. So you need to be self-sufficient, but you also have to need, appreciate and understand the value of partnering with other people and networking with people, so that's really important. I wanted to say something about my 25 Seeds of Success that are in my book because what I did was I wanted to create my story, and then I also understood that there are people out there who are going to maybe not want to read my entire story, maybe they'll read part of it. But they do need to know those 25 Seeds of Success, those lessons learned, if you will, that apply to any business and anyone. It applies whether you're an employee or an owner. And so as I went through my story I put down the Seeds of Success because there's not just one secret, there's a lot of different things that go into making a person a better executive and making a business a better business. So I'm really glad you enjoyed that. One of my Seeds of Success is about wellness. That's more towards the end of the book. I think it's seed number 20. I mention wellness because particularly as you are an entrepreneur if you're not careful you can run yourself into the ground and run yourself ragged. That did happen to me at one point along the way where I was 10 years in and I had planned on certain things, and then the economy didn't go the way I planned and 9/11 happened, and then all my plans literally went up in smoke. My business started declining and I didn't know what to do. Ironically that's when I reached out to take a seminar with a couple, their names are Ariel and Shya Kane. So by taking their seminars, it's all about living in the moment, but it's not just living in the moment. It's also about learning to live a stress-free, more relaxed life, and to say yes to your life so that instead of fighting with what was going on and being annoyed with what was happening, or being worried about what's coming, or upset about what I had done, created in me the possibility to start just being where I was and appreciating everything that I had at that moment and doing what needed to be done. And that's what I love because it's not about sitting back and going, "Oh, the world is great. Let's just sit and relax." It's about relaxing into your possibilities and then moving forward in a way that you could get things done more effortlessly. And it was really cool because that was another opportunity for me to network. That's how I met Susan E. Finch, the voice coach that ultimately is how I connected with you. So I do believe people need to take good care of themselves. It's not just exercise because yes, I do exercise regularly. But also you need to take good care of your mind and learn how to be patient with yourself. I recommend listening to their podcasts. They have a podcast called Being Here with Ariel and Shya Kane. So if you listen to the podcast that would give you an idea of learning how to live this sort of more effortless, less stressful life. Susan Finch: And supporting that point, it isn't just a one-time thing. You need tune-ups. I firmly believe in surrounding yourself, folks, with other people that want to have success. It doesn't have to be a big success, but they are interested in improving their position spiritually, business-wise, personally, and growing, and improving. That's who you want to hang with. Corinne McCormack: That's right. That's absolutely true. It's another reason I started a meetup in New York where I want to create a community of people who are looking to succeed and build their own, either build their own business, so take something that they didn't have and build it, or take what they've got and made it greater, but also to be successful. And it's like you said, when you get a group of like-minded people together it's very, very powerful. So definitely, and I love your point about it's not a one-time thing because it's just like if you go to the gym, and you work out really, really hard, you can't go, "Wow, that felt great. I'm done. I've worked out, I feel great." Or even if you want your body to look good, and you work really hard vigorously for three months, and you get your body in great shape, and you can't stop because if you stop, guess what? It's not going to look as good three weeks later. So it really is finding what works for you, and being consistent, and continuing to take care of yourself and those around you. Susan Finch: You'll get the second half of her story in the next installment of this interview, but before we wrap up our first half, I want everybody to know where to find your book. It is on Kindle. It's on Amazon. You can find it everywhere. You just search for, look for this cover. It'll come up in the results From Living Room to Boardroom: by Corinne McCormack. Also, go to corinnemccormackconsulting.com, and on Instagram @corinneconsults. Never miss an episode. Check out, rootedinrevenue.com and subscribe on the site to get weekly updates of when new episodes come out or find us on iTunes, Stitcher Radio. We want to be where you are, so go subscribe. We'll get you all the information you need to do your best with the marketing of events and your online presence.
Typos on your site can cost you money - tips to fix it.
Karen and Susan cover where the typos are and how it can affect your credibility and make it more difficult for your sales team to build confidence with prospects. Listen to the full episode to get examples, details and an action list. Susan's List of task reminders to keep it current. Karen's secret tool to help you find the typos fast. Check your own site for links to internal PDF files, videos on a YouTube channel, too - those change over time, especially since people are converting personal channels to business channels. ----more---- Remember to use your Google Analytics or Search Console to: 1. Find the top pages for a YEAR that you need to start with checking, and go through the entire list. 2. In search console, check errors from crawls. Find out what's broken and what site or page is leading them there. Need help? Contact Susan Finch. Sometimes you just need help getting started.
Online Reviews - why you need them, where to find them and how to respond.
This lively visit with real estate agent, Kristina Smallhorn applies to all businesses who need and receive reviews. The video version linked in the bottom will have some how to tips, too. Business reviews are not just for B2C and brick and mortar. ALL businesses need reviews in the right places where their potential clients go when considering them as as solution. This, along with what their colleagues and friends recommend play the biggest role in decision making before they even contact you. ----more---- My guest is Your Real Estate Whisperer, none-other than Kristin Smallhorn, a successful real estate agent in Louisiana. Her engaging YouTube channel is how I knew she was a great guest for this topic. But videos are what you EDIT and produce. Reviews - we do not control what people post. We can hope, we can ask for them when we have a successful transaction, but ultimately, we cannot control what others say about us - this gives reviews more credibility. Why do you think some businesses don't pursue reviews? Well, you may be surprised. Businesses don't want to end up in one of these situations: receiving zero business reviews receiving zero recent online business reviews receiving negative online business reviews or, the business simply has a chaotic presence of online reviews across multiple business review websites OK, listeners, put on your big kid pants. Reputation provides interaction. AND business reviews provide valuable feedback for businesses. Business reviews and social posts help shape a company's online reputation. AND, if you don't like what's being said, well, it may be time to do it better. Your problems are bigger than what people are posting. That's just the result of the issue. Ask yourselves these questions: How your are reviews? Are you are sure you know where they all are? What about when you get a bad review? How do you respond and how quickly? Were you able to turn any around to either remove them or update them to something positive? Have you converted any bad reviews into clients or advocates? PIE IN THE SKY hopes! We cover a couple of stories in this episode you may be able to relate to or find entertaining. What you do to get reviews and testimonials from clients? How do those play into your conversion rate? How do you share reviews with your target farm, audience without constantly blaring the "LOOK AT ME! I'm GREAT!" horn. Time for your do to list, listeners. Where to look for your existing reviews? You can do a quick look on the three major venues in order of weight: Yelp! Look on your Facebook business page. Your Google My Business page - the right hand box. You can also do a search on Yext! without signing up - you'll get links to all of your current profiles and can see what others see. Now, if you are niche - you need to also receive and review your listings on those sites: For Real estate professionals: Zillow, Realtor.com For attorneys: Avvo, Lawyers.com For Medical professionals: Healthgrades, RealSelf, ZocDoc For restaurants: Zomato, TripAdvisor For service providers (contractors, roofers, cleaners, etc.): AngiesList, HomeAdvisor, NextDoor if it's popular in your area. Of course you want to get reviews concentrated on the most important online review sites. That's why we recommend you focus on no more than five review sites total. Listen to this replay and catch the video on Susan Finch's site here >
Which comes first - the why or the how in the first presentation?
Susan welcomes back author and impact training expert, Amy Franko, as a follow up to the book launch episode for The Modern Seller. Update on her book, wildly successful launch propelled her into the number one position for Kindle downloads in the category of Sales Techniques. We've continued to follow her tips, posts, appearances and the topic of The Why and the How came up. Her blog post titled, "What Distinguishes a Standout Seller?" led to this interview. There is not one answer, but Amy helps you determine the questions to have ready in order to guide the meeting, the presentation and ultimately - THE SALE. Be sure to sign up for her newsletters, guides and more. Definitely worth adding to your weekly research list for those AHA moments. AmyFranko.com - you will find her book, The Modern Seller there as well.
When your voice drives the sale away before it started.
Take a breath. Really, take a deep breath before you pick up the phone. While you're at it raise your arms, lower your shoulders, sit up straight, smile then make that call, walk into the meeting, take the stage. Speech patterns and bad habits can tune your audience out, even an audience of one, before you get further than your introduction. This will cost you revenue and waste everyone's time. Take tips from voice and dialect coach, Susan E. Finch. This show should have been a video - it was so much fun and packed with applicable tips to keep you from being annoying. The biggest culprits? Women! Women 17 - 35 and this voice fry issue where they sound like they are swallowing their words. Next, the gutteral hiccup - that punch that only belongs in the Cockney community in London. ----more---- How about the fillers: Like, ya know, sooooo, and.... um, uhhhhh? Time to break yourself of those habits. They scream insecurity and require your listener/audience to strain to get to the point you are attempting to make. When we need to hire someone, we go through the interview process, background checks, checking to see if their past is linked to a bunch of workman's comp cases with former employers.... but once we decide to hire them, do we assume they are articulate? Do they know how to present ideas to their new team? Clients? Speak on behalf of the company? Why don't we teach our staff how to think on their feet and respond articulately? Surely there are Toastmaster's chapters near you. Give them bonus points for going through it or pay for it for them. You'll be glad you did. You'll give them confidence. AND if they really have bad habits, consider a speech coach, like Susan E. Finch. These professionals can quickly identify and help them work through bad habits. May not hurt you, either. Susan suggested the movie, "In a world" from 2013. GREAT examples you can remember. It's about the voiceover industry. Challenge: RECORD yourself to see how you sound. Use video if possible. Introduce yourself to you. Would you buy from you? Would you want to slug you? Would you TRUST you? Really listen and ask an HONEST colleague to do the same and give feedback. Do it for your department. You'll all benefit from this improvement. About our guest, Susan E. Finch. Susan Finch is a voice and speech coach who is passionate about supporting people in becoming clear and connected communicators. As her background is in theater she is able to bring vitality and fun to her clients. Specialties include: - accent reduction - vocal production (finding power, ease, volume and range) - clarity of articulation - ease in communication (eliminating fear of public speaking) She coaches people how to communicate with confidence and excellence. | {
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Tom with the BTRTN September 2018 Month in Review. By the way, we were just named one of the Top 100 Political Blogs by Feedspot, check it our at their site: https://blog.feedspot.com/political_blogs/ .
For the very first time in Donald Trump's presidency, he was eclipsed by another newsmaker for an entire month. There certainly have been compelling figures who have joined Trump in the spotlight at various times, including, for example Jim Comey and Kim Jong Un. And there have been a raft of minor characters in the ongoing drama, such as Steve Bannon, Anthony Scaramucci, Javanka, John Kelly, Mitch McConnell, Paul Ryan, Jeff Sessions, Rod Rosenstein, Michael Cohen, Stormy Daniels, Omarosa Manigault Newman and, ever so briefly, Bob Woodward. Robert Mueller has been almost a spectral presence, always hovering in the room, emitting sudden bursts that give evidence of his handiwork, but no real sign of the man himself.
September was dominated instead by Brett Kavanaugh. But in an eerie way, Brett Kavanaugh chose, ultimately, to deal with the disaster that befell his nomination by becoming Donald Trump. And so, perhaps, this month really was all about Donald Trump after all: the "Mini-Me" version.
Kavanaugh's testimony on September 27 had the Trump act down to a tee. There was the knuckles-bearing screeching assault on the Democrats and the Clintons. The complete and total denial of the allegations of sexual assault in the face of all-too-credible evidence. There was the unhingedness of it all, the angry, self-righteous mania, the loss of control, the utter lack of dignity, the monstrous ego, the reversing of questions back to the questioners, the smarminess, the contempt. These characteristics were alien to the prior 43 Presidents of the United States, except in very small (and often private) doses, and they were and are alien to the 113 justices who have served on the Supreme Court, who are typically more spectral presences than even Mueller.
You may have seen Matt Damon's channeling of Kavanaugh in the "cold opening" of Saturday Night Live last week. But while Damon was excellent, and hit the mark nicely, SNL missed an opportunity: perfection would have been achieved if Alec Baldwin had portrayed Kavanaugh, instead of Damon. Trump and the White House made it clear to Kavanaugh that the quiet, choir boy defense of the FOX interview was not going to cut it – only a Trumpian blast would properly shift attention elsewhere, with Lindsay Graham as chief accomplice. And with his testimony, apart from the Blasey Ford charges, "judicial temperament" and "partisanship" came into play as confirmation factors.
The GOP had hoped to have Kavanaugh seated on the bench by the traditional First Monday in October high court opening, but that date has come and gone. With the last minute Jeff Flake-inspired compromise, the story continues, as the FBI conducts an "investigation" that is totally controlled by the White House and is amounting to little more than an exercise in futility in its narrowness. It is unclear, for example, whether any of the 20 names given by Deborah Ramirez as potential corroborating witnesses will be interviewed. Will this fig leaf of a process satisfy Flake, and/or fellow fence-sitters Lisa Murkowsky, Susan Collins and must-keep Democratic Senator Joe Manchin? The answer is almost surely "yes", barring a total collapse of Mark Judge. This will all likely go down on Friday when the report is due.
There were other consequential events this month – the narrow escape of Rod Rosenstein from a firing and our country from a constitutional crisis; the escalating China trade war; the brand new, snappily titled "United States-Mexico-Canada Agreement" with the cumbersome "USMCA" acronym (you have to admit, "NAFTA" was cooler). And, rolling down the tracks, the mid-terms thumbs-up-thumbs-down referendum on Donald Trump. That verdict is now only 33 days away.
But September was basically all Kavanaugh, all the time, right up until, and now beyond, the moment he morphed into Donald Trump himself.
Trump himself was relatively quiet this month, apparently taking his advisers' advice to stay out of the Kavanaugh fray. He did not always completely stick to that script, with a number of notable outbursts, but far less than might have been expected. And Trump thus held steady yet again in a rocky time, recording a 43% approval rating for the fourth straight month, in line with his entire 2018 average.
The generic ballot for September remained at +6 in favor of the Democrats, and inched up to +7 in the last two weeks of the month. This too has been a steady measure for 2018. Using our proprietary BTRTN regression model, this lead would suggest a 42-seat pick-up for the Dems in November (if it held). We calculate the Dems' odds of taking over the House to be 88% as of this moment.
The "Trumpometer" increased marginally to +30 in August, from +28 in July. The stock market and consumer confidence increased a bit in the last month, but so did the price of gas, while the unemployment rate and the latest Q2 GDP figures were unchanged. The +30 Trumpometer reading means that, on average, our five economic measures are +30% higher than they were at the time of Trump's Inauguration.
He sure sounded and acted just like Trump. Belligerent, nasty and self-righteous. And hypocritical, of course. What a joke of an investigation it appears to be. Thanks for labelling it so accurately - the "fig leaf" for the three Republicans. | {
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Wichita Falls Woman Does Everything One Should Not Do While Being Arrested
WFPD
When being arrested, there are several things a suspect probably should not do, such as banging their head on the window of the patrol car, kicking the partition between the back and front seat of a patrol car and biting a cop. This genius did all of them and more.
Meet 25-year-old Hazel Walden of Wichita Falls. Ms. Walden was pulled over by a Texas Game Warden in the 1500 block of Singleton on Monday when the officer noticed her driving erratically. Wichita Falls Police were called to the scene to back up the game warden. Hazel decided to have a tantrum and began banging her head on the side window glass of the game wardens truck. WFPD Officers offered to transport her as their vehicle is better equipped for the job.
Ms. Walden's bad attitude continued in the patrol car, banging her head on the side window and the partition glass in between the back and front seat. As she became more combative on the drive to jail, the officer pulled over and called for an additional officer with leg restraints. The officers pulled Warden from the car and proceeded to put her in the leg restraints. At this point, Ms. Walden decided that biting one of the officers seemed like a good idea. She was, of course, sadly mistaken.
Upon arriving at the Wichita County Jail, Ms. Walden continued with her less-than-cooperative attitude, forcing jail staff to restrain her. Not surprisingly, Warden was found to have been intoxicated.
Warden was eventually booked into the Wichita County Jail. Her list of charges includes resisting arrest, assault on a public servant, driving while intoxicated with a child under the age of 15 and driving with an invalid license. As of Tuesday afternoon, she remains in the Wichita County Jail.
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\section{Introduction}
The cross section of the $e^+e^-\to\pi^+\pi^-$ process in the energy region
$\sqrt[]{s}<1000$ MeV can be described within the vector meson dominance model
(VDM) framework and is determined by the transitions $V\to\pi^+\pi^-$ of the
light vector
mesons ($V=\rho,\omega,\rho^\prime,\rho^{\prime\prime}$) into the final
state. The main contribution in this energy region comes
from the $\rho\to\pi^+\pi^-$ and from the G-parity violating
$\omega\to\pi^+\pi^-$ transitions. Studies of the
$e^+e^-\to\pi^+\pi^-$ reaction allow us to determine the $\rho$ and
$\omega$ meson parameters and provide information on the $G$-parity
violation mechanism.
At low energies the $e^+e^-\to\pi^+\pi^-$ cross section gives the
dominant contribution to the celebrated ratio
$R(s)=\sigma(e^+e^-\to\mbox{hadrons})/\sigma(e^+e^-\to\mu^+\mu^-)$,
which is used for calculation of the dispersion integrals. For example,
for evaluation of the electromagnetic running coupling constant at the
$Z$-boson mass $\alpha_{em}(s=m_Z^2)$, or for determination of the hadronic
contribution $a^{hadr}_\mu$
to the anomalous magnetic moment of the muon, which nowadays is
measured with very high accuracy $5\times 10^{-6}$ \cite{bnl1,bnl2}.
Assuming conservation of the vector current (CVC) in the isospin symmetry
limit,
the spectral function of the $\tau^\pm\to\pi^\pm\pi^0\nu_\tau$ decay can
be related to the isovector part of the $e^+e^-\to\pi^+\pi^-$ cross section.
The spectral function was determined with high precision in
Ref.\cite{aleph,opal,cleo2}. The comparison of the $e^+e^-\to\pi^+\pi^-$
cross section with what follows from the spectral function provides
an accurate test of the CVC hypothesis.
The process $e^+e^-\to\pi^+\pi^-$ in the energy region $\sqrt[]{s}<1000$ MeV
was studied in several experiments \cite{augu,ausl,bena,quen,vas1,buki,vas2,
vas3,kur1,kur2,spec,olya,kmd2,kloe} during more than 30 years. In present
work the results of the $e^+e^-\to\pi^+\pi^-$
cross section measurement with SND detector at $390\le\sqrt{s}\le 980$ MeV
are reported.
\section{Experiment}
The SND detector \cite{sndnim} operated from 1995 to 2000 at the
VEPP-2M \cite{vepp2} collider in the energy range $\sqrt[]{s}$ from 360 to
1400 MeV. The detector contains several subsystems. The tracking system
includes two cylindrical drift chambers. The three-layer spherical
electromagnetic calorimeter is based on NaI(Tl) crystals.
The muon/veto system consists of plastic scintillation counters and two
layers of streamer tubes. The calorimeter energy and angular resolutions
depend on the photon energy as
$\sigma_E/E(\%) = {4.2\% / \sqrt[4]{E(\mbox{GeV})}}$ and
$\sigma_{\phi,\theta} = {0.82^\circ / \sqrt[]{E(\mathrm{GeV})}} \oplus
0.63^\circ$. The tracking system angular resolution is about $0.5^\circ$ and
$2^\circ$ for azimuthal and polar angles respectively.
In 1996 -- 2000 the SND detector collected data in the energy region
$\sqrt[]{s}<980$ MeV with integrated luminosity about $10.0~\mbox{pb}^{-1}$.
The beam energy was calculated from the magnetic field value in the bending
magnets of the collider. The accuracy of the energy setting is about 0.1
MeV. The beam energy spread varies in the range from 0.06 MeV at
$\sqrt[]{s}= 360$ MeV to 0.35 MeV at $\sqrt[]{s}=970$ MeV.
\section{Data Analysis}
The cross section of the $e^+e^-\to\pi^+\pi^-$ process was measured in the
following way.
\begin{enumerate}
\item
The collinear events $e^+e^-\to e^+e^-,\pi^+\pi^-,\mu^+\mu^-$ were selected;
\item
The selected events were sorted into the two classes: $e^+e^-$ and
$\pi^+\pi^-,\mu^+\mu^-$ using the energy deposition in the calorimeter
layers;
\item
The $e^+e^-\to e^+e^-$ events were used for integrated luminosity
determination. The events of the $e^+e^-\to\mu^+\mu^-$ process were
subtracted according to the theoretical cross section, integrated
luminosity and detection efficiency;
\item
In order to determine the cross section of the
$e^+e^-\to\pi^+\pi^-$ process, the number of $e^+e^-\to\pi^+\pi^-$
events in each energy point were normalized on the integrated luminosity
and divided by the detection efficiency and radiative correction.
\end{enumerate}
The detection efficiency was obtained from Monte Carlo (MC) simulation
\cite{sndnim}. The MC simulation of SND is based on UNIMOD \cite{unimod}
package. The SND geometrical model description comprises about 10000
distinct volumes and
includes details of the SND design. The primary generated particles are
tracked through the detector media taking into account the following
effects: ionization losses, multiple scattering,
bremsstrahlung of electrons
and positrons, Compton effect and Rayleigh scattering, $e^+e^-$ pair
production by photons, photo-effect, unstable particles decays, interaction
of stopped particles, nuclear interaction
of hadrons \cite{union,umnuc1,umnuc2}.
After that the signals produced in each detector element are simulated.
The electronics noise, signals pile up, the actual time and amplitude
resolutions of the electronics channels and broken channels were taken into
account during processing the Monte Carlo events to provide the adaptable
account of variable experimental conditions.
The MC simulation of the processes $e^+e^-\to e^+e^-,\mu^+\mu^-,\pi^+\pi^-$
was based on the formula obtained in the Ref.\cite{berkl,arbuzqed,arbuzhad}.
The simulation of the process $e^+e^-\to e^+e^-$ was performed with the
cut $30^\circ<\theta_{e^\pm}<150^\circ$ on the polar angles of the final
electron and positron.
The $e^+e^-\to e^+e^-$, $\mu^+\mu^-$ and $\pi^+\pi^-$ events are
differed by energy deposition in the calorimeter. In $e^+e^-\to e^+e^-$
events the electrons produce the electromagnetic shower with the most
probable
energy losses about 0.92 of the initial particle energy.
The distributions of the energy deposition of the electrons with the
different energies are shown in Fig.\ref{enee}. The experimental and simulated
spectra are in good agreement. Muons lose their energy by ionization
of the calorimeter material through which they pass and
their energy deposition spectra are well modeled in simulation
(Fig.\ref{enmm}). The similar ionization losses are experienced by charged
pions and this part of the charged pion energy deposition is well described
by simulation (Fig.\ref{enppi}). But pions lose their energy also due to
nuclear interactions which is not so accurately reproduced in simulation.
This leads to some difference in energy deposition spectra in
experiment and simulation for charged pions (Fig.\ref{enpi300}).
The discrimination between electrons and pions in the SND detector is
based on difference in longitudinal energy deposition profiles (deposition
in calorimeter layers) for these particles. To use in the most complete way
the correlations between energy depositions in the calorimeter layers,
the corresponding separation parameter was based
on the neural network approach \cite{neural1}. For each energy
point the neural network -- multilayer perceptron was constructed.
The network had input layer consisting of 7 neurons, two hidden layers
with 20 neurons each and the output layer with one neuron.
As the input data the network used the energy depositions of the particles in
calorimeter layers and the polar angle of one of the particles. The output
signal $R_{e/\pi}$ is a number in the interval from -0.5 to 1.5. The network
was trained by
using simulated $e^+e^-\to\pi^+\pi^-$ and $e^+e^-\to e^+e^-$ events.
The distribution of the discrimination parameter $R_{e/\pi}$ is shown in
Fig.\ref{mlp2}. The $e^+e^-\to e^+e^-$ events are located in the region
$R_{e/\pi}>0.5$, while $e^+e^-\to\pi^+\pi^-,\mu^+\mu^-$ events at
$R_{e/\pi}<0.5$.
\begin{figure}
\epsfig{figure=pi2_edep_ee.eps,width=15.0cm}
\caption{Energy deposition spectra for electrons with the energies
180, 300, 390 and 485 MeV in experiment (dots) and simulation
(histogram).}
\label{enee}
\epsfig{figure=pi2_edep_mm.eps,width=15.0cm}
\caption{Energy deposition spectra for the 500 MeV muons in experiment (dots)
and simulation (histogram).}
\label{enmm}
\end{figure}
\begin{figure}
\epsfig{figure=pi2_yad_i.eps,width=15.0cm}
\caption{The spectra of the ionization losses of the pions with energy
$E_\pi>360$ MeV in the first calorimeter layer. Dots -- experiment,
histogram -- simulation.}
\label{enppi}
\epsfig{figure=pi2_yad_300.eps,width=15.0cm}
\caption{Energy deposition spectra of the pions with the energy $E_\pi=300$
MeV. Dots -- experiment, histogram -- simulation.}
\label{enpi300}
\end{figure}
\begin{figure}
\epsfig{figure=pi2_mlp_lt80.eps,width=15.0cm}
\caption{The $e/\pi$ discrimination parameter distribution for all collinear
events in the energy region $\sqrt{s}$ from 880 to 630 MeV.
Dots -- experiment, histogram -- simulation.}
\label{mlp2}
\end{figure}
\subsection{Selection criteria}
During the experimental runs, the first-level trigger \cite{sndnim} selects
events with one or more tracks in tracking system and with two clusters in
calorimeter with the spatial angle between the clusters more than
$100^\circ$. The threshold on energy deposition in cluster was equal
to 25 MeV. The threshold on the total energy deposition in the calorimeter
was set equal to 140 MeV in the energy region $\sqrt{s}\ge 850$ MeV,
and to 100 MeV, or was absent at all, below 850 MeV.
During processing of the experimental data the event reconstruction is
performed \cite{sndnim,phi98}. For further analysis, events containing two
charged particles with $|z| < 10$ cm and $r < 1$ cm were selected. Here $z$
is the coordinate of the charged particle production point along the beam
axis (the longitudinal size of the interaction region depends on beam
energy and varies from 1.5 to 2.5 cm); $r$ is the distance between the
charged particle track and the beam axis in the $r-\phi$ plane.
The polar angles of the charged particles were bounded by the criterion:
$55^\circ<\theta<125^\circ$ and the energy deposition of each of them was
required to be greater than 50 MeV. The following cuts on the acollinearity
angles in the azimuthal and polar planes were applied:
$|\Delta\phi|<10^\circ$ and $|\Delta\theta|<10^\circ$. In the event sample
selected under these conditions one has the $e^+e^-\to e^+e^-$,
$\pi^+\pi^-$, $\mu^+\mu^-$ events, cosmic muons background and
a small contribution from the $e^+e^-\to\pi^+\pi^-\pi^0$ reaction at
$\sqrt{s}\simeq m_\omega$. The muon system $veto$ was
used for suppression of the cosmic muon background ($veto=0$).
\subsection{The background from the cosmic muons and from the
$e^+e^-\to\pi^+\pi^-\pi^0$ process.}
\begin{figure}
\epsfig{figure=pipimpi0.eps,width=15.0cm}
\caption{Two-photon invariant mass $m_{\gamma\gamma}$ distribution at
$\sqrt{s}\simeq m_\omega$.}
\label{mpi0}
\epsfig{figure=pipiz.eps,width=15.0cm}
\caption{The distribution of the $z$ coordinate of the charged particle
production point along the beam axis for collinear events at
$\sqrt{s}=180$ MeV. Histogram -- all events, dashed distribution
-- events with muon system $veto$ ($veto=1$).}
\label{actz}
\end{figure}
The number of background events from the $e^+e^-\to\pi^+\pi^-\pi^0$ process
was estimated in the following way:
\begin{eqnarray}
\label{bg}
N_{3\pi}({s}) = \sigma_{3\pi}({s}) \epsilon_{3\pi}({s}) IL({s}),
\end{eqnarray}
where $\sigma_{3\pi}({s})$ is the cross section of the
$e^+e^-\to\pi^+\pi^-\pi^0$ process with the radiative corrections taken
into account, $IL({s})$ is the integrated luminosity, $\epsilon_{3\pi}({s})$
is the detection probability for the background process obtained from the
simulation under the selection criteria described above. The values of
$\sigma_{3\pi}({s})$ were taken from the SND measurements \cite{pi3omeg}.
Although $\sigma_{3\pi}(m_\omega)\approx 1300$ nb, the $e^+e^-\to 3\pi$
process contribution to the total number of the collinear events at the
$\omega$ resonance peak is less than 0.3 \%.
The leading role in the suppression of this background was played by the cuts
on the acollinearity angles $\Delta\theta$ and $\Delta\phi$.
In order to check the estimation (\ref{bg}), the events containing two and
more photons with energy depositions more than 200 MeV were considered.
The constraint on the photons energy deposition greatly suppresses
not the $e^+e^-\to 3\pi$ events, as a result of the fact that our
selection criteria select the
$e^+e^-\to 3\pi$ events with collinear charged pions and therefore
the neutral pion in this events has relatively low energy.
In order to obtain $e^+e^-\to 3\pi$ events number $n_{3\pi}$,
the invariant mass spectrum $m_{\gamma\gamma}$ (Fig.\ref{mpi0}) was
fitted by the sum of Gaussian and the second order polynomial:
$G(m_{\gamma\gamma})\times n_{3\pi}+P_2(m_{\gamma\gamma})\times(n-n_{3\pi})$.
The value of $n_{3\pi}$ agrees with events number calculated according
to (\ref{bg}).
The cosmic muon background was suppressed by the muon/veto system.
The $z$ coordinate distribution for the charged particle production point
along the beam axis is shown in Fig.\ref{actz} for collinear events.
The $e^+e^-$ annihilation events have the Gaussian distribution peaked
at $z=0$, while the cosmic background distribution is nearly uniform
and clearly extends outside the peak. As the Fig.\ref{actz} shows, the
muon system $veto$ ($veto=1$) separates cosmic muons from the $e^+e^-$
annihilation events. The residual events number of the cosmic muon
background was estimated from the following formula:
\begin{eqnarray}
N_\mu=\nu_\mu \times T.
\end{eqnarray}
Here $\nu_\mu\simeq 1.3\times 10^{-3}$ Hz is the frequency of cosmic
background registration under the applied selection criteria,
$T$ is the time of data taking. The value of $\nu_\mu$ was obtained by using
data collected in special runs without beams in collider. The first-level
trigger counting rate in these runs was 2 Hz.
The contribution of the cosmic background to the total number of selected
collinear events depends on energy $\sqrt[]{s}$ and varies from 0.1 \%
to 1 \%.
The $e^+e^-\to\pi^+\pi^-\pi^0$ events are concentrated in the $R_{e/\pi}$
discrimination parameter region $R_{e/\pi}<0.5$. The cosmic background
events at the energies $\sqrt{s}>600$ also fall in the area $R_{e/\pi}<0.5$,
because the energy deposition of the cosmic muons is much lower
than the energy deposition in the $e^+e^-\to e^+e^-$ events. For the lower
center of mass energies the cosmic background moves to the area
$R_{e/\pi}>0.5$, because in this case the energy depositions are close.
\subsection{Detection efficiency}
The $\Delta\phi$ and $\Delta\theta$ distributions of the $e^+e^-\to e^+e^-$
and $e^+e^-\to\pi^+\pi^-$ events are shown in Fig.\ref{dphiee},\ref{dphipp},
\ref{dtetee} and \ref{dtetpp}. Experiment and simulation agree rather well.
As a measure of systematic uncertainty due to $\Delta\theta$ cut the
following value was used:
\begin{eqnarray}
\delta_{\Delta\theta} =
{\delta^{\pi\pi}_{\Delta\theta} \over \delta^{ee}_{\Delta\theta}},
\end{eqnarray}
where
$$
\delta^{x}_{\Delta\theta}=
{n_x(|\Delta\theta|<10^\circ)\over N_x(|\Delta\theta|<20^\circ)} \mbox{~} /
\mbox{~}
{m_x(|\Delta\theta|<10^\circ)\over M_x(|\Delta\theta|<20^\circ)}, \mbox{~~}
x=\pi\pi(ee).
$$
Here $n_x(|\Delta\theta|<10^\circ)$ and $m_x(|\Delta\theta|<10^\circ)$ are
the numbers of experimental and simulated events, selected under the
condition $|\Delta\theta|<10^\circ$, while $N_x(|\Delta\theta|<20^\circ)$ and
$M_x(|\Delta\theta|<20^\circ)$ are the numbers of experimental and simulated
events with $|\Delta\theta|<20^\circ$. The $\delta_{\Delta\theta}$ does not
depend on energy, its average value is equal to 0.999 and it has systematic
spread of 0.4 \%. This systematic
spread was added to the error of the cross section measurement in each
energy point. Systematic error due to the $\Delta\phi$ cut is significantly
lower and was neglected.
The polar angle distributions for the $e^+e^-\to e^+e^-$ and
$e^+e^-\to\pi^+\pi^-$ processes are shown in Fig.\ref{tetee} and
\ref{tetpp}. The ratio of these $\theta$ distributions
is shown in Fig.\ref{epcpab}.
The experimental and simulated distributions are in agreement. In order to
estimate the systematic inaccuracy due to the $\theta$ angle selection cut
the following ratio was used:
\begin{eqnarray}
\delta_\theta={\delta(\theta_x)\over\delta(55^\circ)},
\end{eqnarray}
where
$$
\delta(\theta_x)=
{N_{\pi\pi}(\theta_x<\theta<180^\circ-\theta_x) \over
N_{ee}(\theta_x<\theta<180^\circ-\theta_x)} /
{M_{\pi\pi}(\theta_x<\theta<180^\circ-\theta_x) \over
M_{ee}(\theta_x<\theta<180^\circ-\theta_x)}, \mbox{~~}
50^\circ<\theta_x<90^\circ.
$$
Here $N_{\pi\pi}(\theta_x<\theta<180^\circ-\theta_x)$,
$N_{ee}(\theta_x<\theta<180^\circ-\theta_x)$,
$M_{\pi\pi}(\theta_x<\theta<180^\circ-\theta_x)$,
$M_{ee}(\theta_x<\theta<180^\circ-\theta_x)$
are the experimental and simulated $e^+e^-\to\pi^+\pi^-$ and
$e^+e^-\to e^+e^-$ event numbers
in the angular range $\theta_x<\theta<180^\circ-\theta_x$.
The maximal difference of $\delta_\theta$ from unity was found to be 0.8\%.
This value was taken as a systematic error $\sigma_{\theta}=0.8$\%
associated with the angular selection cut.
\begin{figure}
\begin{center}
\epsfig{figure=pi2_dphi_ee.eps,width=15.0cm}
\caption{The $\Delta\phi$ distribution of the $e^+e^-\to e^+e^-$
events. Dots -- experiment, histogram -- simulation.}
\label{dphiee}
\epsfig{figure=pi2_dphi_pp.eps,width=15.0cm}
\caption{The $\Delta\phi$ distribution of the $e^+e^-\to\pi^+\pi^-$
events. Dots -- experiment, histogram -- simulation.}
\label{dphipp}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_dtet_ee.eps,width=15.0cm}
\caption{The $\Delta\theta$ distribution of the $e^+e^-\to e^+e^-$
events. Dots -- experiment, histogram -- simulation.}
\label{dtetee}
\epsfig{figure=pi2_dtet_pp.eps,width=15.0cm}
\caption{The $\Delta\theta$ distribution of the $e^+e^-\to\pi^+\pi^-$
events. Dots -- experiment, histogram -- simulation.}
\label{dtetpp}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_tet_ee.eps,width=15.0cm}
\caption{The $\theta$ angle distribution of the $e^+e^-\to e^+e^-$
events. Dots -- experiment, histogram -- simulation.}
\label{tetee}
\epsfig{figure=pi2_tet_pp.eps,width=15.0cm}
\caption{The $\theta$ angle distribution of the $e^+e^-\to\pi^+\pi^-$
events. Dots -- experiment, histogram -- simulation.}
\label{tetpp}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_e_pi_cpab.eps,width=15.0cm}
\caption{The ratio of $\theta$ distributions of the $e^+e^-\to\pi^+\pi^-$
and $e^+e^-\to e^+e^-$
processes. Dots -- experiment, histogram -- simulation.}
\label{epcpab}
\epsfig{figure=pi2_non_50.eps,width=15.0cm}
\caption{The $\delta_{E>50}$ correction coefficient associated to the pions
energy deposition
cut in dependence on the pion energy $E_\pi$.}
\label{non50}
\end{center}
\end{figure}
In the tracking system the particle track can be lost due to reconstruction
inefficiency. The probabilities to find the track was determined by
using experimental data themselves. It was found to be
$\varepsilon_{e}\simeq 0.996$ for electrons and
$\varepsilon_{\pi}\simeq 0.995$ for pions. In simulation these values
actually do not differ from unity, while in reality the track finding
probability for electrons is slightly greater then for pions. So the
detection efficiency was multiply by the correction coefficient:
\begin{eqnarray}
\delta_{rec} =
\Biggl[ {\varepsilon_{\pi} \over \varepsilon_{e}} \Biggr]^2 = 0,997
\end{eqnarray}
Pions can be lost due to the nuclear interaction in the detector
material before the tracking system, for example, via the reaction
$\pi^\pm N\to\pi^\pm N$ with the final pion scattered at the large angle
or via charge exchange reaction $\pi^\pm N\to\pi^0 N$.
As a measure of systematic inaccuracy associated to this effect the
difference from unity of the following quantity was used:
\begin{eqnarray}
\delta_{nucl} =
\Biggl[ \biggl(1 - {n \over 3N}\biggr) /
\biggl(1 - {m \over 3M}\biggr) \Biggr]^2,
\end{eqnarray}
where $N$ and $M$ is the pions numbers in experiment and simulation; $n$ and
$m$ is the pions numbers in experiment and simulation which had a track
in the drift chamber nearest to the beam-pipe, but the corresponding track
in the second drift chamber and associated cluster in the calorimeter were
not found. The particle loss probability
was divided by 3 -- the ratio of amounts of the matter
between the drift chambers and before the tracking system. The deviation of
$\delta_{nucl}$ from 1 was taken as a systematic error $\sigma_{nucl}=0.2$
\%.
Uncertainties in simulation of pions nuclear interactions imply that the cut
on the particles energy deposition leads to an inaccuracy in detection
efficiency of the $e^+e^-\to\pi^+\pi^-$ process. In order to take
into account this inaccuracy, the detection efficiency was multiplied by the
correction coefficients. The correction coefficients was obtained by using
events of the $e^+e^-\to\pi^+\pi^-\pi^0$ reaction
\cite{phi98,pi3omeg,dplphi98}. Pions energies in the
$e^+e^-\to\pi^+\pi^-\pi^0$ events were determined via the kinematic fit.
The pion energies were divided into the 10 MeV wide bins . For each
bin the correction coefficient (Fig.\ref{non50}) was obtained:
\begin{eqnarray}
\delta_{E>50} = \biggl[{ {n_i/N_i} \over {m_i/M_i} }\biggr]^2,
\end{eqnarray}
where $i$ is the bin number, $N_i$ and $M_i$ are the pions numbers in
experiment and simulation selected in the $i$th bin by the kinematic fit
without any cut on the energy deposition in the
calorimeter ; $n_i$ and $m_i$ are the pions numbers in
experiment and simulation under the condition that the pion energy
deposition is greater than 50 MeV. To estimate systematic errors in
determination of these correction coefficients, the ratio of the probability
that both pions in simulated $e^+e^-\to\pi^+\pi^-$ events have energy
deposition more than 50 MeV to the quantity $(m_i/M_i)^2$ was consider.
This ratio is 0.994 at
$\sqrt{s}>420$ MeV and about 0.97 at $\sqrt{s}<420$ MeV. The difference
of this ratio from unity was taken as a systematic error $\sigma_{E>50}$ of
the $\delta_{E>50}$ correction coefficient determination:
$\sigma_{E>50}=0.6$ \% at
$\sqrt{s}>420$ MeV and $\sigma_{E>50}=3$ \% at $\sqrt{s}<420$ MeV.
In the energy region $\sqrt{s} = 840$ -- $970$ MeV the probability to hit
the muon/veto system for muons and pions varies from 1\% upto 93\%, and
from 0.5\% to 3\% respectively. The usage of the muon system $veto$ for
events selection ($veto=0$) leads to inaccuracy in the measured cross section
determination due to the uncertainty in the simulation of the muons and pions
traversing through
the detector at $\sqrt{s}>840$ MeV. In order to obtain the necessary
corrections, the events close to the
median plane $\phi<10^\circ$, $170^\circ\phi<190^\circ$, $\phi>350^\circ$,
where the cosmic background is minimal, were used.
The $e^+e^-\to\pi^+\pi^-$ cross section was measured with ($veto=0$) and
without ($veto\ge 0$) using the muon system, and the following
correction coefficient was obtained for each energy point:
\begin{eqnarray}
\delta_{veto} ={ \sigma(e^+e^-\to\pi^+\pi^-;veto\ge 0) \over
\sigma(e^+e^-\to\pi^+\pi^-;veto = 0)}
\end{eqnarray}
It was found that $\delta_{veto}=0.95$ at $\sqrt{s}=970$ MeV and quickly
rises up to 1 for lower energies.
The detection efficiencies of the processes $e^+e^-\to\pi^+\pi^-$,
$\mu^+\mu^-$ and $e^+e^-$ after all applied corrections are shown in
Fig.\ref{eff_peak}. The detection efficiency of the $e^+e^-\to e^+e^-$
reaction does not depend on energy, while for $e^+e^-\to\mu^+\mu^-$ and
$\pi^+\pi^-$ processes it does. The decrease of the
$e^+e^-\to\mu^+\mu^-$ process detection efficiency at
$\sqrt{s}>800$ MeV is caused by the fact that
the probability for muons to hit the muon system
rises with energy. The detection efficiency of the
$e^+e^-\to\pi^+\pi^-$ process at $\sqrt{s}>500$ MeV is determined
mainly by the cuts on the pions angles. Below 500 MeV the detection
efficiency
decreases due to the cut on the pions energy deposition in the calorimeter.
The statistical error $\le 1\%$ of the detection efficiency determination
was added to the cross section measurement error in each energy point.
The total systematic error of the detection efficiency determination
$\sigma_{eff}=\sigma_{E>50}\oplus\sigma_{nucl}\oplus\sigma_{\theta}$
is $\sigma_{eff}=1$ \% at $\sqrt{s}\ge 420$ MeV and
$\sigma_{eff}=3.1$ \% at $\sqrt{s}<420$ MeV.
\begin{figure}
\begin{center}
\epsfig{figure=pi2_eff_peak.eps,width=15.0cm}
\caption{The detection efficiencies $\varepsilon_{\pi\pi}$,
$\varepsilon_{ee}$, $\varepsilon_{\mu\mu}$, of the
$e^+e^-\to\pi^+\pi^-, \mu^+\mu^-$ and
$e^+e^-$ processes.}
\label{eff_peak}
\end{center}
\end{figure}
\subsection{Measurement of the $e^+e^-\to\pi^+\pi^-$ cross section.}
The number of selected events in the regions $R_{e/\pi}<0.5$ and
$R_{e/\pi}>0.5$ are:
\begin{eqnarray}
N=N_{\pi\pi}+N_{ee}+N_{\mu\mu}+N_{\mu}+N_{3\pi},
\end{eqnarray}
\begin{eqnarray}
M=M_{\pi\pi}+M_{ee}+M_{\mu\mu}+M_{\mu}+M_{3\pi}.
\end{eqnarray}
Here $N$ and $M$ are the events numbers in the regions $R_{e/\pi}<0.5$ and
$R_{e/\pi}>0.5$ respectively. $N_{\mu}$, $M_{\mu}$ and $N_{3\pi}$,
$M_{3\pi}$ are the number of background events due to cosmic muons and the
$e^+e^-\to\pi^+\pi^-\pi^0$ process, calculated as was described above. The
$e^+e^-\to\mu^+\mu^-$ process events number can be written as:
\begin{eqnarray}
N_{\mu\mu}=\sigma_{\mu\mu}\times\varepsilon_{\mu\mu}\times
(1-\epsilon_{\mu\mu})\times IL,
\end{eqnarray}
\begin{eqnarray}
M_{\mu\mu}=\sigma_{\mu\mu}\times\varepsilon_{\mu\mu}\times
\epsilon_{\mu\mu}\times IL,
\end{eqnarray}
where $\sigma_{\mu\mu}$ is the $e^+e^-\to\mu^+\mu^-$ process
cross section obtained according to Ref.\cite{arbuzqed},
$\varepsilon_{\mu\mu}$ is the process detection efficiency,
$\epsilon_{\mu\mu}$ is the probability for the $e^+e^-\to\mu^+\mu^-$ process
events to have $R_{e/\pi}>0.5$.
$IL$ is the integrated luminosity:
\begin{eqnarray}
IL = {M_{ee} \over {\sigma_{ee }\times\varepsilon_{ee }\times
\epsilon_{ee }}},
\end{eqnarray}
where $\varepsilon_{ee }$ and $\epsilon_{ee }$ are the detection
efficiency and the probability to have $R_{e/\pi}>0.5$ for the process
$e^+e^-\to e^+e^-$, $\sigma_{ee }$ is the process cross section
with the $30^\circ<\theta<150^\circ$ angular cut for the electron and positron
in the final state. The cross section
$\sigma_{ee }$ was calculated by using BHWIDE 1.04 \cite{bhwide} code with
accuracy 0.5 \%. The $e^+e^-\to\pi^+\pi^-$ process events number
with $R_{e/\pi}>0.5$ and the $e^+e^-\to e^+e^-$ process events number with
$R_{e/\pi}<0.5$ can be written in the following way:
$$
N_{ee}={{1-\epsilon_{ee }} \over \epsilon_{ee }} \times M_{ee}
=\lambda_{ee} \times M_{ee}, \mbox{~~~}
M_{\pi\pi}= {{1-\epsilon_{ee }} \over \epsilon_{ee }}
\times N_{\pi\pi}
= \lambda_{\pi\pi}\times N_{\pi\pi}.
$$
The $e^+e^-\to e^+e^-$ process events number with $R_{e/\pi}>0.5$
and the $e^+e^-\to\pi^+\pi^-$ process events number with
$R_{e/\pi}<0.5$ are equal to:
\begin{eqnarray}
M_{ee}={{M-M_\mu-\lambda_{\pi\pi} \times (N-N_{\mu})} \over
{\kappa - \Delta \times \lambda_{\pi\pi}}},
\end{eqnarray}
\begin{eqnarray}
N_{\pi\pi}=N-N_{\mu}-M_{ee}\times \Delta.
\end{eqnarray}
Here
$$
\Delta = \lambda_{ee} +
{{\sigma_{\mu\mu}\times\varepsilon_{\mu\mu}\times
(1-\epsilon_{\mu\mu})+N_{3\pi}/IL} \over
{\sigma_{ee}\times\varepsilon_{ee}\times\epsilon_{ee}}},
$$
$$
\kappa = 1 +
{{\sigma_{\mu\mu}\times\varepsilon_{\mu\mu}\times
\epsilon_{\mu\mu}+M_{3\pi}/IL} \over
{\sigma_{ee}\times\varepsilon_{ee}\times\epsilon_{ee}}}.
$$
The percentage of each process in the selected events in dependence on
energy $\sqrt{s}$ is shown in Fig.\ref{doli}. The experimental angular
distributions agree with the sum of distributions for each process weighted
according to its contribution (Fig.\ref{tetbce2}).
The $e^+e^-\to\pi^+\pi^-$ process cross section is calculated
from the following formula:
\begin{eqnarray}
\sigma_{\pi\pi} = {N_{\pi\pi} \over
{IL \times\varepsilon_{\pi\pi}\times(1-\epsilon_{\pi\pi})}} =
{{\sigma_{ee}\times\varepsilon_{ee}\times\epsilon_{ee}}
\over
{\varepsilon_{\pi\pi}\times(1-\epsilon_{\pi\pi})}} \times
\Biggl[{ {\kappa-\Delta\times\lambda_{\pi\pi}} \over
{ { {M-M_{\mu}} \over {N-N_{\mu}} }-\lambda_{\pi\pi}} }-\Delta \Biggr].
\end{eqnarray}
In order to estimate the systematic uncertainty due to $e-\pi$
discrimination, the pseudo $\pi\pi$ and pseudo $ee$ events in the experiment
and simulation were formed. The pseudo $\pi\pi$ events were constructed by
using pions from the $e^+e^-\to\pi^+\pi^-\pi^0$ reaction.
In order to construct
the pseudo $\pi\pi$ event with the pions having energy $E_0$, two charged
pions with energies $E_\pi$ such that $|E_0-E_\pi|<10$ MeV were used from
two separate $e^+e^-\to\pi^+\pi^-\pi^0$ events.
Of course, such pseudo
$\pi\pi$ events are in general not collinear but this is irrelevant for our
purposes here.
The pseudo $ee$ event was constructed analogously from the particles of
two separate collinear events such that their partners in these events have
energy depositions in the calorimeter layers
typical for electrons. Fig.\ref{mlp_nce_nn} and \ref{mlp_nce_ee} show
probabilities for the discrimination parameter to have values
less than some magnitude in experiment and simulation for such pseudo events.
Using these distributions, the corrections to the probabilities for
the separation parameter $R_{e/\pi}$ to be greater or less than 0.5 was
obtained.
The difference between cross sections measured with and without
these corrections was taken as a systematic error and its
value does not exceed 0.5 \% for different energy points.
\begin{figure}
\begin{center}
\epsfig{figure=pi2_doli_peak.eps,width=15.0cm}
\caption{The percentage of the $e^+e^-\to e^+e^-,
\pi^+\pi^-,\mu^+\mu^-, \pi^+\pi^-\pi^0$ and
cosmic background events in dependence on energy $\sqrt{s}$}
\label{doli}
\epsfig{figure=pi2_tet_lt80.eps,width=15.0cm}
\caption{The $\theta$ angle distributions of all collinear events at
$\sqrt{s}$ from 880 MeV to 630 MeV.
Dots -- experiment, histogram -- simulation.}
\label{tetbce2}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_mlp_nce_nn.eps,width=15.0cm}
\caption{The probability of the pseudo $\pi\pi$ events to have $R_{e/\pi}$
value less than some $R_0$.
Dots -- experiment, histogram -- simulation.}
\label{mlp_nce_nn}
\epsfig{figure=pi2_mlp_nce_ee.eps,width=15.0cm}
\caption{The probability of the pseudo $ee$ events to have $R_{e/\pi}$
value greater than some $R_0$.
Dots -- experiment, histogram -- simulation.}
\label{mlp_nce_ee}
\end{center}
\end{figure}
\begin{table}
\begin{center}
\caption{The results of the $e^+e^-\to\pi^+\pi^-$ cross section measurements.
$\sigma_{\pi\pi}$ is the
$e^+e^-\to\pi^+\pi^-$ cross section taking into account the
radiative corrections due to the initial and final state radiation,
$\delta_{rad}$ is the radiative correction due to the initial and
final state radiation, $\sigma_0$ and
$|F_\pi|^2$ are the cross section and the form factor of the
$e^+e^-\to\pi^+\pi^-$ process after the radiative corrections were
undressed, $\sigma^{pol}_{\pi\pi}$ is the
$e^+e^-\to\pi^+\pi^-$ undressed cross section without vacuum
polarization but with the final state radiation.
Only uncorrelated errors are shown.
The correlated systematic error $\sigma_{sys}$ is 1.3 \% for
$\sqrt{s}\ge 420$ MeV and 3.2 \% for $\sqrt{s}< 420$ MeV.}
\label{tab1}
\begin{tabular}[t]{cccccc}
$\sqrt[]{s}$ (MeV)&$\sigma_{\pi\pi}$(nb) &
$\delta_{rad}$&$\sigma_0$ (nb)&$|F_\pi|^2$&
$\sigma^{pol}_{\pi\pi}$(nb) \\ \hline
970.& 118.12$\pm$ 2.76&1.491& 79.20$\pm$ 1.85& 3.91$\pm$ 0.09& 77.53$\pm$
1.81 \\
958.& 137.16$\pm$ 2.94&1.454& 94.34$\pm$ 2.02& 4.56$\pm$ 0.10& 92.16$\pm$
1.97 \\
950.& 150.02$\pm$ 2.85&1.430& 104.88$\pm$ 1.99& 4.99$\pm$ 0.09& 102.35$\pm$
1.94 \\
940.& 166.55$\pm$ 2.27&1.400& 119.00$\pm$ 1.62& 5.56$\pm$ 0.08& 116.01$\pm$
1.58 \\
920.& 204.99$\pm$ 7.14&1.340& 152.96$\pm$ 5.33& 6.89$\pm$ 0.24& 148.60$\pm$
5.18 \\
880.& 310.82$\pm$ 3.52&1.220& 254.67$\pm$ 2.88& 10.65$\pm$ 0.12& 245.94$\pm$
2.78 \\
840.& 513.80$\pm$ 4.76&1.106& 464.48$\pm$ 4.30& 17.99$\pm$ 0.17& 446.64$\pm$
4.13 \\
820.& 676.03$\pm$ 5.99&1.055& 640.60$\pm$ 5.68& 23.86$\pm$ 0.21& 614.57$\pm$
5.45 \\
810.& 760.19$\pm$ 6.58&1.032& 736.34$\pm$ 6.37& 26.90$\pm$ 0.23& 704.79$\pm$
6.10 \\
800.& 856.66$\pm$ 7.32&1.013& 845.61$\pm$ 7.23& 30.28$\pm$ 0.26& 807.33$\pm$
6.90 \\
794.& 890.86$\pm$ 7.43&1.009& 883.09$\pm$ 7.37& 31.25$\pm$ 0.26& 838.38$\pm$
7.00 \\
790.& 892.35$\pm$17.70&1.015& 879.09$\pm$17.44& 30.86$\pm$ 0.61& 829.16$\pm$
16.45 \\
786.& 926.47$\pm$ 7.84&1.031& 898.19$\pm$ 7.60& 31.28$\pm$ 0.26& 842.92$\pm$
7.13 \\
785.& 941.34$\pm$ 9.33&1.032& 911.99$\pm$ 9.04& 31.70$\pm$ 0.31& 858.12$\pm$
8.51 \\
784.& 989.76$\pm$20.12&1.025& 966.05$\pm$19.64& 33.51$\pm$ 0.68& 915.22$\pm$
18.61 \\
783.&1060.12$\pm$11.38&1.010&1050.08$\pm$11.27& 36.35$\pm$ 0.39& 1005.99$\pm$
10.80 \\
782.&1123.55$\pm$26.83&0.989&1136.34$\pm$27.14& 39.26$\pm$ 0.94& 1102.62$\pm$
26.33 \\
781.&1158.03$\pm$10.80&0.971&1192.83$\pm$11.12& 41.13$\pm$ 0.38& 1169.48$\pm$
10.90 \\
780.&1211.67$\pm$ 9.98&0.957&1266.56$\pm$10.43& 43.59$\pm$ 0.36& 1252.62$\pm$
10.32 \\
778.&1273.38$\pm$ 9.47&0.944&1349.27$\pm$10.03& 46.25$\pm$ 0.34& 1343.80$\pm$
9.99 \\
774.&1282.06$\pm$ 9.49&0.938&1366.85$\pm$10.12& 46.48$\pm$ 0.34& 1361.99$\pm$
10.08 \\
770.&1249.25$\pm$ 9.26&0.935&1336.51$\pm$ 9.91& 45.08$\pm$ 0.33& 1330.42$\pm$
9.86 \\
764.&1247.24$\pm$ 9.35&0.932&1338.62$\pm$10.04& 44.61$\pm$ 0.33& 1331.35$\pm$
9.99 \\
760.&1244.74$\pm$ 9.58&0.927&1342.60$\pm$10.33& 44.39$\pm$ 0.34& 1335.30$\pm$
10.27 \\
750.&1219.07$\pm$21.50&0.920&1325.56$\pm$23.38& 42.95$\pm$ 0.76& 1321.82$\pm$
23.31 \\
720.& 989.95$\pm$ 6.62&0.910&1087.59$\pm$ 7.27& 33.15$\pm$ 0.22& 1091.88$\pm$
7.30 \\
690.& 717.99$\pm$ 7.78&0.915& 784.79$\pm$ 8.50& 22.50$\pm$ 0.24& 789.95$\pm$
8.56 \\
660.& 515.95$\pm$ 5.87&0.923& 558.83$\pm$ 6.36& 15.07$\pm$ 0.17& 561.19$\pm$
6.39 \\
630.& 382.69$\pm$ 8.35&0.933& 410.32$\pm$ 8.95& 10.41$\pm$ 0.23& 411.22$\pm$
8.97 \\
600.& 287.18$\pm$10.56&0.940& 305.50$\pm$11.23& 7.30$\pm$ 0.27& 305.61$\pm$
11.23 \\
580.& 255.24$\pm$14.39&0.945& 270.24$\pm$15.24& 6.22$\pm$ 0.35& 269.85$\pm$
15.22 \\
560.& 226.60$\pm$12.41&0.948& 239.01$\pm$13.09& 5.30$\pm$ 0.29& 238.63$\pm$
13.07 \\
550.& 217.52$\pm$17.51&0.950& 228.99$\pm$18.43& 4.99$\pm$ 0.40& 228.29$\pm$
18.37 \\
540.& 212.67$\pm$13.55&0.952& 223.47$\pm$14.24& 4.78$\pm$ 0.30& 222.82$\pm$
14.20 \\
530.& 200.04$\pm$22.75&0.953& 210.00$\pm$23.88& 4.42$\pm$ 0.50& 209.43$\pm$
23.82 \\
520.& 178.13$\pm$10.25&0.954& 186.73$\pm$10.75& 3.87$\pm$ 0.22& 186.26$\pm$
10.72 \\
510.& 174.28$\pm$16.65&0.954& 182.60$\pm$17.45& 3.73$\pm$ 0.36& 181.82$\pm$
17.38 \\
500.& 175.22$\pm$10.78&0.955& 183.52$\pm$11.29& 3.70$\pm$ 0.23& 182.77$\pm$
11.24 \\
480.& 165.18$\pm$ 9.58&0.955& 172.90$\pm$10.03& 3.41$\pm$ 0.20& 172.29$\pm$
9.99 \\
470.& 143.94$\pm$13.21&0.955& 150.71$\pm$13.83& 2.94$\pm$ 0.27& 150.22$\pm$
13.78 \\
450.& 141.32$\pm$14.21&0.954& 148.10$\pm$14.89& 2.86$\pm$ 0.29& 147.42$\pm$
14.82 \\
440.& 116.15$\pm$15.58&0.953& 121.86$\pm$16.35& 2.35$\pm$ 0.32& 121.34$\pm$
16.28 \\
430.& 111.27$\pm$12.60&0.952& 116.86$\pm$13.23& 2.26$\pm$ 0.26& 116.41$\pm$
13.18 \\
410.& 127.38$\pm$19.11&0.949& 134.23$\pm$20.14& 2.64$\pm$ 0.40& 133.84$\pm$
20.08 \\
390.& 121.81$\pm$22.48&0.944& 128.98$\pm$23.80& 2.65$\pm$ 0.49& 128.76$\pm$
23.76 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}[ccch]
\begin{center}
\caption{Various contributions to the systematic error of the
$e^+e^-\to\pi^+\pi^-$
cross section determination. $\sigma_{sys}$ is the total systematic
error, $\sigma_{eff}=\sigma_{E>50}\oplus\sigma_{nucl}\oplus
\sigma_{\theta}$
is the systematic inaccuracy of the detection efficiency
determination.}
\label{tabcuc}
\begin{tabular}[t]{lcc}
Error&Contribution at $\sqrt[]{s}\ge 420$ MeV&Contribution at
$\sqrt[]{s}<420$ MeV \\ \hline
$\sigma_{E>50}$&0.6 \%&3.0 \% \\
$\sigma_{nucl}$&0.2 \%&0.2 \% \\
$\sigma_{\theta}$&0.8 \%&0.8 \% \\ \hline
$\sigma_{eff}$&1.0 \%&3.1 \% \\
$\sigma_{sep}$&0.5 \%&0.5 \% \\
$\sigma_{IL}$&0.5 \%&0.5 \% \\
$\sigma_{rad}$&0.2 \%&0.2 \% \\
\hline
$\sigma_{sys}$&1.3 \%&3.2 \% \\
\hline
\end{tabular}
\end{center}
\end{table}
The obtained cross sections together with the radiative corrections
$\delta_{rad}$, including the
initial and final state radiation, are presented in Table~\ref{tab1}.
The $\delta_{rad}$ radiative correction was calculated according to
Ref.\cite{arbuzhad}.
The accuracy of its determination is 0.2 \%. Having at hand the radiative
corrections the Born cross section for
the $e^+e^-\to\pi^+\pi^-$ process can be extracted as
follows
\begin{eqnarray}
\sigma_0(s) = {\sigma_{\pi\pi}(s) \over \delta_{rad}(s)}
\end{eqnarray}
The value of $\delta_{rad}(s)$ depends on the cross section at lower
energies, so it was calculated iteratively. The iteration stops then its
value changes by not more than 0.1 \% in consecutive iterations.
The form factor values
$$|F_\pi(s)|^2={{3s}\over{\pi\alpha^2\beta^3}}\sigma_{\pi\pi}(s),
\mbox{~~} \beta=\sqrt{1-4m_{\pi}^2/s}$$
are also listed in Table~\ref{tab1}. To evaluate the value of
$R(s)=\sigma(e^+e^-\to\mbox{hadrons})/\sigma(e^+e^-\to\mu^+\mu^-)$,
which is used in dispersion integrals calculation, the bare cross section
$e^+e^-\to\pi^+\pi^-$ is used (the cross section without vacuum polarization
contribution but taking into account the final state radiation):
\begin{eqnarray}
\sigma^{pol}_{\pi\pi}(s)=\sigma_0(s)\times |1-\Pi(s)|^2 \times
\biggl(1+{\alpha\over\pi}a(s)\biggr),
\end{eqnarray}
where $\Pi(s)$ is the polarization operator calculated according to the
Ref.\cite{arbuzqed} from the known $e^+e^-\to\mbox{hadrons}$ cross section
\cite{fedor}.
The last factor takes into account the final state radiation, and $a(s)$
has the form \cite{shw}
$$
a(s)={1+\beta^2 \over \beta}\biggl[
4Li_2\biggl({1-\beta \over 1+\beta}\biggr) +
2Li_2\biggl(-{1-\beta \over 1+\beta}\biggr)-
3\ln{2\over 1+\beta}\ln{1+\beta \over 1-\beta} -
2\ln{\beta}\ln{1+\beta \over 1-\beta} \biggr] -
$$
$$
- 3\ln{4\over 1-\beta^2} - 4\ln{\beta} +
{1\over\beta^3}\biggl[ {5\over 4}(1+\beta^2)^2-2 \biggr] \times
\ln{1+\beta \over 1-\beta} + {3\over 2}{1+\beta^2\over\beta^2}.
$$
Here
$$
Li_2(x) = -\int\limits^x_0 dt\ln(1-t)/t.
$$
The values of $\sigma^{pol}_{\pi\pi}(s)$ are listed in Table~\ref{tab1}.
The total systematic error of the cross section determination is:
$$
\sigma_{sys}=\sigma_{eff}\oplus\sigma_{sep}\oplus\sigma_{IL}
\oplus\sigma_{rad}.
$$
Here $\sigma_{eff}$ is the systematic error of the detection efficiency
determination,
$\sigma_{sep}$ is the systematic error associated with the $e-\pi$
separation,
$\sigma_{IL}$ is the systematic error of the integrated luminosity
determination, and $\sigma_{rad}$ is the uncertainty of the radiative
correction calculation.
The magnitudes of various contributions to the total systematic error are
shown in Table~\ref{tabcuc}. The total systematic error of the cross section
determinations is $\sigma_{sys}=1.3$ \% at $\sqrt{s}\ge 420$ MeV and
$\sigma_{sys}=3.2$ \% at $\sqrt{s}<420$ MeV.
\section{The $e^+e^-\to\pi^+\pi^-$ cross section analysis}
\subsection{Theoretical framework}
In the framework of the vector meson dominance model, the cross section
of the $e^+e^-\to\pi^+\pi^-$ process is
\begin{eqnarray}
\label{cspp}
\sigma_{\pi\pi}(s)={4\pi\alpha^2\over s^{3/2}} P_{\pi\pi}(s)|A_{\pi\pi}(s)|^2
\end{eqnarray}
Here $P_{\pi\pi}(s)$ is the phase space factor:
$$
P_{\pi\pi}(s)= q^3_{\pi}(s), \mbox{~~~} q_\pi(s)={1\over 2}\sqrt{s-4m^2_\pi}.
$$
Amplitudes of the $\gamma^\star \to \pi^+\pi^-$ transition have the form:
\begin{eqnarray}
\label{amp2p}
|A_{\pi\pi}(s)|^2 = \Biggl| \sqrt{3\over 2} {1\over\alpha}
\sum_{V=\rho,\omega,\rho^\prime,\rho^{\prime\prime}}
{ {\Gamma_V m_V^3 \mbox{~} \sqrt[]{m_V\sigma(V\to\pi^+\pi^-)}} \over
{D_V(s)} }
{ {e^{i\phi_{\rho V}} \over {\sqrt[]{q^3_{\pi}(m_V)}}} }\Biggr|^2,
\end{eqnarray}
where
$$D_V(s)=m_V^2-s-i\mbox{~}\sqrt[]{s}\Gamma_V(s), \mbox{~~~}
\Gamma_V(s)=\sum_{f}\Gamma(V\to f,s).$$
Here $f$ denotes the final state of the $V$ vector meson decay, $m_V$ is
the vector meson mass, $\Gamma_V=\Gamma_V(m_V)$. The following forms of the
energy dependence of the vector mesons total widths were used:
$$ \Gamma_\omega(s) = {m_\omega^2 \over s}{q^3_\pi(s) \over q^3_\pi(m_\omega)}
\Gamma_\omega B(\omega\to\pi^+\pi^-) +
{q^3_{\pi\gamma}(s) \over q^3_{\pi\gamma}(m_\omega)}
\Gamma_\omega B(\omega\to\pi^0\gamma) +
{W_{\rho\pi}(s) \over W_{\rho\pi}(m_\omega)}
\Gamma_\omega B(\omega\to 3\pi),
$$
$$
\Gamma_V(s)={m_V^2 \over s}{q^3_\pi(s) \over q^3_\pi(m_V)}\Gamma_V
\mbox{~~~} (V=\rho,\rho^\prime,\rho^{\prime\prime})
$$
Here $q_{\pi\gamma}=(s-m^2_\pi)/2\sqrt{s}$, $W_{\rho\pi}(s)$ is the phase
space factor for the $\rho\pi\to\pi^+\pi^-\pi^0$ final state
\cite{phi98,pi3omeg,dplphi98}. In the energy dependence of the
$\rho,\rho^\prime,\rho^{\prime\prime}$ mesons widths only the
$V\to\pi^+\pi^-$ decays were taken into account.
Such approach is justified in the energy region $\sqrt{s}<1000$ MeV.
Nowadays the $\rho^\prime,\rho^{\prime\prime}$ decays are rather poorly known
and therefore the same approximation was used also for
the fitting of the data above 1000 MeV.
The $\omega$-meson mass and width were taken from the SND measurements:
$m_{\omega}=782.79$ MeV, $\Gamma_{\omega}=8.68$ MeV \cite{pi3omeg}.
The relative decay probabilities were calculated as follows
$$B(V\to X)={\sigma(V\to X)\over\sigma(V)}, \mbox{~~}
\sigma(V)=\sum_{X} \sigma(V\to X), \mbox{~~}
\sigma(V\to X) = {{12\pi B(V\to e^+e^-)B(V\to X) } \over {m_V^2}}.$$
In the analysis presented here we have used $\sigma(\omega\to\pi^0\gamma)=
155.8$ nb,
$\sigma(\omega\to 3\pi)=1615$ nb obtained in the SND experiments
\cite{pi3omeg,pi0gam}.
The parameter $\phi_{\rho V}$ is the relative interference phase between the
vector mesons
$V$ and $\rho$, so $\phi_{\rho\rho}=0$.
The phases $\phi_{\rho V}$ can deviate from $180^\circ$ or $0^\circ$,
and their values can be energy dependent due to mixing between vector
mesons. The phases $\phi_{\rho\rho^\prime}$ and
$\phi_{\rho\rho^{\prime\prime}}$ were fixed at $180^\circ$ and $0^\circ$,
because these values are consistent with the existing experimental data
for the $e^+e^-\to\pi^+\pi^-$ reaction.
Taking into account the $\rho-\omega$ mixing, the $\omega\to\pi^+\pi^-$ and
$\rho\to\pi^+\pi^-$ transition amplitudes can be written in the following
way \cite{thrhoom,akozi}
\begin{eqnarray}
\label{rhoom}
A_{\omega\to\pi^+\pi^-} + A_{\rho\to\pi^+\pi^-} =
{ {g^{(0)}_{\gamma\rho}g^{(0)}_{\rho\pi\pi}} \over {D_{\rho}(s)} }
\biggl[1-{g^{(0)}_{\gamma\omega}\over g^{(0)}_{\gamma\rho}}\varepsilon(s)
\biggr]+
{{g^{(0)}_{\gamma\omega}g^{(0)}_{\rho\pi\pi}}\over{D_{\omega}(s)}}
\biggl[\varepsilon(s)+{g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}
\biggr],
\end{eqnarray}
where
$$\varepsilon(s) = {-\Pi_{\rho\omega} \over {D_\omega(s)-D_\rho(s)}},
\mbox{~~}
|g_{V\gamma}| = \Biggl[ {{3m_V^3\Gamma_VB(V \to e^+e^-)} \over
{4\pi\alpha}} \Biggr]^{1/2}, \mbox{~~}
|g_{V\pi\pi}| = \Biggl[{{6\pi m^2_V\Gamma_VB(V\to\pi^+\pi^-)} \over
q^3_\pi(m_V)} \Biggr]^{1/2}.$$
The superscript $(0)$ denotes the coupling constants of the bare, unmixed
state. $\Pi_{\rho\omega}$ is the polarization operator of the $\rho-\omega$
mixing:
\begin{eqnarray}
\Pi_{\rho\omega}(s) = \mbox{Re}(\Pi_{\rho\omega}(s)) +
i\mbox{~}\mbox{Im}(\Pi_{\rho\omega}(s)).
\end{eqnarray}
The $\mbox{Im}(\Pi_{\rho\omega}(s))$ can be written as
\begin{eqnarray}
\mbox{Im}(\Pi_{\rho\omega}(s))=\sqrt{s}\biggl\{
{g^{(0)}_{\rho\pi\pi}g^{(0)}_{\omega\pi\pi}q^3_\pi(s) \over {6\pi s}} +
{g^{(0)}_{\rho\pi\gamma}g^{(0)}_{\omega\pi\gamma}q^3_{\pi\gamma}(s) +
g^{(0)}_{\rho\eta\gamma}g^{(0)}_{\omega\eta\gamma}q^3_{\eta\gamma}(s)
\over 3},
\biggr\}
\end{eqnarray}
where
$$
g_{VP\gamma}=
\biggl[{3\Gamma_VB(V\to P\gamma)\over q^3_{P\gamma}(m_V)}\biggr]^{1/2}.
$$
We neglected the contributions to $\mbox{Im}(\Pi_{\rho\omega}(s))$ due to
$VP$ intermediate state ($V=\omega,\rho$,$P=\pi,\eta$).
The $\mbox{Re}(\Pi_{\rho\omega}(s))$ can be represented as
\begin{eqnarray}
\mbox{Re}(\Pi_{\rho\omega}(s)) = \mbox{Re}(\Pi^\gamma_{\rho\omega}(s)) +
\mbox{Re}(\Pi^\prime_{\rho\omega}(s)),
\end{eqnarray}
where
\begin{eqnarray}
\mbox{Re}(\Pi^\gamma_{\rho\omega}(s))=
{-4\pi g^{(0)}_{\rho\gamma}g^{(0)}_{\omega\gamma}\over s}
\end{eqnarray}
represents the one-photon contribution to the
$\mbox{Re}(\Pi_{\rho\omega}(s))$. Let us assume that the energy dependence
of the $\mbox{Re}(\Pi^\prime_{\rho\omega}(s))$ is negligible, then
it can be expressed by using the measured branching ratio
\begin{eqnarray}
B(\omega\to\pi^+\pi^-)={\Gamma_{\rho}(m_\omega)\over\Gamma_\omega}
\biggl| \varepsilon(m_\omega)+
{g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}
\biggr|^2
\end{eqnarray}
as follows
\begin{eqnarray}
\mbox{Re}(\Pi^\prime_{\rho\omega}) =
{4\pi g^{(0)}_{\rho\gamma}g^{(0)}_{\omega\gamma}\over m^2_\omega} +
{g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}(m^2_\omega-m^2_\rho) +
\nonumber \\
+ \sqrt{
{\Gamma_\omega B(\omega\to\pi^+\pi^-)\over\Gamma_{\rho}(m_\omega)}
\biggl|D_\omega(m_\omega)-D_\rho(m_\omega)\biggr|^2-
\biggl[{g^{(0)}_{\rho\pi\gamma}g^{(0)}_{\omega\pi\gamma}q^3_{\pi\gamma}
(m_\omega)+
g^{(0)}_{\rho\eta\gamma}g^{(0)}_{\omega\eta\gamma}q^3_{\eta\gamma}(m_\omega)
\over 3}+
{g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}m_\omega\Gamma_\omega
\biggr]^2}
\end{eqnarray}
Equation (\ref{rhoom}) can be rewritten as follows
\begin{eqnarray}
\label{amprhoom}
A_{\omega\to\pi^+\pi^-} + A_{\rho\to\pi^+\pi^-} =
\sqrt{3\over2} {1\over\alpha}
\sum_{V=\omega,\rho}
{ {\Gamma_V m_V^3 \mbox{~} \sqrt[]{m_V\sigma(V\to\pi^+\pi^-)} }
\over {D_V(s)} }
{ f_{V\pi\pi}(s)\over\sqrt[]{q_\pi(m_V)}},
\end{eqnarray}
where
$$f_{V\pi\pi}(s) = {r_{V\pi\pi}(s) \over r_{V\pi\pi}(m_V) }, \mbox{~~}$$
and
$$r_{\rho\pi\pi}(s) =
1-{g^{(0)}_{\gamma\omega}\over g^{(0)}_{\gamma\rho}}\varepsilon(s),
\mbox{~~} r_{\omega\pi\pi}(s)=\varepsilon(s)+
{g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}$$
The theoretical value of the phase $\phi_{\rho\omega}$ can be calculated from
the above given expressions:
$\phi_{\rho\omega}=\arg(f_{\omega\pi\pi}(m_\omega))-
\arg(f_{\rho\pi\pi}(m_\rho))\simeq 101^\circ$.
The phase $\phi_{\rho\omega}$ almost does not depend on energy. In this
calculation we assumed that the $\omega\to\pi^+\pi^-$ transition proceeds
only via the $\rho-\omega$ mixing, that is $g^{(0)}_{\omega\pi\pi}=0$. In
order to determine the $g^{(0)}_{\rho\pi\pi}$, $g^{(0)}_{\gamma V}$ and
$g^{(0)}_{VP\gamma}$ coupling constants, the corresponding measured decay
widths were used.
\subsection{Fit to the experimental data}
The $\rho^\prime$ and $\rho^{\prime\prime}$ parameters were determined from
the fit to the $e^+e^-\to\pi^+\pi^-$ cross section measured at
the energy region $\sqrt{s}<2400$ MeV by OLYA and DM2 detectors
\cite{olya,dm2}, together with the isovector part of the
$e^+e^-\to\pi^+\pi^-$ cross section calculated by assuming
the CVC hypothesis from the spectral function of the
$\tau^-\to\pi^-\pi^0\nu_\tau$ decay measured by CLEO II \cite{cleo2}:
\begin{eqnarray}
\sigma_{\pi\pi}(m_i)={4(\pi\alpha)^2\over m_i}
{B(\tau\to\pi\pi^0\nu_\tau)\over B(\tau\to e \overline{\nu}_e\nu_\tau)}
{m^8_\tau\over 12\pi |V_{ud}|^2}{1\over S_{EW}}
{1\over m_i(m^2_\tau-m^2_i)^2(m^2_\tau+2m^2_i)}
{1\over N} {N_i\over\Delta m_i},
\end{eqnarray}
where $m_i$ is the central value of the $\pi^-\pi^0$ pair invariant mass for
the $i$-th bin, $\Delta m_i$ is the bin width, $N_i$ is the number of
entries in the $i$-th bin, $N$ is the total number of entries, $|V_{ud}|$
is the CKM matrix element, $S_{EW}=1.0194$ is the radiative correction
\cite{aleph,cleo2,radtau}.
\begin{figure}
\begin{center}
\epsfig{figure=pi2_ce_snd.eps,width=15.0cm}
\caption{The $e^+e^-\to\pi^+\pi^-$ cross section.
Stars are the SND data obtained in this work, curve is the fit
result.}
\label{sndfit}
\end{center}
\end{figure}
The obtained $\rho^\prime$ and $\rho^{\prime\prime}$ parameters were used
in the fitting to the SND data (Table~\ref{tab5}, Fig.\ref{sndfit}).
The free parameters of the fit were $m_\rho$, $\Gamma_{\rho}$,
$\sigma(\rho\to\pi^+\pi^-)$, $\sigma(\omega\to\pi^+\pi^-)$,
$\phi_{\rho\omega}$ and $\sigma(\rho^\prime\to\pi^+\pi^-)$.
The first fit was performed with $\sigma(\rho^{\prime\prime}\to\pi^+\pi^-)$,
$\rho^\prime$ and $\rho^{\prime\prime}$ masses and widths fixed at the
values obtained from the fit to the CLEO II and DM2 data. The second and
third fits were done without the $\rho^{\prime\prime}$ meson. The
$\rho^\prime$ mass
and width were fixed by using results of the fit to the CLEO II and DM2 data
(the second variant in the Table~\ref{tab5}) and to the OLYA data (the third
variant in the
Table~\ref{tab5}). The values of the $\rho$ and $\omega$ parameters exhibit
a rather weak model dependence.
\begin{table}
\caption{Fit results. The column number $N$ corresponds to the different
variants of choice of the $\rho^\prime$ and $\rho^{\prime\prime}$
parameters.}
\label{tab5}
\begin{center}
\begin{tabular}[t]{llll}
N &1&2&3 \\ \hline
$m_\rho,$MeV&774.9$\pm$0.4&774.9$\pm$0.4&774.9$\pm$0.4 \\
$\Gamma_\rho,$MeV&146.2$\pm$0.8&146.4$\pm$0.8&146.3$\pm$0.8 \\
$\sigma(\rho\to\pi^+\pi^-),$ nb&1222$\pm$7&1218$\pm$7&1219$\pm$7 \\
$\sigma(\omega\to\pi^+\pi^-)$,nb&30.2$\pm$1.4&30.3$\pm$1.4&30.3$\pm$1.4 \\
$\phi_{\rho\omega}$, degree&113.6$\pm$1.3&113.4$\pm$1.3&113.5$\pm$1.3 \\
$m_{\rho^\prime}$, MeV&1403&1403&1360 \\
$\Gamma_{\rho^\prime}$, MeV&455&455&430 \\
$\sigma(\rho^\prime\to\pi^+\pi^-)$,nb&3.8$\pm$0.3&1.8$\pm$0.2&1.9$\pm$0.2 \\
$m_{\rho^{\prime\prime}}$, MeV&1756&&\\
$\Gamma_{\rho^{\prime\prime}}$, MeV&245&&\\
$\sigma(\rho^{\prime\prime}\to\pi^+\pi^-)$, nb&1.7&&\\
$\chi^2/N_{df}$&50.2/39&48.8/39&49.4/39 \\ \hline
\end{tabular}
\end{center}
\end{table}
\section{Discussion.}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_otn1.eps,width=15.0cm}
\caption{The ratio of the $e^+e^-\to\pi^+\pi^-$ cross section obtained
in different experiments to the fit curve (Fig.\ref{sndfit}).
The shaded area shows the systematic error of the SND measurements.
The SND (this work), CMD,OLYA and DM1 \cite{quen,olya} results are
presented.}
\label{otn1}
\epsfig{figure=pi2_otn2.eps,width=15.0cm}
\caption{The ratio of the $e^+e^-\to\pi^+\pi^-$ cross section obtained
in different experiments to the fit curve (Fig.\ref{sndfit}).
The shaded area shows the systematic error of the SND measurements.
The SND (this work), DM1, OSPK \cite{quen,bena} results are
presented.}
\label{otn2}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_otn3.eps,width=15.0cm}
\caption{The ratio of the $e^+e^-\to\pi^+\pi^-$ cross section obtained
in different experiments to the fit curve (Fig.\ref{sndfit}).
The shaded area shows the systematic error of the SND measurements.
The SND (this work), OLYA and CMD \cite{olya} results are presented.}
\label{otn3}
\epsfig{figure=pi2_otn4.eps,width=15.0cm}
\caption{The ratio of the $e^+e^-\to\pi^+\pi^-$ cross section obtained
in different experiments to the fit curve (Fig.\ref{sndfit}).
The shaded area shows the systematic error of the SND measurements.
The SND (this work), CMD2 and KLOE \cite{kloe,kmd2} results are
presented.}
\label{otn4}
\end{center}
\end{figure}
The comparison of the $e^+e^-\to\pi^+\pi^-$ cross section obtained in SND
experiment with other results \cite{bena,quen,olya,kmd2,kloe} is
shown in Fig.\ref{otn1},\ref{otn2},\ref{otn3}~and~\ref{otn4}. In the
energy region $\sqrt{s}<600$ MeV all experimental data are in agreement
(Fig.\ref{otn1}). Above 600 MeV the OSPK(ORSAY-ACO)\cite{bena} and DM1
\cite{quen} points lay about 10 \% lower than the SND ones (Fig.\ref{otn2}).
The SND cross section exceeds the OLYA and CMD measurements \cite{olya}
by $6\pm 1$ \% in this energy region (Fig.\ref{otn3}).
The systematic error of OLYA measurement is 4 \% and the OLYA data agree with
the SND result. The systematic uncertainty of CMD result is 2 \%, so the
difference between the SND and CMD results is about 2.5 of joint systematic
error. At the same time
the SND and CMD data below 600 MeV agree well (Fig.\ref{otn1}). The
average deviation between CMD2 \cite{kmd2} and SND data is
$1.4 \pm 0.5$ \%, the systematic inaccuracies of these measurements are
0.6 \% and 1.3 \% respectively. In the KLOE experiment at $\phi$-factory
DAF$\Phi$NE the form factor $|F_\pi(s)|^2$ was measured by using
``radiative return'' method with systematic error of 0.9 \% \cite{kloe}.
In Ref.\cite{kloe} the bare form factor is listed. So in order to compare
the KLOE result with the SND one, the form factor was appropriately dressed
by us. The results of this
comparison are shown in Fig.\ref{otn4}. The KLOE measurement is in conflict
with the SND result as well as with the CMD2 one.
The $\rho$-meson parameters $m_\rho$, $\Gamma_\rho$,
$\sigma(\rho\to\pi^+\pi^-)$ were determined from study of the
$e^+e^-\to\pi^+\pi^-$ cross section. The $\rho$ meson mass and width were
found to be
$$ m_\rho = 774.9 \pm 0.04 \pm 0.05 \mbox{~~MeV}, $$
$$\Gamma_\rho = 146.5 \pm 0.8 \pm 1.5 \mbox{~~MeV}.$$
The systematic errors is related to the accuracy of the collider energy
determination, to the model uncertainty and to the error of the cross
section determination. The $\rho$-meson parameters were studied in other
$e^+e^-$ experiments by
using the processes $e^+e^-\to\pi^+\pi^-$ \cite{kmd2,olya},
$e^+e^-\to\rho\pi\to\pi^+\pi^-\pi^0$ \cite{kloe3pi,dplphi98} and the
$\tau^-\to\pi^-\pi^0\nu_\tau$ decay \cite{cleo2,aleph}. The SND results
are in agreement with these measurements as is shown in
Fig.\ref{massa} and \ref{shira}.
The parameter $\sigma(\rho\to\pi^+\pi^-)$ was found to be
$$\sigma(\rho\to\pi^+\pi^-) = 1220 \pm 7 \pm 16 \mbox{~~nb},$$
which corresponds to
$$B(\rho\to e^+e^-)\times B(\rho\to\pi^+\pi^-)=
(4.991\pm 0.028\pm0.066)\times 10^{-5},$$
$$\Gamma(\rho\to e^+e^-)=7.31\pm 0.021\pm0.11 \mbox{~~keV}.$$
The systematic error includes the systematic uncertainties in the cross
section measurement and the model dependence.
A comparison of the $\Gamma(\rho\to e^+e^-)$ obtained in this work with
other experimental results \cite{kmd2,olya,bena} and with the PDG world
average \cite{pdg} is shown in Fig.\ref{poee}. The SND result exceeds all
previous measurements. It differs by about
1.5 standard deviations from the CMD2 measurement \cite{kmd2} and by 2
standard deviations
from the PDG world average \cite{pdg}. The difference of the $\rho$-meson
leptonic widths obtained by SND and CMD2 should be
attributed mainly to the difference in the total widths of the $\rho$-meson
rather then to the difference in the cross section values. The value
$\sigma(\rho\to\pi^+\pi^-)=1198$ nb, which can be obtained by using CMD2
cross section data
reported in Ref.\cite{kmd2}, agrees with the SND result within the
measurements errors.
The parameter $\sigma(\omega\to\pi^+\pi^-)$ was found to be
$$\sigma(\omega\to\pi^+\pi^-) = 29.9 \pm 1.2 \pm 1.0 \mbox{~~nb},$$
which corresponds to
$$B(\omega\to e^+e^-)\times B(\omega\to\pi^+\pi^-)=
(1.247\pm 0.062\pm0.042)\times 10^{-6}.$$
The systematic error is related to the model dependence, to the error of the
cross section determination and to the accuracy of the collider energy
determination.
In the previous studies of the $e^+e^-\to\pi^+\pi^-$ reaction the
relative probability of the $\omega\to\pi^+\pi^-$ decay was also reported.
The comparison of $B(\omega\to\pi^+\pi^-)=0.0175\pm 0.0011$ obtained by using
the SND data and the PDG value of the $\omega\to e^+e^-$ decay width
\cite{pdg} with the results of other experiments is shown in Fig.\ref{om2p}.
The SND result is the most precise.
\begin{figure}
\begin{center}
\epsfig{figure=pi2_mpo,width=15.0cm}
\caption{The $\rho$-meson mass $m_\rho$ measured in this work (SND-05)
and in Ref.\cite{kloe3pi,dplphi98,kmd2,cleo2,aleph,olya}.
The shaded area shows the average of the previous results.}
\label{massa}
\epsfig{figure=pi2_rpo,width=15.0cm}
\caption{The $\rho$ meson width $\Gamma_\rho$ measured in this work (SND-05)
and in Ref.\cite{kloe3pi,dplphi98,kmd2,cleo2,aleph,olya}.
The shaded area shows the average of the previous results.}
\label{shira}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\epsfig{figure=pi2_rpoee,width=15.0cm}
\caption{The value of $\Gamma(\rho\to e^+e^-)$ obtained in this work (SND-05)
and in Ref.\cite{kmd2,olya,bena}.
The shaded area shows the world average value \cite{pdg}.}
\label{poee}
\epsfig{figure=pi2_rom2p,width=15.0cm}
\caption{The value of $B(\omega\to\pi^+\pi^-)$ obtained in this work (SND-05)
and in Ref.\cite{kmd2,olya,quen,bena}.
The shaded area shows the world average value \cite{pdg}.}
\label{om2p}
\end{center}
\end{figure}
\begin{figure}
\epsfig{figure=pi2_fazapp,width=15.0cm}
\caption{The $\pi\pi$ scattering phase in the P-wave. Dots and circles are
results of the phase measurements in Ref. \cite{pwa1,pwa2} by using
the reaction $\pi N\to\pi\pi N$ . The curve is the phase
of the amplitude $A_{\rho\to\pi\pi}+A_{\rho\to\pi^+\pi^-}$ obtained
from the fit to the SND data presented in this work.}
\label{ppfaz}
\epsfig{figure=pi2_tau1,width=15.0cm}
\caption{The ratio of the $e^+e^-\to\pi^+\pi^-$ cross section calculated
from the $\tau^-\to\pi^-\pi^0\nu_{\tau}$ decay spectral function
measured in Ref.\cite{cleo2,aleph} to the isovector part of the
$e^+e^-\to\pi^+\pi^-$ cross section measured in this work
The shaded area shows the joint systematic error.}
\label{tau1}
\end{figure}
The phase $\phi_{\rho\omega}$ was found to be
$$\phi_{\rho\omega}=113.5 \pm 1.3 \pm 1.7 \mbox{~~degree}.$$
This value differs by 6 standard deviations from $101^\circ$ expected
under assumption that the $\omega\to\pi^+\pi^-$ transition proceeds through
the $\rho-\omega$ mixing mechanism. If instead of the phase
$\phi_{\rho\omega}$,
the ratio ${g^{(0)}_{\omega\pi\pi}/ g^{(0)}_{\rho\pi\pi}}$ is the free
parameter of the fit it follows that
$${g^{(0)}_{\omega\pi\pi}\over g^{(0)}_{\rho\pi\pi}}=0.11\pm 0.01.$$
This ratio corresponds to the too large direct transition width
$\Gamma^{(0)}(\omega\to\pi^+\pi^-)=1.82\pm 0.33$ MeV, while the natural
expectation is
$\Gamma^{(0)}(\omega\to\pi^+\pi^-)\approx\alpha^2\Gamma_\rho\approx 8$ keV.
Let us note, that the analysis of the OLYA and CMD2 data \cite{kmd2,olya}
give the similar values of the $\phi_{\rho\omega}$ phase. This result can
point out that the considerable direct transition $\omega\to\pi^+\pi^-$
exists. On the other hand this discrepancy can be attributed also to
inadequacies of the applied theoretical model.
The comparison of the phase
$\arg(A_{\rho\to\pi^+\pi^-}+A_{\rho^\prime\to\pi^+\pi^-})$ with the
$\pi\pi$ scattering phase in the P-wave \cite{pwa1,pwa2} is shown
in Fig.\ref{ppfaz}. These phases must be equal in the purely elastic
scattering region. The agreement is satisfactory, in any case in the
energy region $\sqrt{s}\approx m_\rho$ no essential difference is
observed.
The comparison of the $e^+e^-\to\pi^+\pi^-$ cross section, obtained
under the CVC hypothesis from the $\tau$ spectral function of the
$\tau^-\to\pi^-\pi^0\nu_{\tau}$ decay \cite{cleo2,aleph} with isovector
part of the cross section measured in this work is shown in Fig.\ref{tau1}.
The cross section obtained by SND was undressed from the vacuum polarization
and the contribution
from the $\omega\to\pi^+\pi^-$ decay was excluded. The cross section
calculated from the $\tau$ spectral function was multiplied by the
coefficient which takes into account the difference of the $\pi^\pm$ and
$\pi^0$ masses:
$$
\delta = \biggl({q_\pi(s) \over q_{\pi^\pm}(s)}\biggr)^3
{|A_{\pi^+\pi^-}(s)|^2 \over |A_{\pi^0\pi^\pm}(s)|^2}, \mbox{~~~}
q_{\pi^\pm}(s) = {1 \over 2\sqrt{s}}
\bigl[(s-(m_{\pi^0}+m_{\pi^\pm})^2)(s-(m_{\pi^0}-m_{\pi^\pm})^2)\bigr]^{1/2}.
$$
The average deviation of the SND and $\tau$ data is about 1.5 \%.
For almost all energy points this deviation is within the joint systematic
error $\simeq 1.6\%$. The 10\% difference between $e^+e^-$ and $\tau$ data
at $\sqrt{s}>800$ MeV, which was claimed in Ref.\cite{eetau}, is absent.
Using the $\sigma^{pol}_{\pi\pi}(s)$ cross section (Table~\ref{tab1}),
the contribution to the anomalous magnetic moment of the muon, due to the
$\pi^+\pi^-(\gamma)$ intermediate state in the vacuum polarization, was
calculated via the dispersion integral:
$$ a_\mu(\pi\pi, 390\mbox{MeV}\le\sqrt[]{s}\le 970\mbox{MeV})=
\biggl({\alpha m_\mu \over 3\pi} \biggr)^2 \int^{s_{max}}_{s_{min}}
{R(s)K(s) \over s^2} ds,
$$
where $s_{max}=970$ MeV, $s_{min}=390 MeV$, $K(s)$ is the known kernel and
$$
R(s) = {\sigma^{pol}_{\pi\pi} \over \sigma(e^+e^-\to\mu^+\mu^-)},
\mbox{~~} \sigma(e^+e^-\to\mu^+\mu^-) = {4 \pi \alpha^2 \over 3 s}.
$$
The integral was evaluated by using the trapezoidal rule. To take into
account the numerical integration errors, the correction method suggested
in Ref.\cite{aki} was applied. As a result we obtained
$$a_\mu(\pi\pi, 390\mbox{MeV}\le\sqrt[]{s}\le 970\mbox{MeV}) =
(488.7 \pm 2.6 \pm 6.6) \times 10^{-10}.$$
This is about 70 \% of the total hadronic contribution to the anomalous
magnetic moment of the muon $(g-2)/2$.
If the integration is performed for the energy region corresponding to the
CMD2 measurements \cite{kmd2}, then the result is
$a_\mu(\pi\pi)=(385.6\pm 5.2) \times 10^{-10}$, which is
1.8 \% (1 standard deviation) higher than the CMD2 result:
$a_\mu(\pi\pi)=(378,6\pm 3.5) \times 10^{-10}$. So no considerable
difference between the SND and CMD2 results is observed.
\section{Conclusion}
The cross section of the process $e^+e^-\to \pi^+\pi^-$ was measured in
the SND experiment at the VEPP-2M collider in the energy region
$390<\sqrt[]{s}<980$ MeV with accuracy 1.3 \% at $\sqrt{s}\ge 420$ MeV and
3.4 \% at $\sqrt{s}<420$ MeV. The measured cross section was analyzed in the
framework of the generalized vector meson dominance model.
The following $\rho$-meson parameters were obtained:
$m_\rho=774.9\pm 0.4\pm 0.5$ MeV,
$\Gamma_\rho=146.5 \pm 0.8 \pm 1.5$ MeV and
$\sigma(\rho\to\pi^+\pi^-)=1220\pm 7\pm 16$ nb. The
parameters of the $G$-parity suppressed process
$e^+e^-\to\omega\to\pi^+\pi^-$
were measured with high precision. The measured value
$\sigma(\omega\to\pi^+\pi^-)=29.9\pm 1.4\pm 1.0$ nb corresponds to
the relative probability $B(\omega\to\pi^+\pi^-) = 1.75 \pm 0.11 \%$.
The relative interference phase between the $\rho$ and $\omega$ mesons was
found to be $\phi_{\rho\omega} = 113.5\pm 1.3\pm 1.7$ degree. This
result is in conflict with the naive expectation from the $\rho-\omega$ mixing
$\phi_{\rho\omega} =101^\circ$.
The SND result agrees with the cross section calculated from the $\tau$
spectral function data within the accuracy of the measurements.
Using measured cross section, the contribution to the anomalous magnetic
moment of the muon due to the $\pi^+\pi^-(\gamma)$ intermediate state in the
vacuum polarization was calculated:
$a_\mu(\pi\pi, 390\mbox{MeV}\le\sqrt[]{s}\le 970\mbox{MeV}) =
(488.7 \pm 2.6 \pm 6.6) \times 10^{-10}.$
\acknowledgments
The authors are grateful to N.N.Achasov for useful discussions.
The work is supported in part by grants Sci.School-1335.2003.2,
RFBR 04-02-16181-a, 04-02-16184-a, 05-02-16250-a.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 856 |
Parallax View
May 2, 2013 · by Grain&Noise · in Reviews · Leave a comment
(Isn't this poster awesome!? A little Mad Men-esque right? I found it online but I don't think it's legitimate.)
The Parallax View (Dir. Alan J. Paukula, 1975)
"That's awful. I don't care what your politics are, this is America. You don't just shoot the president." – Trudy Campbell
"You've gotta feel it man, otherwise it's just a cold piece of wax." – Sam Cooke (as told by Herb Alpert)
Remember Occupy Wall Street? (How's that for an opening line? Raise your hand if you're immediately turned off!) Here was this grassroots uprising of young people, rightfully upset that in the richest, most democratic country in the world, one percent of the population controls half of the country's wealth. At a time when unemployment was high, and underemployment was even higher, Occupy was asking the question: "why is our country's wealth concentrated within a few households?". And do you remember that Occupy Wall Street was mocked, not just by the right and the wealthy, but by the very people on the left who were supposed champion economic justice? The whole ordeal made me realize that modern countries have no use for political assassinations. Our current political system uses something far more insidious, apathy. In Occupy's case, if you portray the people protesting against inequality as slackers, bums, and spoiled you make all the people in the middle indifferent. You drain the movement of its most necessary element, energy. After all, there are still assassination's elsewhere in the world, whether it's political massacres in the Philippines or the assassination of Benazir Bhutto. But here, for the most part, the gunshots have been replaced by sarcasm. There's no need to shoot the people who stand up if they can just as easily be convinced to sit down.
(Sorry for soap-boxing there, but I needed an opening and I couldn't think of any snappy personal anecdotes about political assassination)
But back in the 60's and early 70's, the opposition, whether it be right or left wasn't so cunning. This was an era of actual assassinations, John F. Kennedy, Robert Kennedy, Martin Luther King Jr., Malcom X, to name a few. It was a time when enemies of the status quo were murdered. That time period and tone are squarely where Alan J. Pakula's film The Parallax View begins. It starts with a brilliantly shot, brutally nonchalant, political assassination. The murder that opens the film is disturbing, not because you can see the sinister machinery running, precisely the opposite. There's no set up. No guy in a building across the street looking through a scope. It's just a political fundraiser at Seattle's Space Needle. A group of fundraisers having drinks. Suddenly, pop! Blood splatters against a glass window. Screams. Commotion. And through the chaos we can make out that a senator has been shot. The killer is then chased onto the top of the Space Needle where, after a fist fight, he falls to his death. But this was the 70's, so it's not a calculated, choreographed chase sequence. The chase happens slowly, people stumble, they lose their balance, and my heart was frozen until we finally cut away…
…to tell the story of Joseph Frady (Warren Beatty) a newspaper reporter who was present on the day of the assassination. Frady's the kind of no-nonsense, rable-rousing journalist that every great thriller needs. He wears denim. He doesn't tuck in his shirt. He puts his feet up on his desk. You get it.
Anyway, Frady realizes that everyone else who witnessed the assassination has died in bizarre "accidents". This realization inspires him to poke around. What follows is a film that's part investigative drama, part classical action film, and part Bourne-esque spy thriller. As Frady digs deeper into the senator's assassination, he uncovers a secret organization, the Parallax Corporation, that takes mentally disturbed people and trains them to perform political assassinations. Eventually Frady ends up infiltrating the organization and getting lost in their dark world.
The Parallax View pre-dates The Bourne series by what? Forty years, and it has the exact same secret organization of trained political killers. In fact, one of the most effective scenes comes when Frady is being tested for duty by the Parallax Corp. He's forced to sit through a disturbing re-education video. This film within a film evokes similar famous brainwashing scenes, A Clockwork Orange for one, and it made me wonder if forced propaganda would actually work? Granted actual propaganda, even in a place as crazy as North Korea, seems a lot more tame. Kim Jong Un watching soldiers do karate, or whatever.
Also, for an action/thriller The Parallax View shows a lot of restraint. Yes, there are set pieces, including a Dukes of Hazzard style car chase through a Northwestern logging town. I don't know why but the 70's loved car chases more than other decades? I guess the best explanation would be that Hollywood was in search of an urban equivalent to the western horse chase, so they replaced the horses with Pontiacs. Here's a list of TEN. There were so many car chases in the 70's that they reached the point of parody in The Blues Brothers, where an estimated 103 cars were destroyed during filming. And while The Parallax View does have a token car chase scene and some other larger scale set pieces (one at a Dam works pretty well), the film creates a lot more tension and is more effectively disconcerting when it trains the camera on small moments.
I'll give you a quick two examples. The first is a sequence where Frady needs to alert a stewardess that there's a bomb on their plane without calling attention to himself. He decides to write a note on a cocktail napkin and hope that when the stewardess hands it out, she notices. And Pakula makes us wait. She gives out one, two, three, four, five napkins with nothin and the whole time I was on the edge of my seat.
The second example comes near the end of the film. A senator's driving his golf cart through an enormous gymnasium that's been set up for a political banquet. A shot rings out and we cut wide. We watch as the politician slumps over, dead. The golf cart slowly runs off course. We see this huge shot with nothing but tables, chairs and his golf cart. The golf cart continues to creep forward, pushing aside the banquet tables and chairs in undramatic fashion. It's a haunting image. Again, the nonchalance. The complete absence of fanfare. Watching his golf cart slowly push aside tables is enough. No dramatic music. No dramatic techniques.
The other standout aspect of The Parallax View is the cinematography. It was shot by the incomparable (so incomparable that I'm willing to use a word as annoying as "incomparble") Gordon Willis. He's the guy who shot the entire Godfather trilogy, all the classic Woody Allen 70's films (including one of the most gorgeous films ever made, Manhattan), as well as all of the Pakula "Paranoia trilogy" (The Parallax View, Klute, and All the President's Men).
Willis was nicknamed by Conrad Hall "the Prince of Darkness" and that name holds true throughout the film. In fact Willis's contrast between light and shadow are so potent that I feel bogus trying to articulate them. Lots of films include breathtaking shots or sweetly lit scenes, but the photography of Gordon Willis, aside from establishing tone, is a pure reflection of the emotional dynamic within a scene. One night when Frady returns home after infiltrating Parallax Corp, there's a member of the corporation waiting for him The only thing visible in the scene is the glint of the member's shoe. His face and body are shrouded in darkness. We cut to Beatty under a dim light bulb and then back to darkness. Frady is having a conversation with the dark. He's powerless and scared and any other adjective you want to use. The man in the shadows has the power. Until Beatty starts to gain the upper hand… and then the lighting begins to creep even.
I highly recommend The Parallax View. It's not perfect. The middle drags. Frady's editor apparently never leaves his office and is inexplicably available to chat even in the middle of the night. But The Parallax View is worth seeing for the tone, the photography, the tension, and the ending. It's an ending that, much like The Candidate (which I reviewed a few months back), leaves you on a down, jaded note that perfectly captures the mood of the era. I won't give it away…just trust me.
Random notes:
– Warren Beatty is on the one hand a great artist who helped Robert Towne (responsible for an uncredited re-write of the The Parallax View) achieve success, directed Oscar winning movies, acted in a zillion classics (Mccabe and Mrs. Miller, Shampoo, Bonnie and Clyde, Dick Tracy, Reds, basically everything). But on the other hand he's a notorious horn dog. Jack Nicholson (no slouch) refers to him as "the pro" because of his films and his ability to seduce women. I guess it's not really hard to square Beatty's output and his putting out. Although it does add another element to his films. Scene by scene I find myself wondering how many of Beatty's co-stars woke up in his trailer before that day's shoot.
– I have a soft spot for Alan J. Pakula. There're a few films that I don't want to re-watch because the first viewing was so special that I'm afraid seeing them again might diminish the magic. One of those films is All The President's Men. I rented it from the library as a seventh grader (one of the few bright spots of seventh grade in between the gelled hair and baggy shirts). The movie was so intense that the memories still produce a gut reaction.
Tags: 1970s, Alan Pakula, assassination, bumpin' ugly, cars, Cinema, Film, Gordon Willis, Kennedy, Logs, Politics, suspense, the parallax view, warren beatty
← A Chance to Reflect
For Every Car, There Is Dirt → | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,381 |
The Founding Partners of The Powering Agriculture: An Energy Grand Challenge for Development (PAEGC) have announced the 21 Finalists chosen to advance to the next stage in the second global innovation call, that is Stage 3: Innovator Evaluation Board (IEB) interviews.
Funding type requested: 33% applied under Funding Window 2 to scale-up their clean energy solutions while 67% applied under Funding Window 1 on the design of their clean energy solution.
Innovator Evaluation Board (IEB) interviews have just concluded during which the 21 Finalists were asked questions on their clean energy solutions, proposed activities and implementation plans. PAEGC will notify and issue awards to top Finalist Applicants in September 2015. See the full list of finalists at the story below.
The Founding Partners of the Powering Agriculture: An Energy Grand Challenge for Development are pleased to announce that 21 Finalists have been selected to advance to the Stage 3: Innovator Evaluation Board (IEB) interviews.
Read more about Second Global Innovation Call Finalists Announced! | {
"redpajama_set_name": "RedPajamaC4"
} | 4,856 |
package org.springframework.security.web.context;
import java.io.IOException;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpServletResponseWrapper;
import org.springframework.security.core.context.SecurityContext;
import org.springframework.security.core.context.SecurityContextHolder;
/**
* Base class for response wrappers which encapsulate the logic for storing a security context and which
* store the with the <code>SecurityContext</code> when a <code>sendError()</code> or <code>sendRedirect</code>
* happens. See issue SEC-398.
* <p>
* Sub-classes should implement the {@link #saveContext(SecurityContext context)} method.
* <p>
* Support is also provided for disabling URL rewriting
*
* @author Luke Taylor
* @author Marten Algesten
* @since 3.0
*/
public abstract class SaveContextOnUpdateOrErrorResponseWrapper extends HttpServletResponseWrapper {
private boolean contextSaved = false;
/* See SEC-1052 */
private boolean disableUrlRewriting;
/**
* @param response the response to be wrapped
* @param disableUrlRewriting turns the URL encoding methods into null operations, preventing the use
* of URL rewriting to add the session identifier as a URL parameter.
*/
public SaveContextOnUpdateOrErrorResponseWrapper(HttpServletResponse response, boolean disableUrlRewriting) {
super(response);
this.disableUrlRewriting = disableUrlRewriting;
}
/**
* Implements the logic for storing the security context.
*
* @param context the <tt>SecurityContext</tt> instance to store
*/
protected abstract void saveContext(SecurityContext context);
/**
* Makes sure the session is updated before calling the
* superclass <code>sendError()</code>
*/
@Override
public final void sendError(int sc) throws IOException {
doSaveContext();
super.sendError(sc);
}
/**
* Makes sure the session is updated before calling the
* superclass <code>sendError()</code>
*/
@Override
public final void sendError(int sc, String msg) throws IOException {
doSaveContext();
super.sendError(sc, msg);
}
/**
* Makes sure the context is stored before calling the
* superclass <code>sendRedirect()</code>
*/
@Override
public final void sendRedirect(String location) throws IOException {
doSaveContext();
super.sendRedirect(location);
}
/**
* Calls <code>saveContext()</code> with the current contents of the <tt>SecurityContextHolder</tt>.
*/
private void doSaveContext() {
saveContext(SecurityContextHolder.getContext());
contextSaved = true;
}
@Override
public final String encodeRedirectUrl(String url) {
if (disableUrlRewriting) {
return url;
}
return super.encodeRedirectUrl(url);
}
@Override
public final String encodeRedirectURL(String url) {
if (disableUrlRewriting) {
return url;
}
return super.encodeRedirectURL(url);
}
@Override
public final String encodeUrl(String url) {
if (disableUrlRewriting) {
return url;
}
return super.encodeUrl(url);
}
@Override
public final String encodeURL(String url) {
if (disableUrlRewriting) {
return url;
}
return super.encodeURL(url);
}
/**
* Tells if the response wrapper has called <code>saveContext()</code> because of an error or redirect.
*/
public final boolean isContextSaved() {
return contextSaved;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,603 |
Q: Spring Boot https redirect I deployed a Spring Boot web application to AWS and configured SSL certificate for a domain. Every time I click a Login button mapped to:
@RequestMapping("/login")
public String login(){
return "login";
}
I'm redirected to https login page. However, when a user tries to access a page that requires authorization, he is redirected to unsecured http login page.
My Spring Security look like follows:
http
.authorizeRequests()
.antMatchers(HttpMethod.GET,"/","/css/**","/images/**","/js/**").permitAll()
.antMatchers("/").permitAll()
.antMatchers("/index").permitAll()
.antMatchers("/admin/**").hasRole("ADMIN")
.anyRequest().authenticated()
.and()
.formLogin()
.loginPage("/login")
.permitAll()
.and()
.logout()
.logoutUrl("/logout")
.deleteCookies("remember-me")
.logoutSuccessUrl("/login?logout")
.permitAll();
Here is live example: test4test.io
A: Assuming that connection is secure until it hits application, you will have to add following to security config to make all requests secure.
http.requiresChannel().anyRequest().requiresSecure();
If the tls is terminating at the load balancer(which may not be ideal but there are cases) then this may not work. In such circumstances, in aws alb/nlb, a listener can be added on port 80 which can redirect to port 443. This would not require any change in the application as the redirection happens from hte load balancer before the application gets the request.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,133 |
TelegramA: Telegram A Edition
========
My experimental version of Telegram based on open-source created by Stepan Korshakov
[Telegram S Edition Android App](https://github.com/ex3ndr/telegram)
[telegram-api](https://github.com/ex3ndr/telegram-api)
[mtproto](https://github.com/ex3ndr/telegram-mt)
[tl-core](https://github.com/ex3ndr/telegram-tl-core)
More information
----------------
####Telegram project
http://telegram.org/
#### Telegram api documentation
English: http://core.telegram.org/api
Russian: http://dev.stel.com/api
#### MTProto documentation
English: http://core.telegram.org/mtproto
Russian: http://dev.stel.com/mtproto
#### Type Language documentation
English: http://core.telegram.org/mtproto/TL
Russian: http://dev.stel.com/mtproto/TL
#### Telegram S Edition
[](https://play.google.com/store/apps/details?id=org.telegram.android "Telegram S")
Building project
------------
#### Build variants
There are multiple configurations of building app, some of them:
1. ````gradle assembleDevDebug```` - Development build for IDE, recomended for daily usage
2. ````gradle assembleCommonRelease```` - Release version for Google Play. Release versions need additional configuration for signing keys.
3. ````gradle assembleCommonDebuggable```` - Release version with debugging enabled for testing
4. ````gradle assembleBetaRelease```` - Builds [beta-version](https://play.google.com/store/apps/details?id=org.telegram.android.beta) of an app. Includes russian translations.
5. ````gradle assembleMdpiRelease```` - Release version for MDPI devices
6. ````gradle assembleHdpiRelease```` - Release version for HDPI devices
7. ````gradle assembleXhdpiRelease```` - Release version for XHDPI devices
8. ````gradle assembleXxhdpiRelease```` - Release version for XXHDPI devices
9. ````gradle dist```` - Building release distributive
#### Build from Sources
1. Checkout sources with all submodules
2. Select required build configuration and run required ````gradle```` command
#### Using from IDE
This sources are prepared for Android Studio.
License
----------------
Telegram A Edition uses [Apache v2 License](LICENSE) based on libraries that use [MIT Licence](LICENCE)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,795 |
Q: Environment Variables Not Loading Rails Hello I am having issues with getting environment variables working. I exported them onto the server doing this:
Export username=name password=password
And when I do Irb and type of the variable I get it back:
2.2.1 :001 > ENV["password"]
=> "password"
However I am getting this error in postgresql:
PG::ConnectionBad: FATAL: password authentication failed for user "ENV["username"]"
It seems my Environmental variables aren't loading into the system. This is my database.yml file:
production:
<<: *default
database: postgresql
username: ENV["username"]
password: ENV["password"]
When I put in the raw string it works perfectly. Any help would be awesome.
A: Yaml itself knows nothing about environment variables, however rails runs the file through erb before parsing the yaml and that's where you can do things like load environment variables.
You need to use erb tags ( <%= %> ) or else rails will use the literal ENV['password'] as the password, for example:
password: <%= ENV['password'] %>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,618 |
if [ -f "/root/.config/cherrymusic/cherrymusic.conf" ]; then
exec python3 /opt/cherrymusic/cherrymusic
else
exec python3 /opt/cherrymusic/cherrymusic --setup --port 8070
fi
fi
| {
"redpajama_set_name": "RedPajamaGithub"
} | 567 |
{"url":"https:\/\/metric2011.wordpress.com\/2011\/03\/10\/notes-of-stefan-wengers-lecture-nr-3\/","text":"## Notes of Stefan Wenger\u2019s lecture nr\u00a03\n\nToday, we show that isoperimetric inequalities pass to asymptotic cones (this requires the theory of currents in metric spaces). I intend to prove the proposition about Lipschitz disks with positive area, and use it to prove non exactly polynomial Dehn function for certain nilpotent groups.\n\n1. Currents in metric spaces\n\nStarted by Ambrosio and Kirchheim in 2000. Urs Lang, and indepedently Thierry de Pauw and Bob Hardt recently gave alternate versions.\n\nThe idea, going back to De Giorgi, is to replace differential forms with tuples of Lipschitz functions,\n\n$\\displaystyle \\begin{array}{rcl} f\\,d\\pi_1 \\wedge \\cdots \\wedge d\\pi_m \\leftrightarrow (f,\\pi_1 ,\\ldots,\\pi_m). \\end{array}$\n\n1.1. Definition\n\nDefinition 1 Let ${X}$ be a complete metric space. Let\n\n$\\displaystyle \\begin{array}{rcl} \\mathcal{D}^m (X):=Lip_b (X)\\times Lip(X)^m . \\end{array}$\n\nA function ${T:\\mathcal{D}^m (X)\\rightarrow{\\mathbb R}}$ is a metric ${m}$-current if\n\n1. Multilinearity: ${T}$ is multilinear.\n2. Continuity: If ${\\pi_i^n}$ converge pointwise to ${\\pi_i}$ with uniformly bounded Lipschitz constants, then ${T(f,\\pi_1^n ,\\ldots,\\pi_m^n)}$ converges to ${T(f,\\pi_1 ,\\ldots,\\pi_m)}$.\n3. Locality: If some ${\\pi}$ is constant on the support of ${f}$, then ${T(f,\\pi_1 ,\\ldots,\\pi_m)=0}$.\n4. Finite mass: There exists a Borel measure ${\\mu}$, concentrated on a ${\\sigma}$-compact set, such that, on ${\\mathcal{D}^m}$,\n\n$\\displaystyle \\begin{array}{rcl} |(T(f,\\pi_1 ,\\ldots,\\pi_m)|\\leq\\prod_{i}Lip(\\pi_i)\\int_{X}|f|\\,d\\mu. \\end{array}$\n\nWe denote by ${M_m (X)}$ the space of metric ${m}$-currents.\n\nRemark 1\n\n\u2022 Locality forces ${T(f,\\pi_1 ,\\ldots,\\pi_m)}$ to depend on ${d\\pi_i}$ rather than on ${\\pi_i}$ itself.\n\u2022 Continuity axiom is stronger than in Euclidean geometric measure theory. For instance, the evaluation of a differential form at a ${m}$-covector at some point is a current in the sense of Federer and Fleming, but it does not satisfy our continuity axiom (test on\n\u2022 Finite mass implies that ${T}$ continuously extends to bounded functions ${\\times Lip(X)^m}$.\n\nProposition 2 Let ${T\\in M_m (X)}$. Denote by ${\\Lambda}$ the collection of measures ${\\mu}$ as in axiom (4). Define, for a Borel set ${B\\subset X}$,\n\n$\\displaystyle \\begin{array}{rcl} \\|T\\|(B)=\\inf\\{\\sum_{i}\\mu_i (B_i)\\,;\\, (\\mu_i) \\textrm{sequence in }\\Lambda,\\,B=\\coprod_i B_i\\}. \\end{array}$\n\nThis is a finite Borel measure, and\n\n$\\displaystyle \\begin{array}{rcl} |T(f,\\pi_1 ,\\ldots,\\pi_m)|\\leq \\prod_{i=1}^m Lip(\\pi_i)\\,\\int_{X}f\\,d\\mu. \\end{array}$\n\nMoreover\n\n$\\displaystyle \\begin{array}{rcl} \\|T\\|(B)=\\sup\\{\\sum_{n}|T(\\chi_n ,\\pi_1^n ,\\ldots,\\pi_m^n)|\\;\\,B=\\coprod_i B_i,\\,Lip(\\pi_i^n)\\leq 1\\}. \\end{array}$\n\nRemark 2 In Federer and Fleming\u2019s theory,\n\n$\\displaystyle \\begin{array}{rcl} \\|T\\|({\\mathbb R}^n)=\\sup\\{|T(\\omega)|\\,;\\,\\|\\omega\\|_{\\infty}\\leq 1\\}. \\end{array}$\n\nDefinition 3 The measure ${\\|T\\|}$, as well as its total mass ${M(T)=\\|T\\|(X)}$, are called the mass of current ${T}$.\n\nCorollary 4 Mass is lower semi-continuous with respect to weak convergence, i.e. if\n\n$\\displaystyle \\begin{array}{rcl} \\lim_{n\\rightarrow\\infty}T_n (f,\\pi_1 ,\\ldots,\\pi_m)=T(f,\\pi_1 ,\\ldots,\\pi_m) \\end{array}$\n\nfor all ${(f,\\pi_1 ,\\ldots,\\pi_m)\\in\\mathcal{D}^m (X)}$, then\n\n$\\displaystyle \\begin{array}{rcl} M(T)\\leq \\liminf M(T_n). \\end{array}$\n\n1.2. Constructions\n\n\\subsubsection{Boundary operator}\n\nFor ${T\\in M_m (X)}$, m${\\geq 1}$, define\n\n$\\displaystyle \\begin{array}{rcl} (\\partial T)(f,\\pi_1 ,\\ldots,\\pi_{m-1})=T(1,f,\\pi_1 ,\\ldots,\\pi_{m-1}). \\end{array}$\n\nThen ${T}$ satisfies axioms (1) to (3). Say that ${T}$ is a normal current if ${\\partial T}$ has finite mass, i.e. is again a current. Notation\n\n$\\displaystyle \\begin{array}{rcl} N_m (X)=\\{T\\in M_m (X)\\,;\\,\\partial T\\in M_{m-1}(X)\\}. \\end{array}$\n\nRemark 3 This fits with the classical definition. Furthermore, by locality, ${\\partial\\partial=0}$.\n\n\\subsubsection{Push forward}\n\nIf ${\\phi:X\\rightarrow Y}$ is Lipschitz, ${T\\in M_m (X)}$, define\n\n$\\displaystyle \\begin{array}{rcl} (\\phi_{\\#}T)(f,\\pi_1 ,\\ldots,\\pi_{m})=T(f\\circ\\phi,\\pi_1 \\circ\\phi,\\ldots,\\pi_{m}\\circ\\phi). \\end{array}$\n\nThen ${\\phi_{\\#}T\\in M_m (Y)}$ and, as positive measures,\n\n$\\displaystyle \\begin{array}{rcl} \\|\\phi_{\\#}T\\|\\leq Lip(\\phi)^m \\phi_{\\#}\\|T\\|. \\end{array}$\n\n\\subsubsection{Multiplication with Borel functions}\n\nLet ${g}$ be a bounded Borel function on ${X}$. Define\n\n$\\displaystyle \\begin{array}{rcl} (T \\llcorner g)(f,\\pi_1 ,\\ldots,\\pi_{m})=T(gf,\\pi_1 ,\\ldots,\\pi_{m}). \\end{array}$\n\nThen ${T \\llcorner g\\in M_m (X)}$. In particular, if ${U}$ is a Borel set, the restriction of ${T}$ to ${U}$ is ${T\\llcorner 1_U}$.\n\n\\subsubsection{Standard example}\n\nLet ${\\Theta\\in L^1 ({\\mathbb R}^n)}$. Define\n\n$\\displaystyle \\begin{array}{rcl} [\\Theta](f,\\pi_1 ,\\ldots,\\pi_{m})=\\int_{{\\mathbb R}^n}\\Theta fdet(\\nabla\\pi_1 ,\\ldots,\\nabla\\pi_{m}). \\end{array}$\n\nThen ${[\\Theta]\\in M_m ({\\mathbb R}^n)}$.\n\nRemark 4\n\n\u2022 Only continuity is non trivial.\n\u2022 For ${f}$ and ${\\pi}$ smooth, ${[\\Theta](f,\\pi_1 ,\\ldots,\\pi_{m})=\\int_{{\\mathbb R}^n}\\Theta f\\,d\\pi_1 ,\\ldots,d\\pi_{m}}$.\n\u2022 If ${\\Theta}$ has bounded variation, then ${[\\Theta]}$ is a normal current, and ${\\|\\partial[\\Theta]\\|=|D\\Theta|}$ in the notation of ${BV}$ theory.\n\n1.3. Compactness theorem\n\nTheorem 5 Let ${X}$ be a compact metric space, ${T_n}$ a sequence of normal currents with\n\n$\\displaystyle \\begin{array}{rcl} \\sup_{n}M(T_n)+M(\\partial T_n) <\\infty. \\end{array}$\n\nThen there is a subsequence which weakly converges to a normal current.\n\n1.4. Integral currents\n\nDefinition 6 A ${0}$-dimensional current ${T\\in M_0 (X)}$ is called integral rectifiable if there exist points ${x_i \\in X}$ and non zero integers ${m_i}$ such that on Lipschitz functions ${f}$,\n\n$\\displaystyle \\begin{array}{rcl} T(f)=\\sum_{i}m_i f(x_i). \\end{array}$\n\nIf ${m\\geq 1}$, a current ${T\\in M_m (X)}$ is called integral rectifiable if\n\n1. ${\\|T\\|}$ is concentrated on a countably rectifiable set, i.e. a countable disjoint union of biLipschitz images of subsets in ${{\\mathbb R}^n}$, and ${\\|T\\|}$ vanishes on sets of vanishing ${m}$-dimensional Hausdorff measure.\n2. For every open ${U\\subset X}$ and Lipschitz ${\\phi:U\\rightarrow{\\mathbb R}^m}$, there exists an integer valued function ${\\Theta\\in L^1 ({\\mathbb R}^m)}$ such that\n\n$\\displaystyle \\begin{array}{rcl} \\phi_{\\#}(T\\llcorner 1_{U})=[\\Theta]. \\end{array}$\n\nWe denote by ${\\mathcal{I}_m (X)}$ the space of integral rectifiable ${m}$-currents.\n\nTheorem 7 (Representation theorem). Let ${T}$ be an integral rectifiable ${m}$-current. Then there exist subsets ${K_i \\subset {\\mathbb R}^m}$, biLipschitz maps ${\\psi_i : K_i \\rightarrow X}$ and integer valued ${L^1}$ functions ${\\Theta_i}$ on ${K_i}$ such that\n\n$\\displaystyle \\begin{array}{rcl} T=\\sum_{i}\\psi_{\\#}[\\Theta_i], \\end{array}$\n\nand\n\n$\\displaystyle \\begin{array}{rcl} M(T)=\\sum_{i}M(\\psi_{\\#}[\\Theta_i]). \\end{array}$\n\nDefinition 8 An integral current is a normal current which is integral rectifiable. The space of integral ${m}$-currents is denoted by ${\\mathbb{I}_{m}(X)}$.\n\nNote that ${\\partial\\mathbb{I}_{m}(X)\\subset \\mathbb{I}_{m-1}(X)}$. A ${m}$-cycle is an integral ${m}$-current ${T}$ with ${\\partial T=0}$.\n\n1.5. Slicing\n\nLet ${T}$ be a normal current and ${\\phi:X\\rightarrow{\\mathbb R}}$ a Lipschitz function. The slices of ${T}$ with respect to ${u}$ are the currents\n\n$\\displaystyle \\begin{array}{rcl} \\langle T,u,r \\rangle=\\partial(T\\llcorner1_{\\{u\\leq r\\}})-(\\partial T)\\llcorner 1_{\\{u\\leq r\\}}. \\end{array}$\n\nIn some sense, this is the restriction of ${T}$ to the level set ${\\{u=r\\}}$.\n\nTheorem 9 (Slicing Theorem). For almost every ${r}$,\n\n\u2022 ${\\langle T,u,r \\rangle}$ is a normal ${m-1}$-current, with its mass concentrated on ${\\mathrm{support}(\\|T\\|)\\cap\\{u=r\\}}$.\n\u2022 ${M(\\langle T,u,r \\rangle)\\leq Lip(u)\\frac{d}{dr}\\|T\\|(\\{u\\leq r\\})}$.\n\u2022 If ${T}$ is an integral current, so is almost every ${\\langle T,u,r \\rangle}$.\n\nProof: Think of coarea formula\n\n$\\displaystyle \\begin{array}{rcl} \\int_{{\\mathbb R}}\\mathcal{H}^{m-1}(\\{u=r\\})\\,dr=\\int_{{\\mathbb R}^n}|\\nabla u| . \\end{array}$\n\n$\\Box$\n\n1.6. Closure Theorem\n\nTheorem 10 If ${T_m}$ is a weakly converging sequence of integral currents with uniformly bounded ${M(T_n)+M(\\partial T_n)}$, then the limiting normal current is again an integral current.\n\nThis allows to solve Plateau\u2019s problem in the class of integral currents.\n\n2. Isoperimetric inequalities and asymptotic cones\n\nUp to now, we insisted on filling cruves with disks. We need compactness, and for this we shall replace disks with currents. Since currents do not have prescribed topology, one may view the filling function for currents as a homological version of the disk filling function.\n\n2.1. Homological filling function\n\nDefinition 11 For ${T\\in\\mathbb{I}_{1}(X)}$, define\n\n$\\displaystyle \\begin{array}{rcl} Fillarea^{Y}(T)=\\inf\\{M(S)\\,;\\,S\\in\\mathbb{I}_{2}(Y),\\,\\partial S=T\\}. \\end{array}$\n\nA Lipschitz curve ${c:[0,1]\\rightarrow X}$ defines an integral current ${c_{\\#}1_{[0,1]}}$, again denote by ${c}$, whose mass is the length of ${c}$, and we define\n\n$\\displaystyle \\begin{array}{rcl} FA_{X,Y}=\\sup\\{Fillarea^{Y}(c)\\,;\\,c \\textrm{ closed curve }, \\mathrm{length}(c)\\leq r\\}. \\end{array}$\n\nA priori, ${FA^{X,Y}\\leq \\mathrm{const.}\\,FA_0^{X,Y}}$, with ${const.=1}$ for Riemannian manifolds, but only ${const.\\leq\\sqrt{2}}$ in general, since the mass of integral ${2}$-currents is not exactly equal to area.\n\nTheorem 12 (Wenger 2010) Let ${X}$ be a geodesic metric space, let ${Y}$ be a geodesic thickening pf ${X}$. If\n\n$\\displaystyle \\begin{array}{rcl} FA^{X,Y}(r)\\preceq r^2 , \\end{array}$\n\nthen there exists ${C}$ such that for every asymptotic cone ${X_{\\omega}}$ of ${X}$, and for all ${r\\geq 0}$,\n\n$\\displaystyle \\begin{array}{rcl} FA^{X_{\\omega}}(r)\\leq C\\,r^2. \\end{array}$\n\nRemark 5 Since every integral ${1}$-current ${T}$ with ${\\partial T=0}$ is a countable sum of curves, quadratic filling for curves implies a quadrating filling inequality for all integral cycles.\n\nCorollary 13 Let ${\\Gamma}$ be a finitely presented group with quadratic Dehn function. Then every asymptotic cone ${\\Gamma_{\\omega}}$ has quadratic filling for ${1}$-cycles.\n\nPanos Papasoglu shows that quadratic Dehn function implies that ${\\Gamma_{\\omega}}$ is simply connected. Does quadratic Dehn function imply that ${FA_0^{\\Gamma_{\\omega}}}$ is quadratic ?\n\n3. Completion of proofs\n\n3.1. Proof of the proposition about cones of non hyperbolic spaces\n\nProposition 14 (Wenger 2008) Let ${X}$ be a geodesic metric space, ${Y}$ a geodesic thickening with quadratic filling. If ${X}$ is not hyperbolic, there exists an asymptotic cone ${X_{\\omega}}$ of ${X}$, a compact set ${K\\subset {\\mathbb R}^2}$ and a Lipschitz map ${\\psi:K \\rightarrow X_{\\omega}}$ such that ${\\psi(K)}$ has positive ${2}$-dimensional Hausdorff measure.\n\nProof: of Proposition from Theorem 12.\n\nLet ${X_{\\omega}}$ be an asymptotic cone which is not a tree. Then there is a closed Lipschitz curve ${c}$ in ${X_{\\omega}}$ such that the corresponding current is not identically zero. Take for ${c}$ a constant speed parametrization of a geodesic triangle ${xyz}$ such that ${[x,y]}$ is not included in ${[y,z]\\cup[z,x]}$. Let ${\\pi}$ denote distance to ${x}$ and ${f}$ the maximum of ${0}$ and ${1-\\frac{1}{\\epsilon}d(\\cdot,[x,y])}$. For ${\\epsilon}$ small enough,\n\n$\\displaystyle \\begin{array}{rcl} c(f,\\pi)=\\int_{0}^{1}f\\circ c(t) (\\pi\\circ c)'(t)\\,dt\\not=0. \\end{array}$\n\nTheorem 12 gives an integral current ${S}$ filling ${c}$. Then ${S\\not=0}$. According to the Representation Theorem 7, ${S=\\sum_{i}\\psi_{\\#}[\\Theta_i]}$, ${M(T)=\\sum_{i}M(\\psi_{\\#}[\\Theta_i])>0}$, so there is ${i}$ such that ${M(\\psi_{\\#}[\\Theta_i])>0}$. $\\Box$\n\n3.2. Preparation for the proof of Theorem \\ref\n\n}\n\nIn order to apply the Compactness Theorem 5, we must arrange a sequence of fillings in ${X}$ to sit in a fixed compact metric space. For this, thanks to Gromov\u2019s compactness criterion for metric spaces (in the Gromov-Hausdorff distance), it suffices to control the size of nets on fillings. For this, one constructs fillings which leave a definite fraction of their mass in balls.\n\nProposition 15 (Ambrosio, Kirchheim) Let ${Y}$ be a metric space. Assume that ${Y}$ has a quadratic filling inequality for ${\\mathbb{I}_1 (Y)}$. Let ${T\\in \\mathbb{I}_1 (Y)}$ be a cycle and ${\\epsilon>0}$. There is ${S\\in\\mathbb{I}_2 (Y)}$ with ${\\partial S=T}$ such that\n\n1. ${M(S)\\leq\\min\\{C\\,M(T)^2 ,(1+\\epsilon)Fillarea^{Y}(T)\\}}$.\n2. For each ${y\\in \\mathrm{support}(\\|S\\|)}$ and all ${r\\in [0,d(x,\\mathrm{support}(\\|T\\|)}$,\n\n$\\displaystyle \\begin{array}{rcl} \\|S\\|(B(x,r))\\geq \\frac{1}{4C}r^2 . \\end{array}$\n\nProof: Assume first there exists a mass minimizing ${S}$ with ${\\partial S=T}$. Let ${g(r)=\\|S\\|(B(x,r))}$ and ${d_x}$, the distance function to ${x}$. For almost every ${r}$,\n\n$\\displaystyle \\begin{array}{rcl} \\langle S,d_x ,r \\rangle=\\partial(S\\llcorner 1_{B(x,r)})\\in \\mathbb{I}_1 (Y). \\end{array}$\n\nBy minimality,\n\n$\\displaystyle \\begin{array}{rcl} g(r)&=&\\|S\\|(B(x,r))\\|\\\\ &=&M(S\\llcorner 1_{B(x,r)})\\\\ &\\leq& C\\,M(\\langle S,d_x ,r \\rangle)^2 \\\\ &\\leq&C\\,(\\frac{d}{dr}\\|S\\|(B(x,r)))^2 \\\\ &=&C\\,g'(r)^2 . \\end{array}$\n\nIntegrate this differential inequality to get ${g(r)\\geq\\frac{1}{C}r^2}$.\n\nIn general, consider the set ${Z}$ of integral ${2}$-currents filling ${T}$ with mass ${\\leq L}$. For every ${\\delta\\in(0,1)}$, there exists in ${Z}$ an ${S}$ such that for all ${S'\\in Z}$,\n\n$\\displaystyle \\begin{array}{rcl} M_{\\delta}(S):=M(S)+\\delta M(S'-S)\\geq M(S). \\end{array}$\n\nThis is a very general fact which follows from completeness (and not compactness) of ${Z}$ (known as Bishop-Phelps, or Ekeland variational principle).\n\nFor every competitor ${R}$,\n\n$\\displaystyle \\begin{array}{rcl} M(S)=M_{\\delta}(S)&\\leq& M_{\\delta}(S\\llcorner B(x,r)^{c}+R)\\\\ &\\leq&\\|S\\|(B(x,r)^c )+M(R)+\\delta \\|S\\|(B(x,r))+\\delta M(R). \\end{array}$\n\n$\\displaystyle \\begin{array}{rcl} \\|S\\|(B(x,r))&\\leq&\\frac{1+\\delta}{1-\\delta}M(R)\\\\ &\\leq&\\frac{1+\\delta}{1-\\delta}C\\,M(\\langle S,d_x ,r \\rangle)^2 , \\end{array}$\n\nand the proof ends as before. $\\Box$\n\n3.3. Sketch of the proof of Theorem \\ref\n\n}\n\nWe assume that ${X}$ has quadratic filling, and show that asymptotic cones do as well. Step 1. Show that there exists a geodesic thickening ${Y}$ of ${X}$ which has ${Fillarea^{Y}(r)\\leq C\\, r^2}$ for all ${r}$. For this, cover ${X}$ with balls which sufficiently overlap, then replace them by their injective hulls.\n\nStep 2. Let ${c}$ be a Lipschitz loop in an asymptotic cone ${X_{\\omega}}$. Pick a partition ${(t_i)}$ of ${[0,1]}$. Show that there exists a Lipschitz loop ${c'}$, with ${c(t_i)=c'(t_i)}$, with shorter lengths between successive ${t_i}$\u2018s, and an integral ${2}$-current ${S}$ filling ${c'}$, with ${M(S)\\leq C\\,\\mathrm{length}(c)^2}$. This suffices, since holes between ${c}$ and ${c'}$ can be inductively filled, achieving a convergent series of currents whose sum fills ${c}$.\n\nTo construct ${S}$, let ${x^i =c(t_i)}$, view ${x^i}$ as a sequence ${(x_n^i)\\in \\hat{X}}$. Complete ${x_n^1 ,\\ldots,x_n^m}$ into a geodesic polygon ${c_n :[0,1]\\rightarrow X_n =(X,\\frac{1}{n}d)}$. Use Proposition 15. Since ${c_n}$ are uniformly Lipschitz, they can be filled with integral ${2}$-currents ${S_n \\in \\mathbb{I}_2 (Y,\\frac{1}{n}d)}$ in such a way that\n\n\u2022 ${\\partial S_n =c_n}$.\n\u2022 ${M(S_n)\\leq C\\,\\mathrm{length}(c_n)^2}$.\n\u2022 ${\\|S_n\\|(B(x,r))\\geq \\frac{1}{4C}r^2}$ for all ${x\\in\\mathrm{support}(S_n)}$, ${r\\leq d(x,c_n)}$.\n\nThe sequence of metric spaces ${A_n =(\\mathrm{support}(S_n),\\frac{1}{n}d)}$ is uniformly compact, since we have upper bounds for the size of ${\\epsilon}$-nets on it for all ${\\epsilon>0}$. Gromov\u2019s compactness theorem implies that all these spaces simultaneously embed isometrically into a fixed compact metric space. Apply the compactness theorem 5 in that space to extract a subsequence such that\n\n\u2022 ${A_n}$ converge in Gromov-Hausdorff sense to a compact metric space ${A}$.\n\u2022 The curves ${c_n}$ converge to a curve ${c''}$ in ${A}$.\n\u2022 The currents ${S_n}$ converge to an integral ${2}$-current ${S}$ in ${A}$.\n\u2022 The (inverse) isometric embeddings ${\\psi_n : A_n \\rightarrow X_n}$ converge to an isometric embedding ${\\psi:A'\\rightarrow X_{\\omega}}$.\n\nThen ${\\partial S=c''}$ in ${A}$, ${\\partial\\psi_{\\#}(S)=\\psi_{\\#}(c'')=c'}$ in ${X_{\\omega}}$ and\n\n$\\displaystyle \\begin{array}{rcl} M(\\psi_{\\#}(S))&=&M(S)\\\\ &\\leq& \\liminf_{n\\rightarrow\\infty}M(S_n)\\\\ &\\leq&C\\,\\liminf_{n\\rightarrow\\infty}\\mathrm{length}(c_n)^2\\\\ &=&C\\,\\mathrm{length}(c')^2 . \\end{array}$\n\n4. Carnot groups with non exactly polynomial Dehn function\n\nTheorem 16 (Wenger 2010) Let ${G}$ be a ${2}$-step nilpotent Lie group with Lie algebra graded as ${\\mathfrak{g}=V_1 \\oplus V_2}$. Assume that there exists ${u\\in V_2}$ which is not a bracket ${u=[v,w]}$ for any vectors ${v}$, ${w\\in V_1}$. Consider the Lie group ${H}$ with Lie algebra ${\\mathfrak{h}=V_1 \\oplus (V_2 \/\\langle u \\rangle)}$. Endow ${H}$ with a left-invariant Riemannian metric. Then\n\n$\\displaystyle \\begin{array}{rcl} \\lim_{r\\rightarrow \\infty}\\frac{FA^{H}(r)}{r^2}=+\\infty. \\end{array}$\n\nRemark 6 If ${\\mathrm{dim}(V_2)\\geq 2\\,\\mathrm{dim}(V_1)}$, then there exists ${u}$ satisfying the assumption in Theorem 16.\n\n4.2. Application to central products\n\nLet ${G}$ be a ${2}$-step nilpotent Lie group with Lie algebra graded as ${\\mathfrak{g}=V_1 \\oplus V_2}$. Given ${m\\geq 2}$, let ${H=G\\times_{Z}\\cdots\\times_{Z}G}$ denote the Carnot group with Lie algebra\n\n$\\displaystyle \\begin{array}{rcl} \\mathfrak{g}'=(V_1^1 \\oplus \\cdots \\oplus V_1^m) \\oplus V_2 \\end{array}$\n\nwith Lie bracket ${[(v_1 ,\\ldots, v_n),(w_1 ,\\ldots, w_n)]=\\sum_{i=1}^{m}[v_i ,w_i]}$. This will be called the ${m}$-fold central product of ${G}$.\n\nExample 1 If ${G=H^1}$ is the first Heisenberg group, ${G\\times_{Z}\\cdots\\times_{Z}G =H^m}$ is the ${m}$-th Heisenberg group.\n\nCorollary 17 Let ${G'}$ be a ${2}$-step Carnot group with Lie algebra ${\\mathfrak{g}'=V_1 \\oplus V_2}$. Suppose ${m\\geq 2}$ and there exists ${u'\\in V_2}$ which cannot be written\n\n$\\displaystyle \\begin{array}{rcl} u'=\\sum_{i=1}^{m}[v_i ,w_i]. \\end{array}$\n\nLet ${H'}$ be the Lie group with Lie algebra ${\\mathfrak{h}=V_1 \\oplus (V_2 \/\\langle u' \\rangle)}$ and ${H}$ the ${m}$-fold central product of ${H}$. Then\n\n$\\displaystyle \\begin{array}{rcl} \\lim_{r\\rightarrow \\infty}\\frac{FA^{H}(r)}{r^2}=+\\infty. \\end{array}$\n\nProof: The central product ${H=H'\\times_Z H'}$ can be viewed as ${G\/\\exp(u')}$ where ${G=G'\\times_Z \\cdots \\times_Z G'}$. So Theorem 16 applies provided ${u'}$ is not a bracket in ${\\mathfrak{g}}$, i.e. ${u'}$ is not a sum of ${m}$ brackets in ${\\mathfrak{g}'}$. $\\Box$\n\nExample 2 Start with the free ${2}$-step nilpotent Lie algebra with ${\\mathrm{dim}(V_1)=2k}$. Set ${u=e_1 \\wedge e_2 +\\cdots+e_{2k-1}\\wedge e_{2k}}$. Then ${u}$ is not a sum of ${m}$ bracket of two vectors if ${m.\n\nIndeed, as an alternating bilinear form, its rank is ${2k}$, whereas a sum of ${m}$ brackets has rank at most ${2m}$.\n\nTheorem 18 (Olshanskii, Sapir, Young) Let ${H}$ be a ${2}$-step Carnot group containing a lattice. Then its ${m}$-fold central product, ${m\\geq 2}$, has\n\n$\\displaystyle \\begin{array}{rcl} FA_{0}^{H}(r)\\preceq r^2 \\log r . \\end{array}$\n\nIf furthermore ${H}$ is free ${2}$-step nilpotent, then\n\n$\\displaystyle \\begin{array}{rcl} FA_{0}^{H}(r)\\sim r^2 . \\end{array}$\n\nCorollary 19 There exists a ${2}$-step Carnot group ${H}$ such that\n\n$\\displaystyle \\begin{array}{rcl} FA_{0}^{H}(r)\\preceq r^2 \\log r . \\end{array}$\n\nbut ${FA_{0}^{H}(r)}$ is not ${\\leq O(r^2)}$.\n\n4.3. Preparation for the proof of Theorem \\ref\n\n}\n\nA Carnot group has Lie algebra graded as ${\\mathfrak{g}=V_1 \\oplus \\cdots \\oplus V_k}$. The map ${\\delta_r :\\mathfrak{g}\\rightarrow\\mathfrak{g}}$ defined by\n\n$\\displaystyle \\begin{array}{rcl} \\delta_r (v_1 +\\cdots v_k)=\\sum_{i=1}^{k}r^i v_i \\end{array}$\n\nis an automorphism. It integrates into a group automorphism.\n\nThe Carnot-Carath\u00e9odory metric ${d_c}$ is the left-invariant geodesic metric obtained by minimizing length of curves tangent to the distribution of left-translates of ${V_1}$. It is homogeneous of degree ${1}$ under ${\\delta_r}$.\n\nIt follows that every asymptotic cone of ${G}$ is biLipschitz to ${(G,d_c)}$. In fact (Pansu 1983), the asymptotic cone is unique.\n\n4.4. Proof of the lower bound on Dehn function\n\nLet ${G}$ be a ${2}$-step Carnot group, let be ${H}$ the group with Lie algebra ${\\mathfrak{h}=V_1 \\oplus (V_2 \/\\langle u \\rangle)}$. We show that the second homology of the asymptotic cone ${(H,d_c)}$ does not vanish.\n\nClaim: There are Lipschitz loops ${c}$ which do not bound any integral current in ${H}$.\n\nTo construct ${c}$, merely pick a Lipschitz horizontal curve in ${G}$ joining the origin to ${\\exp(u)}$, and project it to ${H}$. Assume that there exists an integral ${2}$-current ${S}$ in ${H}$ such that ${\\partial S=c}$. By the representation theorem 7,\n\n$\\displaystyle \\begin{array}{rcl} S=\\sum_{i}(\\psi_i)_{\\#}[\\Theta_i] \\end{array}$\n\nwhere ${\\psi_i :K_i \\rightarrow (H,d_c)}$ is Lipschitz, ${K_i \\in{\\mathbb R}^2}$, ${\\Theta_i \\in L^1 (K_i)}$.\n\nNote that projection along ${V_2}$ defines a Lipschitz map ${\\eta:H\\rightarrow V_1}$. ${\\eta_{\\#}S}$ is an integral current in Euclidean ${V_1}$ filling ${c_1 :=\\eta(c)}$. Let ${Q}$ be a linear functional on ${{\\mathbb R}}$ which does not vanish on ${u}$. Then ${Q}$ defines a ${1}$-form on ${V_1}$ as follows:\n\n$\\displaystyle \\begin{array}{rcl} \\alpha(x)(v)=Q([x,v]). \\end{array}$\n\nThen\n\n$\\displaystyle \\begin{array}{rcl} d\\alpha(v,w)=Q([v,w]), \\end{array}$\n\n$\\displaystyle \\begin{array}{rcl} 0\\not= Q(u)&=&c_1 (\\alpha)\\\\ &=&(\\partial\\eta_{\\#}S)(\\alpha)\\\\ &=&(\\eta_{\\#}S)(d\\alpha)\\\\ &=&\\sum_{i}(\\eta\\circ\\psi_i)_{\\#}[\\Theta_i](d\\alpha)\\\\ &=&\\sum_{i}\\int_{K_i}[d(\\eta\\circ\\psi_i)(e_1),d(\\eta\\circ\\psi_i)(e_2)] \\end{array}$\n\nwhere ${(e_1 ,e_2)}$ is the canonical basis of ${{\\mathbb R}^2}$.\n\nLet us show that ${[d(\\eta\\circ\\psi_i)(e_1),d(\\eta\\circ\\psi_i)(e_2)]=0}$ for all ${i}$ and almost everywhere on ${K_i}$. At almost every point of ${K_i}$, all Lipschitz maps ${\\psi_i}$ are differentiable. The differential ${d^P \\psi}$ is a group homomorphism ${{\\mathbb R}^2 \\rightarrow H}$. The image of the corresponding Lie algebra homomorphism is an abelian subspace in ${\\mathfrak{h}}$. Its image by ${d^P \\eta}$ is an subspace of ${V_1}$ on which the ${\\mathfrak{h}}$-bracket vanishes, i.e. the ${\\mathfrak{g}}$-bracket is colinear to ${u}$. Since we assumed that ${u}$ is not a bracket of ${2}$ vectors from ${V_1}$, the ${\\mathfrak{g}}$-bracket vanishes on the image of ${d(\\eta\\circ\\psi_i)}$. So ${[d(\\eta\\circ\\psi_i)(e_1),d(\\eta\\circ\\psi_i)(e_2)]=0}$.","date":"2017-09-22 04:11:17","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\": 0, \"img_math\": 403, \"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\": 0.9894754886627197, \"perplexity\": 406.9762737875504}, \"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-2017-39\/segments\/1505818688208.1\/warc\/CC-MAIN-20170922041015-20170922061015-00050.warc.gz\"}"} | null | null |
Q: Simulating multiple-inheritance in Scala I am working on a project that basically requires multiple-inheritance in the formal sense:
class X
class Y
class XY extends X,Y
I have two classes which have some definitions and are used throughout code, i.e:
def alpha(x: X)
def beta(y: Y)
I want to dynamically create a class XY which is just merges all definitions from X and Y but still retains the type-safety. More specifically that the previously defined alpha and beta still accept this merged class.
I know that Scala allows mixing in traits, for example:
trait T
class A
val ta = new A with T
That works fine.
However, I cannot do it with classes:
class X
class Y
val xy = new X with Y
As the with .. must be a trait.
I have tried circumventing this by doing the following:
trait xV extends X
trait yV extends Y
val xy = new xV with yV
Unfortunately this does not work and gives the following error:
Error:(33, 26) illegal inheritance; superclass X
is not a subclass of the superclass Y
of the mixin trait yV
val xy = new xV with yV
Any help would be appreciated.
Edit:
To clarify, I cannot modify classes X or Y.
A: Scala does not have the multiple inheritance C++ style, in order to avoid the dreaded Diamond Shape inheritance pattern.
The (only) solution provided by Scala is to provide mixins in the form of Traits. To resolve method implementation conflicts, the last Trait implemented (the one the most to the right) is chosen.
So unless, at least one of X or Y is a Trait, A will not be able to inherit (methods) from both
A: Doing this literally is impossible. But
More specifically that the previously defined alpha and beta still accept this merged class.
This specific requirement can be achieved by using implicit conversions:
class XY {
val x = new X
val y = new Y
}
object XY {
implicit def toX(xy: XY): X = xy.x
implicit def toY(xy: XY): Y = xy.y
}
You'll also be able to call X's and Y's methods directly.
But e.g. xy match { case x: X => ... won't match, and similarly xy.isInstanceOf[X] will be false. If X or Y override any of the Object methods: equals, hashCode, or toString, they won't be inherited by XY.
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# Cover
# Title Page
# Copyright Page
© 2017 by Shawn Smucker
Published by Revell
a division of Baker Publishing Group
P.O. Box 6287, Grand Rapids, MI 49516-6287
www.revellbooks.com
Ebook edition created 2017
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—for example, electronic, photocopy, recording—without the prior written permission of the publisher. The only exception is brief quotations in printed reviews.
Library of Congress Cataloging-in-Publication Data is on file at the Library of Congress, Washington, DC.
ISBN 978-1-4934-1107-8
Unless otherwise indicated, Scripture quotations are from the Holy Bible, New International Version®. NIV®. Copyright © 1973, 1978, 1984 by Biblica, Inc.™ Used by permission of Zondervan. All rights reserved worldwide. www.zondervan.com
Scripture quotations marked NLT are from the Holy Bible, New Living Translation, copyright © 1996, 2004, 2015 by Tyndale House Foundation. Used by permission of Tyndale House Publishers, Inc., Carol Stream, Illinois 60188. All rights reserved.
This book is a work of fiction. Names, characters, places, and incidents are the products of the author's imagination or are used fictitiously. Any resemblance to actual events, locales, or persons, living or dead, is coincidental.
# Dedication
To
Cade, Lucy, Abra,
Sam, Leo, and Poppy,
for being the main characters
in my favorite story.
And most of all,
to Maile.
Along with everything else,
this is for you.
# Contents
Cover
Title Page
Copyright Page
Dedication
Epigraph
Part 1: The Storm
Part 2: The Tree
Part 3: The Sword
Part 4: The Fire
Part 5: The Secret
Sneak Peek of the Next Enthralling Novel
Acknowledgments
About the Author
Back Ads
Back Cover
# Epigraph
# Part 1: The Storm
## 1
I AM OLD NOW. I still live on the same farm where I grew up, the same farm where my mother's accident took place, the same farm that burned for days after the angels fell. My father rebuilt the farm after the fire, and it was foreign to me then, a new house trying to fill an old space. The trees he planted were all fragile and small, and the inside of the barns smelled like new wood and fresh paint. I think he was glad to start over, considering everything that summer had taken from us.
But that was many years ago, and now the farm feels old again. The floorboards creak when I walk to the kitchen in the middle of the night. The walls and the roof groan under the weight of summer storms. There is a large oak tree in the front yard again, and it reminds me of the lightning tree, the one that started it all. This house and I are two old friends sitting together in our latter days.
I untie my tangled necktie and try again. I've never been good at these knots. My last friend's funeral is this week and I thought I should wear a tie. It seemed the right thing to do, but now that I'm standing in front of a mirror I'm having second thoughts, not only about the necktie but about even going. She was my best friend, but I'm not sure I have the strength for one more funeral.
Someone knocks on the front door, so I untangle myself from the tie and ease my way down the stairs, leaning heavily on the handrail. Another knock, and by now I'm crossing to the door.
"Coming, coming," I say. People are in such a hurry these days. Everyone wants everything to happen now, or yesterday. But when you're my age, you get used to waiting, mostly because you're always waiting on yourself.
"Hi there, Jerry," I say through the screen, not making any move to open it.
"I won't come in, Samuel. Just wanted to apologize for my boy again."
Jerry is a huge bear of a man with arms and hands and fingers so thick I sometimes wonder how he can use them for anything small like tying shoes or stirring his coffee. He's always apologizing for his boy. I don't know why—seems to me his boy simply acts like a boy. And because Jerry is always calling him "boy," I can't remember the child's name.
"I heard he was throwing smoke bombs up on your porch this morning."
"Oh, that. Well . . ." I begin.
"I won't hear of it," Jerry says. "In fact, as soon as I find him he'll be coming here in person to apologize."
"That's really not necessary," I say.
"No. That boy will apologize."
I sigh. "Anything else, Jerry? How are the fields this summer?"
"Green. It's been a good one so far."
"All right," I mumble, then turn and walk away because I'm too old to waste my time having conversations that don't interest me. "All right."
"Oh, and I'm sorry about your friend," Jerry calls to me as I begin the slow ascent up the stairs. His words hit me like a physical object, make me stop on the third step and lean against the wall. They bring a fresh wave of grief to the surface, and I'm glad he can't see my face.
"Thank you," I say, hoping he will leave now.
"The missus says she was a good, close friend of yours for many years. I'm very sorry."
"Thank you," I say again, then start climbing the stairs. One foot after the other, that's the only way to do it. I wish people would mind their own business. I have no interest at my age in collecting the sympathy of strangers. Or near strangers. In fact, I can do without sympathy at all, no matter the source.
I still imagine myself to be self-sufficient, and in order to maintain that illusion I keep a small garden at the end of the lane. Sometimes, while I'm weeding, I'll stop and look across the street at where the old church used to be. After the fire they left the lot vacant and rebuilt the small brick building on a lot in town, but the old foundation is still there somewhere, under the dirt and the plants and the trees that came up over the years. Time covers things, but that doesn't mean they're gone.
If I'm honest, though, I have to admit that during some gradual phase in my life I became too old to work the farm myself. There was a time not long ago when my farm fell into disrepair, and I thought it would be the end of me as well, because I couldn't bear to watch so many memories collapse in on themselves. Then the family that moved into Abra's old farm, Jerry and "the missus" and his "boy," asked if they could rent my fields and barns. I said yes because I had no good reason to say no. Now they take care of everything and I live quietly in the old farmhouse, puttering in my garden or sitting on the large front porch, trying to remember all the things that happened the summer my mother died.
Jerry's son looks to be about eleven or twelve, my age when it happened. I wonder what he would do if his mother died.
I think he's scared of me, and I don't blame him. I don't shave very often and my hair is usually unruly. My clothes are old and worn. I know I smell of old age—I remember that scent from when my father started walking with a cane.
Sometimes Jerry's son will hide among the fruit trees that line the long lane and spy on me, but I don't mind. I pretend not to see him, and he seems to have fun with it, climbing up to the highest branch and peering through an old tube as if it's a telescope. Sometimes, though, when he gets to the top, I find myself holding my breath, waiting for him to fall. Everything falls in the end, you know.
I stare at the mirror again after climbing the steps and wonder where all the time has gone. I pick up the necktie and try again, but my old fingers can't quite get it right. I remember when I was a very young boy my mother would sometimes put a tie on me, her delicate hands weaving the smooth fabric in a magical way.
"There," she would say, patting the knot of the tie and looking rather pleased with herself. "Now you look like a young man."
The boy reminds me of myself when I was his age. He runs around the farm with sticks and pretends they are swords and magic staffs. Those days seem so long ago. Now I move slowly, carrying only a cane that is nothing more than a cane. I don't know if I have the power anymore to turn this cane into anything exciting, anything like a sword pulled from a stone or a gun that could kill an Amarok. Sometimes I feel like I have forgotten how to pretend.
I give up on the tie and sit with relief at the desk by the window that looks out over the front yard and the garden. It's rather eerie how the farm has returned to almost the same condition it was in the summer my mother died, the summer of the fire. Sometimes when I look down the lane I expect to see her walking back up from the mailbox, or my dad to wander in from the barns, dirty and ready for dinner.
After many years of wondering if I could get the story of that summer exactly right, I have decided to simply write it as I remember it. There's no one else left who was there when it happened, no one to compare stories with, no one to agree or disagree with my own version. As I think through the story, I wonder if it's even possible that everything happened as my memory tells me it did. It all seems rather incredible.
But one thing I'm sure of: after everything that happened that summer, life seemed fragile, like an egg rolling toward the edge of the table. It seemed like anyone I knew could die at any moment. But now that I'm old and all my friends have died or moved away, my own life feels almost unbreakable, like it will never give up.
Which reminds me of something that Mr. Tennin told me in his thin, wispy voice, right at the end.
"Samuel," he whispered. "Always remember this."
I leaned in closer as the fire roared on the far side of the river.
"Death," he said, then paused. "Is a gift."
I stare at the obituary sitting at the corner of my desk, the one I cut out of the paper yesterday—such a small amount of writing meant to tell the story of someone's entire life. I lift it up and it's light, almost see-through, and for a moment life seems fragile again, and temporary.
Death, a gift? I would have shouted at someone had they said that to me at my mother's funeral. But I've been on this earth for many years now, and I've seen many things, and I finally believe that Mr. Tennin was right.
Death, like life, is a gift.
This is how I remember that summer.
## 2
I WAS TWELVE YEARS OLD, and because I was crouched down in left field, picking at random blades of grass and not paying attention, I didn't notice the darkness gathering in the west. My father signed me up for baseball every year, even though I wasn't very interested in a game that seemed to be made up mostly of standing around and waiting, and on that particular day I was feeling happy the season was almost over. I stared at a small ant pile and poked at it, spreading panic. The ants dashed here and there, trying to rebuild what I had brushed away in an instant.
I heard the faint sound of distant thunder.
It would be remembered as the summer of storms. Nearly every week, massive dark clouds rumbled down over the western mountain range and drenched the valley. The fields outside of town were green from all the rain, and the creeks were muddy and full, bulging at the seams.
While I heard the distant thunder, it wasn't enough to get my attention, and I continued tormenting the ants. I glanced up at the parking lot and noticed that my mother wasn't there yet, which was unusual because she almost always came to pick me up well before practice was over. She normally parked up from third base and sat on the hood of the car, her feet on the bumper, until I saw her and waved. Then she'd get out a book and read until practice was over.
I had never had to wait for her before.
I heard a loud ping come from home plate, and I looked at the batter, maybe 150 feet away. It was Stony DeWitt, the biggest kid on the team, and he slammed a screamer that was rising, sailing over my head. I left the ants to recover what they had lost and started running back, back, back. The rest of the kids shouted at me to hurry. We grew tired of Stony hitting home runs every time he was up to bat, and we roared with delight whenever we could get him out.
The ball traced an arc over my head, bounced, and rolled to the short outfield fence. Beyond the fence was the town of Deen, Pennsylvania, which was nothing more than the intersection of two roads.
I reached for the ball, and the instant I touched it—the very instant, I tell you—lightning struck, and it was so close that the thunder clapped at the same time. It scared me and I dropped the ball. There are times in those kinds of storms when you begin to feel that there is no safe place, that the lightning will strike anywhere, that you have a target on your back and it's just a matter of time.
My breath caught in my throat and I scrambled after the ball, my insides jumping every which way. I turned to run toward the safety of the infield, but I realized the baseball diamond was empty. The lightning had scattered the kids to their parents' cars. Even Mr. Pelle, my baseball coach, who smoked the delicious-smelling pipe full of cherry tobacco, was running up the small hill to the parking lot, one hand holding a rubber home plate over his head, the other dragging a large red canvas equipment bag behind him. He stopped long enough to drop everything and cup his hands around his mouth.
"Go into the store!" he shouted, waving me off. "Get inside!"
My eyes scanned the parking lot again, the one that ran along the baseball field, but my mom still wasn't there. I turned and ran back to the chain-link fence, climbed over it, and raced toward the edge of town, only a few hundred yards away. Heavy drops hit the ground all around me. There were large amounts of time between the drops, and I could hear each individual one collide with the ground. When they hit my baseball cap or my arms they seemed far larger than normal, the size of marbles that exploded into patches of water wherever they landed.
I ran for Mr. Pelle's antique store, which was right at the intersection. I had made it into the parking lot by the time the next lightning missile struck, and this time I not only heard the crash but felt the sizzle in the air, the electric pulse spreading outward. The air woke up, like a viper sensing a small mouse dropped into its cage.
The rain turned into a constant sheet of water, and I felt like I was trying to breathe underwater. The air was lost, taken over by the downpour. There was no space between drops anymore. Everything, including me, was soaked in seconds. Water dripped from the brim of my ball cap, and my shirt clung to me, suddenly heavy, like a second skin.
On one side of Pelle's Antiques was Uncle Sal's pizza, and the smell of delicious cheese and pepperoni came at me through the rain. I ran into the small alley between Uncle Sal's and Pelle's, through the small waterfall tumbling out from the gutters where the rain already overflowed. I pushed open the heavy brown steel door and vanished into the stockroom of Pelle's Antiques.
The door slammed behind me, and I went from a white-gray day full of the sound of pounding rain and splitting thunder to shadows and quiet and the smells of old cedarwood, dust, and paint. I stopped inside the door as my eyes adjusted to the darkness. Outside, when the rain was coming down through that July day, the falling water had felt almost warm, but in the air-conditioned back room of the antique store, the water spread a chill over my body, and I crossed my arms, clutching my baseball glove as if it might bring me some warmth.
The rain made a distant rushing sound on the roof, and as I meandered through the irregular rows of furniture, I wondered again why my mother had been late, and where she was, and who would take me home. I passed high-backed armchairs standing upside down on barn-door tables, and under them were old windows without any glass panes. There were desks and side tables and large hutches. Wardrobes stood closed and ominous, daring me to open them. Lamps of every shape and size filled in the gaps: tall, skinny ones and short, fat ones, lamps with shades and lamps without shades, some with small white bulbs perched at the top like crystal balls, others with empty sockets.
I stopped in front of an old mirror framed in black, twisting metal, and I stared at my reflection in the peeling surface. I was a skinny kid and, being soaked through, looked even thinner than usual. I'm sure I didn't look as old as I wanted to look. My brown eyes were still the eyes of a child. I spent most of my childhood wanting to be bigger, stronger, older.
I heard voices in the prep room. It was the space between the large storage room and the sales floor, where Mr. Pelle stained and repaired and prepared one piece of furniture at a time before taking it to the store out front with the big glass windows that looked out onto Route 126. It was unusual for anyone besides Mr. Pelle or his family to be in that middle room.
I moved to the door. I could hear my own heart thumping in my ears, and my breath seemed suddenly loud. My sneakers, waterlogged, squeaked with each step.
But as I got to the swinging door, it was already leaning open a few inches. Outside, another lightning strike sent thunder through Deen. The sound of the rain was a constant hum, but the voices were loud. I peered through the crack in the door.
Three old women sat on one side of a large, square table. They were dressed like gypsies, with long, flowing robes that draped down from their shoulders. Scarves were wrapped around their heads, with gray and white hair peeking out from under the colorful fabric. Large golden earrings dragged their flabby earlobes toward their shoulders, and their arms were lined with bracelets that clinked when they moved. They sat so close together that their robes folded into each other, so close that they almost looked like one wide, colorful body with three heads.
They looked intently across the table, but I couldn't see that side of the room through the crack in the door. Someone was there, though. Their shadow, short and wide, draped itself across the table and toward the women. When the person spoke, it was a man's voice. At first he muttered and grunted to himself, the words all jumbled together. But I could only see the three old women, and they stared at him as if trying to decide if they should stay or go.
Out of nowhere, the three old women interrupted him, quietly at first and then louder. They chanted words, but not English words, not old, dead words that can barely stand on their own two feet. No, the words they chanted were alive, words I couldn't understand, words that had a fluttering, startling life of their own. Their words terrified me, but they also intrigued me. I was like a confused magnet, repelled and attracted all at once.
Part of me wanted to turn and run back out into the storm I had escaped from, back into the hair-trigger lightning and the thunder and the rain that had drenched me, but their words pulled me forward until I was braced against the frame, fighting to stay outside the room.
The lights in the building flickered, then went out.
## 3
THE STORM RAGED OUTSIDE. The women's faces held a grayish tint from the stormy light dripping in through the one small window in the prep room. Sometimes, when the lightning flashed, their skin went white, almost transparent, and the man's shadow appeared solid black on the table. I kept expecting one of the women to look at me in those flashes of lightning, those moments of clarity, but their eyes focused on the table, where their fingers had joined together in one big pile. They swayed with the words, and their six hands writhed in an uneven rhythm.
I wondered if those women were traveling with the fair that had recently arrived in town. My dad called them "carnies," that rough group of travelers who brought wonder to our small community every summer, leaving behind deep tire tracks in the park outside of town and puddles filled with unredeemed ride tickets. These women could have been anything—funnel cake vendors or ticket takers outside the mirror maze or fortune-tellers. They might have been the ones who try to guess your age or spin the prize wheel. They could have been anything.
Their chanting stopped as quickly as it had started, and the world fell back into its natural order. I could hear the rain softening on the roof and the wind tapering down to random gusts through the alleyway, but the front of the storm had passed and the thunder had moved off into the distance. The woman in the middle straightened the large scarf tied around her head and pushed all those jingling bracelets and rings and necklaces back into place. She didn't seem to realize she had been saying anything out of the ordinary. She looked up as if expecting the person in the shadows to tell them what to do next.
"Is that it?" the man's voice rumbled. It growled with thick phlegm and the beginnings of an earthquake.
"Is what it?" the woman in the middle asked, leaning forward. She raised her stenciled eyebrows toward the ceiling. Some of her teeth were so sideways that they looked backward. There was nothing straight about her.
"I paid you good money for my fortune, the future, whatever you want to call it. Chanted words, spooky humming . . . is that it? Is that all I get?"
She looked back and forth at the women on either side of her and whispered over one shoulder as if consulting with someone. Someone who wasn't there.
"But you didn't tell us who you were," she said in a polite voice that I realized carried hints of a foreign accent. "The fortunes of your kind are dark. Men are easily read, but you?"
She stared at him with a face completely at peace. His threatening tone of voice did not seem to affect her in the least. The room was quiet for a moment, and then she spoke again.
"You didn't tell us what you were."
The man cleared his throat.
"But you saw something?" He sounded unsettled, even a bit distracted, by her knowledge of "what" he was.
"Something to write with?" she asked.
The man grunted and threw a pen onto the table. It slid toward the women. The one in the middle grabbed the pen before it stopped moving and began scribbling on the table. I cringed—Mr. Pelle would not be happy if he saw them doing that. But she kept writing. She'd cross out what she wrote and write again. And again. She spent a solid five minutes defacing that table with more ink than I thought any pen could hold, and it looked like she crossed out and scribbled over every single word she wrote.
Finally, with the sound of fluid clothes and wind-chiming jewelry, the three women stood up.
"This is for you," the one in the middle said, pushing the point of the pen into the table, where it stuck for a moment before falling over. "You may read it after we leave."
The man grunted again.
"The rest of the money?" the woman asked.
At first nothing happened, and I thought they might keep arguing. But three green bills floated down onto the scribbled surface. The woman picked them up and stuffed them into the recesses of her long, flowing skirt. She was clearly impatient to leave, and when she stood up her movements seemed anxious. The other two women were a half second behind her, as if they were three marionettes all controlled by the same puppet master.
Then something strange happened.
She glanced at me.
Or at least she glanced at the crack in the door. But I thought it was more than that. I thought I felt her eyes locking onto mine, and I was sure that if the man wasn't in the room, she would have come over and told me something. Something very important. But her sudden look scared me, and I spun around, stood with my back to the wall. I held my breath and listened, hoping no one would come that way.
The women must have left through the other door, the one that led into the front area of the antique store. Moments later I heard, far away at the front of the building, the bell ring over the entrance. They were gone.
There was a loud sound from outside the window—the last strong rumble of thunder, or a downspout leaning under so much weight—and the man left without getting a chance to spend much time looking at the table.
"Nothing," he mumbled. "Nothing, nothing, and more nothing."
He walked quickly toward the same door the women had gone through. I didn't get a look at his face, but I did see him from behind. He was short and wide. There was something very powerful about his neck and shoulders. He turned sideways so that he could fit through the narrow door.
The room was empty now. I pushed the swinging door aside and approached the table. The storm seemed to have passed. Sunlight lit up the room, and for the first time I noticed the window was open. The floor had a large puddle on it that reflected the light. I could hear water still running through the gutters and downspouts, splashing into the alley.
The woman with the pen had made a complete mess of the table. Ink was everywhere, filling deep gouges in the wood. She had written many things. Many things. But everything had been scratched out so effectively that it was all impossible to read.
Everything, that is, except for one small sentence I almost missed in the middle of that black cloud of dead, crossed-out words.
Find the Tree of Life.
Voices. The sound of someone coming back from the front of the antique store. If it was Mr. Pelle, I didn't want him to find me there with the window open, the water on the floor, and the ruined table, so I raced through the swinging door, through the storeroom, and out the side door into the alley. There wasn't a sidewalk back there, only a six-foot strip of dirt and loose rocks separating Mr. Pelle's store from Uncle Sal's.
I wasn't sure what I had just seen, but I knew I had never seen anything like it, not in my small town. I turned to walk back the way I had come, away from the main street, back toward the baseball field. I hoped my mother would be waiting there for me. But I stopped. I heard someone walking, their feet crunching slow steps over the loose gravel.
Drip. Drip. Drip. Water fell from a clogged gutter at the top of the building. I turned around. Coming toward me was the woman I had seen sitting at the table inside, the one in the middle who had written everything. She was alone, the other two women nowhere to be found. She walked unsteadily, in the trembling way of someone very old, and I froze. I stood there, staring. She was sort of hunched over, and her robe flapped every once in a while as leftover gusts of wind dashed through the alley, chasing the storm that had left them behind. The air felt cool for July, that kind of after-storm coolness that reminds you summer will not last forever.
She smiled as she walked, and her mouth opened as if she was about to say something, but then she closed it again. She stopped a few feet away, and I saw the stick she carried. It was a gnarled, barkless thing that bent this way and that. She grasped it with both hands, plunged it into the ground, and limped around me, muttering a small stream of those living words. The stick made a harsh, scratching noise in the dirt and the rocks. Her strength amazed me—the line she made was deep. A small trickle of rainwater welled up and filled it.
At that point I almost started to feel bad for her. She was obviously losing her mind. I held my breath, waiting for her to finish, trying to think of something nice to say. She made a circle in the dirt all the way around me with that stick, and I got another glimpse of those sideways teeth crowding for space in her mouth. Her eyes were kind and knowing.
I nodded at her, and she walked away. I sighed with relief and watched her turn the corner.
But I couldn't leave the circle she had made.
## 4
THERE WASN'T ANYTHING IN THE AIR, nothing that I could see that might be keeping me in that spot. I could hear everything going on around me. And I could move, but there was some kind of force keeping me inside the circle she had drawn.
"Sam!" I heard a voice shout. It was my friend Abra coming down the alley.
I tried to lift my arm to wave her over, but the circle kept my arms tight to my sides.
"Come on," she called out. "Your mom's been looking for you. She's going to take us home."
At that point I realized I couldn't talk. I could breathe, but that was it. My voice was gone. Nothing.
"Why are you standing there?" she said. "Your mom is waiting. C'mon!"
When she got closer she slowed down. I stared at her, and she looked confused. She reached out and pushed me playfully. Her foot scuffed mud and stones over the circle the old lady had drawn, and suddenly I could move. I jumped away from the circle.
What had just happened?
"What's your problem?" she asked. "Let's go. The Ferris wheel is going up and the livestock tents are out. I'm pretty sure I saw Steve and Bo sneaking onto the fairgrounds over by the break in the fence, where the cotton candy always is . . ."
She chattered on and on about the fair, and I followed her through the alley, expecting the old woman to jump out at us or that huge man to sweep down and question me. But nothing happened. We wandered out onto the sidewalk that ran in front of the antique store and walked toward my mother waiting in her car.
I climbed into the passenger seat and didn't say a word. I couldn't get the image of that woman out of my mind, the way she scraped that circle, the way it held me frozen.
"Hey," my mom said, disapproval on her face, "where were you? And where's your glove?"
I realized I had left my glove in Mr. Pelle's back room.
"Where was I?" I said. "Where were you?"
She could tell I had been upset when she didn't show up, so she let me get away with talking back to her.
"I'm sorry, Sam," she said, tilting her head and frowning. "I know I'm never late, but I got caught up talking to Abra's mom, and she asked if I could pick Abra up at the school, so by the time I got to practice you were gone. What a storm!"
Abra sat in the backseat and put her bag beside her. She kept glancing at me with a strange look on her face, but I tried to ignore her.
Yeah, what a storm, I thought, once again picturing the dark cloud of scribbles on the table around those words.
Find the Tree of Life.
We drove north onto Kincade Road. That's where the fair was setting up, in a park on the outskirts of town. The workers swarmed the area, building rides and putting up food tents, pulling trailers and backing up trucks. I looked and looked for the three old ladies, but I didn't see them.
"Look, the Ferris wheel!" Abra said. "I can't wait."
There was a whimsical sound to her voice, and I knew exactly how she felt. The rides, the food, the lights—everything about the fair embodied summer and freedom and being young.
At the far end of the fair I saw the Ferris wheel going up, section by section. Three or four large men joined the massive, curving pieces of iron pulled from the back of a semi.
We left town. Abra and I both looked out the back window of my mom's car for as long as the fair was visible. It was the best part of the summer, and I couldn't wait.
Today's Friday, tomorrow's Saturday, then Sunday night the fair opens, I thought.
"Can we come on Sunday night?" I asked my mom.
"Of course we can," she said.
We always think we have one more day. We always think tomorrow can do nothing but come around. It's one of the great illusions we live with, that time will go on and on, that our lives will never end.
"Of course we can," she'd said, but my mom wouldn't make it to the fair that year.
Route 126 and Kincade Road were both lined with restaurants and gas stations and a small grid of houses in those days, population 1,931 (or so said the small sign as you drove into town, and so said that sign for many years). Route 126 traveled east to west. Kincade Road was my road, the road that went north into the farmland and the valley where the eastern and western mountain ranges started pinching together.
We had already dropped Abra off at her farmhouse and were driving the last stretch of Kincade Road before getting to our place. There was only one more farm north of us, and Kincade Road ended just past its lane, giving way first to woods and then to the two mountains that lined the opposite sides of our valley as they converged to a point. A river spilled out of their collision and drifted south through the valley, all the way to Deen.
When I was a kid, that valley was my entire world, and the mountains that lined it were the boundaries. Beyond them, there was nothing. I loved my life there at the edge of the world. I feel sorry for children who live in the midst and never have a chance to wander close to where everything ends.
A clean, delicious wind rushed into the car. We had driven mile after mile out of town until the houses dispersed and gradually gave way to cornfields. The cornstalks were about two feet tall, their narrow green tassels waving back and forth. In most places the fields went all the way from the edge of Kincade Road to the forests that lined the mountains. Everything smelled like cut grass and blue sky. The farming families in the valley tried to squeeze as much out of the land as we could, and as I had grown older I had begun to feel part of the earth, part of the struggle for life.
We approached a meaningless stop sign. The road that used to cross Kincade Road was no longer there, but my mom still insisted on stopping. I wondered if anyone would ever take that sign down. As I glanced over at the grassy bank that kept the cornfields at bay, I saw the cat.
"Wait! Pull over!"
It was pure white, really small, practically a kitten, and it walked like it was proud of itself, flicking its tail behind it like a tall, white snake.
"What, for a cat?" my mom asked, but she was already pulling over. That's the kind of mom she was.
"Yeah, for a cat." I opened my door. The cat turned and looked at me.
Now, decades later, I still wonder why that cat couldn't have simply run away from me, disappearing into the corn and saving everything. Why did it have to come so willingly?
"Look at that," I said. "He likes me."
"How do you know it's a he?" my mom asked.
"Can we take him home?" I asked, reaching out to the cat. It paused for a moment, moved away from me, then leaned back into my reach.
"I don't know if your father will like that," Mom said, but I had already brought the cat into the car and closed the door. I looked at my mom and made sad eyes, a great big pretend frown.
She laughed. I loved how my mom laughed.
Then she sighed and shook her head, but she couldn't stop smiling. "You are going to get me into trouble," she said. "What will you name him?"
"I think I'll name him Icarus."
"Icarus? Where's that from?"
I shrugged. "Remember the story Dad told us the other night after dinner? The story about the father who built wings for himself and his son out of wax and feathers so they could escape the island they were on?"
"I think I was washing the dishes," Mom said, looking at me out of the corner of her eye. "By myself."
"It was a good story," I said, rolling my eyes. "You missed out."
"Well, what happened?"
"The father warned his son about flying too low because the sea's spray would clog his wings. But he couldn't fly too high or the sun would melt them."
"And?"
"He flew too high, the wings melted, and he drowned in the sea."
"That's depressing."
I shrugged again. "I like the name. Icarus."
"You'll have to buy food," she warned me. "Where will you get money for that?"
"Oh, I've got tons of money," I said, and we both laughed.
I wasn't exactly rich, but I made five dollars a week mowing Mr. Jinn's grass. Mr. Jinn owned the farm to the north of us, but I had never seen him in my life. Not ever. He was an old hermit and never left his house. His farm was all grown over with weeds, and the barns were falling in on themselves. He had a small yard that he kept mowed, though sometimes he called my mom and, in as few words as possible, asked if I could mow it for him. When I did, he left a five-dollar bill in an empty birdbath close to his house. Whenever I took the money from the birdbath, I could feel his eyes staring at me through one of the dark windows.
"Well, I guess you can name him whatever you want to name him if you're footing the bill," she said. The car turned in to the stone driveway that led to our house. "Just remember," she said as she turned off the car, "names are powerful things. Sometimes they can even form us into who we become."
But I wasn't thinking about who I was becoming, or who the cat would become, because that's how it is when you're young and feel like you have all the time in the world.
I tried to tuck Icarus under my arm when we got out of the car so that my dad wouldn't see, but at that moment he came walking in from the barn. He strolled over to my mom and kissed her on the cheek.
I murmured, "Gross."
They both laughed. My dad stopped laughing when he saw what I had under my arm.
"What's that?"
"What, that cute little cat?" my mom said, moving over to stand beside me.
Dad sighed. "As if we need another animal around here to feed." He looked at me and raised his eyebrows as if to ask, And what do you have to say for yourself, young man?
I pulled the cat in tighter against my side and stroked his head. "I'll take care of him, Dad, don't worry. I'll pay for the food. You won't have to do a thing."
He looked back over at my mom.
"He named the cat Icarus," she said, as if that was her only argument on my behalf.
"What am I going to do with you two?" he said, trying not to smile. He turned and walked away. When he was far off, he shouted without turning around, "I'm fine with the cat. But not in the house!"
I looked at Mom and she smiled, and we walked to the house together. I put the cat down and waited to see what he would do. Without hesitating, he ran up beside my mom and walked with her, trying to move between and around her feet.
"He likes you, Mom!" I shouted.
"How do you know it's a he?" she asked again.
"Because his name is Icarus."
"Is that your cat?" a voice shouted to me from down the lane. Abra rode her bike up beside me. She had a goofy grin on her face.
"I got a cat! Can you believe it? Meet Icarus!" I laughed.
"Cats are for sissies," she said, but I could tell she was jealous.
"Abra, would you like to stay for supper?" my mom called from the house, and we grinned at each other.
At about six o'clock I ran out to the barn to find my dad and tell him supper was ready. Abra stayed inside to help my mom set the table.
"Dad?" I shouted into the dark barn, where he usually finished up before supper. "Are you in here?"
My voice sounded thin and vanished quickly in the aisles between the pens and the holes in the ceiling that went up to the musty haymow. Sometimes we'd throw a few bales of hay down and then jump through the hole, landing on them. It was a good ten feet from the ceiling to the floor, and the rush took my breath away. Inside that old barn, when the sun was going down but we hadn't turned on the lights yet, it was a dark place with a lot of deep shadows. It was the kind of place where you could believe in just about anything.
I thought back to the old lady who had drawn a circle in the ground around me. Who was the man in the shadows? Why were they all in the back room? What did Find the Tree of Life mean? I kept expecting one of the three women to walk out of a corner of the barn, holding that stick, looking at me with those eyes.
"Dad?" I shouted again.
"Over here, Son," he said. I walked through the half-light to the back corner of the barn, where he kept one of the lambs that had been rejected by its mother. "Hold this bottle for me."
It was warm in the barn, and flies buzzed everywhere. They dodged my steps and buzzed around me in a cloud. I grabbed the oversized bottle and stuck it between the bars of the gate, holding it with two hands. The little white lamb latched on and sucked, bucking its head and wagging its stumpy little tail a million times a minute. I reached out and petted the curly wool on its head.
"Thanks, boy," my dad said, ruffling my hair and smiling. "I'm going to go hook up the tractor. You finish up that bottle for me and I'll meet you inside."
When he left, the barn felt dark and still. I jumped at every shadow. As I helped the lamb gulp down the last of the bottle, I stared into a corner where a beam of sunshine fell through one of the dusty barn windows. The light illuminated a spiderweb, and as I watched, a fly collided with the sticky strands. It fought and churned and spun until it was hopelessly entangled. A small black spider darted out from the shadows, hovered over the fly, and began wrapping it in a sticky cocoon.
A strange sense of fear burned inside me, and I backed away from the lamb. But there was something else, some feeling I couldn't identify. I don't know what it was. Maybe it was nothing. Or maybe I could somehow sense the coming storm, the fact that things were about to change.
We ate supper together that night, our last supper together, though I didn't know it at the time. New potatoes and green beans from our garden, and a roast my mom had cooked in the oven all day.
We never spoke much at supper, the three of us. Sometimes Mom would try to get us going with simple questions: "What's the best thing that happened to you today? What's the worst thing?" And my dad and I cooperated, more or less.
There was definitely more talking when Abra was there. My mom was always asking about her family—how they were going to spend their summer and how her baby brother was doing. My dad always tried to get information out of her about what crops her father was planting, how the animals were faring, that sort of thing. Her family's farm was just to the south of ours, and we saw them a lot.
Every once in a great while my dad would tell a story during suppertime, and when he did I would listen with wide eyes. They were normally stories from his childhood injected with fictional characters or fantastic events. It was usually difficult to strain the truth from the fantasy, but they were always wonderful stories.
That night he cleared his plate and took a long drink of ice water. The outside of the glass was sweating because it was warm in the house, and it left a small, glistening ring on the table. He crossed his arms and leaned his chair back on two legs. When he sat like that he looked huge and old and wise, and I was reminded of how different a boy is from a man, how different I was from him.
"When I was a boy," he said, "there was a great big tree in the front yard of this farm."
"Like the oak?" I asked, looking over at Abra. But she didn't even notice me—she just stared at my dad. We both loved when he told his stories.
"Just like the oak," he said. "Only larger. And taller. Some of the boys in my neighborhood said that if you climbed all the way to the top, you'd be up in the clouds, maybe even in heaven. But that's a different story. In this story, I had a dog, a wonderful dog named Ike. Ike was a German shepherd my grandfather gave me for my tenth birthday. Ike was eight weeks old when he came to live at the house. He was a beautiful dog."
My mom stood up and took a few plates over to the sink, then came and sat down. She put her elbow on the table and leaned her face into the palm of her hand. She was a good listener.
"Ike didn't always know what was best for him, and one day he chased a rabbit around the barn as my dad was backing out the tractor. Well, my dad backed over Ike, and he died. I was very sad. I cried for hours. Finally, as it started to get dark, my dad and my grandpa came in and asked if I'd like to help them bury Ike under the old oak tree. I said I would, and we took turns with the shovel, digging the hole and burying good old Ike.
"The next day it started to rain, and it hadn't rained all summer. We'd been in a drought, and the farmers were happy to see the rain. Well, someone heard that we had buried Ike the night before out under that oak tree, and there were some superstitious people in the town. They started to think that old oak tree had the power to bring rain, and all you had to do was sacrifice an animal and bury it close to the roots."
"That's weird," Abra said, wrinkling her nose.
"Me and my grandpa and my dad, we all knew this was hogwash, but someone kept coming out at night and burying animals under our tree. It got to be pretty bad, and the rain came down harder and harder until it looked like it might flood. So one night my grandpa went out there with a can of kerosene and doused the tree and burned it down. You should have seen the flames."
For a moment he stared at the ceiling as if he were watching a massive tree burn.
"Everything went back to normal after that. But I was sad to see that tree go."
It was very quiet around the table as we sat there thinking about Ike and the tree and the generations of farmers that had come before us. I wished I knew how much of that story was true. You never knew with my dad.
After dinner, Abra helped Mom with the dishes while Dad and I went back out for a few more hours of farm work. By the time I got back to the house, Abra had already ridden her bike home. We did that a lot, biked to each other's houses, because there wasn't anyone else who lived on Kincade Road once you got outside of town, and the ride wasn't that far, maybe a mile or two. Well, there was Mr. Jinn, but no one ever saw him.
I made a house for Icarus by cutting apart a cardboard box, and Mom donated one of her old sweaters for the bedding. I put the box under the huge, green front porch of our farmhouse. I sat there on the steps and looked out over the massive garden, and the cat weaved a circle around my legs, purring.
The sun had gone, but there was still a bit of light in the western sky. The smell of cut hay filtered through the sunset. A few lightning bugs turned on and off and on and off, their yellow-green lights sharp like stars.
I saw the storm rolling in from the east, the clouds heavy and flashing with lightning. It sounded like some kind of war in heaven, a vicious battle that would end only after one side had completely destroyed the other. I had always thought of thunder coming after the lightning, a natural cause and effect, but that night I saw it in a new way. It felt like Thunder and Lightning were two beings battling each other, Lightning always striking first, Thunder coming later with the counterpunch.
The lightning and thunder grew close, and I thought again about what I had seen at the back of the antique store through the crack in the door. I remembered how the thunder had sounded, how the lightning had lit up the three women's faces, pale and clear, and how the scratched-out words on the table had looked like an angry cloud.
But that storm, the one coming in through the dusk, wouldn't be like scratches on a table. That storm would bring death and set everything else in motion.
## 5
I SAT OUT THERE WITH THE CAT, and the storm drifted in. All the limbs started to dance and the bright green undersides of the leaves turned up, silver in the near darkness. Some of the tips of the branches blew off when the wind came gusting in, and because the storm arrived from the east and the sun was setting in the west, there was an eerie, low-lying light that stretched all the shadows in the direction of the storm. It looked like the storm was sucking the darkness out of everything, or maybe chasing away all the light.
The lightning arrived in the valley, bright flashes followed by a moment of silence. Then, KABOOM! The thunder rumbled over the fields. It was right at that first peal of thunder that my little cat ran to the oak tree in our front yard, about forty yards from the porch. That crazy cat clawed its way up to where the first thick branches formed, about ten feet off the ground.
I always thought that particular part of the tree looked kind of like the palm of a giant hand with five fingers branching out, as if the hand was going to pick a piece of fruit or catch something falling from the sky. There was a little hollowed-out place up there—I knew because sometimes I used a ladder to climb up and sit in that spot.
I ran to the shed, and as I stepped inside to look for the ladder, the rain started to fall, tapping loudly on the roof and the walls and the small glass windows. I had to turn the light on inside the shed. I found the extension ladder buried under cobwebs and a thick layer of dust and dragged it through the rain to the tree. It banged on the ground and hit me in the knee a bunch of times—it was so long I could barely carry it. Eventually I propped the ladder up and leaned it against the rough bark.
That oak tree was like an old friend. It was way older than I was. We had picnics under that tree. I had played with my toys all among its gnarled roots. I had helped Mom and Dad rake up all of its leaves every autumn and put them in a big pile so I could jump in them. Its bark was an old man's skin, rough and peeling. That oak tree was practically a grandparent.
I scrambled up the ladder, now slick with rain, and peeked into the small area where all the largest branches forked out from the trunk. There was that silly white cat. Its eyes glowed.
"Here, kitty, kitty," I said gently as the rain came down harder, soaking me for the second time that day. My hair clung to my forehead while huge drops fell into my eyes. I climbed up a few more steps into the darkness, into the shadowy heart of the tree. I knew you aren't supposed to climb up onto the top step of a ladder, but I couldn't reach the cat without going up as high as possible. I stretched again, now up on my tiptoes. The ladder shook underneath me as another bolt of lightning fell to the earth.
KABOOM!
"Here, kitty, kitty!"
Still it wouldn't come to me. It huddled under a tiny branch. If I wanted to rescue that cat, I was going to have to climb over and get it.
I pulled myself up into the tree and stood in that area where all the branches started. I leaned over to grab the cat, but it jumped away and scampered out on one of the branches.
"Icarus, you stupid cat!" I shouted. "Come back here!"
Just then I heard my mom shouting from the porch. Her voice sounded worried and mad.
"Sam, what are you doing up there? You'll get struck by lightning! Come down this instant!"
"It's my cat," I shouted through the rain. "He climbed out onto one of the branches."
"He'll come down when it stops raining. Now listen to me and get down here!"
As if to emphasize Mom's words, the storm threw down a lightning strike that was followed quickly by an explosion of thunder.
When the lightning flashed it was like everything became midday, just for a moment. I could see the yard and the grass and the house and the church across the road. But after the lightning, everything seemed darker than usual.
I had second thoughts about the rescue mission. Maybe I should go back in the house. I stood there for a moment, trying to make up my mind about what to do. I decided to go inside, but then I saw my mom's hands at the edge of the tree's palm. She pulled herself up and scrambled into the nest of branches where I stood. Now we were both standing there in that hand, wet to the bone.
"Where is Icarus?" she asked. I could tell she wasn't happy.
I pointed out the largest branch.
My mom sighed and shook her head. "I am not doing this until you are safe inside. Do you hear me? Now go. I'll take care of this."
She held on to me and eased me down until my feet found the top of the ladder. I looked up into her face. She had a sad, resigned look, as if she knew what was about to happen and had resolved to let it happen. But that's impossible. Right? She couldn't have known, and if she had known, why would she have stayed there?
I scrambled down four rungs and jumped the rest of the way. I ran into the house, up the steps to the second floor, and around the corner to a window where I could see the tree. At first I could hardly see anything. But as I stared into the darkness, the lightning flashed, and I saw my mom walking out that large branch and holding on to overhead limbs. I had never seen her do anything like that before.
I couldn't always see her, what with the rain coming down in sheets and the wind blowing the branches all around and the night having fallen. But once, when the wind held and the lightning struck, I saw her edging farther out on the branch, farther out. She bent over a little and put her hand out for the cat. Her fingers curled up as she sort of waved it to come over to her. Her wet hair hung heavy around her face, and her clothes stuck to her body. I imagined her saying the same words over and over again. "Here, kitty, kitty, kitty. Here, kitty, kitty, kitty."
That's when the lightning bolt struck.
KABOOM!
It lit up the window so bright and close I could have reached out and touched it. The sound of the thunder shook me where I stood—the floor rumbled. In the moments that followed, I heard loud thuds as pieces of the oak tree rained down on the house and all over the farm. In the following days, as neighbors came to help us clean up, someone found a six-foot-long piece of that tree on the other side of the cattle barn, a few hundred yards away.
I regained my senses and looked out the window. Darkness. I peered through the night and wondered if Mom was okay. I thought about my dad, what he was doing, why he hadn't come running. A flash of lightning gave me another glimpse—the branch my mom had been standing on was shredded and hanging.
My mom was gone.
The ambulance arrived along with one police car, and they parked in our lane, their lights spinning and making me dizzy. I watched, never having moved from the window. I didn't want to go down, because as long as I didn't no one could tell me what I already knew.
Eventually I drifted to my bedroom, numb, and my dad came up and said words, but he could barely talk and the words he said didn't make a whole lot of sense. Sometimes there are no words that fit into the space provided. But I didn't need to hear any words, because when that lightning bolt had struck the tree, in that instant it was like a piece of me had vanished. I felt it flutter around inside my chest, a tiny, frantic moth, and then it was gone.
I knew that fluttering sensation was my mom leaving.
After my dad talked to me, he went back downstairs because neighbors had started to arrive and he had to call the funeral home and there was a lot to do in the face of such devastation. I walked quietly down the stairs, through the kitchen, and out the back door without saying hello to anyone. I felt eyes on me, the eyes of people who didn't know what to say, who had also come to the realization that words can at times be powerless. I wandered into the cornfield, the stalks whispering around my knees, and cut out to the road. I didn't want to go out the lane because I'd probably have to talk to someone.
I walked north, past Mr. Jinn's lane, as far as you could go on Kincade Road. Where it ended in the trees, the ground was flat and graded for a longer road, but the work had never been completed. Abra and I called it the Road to Nowhere. Before I walked into the shadows, I looked over my shoulder toward the town. I remembered that the fair was being set up, and I searched for the towering Ferris wheel. Maybe they hadn't put it together yet, or maybe the swells of the fields were too high. In any case, I couldn't see anything. Only the darkness of a storm giving way to the dark of night, and the flashing lights of the ambulance that for some reason no one had turned off.
At the northern edge of the Road to Nowhere there was a path that led even deeper into the woods, all the way to the river. At one point, where the eastern and western mountains began to converge, the river rammed right up against a stone wall. The rock climbed thirty feet into the air, a kind of cliff. And at the base of that cliff, at the very end of the path, was a small cave, barely big enough for me to sit in.
Not far from the small cave was an old graveyard. The stones were mostly ancient and covered in green moss, and quite a few of them were broken off or leaning to one side. The lettering was worn and nearly impossible to read, and some of the graves were actually old crypts, tombs large enough to walk into if the doors still would have opened. The church had its own cemetery, and that's where most of the folks in Deen were buried. This graveyard, the one out in the woods, was from a different era, and a lot of people talked about it being haunted, but it never really frightened me. There were even trees growing up among the headstones, so to me it felt like just another part of the forest.
From that spot in the small cave I looked out over the river beyond the graveyard, maybe fifty yards wide at that point and rushing fast with all of the day's rain. In the winter you could see the eastern mountain from there, up through the leafless branches, but in the summer everything was close and thick and stifling.
I sat in there for a long time and watched the water and wished I had never seen Icarus, wished I had never chased after him into the rain. The storm had stopped and the moon was out and a silvery light fell down all around me through the trees, sparkling on the river.
When I thought that maybe everyone had left my house, I walked back through the darkness. But some of that darkness stayed inside me. I barely recognized it at the time, but it would grow into a heavy shadow, something that would cause me to do many things I never would have done otherwise. Darkness can do that if you let it. It can move you.
By the time I got home it was much later, at a time of night when I was usually fast asleep, but I could still hear people milling around. I crept in through the mudroom, kept my head down while walking through the small crowd in the kitchen, and went up into my room. Silence followed me through the room, and I could feel their eyes again. I could feel the powerless words no one was saying.
From my room upstairs I heard the coffeemaker in the kitchen sputter out another pot of coffee and muffled voices offering condolences. Someone knocked on my bedroom door. I didn't want to answer because I didn't want to talk to anyone. Earlier, when my dad had come to my room, he had said a few quiet words about doing whatever I wanted to do. I could stay upstairs or I could come down. Whatever I wanted. I had hoped that meant I didn't have to talk to anyone.
But out of curiosity, I walked over and opened the door.
It was Abra. As soon as she saw me, she burst into tears and hugged me and put her face against my shoulder. She wept, sobbing like I myself hadn't yet sobbed, and it made me feel good to know that she missed my mom as much as I did. But it also made me feel jealous, or guilty, because I hadn't been able to cry very much, and it felt wrong, the not crying, so eventually I kind of pushed her away. The two of us walked over to sit on my bed, leaving the door open.
"It's just . . . it's just . . . awful," she said. "Are you okay?"
I nodded. Outside the storm had started up again. Rain pelted the glass, but there was no more thunder, no more lightning. That had been reserved for my mother's death, and once she was gone the storm had no more use for it.
"Did you see it happen?" she asked with a very serious face.
"Kind of," I said.
"Was it horrible?"
"Yeah, I guess."
"What will you do?"
"What do you mean?"
"Do you think you'll stay here, on the farm? Or do you think you'll . . . move?"
I shrugged, but the thought of moving hurt. That felt like something I could cry over. I had never lived anywhere else. Besides, the farm's roots went deep in our family. My grandfather had bought that farm when he first got married. He and my grandmother were both gone, but the farm was a part of me. It felt like blood and bone.
"I don't think my dad will want to leave," I said, but my voice betrayed my uncertainty.
She nodded, and I must have convinced her with those few words, because she seemed happier after that, as if not all had been lost.
"Abra!" her father's voice called from downstairs. "Time to go."
She stood, and I knew she wanted to hug me again, but I was done with hugs. I was done with everything.
"How's your little brother?" I mumbled.
"He's good. Really good. Just starting to roll over and get into my stuff."
"That's pretty neat," I said, but my voice was hollow and the words didn't come out all the way.
"Yeah," she said, nodding. She acted like she was going to give me a hug, but that started to feel strange, so she didn't. She just walked out.
I followed her into the hall, but when she went downstairs I drifted into the neighboring bedroom, the empty spare room where I had watched everything happen, since it had a better view of the driveway. The attic door was in that room, and I never completely turned my back on it, because who knows what will come through an attic door when you're not paying attention?
From there I watched Abra and her father walk through the rain, dimly lit by the light pouring from our windows. Abra turned once, looked up to where I was, and waved. I waved back, a small wave with only my hand, not moving anything else. She and her father walked through the night, and soon they were gone.
I had strange dreams that night.
I'm flying over a dark ocean, my wings sturdy and strong. The sky stretches out ahead of me, and there is no reason to go back. But the sun is hot and feathers strip from my wings, one at a time. I glance back and see them all dropping like a trail of bread crumbs or falling stars. I start going down, drifting toward the waves.
Then I see land! I crash onto a flat island that is nothing but a grassy plain. I hike for miles, the blades of grass soft and long, and when I look back I see the dark green trail of crushed grass I leave behind me. When I arrive at the very center of the island there is an oak tree, the tree my father told me about in the story, the one that brought the rain. I know this not because someone told me but only in the way you know certain things in dreams.
I look up and my mom is in the tree, high up and calling for my help. She wears a white dress that billows around her like a sail. I start climbing, climbing, climbing, but the tree grows taller and my mother lifts farther and farther away. When I look down there is no island anymore, just the tree I'm in, growing in the middle of a vast ocean, and the water is rising.
Then I woke up.
It was still the middle of the night, but suddenly I wasn't sad anymore. I knew what I would do—it was as clear as anything I had ever known.
I would bring back my mother.
Somehow, somewhere, there would be a way to do it. Maybe it would be through the magic of a tree like the one my father had told me about. Maybe it would happen after I built myself a set of wings and flew to wherever it was she had gone. If I found her, I could convince her to come back with me. Maybe I'd have to travel to a faraway land and find the secret to bringing someone back from the dead.
It didn't matter. My father had told me many stories of warriors and heroes who had managed to travel to that place people go when they die, and I thought there must be some truth behind all those stories. I would find the way. I felt an immense sense of purpose and peace in knowing I had a mission, and that mission was to bring her back.
I remembered the three women. If anyone knew what I had to do to bring back my mother or where I could go to find her, it seemed to me that they would know. There was something about them that felt like the answer to every unknown thing. It was easy to believe that hidden somewhere in the folds of those great gowns was the truth I needed. I would go to the fair and I would find them and they would tell me how.
I fell asleep and slept peacefully the rest of the night. But the darkness I had taken with me from the cemetery grew just a little bit inside me.
## 6
"WHY DON'T YOU TWO meet me back here in one hour?" Abra's mom suggested. She was a plump woman with curly brown hair. She smiled a lot, but worry clung to her like a subtle perfume, and it took all of Abra's cunning to get her mom to approve of anything that might be even slightly dangerous. I have no idea how Abra talked her mom into dropping us off at the fair on opening night, but somehow she had. I can only believe that my memories of those days are true, that they were simpler times when children were safe walking the streets alone, at least in Deen.
"Mom!" Abra complained. "That's not any time at all!"
Mrs. Miller sighed and looked down at her watch. Cars coasted past us along Kincade Road, dropping people off at the sidewalk before turning off into one of the large grassy areas to park. The lights from the fair reflected off Mrs. Miller's face, blinking and changing color.
"Okay, two hours, but that's it."
Abra squealed. "Thanks, Mom! Thank you thank you thank you thank you—"
"Fine, fine," she said, smiling, but her face grew serious. "Listen to me right now, both of you. You are allowed in the food area and the front part of the ride area, but no going back into all of that . . ."
She couldn't seem to come up with a word for the part of the fair that was the farthest from the road, the area down the hill beyond the rides. She waved her hand at us, knowing that we knew what she meant.
"That darkness," she muttered.
Our fair had five parts. Not that they were divided into specific categories or marked with boundaries, but you could tell as you went from one part into the next. As you left the road and went down the hill, you descended deeper and deeper into the various sections.
The first part of the fair was made up of the place where everyone parked, plus the road, plus a large chunk of food tents. It was always packed full of people of all ages, and it smelled the best too. Cotton candy, funnel cakes, fried anything-you-wanted-to-eat, candy apples—my teeth began to ache as soon as I so much as walked into that area. The lights there were bright as vendors tried to outdo each other with flashing bulbs and gaudy signs. Here everyone was in a happy and smiling stupor brought on by sugar and grease.
Down the hill a short distance—the tents and pavilions were all laid out roughly in rows—you got to the animal pens. Here you could find various award-winning beasts on display: sheep, cows, horses, chickens, rabbits, that sort of thing. The lights in this area were bright and glaring and uniform. Plain white. You always knew when you had wandered out of the food area because the animal area smelled like horse poop, the people had serious looks on their faces as they waited for the judges' scores, and they all wore overalls.
Past the food, past the animals, were the kiddie rides. Tiny Tilt-A-Whirls and miniature roller coasters roared around slides and the crown jewel of that area, the carousel. Loud, happy carnival music pierced your ears. This far down the hill, the smell of the food was a distant memory. The carnies who ran the kiddie rides had abnormally large smiles and probably doubled as Santa's creepy elves in the winter. Parents surrounded the rides, pointing and waving and laughing.
Farther down, farther in was the fourth area of the fair. These were the serious rides. The ones that threatened to steal the food you had just eaten at the top of the hill. This area was marked by teenagers hanging on to each other, screaming voices, and large chunks of shadows. Sometimes, if you didn't pay attention to the general flow of traffic, you would end up behind a ride in some kind of dark dead end.
This area housed the Ferris wheel, the House of Horrors, and anything that spun you wrong-side up or tried to turn you inside out. There the carnies were indifferent, even mean. They sneered when they took your tickets and took pleasure in stopping the rides at the most awkward moments, like when you were upside down. I think they kept track of how many kids they could make throw up, as if it was a contest they held among themselves.
At the very bottom of the hill, past the serious rides, was the "darkness" Mrs. Miller had mentioned. There the trees came up close to the small tents and dark trailers. There, for only one dollar, you could see a woman with two heads or a man with the body of a snake. Old, blind hags would tell you your fortune for fifty cents, or put a curse on your enemy.
When I was in kindergarten, one of my friends was accidentally stabbed with scissors in the art room when he tripped and fell. His blood spilled all over the floor like paint, more blood than I had ever seen. One of the girls passed out, and the art teacher's skin turned clammy and white as she called for help through the intercom. Later we found out that he had been to the dark part of the fair—who knows what someone his age had been doing there, or if it was even true. The kids all said he had mouthed off to one of the old carnies, who had in turn cursed him, calling down his death, and that the curse had almost worked.
There, among the trees, you could also see the remnants of campfires and tattered tents strung up with the help of low-lying branches. That's where the carnies lived during the weeklong fair, down at the bottom of it all—the darkest place—where the air smelled of wood smoke and porta potties, and a constant fog drifted like a lazy river.
But when Mrs. Miller dropped off Abra and me, we were still on the sidewalk surrounded by the light and the laughter of happy people eating fair food. She put a five-dollar bill in each of our hands, and we turned to face the fair, our eyes transfixed by the glory and freedom spreading down the hill in front of us.
"Two hours!" she called again with that same old worry in her voice as she drove away.
"Ready?" Abra said. I nodded and followed her.
It had been only forty-eight hours since my mother had died, but I couldn't wait to get to the fair. I knew the old women were there—I could feel it.
My mind raced. Abra would never disobey her mother and join me if I had to go into the Darkness. How could I get away from her? The words the woman had etched into the table had somehow found their way into me, and nothing could erase them.
Find the Tree of Life.
"What do you want to do first?" Abra asked.
"Bumper cars?"
She laughed and nodded and led the way through the crowd. We would buy food at the end if we had any money left. She reached back and grabbed my sleeve and pulled me along. That first hour passed quickly: bumper cars, the large Tilt-A-Whirl, and finally running into some friends from school who convinced us to join them on rides I was too scared to go on when it was only Abra and me. They ran back up to the street to meet the parent who was picking them up, and Abra and I still had some time left before her mother was going to meet us.
The best part about that night was that I forgot about real life for entire patches of time. Later I would feel guilty about it, but while we were on the rides and screaming and laughing with our friends, for brief moments I forgot that my mom had died. I forgot about the lightning tree. I forgot that my dad waited at home for me, silent and lost. So we ran from here to there and the lights flashed and the sadness inside me receded, like the slipping of the waves as they approach low tide.
"What next?" she asked.
"I could use a break," I said.
"Me too. How about the Ferris wheel?"
So we wandered all the way down to the bottom of the area where the rides were located, just on the edge of the Darkness. It was getting late, so the line for the Ferris wheel wasn't very long—it was mostly made up of teenagers hoping to get some time alone with their boyfriends or girlfriends. Eventually Abra and I were in and riding to the top, stopping every few seconds as more people got on.
The Ferris wheel stopped for longer than usual when we got to the top. It always sort of took my breath away, being up that high. I could see Kincade Road, and I followed it with my eyes to the main intersection in town. I could even see the antique store and the baseball field behind it, although the field was mostly dark. Cars were lined up on the street because of the fair, trying to get out of town, and their headlights and brake lights formed a perfect T where Kincade Road ran into Route 126.
I looked the other way, north on Kincade Road into the darkness of the countryside.
"Hey, Abra, there's your farm," I said.
"And there's yours," she replied.
They looked like lonely outposts, those individual pinpoints of light surrounded by so much night.
I looked closer, down toward the bottom of the fairgrounds, and a strange sense of foreboding filled me. Mrs. Miller had been right to call it the Darkness because it was empty and black. There was something alive about that Darkness, something moving and throbbing. It felt like something barely contained, as if it might break out at any time and take over. My eyes scanned the dim light around the low-burning embers of dying fires, searching for the three women I had seen on Friday.
I saw a few dogs tied to stakes, the kinds of dogs that looked like they would rip your head off first and bark later. There was a group of six tents at the back, under the trees. They caught my attention because their stakes barely held them to the earth. The tents' canvases flapped wildly in even the lightest of breezes. They billowed like robes.
Then I saw them. Three old ladies, hunched over, worked among those tents. They gathered things off the ground, then threw them into the fire. This sent up writhing flames at each offering. I couldn't be sure the ladies were the same three from the antique store, not from that distance, but they looked old and fragile, and one of them had a thick stick in her hand that she leaned on.
I tried to memorize the quickest way back to where they were, but the tents and trailers and trucks in that part of the fair made up a kind of scattered maze. If I was going to find that spot, it would be based simply on my sense of direction.
"What do you see?" Abra asked.
"See those ladies?" I said.
She nodded.
"They were in the back of the antique store on Friday, when you and my mom came looking for me."
"Huh." She shrugged, and I could tell she wasn't impressed.
I couldn't keep it in any longer. I had to tell someone. So I told her what I had seen inside Mr. Pelle's prep room. I told her what I had read on the table.
Abra's eyes squinted in thought, her mouth in a straight line. I could tell she understood why it was such a big deal to me. But I didn't tell her about the one old woman who had drawn a circle around me, the way the stick grated against the stones, the way I couldn't move when it was completed. I was having enough difficulty believing that one myself. So much had happened since that moment.
The Ferris wheel crept back toward the earth.
"C'mon," Abra said with resolve. "We need to talk to those old ladies."
"Really?" I asked. It was something I desperately wanted to do, but when she said it out loud it kind of scared me.
"Hey!" she shouted at the carnie operating the ride. "We're getting off here."
He didn't stop the Ferris wheel, but that didn't stop Abra. She pulled the bolt that locked the door, opened it, and hopped out of the slow-moving car. I was right behind her.
"Hey!" the man called out. He had a patch over one eye and an unlit cigarette propped in his mouth. It stuck to his top lip when he talked. "You can't get out when the ride is moving."
"So kick us off!" Abra shouted back at him.
We ran around the side of the Ferris wheel. That bottommost part of the fair was unofficially portioned off by a line of 18-wheelers parked on a stone lane. We peered between the trucks. It seemed especially dark back there. Somewhere off in the distance I heard voices and laughter from the food section at the top of the hill, but there, as we faced the Darkness on the other side of the trucks, those sounds seemed to be a million miles away.
"Well, what are we waiting for?" Abra asked, and even though she was trying to sound brave, fear left little edges in her voice, edges that caught in the air. I stood there, frozen in space, but she took a few quick steps and vanished on the other side of the trailers, melting into the shadows.
I followed her.
## 7
THE FIRST THING I NOTICED when we entered that lowermost part of the fairgrounds was the lack of sound. The fair we had left behind on the other side of the huge trucks suddenly sounded muffled, like a thick curtain had been drawn between two worlds. The air around us felt ancient and full. Almost all the carnies were working the fair, so the Darkness was empty too, like a ghost town.
But there was a sound, the kind of sound that grows on you in the silence, the kind of sound that's always been there but you haven't noticed before. As we snuck farther in, I realized it was the sound of classical music playing on an old record player. After about a minute, the record got stuck, always at the same exact sequence of notes, and those notes would scratch and repeat and scratch and repeat for as long as it took the listener to walk over and put the needle back at the edge of the record. The music started up again, loud and moving, headed inevitably for the scratch that would knock the needle into repeat.
"Shh," Abra said, raising her finger to her mouth, listening. "Which way?"
I pointed down the hill to the right. Abra nodded and walked ahead. I followed her. Because grass covered the ground in that part, it was possible to walk without making any sound. It was possible to creep around corners and stand quietly in shadows while strangers walked by, muttering or crunching up beer cans in their hands and throwing them under the trailers. The air seemed to grow warmer and heavier as we descended. High up above us, the moon shone through that hazy July night.
I wasn't even sure why we were there. What did those three old women have that I wanted so badly? Why did those words that I read, etched into the table in the back room of the antique store, mean so much to me?
"Look . . . at . . . this," a shattered voice said, the three words coming slow and spaced apart and filled with wonder at some unexpected gift. We turned. The voice belonged to a man. He wore a white tank top, jeans, and unlaced, heavy work boots perfect for stomping on things. When he took another step closer, the boots flopped around, loose on his feet. Black hair covered his arms and the backs of his hands and sprouted out of the edges where his tank top ended. He had a beard that tangled its way down his chest, and his eyes were hidden in deep shadows. He held a leash in his hand that restrained a medium-size, powerful-looking dog that growled when he spoke.
Abra and I leaned closer to each other. I felt her grip on my arm.
"Now what on God's green earth are two pretty little children doing . . . back . . . here?" he asked, and his smile was all blackened teeth and cracking lips.
"We're looking for three old women," I mumbled.
"What's that?" he said, smiling bigger and letting his dog drag him one step closer. "I can't hear you, kid. You scared or something? Your voice is all shaker-y."
I don't know if he was just trying to scare us or if he would have done something terrible, maybe cut us up into little pieces and feed us to his dog. I had visions of my bones lining whatever hole he kept that animal in. I imagined his canine going back days later and gnawing on my femur.
"We're looking for three old women," I said louder.
"You don't want to find them," he said, still mean and aggressive, but the mention of the three old women had changed something in him.
"Why not?" Abra asked. She was always asking why. Always.
The man loosened his grip on the leash, and the dog jumped at us, only to be jerked backward when it reached its new limit.
"It doesn't matter," he said. "My dog's hungry. And little children shouldn't be wandering around back here behind the scenes."
Then he stopped and pulled the dog closer. The change that came over him was almost comical. He went from leering and confident to skittish and uncertain. The dog crept backward and hid behind the man's legs, the hair on its back standing up.
The three old women came out of the shadows. I hadn't even noticed them until Abra tightened her grip on my arm. I glanced at her, and her wide eyes stared off to the side, into the trees. At first I thought the women were floating. They walked with light steps, and the remaining parts of their fragile bodies stayed very still. Instead of those gypsy scarves they had worn in the antique store, they were donned in cloaks with hoods pulled up, casting shadows over their faces.
"Aw, no, that's not, it's not, you know . . ." His voice went on and on, making no sense, explaining himself even though no questions had been asked of him.
The three women got closer. The one in the front held a stick. The second woman held a large bowl in her hands. The third woman hung back. She stopped and crossed her arms, her bony wrists vanishing in the thick folds of her cloak.
The man kept talking, but his voice was now a whisper. The woman with the bowl walked over and held it out to him. She didn't say a word, but somehow I knew that she wanted him to take it.
"You hexin' me?" he asked in a frightened, belligerent voice. "You know you ain't allowed to be hexin' us. You know that, not if you wanna keep traveling. They won't let you stay, you know that."
The woman sighed but didn't say a word, just pushed the bowl closer to him. He took it from her, and it must have been very heavy because he nearly dropped it, and when he walked away he had to keep balancing it on his legs or his hips to get another grip on it. Sometimes he set it down and stretched, as if his arm muscles were tired, but he always picked it back up again. He walked away into the shadows, finally crouching and disappearing inside a green tent that had a bright blue tarp as a door.
"Remember," she called after him, the single word carrying more meaning in it than an entire book of stories. Her voice surprised me. It sounded young and beautiful.
I was relieved. As far as my imagination was concerned, the dog's teeth had come all too close to ripping the flesh from my bones. I wanted to say thank you. I looked over at Abra and smiled, overjoyed at our unlikely salvation. I expected her to return my relieved glance, but the look on her face sent a jolt of uncertainty through me. She didn't look relieved at all. She looked horrified.
The three women walked toward us, but somehow they looked completely different than before, when I had seen them in the antique store. All three of them had their mouths open, as if gasping for air that never came. Their eyes formed hollow, dark caves, and the whites were barely visible. Their cloaks weren't black or brown or gray but shadow colored—which didn't make sense to me at first, but I don't know how else to explain it—and around the edges of the hoods I thought I saw thin worms crawling all around their heads. I realized it must be hair, silver and wiry and somehow moving on its own.
They were in some kind of a trance, and the one with the stick nudged us apart and began drawing a circle around Abra.
"No!" I said, pulling Abra toward me.
The old woman looked at me, and I could tell she was annoyed. She tried again, pushing her stick between us and plunging it into the earth.
"No, I won't let you do it," I said, suddenly aware that the faraway recording of classical music was stuck and repeating itself.
The other two hovered over to us, and the three of them stood there for a long time, staring. They looked disgusting, like rotted corpses somehow moving, somehow alive. A kind of reluctance moved around them like a cloud, and they turned to go.
Off in the distance I heard the record scratch and start over again.
"Who were you talking to in the antique store?" I asked, my voice loud and out of place.
They stopped, and one of them answered, or all three of them answered, but we couldn't tell who was talking because they never faced us.
"Jinn," I thought I heard them say.
"Jinn?" I asked. "You mean my neighbor?"
But they didn't give an answer.
"What's he got to do with anything?"
"His story, not yours," one of them said in a weary voice.
"Well, what's it got to do with me?" I asked, feeling bolder with each question answered.
"There is a certain kind of death that leads to life," they said, and in that moment I remembered my mom, and it made me tired and sad and homesick. I didn't care so much anymore about this great mystery. I wanted to go home and find my dad and sit with him. But all the questions I had, all the things I wondered about, fought through my sadness.
"Why did you write 'Find the Tree of Life' on the table?"
"Because the Tree is here. Now."
Their answers frustrated me, but even more than that, my questions frustrated me. I'd had this idea that if I asked the women the right questions, they would tell me everything. But the right ones eluded me.
"The Tree of Life? What is it? Where is it?"
They took a few more steps away.
"Why'd you draw a circle around me?" I asked.
"For protection," they said, still drifting away.
"Protection? Protection from what?"
"Protection from what lives in the shadows," they said.
They were almost gone, off into the shadows.
"What if I need to find you again?" I blurted out.
They turned a corner, one after the other, still walking slowly, still hunched over. In the silence around us I could hear the gentle thud of the first woman's stick against the ground.
"What is coming?" I shouted after them. When they didn't say anything, I moved to chase after them, but Abra grabbed my arm.
"No. We're out of time. We have to go."
"I don't know what you were thinking, young lady," Mrs. Miller said from the front seat for at least the tenth time. Abra and I were both in the back. Her mom had been talking nonstop since we had found her walking up and down the sidewalk along the road. She had looked frantic, pacing and craning her head to look into the fairgrounds.
We knew the best defense in that case was not to say anything, so we sat quietly. Eventually Mrs. Miller's voice faded in my mind as I thought about everything I had seen and heard the previous few days. What had happened to the small town I knew and loved? Why were all of these strange things happening?
"Answer me, you two!"
I looked up. Abra looked at me. She must have stopped paying attention about the same time I had.
"Um . . . what's the question again?" she asked.
"What! You haven't even been listening! Young lady, you just wait until I speak with your father. The question was, 'What will you do next time?'"
"Come straight to the car."
"That's right. Straight to the car. No dillydallying."
We had to look away from each other so we wouldn't start laughing, but as I stared out into the night, a seriousness settled over me. Something very big was going on in Deen. Something important.
We cruised north into the valley, leaving the blinking fair lights behind us and drifting into the open space of farm country. But it was such a different darkness there than the Darkness at the bottom of the hill at the fair. The darkness in the country was warm, welcoming. It was punctuated by stars and fireflies, and when we stopped at the unnecessary stop sign I could hear the distant rushing of the river as it drifted south, nearly overflowing its banks. It was at that age that I learned there is darkness and there is Darkness, and the difference between the two is day and night.
Mrs. Miller turned left at the church, drove up my lane, and stopped, not turning off the car. Between the lane and the house was the yard, and in the yard was the tree. The lightning tree. I tried not to look at it.
"Thanks, Mrs. Miller," I said, feeling sheepish after the scolding she had given us.
"Good night, Samuel," she said, sounding stern, but when I glanced up at her there was a softness in her eyes. I guess she was remembering that I had just lost my mother, and as the sadness gathered and tugged at her face I wanted to reassure her, tell her not to worry. I was going to bring my mother back—she would see. The three old women would help me, and I would go wherever I had to go, do whatever I had to do.
But I didn't say anything. I only nodded at her.
"See ya, Abra."
"See ya, Sam."
I climbed out and walked through the darkness to the farmhouse. I went inside and the screen door slammed behind me. I left the main door open because it was warm inside, and outside the cool night air had started to settle. It felt more like the end of September than the beginning of July.
My dad was on the sofa watching a baseball game. There were no other lights on in the house, so the light from the television flashed and swam all around him. His face was blank, and when I got close to him I could see the white square of light from the television reflecting in his eyes. For a moment I realized what he had lost, or came as close to understanding as a child can come.
"Hey, Dad," I said.
No response.
"Had a good time at the fair tonight," I said, shuffling my feet, kicking at the worn carpet. "Crazy stuff going on over there."
He still didn't move, just sat there staring at the game, unblinking. I backed away slowly, wishing I had gone straight up to my room without speaking. At least then I wouldn't have had to endure him not saying anything.
"'Night, Dad." I walked up the steps, each stair creaking under the weight of my sadness.
# Part 2: The Tree
## 8
SO MANY YEARS HAVE PASSED. I sit out there with the oak tree not far away, my chair creaking on the old porch, and I light my pipe filled with cherry tobacco, the scent of which reminds me of Mr. Pelle and playing baseball and being a boy. Dusk is my favorite time of day, especially during the summer when it stretches long and lazy and the stars whisper to each other in the heat. Before coming outside, I opened all the windows on the main level, something that took me a bit of time to do, but the house needs to breathe at the end of a long summer day. I will spend the rest of the evening here on the porch, watching the fireflies blink and the day fade to black.
So many years have passed.
Tonight, as I walk through the screen door, I realize Boy is sitting on my porch roof, his legs dangling down. He surely hears me come outside but doesn't say anything. He doesn't pull his legs up, so he must not be hiding. I guess he's waiting for me to say the first word. Two can play at this little game, and I can guarantee you that an old man can outlast a boy when it comes to waiting. I've been waiting for decades longer than he's been in existence. Waiting for what? I'm not sure. But I'm good at it.
As I sit in the chair, I sigh with relief and pull my pipe and tobacco out of my pocket. I slowly go about packing the leaves into the pipe with my finger, the nail of which is stained brown along the edges from so many nights. I pull out a stainless steel lighter with the engraved letters SC on the front and spin the wheel. The flame dances into being. I hold it over the pipe and puff until it comes alive.
He makes me smile, this boy and his antics. I remember climbing up on that very roof when I was a boy, and I remember feeling bigger than everything, bigger than the world. There's something about climbing, something about the possibility of falling, that takes your breath away.
I become so engrossed in my nightly routine that I nearly forget about the boy, his feet dangling down from the sky.
"You know smoking is bad for you, right?" he says.
"Zat so," I say, inhaling, then sighing the smoke into the night. Sweet relief.
"Yep. Gives you cancer."
"Huh," I say. "So if I smoke, I might die of cancer before I can live a long, full life?"
He doesn't respond to that. He climbs down one of the decorative iron rails that prop up the front porch and sits on the step in front of me, keeping his face toward the night. Now that he's up close I notice for the first time that he's a rather small boy, not frail but wiry. When he talks it's like he's playing a chess match, not moving unless he can predict his opponent's next move. He doesn't say anything open-ended, anything that might lead the conversation in a way he cannot predict. It's a rather intriguing trait for such a young boy, this measured way of talking. His hair is curly and unruly, and his nose is round. When he looks at me over his shoulder, his green eyes flash in the light coming through the screen door.
"I guess you know why I'm here," he says in a glum voice. His eyes dart up and meet mine, then he turns again to face the darkness.
I lay the pipe down on the arm of the wooden rocking chair and shake my head. "No, I guess I don't."
He looks at me with surprise. "Thought my dad came by here today," he says. "Didn't he tell you?"
I shrug. "Let me ask you something before you get into all that."
"Okay."
"Do you like hot chocolate?"
"Hot chocolate?" His eyes light up, but he recovers his defenses and tamps down his happiness. "In the middle of the summer? Don't you have any ice cream?"
Kids these days. They don't know nothing about nothing.
"I guess I do," I say, trying not to grit my teeth. "But I've only got vanilla. I'm not much for all of these newfangled flavors with the fixin's already inside."
"I only ever eat vanilla," he said in a determined voice, as if it was a sore temptation to eat all the other delicious flavors and it was only by a supernatural feat of self-discipline that he managed to remain unswerving in his devotion to that plainest of ice cream.
"Well, then, vanilla ice cream it is."
I stand up and walk back inside, leaving my pipe on the arm of the rocking chair. A thin wraith of smoke rises out of it. At first I'm not sure if he will come inside with me, but I go into the kitchen anyway and take down two bowls. I open the freezer and find the ice cream, and by the time I'm closing the freezer door, Boy has come inside and made himself at home in the kitchen.
"Sure does smell funny in here," he says.
"It's because I'm old," I reply. These things don't bother me anymore. "You'll smell funny too when you're my age."
I bring two bowls of plain vanilla ice cream over to the table and set one down in front of Boy.
"I guess I have something to say before I eat your ice cream," he states in the same voice he used to proclaim his undying love for vanilla.
"I guess you'd better say it and get it over with before this melts."
He takes a deep breath, and when he speaks the words come out much quicker than usual. "I'm-sorry-for-the-smoke-bombs-even-though-I-saw-you-kick-the-cat-and-you-kind-of-deserved-it."
I try hard to keep from laughing. "Boy, did anyone ever tell you that you're incorrigible?"
He shakes his head.
"Well, you are. I kick cats sometimes because I hate cats, but it's a mean, nasty habit, and all it does is show that I've got some meanness stuck inside me. I'll try to do better."
He nods.
"That is," I say, glaring at him, "if you agree to stop hitting me with corncobs."
He nods again and takes a big bite of ice cream. Through the cold whiteness he murmurs, "I guess I have some meanness stuck in me too."
We eat quietly.
"I hear your friend is dead," he says. It's hard to get used to, the unrelenting nature of his words, the way they dart out of nowhere and stick you in the most sensitive places.
I take a deep breath, nod, and sigh. "Yes, indeed. My friend is dead."
It sounds rather bleak when I say it that way and not in the normal past tense: My friend died. It's much more polite to talk about death in the past tense, and it doesn't feel as bad.
But it's true all the same, I think. She is dead.
"Was she nice?" he asks.
I nod again. I feel the need to do something physical like nod or sigh before saying words to this boy. I feel the need to create space between the sentences.
"The nicest of all."
"When are they going to bury her?"
"The funeral is in a couple of days," I say, shrugging.
"Are you worried about it?" he asks, and I wish he would focus on his ice cream.
"I've been to many funerals in my life," I say. "I suppose one more won't hurt."
"But she's your last friend."
I look up at him and chuckle, because if I don't I might cry. "Where in the world did you hear that?"
"My mom told my dad."
I shake my head the way a boxer shakes his head after taking an uppercut to the jaw. "Yes, she was my last friend."
Outside, the crickets have begun to chirp and some other noisy bugs have started up alongside them. I'm hoping Boy leaves soon so I can return to my pipe. Conversations tend to exhaust me. I'm not used to them anymore. I'm not used to sharing the inside of my brain with someone else.
"What's your name, anyway?" I ask.
"Caleb," he says.
"Really? Caleb?"
This boy is full of surprises.
"Yeah, why?"
"Oh, I had a friend named Caleb when I was a boy."
"What happened to him?"
"What happened to Caleb?" I ask myself. "What happened to Caleb? That's the question, isn't it. What happened to Caleb."
I remember Caleb Tennin lying on the forest floor. I remember the way the rain sounded coming through the trees and the sound it made falling on the Amarok right there beside me. I remember how the Tree of Life shimmered behind me like a mirage.
Caleb, where did you go?
## 9
I'M NOT SURE WHY I thought news about three strange dogs would make my dad finally speak to me. My mom had died in the lightning tree on Friday, and he'd barely said a word since. His voice seemed to have passed right along with her. Our paths crossed in the house and in the barn, and he made meals at the proper times, but his eyes were somewhere else.
When I saw the dogs in the front yard, walking around and nipping at each other, they gave me a strange feeling, like something out there was watching me, keeping an eye on me, and not in a good way. I hadn't seen them before, and it was unusual to see strange dogs in the valley. They foamed at the mouth and didn't behave like normal dogs, and even though they looked like black German shepherds, they were bigger, like wolves. But we didn't have any wolves in Deen. At least I didn't think so. I wondered if they had come down from the mountain.
I walked into our small living room. It was hot in there. The windows were open and a breeze smelling wet and green came through the screens, a summer day after a storm. In fact, it had rained, with thunder and lightning, off and on since Friday. Ever since my mom died. Every time lightning struck, I had this image of the tree, its largest branch shredded and broken, hanging down toward the ground. But on the day I saw the dogs, the storms had cleared and the July sun threatened to get hot.
"I saw three dogs," I told my dad quietly, not sure if he would even look at me. "I think they were sick."
My dad glanced up from his brown armchair. I missed being a little kid and sitting there with him, cheering on our favorite baseball team or pretending to watch world news in the evenings. I used to fall asleep there, and he'd carry me up to my bed. Sometimes I'd pretend to be asleep so he'd carry me.
It was strange, him sitting there. I couldn't remember anything like it ever happening in my entire life, not on a Monday morning—Monday was a day for work, a day to make up for not working on Sunday. What would happen to our farm if Dad didn't recover? I wondered if the world would fall in on us.
"Why?" he asked.
The sound of his voice sent a shock wave through me, a pulse of joy and sadness, and I didn't know if I could answer his one-word question without crying. I hadn't heard his voice since Friday night.
"Their eyes didn't seem right. They were foaming at the mouth. They didn't run away, not even when I shouted at them."
"Rabies," he mumbled. "Are they still out there?"
"Not last time I checked," I said.
"Let me know if you see 'em again. I'll have to shoot 'em."
I nodded. It was good to hear his voice again, but it was different. He sounded tired and sad and on the edge of giving up. He leaned back in his brown armchair, sighed, and turned the television up even louder. The announcer's voice tried to drown out the emptiness in the house, but nothing could do that.
Just a bit outside for ball three. He's having some trouble controlling those pitches today. Not sure how much longer he'll be in the game. And now the bull pen is warming up.
I backed slowly out of the room. Ever since my mom died, Dad had kept the volume on the television louder than usual. It made my brain feel garbled and overwhelmed.
Suddenly there was a snarling outside, by the lightning tree.
I pushed open the screen door and it slammed behind me. Dad was always reminding me not to let the screen door slam. I stopped on the porch. Huge puddles sat everywhere in the yard—hidden in the grass and filling the potholes in the lane—and they were as blue as the sky they reflected. I heard a loud yelp and looked at the tree. Right there at the base, right there where the lightning scar met the grass, a crowd of animals was fighting.
"Dad!" I shouted. "Dad!"
There they were, the three large dogs. The other two animals were brown and furry and low to the ground, stocky and thick. When the animals drew apart for a moment, I realized the two small ones were groundhogs, and they seemed to be fighting the dogs. Then they were all back together, rolling and snarling and biting and clawing, a pile of chaos and teeth.
My dad charged through the door, raised his gun to his shoulder, and BANG!
The three dogs ran down the lane. My dad released the spent shell and moved the bolt back and then forward, pushing another bullet into the chamber of the gun.
BANG!
A small burst of dust flew up right beside the dogs. They ran faster over the road, dashed past the church across the street, and disappeared into the graveyard. Dad ran after them, his gun in hand. I walked toward the oak tree.
One of the groundhogs had disappeared into the garden, but the other one was still at the base of the lightning scar, and it wasn't moving. As I got closer, I could see it was still breathing, its furry chest rising and falling. Blood oozed from a bullet wound close to one of its front shoulders, matting its fur.
I picked up a small stick and nudged it. It shifted its weight a bit, but it couldn't seem to move. I got down on my knees beside it. I had never seen anything die, at least not until the Friday before, but even then I hadn't actually seen my mom pass away. Just a lightning bolt, darkness, and the space where she had been.
The groundhog's eyes were still open and shining. Its little tail twitched once, twice. Besides that, it didn't move much at all. Even its breathing came on either side of a long stillness. When I looked back at its eyes, I noticed that the groundhog was studying me, taking me in, as if he had heard a lot about me from someone else and was now seeing me for the first time.
The groundhog made a funny sound, so I moved even closer. But it went limp. It was dead.
My dad came walking slowly back up the lane. A strong breeze blew the lightning tree above me, and a thousand drops of rain from the previous storm fell on me and the dead groundhog—cold, wet drops that went down the back of my shirt and hit me hard on the top of the head. I knew my dad hadn't gotten any of the dogs because he walked slowly and came with only his gun in his hand.
I sat down on the wet ground with my back against the tree. My dad walked past me and into the house without saying a word. The farm seemed saturated with a great emptiness.
A few hours later I was back in bed. It felt strange lying in my bed during the day, sunlight streaming through my window, but nothing else felt right either. I heard my dad watch the end of the ball game, and he kept the volume loud—so loud, in fact, that I could follow the game pretty well from up there in my room.
My mother's funeral was scheduled for the next day, Tuesday, but all I could think about was the groundhog and everything that had happened in town that week—the man in the shadows at the antique store and the three old women. Mostly, though, I kept replaying the words I had seen written in the middle of the table.
Find the Tree of Life.
Had I really seen that? Or was my mind making stuff up? If I went back there, would that table still be there with the words scratched on it? I wondered if Mr. Pelle would let me go to the prep room or if I'd have to sneak in.
The sound of the television stopped. Dad must have turned it off. I heard his footsteps move across the creaky floor to the steps. He came up the stairs very slowly and stopped outside my room. I could see his shadow through the crack under the door. For a moment I wanted to run over, fling wide the door, and give him a huge hug. I didn't want to feel so alone anymore.
But I didn't. I was angry. Angry that he had killed the groundhog. Angry that he wouldn't talk to me now that Mom was dead. Angry that Mom was dead. Angry that life was changing. Angry that I had to figure out how to bring her back on my own.
The door started to open.
I fell back onto my pillow, held my breath, closed my eyes, and pretended to sleep. I could feel my dad looking at me from the doorway. Again I fought the urge to jump up and run to him. I heard the door creak shut. He was gone. I took a deep breath and let out a long, confused sigh.
I crept over to my window and put my chin down on the windowsill. I stared hard at the massive oak tree now marked by the lightning, the sunlight glinting off the leaves. I peered toward the church, searching for signs of the dogs. I didn't see any of them, or the remaining groundhog. They were gone.
Then I saw a man.
He walked up our lane, limping. He was a short, round person with a thick neck. He wore navy blue work pants and a button-up shirt. He wasn't walking fast, and he stopped every thirty seconds or so to take a comb out of his front shirt pocket and brush his hair straight back. And he was constantly frowning. Or scowling. Or muttering words to himself.
He stopped by the oak tree, in the spot where the animals had been fighting, and he got down on one knee and reached toward the ground. He touched the wet grass and raised his hand up close to his face, scowling the entire time. He ran his hand down the long, pale scar the lightning had left.
He turned and walked toward the house, and as he got closer, I thought I had seen him before. The way he hobbled from side to side, the shape of his shoulders and the roundness of his body—all of it reminded me of the man in the antique store. Granted, I hadn't seen the man's face, but I couldn't help but think this was him.
He kept walking slowly, always limping, sometimes stopping to comb his hair, and when he got close enough to the house I could no longer see him. I heard his footsteps go up onto the front porch and move toward the front door. All went silent.
And then I heard a loud knock.
## 10
WHEN I HEARD THE KNOCK AT THE DOOR, I knew I'd have to go answer it. There was no way I could stay up in my room and pretend I wasn't there. I felt certain there was some connection between this man and everything else that had been going on. I wondered if he might be a piece of the puzzle in bringing my mom back. He had connections with the three old women. He might be able to help me.
So I left my room and walked down the stairs, trying not to make a sound. I wasn't even breathing. I crept to the edge of the door and stood there, my back against the wall, waiting for who knows what. It's one thing to decide you should talk to a complete stranger who you think might be a little bit crazy. It's another thing entirely to open the door and let him into your house.
I heard a knock again, really loud, so hard on the wooden frame that it made the screen door rattle. I took a deep breath, and as I was about to look through the door, I heard a voice I didn't expect.
"Sam? Are you in there?"
I looked through the screen. It was Abra.
"What are you doing here?" I asked as I opened the door.
"I don't know. I'm just here."
"No, no," I said. "There was a guy out by the tree. He started walking up to the house. I heard a knock . . ."
"Which was obviously me," Abra said, then asked in a quieter voice, "Are you sure you're feeling okay?"
Her blue eyes got all sad, and I knew she was thinking about my mom, which made me feel sad.
"I'm fine," I muttered. I pushed past her and walked down the porch steps and out into the yard.
"What's wrong?" she blurted out. "I mean, I know what's wrong, but is there something else?"
We walked through the soft ground over to the tree, and I leaned against the trunk. I looked at the lightning scar that had split the bark, and there were definitely red marks on it from where the old guy had been touching it. He must have touched the blood on the ground where the groundhog died and used the same finger to examine the tree.
"There was an old man here not thirty seconds ago," I said, looking hard into her eyes. "These are his fingerprints. I don't care if you believe me or not."
"I believe you," she said, and I knew she was telling the truth. She gave me a hesitant smile and pushed some strands of her blonde hair back behind her ears. I went ahead and told her about the three dogs and how they fought with the groundhogs, how one of the groundhogs had died, and how it gave me a strange feeling.
"It's all connected somehow," I said, wishing I could figure it out. My voice trailed off under the weight of that uncertainty. We sat there in silence for a long time. I noticed a shovel stuck in the ground in the corner of the garden, so I walked over to it. Abra followed me, her shoes squeaking in the wet grass.
"I'll bet my dad buried the groundhog here," I said, looking over at Abra. But she was looking up at the sky, shielding her eyes.
I actually heard them before I saw them. Whoosh, whoosh, whoosh, long and sinister, like someone saying "Sh!" over and over again. I looked up.
There were at least thirty vultures. They glided through the air like dark holes in the sky, following each other around and around, looking for a place to land. The sound came from the long flaps of their wings—whoosh, whoosh, whoosh, the sound made when you swing a green branch through the air.
"Where did they come from?" Abra asked. Usually the vultures traveled the valley in groups of two or three, looping lower and lower to clean up roadkill, but I'd never seen that many in one group. The highest ones were nothing but black dots, but I could see the feathers ruffling on the wings of the lower ones, and their pink heads were bare and gaunt.
Suddenly they wheeled and flew in an almost straight line for the northern end of our farm, the side that bordered our neighbor Mr. Jinn's place.
"Jinn," I said.
"What?" Abra asked.
"Remember what the three old ladies at the fair said? They had been talking to Jinn at the antique store. Mr. Jinn."
"So what?"
"So what?" I said. "I want to find out what they meant by 'Find the Tree of Life.' If that was Jinn in there on Friday, he can tell me."
"Sam," Abra said, concern in her voice, "why do you care so much about this Tree of Life?"
I couldn't explain it because I didn't think Abra would believe me if I told her I wanted to bring my mom back. Or at least I was pretty sure she'd think I had lost my mind. I think I was scared that I wouldn't believe myself if I heard the words out loud, outside of my own mind. So I didn't try to explain.
But I knew there was something there, some connection between all the strange happenings and Mr. Jinn, the neighbor I had never seen before. Everything felt like pieces to a larger puzzle, a puzzle I didn't even have the picture for.
I put my hand on the shovel in the corner of the garden and yanked it out of the ground. It was a little long for me to use, and kind of heavy. I carried it in two hands, and my walk turned into a run as I passed the house and entered the cornfield, the same direction the vultures flew. I looked over my shoulder, and Abra was right behind me.
It was deep in the afternoon, that time during a summer day when it feels like the sun will never set. By the time we approached the northern edge of my father's fields, the vultures were already circling again, this time over a spot close to Mr. Jinn's ramshackle farmhouse. A few of them had landed and were hopping through the almost-waist-high corn, pecking at something.
I slowed to a walk and Abra practically ran into me. When I looked back past her, I could see the farmhouse where I lived way off in the distance, tiny against the southern sky. I was startled at how far away I had gone, and how quickly my familiar surroundings had faded. On both sides of us, off in the distance, the mountains stood like walls covered in the deep green of summer trees.
I held my finger up to my lips, bent over as low as I could, and crept forward. My jeans were already wet from running through all that corn. The stalks still held a lot of rain from the previous storms. A strong breeze came down from the mountains and raced through the valley. The sky was cotton-candy blue with puffy white clouds drifting from west to east.
Most of the vultures had landed. A few stragglers glided in and skidded to a stop. They tore at whatever it was they were eating, and they fought among themselves for the strips of dead flesh. I thought it must be a huge animal if all of those vultures were trying to eat from it.
"On three, we'll stand up and scare them off," I said.
Abra nodded, her big blue eyes reflecting the sky. "Sure must be something big," she muttered.
"One . . ." I gripped the shovel tightly in my hands. "Two . . ." I turned away from her, toward the host of vultures.
"Three!" we said together, and we both stood up and started shouting, waving our arms.
I didn't expect what happened next.
They came at us.
As soon as we stood up, they looked at us, cocking their heads to the side. Most of them raised their wings up as if they were trying to frighten us away. But as we kept yelling and I kept waving the shovel, they came at us, half flying, half hopping through the corn that was just about as tall as they were.
Abra scooted behind me, and I started swinging the shovel at whatever black shapes I could find.
"Get some rocks or something!" I shouted. Soon baseball-sized rocks started humming over my shoulder toward the approaching birds. She had a good arm and managed to hit a few. The first wave of birds paused, but when more started coming, they joined back in.
I had never seen anything like it. Vultures always fly away. Always. They might fly a short distance away and perch in the upper branches of a tree. They might drift to the other side of the road and wait for you to pass by. But they never stayed. They never advanced. And they most certainly never attacked.
What was going on?
I brought the shovel down hard on the first one that approached us. It didn't get back up. I caught the second one with a glancing blow and it kept coming, so I had to hit it again. And again. Which made me feel kind of sick because I had never killed anything with my hands before. I'd shot small animals with a pellet gun, and more recently with my dad's .22 rifle, but I'd never felt the impact. I didn't like it.
But I kept swinging because now they were on us. I heard Abra scream and saw that they had circled around behind us. She was flailing, and I realized she had one on her hands. She threw it away from her, but it came back faster than before. They tangled their claws in our hair and our clothes, and I imagined that they leered at us, suddenly aware that we were nothing more than scared children.
Soon all I saw was flapping black feathers and their naked little heads. Their beady eyes. Their beaks pecked at our faces and their talons reached for us. They were all over us. Abra let out a few screams as the birds started to overwhelm us, but I was silent. I don't know why—maybe I couldn't catch my breath with all those beating wings. Maybe I was so focused on fighting that my mind didn't have room for calling out. Maybe I didn't think there was anyone in the whole world who could save us.
I had always heard that vultures aren't strong creatures, that they can only eat food that's already been torn apart for them. Maybe that's true, but in that moment, covered with flapping, scratching birds, I thought we were goners. I thought for one moment that I was about to die.
At least I'll be with Mom.
I heard the blast of a shotgun as loud as thunder. Then another. The birds rose and heaved their bodies into the sky. I lay on my back in the corn and heard another shot. One of the vultures plummeted from the blue, and the rest flew west as quickly as they could. Another shot, and another vulture fell.
I reached around and found Abra, and the two of us helped each other to our feet. She had scratches on her face and her shirt was torn at her shoulder. I reached up to wipe away a bead of sweat, only to realize I was bleeding from a few cuts on my forehead. Both of us were covered in mud from falling into the field.
What had just happened? What was going on?
But nothing about those vultures shocked me as much as when I turned and saw the person wielding the shotgun—or when I finally got a look at what the vultures had been eating.
## 11
IN THE SILENCE I HEARD the whooshing sound of the vultures' wings fading up into the mountains. Soon even that sound stopped. The breeze died down and the corn stopped rustling. Through the heavy silence I stared at the man holding the shotgun, the very same man I had seen snooping around the large oak tree in my front yard only an hour or so before.
He had the same clothes on that I had seen him wearing at my house, only this time everything was covered by a tattered brown overcoat that looked way too hot for July. He had the same squinting eyes and the same slicked-back hair. He held the shotgun against his shoulder and looked very relaxed, as if nothing exciting had just happened.
Halfway between him and me was a large white animal lying among the corn, but I couldn't get a good look at it from where we stood. It seemed that Abra and I both had the same question at the same time, because we started walking through the corn, one hesitant step after another, trying to see what it was that had drawn so many vultures. But as we grew close to it, the old man's voice erupted, breaking the silence.
"Come along, come along," he said gruffly. "It isn't safe for you out here, not anymore."
He moved quickly, without a limp, and for a moment I doubted that he had been the one in my lane because his steps were so sure and quick. He grabbed Abra roughly by the arm and pushed me along in front. Whether it was intentional or not, he led us on a way that avoided the dead animal. Still, I got a look at it.
At first I thought it was a horse, or even something a little larger, but what in the valley would be larger than a horse? And there seemed to be a lot of feathers around, but not black feathers from the vultures—they were white feathers, and they were big. Then my attention shifted from wondering about that animal to wondering how it had died. It looked like something had taken a bite out of it. One large bite.
The old man kept looking up at the sky and ducking his head, as if at any time something might come swooping down and carry us all away. Once we were in Mr. Jinn's weed-infested yard, he let go of us and plowed ahead, muttering the entire time.
"Hurry now, almost there. No time for chitchat. Have to get inside."
Abra and I looked at each other.
"Why are we following him?" she whispered. "Shouldn't we run?"
I understood how she felt. It was one thing to go with that man when he was pushing us along. It was another thing entirely to follow him on our own. But I wanted to talk to him, now more than ever. I wanted to ask him about the women and what they had written on the table.
Find the Tree of Life.
"What about the vultures?" I asked. "Won't they attack us if we walk back through the field?"
She frowned. We kept walking.
"That's the man I saw at my house," I said. "The one who came up the lane before you."
"Are you sure?" she asked.
"I'm pretty sure," I said. "Same clothes, minus that ridiculous-looking overcoat. But I didn't think he could walk this fast. He limped when I saw him. And he must have been cruising to make it back here so fast."
"Hurry, hurry!" he shouted from the porch of Mr. Jinn's dilapidated house. "The spies are everywhere now. No safe place."
"Stay close," I whispered to Abra.
"We have to stay together," she said.
When we got to the porch, the old man had already gone inside. I saw the birdbath where Mr. Jinn usually left my lawn-mowing money. The outside of the house needed paint—what was left of the siding had peeled and twisted away, exposing rotted wood. A few of the porch floorboards had fallen through. The windows weren't broken, but there was such a thick layer of pollen and dust on them that from the outside it was impossible to tell if there were any curtains. Not that he needed any. The grime would have blocked anyone from peering in.
We stopped for a moment, and I walked over and held open the door for Abra. "Ladies before gentlemen," I said.
She smirked and we walked inside.
"Close the door. Quickly!" the old man shouted from inside the house. I pulled the door up against the frame, but as I was about to close it the entire way, I stopped. Something inside me said, Don't. Don't close the door. So I left the door leaning up against the frame, but not latched.
What surprised me most about the inside of Mr. Jinn's house was that it was immaculate. While it was not brightly lit, I could still tell the carpets were vacuumed and the surfaces dusted. He didn't have much furniture, but the furniture he did have was well placed and relatively new. It was strange to think of that untidy man living here, in such a clean place.
We followed his voice back to the kitchen. A very clean kitchen. In the middle was a small green table with two chairs. The table had deep, random scratches going in all different directions, like a three-dimensional road map. As we entered the kitchen, he came bustling in from some back room bearing a third chair, which he slid up against a third side of the table. He sat down in that chair and motioned for us to sit at the other two, one on either side of him, but just as we moved toward our seats he stood again.
"Go ahead, sit down. I'll get you some water."
I sat down in his chair so that he would not be between us. It seemed a silly thing to do, but Abra's words from outside still stuck in my mind.
We have to stay together.
He didn't seem to notice that I had taken his seat. He placed two glasses of water on the table and handed each of us a wet washcloth to clean up with. He took a seat at the end. I say "the end" even though it was a very small table, and if we all would have leaned forward at once, it's likely we would have banged heads.
He stared at us. His eyes were dark, his pupils large so that very little white showed around the edges, and when I stared at them they felt like deep pools, a swirling mass of shadow from another universe. Time slowed. His eyes scared me.
"Well, go on," he said, the first non-gruff words I had heard him utter. "What do you want to know? Ask away."
Abra and I looked at each other out of the corner of our eyes. I might have been the curious one, but when it came to situations like this, Abra was the most straightforward.
"Who are you?" she asked.
"My name is Mr. Jinn. Yes," he said, as if reassuring himself of his identity, "Mr. Jinn."
"Why don't you ever come out of your house?" she asked.
"I don't like people very much."
"So why did you help us?"
"Because I like children. Children aren't people."
That stopped her in her tracks, but just for a moment. "Yes they are!" she said, sounding deeply offended.
"What ate the dead animal in the field?" I asked quietly.
"Mmm," he said, as if tasting a delicious food for the first time. "Finally a good question. But I don't know if you're ready for the answer."
He took a comb out of his shirt pocket and combed his hair straight back. I realized he still had his overcoat on, but he wasn't sweating.
"What do you mean?" I asked.
He stood up and walked over to one of the kitchen windows. A small fly buzzed up against the glass, colliding over and over again with the frame. It stopped and wandered up to the top of the window before buzzing and flying again, twitching in its flight. Mr. Jinn opened the window. I thought he was going to let the fly out, but instead he clapped his hands together. The dead fly stuck against his palm. He flicked it out through the window and slammed the window shut.
"Some people aren't always ready for the truth," he said. "Some people are so blinded by what's real that they're not ready for what's true."
"I think we're ready," Abra said, still sounding indignant after being told children aren't people.
Mr. Jinn looked at me. "What was written on the table in the antique store?"
Abra turned to me, waiting for me to answer the question.
I stared at my water and took a sip. I looked at Mr. Jinn. Why would he ask me that? He had been there. He had looked at the scribbled table.
"I don't know," I said. "I don't know what you mean. I thought I saw something, but now I'm not so sure."
There was something inside me that felt hesitant about telling him. What if he hadn't been the man in the shadows? What if the writing was important information, information that Mr. Jinn shouldn't know about? He made me nervous, and I wanted to leave.
"Just as I suspected," he said with a hint of sadness in his voice. "I guess you're not ready."
Abra didn't say anything, but she stared hard at me, and her eyes asked the question, Why won't you tell him?
I shook my head. "Do you know what ate that animal in the field?" I asked Mr. Jinn.
He squinted those dark eyes, and when he nodded his entire body moved forward and back, forward and back, and the chair he sat on creaked under his enormity.
I sighed. I thought he might know a lot of things that I needed to know, and we wouldn't get anywhere if we stayed stuck at this part of the conversation. Reluctantly, I let the words escape in a whisper.
"I thought the words on the table said, 'Find the Tree of Life.'"
At this Mr. Jinn leaned forward and stared at me. "Is that right?" he asked. "Is that what you saw?"
There was something eager in his face, something hungry. I wondered how he had missed it, why I had seen it but he hadn't. I nodded slowly, feeling as though I had told him something I shouldn't have. It was a feeling I would always have around him, that I was letting things slip, that I was saying more than I should.
"'Find the Tree of Life,'" he said quietly to himself. "So it is finally here."
He stood up and paced back and forth in the kitchen. When he passed by me, his overcoat flapped, and it smelled like mud and summer. He snapped out of that short reflection and looked at me again, saying matter-of-factly, "It was an Amarok."
At first I didn't know what he was talking about.
"What?" Abra said in a sharp tone. She sounded almost angry, as if she believed Mr. Jinn was trying to make her look silly.
"You heard me."
"An Amarok?" I asked. I didn't even know what that was.
"Is that even a real animal?" Abra asked.
"What is real?" he asked. "What is true?"
Abra jumped to her feet, her chair shooting out behind her. "I want to go look at that dead animal," she said. "Let's go right now."
Mr. Jinn didn't look upset or bothered. "It won't be there any longer," he said, shaking his head and pulling his comb from his pocket. "They'll have taken it."
"The vultures?" I asked.
"The vultures may have come back," he said. "Or maybe the black dogs." He gave me a knowing look. "Maybe the Amarok came back for it. If it did, you probably won't make it home through the field. But that's not likely in the day. The Amarok prefers, shall we say, the shadows."
I remembered the combined voices of the three old women, and a chill swept through my body.
Protection from what lives in the shadows.
He raised his eyebrows and shook his head, and his mouth showed regret. His voice hardened. He stared first at me, then at Abra, who was still standing.
"Do you know what it means to 'Find the Tree of Life'? Do you want to know why the old women wrote those words on the table?"
He paused. Abra looked at me. I nodded.
"Your mother and that oak tree were killed at the exact same moment by that lightning strike."
"The tree's not dead," I interrupted. "It's still green."
"That tree won't survive the year," he snapped. "Your mother substituted her life for yours. Her sacrifice, combined with the death of the oak tree, brought something wonderful into the world."
I stared at him. All of his talk about my mother made me angry. Who was he to talk about her? What did he know, this man who never left his house, this man who wore overcoats in the summer? But he just kept talking.
"Now the Tree is here, somewhere." He waved his arms around. "The war is beginning. They are gathering and taking sides."
When he said "the Tree," he sounded like he was talking about something very holy or very dangerous or both. And he liked it. There was a lust for blood in his voice, a desire for destruction. He seemed excited at the idea of war.
"Who's taking sides?" I asked.
Abra backed away from the table. "Let's go, Sam," she said. "We need to go."
"What do you mean by sides?" I asked him again.
"You would do well to heed the words you read on the table," Mr. Jinn said, his eyes piercing me. "You would do well to find the Tree."
"You still haven't told us what an Amarok is, or what it was doing in the field, or what that animal is that it killed."
"The Amarok being here, it's a sign," he said, and in his voice was a pleading for us to understand, as if a greater understanding would lead to our being on his side. "A sign! Just one of many signs that prove what I told you about your mother is true, and that the Tree is close. The Amarok is drawn to the Tree. It is always drawn to the Tree. It's how we know the Tree is here."
His voice sounded more and more like a plea. We stared at him, and I wondered if he was sane.
Abra pulled at my shoulder and I stood up.
"She's right," Mr. Jinn said, looking at the window in the kitchen. "You should go. Before it gets too late in the day. You don't want to be walking by yourselves at night anymore."
We walked quickly out of the kitchen and across the porch. The sun was already dropping behind the western mountain. I saw small black specks against the darkening sky, some of them flying, some of them perched in the highest branches of faraway trees. Vultures? Or my overactive imagination?
We half walked, half jogged through the weeds to the cornfield. We stopped for a moment where the white animal had been, but Mr. Jinn was right. There was nothing, not even any blood. Only broken cornstalks and feathers, some black, some white.
Mr. Jinn shouted to us from his house, "Don't worry. I'll come to your house tomorrow, after your mother's funeral. We have a lot to talk about and even more to do. Remember, find the Tree! Now run! Run! The darkness is coming!"
The sun was barely over the mountain as we ran through the corn, our shadows dashing along beside us.
## 12
I HAD A DREAM the night before my mother's funeral.
I'm standing at the window and the rain pours down, battering the glass. The sky is a greenish-gray and the clouds bubble like a pot of boiling water. I wonder if the barns will be okay, or if the wind will tear them into small pieces and drive them up against the house.
I see my mom. She's up in the oak tree, walking out on the branch. Her wet clothes whip around her and her hair dangles down in her face. I suddenly wonder if I might be able to warn her. If I run out to the tree and tell her to get down, will she be spared? Will the lightning miss her?
Before I know it, I am running through the warm summer rain. The dream is so real that I can feel the squishing of my shoes in the muddy ground. I get to the base of the tree, but I'm too late. The lightning strikes. The tree explodes. I see a bright light.
But something changes. The weather goes from stormy to sunny, with the bluest sky ever. I climb the old oak and it is perfect. No missing branches. No long, white scar from the lightning. And it's bearing fruit! It's not an oak anymore, or at least that's what I think. I climb higher and higher, and I look off in the distance and see my mother in a white dress, sleeping on the green grass.
Sleeping? Or dead?
I realize that the fruit of this new oak tree will bring her back. I grab a piece and it's soft in my hand. It's speckled, a mixture of red and orange and yellow, and oblong like a pear. But by the time I get to the ground, it is rotten in my hands, and it smells terrible. So I climb the tree again, grab a new piece, and race back down.
The bark is like sandpaper on my knees and my hands. My legs start to feel dream-heavy, nearly impossible to lift. And every time I climb down, the fruit rots. I look over at my mother lying in the grass, and I feel so sad that I cannot take her any fruit.
I hear a loud growl behind me. I turn. It's the largest wolf I've ever seen, much bigger than any of the three dogs. It's black with brown paws, and its teeth are like white daggers. Its nose wrinkles back in a snarl, and it speaks in an angry voice.
"That fruit does not belong to you."
The wolf springs at me, and just as its jaws are about to close around my face, I wake up.
My window was open and the early morning sun shone in, fresh and new. Personally, I had hoped for rain. It was the morning of my mother's funeral, and I didn't think sunshine was appropriate.
My dad knocked on the door, and even his knock sounded tired. I walked over, rubbing my eyes. The day didn't seem real. I thought that maybe if I rubbed my eyes and didn't open them, it wouldn't happen. None of it would happen. But as soon as I opened the door, I knew it was real. All of it.
"Time to get ready, boy," my dad said. He turned and walked back downstairs.
I liked hearing his voice. I turned around and pulled some clothes from my closet, though I didn't have very many dress clothes. Most of what I owned had been slightly ruined from working and playing and living on a farm my entire life. But I managed to find a nice shirt, a pair of slacks, and some black socks buried at the bottom of my drawer.
My dad made breakfast for both of us, and as I sat there waiting for the eggs to fry, I found myself running my index finger along a scratch on our dining room table. That reminded me of the table in the antique store, and of Mr. Jinn, and of all that he had said the day before.
Find the Tree.
And what was an Amarok?
"What's an Amarok?" I asked my dad as he put two plates of eggs and toast on the table and sat down beside me. I hadn't really thought about the question. The words escaped from my mouth before I had a chance to check them out, and if I could have, I would have chased them down and swallowed them again. I was too tired of not getting a response from him. I was weary of the one-sided nature of our new relationship, the one created in the wake of my mom's death.
But he surprised me.
"Where did you hear about that?" he asked.
I didn't know what to say. I didn't want him to know that I was sneaking all over the valley, visiting with Mr. Jinn and being attacked by vultures. And everything else. He'd think I was losing my mind. He'd never believe me.
I shrugged. "I don't know. I think we might have talked about it at school or something."
He nodded. "There are a lot of great stories out there. The Inuit people have legends about the Amarok. Do you know the Inuits?"
I shook my head and kept eating, trying not to scare him back into his silence with too much attention. It was like watching a snow leopard in the wild.
"The Inuits, I guess they're a type of Eskimo. They have legends that the old men pass down to the young," he said. His voice was musical again, if only for a few moments. Stories will do that for us, bring beauty back even in the midst of such overwhelming darkness. "They're wonderful legends. Terrifying stories. Some of them involve an Amarok."
He took a bite of breakfast, then continued with his mouth full. If my mother had been there, she would have given him a look that said, "Don't talk with your mouth full." But she wasn't there. So much was changing. I was running around the fair with only Abra. I had met the mysterious Mr. Jinn. Dad was talking with his mouth full.
The entire world felt upside down.
"The Amarok is a legendary wolf, as big as a horse and black, the color of a shadow. Unlike normal wolves, it hunts on its own. Not in a pack."
I shuddered. What if there was an Amarok prowling the valley right now? My dream swept back into my mind, and suddenly I wasn't hungry anymore. I remembered the black wolf that had stared at me in my dream and told me in a growling voice, "That fruit doesn't belong to you." Was that an Amarok?
"But there's one thing to remember about the Amarok—it only devours those who are foolish enough to hunt alone," Dad chanted in a voice that made it sound like he had memorized that phrase once, long ago.
He shrugged, and the music fell out of his voice, and it was just me and him again—no stories, no legends, eating breakfast a few hours before we buried the body of someone we loved more than anything else.
"Or at least that's how the legend goes."
I had been alone in my dream. I shuddered again, and Abra's words echoed in my mind, the words she had said before we had walked into Mr. Jinn's house.
We have to stay together.
"You don't have to worry," my dad said. He must have seen the fear in my eyes. "Amaroks aren't real."
And once again I heard a voice in my head, but this time it was Mr. Jinn's from the day before.
Some people are so blinded by what's real that they're not ready for what's true.
My dad and I walked down the lane. My fancy shoes rubbed around the bottom of my ankles, and the shirt tugged under my arms. The sun refused to go behind the clouds, and the sky was a beautiful blue. The recent rains had turned every plant and crop and tree a deep, lush green. The oak, however, didn't look quite right. The edges of the leaves looked black, and the branches drooped like a wilting plant. The lightning scar that went all the way down the tree and disappeared at the roots had gone from bright white to a sickly yellow, like someone's last, decaying tooth.
We crossed the street and walked into the church. The parking lot was full. My mother was well loved by many people in the neighborhood, and her passing was a great tragedy in Deen. The main auditorium of the small church held maybe two hundred people, and it was standing room only. Ushers walked my father and me to the front row, and we sat down. My mother's casket was there in front of us. I couldn't believe she was in there.
The pastor across the street had agreed to have the service there. He was a tall man, mostly thin but with a little round ball for a belly. His nose was sloped, and his eyes were sad and eager to show you that sadness. His voice had a wavering quality to it, the way it sounds when you're talking to someone underwater.
We sat there, listening to him drone on and on about my mom, someone he barely knew, and my attention began to fade. I wanted it to be over and done. I wanted this part to be in the past so I could focus all of my energy on the future and figuring out how to bring her back. This all seemed like an unwelcome distraction that I didn't have time for.
I heard the sniffles and quiet crying around me more than I heard the words the pastor said. But there was one verse he read from his black book that caught my attention.
"Our final reading today comes from Revelation." He paused and closed his eyes. When he opened them again, he read the passage with a somber, reverent voice that somehow swept me up and carried me to a far-off place.
"Then the angel showed me the river of the water of life, as clear as crystal, flowing from the throne of God and of the Lamb down the middle of the great street of the city. On each side of the river stood the tree of life, bearing twelve crops of fruit, yielding its fruit every month. And the leaves of the tree are for the healing of the nations."
The Tree of Life. Healing for the nations. Again, the phrase echoed over and over in my mind.
Find the Tree.
Find the Tree.
Find the Tree.
My father had petitioned the county to allow him to bury my mom in the graveyard in the forest at the end of the Road to Nowhere. It had taken some convincing, but eventually they gave in, not wanting to have a public fight with a grieving man. So the hearse drove away from the church and headed north on Kincade Road. It was one of the first cars to drive that way for a very, very long time.
I caught a glimpse of Abra as we walked from the church to the graveyard. I wondered if the pastor's words about the Tree had caught her attention too. She wore a long black dress and had a black ribbon in her hair. A thought entered my mind, something I had never considered before: Abra was pretty. Prior to that funeral, I had only ever seen her as a friend, someone to run around with, to have fun with. It seemed strange to me that I would notice her beauty at my mother's funeral, but I did, and I kept stealing glances at her, wondering if she thought I looked handsome in the clothes I had managed to rummage from the bottom of my drawer.
Because the road didn't go all the way to the cemetery but stopped beyond Mr. Jinn's driveway, a group of my father's friends and fellow farmers served as pallbearers. They bore the coffin from the hearse and over the crumbled-up pavement where the road ended. They forged through the weeds and wound in and out among the trees, trying not to stumble on the roots. Finally, they arrived at the ancient cemetery, the one close to the cave, my hiding place. The river was loud there, rushing as it did through the green forest.
The funeral director had managed to erect a small white canopy over the open grave. The men brought my mother's coffin through the forest, passed it over the low iron railing that surrounded the mossy headstones, and set the coffin on straps that lowered her slowly into the summer earth. I looked toward the river but could barely see it through the trees. It was still full to overflowing and muddy. It raced along even though I thought it should stop and pay its respects.
How could the world keep going? Why didn't everything stop, as my life had stopped, and watch as my mother vanished from the earth?
We stopped by the stone, and I stared at the letters. I knew by the phone conversations I had overheard that my father had paid a lot of money to have that stone ready for the day of the funeral.
Lucy Leigh Chambers
Wife and Mother
Meet Me at the Edge of the World
Below that was a picture of a tree. I thought it looked like the oak tree in our yard, and it filled me with a strange sense of awe. It seemed appropriate that my mother and that tree would be joined together forever, or at least as long as that gravestone could withstand the passing of time.
It's a tradition in our town to fill in the grave by hand, so people who knew my mother took turns using the shovels provided by the church and scooped in those dark brown shovelfuls. The clods made a thumping sound as they fell into the hole.
Eventually it was over. The hole was filled and, like the river, overflowing in the form of a small mound. People shook my father's hand and patted me on the head and walked slowly back through the woods to their cars, high stepping through the mud and the weeds, relieved to go back to their normal lives.
But I was left there with nothing. Nothing normal to go back to. I stared at the earth, and it reminded me of when we first tilled up our garden in the spring. It looked like earth that was ready to have something planted in it.
Abra came up beside me and grabbed my shirt sleeve down where it wrapped around my wrist. She wasn't holding my hand, but she was holding on to me.
We have to stay together.
I stared at that filled-in hole, and I felt her holding on to my sleeve, and I thought about the Tree of Life the pastor had read about. It seemed too good to be true, that the very Tree of Life might be here, somewhere in the valley, waiting for me to find it. But after all I had seen and heard in these few days, that's exactly what I believed, and the preacher's words confirmed it for me. I stared at my mother's freshly filled-in grave and thought, if there ever was a place to plant a Tree of Life, that would be the soil for it.
"C'mon, boy," my father said, and Abra and I followed him away from the cemetery. Everyone else had left. Everyone, that is, except for one man.
"Mr. Chambers?" the man said, walking up to my father.
"Adam," my dad said in a tired voice. "Call me Adam."
"My name's Caleb Tennin. I'm sorry for your loss."
The man was dressed in all black, with pointy black shoes and creased black pants and a black shirt with a black tie, all covered by a jet-black suit coat. He had tan skin and long, thin eyes and a shaved, bald head.
"I know this might not be a good time," he said, looking away for a moment before looking back at my father. "But I hear you're looking for some help around the farm."
"You're right," my father said without any anger or emotion at all. "It is a bad time."
"And I apologize," Mr. Tennin said, bowing and backing away.
"Who'd you hear that from?" my dad asked, and I was shocked that he was continuing the conversation. I think he was too curious not to ask.
"Oh, you know, around," Mr. Tennin whispered. He stopped backing up, paused, waited.
"Well, I can't recall telling anyone I was looking for help." My father paused as he continued to stare at the man with interest. I wondered if he had the same doubts I had regarding this man's ability to put in a good day's work. The suit, the fancy shoes, the soft hands—everything about this man suggested he hadn't done a day of hard labor in his life.
"Any experience?"
"Enough," Mr. Tennin said with confidence. "I spent many years in a garden. And I have a way with animals."
My father shrugged, and he spoke every word reluctantly, as if he was running out of words, as if his daily allotment was nearly dry. "Well. When can you start?"
"Now, if you'll have me."
My dad clenched his jaw and nodded. "Okay. Join us for lunch?"
Mr. Tennin nodded back.
Abra and I followed them out of the woods and back to the crumbling road, past Mr. Jinn's lane, and everything seemed to fall into step, fall into rhythm. But it only felt that way for a moment, because Abra nudged me in the side and pointed toward the northern fields that ran alongside the Road to Nowhere. Limping through the field, this time with a walking stick in his hand, was Mr. Jinn. High above him, so high that they were merely tiny black specks in a great blue sky, the vultures circled.
## 13
"SO THIS IS WHERE IT HAPPENED?" Mr. Tennin asked with deep concern in his voice, stopping under the oak tree.
My father nodded, not saying anything. Mr. Tennin moved closer to the tree. He reached up and put his hands on the scar, running his fingers along it. He closed his eyes and said something too quietly for me to hear before speaking louder to us.
"So sad," he said, shaking his head, and his words sounded genuine. "So sad."
A gruff voice called out from the other side of the yard, the side that grew up against the northern fields.
"That's the tree?" the voice asked, and I knew without looking that it was Mr. Jinn, though I couldn't figure out how he had gotten through the field that fast. I had thought we would have at least a few minutes to get my dad and Mr. Tennin inside before he arrived.
My father looked bothered by Mr. Jinn's intrusion. "I'm sorry," he said. "Who are you?"
"Condolences, condolences," Mr. Jinn said, pulling his comb from his shirt pocket. He wore the same gray mechanic shirt with thin, barely visible red stripes and the same navy blue pants I had seen him in before. His dark brown boots were muddy from walking through the field. He ran his comb straight back through his hair, returned it to his pocket, then held out his hand. "I'm your neighbor, Jinn."
"Mr. Jinn," my father said, looking surprised. The reclusive nature of Mr. Jinn had been legendary in our area. My father gathered himself and began introducing everyone else. "This is Mr. Tennin. We're discussing terms to have him join on here as a hired hand."
"I could use one myself," Mr. Jinn said. "If you need more hours, I'm the farm straight back that way."
But Mr. Tennin didn't seem to pay any attention to him.
"This is my son, Sam," my dad continued. "And this is his friend Abra."
"How do you do?" Mr. Jinn said, not mentioning that we had met the day before. When he bent close to shake my hand, our eyes met. His gaze was heavy with one unspoken question.
Did you find the Tree?
I said nothing.
An awkward silence filled that warm July day as the five of us stood there, no one saying anything. Mr. Jinn didn't seem to mind. He just stared up into the branches of the tree. Mr. Tennin still hadn't taken his hand from the long, jagged lightning scar. Abra's eyes were wide open, and I knew how she felt, waiting to see what would happen next.
Finally my father sighed, and when he spoke there was a heaviness in his voice. I could tell he wanted to be alone. I couldn't figure out why he didn't send everyone away.
"Why don't you all come in for lunch," he said, a reluctant invitation. "We can make some sandwiches, and there's some fresh milk in the fridge. But I need to get back to work in about an hour."
He walked toward the house, not waiting to find out who would take him up on the offer. Mr. Tennin and Mr. Jinn followed him, walking side by side.
"This is strange," Abra said, shaking her head, and the two of us followed the three men into the house.
Mr. Jinn took a huge bite out of his sandwich, leaving a piece of ham and a sliver of bread crust hanging from his mouth for a moment. He attacked his food like a man who hadn't eaten for days.
"So tell me about that oak tree out there," Mr. Tennin said. "That's one of the oldest I've ever seen."
My father nodded, finished eating what was in his mouth, and took a drink of milk. "There used to be two oaks in the front yard. The other one was much older than this one and a little closer to the house, but we had some problems with it, so my grandfather took it down."
I thought about the story my father had told me, of how his dog had died and brought the rain and how people had started sacrificing animals to the tree. I wondered if all of that was true.
"Two trees," Mr. Jinn repeated, as if verifying an important fact.
"I believe my great-grandfather planted both of them," my father confirmed. "This one maybe seventy-five, eighty years ago?"
"I can only imagine the amazing stories that tree would have to tell us if it could talk." Mr. Tennin took a bite of his sandwich, and I could tell he was deep in thought.
"Tell them the story you told us," I said to my dad. "Tell them about how the tree brought the rain."
My father looked embarrassed. "Not now, boy."
"That sounds intriguing," Mr. Tennin said, looking at me.
"My dad loves stories." I looked over at him, but Dad was looking at me in a way that said, "You should stop talking," so I took another bite of my sandwich.
"I know a wonderful story about a tree, if you'd like to hear it." Mr. Tennin ate the last of his sandwich, drank the rest of his milk, set his cup down on the table, and smiled. "Delicious." His voice sounded both mysterious and hopeful, like wind through the leaves. "Delicious."
"We like stories too," Abra whispered, but she couldn't hide the eagerness in her voice.
"It's a story about the most important tree in the history of the world," Mr. Tennin said. "But it's rather long." He looked at my father and raised his eyebrows as if to ask for permission.
My father looked curious. "We need to get to work." He glanced at his watch. "But I think we have a little time."
Mr. Tennin cleared his throat. He looked at each of us around the table, including Mr. Jinn, who by now was combing his hair again and muttering things to himself. This is the story Mr. Tennin told us, in a lyrical voice that sounded like the wind and the river.
In the beginning of time, when all the world was young and the trees had only just begun to grow, there were two people. The first two people. Perhaps you've heard this story, or at least the beginning of it.
The first two people lived in a beautiful forest that contained everything they could ever want. There were trees with fruit, good for eating, and there were four rivers with clear water. These two people, one man and one woman, walked the paths and tended to the trees. And there was a lovely Voice that guided them, a beautiful Voice that lived among them.
But there was also evil in that garden forest, because there are always shadows, there is always darkness. There is the hidden side to what we can see. Lurking in the shadow was a Darkness that sang dark songs, one who wanted to destroy the beauty that the Voice had created.
When the Voice had first guided the two people to the forest, he encouraged them to take whatever fruit they wanted. There was nothing in the forest they could not have, except for one thing. They were not permitted to eat from one of the trees, because if they did their eyes would be opened. Not their physical eyes, mind you. The Voice was talking about their inner eyes.
"Eat of any other tree," the Voice said. "But do not eat of the tree that will open your eyes."
For a long time, peace reigned in the forest. But always there was the Darkness in the shadows, waiting.
Until one day the Darkness sang its song and convinced them to eat from the tree, and just as the Voice had said, their eyes were opened. They realized they were naked. They realized they were not perfect. They realized they had done a terrible thing, and they hid. But of course the Voice found them.
Now there was a problem, because there was a second Tree (and for a moment Mr. Tennin looked knowingly at my father) in the middle of the forest. This was the Tree of Life. The Voice knew that if the two people ate from that Tree, they would live forever. They would be like gods, because they would live forever with open eyes. So the Voice cast them from the forest. They were not permitted to reenter. Ever again.
And the Voice gave them a gift—it was called Death. It was a gift because it would be the path they would follow that would take them back to who they had been before their eyes had been opened, a path back to innocence and pure joy. Without Death, they would have been forced to wander the earth forever without any hope of returning to perfection, always decaying, always rotting, until they were nothing but scattered particles of dust trying to come back together, molecules lost from one another, forever separated.
This is what the gift of Death keeps from happening.
Just to make sure that those first two people didn't try to come back and eat from the Tree of Life, something that would steal the gift of Death from them forever, the Voice sent two cherubim, a type of angel, to guard the way into the forest. And there was a flaming sword to frighten anyone who might wander near.
That is the story that is well-known. But what most people do not know is what happened after that.
(Here Mr. Tennin paused and stared at the table for a short while, as if weighing the cost of revealing the rest of the story.)
The two cherubim remained there guarding the entrance to the forest, guarding the Tree of Life. Decades passed. Centuries. Eventually one of the cherubim allowed his mind to wander. He thought about how humans had spread throughout the earth, and how they lived a hard existence. More than anything else the humans feared Death. They didn't remember where Death would lead them, so they didn't realize it was a gift and not something to be feared. This cherub realized that if he could possess the Tree of Life, humans would worship him. They would do whatever he wanted them to do.
But even more important to that cherub was the knowledge that if humans ate of the Tree of Life, they could never escape earth, and they would be forced to live in his kingdom forever. He knew that humans are often weak, and they would do anything to avoid Death, something they knew so little of, and trade it for the endless stay on earth that the Tree of Life would give them. They could not possibly imagine the horrid existence that awaited them without Death.
That cherub's own inner eyes began to envision the throne upon which he would sit, the scepter with which he would rule. And lust for power grew in his heart. More than anything, he began to desire the Tree of Life so that he could give its fruit to humans and make them his servants forever, with no escape.
One day he moved toward the Tree to steal a piece of its fruit. He planned to run away with it, plant it, and nurture it. For many different reasons he could not possess the Tree itself, but with a piece of its fruit he hoped to fashion a tree of his own, a powerful tree. He could have his own Tree of Life. The Voice could never destroy him, and people desiring the Tree and its fruit would worship him and do whatever he told them to do, and once they ate from the Tree they would be trapped on earth.
But the second cherub saw him move for the Tree and tried to stop him, and the two of them fought. For forty days and forty nights they wrestled in the forest. Both of them grew weary, yet neither would give up. As they fought, their fury turned to fire, and as they rolled through the forest the trees caught and burned. Finally, their battle took them to the center of the forest, where the Darkness had deceived the first two people long, long before.
The tree from which the first two people had eaten—the tree that had opened their inner eyes—had become small and twisted, like an old cedar that cannot reach the sun. The fire from their fight lit this old tree and it went up in hot smoke.
But the Tree of Life had grown tall. Its leaves were broad and green, and its branches reached up nearly to heaven. Its fruit, untouched for thousands of years, hung heavy and ripe. When the fury of the cherubim lit the Tree of Life, it burned for another forty days and forty nights. Humans gathered in the surrounding mountains and plains and watched with terror, because at night the burning Tree looked like a comet ready to collide with the earth, and during the day it looked like the beginning of an eclipse that might drown the sun forever.
When the cherubim realized what had happened, they stopped fighting and sat quietly beside one another, spent and waiting. And the Voice came down to them.
To the first cherub, the Voice said, "You have desired the Tree of Life more than anything else, and so you are cursed. For eternity you will try to find the Tree. Your only desire shall be to possess it, and your fate will be tied to it."
With that, the first cherub vanished and began to roam the earth, always searching for the Tree of Life, because it is always reborn after it is destroyed.
In the peace that remained in that smoldering garden forest, the Voice said to the second cherub, "You have done well, good and faithful servant. Will you take on this purpose? Will you also roam the earth, but to keep the other cherub from possessing the Tree? The Tree of Life, because of its nature, can never be completely destroyed, and even now it is being remade and will reappear where someone who is faithful gives up their life for a friend. But when it is reborn, you must destroy it so that humankind does not lose the gift of Death."
The second cherub nodded, took flight, and roamed the earth, always looking for the Tree of Life in order to destroy it, keep the first cherub from possessing it, and preserve the gift of Death for humanity. This cherub, legend says, has destroyed the Tree many times—maybe a hundred times, maybe a thousand—but the Tree of Life must be destroyed many more times before the end.
Mr. Tennin leaned back in his chair.
I glanced at Mr. Jinn, and he was glaring at Mr. Tennin, his eyes thin slits. He sat unmoving, still as a cliff, and somehow, in that motionless stare, I sensed a kind of recognition, as if he had finally realized something, as if he had spotted the one missing piece to a puzzle he had been working on for years.
My father looked impressed. He always loved a good story. He even chuckled to himself and shook his head, smiling.
But me? I felt an urgency rising up. The Tree, the Tree, the Tree—everywhere I turned, people were talking about it. Telling stories about it. I thought it must be real. It must be close. And who were these two men, Tennin and Jinn, wrapped up as they were in the life of the Tree?
"Where did you hear that story?" my father asked. "I've never come across anything like it."
Mr. Tennin gave a tired smile. "Some stories, you don't know where they come from. Some stories, they just grow up inside you."
I wanted to stay silent, to not draw attention to myself, but my curiosity got the better of me. I had to ask.
"You said the Tree of Life could keep people alive," I said quietly. "Could fruit from the Tree of Life bring someone back from the dead?"
The man grew silent. I knew that everyone around the table realized what was on my mind: the fresh grave of naked dirt at the end of the Road to Nowhere.
Mr. Tennin had a sad look on his face. "Sam, the Tree of Life, as spoken about in this legend, was a powerful tree. That's certain. If anything could bring someone back from the dead, it would be fruit from this Tree. But even if it could, would that be the best thing to do?"
I stared at the table, embarrassed. "So you think it could?" I asked again, not looking up.
"Sam," my father said with the sound of warning in his voice.
Mr. Tennin held up his palm toward my father. "It's okay. It's an important question." He turned back to me. "It might be able to, Sam. But sometimes the correct question isn't, 'Can we?' Sometimes the correct question is, 'Should we?'"
I glanced over at Abra. She stared at Mr. Tennin, as if waiting for him to start telling us another story.
"Imagine this, Sam," Mr. Tennin continued. "What if death isn't as dark and scary as we think it is? What if death is simply the path from this world, full of hurt and pain, to a better place?"
He waited and let that sink in.
"Now imagine destroying that path, covering it up so that no one could follow it. Imagine eliminating the only way to escape from this broken world. Because the Tree of Life doesn't eliminate pain, at least not forever. It doesn't eliminate disease or old age or scars. So when you introduce the Tree of Life, you eliminate the only means of traveling away from all of those things. If people would eat from that Tree, they would be trapped here. Their bodies would eventually decay even as they lived, and their skin would grow thin and their eyesight would dim and eventually they would be nothing but bones, wearing away in the wind and the water, and still they would be here, alive. Do you know what this earth becomes when people are trapped here for thousands of years in their pain and their decaying bodies?"
I shuddered.
"Hell," he said. "That's what this earth would become if there was a Tree of Life and everyone ate from it."
"But it's not real, right?" Abra interrupted. "I mean, you're talking about this Tree as if it exists for real."
Mr. Tennin smiled at her, and it was kind of a sad smile, but he didn't say anything.
"What's real? What's true?" he asked, and my gaze darted over to Mr. Jinn.
"Yes, yes, a good story," Mr. Jinn said. When he had ambled into our yard, he had the look of a man staring down a day of leisure, but now he seemed nervous, anxious to leave. "Moving and all that. Now it appears lunch has come and gone."
He stood up and took his plate into the kitchen, and the rest of us followed. But I couldn't stop thinking about this Tree of Life. I thought about the words scribbled on the table and the words the preacher had read at my mother's funeral. I thought about Mr. Tennin's story. And my mind became obsessed with one thing: finding the Tree of Life and bringing my mother back from the dead. I wanted her there with me. I wanted to hug her and hear her voice in the kitchen. I wanted to see her waving from the third base line at the ball field. If we both ate from the Tree of Life, we could figure out the future together.
I felt a certain kinship with that first cherub. I would do many things in order to possess that Tree. In fact, I couldn't think of anything I wouldn't do, if it meant plucking one piece of fruit from that Tree, if it meant bringing my mother back from her dark grave.
My father and Mr. Tennin walked out toward the barns. Mr. Tennin didn't look ready for work, still dressed in his all-black fancy clothes, but he had taken off his suit coat and rolled his sleeves up, and my father had lent him a pair of knee-high boots. I figured they wanted to have a look around and talk about pay out of the hearing of nosy children. I watched them both disappear into the dark shadows of the barn, where only a few days before I had bottle-fed the lamb.
"We've no time to lose," Mr. Jinn said once they were out of sight. He put his comb back into his pocket. "That much is clear to me now. We'd best do what that old hag wrote on the table. We'd best find the Tree."
He stomped out onto the porch, hurried down the steps, and crossed the yard to the lightning tree. I looked at Abra, and we both followed him.
## 14
"SO YOUR MOTHER was right up there in the tree when the lightning struck?" Mr. Jinn asked, his round head leaning back, his thick neck bulging.
I bristled at the casual way he talked about my mother's death, especially considering we had buried her body in the ground not three hours earlier. I didn't know what to say. Abra moved up beside me and grabbed my sleeve again. I thought I might start crying. In that moment I was thinking about how my mother had been such a good mother. And once again I thought, I would do anything to bring her back.
Mr. Jinn looked over at me and squinted, as if he was trying to figure out what was wrong.
"Oh my," he said, shaking his head. "Oh my. Come here, kid. Come here."
I went to him, Abra reluctantly letting go, and Mr. Jinn raised his arm and welcomed me against his side.
"There, there," he said. "There, there."
But it didn't comfort me. It didn't comfort me at all. He smelled like the stone road after a storm—heavy and dark. His embrace felt more like he was luring me in than trying to make me feel better. And once his arm came down around me, I felt stifled, trapped. Still, I wasn't sure what to do. I had never had to pull myself away from an adult before.
"Listen," he said, and then, as if on second thought, he shook his head. "No, sit down. Both of you. You might as well know."
We sat down on either side of Mr. Jinn, but once he had settled in, Abra stood up and came around to my other side, which put me in between both of them. I looked up over my shoulder, and the lightning scar in the tree crashed down right on top of Mr. Jinn's head and continued down where his back rested against the tree. The sky was very blue, and carefree clouds wandered over the fields from one mountain to the other.
"What would you do to bring back your mother?" Mr. Jinn asked me.
It shocked me, like he had been reading my mind. He didn't wait for an answer.
"I know. You'd do anything. Anything. Just as I would. Or you," he said, pointing over my head at Abra. "When someone we love dies, we'd do anything to bring them back."
He was right. A sense of resignation washed over me, from the tips of my brown hair to the soles of my nice shoes that I hadn't taken off after the funeral. I would do anything, and I wasn't the only one. I was justified in how I felt. It was an admission that filled me with both relief and guilt.
"Here's another question. What would you say if I told you I could help you bring her back?"
A wondrous hope surged through me like a jolt of electricity. That thing I wanted—here was someone willing to talk about it, someone willing to help. To feel her skin again, to hear her laugh, to smell her hair as she bent over my bed and kissed me good night—he could bring all of that into reality. Deep inside, I knew it was true.
But all of that hope, all of those good feelings, popped like a soap bubble at the sound of Abra's voice.
"You're crazy," she said. "No, you're not crazy. You're evil."
Panic rushed through me. I wanted her to keep quiet. I wanted Mr. Jinn to keep talking and feed the small flame of hope growing inside me. I didn't want to face life without my mother. I wanted to chase after her return, no matter how long it took, no matter what I had to do.
"Shut up!" I said. "Wait."
I had never told her to shut up. She was my best friend, and it didn't feel right. She looked at me as if I had slapped her.
"I can do it," Mr. Jinn said in the softest voice I had ever heard him use. He pulled out his comb and made long, sweeping motions as he slicked back his hair again and again. "I can do it. But I need your help."
Abra stood up. "If you don't stop it, I'm going to tell his father about your lies. If you don't stop saying these things, I'm telling everyone."
"You think they'll believe you?" Mr. Jinn said, still in his soft voice. "Will you tell them about being attacked by the vultures? Will you tell them about the Amarok?"
Abra's face went empty. No one would believe her. No one would believe any of it.
"So what if you bring her back?" she asked. "What if it works? Do you have to go dig her up out of the ground? Will she still have all that stuff in her from the funeral home? You can't bring someone back from the dead! It's impossible."
At the mention of digging her up, I stood to my feet and stared into her eyes. And in that moment I hated her, or at least I hated what she represented—the end of my hope and the finality of death.
"Don't you dare talk about my mother that way," I said. "It's disgusting."
Fury rose up in me, and I let it take over. It felt good to be out of control, to let that simmering anger boil over, and I could tell immediately that it rose up out of the darkness I had been nurturing inside me. I stared hard at Abra, and the words that came out surprised even me.
"Leave. Now."
And I pointed down the lane.
This time it was worse than slapping her. Her face pulled back, hurt and red. Her eyes filled with tears, like new puddles in a spring rain. She pushed past me, crying for real, sobbing and sniffing and trying to cover it all with a stubborn scowl. Once she was out from under the shade of the old oak tree, the lightning tree, her walk gradually turned to a jog, then a run. At the end of the lane she glanced back toward us, slowed to a walk, and slid out of sight down the long country lane. I watched her the whole time.
"I can do it," Mr. Jinn said, as if none of that had happened. As if Abra had never even been there. "But I need your help."
I looked away from him, up into the lightning tree. "I would do anything," I said, and it felt like a handshake. It felt like an agreement that I would not be able to back out of.
I waited for him to say something, to continue the conversation, but when I looked over at him he was staring at the church. I followed his gaze. Three large, black dogs came trotting up the lane. They looked like German shepherds except they were all black and their noses were shorter. Long, pink tongues hung out between their oversized white teeth. They were the same three dogs that had been in the fight with the groundhogs.
The darkness inside me seemed to swell with the approach of those animals. It felt like a living thing, that darkness, and my insides twisted, the way my mom had twisted a dishrag before she hung it to dry on the spigot. And like that rag, all the goodness was wrung out of me, and I was focused on finding the Tree. Bringing back my mom. That's all I cared about.
The dogs seemed to be headed right for us, and even though the darkness had grown inside me, I still felt fear as they got closer. They looked unpredictable. They looked angry. I glanced up into the tree but knew I could never make it to the first branches without a ladder, so I got ready to run. I looked at Mr. Jinn to see what he was going to do, and I saw him make these subtle shooing motions with his hands. He whispered something, and the dogs somehow seemed to hear him, even from that distance. They curled off to the side, cut through the small pasture back out to the road, and headed the same direction as Abra.
"What are you doing?" I asked.
"They're here to protect us," he said.
"Like the vultures?" I don't know if I meant it to, but it came out as an accusation.
"Now that the vultures know you and I are working together, they won't do you any harm either."
"They were protecting you?" My mouth dropped open.
He didn't reply.
"Did you send those dogs after Abra?" I could feel the edges of panic gathering inside me.
"They won't hurt her," he said. "They're here to protect us."
He emphasized the word us as if Abra was no longer us. As if Abra was on the other team, and the dogs would do what they needed to do to protect "us" from "her."
"This tree right here, the one where your mother died," he said, as if still trying to explain the presence of the dogs. "There will be more and more coming for it. The Tree of Life is close by. It must be."
I felt heavy inside, sad, and unsure of myself. It was hot and I was still in my nice clothes. The sun moved slowly toward the west, but we had four or five more hours of heat ahead, and even after the sun set the night would be warm. I wanted this to all be a dream. I wanted everything to be the way it had been before lightning struck the tree, before my mom stopped the car so that I could pick up Icarus, before I ran into the antique store and saw the words Find the Tree of Life.
"Why will the animals come looking for the tree?" I asked.
His words came out in the form of a spell, a monotone recital of a long-dead incantation. "It's the nature of everything to seek unending life. Nothing, no one, wants to die. And the Tree of Life will be somewhere close to this tree, the one that died."
The words fluttered around us, and they reminded me of the words of the three women in the darkened room, the words I hadn't been able to understand. The living words.
"What do I have to do?" I asked.
"The Tree is important, but we need more than the Tree. We need a suitable container to hold it in, something made of stone. We need the right kind of water. And we need the right kind of sunshine." When it was clear I was more confused than ever, he spat out a list. "Four items. Four seasons. Four rivers. Do you see?"
I nodded, but I didn't see. Not completely.
He shook his head and waved his hand at me. "No matter. All you need to know is this: we need to find the Tree. It will still be small, maybe six inches tall, maybe only an inch or two. A tiny green thing is all. At first you might think it's a plant." His eyes came alive as he spoke of it, like an old man reciting tales from the glory days of his youth. "It will have two or three small white flowers on it by now. The flowers are important. We mustn't break the flowers."
"Only an inch or two?" I sighed. "It could be anywhere."
He didn't say anything, and I looked closer into every nook and bend of the tree.
"It has to be up there somewhere," he said. "It always forms around or inside the tree that died. Do you have a ladder?"
I hurried to the shed and dragged the extension ladder over, and it banged against the ground, banged against my legs. I couldn't carry it across that stretch of grass without thinking back to the night my mom died, the night I propped the ladder up against the tree and climbed up.
What happened to Icarus? I wondered for the first time. And it felt strange, because I had barely thought of the cat since the lightning had struck and I saw the branch was missing. I didn't think I could care for that cat anymore, not after what it had brought about.
I propped the ladder against the tree and climbed up, then pulled myself into that first nest of diverging branches. I looked for the small tree that Mr. Jinn had described, but I saw nothing.
"A bit higher!" he shouted up to me, so I climbed higher. "A bit higher!" he shouted again, and up I went.
I was so high I started to shake. I didn't enjoy heights. From there I saw Mr. Jinn's house out across the field. I turned and saw Abra's family's farm to the south. I saw the three large dogs sitting in the middle of the road and vast fields of corn waving at me, waving in great green ripples of movement like an ocean. The vultures flew across the valley in a straight line, wheeled in a circle, and continued over to the other mountain. But I didn't see any small tree or plant, either hidden in the branches or anywhere else.
"Nothing!" I shouted down. "I can't go any higher. I'm too big for the branches."
"Fine, fine. Come down," he muttered reluctantly.
I made my way back down the tree, and it was like moving backward in time, back past all of these different choices to the heart of the matter. The beginning point. The beginning of all things. I stood there on the bottommost branches, in that palm of the tree's hand, and I didn't want to go back down. I wanted to stay there, and I wanted Abra to come up to where I was and hang on to my sleeve as she had done at the graveside service.
"Hey," a voice called up to me, and it wasn't Mr. Jinn. "What are you doing up there?"
I looked down. It was Mr. Tennin.
## 15
MR. TENNIN SHIELDED his eyes from the sun. Mr. Jinn looked annoyed.
"You climbed pretty high. Impressive. I bet you could see a lot of things from the top of that tree."
"Yeah," I said, feeling like a kid caught with his hand in the cookie jar. Mr. Tennin had a kind voice, the type of voice that was so kind it was almost unnerving. I thought back through our brief conversation after lunch about the Tree of Life, and it made me feel uncomfortable. I felt weak for the determination I had shown to bring someone back from the dead, and I felt more than a little foolish for putting all of this hope in someone like Mr. Jinn. He seemed convincing when it was just him and me, but when someone like Mr. Tennin came around, someone so full of kindness, Mr. Jinn seemed like a poor copy.
"I'm going to be moving into your house," Mr. Tennin said, spreading his arms wide the way people do when they make an announcement that surprises even them. "Your father said I could stay in the spare room, the one right next door to yours."
I nearly fell out of the tree. That room had been empty for as long as I could remember. I didn't like going in there because the door to the attic was in that room. I didn't say anything, but I sensed a movement and glanced quickly down at Mr. Jinn. He looked agitated at the news.
"Great," I finally said, but the word came out flat, devoid of meaning.
"I'm going to walk over to the church and drive my car back over here. It's got all of my things in it. I'll talk to you later," Mr. Tennin said.
I watched him walk down the lane in my dad's oversized rubber work boots. They jerked forward and backward as he walked, the way big boots tend to do if they're not tight. He looked all around, taking things in. His hands were halfway in his pants' pockets with his thumbs outside, and his bald head gave off a glare in the sunshine.
I looked to the north. "The vultures are circling again."
"They're helping us," Mr. Jinn said. "They're searching for the Tree." He paused. "You be careful about that Mr. Tennin."
"What do you mean?" I asked.
He waved his hand at me as he did whenever we discussed things he didn't think I would understand. "You be careful."
I looked all around the farm, and I noticed a lot of activity. I saw a groundhog in the far corner of the garden, standing up on its hind legs the way they sometimes do. Then I saw Icarus! He was walking along one of the rain gutters, high up on the second floor of the house. Icarus. My cat. He disappeared behind the house.
I saw the vultures too, still circling.
Up there in the tree, among the twigs and the leaves and the shattered branches, things moved all around me. Squirrels scampered from here to there. A trail of ants followed the scar up, up, up the tree. A large hawk perched in the uppermost branches, surveying the grounds.
So many animals. So much going on around me. I wondered which side was good and which side was evil, because that's how I thought of things—in pairs, with one thing on one side and the other thing on the other. I looked down at Mr. Jinn.
Which side was he on?
Then a small thought caught in my mind like a thorn. What if Mr. Jinn was the cursed angel, the one whose only desire was to possess the Tree? It wasn't the first time that thought had perched in my mind, but it was the first time I had looked directly at it, considered it seriously. Mr. Tennin's story might be real. The Tree might be here.
I took a deep breath, and as I turned around and reached my foot down for the ladder, another question came into my mind, a question I realized I couldn't answer.
Whose side would I join?
Mr. Jinn went back to his farm to, in his words, "Eat, take a nap, think, and call for more helpers." And when he said the word helpers, it sounded like the name of something specific, as if it should have been a proper name with its own capitalized letter: Helpers.
I went back into the farmhouse and thought about Abra, but I didn't let myself think about her too long because it made me wonder again whose side I was on. How could I have ended up on a side that didn't include her? It was lonely, facing an uncertain future without my best friend.
I turned on the television and found a baseball game, but on second thought I left it and walked up to my bedroom. My window was open and somehow that warm July day managed to send a cool breeze in through the screen. Flies buzzed around the window, trying to get in. I lay down on my bed and thought about Mr. Jinn and Mr. Tennin, and I wondered what my father was doing. It was unusual for him not to ask for my help, especially during the summer when I was home from school and bored. Perhaps he thought I should have the day off, the day of my mother's funeral. But I would rather be busy mucking out stalls or bottle-feeding the lamb.
I heard the screen door open downstairs, and then it slammed shut. I knew it wasn't my dad. He never let the door slam like that. He said it was lazy and worked the hinges loose. I heard someone walking up the steps, slow and heavy. Would Mr. Jinn come into our house without being asked?
I walked out into the upstairs hall and waited. Just as the person rounded the stairs I remembered: Mr. Tennin had been going to get his car. He would be collecting his things and bringing them upstairs. And there he was.
"Hi there, Sam," he said in a friendly voice.
"Hi," I said, and it felt awkward having a strange man in the house. I felt like I had to be more careful, but I wasn't sure why.
"Is this my room?" he asked, motioning toward the first door on the right at the top of the stairs. His voice was timid and his eyes were hesitant, as if he was trying to figure out what I was thinking, where I was settling in the whole scheme of things. His eyes gave me the same feeling I got when I first looked at the stars after learning the light that came from some of them was thousands of years old.
I nodded and pointed to the next door. "That's my room. Dad's room is there at the end. The bathroom is the door straight ahead."
"Thank you, Sam," he said in a smooth, quiet voice. He carried his two bags into his room, turned on the light, and closed the door behind him. I heard the lock turn, the smallest click.
I went back into my room and left the door open. Everything felt still, as if the house was holding its breath, but that's probably because I was listening more intently than I usually did. I lay down in my bed. What was Mr. Tennin doing over there? And as I wondered if he knew the door to the attic was in his room, I heard it open.
I knew it was the attic door because every so often my dad would go up there to look for something he couldn't find, and whenever he opened that door, it made a long whining sound followed by a loud snap. When you opened the door the whole way, it popped up right at the end and collided with the door frame.
Lying there on my bed, I heard the long, slow whine and the snap. Very far away, or what felt like it, I heard the slow thudding of footsteps as Mr. Tennin walked up the attic stairs. I didn't envy him that. You couldn't have paid me to go up there. All those spiders and boxes of mice-infested clothing and old keepsakes. My baby clothes were up there somewhere. And my old papers from kindergarten. My mom had kept a box up there with all of my old stuff in it. She could never throw anything away.
I heard him walking through the attic. Soon he was directly above me. The only thing I moved was my eyeballs as I looked straight up above me. I heard him slide a few cardboard boxes around, and they sounded like sandpaper moving slowly over rough wood. Then he slid the boxes right back to where they had been.
At first I didn't know what to think. Is he going through our stuff? Is he here because he wants to rob us?
But then I heard him walk back through the attic and down the stairs, and as I heard the door snap and whine all the way closed, I realized what was going on.
He's hidden something up there. He's hidden something very important, because he's worried that someone might snoop through his car or his room and he doesn't want anyone finding it.
He opened his door and walked out into the hall, then peeked his head around the corner of my doorway.
"Have a good afternoon, Sam," he said, nodding his head at me before turning and walking down the steps. I heard his footsteps again, and I was beginning to recognize the cadence to them, the particular rhythm of his movement. The screen door slammed shut.
I darted over to my window, and while I couldn't see him walking through the part of the yard hidden by the rest of the house, I saw his shadow stretching long and thin and moving toward the barns. I waited. I waited some more. I could hear the baseball game announcer still on the television, still talking about baseball in his slow, easygoing, summery voice. One thought took over my mind.
I have to go up there and find out what he's hiding.
So I moved away from the window, walked into the hallway, and stared at his closed door. I reached over, and the knob felt cold in my hand. I turned it, and the door swung open on well-oiled hinges, but the breeze coming in the open window threatened to slam the door shut again. I went into the room and let the door close behind me.
His small, single bed was against the wall that separated his room from my room. Directly in front of me was a window that looked out over the porch roof. Since his room was a corner room, there was also a window to the right. That was the window where I had watched my mom try to rescue Icarus. I had stood in that spot as Abra walked away from the house after my mother was gone. Now I stayed to the side of it and glanced out. No one was in the yard. No one was coming.
There it was—the lightning tree, looking more wilted than ever. I didn't know if a lightning strike could kill an entire tree, as Mr. Jinn claimed it could. Could lightning go all the way down and char the roots under the earth? I didn't know anything about lightning or the life cycle of an old oak tree.
I heard a small buzzing noise and looked up. A hummingbird hung in the air on the other side of the glass, no more than two feet from my face. It was a brownish gray, the size of my fist, and its whirring wings moved so fast that they were invisible. It cocked its head and seemed to be asking me a question, a simple question, one I could answer if I only spoke hummingbird.
Or maybe it wasn't asking me a question—maybe it was trying to read me, trying to figure me out, trying to find out what I was going to do next. I raised my finger up to my lips and said, "Shh." I don't know why, but I did. It flew away in fits and starts, darting here and there and disappearing in the distance. I had the strangest feeling that it had been sent there by someone, and that it would now report back.
Still, no one was coming. I took a deep breath. I didn't like going into the attic for normal reasons, much less to try to find an object hidden by a stranger who had just moved into our house. But I opened the attic door anyway. It whined slowly all the way to the end, where it gave that loud snap! I had terrible visions of the attic door closing on me and somehow getting stuck, trapping me in the attic until Mr. Tennin came back. So I pulled his suitcase over and used it to hold the door open.
The stairwell was dark, but I knew there was a light switch at the top. The unpainted wood steps were worn smooth by many years of rough use, and they were steep and tall so that I had to reach my foot up with each step. A narrow handrail ran the length of the steps, but the screws that held it in place were loose, so if I pulled too hard on it for support, it wriggled in and out of the housings and felt like it would fall out.
Under my bare feet I felt the smoothness of the wood, the way it had been worn down in the middle by a hundred years of footsteps. I stopped at the top and waited for my eyes to adjust, realizing that it was much, much warmer in the attic than the rest of the house. I started sweating immediately. Once my eyes adjusted to the dim light, I found the light switch and flicked it on, but nothing happened.
The bulb was dead. The only other source of light was a small, round window at the end of the attic, and it was covered in a thick layer of dust, like Mr. Jinn's farmhouse windows, so the light that fell through was dim and filtered. I listened carefully, wondering if anyone had come into the house, but I heard nothing besides the normal summer sounds of the farm: some bugs buzzing and chirping, a bird singing, and a tractor engine lurching and working its way through a wet field. They all sounded far off, as if I were in the bottom of a well, listening to a world high above me.
One main clearing formed a path down the center of the attic, and it was flanked by boxes, black trash bags, and huge plastic containers. There were cedar chests and old trash cans full of photos and memories and Christmas decorations. Ghosts from the past. Every so often a narrower cleared aisle led off the main one, an empty alley that gave access to the far corners of the attic. I thought Mr. Tennin must have hidden whatever it was he had hidden at the end of one of those narrow walkways.
I tried to figure out where to walk so that I'd be directly above the corner of my room, where I had heard Mr. Tennin moving things around. I found a small path through boxes that led back into the eaves of the house, toward the corner of my room. I had to turn sideways at some places where the boxes jutted out or the dusty plastic bags reached out to grab me.
The farther back I went down the row, the lower the ceiling, so eventually I had to duck down to avoid the beams. It was very dark. At the end, I had to get down on my hands and knees. Everything was covered in a layer of dust, and cobwebs, real and imagined, clung to my hair. I reached around with my hands, trying to find a few small boxes that I might be able to slide away, small boxes that might have Mr. Tennin's secret stash hidden behind them.
About this time the heat started to overwhelm me. The air felt unbreathable. I thought I should go back down to my room and get a flashlight.
That's when I heard a sound that sent a surge of panic through me. It was a far-off sound, but close enough and familiar enough for me to know that it was inside the house.
It was the sound of the front screen door slamming shut.
# Part 3: The Sword
## 16
THIS IS THE LIFE of an old man whose friends are gone, who lives alone on the farm his father rebuilt, miles north of town. I stare at the large calendar on my desk, the one with an empty block for each and every day of the year. Most of the blocks are empty, except a few with things written in them in pencil, phrases like, "Plant the last of the corn" and "Give zucchini to Jerry." Most blocks, though, are empty white spaces, blank days that repeat again and again.
The block that is tomorrow is filled with one word that I, for some reason, wrote in all capital letters.
FUNERAL.
I look up from the calendar and find my eyes drifting back and forth between two things. One is the beautiful day outside my open window, unseasonably cool for a summer day. I can see the oak tree and the lane and, if I lean to the right, the space where the church used to be. On some afternoons the beauty of this farm overwhelms me, and I can sit and stare at it for hours. Of course, this might also be because I am getting older, and because of all the blank-space days in my life.
My eyes leave the window and focus on the box in front of me, the box I brought down from the attic just this morning, the box I haven't opened for decades. It's covered in years and cobwebs. I wipe some of the dust off the top and it sticks to my fingers, a fine layer.
Ashes to ashes, dust to dust.
I hear a knock at the screen door. I sigh. It's probably Jerry, and it's no good pretending I'm not home because he knows I never go anywhere. I rise slowly and walk to the stairs. He knocks again.
"Coming, coming," I say, and I wonder again why everyone is in such a hurry these days, such a hurry. What are they hurrying toward? What is there out in front of every single one of them that they can't wait to get to? What happened to this present moment?
"Mr. Chambers?" he says again while I'm walking down the stairs. "Samuel? Are you there?"
"For goodness' sake, man." I can't hide the irritation in my voice any longer. "It takes me a while to get to the door. At least allow me that."
I get to the bottom of the steps and walk over to the door, and there I find Jerry standing up rather straight. His son Caleb is beside him, reluctantly. I stare at the boy, and his glance, which at first looked defiant and aggressive, darts away into some corner to hide.
"Hello," I say through the screen without opening the door. I'm not in the mood for people today. Caleb interrupting my pipe smoking the night before took me to the end of my rope. I needed a few days of solitude to gather my strength. Maybe a few weeks. Of course, the funeral is tomorrow, so there is no clear end in sight, and that makes me tired.
Jerry moves his hand to open the door, but it doesn't budge when he pulls on the handle. It's locked. He looks first at Caleb, then at me, and finally back at Caleb.
"I think you have something to say to Mr. Chambers," he says.
I roll my eyes. "Goodness, boy, what now?"
But the boy stares down at the porch floor. His father nudges him with his elbow, but he refuses to look up.
"Is that all?" I ask, moving from the door. "I have other things to do."
"Caleb!" his father says in a sharp voice. I've never heard either of his parents call him by his first name before. I don't think the boy hears it much either, because he springs into full confession mode.
"I climbed up on your roof," he blurts.
I look at his father. "Is that all?"
His father nudges him again.
"To spy on you," he continues.
I roll my eyes again and send out an exasperated breath. "Am I going to have to put an electric fence around my house?"
"And I broke the downspout when I was climbing down," he says, and I can tell he is finished talking because a wave of relief washes over his face.
"Well, I'm sure your father will take care of that." I back away again, trying to pry myself out of a conversation that is going nowhere.
"No, no, Samuel," Jerry says in a determined voice. "Caleb will make it up to you. Of course I'll fix the downspout. But he needs to make it up to you."
Oh, these people and their endless quest to make it right. What scale do they measure by that must always be brought back to level? But an idea comes into my mind. I didn't call for it. I'm not sure where it came from, unless perhaps I've been thinking about it without knowing.
"Fine," I say. "He can come with me to the funeral tomorrow. That can be his penance."
Jerry looks rather shocked. The boy looks terrified.
"Well," Jerry begins, "I'm not sure how that—"
"I see," I interrupt. "I need someone to help me with something at the funeral. But if your offer isn't real, if it is, in fact, a false offer, I'll be going back upstairs, thank you very much." I say the last four words on their own, like a hammer striking a nail, and I turn to go.
"Of course he'll go with you," Jerry blurts out. "Won't you, boy?"
I don't even stop long enough to look at Caleb's face. I'm afraid I may start laughing.
"Eight a.m. sharp," I say, and I leave the two of them standing at the door. But when I get to the bottom of the stairs, I change my mind. I turn around and go back to the door. They are already down the steps and walking through the yard.
"Caleb!" I shout.
The boy turns.
"Come here."
He looks up at his father, Jerry nods his head, and the boy walks back to the door. I bend down as low as these knees will let me.
"Now listen here," I say, and he stares at me, his eyes unblinking. "I need someone at the funeral who can do something very brave for me. Very brave."
"Is it illegal?" he asks, looking mildly interested.
I think for a moment. "I don't think it's illegal. But some people wouldn't like it. Which is why I'm going to need your help."
He looks at me, but he doesn't say anything.
"Do you think you can help me?"
He nods. "Yeah, I can help."
"Bring some of your smoke bombs."
His eyes light up.
Upstairs, I sit back down at my desk and pull the lid from the box. Inside I find what I expected to find: a pack of articles and an atlas, its margins full of notes and dates and questions, but when I look at the writing I can't tell if it's my own from childhood or someone else's. The small sword is gone. I hoped it would be there. I thought the heat from it would convince me that everything I remember is true. Could it all have been an adventure I made up in my mind? Could it be nothing more than the way Jerry's Boy wanders the farm carrying a sword that is really a stick?
But I have a faint memory of giving it to her long ago. It's like the memory of a dream, but it feels familiar. In any case, the blade isn't there. I put the lid back on the box and slide it to the side of the desk. I pick up the necktie and walk over to the mirror. And I try again to weave that elusive knot.
## 17
AT THE MOST CRUCIAL POINTS in your life, either you move without thinking and accomplish what needs to be done in the nick of time, or you hesitate, the moment passes, and you're left facing an entirely new set of problems. When I heard the screen door slam, I should have raced out of the attic without waiting one moment, pushed the attic door closed behind me, and dashed into the upstairs hallway. Even if Mr. Tennin found me there, breathless and looking very suspicious, he couldn't have proven a thing.
But I hesitated. I tried to think my way out of the situation. Which meant I acted too late.
By the time I got to the bottom of the attic steps I could hear him coming up from downstairs. I pushed his suitcase down so that it wasn't propping the door open, let the attic door close (whine, snap!), and retreated back up into the dark, dusty attic, moving as quickly and quietly as possible. I went down the main aisle and slipped back through one of the side paths across from where I thought he had hidden whatever he had hidden. I pulled myself under a fake Christmas tree we kept in a black garbage bag.
And I waited.
I heard him open the door to his room and close it behind him. I hoped Mr. Tennin was just in there to grab something and then head back out to work. But he wasn't. In fact, it sounded like he was going through the entire contents of his two bags. I heard him muttering to himself, and I heard things dropping onto the floor.
The sound of his footsteps moved over the creaking floorboards in his room and toward the attic door. The long whine and the loud snap at the end, and the door was open. The attic ceiling lit up with daylight from Mr. Tennin's room. His heavy, plodding footsteps climbed the steep, tall steps, all the way to the top. Through an empty space between boxes I could see him.
And it wasn't Mr. Tennin.
It was Mr. Jinn.
What was he doing up there? Part of me wanted to jump up and tell him to get out of my house. Who goes into someone else's house without asking? Who sneaks into someone else's attic for no reason?
But maybe he had a reason.
So I stayed quiet, and I watched, and I waited.
Mr. Jinn flicked the light switch and muttered under his breath when the light didn't turn on. He walked down the middle of the attic, opened a few boxes here, moved a few boxes there, but he didn't look very dedicated. To be fair, it was a large attic, and it was dark, and he had no idea where to begin, not like I had. But he did stop when he got close to my row, and I was sure he turned his head and looked right at the bag I was hiding under. But if he saw me, or if he knew I was there, he didn't say anything. He turned around and walked back to the stairs. And he descended.
I heard it again.
The front screen door slammed, but not because Mr. Jinn had left. No, someone else was coming into the house.
I heard Mr. Jinn hurry the rest of the way down the attic stairs, moving way faster than I thought he ever could have moved. He closed the attic door without a sound, which was strange.
Another set of footsteps came up the stairs from the main level to the second level. Meanwhile, I was getting hot. Sweat dripped into the corners of my eyes and off the tip of my nose. The dust stuck to my arms and my fingers and turned to a thin layer of grime. But I didn't move.
The bedroom door opened, then slammed shut, and I heard the lock turn fast. Footsteps dashed across the room and the attic door popped open. The person raced up the stairway, and as he came into the light I could see the bald head of Mr. Tennin.
"Oh my," he said quietly. He sounded worried.
He got to the space in the main aisle just in front of the row where I was hiding. He stopped and looked around. He stared in my direction. I could just see the one side of his face, the side facing the small attic window, and he looked suspicious. But he didn't stop for long. Instead he raced down one of the smaller rows.
I realized I had been searching the wrong area. I watched as he went down that row, moved a few boxes, and stood on them. He reached up onto one of the crossbeams and pulled down a small box. The inside of the box glowed orange when he opened it, as if it had some kind of small, battery-powered light inside. So, that was where he hid it. On top of the beam.
He seemed to take a quick inventory of what was in the box. He put it back up onto the beam, pushed the boxes into place, and ran back down the attic steps and into his room. I heard him slam the window closed. Mr. Jinn must have climbed out the window.
Mr. Tennin left his room, closed the door behind him, and walked down the stairs. The screen door slammed. I breathed a huge sigh of relief, climbed out from under the fake Christmas tree, and moved quickly down the correct row. I pulled a few boxes out and climbed on top of them, reached up onto the beam, and grabbed the box.
I wanted to open it right there, but I decided that would be best to do in the light of my own room, so I pushed the boxes back in place and walked down the stairs. The box wasn't that large, but I still needed two hands to carry it, and at two different spots I nearly lost my footing and tumbled down the steps. At the bottom, I opened the attic door, relieved to find that it wasn't stuck.
Mr. Tennin's room was a mess—clothes everywhere, papers scattered on the floor, the mattress pulled off the bed frame. Mr. Jinn must have searched the room. For what? Probably for what was in my hands.
I raced through the room, closed the door behind me, and hurried into my bedroom. I locked the door, which I never did, and then ran to my two windows. I closed them, locked them, and pulled the curtains shut. I didn't know how Mr. Jinn had managed to escape through Mr. Tennin's window, but I didn't want him climbing in through either of mine.
I walked to my bed, set the box down, then lifted my shirt and wiped the sweat and dust from my face. The July air in my room felt wonderful and cool compared to the stifling attic. I sat on the bed and pulled the lid off the box.
It was almost dinnertime, and when I had closed and locked the windows I had noticed the sky growing darker in the east, over the church, as though another summer thunderstorm might be rolling in. The upper branches of the oak tree waved back and forth in a menacing manner. But I didn't dwell for too long on the weather. I just wanted to open the box. So I did.
There were three things inside. I would spend the next few days poring over them all with great interest, but I was twelve, so the one that grabbed my attention immediately was a twelve-inch blade that lay diagonally across the top, tied in place with two small leather straps. The hilt and the blade of this small sword were the same dull gray color and appeared to be made of the same metal.
I reached down to unstrap the sword from the box, but when my fingers touched the metal they were immediately scorched. It was like touching the burner on the stove. My thumb, index finger, and middle finger turned red, and each welled up with a tiny blister, like a teardrop.
"Ouch!" I shouted, grabbing my hand. I looked at my bedroom door to make sure no one was coming in.
I grabbed a piece of paper from my small bookshelf and held it against the metal. Nothing. It didn't burst into flame or even smoke. Nothing that I held against that small sword appeared to be burned, or even heated up, in any way. Yet when I tapped the hilt again, this time with my left hand, it was roasting hot to the touch.
Even though it had burned me, something strange happened on my insides. The darkness that seemed to fill me when Mr. Jinn and I were together—that darkness receded. Its presence wasn't as stifling, as suffocating. There was something about the sword that made me feel almost brave. Memories of my mother came and went, but they had joy in them, not bitter sadness. The desperation to bring her back faded.
I turned my attention to the other two items. One was a small book about six inches long by four inches wide. The other was a stack of papers, note cards, and newspaper clippings, all held together in a small leather strap tied in a knot.
The book was thick, four or five hundred pages at least. I picked it up and placed it on my bed, waiting for it to explode or cause my blankets to burst into flames. But nothing happened. Nothing extraordinary.
So I opened it. As I moved through the book, gently turning its light, thin pages, I realized that it was an atlas of the world. There were the occasional footnotes and headnotes, and at the end of a section—each of which spoke about a particular continent—there were various things that each continent was well known for.
But what drew my eye the most were the handwritten notes in the margins. All around the edges of one map, which appeared to be Turkey, I read the following:
Entry 7. The Tree appears to have taken root in a small canyon. Have secured the perimeter. Waiting.
I went further into the book and found more handwritten notes in a very fine cursive script, looping around a map of Iran.
Entry 12. The building has reached forty-three levels. They will now attempt to plant the Tree on a terrace overlooking the city before building higher. The end is near.
The end is near?
Entry 21. Forced to destroy the entire city in order to destroy the Tree. One family escaped.
I felt like I could spend the rest of the day exploring that book of maps with its writing in the margins, but I wanted to see what the stack of papers contained. Once again I tapped the strap with my fingers to make sure the stack of small papers wouldn't burn me. It sounds funny, I know, but the blisters on the ends of my fingertips were painful reminders.
I placed the papers beside the atlas on my bed and looked at the top one for a moment. Some of the newspaper clippings were brown and old, but others looked like they could have come out of yesterday's paper.
"Mysterious Monster of Loch Ness" (October 18, 1933)
"Hitler's Sea Wall Is Breached; Invaders Fighting Way Inland; New Allied Landings Are Made" (June 6, 1944)
What did all of these world events have to do with Mr. Tennin or the contents of the box? What was the meaning of all the writing in the margins of the small atlas? How did that sword stay so hot without burning its way through the leather straps that held it in the box?
There was only one thing to do. I had to take this box to Abra's house—she would know what to do. I cringed as I thought about how I had treated her. The image of her walking down the lane toward her house, staring down at the dirt, was one I couldn't get out of my mind. I pulled a duffel bag out from under my bed and gently placed the box in it with the papers, the book, and the short sword. The zipper barely closed around the box, but it did, and I threw the strap over my shoulder and left my room.
I walked quietly down the stairs, listening for anyone who might be on the ground floor, but I didn't hear anything. Only the television, which was still on. I was so anxious to get to Abra's house that I burst through the front screen door without even thinking to check if anyone was out there.
"Hey there, Sam," Mr. Jinn said from where he sat on the porch steps. Icarus sat on his lap. The cat jumped up when I came through the door and fled under the porch.
"Find anything yet?" he asked.
## 18
"NO, I, UH, I KIND OF FELL ASLEEP," I lied.
He nodded, and his mouth turned into a line of regret, as if he was very disappointed but not very surprised. He pulled his comb from his shirt pocket and brushed his hair straight back, as he always did. He put it back in his pocket. But then his calm demeanor snapped and he thrust his hand straight down. The muscles in his neck and shoulders bulged as his thick hand sent a crack through one of the boards he was sitting on, and the wood made a wrenching sound as it split.
"I am normally a very patient man. But this . . ." He stopped and shook his head back and forth. "This is very important. I thought you said you would do anything to bring her back. Anything."
I put my hands on my duffel bag and clutched it to my side. "I would," I said. "I mean, I will. I just—I have to go apologize to Abra. I think she could help us. She's super smart. I think with her help we'd find it a lot faster. Honest, I do."
Finally he turned and stared at me. He didn't speak for a few moments as he scratched one of his eyebrows with his thumb. "She's not going to help," he said, as if trying to explain a confusing concept to a child. "She doesn't believe. And even if she did believe, she doesn't think you should do it. She thinks your mother should stay . . . there. Why would we want that girl on our side? Why would we be allies with that kind of thinking?"
He stood and, stepping over the broken step, came up onto the porch. He walked toward me, and suddenly I knew that the topic at hand was not Abra or my mom or even my willingness to help him find the Tree. We were talking about the box in my bag. He knew it. I knew it. And he was coming for it.
I put my hand on the screen door, prepared to run back into the house, but at that moment Mr. Tennin and my father came around the corner of the house.
"Hey there," my father said. "Mr. Jinn. What can I do for you?"
Mr. Tennin looked surprised, almost alarmed. Mr. Jinn cleared his throat and took a step back, away from me.
"Oh, nothing much. Just coming by to say hello to the boy here. See how he's doing after the funeral."
"Very kind of you," my father said, but he didn't sound convinced. He stared at the broken step but, oddly enough, didn't comment on it. Something looked different about him. His face appeared brighter, and the fog in his eyes had cleared. I looked over at Mr. Tennin and wondered if it was because of him. But he didn't meet my gaze—he was staring at Mr. Jinn.
"Actually, Dad," I said, "Mr. Jinn here wanted to hear the story of the old oak tree. The story you told Abra and me the other day? I told him you'd be back in a minute and that maybe you could tell him while you washed up for dinner. Please?"
It was a lame attempt, but I said "please?" with such desperation that my father stared at me for an extra moment and then nodded. I think he could tell something was wrong.
"Sure, boy. If that's what you want."
I nodded, my head moving up and down so fast it's a wonder it didn't fly right off.
"Well, now, that's okay," Mr. Jinn began, but Mr. Tennin interrupted him.
"Come on, Mr. Jinn. Join us! I'm making dinner to celebrate my first night here. We'll pull up an extra chair."
I ran past Mr. Jinn and stood on the other side of Mr. Tennin and my father.
"Actually, Mr. Jinn can have my seat," I said as I continued walking away. "I'm going to Abra's for dinner tonight."
"Okay, boy," my dad said. "But don't stay too late. I'd like you to start helping with chores again tomorrow. We've gotten into a bad habit."
Chores seemed so bland in the face of all that was happening. I was still determined to bring my mother back—I didn't have time for feeding baby lambs and collecting eggs. But there was also something about the fact that my father wanted me to help him that made me think he must be getting better, back to his old self.
"Okay, okay," I said. But as I turned to run, Mr. Jinn called out after me.
"You'd best watch your way on Kincade Road, Sam. People in town said they saw some nasty-looking dogs roaming between here and the fair. Probably the carnies' dogs."
I turned and walked backward for a few steps. Was he threatening me? He shrugged, not looking very worried, and walked into the house. I continued walking backward, away from the house, then turned and ran down the lane, each of my steps kicking up a cloud of dust, small clouds that disintegrated quickly in the stiff breeze coming down from the eastern mountains.
I tired out fast and my run turned into a walk. I had decided not to ride my bike because Mr. Tennin's box was heavy in the duffel bag and I wasn't sure of my ability to ride while balancing it. But walking was slow. Very slow.
The road south of our farm ran along Abra's father's fields, but they were barbed-wire-lined pastures filled with a few hundred dairy cows, their lazy tails swatting at flies, their jaws chewing, chewing, chewing. They never stopped working over their food, not even when they looked up at you through those deep black eyes.
Those cows knew me, and a few of them meandered over to the fence where it ran along the road. I walked over and stopped for a moment, holding my hand out over their heads as if I was blessing them. They tried to lick me, their massive tongues curling out toward my fingers. They made me laugh, those long tongues.
But laughing felt so foreign. I hadn't laughed for days. And I remembered why. My mother had died because of me. Because I had insisted we stop and pick up Icarus.
I sighed and turned away from the cows, feeling torn. Should I continue on to Abra's house, or should I go back and spend what was left of the day looking for the Tree? It felt like time was running out. It felt like, if I was going to bring my mom back, it had to happen soon, or some kind of doorway would close.
That's when I saw the three large, black dogs, the same ones that had been fighting with the groundhog. They sat there in the middle of the road, just south of me. They didn't look aggressive, but they didn't look like nice dogs either. It seemed like they were waiting for me to make a decision, and that decision would determine their course of action. I had to pass them if I wanted to go to Abra's house, and they didn't look like they were going to move.
"Out of the way!" I shouted, waving my hand at them.
I thought about going home. But then it hit me: Mr. Jinn had sent them after me. He didn't want me meeting up with Abra. For some reason he wanted the two of us to remain separate.
I took a step.
The one in the middle bristled, and I heard it growl, a sound that came at the same time as a far-off peal of thunder. The storm approached. Low gray clouds boiled with anger and rolled in overhead. It was getting darker, too, as the day wore on. Large drops of rain exploded on the dusty road. The other two dogs walked around either side of me as if they were distracted, but I knew what was going on. They were surrounding me.
"Get out of here!" I shouted, but they only smiled at me the way dogs can sometimes smile, with their lips pulled back, their teeth bared, their tongues lolling to one side.
The rain came down in stinging pellets, and I knew I was about to get drenched. I was also about to get eaten. One of the dogs snapped at my foot, and I kicked it in the nose. It yelped and growled even louder, coming back in to take a snap at my elbow.
While I kicked that one back, another grabbed the duffel bag and pulled it away from me. The contents of the box spilled onto the ground, and I ran to it in a panic, trying to keep the book and the articles from getting wet. Then I saw that the sword lay in the road.
It looked like it was on fire, and it seemed to be growing larger. The rain wasn't hissing or steaming when it hit the sword. In fact, the rain came down even harder, but the blade and the hilt were writhing in flame, and nothing could extinguish it.
At first the dogs drew around it, forgetting about me at least for a moment. I scrambled backward away from them, getting ready to run for Abra's house, though I hated to leave all that stuff behind.
Then the dogs started yelping and howling. They bit at their own fur as if trying to pull hot embers out of their skin with their teeth. These enormous black dogs were reduced to rolling on the road. It was like the heat from the sword had gone inside them.
They rolled over and over on the road.
Then they stopped moving.
I was both relieved and horrified. Were they dead? I wasn't going to get close enough to find out. But seeing those dogs lying there, I suddenly realized how serious this quest had become.
I stared at the sword. What should I do with it? I couldn't leave it in the middle of the road.
It no longer glowed. It was no longer in flames. I tried to touch it but it was still hot. I bunched up my duffel bag and used it to pull the sword from the earth, then dropped it into the box, nudging it into place. Even through the duffel bag I could feel the heat. I placed the book and the articles back in their spots. They were soaking wet, and I hoped they weren't ruined. I placed the lid on the box and managed to fit the box back inside the duffel bag.
I looked at the dogs. They were actually quite majestic creatures. There was something very old about them, something ancient and mythical. Their fur was a deep, deep black, the night sky around a new moon. I wondered if they had been that mean when they were puppies, if that's how their breed was born, or if they had been trained to attack. I thought I knew the answer. I couldn't bring myself to believe that anything was born evil. It seemed that evil had to be constructed, usually in the empty places left by pain or rejection or manipulation.
It wasn't too much longer before I arrived at Abra's farmhouse, but I was soaked through. The rain stopped and the sky darkened as night fell. The clouds had spilled over the western mountains, and now hints of a long, slow sunset peeked out from the edges, pink and indigo.
I walked up Abra's long lane and there she was, sitting on the porch alone. She looked tired and sad, but when she spotted me coming up the lane, her face brightened and she hopped up, ran through the wet grass, and hugged me. The light in the sky looked strange, as if it had been strained through many filters and what was left was light without any of the normal impurities. It was like the first day.
"I'm glad you came," she said.
"Abra," I began, "I'm sorry about—"
"Don't worry," she said. "I don't want to talk about that. I have something to show you. You're not going to believe what I found."
## 19
SHE GRABBED MY SLEEVE, then my hand, and jogged toward the house, dragging me along behind her. The duffel bag strap dug into my shoulder, and the bag itself banged against my leg as we ran.
"Wait, wait," I complained. "Not so fast. This bag is heavy."
She dropped my hand. "What do you have in there anyway?"
"I brought a surprise of my own. I've been busy too," I said, not wanting to be outdone by her.
"I think you're really going to like this," she said. "I think it's a sign."
Her house was similar to mine, with a large front porch attached to an expansive farmhouse. But their house was made up of two dwellings, and they often rented the other side out. That summer the other side was empty. We would often sneak into the empty half and pretend it was haunted. We would run from window to window, breathless with fear or excitement, until we'd hear her mother's voice calling out that supper was ready.
We walked quickly into the house. I heard Mrs. Miller putting the dishes away, the ceramic plates making loud sounds as they crash-landed into the appropriate cupboards. Her mom was always moving, always busy, and you could tell where she was in the house just by listening.
"Mom, Sam's here," Abra said as we passed the kitchen.
"Hi, Sam," she called out.
"Hi, Mrs. Miller," I said, but Abra pulled me in the opposite direction, into the dining room with its wood floor and echoing, high ceiling.
"I have ice cream if you want," her mom called after us.
"Okay, Mom, in a minute," Abra said.
At the far side of the dining room was the door that led to the empty side of the house. An old-fashioned key was in the lock, the huge kind with oversized teeth on the end. Abra turned the key and the lock clicked. She cringed, and I hoped her mother hadn't heard—her parents didn't really like when we played on that side of the house. We both froze in place, waiting for a voice telling us not to go over there. When none came, she turned the knob and pulled the door open, and we vanished into the other side of the house.
She closed the door behind us and picked up a flashlight. It always seemed so still in the empty side of the house. It felt like we had traveled to another time, another place, where we were the only two people alive. Who knew what kind of world we would find waiting for us if we dared to venture outside? Maybe everyone else had disappeared. Maybe everything was starting over again.
"I kept this here in case you came," she whispered. Light from the dusk outside drifted through the windows, but it wasn't much, and it left the rooms coated in a kind of blue darkness that was difficult to navigate. The flashlight pointed the way, a round circle of light with a dim inner core.
She led us up the stairs. My shoulder was weary from carrying the bag, so I changed it to the other side. We got to the top of the steps and doubled back to the landing to the front bedroom, the one that had a window that looked out over the lane.
"Here, hold this," Abra said.
I dropped my duffel bag and took the flashlight.
"Point it into the closet," she said, so I did.
She walked into the shadows and came out carrying a chunk of log that was almost too heavy for her, about a foot in diameter. She had to carry it with two hands and kind of leaned back as she bore its weight. She carried it tenderly, as if it might break, and placed it on the floor in front of me.
"What's that?" I asked.
She looked up at me, her blue eyes large and expectant. "It's a piece of log from your tree." Her voice came faster now. "The lightning must have blown that branch to bits, because this piece was all the way in our pasture. I saw it when I was walking back from your house."
"Wow," I said, but I wasn't that impressed. I'd seen similar chunks of wood littering our farm after the lightning strike. She treated the branch as if it was holy, as if it was some kind of a sign, but I just didn't get it.
"Look on this side," she said, pointing to the thick end of the log facing her.
I walked around, and then I understood.
First of all, I saw how she could carry such a thick piece of wood. It was hollow. Or at least part of it was hollow. I shone the light into the hollowed-out place of the thick branch, and that's where it was.
A small green thing, no more than three inches tall. It looked like a miniature tree in the winter, without any leaves, except even the trunk and branches were bright, shiny green. And while it didn't have any leaves, there were three white flowers, each the size of a pea, hanging on the tree, heavy and ripe. The branches those flowers hung on were weighed down and looked like they might break at any moment.
"That's . . . that's . . ." I said, unable to speak further.
"Isn't it amazing?" she said. "I've never seen anything like it. I think it's a sign, Sam. I think it's a sign that your mother, she's okay, right? I mean, this is a chunk of the tree where she died, and somehow there's this flower, this beautiful flower inside it, protected? I think it's just beautiful."
She was nearly in tears, and then I remembered. She hadn't heard Mr. Jinn's description of the Tree of Life—what it looked like or where I might find it or what it would need to survive and grow. She had already left before he told me those things. But this was it, for sure.
This was the Tree of Life.
"Amazing," I said, and with that one word I decided I couldn't tell her. I couldn't tell her what I knew, at least not right away. I couldn't show her what was in the duffel bag. I couldn't tell her about the three dogs or the flaming sword, because who knew how she would respond? She might laugh at me or try to convince me not to use the Tree to bring back my mother. She might even hide the Tree, or kill it.
I took in a sharp breath.
She might kill the Tree. I looked at it again. It was so fragile. It wouldn't take much to kill it. Just a deliberate movement of the hand. A swift kick. So much could be destroyed so quickly.
"What is it?" she asked. "What's wrong?"
I shook my head. "I don't know. I just don't know."
I felt evil again. I felt like she was good and I was keeping things from her, so surely that made me evil, right? Darkness spread in me, I could sense it, but I felt powerless to stop it. The only way I could stop it would be to give up on my mother, and I couldn't do that. I couldn't.
I would do anything to bring her back.
Right?
Anything?
"Thanks for showing this to me."
She put it back in the closet. "We can keep it here for now," she said. "Maybe your dad can come and get it in the car. It's kind of heavy."
"I can't believe you carried it all the way here," I said.
"I know! But I really wanted you to see it," she said, suddenly bashful. "So, what do you have in there?"
My mind darted here and there. "You know what? Nothing compared to that," I said, motioning toward the closet. "Nothing at all."
"But I'm curious now!" she protested, laughing. "You can't do that."
"Honest, it's nothing. Just a few old things I found in the barn."
"Whatever it is, it looks heavy," she said, and I was relieved that she seemed content to let it go, to move on. "You should leave it here. I could even lock the closet. When you and your dad come for that log, you can get your bag."
At first I panicked. I thought she was trying to steal it from me, to separate me from the blade and the atlas and the articles. But I calmed myself quickly. She didn't know. She was only trying to be nice.
"Do you think if we locked it in there tonight, I could take the key with me?"
She looked confused. "Sure, I guess. Why? Do you think I'm going to steal it?" She looked bothered, as if she had stubbed her toe on something in the dark, something strange, something she couldn't identify.
"'Course not." I forced a laugh, but it came out sounding hollow. "I just, you know, I really like it. I'd like the idea of knowing that little plant is mine. That the sign is mine and no one else can get to it."
"Okay . . . weirdo," she said, smiling.
We both laughed, and that time I laughed for real. It felt good. There is something about laughing that pushes back against the darkness, even if only for a moment.
"Thanks for coming," she said. "I was hoping you would."
I smiled, and it was genuine, because I had missed her too.
"What are friends for?" I asked, but those words made me feel worse, as if cementing my betrayal.
I clutched the closet door key tightly in my pocket as I got into the car with Mrs. Miller. She had agreed to give me a ride home since it was already dark and I didn't have my bike. They had one of those old station wagons with the fake wood panel that ran down the side. It always smelled like a pine forest in there, thanks to the little green tree hanging from the rearview mirror. It felt strange sitting in the passenger seat with only Mrs. Miller and me in the car.
"How is your father doing?" she asked.
"He's okay," I said.
"And how are you?"
"I'm okay, I guess."
"The funeral was beautiful this morning," she said, wiping her eyes. She glanced over at me while she drove. "You know, it's okay to be sad. It's okay if you cry from time to time."
Silence. Only the sound of the tires spitting out muddy rocks and the clattering they made on the underside of the car.
I nodded and turned away, looking out the passenger-side window. It was strange how talking about crying made me want to cry. It sounded like something my own mother would have told me, if she hadn't died. But I didn't believe Mrs. Miller. Adults rarely cried. I hadn't once seen my father cry, not in my entire life, not even since the funeral, though sometimes when I came into a room unannounced or unexpected, his eyes were red-rimmed and tired.
No, what she said wasn't true. We weren't supposed to cry. I didn't know why she was trying to tell me any different.
That's when I saw it—a deeper shadow moving against the night. A blackness within a blackness. It stood on the eastern side of the road toward the river, in a clump of trees that led up into the mountain. At first I thought it was only a strange shadow, a trick of the early night. But after we passed it, and just before it went out of my view, it gathered itself, sprang out of the glade of trees, and ran alongside the car.
## 20
I COWERED IN MY SEAT, moving down farther until only my eyes and the top of my head were visible in the glass.
"That's okay, dear," Mrs. Miller said, reaching over and patting my leg. She must have thought I was bent over with emotion after her kind speech about the acceptability of mourning. But that wasn't it. I was scared. More scared than I'd ever been.
The thing that ran along beside us, off the side of the road, reminded me of the three dogs that had attacked me earlier on the road, except it was so much bigger. If it would have stood on its hind legs at the base of the oak tree, its forepaws and head would have easily reached into that small nest of branches where my cat had hidden, where I had stood in that terrible storm. And even though it was running alongside the car, it kept up with us easily. It didn't look tired or like it was trying very hard. It looked like it was loping, running for the fun of it.
Sometimes when I blinked I lost sight of it. It was a shadow within a shadow, a deeper blackness. It was a hole in reality. I couldn't see it. And then I could. And every time I caught sight of it, every time its shape became recognizable, I ducked down again, fear gripping me.
We slowed to make the turn into my lane, and it stopped in the church parking lot. It bared its teeth at me as we drove away, a silent warning.
That fruit does not belong to you.
I remembered it. The fierce thing that had come to me in my dream, when the fruit kept rotting and I couldn't get a piece of it to my dying mother.
"An Amarok," I muttered to myself, and I realized what it had come for. It had come for the Tree.
I remembered my father's words.
It only devours those who are foolish enough to hunt alone.
"Sam?" Mrs. Miller asked in a kind voice. "Are you going to get out?"
We were parked in the lane, fifty yards from the house. I hadn't even realized she had stopped. I looked in the side-view mirror, backward down the lane, desperately searching for the Amarok. There were strange shadows in the church parking lot, sliding shadows cast by the single flickering streetlight mounted on the corner of the church. But I didn't see anything else.
"Sam?" Mrs. Miller asked again.
"Thank you, Mrs. Miller," I said, trying to contain the fear in my voice. "The ice cream was delicious."
I opened the door and cringed, expecting to feel the savage bite of an Amarok on my leg as it yanked me into the darkness, devouring me after I told it all of my secrets. But nothing happened. I only heard the rumble of the station wagon's engine more clearly, mixed with the summer sound of crickets chirping.
"Are you okay, Sam?" she asked.
I put my foot on the ground. I looked around the car. Every shadow was suspect. Every shadow was an Amarok waiting.
"Bye," I said, but at first I didn't move. I turned and looked at her with what was surely a desperate gaze. "Bye," I said again, dashing from the car and sprinting through the darkness, holding the key in my hand as if it were the one thing that could save me from the Amarok.
"Sam!" Mrs. Miller called out from the car, her words barely fast enough to catch me. "Sam! You forgot to close the door!"
My father's hand shook my shoulder, leading me away from the nightmares. Shadows. The Amarok running alongside our car before hiding in the blackness surrounding the church. The lightning tree exploding over and over again. And there was a key, always a key that I could never find or hide or fit into the lock. A key that slipped from my fingers and fell down, down through the cracks in the floor to a place I could never reach.
"Sam," my father said, shaking me again. "Sam, it's time for morning chores."
I was happy to escape those dreams, and I rolled over and climbed out of my bed without a single complaint. I was also happy to hear my father's voice again. He walked downstairs while I fumbled my way into my work clothes: jeans, holey socks, and an old T-shirt. My boots waited for me in the mudroom inside the back door. I put the key Abra had given me into my pocket, and while the dreams began to fade, that key felt very, very real. I rubbed my finger along the edges of the sharp teeth. I felt the ring at the top, smooth and cold.
I followed the smell of bacon downstairs.
"Breakfast is served," Mr. Tennin said, loading eggs and bacon onto the three plates on the table. He looked wide awake, refreshed. Had he slept? Did he even need to sleep?
I didn't want to make eye contact with him. I couldn't tell whether or not he knew his box was missing. It didn't seem as though he did—nothing was said about it, and I hadn't heard him up in the attic after I got home the previous night. But he could have easily been up there while I was over at Abra's house. He even would have had time to search my room. On the other hand, he seemed happy enough. Still, it made me nervous even looking at him, so I kept my eyes down, focused on my food, and decided to answer any of his questions quickly, with as few words as possible. For some reason I was worried that he might find the truth somewhere in the sound of my voice.
Thankfully, we ate without talking, but breakfast was still a noisy business of tired breathing and silverware clanking on plates and the sound of chewing. It was a fast meal because there was always too much work to be done and not enough time, and soon our dishes were in the sink and we were walking out the front door into the mostly dark early morning. The eastern sky held a faint glow. The sun would rise in less than an hour.
Mr. Tennin and I followed my dad into the main level of the barn, and Dad turned on the lights. Five or six lightbulbs blinked on, reminding me of the attic, that the bulb up there needed to be replaced.
"Boy, why don't you go back and feed that lamb before I forget about it? Mr. Tennin and I will be up in the hayloft throwing down some hay."
He handed me the bottle and I walked back through the barn, past the cows waking up in their stalls, past the chicken run that connected to a small opening that allowed the chickens free access to the outside world. There in the back corner, where dusty light fell through a small window, I saw the lamb. As soon as it saw me it started bleating and shaking its little tail back and forth, back and forth, as fast as it could. Its face was tiny. Its whole body shook with excitement at the sight of breakfast.
I took the bottle my father had given me and stuck it between the bars. The lamb squatted down, stuck its butt up in the air, and reached up with its mouth, jerking on the bottle and wagging its tail. I laughed and patted it on the head. I thought about how my mom used to love to come out and feed the lambs. She wasn't much for the other farm work, the milking or the mucking out of the stalls. But she loved the lambs.
I thought, too, of Abra. She'd probably like to meet this little guy.
"Yeah, you'll have some more friends before this summer is out," I said quietly to the lamb.
I heard the sound of hay falling down through the large holes in the ceiling as my dad and Mr. Tennin used their pitchforks to shovel it from the upper level of the barn. It made a wispy, hushing sound, and hay dust swirled around in the light.
A shadow fell over the lamb, and at the same time the light coming through the dusty window was blocked out. I couldn't tell what was outside the barn that might be casting such a large shadow, but there was also something behind me. I looked over my shoulder.
Mr. Jinn stood there, his arms crossed, his eyes stern. His presence startled me and I jumped, banging my head on the bars. I looked around, but I had nowhere to run. When I finally caught his gaze, I could tell he wasn't happy.
"Hello, Sam."
"Mr. Jinn," I said.
The lamb jerked the bottle out of my hands. When it hit the concrete on my side of the bars, the glass shattered, sending milk everywhere. I groaned.
Mr. Jinn looked at the ground and kicked lightly at the concrete, his foot sending up small clouds of dust and straw. He looked back at me, squinting. "I don't get the feeling that you're helping me very much."
"With what?" I asked, but I knew what he was talking about. When I first realized he could help me find the Tree, his presence had filled me with a kind of hope. Leery hope, perhaps, but still hope. Now? He made the pit of my stomach drop. I found it hard to breathe when he was around. I could feel my pulse beating solid and fast in my neck. But right alongside the fear he filled me with was the sense that I needed him. I needed his help.
He stared at me but didn't say anything, so I continued, stammering through whatever story I could come up with.
"Well, it's just that I had to show Abra something last night, and now this morning I've got to do my chores. I don't have much choice with that. But this afternoon—this afternoon I'll spend the whole rest of the day looking for the Tree. Honest. I'm sure we'll find it."
"Oh, I'll find it," Mr. Jinn said. "I always do. But we're running out of time. Your mother is running out of time." He paused and let those words sink in.
They sank in deep, resonating with me, and I had a moment of clarity.
Oh, I'll find it. I always do.
Mr. Jinn was the angel who wanted to possess the Tree. He was the one. A chill spread over my body, tingling in every hair on my head. He was the cursed angel. The realization should have shut down any other plans I had—knowing his true identity should have scared me off. But it didn't. It only entangled me with him even more. I needed his knowledge and I needed him, because he could help me with the Tree.
"This Tree doesn't hang around forever, Sam, and I've waited a long time for this. We've got about ten days from when your mom died until the Tree withers. If we don't find it before that"—he lifted clenched hands, then opened them suddenly—"pow. The small white flowers fall off and it will die, and that will be the end. The Tree will not show up here again. It might not even regrow in your lifetime."
I pictured those white flowers on the small tree Abra had shown me. They were heavy, all right, and weighing down their branches. I could imagine them snapping off at any minute.
"I'll help. Honest."
I tried to erase the images from my mind. I had a strange sense that he could go in there, inside my brain, and help himself to whatever it was I happened to be thinking about.
"I hoped you would," he said, "but I wasn't so sure. So I had to call in the big guns. I had to call in the helpers. Specifically, one helper."
I knew what he was talking about. The Amarok.
"I think you saw him last night on the way home from Abra's house, didn't you?"
I nodded.
"Sam," he said, suddenly very serious, "the Amarok will not . . ." His voice trailed off, and he sighed. I pictured the large shadow loping alongside Mrs. Miller's car, the long tongue, the eyes.
When he spoke again, his words came out with resignation, as if things had moved somehow beyond his power. "The Amarok is not easily appeased. It hunts for one thing: the Tree. It wants to feed on one thing: fruit from the Tree. But anything that stands in the way?"
He raised his eyebrows as if to ask me if I understood. I nodded again.
"It devours," he said with a shrug.
I looked over my shoulder through the dusty window, but that shadow was gone.
"Come to my house when you're finished here," he said. "We have a lot of work to do."
So that's how I found myself just after lunch, walking through the knee-high corn to Mr. Jinn's house. I had lied to my father, telling him that Mr. Jinn had some chores he'd like me to help with. I guess it wasn't a complete lie, but it felt like one. Anyway, my father said I could go but I had to be back in time for dinner and after-dinner chores. I agreed.
As I walked through the field, my own house growing smaller and smaller behind me, I noticed the vultures were circling. All of them wheeling and gliding, occasionally flapping their giant wings, their bare heads barely visible from the ground. They hovered over me as if they were protecting me, or perhaps pointing me out to someone or something.
I left our fields behind and entered the tall weeds, glad for the boots I still wore after morning chores. The small path used to have walking stones, but those were mostly buried by mud and time. I walked up the rickety steps to the porch and knocked softly on the door.
"Yeah," Mr. Jinn said from deep inside the house. "Come on in."
I pushed the door open, walked inside, and reluctantly pulled the door closed behind me. The latch made a loud click, and I stood there for a moment, wishing Abra was there with me.
We have to stay together.
I was so far from that.
"Hungry?" Mr. Jinn asked from the kitchen.
"No thanks. I just ate."
I walked in and sat down in the same chair I had sat in the first time I was there. Mr. Jinn's back remained turned toward me as he chopped something that smelled like onions with a large knife on the counter. The chopping made a solid sound, a kind of knocking that ran around the otherwise silent house.
"How's your friend?" he asked.
Chop-chop-chop-chop-chop.
I grew nervous. I couldn't think of her without picturing the Tree of Life, its small green shininess, its three white flowers. I tried to keep it out of my mind. I worried that if it was there, Mr. Jinn would see it and pluck it out of my head, bring it into reality.
Yet wasn't that exactly what I wanted? Didn't I want Mr. Jinn to have the Tree so that together we could bring my mother back? I thought that was what I wanted. I thought that was why I was there. But something in me hesitated.
"Fine," I said. "She's fine."
He threw a large slab of meat into a frying pan and added the onions on top. It fried and it spit and it hissed, and the rich smell of it filled the house. Still, Mr. Jinn didn't turn around.
Suddenly, I knew that he knew that I knew where it was. And he was angry. And he would get angrier and angrier until I told him. And if I didn't tell him, my mother would be gone forever.
Forever is a very long time, especially to a twelve-year-old boy.
"I know where the Tree is," I said quietly.
He flipped the large piece of meat in the skillet. I thought I recognized it as a slab of liver. I had never liked liver very much. The texture reminded me too much of sawdust. I was glad I'd eaten before I came. But he didn't say a word. I wondered if he had heard me.
"I know where the Tree is," I said, louder and with more confidence.
"'Course you do," he said, turning to the side and emptying the meat and the onions onto a plate, which he carried to the table and put down with a loud thud. "'Course you do."
He started cutting and the meat was very bloody. Soon the bottom of his plate was nothing but a red pool of onions. He ate like a man who hadn't eaten in weeks, like a man who was eating for the very first time. He savored every massive bite.
"It's in Abra's house."
He stopped. He placed his knife and fork on the table quietly. He leaned back and stared at me, chewing and chewing that bite. When he swallowed, the whole thing went down. I could follow the lump in his throat as the food descended. It was like watching a snake consume a rat that was too big for it.
"That's not good."
"It isn't?"
"No," he said. "That's not good at all."
"What's wrong?" I asked.
"I can't go over there. You'll have to bring it here."
"Bring it here? Can't we go get it together?"
"Absolutely not," he said, shaking his head. "Absolutely not."
We sat in silence. I could tell he was thinking. It seemed he had completely forgotten about the liver and onions cooling on the plate in front of him.
"You'll have to go and get her. Bring the Tree here. Bring her here too. That's what we need."
"I don't know if she's going to—"
"Bring her!" he shouted.
A shadow darkened the dirty kitchen window. I looked through it, but I couldn't see anything.
"Bring her," he said in a calm voice, as if he regretted losing control. "Once she is here, once the Tree is here, we can find the rest of the things we need."
"The rock, the water, and . . ." I couldn't remember the final item.
"And the sunlight. That's right," he said. "But first, bring your friend here. And bring the Tree."
He seemed satisfied. He took another large bite, and the red juice ran down his chin.
I stood up. I knew that if I was going to do it, I would have to do it quickly. "Okay."
I walked out of Mr. Jinn's house and started the long walk to Abra's. It was a mild July day, and I realized the shadow I had seen in the window had not been from a storm cloud. The sun shone in a clear, blue sky. But I felt a darkness surround me, and the vultures came again, circling high above.
## 21
ONCE I WAS ON THE ROAD, everything seemed less mysterious. Without the thousands of rustling cornstalks all around me, the day took on an almost boring note. The July heat came up off the stones like a mirage. Even the cemetery and the church, both vacant, seemed drab and normal.
Soon I walked the stretch where the dogs had attacked me the day before. But again, the earth seemed to deny that anything supernatural had ever occurred. I wondered what had happened to the dogs' bodies. I thought about the tiny plant in the log, and it all seemed silly and impossible.
By the time I arrived at Abra's house, I fully expected us to find the closet empty. Maybe there was no Mr. Jinn. Maybe there was no Mr. Tennin.
Maybe my mother had never died.
Yet when I walked up Abra's driveway and slipped my hand into my pocket, there was the key. The skeleton key that would unlock the door. It was hard and metal and very, very real in my pocket. I knew that all of it had happened, every last strange thing, and in that moment I also knew that I would have to make a choice soon about what I was going to do with that Tree, a very real choice that would have very real consequences.
Abra's baby brother was crying when I knocked on their front door. I walked in without anyone answering or inviting me in.
"Hello?" I called out to the house.
Mrs. Miller came into the room, carrying the baby. I could never remember his name. He cried a lot.
"Hi, Sam," she said with an apologetic smile. "Abra went out with her father to the milk barn. She'll be back in a minute. Can I get you a drink?"
"No thank you," I shouted over the loud cries of the baby.
"Oh my. Oh my," Mrs. Miller said to the baby. She placed him on one of the sofas, on his back, and looked over at me. "Would you watch Francis for just a minute? I have to run upstairs for something."
That's right. His name was Francis.
"I'm not so sure," I said.
"Just one minute. I promise. Here." She waved me over. "Sit here, like this, and make sure he doesn't roll off."
I walked to the sofa, but I didn't want to watch the baby. Babies were breakable, like fancy glasses with stems.
"Oh, stop it," she said, laughing at my hesitancy. "You'll be fine."
She was off and I was left sitting there on the edge of the sofa, my skinny, twelve-year-old legs the only things that separated the baby from a long fall and certain death. But he clearly didn't appreciate the crucial role I played in keeping him alive, and he kept crying.
"Francis," I said in a singsong voice. "Francis. Stop crying. Stop crying."
For a moment his cries grew even more shrill, making me even more nervous, but then his eyes caught mine, and he stared up at me. His mouth uncurled, smoothed out. His eyes went from that squinty crying position to wide open, though still filled with tears.
I looked down and understood what it was about babies that so fascinated people. Inside those bright blue eyes, eyes that reminded me of Abra, I saw the essence of life. A spark resided there that could not be explained biologically. It was life, and it was moving and beautiful and a little scary, like a flash of lightning or a fish showing its shiny self for a moment in a fast-moving river.
Francis looked up at me and, as if disappointed by what he found in my own eyes, started crying again. This time a louder, more persistent cry than before. Abra came running in the front door.
"Francis?" she called, dashing over to where I sat.
"He's crying," I said, shrugging.
"Is Sam being mean to you?" she asked the baby, picking him up.
Mrs. Miller came down and reached for Francis. "Aw, you poor thing. Thanks, Abra. Thanks, Sam."
Abra looked at me and raised her eyebrows, wondering why I was getting any praise.
"Hey," I said, "I was watching him."
"Is that what you call that?"
"I'm taking him up for his nap," Mrs. Miller said. "You two have fun. And be careful." She looked at Abra. "Your father found an enormous set of tracks by the river. He's still not sure what it might be. So stay close to the house."
She walked up the stairs, carrying little Francis, who by now had stopped crying and was sucking on his fist. He looked over at me with obvious contempt. Or at least that's what I thought I saw.
Once Mrs. Miller had disappeared upstairs, Abra looked over at me. "Want to go see it again?" she asked.
I nodded.
"Did you bring the key?" she asked.
I reached into my pocket and held it up like it was the answer to every question anyone had ever asked.
The feel of the correct key turning in a lock is a satisfying feeling. I pulled the skeleton key back out of the slot and looked at Abra before turning the knob and opening the closet door. Everything was where we had left it. The log was back in the shadow, the hole facing away from us just as I had placed it the night before. The duffel bag sat on the other side of the closet, the square edges of the box visible.
"There it is," I said, not knowing what else to say. I walked into the closet, picked up the log, and carried it out into the room. It was heavy. I wasn't sure how I would carry it all the way to Mr. Jinn's house.
"Oh no," Abra said in a sad voice, pointing to the hollow side of the log. "That little plant is gone."
I practically dropped the log and looked upside down into the end where the Tree of Life had been the night before. Nothing. I turned around, got down on my hands and knees, and peered deep inside the log, hoping that maybe it had fallen in further. But there was nothing there, nothing except the rich dirt and small patch of moss that I pulled out and held in my hands.
I thought I was going to cry. Every dream I had ever had about my mom returning evaporated into that hollow log.
"It was so pretty," Abra said. "But it was a sign. Your mom is watching over you."
No! I wanted to shout. No! That was the thing that would make my life normal again. It would bring back everything I've lost! That little plant was what I needed. I had to have it.
But it wasn't there. It wasn't dead, at least not in the log. Someone must have taken it.
Who?
I stared over at Abra. The darkness that had moved into my soul flared up.
"Did you take it?" I asked.
She looked hurt. "Take it? I gave it to you! I gave you the key to the closet. Why would I take it?"
The darkness subsided. She was right. If she had wanted it, she could have chosen never to show it to me. And she didn't even know what it was.
"What about your parents?" I asked. "Were they in here?"
"They never come over here," she said. "Why are you so paranoid? Why would anyone even want that thing? It was pretty, but that was it. It was just a flower."
I sat down under the weight of loss and shook my head, and before I could stop them, the words came pouring out.
"It wasn't. It was the Tree. The Tree of Life. Mr. Jinn told me to bring it to him so that we could bring my mom back. He said he could do that."
I wondered what she would say. I knew she had been skeptical from the beginning. But her response surprised me.
"So what's he going to do if we don't have it?"
"You believe me?"
"What's he going to do?"
"He won't be happy."
"Were you going to tell me, or were you just going to take it to him?" she asked.
"I don't know," I said. "I didn't know what to do."
She sat down on the floor beside me. We both stared into that empty log for a long time. And strangely enough, I felt a small seed of peace.
"So what's in the bag?" she asked.
I stared at it. The box seemed suddenly important again. Even without the Tree, I was left with something. Maybe something in there would lead me to it. Maybe something in that box would put the whole thing back on track.
"This has been one crazy summer," I said, looking over at Abra. She smiled, and it made me smile.
"What's in the bag?" she asked again, this time punching me in the shoulder, but not very hard.
"You're not going to believe it," I said, shaking my head. There was nothing believable about that summer. Not one single thing.
I pulled the bag over to where we were sitting. Everything seemed to grow serious, but the sun still shone in the window. The empty half of the house we were in felt even emptier. I felt like I always did on that side of the house, like we were the only two people in the entire world. But maybe that wasn't it—maybe we were the first two people in the whole world, and this was the first day.
"You're not going to believe it," I said again as I pulled the zipper back and lifted out the box.
"Try me," she said, staring as I drew the lid back.
## 22
THE SWORD SEEMED LARGER SOMEHOW. I didn't know why. But there it was in the box on top of the atlas and the clump of news clippings and notes. More than anything, though, the sword felt significant. In my mind, it had replaced the missing Tree as the thing I must hang on to. I wasn't sure why.
Movement across the window caught my attention, but when I looked up I didn't see anything. I walked over and looked through the glass. The vultures circled high overhead. I must have seen one of them as its dark shape passed by. I was tired of seeing them. I wanted them to leave.
"The vultures are still out there," I said, turning back to Abra.
She was sitting there quietly, holding the sword and running her fingers over the blade.
"Abra!" I shouted, taking three quick steps toward her. She backed away from me, holding the sword by its small hilt. The blade was short, but for her, for both of us really, it was almost long enough to be a normal-sized sword.
"What?" she asked, inadvertently pointing it at my gut.
I stared at her hands. "Isn't that . . . doesn't that hurt?"
"Hurt? Why?"
"It's not burning your fingers?" I asked.
She laughed. "No. Why?"
I reached out for it. She stretched out her arm to give it to me. But as soon as it touched my fingers, it burned me again.
"Ouch!" I said, jerking my hand away.
"What?" she asked. "What's wrong?"
I shook my head. I didn't get it.
"That thing burns me if I touch it," I said. I showed her the red marks on my fingertips.
"Really?" she said, looking it over, staring down the sharp edge of the blade. "What else is in your box?"
I could tell she was excited, that she thought we were on the edge of something. The strange nature of the sword definitely got her attention.
Some of the things had gotten wet when I brought the bag over, and now they had that crinkly, dried-again look to them. But nothing had been permanently damaged, and all the papers I saw were still readable.
I showed her the atlas and we started scrolling through the pages. There were at least one hundred pages with notes on them. Some of them were places we knew or at least had heard of, like New York City or Jerusalem. But there were also strange places and names that felt ancient. Meshech. The land of Havilah. Miletus. The places that had smaller numbers beside them tended to be the ones we didn't recognize, while the pages that were numbered in the sixties and above were places we knew about.
"What do you think this is?" I asked her. "And why all of the numbers?"
"It looks like the kind of map someone would keep of their journeys. Maybe they went to all of these places and numbered them?"
"All the places with numbers beside them?" I asked. "You'd have to be super old. Or super rich. Or both."
She nodded. "Yeah, but why else would you number different places?"
I skimmed through the atlas. "Maybe they're all places the person wants to go?"
She shook her head. "No. A lot of the notes are observations. Whoever took the notes had definitely been there. In person."
"If you were traveling to all of these places and you were going to number where you went, wouldn't you go to the closest place next? This person looks like they were skipping all over the world for no reason. Look here, in Turkey—#1 and #46. Why wouldn't you do those #1 and #2? Or #45 and #46?" I looked at her with my eyebrows raised, as if I expected her to have an answer.
"I don't know, Sam," she said, sounding frustrated. "I don't know. Why would you skip all around?"
I thought for a moment. "I guess if you didn't know where you were going next."
Her eyes lit up. "Or if you weren't in charge of where you were going next—"
"Or if someone else was telling you where to go!"
"Yes! That's it," she said. "Mr. Tennin works for someone else, some huge, rich, important company. Probably an oil company or something. And they send him all over the world to do his job!"
"With a short little sword," I said, unconvinced. "And a pack of old newspaper clippings."
Abra frowned at me. "I think we're onto something," she said. "It kind of makes sense."
"Maybe."
"Let me see those." She gestured to the papers.
I handed the entire wad to her—it was probably about an inch thick. She unwrapped the rubber bands and started spreading the articles on the floor in front of her. Some of them were stuck together from getting wet, and we had to gently peel them apart. Some weren't from newspapers but were old note cards with writing in foreign languages. Some were in English and some weren't. But all of them—the newspaper clippings, the note cards, the torn-off pieces of paper—had a number written in the top corner.
"Hey, careful," I said. "What if they're in some kind of order? Mr. Tennin's not going to be happy about us messing it up."
"That's it!" she said. "In order. Sam, look up this place." She handed me the atlas.
"What place?" I asked.
"Look, an article about a tree called L'Arbre du Ténéré."
She paused, and I saw her gaze flitting down the small newspaper clipping.
"It was the most isolated tree in the world, 250 miles from any other tree! A Libyan truck driver ran it over." She looked up at me. "Look, here's the number on the article—60. Can you find the Sahara Desert in the atlas?"
I looked in the back and found a page number for the Sahara. I scrolled through the book until I came to the page. There, in tiny script, right in the middle of the desert, was a number.
#60.
"You figured it out," I said in a solemn voice.
"Let's try another one," she said with excitement. "How about this? It's another article with a number in the top corner." She skimmed over the note card. "Okay, this one is about a tree too. Its name was Prometheus and it was almost five thousand years old!" She looked up at me again, amazement on her face.
"Go on," I said. "Then what?"
"It was in the White Mountains of Nevada, and it was the oldest living thing on the planet. A graduate student was given the responsibility to count the rings." She paused, reading some more of the article. "But instead of taking a core sample, the student requested to have the tree cut down? And the park service agreed! That's ridiculous. Why would they give someone permission to cut down a five-thousand-year-old tree?"
"What's the number?" I asked.
"Sixty-two," she said.
I looked up the White Mountains in the atlas. Right there, along the mountain range, was another number.
#62.
She looked up at me, and I could tell she was connecting the dots. She spread out all the articles and note cards.
"Every single one of these is about a tree, either a really old tree or a tree that was vandalized or destroyed. At least the ones that are in English." She held up a note card written in some kind of strange slanting script that neither of us could read or understand. "So, what kind of a company would send Mr. Tennin to places with trees like that?"
"A tree company?" I asked.
She rolled her eyes. "I don't think so."
"How about one of those preservation societies—you know, the ones that try to save the environment?"
Abra didn't look convinced. "I don't think so," she said again.
What was the connection between the contents of Mr. Tennin's box and us? Where did he come from? Why was he here?
"What if he's here because of the lightning tree?" I asked quietly.
Abra looked at me. "What do you mean?"
"Well, what if my grandfather's oak tree is another tree that's been damaged, and that's why he's here?"
"That might be what brought him here, but we still don't know why he does this over and over again," Abra said. We were thinking on the same track. "Here's a question. If he's here for another company, why is he pretending to work for your dad? He doesn't need the work, not if he's working for this business that has enough money to send him all around the world."
"So he's lying," I said. I felt justified in stealing his box, and that gave me a certain sense of relief.
Abra nodded. "He's here for something else."
"The Tree of Life," I said without even thinking. Our eyes met. "He's here for the Tree of Life."
I thought about Mr. Jinn's words again, when he had said that he'd find the Tree. That he always found it.
"Mr. Jinn is the angel who tries to find the Tree. The one from Mr. Tennin's story."
Abra stared at me, curiosity mixed with excitement and a little bit of skepticism covering her face. "And?"
"Maybe Mr. Tennin is the other one. The angel whose job it is to find the Tree and destroy it before anyone eats from it and lives forever."
We knew this was serious.
"Maybe one of them already stole the Tree from the closet," Abra said.
"Could they have come in here?"
"I doubt it," she said. But neither of us felt safe anymore.
I looked out the window. "It's getting late. I promised Mr. Jinn I'd bring you and the Tree to his house this afternoon. But I have to be home in time for dinner and to help with chores."
I couldn't decide what to do. If I didn't go back to Mr. Jinn's house, it would seem suspicious. But what would he do if I went back without the Tree? Without Abra?
"I don't think you should go back there," she said. "I don't think it's safe."
"Me neither."
We sat there quietly for a moment.
"We have a lot to figure out," I said. "But I have to go home. Can we leave everything here, locked in the closet?"
"Do you think it's okay here?" she asked. "The Tree was stolen from there."
"Do you have any other good hiding places?"
We went into a different room and found a different closet with a key in the lock. It didn't feel completely secure, but we didn't know where else to put the box, and I didn't feel right carrying it home with me, so close to the clutches of Mr. Tennin. He had seemed so nice, but now that I knew he was lying about why he was here and that he would do anything in his power to destroy the Tree, everything about him seemed dark and twisted.
I gave Abra the old key. There wasn't any reason for me to take it. She was in on this now. We were in this together. It felt comforting not having to bear everything on my own. But I still wondered, if it really came down to it, would she help me bring my mom back to life?
I told her about the three dogs that had attacked me on the road and the Amarok I had seen running alongside her mother's car.
"I'll come back tonight," I said, "after my chores are finished. Around eight?"
"Yes," she said, "but be careful."
"Don't worry, I'll get my dad to give me a ride. Don't walk onto our property unless it's an emergency," I said. "I think it's safe here, on your farm, but I'm not sure why. Mr. Jinn said he couldn't come here, or at least he didn't want to come here."
"Be careful," she said again.
She led me back to the side of the house where her family lived. I said good-bye to her mother. When her baby brother saw me, he started crying again. I rolled my eyes at him.
Mr. Tennin ate his dinner up in his room that night, so it was only Dad and me at the table. He had sunk back into a state of despair about my mom, so he wasn't saying much. Actually, he wasn't saying anything. We ate in silence, and he didn't ask me about Mr. Jinn or what the man had wanted me to help him with.
After dinner we went out to the barn and I did my chores. Mr. Tennin came out and worked mostly with my dad. He didn't say anything either. It felt strange. Why wasn't anyone talking? Why was everyone being so quiet?
Not only that, but I kept looking over my shoulder, waiting for Mr. Jinn or the Amarok to show up. I knew the Amarok would devour anything that came between it and the Tree. I wasn't necessarily between it and the Tree, but Mr. Jinn might think I was. What if he sent it here to devour me?
I stayed close to my dad all evening.
Finally, my part of the chores was nearly finished. All I had to do was get this bottle of milk into the lamb and I'd be free. My dad was in the cow stalls, shoveling out the manure. Mr. Tennin had vanished.
"Dad, could you drive me down to Abra's?" I asked.
"Drive you? Since when do you need a ride there?"
I shrugged. "I don't know. I thought it would be quicker."
"Sorry, boy, I don't have time to drive anyone anywhere tonight. Just ride your bike or walk."
Mr. Tennin spoke from the shadows. "I'll drive you down. I don't mind."
I shuddered. The lamb finished its bottle and I placed it up on the shelf.
"There you go, boy," my dad said. "There's your ride. Thanks, Mr. Tennin."
I didn't know what to say. For once I wished that Mr. Jinn would come walking in and interrupt us like he always did. I could go with him and he would probably—maybe—keep me safe from the Amarok. But I didn't have much choice. I didn't trust going in the dark all the way to Abra's house. I'd have to let Mr. Tennin give me a ride.
"Okay," I said.
"When do you want to go, Sam?" he asked.
"Whenever you're ready."
"Okay." He turned to me with a large smile. "Let's go now."
# Part 4: The Fire
## 23
I FIGHT WITH MY TIE AS BEST I CAN, and it doesn't feel like a dress rehearsal anymore—this is the real deal. Somehow I manage not to strangle myself in the process, and it is crooked and a little lumpy, but no one will notice. That's what I tell myself. No one will notice the crooked tie of an old man, even if he is attending the funeral of his last friend. Perhaps they will simply see it as a sign of my profound grief. I make my way downstairs.
Dress shoes have always put me in a bad mood. Maybe that's why I stopped going to church some years back. I hated wearing those black shoes. I despised shining them, the smell of the shoe polish, and the way it got all over my hands. They pinched my heels and grated against my bony ankles, and they never felt quite right. I was always aware of them, which is perhaps the worst thing that can ever be said about a shoe. A good shoe isn't even there. You completely forget about it.
Anyway, I walk down the stairs in my pinching dress shoes and am surprised to hear a knock at the door. There's Caleb, dressed up and ready to go to the funeral. I hadn't actually expected him to show up. I look past him, out toward the barn, and his father is in the car, waiting to drive us. I nod at Caleb.
"Hello," I say.
"Hi," he says. That's it. His one-word response is almost as surprising as the fact that he showed up, on time.
"Did you bring your smoke bombs?" I ask.
He nods.
"And this. Can you carry this for me?" I hand him the old box. "It's very fragile. You'll have to be careful."
"Okay," he says, and I wonder who has possessed the body of this boy who used to wield his words like weapons.
"Okay," I say. "Well, let's go."
No one talks in the car. In my experience, no one ever talks in the car on the way to a funeral. What is there to say in the face of death? What is there to say when we are forced to remember that we have come from dust, and to dust we shall return?
"Careful," I say to the boy holding the box as we hit a bump on Kincade Road. It's paved now, the road to town, and Jerry drives faster than we ever drove down that straight stretch. The stones used to jump up and bite the bottom of the car, but now the only sound I hear as we fly down the road is that constant whirring. It reminds me of the river, or of eternity.
We get close to town and pass the park where they still set up the fair every year. The old dusty paths have been paved, and I don't think the carnies are allowed to camp out at the bottom of the hill anymore. The Darkness seems less, or at least it seemed less the last time I was at the fair, fifteen years ago or so. But it's still too early in the summer for the fair, and the park is abandoned.
The town comes up Kincade Road a little farther than it used to, but other than that not much has changed. A few of the restaurant names are different, and the houses look tired, but Pelle's Antiques is still there at the crossroads, run by his grandson, if you can believe that, who is not much younger than me. I wonder if that old back room is still there. I wonder what they ever did with that table the old woman scribbled on.
Find the Tree of Life.
Jerry says he will wait in the car.
"I'm not a fan of funerals," he says, looking away awkwardly because he realizes the obvious nature of his words. Who is a fan of funerals? Caleb and I walk toward the church, and there are a few dozen other people making their way through the parking lot. They wear black and carry a heavy burden on their shoulders, and it is strange for me to think that I could have perhaps stopped all of this from happening with the Tree of Life. All of this death. All of these heavy burdens.
What would these people say to me if they knew I could have stopped death in its tracks?
The boy carries the box, the dust leaving marks on his shirt and his clip-on tie and the lap area of his black dress pants. The contents rattle around inside as he walks, and I know he is desperate to look inside. I stop him before we get too close to other people.
"This is what I need you to do," I say, then whisper in his ear.
He shrugs. "No big deal. But where should I go after I do it?"
"Hide somewhere," I say. "Or go out and get in your father's car. But don't leave without me. I don't have any other way of getting home."
"Okay," he says.
I hold the dusty box on my lap and sit at the front right-hand side of the church. The preacher is a tall man with blond hair and kind green eyes. I have never seen him before, but that doesn't surprise me since I rarely leave the house—I just don't have much desire to get out. I go into town when I must. The only person I considered looking up was Abra, but after so many years of not being in touch, picking up the phone and calling her felt awkward, or somehow inappropriate. And now, well, that's gone.
The preacher seems to have been personally acquainted with the deceased, and emotion keeps leaking into his voice while he talks. The church is not as full as I thought it would be, but of course we are old now, and nearly everyone we knew growing up has left. She has a family, which accounts for most of the people there. I look around as the preacher's voice trips and skips, and I wonder who, if anyone, will come to my funeral. I can't think of a single person.
The casket is open at the front of the church, and some people walked by it before the service began, but I didn't have the heart. I didn't think I was ready to see her. Not yet. I grip the box tighter on my lap, and I shake it slightly to make sure the things are all still inside. The woman beside me gives me a nasty look for making so much noise. Some people.
The preacher keeps talking, and his voice fills in the empty spaces of the room. I look for her husband, and I see him sitting at the very front, to the right of the aisle. I can't remember his name for sure, but I think it might be John. Or Simon.
My heart starts to race, and I wonder if maybe the plan I came up with wasn't the best idea. Maybe I should have simply spoken with her husband, asked permission. Maybe he wouldn't have minded. But as I decide to walk out, find Caleb, and abort the plan, I hear the ear-piercing sound of the fire alarm going off. I sigh. Too late.
The people look around nervously at each other the way people always do when a fire alarm first goes off. Everyone wonders if it is just a drill, if it's a sound that can be overlooked. Lights flash brightly in the church, and the pastor looks around uncertainly. Just as he is about to reassure everyone that they can stay where they are for the time being, smoke pours in over the balcony and billows through the back doors.
Someone screams.
Everyone stands together, and the pastor tries to guide them with his voice, tries to calm them, but they are frantic, as most people are when facing death. Panic and pushing and shouting. Soon the smoke is thicker, but it is settling into an empty sanctuary. Everyone except for me has left.
I walk over to her coffin, and there she is.
Abra.
She is still as beautiful as I remember, though I haven't seen her for years. Her hair is white, the color of frost, and her skin, though old, still holds something of her youth. Her nose reminds me of how stubborn she could be, and I wish I could look into her eyes again, see those sparks fly during a disagreement or the way they softened in friendship.
Our last encounter is one I'd rather forget, one full of questions and doubt. I felt she had forgotten me, and perhaps she had, but it was no excuse for the things I said. She only stood there and took it, and we parted with a painful silence. Now there is only this: her closed eyes, her folded hands, and me, wishing there was a way to follow after her.
I pull back the blanket that lines the coffin and place the box inside with her. Where it belongs.
Outside the church, the crowd mills around. Their voices are full of chatter, and everyone wants to know what's going on, but as the minutes pass their curiosity dies down and they form small groups of people, friends and family. They make small talk—the weather, the town, the baseball season. They fill the morning with words because the silence is unbearable.
I decide suddenly that I have had enough. I got what I came for—a last view of Abra and one last gift from me to her. I weave my way through the crowd, trying not to push my cane down on anyone's toes.
I feel a hand on my shoulder. The pressure of fingertips. I turn around.
"Excuse me, are you Samuel Chambers?"
It's Abra's husband.
I nod, wordless, expecting to be charged (and rightly so) with disturbing her final peace. What right did I have to put things in her coffin, objects that would remain beside her body for decades to come? But he does not say what I expect. In fact, he hands me a small box of his own, and he gives me a sad smile.
"This is from Abra," he says. "She wanted you to have it."
I nod again, clear my throat to speak, but find there are no words waiting to come out. So I turn and walk away, wishing I would have asked him for his name.
I get to the car and climb in. "Thank you, Caleb."
"Sure," he says. "What's that?"
I look down at the box again. "I'm not sure," I say. "I haven't looked inside yet."
Jerry turns on the car and drives away.
## 24
I FOLLOWED MR. TENNIN out to his car, and something inside me was saying, "Run!" But I didn't listen. I crawled into the passenger seat of his old black car, and he started it up. The engine rolled over a bunch of times before catching, and it sputtered and spat before settling into a rhythm.
"There we go," Mr. Tennin said in his soft voice. He put the car in reverse, backed out of his space in the grass beside the barn, and drove down the lane toward the road.
I kept reminding myself that it would only take four or five minutes to get to Abra's house, and I resolved to say as little as possible. I didn't know how I'd answer if he asked me about the box with the blade and the atlas and the articles. Who else would have it? But then I remembered Mr. Jinn sneaking around Mr. Tennin's room and even going up into the attic. Maybe Mr. Tennin knew that Mr. Jinn was spying on him. If he did, he probably thought that Mr. Jinn stole the box, which put me in the clear.
I stared hard out my window and into the empty darkness of Abra's family's pastureland. I knew the cows would all be in the barn for the night, but still I peered into the shadows, thinking about the Amarok. I wondered if I would be safe walking from the driveway to the house. I imagined it jumping on top of the car and ripping through the roof, tearing Mr. Tennin and me to shreds.
As we got to Abra's long lane, Mr. Tennin pulled the car off to the side of the road so that two of the tires were in the grass. Then he turned off the car. It was so dark I could barely see his face. I felt for the door handle, getting ready to yank the door open and run for my life.
"I wouldn't do that," he said quietly. "You know as well as I do that it isn't safe out there tonight. Not for anyone."
He looked at me in the darkness, and I knew that he knew everything. He knew what was going on with the Tree. He knew the Amarok was on the loose. He knew about Mr. Jinn and probably even about the box stashed in an old closet in the empty side of Abra's house.
"What do you know?" I asked, trying to stay calm. I surprised myself with how steady my voice came out.
"I know much more than you do, so that's a start," he said. He continued with something like reluctance. "I know Mr. Jinn is searching for the Tree of Life. I know you would like to find it in order to bring your mother back from the dead. I know the Tree is on your property because of the sacrifice your mother made, and because of the presence of an honorable, dead tree. I found the remains of three large, dead dogs in the woods, so the time is almost here. Perhaps worst of all, I've seen the shadow of the Amarok." He paused. "There are many other things that I think I know but am unsure of. I'll spare you all my guesses."
His straightforward answer came out full of truth. He didn't seem worried at all by what I might do with the information. For the first time in my life I realized the power of truth and of truth telling, how knowing and telling the truth will always give you the upper hand over someone who is being malicious or deceitful or even simply withholding information. But I was too afraid to tell the truth. It's always one fear or another that makes us lie.
"I have the Tree, but I don't want it only to bring my mother back," I lied. I felt that old darkness stir inside me.
"If you don't want it," he said in a kind voice, "give it to me."
Even though his words were kind, they also held power, a terrible power that I feared almost enough to rival my fear of the Amarok, and my hand moved to the door handle again. His words held the power of truth.
"I can't do that," I said. "I've promised it to someone else in exchange for . . . something. But I'll . . . I'll . . . Listen, I can make a trade with you if you'll help me."
"How can you offer it to me if you have already offered it to someone else?"
"I haven't offered it to anyone," I said, working hard to assemble these intricate layers of lies. "What I meant was that I need to have the Tree in order to fulfill my promise, but I don't have to give it to them. I can still give it to you and make good on my promise to them."
Where were all of these lies coming from? I couldn't figure it out. I wasn't a liar by nature, but there I was, scrambling to create some kind of reality in which Mr. Tennin would help me find the other three things I needed.
He didn't say anything, but I knew he was waiting to hear the terms.
"If you tell me about the stone, the water, and the sunlight, and help me find them, I'll give you the Tree."
He didn't seem surprised that I knew about those items required to grow the Tree, and that surprised me.
"Why would I give you what the Tree needs to grow? And why would you even want them unless you wanted to keep the Tree for yourself?"
I was done. I couldn't come up with anything. My lies had reached that natural end point where they collapse in on each other and begin to contradict every obvious bit of sense.
"I can't explain it to you now," I said. "But if you help me find those things, I'll give you the Tree. I promise."
I reasoned with myself that if he helped me do those things, I could somehow take a piece of the Tree, anything that would help me in bringing my mother back. I no longer even factored in that I didn't have the Tree to give, or that I told Mr. Jinn I'd give it to him first. In that moment the only important thing was for Mr. Tennin to tell me about the stone, the water, and the sunlight.
"I don't want you to misunderstand me," he said slowly in a kind voice. "I know you're not telling me the truth, or at least not all of it. I don't think you actually have the Tree. But I think you will lead me to it one way or another, willing or not. So I will help you. But I'm warning you with a reminder of your own words—you have promised the Tree to me. You might be surprised at how seriously your oaths are taken, if not by you, at least by others. Even by the Tree itself."
I sat there in his car, barely breathing.
"I'll tell you about each item one at a time. Once you find the item, come to me and I'll tell you about the next one. Understand?"
I nodded.
"First, the stone." He paused as if still considering whether or not he wanted to help me. But then he continued. "The stone is the first item. If the Tree represents life, the stone represents death. The stone is the foundation that all of the other objects build upon. Without it, the Tree will die quickly."
"What is it? Where can I find it?"
"The stone is not just a rock. It will be in the form of a vessel. Something that can hold the other items."
Immediately I thought of the bowl the old ladies had given to the man when we first saw them in the Darkness of the fairgrounds.
"Okay," I said.
"You know where it is?"
"I think so."
"Do not go by yourself."
I nodded. "Because of the Amarok?" I asked quietly. "Because of the Amarok controlled by Mr. Jinn?"
Mr. Tennin gave a grim smile. "Mr. Jinn does not control the Amarok," he said, and his voice was whimsical. It was his storytelling voice. "He may have called it here, but the Amarok is controlled by no one. By no thing. Enemies of Good are almost always enemies of each other, as allies of Good are almost always allies of each other. The Amarok is its own, and if the Amarok decides to devour Mr. Jinn, well, Mr. Jinn would have a fight on his hands."
He turned on the car, turned on the headlights, and drove up Abra's lane. I looked at him for a moment. He was nothing like what I expected an angel to look like. Could it be possible? Could he and Jinn be the cherubim who had been there for the creation of the world? Could they have seen when it all first fell?
"Thank you," I said, getting out of the car.
He nodded his bald head at me in the darkness. "Make sure you get a ride home," he said.
When Abra and I snuck into the empty side of the house and entered the upstairs bedroom where we had last hidden the duffel bag, I could tell she had spent a lot of time in there that afternoon. I stared around the room in astonishment, and she gave me a sheepish grin.
"I wanted to get things organized," she said. "Besides, some of the articles were still stuck together."
"This is incredible."
All the articles had been spread out in order by their number. There weren't as many as I had previously thought, maybe less than a hundred.
"Some of these earlier ones, I couldn't even read them," she said, pointing at some ancient-looking pieces of paper with scribbles and notes on them in foreign languages. "But the most recent half of the cards and articles are in English."
I glanced over them. One was about a five-hundred-year-old mesquite tree in Bahrain that the article called the Tree of Life. Another was about the Cotton Tree in Freetown, Sierra Leone. There was the Lone Cypress near Monterey, California, now held in place by cables.
"Tree after tree after tree." She poked a new article each time she said the word tree. "Ancient trees, and most of them burned down, cut down, or destroyed. Or trees that people are protecting or hiding. But every article is about a tree."
She waited and let me skim through some more of the articles.
"Mr. Tennin has a serious interest in these trees," she said. "Why else would he keep track of how each of them has been destroyed or hidden? Why would he have a matching map showing where each one was located? And why would he have taken special note of this?"
She pointed at the article at the very end, the most recent of all the newspaper clippings. It was one I had seen somewhere before.
"I think you were right," she said solemnly. "I think he is here to destroy the Tree."
Valley Woman Dies When Lightning Strikes Ancestral Tree
It was the story of my mother's death, with #68 in the top right corner of the article. I looked at Abra. She nodded, holding the atlas out to me. There was our small town in central Pennsylvania, flanked by the curving slopes of two mountains. Our valley.
"But our tree is already dead," I said, thinking out loud.
"You said it yourself earlier today. He's here for the Tree of Life."
I told her about the conversation I had just had with Mr. Tennin.
"How did he know it was here? It must have something to do with all these." I pointed to the articles spread out over the floor.
"I wonder," Abra said. "Do you remember the story he told us about the Tree of Life when he first arrived at your house?"
"Of course," I said. "But keep going."
"What if these are all times when the Tree of Life appeared?"
My eyes scanned the photographs that some of the articles contained, pictures of charred trees or lopped-off stumps, rings within rings. There was a picture of our old oak, dashed as it had been after the lightning struck and before the neighbors had come over to clean up.
I nodded. Not only was he the angel charged with destroying the Tree, but these were his notes on all the times he had already done it.
"You're brilliant," I said.
She blushed. "Well, if it's true, it's great that we know it," she said. "But that doesn't solve our biggest problem."
"What's that?" I asked.
"What do we do next?"
## 25
"WHAT WE DO NEXT kind of depends on who has the Tree. Who do you think has it?" I asked.
She paced back and forth from the window to where I sat among the newspaper articles. "It has to be Mr. Tennin or Mr. Jinn," she said. "Mr. Tennin doesn't have it, or he would simply destroy it. And if he had it, why would he be helping us find the other things?"
"So it's Mr. Jinn?" I said.
She nodded.
"Which would make sense, because he hasn't come looking for me or the Tree. But how did he get it? He told me he couldn't come here. He wasn't in your house, was he?"
"Who knows," she said. "Maybe he snuck in during the day when no one was paying attention or we were all out in the barns. Maybe he can just appear places."
"No, I don't think so," I said. "When he came into my house he definitely walked in like a normal person. I heard him come in through the screen door, and he crawled out the window."
She shrugged. "Does it matter how he got it? He controls the vultures, right? Maybe he sent in little mice to steal it and take it out."
"I don't think he actually controls them," I mumbled, creeped out at the thought of Mr. Jinn sending rodents into my house to look for things.
"We'll have to deal with that later," Abra said. "I think our best bet is to start finding the other three things. Maybe we'll find it along the way. Maybe the three things will even lead us to it."
"We know the first thing to find is the stone bowl," I said. "It has to be the one the old ladies gave to that guy at the fair."
Abra sighed. I knew what she was thinking. The Darkness at the bottom of the fair was not a place we wanted to go back to, and the man with the bowl was not someone I wanted to look for, much less find.
"We'll have to do that tomorrow," she said. "I don't think my mom would take us to the fair tonight. It's too late."
Outside, the moon emerged from behind a small cloud and sent ivory light through the window.
"You should probably get home," she said. "It's getting late."
"Yeah, I don't want my dad worrying about me. He's been quiet again. Real quiet."
"I'm sorry," she said, staring hard at me as if I were a puzzle she was trying to put together.
Abra started gathering all the news articles into a pile to put back into the box. The next thing she said came out quiet and timid, not at all like the boisterous mystery solver who had been shouting out possible explanations not too long before.
"Sam, do you still want to find the Tree so you can bring your mom back to life?"
I didn't answer. I reached over and put the atlas in the box and stared at the sword.
"Because if you do, well, I still think it's wrong. But there's something inside me that keeps telling me I'm supposed to help you find the Tree. I don't think you're supposed to use it to bring your mom back, but I'm going to try to . . . to be part of this."
I nodded. I appreciated her honesty, but I didn't want to get into that conversation again, the one about bringing back my mother. If she was willing to help, that was good enough for me.
I pointed at the gray sword. "I think you should hang on to that. There must be some reason it doesn't burn you. I think you should keep it with you, in case . . ." My voice trailed off and the image of the Amarok rose in my mind. Abra hadn't seen it yet. I was glad she hadn't, but I wanted her to have some way of protecting herself if she ended up coming between it and the Tree.
She picked up the sword, and the drab grayness of the blade seemed to turn into something brighter, something closer to glass than metal. I could see it shimmering in the reflection in her eyes.
Mrs. Miller agreed to drive me home again, which was very kind of her, seeing as how Mr. Miller was out in the barn and Abra didn't want to stay at home alone with the baby.
"I don't understand why you insist on coming along," Mrs. Miller said as the four of us went out to the car. "It's seven minutes up the road, and Francis should be in bed."
She buckled the baby into his seat and gave Abra a quick glare. The truth was I was the one who didn't want Abra staying home alone. She was quite prepared to take the risk, but I didn't want her there by herself with the Amarok on the loose.
Fortunately, the baby kept sleeping, even through all of that movement. I sat beside the window and Abra sat in the middle, between me and the baby. This meant the front passenger seat was empty. Mrs. Miller started the car and pulled out of the long lane.
The bright moon cast dim shadows across the stone surface of Kincade Road. Every shadow seemed to move, to shift, and I kept looking up at the moon, hoping the night would stay bright until I made it through my own front door.
We got about halfway down the road to my house when the car sputtered.
"Uh-oh," Mrs. Miller said.
"What do you mean, 'uh-oh?'" Abra asked.
She groaned. "I forgot to get gas today when I went into town. I think we're going to run out."
"Mom!" Abra said. "Why do you always do this?"
As she said that the engine sputtered again, this time louder and more persistently. Before I even had a chance to hope that we'd at least make it to my driveway, the engine stalled out and Mrs. Miller guided the car to the side of the road.
Everything was very quiet. Abra's baby brother slept beside us, his face oblivious to the world. Mrs. Miller sat in the driver's seat, not yet accepting that we had run out of gas. She tried to start it again. Nothing. Abra and I looked at each other. I was more scared than I could ever remember—more scared than when I had been hiding in the attic, more scared than when I saw the lightning strike the tree, even more scared than when the three dogs attacked me. During all of that stuff I had been in the middle of the action, but there in the car, on that moonlit night, I was waiting. Waiting to see what would happen next. And the waiting filled me with fear.
"Well, who's walking to Sam's house?" Mrs. Miller asked with a wry smile.
I tried to think it through. I remembered my father's words about the Amarok.
It only devours those who are foolish enough to hunt alone.
"Why don't you two stay here with the baby and I'll go?" Mrs. Miller suggested. "It's not very far. The church's parking lot light is right up there."
"No," I said. "No. Abra and I will go."
"You just don't want to watch the baby again," Mrs. Miller teased. "Okay. Please ask your dad to bring me some gas, just enough to get me home. And tell him I'm so sorry."
Abra and I stared at each other across the dark backseat of the car, and I opened the door. The two of us got out. A cool breeze blew through the valley, much colder than you would expect to have on a July night. I slammed the door behind us. The sound of it closing felt sudden and irrevocable. There was no going back.
We walked quickly, our feet making far too much noise on the gravel road. Abra grabbed on to the side of my shirt exactly as she had held my sleeve at the funeral. But there was nothing affectionate about the way she latched on to me that night. She was scared, and I could sense it in her grip.
Halfway from the car to the lane, I stumbled, my feet kicking up loose stones.
"Shh!" Abra said quickly.
"I know, I know," I whispered.
We were getting closer and closer to my mailbox. The church light was getting brighter and brighter, and the nearer we got to that light, the better we felt. I looked over at Abra, and because of that light I could clearly see her face. She looked back at me and smiled. We would make it. We were almost there.
The church light blinked out.
I've always found it eerie when a streetlight blinks out, but usually where there's one streetlight there are many, and when one goes out it leaves a dim gap in the long line of those that stayed on. But this was different because there was only one light, and we were in the middle of the country, so when it blinked out everything went dark. We were left with the pale face of the moon and the faraway pinholes of light that came from my house.
We moved closer together and walked slower, quieter. We listened for any other sounds, and when we thought we heard something we stopped, my finger on my lips, Abra barely breathing. Then we took a few more slow steps, cringing at every crunch the gravel made under our feet.
Nighttime shadows can be tricky things, shifting and moving in ways that daytime shadows don't. The breeze rustled the weeds that lined the small space between the road and the fields, so the dim shadows on the road were always moving, waving back and forth. The trees, too, faded here and there, as if they weren't rooted to the ground, as if that cool wind had somehow freed them.
But from the depths of these nighttime shadows, a darker thing appeared. It moved toward us from the church, and the closer it got, the colder the wind became. The darkness I had felt in my heart during those days after my mother's death seemed drawn to it. All the lies and deceit and anger at my mother's passing gained lives of their own and rose inside me, as if they were given new life. As if they were rising from the dead.
Abra and I stopped walking.
"What's that?" she whispered.
I shook my head as if I didn't know, but I knew. I just didn't want to say the words.
It's the Amarok.
That dark shadow moved faster as it approached, and it raced past us along the side of the road. Everything in me screamed, Run! Run into the woods and hide! But Abra clung to my shirt and I knew I couldn't leave her. The darkness inside me shouted, Leave! The Amarok isn't here for you. Run away, and it will take Abra but you will be safe. Better one of you is devoured than both of you.
That voice, it was calm and convincing, and what it told me made sense. I grabbed Abra's hand, the one clinging to my shirt, as if I was going to hold it, but instead I dropped it down to my side.
"What are we going to do?" she hissed as the shadow blew past us again, back up the other side of the road.
Every time it passed us, the darkness inside me grew, and my desire to run became almost overwhelming.
"What about this?" Abra asked, pulling the sword out from behind her.
"You have it?" I asked.
There it was, the moonlight glinting off its surface.
"I tucked it in the back of my pants, under my shirt," she whispered.
She pushed it slowly out in front of her. The shadow paused, then approached. I could finally see its form—the wolflike shape, the massive size, the huge paws, agile and ready on the gravel. Its eyes glittered in the moonlight, and something else shone.
Its teeth.
Abra brandished the blade, but the Amarok only drew into itself before expanding larger, taller, fiercer. Before, it seemed ready to play with us, to bat at us with its paws and devour us happily—but once it saw the sword, it seemed full of rage. It took one step toward us. Another. Its eyes squinted, and I could hear the softest movement of gravel as it approached. Soon it was so close that even in the dim moonlight I could see its nose curling. I remembered what it had said to me in my dream.
That fruit does not belong to you.
I got ready to run.
Then I saw a bright light and heard a voice calling out to us through the darkness. The nighttime breeze got warmer and stronger, and I caught the smell of cut hay coming from a neighboring field, mingling with the far-off sound of the river. The Amarok melted away, like a shadow when the light comes on.
## 26
THE APPROACHING LIGHT got brighter and brighter, and for a moment I felt like we were rushing forward through a tunnel, toward the light and the way out. I shielded my eyes, and the light dropped. Mr. Tennin came into view, and the church light winked back on.
"What are you kids doing out here?" he asked.
I wanted to run to him and give him a hug. I wanted to tell him all about what we had seen. But I didn't. Instead I turned to Abra. "Hide the sword," I whispered.
"Mr. Tennin," I said when he got closer. My voice still shook from the close call with the Amarok. I coughed and tried to steady it. "Abra's mom was bringing me home, but she ran out of gas."
"Everything okay?" he asked. "You sound a little shaken up."
In the darkness, when I couldn't be distracted by his boring, humdrum physical appearance, I remembered that Mr. Tennin's voice was deep and beautiful. The deepness wasn't in the sound it made, but more in the way it seemed to lead to other things, long-ago stories or forgotten tales.
"Yeah, we're okay," Abra said, but her voice sounded as weak and unconvincing as mine.
"C'mon," he said. "Let's go find your dad."
We walked the rest of the way together, turning into the lane past the mailbox, walking along the garden and the growing-heavier-by-the-day apple trees. We came up to the barns and walked through the yard, past the lightning tree, to the front porch. Our feet made loud thudding noises on the boards. It was as if we had finally returned to reality.
We walked into the bright house. I could hear a baseball game on the television heading into its final stages.
"Mr. Chambers?" Mr. Tennin said. "You in there?"
"Yeah," my dad said.
"Abra's mother ran out of gas on the way here. You want me to drive back out there with a little gasoline to fill up her car?"
"Sure," my dad said. "Thanks, Tennin."
Soon Mr. Tennin and Abra headed back out into the night. I waved to Abra, and when she turned around I could see the bulge in the back of her shirt where the sword's handle stuck out. I hoped she would keep it safe. I hoped she would keep it secret.
All I wanted to do was go to bed. But as I got to the steps, my dad called out to me from the living room.
"Boy, Mr. Jinn was here earlier this afternoon. Said he expected to see you. He left a note for you in the kitchen."
"Okay," I said. I walked into the kitchen and there it was, a note written in scratchy handwriting on a small white piece of paper.
I wanted to come by and talk to you about that unfinished project and give you what I owe you. Make sure you're here tomorrow at one so I can talk to you about that. If you're not here, I can always give your payment to your father.
I knew what he was saying. He was angry that I hadn't yet found the Tree of Life or gone back to his house to talk about it. He wanted to feed me to the Amarok, or something worse, and that's what he was going to do tomorrow. That's what he meant by giving me what he owed me. And if I wasn't there, he would do to my father what he wanted to do to me.
"You see the note?" my father asked, his voice from the next room mingled with called strikes and balls.
"Yeah," I said, holding it in my hands, trying not to let fear fill me up and knock me over.
"Well, make sure you're around tomorrow. He seemed pretty intent on seeing you."
"Okay," I said. "I will."
I had another dream that night.
I'm playing hide-and-seek with my dad in the farmhouse. I'm very small, maybe four or five years old. I hear him counting in the kitchen.
"One . . . two . . . three . . . four . . . five . . ."
He keeps counting as I climb the steps. I stop for a moment in the hall and look at each of the doors: the bathroom door at the end of the hall, the door to my parents' room right there beside it, my door in the middle, the empty guest room to the right. It's not day and it's not night. Dusk maybe. A whisper of light drifts in the windows and under the doors.
"Twenty-three . . . twenty-four . . . twenty-five . . . twenty-six . . ."
He keeps counting, and I can't decide which room to go into. I get scared. This is when I usually run to my mother, but suddenly I'm twelve again, no longer four or five, and I remember that my mother is dead. I don't have anyone to run to, and my dad is about to come looking for me. I don't like the feeling of not having a safe place, a safe person.
"Thirty-eight . . . thirty-nine . . . forty . . ."
I run into the spare bedroom and look out the window. The streetlight on the corner of the church building winks on and off. Then back on again. I look to the right, and the tree blows in the wind. It's getting dark, and lightning strikes over the eastern mountain.
"Forty-eight . . . forty-nine . . . fifty. Ready or not, here I come!"
Silence.
I wait. I picture my father searching the main level of the house. I can hear him calling out.
"Sam, are you in there? Sam, are you in here?"
I hear his feet climbing the steps, one slow step at a time. I look around the room for someplace to hide, but there's no furniture in there, not in my dream, so I stand by the door. I decide I'll have to let him find me, but then something strange happens.
"Sam, where are you?" the voice calls out.
But it's not my dad's voice anymore.
It's Mr. Jinn's.
I dash over to the attic door and pull it open. It doesn't make a sound and I wonder about that. I run up the stairs and hide among the boxes. I hear his voice again, and he's in the spare room.
"Sam, where are you?" he asks in a singsong kind of voice, and I know for sure that it's Mr. Jinn. "I'm here to give you what I owe you."
I tuck myself away in the back and hear thunder outside the attic. I hear his footsteps coming up the attic stairs.
Then, in the way dreams can change, I'm out in the lightning tree, way up high in the branches, and I'm reaching for a piece of fruit. I look down, and Mr. Jinn is climbing up the tree. He reaches up and grabs my foot, and I don't know how he managed to climb so high. He's so big and the branches are so small, and where his hand touches my heel I feel his nails claw a deep cut into my skin.
"That fruit doesn't belong to you," he says, and he turns into the Amarok. Then both of us are falling, falling, falling through the branches, the bright green grass rushes up at me, and as I make contact with the ground, I wake up.
"Finish feeding the lamb and come in for lunch," my dad shouted down from the upper level of the barn. I was down on the ground floor, sweeping the walkways. I heard him and Mr. Tennin walk out the back of the barn, where the second level was even with the hill. The massive barn door slid closed behind them, the sound of it grating and far away. It became very quiet.
I walked to the corner and leaned the broad broom against the wooden wall. My sweeping had stirred up dust, so the air was full of particles floating through the rays of light like a million planets. I stopped by the lamb's stall and picked up the fresh bottle full of milk. The lamb jumped over to the bars and bleated in a pleading voice. I smiled at it and patted it on the head. It tried to suck on my fingers, thinking everything was a bottle of some kind.
I leaned against the bars and fed the lamb. Its short tail wagged back and forth, and it jerked its head to move the milk out of the bottle. I thought about my mother and it made me want to cry again, and I got mad at myself for always wanting to cry. But still I thought about her. I remembered our last day together, how she brought me home from practice, how she stopped to let me pick up the cat, how she climbed up in the tree during the storm to save me.
The more I thought about her, the greater the ache. The more I thought about her, the more I found myself visiting old ground—I needed that Tree of Life.
Another thought lodged itself in my mind. I reviewed the previous days, and I knew who had the Tree.
Abra.
It had to be Abra.
Who else had access to it? Who else knew it was there? Only her.
That old familiar darkness simmered inside me, and I couldn't understand why I hadn't seen it before. Of course she had it! She must have realized what it was before I came back, picked the lock or used a spare key, and taken it. She either hid it or destroyed it.
Destroyed it.
The lamb wasn't quite finished, but in my disgust I yanked the bottle away and put it up on the shelf. Turning, I saw Mr. Jinn behind me, surrounded by the swirling particles of dust drifting through the sunlight. And standing beside him, leaning into the shadows and almost too big to fit into the barn, was the Amarok.
I saw a flash of movement at the opposite corner of the barn and glanced over in time to see Icarus slip through the bars and flee into the shadows.
I looked back at Mr. Jinn and the Amarok, but I wasn't scared. Why wasn't I scared? I didn't know, but I didn't care.
"She took the Tree," I said. "She hid it somewhere."
Mr. Jinn nodded slowly. "Doesn't surprise me," he said. "Doesn't surprise me one bit."
"She'll be here soon. Should we ask her about it?"
He thought about it for a moment. "No. Not yet. Let's leave it. Let sleeping dogs lie and all that."
He looked over at the Amarok. It hadn't taken its eyes off me, as if it still waited for Mr. Jinn to give it the order to attack. It took a step in my direction, saliva hanging from its lower row of snarling teeth.
"Don't worry," I said. "Mr. Tennin is going to help me find the other three things. Help us find the other three things."
"Is that right?" Mr. Jinn said, and he looked downright happy to hear it. "Mr. Tennin? Well, that's a pleasant surprise for sure."
He seemed very pleased with everything, which I couldn't understand based on the fact that Abra had the Tree. Why wasn't he more worried? I was very worried.
"We're not too late, are we? We can still bring my mom back, right?"
"Sam," he said, "if we can get that Tree of Life, it won't be too late for anything."
He turned and walked away. The Amarok backed away alongside him, ducking to miss the low crossbeams in the ceiling. But before it got too far away it became unrecognizable, blending in with the midday shadows in the corners of the barn.
"What should I do?" I asked, suddenly overwhelmed at what remained to be done.
"Keep doing what you're doing," he said loudly without turning around. "Find the remaining items and bring everything to me."
I heard the barn door opening. He shouted one more thing back to me.
"It's never too late!"
I sat down and realized I was shaking. I closed my eyes and put my head back against the wall. Why did things have to change so much? Why did my mom have to die? Why did I have to make all of these decisions on my own?
When I opened my eyes, I saw the door open at the far end of the barn. Abra came down the long aisle.
"Hey," she said.
I looked at her, and I wondered, did she have it? Was she the only thing standing between me and bringing my mom back?
"Hey," I said.
"Everything okay?" she asked.
"Yeah," I said. "Mr. Jinn came by."
"He did?"
"Yeah. He did."
"What did he say?"
"He said to get the remaining items. He'll take care of the rest."
"So he does have the Tree," she said.
"What?"
"Mr. Jinn. We were right," she said as if everything had been revealed to her. "He has the Tree. Why else wouldn't he be concerned about you not having it? He didn't even push you for it. When's the last time you had a conversation with him and he wasn't asking you over and over again for the Tree?"
I wanted to scream and shout and accuse her of being a terrible friend, a liar, someone who wanted to keep my mom under the ground in that cold, damp grave. But for some reason the darkness inside me felt stronger than ever, and it told me to remain calm. So I listened to it.
"Yeah, I guess," I said.
"My mom said she'll take us to the fair, but only for an hour or so," Abra said.
"Let's go find the stone bowl," I said, standing up and walking past her.
## 27
ABRA'S MOM DROPPED US OFF at the fair entrance and drove into town to run some errands, and as Abra and I walked onto the fairgrounds, I found myself feeling disappointed. At night, the fair seemed edgy and exciting. The flashing lights seared their images into my brain. The mirror maze and the haunted house felt like truly dangerous undertakings, and the shadows that drifted in the margins of the snapping tent flaps held mysteries and unknown terrors.
But during the day, the fair was ordinary. The gravel paths were filled with stale cigarette butts, and the toothless old man collecting the trash, who at night bore the appearance of a man who might steal little children, looked harmless. He even smiled at us as we walked past. Carnies lounged in their tents that lined the midway, napping or staring off at the horizon. They looked like real people during the day, not like the caricatures from fairy tales that they were at night.
When we had been at the fair after dark, finding the Tree of Life had felt like a distinct possibility. But in the light of a normal weekday, it all seemed too fantastic to be true. The Tree of Life? An Amarok? A stone bowl? Three old women and angels and a sword that burned me when I touched it? All of it seemed hard to believe, like a dream I had awoken from.
Still, we wandered down through the various sections of the fair, past the food and the animals and the kiddie rides. The rides' lights were on, but they were bleached out by the sun. A few small children screamed as the rides whipped them around. A few of the carnies called out to us, encouraging us to try their games of skill, but their voices were ordinary and tired, and they weren't very persistent.
We passed the Ferris wheel and the large trucks parked just below it and wandered into the section of the fair where the carnies lived during the week. It was as boring as the rest of the fair, perhaps even more so because it was completely quiet. I guess they were all still in bed after a long night. A stale summer breeze wandered through the tents and RVs, rustling the canvas and tossing the long grass from side to side. A black and white dog, tied to a stake outside the entrance to a tent, perked up its ears as we walked past but must have decided it couldn't be bothered. It set its head back down on its paws and watched us pass without making a sound.
"There's the tent," Abra said, pointing down the hill to a green tent with a blue tarp over the door. I nodded. That was the tent the man had disappeared into with the bowl. Like everything else, it looked ordinary.
Could we just go in and take the bowl? If he was there, how long would we have to wait until he left? We only had an hour. We walked through the long, trampled grass and stopped outside the tent.
"Now what?" I whispered to Abra.
"Hello?" she said in not much more than a loud whisper. "Hello? Anyone in there?"
She took a deep breath, shrugged, pulled back the tarp, and looked inside. She glanced back at me with surprise on her face, then snuck carefully through the flap. I followed.
The first thing I noticed was a loud, raspy sound, so intense that I was surprised I hadn't heard it from outside the tent. I looked around, expecting to see some kind of machine click-click-clicking. I saw the man who had taken the bowl from the old women, lying on a mat on the floor, asleep.
The sound was him snoring. Each inhale caught and snagged like a door on uneven hinges, and each exhale swept out like a new start. Abra and I took a few more steps into the large tent and stood there for a moment, staring at him. Resting on his stomach, clenched by both of his hands, was the stone bowl.
It was the only thing I saw there that didn't seem ordinary. The stone was a gray white, and it had flecks of something in it that sparkled, the way sand glints in the morning light, or the way a granite headstone sparkles when the sun comes out from behind a cloud. It was about a foot in diameter and hollowed out, the shape of a contact lens.
"The dog?" Abra whispered and pointed, and I saw the man's pet lying beside him, on its back, paws in the air, tongue lolling off to the side. It was asleep too. I looked at her and shook my head. I didn't know what to do. We both took another step closer to the sleeping man and his dog. Then we heard the tent flap open just a few feet behind us.
A woman came in through the opening. She was one of those particular creations of the fair, someone you see nowhere else. Her hair was shoulder length, her face was as wrinkled as a balled-up piece of tissue paper that's been stretched flat again, and her body was skinny, a sack of bones. A cigarette perched between her purplish lips, and the watery whites of her eyes were more yellow than white. She wore a T-shirt three sizes too big for her, and it hung down around her knees. Her jeans were torn and dirty, and she wore work boots.
In one hand she carried a butcher knife, and in the other hand she carried a white grocery bag dripping blood from the bottom corner.
Abra leaned over closer to me, and I put my hands up, preparing to talk her out of murdering us. I kept expecting her to raise the knife and charge, or cry out to the man to wake up and bash us over the head with his stone bowl, or maybe she'd even wake the dog and tell it to attack us. But she did none of these things.
She fell to her knees, dropped the knife and the bag, and started crying.
"You're here," she cried out. "You're really here."
Abra and I looked at each other. I probably would have been less startled if she had charged at us.
"Thank God," she said, sitting back on her ankles before taking a long drag from the cigarette. She exhaled the smoke. It hung heavy in the tent, and the longer we stayed, the foggier the tent became.
"I'm sorry?" Abra said.
"You're here," she said again. "Those three old hags said you'd come."
"They did?" I asked.
She nodded. "They cursed my man with that bowl, and he's been asleep ever since."
I looked over at her "man." I found it hard to believe he was under any spell other than alcohol and laziness.
"He's been sleeping there ever since that night?" Abra asked her.
She nodded again. "Came in here and lay down, and I didn't think he was ever gonna wake up again," she said, a fresh batch of tears flooding her eyes.
"So . . . now what?" I said.
"Take the bowl," the woman said. "Just take that bowl and get outta here. That's what those three old hags said, yes they did. 'When two children come here for the bowl, and when they take the bowl, this man will wake up.' That's what they said, they did."
I looked at Abra and she looked at me.
"What about the, um, dog?" I asked.
"Him too," she said, shaking her head, regret on her face. "Him too."
So I took a few steps toward the man, bent over, and lifted the stone bowl. His hands let go of it easily, as if he was relieved to give it up. It was heavy, with a texture like sandpaper.
When I first touched it, I thought I saw something in the bowl, like a shooting star traveling from one side to the other. But when I looked closer, all I saw was the shimmering of the stone. It had glints in it as if it were from another planet, another part of the universe. Or maybe another time.
Abra held open the tent flap for me, but the woman never got up. In fact, she leaned forward, then back on her knees, and it sounded like she was praying as we left, or saying something like a prayer. I heard the man shift on his mat, and the dog made a whining sound. We emerged into the light and I had to squint—the sun was bright outside the tent. We walked, the two of us, through that quiet, ordinary day.
Abra's mom was so happy we showed up on time that she didn't even ask us about the stone bowl, if she even saw it. We climbed into the back of the car without a word and put it on the seat between us. Once we got to Abra's house, Mrs. Miller rushed inside to relieve Abra's father of baby duty, and we were left staring at each other in the backseat of the car.
We decided to hide the bowl in the cave in the cliff at the end of the Road to Nowhere. It was a long walk and the bowl was heavy, but we made our way through the woods, always looking around, always waiting for the sound of the Amarok in the shadows.
We arrived at my mother's grave in the cemetery in the woods. My breathing came faster, and I approached the bare, brown earth that had so recently been put on top of her coffin. Someone had left a bouquet of tulips resting against her headstone. They were yellow with streaks of red from the stem to the end of the petal. It was a deep red, like the low, evening sun. I got down on my knees and read the inscription on her stone.
Lucy Leigh Chambers
Wife and Mother
Meet Me at the Edge of the World
I noticed something protruding from under the dozen or so tulips, so I picked them up and set them on top of the headstone. And there it was, small and bright green with its own white flowers.
The Tree of Life.
Someone had removed it from the log, brought it here, and planted it in a shallow hole. The green had faded a bit, and the flowers weren't so much white as they were ivory, a sickly version of off-white. The Tree was dying, that was easy to see. I felt the old darkness rise inside me.
"Who brought that here?" Abra asked, awe in her voice.
I didn't know what to say. We sat there in silence. I was relieved that Abra hadn't taken the Tree, and I was frustrated with myself for not believing her. What was happening to me that I was so suspicious of my best friend?
Yet, as I saw the plant right there in front of me, both my disbelief and my determination grew. On one hand, I found it even more difficult to believe that this small plant could somehow snatch my mother from the strong jaws of death. It was so tiny, so fragile. On the other hand, there it was—it just kept coming back to me. I thought that must mean something.
"We should leave it here," I said.
So we did. It looked too fragile to move again anyway, so I leaned the yellow tulips with the bloodred streaks over it, keeping it mostly out of sight. I took a deep breath and stood up. I set the stone bowl up on my mother's headstone, and I walked away.
I left Abra and the cemetery, drifting away from the rock cliff with the cave in it. I could feel Abra watching me. I could hear the river rushing out there somewhere in the trees. It was a never-ending sound, the sound of life. The roaring it made as it spilled into the valley and swept toward Deen was the sound of thousands of years of history, moving, carrying me away. I heard Abra walking along behind me, but I didn't say anything to her. I needed a minute to think.
There were three large granite crypts between the cemetery and the river, and I wondered why they were there, planted by themselves like some kind of strange orchard. I thought people had used crypts down there in case the creek overflowed its banks, to keep the bodies up out of the floodwaters, but I didn't know for sure.
I noticed that one of the crypts was covered in writing, a thin cursive script that stretched along the roof of the grave.
In Grateful Remembrance of Josephine M. Jinn
Going down each side of the crypt were the dates of her birth and death.
"Seventy years old," Abra said, and I was surprised to hear her voice. I hadn't realized she had trailed along behind me. "I wonder if she was related to Mr. Jinn?"
There was a small metal plate attached to the pillar, and there were words etched into the plate, faded words no longer legible.
I looked over at Abra. She stared at me.
"I don't think we should give the bowl to Mr. Jinn," she said.
"Not Mr. Tennin either," I said.
"I don't know," she said quietly. "I think I trust Mr. Tennin."
I didn't trust anyone. I realized I resisted choosing sides, resisted choosing between Tennin and Jinn, because I was the only person I could trust. I was on my own side now, getting as far as I could with the help of anyone who would aid me.
For a moment we stood there in the heat, and the river, still hidden off in the trees, sounded so appealing. I wished the summer had turned out differently. I wished we were boating in that river, floating down behind the church and winding our way toward town. I wished that when we finished swimming we could go back to my house, and as we went through the screen door we'd smell the chocolate chip cookies my mom was baking.
I wished. Instead we were sweating in a silent graveyard on a sweltering day, trying to figure out what to do with a stone bowl.
We walked back to my mother's grave, and I picked up the bowl again. It was heavy, but it didn't seem as heavy as when I had first lifted it, as if my arms were getting used to it. Or perhaps it was getting used to me.
"Are you ready to put it in the cave?" Abra asked.
As far as locations went, I thought it was a good idea. It was past Mr. Jinn's house in a direction no one ever traveled. As long as he didn't see us coming or going, he would never suspect that we had hidden it there.
I carried the bowl to the small cave, only fifty yards away through the trees, where the cliffs came down from the mountains. Some of the rocks were wet and slippery from recent rains, making it hard going. At one point I got caught up in a few trees and we had to climb up a short outcropping of rock, so I had to pass the bowl to Abra. I imagined her dropping it on purpose, the bowl shattering against the rocks. I imagined her laughing at my sorrow. But she didn't drop it. She handled it as carefully as I did.
We arrived at the cave, and you could see the muddy river from there, moving fast with all the rainwater. The cliff was a huge piece of rock, nearly as big as a house, and it reached out toward the river. The cave was at the base of the cliff, about three feet high and two feet wide, and it was dark, like an empty spot where an eye used to be. I pushed the bowl in along the ground, and the weight of it made a divot, a short, hollowed-out path.
"One down," I said. "Two to go."
That evening after dinner I walked into the barn with my father and Mr. Tennin. The three of us stacked hay bales and cleaned out the barn. At one point my dad went down to the lower level for something, and Mr. Tennin and I were left alone, picking up the loose hay with our pitchforks and throwing it down through the hole in the floor.
"I found it," I said quietly. "I found the first item. The stone."
He kept working as if I hadn't said anything, and when he spoke he barely moved his mouth, as if someone was watching us.
"Good," he said. "Good. Now you have to find water."
"What kind of water?" I whispered.
"It's not water. It's blood. Innocent blood."
"What?" I pictured some kind of terrible sacrifice. An animal dying on an altar. A high priest raising a stone knife.
"It doesn't have to be much," he said. "Only a drop. Place a drop of innocent blood in the middle of the stone bowl, directly under the Tree." He stopped and looked at me. "Have you found it yet?"
"No," I said. The word came so quickly from my mouth that I didn't realize what I was saying. I lied before I knew I was lying.
He stared at me for a moment. He threw another forkful of hay down the hole, and it vanished into the dark lower level. A cloud of hay dust came whooshing back up and settled all around us.
"Remember your promise to me," he said, not looking at me as he plunged his pitchfork into the pile of straw, "because I won't forget."
The kindness in his voice was still there, but it was edged with force, and I knew he wouldn't forget. Not ever.
## 28
"INNOCENT BLOOD?" Abra asked, sounding nervous.
The whole long Friday afternoon stretched in front of me, chore free. It had always been something my mother insisted on. My father could have me working hard on the farm all week, but on Friday afternoon I got a break. I was free. No work, no responsibilities. "Just time to be a kid," she had said, messing up my hair and giving my dad those pretend pleading eyes.
"What does Mr. Tennin mean by innocent blood?" Abra asked.
"Innocent blood," I said, as if the two words explained themselves.
The two of us sat there in the lightning tree, one week after my mother had died. The tree itself was definitely dying. Its leaves were still there but were dry and brittle. Some of the branches that had been nearer to the lightning strike were charred, and those leaves were brown.
We sat in the flat area where the cat had been hiding, the palm of the tree's hand, the place I had been standing when my mother pulled herself up and told me to run inside. It might seem strange, but as I sat there with Abra on that Friday afternoon, it was the first time I realized how close I had come to death. I imagined the valley without me, Mom and Dad standing in the kitchen doing the dishes, my mom crying. My dad looked the same in my vision as he did in reality—tired and sad.
I wondered what Abra would be doing on that day if I had died in the tree. Would she be at her house, remembering me? Or would life already have gone on, seven days later? Time passes and people leave, and those of us who are left eventually move on in one way or another. Maybe that's the saddest part of death, the knowledge that when we die, we will eventually be forgotten.
The sky was low and gray and looked like rain, or at least a shower or two. But it wasn't stormy, and I didn't expect any lightning or thunder.
"Maybe he knows someone named Innocent and we have to get her blood," Abra said. "You know. Innocent blood."
"Do you know anyone named Innocent?" I asked her, shaking my head.
"I was kidding," she said. A breeze came through the lightning tree just for a moment, and all those dry leaves rustled against each other, a strange sort of shushing sound that made me eager for fall. Abra's blonde hair blew up around her face and she pushed it away. Her blue eyes looked silver in the light.
"So what's the most innocent blood we know about?" I asked.
"You're not touching my little brother," she said quietly.
"I wasn't even thinking about him," I said, which was completely untrue. Her baby brother was the first person who came to mind when I thought about innocent blood.
"What about your lamb?" she asked.
I didn't know if that would be good enough. I shrugged. "That might work. Mr. Tennin didn't say it had to be a person."
I thought back over the seven days since Friday when the lightning struck, and I wished none of it had happened.
"Well, should we go try?" I asked her.
"Sure," she said, but she didn't sound committed to it, and the more I thought about it, the less sure I became.
I reached my foot down for the ladder and climbed to the grass. Abra came scrambling down after me, and the two of us walked into the barn, back through the shadowy aisles, past the chickens, and into the farthest corner.
Something sprang from the dirty windowsill that let in filtered light, and I jumped. But it was just Icarus running away from us. I wondered where he was sleeping, what he was eating. I didn't have the heart to chase him, though.
We got to the pen at the back of the barn, and the lamb looked up at us, its little tail wagging back and forth. I think it thought I was there to give it a bottle.
"So," Abra said, "how do you get blood out of a lamb?"
The whole proposition had seemed so simple. All we needed was one tiny drop of lamb's blood. But there in the barn with the white lamb staring up at us, well, Abra's question was valid. How would we get blood out of the lamb? I didn't want to hurt it.
"What will we use?" I asked. I looked around. There was a shovel, a broom, and a pitchfork leaning against the wall, back in the shadows. I thought I could find a screwdriver if I looked hard enough. I'd have to go back inside for a knife, but if I saw my dad along the way, who knows what he would say. How would I explain why I was carrying a kitchen knife to the barn?
Abra reached around behind her and pulled out the small sword. I didn't even know she had it with her.
"We could try this," she said.
It made me jealous, seeing her with that blade. I wanted to be the one to hold it, to be the one with a weapon. I had found it—I should be the one possessing it, protecting us. But there she was, holding it, not being burned by it.
"Can I see it?" I asked.
"Okay."
I reached for it, and she grabbed it by the bottom of the blade, pointing the handle toward me. But as soon as I touched it, it burned me, and I dropped it. The sound it made as it hit the cement walkway was deep and heavy, as if it weighed ten times what it actually did. Abra reached down for it, and based on the sound it had made, I didn't expect she'd be able to pick it up. But she lifted it as if nothing had changed.
"I guess you'd better keep it for now," I said, rubbing my hands together, trying to get the burn out.
She held it in front of her and stared at the blade as if looking for hidden stories in its reflection. For a moment she didn't look like herself. She looked like some visiting angel, preparing to protect the entire world from an enormous evil. I was scared of her in that moment, and I felt small. I was scared of what she could do.
"Should we try?" she asked.
I moved toward the pen and the lamb came to the bars, trying to stick its head through. I stroked its soft wool. It felt like a great betrayal, what we were about to do.
"Where should I . . . you know?" Abra asked.
I wasn't sure. Lambs are all soft and white, but their legs and hooves are bony and hard, their skulls miniature boulders.
"Maybe on the leg?" I said. "There's not a lot of flesh. Maybe it would just feel like it was banging its shin on something."
She got down on her knees beside me.
"Wait!" I said. "What will we put it in?" We didn't have any containers with us, nothing for keeping the blood.
"Maybe if we get it on the blade, we can carry it to the bowl and scrape it in."
"Okay."
She reached the blade through the bars. Where it almost touched my arm, I could feel its heat.
"Watch it," I said. "That's hot."
I wondered if it would feel hot to the lamb, but when she propped the blade up against the lamb's leg, it didn't move. It didn't even seem to notice. It moved closer to me, and I held it tight so it wouldn't jump away.
"Go ahead," I said. "Go."
She grimaced and slid the blade slowly along the lamb's leg.
Blood poured out.
"Whoa!" I shouted. "What are you doing?"
She screamed and there was fear in her voice, and horror. She inched backward, away from the lamb, and her eyes opened up wide and alarmed.
"I didn't try it," she kept saying over and over. "I didn't try it. It's just so sharp."
The lamb jumped away from us and ran to the back of the pen. It huddled there in the shadows, quivering, and I could see its leg was bleeding badly.
"We have to do something," I said.
Abra stared at the blade. It was wet with blood.
"Keep that flat," I said. "Don't let it run off."
She placed the sword on the floor and helped me climb over the bars into the pen. I took off one of my boots, then took off my sock and put my boot back on.
I crawled in close to the lamb, through the hay, talking to it all the time. "It's okay, little guy. You're going to be fine."
Its ears were limp on the side of its head. Its eyes were jumpy.
"Wow, it's really bleeding," I said.
Abra couldn't keep her own cries quiet anymore. She sobbed right there in the barn. I remember her sobs, and now I know they were the cries of someone who has lost their innocence in one way or another, the cries of someone who has realized not only that there is pain in the world but also that they can cause it, that they will cause it. We all will.
I tried to wrap my sock around the lamb's wound. Abra had cut it on the back of its hoof, right where its heel would have been if it had one. It reminded me of my dream and how Mr. Jinn had chased me up the tree, burning or slicing my foot. For a moment I felt that same panic of trying to climb faster than him, of looking for that next branch. But that was just a dream.
I focused on the lamb. I kept trying to tie the sock on, but the crazy animal jumped and ran away from me.
"Come here, you." I reached for the lamb, but it kept running. "Abra, I need you to hold it still. I can't hold it and tie the sock at the same time."
By now my own hands were covered in blood and straw and dust. Abra came over the bars and got down there in the dirt with me, wiping the tears from her eyes and sniffing loudly.
"Here you go, little lamb," she whispered, and the lamb calmed. She walked toward it and got down on her knees. "It's okay." She reached out her hands. It walked slowly to her, and she held it tight. She put her face on its back, and I could tell she was crying into its wool.
I crawled over to where they were. "Hold tight. Here goes."
I reached down and wrapped the sock around the still-bleeding cut. The lamb trembled, but Abra held it tight. I tied the sock in a tight knot and hoped it would stay.
"We'll have to clean it up later." I hoped my dad wouldn't see the state of the poor lamb. That would be a hard one to explain.
Abra nodded quietly, wiping her eyes again. We both climbed out of the pen and she picked up the small sword, always holding it flat. The blood sat in a straight line, one long run. And that's how we walked all the way from the barn, through the woods, and to the cave—carefully, eyes always on the lamb's blood.
"You'll have to put the drop in the bowl," I said. "I can't hold the knife. It'll burn my hand off."
She nodded, and she went inside and didn't seem scared, not at all. When she came out she looked somber, as if she had just come from another funeral.
"It's done." She bent down and wiped the blade on the grass, cleaning off the rest of the blood.
"Was there enough to go into the bowl?"
Her face crinkled up and she started to cry again, I guess at the thought of all the blood she had let out of the lamb. She nodded, leaned the hilt up against the rock, and put her face in her hands. I walked over and put my hand on her shoulder. We both took a deep breath.
"Only one thing left to find." I hoped that was the worst of it.
But Abra went back to a small patch of grass in the forest just beyond the cemetery, and she kept wiping the bloody blade on the green blades, as if removing every last stain would somehow mean she hadn't cut the lamb. A clean sword would somehow mean that none of this had happened.
I watched her, and I wished there was something I could clean that would take away what had happened to my mom. I stared into the cave. It looked like a wound, and the darkness that seeped out was an infection, the same one I had inside me, the same one driving me forward, propelling me to do anything to bring her back.
I walked the short distance to a small pool that formed off the side of the river and washed my hands in it. The water seemed louder and louder every time we returned. Either the rainwater was finally making its way down from the mountains, or nature itself was beginning to roar at the thought of what we were bringing into being. The Tree of Life.
We were close. We were getting so close.
Abra and I walked back to the house. It still wasn't time for supper. The sun was well over the western mountains and the vultures were nowhere to be seen.
Something about the whole situation felt wrong. Even though I knew what I was doing and I wanted to do it, I still felt like I was being set up. But by whom?
Abra? What did she care about the whole thing, other than the fact that she thought it was wrong to bring my mom back?
Mr. Jinn? More likely. Now that I knew I was alone, taking care of my own interests myself, I realized I didn't trust that man for anything. Him and that Amarok of his. I wouldn't be surprised by anything he did, good or evil, heroic or heinous. Actually, that's not true. If he did anything heroic, that would have surprised me.
Mr. Tennin? He had started off being such a nice guy, so soft-spoken and polite. But each time I talked to him he seemed to grow sharper around the edges, as if some fake self was wearing away, revealing a harder core.
I said good-bye to Abra and she started walking home, the handle of the sword still bulging slightly from the middle of her back. She walked quickly, on the verge of a run, and even though we had both agreed she would be safe in the daylight, especially once she got to her property, I think we were both less than convinced. I took a deep breath as she disappeared down the road. I hoped she would be okay.
The rain had never arrived that day, and I wandered over to the lightning tree and followed the long, ivory scar running down it. I didn't know the exact nature of lightning, its power or its speed. Would my dad cut down the tree now that it was dead? Would we even stay here on the farm, with all the memories of my mother, or would we leave?
I didn't want to leave.
"Sam!" Mr. Tennin shouted from the barn. His voice contained an edge of panic. "Sam, where are you!"
"Over here, by the tree," I yelled back.
He came running as fast as he could, and he could run fast. I was surprised. Mostly I had taken him for a middle-aged balding man who knew how to work and wear boots but who didn't have much in the way of athleticism. But his stride was long and strong, and even in work boots his feet were light.
"Sam," he said, bending over and catching his breath. Perhaps his endurance wasn't so great. "It's the lamb."
I ran past him toward the barn. I thought maybe my dad had found the lamb and now I was going to be in big trouble. Huge trouble. I ran through the dark doorway and into the barn. I slid around the corner and ran the long straightaway to the back, past the chickens and the cows in their pens, to the lamb's stall. My dad was inside, squatting down beside the animal.
He looked over his shoulder at me as I climbed the bars and swung my leg over. I dropped down into the pen beside him.
"Dad, I'm so sorry," I began, but he interrupted me.
"I'm sorry, boy," he said. "We found him too late."
What?
I looked around him and then looked away. Could all of that blood have come from Abra's small cut? I didn't want to, but I looked closer. I had to see what had left that huge pool of blood around the soles of my father's work boots.
## 29
MY LAMB WAS DEAD.
My father's hands rested on the lamb's head, and his large, calloused fingers looked soft against the white wool. I noticed his wedding ring. He still had his wedding ring on, and for the briefest moment I comprehended the pain he must have felt when my mother died, the loss, perhaps even greater than mine. Yet he was moving on with his life. He was trying to survive without her. I felt selfish and small for wanting to bring her back.
He looked over at me.
"I'm sorry, boy," he said again.
I looked down at the lamb's leg, afraid of what I might see, afraid that Abra's cut had somehow opened up into a gaping wound. But what I saw immediately removed that fear and introduced a new one. The lamb's entire back half was gone, ripped off.
"What was it?" I asked. My voice came out in a hushed whisper, because I knew what it was. The Amarok.
My dad shook his head, pushed the ball cap back on his head, and rubbed his forehead. "I don't know," he said. "Might be the same thing that made the tracks Mr. Miller saw a few days ago along the woods. Maybe some kind of crazy coyote, but the bite looks way too big for that. And the tracks they found by the Millers' farm, well, that wasn't a coyote. Too big even for a wolf, which we don't have around here anyway."
He pointed to a large arc that ran along the lamb's hindquarters, and I could tell he knew it wasn't a coyote. But we always try to fit the things we see into the world we understand, the world we can comprehend. Anything that doesn't fit into our tidy understanding brings fear.
"See that? That's a bite that didn't hold. Part of a bite." He looked at me. "That's a big bite," he said in a serious voice. "Bigger than anything I've ever seen. I don't want you wandering around anywhere from now on. You hear me? Not anywhere. At least not by yourself."
I nodded.
"You hear me?" he asked again, as if he wasn't convinced that I had actually committed to following his instructions.
"Yes, sir," I said.
And because he understood the wild heart of children and the ways they will convince themselves to disobey, he said it again. "I'm serious, boy. I don't want to find you like this."
"Yes, sir," I said again.
He sighed a heavy sigh that had more than a lamb's death in it. There was a tree and a lightning strike and a wife gone as well, and the fear that he might lose the only thing he had left. He stood slowly, the weight of it all trying to hold him down. He put his hand on the top bar and pulled himself over in one smooth movement.
"Tennin," he said. He had taken to calling Mr. Tennin by his last name only. "I'm going to go get some stuff to clean up this mess. You mind digging a hole in the corner of the garden? There's already a groundhog there. Might as well turn it into our own small graveyard."
He looked sad, sadder than he had been since the funeral, and I knew he was thinking of a different graveyard. He walked past Mr. Tennin, who grabbed a shovel from the wall and turned to follow him. But then Mr. Tennin stopped by the corner and turned back toward me.
"You'd better come with me, Sam. None of us should be alone, not for now."
Mr. Tennin asked if I wanted to dig a few shovelfuls, so I took the shovel from him and with my twelve-year-old strength dug some feeble bites from the summer earth. He took the shovel and clawed a little deeper. A small mound of earth built up there at the edge of the grass and the garden. Earthworms flailed as they were exposed in broken clods of dirt. The deep brown stood in contrast to the sharp green, and everything smelled alive and rich.
Above us, above the lightning tree, the vultures circled, perhaps drawn by the death of the lamb. Or maybe they were sent by Mr. Jinn to watch and report back. Whatever the case, their presence felt ominous. Their naked, pink heads looked greedy, and I wanted them gone.
"So where do I find the sunlight?" I asked.
"You got the water already?" He sounded surprised.
"Yeah."
"And you put it in the center of the stone?"
"Yeah."
He frowned and stuck the shovel in the earth. He looked at me, his head cocked to the side. "You're serious about making this happen, aren't you?"
"Aren't you?" I asked.
He stared at me, and his stare evolved into a subtle nod, a determined yes. "Yeah," he said. "I am. I always have been. I just wasn't sure if that"—he nodded toward the barn and the dead lamb—"would make you change your mind."
I shook my head. "If I can bring my mom back, nothing will change my mind."
"Fair enough," he said. He looked around. "I thought it was going to rain today. Guess it's going to hold off now."
I looked up, but I was looking at the lightning tree and at the vultures high above us. Finally I scanned the clouds on the horizon. They were breaking up, and it looked like we might get a little bit of a sunset under the rim of those slate-colored clouds.
"Your father isn't going to be happy if you're off traipsing around the valley. Not after this. Not until they find that Amarok."
"Can they find it?" I asked. "Is that even possible?"
He looked at me, and I could tell he didn't understand what I meant.
"I mean, is it really real?" I asked. "Is it something you can see and hunt and kill?"
"Sam, what do you mean by real?"
He waited while I thought about that. Then he continued.
"All the myths you've ever heard, they're real in some sense. All the mythical creatures you've ever read about, they're out there, or at least they were at one time, in some form or another. This Amarok, of course it can be killed."
His words swirled around me, new and exciting. I didn't know what to say. I didn't know what to think.
"But beasts are mythical for a reason, usually because there's an aspect of them that you don't understand, something that doesn't fit with the rest of what you know about the world. The Amarok, it's part shadow. As real as you or me, but part of it lives in darkness."
I thought I understood.
"So, for someone to kill the Amarok, the Amarok—and there is only one, thank God—that person would have to figure out how to enter the shadow, at least partly, and hunt it there. And that may never happen."
"So it's old?" I asked.
"The Amarok? It's older than you even know how to imagine."
Mr. Tennin looked toward the house, and I looked back over my shoulder. My dad came through the door and walked down the porch steps. He didn't see us there at the edge of the garden, not right away, maybe because the light was dimming, or maybe his mind was elsewhere. Maybe it was because he was staring up at the lightning tree, searching for something. Someone.
My dad saw us then, so he changed direction and crossed the yard.
"The sunshine," Mr. Tennin said quickly under his breath, "is simply the light from a hot fire burning at night. It can't be too close to the Tree, and it can't be too far away. But once the Tree is in the stone on top of the water, and the fire is at the right distance, you'll know, because the blossoms will fall off and the Tree will begin to grow. Visibly."
He said that last word at the same time as he looked up and greeted my father. "Mr. Chambers," he said. "This look big enough?"
He gestured down toward the hole in the ground. It was dark, and for a second it reminded me of the cave holding the stone and the water.
My father nodded. "That'll do." He held up a host of old towels and rags and cloths. "You boys ready to do some cleaning up?"
We both nodded, and the three of us headed for the barn, but Mr. Tennin stayed back a little ways, held on to my arm, and kept me walking at his own slow pace. My father vanished into the barn ahead of us, and Mr. Tennin turned to me with serious eyes.
"Don't forget our deal," he said. "Don't forget."
I walk out of my room through moonlight that casts shadows all around me. I walk over to the fresh grave where Mr. Tennin and I buried the lamb just that night. I sit down beside it for some reason, and the grass is wet underneath me, I guess from the dew.
The dirt starts to move over the grave. I slide back, my eyes wide. First it crumbles, then it shakes, and soon it is being pushed away. Something isn't dead. Something is crawling out. I expect to see the lamb, and I'm terrified. A hand comes out. An arm reaches its way up out of the earth.
It's my mother.
I run to her and she hugs me tight.
Lightning strikes.
I wake up.
I looked at the small clock beside my bed. Just after midnight. I lay there for a moment and listened, but my dad had gone to bed long before and the television was turned off. I heard Mr. Tennin snoring in the neighboring bedroom. Outside my open window, an entire chorus of crickets and nighttime bugs chirped and screeched and hummed. I pushed my blankets down and got up.
In the backpack under my bed I had already packed a flashlight, matches, some newspaper, and an old pocketknife. I had also hidden a change of clothes down there, so I pulled those out and slipped into them as quietly as I could. My breathing felt way too loud. Every time my bed creaked under my weight, I held my breath, waited for the inevitable sound of footsteps in the hall.
But they never came. All was quiet in the house.
I crept across the room, and as I passed through the doorway I realized this was it. I would grow the Tree. I would finally see my mother again. There was no turning back from here.
## 30
I GUIDED THE SCREEN DOOR until it came to a quiet stop against the door frame and slid out into the warm, still air. It felt like I was the only moving thing on earth. I walked gingerly, as if the grass under my feet might explode into sound at any careless step, and I headed for the bright streetlight at the corner of the church. It was working again. I tried not to think about the night the light had gone out, the night the Amarok stood on the road and growled at Abra and me. I looked over my shoulder one more time to make sure no one had followed me from the house. I wondered where the Amarok was, which shadow it was clinging to. I didn't have to wait long to find out.
Somewhere between my house and the beginning of the Road to Nowhere, the Amarok ran past me, and I felt my insides turn cold. I knew it had devoured the lamb, and I knew it could have devoured me in that moment, but that's not what sent a shiver through my body. I grew cold because I realized there was a reason it kept me alive. It wanted me to grow the Tree so it could feed on it. Nothing that anyone could have told me would have dissuaded me from moving ahead with my plan to bring my mother back, but knowing that I was somehow on the same side as the Amarok made me feel lost.
Before bed that night, I had told myself I would go get Abra first. I had convinced myself that this was something we should do together—start the fire, grow the Tree, take off a piece of the fruit. But as soon as I woke in the middle of that Friday night turning to Saturday, I knew I had only been kidding myself. From here on out, I would have to do it alone. No Mr. Jinn, who might steal the Tree. No Mr. Tennin, who might destroy it. No Abra.
Only me.
My jog slowed to a walk, both because I was out of breath and because I didn't know what to do. I had told Mr. Jinn I would bring him Abra and the Tree. I had told Mr. Tennin the Tree would be his if he helped me find the stone, the water, and the sunshine. I knew I had to keep my word, but I didn't know how to do that when I had promised the Tree to each of them. What would they do to me if they found out?
But you can't tell them yet, I convinced myself. Not yet. First I have to keep the Tree alive.
I eventually passed Mr. Jinn's lane. I kept expecting the Amarok to double back and devour me, but when I looked into the shadows of my mind I couldn't find it. It wasn't anywhere close. So I disappeared into the shadows under the trees, down the Road to Nowhere. I walked through the dark toward the sound of the river and arrived at the old graveyard in the middle of the woods. I turned on my flashlight.
I didn't waste any time moving to my mother's grave site and gently prying the Tree from the earth with my pocketknife. The ground was soft and warm. My knife scratched against a few small pebbles in the ground, but most of the dirt was rich and clean. I picked up the Tree and stared at it in the darkness. I held it, and it felt like it was mine. I looked at the hole I had left in the loose dirt, and I thought, if I planted a piece of fruit directly over her grave, right there in that small hole, would that be enough to bring her back?
I walked over to the cave and looked into the shadows cast by the stones on that moonlit night, and I wondered what my mother would think of all this. It didn't take me long to come to a conclusion. I knew she would think I was being selfish, that I wasn't making a good decision. It hurt me to think she wouldn't be happy with me, but I still walked on. I didn't look back. I knew I could change her mind if I could simply have her there in front of me, with me.
I shone my narrow beam on the bowl where it sat at the back of the cave, and I placed the limp Tree inside, its tired roots barely held together by the dirt I had managed to dig up. I thought about the few drops of lamb's blood beneath it. The Tree looked pitiful there, sagging to one side.
It's nothing but a dying plant, I thought. It's nothing but a hope that will never happen.
And I laughed at myself. Why did I think this would change anything? Why did I believe?
But I did believe, no matter how silly the whole thing seemed. There was something spectacular about the small white blossoms that still clung to the tired green of the Tree. There was a smell about it, something that had come into the air when I dug up the roots. There was hope there, the kind of hope that makes anything seem possible.
I went to work making a fire, the sunlight Mr. Tennin had told me about. I gathered small twigs and leaves and pulled some paper out of my backpack. I peered into the shadows. I jumped at every sound, wondering if I had been found out.
I lit the match. A wind kicked up out of nowhere and blew it out. A small wisp of smoke twisted from the dead end of it, up through the narrow beam of my flashlight. I sighed and tried again. Match after match sputtered to life, only to be blown out. I was down to three matches when the flame managed to survive the transfer.
The fire grabbed at the paper and the leaves first, and a small stream of smoke rose. I blew lightly on the baby flame, and it reached up to the twigs and crackled, sending one or two sparks toward the sky. I scurried for a few larger twigs and small branches. At that point the fire was about three feet from the cave.
The Tree of Life started to look a little more withered, as if the fire was melting it, so I nudged the flaming branches a few feet farther from the cave with my foot and added some more branches. Light danced all around me, and I turned off my flashlight and put it into the backpack. I checked on the Tree again. It looked suddenly sturdy, and the small white flowers weren't drooping. They turned slowly, the way sunflowers lean toward the sun, and faced the fire. The blossoms opened wide, drinking in the light.
I sat down with my back against the stone cliff and stared into the fire. Every so often I glanced over my shoulder and into the cave, checking on the Tree, and each time it seemed a little healthier.
The warmth made my eyes heavy. The dancing light put my mind at ease. I leaned my head back against the stone. I had done it. Now all I could do was wait.
The shadows shifted like a hypnotist's locket. It was me and the fire and the stone behind my head and the Tree of Life and the changing shadows. I imagined there was an ocean on the other side of the trees, an ocean instead of a river that stretched out into eternity. And maybe, just maybe, if I sailed long enough and hard enough and didn't let the storms sink my ship, I could reach the other side, where I'd find my mother waiting, standing at the top of white cliffs, her hand shielding her eyes from the sun glaring off the crystal sea.
Because it was only me and the rock and the fire and the trees, it felt like the beginning of time. It felt like I was the first person and that all possibilities and hopes began and ended with me and that small Tree of Life in the cave behind me. The fire wasn't a fire anymore—it was our planet's sun, young and new. The trees weren't mature trees anymore—they were moments old, newly created. Even the shadows shed their strange nature and became young shadows, playful and harmless.
All of these thoughts swirled through my mind and I fell asleep, dreaming of the beginning of the world.
I woke up once in the night and the fire had grown low, so I threw on some more branches. As the fire rose back to life I thought I saw the Amarok moving among the treetops, its dark outline swaying with the movement of the highest branches. I ducked down and held very still, hoping it wouldn't see me pressed up against the rock. While it didn't come down from the trees, I thought I saw it stop and look at me, waiting for something to happen.
I saw the outline of a man as well, or something like a man but taller and somehow more beautiful, even though it was only a shadow. But as I threw more branches on the fire, the shadow man dissolved in the light.
I fell back to sleep.
I'm not sure what woke me. It could have been that my back had grown stiff from sleeping against the rock wall. It could have been the dim fog lit by a gray light that filled the forest or the distant rumble of approaching storm clouds. It could have been the realization that the fire had gone out, its dying breaths blowing smoke in my direction, a smoke that swirled and combined with the mist. It could have even been that I sensed someone approaching from the Road to Nowhere, their light footsteps snapping tiny twigs and breaking last fall's leaves.
Or it could have been the brief sighting I had of the Amarok, far off in the trees and the fog. I could barely see it, its black coat moving silently through the green. It padded off in the opposite direction, disappearing once again.
The sound of footsteps grew closer. I looked into the trees. The fog revealed only the outline of a person sneaking here and there through the shadows. A voice called out.
"Sam? Sam! What are you doing here?"
It was Abra, and I was filled with both relief and anger. Relief because I was scared of being there alone, with the Tree and the Amarok and the fog. But I also felt anger, because what was she doing there without me? Had she come to steal the Tree, only to find that I already had it?
Thunder rolled again, loud and close, and I could almost smell the rain.
"What am I doing here?" I asked. "What are you doing here?"
My accusation didn't bother her.
"Everyone's looking for you!" she said. "They're all nervous after what happened to the lamb and the tracks they found. Your dad came to our house not long ago and said you were missing when he went out to do chores this morning. Everybody in the whole town is on the move, looking for you. My dad went searching in the mountains along the river . . ."
Her voiced stopped as she came closer. I saw her staring at the coals, still warm on the ground in front of me. They shone like small pieces of wet fruit. Smoke rose, a confession. She looked behind me and her face gave in to a weary sadness.
"Sam, what have you done?" she asked.
Various realizations flooded through my mind in that moment. My back wasn't resting up against the cliff wall anymore, although I hadn't moved. My hands, down at my sides, were holding on to massive tree roots so gnarled and twisted and large that they had to be roots from a tree that was thousands and thousands of years old. And even though the smoke from the fire still drifted toward me, I couldn't smell it. Instead, the sweetest fragrance surrounded me, the smell of new things, the smell of hope.
I turned and looked behind me. The Tree of Life had taken root, and it was huge. It had completely taken over the cave and grown up the side of the cliff wall until it stretched nearly as high as any of the surrounding trees. Branches spread out in every direction, each one drooping heavy with white blossoms the size of my fist.
Time seemed to stop as I examined the Tree. I stood up and touched the bark, surprised to find that it was soft like felt, and when I pressed on it my fingers left indentations. The leaves were large and almost oval, sort of like magnolia leaves, and they grew in an alternating pattern on the branches.
Some of the blossoms had yielded a lime-green fruit that blended in with the leaves. In fact, it was so close in color to the leaves that at first the fruit was invisible. But as soon as I saw one piece of it, I realized the entire Tree was covered with it. There was so much fruit that it weighed some of the lower branches down to where they almost touched the ground.
Lightning struck somewhere up in the mountain, and a few moments later it was followed by the growl of thunder. I walked over to one of those low branches and stared at the fruit. I could almost see inside it. Each one was like a tiny crystal ball, swirling with images and dreams and years. I reached up and touched the fruit, and it was as smooth as glass. I pulled my hand away, worried that I would shatter it, and that somehow the shattering of one piece would ruin the entire tree. When I pulled my hand away, one of the leaves caught in my fingers and stayed in my hand. I stared at it, stared into its waxy surface, but it didn't have the same quality as the fruit. There was nothing there to see, except perhaps the deepest green in the universe. I held it tightly in my hand.
Abra seemed to be staring at all the same things I stared at, and her eyes went from disappointment in me to wonder at that impossible Tree. She walked to a different branch and did the same thing I had done—touched the smooth fruit, felt the soft bark of the branches.
"This is it," she murmured. "This is the Tree of Life."
"What did you expect?" I asked.
"What did I expect? Sam, I helped you because I realized that if I was going to be your friend, I had to help you. But I didn't actually believe it. I didn't believe this would happen. And I thought that even if it could happen, you would still do the right thing."
Her blue eyes stared desperately into mine. "I never believed it," she whispered.
"And now what?" I asked. "Now that you see it's true?"
She pulled her hands away from the Tree reluctantly. "You can't do this, Sam," she said. "It's not right. You can't bring your mother back."
When she said those words, I felt that old darkness rise up inside me like a fire that had been fanned.
"Can't?" I pointed toward the branches above us, as if every single piece of fruit stood as a reason it could be done.
"Shouldn't," she said, shaking her head. "Shouldn't. She's at peace now! You want to bring her back to this?"
"What do you think I should do?" I asked, trying hard to control the anger I felt. "This is it! This is what everyone wants, isn't it? Death, gone! No more sadness! No more loss!"
My pleading anger grew into a rage, fueled by the more frequent lightning strikes and the pattering sound of the rain beginning to hit the highest leaves of the trees. A storm was brewing.
"Sam, you have to destroy it! This is the story Mr. Tennin was telling us about! This Tree isn't meant for us."
"Destroy it?" I said, almost laughing. "Destroy it? How could we destroy it now? Even if I wanted to, how could we—you and me, two kids—keep this from happening?"
She answered quietly, "With fire."
## 31
I SHOOK MY HEAD. I prepared to argue with her, to tell her all the reasons for bringing my mother back—that she didn't want to be dead, that she was waiting for me on the other side of the water, that she was fighting her way back up from under the ground. I tried to figure out how to explain the emptiness her absence had left inside me. But before any of the words came out, a huge shadow fell from the surrounding trees.
It was the Amarok, and it walked slowly toward Abra, baring its teeth and giving a growl that shook the earth under my feet, a growl that mingled with the thunder and the lightning. It felt different from when we had seen the Amarok on the road. At that point it had seemed curious. But there, in the shadow of the Tree of Life, the Amarok was different. It was angry, and it perceived Abra as a threat to the life of the Tree. Somehow it knew that she would destroy it if she was given a chance.
Abra looked tiny, staring at the Amarok approaching through the mist, its massive paws snapping branches and crushing leaves. She turned slightly away from me to face the Amarok, but I could still see her bright blue eyes flashing as they faced the east and the coming storm.
"You don't belong here," she said, and I was surprised at how little fear there was in her voice.
Even though the Amarok walked slowly, it covered a lot of ground with its long strides. Its eyes were black, two glittering pieces of coal, and there was a depth there, a darkness so deep that it didn't have a bottom. The Amarok's growl turned into a low, slow voice.
"That fruit does not belong to you," it said, and I shuddered, hearing the words from my dream.
"I don't want the fruit. I want to destroy it," she said, gritting her teeth with determination.
It growled again, so close it could have reached out and put one of its massive paws on her shoulder. She bent her knees slightly and reached around behind her, and I noticed the bulge at her back. She pulled the sword out from where she had been hiding it and held it out in front of her. The tip of it trembled, and I knew she was afraid.
The sword was definitely longer than it had been before, or maybe it grew after she pulled it out, because it was more the length of a normal sword, and it wasn't a dull gray anymore. It glowed a silvery white, like glass covered by a winter frost and lit up by the morning sun. The Amarok stopped moving for a moment. The sword changed things. It filled that early Saturday morning with all kinds of new possibilities.
The rain fell, heavy and clean. The drops disturbed everything, rustling the branches, causing the rocks to glisten, and making the dead leaves on the forest floor dance around. I guess that's what made Abra, the Amarok, and me stand out so much—everything else was moving, twitching, yet the three of us stood there completely still, unwavering, waiting to see who would make the first move.
The Amarok circled Abra again, and I found myself worried that the animal might somehow damage the Tree. That thought brought to the front of my mind how far I had fallen. I was more worried about the Tree than I was about my own friend.
"That fruit does not belong to you, to keep or to destroy," it growled at her, and I could barely understand its words. They were a combination of human sounds and animal growls. They spilled into being like vomit.
Without warning the Amarok lunged at Abra and she swung the sword, but the huge wolflike beast dodged her swing. It kept drifting around her from side to side. It darted at her, she swung the sword again, and the Amarok feinted to the side. She took one swing that knocked her off balance, and the massive black wolf plunged in and grabbed her entire body in its jaws, its mouth wrapping around her waist.
For one heartbreaking moment, I remembered the lamb, but for some reason the Amarok didn't bite clean through. It shook her viciously and she went limp. I felt a numbness spread through me, disbelief that all of this was happening, and the numbness slowly turned to horror and fear as the Amarok tossed Abra at me, knocking me over. She was completely limp, lifeless.
What had I done? First my mom, dead because I had to have a stupid cat. Now Abra lay on the ground, dying because I insisted on regrowing the Tree. Was my dad next? Would I lose everyone I loved, one by one, because of my selfishness?
Abra's body had knocked me onto my hands and knees, and the leaf I held from the Tree of Life was crushed. There was a stickiness inside it that oozed out onto my fingers.
"Now what about you?" the Amarok growled. "Whose side are you on?"
But the words came from a faraway place. The crushed leaf's thick, sticky sap was like the gel from an aloe plant, and it had a strong aroma. In the midst of that smell, the voice of the Amarok faded off to somewhere distant, somewhere far away, somewhere insignificant. I had the clearest vision of my mother's face that I had had since her death, and she was smiling at me. I realized that some of my visions had been true, that she actually was watching for me from the top of a tall white cliff on the other side of an eternally wide body of water, but she wasn't waiting for me to bring her back.
She was waiting to see what I would do.
And the smell of the leaf from the Tree of Life brought back so many good memories of my mother, memories of her taking me to the pumpkin patch in the fall when the shadows were long and cool, memories of the flowers we had planted together and of sledding down the small hill behind the barn when I was young. I even remembered things I couldn't possibly have remembered, like the way she looked at me when I was born, as if I was a treasure she would never give up, and how she fed me a bottle and sang me her favorite songs with her eyes closed and her voice clean and clear.
I remembered the songs, all the verses and choruses, the notes and the silence in between. They swirled around me in the fragrance of the broken leaf, and as those words and notes faded, the verse the preacher had read at her funeral service rose up through them.
On either side of the river is the Tree of Life with its twelve kinds of fruit, producing its fruit each month, and the leaves of the Tree are for the healing of the nations.
"The Tree is mine," I said. "I brought it here, and I grew it. Now I can do whatever I want with it."
The Amarok moved toward me, sensing my doubt. I think it knew somehow that I wasn't sure anymore, that I didn't know what to do, that I was as likely to destroy the Tree as I was to keep it.
"That Tree is not yours."
But I could see inside the Amarok, and in the midst of that darkness was a heart of fear and doubt. The darkness inside me was dying, withering under the influence of the broken leaf, and I could see clearly. I could see things for what they truly were.
I reached down and picked up the sword. There was no time to find something to protect my skin—I had to grab it immediately. It burned my hand, but I gritted my teeth and held it tight. The pain was excruciating, and I could feel my skin blistering, bubbling up and melting and sticking to the hot metal, but I knew I had to hold on. My entire arm went numb from the pain.
I cried out, a primal sound, as the physical pain mixed with my deep sadness.
Abra lay still on the ground behind me, and I didn't know if she was alive or dead. The Amarok stared me down, growling, saliva dripping from its glistening teeth. The Tree was still growing, slowly, and the movement it made as it grew was like a tree in the midst of a breeze, its leaves rustling, its fruit swaying. Lightning tore through the sky, followed by an immense explosion of thunder. The rain came down heavier.
Two flashes of light fell down in the midst of all this chaos. Those lights pounded into the ground and took form, and I knew right away that one was Mr. Jinn and the other was Mr. Tennin and that they were the two cherubim who had been fighting over the Tree of Life since the beginning of time. They shimmered and were of human form but were also something more, as if all my life I had seen humans only in a cloudy mirror until that moment. What I saw of them when they slowed was beauty and strength and power.
They didn't speak, but sometimes I could sense what they were saying to each other. It was as if their thought, their consciousness, was all around me, but instead of individual words, their communication was made up of streaming raw emotion and calculated movements. They streaked through the fog and the smoke like comets, and the sound of their rising was the screaming of jet planes or the roar of rockets.
They would stop for a moment, and that was when I saw their form, but mostly they moved and flew in a blur around the Tree and over the river, and sometimes their collisions with each other made loud cracks, like the snapping of an electric cable when it comes loose from the pole and strikes the ground. There were bursts of flame when they collided too, and the fire fell at the base of the trees on the far side of the river and licked at the broad trunks. Soon smoke from that fire mingled with the fog.
For brief moments I recognized them as two powerful men, and they wrestled there among the trees. Mr. Jinn's face was desperate and determined. His mouth was a firm line of desire, and it propelled him, strengthened him. He pushed Mr. Tennin to the brink of the river, and then they were in it, Mr. Jinn holding Mr. Tennin under.
I found myself holding my breath, wondering if he would come up. But I didn't have much time to worry about him—the Amarok roared, and the roots of the forest groaned in reply. It was like thunder in the earth, the sound of a thousand fault lines slipping out of place. I held the sword up again and glanced over at Abra.
Mr. Tennin rose out of the water, and when he did I recognized in him the quiet confidence of Truth. I could tell that he would stand not by the sheer power of emotion but in the conviction of someone acting simply out of love. I felt an ache for him, the same ache you feel looking out over a snow-peaked mountain range or walking through an ancient temple.
The Amarok came at me again, and I held the sword out toward it. It dodged off to the side and snapped at my face, but I moved and ducked and swung the sword like a baseball bat. The air around us crackled with the fighting of the cherubim, and the morning lit up as the sun prepared to rise over the eastern mountain, illuminating the back of the gray storm clouds. Abra still wasn't moving.
I held the sword in front of me, my arm still numb with pain. The Amarok circled. Behind it, Mr. Tennin and Mr. Jinn flew straight up into the sky like fireworks heading for their apex. Through the trees, through the smoke, and up into the low, gray clouds of morning. I tried to watch, but the Amarok growled. I waved the sword at it again.
The blade grew brighter and brighter. I wondered if it was getting ready to explode. Then two things happened at once: I took a swing at the Amarok as it snapped at me, and one of the lights fell from the sky so hard and fast that it sank down into the earth. Everything seemed to go completely still.
I realized the top half of the glowing blade was covered in blood, a dark blood almost black, and I looked at it strangely, wondering if somehow it was my blood. Was I dying? Was this the end?
The Amarok looked stunned, stopped in its tracks, and fell over dead—my last desperate swing had cut clean through its throat. I threw the sword to the ground and cried out as it tore the burned skin away. I held my hands palms up so they wouldn't touch anything, and I ran over to see which of the cherubim had fallen.
I think I was crying then, although I can't remember exactly why. Maybe it was the terrible pain from my burns finally registering in my brain. Maybe they were tears of relief that come after a terrible fright—the Amarok, after all, was dead. The great shadow had passed. Or maybe I was crying because somehow I knew who I would find in that hole in the ground. Maybe I sensed, even without seeing it, that something deep had shifted in the world.
I fell to my knees, my palms still facing up, and looked down into the hole the fallen cherub had created.
It was Mr. Tennin. And while it was the force of his fall that had caused the ground to rise up around him, for a moment it seemed the earth had done that of its own accord—had swelled up, maybe to protect him, maybe to hold him. It was almost as if even the earth itself knew what was taking place and wanted to help, wanted to play a part.
He wasn't bald and skinny anymore. It's impossible for me to describe exactly what he looked like besides this: he was beautiful and strong and there was power there, even after he fell. But I also had the sense that what power remained was leaving him fast, that he had somehow sprung a leak and everything that was bright and magnificent about him was growing dim. I wanted to reach out and touch his face, but my hands were so badly burned that I simply held them out over him, as if I was trying to hold down his fleeing spirit.
"Mr. Tennin," I said. "What . . . what happened?"
He turned a weary face to me, and all the words he said from that moment until the end came in a whisper.
"I fell."
There was weariness in his voice, but there were also tiny strands of relief.
"But what does that mean?" I asked. "Are you dying?"
He shook his head slowly. "No. It just means I can't stay."
"Where will you go?"
He looked me in the eyes, and I realized that he somehow knew my thoughts, that he had seen my visions or perhaps I had communicated them to him unknowingly.
"First I will go across the ocean, beyond the white cliffs, and then, who knows?"
I felt desperation rise inside me. "What if you can't come back?" But even as I said it, I knew what his response would be.
"Come back? Why would I care about coming back? Sam, if there's anything you should know, it's this: death is not a destination. It's a passing, a transition into eternity, the rest of time. When you leave this place, everything you have known will seem like only a dream or the memory of a dream. Dying is the shedding of one cloak and the taking on of another. Death is a gift."
I put my head down and wept. "I find that so hard to believe." I felt helpless, as if everything that had ever mattered to me was passing through my fingers.
"Life is not only made up of what you can see. This is the beginning of belief."
"It seems like so much," I said in a whisper. "So much to believe in. So much to give up."
"Samuel," he whispered. "Always remember this."
I could smell wood smoke drifting around me, the only slow thing in the midst of the gathering storm.
"Death," he said, then paused before whispering the last three words, "is a gift."
I looked at Mr. Tennin and had this sudden realization that he had been there for me all along. He had moved into our house to find the Tree, yes, but also to keep watch over me. He had protected me from the Amarok on the night we ran out of gas. He had helped me grow the Tree so that he might destroy it and keep me from yet another mistake. And now he was showing me that this path through death was one that could be traveled bravely, with dignity.
He shimmered like the flickering of a lightbulb nearly out. Then he was gone, and I stayed there, kneeling beside an empty hollow in the ground. I had so many more things I wanted to ask him.
A fire raged in the forest on the other side of the river. I thought it would cross over and consume all of us, leaving nothing. No one would ever know what had happened. The story would die with me and Abra. This was the end.
A shadow fell over me, the shadow of a person. I turned from where Mr. Tennin had fallen and looked over my shoulder. It was Mr. Jinn, not as the cherub who had just proven himself victorious, but as the dirty, straggly farmer still wearing that old brown overcoat, still walking with a limp.
"You killed my Amarok," he said, staring not at my face but at my blistered hands.
"Your Amarok? It wasn't yours," I said.
He waved his hand at me. "We have more important things to discuss," he said.
"Like what?" Pain shot through my hands again, and I let the cool rain fall on them, run over them.
"You're powerful, Sam," he said in a reluctant voice. "If, as a boy, you can kill an Amarok, well, there's nothing you can't do." He paused, and his eyes searched my face, searched for any signs of weakness. "You could bring your mother back, Sam. Think about it. You could bring her back. And you could be a prince among men, wealthier than Solomon, because you could sell what everyone wants: life. Forever life."
I shook my head, but the alluring smell of the leaf had faded and neither of us knew what I would do.
He pointed at one of the low-hanging branches above my head. "There it is, Sam! You did everything you had to do. You found the Tree, the stone bowl, the water, the sunlight. You did it all yourself. You even killed the Amarok, something no one else has been able to do, not for all of time. Now all you have to do is reach up and take a piece of fruit. Bury it deep in the earth above your mother's coffin. You can bring her back with it. Life from this fruit goes down deep. It's so close. Everything you wanted is here for the taking."
I stood up and looked at the fruit above my head, noticing for the first time that it came in various shapes and shades of green. Some were shaped like pears, the color of dark green grass. Others were round like limes, but so light green they were almost yellow. Still others looked like apples, but smaller and softer. The leaves hung heavy and thick, and I imagined all of that beautiful sap in each one. What people would pay for such healing power!
I would never have to die. My father would never have to die. And in my naïve youth, it all seemed so good. Living forever seemed like a wonderful fruit to eat.
I reached for a piece of it, then glanced at Mr. Jinn. His eyes followed my hand. They were hungry and intent and scanned the Tree as if he was looking for something. His tongue flicked at the edges of his lips, and the hint of a smile turned up the corners of his mouth. His hands came out of the deep pockets of his overcoat, and they were round and heavy and trembling. I remembered those hands from the room at the antique store, the way they had pounded the table.
I realized he couldn't see the fruit. He was waiting for me to pluck it and give it to him.
"Just imagine, Sam," he said. "Your mother here again, in the flesh. Welcoming you home from school and making you breakfast and tucking you into bed at night. Think of it."
Whether it was because of some special power he had or the recent sharp visions the sap had brought to mind, I could picture it all perfectly, what life would be like with my mother. I shook my head again, but my hand reached closer for the glassy fruit, and in each one I saw a vision of my mother's face, smiling.
That beautiful fruit!
"No," I said. "The Tree is mine. I found it. I brought it here. I grew it. It's mine and I won't give it to you."
The desire for it was too great, and I couldn't imagine sharing it, not even with Mr. Jinn, the one who had helped me find it.
"Yours?" Mr. Jinn's voice grew terrible and strong, and rays of the same glorious power I had seen in Mr. Tennin shone through the rags of his clothing. He was rising.
"You won't?" he asked, and this time his laugh filled the valley and the sky and made the trees bend away from us, trying to escape from some unseen power.
He shook his head, and I felt fear tremble inside me because something in his face switched from mirth to regret. He was about to do something to me that he didn't want to do. He reached his hand out, and my entire body clenched tight in an unseen vise. I couldn't move. It was as if he had drawn a circle around my soul. But then he dropped me in a heap and looked past me, toward the trunk of the Tree of Life, and surprise showed on his face, and disappointment.
I looked over at the Tree, and there was Abra. She sat beside the Tree, and the hilt of the sword stuck out from the soft trunk. A blackness had already begun to spread from where she had plunged the fiery sword into the Tree, and the branches had all begun to sink, as if it was deflating.
Mr. Jinn was overcome with anger. Multiple lightning strikes lit up the fog, shattering tree branches and exploding limbs, and were immediately followed by the sound of thunder. He ran at Abra, hands raised, coat billowing out and away from him, the light of a powerful, angelic glory streaking out in rays.
Abra stood up and pulled the sword from the dying Tree. It came out easily, like a knife pulled out of butter. She grasped it with two hands, raised it over her head, and threw it at Mr. Jinn. I was amazed at the force with which she threw it, and as it moved away from her, it seemed to increase in speed, as if it was obeying not only her physical will but also her emotional desire. It stuck into Mr. Jinn's chest as easily as it had gone into the Tree.
He stopped. He stared at her. He ripped the sword out as he fell, and it clattered onto the rocks.
The fruit all fell in one dropping motion, one thousand visions, and when they hit the ground each piece shattered and a strong wind blew through the valley. Every single shard of fruit was blown away into the sky. I closed my eyes and imagined those shards spreading out over an eternal ocean, then sinking into the water and dissolving. I imagined the waves rolling in huge breakers against a perilous, rocky coast, each wave carrying tiny glass-like pieces of fruit from the Tree of Life. I imagined the beach made up of sand from that pulverized fruit, and I could see the white cliffs rising out of the sand. And there, at the top of the cliff, I saw my mother smile one last time, turn, and walk away.
She was gone, and I couldn't bring her back.
Death is that ocean, filled with the dissolving shards of fruit from the Tree of Life. It is the sound of waves that crest but never break, a sound that rolls on forever.
## 32
ABRA CLOSED HER EYES for a moment, and I crawled to her, past the small depression in the ground where Mr. Tennin had fallen, past a fading Mr. Jinn, past the dead Amarok and the pile of ashes that had been the fire from the night before. We both sat with our backs against the Tree of Life, and we watched it die.
We leaned our heads back against the Tree, and I looked up at the top branches. The leaves had begun to change color, from that dark green to a blackish green, then to a reddish black, and finally to a deep, blood red. Autumn came for the Tree of Life in a matter of minutes. Seasons passing in a moment. Soon the entire Tree was waving crimson in the strong breeze.
The leaves fell and swirled in miniature twisters, and the breeze blew some of the leaves into the river and others into the flames or down the path to the Road to Nowhere. I caught a few as they fell and broke them apart. Too late. They were dry inside, and they crumbled in my hands. But even their dust soothed my skin. The blisters did not heal, but the pain dissolved. I grabbed more as they fell, and Abra rubbed them over her stomach where the Amarok had held her in its jaws. We were, both of us, in need of something to take our pain away.
Soon the entire Tree was leafless and old, and the branches clattered together like bones. The wind grew stronger and a few brittle branches fell around us. The fire rose like a wall up against the far side of the river, and a few of the trees that reached toward it from our side smoked and burst into flame. All that remained beyond the stream was ash and the blackened skeletons of tall, skinny trees still blazing, and among all of it the rocks that led up into the eastern mountain. The fire moved, devouring, looking for more fuel.
We were too tired to move, too tired to think through what had happened, but I knew we had to get out of the woods. Quickly. There was the pungent smell of smoke, the way it stung my eyes and burned in my throat, the glistening, black fur of the Amarok, the storm clouds passing over us, giving way to strands of wispy sky. The blue peeking through reminded me of the water in my dream, the eternal waves, and the white cliffs at the far side.
"My mom's the one who took the Tree to the cemetery," Abra said quietly, as if talking to herself.
"What?"
"My mom. She had wondered what we were doing over in the other side of the house, and she thought it was weird that the closet was locked, so she asked my dad to open the door. She found the Tree inside. 'It reminded me of Lucy,' she said, so she took it to her grave."
I started weeping, full of so many emotions. Regret. Sadness. Relief. Abra reached over and held on to my hand. It hurt, but I did not pull away. My own tears felt good on my face, as if some buried piece of me had finally fought to the surface, and something about those tears reminded me of the aloe from the leaves on the Tree. There is healing, after all, in sadness, and sometimes only tears will bring it. Abra's grip reminded me that I was human. I was here. I felt real again. I felt alive.
Mr. Jinn made a sound. He was laughing.
Abra and I stood together and walked toward him. Mr. Jinn reminded me of Mr. Tennin in the moments before he had vanished—he was weak, though not entirely powerless, but what power remained seemed to be easing its way out of him.
He moved only his eyes as he looked at us, and he kept laughing.
"What?" Abra asked, and we couldn't show him the contempt we wanted to because part of the glory he had shown earlier lingered there with him, like a mist within the fog. It was a wonder and a splendor, even hidden as it was beneath the curse he had carried for centuries. For millennia.
He shook his head back and forth, barely, and his laughing dimmed to a weak smile. "You don't even know, do you?" he asked. "You don't even realize what you have done."
That's when I recognized it. The darkness inside me was gone. After everything that had happened, I had given it up. I believed Mr. Tennin. I hadn't wanted the Tree to die, and maybe I couldn't have killed it if it had been up to me, but it was gone now.
I was free.
"What don't we know?" Abra asked.
"His mother," he whispered, staring at me. "There's nothing you can do to bring her back."
He looked over at Abra. "And you . . . You have only just begun."
He disappeared.
Abra retrieved the sword where it lay in the depression. It had returned to its normal color and size, and she held it tightly. But Mr. Jinn's words didn't fill me with terror anymore. I was okay, relieved even, that my mother could rest in peace. I looked around at the burning world, and I realized this was no place to bring her back to. The beach and the cliffs and the green fields beyond seemed like a wonderful place to be. Instead of anger or bitterness, I was filled with a sense of hope that I would see her again, that I could join her there. Maybe someday I could leave all of this behind.
"We have to go," I said, feeling the heat from the fire. We hurried back to the Road to Nowhere through smoke that filled the trees like fog, then continued on to where the road was paved with stones, past Mr. Jinn's house. We were both exhausted and coughing, our lungs burning. Abra put her arm around me and we stumbled down that road together.
I saw my father's car careening up Kincade Road, a cloud of dust billowing out behind him. As he got closer I could see him hunched over the steering wheel, a look of desperation on his face. My father was like an approaching storm.
"Look," I said to Abra, pointing west, away from the fire and the river, over the fields of deep green corn now approaching waist height. A long, straight line of vultures flew out of the valley and disappeared over the mountain.
My father took us to the hospital, but I remember very little about the drive. There was the rough road we bounced over, and the loose gravel pinging up under the car. There was the smell of smoke coming through the open windows, mingled with the heavy moisture of a wet July morning. There was the smooth hum of wheels on the highway, the gradual slipping in and out of sleep. There was Abra and me leaning against each other, exhausted, relieved.
The time I spent in the hospital was also a blur.
"Smoke inhalation," the doctors said. "Third-degree burns."
I guess the leaves hadn't healed me completely.
Abra was in worse shape, and the two of us had trouble explaining her injuries: a series of deep punctures in her chest, in her abdomen, and down her back. A broken rib. A sliced foot. In the end, our parents and doctors chalked it up to two children who had nearly been killed in a forest fire, who had injured themselves while fleeing the oncoming flames. We were okay with that. There seemed very little benefit in explaining the details of what we had been through, and even less chance that anyone would believe us if we did.
But I do remember one thing now. Something I had forgotten for many, many years.
I remember lying in my hospital bed that first night after everyone else had left. I knew Abra was in her own room, recovering. I was thinking about how close we had come to death, and I realized I was both relieved and disappointed not to have made that journey. I missed my mom, but I realized I loved life. I wasn't quite ready to die.
The doctor came in. I say she was a doctor, though in hindsight I have very little idea who the woman actually was. At first I thought I was dreaming because she looked so much like my mother. I thought I was having another one of my nighttime visions, and I settled into it, believing. I had come to enjoy those moments with my mother, even if they weren't strictly real. One of the machines I was connected to let out its rhythmic beep. Another hummed on into eternity.
But then she spoke, and I knew it was no dream.
"Sam," she said, and she even carried herself like my mother, so that I lifted myself up on my elbows and stared closer.
Could it be? I wondered if the Tree, during its brief time beside the river, had leached its life into the ground, enough that it brought her back. Maybe the roots of the Tree had reached far enough into the forest, all the way to the small cemetery and my mother's grave. Maybe this was the beginning of some new era, when all the once-dead people in our valley would come to life, walk among us, reunite with the people they loved. For a moment I imagined the celebrations, the surprise, the joy.
But it was only the late hour talking, or the medication, or my last hopes, because when she got closer I looked into the woman's eyes and recognized immediately that this was not my mother. The blue was not there. The humanness was missing. This person's eyes were dark and endless.
If you've ever looked into the eyes of one of them, you'll know what I mean. Her eyes were exactly like those of Mr. Jinn and Mr. Tennin—eternal, like the space between the stars.
I suddenly realized what she was.
"Why are you here?" I asked. I stared hard at her. She was dressed like a nurse, but she didn't have a name tag on. "Who are you?" Before, when I thought she was my mother, I had wanted to get as close as possible, but now I pushed myself backward in my hospital bed, as far away from her as I could get.
She looked sad for me, as if I would never understand.
"How are you feeling?" She held up a clipboard, writing a few notes on it, and for a moment I was confused. Maybe I was imagining things. Maybe she was only trying to do her job.
"I'm okay," I said. "It's the middle of the night. Can we do this in the morning?"
She nodded and scribbled a few more things on her clipboard. "Your appetite okay?"
I nodded.
"Are you feeling achy at all? Sick to your stomach? Trouble breathing?"
"No," I said. She made me feel tense, uneasy. It wasn't the questions she was asking. It was her. It was her presence.
"Exactly what happened in the forest beside the river?" she asked, eyebrows arched, as if it was a completely normal question for a doctor to be asking a patient.
"What?" I asked, confused.
"I believe there was a gentleman there with you in the woods?"
I closed my mouth tight, bit my lip.
"Isn't that right?" She bent closer. "I believe he worked for your father."
"Mr. Tennin?" I whispered, and for a moment it felt like I didn't have any control over my mouth. It felt like my lips and tongue were going to say whatever information was in my brain. She would ask, and my mind would tell her whatever she needed to know.
I shook my head. Maybe I was trying to clear the cobwebs. Maybe I was trying to wake up.
"What happened to Mr. Tennin?" she asked, and I could tell that for her, everything rested on the answer to this question.
"He fell," I whispered.
She sighed, but I could not tell if it was a sigh of sadness or relief, or the kind of sigh when someone tells you something you already thought to be true but didn't know for sure.
"Do you have it?" she asked, and I knew she was talking about the sword.
I couldn't help it. I shook my head, hoping that would be enough to protect me.
"Do . . . you . . . have . . . it?" she asked again.
"No," I said.
"Does your friend have it?" she asked.
I shook my head again. I remembered seeing Abra retrieve the sword after Mr. Jinn disappeared, and I remembered that it had seemed suddenly small, almost insignificant, like a pocketknife, as she tucked it back in her waistband. It took a great amount of willpower not to answer the woman's question. It was like trying not to respond to someone who says something untrue about you. Words started escaping, but instead of holding them in, I turned them into my own question.
"Who are you?" I asked again.
I sensed a great tension rising in her, and it spilled into the air between us. It was a cloud of anger and resentment, and for a moment I thought she had been sent to avenge Mr. Jinn.
Whose side was she on?
"I need to talk to your friend Abra." She said the words as if explaining something to a very small child who might not understand.
But I shook my head once again. "Who are you?"
She leaned forward and whispered her name. Her breath was ice-cold against my ear, and she lingered there a moment longer than necessary, seeming to enjoy how uncomfortable she made me. Her name was one I had never heard before, but it filled me with darkness, the kind that you can feel closing in around you.
I slept.
When I woke up the next morning I couldn't remember exactly what had happened, though her name was etched in my mind. I doubted for many years if it had actually even happened.
I never told Abra.
Koli Naal. That was her name. Koli Naal.
## 33
IT WAS A SUNDAY MORNING in the fall. The fire had ravaged the valley. The trees that lined the eastern ridge of mountains had been scorched all the way along the river, all the way down to Deen. The town had nearly caught fire as well, but the townspeople had fought it, and the wind had changed, and that storm had finally come in. Mr. Jinn's farm was reduced to ash, as were our house and barns and most of the fields. It was a fire unlike anything anyone had ever seen, and even the green things had caught.
But small signs of life reappeared: tractors had dug out new foundations, and structures rose from the desolation. My father had decided to rebuild, and the new farmhouse was taking shape. It seemed like my father knew more than he was letting on—there was no other explanation for his lack of questions. Why didn't he ask about my injuries? Why didn't he talk about Mr. Tennin's sudden disappearance? In any case, it looked like our new home would be finished before winter. The leaves of the trees on the western mountains, unaffected by the fire, had turned red and yellow and orange, as if the whole mountainside was ablaze.
Abra came to the partially rebuilt house as she had been in the habit of doing on Sunday afternoons. Sometimes we would walk out to the Tree of Life and sit there with our backs against the hard wood, surrounded by the blackened poles of burned trees and the smell of an old fire. But every Sunday that we went out, we found more and more signs of life. The animals returned, creeping through the barren trees, and the tiny green plants created a haze over the gray ash. The trees would be replaced. Life would come up out of that dead ground in the spring.
Everything felt like recovery. Everything, that is, except the Tree of Life. It somehow looked even more lifeless than the other burned trees.
We never said much when we went out there. Mostly we just waited for something, although we weren't sure what.
On that particular Sunday afternoon, about three months after the day the angels fell, Abra and I looked through Mr. Tennin's box again. We sat on the porch and examined all the articles, paged through the atlas. We tried to find the pattern in the appearance of the Tree of Life, but it all seemed so random, those strange trees that sprang up all around the world and then were killed or died under mysterious circumstances.
"Look!" Abra said, pointing toward the church.
Icarus meandered along the road, his tail tall and curling.
"The cat," I said, and the strangeness of that entire summer seemed somehow summed up in those two words. We watched as he disappeared behind the church, walking slowly through the decimated forest toward the river.
"Maybe there isn't a pattern," Abra said, her attention back on the articles and the atlas. "Maybe there's no way of telling where it will appear again."
I shook my head. "But Mr. Jinn knew. He knew it was coming here."
Mr. Jinn's farm was a mystery. When no one showed up to claim it, he was officially declared dead and the farm was eventually auctioned off. We never found out what had happened to the real Mr. Jinn—the man, not the angel who took his name. New people moved in, strange people nearly as private as Mr. Jinn had been. But their neatness extended outside the house, and as the years passed, the grounds of the farm eventually looked immaculate. Silent and lonely, but immaculate.
We studied the contents of Mr. Tennin's box and made maps and charts and long lists of numbers, but we didn't get any closer to figuring it out.
I walked with Abra all the way out the lane. My dad must have been burning debris somewhere, because there was smoke in the air—the smell of fall, the warning of winter. It took me back to the day the angels fell. The smell of wood smoke always did after that.
"Let's go say hi to Lucy," Abra said. In those months after the fire, she had taken to calling my mom by her first name, and something about it seemed right, as if she was one of us, a friend, walking right there beside us.
So we went up Kincade Road, into the forest, all the way to the cemetery, and as we meandered among the stones, Abra let her hands rise up from her sides as if she was flying.
At my mother's grave, we sat down. I told Abra all of my favorite stories about my mom, and she listened, even though I had told them all to her before. I felt that sense of peace again, a peace I couldn't explain, that what had happened would be okay, and anything that wasn't all right would be made right before The End.
I remembered Mr. Tennin's words, and I tried hard to believe them.
Death is only a passage.
Death is just the exchanging of cloaks.
Death is not a destination.
Death is a gift.
I grabbed a red leaf and held its stem in one of my scarred hands. The wind had blown it all the way from the western mountain, where the trees were still alive and in their full autumn glory. Suddenly, a cloud of those leaves from the other mountain swept into the woods and swirled around us, red and yellow and orange, like fire.
# Part 5: The Secret
## 34
"WAIT," I SAY TO JERRY. "Keep driving."
He looks over at me, confused. "But there's nowhere to go from here," he says.
"Just keep going. Please."
The word "please" sounds strange coming out of my mouth. I can't remember the last time I used that word. Jerry drives straight past the lane to my farm, past the old cemetery on the right, the one that used to have a church right beside it. He drives all the way back to the Road to Nowhere, as we used to call it. He passes the lane to Mr. Jinn's old farm, then stops the car when he can go no farther.
"Okay. Thank you," I say, getting out of the car with my cane and the box Abra's husband gave me.
"Should I wait here?" he asks.
"No, no, I'll manage."
"Where are you going? There's nothing back there. No road. No path. Nothing."
I push the cane down into the soft ground and look over my shoulder through the open car window. "Things aren't always the way they appear. I'm going to see an old friend."
Jerry and Caleb glance at each other, and I know that look. They think my mind has wandered off without me. But it is the privilege of old age not to care when people look at you as if you're going crazy. And anyway, who knows, maybe I am. I turn away from the car and pick my way through the trees, my cane in one hand, the box in the other.
The old path is gone. It's as if it never existed. But I know the general direction, even after all these years. Everything is green and overgrown, and it makes me feel old that I have been alive long enough to witness the regeneration of an entire forest, one that was, in my lifetime, charred and lost. It says something, I think, about the heaviness of patience, the power of waiting.
The ivy snags at my cane and it's slow going. I push branches away from my face and walk through spiderwebs.
Eventually I come to the cemetery where my mother was buried. The old iron fence still surrounds the small space, though it's rusty, like an orange weed, and leans over so far in some places that it looks like it might topple. The gate is stuck open. Someone must have opened it a long time ago and never closed it. Some of the headstones have fallen over—broken teeth—but others are still in one piece, drowning in weeds.
My mother's gravestone still stands, and I wonder why it has been so long since I've come this way. I remember her funeral. How long ago that day seems! It feels more like something I read about in a book than something I saw with my own eyes. I place the box on top of her grave, then put my hand on the stone and close my eyes. It's warm in the summer heat.
I have never forgotten the verse the preacher read in the church. I looked it up many times as a child until the words were etched in my mind.
Then the angel showed me the river of the water of life, as clear as crystal, flowing from the throne of God and of the Lamb down the middle of the great street of the city. On each side of the river stood the tree of life, bearing twelve crops of fruit, yielding its fruit every month. And the leaves of the tree are for the healing of the nations.
How I hope that is true.
But I haven't come here to stand at my mother's grave site all day. No, this is not my destination. I turn away and walk through the narrow gate and continue back through the woods. The going is even more difficult, and for a minute I'm not sure if I can make it over the rocks and the roots, through the weeds and the soft earth. But I get there, my black shoes pinching my feet.
I see it. It's still there.
The Tree of Life.
The outside of it is smooth like worn leather, and it's the color of a cloudy sky, a slate gray that's just beyond white. The bare branches are tangled in the leaves of other, living trees. I sit down with my back against it and lay my cane down on one side of me, the box on the other. I lean my head back against the old trunk and close my eyes. I can still feel the amazement I felt that morning when I looked up into its branches and saw all that glistening, almost-clear fruit. I feel a burning in my hands, or imagine I do.
I wonder what would have happened if I had taken a piece of that beautiful fruit and planted it in the loose earth of my mother's grave.
Would she be with me today?
Would we have been able to save the Tree?
Would she go on to live forever as I wasted away and eventually died, leaving her here alone? Or would I have eaten from the Tree too, sealing our fate, forcing us to roam this old world forever, never to see the other side of that vast water?
In the midst of all these thoughts, I hear the river.
I open my eyes and lift the box up onto my lap. I remember the other box, the one from the attic, the one I had kept for so many years without looking inside, the one that is now inside Abra's coffin and will soon be buried under the ground. And now another box, another mystery.
What could Abra have left me?
I lift off the lid and am not surprised.
The small sword is sitting over to one side, the same dull gray color of unpolished metal. I reach toward it carefully, but when my finger glances against it, it is still terribly hot. It would burn me again if I held on to it. Again, the burns tingle in my hands. I can see the Amarok again, and the fire raging in the forest, and the angels streaking through the sky.
I look beside the blade and see a kind of leather journal tied closed with a thin leather strap. I lift it out and untie the knot and gently ease it open. A breeze blows through the trees and flaps the pages. A few leaves drift down to the ground. It's the sound of fall in the middle of summer.
Then, there it is—something like a title page, written in Abra's childhood scrawl.
The Adventures of
Abra Miller:
My Many Quests to Destroy
the Tree of Life
I sigh. So many years have passed. So many things have been lost. Where will we find the courage we need?
I turn to the first page, and I can almost hear her voice reading the opening sentence to me.
After the death of the Amarok, I went to New Orleans. It is a city surrounded by water, a city full of magic. The sword took me there.
# Sneak Peek of the Next Enthralling Novel
"I DIDN'T SPEAK WITH ABRA for many years, you know," I say, trying to sound convincing. "Many years. We grew apart."
I pour two cups of coffee, my nerves on edge. The porcelain spout of the coffeepot chatters against each of our porcelain mugs like the teeth of a cold man. Steam rises, swirling, and the smell calms my nerves.
"Yours is here on the counter," I say as I make my way to the table, holding my own scalding mug.
I had forgotten the very particular feeling that comes when sitting across the table from someone like him, someone who is what he is, but when he returns to the table and settles in, it comes rushing back: the sense that you are not sitting across from a person as much as you are sitting across from an era, an epoch. Looking at this man was like looking at the Grand Canyon and seeing all those lines in the rock, all those different ages of the earth.
"Did you know anything about what she did after your mother died?" he asks.
"How do you know about my mother?" I ask.
"Everyone knows about your mother," he says with a hint of impatience. "Your mother was . . . What do you know about what Abra did after your mother's passing?"
"She was my best friend. I gave her some things. Our friendship died. No, it didn't die—it wasn't that dramatic. We grew apart."
"You could have helped her, you know," he says, sipping his coffee, glancing at me over the rim.
I shake my head and look down. "No," I murmur into my coffee. "I was never strong enough."
"Come now. That's not true?" he says, but his voice turns the words into a question.
I look at him. "Apparently you know the story," I mutter. "I don't have to tell you about it."
"Our weaknesses are poised to become our greatest strengths. If we are patient and if we believe, the switch will often happen when we most need it to. Weakness"—he pauses, tilting his head from one side to the other—"to strength."
"I don't think that switch ever happened in me."
"Maybe you haven't needed it yet," he says. "What did you give her?"
"She ended up with the box. With everything."
He nods. He knows about the box. Of course he does. Mr. Tennin had it—they probably all wanted it after what happened at the Tree.
"Recently. Did you give her anything recently? Or did she give you anything?"
I stare into the black depths of my drink, and it feels like I'm still staring into this man's eyes. His eyes are everywhere.
I picture the box I put into her coffin.
The atlas.
The notes.
I envision the sword and the journal given to me by her husband. This was the moment. It was why this man was here.
I look up at him. "I can't help you. I don't know you."
I say these things in a voice that I hope will communicate that it's time for him to leave. I have been kidding myself thinking I can perhaps climb back into that adventure from my youth. I am too old for this. I have nothing to do with whatever real or imagined saga is going on around me, behind the curtain.
That phrase sticks in my mind: "behind the curtain." That's how Abra and I used to talk about the strange things that happened, as if normal life was on one side of a veil, and the other things—the Tree, the angels, the Amarok—were behind it. If we looked hard enough in those days, we could see the rustling. But not now. Not for many, many years.
"I appreciate your . . . discretion. But there is something Abra had that we need." He waits, then speaks again in a careful, insinuating tone. "I think you might have it. Here."
My heart pounds in my chest. I have no way of knowing which side this man is on. I have no way of knowing if he is a Mr. Tennin or a Mr. Jinn. I look in his eyes, desperately searching for something. Kindness, maybe.
"There's nothing here for you," I say, nerves stealing my breath.
He nods. His dangling earlobes sway. He reaches up and strokes his eyebrow with its seven small piercings all in a line. The space between them is the space between stars, which means that he and I, across the table from each other, must be light-years apart. How long is it taking his words to reach me? How many worlds have fallen in the time it takes me to refill his coffee?
"Do you have time for a story, Mr. Chambers?" he asks.
"I have as much time as I have." I shrug. "Look at me. I have no friends. I have no family. I have very little money. Time is all I have."
He smiles a sad smile. "You have less time than you think. This is a long story."
I take a long drink of coffee.
"It's about Abra," he says.
I nod, and the sadness rises again, this time without the apprehension.
"Let me put it this way," he says. "It's primarily about Abra, but there are others involved. It took me time to gather all these stories together. Decades. There were large gaps. Recently, I had to reopen doors that were not meant to ever be opened again. I sat in the shadows for years, looking for answers, always looking, never finding. Always seeing, never comprehending. I went very close to The Edge."
His voice fades. The wind kicks against the door. The windows rattle. Sleet falls for a minute or two, tapping against the glass, but it turns to snow, a swirling cloud of thick, hypnotic flakes.
"Do you know about her trip to New Orleans?" he asks.
"Only the basics," I say. "She mentioned it in her journal, but it was only a few paragraphs. Something terrible happened there, something she didn't want to write about. She was different after that. Her journal went from descriptive and flowery to matter-of-fact."
He sighs and nods. "How about Egypt?" he asks. "Jerusalem? Paris? Rio? The South Pole? Sydney?"
I am stunned but try not to let it show. I had no idea.
"Those are only the major journeys she took. There were smaller trips. Side trips, you might say. New Orleans was . . . unexpected. For all of us. And we only knew about the Tree growing there after Tennin fell. By then Abra held the sword. The Shadows were rising everywhere. People like me were turning. No one could be trusted. Two Trees at once! Who could have ever imagined? Jinn's replacement was . . . ruthless. Her name was Koli Naal. She wanted it all." He shakes his head. "She wanted every last thing. Not only the Tree. Not only everything and everyone here."
The name shoots through me like the memory of an intense pain.
Koli Naal.
I had never spoken that name to anyone.
He stares hard at me to see if I understand what he's saying. "You've heard that name before," he says, and it sounds like he feels sorry for me.
I nod.
"She wanted every last thing," he repeats. "Those who came before her, the Mr. Jinns of the world, wanted all of this." He raises his arms to take in the walls of the house, the ends of the earth. "Those who came before her wanted all of you—all of humanity and all of this earth. But Koli Naal wanted even more than that. She wanted everything."
When it's obvious I'm not catching on, he says something in a whisper, something I can barely hear. He says it as if it's blasphemy.
"She wanted Over There too."
"Over There?" I ask.
We stare at each other there in my little farmhouse, frost on the windows, the snow sliding along the hard ground. We stare at each other over mugs of coffee that are cooling. We stare at each other over eternities and galaxies, cities and friendships, swords and shadows.
He shrugs as if it will all make perfect sense to me at some point. "There was no one else who could go inside and do what needed to be done. Only Abra. Those were dark times."
"They must have been," I say in an even voice, "if you had to turn to a young girl to rescue you."
When he speaks again, there is something tender there, something that begs me for understanding. Or forgiveness. I wonder if he can be trusted after all. Perhaps.
"She was the only one who could go," he insists. "I would have gone. I hope you understand that. But it had to be her."
I wait, and the steam from our mugs rises between us like spirits.
"The story starts four years before the Tree appeared in Deen. Four years before the two of you killed Jinn and the Amarok and Mr. Tennin fell. Four years before your mother died."
"I didn't actually kill Jinn, you know," I say in a quiet voice. "Abra took care of that."
It feels a cowardly thing to have said, as if I'm trying to pawn all the dirt of that summer onto Abra, trying to save my own skin in case this man has come for revenge. I have a feeling that he knows far more about those events than I do, even though I was there and he was not.
He keeps talking as though he didn't hear me. I stare past him out the window. The snow is really coming down now. It looks like a blizzard is on the way.
"This is what happened," he begins, "the day Ruby vanished from the world."
This is the story he told me.
# Acknowledgments
MANY, MANY YEARS AGO, a skinny kid sat on a farmhouse porch under the reaching arms of two large oak trees, shooing away the flies, putting off his chores, and devouring any books he could get his hands on. His greatest dream was to someday write a novel.
That boy was me, and this book is the realization of that dream. So many of you played a part.
Ruth Samsel, this wouldn't have come about without your encouragement and patience. Thank you.
Sarah Hoover, you (very rashly, I might add) forwarded my email to your literary agent, and without that one quick click, this would not have happened. Thanks for your friendship and your belief in my writing.
Kelsey Bowen and the rest of the team at Revell, your vision and kindness and enthusiasm have overwhelmed me. Thank you for reading the manuscript of an unknown novelist and believing.
Bryan Allain, thanks for the many years of breakfasts where we talked writing and built huge dreams for ourselves.
Jeremy Martin, your long friendship and kind words have led me through many a dark place, including a time in my life when discouragement nearly stopped me writing fiction.
Thanks to DC for all of your constant friendships.
There are many families who embraced this book and continue clamoring for a sequel, including the Harveys, the Schneiders, the Haineses, and many others. Thanks for welcoming this child of mine into your own families.
Andi and Philip, God's Whisper Farm is a haven. Thanks for letting me do a reading there and for welcoming my family so often.
Thanks to those who made special contributions to the initial self-publication of this book, including Tim Lapp, Scott Bennett, David McCarty, Tamara Perry-Lunardo, and Gwyn McVay.
I also owe a huge debt of gratitude to those of you who supported my Kickstarter campaign and helped make this book possible. I'm going to list you all here because you're awesome: Steve Goble, Carl and Fan Smucker, Leanne Shirtliffe, Ryan Haack, Meghan Diller Glick, Dave Stoltzfus, Merrill and Verna Smucker, Dan and Jamie Smucker, Brenda Lee Sieglitz, Andrea Cumbo-Floyd, Dianne Yuninger, Jessie Buttram, Tor Constantino, Bryan and Erica Allain, Jesse and Sarah Hoover, Stewart Conkle, Christine Niles, Gordon Delp, Tammy Turney, Laura Stocker, Jim and Suzy Ogle, Ben and Shar Halvorsen, Susan M. Andrews, Deanne Bullock, Matt and Suzanne Silva, Brian and Angie Schmidt, Noah Martin, Jon Martin, Jay and Dena Riehl, Diana Trautwein, Preston Yancey, Robert and Bethany Woodcock, John and Kim Sanderson, Jason Boyett, David McCarty, Milynda Foushee, Jon Fisher, Jon Hansen, Jason McCarty, Patricia Gibbons, Corri Gross, David and Orpha Longenecker, Sean McCarty, Joshua Samuelson, Todd Adams, Ryan and Janae Dagen, Brandon Fisher, Rich Hartz, Samantha and Lauren Good, Justin and Cindy Smucker, Mark and Heather Buckwalter, Rob Stennett, Roxanne Stone, Jim and Sharon Silva, Alicia Sierra, Tamára Lunardo, Dustin Sangrey, Jill and Brad Kane, Sharon Osielski, Matthew and Jessica Turner, the Arthurs, Joel Cornett, Michelle Woodman, Anna Haynes, Arne Radtke, Chris Davis, Susan Pogorzelski, Kevin Hostetter, Paula Aamli, Eric Wyatt, Evan and Laura Brownstein, Paul and Julie Peachey, Janice Riley, JR Forasteros, Gabe and Michelle Harvey, JJ Landis, Jeanne Befano, Chuck Blair, Patrick and MJ Miller, Samuel Gray, Blaine Houger, Robyn Pretorius, Nissa Day, Alexandria Gilbert, Seth and Amber Haines, Clay Morgan, Marilyn Coblentz, Caleb McNary, Allison DeHart, Daniel Fedick, Tamara Thompson, Paul Heggie, Doug and Shannon Schneider, Burnie Smucker, Donna Coleman, Gregg and Lize Landis, and Ashley Smucker.
To the entire family of Peter Perella, for enduring such a difficult loss and bearing it with grace and hope, and then supporting a book that made the audacious claim that "death is a gift." I thank you.
To Jason Darity, my friend.
Aunt Lin, I wish I could hand this book to you. And number six was a girl, but you probably already know that.
Mom and Dad, thanks for all the books. And everything else.
To my sisters, Sharalee, Angela, and Ashley, for putting up with me for so many years.
To my children, Cade, Lucy, Abra, Sam, Leo, and Poppy. You helped me create this story around the dinner table one spring evening in Holtwood in the middle of our forty-acre wood. Your imaginations inspire me and remind me to stay childlike.
And to Maile. We actually did it. We did it! Without you, my life would be unrecognizable. Without you, this book would not exist.
# About the Author
Shawn Smucker lives with his wife and six children in Lancaster, Pennsylvania. The Day the Angels Fell is his first novel. You can find him online at www.shawnsmucker.com, where you can also sign up for his newsletter if you would like to be notified when and where the Tree of Life grows once again.
# Back Ads
ShawnSmucker.com
Sign up for announcements about upcoming titles.
Twitter: RevellBooks
Facebook: Revell
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Mayenne este un departament în vestul Franței, situat în Pays de la Loire. Este unul dintre departamentele originale ale Franței create în urma Revoluției din 1790. Este numit după râul omonim care îl traversează.
Localități selectate
Prefectură
Laval
Sub-prefecturi
Château-Gontier
Mayenne
Diviziuni administrative
3 arondismente;
32 cantoane;
261 comune;
Legături externe
Prefectura
Consiliul General | {
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Gumowo – wieś w Polsce położona w województwie mazowieckim, w powiecie płońskim, w gminie Dzierzążnia. Leży nad Płonką.
Wieś szlachecka położona była w drugiej połowie XVI wieku w ziemi wyszogrodzkiej. W latach 1975–1998 miejscowość należała administracyjnie do województwa ciechanowskiego.
Zobacz też
Gumowo
Przypisy
Linki zewnętrzne
Dzierzążnia (gmina)
Wsie szlacheckie I Rzeczypospolitej (województwo mazowieckie) | {
"redpajama_set_name": "RedPajamaWikipedia"
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McIlroy, Mickelson in confident mood in Abu Dhabi
Rory McIlroy and Phil Mickelson added a new twist to traditional Emirati Al Razfa dancing. (SUPPLIED)
Published Wednesday, January 15, 2014
Two of the biggest names in golf today performed an impressive opening act ahead of Thursday's Abu Dhabi HSBC Golf Championship opening when they added a new twist to traditional Emirati Al Razfa dancing.
As the world's top players roll into the UAE capital for the four-day 'Gulf Swing' opener, Rory McIlroy and Phil Mickelson eased themselves into the season by joining a select Emirati dance troupe for an energetic, hair raising prelude to the showpiece event.
Holding aloft their clubs, the pair swayed to the sounds of Emirati drums and chants as they learnt the finer art of Al Razfa - a dance traditionally performed by male warriors who brandish and twirl sticks as they celebrate heroes.
"That was a bit of fun and a great way to get into the rhythm of the season," said McIlroy. "I enjoyed learning the traditional Al Razfa dance and putting my own spin on it. It's harder than it looks – some skilful finger work and balancing is needed here. I suspect it's like golf, practice, practice and practice can make the difference but anything can happen when you have to go out there and perform."
Mickelson, who returns to Abu Dhabi Golf Club for the first time since 2011, enjoyed experiencing a traditional art that has been part of Emirati culture for generations.
"I love learning about different cultures, and although I have been to Abu Dhabi before, this was a chance to really experience and understand the emirate's traditions a little better," said Mickelson. "I thoroughly enjoyed it, and was just glad I could keep pace with the dancers who did a wonderful job in showing us how it's done."
McIlroy and Mickelson headline a stunning line-up of the world's best players, which includes Super Swede and current world number three, Henrik Stenson, as well as Spaniard Sergio Garcia, who surged up the rankings to world number ten after winning the Thailand Golf Championship late last year.
Three-time Abu Dhabi champion Martin Kaymer, who first made a name for himself lifting Abu Dhabi's Falcon Trophy in 2008 and again in 2010 and 2011, along with Italian hotshot and Abu Dhabi Ambassador Matteo Manassero join the fray alongside former world number one, Luke Donald, and Irish charm, Padraig Harrington.
McIlroy and Mickelson start their season at the Abu Dhabi HSBC Golf Championship this week, confident 2014 will be one of their best ever seasons.
That won't be such a tough task for world number seven McIlroy, whose struggles in 2013 are well documented with troubles on and off the golf course.
But world number five Mickelson won three times, including an Open win at Muirfield that he described as the finest achievement of his career so far.
It was with much fanfare in the same city exactly one year ago that McIlroy was announced as a Nike ambassador following a world record sponsorship contract.
But the 24-year-old went on to miss the cut that week, and then did not win any tournament for 11 months before closing the season with a superb come-from-behind win over Adam Scott at the Australian Open.
McIlroy, who got engaged to girlfriend Caroline Wozniacki over the New Year, said all the things happening around him last year caused "instability" in his life, but he is in a "good frame of mind" and looking forward to 2014.
"I'm really looking forward it. I feel like I'm much better prepared heading into the first event of the season than I was last year.
"The swing is in a much better place. I've done some really good work on that, the end of last year, and just in the couple of weeks that I've had here leading into this tournament," said McIlroy.
"There was just loads of stuff going on around me and that didn't let me focus 100 per cent on what I needed to do which was to try to play the best that I could.
"This year is polar opposite. Things are really looking good. I'm in a really good frame of mind. Everything seems to have just fallen into place nicely, and I can just go out there and focus on my golf and try and play it as well as I can."
Mickelson said his confidence stems from the fact that he seems to have finally found a driver that suits his game best.
There have been several tournaments in the past few years where the American has played without any driver in his bag, relying mostly on his three-wood.
"There's one thing that makes me very excited about 2014; and as I look back on 2013, I played some of my best golf and had some huge breakthroughs.
"But I did most of it without a driver," said the five-time Major champion.
"And this year, we have the best driver I've ever hit that lowers my spin rate just like my 3?wood. I drive it longer and straighter with my driver than I did with my 3?wood. It's a whole different weapon in my arsenal now.
"And if I drive the ball well, like I have been in practise and I have been this off-season, heading into this 2014 season, could be the best year of my career for that simple reason." | {
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Q: How does zookeeper call complete function in asynchronous APIs I found some callback signature such as data_completion_t, string_completion_t. But I wonder how zookeeper call those functions in asynchronous APIs.
Does it use a single thread to receive response from zookeeper? So I have to add mutex to protect user_data in callback. Or does it check callbacks every time another asyn API has been called?
A: I tested the C mt library, and found that zookeeper created another 2 threads for IO and completion, the completion function is called in the completion thread, so that those functions should be called sequentially.
2012-10-09 15:35:36,904:60028(0x7fff7d0f7180):ZOO_INFO@zookeeper_init@786: Initiating client connection, host=127.0.0.1:3000 sessionTimeout=5000 watcher=0x0 sessionId=0 sessionPasswd=<null> context=0x0 flags=0
2012-10-09 15:35:36,904:60028(0x7fff7d0f7180):ZOO_DEBUG@start_threads@221: starting threads...
2012-10-09 15:35:36,905:60028(0x10af45000):ZOO_DEBUG@do_completion@459: started completion thread
2012-10-09 15:35:36,905:60028(0x10aec2000):ZOO_DEBUG@do_io@367: started IO thread
2012-10-09 15:35:36,905:60028(0x7fff7d0f7180):ZOO_DEBUG@zoo_aset@2700: Sending request xid=0x5073d3c9 for path [/mm/mmidc] to 127.0.0.1:3000
2012-10-09 15:35:36,905:60028(0x10aec2000):ZOO_INFO@check_events@1703: initiated connection to server [127.0.0.1:3000]
2012-10-09 15:35:36,909:60028(0x10aec2000):ZOO_INFO@check_events@1750: session establishment complete on server [127.0.0.1:3000], sessionId=0x13a43632d85000f, negotiated timeout=5000
2012-10-09 15:35:36,909:60028(0x10aec2000):ZOO_DEBUG@check_events@1756: Calling a watcher for a ZOO_SESSION_EVENT and the state=ZOO_CONNECTED_STATE
2012-10-09 15:35:36,909:60028(0x10af45000):ZOO_DEBUG@process_completions@2107: Calling a watcher for node [], type = -1 event=ZOO_SESSION_EVENT
2012-10-09 15:35:36,910:60028(0x10aec2000):ZOO_DEBUG@process_sync_completion@1868: Processing sync_completion with type=1 xid=0x5073d3c9 rc=-101
zoo_set2: no node
the very simple code for the test, the zookeeper server is a standalone listening localhost:3000
int main()
{
zoo_set_debug_level(ZOO_LOG_LEVEL_DEBUG);
const char* host = "127.0.0.1:3000";
zhandle_t *zh;
clientid_t myid;
zh = zookeeper_init(host, NULL, 5000, &myid, NULL, 0);
struct Stat stat;
const char* line = "/test";
const char* ptr = "hello, world";
int ret = zoo_set2(zh, line, ptr, strlen(ptr), -1, &stat);
printf("zoo_set2: %s\n", zerror(ret));
}
Actually, these are explained in the document. http://zookeeper.apache.org/doc/r3.1.2/zookeeperProgrammers.html
C Binding
The C binding has a single-threaded and multi-threaded library. The multi-threaded library is easiest to use and is most similar to the Java API. This library will create an IO thread and an event dispatch thread for handling connection maintenance and callbacks. The single-threaded library allows ZooKeeper to be used in event driven applications by exposing the event loop used in the multi-threaded library.
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Walgreens pharmacist in Peoria denies mother miscarriage medicine due to moral objection
Peoria resident Nicole Arteaga went to a Walgreens to pick up her medication, but a pharmacist refused to fill the prescription over moral objections.
Walgreens pharmacist in Peoria denies mother miscarriage medicine due to moral objection Peoria resident Nicole Arteaga went to a Walgreens to pick up her medication, but a pharmacist refused to fill the prescription over moral objections. Check out this story on azcentral.com: https://azc.cc/2IpGDdQ
chenderson and Bree Burkitt, Arizona Republic Published 8:16 p.m. MT June 23, 2018 | Updated 2:34 p.m. MT June 27, 2018
After a miscarriage, Nicole Arteaga had a doctor prescription filled at Walgreens. She went to pick it up, the pharmacist refused to give it to her. Patrick Breen, The Republic
Nicole Arteaga tells her story, about how a Walgreens employee denied her prescription because it was against his ethics, inside her home in Peoria on June 23, 2018.(Photo: Patrick Breen/The Republic)
Nicole Arteaga wanted nothing more than to be a mother again.
But doctors gave the 35-year-old mother heartbreaking news during her 10-week pregnancy checkup.
The baby's development had stopped. There was no heartbeat. The pregnancy would end with a miscarriage — a pain Arteaga has faced before.
Grieving, Arteaga went to her local Walgreens in Peoria on Thursday to pick up medication prescribed by a doctor to manage her health and the miscarriage by terminating the pregnancy.
UPDATE: Board to investigate complaint over denial of miscarriage medication
Instead, Arteaga was turned away, without the medicine she needed.
A Walgreens pharmacist refused to fill the prescription, she said.
"I don't have control over my body and I don't have control of the situation," Arteaga said. "I was seeking help for the medication I needed and he refused."
"I completely lost it and was in tears."
Arteaga walked into the Walgreens at Peoria and 91st avenues on Thursday with her 7-year-old son to grab dinner, choose a movie and pick up the medications prescribed by her doctor.
The day before, she learned her pregnancy would end in a miscarriage.
Arteaga said she opted to take prescription medication instead of undergoing an invasive medical procedure.
"I didn't want to need those pills," Arteaga said. "This is not how I wanted my pregnancy to go, but this is my situation."
An already difficult reality soon took another complicated turn when the pharmacist refused to fill the order from her doctor.
Nicole Arteaga tells her story, about how a Walgreens employee denied her prescription because it was against his ethics, inside her home in Peoria on June 23, 2018. (Photo: Patrick Breen/The Republic)
"I stood at the mercy of this pharmacist explaining my situation in front of my 7-year-old, and five customers behind only to be denied because of his ethic(al) beliefs," she wrote in a Facebook post that as of Saturday evening had already been shared nearly 19,000 times and garnered nearly 8,000 comments.
Arteaga said the he did not explain any further. Despite two other pharmacists working behind the counter, she said, he told her she could come back the next night or go to another pharmacy to see if they would fill the prescription.
She struggled to tell the pharmacist why she needed this medication with her young son standing beside her.
"His mind was pretty much made up," Arteaga said. "I tried to explain to him. I have to take this medication because it is an undeveloping fetus inside of me and he still refused, standing there silent and looking at me."
She said the embarrassment added to the emotions she is experiencing after losing a child.
RELATED: Protesters rally outside Walgreens that denied miscarriage medicine
"I couldn't believe what he was telling me," Arteaga said. "He has no idea what it's like to want nothing more than to carry a child to full term and be unable to do so."
Her husband was met with the same response when he returned to the store to try to explain their situation.
"He wasn't compassionate about it," J.R. Arteaga said. "He didn't seem to care what we were going through already."
Arteaga later learned the pharmacist sent her prescription to another Walgreens location. She was able to pick up the medication with no issues Saturday.
Walgreens responds, explains 'moral objection'
Walgreens said in a statement Saturday that pharmacists are allowed to step away from filling a prescription anytime they have a moral objection under company policy.
Employees are required to refer the prescription to another pharmacist or manager to ensure the needs of the patient are met "in a timely manner."
Arteaga explained that there were other pharmacists at the Walgreens when the man denied filling her prescription, yet he did not refer her medical needs to another employee.
"We are looking into the matter to ensure that our patients' needs are handled properly," the statement said.
MORE: Atlanta toddler hospitalized after officials deny kidney transplant
A representative for Walgreens said someone reached out to Arteaga to apologize for how the situation was handled.
Arteaga disputed the company's statement, saying the only time she spoke to anyone from the company was when she called the manager of the Peoria store to complain.
The manager did not offer an apology at the time, she said.
Walgreens later told The Arizona Republic, after Arteaga's dispute was brought to their attention, that a representative will reach out to her Saturday evening.
Arteaga has also filed a complaint with the Arizona State Board of Pharmacy.
The laws governing pharmacies vary from state to state.
In 2016, the U.S. Supreme Court declined to take up a challenge to a Washington state law that made it illegal for pharmacies to refuse to dispense medications based on religious grounds.
But, according to the National Women's Law Center, the pharmacist was within his rights.
ALSO: Was a Walgreens pharmacist legally justified in denying medication?
Arizona laws specifically allow pharmacies and pharmacists to refuse to fill a prescription for religious or moral reasons.
The pharmacy isn't required to refer or transfer any refused prescriptions. However, companies may make workplace polices for employees who choose to work for the business.
'I experienced something no woman should ever have to'
Arteaga first shared her frustrations online Thursday night by writing a review for the Walgreens pharmacy on Yelp.
The comment about her experience unknowingly posted on her Facebook page, which she deleted upon discovery.
But the accidental posting brought messages of support and tales of similar experiences from multiple friends.
"I had a friend who reached out and told me not to be ashamed or embarrassed. That she too had left a pharmacy with the same feelings," Arteaga said. "She helped me realize that my feelings were valid … that this might be something that is happening to others and it's not OK."
Overcome with emotion, Arteaga did something she normally doesn't do during a sleepless night: She shared her story on Facebook Friday.
Nicole Arteaga talks about a Walgreens pharmacist denying her medicine
Nicole Arteaga tells her story, about how a Walgreens employee denied her prescription because it was against his ethics, inside her home in Peoria on June 23, 2018. Patrick Breen/The Republic
"I experienced something no woman should ever have to," she wrote.
Her account of the incident was met with thousands of sympathetic comments from other mothers who had lost a child. Others shared their own stories of being denied access to similar drugs.
She said the reactions validated her beliefs that she had been wronged.
"No one should have to go through this, but it was comforting to know I'm not the only one," she said.
Arteaga says she wants her "humiliating" experience to help other pharmacists better understand the effect of their actions.
"I honestly hope that a pharmacist who is indecisive in the same situation (will) think how their personal choices to deny people medication can be more impactful than they may think or be able to see," she said.
Want news on the go? Get azcentral news on Google Home and Amazon Alexa.
Read or Share this story: https://azc.cc/2IpGDdQ
Salary database prompts officials to address concerns of 'woefully underpaid'
Man arrested in connection to double hit-and-run
Missing Northern Arizona man found dead in Wyoming river
ADOT employee accused of tampering with motor-vehicle records | {
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**Also by Tiya Miles**
_Ties That Bind: The Story of an Afro-Cherokee Family in Slavery and Freedom_
_The House on Diamond Hill: A Cherokee Plantation Story_
_The Cherokee Rose: A Novel of Gardens and Ghosts_
_Tales from the Haunted South: Dark Tourism and Memories of Slavery from the Civil War Era_
© 2017 by Tiya Miles
All rights reserved.
No part of this book may be reproduced, in any form, without written permission from the publisher.
Requests for permission to reproduce selections from this book should be mailed to: Permissions Department, The New Press, 120 Wall Street, 31st floor, New York, NY 10005.
Published in the United States by The New Press, New York, 2017
Distributed by Perseus Distribution
LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Names: Miles, Tiya, 1970- author.
Title: The dawn of Detroit: a chronicle of slavery and freedom in the city of the straits / Tiya Miles.
Description: New York: The New Press, 2017. | Includes bibliographical references and index.
Identifiers: LCCN 2017018381 (print) | LCCN 2017031043 (ebook) | ISBN 9781620972328 (e-book)
Subjects: LCSH: Detroit (Mich.)--History--18th century. | Detroit (Mich.)--History--19th century. | Detroit (Mich.)--Race relations. | Slavery--Michigan.
Classification: LCC F574.D457 (ebook) | LCC F574.D457 M55 2017 (print) | DDC 977.4/3401--dc23
LC record available at <https://lccn.loc.gov/2017018381>
The New Press publishes books that promote and enrich public discussion and understanding of the issues vital to our democracy and to a more equitable world. These books are made possible by the enthusiasm of our readers; the support of a committed group of donors, large and small; the collaboration of our many partners in the independent media and the not-for-profit sector; booksellers, who often hand-sell New Press books; librarians; and above all by our authors.
www.thenewpress.com
Book design and composition by Bookbright Media
This book was set in Palatino and Engravers' Oldstyle
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
For the renegades closest to my heart: Sylvan David Gone, Erik Miles, Seante Lackey, and Fred Johnson; and in loving memory of Adrian Gaskins
Hence then, commences the history of Detroit, and with it, the history of the Peninsula of Michigan. . . . No place in the United States presents such a series of events, interesting in themselves, and permanently affecting. . . . Five times its flag has changed, three different sovereignties have claimed its allegiance, and since it has been held by the United States, the government has been thrice transferred; twice it has been besieged by the Indians, once captured in war, once burned to the ground. Identified as we are with its future fate, we may indulge the hope, that its chapter of accidents has closed, and that its advancement will be hereafter uninterrupted.
_—Governor Lewis Cass, State Historical Society of Michigan Inaugural Address, 1828_
The story of the new world is horror, the story of America a crime.
_—Jodi A. Byrd,_ The Transit of Empire: Indigenous Critiques of Colonialism, _2011_
Contents
_Introduction: The Coast of the Strait_
1. The Straits of Slavery (1760–1770)
2. The War for Liberty (1774–1783)
3. The Wild Northwest (1783–1803)
4. The Winds of Change (1802–1807)
5. The Rise of the Renegades (1807–1815)
Conclusion: The American City (1817 and Beyond)
_A Note on Historical Conversations and Concepts_
_Acknowledgments_
_Bibliographic Abbreviations and Quotations_
_Notes_
_Index_
Captain D.W. (David William) Smith, _Rough Sketch of the King's Domain at Detroit_ , 1790. Courtesy of the Clements Library, University of Michigan. This rare, hand-drawn map of Detroit in the British period was identified and authenticated in 2016. Clements Library associate director and curator of maps Brian Leigh Dunnigan has pointed out that key features distinct to this map include the depiction of private landholder "encroachments" within the town walls. Landholders identified by Dunnigan thus far include the prominent slaveholders William Macomb (letter A), John Askin (letter D), and Captain Henry Bird (letter E). The map also shows the rivulet, Savoy Creek, flowing behind the settlement and the abatis, intertwined tree branches used as a defensive barrier, around the fort at the rear. Smith, the creator of the map, expressed support for slavery.
Introduction:
The Coast of the Strait
It has risen from the ashes. We hope for better things.
_—Seal of the City of Detroit, 1827_
Detroit is a city of ash, the charred remains of a burning. For centuries the fire has raged, consuming lives, igniting passions, churning up the land and animals, swallowing humans whole. The burn that Detroiters feel—that the nation uncomfortably intuits as it looks upon the beleaguered city as a symbol of progress and of defeat—traces back through distant time, to the global desire to make lands into resources, the drive to turn people into things, the quest for imperial dominance, and the tolerance for ill-gotten gain. We attach a series of words—coded and clean—to the residue left behind by that fire: racial tension, white flight, industrial decline, financial collapse, political corruption, economic development, even gentrification and renaissance. But the challenges faced by the residents of this city, and increasingly by residents of all of our industrial urban places, are not neat or new. Deep histories flow beneath present inequalities, silent as underground freshwater streams. The racial and class divisions that set groups against one another are old, aquatic creatures. We sometimes sense this. We sometimes feel the nearness of history—the imprint of people acting and events unfolding in the past. Beneath the popular culture chatter that calls Detroit a "ruin," grotesquely suggesting some natural process of decay at work, we can dip our fingers into the water and touch the outlines of an alternate, historical dimension. In this dimension, the firestorm that engulfed Detroit was not the result of inevitable decline brought on by invisible market shifts akin to the force of gravity. In this dimension, Detroit is not the scene of natural disaster, but rather the scene of a crime—a crime committed by individuals, merchant-cabals, government officials, and empires foaming at the mouth for more. This book reconstructs that crime, tracing it to the intertwined theft of bodies (both human and animal) and territories (both lands and waters) that we call slavery and settlement. The perpetrators are not always evil, the victims not always noble, and, at times, they join forces for reasons admirable or lamentable. This is the human relational muck of how a great city—how a great nation—came to be, pushed from the guts of an all-consuming capitalism.
Detroit was born of the forced captivity of indigenous and African people and the taking of land occupied by Native people. Captivity and capture built and maintained the town, forged Detroit's chin-up character as a place of risk and wild opportunity. Detroit was formed not only by the labor of enslaved people on indigenous lands, but also, and as importantly, by what those enslaved people came to signify for the identity of the city. It was ultimately through the dauntless acts of fugitive slaves, and the changing ideas about slavery held by free residents of the working and political classes, that Detroiters began to perceive themselves as distinctly American. Black and red people traversing the river between the United States and Canada compelled Detroiters to confront their long-standing, multinational practices of slaveholding. The presence of renegade bondspeople from British Canada tested Michigan's limits on the legalization of slavery and led Detroit dockworkers, hat-makers, and sailors of European descent to threaten their own lawmakers if they returned runaway slaves. By the end of the War of 1812, the second war for U.S. independence, Detroit was an American metropolis that slavery had made.
This is a chronicle of Detroit, an alternative origin story that privileges people in bondage, many of whom launched gripping pursuits of dignity, autonomy, and liberty. To tell the history of the dawn of Detroit with a focus on the experience of enslaved people reveals yet another chapter in the larger narrative of a national truth: America was a place ridden by slavery, where chains stretched as wide as the midnight sky, trapping diverse peoples in an ironclad hold that took generations and bloodshed to break. Even in Detroit, in the North, and in Canada—places that we like to imagine as free—slavery was sanctioned by law and carried out according to custom. And where there was slavery, there were efforts to wrest away indigenous territory, the lands from which elites could draw wealth by means of exploited slave labor. Slavery and colonialism were bundled together in Detroit as in the rest of North America, creating a complex ecosystem of exploitation and resistance. The Ojibwe historian Michael Witgen has succinctly observed about the Great Lakes region: "The two primary sources of wealth for Europeans who came to North America during the seventeenth and eighteenth centuries had been the profits made from this vast inland trade, and land." He need only have added "slaves" in order to complete this catalogue. Productive plots, beaver pelts, black and red bodies—all were viewed as natural resources ripe for commodification.
Remapping Detroit
Please rip your mental map in half and turn it upside down—the one that sees Detroit in Michigan, Michigan in the Midwest, the Midwest as fly-over country in the United States of America. That is a modern map, developed long after Detroit was settled by Euro-Americans and the grinding process of westward expansion gave some Americans a new West from which to turn back and view a "Middle West" and an "Old Northwest." In the 1600s, _Bkejwanong_ (an Anishinaabe place name) was a hunting ground and transitional village site for the many indigenous groups who peopled the lake country, expertly moving across this wetland terrain to suit their subsistence needs from season to season. At the end of that century, French explorers associated this spot with another name, Détroit, or "strait," a narrow channel joining two bodies of water. It was the French who built the first permanent European post here—to foster the lucrative trade in fur-bearing animal skins. Detroit was therefore seen for over a century by Europeans and Americans alike as a Francophone place, as a subordinate and marginal "dependency" of French Canada to the north, and then of British Canada following a French military defeat. It would take two wars between Great Britain and the fledgling United States before the American claim on Detroit, and on the loyalty of Detroiters, was actualized. When Detroit became American in 1783 (or 1796, or 1815—the date was always in motion and a French elite maintained economic and social influence well into the 1830s), it was located in the "West," a frontier post not yet matched by Chicago (in the Anishinaabe language, _Chigagou_ , "the wild-garlic place"), let alone cities on the horizon of that mangled mental map. A linchpin port town in the Great Lakes by the mid-1700s, Detroit is the second oldest French settlement in what is now the United States, with roots dating back before New Orleans and St. Louis.
The strait that inspired Detroit's first European name stretches thirty-two miles in length and shelters twenty-one islands. This waterway, now the Detroit River, was the hinge that joined the Lower and Upper Great Lakes, a "junction of the continent's major watersheds" that served as a hub of ancient indigenous travel and trade. Centuries later, these massive lakes so central to the continent would form the heart of America's Old Northwest Territory. Water was the earth's blood pumping to and from that heart, making all life and the growth of human societies possible. _Le détroit_ joined Lake Erie to the south with Lake Huron to the north by way of the relatively delicate Lake St. Clair. Narrowing above Lake Erie and again below Lake Huron, the strait could duplicate itself, being first one channel, and then two. This waterway, fanciful in configuration, linked the Great Lakes freshwater chain, which merged with the St. Lawrence River, then spilled into the Atlantic Ocean that bound four continents together. North America, South America, Europe, and Africa joined in an embrace at once enigmatic, abusive, and consequential, reverberating inland by way of the rivers and lakes, a fluid "transit of empire."
The swaths of land rimming the Detroit River teemed with plants and wildlife at the moment French explorers arrived in the late seventeenth century. Father Louis Hennepin, a Recollet priest who traveled with René-Robert La Salle on the ship _Griffon_ in 1679, called the river a "most agreeable and charming Streight," overflowing with deer, bears, turkey hens, and swans. When Frenchmen journeyed there in the decades that followed, they encountered indigenous people who already knew the place and its bounty, principally Hurons (who came to be known as Wyandots in this region) and Ottawas. The Detroit River zone was chosen ground for Native hunters, including local Algonquian speakers and Iroquoian speakers from the northeast. Hurons, originally from Georgian Bay of Lake Huron, traveled frequently through the area from villages southeast of Lake Michigan and near the straits of Mackinaw. As intimates of the place, they called the Detroit riverbank "the Coast of the Strait." This evocative Huron phrasing brings to mind not only the thin waterway connecting "inland seas," but also land: the marshes, meadows, fields, and forests abutting that river. The strait formed a shoreline from which a signature city would spring. This was a place where the ground met the waters, as much riverscape as landscape. The indigenous phrase "Coast of the Strait" captures the sense that Detroit took shape on organic borders, edges between one kind of environment and another. Social and political life there would come to mirror that aspect of nature, taking on the quixotic qualities of a coastline surrounded by land. Here, where waters and lands made enduring and unpredictable contact, a diverse collection of individuals settled and built their lives. They would become River People who lived, in the words of Midwestern poet Richard Quinney, "on the border, on the edge of things." The edge is not the most comfortable space for habitation, as the Chicana feminist theorist Gloria Anzaldúa explained when she characterized zones like this as "borderlands." In her classic treatise on the U.S.-Mexico border, Anzaldúa called the borderlands ( _borderlands/la frontera_ ): "This thin edge of barb wire." For her, and for many others such as Detroit River People, spaces of merger shaped by conflict are difficult places to reside and, at the same time, are "home." They were a motley bunch, the human inhabitants that would gradually populate the fertile strip along the Detroit River and give it the character of a bustling fur trade town. Hailing from points near and far—indigenous North America, French Canada, Great Britain, Africa, and what would eventually become the United States—with ranging ethnic and national backgrounds and competing cultural sensibilities, Detroit's residents perfectly reflected the quality of the place where they dwelled. These inhabitants lived on the Coast of the Strait, on the edges of each other's cultures, on the line between warring empires, on the border between bondage and freedom. Most of Detroit's early residents arrived at the strait as free individuals, but a significant number of them were held as slaves. Working with, and just as often against, one another, free and enslaved Detroiters built a distinctive community that has faced down time despite its trials.
While the history of colonial and early Detroit has been told from many perspectives and is now a growing area of historical inquiry, published studies tend to render invisible or inconsequential the existence, struggles, and contributions of enslaved people in the city. In contrast to the existing historical literature, and as a hoped-for contribution to it, this book chronicles the rise, fall, and dawn of Detroit while centering the experiences of those who were held in bondage there from the mid-1700s to the early 1800s. In the mercantile settlement that would eventually become an American urban behemoth, hundreds of people—Native Americans, African Americans, men, women, and children—were kept captive, stripped of autonomy, and forced to labor for others. The composite story of their lives across five decades and under three imperial governments illustrates the extraordinary and all-too-ordinary character of Detroit, reveals the role of enslaved people as key actors in the history of the city, and illuminates a defining theme, and indeed paradox, of American history: the breadth and elasticity of slavery and the epic, ongoing quest for liberty.
Native Americans, African Americans, and Euro-Americans were differently positioned in this quest. The Coast of the Strait was a place where their varied fights to realize freedom played out in stark comparative relief, from the colonial conflict known as Pontiac's War in 1763, to the American Revolution from 1775 to 1783, to the War of 1812 in which the young United States sought to reaffirm its political separation from Great Britain. Like the American revolutionaries who called themselves Patriots, enslaved people in Detroit exhibited a deep-seated drive for independence. They verbally and physically challenged their owners and, in the ultimate blow to the system of bondage, fled across the Detroit River to secure their freedom in another country. Native communities living near Detroit likewise adopted a rebellious stance against authoritarian imposition, laying siege to the city and competing with colonial authorities in the battle to retain autonomy in the region. Often these various freedom dreams clashed, but sometimes they coincided, when indigenous groups sided with the Redcoats or Patriots to better their own position, or when enslaved blacks took advantage of wartime chaos to launch escape attempts. Red, black, and white American freedom bids, three streams of purpose and passion in the late eighteenth and early nineteenth centuries, merged at the turbulent site of Detroit just as the waters did.
Cadillac's Town
Surrounded by rich, moist soils and deciduous woodlands, a community, a town, and even an empire, could be anchored at _le détroit_. Such a town could extend its economic reach across the western interior, accessing a vast array of indigenous trade alliances and moving prized materials from the Great Lakes hinterlands into the lucrative markets of North America's eastern colonies and western Europe's populous cities. These materials consisted in the main of treated and untreated animal skins and items crafted from peltry, like textured beaver hats of the kind we can imagine on the head of a mature Benjamin Franklin. The eighteenth century was the height of the international fur trade, which locked European colonial powers in fierce competition for indigenous trading partners: Indian men who had the skills to hunt the animals that were driving a fashion frenzy among the transatlantic cosmopolitan set. The vessels that launched from a site such as Detroit carrying away beaver, fox, and deer parts would return from the East with capital in the form of credits and payments, as well as with sundry practical wares like cloth, guns, and kettles. The town that stood at the western edge of so abundant a trading system would grow fat and important over time, raising its own status beyond that of outpost and stretching the imperial girth of its mother country, France.
This was the vision imagined by the officer and "opportunist" Antoine Laumet de La Mothe, Sieur de Cadillac, when he founded Fort Pontchartrain du Detroit in 1701. Cadillac sought to expand the reach of the French Empire, then situated in the northerly region known as New France (now Canada), to block a growing exchange between Anishinaabe and Iroquois traders at the British post of Albany and thereby hem in the trading activity of British rivals, and to benefit personally from the results. He bet that by building a fort along the Detroit River, what was then a far western point for European colonists, the French Crown could hold back a British advance, buffer economic partnerships that French traders had cultivated with Ottawa, Huron, Ojibwe, and Potawatomi hunters, and gain still more trading partners to the west. "Dream[ing] of the personal riches that would accrue to him by making Detroit the preeminent post for a vastly extended trading network," Cadillac proposed a trial settlement at the strait that would entice indigenous groups to move nearby, hence ensuring immediate access to the animal pelts brought in from their hunts. Native men were "procurement specialists" of these sought-after furs, and the women of their villages were expert at tanning and drying. By keeping Native trade partners close at hand, Cadillac aimed to dominate the region's market in furs, thereby shoring up French supremacy in the eastern Great Lakes and stretching French influence farther west.
From the 1600s through the mid-1800s, the fur trade economy was an Atlantic world phenomenon that linked European and American continental societies by a common ocean and drive for profit. The European rage for apparel fashioned from beaver skins, "a scarce luxury product" then available only in the so-called New World, was augmented by a more mundane use for leather goods made from the thicker hides of species like deer and bison, including "shoes, belts, clothing, bags, book covers, housing, straps, fasteners, and floor coverings." Although there were rises and dips, periods of growth and recession, in the fur trade over the centuries, the historian Claudio Saunt has estimated that in the last thirty-five years of the eighteenth century alone, nearly "six million beaver pelts were exported from North America." The bodies of local animals became sought-after commodities and sources of startling profit, akin to oil in the twentieth century if only people could wear it (and we do, in the synthetic materials that make up much of our thin, breathable, water-resistant yoga and outdoor apparel, not to mention those millennial stretch-style "skinny" jeans).
Skins fueled European expansion into the interior of the continent, becoming, as the historian Anne Hyde has put it, "an industry that dominated commerce in North America and provided the underpinning for its first capitalist boom." That commerce had drawn whole villages and tribes into ferocious combat over position and primacy, including a series of bloody conflicts between Haudenosaunee (Iroquois Confederacy) people and French-allied Anishinaabe (Ottawa, Ojibwe, and Potawatomi) people, as well as Hurons, in the mid- and late 1600s. These wars ended in a costly victory for the French alliance in the form of the Great Peace Treaty of Montreal in 1701. In a contest between European empires dedicated to a modern capitalist ideology and longing to control the natural riches of North America, principally the animal pelts and hides of the trade, Cadillac vowed to deliver France the upper hand and schemed all the while to increase his own wealth and local authority. The French minister of marine, Jérome Phélypeaux, Comte de Pontchartrain, championed Cadillac's cause, leading reluctant officials in Quebec to grant him settlement rights.
Aware that the cost for prime positioning within the fur trade had meant warfare and bloodshed in the all-too-recent past, Cadillac nevertheless did precisely what he had plotted. He established a fort along the strait that joined the Great Lakes together as one mammoth commercial waterway. Westerly enough to connect French traders with untapped sources of furs in the interior, and far enough to the south to provide a longer agricultural growing season than could be had in Montreal or Quebec, or in the older French Great Lakes posts of Michilimackinac and Sault Ste. Marie, Cadillac's preferred location seemed ideal for a settlement with staying power in the French _pays d'en haut_ , "Upper Country" or "High Country." From this strategic strait, he hoped to control one of the most powerful resources in the development of human civilization: water. Together with the interconnected major rivers that flowed across this central region—the Missouri, the Mississippi, the Red River, and the St. Lawrence—this tucked-away strait formed approximately "eighteen thousand miles of Inland navigation."
Cadillac sited his military fort where the gleaming skyscrapers of downtown Detroit still tower today, favoring a spot on a slight incline at what he believed was the narrowest stretch of the river. The rise provided good sight lines and higher ground for the essential protection of the military post, while the river provided a ready thoroughfare for the transport of goods as well as people. A proximate stream flowing parallel to the river dipped below this incline, forming a natural barrier to the rear. Cadillac's settlement on the ridged slope at the strait was special from the beginning. He had the self-advantageous insight to invite disparate Native groups to settle new villages on the outskirts of his fort, which some did in the hopes of bypassing tedious trading treks to Montreal. Cadillac also exhibited the unusual commitment to sustain long-term residency for not just lone French Canadian men but also their families, through extensive agriculture. Unlike other commandants of French forts and trading posts in the Great Lakes woods, Cadillac brought a sizeable contingent of one hundred people along, including farmers and artisans as well as military personnel. Enslaved people were likely among this group that settled Detroit and planted a crop of winter wheat that first season. By the fall of 1702, French wives of the leading officers had begun to arrive, making Detroit a settlement where families would grow in the houses abutting the wheat fields. The settlers established "ribbon farms," vertical homesteads of just four hundred to five hundred feet in width that opened onto the banks of the river and backed into fragrant orchards and dense forestland. These ribbon farms, poetically named because of their thin, elongated shape, would, a few decades later in the 1730s, cradle French Canadian style homes inspired by those in the north of France. Dwellings featured wood plank or shingle-sided exterior walls, sloped thatch cottage-style roofs, massive chimneys made of stones, and distinctive glass windows of petite geometrical panes. Residents cultivated the fertile land around their homes, planting orchards of peach, apple, and most notably pear trees, which would come to signify the French botanical heritage of the settlement. The look of this charming, rustic village behind its protective walls was that of a European "fortress town."
In time, the population increased at the fort that came to be known as Detroit, a truncated version of its formal designation, Fort Pontchartrain du Detroit. As the settlement grew beyond its walls, it encompassed farms along both sides of the river to take full advantage of that magical liquid highway. The town grew long and slender, following the water's edge and shaping Detroit's early footprint into what we might now call sprawl. The settlement came to engulf the bight of the river, or bend in the coastline, stretching eastward to westward just as the river flowed. And as social relations became more strained in a vise grip of proximity and exploitation, the people there would soon come to feel in their own skins the second meaning of the word bight: a loop in a taut rope.
In 1710, Cadillac was appointed governor of Louisiana, which would become the site, in 1718, of another famed French colonial settlement: New Orleans. The commandant had made a timely exit. After Cadillac's departure, his town on the Coast of the Strait remained, made up of diverse inhabitants who dwelled together in unsettling intimacy: indigenous people of the Huron, Ottawa, Potawatomi, Ojibwe, and Miami societies, French people from New France and old France, the children of Indian and French unions, and enslaved people of indigenous descent. The forced diversity and social hierarchy of Detroit made it a tinderbox. In 1712–13, a conflict called the Fox War broke out between Native villages near the fort. Cadillac had asked more than one thousand members of the Fox, Kickapoo, and Mascouten tribes from the west to move to Detroit in 1710, just before he relocated to New Orleans. A rivalry developed between hunters from these new groups and previous Native residents already established near Detroit. Indigenous men vying for the primacy of their own bands began killing each other in the woods of their hunting grounds. The tension escalated into group attacks that the French authorities did little to settle, leading to the death or captivity of hundreds of Fox and Mascouten people, many of whom would remain in Detroit as slaves.
_La Riviere du Detroit_ , 1701. Courtesy of the Clements Library, University of Michigan.
The racial, cultural, and national multiplicity of Detroit would only increase over the following hundred years to include British residents of English, Scottish, and Irish heritage, African Americans held in bondage, and white Americans from various points east and south. The Coast of the Strait was a place of overlapping borders—natural, cultural, and political—where peoples of various backgrounds struggled to make their lives in a context of growing economic disparity and political volatility. The most vulnerable of those people are also the most invisible in traditional historical treatments of Detroit and the greater Midwest. They are those whose presence was compelled rather than freely chosen, the enslaved who were integral to the town that would one day become the Motor City.
Remnants of Slavery
At the post of early Detroit, free white residents were fiercely resourceful. They invented effective ways to live in an isolated riverine environment, and they plundered natural resources in order to profit beyond their needs. Unfree people were just as creative, as subjects of their own lives and as objects of chattel slavery. Participants in the innovative process of supporting life in a difficult place out of the raw materials around them, they were at the same time viewed as a kind of natural resource themselves. Like the hunted beaver, enslaved people could be trapped and traded, their best parts—intellect, feeling, strength, and versatility—extracted to further what was then a model mercantile experiment. Straining to live worthwhile lives and contributing to the cultural mosaic that characterized this rough-hewn trading post town, enslaved residents of Detroit shared close quarters with those who exploited them like animals. Their owners ran the gamut of society: merchants, traders, gentleman farmers, political leaders, belles of the balls, and even priests.
Piecing together a composite picture of enslaved people's experience in Detroit has depended on scant documentation. Unlike many locales in the American South (and even some places in the Midwest, such as Indiana), Michigan has yielded no full-length slave narratives or WPA slave interviews recorded by employees of the Federal Writers' Project. Even narratives of African Americans who escaped to Ontario in the 1850s do not include fugitives who had been enslaved in Detroit. In a few rare instances, the cloaked thoughts of unfree people filter through formulaic documents like criminal proceedings and dictated wills. But for the most part, we must read the minds of those who were enslaved by identifying and interpreting their actions—by closely examining the things they did—in the light of their circumstances. Although there is a nearly nonexistent record of Detroit bondspeople's direct words, several Detroit slaveholders wrote about their human possessions in matter-of-fact language captured in letters and financial account books. Due to Detroit's character as a swashbuckling fur trade settlement that tolerated a loose legal and political infrastructure for close to a century, and due to a devastating fire in 1805 that destroyed businesses and private homes, even slaveholder records from the town are limited. Perhaps because of the slim nature of the Detroit slavery archive, very few scholarly works, and no full-length books, had yet been written about this subject. (For a discussion of the related historical literature, please see the essay at the end of this book.) But not having at our disposal the sources that make for a fuller history does not mean we should ignore the enslaved in Detroit. Their lives had meaning to them, to their families, and to the region, and can, when illuminated even by the refracted light of limited sources, have meaning for caretakers of the city today. The odds have been against some Detroiters from the dawn of the city's founding, and yet they still fought and fled, created alliances and evaluated circumstances, crashed across international borders and challenged entrenched racial biases. We owe it to them, and ourselves, to bear close witness to their triumphs as well as their trials.
Primary sources for this book consist, in the main, of the wills, letters, and account ledgers of Detroit slaveholder-merchants such as William Macomb, John Askin, and James May. Legal cases in the Michigan Territory Supreme Court involving slave freedom suits and attempts to recapture runaway slaves, together with the papers of prominent Detroit attorneys like Elijah Brush and Solomon Sibley, also provide crucial material. The registry of Ste. Anne's Catholic Church, the only religious institution in Detroit for decades, as well as diaries of Protestant Moravian missionaries who settled in the area, contribute ritual and observational details about enslaved people's daily and religious lives. Census lists, receipts, and bills of sale partially fill the many gaps inherent in this historical reconstruction.
The scattered nature of the archival record on slavery in Detroit resists the wish that we might have for a comprehensive story that includes beginnings, middles, and endings for each individual and family that will emerge on these pages. Rather, the fragmentary state of the Detroit slavery archive reflects the rough, unpredictable nature of enslaved people's experiences. So instead of pushing for story in some coherent and seamless sense, I have striven to offer what I see as a quilted chronicle: a chronological but oftentimes broken account of important events that stitches together historical interpretation, context, and causes, while patching in intuitive descriptions of people moving through a fraught place. What we can come to understand through this patchwork project is that Detroit was both common and uncommon as a site of American slavery. Detroit was a place built not on tobacco, sugar, or cotton but on the skins of animals often prepared and transported by slaves. Its geographical centrality in the fur trade circuit during the heyday of the industry made Detroit unusual even in a broader context of slavery as it was practiced in the Midwest. Most slaveholding settlements in the areas of Indiana, Illinois, Wisconsin, and Minnesota applied stolen labor to military officers' personal services at various forts, domestic duties, wheat production (Indiana and Illinois), mining (Illinois and Wisconsin), and resort hotels for vacationing southerners (Minnesota). In contrast, Detroit's enslaved, while certainly employed to cushion daily life for others through domestic pursuits and in small-scale agriculture, were critical among the labor force that greased the wheels of trade. A close look at life in Detroit therefore draws together two aspects of the U.S. past that are often narrated separately: the fur trade of the great West (often imagined as involving whites and Indians) and chattel slavery (often imagined as involving whites and blacks). Trading in the pelts of beavers and trading in the bodies of persons became contiguous endeavors in Detroit, forming an intersecting market in skins that takes on the cast of the macabre. While black men's backs and legs served as the locomotives that moved these furs across vast distances, indigenous women's bodies were plundered for sexual riches, much like the land was stripped of beaver and other fur-bearing mammals. The theft of unfree people in Detroit, of their knowledge, skills, and corpuses, made the city we know today possible. But out of the shadows of exploitation, enslaved people rose to accomplish a set of rare, phenomenal feats: they ran away consistently, testing new laws of the territory; they contributed to the growth of a subversive Afro-Native community that came to be known as "Negrotown"; they formed an armed fighting force that paraded the streets of Detroit while conflicted officials looked on with worry. In spirit, and surely in flesh for some, they were the ancestors of modern-day Detroit.
Inspired by passionate public discussions about Detroit's past spurred by commemorations of the Underground Railroad, the sesquicentennial of the Civil War, and the bicentennial of the War of 1812, I took up this research project in the summer of 2011 with the aid of a small team of student researchers. I had the privilege of following these public conversations and sometimes contributing to them in spaces such as the Detroit Historical Museum, Wayne State University, the University of Detroit Mercy, the University of Michigan, the Michigan Local History Conference, Underground Railroad tours in the city, and the River Raisin National Battlefield Park. No doubt, the intensity of dialogue among residents and scholars from Detroit and beyond took some sense of urgency from media accounts that repeatedly described Detroit as a symbol of ruin and collapse. But History may have a constructive rebuttal for this demoralizing rhetoric. One of Detroit's prominent slaveholders once called the city "ruined," and yet, from the vantage point of Detroit's most vulnerable residents in his time—enslaved men and women—disarray meant the opportunity for reinvention.
Contradictions of the Coast
A "strait" is a channel of water and also a state of difficulty. Native American and African American slaves in Detroit experienced dual and dire straits. The life they knew along the Detroit River was hard and rife with risk. Most of them had been snatched away from their families of origin in indigenous lake country and the plains, French Canada, New York, Kentucky, or Virginia, and were then sold and shared among members of the area merchant class. Tasked with the essential work of making a distant settlement habitable and even comfortable for their needy owners, slaves cleared land and built dwellings, chopped wood and tended livestock, grew food and prepared meals, and did the onerous heavy cleaning required in a location seasonally soggy with river mud and marshlands. Many of them were compelled to perform intense and dangerous labor as sexual servants or as crewmembers on boats that plied the rough, local waterways. Some slaves in the Detroit area, forced to do work out of doors without proper protection, succumbed to the harsh winter weather of the blustery lakes. An unknown number dwelled in an emotional cloud of anxiety, fearing physical restraint, injury on the waters, separation from loved ones, and violent punishment.
But at the same time that enslaved people in Detroit confronted certain hardship, they lived in a place that afforded them a degree of constructive mobility that was not without significance. Detroit was on the far periphery of European settlement. In some senses the town was like an island in an archipelago, separated from other colonial cities by long stretches of water but connected to imperial networks through trade. Surrounded by indigenous villages and hunting grounds, Detroit had no immediate support from either European colonial or American territorial infrastructures. It possessed what legal historian Lea VanderVelde has described as "frontier characteristics," which meant the town was perpetually engaged in "building itself up, inventing first generation solutions in the absence of long-standing institutional foundations." Far from being strong enough to comprehensively enforce the subjugation of enslaved people, Detroit depended on the cooperation of captives in the city. The tiny free white population of this borderland town always felt itself vulnerable to Indian, British, or American attacks, which meant the settlement needed combined efforts for defense from residents across the class hierarchy. Members of the Detroit elite marginalized, exploited, and punished their slaves, but only to a point. References to whippings and beatings are few in local slaveholders' records. The callous separation of family members, emotional coercion, physical restraint, and imprisonment appear more frequently as mechanisms of control. On an inland coast in a frontier town that stood at the far reaches of European, and later American, centers of finance and government, enslaved people could, to a certain extent, negotiate their immediate circumstances. They seized the opportunity to broaden the scope of their personal actions, to push out the walls of their containment, to adjust relations of power, and, sometimes, to escape. In a lightly populated northern area bordered by Native towns and a navigable river, enslaved men and women found leverage that they applied to the goal of gaining freedom.
Detroit, the experience of enslaved people shows, was a compelling and confounding place in the history of American slavery. Besides being sited near multiple indigenous villages and at a great distance from established white towns, Detroit was shaped by diverse cultural influences, including indigenous practices and the religious mores of the Catholic Church. And just as significantly, Detroit was positioned on a pivotal waterway that, after the Revolutionary War, comprised an international border between the United States and British Canada, guaranteeing freedom for slaves who managed to cross in either direction. In this culturally heterogeneous frontier-borderland environment, slavery evolved as a palimpsest, with subsets of the population enacting and challenging slavery in different ways, and with new cultural practices of human bondage inscribed on top of old. The history of Detroit reveals long-term Indian bondage originating in Native American captive-taking practices that the French adopted and elaborated, as well as African bondage derived from French, British, and American norms. Three categories of enslaved people therefore lived in Detroit: those possessed by the French and their Indian allies, those owned by British officers and businessmen, and those held during the period of American occupation and settlement prior to Michigan statehood. Beyond demonstrating that Detroit was a distinctive site of American slavery due to its geographical, multiracial, and international makeup, this book illustrates the way in which early America was nowhere a place that guaranteed the enjoyment of freedom for peoples of color. Even in the Old Northwest, on the border with Canada, America was a land where freedom necessitated a hammering out blow by blow, and moment by moment, like molten iron in the blacksmith's forge. In this way—in the torpid forging of freedom and long denial of corporeal security and meaningful citizenship for former slaves—the fort town of Detroit was all too common.
The five chapters in this book unfold chronologically. Chapter 1 describes the practice and experience of slavery in the era of Pontiac's siege of Detroit in the 1760s, detailing how slavery came to the settlement with the French and their Native allies and how the practice persisted and changed under British jurisdiction following the French and Indian War. Chapter 2 traces the activities of a circle of British slaveholders in the period of the American Revolution in order to offer glimpses into the world of their slaves, whose numbers reached a high point and shifted demographically during and following the War for Independence. Chapter 3 uncovers the fiction of a free Northwest Territory by detailing the ways that slaveholders evaded the ambivalent antislavery clause of the Northwest Ordinance as well as the ways that enslaved people used the new federal legislation to their advantage. Chapter 4 explores the initial period of American authority in Detroit's history, after the British finally relinquished key military posts in the Great Lakes. It traces the pace and scope of Americanization in the town and evaluates the effect of this political shift, as well as the impact of the great fire of 1805, on the enslaved. It also details a series of cases in the Michigan Territorial Court in 1807, a year that saw a surge in slave freedom suits and formal attempts by owners to recapture runaways. Peter and Hannah Denison, a black couple suing for their children's freedom, launched the first such case that year, setting a precedent for the limits of slavery in Michigan law and establishing a route of escape to Canada that others would follow as an Underground Railroad network developed decades later. Chapter 5 traces the formation of a unique fighting band of runaway slaves known as the "Negro Militia." After an international maritime incident, the Chesapeake-Leopard Affair, raised American fears of an Indian attack backed by the British, Michigan Territorial Governor William Hull authorized the formation of a defensive force made up of Canadian ex-slaves led by Peter Denison. This chapter concludes with an overview of the War of 1812 and speculates on the role of Detroit's black militiamen in the conflict. The conclusion of the book follows the surprising adult life of the eldest daughter of Peter and Hannah Denison, Elizabeth Denison Forth, and reflects on the history of slavery in Detroit in relation to public memory. A final essay briefly positions the book and its arguments within various streams of historical and academic conversation.
The City of the Straits, yet another name for the venerable Detroit, brims with untold stories of crisis and courage, of bold bids and daunting defeats. Although the people once held as slaves have disappeared from public consciousness and have no marker to their memory on the streets of that metropolis, their stories lend meaning and urgency to our understanding of the city's past. By bringing hundreds of captive people into the light of our awareness, people who were expected to fade into the dim recesses of history, I hope to show the struggles, the strivings, and maybe even the soul of Detroit, a place like no other.
Slavery has a deep history on the Coast of the Strait, and echoes of that era sound beneath the surface even now. In 2012, a man named Sedrick Mitchell was convicted and sentenced for holding women captive in the city of Detroit. For months he had secreted away two African American girls in a nondescript house on the east side of town. Mitchell demeaned and physically assaulted the fourteen- and fifteen-year-old girls, forcing them to perform certain acts against their will. His case and others have been investigated by the Michigan attorney general's Human Trafficking Unit. Still, sufferers of modern-day slavery in Detroit, and hundreds of missing and murdered aboriginal women in neighboring Canada, continue to await liberation and justice. It seems that the old streets of Detroit are still drawing traffickers, who rely on the unwieldy size of the 139-square-mile city, its decreasing population, its proximity to major highways and bridges, and its status as America's most active border for international trade to ensure ease of passage and anonymity for dreadful deeds. Centuries ago, slaveholders used the same waters of this river to hike their profit margins, forcing enslaved people to ply the vessels carrying goods processed by still more slaves. But bondsmen and women turned this waterway to their advantage and hijacked the river as a route to liberation. Emancipatory action in our time, too, might be waterborne—ferried by the physical waters that embed social power, fed by the underground stream that is history. On the borderlands of bottom-line globalization, capitalistic expansion, and postindustrial flux, recognizing the historical links between land-seizers and body-snatchers, and exposing the tools and techniques of bondage as well as liberation, are incremental but purposeful ways to make room for visions that see the earth and all of its creatures free.
The Straits of Slavery (1760–1770)
How can we make these barbarians, Christians, if we do not first make them men? How make them men, if we do not humanize them? . . . How can we conquer them and make them subjects of the king if they have neither docility, nor religion, nor friendly commerce? All of this is easily accomplished by the means spoken of in my memoir, and by perfecting the establishment at Detroit.
_—Cadillac to M. de Pontchartrain, 1702_
Hundreds of ten-foot-high hardwood planks encompassed Fort Pontchartrain du Detroit, just as the French commandant had originally envisioned it in 1701. Antoine Laumet de La Mothe le Sieur de Cadillac had specified oak as a strong material from which to construct the defensive walls of the post. Fashioned from the solid cores of sheltering trees that grew plentifully in the forestland of the southern Great Lakes, Cadillac's stakes still rose to sharp points above eye level and bored into the rich earth three feet deep. The French fort that had just seen its sixtieth birthday was not only picketed but also manned. Sentries guarded the gates of this old-world village, monitoring the comings and goings of outsiders. A water gate shuttered the river; a rear gate faced down the forest; side gates capped either end of the main road called Ste. Anne's. These fortified barriers were meant to secure the vulnerable populace of a small and fledgling trading town. Here, within a 372-by-600-foot expanse tucked beside an ambling river, streets such as Rue Ste. Anne, Rue St. Louis, and Rue St. Jacques were packed to bursting with buildings: private homes, merchant houses, a bakery, a church, a guardhouse, a storehouse, military barracks, and military commanders' stations. On Ste. Anne's Street, the major thoroughfare running east and west, perched Ste. Anne's Church with its newly erected belfry, dating, the rugged residents would tell any properly admitted guest, to 1755. Saint Anne, blessed mother of the Virgin Mary, was a favorite saint in Quebec, Canada, and a spiritual match for this riverine coastline, as she was believed to be a protector of sailors and safeguard from storms. Rocking up to the churchyard like so many wooden boats with sails were neat rows of family homes with steep, triangular rooflines. The King's Gardens, a parcel of land set aside for commanding officers, grew near the water southeast of the fort. Below the unwieldy incline of the southern wall, windmills spun beside the river, their oblong fans producing power to grind the wheat so carefully cultivated to sustain the survival of the remote, western settlement.
Past the fortified town that sat on the northwestern edge of the river, elongated "ribbon farms" unfurled along the banks. Indigenous villages curled like strings of gleaming glass beads beyond them, on the north side as well as across the water to the south. A Potawatomi village to the west of the fort marked the border of settlement on the north bank of the river, where present-day Michigan is located. An Ottawa village could be sighted just across the river in the area of present-day Ontario, Canada. Farther west on the southern side, a Huron village was neighbor to an Ottawa settlement, and below the Hurons, French farmers had established another stretch of homes at a bend of the river known as _la petite cote_ , "the little coast." The portion of Windsor, Ontario, as we know it today, that shares the coastline with Detroit and is often viewed as a northern destination on the Underground Railroad of the pre–Civil War era, actually lies south of Detroit city. But in the 1760s, there was no Michigan and no United States; there was no Ontario and no international border that drew a stark political line between two nations, or marked a bloody line of desire and loss between two states of being: slavery and freedom. There was, instead, a wooden fort surrounding a French Catholic town that had recently fallen to the British in a costly, protracted imperial war.
To the rear of the fort called Detroit marshlands spread into a dense thicket of forestland used by Native peoples as hunting grounds. To the front of the fort a wooded swath buffered the rich bank of the river, below which sundry boats regularly approached to trade in goods. These waterborne vessels delivered textiles, household supplies, and metal weaponry, and carried away animal pelts headed for distant markets, as well as the flour, oats, and meat that Detroit regularly supplied to the smaller population of Fort Michilimackinac, located at the straits of Lakes Michigan and Huron, nearly three hundred miles to the north. The town on the bluff and its satellite settlements embraced the strait of Detroit, a waterway toward which all life here oriented. For this was a river that flowed into the rippling Great Lakes and, through them, the St. Lawrence River, the Atlantic Ocean, and the greater world. When Cadillac selected this site for his fort in 1701, he described the Detroit waterway as a channel made wondrous by versatility. The river could be accessed for trade and sealed off for defense, depending upon the circumstances. "The situation is agreeable," Cadillac wrote about his chosen spot, "it is none the less important because it opens and closes the door of passage to the most distant nations which are situated upon the borders of the vast seas of sweet water. None but enemies of the truth could be enemies to this establishment so necessary to the increase of the glory of the king."
Fort Detroit was at once a strategic military stronghold and a pivotal commercial trading post set in the hinterlands of the _pays d'en haut_ , a French term for Upper Country. Besides the French farms and Indian villages that spun around the picketed town like spokes on an elongated carriage wheel, Fort Detroit was positioned in an interior spot far from any European urban center. Montreal and Quebec, the bustling cities of colonial New France (the province to which the post at Detroit had previously been attached) were 560 and 723 long and tedious miles to the north and east. Although Great Britain had won the war and now claimed this post, the British colonies of the Atlantic seaboard had no effective influence here. Even New York, a principal city with which Detroit did business on an annual basis as the trading boats made their slow circuits in warmer months, was a full seven hundred miles away.
The fur trade formed the economic core of this chiefly mercantile community, with the preponderance of its residents engaged in the business. As an inland hub of the trade, Detroit hosted the people and attracted the activities that kept enterprise alive and thriving. Resident merchants received goods from crewmen from the east, procured furs from indigenous hunters in local villages, imported a portion of those furs through the services of French _voyageurs_ (rowers and traders), employed free and enslaved laborers to process and pack those furs, and then exported the products to eastern and Atlantic markets by way of combined free and slave labor power. Intimately attached to the cities of the east through the flow of this global trade, Detroit was at the same time a world apart: small, rustic, and surrounded by Native hunting grounds, villages, trails, and preexisting trade networks.
John Montresor, _Plan of Detroit_ , 1764. Courtesy of the Clements Library, University of Michigan.
Various classes of French men and women, as well as inhabitants of mixed Native and French descent, peopled the riverside town's dirt-packed roads. On the streets of Detroit in the latter half of the 1700s, a newcomer, perhaps a trader relocating from British New York who had arrived in early summer after the lakes had thawed, would have noticed the elided tones of the French language, along with Algonquian and Iroquoian dialects and a smattering of the English tongue. He would note the formal style of local merchants, the highest class of folks in town, who dressed to signify their position. For even in the so-called backcountry, these wealthier residents kept in step with trends of the cosmopolitan Atlantic. The men wore their hair powdered in white and paired brocaded waistcoats with breeches that buckled at the knees. Their wives donned long gowns wrapped with shawls and accented by strands of hair delicately piled atop the head. Merchant-class women in Euro-Native mixed-race families would have been similarly appareled as they stood on the shop floors with their husbands, co-managing the affairs of the fur trade.
The harvest produced by family farms, especially wheat and orchard crops, fed the town and brought returns in local exchange. So farmers would have been present in this streetscape too, doing business within the fort, although their homes were mainly situated outside the enclosure walls. French farmers and craftsmen in the town would have worn shirts in brilliant shades, trousers with belts or sashes, and Indian-style moccasins. The women in these families that worked so intensively with their hands out of doors would have dressed in knee-length gowns, petticoats to the ankles, and straw hats for sun protection. Farming women, like merchant women, applied themselves both inside and outside. They kept house, tended kitchen gardens, prepared food, made household items, and raised children in a settlement with no schools. Prominent merchants were often also farmers, commanding large tracts of land derived from Cadillac's early claims or acquired, unlawfully, in purchases from indigenous groups. The New Yorker would surely have noticed, too, Father Bonaventure, the local priest draped in stern black robes. Charged with the moral well-being of residents in a town with only one church, the father kept the community's sacred rituals: marriages, baptisms, funeral services, regular masses, and holiday celebrations in honor of the saints.
Any one of these members of Detroit society, from longtime French merchants, farmers, and priests to newcomers from Great Britain, could be the owner of another Detroit resident, that is, the owner of a slave. This would have come as no surprise to a sharp-eyed merchant from New York, as that colony was becoming a primary location from which Detroit slaves were sourced. Black people arrived via boat and on foot through the trading networks that also circulated animal pelts. The connection between slaves and skins in Detroit and other Great Lakes markets was so close, so uncanny, that a French Canadian attorney general had once proposed manipulating slaves' need for clothing as a means to process furs for market.
It was Ruette d'Auteuil who seized upon the notion, in 1689, that the African slaves imported to New France could wear beaver fur as apparel, thereby transforming the rough but valuable animal skins into a prized variety of processed fur. Softened and tempered by long-term wear in which contact with the natural oils of human skin rubbed out the roughest hairs, leaving behind the soft underfur that felted so well into headwear, "coat beaver" or "fat beaver," as it was sometimes called, commanded luxury prices. Ruette d'Auteuil figured that black slaves could be put to work at building "all sorts of manufactures" in French colonial North America while dressed in the prickly skins of another captured species. The black men's bodies would finish the furs while at the same time erecting the infrastructure of the colony, producing extra surplus value by way of the sweat of their stolen labors. While this plan was never enacted in New France, in part because of the easy availability of Indian slaves, the vision behind it reveals an eerie alignment between the fur trade and the slave trade, capturing the ideological intersection of these two seemingly separate exploitative enterprises. The beaver and the black man, both, were reduced to natural resources in the eyes of capitalist body brokers.
We tend to associate slavery with cotton in the commercial crop heyday of the southern "cotton kingdom," but in this northern interior space, slavery was yoked to the fur industry. The cycles and routes of the fur trade, as well as its vessels—Indian canoes, French batteaux, and British schooners—were the cycles, routes, and vehicles of the slave trade in the place we now call Michigan. If the outlines of a triangular trade can be sketched in these thick, forested lands, it existed between upstate New York, southern Michigan, and the northern straits of Mackinac. Along the Detroit River and at trading posts linked by Lakes Erie, Ontario, and Huron, merchants bought and sold peltry as well as people, shaping a _skin_ trade of dual nature. The dark underside of fur trade imperialism was not only the rise in conflict among various Native groups and the near destruction of beaver and the lush riverine habitat that the meticulous animal maintained, but also the consumption of human beings in an insatiable for-profit enterprise.
Bound for Detroit
Detroit's strategic location between Lakes Erie and Huron, as well as between the eastern port cities and western Indian nations (such as the Foxes, Dakotas, and Lakotas), made it a prize in the eyes of European imperialists. The ongoing purpose of the fort was to secure and control a flow of goods between indigenous hunters, white traders, and global markets that would shore up the economic primacy of the European empire that claimed it, formerly France, and, at this moment in our chronicle, Britain. When, between 1757 and 1760, France and Great Britain waged a war over the fates of their North American colonies, Detroit was one of the most valuable chips in play. France lost this Seven Years' War (or French and Indian War, as the British called it), forcing French King Louis XV to relinquish all of that country's posts in the Great Lakes region. The once wide-ranging French-claimed territory in North America, a "corridor" stemming from the St. Lawrence River Valley of Canada, through the Upper Great Lakes and southern Illinois country, southwestward into the Missouri River region of Louisiana, was rudely sliced in two. The English took swift command of the Great Lakes posts, including Fort Pontchartrain du Detroit, though the limits to their actual authority were extreme in a country surrounded by Indians. After a small cadre of British commanders trekked from the East to settle inside the old French fort, they purchased dwelling places from local residents, some of whom relocated to homesteads beyond the walls.
French villagers who remained at Detroit were permitted to keep their property after first swearing allegiance to the new Crown that dominated the region. This property could include unfree blacks and Indians. As spelled out in Article 47 of the Capitulation of Montreal following the war: "The Negroes and Panis [Indians] of both sexes shall remain in their quality of slaves in the possession of the French and Canadians to whom they belong; they shall be free to keep them in their service in the colony or to sell them; and they may also continue to bring them up in the Roman Religion." With the promise of French property protections firmly in place and the residents placated, if still wary, the British endeavored to turn Detroit into a central command post for their military operations in the Indians' west.
At Detroit, civilian government had no foothold. In this militaristic and mercantile town, British officers held sway in a tenuous truce with wealthy French merchants, whose economic and social influence was long-standing and deep-seated. In 1760, Detroit was a village on edge, a place on _the_ edge—of empires and interest groups. Dangerous and unpredictable, a space of extreme risk and ample opportunity, Detroit drew people—and conflict—like a magnet. White, red, or black; enslaved, indentured, or free, new people were bound for Detroit in the aftermath of the French and Indian War, and when they arrived, they twined their fates with that of the city.
Even under formal British jurisdiction, Detroit remained French and Indian in character. Within the walls of the fort and alongside the sloping shoreline, nearly one thousand people went about their daily lives, keeping hundreds of homes and farms in as good a working order as could be expected in a place where supplies might arrive or might not, depending upon the season and the flowing or frozen state of the river. When the populations of nearby Native villages are included in the count, greater Detroit residents numbered around two thousand. These _habitants_ were French in the main, as well as mixed-race French and Indian, with a substantial number of Native people regularly visiting the fort from their villages just beyond town. French-speaking people of African descent resided at the fort in small numbers, but very few were free. Detroit residents traded furs and sundry goods with one another, attended mass, rites of passage, and celebrations at Ste. Anne's Catholic Church, ran exuberant foot races, and threw festive dances and sledding parties in an atmosphere characterized by a lively communal life.
But while the fur trade flourished, bringing wealth and social stability to European colonists in Detroit, enslaved women toiled behind those festive scenes, keeping the homes and gardens of others, processing and preparing food, caring for their mistresses' children, making clothing and household linens, cleaning private and public spaces, and providing sexual services according to the demands of their masters. Enslaved men in Detroit were likewise taxed by arduous labor, plying the boats that kept the system of long-distance trade running across the formidable lakes, hauling goods, applying the skills of various crafts, building structures and containers, and working the land obtained by their owners.
Free French and mixed-race _habitants_ , soon joined by British soldiers and a smattering of British merchants, enjoyed a position of relative safety afforded by town walls and armed patrols. Most French residents made peace with the new political reality, accepting British authority and clinging fast to the things that produced and secured their wealth: healthy trade relationships with Native people, land, and slaves. The picketed walls of Fort Detroit shielded these privileged residents from the threat of attack that could originate from any direction in an era of ongoing imperial warfare: from Indian villages close to the fort, Native communities far afield, or even the vanquished French military that had receded to the jointly occupied French and Indian Illinois territory. But for those individuals who were not free, the palisade may have symbolized physical confinement within the fort and containment within the status of "slave," even as it promised protection from unknown threats outside the common walls.
Detroit counted 33 slaves among 483 residents in the year 1750. By 1760, that number had increased to 62 slaves as the arriving British officers brought their black bondspeople along with them.
This Great, Disastrous Catastrophe
Perhaps James Sterling should have known what trouble loomed. He was, after all, a merchant doing steady trade with the Indians who would soon conspire to attack the fort at Detroit. Born in Ireland, Sterling had lived in North America since the 1750s, serving in Pennsylvania during the French and Indian War and working as a commissary at various British forts. He had relocated to Detroit in 1761 to stand as the western agent of a trading firm with the very long name of Livingston, Rutherford, Duncan, Coventry & Syme. Charged with overseeing the movement of goods between traders in New York and traders in the west, Sterling was not keen at first on his relocation from the populous east. In the fall of 1762 he disdainfully described his new town as "this place of Exile (as I may justly term it)." But business proved good for Sterling, an ambitious bachelor with an eye out for the main chance even in exile. He developed a steady exchange with nearby Native hunters and added a degree of Indian language facility to his proficiency in English and French.
Sterling's correspondence made clear that his thriving business depended on the work of enslaved blacks, especially black men whose muscles became the mode of movement for trade goods. In 1760, in advance of setting up shop in Detroit, Sterling attempted to acquire black slaves from merchants Phyn and Ellice in upstate New York. A letter from the company's owners informed Sterling: "we have tried all in our power to procure the wenches and negro lads, but it's impossible to get any near your terms. No green Negroes are now brought into this Province. We can purchase negroes from eighty pounds to ninety pounds, and wenches from sixty pounds to seventy pounds. If such will be acceptable, advise, and you shall have them in the spring." Sterling's inquiry about the availability of slaves in advance of founding his shop in Detroit reveals his conviction that blacks in bondage were necessary to his western venture. And at the same time that Sterling sought black slaves from New York, upstate New Yorkers were holding black as well as Indian slaves. Isabella Graham, the spouse of a British military doctor stationed at Fort Niagara, wrote in 1769 that her husband "bought me an Indian girl and has since purchased another." This meant that Isabella Graham had "another one to cloak," she wearily yet proudly explained to her parents in a letter. Graham therefore increased her clothing wish-list to include several items of "coarse" material "for each of them" and sent the list to her parents in Britain by way of a ship bound for Detroit. Lamenting the isolation promised by the impending winter weather, Graham's spirits lifted at the thought of "sending one of the Savages thru the roads to York in winter" to collect her return correspondence.
Back in Detroit, over the course of five years, James Sterling mentions several black slaves in his unpaid employ or in the employ of his trading partners. In 1761, Sterling is pleased with a new and important purchase, writing to a ship captain and business associate: "I have bought a Negro here for whom I am to give £75—he speaks French, English and a little Indian language here, seems to be a good lad and I believe will suit very well." In the same missive, Sterling noted to the captain that "your Negro man Charles" was accompanying a group to Niagara. Sterling allowed to another associate, Mr. Collbeck, that the "negro Jack" could be kept in Niagara "during the winter to take care of [Collbeck's] oxen." When a slave of Sterling's ran away, Sterling was concerned that he had been "taken up by a Frenchman." Relieved to later recover his human property, Sterling had the man "secured" by force.
James Sterling used black men like railroad cars in a pre-industrial transit system that connected sellers, buyers, and goods, and he did not hesitate to protect his investment in this human infrastructure of the fur trade. These men of African descent would carry furs to the east in warm weather, winter over with Sterling's partners who used their labor while the waterways were impassable, and then return to Detroit with goods for Sterling's shop in the springtime. Sometimes the "goods" that black men helped to move might include other enslaved people. Like the beaver bodies they transported, these men were viewed by slaver-traders as little more than fur-bearing animals.
With his talented unpaid laborers transporting wares across the waters and creating goodwill in the business circles that benefited from the borrowed use of their labor in the cold season, Sterling was able to focus on the nitty-gritty details of commercial transactions on the ground in Detroit. And so he should have intuited, perhaps, that conflict was brewing in the summer of 1762, when many of his Native trading partners began to ask for weapons. That season, Sterling took orders for "Three Thousand Weight of the best & hardest Corn'd Powder" and "all the Scalping Knives" that his distant business associates could acquire. Sterling was unable to get his hands on that much weaponry; neither did he record any sense of foreboding at the sheer volume of the requests. But one year later, Sterling would find himself in the thick of a battle that had been brewing since the British assumption of control in the Upper Country in 1760. Fighting beside trained officers of the British military, he would command the Detroit militia in Pontiac's impending war.
Pontiac's Rebellion, also known as Pontiac's Conspiracy and Pontiac's War, is one of the most dramatic and, indeed, celebrated, moments in the annals of Detroit history. It is so famous an event that in addition to the numerous books that have been written about it, pageants have been performed around it, and places (Pontiac, Michigan) as well as things (the Pontiac car and Pontiac Silverdome Stadium) named for its intrepid leader. Pontiac, the son of an Ottawa man and Ojibwe woman, was a skilled orator and warrior who sought to inspire an all-out war against the British Empire, which had spread its reach into his Great Lakes homeland. A French collaborator who had sided with that country in the French and Indian War, Pontiac aimed to gather Ottawa, Ojibwe, Huron, Seneca, Delaware, Shawnee, Miami, and French combatants—some of whom had had group rivalries in the past—to wage war against the British and undercut their newly won military and hence commercial victory in the region. Spurred by the vision of Delaware prophet Neolin, who pictured a world free of white influence in which Native sacred power could be restored, Pontiac planned his attack for months, gathering and sometimes pressuring Indian allies to join him.
For Pontiac, frustration at the shift from French to British rule swelled into irreconcilable anger. Native people in the northern regions had learned to coexist with the French, who had set about cultivating relationships since their earliest explorations. The French object in North America had traditionally been to derive wealth through the manipulation of trade as well as to convert the Indians in order to strengthen the Catholic Church. Unlike the British, who came to establish Protestant towns in New England and profit-making plantations in the South, all of which required massive tracts of land, the French focus had been on controlling trade and extracting natural resources (principally fish and beaver). This meant that French colonists did not arrive in the Upper Country with an eye toward developing sizeable family-friendly settlements. The first French forays into the Great Lakes were made by military men, Recollet and Jesuit missionaries, and traders. Detroit was in some ways an exception to the French rule in its attention to keeping family units intact (bringing officers with their wives) and practicing settled agriculture, though even Detroit was a far cry from the land-intensive intrusion of a Boston or Jamestown. Entering the North American scene with a relatively light but nonetheless self-serving footprint, the French needed to quickly build strong alliances with Native people who knew the environment and geopolitical status quo. Over several generations of the French colonial presence, some French residents and various groups of Indians had formed mutually intelligible aims, bicultural families, and shared habits of life. But the British were a different breed. Not only did they hold Native people at a greater social distance than had the French, but they also approached Indian diplomacy in markedly contrasting ways.
While French explorers, voyageurs, and traders had smartly adopted indigenous customs, intermarried with Native women, and bestowed Indian trading partners and their communities with generous gifts to establish goodwill and grease the wheels of trade, the British took a different tack. British commanders at Detroit gave far fewer gifts to the Indians, thus refusing to engage in a cultural ritual of good faith and social connection that undergirded economic alliances. British military commanders also refused to regularly meet with Native leaders, treating them with a level of disrespect that was unprecedented in the former French territory. Finally, British officials blocked the dispersal of rum to Indians and reduced the trade value of beaver skins. Frustrated with the dismissive treatment of British leaders and propelled forward in his view by Neolin's vision of a return to ancestral ways, Pontiac went on the attack, seeking to put the British down and to help restore French rule at the Great Lakes European posts.
At a series of conferences with leaders of various tribes, Pontiac made his case against the British, whom he deemed "liars" and "dogs clothed in red." Together with his allies, Pontiac adopted a bold plan: he would orchestrate a reconnaissance mission in which he and his fellows would perform a disingenuous "peace-pipe" dance for British officers inside Fort Detroit; meanwhile, others in the scouting party would surreptitiously assess the number of enemy soldiers and guns. He also called for warriors to attack British citizens wherever they found them, to strike the settlers randomly in so many places that they would be overwhelmed. Pontiac's own part in this great battle would be to lead a contingent of warriors in an assault on Detroit. His goal: to isolate the British commanders inside the fort, cut off their food supply, compel them to surrender, and push them back across the Allegheny Mountains to their former eastern posts. Pontiac expected that the French military would abet his multipronged assault, leading to a victory that would ultimately return to the French territories lost in the Seven Years' War and return to the Native tribes more agreeable trading partners.
Pontiac and his supporters planned their attack for early May of 1763, but the British commander in the fort, Major Henry Gladwin, had received a warning about the plot from a disaffected Ottawa leader. The British subsequently increased their sentries and gathered their arms, forcing Pontiac to regroup on what he had intended to be the first day of the siege. His men bided their time for a few days and then split ranks, executing a surprise attack on a family farm behind the fort as well as on residents of Hog Island (present-day Belle Isle), the Detroit River islet treated as common land where the French had allowed their pigs to graze. Leaving a trail of bodies behind on Hog Island and taking three white children captive, Pontiac and his allies pummeled the fort walls with gunfire.
It was the ninth of May. Springtime, a most beautiful season in the Great Lakes, had morphed into a time of crisis, as the fearsome smell of gunpowder in the air mixed with the heady scent of pear and apple tree blossoms. Unable to penetrate the wooden pickets of the fort, Pontiac's six or seven hundred warriors patrolled the riverbank to the east and the woods behind the settlement, seeking to block the delivery of provisions and reinforcements that would come to Detroit from the northward fur trade post of Michilimackinac or from British Canada via the river. Merchants, farmers, and those they held as slaves cowered behind the wooden gates as Native forces penned them in, laying siege to the town.
The assault on Detroit continued unabated. At the end of a failed peace meeting in the home of a French _habitant_ on May 10, Pontiac took hostage two leading British officers, Donald Campbell and George McDougall. He threatened to hold them unless Major Gladwin surrendered the fort, relinquished all arms and ammunition, and departed for the east. When Gladwin refused, Pontiac softened his offer, saying the British could take their property with them but insisting that they leave behind a certain "Negroe boy" who served as a "Valet de Chambre" to a British officer. This unnamed African American boy would be retained for Pontiac's exclusive use. Pontiac's request for a slave, as reported in the journal of Detroit merchant John Porteous, a New York trader who would soon come to work for James Sterling, as well as in the journal of Lieutenant James McDonald, who was stationed at Detroit, is a telling moment in the midst of this battle that bespeaks the entrenchment of human bondage among Europeans as well as Native people in the region. Pontiac's desire for a black boy in particular indicated that young black male slaves carried a special kind of status in the Upper Country. Though bondspeople of African descent had been circulating in the urban areas of New France since the 1600s and trickling into the rural Great Lakes by the middle 1700s, they were harder to come by than Native slaves and twice as expensive. Pontiac likely saw the boy not only as a practical asset but also as a symbol of his personal leadership status. This boy would have been war booty for the Ottawa leader, a valuable prize and a visible trophy. Gladwin did not relent, however.
Meanwhile, inside the walls of the fort, British officers used slaves at their disposal to strengthen their hand. On the first day of the siege an enslaved " _Panis_ " (Native) man formed part of a scouting party to assess whether a ship could make it past Pontiac's warriors on the river. All in the party, except for the man and a resident teenaged boy, were killed by their enemies. The unnamed Indian slave was captured by Native warriors, to be held again as a captive or traded to others. Later in June, another enslaved Native man reported to Major Gladwin that he had sighted a supply boat drawing near on the Detroit River. This information was essential for the sustenance of those within the fort. These two indigenous men are among the few enslaved Detroiters mentioned in primary accounts of the siege, but dozens of other unfree people in the town were also witnesses and victims. While Pontiac's contingent was unable to bring Detroit to its knees, neither was Gladwin able to free Detroit from the onslaught. A stalemate followed. As the prolonged assault continued, an unfree man belonging to one of the town's largest slaveholders, Mr. Beaubien, was suspected of joining Pontiac's warriors and faced arrest by the British.
By June, nearly 850 warriors were amassed beyond the walls of the fort at Detroit. Across the Great Lakes, Ottawa, Ojibwe, and Huron warriors were bringing down other British forts like so many dominoes. The fort at Sandusky, Ohio, fell, along with the fort at Miami, Ohio, and the fort up north at Michilimackinac. As word of the defeated forts traveled back to Detroit, the anxiety of the people trapped inside surely increased. Now it was summer on the strait, humid and stifling. The fortified town of Detroit sizzled inside its pickets, steaming as river water rose into vapor, adding to the thickness of tension in the air. Those trapped within the fort expected to be fallen upon at any moment by the Indians outside, even as their commander, Major Gladwin, refused to give in to Pontiac's demands. The walls of the fort had been built to keep danger out, but for weeks in the spring and summer of 1763, these barricades locked danger in, containing even those Detroiters who were accustomed to their freedoms.
Pontiac's major obstacle as the siege continued was his inability to breach the defensive schooner that Gladwin had planted on the river right alongside the town. Neither could Pontiac realize the once possible aim of starving the British into submission, as they had used the purported peace meeting in the home of a French resident as cover for collecting all of the edibles in the fort and amassed a store that could last them for weeks. The British soldiers had also cleared away trees and brush around the town, reducing cover for the Native fighters that shot their weapons into the pickets. The French military support that Pontiac hoped for never arrived, since the French commander in Illinois hesitated to violate the Treaty of Paris signed between his nation and Great Britain.
Pontiac's allied fighters withered in number as the conflict waged on with no decisive victory at Detroit. Just weeks into the siege, bands of Potawatomi and Huron warriors sought meetings with Gladwin and agreed to his terms to end their part in the conflict, damaging the strength of Pontiac's Indian alliance beyond repair. By July of 1763 merchant-militiaman James Sterling could disclose to his business partner in New York that "the Seige [sic] continues here as formerly, tho' we are not so much harassed as at the beginning, having burn'd & destroy'd all the houses, Fences, gardens & c. that were within [800] yards of the fort; not only so, but our garrison is much stronger than it was & the Enemy weaker at present, tho' there are vast numbers of the Northern Nations expected every day."
The gathered force of allied warriors, though great, was unable to overcome Fort Detroit's defenses and soon received word from the French at Illinois encouraging them to retreat. In October of 1763, Pontiac lifted the siege. That same month, James Sterling's mind turned toward vengeance. He wrote to his brother: "we will repay the white and black savages for their rascally behavior." By "white savages," Sterling referred to the small minority of French residents at Detroit who had lent active support to the warriors; by "black savages" he meant the Indians themselves, reiterating a longtime English cultural belief in the association between blackness and evil, and hinting, perhaps, at an elision between the racial categories "red" and "black" in the mind of a man whose society owned members of both groups as slaves.
Sterling's anger, wrapped in ethnocentric language, was warranted from his perspective. The war had taken a great toll on the British, lasting nearly a year and a half and costing "the lives of an estimated two thousand Anglo-American settlers and four hundred British soldiers." Out of thirteen British posts attacked between 1763 and 1765, only four remained standing at the end of Pontiac's War. Detroit, a gem in the crown of the British West, was one of them. Pontiac, for his part, was dissatisfied despite the damage he and his allies had managed to inflict on the British. After all, the British were still there. For the next two years, and to the consternation of the British, Pontiac traveled to various Native gatherings spreading his discontent and voicing the notion that war might be rekindled.
British military leaders agreed with James Sterling that vengeance should be theirs and that Indian warriors must be crushed. Major General Thomas Gage, commander of the British forces in North America at the time, ordered retaliatory assaults on tribes allied with Pontiac, even though the Huron leader, Teata, the Ottawa leader, Manitou, and the Ojibwe leader, Wasson, sought a peace with the British. After pressing surrender through military action, Colonel John Bradstreet, commander of one of the two retaliatory British armies, entered into a series of informal peace treaties with Native groups in Ohio and then in Detroit. Finally, at a meeting in Detroit in July of 1765, Pontiac himself formally relented. Yet the British would not soon forget his actions. The ultimately failed assault that a nineteenth-century Ottawa writer would later call "this great, disastrous catastrophe" had taken many lives on both sides and convinced the British that they would never be fully secure as long as they trod on indigenous ground. The response of British colonial officials, such as Superintendent of Northern Indian Affairs Sir William Johnson, was to cook up plans to "Settle and Enlarge our Frontier and in time become an over Match for them [the Indians] in the interior part of the country." With rebellion quelled, at least for the time being, Johnson hoped to populate and expand their North American empire. Multiplying the number of British settlers until the indigenous residents were outnumbered, Johnson felt, would be the only means of forestalling future threats.
As Pontiac's Rebellion stuttered to a messy end, scores of enslaved people were still being forcibly held in Detroit. They were the property of French Canadians who had built the settlement, of mixed-race French and indigenous families who controlled a large portion of the fur trade, and, increasingly, of British soldiers who had arrived after 1760 to administer the post. They were also, rarely, the property of Native traders who lived inside the fort. Detroit survived, with most of its residents free to run their own affairs under the aegis of the ruling British power, while others—a black and Indian enslaved minority—were just as trapped as they had been before the siege began.
But if Pontiac and his allied forces had ousted the British and returned French authority to western posts, would enslaved people have fared any better than they ultimately did beneath the Union Jack? By the time of Pontiac's Rebellion, 1,500 enslaved people were living and working in the territory of New France. The evidence of two hundred years of slavery in Quebec indicates that little would have improved for them had Pontiac succeeded. Like the British, the French in Canada kept, used, and sometimes abused slaves of African and indigenous ancestry. To unfree people—Indians as well as blacks—the French were enemies and captors.
Captives in Canada
The history of slavery in New France, or present-day Canada, has only been confronted in the past half century. Canada imagines itself—and is imagined by Americans—as a safe zone for blacks who fled there to escape lifelong bondage via the secret network known as the Underground Railroad. But contrary to this belief, New France was a society with slaves for close to two hundred years. French Canadian merchants, government officials, tradesmen, and farmers incorporated slavery into the workings of everyday life, depended upon the labor of slaves, and legalized their reduction of people to property.
The first African-born person held as a slave had arrived in the St. Lawrence River Valley in 1628 or 1629. A French trader based in Quebec purchased this young boy, likely from Madagascar or Guinea, from an English pirate. Nearly a century passed before more captive Africans began to trickle into the colony. Meanwhile, indigenous captives, mostly women and children, were slowly falling into the hands of the French, who received them as gifts from indigenous allies. By the 1670s, French Canadians were not only accepting slaves as presents but were purchasing Indian slaves outright on their own initiative. Members of various and often distant tribes—the Kansa, Iowa, Arkansas, Natchez, Shawnee, Cahokia, Sioux, Assiniboine, Pani, Pawnee, Fish, Ojibwe, Fox, Menominee, Mascouten, Potawatomi, Ottawa, Iroquois, Mohican, Inuit, and other groups—spanning from the Mississippi River Valley to the south, to the Missouri River at the northern plains, found themselves owned by Frenchmen via capture or sale by members of other indigenous groups.
Despite their practice of slavery, the French did not see indigenous people as a separate caste of human being marked for bondage due to racial difference. In this way, their ownership of Native slaves differed initially from their ownership of African slaves, whom they viewed as occupying a fixed inferior status that was racially derived. Neither were the French indiscriminate about the Indians they were willing to hold. They had formed close economic and political ties with some Native groups, such as the Hurons and Ottawas, and did not wish to jeopardize these relationships. But boundaries blur in the avaricious traffic in human bodies. Although French colonists intended to acquire slaves from Indian groups with whom they were in conflict (enemies) or with whom they had no connection (strangers), the number of tribes named in the long list above reveals that people from allied groups were also taken. Indigenous slaves could be challenging to hold, however, because they were often located fairly near home territory to which they might escape. This was far from the case for the smaller number of African slaves who had been transported thousands of miles from their homeland to labor in North America. With the colonies of New England serving as a persuasive example of the ways that African slave labor could be successfully employed in cold northern climes, more French Canadians began to seek access to black bodies just as eagerly as they had harvested beaver carcasses.
In 1688, leading officials in New France, including the governor, requested the king's permission to import African-descended slaves. Permission was granted and, in 1701, augmented by an authorization by Louis XIV for New France colonists "to own slaves . . . in full proprietorship." Although no slave ship actually landed in New France at the auspices of the king due to a concern about the financial viability of Africans surviving the frigid weather, a limited number of black slaves could be obtained from French territory in the Caribbean islands and, later, Louisiana, or from the British colonies as spoils of war or smuggling. In the two hundred years between 1632 and 1834, 1,443 enslaved blacks appear in French records. Indigenous slaves outnumbered blacks almost two to one in New France, reaching an estimated total of 2,700 over the time period that French Canadians owned people. Of 4,185 total slaves in the territory (some with unmarked racial categorization), 874 resided in the Great Lakes area of the present-day American Upper Midwest.
French slavery was governed by a set of rules called the Code Noir, which strove to align the practices of owning human beings with the ethics of Catholicism, France's state religion. Adopted in 1685 in the French Caribbean colonies where lucrative sugar plantations dominated, the Code Noir was adapted for use in Louisiana in 1724 and applied loosely to the northern colony of New France. The Code Noir allowed masters to physically punish slaves but discouraged excessive brutality. It discouraged owners from separating families through sale and legislated free Sundays for slaves to honor the Sabbath. In the Great Lakes, as in the Caribbean and Louisiana, slaveholders did not completely abide by the tenets of the Code Noir, which was not uniformly enforced, especially in distant settlements. But French slaveholders, who often took their Catholic faith seriously, were aware of the expectations inscribed within the code. Many had their slaves baptized. Enslaved people could be married in the church and have those unions legitimized as sacrosanct; the church also recognized "natural marriages," or informal intimate unions, between slaves. The children of slaves were baptized under the auspices of their parents' owners and assigned godparents within the church. The French practice of slavery therefore provided a small measure of legal protection for families and a vehicle for social inclusion in the form of religious participation.
Colonists in New France used the unusual term "Panis" to designate Indian slaves, a word that may have several derivations. Many Indian slaves were not originally from the Great Lakes region but instead had been captured farther west, beyond the Missouri River. Members of the western Pawnee nation made up a notable number of Indian captives around the lakes, as this group was a target of slave raids carried out by Missouri and Little Osage bands in order to produce captives to sell to French traders. In addition, Ottawas may have captured and integrated Pawnee people. The late nineteenth-century Ottawa interpreter and writer Andrew Blackbird described his own family background as being rooted in the plains. His ancestors had been taken captive by Ottawa warriors who raided as far west as the Rocky Mountains, and then had been incorporated into the tribe through adoption and intermarriage. Blackbird described these distant ancestors, known to the Ottawas as "the Undergrounds," because they built "their habitations in the ground by making holes large enough for dwelling purposes." Pawnees of the Great Plains loosely fit this description, as they lived in earth lodges built into the high bluffs of riverbeds. For these reasons, a term that sounded close to the name of the Pawnee tribe—"Panis"—came to stand in for Indian slaves as a category and a caste. What is more, a number of smaller Indian groups whose members were vulnerable to capture by Illinois raiding parties had tribal names beginning with the letters "Pan," supporting the theory put forward by historian Brett Rushforth that the partial names of a series of tribes who suffered great losses to slave raids led to the composite word "Panis."
Wide use of the term "Panis" in the eighteenth century resulted in the belief that the Indians called "Panis" represented a single nation. While we now know that the people designated as "Panis" came from a range of ethnic and tribal backgrounds, we can see, in the historical use of this flattening term, that those individuals did have something fundamental in common. They had each been reduced to a state of nonpersonhood in the eyes of their captors. Native people from various tribes reclassified as generic "Panis" now shared a key characteristic with people of African descent who were viewed by the French as natural slaves: unlike other Indians, "Panis" could be deprived of their right to freedom. Central to the significance of the catchall term "Panis," then, was the implicit notion that an Indian slave was no longer a recognized member of a specific tribe or nation. From the perspective of slaveholders, she or he had been stripped of national belonging; she or he had become a no one. The surviving records of early Detroit emphasize this erasure of group connection, as slaves denoted as "Panis" very rarely had a tribal signifier added to records that list them. Although many French colonists had close relations with free Native people and even, for a time, sought to acculturate Indians into French identities, they could nonetheless turn certain Indians into possessions with a crude linguistic act of recategorization. "Panis" came to signify a Native person detribalized, a Native person who, due to a lapse of the kind of protection that came with a recognized national status, could be treated like an African slave, the basest category of "person" in the increasingly capitalist, increasingly race-conscious transatlantic and inter-lake modern world. The magic word "Panis" transformed a Native subject into an objectified slave, a mode of linguistic transit akin to captured Africans crossing the Middle Passage.
All the Panis and Negroes
On April 13, 1709, New France's leading civil official, Intendant Jacques Raudot, issued a proclamation defining the status of slaves in that territory. "All the Panis and Negroes," Raudot announced, "who have been bought, and who shall be bought hereafter, shall be fully owned as property by those who have purchased them as their slaves." Revealing the underlying reason for this declaration, Raudot further asserted that slaves: "are needed by the inhabitants of this country for agriculture and other enterprises." In making this bare statement that was read aloud to the populations of three major cities—Quebec City, Trois-Rivières, and Montreal—Raudot clarified for all residents of New France that unfree people in that territory, both black and Indian, could be held as slaves. Slaveholders in New France need not be concerned about the legality or the morality of their actions because slaves here were property in the very same way as slaves held by masters on the plantations of the French West Indies. As Intendant Raudot stressed to the populace, inducing slaves to run away was a criminal offense in New France; this category of people—people defined as things—had no natural right to liberty.
As in New York on the British side of Lake Ontario, slavery in New France took hold mostly in urban areas. The labor required from these captive people would be domestic, commercial, and, to a certain extent, agricultural, but the scale of large farms and plantations common to the American South, and the constant field work required in that region, would not take root in the cooler climes of the St. Lawrence River, Great Lakes, and strait of Detroit. Here in this northern, water-bound, trade-oriented terrain, slaves would operate boats, package and cart goods across land and water, work at skilled tasks in shops and manufactures, organize and clean homes, make clothing and wash laundry, grow, gather and prepare foodstuffs, cook and serve meals, and tend to the brutally intimate demands of their owners. The gendered breakdown of these labors is both predictable and surprising. Men toted trade goods and worked as ship crewmen. Women worked in domestic and private spheres. And although direct evidence is evasive due to the fragmented nature of slaveholder records in Detroit, it is likely that enslaved Native women were sent to local shop-based factories to process animal skins by scraping, waterproofing, and tanning hides, since transforming furs into useful items was a skill they would have acquired in their communities of birth. Just as likely, enslaved Native women were tasked with turning those finished hides into consumer goods, especially the "frontier" style deerskin moccasins that became fashionable for white residents of Detroit as well as northeastern cities by the mid-1700s. In the Great Lakes, moccasin-making had long been the craft of women, and just as slaveholders in South Carolina took advantage of West Africans' rice growing knowledge to further elite economic interests, slaveholders in Detroit would have sought to channel indigenous women's knowledge. Many of the soft leather shoes that became an "imperial fashion" worn by French Canadian voyageurs and well-heeled Boston ladies alike probably passed through the hands of unnamed Native craftswomen held as slaves in Detroit, the center of moccasin manufacture. Enslaved men and women were essential to the economic viability of this fur trade town, as well as to the maintenance of free residents' homes, farms, and families. Escape from bondage was therefore prohibited and punished. If captive residents of greater French Canada tried to run and were unfortunate enough to be apprehended, they could be branded on the shoulder with the image of a _fleur de lys_ , the delicate floral motif that served as the symbol of imperial France.
Ships crossing the Atlantic carried African slaves to New France in limited numbers. In this part of the world considered remote to Europeans, overland trails and inland lakes served as major channels for the delivery of unfree people as pillaged indigenous communities became the most regular source of slaves for northerly French colonists through the mid-eighteenth century. These human beings, often described as bits of "flesh" even by the Native Great Lakes and eastern woodlands people who captured and traded them, were exchanged in a number of ways that carried multiple meanings. Native groups, who had long histories of taking war captives themselves, gave away captives as gifts to French trading partners or respected political leaders. They also offered slaves to "cover" or appease the deaths of loved ones in the families of valued associates. French colonists could buy slaves in trades with Indians who had acquired them through warfare, previous transactions, or, increasingly, as the European demand for slave labor grew, through slave raids. French as well as mixed-race French-Indian families could and did pass down their slaves as property to the next generation, begetting inherited wealth and advantage.
Members of numerous Great Lakes Native societies—Ottawas, Ojibwes, Potawatomies, Miamis, Foxes, and Hurons—all engaged in captive-taking practices that bled into forms of slavery. The seizure of members of other groups, the abuse of those captives, and their forced assimilation into the captor community is a documented feature of most indigenous societies on the continent. These actions on the part of Native people are further evidence that slavery was a global force, and that viewing some human beings as less than full persons was a transcultural phenomenon and widely shared human failing. At the same time that Native societies participated in a worldwide, inhumane practice of stealing lives, their captive taking included elements that differed substantially from the form of Atlantic slavery in the Caribbean and North America visited mainly upon Africans. In the eastern and Great Lakes regions, Indian people who seized captives in raids or wars with other tribes usually took one of three courses of action: ending the life of the captive through ritualized torture and murder, adopting the captive into the household of a tribal member that had lost a loved one, or trading that captive to slave-hungry Europeans.
Becoming a captive within a Native community meant losing one's life or former subjectivity; it meant murder or forcible incorporation. Being adopted, surely the outcome preferable to death for many captives, was not an easy process, however. Captive people were often forced to do heavier labor than biological family members, facing intense scrutiny and supervision. Captives could be beaten and harshly treated, and women and girls were regularly compelled to serve in the place of a wife, performing domestic and sexual duties. The captive-taking practices of Dakotas, Anishinaabeg (Ojibwes, Ottawas, Potawatomies), Foxes, Sauks, Miamis, Illinois, Crees, and other groups, in fact, favored foreign indigenous women and girls who could be integrated into families and produce new kin. Women captives were thus valued as domestic laborers, sexual consorts, and bearers of children. Since most captives retained in raids were women and children, the trauma of sexual coercion and violence was integral to their experience.
Captive people in indigenous societies were often themselves from groups that took captives in a similar fashion, and so, while gravely disadvantaged and vulnerable, they knew what was expected of them. The better they fit into their adoptive family, the more bearable things were likely to be and the swifter they would be accepted by their new tribe. Full social inclusion was possible—at a cost. Captives were required to shed previous familial and tribal ties and become members of a different community in order to have renewed lives. In contrast to black or Atlantic slavery in which slaves were kept at a social distance from their owners and intimate relations between masters and slaves, though frequent, were viewed as violations of a strict racial and class order, Native people roped captives into the family circles of captors, "toward full, if forced, assimilation." Surely the psychological adjustments of compulsory assimilation were shadowed by mourning and an abiding sense of loss. Slaves in Native societies were people ripped from their families of origin and forced to fit into foreign families in order to save their own lives.
The situation was even less certain for Indian people taken captive and then traded to Frenchmen. The French, who had been enmeshed in trade relationships with Native people for more than a century, brought multiple streams of experience together in their approach to owning slaves in New France. They possessed a long history of race-based, exclusionary African slavery in the Caribbean context (where indigenous slaves were held as well, but in significantly reduced numbers due to massive deaths from disease and hard labor); they had observed the foreign practice of incorporative slavery in Native North America, and they had forged a pattern of marrying into Indian families throughout their colonial history on the continent. Each of these strands of experience made an imprint on the layered forms of slavery the French would adopt in the Upper Country. They continued holding black slaves as a racialized group viewed as inferior and unworthy of incorporation into French families and society. They attained Native slaves from Indian allies and, in the manner of those allies, allowed for a degree of social incorporation, especially through religious ritual. And they took unfree indigenous women as sexual consorts and domestic helpmeets. While French colonists owned both black and Native people as slaves, they did so with an implicit, subtle difference. Black slaves in New France were associated with black slaves in the Caribbean, a denigrated, separate class. Native slaves in New France were part of a population that theoretically could be, and in some cases had been, economic partners, political allies, cultural brokers, and people accepted as kin. If black slaves were held at a social distance by French colonists in the North, Indian slaves were held with a dangerous degree of intimacy.
A European man with an Indian wife was a common sight in fur trade settlements of the colonial period. These couples comprised the roots of the large mixed-race families that played dominant roles in the trade well into the nineteenth century. By the mid-1700s, Frenchmen and Indian women in the Great Lakes had set in motion a pattern of forming intimate unions or marriages "in the custom of the country," as the French termed it. These unions took place in accordance with the rituals and traditions of local indigenous groups and with the consent of Native families. Often marriages formed to further trade occurred at the behest of influential Indian men—political leaders and successful hunters who sought strategic matches for their daughters that would benefit their families and bands. These marriages provided traders with critical kin relationships and links to Native communities that strengthened, and in many cases, made possible, the business of trade. Besides gaining direct lines of access to pelts procured by Indian hunters, European traders benefited greatly from their Indian wives' varied skills as translators, cultural negotiators, and keepers of homes. The union of Native-white couples also provided indigenous people with greater access to European goods and communication networks.
The majority of these mixed, customary marriages took place between Frenchmen and Native women, but British men also adopted the practice as they penetrated the North American interior. Some white men maintained more than one Indian wife and family, mirroring and perhaps taking advantage of indigenous polygamy practices; others had both a "country" wife in a Native village and a white wife, viewed as more appropriate by European officials, in a colonial town or at the post. Nevertheless, many of these cross-cultural marriages seem to have been consensual and resulted in close bonds between wives, husbands, children, and extended kinship circles. After a generation of Europeans and Native people traded and intermarried, white men shifted toward marrying mixed-race women, the daughters of those first intermarriages who were viewed as being more acculturated to "civilized" European ways of life. Despite implicit cultural biases, both white settlers and indigenous communities had something to gain from these publicly sanctioned interracial partnerships. Even though some French officials frowned on the practice from afar (and many British officials condemned it), local priests, military commanders, and political leaders supported these marriages as a means of stabilizing French-Indian relationships, of controlling illicit sexual liaisons, and of assimilating Native people into French spiritual and cultural practices.
At the ground level of cross-cultural colonial encounter, white men in the _pays d'en haut_ continually and openly sought out well-positioned indigenous women as domestic and intimate partners. But not all Indian women were destined to be wives in formalized relationships. As slave raiding increased over time and white men gained greater access to indigenous women captives who did not come from local, high-status families, these men sought unfree sex partners outside the bounds of customary trade marriages. The long history of interracial sexual intimacy in colonial New France, the symbolic association of indigenous women's bodies with the land and its resources, and the force of lust unconstrained by community norms of mutual obligation all contributed to European men's eroticized objectification of Native women. Just as they had entered a new land and extracted its living bounty, these men began to feel that they possessed an unbridled right to the bodies of Indian women, with or without the consent of Native families or the women themselves.
In New Orleans, the younger, southern sister city to Detroit, the desire of Frenchmen for Indian women was so great as to be alarming. One colonist wrote in his memoir that French Canadian men seeking "sex" would troll "among the Indian nations and satisfy their passions with the daughters of these Indians." As governor of Louisiana in the second decade of the 1700s, Detroit founder Antoine de La Mothe Cadillac raised strong concerns about illicit sexual relations stemming from the presence of enslaved Native women in the homes of Frenchmen. He and the Reverend Henri Roulleaux La Vente worried that these women were being abused in a "scandalous Concubinage," after which fathers sold away their own children. Cadillac's recommended but untenable solution was to remove temptation by selling these Indian women to the Caribbean islands or encouraging French owners to marry their Indian slaves. The problem of French liaisons with unfree indigenous women continued nonetheless, coming to constitute the majority of interracial sexual relationships.
Given their long history of sexual entanglement with Native women, Frenchmen were primed to adopt the indigenous habit of claiming captive women as substitute wives. When French explorers, traders, and colonial officials fused their own cultural practice of slaveholding with local indigenous ones, they continued this pattern of use for female slaves. They also applied the indigenous practice of incorporating slave women as marginal kin, especially through religion. It was not uncommon for French owners, both men and women, to serve as godparents to slaves in the Catholic faith. Frenchmen often accepted the infants of enslaved Panis women—possibly their own sons or daughters—as godchildren. In the French context, the Native custom of adopting captives into families had echoes in the religious ritual of masters serving as godparents to their enslaved spiritual kin. However, unlike indigenous processes of adoption that incorporated the children of captive women as actual kin with rights to freedom and full belonging, French slaveholders were willing to hold and sell the children of Native sex partners as slaves.
Sexual relationships between white men and Indian women, whether those women were enslaved or free, represented complex forms of bondage and intimacy that trapped many Native women in situations of captivity. Although Indian women owned as "concubines" experienced a degree of incorporation into French social networks, they were still essentially a class of people who could be bought and sold. Their children, like the children of black women in North America, inherited their unfree position. As the historian Kathleen DuVal has captured in her summary of this circumstance, "enslaved Indian women had more in common with their African counterparts than with free Indian women living among their own people." In the American territory claimed by France, unfree black and indigenous women shared a similar subjugated status and the expectation of lifelong servitude that they would pass on to their progeny.
Indigenous women redefined by the French as "Panis," a word that would effectively become the equivalent of "Negro," had been stolen from their home communities, sold to Europeans, and unredeemed by manumission or formal marriage. Their fate was linked to the imperial struggle over authority in the Great Lakes being waged among European empires and indigenous societies, but their fate was not the same as that of free Native people in intact tribal units who could ably negotiate the cultural "middle ground" with European interlopers. Intermarriages and intimacies between Frenchmen and Native women existed on a spectrum that blurred into sexual slavery, and it is often difficult, in evaluating existing records, to distinguish among these various relationships. Due to their ambiguous position in relation to Native groups and the pattern of French-Indian intermarriage, indigenous women may well be the most invisible population in the history of American and Canadian slavery.
Lives of Bondage
Detroit was a Catholic town dominated by a Catholic faith that saw no other religious influence until 1800, when a lone Protestant missionary arrived from distant New England. A petite cathedral built of wood and topped by a narrow belfry with a silver gilded bell, Ste. Anne's Catholic Church fronted the street named for it, facing the river near the fort's eastern gate and adjoining a burial ground where Catholics and people of Protestant heritage were interred together. This had been the first building erected in Cadillac's Fort Pontchartrain du Detroit, and it had burned or been torn down and then rebuilt four times by the 1760s. Detroit's oldest institution, one that had outlasted even the French military, Ste. Anne's served as a moral and social center, bringing people together across class status, racial groups, tribal affiliations, and nations of origin. Native people from Huron, Iroquois, Miami, Ottawa, Potawatomi, Sauk, Sauteur (Ojibwe), and Sioux communities participated in church services over the years. In the decades of British rule following Pontiac's Rebellion, even British merchants with Protestant backgrounds attended Ste. Anne's and had their slaves baptized there. For members of Detroit society seeking spiritual and interpersonal connection, this church was the core of community life.
Enslaved people in Detroit were counted among the number who moved through the physical and social space of Ste. Anne's, as their inclusion in spiritual community was a feature of bondage among the French. French slaveholders in the colonies were expected to raise their slaves in the teachings of the Catholic Church, to baptize their bondspeople and care for their souls. Slaveholders served as the godparents of their slaves or the slaves of family members and associates. And rarely, an enslaved person acted as godparent to another slave. Unfree people, like free people, attended church services and joined in the communal life of the parish. Slaveholding families tended to own just a few slaves who resided in or near the homes of their owners. Enslaved people within Detroit households therefore came to know their owners, as well as one another, intimately. Each household was tied to others through the church. Ste. Anne's connected separate domestic spaces within and beyond the walls of the fort, linking otherwise isolated enslaved people across the Detroit River archipelago. Within the yard and walls of the church, enslaved members of various households saw one another regularly, affording the chance to exchange a glance, touch a work-worn elbow, and share the personal stories of their days. And so it is in the Ste. Anne's Church register, a record book kept by priests in the second oldest diocese in the present-day United States, that the shrouded lives of people in bondage during the era of Pontiac's War emerge.
Several of Detroit's French middle-class and wealthy households contained one to two enslaved people, mostly of American indigenous ancestry and very rarely African. Ste. Anne's register mentions the births, deaths, and baptisms of eighty-two slaves in the decade of the 1760s. The largest category of these—thirty-two—are "Panis" girls and women. Eighteen are "Panis" boys and men. Fourteen are "Panis" with gender unrecorded. Three "Black" slaves are listed, along with two "Mulatto" slaves. Several enslaved people are not identified by race and sex in this record, making precise total counts difficult. One fact is clear, however: most enslaved people present in Ste. Anne's Church in this decade, and indeed prior to the year 1800, were women. The greater part of these captive women were indigenous.
At Ste. Anne's in the 1760s, most free congregants were French, one was British (the trader James Sterling), and three were Native people listed by name and tribe (Huron, Métis, Sauteuse). The French Campau (also spelled Campeau) family, whose members appear frequently in Ste. Anne records, typifies the lifestyle of early Detroit elites. The Campau line traces back to seventeenth-century Montreal, where they were, according to French Canadian historian Marcel Trudel, among the "leading" holders of human property, evidencing "an extravagant taste for slaveownership." The Campaus put down roots in Detroit in the early 1700s, when two brothers, Michael and Jacques, moved to the fort, received land grants from Cadillac, and sired an extended clan whose members became influential in Detroit society as landowners, militiamen, and civic leaders. Their progeny would, generations later, co-found the _Detroit Free Press_ newspaper, the Bank of Michigan, and Farmers and Mechanics Bank, amassing a fortune worth millions. Jacques Campau lived in a house on Ste. Anne Street, acquired land, and became a successful farmer. His son, Jacques Campau II, gained and sold still more land around the Detroit River. The Campaus may have brought enslaved people with them when they first arrived, or they may have accessed human property through contacts back in Montreal after settlement. At the age of twenty-eight, Jacques Campau owned one slave according to the 1762 French census of Detroit. Louis Campau owned three slaves that year; Simon Campau owned one; Claude Campau owned no slaves but had two paid employees. All of these men were described as economically "comfortable" in the estimation of the census taker, the French notary for the town, Robert Navarre. Three members of the Campau family (Baptiste, Michel, and Charles) who had no slaves were listed as "poor," suggesting, as would be expected, that slave ownership correlated with rising wealth. The two largest slaveholders on the 1762 census each had five slaves: Zacharias Chicoste is listed as "rich"; Claude Jean Gouen is categorized as "comfortable."
Ste. Anne Church Slavery Data, Race by Decade. Compiled by Michelle Cassidy. Ste. Anne's Church Registers, 1704–1842, Archdiocese of Detroit, available at the Bentley Historical Library, University of Michigan. Courtesy of Ste. Anne Parish (Detroit), Sacramental Parish Register (Marriage, Birth, and Death Records, 1704–1842), Archdiocese of Detroit.
Ste. Anne Church Slavery Data: Race and Gender by Decade. Compiled by Michelle Cassidy. Ste. Anne's Church Registers, 1704–1842, Archdiocese of Detroit, available at the Bentley Historical Library, University of Michigan. Courtesy of Ste. Anne Parish (Detroit), Sacramental Parish Register (Marriage, Birth, and Death Records, 1704–1842), Archdiocese of Detroit.
Ste. Anne's Church records also reveal the Campaus' active ownership of Indian slaves. In 1761 Louis Campau had his slave, Joseph Marie, child of the enslaved Susanne, baptized. In 1763 Simon Campau had his Panis slave Marie Louise baptized with Alexis Campau serving as godfather. When the enslaved infant Cacille (or Cecille) was born in 1763 to Marie Louise, a Panis slave owned by Chauvin Pere, her godparents were Nicolas Campeau and Cacille Campeau, the slave child's namesake. Large slaveholders relative to other Detroiters at the time, Cicotte and Gouin appear frequently in the church register upon the births, baptisms, or burials of their Panis slaves. Not a single child born of a Panis woman is listed as free in the record.
The registry kept by the priests at Ste. Anne's Church in a sprawling French cursive is visually intricate but lacks texture regarding the experience of enslaved people. Nonetheless, a most striking and moving aspect of an otherwise spare record is the litany of deaths of Indian slaves in their infancy or childhood, often described as "small" or "young" "Panis." The story of one enslaved woman in the priests' notations also demands to be told but resists full reconstruction because of the starkness of the record. She was an unnamed "Panis slave" doubly confined in the state of slavery and a cell of the military prison in the winter before Pontiac's siege. The reason for her incarceration went unstated, but it was within the walls of the prison house that she gave birth to a baby, Marie Joseph, with the aid of a midwife. The enslaved infant was baptized "with condition" in January of 1763. The baby had apparently been intended to go to " _Monsieur Goduel Major commandant pour le roy de Detroit_ "—the commander of the fort—but was given instead to the master gunsmith. This change in the plan of who would gain ownership rights to the infant raises questions about paternity as well as clandestine deals between men of influence. It also begs questions about the unnamed mother's imprisonment, her reaction to her and her child's lamentable situation, and her fate after release, if indeed she survived the ordeal. Had this woman been confined because she fought her owner or someone else who had taken advantage of her lack of power? Had she attempted to run away in the weeks before giving birth, realizing that her child would inherit her unfree condition? Certainly other enslaved women in the coming decades in Detroit would take such drastic measures in order to gain a slice of freedom from authoritarianism and abuse. Although we cannot identify the precise conditions of this particular indigenous woman's life, we can try to imagine the bleakness of her circumstances and the possibility that she rebelled against them.
The French Canadian Campaus, the Cicottes, the Gouins, and the master gunsmith who acquired the jailed woman's infant represented some of Detroit's earliest settlers and first slaveholders. Indeed, those categories overlapped, as colonial Detroit seems never to have been a place free from slavery. The British merchants and military men who came to Detroit in the wake of the French and Indian War also owned slaves. With greater access to African-descended bondspeople from the Atlantic coastal markets, British newcomers were more likely than French locals to have black people among their holdings. A chief example is James Sterling, the transplanted merchant from New York who first saw Detroit as a place of exile but soon learned that intermarriage combined with black slave labor was a recipe for success in that place.
In 1762, the "hurry of Business" had kept James Sterling from "having so much pleasure" in the company of the "fair sex," and he was "obliged to content [him] self with that of a Copper Hue," a reference to relations with Native women, likely enslaved. A few years later, his outlook had brightened. In 1765, he reported his marriage to Marie Angelique Cuillerier, a daughter of the slaveholder-trader Antoine Beaubien. For Sterling, this was an excellent match. A reportedly lovely and spirited young French woman who could lightly converse and gracefully dance with equal finesse, Angelique had charmed the first contingent of British officers who arrived in Detroit in 1761. But it was the sharp-eyed Irish merchant seeking his fortune in Detroit who won her hand (as well as her considerable dowry) and used that bond to further his business ventures. Sterling described his bride as "a very prudent woman and a fine scholar" who had "been raised to trade from her infancy and is generally allowed to be the best interpreter of the different Indian languages at this place." Continuing in his rhapsody, Sterling enthused: "Her family is in great esteem amongst the Indians. . . . We shall carry on trade much better and with a great deal less expense than formerly, my wife serving as interpreter and she and I myself as clerks." Besides being multilingual and skilled in the ways of trade, Angelique Cuillerier was a member of a well-connected family with close links to local Native people. She was able to bring unusual Indian items, such as fox fur muffs and beaver blankets, into the channels that her husband used for the trade of foodstuffs and other supplies. Her father, according to Sterling, was trusted by the Indians who had led the attack in Pontiac's War and would likely have been positioned as a French commander in Detroit had the rebellion against the British triumphed. And for Angelique's family, an intimate bond with a subject of Great Britain ensured their staying power after the French defeat. This was a match made in imperial fur trade heaven, where patriotic divides could fade in the face of economic opportunities.
Between their dual nationalities, similar experience in business, access to different sources for goods, and shared zeal for trade (a fact borne out in Angelique's independent control of items in her possession and use of her husband's networks to distribute them), James Sterling and Angelique Cuillerier were the perfect mid-eighteenth-century Detroit power couple. And for each of them, black slaves made up an essential part of this winning package. Sterling is the only person noted as owning black slaves in the Ste. Anne register in the 1760s; he is also one of few British residents listed at all in this early decade of church records. Sterling's human property included a black child named Marie, daughter of the black enslaved couple Babet and Emanue. On the occasion of this child's baptism, her owner was described as "Sieur Sterlin Bourgois commercent of the town." Sterling also owned Antoine, a child born to a black slave, Fébe, in 1768 (with no father named). After Pontiac's War, Sterling continued to procure and distribute black men for his use and the use of his business partners. In fact, he stated a preference for black men over white men who might be employed to do the same work of carrying heavy animal pelts over challenging portages (the miles to be crossed on dry land between waterways on a journey). In a series of letters in 1764 and 1765, Sterling complained about the poor performance of a white worker, Charles Morrison, writing that Morrison was not as good as "negroes" in transporting merchandise (in this case, a massive "eighty-five packs of peltry").
For her part in this successful slaveholding union, Angelique Cuillerier was the child of a slaveholder who probably enjoyed the services of Indian slaves before her marriage to James Sterling. She also secured "a negro wench for her own use" from John Duncan, a business partner of her husband. Angelique paid for this black woman with "the price of the peltry," a trade to Duncan, skins for skin. A black woman held in bondage would have been more than a source of domestic labor for a French elite woman like Angelique. Similarly to the black boy that Pontiac sought in the heat of conflict, such a woman symbolized the status of her owner. A living, breathing ornament that highlighted her mistress's access to exotic, costly things, a black woman in 1760s Detroit was worth her weight in furs. For black slaves were still much more difficult to acquire than Indian ones in the Great Lakes, and females of African descent were the rarest kind of human being transformed into commodities in the settlement on the strait.
Beyond serving as luxury goods for a few European elites, black women could find themselves enslaved in Detroit as a means of keeping black men in line. While French, and to some extent British, men set aside Indian women for their own self-serving sexual purposes, these slaveholders sometimes maneuvered to pair black women with black men. In one recorded example of this kind of strategic purchase of African American women, the explicitly stated reason was to placate black men being held in bondage. James Sterling reveals as much when he writes in 1764 that he has gotten hold of "2 young Negro wenches for the two big negroes whom I have employ'd . . . with the Engineer for the winter. The French are afraid to buy them without wenches for fear they should run away. Yet I have been offered a good deal more than what they cost." Sterling's words indicate not only the high value placed on black women, but also his attempt to allay the fears of French clients by providing sex partners for black male slaves who might otherwise abscond. His stated intention to artificially manufacture couples suggests the existence of more than one sexual market for bondswomen in Detroit. Indigenous women were paired with white men as sexual and domestic servants, and black women were paired with black men as sexual consorts to quell resistance.
Sterling's cynical action here has an element in common with the breeding practices of southern slaveholders who forced black women to lie with black men in order to increase the size of an enslaved population. But rather than explicitly trying to produce greater numbers of slaves through compelled procreation, Sterling is seeking to produce complacency through the formation of black pair bonds. This nuanced exploitation of black women's sexual labor in Detroit is difficult to pinpoint and verify, but trace evidence in the records of merchants like Sterling leaves a trail to follow. The letter book of Schenectady, New York–based merchants provides another example pointing to the constructed coupling of black women and men. The Phyn and Ellice Company often took purchase orders from merchants and residents in Detroit, including several for slaves. In June of 1771, the pair informed Detroit merchant John Porteous: "We have contracted with a New England Gentleman . . . for some green Negroes to be dilver[ed] here. . . . When your wench will be forwarded together with Negro Boy in case she may sometime hereafter choose a Husband we apprehend he will be useful to you or advantageous at the Sloop or you can despose [sic] of him as you find best the price £50 each." In this case, Phyn and Ellice were providing Porteous with the woman slave he had requested (again, an indication of the market for black women) and throwing a young black man in with the deal, assuming that the man would make a fitting sex partner for the woman, prove useful in boat work, and barring either outcome, be resalable in Detroit.
Although the merchants who doubled as slave traders paired black men and women for practical reasons that served their own profit motives, by forcibly arranging enslaved blacks into couples, Detroit elites provided for the formation of black nuclear families. Sometimes enslaved men and women formed ties that endured and entered the state of formal marriage recognized by the Catholic Church. Most of these enslaved couples were composed of black husbands and wives; the few interracial marriages were between black men and Native women. The pattern of these rare Afro-Indian couplings among slaves stemmed from demographic realities: larger numbers of Indian women than Indian men in the enslaved population and increasing numbers of black men in the area due to British merchants' active procurement of them. The children of these couples were labeled as "Panis" or "Negro" in church records, both terms being synonymous with "slave."
This fate of inherited slavery for mixed-race children with Indian mothers and black fathers departs from much of what we know about how indigeneity functioned for Afro-Native people in early America. In the American Northeast and the South in the late eighteenth and nineteenth centuries, having a Native American mother could be a means to freedom for black people of mixed ancestry. This is because the enslavement of Native Americans was outlawed in northeastern as well as southern colonies and states by individual laws passed between the middle and late 1700s. Holding an Indian person as a slave became illegal in most locations in the east. This did not mean that Native people previously enslaved there were not still secretly held on farms and plantations. Certainly they were, and many of these hidden American Indian bondspeople would fade into the recesses of historical consciousness. It did mean, though, that people trying to buy or sell indigenous slaves could come under scrutiny and see their claims challenged in the courts. In many cases, when enslaved individuals with Indian mothers and black fathers brought suit for their freedom in American courts, they prevailed on legal grounds tied to an assumption of the indigenous rights to liberty inheritable through the maternal line. Just as black women were seen as producing slave children nearly as a matter of course, Native American women were seen as producing free children.
But Detroit presented a starkly different context. Here in the western borderlands, Indian slavery was the norm, and the practice of owning Native slaves was sanctioned by governing authorities—the French and then British Crowns—as well as by the Church. Having a Native American mother guaranteed nothing to a mixed-race slave, except the likelihood of lifelong bondage. The situation of Marie-Marguerite, an enslaved Native woman, is a case in point. Marie-Marguerite was owned in Detroit by a mixed-race (French and Miami) woman, Marie Suzanne Richard. Marie Suzanne Richard had retained her slaves as part of her inherited estate after her husband's death in a French legal context that permitted women to own and inherit property with fewer restrictions than in British North America. Marie-Marguerite married Charles, a black man also owned by Richard. When the two had a daughter, Catherine, in 1752, the priest recorded the baby's race as "negresse," making clear that this child was to be considered a slave and drawing a visible line of differentiation between this unfree infant and her owner. This instance also shows, like the example of Angelique Sterling, that white men were not the only slaveholders in Detroit. French, mixed-race, and Native women owned slaves as well. In another case, a Miami woman, Tacumwah, who coupled with a British and then a French man in Detroit, had acquired slaves by trading rum. The Frenchman with whom she lived in the early 1770s was a Beaubien, the same family to which Angelique Sterling belonged and that owned the slave arrested by the British for suspected betrayal during Pontiac's War.
Whether held by white or Native owners, children born to enslaved Indian mothers and black fathers were in the extreme minority in Detroit and other French colonial towns. Even fewer enslaved families with both a Native father and mother existed here, and only one such family was listed in the Ste. Anne register in Detroit: Babet, Piere, and their child Catherine, Panis slaves of Charles Cicotte. This marriage pattern, or lack thereof, for indigenous women strongly suggests that white male owners were claiming sexual rights to their slaves, leaving little room for Indian women to marry enslaved men even in a society that sanctioned such unions. Frenchmen, and the British men who moved into town after them, wanted Indian women, sometimes as free wives, but more often as unfree sexual consorts. This may be why Mr. Collbeck, a British trading partner of Detroit merchant James Sterling, liked to keep the Indian women near his home in Niagara, New York, "frequently drunk." The particular value that Native women were perceived as possessing, a value of erotic and sexual potential long instantiated in the social and cultural expectations of fur trade society, coincided with their value as household laborers. In the 1760s and beyond, uncountable infants born to enslaved Native women had been conceived by white men in Detroit. Most of these babies went unclaimed by their fathers and were listed in the Ste. Anne's registry along with their mother's name, their mother's status as "Panis," and the notation that they were the progeny of an "unknown father." For sixty-nine "Panis" babies born in Detroit, the father was listed as "unknown" or not mentioned at all.
There were, of course, exceptions to the scenario in which the child of an enslaved Indian mother was also consigned to slavery. A small number of French slave-owners in colonial settlements are recorded as formally freeing Indian women in order to marry them, women with whom these men had shared beds and conceived children. The majority of Frenchmen did not bother with this formality, however, and did not bestow on their enslaved consorts the legal protections of freedom. With the turnover from French to British control, British military officers and merchants joined the slaveholding ranks in Detroit, though the cultural prohibition against sexual relations across racial lines was stronger in British colonial society than in the French settlements. Still, Englishmen pursued sexual relations with Native women, too, continuing a pattern that was all too familiar in their adopted region. The best-documented example is that of John Askin, who had braved a trip to Detroit to deliver provisions during Pontiac's siege and would later return to become one of Detroit's most prominent merchants and leather-good manufacturers.
The young John Askin had arrived in North America in 1758, hailing from a family of shopkeepers in Ireland. After building a business in Albany, New York, that chiefly provided supplies to the British army, Askin moved to the northwest fur trade post of Michilimackinac in search of new opportunities in the Upper Great Lakes. In Michilimackinac, most likely in the 1760s, he acquired a Native slave woman named Mannette from a Mr. Bourrass. Mannette was probably Ottawa from a nearby village, and her cultural knowledge and social connections along with her linguistic versatility were beneficial to Askin's trading enterprise. Askin's access to rum smoothed his relations with Native traders as did his intimate ties with this unfree Indian woman. He had three children with Mannette: John Jr., Catherine, and Madelaine, born in 1762 and 1764. Askin claimed, cared for, and educated his children with Mannette. In 1766 he freed the children's mother in a manumission letter in which he promised to "set at liberty and give full freedom unto my Panesse slave named Mannette." Askin vowed, further, that "She is a free woman at full liberty and Mistress of herself to dispose of herself as good Seemeth unto her."
Apparently, what seemed good to Mannette was cutting ties with her former owner, John Askin, even if that meant leaving their little ones behind. The children remained with Askin and his French wife from Detroit, Archange Askin, who raised them in a household served by Indian and black bondspeople. John Askin Jr. would become a trader and Catherine Askin would marry Samuel Robertson, a British employee of the Phyn and Ellice Company, whose job was to captain boats carrying furs, supplies, and, likely, slaves, in the New York–Western circuit. The children of an enslaved mother, they were now part of a mixed-race class that participated in slavery. But after Mannette's manumission, there is no trace of this Ottawa mother in Askin's correspondence; she fades into the shadows of colonial history like so many other Indian women held as slaves across the Great Lakes.
Askin's act of emancipation is a rare recorded example of such largesse among British slaveholders in Detroit. Later, John Askin would hold several more Native women as slaves and one Native woman as his ward. These women may have been vulnerable to sexual advances in a household in which their owner had bedded an Indian slave in the past. While there is no indication in the existing documents that John Askin engaged in relations with any of these women, records often fail us in the search for the experiences of slaves in Detroit. There is one thing we can know for certain: most stories of the women owned by John Askin, like most stories of slaves held in Detroit between Pontiac's Rebellion and the American Revolutionary War, did not end like Mannette's, with "full freedom."
A Dim Force
In the 1760s, Detroit was an isolated place where people lived in a concentrated area, depending upon a local exchange of goods and services for their survival. A dim force drove the growth of this linchpin port town in the Great Lakes. Slavery was integral to the workings of the settlement. Leading French and British families owned one or two slaves, usually of indigenous descent and acquired mainly through Native brokers in exchange for utilitarian items such as guns, ammunition, and blankets. Enslaved people could be found laboring in every capacity in the town—in bedrooms, in kitchens, in wheat fields, and in manufactures. And importantly, enslaved men crafted the storage containers, manned the boats, and transported the bundles that comprised the town's chief economic activity—the fur trade.
More invisible in the historical literature than even these unfree men whose labors supported the frenzy for fur, were unfree women. Most enslaved people in Detroit, as notated in the Ste. Anne's Church register, were indigenous and female. Both the practice of marrying Indian wives according to local customs and the habit of using Indian slaves for sex informed the unspoken view among male slaveholders in Detroit that indigenous women were fit for sexual-domestic roles. Free Native women with a recognized tribal or national designation, and the protections that came with this political identity, were accorded social regard in this French-Indian dominant community. Panis women, by contrast, those stripped away from their families and tribes of origin, were just as vulnerable to sale and abuse as slaves of African descent. Because Indian women could be found in a spectrum of arrangements with white men in Detroit, the lines between free Indian wife, long-term Panis concubine, and casual Panis sex slave blur in the historical record. In popular understandings of Midwestern history, Native women who were owned by Frenchmen have faded into the background behind more positive narratives of Native women who were married to them. But unfree indigenous women lived and struggled in Detroit, too, making up the largest portion of the enslaved population.
In the era of Pontiac's War, slavery in Detroit was a multidimensional, multicultural, multiracial, and malleable tradition. Traders, merchants, farmers, and priests could own people of color in this fortified French-Indian-British town where colonial laws governing slavery were inapplicable, unenforced, or undeveloped. Due to the relatively short life spans of enslaved people in New France (with an average death occurring before the twentieth birthday) most bondspeople in this period were young and Indian; a handful were black. These individuals were compelled, by the theft of their freedom, to meet the fundamental demands of privileged residents in the Detroit River region—residents who sought slaves for mobility (the movement of goods), for intimacy (the satisfaction of sexual desires), for domesticity (the maintenance of households), and for luxury (the pleasures attached to owning prestige goods). On this razor-thin edge of settled life along the strait of Detroit, scores of Indians and a smattering of Africans were held as captives by fur trade elites, and also held captive, along with their owners, by forces that were changing the course of North American history.
The War for Liberty (1774–1783)
If that Post be reduced we shall be quiet in future on our frontiers.
_—Thomas Jefferson to George Rogers Clark about Detroit, 1780_
What was going through Ann Wyley's mind when she entered and burgled the furrier shop of two of Detroit's most successful merchants? Certainly not that she and her accomplice, the Frenchman Jean Baptiste Contencineau, would escape unpunished if caught for theft. Like most British businessmen in the bustling frontier maritime town, James Abbott and Thomas Finchley, targets of the break-in, dealt in furs and imported goods. Their job was to procure skins from local hunters or middlemen and ship those pelts to purchasers in the East in exchange for supplies; they then sold or distributed manufactured items to customers and American Indian trade partners. The pair operated a shop located near a host of others along the northern bank of the Detroit River, the liquid-gold main street of colonial Fort Detroit. And in addition to co-owning the store itself, Abbott and Finchley co-owned Ann Wyley, an enslaved woman of African descent. Abbott was an Irishman by birth whose arrival in 1768 had been timed to take advantage of opportunities afforded by the British assumption of former French posts. Finchley, his business partner, is a more reclusive figure in the records of early Detroit, who appears only infrequently in conjunction with shorthand notations about the pair's firm. Both men were slaveholders, as were other members of the newly arrived British merchant elite. Between Pontiac's Rebellion and the American Revolutionary War, these men joined their French and Euro-Indian mixed-race counterparts in the capitalist enterprise of the Great Lakes skin trade, acquiring the pelts of beasts and bodies of humans to build wealth and influence. Between the waning years of the French period and the rise of the British period, the ratio of indigenous to black slaves tilted only slightly. An approximate count of the Ste. Anne's parish records indicates sixty-four Natives to five blacks in the 1760s and forty-six Natives to eight blacks in the 1770s. It would take a revolution and shifting political balance of power for numbers of enslaved blacks to substantially increase in a town defined as part of the American Northwest Territory.
Ann Wyley was among few blacks, enslaved or free, living in Detroit in the early 1770s. How the firm of Abbott & Finchley came to count her among its assets is unknown. Equally mysterious are the precise details of what took place on the night the storehouse was robbed, as the fragmented testimony of participants varied at the time, and the testimony of Ann Wyley, portrayed as the instigator by her co-conspirator, was not preserved in the record. In the spring and summer of 1774, a series of petty thefts had been taking place inside the walls of the fort, wrangling the frayed nerves and thinning the pocketbooks of resident merchants. Ann Wyley, "a negro slave" of Abbott & Finchley, Jean Contencineau, "a Canadian of humble station" in the employ of Abbott & Finchley, and Charles Landry, another laborer at the firm who worked alongside Jean packing peltry, were all suspected as perpetrators in "a system of small pilfering that had been going on for some time." The most dramatic of these crimes—the burglary at Abbott & Finchley's store apparently facilitated by an act of arson—was the final straw, the bold incident that led to a government crackdown, Ann Wyley's jailing, and Jean Contencineau's death. The violation of property rights within the heavily guarded fort unnerved the moneyed class in Detroit, and "a feeling prevailed that there could be no security until such worthless characters were adequately punished."
In this heist that set the wheels of Detroit's barebones justice system in motion, "eight pounds of beaver skins, two otter skins, and some raccoon skins, to the value of four pounds sterling" along with a handful of domestic items and "little knives" had been stolen. Of the spoils, Ann Wyley had come away with "a purse containing six guineas, the property of James Abbot . . . which purse were found on [her] person," as well as "a handkerchief, containing two pair of women's shoes and a piece of flannel."
Was Wyley making a statement of political import through her illegal action? Did she wish to adorn herself with the feminine items now in her possession, to embellish the rough apparel provided by her owners that likely marked her inferior status as a slave? Did she think she could improve her material condition by taking the goods and selling them on the illicit market? Or was there a deeply emotional element motivating her actions? Perhaps Ann had bonded with or felt indebted to her accomplice, Contencineau, who worked in the shop as a "servant," and might have been indentured (bound for a period of years) to Abbott & Finchley's firm. Perhaps Ann longed to strike a blow against her owners where she knew it would hurt the most—their commercial enterprise, the other valuable "things" they owned.
Whatever her reasons for taking the risk, Wyley, along with her accomplice, faced dire consequences for her actions. Arrested by the authorities, the duo faced indictment for "subtilly, privily [and] craftily . . . steal[ing], tak[ing], and convey[ing] away" the "goods and chattels of the said Abbot and Finchley" as well as "attempting to set fire to the house of the said Abbot and Finchley." Confined to the barracks where prisoners were kept in the fort, the unlikely pair awaited trial for nearly two years, an expanse of time during which Wyley stood at the mercy of her military jailers, much like the unnamed "Panis" slave woman who was similarly imprisoned there for reasons unknown in 1763.
In the spring of 1776 Ann Wyley and Jean Contencineau finally had their day in court, but the proceedings of that court were far from regular. The passage of the Quebec Act in 1774 had established the boundaries of British Canada and included Michigan within the legal jurisdiction of Quebec. Officials in Quebec then appointed military and civil leaders to run the distant posts. In 1775, Henry Hamilton, a captain in the British army described as "overbearing and supercilious," became lieutenant governor of Detroit. As the town's chief civil leader, Hamilton worked closely with Philip Dejean, Detroit's notary and justice of the peace since 1767, who was suspected of being "a bankrupt merchant from Montreal . . . that came west to better his fortune by leaving his debts and creditors behind." Dejean's mandate was never clearly defined by British officials in Quebec; nor were the legal rights of Detroiters in relation to local governance. But there was a sense among residents that Dejean's nebulous authority did not grant him the right to judge serious offenses or exact harsh punishments.
Lieutenant Governor Hamilton and Judge Dejean saw their roles in a different light. Operating within a gap of formal governmental oversight, they tended to settle minor disputes among residents in an ad hoc, heavy-handed, and even authoritarian manner. No regular court proceedings were held in Detroit in the transitional period between French and British rule, but Dejean did assemble a jury of twelve to hear the case of Wyley and Contencineau. Charles Landry, a third suspect in the Abbott & Finchley robbery, had escaped prosecution, having confessed to stealing "some beaver and otter skins . . . in the company of the said Jean Coutancineau." Landry was viewed as a bit player in the crime. But Ann Wyley, according to Contencineau's testimony, was the mastermind of the entire scheme. Contencineau testified that "he knew nothing whatever concerning the cash box that was in the storehouse; that he only saw the negress, Anne, who belonged to Messrs Abbott and Finchelay carry a little box into the kitchen, the day after the fire, but that he did not know what she did with it, and the instant later . . . the negress crushed the cash box with her foot and threw it into the fire." While claiming no personal responsibility for the fire or missing money, Contencineau "confessed, nevertheless, and acknowledged that he stole a beaver skin, conjointly with a man named Landry who was making packs with him for Abbott and Finchelay." Contencineau also stated that when he carried stolen items (the shoes, cloth, and handkerchief) to the house of a soldier's wife, he did so at the direction of Ann Wyley who was "afraid that her master was about to look up his trunk."
Contencineau represented himself as someone who had made a mistake in the petty pilfering of furs and knives, but who lacked the premeditation, insider knowledge, and craftiness of his black female companion. Upon further examination in a second statement to the court, Contencineau even suggested that Wyley had planned the fire, placing "some powder in a horn . . . together in a piece of cloth with a piece of tinder" and "while her master was dining" giving the kindling to Contencineau to "place it upon a piece of English cloth" in the storehouse. He stated further that "after the negress had given him the six dollars [from the cash box], the negress threw the box to him and said 'Empty it and throw it in the fire.'"
In the scant pages of testimony that have survived the centuries, Ann Wyley is only attributed two lines of speech: a directive to her accomplice to hide the evidence, and her own paraphrased testimony in which she "declared that she had given the four silver dollar to Mr Cenette, one of the paper dollars to Mr Chatelain and the other to Mr C Enfant" and that she "had given three pounds in paper to Jean Coutencineau, which said three pounds he carried to Samuel Denny" at her request. Ann Wyley, according to her testimony, was compensating Frenchmen of means with the stolen funds of her masters. Could she have been paying down debts, paying for silence, or purchasing the promise of future assistance in an even larger scheme, such as the theft of her own person from those who claimed her and her release from lifelong captivity?
Jean Contencineau's attempt to shield himself from the worst of the charges did no good. He was viewed as equally culpable with Ann Wyley. In Justice of the Peace Philip Dejean's makeshift court, "the prisoners were found guilty only of the trivial offense of stealing property of a total value of about fifty dollars and there was grave doubt whether the woman was guilty at all." The charge of arson could not be substantiated, as the jury only found circumstantial evidence to support it. The pair was therefore acquitted of the more serious of the two crimes. Nevertheless Philip Dejean determined that the penalty for theft in this case should be death, a decision approved by Lieutenant Governor Henry Hamilton. The punishment was to be carried out on the town commons (at Detroit's present-day Jefferson Avenue) on March 26, 1776.
The handwritten note scribbled by Philip Dejean on the back page of the verdict in French revealed the tenor of his thinking about this harsh decision: "You shall be hanged-hanged-hanged, and strangled until you be dead," he wrote of the pair. And then he entered more intimate words directed toward Contencineau, a fellow French Canadian and likely fellow Catholic whom Dejean addressed as "my dear brother." "You see, my dear brother," the justice penned on his notice of execution, "that it is neither the jury nor myself that has condemned you to death—it is the law that you violated. It is for domestic theft that you are now going to lose your life. According to the English laws, a domestic who steals a shilling, or the value thereof, merits death." Dejean impressed upon Contencineau, in words that may have been read aloud, that even if "bad examples" had come from the servant's own "masters," Contencineau must "understand that God and the laws will not excuse you, and say with me the Lord's Prayer and Ave Maria." Dejean intended to hold the Frenchman accountable not only to the law, but also to a higher power. As a member of the servant class, Contencineau was ordained by God to mind his place in the social hierarchy. Wyley, too, would hang for her crime as part of Dejean's final judgment, but her soul was not of interest to him, and he penned her no parting words.
Dejean's choice to punish Contencineau just as harshly as Wyley points to the quixotic character of slavery in colonial Detroit. This remote fort had nothing like the regimented racial systems of bondage found in larger and older slaveholding communities in places like South Carolina or even New York. A coherent system of laws organizing the practice of slavery did not exist and would never fully take shape in Detroit. The physical isolation and in-limbo jurisdictional quality of the western settlement, which lacked a stable, rationalized civilian government, led to a form of slavery that was fluid and even capricious until its eventual demise in the first decades of the 1800s. In this unusual instance, a white man faced the same punishment as his enslaved, black female codefendant. And the case would take an even more shocking turn when the day of reckoning arrived.
No hangman could be found to put the condemned Frenchman to death, perhaps due to the extremity of the punishment in relation to the scale of the offense. Undeterred, the justice of the peace devised an ingenious solution. He offered Ann Wyley a gruesome choice in order to avoid her own death sentence. The prisoner "was released and pardoned of the said sentenced judgment of death, by the said Philip Dejean . . . on condition that [she], the said negress, would by herself as executioner, execute and put to death, the above named John Coustantininau." Wyley consented, playing the part of hangwoman in exchange for her life, and according to one source, her freedom. If the sinister deal was solely to save her life, it may have been extended in recognition of Wyley's value to Abbott and Finchley. If the offer did indeed include a promise of freedom, it parallels another example of a French colonial practice of bribing enslaved people with the dearest reward in order to compel them to do the government's dirtiest work. In the same period in New Orleans, a black man named Louis Congo won and maintained his freedom as well as his wife's by serving as the city executioner. Ann Wyley's participation in this ghastly affair hints at the desperation of a life lived in slavery, a desperation that exploded into theft, possibly arson, and finally murder.
According to the historical record, Dejean placed the noose in Wyley's hand because no one else was willing to undertake the deed. Perhaps this is so. And just as likely, this sadistic form of retribution in which a slave was made to kill her accomplice, even an accomplice who had betrayed her in his testimony, had a secondary purpose beyond utility. Judge Dejean was no stranger to slaveholding. He had personal stakes in the practice, as evidenced by a transaction in 1777 in which a man named Thomas William had sent Philip Dejean a bill "for vending a Negro." Dejean and other Detroit slaveholders would have been familiar with the toxic effects of holding people in chains. They may well have known about the New York slave revolt of 1708 when a Native man and black woman murdered their owner's family before escaping, or about the larger New York uprising in 1712 when blacks adopted arson as a weapon. They would have worried about such aggressive tactics, the stuff of outright rebellion, being taken up by enslaved people in Detroit. Dejean explicitly fretted, too, about the "domestic" nature of this crime. While James Abbott had been contentedly enjoying his evening meal, his servant and slave had violated the sanctity of his storehouse, testing the security of the entire merchant class. Together, these offenders represented a threat of symbolic proportions—not from outside the fort walls, but from within. Dejean's harshly creative reprisal therefore served as a warning to slaves like Ann Wyley, who might see arson as a tool of self-liberation, as well as to poor whites like Contencineau, who might perceive an interest in common with enslaved people of color.
On the day that a Frenchman was publicly hanged by a black bonds-woman, poor whites and indentured servants living in Detroit could glimpse, in terror, what their fate might be if they dared collaborate with slaves. As late as the 1940s, the descendant of an old Detroit family still recalled the sting of this public rebuke, writing in a family history that: "On the day appointed the Detroit Common witnessed the degrading spectacle of the Frenchman being done to death by the slave woman." Racial categories linked to social status mattered and were monitored, even on the Great Lakes frontier, where a civil official skillfully deployed this social hierarchy to control the behavior of a class-stratified, multiracial populace.
Indigenous people fell into a gray area between the racial boxes taking shape in Detroit, categorized as Negro-like if they were enslaved (as designated by the term "Panis") but viewed as having other essential characteristics that differentiated them from blacks. Unlike individuals of African descent, Indians were members of polities in North America: politically organized groups with military might and economic influence that European imperial powers were compelled to recognize. Pontiac's Rebellion had failed to capture Forts Detroit and Pitt, but did force the British out of several western garrisons and frighten colonial authorities. In order to improve relations with restive Native groups, British military officials restored the practice of gift giving, and the British Crown passed the Royal Proclamation of 1763, which forbade colonial settlement west of the Allegheny Mountains. Because of indigenous political organization and the essential role of Native hunters and traders in the commercial fur trade market that spanned eastern North America and crossed the Atlantic, it was impossible for American Indians as a whole to be reduced to the degraded category of "slave" and hence racialized as a fixed, inferior caste.
Some Natives were being enslaved, but others were free individuals of influence. This did not mean, however, that members of the Detroit elite shied away from trying to control American Indians, even those who were free. The purpose of Fort Detroit, dating back to its founding, had been the formation of a military and mercantile post that structured the presence of indigenous people, strategically leveraging these communities as a source of furs as well as a physical barrier to the advance of European competitors. After ousting the French from their prize western post at Detroit, the British recognized, with irritation, that the Great Lakes Indians had not been conquered or displaced. They then followed the previous prescription of Detroit founder Antoine de La Mothe Cadillac, seeking to keep neighboring Indians amiable and pliable in the interest of building a trade monopoly.
So even as town leaders made an example of Wyley and Contencineau to enforce control over colored slaves and poor white servants, they also sought to exercise authority over free Native people who did regular business in town. Most Indians linked to Detroit lived in their own villages but constantly moved through the fort to engage in trade, attend religious services, and socialize with friends and family members. In the 1770s, at least eighteen free Indians attended Ste. Anne's Church, participating in marriages, baptisms, and burials. Most were identified simply as "Indian" in the priest's registry; three were described as Huron, three as métis, and one as Iroquois. These individuals would have been connected to relatives whose names were not necessarily listed when a religious event was recorded, making the estimated figure of eighteen a certain undercount. The number of free Native people involved in the church amounted to less than half of the "Panis" slaves there, whose population in the church registry of 1770–79 reached forty-six. In a fort that imposed geographical intimacy on its residents and visitors due to its diminutive size and tightly intersecting roads, indigenous people would have made up a highly visible, as well as significant, minority group.
The importance of the indigenous presence in Detroit was readily apparent in the plan and architecture of the town. Negotiating with Native people was so crucial to the security of Detroit that an Indian Council House would be constructed in 1779, long before the existence of a courthouse or school. The wooden building provided a place for military officials to woo Indian allies, for town officials to talk with Native political representatives, and for merchants to meet with Native traders; it also became the only sizeable social gathering spot beyond the austere Ste. Anne's. Trader Alexander Macomb, apparently fond of a lively night out, remarked to Lieutenant Governor Hamilton that the Indian Council House, one of few public buildings other than military structures, was "a very excellent house for haranguing as well as for dancing." Macomb's offhand remark reveals the dependence of Euro-Detroiters on the secondary, as well as primary, benefits of the "Indian trade."
Indians were essential to the mix of diverse peoples that made up Detroit. Nevertheless, church and civil officials felt anxious about having Indians so near. They balked, especially, at what they saw as the "disturbances occasioned by Indians made quarrelsome by the use of liquors." These liquors consisted mainly of brandy and rum customarily provided to Native people in diplomatic exchanges and traded to Indians by European merchants, a practice that, not coincidentally, often had the effect of bettering terms for whites. In April of 1774, the same season that Wyley and Contencineau robbed the store of Abbott & Finchley, British officials compelled Detroit merchants to limit alcohol sales to just one glass per Indian and to stock all rum in a "general" storehouse in order to prevent trouble. Major firms in the town agreed to the prohibition, including Abbott & Finchley. James Abbott then joined James Sterling, Alexander Macomb, and John Porteous to form a committee charged with penalizing Indian liquor transactions. Restrictions on alcohol consumption became just one way in which colonial officials sought to control Native freedoms.
Land Grabs in the Shadow of War
Soon after a Frenchman was hanged by the slave of James Abbott on the orders of the justice of the peace at Detroit, the Continental Congress of the American colonies proclaimed political independence. It was early July of 1776. From Philadelphia, where the Continental Congress met, to the colonial population centers of New York and Boston, news of the momentous decision to sever ties with Great Britain and throw off the mantle of King George III traveled by horseback and word of mouth. In the public houses of New York, officers of the Continental Army proceeded to "testify our joy at the happy news of Independence." When read aloud on July 9 on the order of General George Washington, the potent words of the Declaration of Independence penned by the young Virginia planter and lawyer Thomas Jefferson reverberated across the Philadelphia Commons.
While rebellious residents of the eastern colonies readied themselves to defend these words that formally commenced the American Revolutionary War, Detroit merchant William Macomb was otherwise occupied, sealing a stupendous land deal. Like Thomas Jefferson and George Washington, William Macomb was a slaveholder. Unlike these "founding fathers" of the republic, Macomb would develop his wealth on the riverbanks and islands of the Great Lakes fur trade region rather than in the agrarian South. When William Macomb and his elder brother Alexander strode across the Detroit River's largest island in the summer of 1776, they were aware of the fate of the black slave Wyley and the French servant Contencineau, and they knew something of the trouble brewing back East. New York traders Phyn and Ellice had complained to the Macomb brothers about the disruption that mounting hostilities were causing as early as June of 1775, informing them that shoes on order might not be delivered. "Such is the distressed situation of this Country that nothing can be positively promised," they wrote. "We are not allowed to send Riffles [sic] out of the Country there are not any servants to be had." The brothers were likely unaware, however, of the drastic escalation of the diplomatic impasse that led to the Americans' declaration of independence. The catastrophic impact of a burgeoning revolution had barely rippled through the western populace. Great Lakes garrisons at Detroit and Michilimackinac had seen soldiers transported to Boston via Quebec in the spring of 1775, and some of these men had been present at the Battle of Lexington. But news traveled slowly to the interior, and word of America's formally declared intention to break from Great Britain had not yet arrived.
For the Macomb brothers, the pressing matter in July of 1776 was securing the purchase of Grosse Ile, the largest among twenty-one islands in the Detroit River archipelago. In the 1770s and in the wake of increased British immigration following Pontiac's quelled rebellion, leaders of the Potawatomi, the Detroit-area indigenous group that claimed this island, had been selling several stretches of land to newly arrived residents. These transactions were technically illegal, as only the British Crown held the authority to carry out land transactions with Native people in the West. But British settlers elbowed into off-limits areas despite the Proclamation of 1763. In Detroit, a far remove from effective British political authority, even members of the military participated in and sanctioned illegitimate land exchanges. So on July 6, 1776, two days after the American Colonies declared independence, William and Alexander Macomb signed a parchment contract made of smoothed animal skin. Along with fifteen Potawatomi leaders, who entered their signatures beside exquisitely hand-drawn animal symbols representing their clans, and in the presence of two French witnesses, the brothers entered into an agreement. The contract read: "We the Chiefs and principal Leaders of Potterwatemy nation of Indians at Detroit . . . bear unto Alexander and William Macomb of Detroit, merchants . . . that messuage or Tract of Land known by the name of Grosse-Isle, and call'd in our Language Kitché Minishen or Grand Island, situate, lying, and being in the mouth of Detroit River where it empties itself into Lake Erie." No price of exchange is recorded in the document. Soon after this momentous, under-the-table purchase, Lieutenant Governor Henry Hamilton gave William Macomb permission to take possession of the island. In 1780, this vague deed would be affirmed as a "voluntary act of the chiefs of the Pottawatome Nation" by the British commander in Detroit at the time, Captain Arent Schuyler De Peyster, who would later marry into the Macomb family. In 1820, Alexander Macomb would defend himself against stories that the Macombs bought the island with "only trinkets," writing: "I had little to do on that score. We made several purchases of the Indians, which were in a manner forced on us by their importunities. Our influence with the pottawatomies was great & they were the proprietors of the lands below Detroit."
If Alexander Macomb and his future son-in-law, Arent De Peyster, protested too much in the aftermath of the Grosse Ile deal, insisting that the massive sale was the result of the Potawatomis' entreaties and therefore voluntary as well as ethical, William Macomb quietly profited from the land grab, becoming one of the wealthiest men in Detroit by the time of his death in 1796. Owning vast swaths of land as well as several slaves meant that William Macomb could lay claim to the game hunted there, harvest natural resources, extend agricultural development, and charge other residents for rent, creating capital and income streams that would allow him to do more of the same: trade goods, acquire acreage, buy slaves, and put those slaves to work on his property as caretakers, farmers, builders, transporters, and domestics.
The Macomb brothers' conduct is an exaggerated example of the mode of settlement and urban development adopted by most elite British residents in the late eighteenth-century Detroit River region. They moved to the area, imported and produced goods for the local market, processed and sold furs collected by Indian hunters, acquired tracts of Native land under specious circumstances, built homes and operated farms with slave labor, and used slaves to transport raw materials and finished goods from west to east and east to west. The most successful of these men attached themselves to a branch of official government business, principally supplying the British military or serving as Indian agents, and they used the pressure of rising white land speculation as well as wartime violability to further encroach on Native territories. In short, British subjects, who did not want for ambition, combined access to Indian land and Indian-procured furs, slave labor, and government connections to build their businesses, and with these, the town of Detroit. Like the metropolis of New York whose backstory of black slavery is now widely recognized, the great industrial and cultural center of twentieth-century Detroit had its roots in greed, graft, and forced racialized labor. Those roots crossed the cultural lines of British and French elites, whose family trees began to merge in the 1760s and '70s. Some British merchants were wise enough to marry into wealthy French families, like James Sterling, the well-positioned trader whose shop was in place before the outbreak of Pontiac's War, and like Alexander Macomb, who married Catherine Navarre, daughter of the French notary and slaveholder Robert Navarre. Within decades, the bicultural daughters of these first British residents would be attractive mates to incoming American businessmen who eyed Detroit as a space of new opportunity at the turn of the nineteenth century.
The networks and commercial ventures built by British Detroiters linked that interior hamlet to towns and cities near the eastern Great Lakes. Although Detroit was remote on the map of northern colonial settlements and surrounded by forests and Indian villages, it possessed close ties to colonial New York, which sat on Lakes Ontario and Erie. Indeed, Detroit resembled New York in situation and characteristics. Like New York City, Detroit was sculpted by waterways that moved around and through the town, forming a series of inlets and islands. Like broader New York, Detroit adopted an urban-style slavery oriented around skilled trades, manufacturing, shipping, and small-scale agriculture. Decades into the future, Detroit would follow the ambivalent and stuttering lead of New York in the development of gradual emancipation for its enslaved population. And consequentially in 1776, like New York City, Detroit was a British military and loyalist stronghold. Although they lived at "the edge of the West" and deep inside Indian territory, Detroiters were no country bumpkins as some easterners at the time liked to think. Detroit's intrinsic relationship with the people, goods, and ideas of New York was one essential way in which this fortified frontier town was "poised at the intersection of East and West, empire and frontier, core and periphery, and imperialism and localism."
The power brokers in Detroit at the outbreak of the American Revolution were cosmopolitan British traders who trafficked in slavery and misappropriated indigenous lands. They were also members of a tight-knit economic and social circle, aiding one another, intermarrying, trading goods, and exchanging the bodies of slaves. British loyalists nearly to a man, these English, Scottish, and Irish businessmen found opportunity as well as difficulty as the once distant war for independence exploded, drawing ever nearer to their Great Lakes enclave.
War Comes to the Northwest
William and Alexander Macomb were sons of the British Isles, born to Scottish parents who were living in Ireland in the late 1740s and 1750s. Their father, John Gordon Macomb, relocated the family to Albany, New York, in 1755. There the Macomb men entered the brisk business of trade. With the blessing and financial assistance of their father, the adult-aged Macomb sons moved to Detroit in 1769, where they set up shop as traders and merchants, taking advantage of their father's contacts and access to suppliers in the east. The Macomb, Edgar & Macomb mercantile company supplied British military personnel and other residents in Detroit with imported goods, plunged into the pelt trade that was Detroit's chief commercial activity, and acted as local bankers. Besides the profitable land of Grosse Ile "purchased" from Potawatomi leaders, Alexander Macomb attested: "the Ottawas & Chippewas also granted us large tracts back of the Settlement & from the River." The Macomb brothers did well for themselves despite the eventual refusal of the American Congress to affirm these latter land purchases. While Alexander would move back to New York after the Revolutionary War, William established a strip farm immediately west of Detroit's fort pickets and, later, had a large log home built on Grosse Ile.
In the summertime, William Macomb occupied the "Mansion House," his breezy island abode on Grosse Ile, with wife Sarah Jane Dring Macomb and their children. In cooler weather, the Macombs resided at their townhome on seven acres beside the fort, sending their enslaved woman, Charlotte, to manage the island house. And William Macomb found no shortage of bondspeople to task with work on his various properties. He steadily increased his slaveholdings in the 1770s, '80s, and '90s. In November of 1776, "Mr Macome," a Protestant, had a Panis male slave buried at Ste. Anne's Church. In 1788 he was paying off the price of a "negro wench" to Detroit merchant James May. Macomb would come to own scores of slaves by the time of his death in 1796, and many of these had been acquired in the tumult of the Revolutionary War era. That massive conflict disrupted stability and threw lives into disarray, providing a golden opportunity for Macomb and other prominent Detroiters to snatch up slaves, mostly African Americans from the Upper South who were forced to Detroit at the hands of British soldiers and their Native allies. Gradually, over several years between the Declaration of Independence and the Treaty of Paris that cemented the war's end in 1783, Detroit's enslaved population increased by nearly a third.
Although William Macomb was focused on acquiring land rather than fighting a war in the summer of 1776, by 1777 he and other Detroiters felt a mounting anxiety. William and Alexander Macomb's father, John Macomb, was being frightfully harassed back in Albany for his Tory allegiance. By the summer of 1777 John Macomb was fleeing the Rebels, having, as he described it in an appeal for help to the Governor of Quebec, "just time to leave his House when the Rebels enter'd and Plunder'd it of every moveable thing also every living creature & thing out of doors to a very large amount." John Macomb requested placement in Detroit as "commissary for that garrison," for which he would "Relinquish his Salary." He explained that "all his Family are now settled at Detroit [and] he wishes to live there with them." He also hoped this move would bring relief from Rebel assaults. But given the strategic position of Detroit, the brawl between American revolutionaries and British loyalists would soon extend even there.
General George Washington had firmly felt, since 1775, that the northwestern forts were key to a Continental Army victory. He had written to General Philip Schuyler (uncle of Detroiter Arent Schuyler De Peyster, who stood on the opposite side of the conflict and would marry into the Macomb clan), saying: "If you carry your arms to _Montreal_ , should not the garrison of _Niagara_ , _Detroit_ & c. be called upon to surrender, or threatened with the consequences of a refusal?" Although a Rebel attack on Quebec had failed in 1775, the prolonged conflict and a competition between the Crown and Continental Congress over the allegiance of various Native nations increased Detroiters' fears that they could be targeted. Indigenous people figured prominently in the struggle between the Rebel and British forces, with each side desperately attempting to recruit Indian allies and fretting over the damage that Native warriors could unleash. While British leaders in Detroit managed to secure the support of the Detroit Potawatomies, Ohio Shawnees, and various bands of Ojibwes, Hurons, and Ottawas, they failed to gain the assistance of Potawatomies in Wisconsin and Illinois. By July of 1778, Lieutenant Governor Hamilton in Detroit had succeeded in passing a war belt to Shawnee, Ottawa, Mingoe, Wyandot, Potawatomi, Delaware, Mohawk, and Miami representatives, cementing an alliance that greatly distressed the Continental Congress.
With important Native allies in place, British military officials sought to shore up Detroit's defenses as well as prepare the way for offensive action using the fort as a staging ground. The British concentrated strength and strategy in Detroit, moving personnel to the settlement from New York and making Detroit the center of the western theater of war. Captain Richard Lernoult, reassigned from Fort Niagara in 1776, would oversee the building of a substantial new fort in Detroit located on higher ground behind the dwellings and mercantile shops rather than near the riverbank. Lernoult placed responsibility for the details of construction in the hands of his second-in-command, Captain Henry Bird, who had been transferred from Niagara in 1778. Bird served as the engineer for the new fortification, a star-shaped structure named Fort Lernoult, "which dominated the town of Detroit for almost half a century" (and is marked today by a plaque at Fort and Shelby Streets in downtown Detroit).
Meanwhile, the threat of Rebel attack grew, as Virginia militiaman George Rogers Clark launched an aggressive plan approved by Virginia Governor Patrick Henry to strike at the British in the western interior. Clark's advance into the West was spurred by Thomas Jefferson, who held grave concerns about the fort at Detroit. Jefferson saw Detroit as a pocket of strength that would facilitate Great Britain's ability to maintain Indian allies and attack American settlements in the East and South. "It becomes necessary that we aim the first stroke in the western country and throw the enemy under the embarrassments of a defensive war," Jefferson wrote to Clark on Christmas Day of 1780. "We have therefore determined that an expedition shall be undertaken under your command into the hostile country beyond the Ohio, the principal object of which is to be the reduction of the British post at Detroit." According to Jefferson's instructions, Clark and his men should be ready "at the Falls of Ohio by the 15 of March," when "the breaking up of the ice" on the Wabash River and nearby lakes would allow for water navigation. And Jefferson had more than military strategy in mind when he considered Detroit. He was also thinking forward about financial gains that America would reap. If Captain Clark could successfully capture the post at Detroit, Jefferson wrote, "we shall be at leisure to turn our whole force to the rescue of our eastern Country from subjugation, we shall divert through our own Country a branch of commerce which European States have thought worthy of the most important struggles and sacrifices." But this would depend on the Indians, to whom Jefferson told Clark to "hold out either fear or friendship as their disposition and your actual situation may render most expedient." America, Jefferson imagined, could control the posts of the profitable western fur trade, displacing the British, who had displaced the French only decades prior.
Commander Clark partly succeeded in his invasion of the western front, taking control of former French towns in eastern Illinois including Kaskaskia, which had a large intermarried Native-French population, and Cahokia (where visitors today can tour a reconstructed indigenous Mississippian village). While holding control of the Illinois posts, Clark issued a Christmas Eve statement aimed directly at black and Native slaves. This population, Clark opined in his proclamation of December 24, 1778, had "too great a liberty . . . that prevents them from accomplishing the different pieces of work in which their masters employ them." Clark stated that the mostly French slaveholders of Illinois had "begged" for help, as their slaves' lack of productivity was "causing a total loss of this colony." He intended to crack down on such license by prohibiting alcohol sales to "red and black slaves" and by disallowing "any red and black slaves" from renting private homes or public buildings in which they might gather for "dancing, feasting, or holding nocturnal assemblies." In order to prevent robberies, he planned to forbid "red and black slaves" from leaving their masters' homes after curfew without permission. He would also prohibit them from trading, selling, or buying items such as wood and pigs in exchanges with free residents without a master's permission. Clark's dictate included an enforcement measure, to "enjoin all captains, officers of the militia, and other individuals to enforce the execution of the present proclamation, and all white men to arrest the red or black slaves whom they shall meet in the streets of each village."
George Rogers Clark's proclamation, a wartime slave code, reveals the extent to which enslaved people of Illinois, a Great Lakes area more connected to the South than was Detroit, were biracial in ways similar to Detroit's unfree population. While indicting enslaved people for practicing "disorders, abuses, and brigandage," Clark repeatedly emphasized their color as "red and black." He also called for "white men" in the towns to help police this unruly colored population. Importantly, Clark was highlighting race in a way that had not been so clearly defined in the French and British periods of holding "Panis" slaves. In the eyes of this Virginian, there were categorical differences between "reds and blacks" versus "whites." Indigenous people had been reduced to a color category and thrown in with African Americans, which occluded the tribal specificity of Native backgrounds. Even the French term "Panis" that flattened some Indian people into one subjugated group had been derived from a series of indigenous tribal names (such as Pawnee) and recognized an Indianness—albeit an unfree Indianness, that was not yet reduced to purportedly biological difference. Clark, a southern military man who had penetrated the Great Lakes at a time when "only a handful of American soldiers and settlers" had ever been there, focused on skin color as integral to caste. In his detailed proclamation we can glimpse the beginnings of the American racialization of Native people as "red" in this region, and the yoking together of redness and blackness as inferior states of being. On the cusp of the nineteenth century in the western interior, Americans were already exaggerating these fixed understandings of red, black, and white racial difference.
Captain Clark saw "red and black slaves" as a group gone out of control, but his formal attempt to manage them revealed their own self-actualization, their social ties to one another, and their ability to negotiate with white residents even within a society that held slaves. If Clark had to pass a code prohibiting trade, space rentals, dancing, theft, and evening strolls around town, enslaved people must have been engaging in these activities and finding the wherewithal to gain bargaining power. They were turning to their advantage the needs of white settlers in an isolated environment where slaves were harder to come by and labor was dearly sought. Although Commander Clark stated that enslaved people in Illinois had been fomenting "disorders" "of so long duration," it is probable that they, like enslaved black people in the eastern states, had seized upon the war as an opening for increased disobedience, recalcitrance, and escape. Clark never took the Michigan forts during his campaigns, and so we have no similar record of what he might have witnessed among the unfree population in Detroit. It is possible, though, that enslaved people in that town also used wartime disruption as an opening to push for a greater scope of action.
While George Rogers Clark proved that he could march his men through the dense western territory, British military commanders in Detroit anxiously anticipated a Rebel advance further north. To stave off an attack by the Continental Army and weaken "a wedge of colonial settlement thrust into the heart of Indian America, Captain Henry Bird led expeditions deep into Kentucky." Marching with 150 soldiers and volunteers, hundreds of indigenous allies, and forty-three men charged with carrying supplies and armaments, Bird set out from Detroit in May of 1780, heading for Ohio. The soldiers, most of whom hailed from French families, were being paid by none other than the Macomb brothers, whose company, Macomb, Edgar & Macomb, held the government contract for fiscal agent to the British military. The number of men counted in the supply chain convoy most likely included enslaved blacks. By the time Bird and his contingent reached Kentucky, they comprised a force of one thousand men, large enough to crush the rural settlements of Ruddle's Station and Martin's Fort. And this they did, destroying homes, seizing booty, and taking more than three hundred prisoners.
Bird would write to his superior officer in Detroit, Major De Peyster, that the Indians were the ones responsible for cruelty in excess that had occurred during these raids. While Bird had "entreated every Indian officer that appeared to have Influence among the Savages, to pursuade [sic] them not to engage with the Fort until the guns were up—fearing if any were killed it might exasperate the Indians & make them commit cruelities when the Rebels surrendered," he claimed that he could not control "the Savages" who "tore the poor children from their mothers Breasts, killed a wounded man and every one of the cattle, leaving the whole to stink." Nevertheless, Bird and his men, as well as their besmirched Indian allies, stood to gain from these attacks in the form of prisoners and plunder. Bird wrote of the grueling journey back to Detroit: "I marched the poor women & children 20 miles in one day over very high mountains, frightening them with frequent alarms to push forward, in short, Sir, by water & land we came with our cannon & c 90 miles in 4 days." Although neither Bird nor the other officers mentioned enslaved blacks among the prisoners, several were seized in Kentucky and claimed by these men, as well as by Native combatants.
Bird acquired "the Wench Esther" at Martin's Fort "whereby the Inhabitants and Defenders agreed to deliver up their Blacks and moveables to the Indians as their property, on condition that their persons should be safely conducted to Detroit . . . the said Esther became my Property by consent and permission of the chiefs." Here, as in his earlier report on the raids, Bird disassociates himself from Indian actions that might be viewed as uncivilized. It was not Bird who took this woman in his account of events; rather, it was the Indians, who then bestowed her on Bird, in all likelihood, to strengthen that alliance. Perhaps Bird was aware of the Rebels' penchant to smear British soldiers by describing them as virtual "savages" and used rhetorical distance to protect his reputation. Certainly by 1780, Detroit officials such as Lieutenant Governor Henry Hamilton had come under special attack by American illustrators and writers, charged with barbarity and with accepting the scalps of colonists from bloodthirsty Indians.
The Americans as well as the British positioned Indians as scapegoats, seizing on cultural practices as well as skin color as markers of difference increasingly defined as race-based. While disavowing the Indian allies that were so crucial to his campaign, Captain Henry Bird personally profited from them. He soon turned Esther, the slave he had acquired during a Kentucky assault, into human capital. And by the time Bird sold Esther in 1784, she had borne a son to an unnamed father. Bird decided, as recorded in the deed of sale, to "Make over and give way my right and Property in the said Wench and her male child to William Lee in consideration of his having cleared for me Sixteen Acres of Land." William Lee was a free black man, which raises uncomfortable questions about his purchase of Esther. Was Lee planning to treat Esther as valuable exchange commodity just as Bird had done, or was Lee seeking to help Esther? Perhaps William Lee was a relative or lover of Esther's and sought to secure her freedom by trading his labor. We can only hope that her situation improved, as Esther's documentary trail ends here, with the transfer of herself and child to William Lee. But the cleared land she was traded for, the land that Captain Henry Bird sought, has a traceable future in the record. The parcel would later become part of the ground upon which the defeated British military built a stronghold in their remaining Canadian territory: the town of Amherstberg, home to Fort Malden. In this transaction in which the future of a woman and her child hung in the balance, the value of slaves, as well as land, was paramount to British settlement. Each form of property reinforced and enhanced the other, as slaves were used as capital to acquire land and then to make that land habitable and profitable.
Pathways to Wartime Detroit
When Henry Bird and his compatriots returned to Detroit in 1780, they dragged along "the largest body of people ever gathered in the wilderness of Kentucky . . . about 1,200 of these consisting of the invading force, and about 470 miserable prisoners, loaded down with household plunder from their own cabin homes." Many of these captives, like Esther, were enslaved. Prisoner Agnes LaForce owned thirteen slaves seized by the British and their Native allies during the raids. After having been relocated to Montreal, LaForce, who it turned out was a loyalist from a prominent Virginia family, enlisted the aid of Sir Frederick Haldimand, governor and commander in chief of Quebec, Canada, to recover her slaves. "On the 25th of June last year," she wrote in her appeal, "your petitioner together [with] her five children and thirteen negro slaves belonging to her, were disturbed in their (as they thought) safe retirement by a party of Soldiers and Indians of his Majesty, and were by them taken Prisoners and carried to Detroit where on their arrival said negro slaves were sold and disposed of without your petitioner's consent or receiving any benefit thereby to her great detriment said slaves being her only resource she had and her only property in this country." Despite the governor's effort on her behalf, the petitioner did not recover her slaves, who constituted a valuable infusion into Detroit's labor force. Agnes LaForce's African American property included Scipio, Tim, Ishener, Stephen, Joseph, Keggy (Kijah), Job, Hannah, and Candis—now in possession of French traders, British officers, and Indian interpreters in Detroit—as well as Bess (Betty), Grace, Rachel, and Patrick—now in possession of Indians. Joseph, the son of Bess, and his sister Keggy, were held by Captain Matthew Elliott, who would soon grow rich on such acquisitions. Job, the son of Hannah, fell to Jacques Duperon Baby, one of Detroit's most successful French traders and an Indian interpreter for the military. These black captives joined a Detroit population swelling from an influx of American prisoners (such as Daniel Boone, the famed Kentucky frontiersman, and Jean Baptiste Pointe du Sable, the successful black trader who had married a Potawatomi woman named Kitihawa and became the first non-Native settler of Chicago), as well as many more black southern slaves whose names would never be recorded, and Native refugees from villages devastated by Rebel attacks.
Just as captives, slaves, and exiles were crowding into Fort Detroit, two high-ranking officials were fleeing. Justice of the Peace Philip Dejean and Lieutenant Governor Henry Hamilton saw their past deeds catch up to them. The pair had lost favor by meting out harsh punishments to residents. Their authoritarian bent had irked influential Detroit merchants, like James Sterling and William Macomb, who served as witnesses to a Montreal grand jury that indicted Dejean and Hamilton for "divers unjust and illegal, tyrannical and felonious acts, and things contrary to good government and to the safety of his Majesty's liege subjects." The protest may have begun with an anonymous letter, likely penned by James Sterling, in September of 1777. The letter called Hamilton "cruel and tyrannical" and expressed "how unhappy we are under his government." The complainant then listed among his grievances "the cruel manner in which he [Hamilton] treated Mr. Jonas Schindler, silversmith" as well as the appointment of "a certain Philip DeJean." With Hamilton's approval, Dejean had taken out an "Advertisement" in 1777 announcing that German silversmith James (or Jonas) Schindler had been imprisoned in the garrison and would be driven out "with infamy and sent in the country below" for practicing without an apprenticeship. Dejean had, further, according to the whistle-blower, "passed sentence of death" upon a furrier named Joseph Hecker, accused of killing his brother-in-law in a "quarrel," and "condemned and hanged, also, Jean Contancinau, a Canadian, for having stolen some money &c. from his master, and being concerned with a Negro wench in attempting to set fire to his master's house." While the writer allowed about the servant and slave, that "these criminals deserved death," he angrily queried: "but how dared Lieutenant-governor Hamilton, and an infamous Judge of his own making, take upon them to try them, and execute them without authority?" Even loyalist Detroiters seem to have caught the revolutionary zeal that led them to question undue assumptions of power.
Amidst the turmoil of war, Dejean and Hamilton chose to run rather than face questioning in Quebec. They used the conflict as cover to escape, eluding officials in 1778 by marching out with British troops traveling to Vincennes, Indiana, to retake Fort Sackville from the American army. It was there, in 1779, that Hamilton, caricatured by Rebels with the scathing epithet "the hair-buyer general" for purchasing American scalps, was captured. Captain George Rogers Clark marched him toward Williamsburg, Virginia, where Hamilton, a man who had overseen the jailing of Detroiters, would take his turn as prisoner.
Detroit was tense and full to bursting by 1782, when the enslaved population had increased to 180 souls, when desperate, hungry indigenous people pressed into town seeking assistance and shelter, and when Native military allies came to receive dramatically increased quantities of British gifts, including alcohol. At this moment, slaves of color and free Indians shared a slice of experience, all having been driven to Detroit by the chaos of combat. Native refugees did not always find a warm reception in Detroit. Put off by the expectation that they would support displaced Indians, even though those nations were their allies in battle, military officials sent Native men to attack southern settlements as a means of reducing population pressure in the fort. These attacks led to the capture of slaves from the South, and the vicious cycle of violence, captivity, and disruption continued.
During a period of intense growth born of upheaval, trader John Macomb joined his sons, Alexander and William, in Detroit. He had not been able to secure the commissary post that he had requested as a means of escaping Rebel assaults in New York. Nevertheless, he worked to advance his sons' endeavors throughout the war. Trader John Askin also saw wartime Detroit as a refuge. In 1778, he had suffered the indignity of being fired as deputy commissary at Fort Michilimackinac, for "dispens[ing] the King's stores too loosely." Under Askin's watch, quantities of rum, flour, pork, and butter had come up short, raising the suspicion of his boss, the newly appointed (since 1775) superintendent and lieutenant governor of Michilimackinac, Patrick Sinclair. Sinclair had replaced Askin with local physician David Mitchell, who would later be a supplier of slaves to Detroit, since the role of fort commissary in the Great Lakes came with a secondary, implicit duty: the role of slave trader. Just as historical research on slave traders in the South has found that, unlike the popular stereotype of uncouth and outcast brokers popularized in works like Harriet Beecher Stowe's _Uncle Tom's Cabin_ , these men had close ties with the planter class and often became planters themselves, in the Great Lakes, slave-dealing was not a marginal or socially sullied enterprise. Well-positioned fort officials engaged in the practice, and supplying customers with slaves became part and parcel of supplying them with wheat, rum, and other necessities.
As professional tensions about the distribution of military wares in Michilimackinac grew, John Askin cast his eyes south to Detroit. He was deterred, though, by the hostilities between Great Britain and the colonies, writing in 1778: "I have changed my plann of settling at Detroit untill the war is over, indeed in the present Situation of affairs, it's hard to undertake anything." Moving to Detroit, giving up his farm, and transferring his fleet of trading boats seemed a gamble to Askin, but so did remaining in Michilimackinac, where "everything [was] so scarce and so high-priced" and where he had lost his government position. Disgraced and financially weakened, Askin decided he could not wait out the war after all. He relocated his family and slaves to the hometown of his wife, the French Detroiter Marie Archange Barthe Askin. Archange Askin was a Barthe on her father's side and a Campau on her mother's side, and thus descended from one of Detroit's oldest slaveholding families. Due to the influence of his in-laws, Askin acquired a choice piece of land east of the fort pickets in 1780. This ribbon farm, described as Lot 1 "above the fort" in a 1765 survey of Detroit, had been in the possession of the Barthe family prior to the war. Askin also relied on the help of his friends, like Commander Arent De Peyster, who vouched for Askin's character, and James Sterling, who had been Askin's local agent on the ground in Detroit during Askin's Michilimackinac days. Gradually, Askin rebuilt his trade and mercantile business, as well as his thriving farm, with the essential aid of key local contacts and highly skilled slaves.
Back at Fort Michilimackinac in the 1760s and 1770s, Askin had acquired a handful of African and indigenous people whom he held as property. The Native domestic, Charlotte, cooked and served in the house. Askin's possessions also included two adroit black men, Pompey and Jupiter Wendell, whom Askin had purchased from Abraham Douw of Albany in 1775 for "the Sum of One Hundred & Thirty five Pounds Lawfull Money of the Province of New York." Jupiter Wendell fashioned barrels, an essential task in an economy oriented around the storage and shipping of goods, and he also labored as a maritime crewman. Pompey was a skilled sailor who operated Askin's trading vessels. A man named Toon, whose race was not identified in Askin's records, also worked Askin's ships and lost his life doing so, as Toon "was Drowned out of a small canoe coming from the Vessell" while laboring on the lakes. These ships on which Jupiter and Pompey drudged, and on which Toon had died, skimmed the Great Lakes and interconnected rivers, moving goods from Michilimackinac, north to Sault Ste. Marie, northwest to Grand Portage, and southeast to Detroit, where military Commander Arent De Peyster was a regular customer.
John Askin was fastidious about satisfying those he supplied, holding the view that: "We must never disappoint people in the matter of shipping goods." This is why enslaved men with construction and transportation skills were essential to Askin's enterprise. Pompey was especially valuable, and Askin at times could not "do without him," preferring to hold Pompey in reserve for vital tasks while finding others to fill Pompey's shoes for certain outings. When Pompey sailed Askin's ships, he did so with a multiracial crew. One of Askin's employees, referred to as "the Indian," was a free Native sailor, "a good man," according to Askin, "if one could only understand what he says"; another crewman, Mr. McDonald, was a white employee, "somewhat overbearing," but kept on by Askin due to a wartime labor shortage. Askin supplied all of the men with rum during these trading trips "as an incentive to good work besides keeping them from helping themselves from the cargo." However, "Pomp," as Askin called him, only received "half that quantity," a lesser amount than the free white crewmen on the boat. Pompey was crucial to Askin's outfit, but still a slave, entitled to neither his freedom nor equal rations.
During his time as commissary at Fort Michilimackinac, John Askin had done double duty as a slave broker. In 1778, he informed Jean Baptiste Barthe of Sault Ste. Marie: "I sold your panis to Lavoine for 750 livres. He is too stupid to make a sailor or to be any good whatever." A month before he so crudely sold this man using language that may hint at a burgeoning racialization of "Panis" Indians as unintelligent, Askin also sought to procure young Native female slaves. He wrote at the end of a missive to Mr. Beausoleil in which he had already addressed the need to "divide the merchandise equally" among merchants and reported the delay of a shipment of "liquor and provisions" from Detroit: "I shall need two pretty panis girls of from 9 to 16 years of age. Please speak to these gentlemen to get them for me." The attention paid to the girls' youth and appearance in this order suggests their intended purpose for household ornamentation and eventual sexual service in an eroticized gutter of the Great Lakes slave market. John Askin himself had kept an enslaved Indian woman, Mannette, as a sexual object before freeing her in 1766. These "panis girls" may have been sought by Askin for undisclosed personal reasons, or through him for local male associates with illicit designs on the victims of this trade. The direct reference here to physically appealing Native girls stands alone in the extant Detroit records. However, we can read into the silences in this regional history a pattern that has been confirmed in the southern states. In the U.S. South, white men developed an extremely profitable "fancy trade" in which African American women, most often of mixed-race ancestry, were sought for sexual slavery. Marketed at exorbitant prices, these women referred to as "fancy girls" or "fancy maids," were sexually abused by slave dealers in slave pens, markets and prisons along trade routes, as well as by a string of buyers. While we do not have a record as explicit in its ugliness as that which exists in the South, this particular order for young girls in Askin's letter whispers of unseemly ends, especially when viewed in the context of the numerous Native women who were bearing babies to unknown fathers in Detroit. We have now come to recognize the horrendous trials and compromised survival strategies of "fancy girls" in the southern slaveocracy. On the shores of interior lakes and rivers of the West, women sold as "pretty panis" likely suffered similar fates. And in the Great Lakes, as in the South, protected white women benefited from wealth derived from the sale of "pretty panis." In the same month that John Askin was ordering up Indian girls to satisfy himself or his clients, he was also ordering twelve pairs of fancy shoes in the "French fashion" for his French Canadian wife. But the reality was not so simple in its color coordination; women of Native descent could also be members of the slaveholding class. While attending to his white wife's specialty footwear, Askin also ordered in from Montreal a wedding gown of "light blue Sattin" in "the french fashion" for his daughter, whom he affectionately called Kitty. Kitty was a girl of mixed Euro-Native parentage and herself the daughter of an Indian slave. She nevertheless luxuriated in the lifestyle generated by the sale of other indigenous girls, whose impending sexual subjugation allowed her to enjoy a proper continental wedding.
In another transaction that year, Askin attempted to protect one Native slave at the expense of another whom he deemed less valuable. Askin informed Charles Patterson that an Indian boy in whom Patterson should have an interest was in the possession of Ottawas. This boy was Patterson's son conceived with a Panis mother. Askin, who had claimed and cared for his own children from an Indian slave, including the favored Kitty, wrote in rebuke to his friend: "there is a Boy here who was sold to the Ottawas, that every body but yourself says is yours, he suffered much [,] poor child [,] with them. I have at length been able to get him from them on promise of giving an Indian Woman Slave in his Stead—he's at your service if you want him, if not I shall take good care of him untill he is able to earn his Bread without Assistance." In concern for this mixed-race child, Askin got the boy back by trading an "Indian Woman Slave" for him, proving again the vulnerability of Native women in the Great Lakes slave market. One wonders if this unfortunate woman was the rescued boy's own mother. John Askin's letters reveal nothing of her identity. This indigenous enslaved woman, a member of a class of people whose bodies were "routinely violated," also became disposable in the historical record.
Patrick McNiff, _A Plan of the Settlements at Detroit and Its Vicinity from River Rouge Upwards to Point au Ginglet on Lake St. Clair_ , 1796. Courtesy of the Clements Library, University of Michigan. This map depicts French-style ribbon farms as strips along the river and individual farmhouses as squares on the opposite bank. The farms of wealthy slaveholders William Macomb and John Askin, as well as members of the Campau family, are prominently located near the fort.
At Fort Michilimackinac, John Askin built his wealth by diversifying his interests: serving as a commissary on the payroll of the Crown (while allegedly misappropriating military provisions); managing the infusion of Indian furs from the privileged vantage point of his government position; securing land and operating a farm; acquiring boats for the shipment of goods; and using, selling, and placing slaves to strengthen trade and satisfy desires. He would seek to reproduce this winning pattern in his new home at Fort Detroit, which he made with his wife Archange and their multiracial household of young adult Anglo-Ottawa children (the progeny of Askin and his former slave, Mannette), Anglo-French children, and black and Indian bondspeople. John Askin settled near William and Sarah Macomb, whose farm was located on equally prized riverfront property immediately west of the fort.
The Macombs and the Askins, who would become business associates and family friends, were transplanted Detroiters in the opening years of the American Revolution. Also new to Detroit, but not of their own volition, were Protestant missionaries of the Moravian Church who had run afoul of the British authorities. Accused of harboring an allegiance for the Rebels despite a profession of pacifistic neutrality, Moravian ministers David Zeisberger, John Heckewelder, and others stationed at the church's Ohio missions were captured by pro-British Native warriors in 1781. In 1782, the ministers were ordered to appear in Detroit on suspicion of "sympathy and complicity with the American cause." And indeed, the ultra-observant Moravians _had_ been operating as pseudo-spies, passing along messages to Rebel leaders about intended attacks on a nearby Ohio fort. This may have been why the Moravian's "taciturn" leader in the region, Reverend David Zeisberger, expressed relief when Native combatants burned mission diaries and letters, confessing he was "glad that they fell into the flames and not into strange hands." While their writings escaped capture, the Moravians themselves did not. A forced relocation to Detroit swiftly followed the assault on their missions.
The Moravian Church, which was founded in Moravia, Central Europe, in the seventeenth century and retained a strong German cultural heritage, had its northern American headquarters in Bethlehem, Pennsylvania. A fervent commitment to evangelism had led Moravians to carry the word of their faith into American Indian communities in the West and Southeast in the late 1700s and early 1800s. It is from Pennsylvania and in service of this cause that the Reverend David Zeisberger had set out as the lead minister on a proselytizing expedition to the Ohio country, once depending on an "old Mulatto" who had lived with Shawnees for twenty years "to translate for them." The Moravians made successful forays into Delaware and Shawnee country and saw their Ohio missions enlarged by Native converts who formed a string of small Christian Indian towns. Pro-British forces ransacked these settlements as the Moravian leaders were seized.
On the arduous march from central Ohio to southern Michigan, Reverend Zeisberger described trudging through "deep swamps and troublesome waters" and passing by a constant stream of people in motion: "a multitude of Indians of various nations, who were all bringing from Detroit horse loads of wares and gifts." These were individuals who had spent time in Detroit, trading goods and receiving presents from British officers as tokens of goodwill meant to secure economic and military alliances. When the Moravians finally reached "the city" and saw "the whole country round about, on both sides [of] the river . . . about a mile wide," they had passed through a territory made wild by the vagaries of a natural water-rich environment as well as by the vicissitudes of an unpredictable war. The Moravians had likewise passed through lands inhabited by indigenous people whose villages and trade routes surrounded Detroit from as near as the Detroit River to the southern reaches of Ohio and into the Cherokee territory of the Southeast. The scene was similar far north of Detroit where Fort Michilimackinac was situated and far west of the city at the southeastern shores of Lake Michigan: Native people and Native lands encompassed Detroit, a center for distributing goods, passing information, and crafting wartime strategy that pulled in people of various colors, cultures, and creeds.
At Fort Detroit, Commander Arent De Peyster summoned Reverend Zeisberger and members of his congregation, including Delaware Christians, for questioning. He released the group soon thereafter, apparently convinced of their innocence, but ordered them back to Detroit within a matter of months to hedge his bet. While this subset of the Ohio Moravians was being held captive at the fort, Native converts to the faith back in Ohio faced a horrible fate. In March of 1782, American militiamen from Pennsylvania had attacked two Delaware villages at Salem and Gnadenhütten, taking the lives of nearly one hundred unarmed Indian Moravians in a senseless massacre. Heartbroken by this crime perpetrated by Americans that they had once secretly assisted, the Moravians could do nothing. They stood at the mercy of the British commander at Detroit, who treated them well, according to Zeisberger, but would not let them leave the area. With their remaining missionaries and a smattering of Indian followers, the Moravians moved to the outskirts of Detroit by order of the British, who wished to keep them under surveillance and had secured a parcel of land from a band of Ojibwes on which the Moravians could reside.
Captives of the power-center at Detroit and refugees from the western theater of war, the Moravians established a mission and farm on the Huron River (now the Clinton River), twenty miles northeast of Detroit near the edge of Lake St. Clair. They resumed their longtime habit of diary-writing, observing the soldiers who had intended to keep a watch on them, and jotting notations about the activities of Detroit traders and farmers that offer clues about the slaves these men and women held. Mourning the loss of their fellow congregants, the Moravians and Delaware converts watched developments of the war from their vantage point on the Huron River. In late spring of 1783, upon returning from a supply trip to Detroit, the Moravian Brother Edwards "brought word that peace would certainly be made." One month later, the Reverend Zeisberger penned in the mission diary: "from the articles of peace it is plain to be seen that Niagara, Detroit, and Michilimackinac will be ceded to the States." But even under the coming sway of an upstart nation that had risked all for liberty, slavery would remain a feature of the Detroit landscape as prominent as the river.
The Wild Northwest (1783–1803)
By an ordinance enacted by congress, dated July 3, 1787 . . . there was a clause in Article VI saying that "there shall be neither slavery nor involuntary servitude in the said territory." This was a safeguard by congress to prevent the extension of slavery northwest of the Ohio River. Notwithstanding this wise provision, our ancestors paid little attention to it, for whenever a spruce young negro was brought by the Indians he was sure to find a purchaser at a reasonable price.
_—General Friend Palmer,_ Early Days in Detroit, _1906_
The Great Lakes region could have been different. Acquired by the United States after a bloody revolution that had championed the principles of equality and liberty, and separated from the entrenched slaving stronghold of the South by physical distance, cultural makeup, and economic interdependencies that leaned northeastward, this might have been a place where freedom won in full-throated fashion, matching hot revolutionary rhetoric with reality. In the northern states, the Revolutionary War had generated a sense of disquiet about holding human beings as chattel. Enslaved petitioners and plaintiffs in Massachusetts had exposed the blatant hypocrisy of this upstart would-be country espousing ideals of liberty while maintaining a slave society. Prompted to act by burning desire and the opportunities afforded by wartime disarray, thousands of slaves in the North as well as the South had escaped during the war, evidencing the "contagion of liberty." New England colonists who had employed the rhetoric of slavery as a metaphor to describe their political relationship to Great Britain could not help but see the irony in Americans owning humans as things. This recognition of hypocrisy, and indeed, immorality, at the center of American life fed the gradual abolition of slavery in the New England states, with Vermont at the lead in 1777. In the northern mid-Atlantic states, including New York, emancipation would come even more incrementally as legislatures adopted molasses-like plans for bestowing upon enslaved people the right to personal liberty.
America was no innocent when it came to the beast of slavery. When we look back on decisions made at the founding moments of this nation, we cannot in good conscience claim that political leaders were ignorant of scathing critiques of the practice. Slavery had in fact been a subject of fierce debate in the Constitutional Convention of 1787. Some of the country's leading men were sickened by the vile mistreatment of a whole subset of the populace; others saw slavery as an unfortunate but necessary economic practice that should be phased out over time, and still others felt that slavery was a social and financial good, ordained by a Christian vision of paternalistic social hierarchy based on natural strengths and deficiencies that fell along racial lines. These differences in points of view were mainly, but not fully, regional, with New England and southern states chafing against each other's interpretations of how the new nation should be imagined. But the seeds of deep division that would later explode in a Civil War were buried by the state representatives who met in Philadelphia that May to September in order to establish the nation's governing text. Flushed with their unexpected military victory over a global superpower and chastened by the grave import of their collective task to build the legal scaffolding of a free democratic republic, northern and southern attendees found their way to compromise. They banned the ugly international trade in slaves after the passage of twenty years and developed the callously creative Three-Fifths Clause, which counted enslaved people as equivalent to three-fifths of free people toward congressional representation for the states. This meant that slaveholders, especially those in the South where the majority of unfree laborers lived, could deny enslaved people freedom and citizenship while using these same enslaved people's presence to amass greater congressional power for white male citizens with property. This three-fifths provision, in the words of the historian Edward Countryman, "made slavery the only special social interest that the new national order explicitly recognized."
The freshly acquired region of the Great Lakes, or Northwest, as it came to be called, also triggered tension over the place of slavery in the nation and the boundaries of slavery's expansion into the West. Two months before the delegates of the Constitutional Convention finalized that foundational document in preparation for ratification in the states, the Confederation Congress had laid out a plan for western terrain ceded by Great Britain. Building on a document drafted by Thomas Jefferson and his committee in 1784 that had not been adopted due to perceived insufficiencies, the final legislation written by a new committee in 1787 provided for the division of these lands into three to five states and created a process for the admittance of those states (later, Ohio, Indiana, Illinois, Michigan, Wisconsin, and a portion of Minnesota) into the Union after a temporary territorial stage. The previous text penned by Jefferson's committee had addressed the difficult matter of slavery, recommending that: "after the year 1800 of the Christian aera [sic] there shall be neither slavery nor involuntary servitude in any of the said states, otherwise than punishment of crimes, whereof the party shall have been duly convicted to have been personally guilty." The final legislation adopted in 1787 included this language nearly verbatim, principally to encourage the immigration of white northeasterners into the region.
In July of 1787, during the Constitutional Convention, representatives adopted the Ordinance for the Government of the Territory of the United States North-West of the River Ohio, handily shortened to the Northwest Ordinance, with a prohibition against slavery modified but intact. Always reaching for compromise, architects of the nation's founding documents made the ban on slavery immediate in the Northwest and added a fugitive slave clause. The finalized language of Article 6 included reassurance for southern slaveholders: if their human property should abscond to western lands, that property would be returned. The text also legalized the bondage and forced labor of convicted criminals as a form of punishment. On the issue of slavery, Article 6 of the Northwest Ordinance declared: "There shall be neither slavery nor involuntary servitude in the said territory, otherwise than in punishment of crimes whereof the party shall have been duly convicted: Provided, always That any person escaping into the same, from whom labor or service is lawfully claimed in any one of the original States, such fugitive may be lawfully reclaimed and conveyed to the person claiming his or her labor or service as aforesaid." (The logic of this careful wording that managed to prohibit slavery while simultaneously protecting some forms of it still operates today in the legal use of prison labor to perform some of the country's most dangerous jobs.) But what of the hundreds of Native and African-descended slaves in Detroit who were not runaways from the states and had not been convicted of crimes? They found no safe haven in this new Northwest. As legal historian David Chardavoyne has baldly put it: "The arrival of American rule and enactment of the Northwest Ordinance did not emancipate any slaves in Michigan—on the contrary, for many black and panis slaves, the words of Article VI of the Ordinance were just words, seemingly incapable of freeing them." Riven with loopholes that revealed its ultimately equivocal stance toward slavery, the Ordinance, functionally a constitutional document for the region, left people of color at the mercy of previous customs. Under American jurisdiction, the Northwest would become a wild, wild West for enslaved people, who had very little protection under legislation that upheld a compromised form of abolition and included no enforcement provision. Colonialism and slavery would remain braided together in the new national terrain, as this "foundational document of American expansionism" was careful to protect the property rights of southern slaveholders and to legalize the theft of prisoners' labor on lands still claimed by Native societies.
While the Northwest Ordinance banned blatant slavery in what would later be called the Midwest, it protected access to slave labor. It was not long before the region's slaveholders and would-be slaveholders devised strategies for taking advantage of wiggle room in the federal law. They interpreted the prohibition of Article 6 as applying only to incoming residents in the territory (not to previous settlers) and aided in the seizure and return of fugitives. The Northwest Ordinance, which is often imagined today as outlawing slavery in the interior North, actually allowed for "a _de facto_ slavery through a system of long-term indentures, rental contracts, enforcement statutes, and the recognition of the status of slaves who had been brought to the territory before 1787." In a Revolutionary era characterized by radical talk of natural rights, American leaders came close to abolishing slavery in the new western territory that was, by right of prior occupation, indigenous land—but "close" was not good enough to make an immediate, meaningful difference for those enslaved in Detroit.
Betting on Detroit
To elite Detroiters, the settled peace in 1783 represented a startling turn of events. The Treaty of Paris, negotiated by John Adams, John Jay, and Benjamin Franklin at the behest of the Continental Congress in 1783, called for the relinquishment of the interior region east of the Mississippi to the nascent American government. The specter of occupation by a foreign military force and unfamiliar political authority, and the threat of draconian laws and taxes, hung like a scrim over British Detroit. In a place peopled mostly by loyalists and an even larger longtime French population, the loss carried the potential for political unrest and social instability. Worse, in the aftermath of the war, inflation and a scarcity of goods were ravaging the local economy.
One slice of luck for Detroit's white settlers was the physical soundness of the settlement. Detroit had been a military hub during the conflict but had seen no immediate fighting, which could have devastated buildings and cropland. With the town structurally intact, trade could resume as soon as the market recovered. A second boon was the promised protection of colonists' property under the new American government. Even before the end of the war, Thomas Jefferson, hoping for a capture of Fort Detroit, had directed Commander George Rogers Clark to safeguard the inhabitants' material possessions, writing: "Should you succeed in the reduction of the Post, you are to promise protection to the Persons and property of the French and American inhabitants, or of such at least as shall not on tender refuse to take the Oath of fidelity to this Commonwealth." Clark would have seized upon this directive, especially regarding the security of human property, as he had already demonstrated in his Illinois Proclamation of 1778 that he believed "red and black slaves" should be kept in their place as chattel. Beyond Jefferson's dictate to an officer in the field to guard the property rights of previous settlers from New France and newcomer Americans, the formal Treaty of Paris sought to further ensure Americans' investment in slaves, insisting that: "his Brittanic Majesty shall with all convenient speed, and without causing any destruction, or carrying away any Negroes or other property of the American inhabitants, withdraw all his armies, garrisons and fleets from the said United States." Although the British did in fact remove from American territory former slaves who had been promised freedom for serving on their side of the conflict, Great Britain did not yet condemn slavery unilaterally. Neither did the United States, which would permit certain forms of slavery on Great Lakes lands just as Great Britain had done. Weighing out all of these factors—politics, economics, infrastructure, and slavery—British merchants had to determine whether making a life in Detroit still made sense.
Some British-identified residents, such as John Macomb and his son Alexander Macomb, chose to leave Detroit for New York after the end of hostilities; but others, such as John Askin, stayed on. Askin's neighbor and fellow Scotsman William Macomb wagered on Detroit as well. While the political terrain on which they planted their personal flags was still uncertain, the legal terrain was secure enough in one key respect: the protection of present colonists' right to hold slaves. This proved providential for Detroit's Anglo elite. Men like John Askin and William Macomb would benefit from the weak prohibition on slavery, numbering among the town's eighty-four slaveholding households and steadily accruing more human chattel to work or sell at a profit in the 1780s and '90s.
The slave trade among Detroit merchants boomed during these postwar decades. In 1789 William Macomb was attempting to sell two African Americans belonging to Alexis Masonville for £200. The black woman, he vowed to Charles Morrison, the recipient of his letter, was "very handy & a very good cook." The black man was "a very smart active, fellow and by no means a bad slave." Macomb wanted them "disposed of," preferably by the fall and not on "a longer credit than the first of June." He added in a postscript that he hoped Morrison could purchase him "a very good Carabois [caribou] skin" while he was out making trades, as their "hair" was "most esteemed." Directing the sale of "disposable" black bodies in this letter, Macomb then immediately turned to procuring the skins of valuable beasts whose numbers were then in decline due to overhunting. Macomb was less than pleased a month later about the intended sale of the slaves to a Mr. Ceré and wished Morrison had instead accepted Mr. Ainse's offer. Morrison corrected his error, soon responding that he had indeed made the better sale to Ainse but "had not seen a Carabois skin." The black man and woman had been passed on to other owners in the Northwest. The woodland caribou had perhaps escaped with their lives farther north where their habitat still remained intact. In 1794, James May sold "a certain negro man, Pompey," to John Askin for £45. The next year, Askin made a profit by selling Pompey to James Donnelson for £50. In 1801 John Askin received a request from James Mackelm, a colleague downriver, to "part with your Negro (who can do every thing)." After asking to be informed of Askin's "price" and "line of payment," Mackelm promises to "look for the feathers and Cyder" already on order. In a follow-up letter, Mackelm again presses for the black man, asking if "he is a slave for life, how old he is, and [if] his price [is] payable six months after Delivery." Those who held on to their slaves rather than selling them in a hot market used them to keep business brewing, especially through the transport of goods, including Elijah Brush, Dr. Thompson, and Robert McDougall, who all sent "their" black men and boys to Joseph Campau's general store to pick up silk, bushels of corn, rum, flour, and gunpowder.
Askin, Macomb, and others in their circle also seized the opportunity to grab more indigenous land. The American Revolutionary War had been waged not only between the British and the Americans but also between both these powers and scores of Native nations that strategically fought with either side or strove to remain neutral, all with the goal of maintaining indigenous strength on a rapidly changing continental map. The Revolutionary conflict had therefore been "a continuation of the struggle about Indian land and who was to get it." Now that the United States had proved itself the victor, indigenous lands were among the spoils. The Crown granted the United States sovereignty over the original thirteen colonies as well as over western territory that was predominantly occupied and claimed by Indians, drawing national boundaries between Great Britain (Canada) and the United States across the Great Lakes and northwest waterways. The negotiation of this treaty in Paris neither included nor consulted indigenous leaders, whose lands—at least on paper—were diced and distributed by European and American colonial powers.
Land lust took hold in Detroit as elsewhere. The region became a microcosm of the larger American bid to obtain huge swaths of Indian ground on the cusp of a new century defined by westward expansion. As the historian Alan Taylor has noted, U.S. leaders relied not only on territorial enlargement at the federal level through treaty provisions and massive acquisitions like the Louisiana Purchase of 1803, but also on the actions of individual Americans who sought private land purchases. There was, Taylor writes, a "power of property lines in weaving a settler society." Along the Detroit River, this effective power of private property to extend the footprint of what would become white America was well underway at the turn of the century. William Macomb already owned Grosse Ile and was raking in proceeds from tenants on the island. Before his death he would purchase Hog Island (now Belle Isle, the beautiful island park known as the "gem" of Detroit), which had served as a commons for settlers who kept pigs there during the French period. John Askin purchased land on both the northern (American) and southern (British-Canadian) sides of the Detroit River and engaged in numerous land speculation schemes, including an attempt to purchase the entire Lower Peninsula (the "mitten") of present-day Michigan.
The war would end with a surfeit in slaves and shifts in land ownership that further secured the powerful position of British merchants. And for them, another blessing sailed on the horizon. Despite Americans' wishful plans for the governance of the Northwest, the British Crown did not keep its promise to relinquish control over Great Lakes forts. Instead, the Red Coats stood their ground, defying the terms of the Treaty of Paris while claiming that Americans still owed unpaid debts. And the Americans, now crippled with war debt, a spent army, a citizen revolt against taxes in Massachusetts (Shays' Rebellion), and a barely formed, untested national government, had little power to force the issue. Throughout the 1780s and most of the 1790s, Detroit and the interior Northwest were American in name only. British authorities, now officially ensconced at Fort Malden in Ontario, brazenly ran Fort Detroit. The British were even so bold as to include Detroit in a new political district in 1791—the District of Hesse, located in the province of Upper Canada, Quebec. And the British would continue the practice of slavery in the posts they so blatantly held. In 1793 the Hesse district government official, Detroit military commander, and mapmaker Major David William Smith wrote to his colleague John Askin to share news of a Canadian legislative meeting in Niagara. "We have made no law to free the Slaves," Smith exclaimed in relief. "All those who have been brought into the Province or purchased under any authority legally exercised, are Slaves to all intents & purposes, & are secured as property by a certain act of Parliament."
Slaves to All Intents and Purposes
Despite a spectacular American victory in the Revolutionary War, little had changed on the ground in Detroit, especially for the enslaved. French, Euro-Native, and Native residents still made up most of the population. British military officials dominated the governing structure of the town. Slaveholding merchants constituted the economic elite. African-descended free people of color ( _gens de couleur libre_ ), who comprised sizeable communities in the culturally French towns of New Orleans and St. Louis, were absent in the Detroit records before 1800 and were likely only present in very small numbers. Few people claiming a declarative American identity were anywhere to be seen. And now, from the perspective of those who wished to get ahead through the mechanism of owning slaves, there were even more unfree inhabitants available to operate the town's shops, storehouses, kitchens, industries, ships, wagons, and farms. Ste. Anne's Church records show "Master Girardin, baker of the town" with a "Panis" named Antoine in 1786, and "Mr. Payet, Parish Priest of Detroit," with a black enslaved woman called Catherine in 1785. British military officers also had slaves, acquired through wartime raids and recent trades within slaveholding circles. "Mr. Grand (Grant), commandant in the navy" buried an unnamed black woman in 1784 and baptized a "Panis" man, Jean Baptiste, in 1793 and another "Panis" man, Paul, in 1794. Grant had married into a prominent French Detroit family in 1774, a reliable way for British residents to increase wealth in slaves.
In addition to individual ownership, corporatized groups of Detroiters could collectively leverage their resources in slaves, as when William St. Clair and a "Co of Detroit Merchants" sold Josiah Cutten (also known as Joseph Cotton), a black man, to Thomas Duggan, an officer in the British Indian Department. The price for Josiah Cutten was "One hundred and twenty Pounds New York Currency payable . . . in Indian Corn & Flour." By the time that he was traded for corn, Cutten had already been sold at least once in Montreal. He would later become the property of John Askin, who pledged £50 for a half share in Cutten in 1792 while Cutten languished in prison for robbing Joseph Campau's store. Askin insured this risky investment such that he did not owe when Cutten, a young man just in his twenties, was later executed for theft in Upper Canada.
John Askin Estate Inventory. The Burton Historical Collection, Detroit Public Library.
While a greater supply of slaves existed in Detroit after the war, there was also a higher demand for their labor. Captain Alexander Harrow, an officer of the British navy who had previously manned the king's ships in Great Lakes trades, owned slaves in Detroit but tried and repeatedly failed to acquire more in the 1790s. In 1794 he sent a 33.6 pound payment to Dr. Mitchell at Michilimackinac, the man who held Askin's former job as commissary, for "a little Pawnese" the doctor had sent. In 1794 Harrow wrote to Mitchell about sending "the boy he mentioned of 12 or 16 years old" and added "if the Boy was a little negro the better." As in earlier decades, a preference for difficult to acquire black boys showed in Harrow's request. The preference was, in some ways, irrational, as Indian slaves from the same locality would be better skilled in working the waters or traveling across the region. But the blackness of an enslaved child conferred a certain status upon an owner in Detroit, showing that the person could obtain rare commodities and marking, through oppositional skin tone difference, a starker social division between the owner and the owned. Black slaves were also far less likely to be confused for free people than Indian slaves in a region peopled mainly by Indians, and were less likely to make successful escapes due to a greater distance from their original homes. In May of 1795 Harrow was seeking a "Slave man or woman, Negro or Pawnee," indicating by word order his racial preference but stressing his willingness to buy any slave. Two months later he pressed Dr. Mitchell at Michilimackinac for "a wench for country work" and "a Slave Boy of 10 or 15 who would suit me." In May of 1796 Harrow was expecting "the Pawnese & 2 children if settled by Mr. Robertson for me." He hoped this Indian would prove "a good Kit[chen] wench." In July he was also trying to get "Black Bet and 3 children to get them by all means," and by August, Harrow's demands rose to a fever pitch of desperation, as he was "still looking for a wench, black or Yellow, young or old."
Most Detroit slaveholders continued to hold just one or two slaves after the Revolution, but members of the merchant elite, their pocketbooks fattened by government-military contracts and Indian land purchases, owned several. In 1787 John Askin inventoried his slaves, listing Jupiter and Tom—both "Negro" men, George, a "Ditto [black] Boy," Sam, a "Pawnis Blk Smythe [blacksmith]," Susannah "a Wench & 2 children," and Mary "a Ditto Wench." The combined value of these individuals totaled £760. The women in the inventory whose races went unmarked were valued at just £100 each, but the skilled male laborers of different races—Jupiter, a black boatman, and Sam, a Native blacksmith, were each worth £150. Across the span of Askin's preserved ledger and personal papers, more than thirty enslaved people of indigenous and African ancestry appear, fleetingly, in the non-emotional mentions of acquisitions, sales, tasks, and deaths. Even John Askin's daughter, Catherine or "Kitty" Askin, had a slave of her own. A young mixed-race Ottawa and Scot woman herself, Kitty Askin possessed a female "Panis" named Cecile. The outlines of Cecile's personal history are unknown, omitted from the record that has preserved minute detail about the color and fabric of Kitty Askin's blue satin wedding gown. And as was the case decades earlier under French rule, Kitty Askin was not alone as an indigenous woman with slaveholdings in Detroit. The most flamboyant Native American woman in town, Sally Ainse, was a savvy trader and slave-owner.
Merchant Slaveholders and Misplaced Missionaries
Sally (or Sarah) Ainse, an Oneida woman from Pennsylvania, had ventured into the business of trade back east alongside her husband, the French-Native trader and interpreter Andrew Montour. A "remarkably tall and elegant" woman who dressed in "English mode with a long gown and hair flowing behind," Sally Ainse moved to Detroit during the Revolutionary War after a separation from her husband. There she found ample opportunity to establish her own networks for trade. Ainse acquired a prime lot within the fort next to Ste. Anne's Church, where she had a wood frame home, kept livestock, and produced flour, corn, and cider for the market. Ainse owned three slaves in 1779 and one female slave in 1782, having likely sold part of her human property to others in the interim. Since Ainse had a previous business relationship with John Askin from a period when they both lived in Michilimackinac, and since she had extensive kinship ties through her former husband in the area, Detroit was a fitting place for the reestablishment of her female-run trading venture. Her clothing in the Anglo style was an indication that Ainse adopted as well as flaunted the accoutrements of cultural intermixture. Ainse, like the French and British traders in town, was caught up in the "skin trade" of dual meaning catapulted by the capitalist enterprise of European exploration, colonization, and slavery. A brief notation in John Askin's account book for 1781 notes that "Sarah Anis" (Ainse) received "1 smoaked skin from Thebeau for a boy at Mackina." This exchange of a Native child for a finished animal pelt that transpired between an Indian woman and white man captures in elliptical snapshot form the intricate nature of slavery in the Great Lakes. American Indians participated in this practice as both perpetrators and victims, while navigating changes, challenges, and chances wrought by the meeting of diverse peoples, the advance of European settlement, and the unseemly ravages of war. Indeed, one of Ainse's indigenous neighbors in Detroit was the Shawnee leader and British military ally Blue Jacket, who, according to a white woman taken captive by a different Shawnee warrior in the war, had married "a half French woman of Detroit" and lived there "in great style, having curtained beds and silver spoons" and "Negro slaves" to serve tea.
Sally Ainse, also privileged with tea and slaves, prospered as a businesswoman in Detroit, living at times with a white man named John Wilson, yet acting as an independent trader. She received boatloads of goods and held accounts with various merchants, including her old associate John Askin and William Macomb. At one point the grand sum of her accounts reached over £2,000. The well-being of the bondspeople owned by Ainse is, in contrast, impossible to determine. They are noted by number, and not by name, in the Detroit city census that lists their "elegant" Oneida mistress's property.
Perhaps Sally Ainse ventured out to visit the Moravian missionaries to diversify her business affairs in Detroit. She had proven herself to be an ambitious and capable entrepreneur, and she was no stranger to the Moravian faith. Ainse had hosted missionaries from that church back in Pennsylvania when she shared a household with her former husband, Andrew Montour. She also had family connections to the Moravians of Upper Canada through her ex-husband and to the Moravians of Ohio as well as Detroit through her brother. The Moravians and their German ways would therefore have been recognizable to her, and the Delaware members of the Moravian congregation even more familiar. In addition to being Oneida, Ainse claimed an identity as Shawnee, an Ohio woodlands nation culturally close to the Delawares. Sally Ainse's ability to identify a growing market for her trade goods may have been what previously led her from Michilimackinac to Detroit in the middle of a war. And the Moravians did need all manner of things. They had been forced to rebuild a settlement and seed a farmstead from scratch after their relocation from Ohio. While they had the benefit of Ojibwe lands and wooden "boards" for building that Detroit officials had negotiated for their use, the Moravians required a constant infusion of supplies and cash from town. Indian men of the congregation crafted bark canoes that they sold at the fort to provide "themselves clothes for the winter." Indian women fashioned baskets and brooms, which they likewise sold to townspeople or traded for apples. In order to sustain families in this new environment, Moravian community members gathered wild cherries and whortleberries, dug wild potatoes, and hunted deer and bears. This nascent Protestant community outside of town represented a promising market for Detroit traders like Ainse, some of whom owned acreage near the mission on either side of the Huron River but, according to Reverend David Zeisberger, had "never seen it," as this rural area near Lake St. Clair was considered "the bush" by Detroit urbanites, who rarely ventured so far out into "Indian land."
Whether or not his business associate, Sally Ainse, beat him to it, John Askin was one of Detroit's first merchants to trek into the marshy wilds north of town. He immediately drew the Moravians into his commercial orbit, offering them credit for provisions sourced in Detroit and becoming one of few white visitors to the mission in 1782. Over the next few years, other Detroiters began to stop by to view the Christian settlement, often traveling by sleigh or "sledge" across sheets of heavy ice that connected the Detroit River to the Huron River by way of Lake St. Clair. Visitors came to take in the sights of the mission, including its 117 resident Christian Indians; they also were keen to assess the valuable lands around the establishment, to set terms of trade, and to have marriages and baptisms performed, as, in the words of Reverend Zeisberger, "there [was] no ordained preacher of the Protestant church in Detroit." The desire for Protestant religious services was one sign that Detroit's population was gradually shifting, becoming more Anglicized as British officers, soldiers, and traders put down roots in the former French territory. Still, there were numerous French residents within the fort proper and living on farms alongside waterways, some of whom sold corn to the Moravian Delawares in exchange for venison.
In the winter of 1784 British Captains Alexander McKee and Matthew Elliott came "with two sleighs" to see the Moravian mission for themselves. Both men had accompanied Captain Henry Bird on his raids into Kentucky and come away with valuable African American slaves that they promptly moved across the river after the conflict. McKee, now an official of the British Indian Department, was among the individuals sought out by the slave-hungry Captain Alexander Harrow, who begged McKee for "a wench for kitchen and country work [or] a Black boy or man to dispose of." Elliott, a trader and Indian agent for the British, styled himself like a southern planter with his stolen Kentucky bondspeople. He established a sizeable farm on the Canadian side of the Detroit River where, according to the Moravians, "an overseer and several blacks lived." Elliott's "Indian wife" enjoyed the niceties of an upper-class life and lived in a style even higher than that of Oneida trader Sally Ainse. Slaves attended to this Shawnee woman's needs, and when she was out visiting, the Moravians observed, Matthew Elliott "sent his Negro" to pick her up "with a sled." Trader William Macomb became friendly with the Moravians too, forwarding parcels of "letters and papers from Bethlehem, together with Scripture-verses and texts" for the missionaries. The Moravians surmised that packages from their home church town in Bethlehem, Pennsylvania, which brought them such "joy," had arrived on Macomb's ship.
A comfortable farmer named William Tucker was the most frequent British visitor to the Moravian mission. Like Askin, Elliott, and Macomb, he was a slaveholder deeply entangled with Indians. Originally from a Virginia family, Tucker had been taken captive by a group of Ojibwes along with his brother when they were just boys. After killing the boys' father, the Ojibwe captors adopted the eleven-year-old William and his brother Joseph, eventually bringing the children to the Huron River where the Ojibwes had a settlement. While a young man, William Tucker served as an interpreter at Fort Detroit and worked as a trader for George Meldrum, a Scottish merchant from Schenectady, before returning south to Virginia to marry in 1773. He moved back to Detroit with his wife, Catherine Hezel (or Hazel), and, according to county history, with "a family of slaves, consisting of father and mother and several children." William Tucker's Ojibwe friends then bestowed on him a large tract of land along the Huron River, making him one of the first white settlers in the area. As retold in local lore, the acreage William Tucker acquired amounted to "all the land he could walk around in one day." Tucker built a one-story log house tucked among old-growth trees near the "mouth of the river." He planted apple, pear, and cherry orchards, kept boats for transporting his crops for trade in town, and "settled on his farm with his bride and slaves." His route to prosperity followed the usual pattern for European settlers in the Great Lakes region: trade, government work, Indian land, slaves—except that his enslaved labor force was fully black rather than Native.
William Tucker made his living as a farmer on Indian land "eight miles down the river" from the Moravians, who were among his closest neighbors. Tucker befriended members of the Christian sect and acted as their advocate in tense conversations with nearby Ojibwes, who began to feel that the missionaries were overstaying their welcome on the borrowed parcel of fertile land. While Tucker served as a buffer between the missionaries and local Indians, he also found that he needed the help of Moravian Delawares. In 1783, Tucker came to the mission with his wife, Catherine, asking "for an Indian sister to be at the lying-in of their negro woman." This unusual request revealed not only the expertise of Delaware women as midwives but also the everyday proximity of diverse peoples on the waterways: Europeans of different backgrounds, Native people of various ethnicities, and enslaved African Americans from the South. As the Reverend Zeisberger would record in the mission diary, whites as well as blacks began to attend Moravian services in the 1780s. One of these attendees of African descent may well have been the woman on the verge of giving birth on Tucker's farm in 1783.
Events that unfolded at the Tucker family homestead are hazy, yet pivotal to the larger story of slavery in Detroit. The enslaved woman who gave birth in 1783 with the aid of a Delaware woman was most likely Hannah Denison, mother of the first African American family to file a freedom suit in Michigan. The conflicting nature of limited evidence makes the Denison family's origins difficult to reconstruct. According to probate records, William Tucker owned one black family upon his death in 1805: Hannah Denison, her husband Peter Denison, and their four children: Elizabeth (Lisette), James, Scipio (Sip), and Peter Jr. Local oral history conducted by the historian Isabella Swan in the 1960s suggests that the first child in the family, a girl called Judy, was not listed in this official record. Slaveholder Catherine Tucker would later report that William Tucker had purchased Hannah in 1780 from "Joseph Mantour" at Detroit and bought Peter for "three hundred pounds" in 1784 from "Mr. Paulding," also in Detroit. After Peter's arrival, Hannah and Peter coupled. If there was indeed a first baby within the Denison family whose name was left off the record, she may have been the child born with the aid of a Delaware midwife in 1783. The identity of this child's father is not noted in any source. The spare existing record only reveals a description of Hannah's owner, William Tucker, rushing to the Moravians' farm for assistance with the delivery. The secret of the infant's father may have been intimately known to him and, on an isolated farm, to his wife.
Catherine Tucker's record of the purchase of Hannah and Peter Denison tied the members of this couple to two different routes into slavery. Hannah had been sold by the Montours, in-laws of the Oneida trader Sally Ainse, and she may even have briefly belonged to Ainse. Hannah was therefore a woman who had lived among Native and French people and whose own family history may have stretched back multiple generations in the Great Lakes, tracing to Montreal, Quebec or some other northern urban locale. Peter Denison, in contrast, came from a black family not many generations removed from the Upper South. County histories of the Tuckers trace the origins of the family they owned back to a purchase in Virginia before the Revolutionary War. This information is revealing, but not in the way that it at first seems. Based on a wildly expansive 1609 charter from King James I, the colony of Virginia claimed as part of its territory lands stretching past Lake Michigan. Since Virginia "held" this land until the Treaty of Paris concluded the Revolutionary War, enslaved people born in the Michigan region could, technically, be defined as having been born in Virginia. Peter Denison may have been "Virginia-born" right in Detroit with parents who had been seized from the South. William Macomb of Detroit had among his slaveholdings a man named Scipio, valued at £130, and a woman named Lizette, "Wife of Scipio," valued at £80. It cannot be coincidental that this man and woman bear the names of two of the Denison children in such a small community. The elder Scipio and Lizette were likely captured in southern raids during the war and acquired by William Macomb. They then had Peter, who was later sold to Tucker by a man named Paulding, a broker or subsequent owner. The origin of Peter's surname is unclear. Perhaps his parents carried the name from the South (though Macomb's records do not state as much), as "Denison" does trace back to Scots-Irish settlers in southwestern Virginia. While Hannah had compulsory ties to a French-Native slaveholding circle, Peter came from a British household in which his southern parents were held as slaves. The range in the couple's backgrounds, together with the wide network of people their lives had touched, broadened their combined experience as well as their social connections, positioning them to face a future of drastic change.
The Denisons were essential to the smooth operation of William and Catherine Tucker's farm. While Hannah handled all manner of domestic and gardening chores, as well as helping to care for the Tucker children, Peter performed agricultural and manual labor. Peter may also have honed specialized carpentry and boating skills of the kind evidenced by John Askin's enslaved men, Pompey and Jupiter Wendell. Peter probably rowed Tucker's boats to deliver wheat and fruit to Detroit, affording mobility that allowed for the maintenance of ties with relatives on the Macomb farm. The Denisons were likely conversant in local Native languages, including bits of Anishinaabemowin spoken by the Ojibwes who originally owned Tucker's farm as well as Delaware spoken by the Moravian Indians. Hannah probably spoke French. Hannah and Peter's children would have been linguistically adept by necessity, growing up as the only slaves on a large farm among a diverse population in the Indian country outside Detroit. As a young black couple with multiple skills and cross-cultural literacy, the Denisons were well known, highly valued, and frequently sought after. During the time that William Tucker owned the pair, Captain Alexander Harrow angled to buy them, writing in his journal that he had asked if Tucker "would sell his negro man and woman and at what price for the whole." Years later, Tucker's neighbor across the Detroit River, Matthew Elliott, would also try to claim the Denisons as his property. The Denisons clearly possessed ample talents, which would prove consequential when the town of Detroit finally succumbed to American territorial rule.
Postwar Land Dispossession
After the Peace of Paris was signed and the war formally closed, the Ojibwes on whose land the Moravians lived intensified their complaints about the arrangement. They had agreed to host the newcomers while hostilities ensued and had continued to access the Huron River lands for hunting during that time, sometimes leading to tense competition for game with the Moravian Delawares. But now that the war was over, Ojibwe leaders pressured the Moravians to pack up their things and move on. Reverend Zeisberger was anxious about the increasing pressure, imagining that certain Detroit merchants who wished to become "masters of our settlement" were "the real instigators of the Chippewas" and using the Indians "as tools." While Zeisberger's hunch about merchant land lust was accurate, he too easily dismissed the Ojibwes' own motives. In January of 1786, Ojibwe leaders warned the missionaries that this was Ojibwe land, and the settlers must depart. When the governor at Detroit advised the missionaries that prudence suggested they heed this warning, the Moravians relocated, with reluctance, to Chatham, Ontario.
The contest north of Detroit between the Moravians and local Ojibwes was a microcosm of larger tensions still at play in the decades after the Revolution. Native nations that had been yanked into a devastating colonial war refused to accept the outcome. Many lake country bands had sided with the British, who had been less preferable than the French but better than the Americans when it came to the protection of Indian lands. At the close of the war, the British surrendered to the Americans, whose rising power the western tribes witnessed with a stubborn rage. Native Americans recognized that with the defeat of the British, "a new era had begun." And this transformation worked to the detriment of indigenous land claims and political independence. Groups of Indian warriors in the Great Lakes as well as in the South refused to recognize American authority in their own homelands. They led attacks on settler settlements, continuing the revolutionary fight—this time for their own nations' liberty.
Native people's discontent with the shifting balance of power in North America cut into commercial transactions in Detroit. Due to overhunting and some Native men's focus on attacking American settlements rather than hunting, the number of available pelts plummeted. Deteriorating living conditions worsened economic trials resulting from the scarcity of furs. The winter of 1784 proved relentless, described by "Old settlers" as the hardest they had ever seen. Poor crop yields and famine in 1784, 1787, 1788, and 1789, as well as a scourge of smallpox in 1785 and "pestilence and sickness" in 1789, wreaked more havoc, taking the lives of numerous Detroit River residents.
President George Washington and U.S. leaders in the East grew alarmed at the recalcitrance of Native people in the West, who far outnumbered white settlers in the interior and were organized as well as armed. The Moravian missionaries continued to observe developments from their new settlement on the other side of the river, recording the stealthy advance of American soldiers into the country. In 1791 Zeisberger wrote, "From Capt. Elliott, who came from Detroit, we learned that they had news that a strong army from the States was on the march out against the Indians." In 1793 he recorded "news that those at Detroit fear the Americans under Gen. Wayne might attack." Led by General "Mad" Anthony Wayne, a veteran of the Revolutionary War, American soldiers were tasked with crushing Native military resistance, which had coalesced into a confederated, pan-Indian force centered in the Ohio Valley. In August of 1794, Wayne and his men defeated Miami, Potawatomi, Shawnee, Delaware, Ottawa, Ojibwe, and Iroquois fighters, whose ranks had been depleted by long-distance travel and hunger. One year later, in August of 1795, representatives of seventeen western Indian bands and nations signed the Treaty of Greenville with the United States. The treaty called for Native relinquishment of massive swaths of land in Ohio, Indiana, Illinois, and Michigan, including "the post of Detroit, and all the land to the north, the west and the south of it." This left little else in the way of Indian land in Detroit, and those portions remaining would be taken by 1807. As indigenous people had suspected throughout the long years of war, the Americans fully intended to dispossess them, as the "revolutionaries who fought for freedom from the British Empire in the East also fought to create an empire of their own in the West."
Although the indigenous western resistance seemed to have been quelled after the Battle of Fallen Timbers, one final barrier stood in the way of American expansion into the inland West: the British occupation of Great Lakes forts. A new treaty negotiated by John Jay in London won the Crown's forfeiture of these forts and signaled to Native people the final withdrawal of their British ally. The U.S. Senate ratified the Jay Treaty in the summer of 1795, just before the ink dried on the Treaty of Greenville. One year later, Jay's treaty would take effect. The border established between the United States and Great Britain that separated territory with "lines drawn upon the water" would now be recognized by each country. The Detroit River was no longer a thoroughfare that joined settlers on both banks under the shared identity of Detroiters. On one side of the waterway, American stars and stripes would fly; on the other bank, the Union Jack would sway in the rippling wind.
In 1796, thirteen years after the official close of the Revolutionary War, America would finally seize control of the Northwest Territory won back in 1783. "The States," Reverend Zeisberger penned, "have occupied Detroit." After his decisive victory over the western Indian nations with a force of just over a thousand men, General Anthony Wayne swaggered into town to oversee the departure of the British military. Zeisberger noted the transfer-spectacular in his mission diary: "When Gen. Wayne marched in with the garrison by water, and, when Wayne got to the city, the English commandant discharged his cannon from the ship, and was saluted in return, in like manner, from guns great and small, whereupon the new owners moved in." Despite the fanfare, British officers did not remove a great distance away. They simply resituated across the Detroit River at Fort Malden in Amherstburg, Ontario, on land cleared after the war in exchange for an enslaved woman named Esther. Their close proximity and ongoing ties with indigenous groups meant that tensions between the British and the Americans, while lessened, would not disappear until a second major war purported to settle them.
Meanwhile, the "new owners," or American officers, to whom Zeisberger referred now commanded Detroit. Zeisberger would have described the "old owners" as British officers, but there is a second, more accurate meaning of that phrase. The "old owners" were also Detroit's French and British merchant elite who now faced a concrete changing of the political guard but held a core notion in common with the provisions of the Jay Treaty. Their status as "owners" of people in a slave society would continue to be safeguarded, and now even more emphatically, into the American era. The Jay Treaty, which defined the rights of Detroit's prior residents of European descent, guaranteed: "All Settlers and Traders, within the Precincts of Jurisdiction of the said Posts, shall continue to enjoy, unmolested, all their property of every kind, and shall be protected therein." Now it was not only French slaveholders whose rights to their slaves would be formally honored; British slaveholders could claim the same protections. And any of these Europeans could shift their loyalties to the United States and gain recognition as American territorial "citizens" under the Jay Treaty. They had only to maintain residency for a year or to swear an oath of allegiance if they preferred. The Jay Treaty opened the gate to American belonging for longtime Detroiters and broadly sanctioned their continued possession of Native and African-descended slaves. In a painful irony for enslaved people owned by French Canadian old settlers, France had abolished slavery in its colonies in 1794. Together, the fundamental legal documents of the territory—the Northwest Ordinance of 1787 and Jay Treaty of 1794—functioned in a way that allowed Detroit to become a hub for slaveholders and a prison for captive people decades into the nineteenth century. As Christopher Phillips, a historian of the borderland Midwest and self-identified descendant of slaveholders there, has put it, "slavery and white supremacy were interwoven into the fabric of the entire western region."
William Macomb Account Book (c. 1796). The Burton Historical Collection, Detroit Public Library. A list of enslaved people with their individual monetary values is included in this bound record of Macomb family accounts.
Preserved property records of Detroit merchants demonstrate the robust continuation of slavery. In 1787, when John Askin inventoried his human chattel in a ledger book along with his other accounts, he enumerated eight persons: three men, two boys, two women, and two children of unspecified gender. Half of these individuals were identified as "Negro"; both of the women and a "Pawnis" blacksmith were most certainly Native. In 1796, when the executors of William Macomb's estate estimated his property holdings in the wake of his death, they listed twenty-six slaves: eleven men, seven women, and ten children. Charlotte was the wife of Jerry and mother of two. Bet (or "Black Bet," as Captain Harrow called her in his bid for purchase) had three children. Betta, listed alone without a family, was nine years old; Phillis, also listed alone, was seven. Most, if not all, of these individuals were African American. The racial breakdown of the souls counted among the assets of two of the most prominent British traders, Askin and Macomb, revealed a shift in Detroit's enslaved population. Before the war, indigenous slaves had vastly outnumbered those of African descent, who made up a tiny portion of the captive population. During the war, raiders into southern settlements seized African Americans who then became the property of traders, merchants, officers, and farmers. In the postwar years, the number of captive people reached an apex in Detroit. City census records from 1773 listed eighty-five enslaved people; in 1782 that number had jumped to 180. By 1796, 298 enslaved people lived in Detroit. The registry of Ste. Anne's Church adds precious detail to these raw census numbers. In the decade of the 1780s, ninety-seven enslaved people appeared as principal entrants in the priests' record book; sixty-eight of these were Native American, and twenty-six were African American. In the 1790s, Ste. Anne's priests noted eighty-five enslaved members; fifty-six were Native, while twenty-four were black. In short, over the three decades since James Sterling had been the first British slaveholder to appear in the Ste. Anne's registry with black slaves, the church's African American population had increased nearly eight-fold. British settlers' desire for black slaves and their access to New York markets, together with wartime raiding to the South, gradually shifted the color of Detroit's unfree class. The enslaved population was now approximately two-thirds Native and one-third African American. As the settlement moved into its "first American century," slavery persisted as a more evenly divided biracial phenomenon, shaded black as well as red.
Theft, Fight, and Flight
After the Revolutionary War, enslaved people in Detroit carried on much as they had in prior decades—fighting for dignity, liberty, and a decent quality of life, trying to beat the odds in a frontier community that presented openings as well as barriers. In 1792 a "Panis slave" named Francois stood accused of stealing "two bed covers, two shirts, and some other things" from a house, the mode of rebellion taken by black bondspeople Ann Wyley and Josiah Cutten in previous years. Francois, who lived in "a hut in the rear of the house of Baptiste Meloche," armed himself "with a knife" after the incident. When the homeowner, Michael Houde, pushed into Francois's "hut" looking for evidence of the crime, he promptly withdrew upon seeing the weapon. Afraid to confront Francois directly, Houde took the matter to court. Hearing the case against Francois was none other than John Askin, who was enjoying a new appointment as "one of His Majesty's justices of the peace for the District of Hesse" along with new buildings that he had conveniently acquired on the Huron River after the Moravians' departure.
Besides stealing from wealthy merchants, unfree people attempted escapes from and to Detroit in the 1790s. On a snowy autumn morning in 1794, an enslaved man fled Detroit and made his way to the Moravian mission in Ontario. The Moravians did not aid the runaway, who was captured by "Mr. Parke" (of the prominent Meldrum and Park trading firm in Detroit) and then returned by Park to the town center. In 1798 John Askin lost a slave to escape. His daughter Madelaine Askin attempted to aid in the recovery of the man and wrote to her "dear Papa" in French: "I gave notice to several people that if they see your negro, to arrest him and take him to you, and I told them what reward you would give." Madelaine reported that she had secured the aid of other settlers, who would help to capture the runaway "with pleasure." Sampson, a black man owned by the slave-hungry Captain Alexander Harrow, fled in February of 1797. Sampson's escape plagued Harrow for over a year, and Harrow was not quite sure if he wanted the difficult Sampson back. He determined in March of 1797: "I wish Sampson could be sold for £50 rather than have any more trouble with him." By the summer of 1798, Sampson was working "in the service of Mr. Wells Attorney-at-Law" in Cincinnati. Harrow drew up a bill of sale for Sampson to Wells for "100 Dollars" and tried to hedge by getting Joel Williams of Cincinnati to purchase Sampson if Wells would not. In March of 1799, Harrow had still received nothing for Sampson, and he had not managed to have Sampson sent back to Detroit. Sampson's trail in Harrow's record ends here. Perhaps Harrow eventually collected funds for Sampson; likely, he did not. To engineer his escape, Sampson ran south to Ohio through the swamps rather than toward the legendary North Star. During Sampson's lifetime and that of other slaves in Detroit prior to the turn of the nineteenth century, Upper Canada was as much slave territory as the United States, which meant fleeing either north or south held equal promise and risk.
Before Sampson seized his freedom, plaguing his frustrated owner who dared not enter Indian country to track him, a fugitive from Kentucky took the reverse of Sampson's course. This man fled north into Detroit, where he formed a partnership with a Wyandot hunter and entered the fur trade between Detroit and Ohio. Unnamed in the record, this black trader represented an infinitesimal free black population in eighteenth-century Detroit. Another free man may have been the "coal maker" in town described as "Will the Negro" in John Askin's ledger that recorded a debt Will owed. Perhaps this was William Lee, the man who had cleared acreage to purchase Esther and her son from Captain Henry Bird during the war. If so, and if William acquired Esther to free her, they may have become one of Detroit's scarce free black families.
But many more enslaved people, both black and Native, remained in the town and its satellite communities, failing to find their longed-for freedom in the aftermath of the war. A significant number of Detroit's still-captive bondspeople worked on the farms and river islands of William Macomb, which included: a "farm near the fort . . . on the Detroit River" a "farm at the Grand Marrais," "Hog Island," a "farm on the south east side of [the] Detroit river," three houses "in the fort," "lands in the Ohio," and "Indian grants" at "Grosse Isle, Stony Island & other small islands," and lands "on the north of the river." Before his death in April of 1796, Macomb ensured that his "moveable estate . . . Slaves, Cattle, Household furniture, Books, Plate, Linens, Carriages, and all [his] utensils of Husbandry" would be duly accounted for. He appointed as executors of his estate merchants from New York and Detroit and named his wife, Sarah, followed by their eight children, as heirs. The items listed in Macomb's itemized account of "moveable goods" would be passed down or auctioned off for the proceeds. In September of 1796, the executors began to liquidate by shedding human chattel. They sold Antoine to F. Billettes, transported Ben and Guy to New York, sold Bet and her "three boys," Sam, Isaac, and Charles, for £135, and sold the "Negro girl Betta" for "fifty."
Settling the Country in the Lakes
William Macomb may have been Detroit's wealthiest resident upon his death in 1796, but he would not be among those to lead the town into its first American century. That task fell to men like James May, a slaveholder; Solomon Sibley, a non-slaveholder; and Elijah Brush, a man with two "indentured" slaves. Born in Birmingham, England, in 1756, the nineteen-year-old James May had journeyed to Detroit in 1778, where he married a French woman, Rose St. Cosme, and began to engage in the chief business of the frontier: trade. A man of massive stature, fine tastes, and "a strong virile intellect," May had achieved solid middle-class merchant status by the time that William Macomb died. May further improved that status when he turned up among the crowd at the Macomb family estate auction. On that hot August day, John Askin bought rabbits; Jonathan Nelson bought a fox house, a mare, and a colt; Matthew Dolson and Jacob Flower bought cattle and a horse; and Francis Billettes bought the black man, Antoine, "payable monthly on 5 months." It was James May, however, who made the largest haul. At a time when coins and bills were scarce and most economic transactions were made through a barter and debt system kept track of by local merchants, May paid 252 in "cash" on the spot and still owed 1,269 for the things he bought from Sarah Macomb. Because of the size of May's purchase, his sundry items were not detailed in the Macomb family ledger book like Askin's rabbits or Nelson's fox house, but the purchase probably included unfree people whose lives were devastated by the death of the trader who had formerly owned them. For men, women, and children in bondage, the passing of a master meant certain change: often sale and separation from loved ones. And James May, like many of Detroit's leading residents, dealt in slaves as both an owner and purveyor. In the 1790s, May owned a black woman named Jenny, acquired from a man named Grauchin "in payment of a debt," as well as Jenny's sister Chloe, and an unnamed "Negro boy." May sold John Anderson "a negro woman" in exchange for "200 good raccoon skins + 50 more if he is satisfied with her work." And since Detroit merchants served as bankers for their customers, keeping logs of complex accounts, debts, and exchanges, among May's business records are several transactions that he tracked for other Detroit slaveholders, including John Askin, who owed May for "a Negro Man named Pompey sold you," William Hands, who owed May for "making a pr of shoe packs" (moccasin-like boots) for a "Pawney Girl," and James Abbott, who owed May for "1 oak plank taken by your negro last fall." While some Detroit merchants were struggling in the postwar period when furs decreased in availability and value, May was enterprising enough to continue his upward climb by acquiring more property, leasing what he already owned, and becoming indispensable to the new American government.
Lieutenant Edmund Henn, _A View of Detroit. July 25th, 1794. E.H._ Courtesy of the Burton Historical Collection, Detroit Public Library. This image, rare in its lively depiction of the high level of activity on the Detroit River and its shores prior to 1800, appears to show people of color in the canoe in the foreground.
Chief among James May's calculated moves was the strategic use of his schooner the _Swan_. In 1796, the year the American military assumed control in Detroit, May leased his ship to the U.S. government to transport soldiers to the fort, making the _Swan_ "the first vessel in the lake region to fly the stars and stripes." The next year, May followed the proven European settler pattern of getting hold of cheap Indian land. With two partners, he purchased "several thousands of acres" in Macomb County from six Ojibwe "chiefs" for $50, clothing, and corn. While May was doing well under the occupying government, he lived in an unpredictable place still characterized as western and wild by most Americans in this era, a place where the population was small and culturally heterogeneous, the nearest city (Cincinnati, Ohio) was three hundred miles away, and the raw forces of weather and water could disrupt lives as readily as fluctuating commercial markets.
In the fall of 1801, James May learned what it meant to lose in a contest with the great inland seas. May's schooner _Harlequin_ had set out in late July with its captain, Joseph May, at the helm. Two months later, the ship had not reached any port and James May feared "that her and the Crew" had wrecked. Among the crew lost at sea were three sailors, including May's brother Joseph, and three passengers. "The stroke," May wrote to his colleague John Askin, "is a very severe one for me, the effects of which I shall feel for a long time; perhaps the rest of my days." Askin could commiserate with May. Askin had lost two ships of his own to storms and rough waters back in 1798 and had expressed the agony that ensued when " _madame bad luck_ took a passage" on one's vessels. For May and Askin, the financial losses went beyond damaged ships and included human property never to be recovered. One of May's sailors was an enslaved man, whose death, May feared, would have a disastrous domino effect. "The loss of the Negro man," May confided to Askin, "will probably be the cause of my losing the negro woman, who ever since the misfortune happened, has been delirious and is now very ill, in bed." May reached out to his friend for help in the form of a slave order, writing: "Being now deprived of two of the best servants, in this country, my sittuation [sic] is very distressing, unless you will condescend to let your Boy George, remain with me until I can have time to look about for a servant, his Mother is very anxious to have him stay with her, & says it will be the only comfort she has in this world now she has lost her Husband, to have her son with her."
The tragedy of the shipwrecked _Harlequin_ unveils an extraordinary, if blurry, picture of an enslaved family's circumstances in early American Detroit. James May owned the black father and mother of this family, while John Askin owned the couple's son, George. Although they lived in the same town, this family was physically separated. George's parents did not have the luxury of raising and caring for him. George's mother, a domestic servant in Askin's home, was crushed by the loss of a loved one at sea. This was a feeling she would have shared with other women attached to unfree men who plied the dangerous lakes not by choice and sometimes lost limb or life in the process. A man owned by William Macomb had injured a foot jumping between two vessels, a sloop and a canoe. John Askin's bondsman, Toon, had died at sea while working Askin's trading fleet. Other enslaved men had died in shipwrecks, clung to trees rooted in bare rock along the storm-swept lakeshores, and frozen to death while delivering letters in the harsh northern winter weather.
The wife of James May's drowned sailor, named either Jenny or Chloe (May does not take the time to specify which of his enslaved women he means), was valuable enough to her owner in a town where slave labor was a sought-after commodity that she had a built-in bargaining chip. James May was willing to buy the mother's son to assuage her pain, cut short her mourning, and get her promptly back to work. It is notable that this black family's crisis dominates May's letter to Askin rather than May's own familial loss, the death of his brother Joseph. May revealed to Askin that he could not promise "Money down" on the black boy, but would "endeavor to give you the worth of him some way or other." But despite his feelings of camaraderie with May, business was business. Askin did not make the sale, preferring instead to keep little George among his own property holdings.
John Askin had been living well since the war but was nevertheless anxious about his financial status. He watched the roller-coastering price of animal furs as beaver became scarce, values fell, prices rose slightly (for deer skins but not the more plentiful raccoon skins), and fell again. He chafed at the American government's imposition of duties on trade goods. By 1800, Askin was carrying uncomfortable debts and bemoaning the commercial opportunities in Detroit, woefully penning in his letters: "this Country is Over-done" and "Ruin, Detroit is not far from you." Discouraged, he shifted into semi-retirement and contemplated a move that would mean leaving behind his Detroit landholdings.
James May was not so pessimistic, even after the wreck of his ship _Harlequin_. He doubled down in Detroit, identifying with the fledgling American nationality that John Askin was loath to embrace. May became a justice of the common pleas court of the Northwest Territory and in 1801 accepted an appointment as Wayne County's militia captain. A forward thinker, he obtained a ferry license to transport passengers across the Detroit River—the newly established border between the United States and Canada. He also kept the accounts of Detroit's only printer and continued to trade in furs and goods. May did well in those turbulent years when soldiers, territorial appointees, and incoming settlers from New England transformed Detroit into an American-run place, at least, by all outward appearances. His granddaughter recalled that the family sipped from "solid silver wine cups." May himself remembered Detroit's early American years as a grand string of parties. "The citizens all lived like one family," he fondly reminisced. "They had assemblies for dancing and social intercourse, and the ladies never went without their silks. As a rule assemblies were once a week, and sometimes once a fortnight. Dining parties were frequent, and they drank their wine freely." It would have been black women like Jenny or Chloe who dressed white ladies in rustling silks, tended to guests at these balls, and laundered linens after scrubbing dance hall floors. And while enslaved women lived in close quarters with their owners in what was a densely packed urban environment, they may have differed with May's portrayal of Detroit residents as one big, festive family.
James May became a pillar of Detroit civic society after the American assumption. He championed the rule of law and building of roads and became impassioned about bringing education to the territory. May accepted U.S. authority with little sign of reluctance, but his long tenure in Detroit and close affiliation with British loyalists made him a Tory in the eyes of eager American newcomers moving in from the East, such as Solomon Sibley and Elijah Brush. Sibley, a native of Massachusetts who had been trained at Rhode Island College (now Brown University) viewed May as a pompous Brit and referred to him sarcastically as "Sir James." Sibley had first moved from New England to Marietta, Ohio, where he pursued the practice of law. He then relocated to Detroit in search of opportunity, and, by all indications, a wife. The move to Detroit would have made for dramatic change. Although Sibley had spent time within the Northwest Territory, he had resided in one of the areas most developed by Americans, where flagship Ohio River towns like Marietta and Cincinnati attracted settlers from New England as well as the mid-Atlantic and southern states. As a place where thousands of acres had been wrested from Native people in the Battle of Fallen Timbers and Treaty of Greenville, Ohio would soon become the first state to emerge from the Northwest Ordinance. The southern parts of Ohio, Indiana, and Illinois were nothing like most of Michigan, where indigenous societies still held oceans of land and the infamous Black Swamp that stretched from Michigan to Ohio made land travel treacherous. To a polished man like Sibley, the isolated fort town of Detroit was like another country. Indians, whose motives Sibley would have been unsure of, lived in large numbers in villages across the watershed; French, a tongue unknown to Sibley, was the common language of local residents. But on the bright side for Solomon Sibley, when he arrived in 1798, professional competition in the field of lawyering was slight in Detroit. His arrival made for a sum total of two lawyers working in town. He had hardly been practicing a month when the attorney general of the Northwest Territory, Arthur St. Clair II (son of the territory's governor), took advantage of fresh talent and named him deputy attorney general for Wayne County. Promoted nearly upon arrival to a plum government post, Solomon Sibley, recognizing his good fortune, tried to settle in. He found Detroit rustic at first, complaining that the town was "without taste or elegance," but he also called the bucolic scene of the fortified village at the river's edge "exceedingly pleasing as you approach it." Soon Sibley was writing: "I should feel myself quite contented to spend the residue of my days in this Country—But for one thing, we have no ladies here that I care a fig for—have been in company with some of the young French . . . but take no pleasure in listening to their French nonsense—They speak no English & I speak no French."
Major John Jacob Ulrich Rivardi, Artillerists and Engineers, March 29, 1799. _Plan of Detroit, 1796–1797_. Courtesy of the Clements Library, University of Michigan.
As one of few American civilians in town—they numbered less than twenty at the turn of the nineteenth century—Sibley found himself in a foreign cultural environment. Detroit was not yet culturally American, and the Northwest region as a whole was far from being racially white. The Second Continental Congress had set in place legislation for "a territory that had practically no white population and which, in a sense, did not belong to the United States at all." Most of the 327 inhabitants within Detroit's walls as well as those along the riverine suburbs were still predominantly French when Sibley arrived; even the British settlers who had chosen to stay and, through residency, become de facto Americans outnumbered American patriots. Along the banks beyond the fort's wooden pickets, hundreds of French farmers extended Detroit's social circles, as did indigenous families in settlements stretching beyond Lake St. Clair to the north and Lake Erie to the south.
An alliance of kinship existed between the early French and British settlers since many families were intermarried. Of the leading traders in Detroit during the British era, few wedded women who were not local. John Askin, who coupled with a French Detroiter, wrote many of his letters in the French language. But Solomon Sibley, a high-collared Massachusetts man with broad shoulders and a long patrician nose, was among an American professional class that did not care to mix intimately with the French _habitants_. French ladies, in turn, had their own reservations about "Yankee" men. Miss Navarre, a member of a French first family in town, had the misfortune of sitting in tobacco juice spat in her pew at Ste. Anne's Church by young Americans Frederick Bates and George Wallace. She later opined that these men "had more ill-manners & less decency than even the Yankees generally had." The cultural mosaic of Detroit confounded some Americans and delighted others. Frederick Bates, a quartermaster in the U.S. military, became smitten with the daughters of Commodore Grant, the British naval commander and slaveholder who had married a French wife. Bates, a handsome officer with wavy dark hair, thought Grant's bicultural daughters were "the finest girls in this country." He recognized his disadvantage, however, complaining that "the French girls" thought of Americans as "a rough, unpolished, brutal set of people."
Solomon Sibley had difficulty finding a spouse in the remote French and Indian town with a British influence now ruled by the Americans. If French women thought themselves too sophisticated for the Americans, Sibley thought himself too ambitious for the French. Shaped by a Protestant work ethic honed by a New England upbringing, Sibley characterized the French as "exceedingly ignorant and lazy." Certainly he would not have agreed with James May that luxurious parties once a fortnight were fitting or even proper for a tiny town built of wood on muddy, narrow roads. Detroit left much to be desired when compared to the Americanized cultivation of New England, or even Ohio, in Sibley's eyes.
Although he had been thus far unlucky in love, Solomon Sibley may have taken heart in his immediate rise in politics. The Northwest Territorial Legislature required a representative from Wayne County, where Detroit (and most of present-day Michigan) was seated. Although Judge James May seemed an obvious choice for the spot and ran with the backing of British loyalists, the Americans and, surprisingly, the French as well supported Solomon Sibley. Sibley won the seat in Detroit's first American election, perhaps, May charged, because Sibley's supporters provided free alcohol to voters and turned away others for being unfit for the ballot box. Victor nonetheless, the thirty-year-old Sibley began journeying back and forth to Cincinnati, Ohio, the seat of the Northwest Territory, and Chillicothe, Ohio, a second meeting place of the legislature. He once lost his way while traveling to attend a meeting, passing through forests and swamplands on buried paths.
As Sibley's travels southward show, Detroit reoriented politically toward Ohio (even while continuing to favor suppliers in New York). The majestic Queen City on the Ohio River that bordered the slave state of Kentucky, Cincinnati was the source of the mail in Detroit (which was extremely slow to arrive) and also the source of the news (even more sluggish). Because there was only one newspaper circulating in Detroit and the whole of the territory, the _Freeman's Journal_ published in Cincinnati, Detroiters posted public notices in French and English and dispatched a drummer to the streets when announcements were urgent. None of this sat well with Solomon Sibley. He saw the necessity for drastic change in Detroit, starting with the layout and position of the settlement. He felt that the picketed town was "exceedingly crowded with buildings leaving no room for further improvement." He was aware that his constituents fretted over the proximity of Native communities on the fragments of land that they still held. They urged Sibley to ask the "U. States" to "settle the lines between them & the Indians." These free residents also wished to see more white Americans moving to the area, being "desirous the United States would give full encouragement to the settlement of the Country on the lakes." A fair portion of Indian lands ceded in the Treaty of Greenville had not yet been occupied by whites, and Detroiters of that stripe were anxious to see the acreage settled, thereby "enableing" their region "to defend itself against their Indian neighbors, should a war take place." Not twenty years had passed since the close of the Revolution, and Detroiters were anxious about the start of another major conflict that would set indigenous people lately dispossessed of the bulk of their land base against the village.
Sibley took this desire for local development seriously. His first order of business as Wayne County's representative was to see Detroit recognized as a full-fledged town. On January 18, 1802, the territorial legislature approved Sibley's bill for Detroit's incorporation. Upon returning home from Ohio after this victory, Sibley was greeted by candles lit in every window and a "general jubilee" in Detroit. Loyalist John Askin watched these events unfold with vigilance, wariness, and a bit of pride, writing to an associate: "This place is incorporated. Mrs. Macombs farm and mine are in the Town. The legislature honored me so far as to make me one of five trustees . . . to whom they gave great authority." The French fur trading post and military fort established by Cadillac in 1701 was, one hundred years after its birth, an American town of the new Northwest.
By 1803, Solomon Sibley was scribbling sunny missives too, as he had found a fitting spouse and brought her back to his adopted hometown. "I am now settled at Detroit having removed the whole of my family, To wit, Mrs Sibley, to this place," he wrote in August of that year. "The journey was fatiguing due to the heat of the weather & the lowness of the waters." Despite the tiring travel, Sarah Sproat Sibley, formerly of Chillicothe, Ohio, was "pleased with the Country & its habitants," according to her husband. But while Solomon Sibley no longer felt lonely in Detroit, he was vexed by crucial changes taking place in Washington. In March of 1803, Ohio became the first state to emerge from the Northwest Territory. As a result, Congress placed Wayne County within Indiana Territory, the first territory to be carved from the larger Northwest in 1800. Detroit was now even farther away from the seat of regional government. The territorial circuit court judges who traveled to various locations hearing cases rarely made it to the Great Lakes interior. Sibley himself now had to travel an even greater distance—southwest to Vincennes, Indiana, in order to attend legislative sessions.
At these regional gatherings of territorial representatives, Sibley witnessed the tension that swirled around the subject of slavery. While existing records on Detroit do not reveal internal debates over slavery among town leaders who had mainly emigrated from the Northeast, other white settlers in the Northwest Territory, especially in Indiana and Illinois, vociferously resented the legal prohibition against slaveholding. Some of these individuals already owned slaves, and many of them hoped to acquire some to work in their salt and lead mines, convoys, and corn fields. Local officials on the ground in these parts of the Territory that had closer ties to southern states therefore interpreted Article 6 of the Northwest Ordinance as going into effect at some indeterminate future time. Settlers there submitted petitions to the territorial legislature and U.S. Congress pushing for a repeal or modification of the antislavery clause at the federal level. At a special convention of representatives in Vincennes in 1802, pro-slavery officials asked for the right to bring slaves into the Northwest Territory for the next decade, arguing that they should be "permitted to enjoy their property." In 1805, Illinois residents requested their own separate territorial government and the allowance of slavery. Although acquisitive settlers did not achieve these formal means of legalizing slavery, they concocted and regularized long-term arrangements of indenture that amounted to "de facto" slave ownership in sections of the Northwest Territory. Territorial leaders passed laws to make a virtual system of slavery possible by leaning on the fine line between involuntary and voluntary servitude. Supported by the wink and nudge of local officials, residents found ingenious ways to circumvent the general slavery prohibition of Article 6, principally by filing paperwork in the courts to transform slaves into indentured servants who were said to have freely consented to their status. It was possible, these Illinois and Indiana settlers realized, to find hundreds of "voluntary" servants among the enslaved population who had very little power of self-protection. Solomon Sibley may well have attended the meeting in Vincennes where the slavery issue was most hotly debated, but his own views on slavery are not disclosed in his papers. Sibley's New England background and later assistance to the eldest child of the Denison family suggests that he may have looked askance at underhanded attempts to extend slavery northwestward. Even if this was the case, the son he raised in Detroit, Henry Hastings Sibley, would later become a slaveholder (and the first governor of the state of Minnesota).
Regardless of his personal views, in Sibley's adopted home of Detroit, slavery was a system with deep roots, protected by French and British custom as well as by American law and international treaty. According to U.S. dictates, then, the eighty-four French and British families who owned slaves in Detroit before the close of the Revolutionary War had every right to continue possessing them after the passage of the Northwest Ordinance. Their children could also inherit this human property. The one population legally barred from owning slaves in Detroit was the very small number of newly transplanted Americans. They could not bring slaves into the territory or buy slaves once they were in Detroit without violating the Ordinance. But they _could_ marry into slaveholding French or British families, contract slaves through indenture, and hire the slaves of other residents at will. Although they were never so extreme in the pursuit of slavery as their Northwest territorial neighbors to the south, free Detroiters with an interest in maintaining or accruing wealth also found ways to evade the constraints of Article 6. At the same time, enslaved people in Detroit were pondering what this changed legal context meant for their prospects of freedom. As rules came down from the federal and territorial levels, and in the absence of any local laws structuring slavery in Detroit, unfree blacks and Indians in the town and surrounding suburbs prepared to capitalize on the fresh set of terms.
Between the unpredictable years of the Revolution and the heady first sessions of the Northwest Territorial Legislature, borders had been established and territories occupied in the Great Lakes. New flags had been planted. Imperial rivalries had cooled. But in the wake of a movement loudly proclaiming that "all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness," couples like Charlotte and Jerry, children like Betta, and families like the Denisons were still enslaved in Detroit. Today, reminders of the prominent people who stole the lives, livelihood, and labors of others dot the greening landscape of southeastern Michigan. The home of William Tucker, owner of the Denison family, still exists on the Clinton River, its original plainspoken farmhouse architecture occluded by a modern addition. Macomb County, where the Tucker home stands, carries the family name of Detroit's largest slaveholder. Just off of Belle Isle, the Detroit River island illegally procured by the Macombs and later purchased by the Campeaus, a street named after Joseph Campau bisects the city. And Detroit itself is situated within Wayne County, named for the famously "mad" General Anthony Wayne, who proudly dispossessed southern Great Lakes indigenous peoples, laying the groundwork for American ascendance in the Old Northwest and the world.
Detroit and surrounding area, 1799.
Detroit and surrounding area, 1800.
The Winds of Change (1802–1807)
Ruin, Detroit is not far from you.
_—John Askin, April of 1800_
When the Northwest Ordinance finally went into effect after the American occupation in 1796, Detroit had no applicable laws of its own. French civil law, overlaid by British common law, had previously operated in the settlement. And unlike many towns that would soon crop up in the sparsely populated Northwest region, Detroit stood on an international border and housed a large European settler population with rights protected by the Jay Treaty between the United States and Great Britain. The town was also surrounded by indigenous peoples, whose lands, though greatly reduced by warfare, treaties, and hasty sales pressured by the threat of a coming wave of non-Native migrants, still extended for hundreds of miles between Euro-American settlements. According to the Northwest Ordinance, these remaining Indian lands could not be taken without "consent," except in the case of "lawful wars authorized by Congress," language that anticipated and justified further territorial expansion by the U.S. government. Turn-of-the-nineteenth-century Detroit was a mind-boggling morass of murky rules and unspoken expectations. It was therefore a thrilling place to be a bright-eyed lawyer looking for the challenge of a lifetime, which is exactly what Elijah Brush was when he arrived, eager and unmarried, in the year 1798.
Elijah Brush had been born in Bennington, Vermont, in the early 1770s and educated at Dartmouth College in Hanover, New Hampshire. He came to Detroit to practice law and soon found fortune by making the marriage match of the season. The twenty-something Brush swiftly wooed Adelaide (also called Alice) Askin, the youngest daughter of John Askin and Archange Barthe Askin. Pampered through her girlhood, Adelaide Askin simply adored cosmopolitan fashion and finely crafted things. Despite her physical isolation from urban centers like New York City, London, and Paris, she was always in the know when it came to cutting-edge style. This was in part due to a steady flow of information from her older sister, Archange Askin, who lived in London and was married to a British military officer of the Royal Artillery Regiment. Archange penned letters to Adelaide spilling over with fashion advice and shipped them across the ocean to Detroit. Informed of the latest transatlantic trends by her sister, like the rage for gloves and turbans made of silk, Adelaide eagerly sought out premium fabrics and elegant designs. Ready-made clothing was unavailable in the shops of remote Detroit, so much of Adelaide's wardrobe would have been imported from elsewhere or meticulously hand-sewn by enslaved black women. Beyond being fashionable, Adelaide was well educated, having studied at L'Assomption de Sandwich in Canada. She was fluent in both French and English and had grown up enjoying the domestic services of indigenous and black women who had been stripped of their freedoms.
_Part of St. Anne's Street in 1800_. Engraving by Silas Farmer from a watercolor by Lieutenant Colonel Jacob Kingsbury or George Washington Whistler. Silas Farmer, _The History of Detroit_ (Detroit: Silas Farmer & Co., 1884), 368. Courtesy of the Clements Library, University of Michigan. This drawing of Detroit's main thoroughfare depicts the French village aspect of dwellings prior to the 1805 fire.
By catching the eye of Adelaide Askin, the enterprising Elijah Brush inserted himself into a well-heeled, landholding, bicultural, multilingual old Detroit family. No wonder Brush was filled with "exceeding great joy" at the "prospects of speedily being married to Miss Askin," according to his friend, the fellow New English attorney Solomon Sibley. And Brush was equally enthused, Sibley added, about "a fair way to realize a fortune," which Brush believed was on the near horizon at Detroit, as he had heard that a "New County" was being designated with "the County Town . . . established on the Pra[i] rie." Brush's impending nuptials and Detroit's bright future were intertwined in the eyes of the observant Solomon Sibley.
Elijah and Adelaide chose the festive annual celebration of Mardi Gras, observed enthusiastically in French-Catholic Detroit, as the season for their nuptials. Father Levadoux performed the service at Ste. Anne's Church on a February evening in 1802. The newlyweds, whose wedding had been the social event of the winter, next endeavored to establish their household together. Adelaide Askin likely brought a slave with her into her home with her new American husband, while Elijah Brush busied himself with procuring imported dishware and delicacies for his bride. "I have lately [entered] into a matrimonial life with Miss Askin," he wrote to the merchants he frequented in Albany, New York, "and find myselfe [sic] under the further necessity of troubleing [sic] you again with a further commission, which I expect to be obleiged [sic] to repeat annually." Brush ordered, among other things, from the shop of Robinson & Martin: "one Set of fashionable guilt chinea [sic] complete with coffee cups & c One barrel of loaf Sugar and Coffee, one fourth chest of best hyson tea; 1/2 barrel of best 4th proof 1 dozen handsome knives & forks." While most Detroiters made use of goods provided by merchants in town and could not afford personal imports, Mr. and Mrs. Elijah Brush preferred items of distinction, no matter the expense and waiting time. Elijah Brush ordered one dozen silver teaspoons engraved with his initials from New York, quipping about the low quality of local craftsmanship: "if you give a Silver Smith in this Country Silver to work you'll never get either work or Silver." When his wife was displeased with the color of Rusha sheeting fabric sent by Martin & Robinson's shop, Brush "disposed of it and ordered another piece." He sent to New York, as well, for Adelaide's accessories and clothing, ordering a "fashionable Summer cloak," a "fashionable Bonnet for Summer," and enough kidskin ladies shoes for Adelaide to change her footwear twelve days in a row. When the couple's first son, Edmund, was born nine months after the winter wedding, Elijah ordered shoes for the boy as well. For himself, Elijah requested "1 Superfine fashionable coat Dutch cloth," "1 pair of black Striped Velvet pantaloons and Vest of the finest quality," and "1 fashionable beaver hat" from New York, closing the loop of the fur trade that was his new town's chief enterprise. Detroit produced furs and shipped them East so that cosmopolitan professionals like Elijah Brush could wear the beaver hat as a status symbol all across the coasts of the Atlantic.
For the Brushes, the buzzword was "fashionable," and as a leading lawyer in the town, Elijah Brush could afford to wrap his young family in luxury. In 1803, he ordered an elegant two-wheeled carriage with a folding roof, called a _caléche_ , from Robinson & Martin's firm in New York. The next summer two copycat carriages appeared on the narrow roads of Detroit, ordered by officers at the garrison. The Brushes had become the town's "Joneses," trendsetters who influenced norms and sparked the competitive desire to "keep up." And in a place where slavery was still widely practiced despite the territorial law that curtailed it, the couple's eye for the next best thing soon turned to bondspeople. Peter and Hannah Denison, an African American couple toiling away on the Tucker farm in the countryside of the Huron River, had developed a reputation in the area. Before long the Brushes would seek the same kind of distinction in their choice of servants as they did in consumer goods. They would import Peter and Hannah all the way from the sticks to work in their fashionable urban household.
Elijah and Adelaide Brush House. _Detroit, 1852_ by R. Bürger. Library of Congress, Prints and Photographs Division, LC-DIG-pga-00350. The Brushes purchased this farm from Adelaide's father, John Askin, before he moved across the river. Enslaved people lived here with both families.
Mr. and Mrs. Elijah Brush calling card. Benjamin F.H. Witherell Papers, 1791–1924. The Burton Historical Collection, Detroit Public Library. Adelaide and Elijah Brush were members of Detroit high society who enjoyed convivial entertainments and cosmopolitan fashion. Adelaide was the child of a British merchant and French socialite. Elijah was an American attorney from New England.
The self-confident Elijah Brush met with approval from British-identified John Askin, who wrote to a friend about his American son-in-law: "he promises fair, has a good character and [is] reckoned a good lawyer which is not a bad profession in this quarter." To a business partner, the practical Askin also expressed his approval of young Elijah, writing that Brush was "an able Lawyer, has considerable practice is sober and industrious therefore I believe Alice has made a good choice." Askin's respect for Brush would have made the dilemma that Askin was weighing a little easier to settle. Despite his positive observations that "the Gentlemen on this side" of the river treated him with "nothing but politeness and civility" and "debts are recovered here without delay which is a great Object for a Merchant," Askin had misgivings about continuing to reside in American Detroit. He preferred to live in British territory and, consequently, to avoid American taxes on his business transactions across the border. He therefore elected to relocate with his wife, sell a portion of his real estate, pay off debts, and leave his youngest daughter and son-in-law behind in Detroit. "In the course of two weeks we remove over the River," Askin soon told an associate, "but I will be a great part of my time here to attend to the lands and [etc.] on this side." Near his departure date, Askin wrote to a trading partner, perhaps referring to livestock, perhaps referring to human chattel: "Part of my stock are sent over the River and in about two weeks we will move after them." According to a traditional history of the early American period in Detroit, the town had "lost a grand old man" upon John Askin's leave-taking. Askin's enslaved laborers, who would now become residents of Canada as well, may have thought otherwise.
By the spring of 1802, John Askin was off to Canada, but the relocation to British turf was bittersweet. Settling in at his new abode, charmingly named Strabane after his birthplace in Ireland, meant abandoning the beloved Barthe-Askin farm along the north side of the river. Askin was therefore buoyed by the news that "Lawyer Brush" was "desirous of purchasing" the family estate in Detroit. The newlyweds lacked cash on hand to pay John Askin's £2,000 asking price, but they moved into the home with Askin's blessings and paid taxes on the property. In part because Adelaide Brush wished to remain in Detroit rather than relocating to the Ohio Country as Elijah had at first intended, by 1805 Elijah was planning to "sell some lands he has in the States" and pay Askin for the Detroit property. Adelaide longed to keep the French farm in the family, and Elijah sought to please his nostalgic bride. "She has the same desire of being perpetuated in it that Mrs Askin [her mother] has on account of the family tradition it has already passed through," Brush explained to Askin, his approving father-in-law.
Brush finally purchased the farm at the price of $6,000 U.S. after living there rent-free for nearly four years. He would obtain the "premises with all the appurtenances, privalages and Commodities to the same." The Askin farmland, "being on the Detroit or Streights of Lake Erie" lie "mostly in what is now called the Town of Detroit," and boasted a royal pedigree. It had been "ceded and granted by Charles Marquis-De-Beauharnois knight of the Royal and Military order of St. Louis . . . and Gilles Hocquart Knight and member of the King's privy counsil . . . to Eustache Gamelin . . . and Granted by Piquotee Belestre Military and Civil Commandant for the king at Detroit unto Jaques Pelet" before coming into the Barthe family. Layered into this legal record of land exchange dating back to 1747 are decades of colonial presence and the selling of land as a commodity. Nowhere in the document is an original purchase from Native people indicated. Neither does the sale of the Brush farm reveal the consent of any woman. For this coveted parcel had fallen first into the possession of a British male in-law, and then an American male in-law, the lucky Brush. Handed down in the families of French women, the land would be legally retained by English and American men. Brush could thus buy his own wife's family farm and make this transfer of landed power seem like a gift to her. During his time on the farm, Elijah Brush built his legal practice. Brush and his father-in-law grew all the closer, and Brush began to represent John Askin in land deals that remained essential to free white men's success in the region.
While Askin family members then in Upper Canada sent pleasing treats like an "Indian sack full of Cramberry [cranberry]" over to their cherished Adelaide, Elijah traversed the frozen river many a time to visit with his father-in-law in cold weather months. They were a tight-knit clan. And while Brush may have preferred deep down to strike out for Ohio, where he already owned land, it was plain to see that he had found a plum situation in Detroit. Just as John Askin had benefited from marrying a French wife and settling on her family's farm beside the fort a generation earlier, Elijah Brush married into prime property when he wed Adelaide Askin, daughter of one of Detroit's most prominent traders and largest slaveholders.
Recalcitrance and Rebellion
In order to improve his circumstances, John Askin only needed to sell his properties, tidy up his finances, and move to one of his other plots across the Detroit River. And while this was not a simple proposition given the losses he had taken in the fur trade as well as his failing health due to elder age, it was a readily achievable goal that did not entail the risk of life or sacrifice of loved ones. The lives of enslaved people were entirely different and considerably more constrained. Black and indigenous men and women held in bondage also carefully assessed their situations in the first American years of the late 1790s and early 1800s, scrutinizing shifting structures of governance, flows of capital, and social relationships. The transition from French to British rule at the end of the French and Indian War had meant few changes for unfree Detroiters. Raiding during the American Revolutionary War had brought larger numbers of African Americans from the South into the region, making the 1780s the high mark of slavery in the town in numerical terms. The Americans' passage of the Northwest Ordinance had meant little in the decade when British officials had refused to relinquish western posts. But the wheels of political power, as well as the century, had now turned. What changes would the British withdrawal and the official American presence usher in for those who lived in slavery?
British loyalists who moved to Canada, such as John Askin and Matthew Elliott, brought their bondspeople along with them, increasing the enslaved population along the border with the United States. An ordinance passed in 1793 by the lieutenant governor of Upper Canada, John Graves Simcoe, outlawed the importation of new slaves to Canada and introduced gradual emancipation but permitted British subjects crossing the river to retain their human property. Slavery would be legal in Canada until the British parliament ended it throughout the territories of Great Britain forty years later in 1833. By the time John Askin arrived, former Detroiter Matthew Elliott and his fellow British military officers, Alexander McKee and Henry Bird, had already moved to present-day Ontario and established homes on land bestowed on them in 1783 by Native allies from the Revolutionary War. Elliott "was given the allocation nearest to Lake Erie, and his home and farm were soon to become a landmark for those approaching Detroit via the Lake Erie-Detroit River route." He steadily expanded his land holdings, resulting in a "home and farm that became a show-place in Upper Canada." An unforgettable aspect of that "showplace" to some observers was its striking resemblance to a southern plantation. Matthew Elliott, a British Indian agent with a Shawnee wife (one of several Native women he partnered with in customary marriages or informal liaisons over the years), possessed more than eight hundred acres by the early 1790s and presided over a magisterial farm where "he did not directly engage in farming himself, but ran it as a plantation with a steward or overseer to supervise his Negro and Indian slaves." To a commander at the nearby fort in Amherstburg, Captain Hector McLean, this slaveholding Indian agent was infamous for his wealth. McLean wrote that Elliott "lives as I am informed in the greatest affluence at an expense of above a thousand a year. He possesses an extensive farm not far from the garrison stock'd with about six or seven hundred head of cattle & I am told employs fifty or sixty persons constantly about his house & farm chiefly slaves." Another, more favorable observer traveling through the area enthused: "The farm belonging to our friend, Captain E . . . contains no less than two thousand acres. . . . His house, which is the best in the whole district, is agreeable situated, at a distance of about two hundred yards from the river; there is a full view of the river, and of the island of Bois Blanc, from the parlour window." Elliott's bucolic riverside farm was the setting for whippings of enslaved people who were secured to a locust tree with an iron ring and shackles.
On the American side of the Detroit River, slavery also continued apace. The federally appointed governor of the Northwest Territory and slaveholder, Arthur St. Clair, had widely publicized his view that the provision of the Northwest Ordinance limiting slavery was ideational and meant to curtail future, rather than present, activity. He had written in 1793, and announced to Illinois residents prior, that "the declaration that there shall be neither slavery nor involuntary servitude in the said Territory . . . was no more than a declaration of principle . . . but could have no retroactive operation whatever." In the Northwest Territory, French and British residents still owned slaves, and Americans had access to bondspeople owned by prior settlers. Some free residents across the Northwest Territory took advantage of this flexible situation, attempting to acquire slaves. But ambiguity had its costs. Would-be slaveholders in Detroit felt discomfort about whether their intentions would be legal. They carried the angst of residing in a gray area between the letter of congressional law and common practice on the ground. Governor St. Clair's statements about the "principle" of the Ordinance had been intended to allay such anxieties, but in Detroit, a northerly border town with a stream of New Englanders trickling in, such worries could not be fully assuaged. Slavery in American Detroit was persistent but unstable, reflecting the "fragile legal constructions" that characterized northern slavery in the post-Revolutionary "gradual emancipation era."
Enslaved people in the town and closest farmsteads, counted at thirty-one in the 1796 Wayne County census (after many had been removed by their masters to Canada), saw little immediate improvement to their situations following the passage of the Jay Treaty. But a few years later, by 1800, unfree people were doubling down on their acts of defiance. Just as they had before the Americans took charge, enslaved men and women fought the injustice of exploitation with the limited mental and physical weapons available to them: withholding compliance, pilfering property, battling members of the master class, and stealing themselves away. Attempts at escape increased in both number and boldness. The papers of Detroit merchants who were dissatisfied with their slaves, as well as of Solomon Sibley, who managed local legal complaints, offer glimpses of the range of rebellious actions unfree people took at the turn of the nineteenth century. In 1801, a "Pawney man" belonging to the Frenchman "Mr Barth" was accused of assault against a J.B. Nadau. In March of 1802, Jaco, "a Pauni" owned by Frenchman Simon Campau, acted "contrary to the obedience due to [Campau] as his master." Jaco had "absented himself and doth still absent himself from his said Masters Service." Campau entered a formal complaint in the matter, seeking the territorial circuit court's intervention. Toby, a "Panisman," was arrested and jailed in 1807 for absconding and was returned to George Cotteral, who "claim[ed] the Said Toby as his Slave, and acknowledge[d] that he hath humbled himself to his Satisfaction." Mary Abbott, an Englishwoman, complained in the summer of 1802 that "her slave Susan a Panie has resisted and refused to obey her lawful Command contrary to the obedience due her mistress." Mary Abbott turned to the courts as did other slaveholders, with the result that constables equipped with a warrant were ordered to "apprehend the said Susan a Panie . . . to be further dealt with according to Law." It was a difficult stretch of years for Abbott women in terms of trouble with recalcitrant bondspeople. Elizabeth Audrain Abbott, wife of Robert Abbott, found herself threatened with a whipping by her slave. A black woman named Mary, described as a "negro wench" in the court record, was jailed after "beat[ing] and abus[ing] her mistress, the same Mrs. Abbott." Robert Abbott then endeavored to sell the black woman to Thomas Jones, who declined another offer of a "Pawny Boy" from Mr. Pattinson in order to buy this woman who had been promised as having "no fault except beating his [Abbott's] wife." However, when Jones discovered that the jailed Mary "was rotten with the pox," he took Abbott to court in order to break the contract.
In American Detroit governed by the Northwest Ordinance, long-standing resident slave-owners like the Campaus and the Abbotts had in their favor a more functional judicial system to which they appealed for intervention in controlling their human property. Now masters could use territorial courts to enlist police power in the correction and apprehension of unruly or runaway slaves. But at the same time, the Ordinance limited how enslaved people could be held and transferred in Detroit. Solomon Sibley's handwritten notes on the _Jones v. Abbott_ case, which he argued in court, open with the lines: "1 point—By the common law a negro is no[t] a slave or the subject of property. . . . The Statutes and laws of this Country, do not recognize slavery—But on the contrary expressly negative such a state in society—Vide the ordinance of Congress passed 1787. Article 6." Based on this reasoning, Sibley contended that Abbott was unable to "establish his right in this property," meaning Mary, and therefore the contract was null and void. While Sibley's sense of clarity in interpreting the Ordinance was not shared by everyone, his trial notes hint at the raincloud the Ordinance represented over the heads of slaveholders, whose only umbrella was the Jay Treaty.
Enslaved people in Detroit also proved aware of the import and potential of Article 6, and they were learning to effectively use the courts just as slave-owners had. The case of the Smith family, though sketchily preserved, provides a glimpse into the first documented use of legal strategy by African Americans seeking freedom in Detroit. Antoine and Anna Smith, an African American couple with children, leveraged the law to put an end to their harrowing experience of varied forms of captivity dating back decades. The Smiths were attendees at Ste. Anne's Catholic Church, where a priest recorded fragments of their story. Father Gabriel Richard described the pair as "free negroes ransomed in the past few years from the said Indians who had made them prisoners in their youth." Antoine and Anna had been captured by Native people, probably during the Revolutionary War. They were freed from captivity at Fort Wayne in Indiana and "taken to be husband and wife." For reasons left out by the priest, the couple came to Detroit where they seemed to have a brighter future ahead. In 1803, Anna gave birth to a baby girl, Therése, who was baptized at Ste. Anne's. But by 1805, the Smiths were in dire straits yet again. Anna and the children had been snatched by a local slaveholder, or perhaps sold to him in violation of the Northwest Ordinance. In response, "Anthony Smith, a black man," hired a lawyer to contact the offender who "h[e] ld them as slaves." A.J. Hull, attorney for the plaintiff, wrote to the Frenchman Jacques Laselle that Smith demanded the "release" of "his wife and children, from slavery." Hull's letter continued with the lightly veiled threat: "As you must be sensible as well as myself, that slavery is prohibited, by the ordinance which forms this territory, you cannot hold them as such. By giving his wife and children to him now, you will save yourself much trouble and expense. If you refuse I shall immediately commence my suits, which will be expensive to you, and will surely recover them in August."
Lasalle's reaction to this letter demanding the release of the Smith family does not survive. He probably relented, given the absence of further court documents in the case and the blatant machinations of other local slaveholders to appear as though they were complying with the Ordinance. The Smith family's legal strategy won the day, but their anguish lasted months. Anna and the children were in the hands of Lasalle at least as early as June 5, 1805, when Hull wrote his letter. Hull did not expect to recover them until August. Antoine, a husband and father, must have agonized each passing hour about the suffering of his loved ones during that extended wait. Following their ordeal, the family returned to the multiracial community of Ste. Anne's Church, where a handful of other blacks also worshipped. In 1816 church records show that Anne Smith, "a free negress," gave birth to another daughter named Angelique.
British captain Alexander Harrow, who had already lost a man named Sampson to an escape in the 1790s, encountered difficulties for the second time when Robert Taylor, a black man, absconded from him in June of 1802. Harrow had a warrant issued for Taylor's arrest. But by the next month, an exasperated Harrow was offering Robert Taylor a contract of indenture, in which he attested: "I Alexander Harrow of River St Clair of Wayne & Territory North-West of the Ohio, being willing and desirous that Robert Taylor, a negro man of about Thirty years of age, and a slave servant of mine for life . . . should at a future day & within a reasonable time, obtain, possess & enjoy, full and entire freedom." The term of indenture was set at four years, during which time Taylor was to "well and faithfully, work, labour and serve" Harrow and "at all times during said Term, behave himself, honestly, uprightly and faithfully." If Taylor failed to meet these conditions, his status would revert back to slave for life. If he complied, he would receive at the end of four years "A suit of cloaths adapted to his Station in Life," courtesy of his former master. Harrow, who was losing valuable property to escape, thought it wise to offer a promise of future freedom in exchange for the loyal service of his African American bondsman. Against his preference to simply hold humans as chattel outright, Harrow had been compelled to negotiate with Robert Taylor in a new legal environment that limited slavery.
Captain Alexander Harrow slowly grasped the reality that it had become harder to keep slaves in Detroit, a town where New Englanders were gaining more influence. As enslaved people grew aware of the opening that the Northwest Ordinance created and the changing demographics on the ground, they ran more frequently and refused to return unless they could negotiate better circumstances. Harrow therefore resorted to the practice of indentured servitude, which other slaveholders in Detroit adopted as a method of holding de facto slaves at the same moment. Correspondence regarding John Reed, a black runaway from Kentucky, points to indenture as a tactic used by Detroiters, like others in the Northwest, to take advantage of the language in Article 6 of the Ordinance, which did not prohibit _voluntary_ servitude. After being advertised as a runaway by his master, Reed was "taken up and confined" by Detroit slaveholder James May, now a U.S. marshal, "in the Common Prison of said County of Wayne." Daniel Ransom, an agent of Reed's owner, owed May $200, a price that included the reward money for Reed's capture and the cost of his incarceration. The agent, Ransom, worried about whether the enslaved man could be kept captive in Detroit and therefore included a contingency in the contract for Reed's return. Ransom would not pay May, the contract stated, "should the negro escape."
Reed's plot thickened. Deputy Attorney General Solomon Sibley wrote to John Reed's former owner, Colonel Grant of Licking, Kentucky, detailing the situation and commenting that the bounty hunter, Ransom, wanted to purchase John Reed for himself. This, however, would be difficult in Detroit, as new slaves were not supposed to be bought and sold in the territory. It would likewise be tricky in Canada, where the importation of slaves had been prohibited since 1793. Sibley explained to the Kentucky colonel: "The Negro if he purchase cannot by him be held as a slave on either side. Mr Ransom's only method will be to get the fellow to endent [sic] himself for a term of years. It will rest with you to determine whether it is not better for you to sell him for a much reduced price to what he would command in Kentucky rather than risk taking him thither thro' the Indian Country." Sibley's frank assessment confirmed a further complication in this case: there was a great chance of losing Reed altogether if Colonel Grant sought to transport the bondsman southward. In order to reach Kentucky, Reed would have to be brought through Indian territory, and Reed was "an arch lad" who had "acquired a knowledge of the Indian language." Since Reed could not be sold in Detroit and was a flight risk due to his linguistic skills and Detroit's location in Indian country, Sibley suggested that Reed be pressured into indenture while he languished in jail awaiting an uncertain fate.
Under the Northwest Ordinance and American authority in Detroit, enslaved people had attained a status ambiguous enough that slave-owners now had to think twice about how to transport, retain, and claim them. In addition, the formation of a newly defined international border along the Detroit River highlighted pathways for escape that made calculated risk-taking more possible for bondspeople. Enslaved men and women could run south to Ohio, they could go east and cross the river into Canada, and they could hide out in adjacent indigenous territories that lay between the town of Detroit and both of these routes. Tensions between the U.S. and British governments, as well as between various Native groups and the Americans, meant that enslaved people had now gained an advantage that indigenous tribes had long employed in the region: playing imperial powers off of one another. Slaveholders, wary of both Indian hostilities and the unknown wilds of lake-country nature, were hesitant to track enslaved people into the swamps and Native villages surrounding Detroit. And back inside the wooden pickets of the town, a novel legal environment was leading would-be slaveholders to pursue indentured servitude instead of clear-cut slave ownership.
A record from 1799 further indicates Detroit slaveholder strategies in this altered political context. In order to avoid legal complications for selling a slave, Charles St. Bernard, a merchant of Hamtramck Township, contracted an "indenture" with Henry Berthelet, a merchant of Detroit. In actuality, the document entails the sale of a small child, the "young negro girl, Named Veronique, about five years of age," rather than a time-limited labor agreement. According to the contract, Berthelet is: "TO HAVE & TO HOLD the said young negro girl above bargained & sold, for and during her natural life" for the "Sum of SIXTY POUNDS New York Currency." Bernard and Berthelet take pains to explain that Veronique was "born within this County, when under the Dominion of his Brittanick Majesty, and has never been out of it since the United States have taken possession of same." Carefully spelling out the child's place of birth and permanent residence in British Detroit allows the men to demonstrate that she can be held under the rules of the Northwest Ordinance. Further, to hedge their bets, the merchants introduce their bill of sale by describing it as "this INDENTURE made at Detroit." Their contract was signed, sealed, delivered, and recorded by the Wayne County court.
Too young to fend for herself or broach an escape, Veronique became the property of Berthelet. But John Reed, a grown man who had already shown that he would run, may have been offered a more forthright contract of indenture, as this was the best means for the would-be buyer/bounty hunter to hold on to him, as well as for his Kentucky owner to redeem some value from the loss of him. While being an indentured servant in Detroit could not have been Reed's desired outcome when he first fled, it was a status that offered greater potential for the future than lifelong slavery in the American South.
Elsewhere in the Northwest Territory, indenture was also being employed as a secondary form of confinement. The practice was common in Illinois and Indiana, where a "terrain of unfreedom" developed on the shadow side of the Ordinance. Often, enslaved people were pressed into servitude contracts with only a veneer of consent. In Marietta, Ohio, in 1802, "a negro boy under the age of twenty-one" named Bob signed a contract of indenture with Dudley Woodbridge, using an X as his mark. Stephen Wilson, a man from Virginia, had previously owned Bob but attested: "I have this day received of said Woodbridge the sum of two hundred dollars for a relinquishment of my claim to the said negro boy." Woodbridge paid Stephen for Bob, who then agreed to serve Woodbridge as his master until he reached the age of twenty-one. In Wilson's words, a "bill of sale" was made granting Bob "his freedom, to enable him to bind himself by indenture to Dudley Woodbridge." Bob was sold to "free" him up to sign an unpaid labor contract. Bob did manage, however, to extract something of value for himself in these negotiations. According to the agreement, Woodbridge would: "At the age of twenty-one years . . . provide and furnish the said Bob with good, comfortable and sufficient apparel, meat, drink, washing, & lodging; and will learn him the said Bob to read." If Woodbridge kept this promise, Bob would be literate by the time he attained his actual freedom. The documents describing Bob's sale and indenture found their way into the archives of Detroit when the Woodbridge family moved to town in 1814.
While enslaved blacks like John Reed were able to slightly improve their status through indenture, several individuals held as slaves in Detroit found other ways to inch toward autonomy. They began to collect wages for their work as a trickle of American migrants moved into town in need of labor. Eager American lawyers, merchants, and doctors kept farms in addition to practicing their professions and sought skilled agricultural and domestic workers. This included compensating enslaved people who were hired out by their owners and allowed to retain some of the income, or who were permitted to hire themselves out. David Maney paid Eli[z] abeth Burnutt "for her washing" in September of 1802; she attested to the receipt of this sum by signing with her mark. Evidently a practiced washerwoman, Elizabeth was also a seamstress. The man who owned her, William Burnett, had been owed "Cash to your woman to pay for mending" two years earlier. Merchant James May recorded that William Robertson owed "half pay of Pomps wages for attending cattle [in company] with John Askin" and that Charles La Leavre was owed "By 1 days work of his Man helping to kill pigs By work for self." A woman called Black Betty owed in May's ledger for five pounds of beef, which she may have planned to pay off through the exchange of her labor. This was probably the same Bet sold with her two sons by Sarah Macomb after William Macomb's death in 1796. In the Macomb family account book several individuals received pay for services: Charity for washing, Suana for washing, Sisco for masonry, and Will for chopping wood. A woman called Black Patty, who may have attained her freedom, was earning enough to accrue livestock and pay her debts in cash. In 1801 Patty conducted business with or through James May, had an "account" on file with him, and had paid "10 dollars + Cash 3 dollars" toward "a cow + calf 17 Dollars + 50 Cents."
Beyond creating a market for finite indenture contracts as well as paid work, American jurisdiction in Detroit had a third unexpected benefit for the enslaved: an enlarged geographical community. Raiding during the Revolutionary War had increased the black population in town, which meant more available free labor for slaveholders. But higher numbers also meant the black community as a whole was bigger, potentially more robust and resilient. Having a greater number of African Americans in the area—most of them enslaved, a few of them free—increased the chances for social alliance, communal collaboration, and organized rebellion among blacks as well as among unfree people of indigenous ancestry. One truncated but telling example points to a growing black community in the southern Great Lakes that may have channeled its collective energies toward a radical challenge of slavery in the area. In 1803, a fatigued British captain outlined the "cares" of his French wife in a letter to John Askin, his relative by marriage. The unruly behavior of her slaves had driven his wife to distraction, groused Captain Alexander Grant. Mrs. Grant's bondspeople were "very ungrateful and turbulent," and her "Cursed negroe wench" along with a black man lately purchased from Matthew Elliott, were both in jail for theft. Grant complained that the jailed pair were suspected of carrying "information of a great number of vagarents hovering about here to bring off as many negros as they can And as I am told forming a Town on the other side of Sandusky. at present there is forty Black men there."
Grant's grumbling letter reveals that African Americans clustered on the south side of Lake Erie were rumored to be easing into Detroit River settlements, stealing items, sharing strategic intelligence, and encouraging enslaved people to escape. The specific community described by Captain Grant in 1803 was undoubtedly the same one encountered by Moravian missionaries who followed the Miami River to Lake Erie in 1808 and were the first to document the settlement by name. "After we had passed through a place where twenty years ago an old Wyandotte town had stood, we came to Negro town where about six or seven Negro families live. They have been among the Indians for a long time, and have taken over their way of life," penned one of the fascinated Moravian brothers. After entering the Wyandot-African village just outside of Upper Sandusky near the mouth of the Sandusky River, the traveling missionaries were served by a black woman host, who "spoke English very well," and gave them "cornbread and coffee," the latter being a preferred drink among the villagers. The Moravians took care, while in the home of their host, to follow "Indian custom" and accept the victuals she offered. A Methodist minister called Benjamin Larkin passed through two years later, and remarked upon the same settlement where "some Negroes and Indians dwelled."
These survivors of war, slavery, and migration encountered by the missionaries had come north by various routes in the late eighteenth century and resided with Wyandots, members of the Wendat (Hurons, Petuns, and Neutrals) diaspora set in motion by wars with the Iroquois in the middle 1600s. Some blacks in the village had been brought in as captives but later lived as free people; others may have entered as free. Some of these individuals were mixed-race of African and Native ancestry, but seen as "Negro" by the Moravians due to their darker skin tone. Some may also have preserved African and African American spiritual and folk practices, as not very far away, in Fairfield, Upper Canada, Moravians had observed a black woman with a broom that was "somewhat like the fetishes the Negro in Guinea fashions out of roots" and was believed to bring protection to its bearer from "illnesses and misfortune." This village south of Lake Erie was the same community that produced the free black trader who worked between Detroit and Ohio with a Wyandot partner in the 1790s. When the Wyandots were compelled to sign away territory to General Anthony Wayne after the Battle of Fallen Timbers in 1795, most tribal members moved westward. Several black families who had acclimated to Wyandot ways stayed behind. Tension grew between the groups, as the Wyandots, pressed to remove and take stock of their now meager resources, began to distance themselves from people of African ancestry in the village. The black, mixed-race, bicultural residents who remained rebounded from this rejection and received other African descendants into their midst, especially runaway slaves trickling in from the U.S. South. Negro Town (a name that would stick well into the early twentieth century and later be disparaged as "Nigger Town" by local white Ohioans) became a radicalized community of color out of necessity. Mrs. Grant's black woman and the man with her in jail likely had connections there, suggestive of a free black network based near Lake Erie and the interconnected Detroit River region as early as 1803. In the summer of 1807, James May on the American side complained to John Askin on the Canadian side that his own enslaved man, Nobbin, had escaped and that "a bad set of people about" were also trying to persuade Askin's enslaved boy, George, to run across the river. These "bad people" may well have hailed from Negro Town. Enslaved blacks and Indians in Detroit now had another destination should they take a gamble on seizing freedom: a black village in the remote, semi-protective zone of former Indian lands not yet settled by whites.
Despite the continuation of slavery, circumstances in Detroit had shifted in discernible ways for unfree people as well as their owners several years into the new American era. The disruption of the Revolution had reshaped the racial makeup of Detroit's population, dispersing more African Americans throughout the region. The Northwest Ordinance narrowed pathways to slaveholding for Americans, while the Jay Treaty drew a boundary that highlighted routes for escape to foreign territory for enslaved people. In this environment, captives found greater opportunity for boldness. Escapes were more frequent, and freedom-seekers identified multiple destinations. In addition to fleeing south toward Sandusky or Cincinnati across wild terrain that no white gentleman relished entering, bondspeople made for Native towns, viewed as equally formidable by slaveholders even in the aftermath of the Treaty of Greenville that had stripped indigenous groups of most tribal territory in Ohio. From one community home-base with both a black and Indian imprint, Negro Town of Ohio, clandestine attacks may have been waged against Detroit slaveholders to rile bondspeople, seize goods, and spread the message of freedom. Just as John Askin had sensed when he packed up his things and moved to Canada, winds of change were in the air along the strait.
Legislating Detroit Town
While enslaved people in Detroit pushed for liberty in radical ways, Elijah Brush's professional star continued to rise. His father-in-law, John Askin, wrote that Brush was "an industrious man and except for improvements is by no means extravagant for a man who earns so much for his profession" and noted with paternal pride, "His practice is worth a great deal." In 1803 Brush was appointed as a trustee of the board governing the township of Detroit (as had been his father-in-law before the move to Canada). Brush was responsible, along with a handful of leading men, for devising local rules, ensuring the compliance of the public, and handling complaints. The board's first municipal ordinances addressed fire protection and the sale of foodstuffs. Bread now had to be stamped with bakers' initials and sold for the fixed price of six pence for a three pound loaf. Instead of allowing farmers (primarily French residents) to come to town with carts of eggs, butter, beans, vegetables, and meats on Sunday and commence selling these products following mass at Ste. Anne's, as was the local custom, the board established market days on Tuesday and Friday and designated a set location by the river that would serve as a farmers' market. Tavern keepers were prohibited from allowing "any minors, apprentices, Servants, or Negroes to Set drinking in their houses, at any time, or to have any Strong drink, without Special order & allowances of their parents or masters." This directive indicated the finely graded class stratification in Detroit as well as town leaders' continued efforts to control the behavior of societal underlings. "Negroes," a term nearly synonymous with "slaves," were classed right along with poor laboring whites, minors, and "servants," the latter of which could include members of any racial group as well as lifelong unfree people characterized as indentured servants in contracts.
The absence of the word "slaves" in this edict is representative of all early laws in Detroit, which avoided directly pointing to a class of people held in slavery, likely due to the influence of the Northwest Ordinance and the seriousness with which leading Detroiters, such as Solomon Sibley, took this federal mandate. Detroit would never develop a slave code like other municipalities with slaves; nor did it clearly lay out rules for indenture. Slavery and servitude were old practices instantiated by custom rather than regulated by local law. Enslaved people would therefore fall under the general rules of the community, with their masters held responsible for their infractions. It would take decades before Detroit had a law specifically aimed at enslaved people, which took the form of a Michigan territorial black code, rather than a slave code, in 1827. Following a dramatic act of organized resistance in which Detroiters aided the escape to Canada of Thornton and Lucie Blackburn, runaways from Kentucky, the territorial legislature seated in Detroit passed "An Act to Regulate Blacks and Mulattoes." This punitive legislation required blacks in the city to provide proof of freedom, register with a clerk of court, and pay a registration fee; it also required newcomers of African descent to pay a $500 bond to a free resident within twenty days to guarantee good behavior, or else be forcibly removed. The law charged fines for anyone aiding runaway slaves and, in the interest of maintaining order in the wake of mass action to aid the Blackburns, mandated the punishment of those who kidnapped free blacks. Despite the clause that protected African Americans with proof of freedom from unlawful seizure, this law intended to limit and control the black population, making it harder for free blacks and runaway slaves to call Detroit home. But decades earlier, in 1802, before the existence of Michigan Territory as a discrete place, no such law directed at the black population existed. Blacks and Native Americans held as slaves were legislated alongside people deemed dependents with no reference to enslaved status.
While studiously avoiding the subject of slavery, Detroit's board of trustees spent the bulk of its administrative energies passing and enforcing rules about fire prevention. In a town built almost entirely of wood, fire was a hovering threat and constant cause for anxiety. The board therefore required residents to keep their roofs free of soot, to own ladders tall enough to reach the tops of chimneys, and to maintain personal fire-fighting paraphernalia, including a barrel full of water and buckets. In the evenings, domestic fires had to be covered and candles snuffed. A night watchman patrolled the streets looking for wayward flickers of light and pounded on door planks to question residents about candles left visibly burning. Fire inspectors regularly checked every household for the requisite ladders, buckets, and barrels. Those who broke the fire codes and other regulations were charged by the board and required to pay fines. By 1805 town trustees had put in place scrupulous precautions against a possible conflagration, a regulatory code for the grocery market, fines for noncompliance with municipal rules, and a system of tax collection.
As soon as Detroit's trustees began to make local laws, residents—including those same trustees, began to break them. John Askin was a fire code offender before his move across the river, as was John Dodemead, a relative of James Dodemead, the man in charge of the fire engine. In 1803 merchant-slaveholders George Meldrum, Henry Berthelet, Robert and James Abbott, and James May were all fined for fire code violations; they failed to keep at their houses the required kind and number of ladders and buckets. Elijah Brush "esq[uire]" was also charged for having a "roof-ladder too Short" but was conveniently "excused" from fine payment.
Town officials policed moral dangers, too. In 1803 inspectors filed a report against Henry Berthelet, the purchaser of little Veronique who would soon attain U.S. citizenship, as well as other "Delinquents" for using "profanity on the Sabbath day." In 1802, Deputy Attorney General Solomon Sibley brought suit against Margaret White, "Spinster," for keeping "a common, ill governed, and disorderly house." At White's residence, "for lucre and gain, certain persons, as well men as women, of evil name and fame, and of dishonest conversation" engaged in "drinking, tipling, whoring, and misbehaving themselves." The growing Town of Detroit now had a social counterpoint to Ste. Anne's Church in the form of a rowdy saloon and brothel. We can surmise that indigenous and black women were present here, as the prostitution of enslaved women by their owners had long occurred in Detroit's sister city of New Orleans.
James May, an elected town board member, was a two-time offender for breaking town codes. He violated regulations by sending beef "not Sound" to market, for which he had to pay fifteen dollars. He also broke the law by proxy, since he carried responsibility for the actions of his slaves. In 1802 May was charged twenty-five cents because his "young Negro boy" was caught "carrying filth out of the S. W. gate of the town," which amounted to littering on the public commons. May was also busy accusing others of breaking the rules; in 1803 he complained that the "Negro-man" of John Michel Yack (of French and German descent) was guilty of "Galloping a horse in the streets of the town of Detroit." Yack was fined a dollar for the transgression of his slave.
Although James May could not have been happy about his own fees, he certainly had the means to pay them. In a tax list for Wayne County compiled in 1802, one hundred and four homes and only seven slaves were counted within the pickets of the fort and just beyond the walls to the west. Several enslaved people who lived in farms outside of town were not accounted for, including the Denison family, the bondspeople owned by William Tucker on a tributary of the Detroit River. According to the records of Ste. Anne's Church, between 1800 and 1809, at least twenty-nine individuals were still being held as slaves within the church community. This included ten blacks, fifteen "Panis," one "mulatto," and three individuals with no racial designation listed. James May, who possessed one slave according to the 1802 census, also owned one of the three most valuable homes, assessed at $1,000. In a tax levied in 1805 for ownership of "mules, calashes, carioles, dogs and studhorses," May was the highest taxpayer, followed by Joseph Campau, James Abbott, and Elijah Brush, all slaveholders or beneficiaries of indentured slave labor. Although William Macomb's widow, Sarah Macomb, was not listed among these men and may not have had a fancy calash or studhorse, she was still prospering in the decade following her husband's death. In the spring of 1806, under a list of "Sundry Expenses for the Family," Sarah Macomb recorded the purchase of "Molly the Wench," for whom she paid "70" in "cash." The acquisition of Molly dwarfed all of Sarah Macomb's other expenditures recorded in the same list, including: honey, eggs, fish, work by the blacksmith, a pig, six hens, linen, and cash paid while "shopping at New York."
The serious-minded attorney Solomon Sibley watched national matters as closely as local issues from his home in Detroit. When Ohio achieved statehood and Congress formed Indiana Territory in 1803, the seat of Northwest Territorial governance shifted from Ohio to Indiana. Sibley, who served as a territorial representative, worried about the fate of Detroit in the aftermath of this consolidation, fearing Detroit would fall prey to neglect now that the regional government was at a farther remove. Therefore Sibley, along with other local leaders, pushed for a separate territory that would prioritize Detroit. Two years later, Sibley saw his dream of independence realized. In January of 1805, President Thomas Jefferson approved a division of the lands then encompassed by Indiana Territory. The newly christened Michigan Territory would occupy the boundaries of what had formerly been defined as Wayne County, a land nestled among flowing rivers and glistening lakes. Even better, Detroit would become the territorial capital, and President Jefferson would appoint commissioners to govern from the town beginning July 1, 1805.
Elijah Brush stood in the thick of local town governance as the infant Michigan Territory took shape. Constantly busy with his law office, he also juggled new roles as fire inspector (an elected position) and lieutenant colonel in the Michigan militia (an appointed position) starting in 1805. True to form, Elijah Brush dressed smartly for his militia post, having ordered in from New York "twelve yards of superfine Buff casimure and four doz[en] of the best trible gilt Coat buttons" as well as a stack of instructive military books: "Hayts Cavalry dicipline—Steven's Artillery, Stubons Exercise for the Militia, [&] Fishers Military tactics." During Elijah's long stints at work, Adelaide Askin Brush, little Edmund, and the newest baby Charles sometimes stayed with family across the river in Canada. Adelaide may have been visiting at the home of her father when the greatest calamity since Detroit's founding unfolded. One morning, from the safety of Strabane, his stately home across the river, the venerable trader John Askin witnessed flames leaping across the rooftops of Detroit.
The Great Fire of 1805
It had begun at ten o'clock in the morning of June 11 in the year 1805: the fire that would destroy the original French fort town made charming by shingles and diminutive glass window panes. John Harvey, a baker by trade, kept a stable behind his business where sparks of a mysterious origin ignited, possibly from the pipe tobacco of an employee at the bakery falling into hay. Robert Munro, a witness to the events that would transpire, was employed as the storekeeper at the Indian Factory, where government goods were sold to Native traders. The factory site was located opposite the bakery in Detroit's compressed town center and so made for front-row viewing of the impending disaster. When Robert Munro caught sight of "flames bursting through the doors and windows" of the bakery's outbuilding, he wildly shouted the alarm. His calls, along with the panicked screams of others, were answered by the town's single fire engine, a souped-up horse-drawn wagon manned by twelve volunteers. The bucket brigade, a line of men passing buckets overflowing with water, fell hurriedly into position. Despite the frenzied efforts of community firefighters, a robust wind carried the flames from building to building. Townspeople began to flee, lugging all they could from their homes and making their way to the commons beyond the pickets near the river. Robert Munro at the Indian Factory grabbed what he could and ran. At Ste. Anne's Church, where mass was in session that morning, Father Richard fled as Father Dilhet, with the help of a few devoted worshippers, salvaged "vestments and sacred utensils." Their actions to save cherished church items may be the reason why the Ste. Anne register, in which so many fragments of enslaved people's lives were notated, has been preserved to this day. The church, along with every other structure inside the town walls with the exception of the fort (British Fort Lernoult, soon to become Fort Shelby) at the rear of the settlement, burned to the ground within a few hours. Three days later, Robert Munro opened a letter to William Henry Harrison, governor of Indiana Territory, with the solemn words: "Sir,—I have the painful task to inform you of the entire conflagration of the town of Detroit." He ended lamenting: "I can hardly hold the pen to write these few lines, and my mind is equally affected with the distressing scenes I have witnessed."
Robert Munro was among the first victims of the disaster. Close enough to the fire when it broke out to be injured, he later bore the psychological scars. Canadians like John Askin, at a safe distance along the opposite bank but with friends and relatives remaining on the Detroit side, watched the ominous dark smoke mushroom into the sky with near equal panic that morning. The first Detroiters to escape the smoldering town jumped into rowboats and pushed out onto the waterway. From the sanctuary of the river, they watched, in the words of an early Detroit historian, Clever Bald, "the flames sweeping from house to house across the narrow streets, fire-fighters stubbornly working at their hopeless task, women and children streaming out on the Common, and above, like an angry storm cloud, the thick black smoke hiding the sun." Munro, who had barely escaped the Indian Store with his papers and two thirds of the goods, reported to Governor Harrison that "In less than two hours the whole town was in flames, and before three o'clock not a vestige of a house (except the chimneys) visible within the limits of Detroit. The citadel and military stores were entirely consumed. . . . The situation of the inhabitants is deplorable beyond description; dependence, want, and misery is the situation of the former inhabitants of the town of Detroit." Another eyewitness, awestruck by the incident, described it as "at once sublime and painful, exceeding in awful grandeur perhaps almost any spectacle of the kind which has happened since the world began." But two important people did not see the conflagration and were late in even learning of it. William Hull and Augustus Woodward, Michigan Territory administrators appointed by President Thomas Jefferson, were en route to Detroit from the East while the great fire burned.
William Hull had agreed to serve as the governor of Michigan Territory and Augustus Brevoort Woodward as one of its two active supreme court justices. By the time the men arrived at the seat of their new territorial government, scheduled to become official the next month in July, they found nothing there but the shards of a colonial settlement. The buildings were gone with most of the contents destroyed, and the people were severely distressed. On the cusp of its grand moment as capital of Michigan, Detroit lay in a pile of debris. John Askin may have thought that his prognostication of Detroit falling into "ruin" seemed to have come to pass, though not in the financial realm where he most expected it. Disaster sparked by human hands, rather than an unfavorable business environment, proved to be the first undoing of Detroit. The original French Canadian dwellings were lost to wisps of memory, leaving the town orphaned from its eighteenth-century architectural heritage and its residents orphaned from their sheltering homes.
Out of the Ashes
Judge Augustus Woodward was the first of the incoming U.S. administrators to arrive on the scene after the fire. Judge Frederick Bates was already present, as he lived in the town, had served in the military, and, as his letters have revealed, courted French ladies. Woodward appeared on June 30, having departed from Washington days before with the formal appointment from President Jefferson that he had long sought in hand. Woodward was born in New York City in 1774. He studied at Columbia College and soon made his way to Washington where he began the practice of law and served as a member of the city's first municipal governing council. A voracious reader and fiercely analytical thinker, Woodward found interest in all manner of subjects, from the study of languages (he wrote in Latin, French, Greek, and Spanish as well as speaking fluent French) to literature and poetry, science, leadership, politics, and governance.
A staunch Jeffersonian Republican, Woodward admired Thomas Jefferson and wrote forthrightly that Jefferson was, in his view, "undoubtedly the second character in America in every thing which forms a component part of a great man. Washington alone is his superior." Woodward's handwritten notebooks, full of pictorial foreign language word-trees, a self-made map of Washington City, English word sounds and stenographic shorthand notes, classical quotations, and principles of chemistry, show Woodward to have had much in common with the supple-minded Jefferson, known for his interest and competence in a dizzying array of subjects. In 1790, soon after Jefferson was elected to the presidency, Woodward sought a clerkship with him. But Jefferson informed the avid young student by mail that "I am not able to serve your wishes. . . . There neither is, nor has been a single vacancy in the clerkships in my office since I came to it."
It was not until six years had passed that Woodward had the chance to meet Thomas Jefferson in person. A critical observer who treated Jefferson to the closest scrutiny, Woodward wrote down "Notes on My Visit to Mr. Jefferson," in which he found fault with the president's comportment. Jefferson was too "lively" and attentive, which "detracted from that calm & sublime dignity, which the imagination always attributes to a great & elevated character." Woodward continued in his critique: "Calm & composed he should have waited my approach without an advance on his part; my salutation & accessions . . . should have been readily reciprocated with a mild & engaging condescension." Jefferson was, in other words, too willing to engage Woodward and failed to display a social distance that underscored Jefferson's higher status.
Woodward's desire for Jefferson to politely remind him of his place reveals the young lawyer's own belief in social hierarchy and graces. But at the same time that Woodward disliked Jefferson's outgoing manner, he accused the president of being overly self-promoting. "I rather tho[ugh] t he spoke of his own notes a little too often: he ought not to have presumed that I had read them or had ever seen them," Woodward harped. But Woodward _had_ read Thomas Jefferson's bestselling _Notes on the State of Virginia_ , published in 1785. Jefferson's _Notes_ contained the now well-known passage in which Jefferson lambasts African Americans for being unintelligent, unattractive, and unfit for assimilation into white society. Woodward, writing his own thoughts on blacks in an essay titled "On Habits," had expressed views remarkably similar to Jefferson's. In the essay, Woodward wrote: "in our own country—One sees all the negros in slavery—from his cradle he has known nothing else; the impression made by this custom has habituated him to imagine some kind of natural connection between the Africans and slavery. They are such black ugly creatures with such big lips & flat noses that surely God who is a wise Being & does every thing right w[ould] never put rational Souls into them—They must be hewers of wood and drawers of water forever—At any rate, they must not be put on a par with that dignified being a white man."
Augustus Woodward was certainly influenced by Jefferson's writings in this opinion of African Americans as a subspecies created by God with an inbred irrationality. Nevertheless, he thought it arrogant for Jefferson to assume familiarity with Jefferson's popular book. Woodward's skittish interaction with Thomas Jefferson upon their first meeting was an indicator of his social awkwardness more generally. A tall, reedy man with a prominent, irregular nose and small, piercing eyes, Woodward believed deeply in his own self-evident intelligence and was quick to defend against slights. That he could sharply judge a man whom he admired and whose ideas he incorporated suggested that Woodward readily turned an exacting eye toward those who did not measure up to his standards. Still, Woodward's intellectual gifts and passion for knowledge caught and held Thomas Jefferson's interest. Jefferson became an associate to the younger attorney, lending him an encyclopedia and seeking Woodward's aid in identifying sources on topics of interest to them both. On one occasion, Woodward promised to send Jefferson a work that he would "shortly procure from alexandria" [sic] containing "a great deal of information on the domestic jurisprudence of France." This relationship led to Woodward's appointment as one of Michigan's first two supreme court justices, for which he would take an oath of fidelity to "support the constitution of the United States."
As the first appointee to the court, Woodward became chief justice of the Supreme Court in Michigan Territory. He brought his prejudiced views on race with him to the work as surely as he carried along his educational training and legal experience. The driving intellectual force in a territory that was only required by local law to have one judge present for cases, Woodward would become the only justice to write opinions for the court during his eighteen years on the bench. Several of these cases involved disputes over slavery, a practice limited by the Northwest Ordinance but not explicitly addressed in Michigan Territory laws (that Woodward himself would first pen in 1805) or in Detroit Town edicts established by the board of trustees. Woodward's decisions on slavery cases would soon show his investment in establishing a legal culture in Detroit that reflected the principle of the rule of law, protected U.S. sovereignty over its territory, and maintained peace at the border.
Augustus Woodward arrived in Detroit one day before Governor William Hull, with a personality guaranteed to irk his superior. Woodward was self-posturing, self-important, and spoke in multisyllabic words so as to display his fine education. He was also prominent and fortunate enough to immediately find shelter with James May, whose expensive home was located beyond the borders of the fallen town. From there, Woodward, whose "office and his friendship with President Jefferson gave him prestige in the Territory, and his own imperious nature demanded respect," began to steer the distressed inhabitants. Together with Judge Bates, Judge Woodward convinced Detroit residents to await the arrival of the governor before rebuilding their homes. With no permanent shelter, the townspeople created a refugee camp on the common land beside the river, squatted in the homes of nearby farmers, and depended on the charity of local merchants, like Jacques Girardin, a slaveholder, who provided the people with loaves of fresh bread.
One day after Woodward's appearance and two weeks after the massive fire, Governor William Hull finally reached Detroit. He arrived with his wife Sarah Hull, a son, two daughters, a personal secretary, and the secretary of Michigan Territory, Stanley Griswold. "Shocked and appalled to find his intended capital in ruins, and the inhabitants encamped round about," Hull went about the difficult business of managing a proto-state. Unlike Augustus Woodward, Hull was not able to secure the best of temporary accommodations. Hull wrote to James Madison, secretary of state: "On my arrival (July 1st) every house was crowded, and it was more than a week before I could obtain the least accommodation. I am now in a small farmer's house about a mile above the ruins, and must satisfy myself to remain in this situation during the next winter, at least."
Although an unfortunate man in the summer of 1805 and on key occasions thereafter, William Hull had been born into privileged circumstances in 1753. He hailed from Connecticut, trained at Yale College, and served honorably in the Revolutionary War under General George Washington as well as General Anthony Wayne. Hull had been appointed by Jefferson as governor of Michigan, which also made him military commander of the territory. But any grand hope that he may have harbored for his new western post was dashed from the beginning. Hull was described by his descendants as "a man of considerable ability . . . handicapped in his new job by his total lack of acquaintance with frontier life and problems." As he struggled to recover Detroit from overwhelming disaster, a task that stretched on for years, William Hull would learn too late about the pressure that the Indian presence would foment and the cohesion of the large French population, whose language he did not even speak.
But in the days immediately following the fire, Hull forged ahead with drawing the beleaguered populace together. He called a meeting beneath the pear trees of slaveholder Sarah Macomb's fruit orchard and gave a rousing speech. Hull vowed that a committee would be formed to request aid from the U.S. government, assured the people that they would be made financially whole, and expressed his desire to rebuild the town according to a "Judicious and enlarged plan." Governor Hull saw opportunity in the ruins of Detroit. Some local leaders agreed with his vision of an expanded settlement, such as Solomon Sibley, who had always judged Detroit to be too tight and too French. Stumbling out from the ashes of catastrophe, certain Detroiters began to see strategies for growth that today might be termed "disaster capitalism."
Elijah Brush also approved of the governor's notion of building a bigger and better Detroit. One year after the fire in 1806, Elijah Brush, James May, and John Anderson wrote a letter to President Jefferson representing a view that they described as having been sanctioned "by all the inhabitants here who are in the least Degree interested, or affected thereby." Governor Hull was, in the letter writers' estimation, running "a System of Territorial Government as much to our perfect satisfaction." But the men nevertheless had pressing concerns and urgent requests. They appealed to the U.S. government to recognize all land claims obtained and held during the French and British periods; they wished to see "the Indian Title in this Territory . . . extinguished." They wanted "to open the door to Emigration" and thus see more white settlers enter the country, and they sought "some support and Releif [sic] for the unfortunate sufferers by the late conflagration at Detroit." Finally, they hoped to see "the Plan of the New Town of Detroit" enacted—a town that would marginalize indigenous people and reward settlers of European descent, who by hook or by crook had gained title to those lands in the colonial period. If these measures were not taken, especially regarding land, "our Ruin is completely sealed," the authors proclaimed in defeatist language about Detroit that was already beginning to sound like an echo in the early nineteenth century. Early settlers may have found the wood-shingled village charming and may have tolerated indigenous neighbors to further the fur trade, but the new Americans had another vision in mind. The catastrophe of fire on the heels of the establishment of Michigan Territory created an opportunity for drastic change. The rustic French fort town that hugged the banks of the narrow river could now be remade into an "authentic" American city.
Judge Augustus Woodward was tasked by Hull with designing a spatial layout for the New Town Plan. He seized upon the assignment with gusto, imagining the future Detroit as a grid of long, diagonal streets punctuated by graceful spokes at regular intervals. Much of the design was inspired by the work of a Frenchman, Pierre Charles L'Enfant, who had planned the majestic Washington City for President George Washington. Woodward had kept a hand-drawn map of Washington in his pocket notebook while working as a lawyer there. Perhaps he pulled out that map, worn at the creases of the folds, to examine its specifics before sketching a design for Detroit. He also may have dusted off his reading notes from Columbia College, which included the titles _On the Best Plan for Building a City_ , _Improvements on the Plan of the City of New York_ , _Description of the City of Philadelphia_ , and _Description of the City of New York._ Surely this moment was one the intense man who compulsively sketched in his notebooks had been waiting for all his professional life. In addition to calling upon his broad base of multidisciplinary knowledge as well as his love of the liberal and applied arts, Woodward relished playing a dominant role in the refashioning of Detroit. His ardent belief in nationalism and patriotism, and the need to build up both in America, suggest he would have welcomed the challenge to remake Detroit into the pride of an American West. Although he spoke fluent French and admired French politics of the Revolutionary era, Woodward cared little for English ways. He had created a table in his plentiful notes in which he compared American and British characteristics, the latter group faring poorly in the tally. While American "Patriots" could be counted on for "Modesty, Intelligence, Morality, Eloquence, Decency, Family Ties, and Plainness," the British displayed "Hauteur, Science, Gluttony, Ratiocination, Prostitution, Pride of Birth, and Splendor," in Woodward's humble opinion. Detroit's New Town design rested in the hands of a man who wished to imprint an American stamp with an invisible touch of French influence.
Enslaved Detroiters in Disaster's Wake
Governor William Hull's New Town notion depended upon the wreckage of old Detroit. But he was not the first to realize that disaster presented economic openings. As Detroit's priceless eighteenth- and early nineteenth-century buildings lay in smoldering heaps of ash, merchant James May picked his way from lot to lot, where he "gathered the stones of which the chimneys in the houses were built . . . and built a stone house with them." May's palatial stone home, located on May's Creek, a waterway that once spilled into the Detroit River, was complemented by a gristmill, tannery, and barn. This became the new hub from which May managed "a big business" with his partner, Valentine. May and Valentine rustled cattle from Ohio and Indiana back to Detroit, supplied the military post at Detroit as well as others, and provided "salt and fresh pork and beans" to households along the strait. Later, the large stone building that May called home became a courthouse and a hotel. But the early account of May's stone salvage project raises pointed questions. Who, exactly, waded through the ash and rubble looking for choice chimney stones? Who carried those stones to the undisturbed creek bank miles outside of town? Who built the stone manor house? Who ground the corn in the mill? Who raised the cattle? Who tanned the hides? May's slaves and hired laborers surely performed these tasks, though they garner no mention in the historical record.
Not one existing narrative of the "great fire" of Detroit notes the presence of unfree people during or immediately following the incident. Despite this void, it stands to reason that enslaved people—both black and Native—would have been severely affected by the calamity. Many would have been homeless alongside their owners yet directed to the worst of temporary lodgings. Bondspeople faced hunger and bodily need just like other Detroiters but likely received lesser portions of donated food and none of the funds delivered by the relief ships dispatched from Michilimackinac and Montreal and distributed by wealthy residents. Lots and roads had to be cleared, pickets reconstructed, and new homes and gardens established. Certainly slaves would have been tasked with this work as well as their customary labors. But at the same time that unfree people would have been especially disadvantaged in this moment of crisis—more vulnerable to the vagaries of chance and the burden of excess work in a town struggling to rebuild in the aftermath of destruction—they, like James May and William Hull, could find and exploit hidden opportunities. For enslaved people, disaster could be double edged—painful, but also productive. The Revolutionary War had shown that chaos and disruption could be a boon in slave communities, creating new routes to freedom. In enslaved circles where lifelong servitude was the condition of existence, events defined as crises could spur constructive change.
The Denison Case
Peter and Hannah Denison, a black couple enslaved on the Huron River twenty miles north of Detroit, would have heard about the fire as soon as news could travel. They surely worried about what the loss of the area's central settlement would mean. But even more pressing in the lives of the Denison family than total town destruction downriver was an event that transpired just a few months before the fire. The Denisons' owner, William Tucker, had died in the spring of 1805, and his passing put the Denisons in extreme danger. The death of an owner, as the bondspeople of William Macomb had experienced, often meant the disbursement of slaves. William Tucker left his wife, Catherine Tucker, the bulk of his property, which consisted of "six hundred acres whereof 60 acres are supposed to be leased and under fence . . . With a dwelling house, barn, stable, out houses, and orchard thereon." William also wished Catherine to have: "my Black man and Black woman—Peter and Hannah his wife" who would receive "there [sic] freedom after the decease of Catherine Tucker my wife provided they shall behave themselves as becometh to her . . . during her life." Tucker revealed in his will that he "always meant to give their freedom" to Hannah and Peter. Perhaps William Tucker had even told the couple as much and led them to believe he would free them upon his own death. If so, the pair would have been sorely disappointed upon hearing the specifics of Tucker's will. Peter and Hannah would not obtain liberty yet. For that, they would have to await Catherine Tucker's demise. But their main, heartrending concern as Tucker's estate was settled would have been for their children: Elizabeth, Scipio, James, and Peter Jr., also left to Tucker's wife in the will. Unlike Peter and Hannah, the children would not be freed upon Catherine Tucker's death. Rather, "one sixth share of the negro children" would be inherited by six of the seven Tucker children—all of them boys. (Tucker's only daughter, Sarah, was to receive two cows after her mother's death.) How could four African American children be subdivided into six equal parts? Unless the Tucker sons (William, Edward, John, Jacob, Charles, and Henry) planned to work these slaves on a time-sharing plan, there was just one method: sale and division of the proceeds.
William Tucker's last testament was chillingly clear. He had bequeathed: "unto Catherine Tucker my Trusty and well beloved wife the farm I now live on together with all building stock (I mean, oxen cows sheep young cattle hogs farming utensils household furniture my Negro man and woman Peter & Hannah & their daughter and three sons). The sole use and benefit therof [sic] for & during the whole term of her natural life." As soon as Catherine Tucker died or had the inclination, the Denison children could be sold. Their fate rested entirely in the hands of Catherine Tucker and her male heirs. Peter and Hannah Denison would have felt deep unease and even rage at this revelation. Their family was still together following the death of a man who had claimed mastery over them. But for how long?
It is impossible to know exactly how events began to turn next, who said what to whom and when. The records of Detroit are silent on which person in the transaction initiated the contract of indenture. Perhaps Catherine Tucker sought fast cash to balance the finances of her estate, or perhaps she feared that a resentful Peter and Hannah would run. Maybe Elijah Brush saw the need for skilled labor following the fire and approached Catherine Tucker about acquiring her black man and woman. Whatever the impetus, in 1806, Catherine Tucker transferred Peter and Hannah for an undisclosed signing fee. She "indented" the couple "to Elijah Brush for one year, at the expiration of which they were to have and enjoy their freedom." Elijah Brush had probably paid Catherine Tucker hundreds of dollars to make this deal for the Denisons' removal. The couple's children would remain with Catherine Tucker, however. This loss of their family must have dominated the thoughts of Hannah and Peter as they rowed the river to the remains of the old French port town where they had been purchased in 1780 and 1784 and separated, then, or prior, from their own parents.
The home occupied by Elijah and Adelaide Brush, as pictured in a drawing from the middle 1800s, took up the better portion of a city block. Sprawled across lush park-like grounds surrounded by pickets, the large two-story farmhouse had multiple front-facing windows framed by wood shutters and a long, covered front porch secured at the corners by columns. Crisscrossed by walking paths, the land supported shade trees, fruit trees, and thriving gardens. The house would have had stone chimneys. The doors may have been painted an emerald green, a color at that time viewed as "evidence of the taste and wealth of the householder." The Brush farm, as it came to be known after John Askin's move to Canada, encompassed more than a mile of land with 386 feet of frontage along the Detroit River just outside the fort. When the Denisons walked onto that land and into the home where they would work, they could not have helped but compare it to the more modest farmhouse of William Tucker. The Denisons also would have been quick to perceive the high social status of their new masters: Adelaide, the elegant daughter of a prominent trader, and Elijah, a big man in local affairs. At the time of the Denisons' arrival, Elijah Brush's stature, and hence his influence, were steadily expanding. He had been appointed co-mayor of the town in 1806 along with Solomon Sibley, and he was serving as treasurer of Michigan Territory as well as lieutenant colonel of the Legionary Corps.
Within the wooden walls of the home constructed on land purchased by Adelaide's maternal ancestors in the period of the French and Indian War, the Brushes and the Denisons must have sized one another up. Hannah would have been told to keep the kitchen, clean the house, sew and wash linens and clothing, and serve Mrs. Brush as other enslaved women had done before her, while Peter would have been ordered to take on many of the regular duties of male slaves in Detroit. This included heavy agricultural work, construction and repairs about the place, delivery of parcels and letters, and the application of any specialized craftsman skills. Because Elijah Brush did not engage directly in the fur trade but instead represented clients in the industry, Peter was not dispatched to sea, made to clean and pack furs, or directed to transport malodorous skins across great distances. Instead, he was likely assigned to help clear the rubble in Detroit. All through the year that the Denisons lived with the Brushes, town residents were still homeless due to the fire. During the winter of 1806 and into that spring and summer, Detroit resembled a tent city, with temporary lodgings half open to the elements teetering among refuse piles.
As days turned into weeks and weeks into months, the Brushes may have come to appreciate the particular attributes of the Denisons. We can wonder what the exacting Adelaide first noticed about the capable Hannah. Perhaps Hannah spoke often of her children in the French language, pulling on Adelaide's heartstrings. Or perhaps Hannah, a woman handy with the needle, even claimed the superior skills of a dressmaker and could craft the fashionable clothing that Adelaide so adored. And Elijah may have recognized in Peter a self-possessed nature that indicated an unusual force of inner strength. Elijah may even have regretted the other man's forced condition of servitude, feeling a flash of sympathy for the difference that class and color made. His father-in-law, John Askin, had after all once described Elijah Brush as a "warm hearted fellow." So during the long winter months, when Detroiters relied on fires for heat, stories for comfort, and sleds for transport across icy waters, the Brushes and the Denisons may have gotten to know one another, slowly laying a fragile foundation for common cause. Even given the unequal power relations in place, something transpired between these pairs—perhaps a sense of mutual dependence, recognition, or even respect. By the time the calendar turned to the fall of 1807, the Denisons were suing for their children's freedom, and they had secured as their attorney Elijah Brush, Esquire.
Or maybe this story is inside out as I have told it, with emphases on the wrong elements. Maybe actions less romantic, but more heroic, actually occurred in Detroit that year. Perhaps Peter Denison had an unusual asset that he was able to leverage to change his family's circumstances. He had relatives on the Macomb farm, which was parallel to Brush's place on the other side of town. He was not unknown to Elijah Brush. The two men had probably met and even conversed in the past. Elijah sensed what Peter was made of. So upon the death of William Tucker in 1805, Brush and Denison negotiated an agreement. In exchange for something special from Peter, Elijah Brush would ask Catherine Tucker to release the Denisons under the auspices of a one-year indenture contract that would soon see the whole family freed. But then, a hitch. Catherine Tucker refused to let the children go. So while Peter and Hannah Denison lived in Detroit and worked for the Brushes, they strategized with the Brushes to challenge their former mistress's right to continue holding the children as slaves. Like other enslaved people who engaged the services of attorneys, Peter Denison likely paid Brush's fees by trading even more of his own labor. The case brought forward by Elijah Brush on behalf of the Denisons would test the court system of Michigan Territory as the first freedom suit to be heard there. Brush, in his own words, "had always considered the Subject of Slavery as very doubtful in the Country, and as highly necessary to be Setled by Some judicial decision." He wanted to be the one to argue the matter, "but had no clear idea what the ultimate decision was likely to be" in the suit described many years later by a scholar of African American history as "Michigan's Own Dred Scott Case." _Denison v. Tucker_ , decided in the fall of 1807 by a single judge, constituted the rationale that regulated slavery until Michigan statehood in 1837.
Established in July of 1805 upon the birth of Michigan Territory, the Michigan Supreme Court was a "loosely organized, often whimsical bench." As no physical courthouse existed, sessions were held in any available structure, including the Indian council house, offices, taverns, "and sometimes on a Woodpile." The rough-hewn quality of this arrangement suited Chief Justice Augustus Woodward, whose focus on the life of the mind led him to bathe seldom and dress with scant attention to polish or presentation. Perhaps in part because he was known as "quarrelsome" and "slovenly," Woodward never married, concentrating his energies instead on the tasks and problems set before him as a manic, conceited, and some have said "brilliant" visionary of the territory. One of the mottos scrawled into the pages of his notebooks read: "Tis better to excel in knowledge than in power." While Woodward's pursuit of government posts over the course of his career shows that he was not immune to the allure of status, for him, research, reading, and knowledge in the quest for "patriotism" and "virtue" were paramount endeavors and essential ends. So when Elijah Brush entered a motion on behalf of Peter and Hannah Denison, Woodward—a man who had written just over a decade earlier that blacks "must be hewers of wood and drawers of water forever," consented to hear the case. The Michigan territorial judiciary had borrowed from Ohio law to establish the supreme court with "exclusive jurisdiction" over cases involving land title, matters exceeding $200, crimes allowing capital punishment, divorce, and appeals from the district courts. The Denison children would have been valued at far more than $200 and closer to $2,000. This case therefore fell squarely into the supreme court's purview. Dutifully, Woodward issued a writ of habeas corpus, a right to inhabitants guaranteed by the Northwest Ordinance along with trial by jury. With the use of the writ, Woodward summoned Catherine Tucker into court to present the Denison children and testify as to her claim on them.
Habeas corpus had been applied over the centuries of Anglophone legal culture to prevent wrongful imprisonment and allow captive people to appear before a judge who would determine the reasons for their detention. No person, the practice presumed, should be held without just cause. In the 1700s, the writ became a tool for slaveholders to demand the return of fugitive slaves. The application of the writ in protection of enslaved people was more unusual, and in requesting it, Elijah Brush pursued an edgy legal strategy fit for his location on the borderland-frontier. Catherine Tucker was thus compelled by Judge Woodward to bring him the "bodies" of the Denison children. Unlike most freedom suits, which became more common in the nineteenth century, the Denison case would not turn on whether the Denisons could prove a "free maternal ancestor." Instead, the future of these children would rest on the fine-grained interpretation of territorial and international law.
In the case of _Denison v. Tucker_ , Catherine Tucker's statement on September 24, 1807, began as follows: "In obedience to the commands of the annexed writ of _Habeas Corpus ad subjiciendum_ I have brought before the Supreme court of the territory of Michigan, the bodies, of Elizabeth Denison, James Denison, Sip Denison and Peter Denison Junr . . . together with the cause of their detention by me." Tucker, represented by attorney Harris Hickman, claimed that she held the children "in Servitude, under the Authority of the Ordinances and Laws of Upper Canada, which existed prior to, and at the time of, the surrender of the Post and Settlement of Detroit." Tucker was a British subject who had remained on the American side of the river. She argued that she was therefore due the protection of property guaranteed by the Jay Treaty, as the children were born to Peter and Hannah, slaves of her husband purchased for "a valuable consideration." Because the children "were all born, within the precincts & Jurisdiction of the Post of Detroit, while it was a part of (and subject to the Laws of) the province of Upper Canada," Tucker believed "she was entitled to hold them." She signed this statement with her mark rather than her name, an indication that Catherine Tucker's level of formal education was no higher than that of her bondspeople.
A beneficiary of slave labor who regularly represented his father-in-law and other members of the slaveholding class, Elijah Brush fought hard for the Denisons, arguing their case "at full length" a day after Catherine Tucker's attorney presented hers. The text of Brush's argument does not survive in the Michigan Supreme Court records, but we can intuit the outlines of his position. Peter and Hannah were now free following the year-long term of their indenture contract with the Brushes. Their children should be free as well according to the dictates of the Northwest Ordinance. Brush's allegiance in this case was not to a principle of emancipation but, rather, to individuals with whom he had ties. Brush was loyal to those he claimed as part of his circle, and the Denisons could be counted as such for reasons both altruistic and self-serving. But neither Brush's commitment nor his connections could win the day in court on such a consequential matter as property ownership. This case, as Judge Woodward saw it, went straight to "the question of Slavery" in the territory. And as he wrote in his final decision issued on September 26, 1807: "The question is novel, it is important, it is difficult."
Augustus Woodward devoted thirteen pages, covered in a tight cursive scrawl with numerous lines of crossed out text and length-wise additions in the margins, to thinking through the complexities of the _Denison v. Tucker_ case. Maybe he once again dusted off his books from Columbia, referencing his copy of _On the Abolition of Slavery_ , _Plan of a System of Jurisprudence for the United States_ , or _Commentaries on the Constitution of the United States_ , as he struggled through his deliberation. He solicited information from James Wood, a colleague in Canada, and perhaps from legal associates back East or elsewhere in the western territories. Wood explained in a letter to Justice Woodward that: "Prior to the Conquest of Upper Canada by Great Britain, an Ordinance was passed by Mr. Raudot, Intendant of Canada, dated the 15th of April 1709, by which it was ordained that, under the good pleasure of his Majesty (the King of France) all _Panis_ & Negroes which had been or which should thereafter be purchased, should belong in full property to those who had or who should purchase them in quality of Slaves." Wood also disclosed that Elijah Brush was well informed of this precedent, suggesting, "if you will call on _Mr. Brush_ he will give you a Volume containing the Laws of Upper Canada which I left with him this Spring & in which the Statute you allude to is contained." Wood's letter, dated August 18, 1807, six weeks before the Denison case came to court, is indicative of forethought. Elijah Brush was preparing his case months in advance, and Judge Woodward was expecting the charge against Catherine Tucker. Both men may have been influenced in their actions by a statute passed in Missouri, Louisiana Territory, just months prior in June of 1807, which permitted individuals being held as slaves to sue for freedom on the basis of wrongful captivity.
Augustus Woodward sought information from a Canadian regarding a nearly hundred-year-old French edict and may have looked westward for instructive territorial law. Deciding this slavery case in Detroit required as much. Because Detroit was positioned on a border and at the intersection of territorial, national, and international laws, Woodward had to contend with the legal history of two empires and one aspiring imperial nation, including layers of law dating back to the French colonial period. He had to grapple, as well, with the moral mire of slavery, the citizenship status of Catherine Tucker, and the birthdates and places of the Denisons. Woodward's lengthy written decision began with a history of slavery in Europe (England, Spain, and France) as well as the United States, reviewed the Northwest Ordinance and Jay Treaty, defined the meaning of property, discussed "principles of the law of nations on the Subject of Slavery," quoted the French ordinance on slavery of 1709 and the Canadian act of 1793 preventing the importation of slaves. While weighing all of these matters, Woodward professed that he held absolute the Constitution and authority of the United States. "The American government has promptly, Steadily and uniformly manifested its disposition to introduce its own forms of government, and to apply its own laws," Woodward proclaimed. His chief aim was to affirm and strengthen America's position as an independent nation. He therefore determined that his territorial court must resolutely uphold the international treaties of the federal government. Woodward acknowledged that the Northwest Ordinance mandated: "In this territory Slavery is absolutely and peremptorily forbidden." Nevertheless, he also asserted: "the federal constitution required that provisions in a duly ratified treaty prevailed over any contrary local laws." For him, the U.S. Constitution and treaties ratified by Congress trumped the quasi-constitutional nature of the Northwest Ordinance, which he saw as comparatively "local." Woodward determined that enslaved people born before the effective American era that commenced in 1796, even "after the application of American laws," could be held in a "State of _qualified_ slavery." He accepted that Catherine Tucker was a British citizen, entitled to protections of personal property as spelled out in the Jay Treaty cemented between Great Britain and the United States. He therefore decided that Catherine Tucker was entitled to hold the Denison children as her property.
Woodward rendered a complicated ruling that drew on the Jay Treaty, the Northwest Ordinance, gradual emancipation schemes in the Northeast, and British Canadian slave law. He issued a partial, graduated emancipation decision in which some slaves and slave descendants would never be free, others would be free after twenty-five years, and some—those born after the American assumption of control in the Northwest Territory—would be born free. The ruling stipulated:
The Laws of France and Upper Canada ceased to have any effect in this Territory almost immediately after July 11, 1796, but under Jay's Treaty settlers continue to enjoy their property of every kind. The term property as used in Jay's Treaty includes slaves, as slaves were recognized as property by the countries concerned. Slaves living on May 31, 1793, and in the possession of settlers in this Territory on July 11, 1796, continue such for life; children of such slaves born between these dates continue in servitude for twenty-five years; children of such children, and all born after July 11, 1796, are free from birth.
Because the eldest Denison children had been born between 1793 and 1796, they were consigned to slavery for life; their younger brother, Peter, would be relegated to slavery for another twenty-five years. The devastation in the aftermath of that court session must have been profound. Elijah Brush had lost the case, and Peter and Hannah Denison had lost their sons and daughter to a lesser demon politely deemed "qualified slavery."
Word traveled swiftly along the banks of the river. Catherine Tucker's success in court spurred other slaveholders on. It was only three weeks after this decision that the Detroit slaveholder George Cotteral used the writ of habeas corpus to have the runaway Native man Toby arrested and returned to him. One week after Toby was apprehended, on October 19 of 1807, Judge Woodward had before him another slavery case. Canadian merchant Richard Pattinson petitioned the court to forcibly return his runaway slaves who were living in Detroit. Jenny, a mixed-race woman of African descent, and Joseph Quinn, a Native man, had run away from Pattinson's home in Sandwich, Upper Canada, a year earlier, in the fall of 1806. The two had made it to safety across the river and managed to evade recapture for months. Pattinson described Jenny as a "certain Mulatto girl . . . about the age of twenty years about five feet Six inches high straight and well made." One wonders what the relationship was between Pattinson and Jenny, a young woman whose figure he admired and who, in his words, "refuse[d] to return to his services." Joseph Quinn, the young man Jenny absconded with, was close to her age, at eighteen. He may have been a friend, lover, or relative of Jenny's, such that the two vowed to make their break together. Pattinson asked the Michigan court to arrest both young people and return them to his possession.
Pattinson likely expected a positive outcome given the precedent of the Denison case. But that situation was entirely different in Judge Augustus Woodward's view, which was filtered through a lens of upholding American sovereignty. In the Pattinson case, Woodward emphasized that while the Jay Treaty compelled the recognition of British property rights in Michigan, no such treaty existed between the United States and Canada regarding Canadian slaves. He decided the court had no obligation to return persons held as property who were fugitives from a "foreign jurisdiction." Woodward's decision in this case set important precedent for slavery law in the territory and the strength of U.S. jurisdiction at the border. He later received notice from the postmaster of New York City that copies of his decision on the Pattinson case were circulating in New York, where it was printed in _The American Citizen_ and _Republican Watchtower_ newspapers and sent to the Speaker of the House.
On the same day that the Pattinson case reached the court, a slaveholder in similar circumstances filed a petition. Matthew Elliott, who "had remained at Detroit until about the time of surrendering said Post to the American Government, when he removed to Amherstburg," had lost several of his slaves. He claimed that "Hannah, Peter, Abraham, Scipio, Candus, and James who were born the slaves of said Matthew Elliott of female slaves belonging" to him, had run away to Detroit "last winter and spring." In addition, Elliott stated that Pompey and Jane, whom he bought from John Stockwell, who bought them from George Meldrum, had also "deserted" at the same time. Elliot brought suit for the arrest and return of eight people. Given the replication of several names from the Denison family and the vague time window in which these slaves were said to have escaped, Elliott may have been chasing financial gain by claiming people he did not actually own and taking advantage of what he saw as an opening signaled by the Denison decision. Judge Woodward denied Elliott's request, citing the Pattinson ruling that he had issued that same day. Woodward saw no legal obligation to find, arrest, and return the slaves of British Canadian subjects. Elijah Brush, who argued and lost all of these cases, first on behalf of the Denisons' freedom and then on behalf of Pattinson's and Elliott's right to recover their slaves, confessed he had never been "Sanguine" in his "expectation of Success" in any of the suits. The relationship between slavery and the law in Detroit had been too hazy for Brush to predict an outcome. And Woodward's supreme court decisions may have added still more confusion, as he protected the right to hold slaves for the class recognized as old British settlers, but rejected the right of British-Canadians to recover their slaves with the aid of the court.
Despite his previously expressed views of black inferiority, Augustus Woodward criticized slavery severely in these decisions. In Pattinson's case, he empathized with the runaways as "human beings escaping from chains and tyranny" who "Could find no place in the whole earth to rest." In the Denison case, he approved of the Northwest Ordinance's ban on slavery, writing: "Nothing can reflect higher honor on the american government than this interdiction. The Slave trade is unquestionably the greatest of the enormities which have been perpetuated by the human race. The existence at this day of an absolute & unqualified slavery of the human Species in the United States of America is universally and justly considered their greatest and deepest reproach." These ardent feelings, which seem to represent a change for Woodward over time, had no practical bearing on his decisions for the Michigan court. In the end, he addressed these cases legally rather than morally, or rather, with a view of maintaining American sovereignty as the highest form of his moral duty.
The Denisons surely had little regard for the subtleties of Judge Woodward's musings on the ugliness of the slave trade and assuredness of America's failing. For them, the judge's final decision that stole the liberty of four of their members was what mattered most. The next generation of their family would remain enslaved, most for their entire lifetimes. The Denisons would not abide this. By late October, the Denisons knew Tucker would have trouble recovering the children from Canada, just as Pattinson and Elliott had failed to recapture fugitives who had crossed the international border into Michigan Territory. This was all the incentive the Denison family needed. In the fall of 1807, they fled across the river to Sandwich, Upper Canada, keeping their family unit intact against all odds.
As the Denisons ran _from_ Detroit in search of liberty and security in their personhood, other black and Native captives ran _to_ Detroit from Canada. The river that had once connected two sides of a single settler community but now divided two adversarial nations was being used as a bridge yet again—this time for fugitives escaping the grip of slavery. Detroit saw a surge of freedom suits and runaway slave cases between 1807 and 1809, as enslaved people, and those who claimed them, watched to see how the legal winds would blow. _Denison v. Tucker_ was the first slavery case decided in Michigan Territory, but it would not be the last fight for freedom at the riverside. Before long, Peter Denison would return to his birthplace of Detroit, armed and politically dangerous.
The Rise of the Renegades (1807–1815)
The whole territory is a double frontier.
The British are on one side. The savages on the other.
_—Memorial of the Citizens of Detroit, 1811_
Maybe the story was inside out. Perhaps Peter Denison, the black man formerly enslaved by William and Catherine Tucker, was never really a servant indentured to Attorney General Elijah Brush. The legal record of the Michigan Supreme Court tells us otherwise, explicitly stating that Catherine Tucker indentured both Peter and his wife, Hannah Denison, to Elijah Brush following the death of William Tucker in 1806. But the odd events that soon ensued on the heels of that contract indicate a more intricate and unusual course of events that unfolded in the borderland vortex of turn-of-the-century Detroit.
The onset of the 1800s was difficult for Detroiters. A raging fire had destroyed the old town within the walls and scattered residents across the countryside in search of shelter. Political leaders for the newly designated Michigan Territory, mostly hailing from more refined eastern cities and townships, struggled to find their footing in a frontier environment peopled by inhabitants who spanned a cultural range, including, most especially, indigenous North Americans and French Canadians. The first session of the Michigan Territorial government, led by Governor William Hull, was held two months in the wake of the fire in the corner tavern of Richard Smyth, who, in addition to selling spirits, crafted hats. Enslaved people, often in groups, were making bold bids for freedom by crossing the international borderline that was the Detroit River, a movement that led to a series of controversial cases in Chief Justice Augustus Woodward's outland court. French-speaking _habitants_ harbored suspicions of the radical plan for rebuilding the town put forward by American leaders. Because of the need of constant translation between French residents and the governor, "the intercourse of the heart," Judge Woodward wrote, "seldom pass[ed] through." Neither the British nor the French actually liked easterners, Woodward confessed. The British referred snidely to Americans as "Yankees," while the French maligned them as "Bastonnois," "Sacre Bastonnois," or "sacre cochon de Bastonnois" (Bostonians, blasted Bostonians, or filthy swine of Boston). Eastern newcomers, for their part, often viewed the old western settlers as uncouth and "half savage." The landed elite, many of them from longtime merchant and slaveholding families, pushed for a federal government that they distrusted to recognize existing land claims and mark a fixed boundary between white and Indian territory that would swell the former and shrink the latter. And even as Detroit dragged itself out of the ashes of manmade disaster and negotiated internal social as well as political strife, new threats gathered on the horizon that presaged the possibility of yet another imperial war.
Incoming governor William Hull may have once thought that he was equipped to untangle such a tight knot of conflicts and pressures. Hull was a man possessive of an imposing physique, as well as an impressive military and judicial background. His full girth, patrician nose, and slightly downward turned eyes might even have intimidated those who worked with and beneath him. His history of outstanding service in the Revolutionary War helped him win the appointment as governor of Michigan Territory. Hull had risen to the rank of lieutenant colonel in that conflict and was roundly recognized for his brave and brutal handling of the bayonet, even receiving a personal commendation from General George Washington. After retirement from the military in 1786, Hull served as a common pleas court judge in Newton, Massachusetts, and as a member of the Massachusetts state senate. Being a Democrat and staunch supporter of Thomas Jefferson also buoyed Hull's rise, as it was President Jefferson who tapped Hull for the gubernatorial post that included responsibility for Indian Affairs in the region. For a salary of $2,000 per year, William Hull made plans to move "to a rough frontier society made up of French-speaking settlers intermixed with a sprinkling of Americans who were primarily westerners of an independent spirit." After taking the oath of office in Albany, New York, in the spring of 1805, Hull set off for Detroit with his family by way of a water route. Travel across Lake Erie was unpredictable, with the speed of the crossing entirely dependent on the winds. Nearly two long months after their departure, the Hulls had arrived to find Detroit "vanished."
Sarah Hull, William Hull's wife of twenty-four years, entered a waking nightmare when she arrived with a son, Abraham, and two daughters, Nancy and Maria, by way of the Detroit River. Four years later, she would describe the arduous trek from the Northeast as "a long and perilous journey through the wilderness of six hundred miles." Responsible for the management of her upper middle-class household in a period that elevated white women's roles as Victorian wives and mothers of the Republic, she was expected to create a proper and uplifting home while her husband attended to politics. But there was no home to make in Detroit. The settlement was an ash bin. Sarah Hull and her children were virtually homeless, living with a farm family a mile out of town in crowded conditions worse than those suffered by her husband's headstrong chief justice.
Sarah had not been groomed to live in a refugee zone on the western edge of American expansion. The daughter of a judge in Newton, Massachusetts, she would have been expected by fellow ladies of the genteel class to instill virtue in her children, host teas and charm guests, and lubricate the social wheels of her husband's bright political future. Frontier Detroit promised nothing resembling this picture. The people there were isolated, insular, ethnically oriented toward French and Indian ways, and accustomed to making do in the most extreme of circumstances. In 1805, the population amounted to just 274 souls within the walled village, and most of those residents had been displaced to makeshift lodgings. Outside the central footprint of the riverine fort, farmers, "almost exclusively French," dug in along the various waterways. Sarah Hull could not have missed the precarious nature of Detroit Town: "a long, narrow column of settlers . . . flanked by the British on one side and by the woods and the Indians on the other." But she had shown fortitude in accompanying her husband to military encampments during the Revolutionary War. She had been present at the Battle of Saratoga and helped to tend the wounded. This was exactly the kind of grit that she would need to muster, and more, in adjusting to her new environs of Detroit.
While Sarah Hull struggled to keep her family fed, clean, and morally upright in their temporary, substandard quarters, she observed her husband weighing out the innumerable threats to the territory he now governed. Indians, their large and persistent populations and outstanding claims to Detroit area lands, plagued William Hull. His most active supporters, merchants of an American cast, wanted Native people pushed back and contained. Even more foreboding than the Indian encampments outside Detroit were the hundreds of clans, tribes, societies, and confederations of indigenous people spanning the Great Lakes region from New York to Minnesota and into British Canada. These original inhabitants of the inland seas, chain-linked rivers, fertile coasts, and forested hunting grounds had shown themselves to be fierce protectors of their lands and life ways. Indians had attacked this very settlement and held it hostage in the 1760s. Then they had fought with their former foes—the British military—against the Americans not twenty years later. During the Revolutionary War, Indian warriors had gathered at Detroit in order to collude with British officials and plan attacks on patriot settlements. They were everywhere, the indigenous people of the Great Lakes. These Indians had their own minds. They had a generation of young men itching to retake what had been lost in the Treaty of Paris in which they had had no representation. They also had the friendship of the British who lay in wait, ready to use them as a first line of offense against their former American colonies that had dared to break away. While William Hull pondered the Indian threat that never quite receded, he anxiously watched as tensions between the United States and Great Britain simmered to boiling.
The main issue was impressment. Great Britain boasted the greatest navy in the world and depended upon its ferocious fleet for global financial primacy as well as homeland security. The British navy enabled the small island nation to dominate much of the globe in international trade. But as Britain fought a protracted war with France during the French Revolution and Napoleonic Wars that followed, the country's navy was severely overstretched. The British navy desperately needed more sailors even as British subjects and Irish resisters were defecting to American ships in the hope of better wages, greater independence, and shorter terms at sea. Determined to preserve its military might on the oceans and to put the upstart United States in its place, Great Britain got its back up. The navy ramped up a program of impressment led by burly "press gangs" that searched port town pubs and social spaces, and even private homes, for British defectors. These men were taken aboard British ships and compelled to work for the navy in conditions that approached indentured servitude, with low pay, long terms lasting until the ends of wars, and little if any shore leave. After 1803, the British navy became even more aggressive in its impressment practice, challenging American merchant ships, searching the decks for defectors, and forcing into military service men who claimed American identities by way of affiliation, naturalization, and birthright.
This was the cast of William Hull's mind when an incident foreshadowing the War of 1812 unfolded in the summer of 1807. On June 22 of that season, an American warship floated near the Virginia shoreline with no military mission and only light weaponry. The frigate U.S.S. _Chesapeake_ captained by Commodore James Barron was simply scheduled for a routine commercial trip to the Mediterranean. The deck was loaded with cargo, the ship's cannon stowed away. So neither the captain nor the crew saw the blow coming when the British warship _Leopard_ attacked by cannon at close range. The _Leopard_ struck the _Chesapeake_ thrice as the American captain tried but failed to launch an effective defense. Commander Barron had no choice but to surrender while a party of British naval officers forcibly boarded the ship, physically inspected the bloody crew, and kidnapped four men accused of desertion from British service. Only one of these prisoners, Jenkin Ratford, had actually been born in Britain. Three Americans were killed in the _Leopard_ assault; eighteen were wounded. The _Chesapeake_ was a bundle of shattered boards when finally released to limp back to port. The British defector, Ratford, was punished for his crime with a hanging on board the ship that he had fled months prior. The captured Americans from the _Chesapeake_ crew soon joined the six thousand American men who had already been impressed by the British.
News of the _Chesapeake_ affair leapt across eastern seaboard states as well as western territories. The offended American populace fumed with outrage. President Jefferson declared a risky trade embargo, crippling commercial exchange and the country's overall economy. The American Republic and British Crown were squaring off against one another as events slowly spiraled toward war. The British lords of the sea were on the offensive, and Governor William Hull was steward of an untamed land bordered by massive waters. Michigan Territory was a virtual peninsula with three quarters of freshwater coastline accessible to an aggressive British Provincial Marine. Moreover, the land over which Hull had formal American authority, but not by Native American consent, shared a border with British Canada that was uncomfortably close. A few stone throws across the Detroit River sat in wait Fort Malden, the encampment built by the British military after these same men had begrudgingly vacated Detroit just over a decade prior. And only one month before the _Chesapeake_ incident, Hull had received an alarming letter from an officer stationed at Fort Mackinac, on the island above the Straits of Mackinac. The captain warned that neighboring tribes were communicating by wampum belt and likely planning to attack. So Governor Hull felt the breath of danger when he cast his thoughts to the corners and borders of Michigan Territory in the summer of 1807. The Indians could assault Detroit. The British could besiege Detroit. And the two could join their nefarious forces to fall upon America together, just as they had in the Revolutionary War. Biographers of William Hull have tried to convey and contextualize his fear of an Indian attack fired up by British instigation. For it was this fear (in hindsight, strategically misdirected) that led Hull to act in unpredictable ways that shocked his white contemporaries.
The Renegade Militia
William Hull determined that he needed a strong defense, the best defense that could be obtained in a hinterland settlement with a dangerously low population of free white men. His attempt to organize the local French farmers into a formidable militia, as required by law for every new territory organized through the Northwest Ordinance, had dissolved into conflict when locals complained that the uniforms Hull required were far too expensive. Through a newly devised Michigan law modeled after a New York code, Hull and the judges had bestowed upon Hull the right to dictate militiamen's dress. A proper New Englishman with a penchant for formalities, Hull decided that each member of his militia should don: "a long blue coat . . . white plain buttons, white underclothes in summer, white vests and blue pantaloons in winter, half boots or gaiters, round black hats, black feathers tipped with red, black cartridge and bayonet belts." Hull was more than slightly out of touch with his new frontier environment, judging by his dress code. Elijah Brush, the flashy attorney turned militia leader, was perhaps the only soldier more than happy to comply. Brush had ordered a uniform ready to wear from New York the moment he received his commission. But the majority of Detroit residents who were compelled to defend the settlement could not afford to purchase the fabric that Hull required for uniforms (which he had ordered wholesale and personally sold), let alone spare the time from farmhouse labors that would be required for their wives and daughters to stitch the peacockish outfits. The down-to-earth French residents of Detroit were disaffected. The eager beaver Americans were small in number. Who could Hull turn to, then, as threats outside the town walls mounted? Who, in Detroit, had nothing but their lives to lose?
Governor Hull had no choice that did not involve invention. He was in dire need of new and untried ideas. He might have sought out, in this circumstance, someone like Elijah Brush, an influential American with local ties, a formal role as lieutenant colonel of the territorial militia, and experience in the settlement dating back several years. _I know a man_ , Elijah Brush might have whispered to William Hull, following a meeting of militia leaders in Richard Smyth's candlelit tavern. For surely Elijah Brush did know Peter Denison, the enslaved black laborer of William Tucker famous enough that various Detroiters had tried to buy him. Peter Denison was broadly skilled in physical work and river navigation; he had an unusual strength of mind that inspired respect in others. A man of talents masked in the historical record that paid little attention to slaves, but apparent to all who encountered him in his time, Peter Denison was soon envisioned by Governor William Hull as a chief defender of Detroit. The challenge was getting access to the man when he belonged to Catherine Tucker, a piece of human property bequeathed by her husband.
Elijah Brush must have approached Denison first. Then came the contract of indenture with Catherine Tucker, and the move of Peter and Hannah Denison into the elegant riverside home of Elijah and Adelaide Brush. Peter, in consultation with Hannah, must have extracted a promise for his dangerous work on behalf of the town: freedom for himself and his wife, and probably for their children as well. For in August of 1807, months before the _Denison v. Tucker_ freedom suit was brought before Judge Woodward, Peter Denison was leading a company of men of color whose task it was to defend Detroit. Members of the prominent Askin family were among the first to nervously notate the strange sight of black men drilling with arms right across the waterway. James Askin wrote to his brother Charles from Strabane, the family abode on the Canadian coast of the Detroit River: "at Detroit they are making great preparations. The Town of Detroit is Picketed in from the Water Side until it joins Fort Lernoult. A Company of Negroes mounting Guard, The Cavalry Patroling every night, Batries Erecting along the Settlement, and the Militia called out frequently." James's father, John Askin, was displeased at this unwelcome turn of events, writing to a business colleague in Montreal: "our run Away Negroes have had Arms given them & Mount Guard."
The Askins may not have been taken by utter surprise at this unusual turn of events. They could have been warned of developments by their in-law, Elijah Brush. But British military officials at Fort Malden in Amherstburg necessarily learned of the news through formal channels of command. On August 17, 1807, Lieutenant Colonel Jaspar Grant informed Secretary James Green of Quebec that he had heard from Colonel Isaac Brock of trouble brewing in Detroit. Grant's description was even more detailed than the following excerpt reveals, as his intention was to expose Detroit's advantages and weaknesses should a military conflict unfold. Grant wrote to Green in a lengthy letter:
As the affair of the Leopard and Chesapeake has occasioned much ferment at Detroit, and has also induced the Governor the Territory of Michigan, who resides there, to take steps by no means indicative of friendly intentions, I conceive it my duty to acquaint you . . . [of] what is going forward there. . . . The Militia of Detroit have been constantly assembled for the purpose of Drill, they amount to about 400, are much better disciplined than could well be supposed, are very well appointed, and two Companies are kept in constant pay. There is, besides, a company formed of Renegade Negroes, who deserted from Captain Elliott and several Gentlemen at this side. This company consists of . . . 36 in number, and are kept for such desperate services as may be required at this side.
These armed black men defending Detroit were joined, as Grant described the scene, by a force of "inhabitants . . . called in from the distance of 30 miles." Governor Hull had been inventive indeed, forming a special militia of nearly forty former slaves; and so, it seems, had Peter Denison, their designated leader.
Appointed as the head of a defensive force made up of enslaved men of color, Peter Denison had fished for his men across the river among the farms of Upper Canada's largest slaveholders. Denison's recruitment strategy of enticing enslaved men to Michigan was the unspoken cause behind Matthew Elliott's lawsuit in October of 1807, in which Elliott attempted to recover several fugitives who were living in Detroit. Elliott had listed the Denisons as part of his absent human property although the family had not formally belonged to him. His action may have been as emotional as it was economic, a vindictive attempt to punish Denison for leading away Elliott's bondsmen. Inside and outside the courtroom, Elliott met resistance. His overseer, James Heward, had been tasked with finding the runaways, but met sharp recriminations from white working-class Detroiters when he arrived in town to give testimony. The overseer stopped in at Smyth's tavern "to get a drink of grog," and found himself being verbally accosted by a carpenter named William Daily and a navigator named Peter Curry. As half-pints of brandy made the rounds, Daily called Heward a "British rascal" and "threatened to pull off his wig." The tavern filled with more working men from Detroit. Heward's situation grew dicey. In a defensive move that begged greater forethought, Heward called the men "a damned rascally set of beggars," which they rejoined by calling him "a damned British rascal." By the time the dust settled, Heward had been tarred and feathered on the face and head, his wig tacked up by a nail on a post at a public street corner. In an irony that again revealed the intense social dynamics of Detroit, a thirteen-year-old enslaved boy belonging to the father of Heward's host sounded the alarm that "they were killing Mr. Heward." Heward was not in lethal danger, as it turned out, but his dignity took a blow, and "he had tar on his face" and "his hat full of feathers" by evening time. James Dodemead, a witness to the whole affair who testified before Judge Woodward, said he could think of no motive for the tavern patrons' aggression except for the "offense given by Mr. Heward . . . [in] coming over to give testimony respecting Mr. Elliott's slaves." The only item the attackers took from Heward was his wig, the witness reported—the chief symbol of the victim's social class and national identity.
In addition to throttling Heward outright, the men at the tavern threatened the absent Matthew Elliott with a tarring and feathering and boasted that "if the Court decided the Slaves of Mr. Elliott Should be restored, the Court should be tarred and feathered" too. Attorney General Elijah Brush, who was deposed in this case, said he was told by an irascible Mr. Smyth that Elliott was also targeted for "formerly taking an active part with the Indians against the United States" and that the threat of tarring and feathering extended to "the judge." Harris Hickman, counsel for Matthew Elliott, swore that "Richard Smyth, tavern keeper in Detroit . . . made use of a great deal of violent and abusive language . . . relating to the Case of Mr. Elliott's Slaves" and "Swore very bitterly that they Should not be restored to their master, and that he would Kill any person who Should come to his house to take them, or Should attempt to arrest them, and to carry them across the river." Smyth made this promise on "several other Occasions since," Hickman testified, "with violent language and threats of the Same Kind."
The men in the tavern disdained the forcible seizure of slaves. Richard Smyth, a justice of the peace as well as a hatter and barkeep, was sequestering some of the runaways in his own house. As shown by the ire of these workers, an antislavery spark was flaring in the city along the strait. But objecting to the return of fugitive slaves to the Brits was not just rooted in a rejection of the notion or practice of bondage; it was how these men could sense as well as demonstrate their burgeoning identity as American Detroiters. It offended these residents to see rich slaveholders cross the river and try to enlist the Michigan courts to arrest black bondspeople. The British elite, once occupiers of this soil, were now intruding on these tavern-goers' turf. Defending fugitive slaves in their midst was an act of nationalism, which is why Judge Woodward admonished them in patriotic terms. In court, Woodward chided: "he did not believe any American citizen would So much disgrace their Country" as these men had in insulting Heward and Elliott, "at a time when the United States had so many good Causes of Complaint against the British government." Matthew Elliott, Woodward said, "had a right to be a Suitor in the Courts."
The conflict between the tavern-goers and the slaveholders, between the tradesmen and the justice, was spurred by border tensions. These tensions led Smyth and his mates to see black people held captive by the British as fellows and potential allies. The presence of black runaways stoked political and class consciousness among the white workers, giving them clear ideological adversaries: British slaveholders who sided with Indians, and a pompous eastern judge who might be tempted to side with slaveholders. Slavery became a screen against which these men could project a proud national identity. Daily, the carpenter, Curry, the navigator, Smyth, the hatter, and the several men who joined them, including William Watson, Austin Langdon, Abraham Geel, and others, tested their ideal Americanness against the foreignness of British slave-owners, and even against the definition upheld by Augustus Woodward in which "Americans" should be cautious of causing "offence." Upon witnessing the tarring and feathering of Heward, one among them had cheered his fellows on by shouting: "hurraw my boys." They likely roared at the news that Governor Hull was arming fugitives, including some of Elliott's own bondsmen. But Augustus Woodward saw escaped slaves as "disorderly characters who had Come from the British dominions" and decried Hull as having "resorted" to "low intrigues." To the chief justice, black slaves, unruly workers, and jumpy territorial governors were the real threat to America.
While Smyth and the men at his tavern jolted the establishment, enslaved men of color were crossing the strait to fight in defense of Detroit. Peter Denison resided on the Michigan side of the border, but his men lived on the Canadian side and had pledged their "desperate services" in order to seize freedom in the United States. When they traversed the river and armed themselves beneath a rival national flag, these men were joining a tradition set by enterprising men of color in colonial wars past. During the French and Indian War as well as the American Revolution, black men had fought, mostly for the British, in exchange for promises of freedom. Even that very summer of 1807, as hackles rose in the aftermath of the _Chesapeake_ incident, enslaved black American men had escaped their owners to board British naval ships. But the Detroit militia of formerly enslaved men deviated from this more typical arrangement. Led by officers of African descent, these men had crossed an international border to fight for the other side.
In the Revolutionary War, the War of 1812, and the Civil War fifty years into the future that would divide America from itself, black men were rarely shown the respect of being named officers of their military units. But William Hull, according to a scornful Judge Augustus Woodward, had audaciously formalized black men's martial leadership. Woodward wrote in a complaint to the secretary of war, William Eustis, "Mister Hull had issued three commissions to captain Denison, lieutenant Burgess, and ensign Bosset, black men, not under any law of the United States or this territory." In Woodward's view, Hull had been "insolent in the extreme" when challenged about this course of action and had taken as his authority "some ex parte correspondence with mister dearborne, then secretary of war." Hull made a show of defending his deeds in a letter to Colonel Grant at Fort Malden meant to calm escalating fears that these armed former slaves might attack. "The permission which I have given to a small number of Negroes, occasionally to exercise in Arms," Hull wrote, "I am informed has excited some sensibility among the Inhabitants on the British Shore. Be assured Sir, it is without any foundation, for they only have the use of their Arms, while exercising, and at all other times they are deposited in a situation out of their control." Hull's reassurance that the formerly enslaved Canadian men did not always have access to their rifles and bayonets would have been cold comfort to the British military leader, as well as to the slaveholders in his province, whose human property was not just absent but also armed.
Governor Hull cut a new groove into the pattern of using black fighting men in colonial and early America. Under his auspices, the "first black militia" was formed in the United States. The military titles that Hull bestowed upon leaders in this unit—captain, lieutenant, and ensign—indicate that he viewed the group as akin to a company in the Michigan militia. And very likely, Elijah Brush, or Peter Denison himself, had driven Hull to formulate this arrangement. The fear of an Indian attack was so great at Detroit that Hull hired desperate men for desperate measures. How these rebels must have relished scoffing at their former masters, drilling with weapons in plain sight right across the waterway. Primary accounts describe this unusual militia company variously as a group of men made up of "Negroes" and "slaves." Although the record does not state as much, some of these men may have been Native or mixed-race Afro-Native people enslaved by the British. Their object would have been freedom, rather than allegiance to any single slaving nation, be that nation European, American, or indigenous.
Governor Hull had authorized an unprecedented military organization. Judge Woodward stridently objected, viewing Hull as having gone a bridge too far when he armed the slaves of the neighboring nation. Woodward directed his concerns to Secretary of State James Madison in July of 1807, writing: "There is however one point on which the inhabitants of the different sides of the river are at variance. This is the desertion of the slaves. I expect complaints will be made to you on this head by the British minister. I do not approve the temper, principles and conduct of the inhabitants of this side, on the subject. I thought something ought to be done to check it." In a set of resolutions addressed to a Michigan territorial special committee in 1808, Judge Woodward continued to criticize Governor Hull on this issue, stating that Hull had been responsible for the "embodying of slaves belonging to the subjects of his Britannic Majesty residing in the province of Upper Canada into a militia company, and the issuing of commissions, or other authority, to such persons, or other slaves, or black persons, to be officers in such militia company." Woodward viewed Hull's actions as stoking the flames of discord between the United States and Great Britain and, most importantly to him, of violating American civil law. In order to have gone forward with a plan to arm escaped slaves, Hull should have sought higher legal approval. "In our government," Woodward asserted, in a separate letter of complaint to the secretary of war, "we had no masters but the law." Although Woodward's comment was not consciously ironic, it highlights a difference in status that fueled the dispute; the enslaved men in Hull's militia could not have made so bold a claim to having just one master in the abstract form of law. Their masters were men and an immoral slave system wielded by men that sometimes bested the law. The special committee responded to Woodward's complaint that Hull had acted out of bounds by quoting the territorial dictate regarding the governor's military powers. "'The governor, for the time being, shall be commander-in-chief of the militia, appoint and commission all officers in the same below the rank of general officers,'" the committee reminded Woodward, then stated further that they had paid "particular attention" to Woodward's charge that Hull had "formed negroes, who were slaves, into a military company." The committee found it to be "true that the governor has given permission to the black male inhabitants to exercise as a military company; that he has appointed a black man by the name of Peter Denison to command them; and has given him a written license for the purpose; though not in the form of a military commission. . . . This company has frequently appeared under arms, and has made considerable progress in military discipline. That they have ever conducted in an orderly manner, manifested on all occasions an attachment to our government and a determination to aid in the defense of the country whenever their services should be required."
Not surprisingly, the territorial special committee (made up of the judges and Hull himself) sided with Hull, but, remarkably, the committee heaped praise on the discipline and patriotism of black men. The committee's response went on to assert that Woodward's emphasis on these men's status as slaves was an irrelevant point: "With respect to any of them being slaves, the committee only observes that they were black persons, who resided in the Territory, and were not claimed as slaves by any person or persons in the original States." The committee members had decided against Judge Woodward, but by using the same logic as Woodward's own legal decisions in the Pattinson and Elliott cases: if these black militiamen were runaway slaves of British owners, it was not Michigan Territory's affair. Michigan was only beholden to slaveholders from their own nation: the United States. "Under this view of the subject," the committee report concluded on this matter, "the committee is of the opinion that the conduct of the executive in availing the country of the services of their black people, was not only proper but highly commendable; especially as it was at a period when the safety and protection of the Territory appeared to require all the force which could be possibly collected." Black men formerly from Canada would now be considered "their," meaning Michigan Territory's, "black people," members of "the country." Woodward was not convinced. He rebutted this finding in a letter to the federal government, noting again his doubts about the "propriety of organizing a military company composed of slaves who had run away from gentleman residing opposite" and of "negroes commanding the company as officers being alike unauthorized by the town and the gen. [general] gov. [government] ."
Augustus Woodward's pointed criticism of the formation of a black militia in Detroit exposed the issues of racial bias, slave status, international relations, and military readiness in a way that forced a clear and revealing response from territorial representatives. These men, like Governor Hull, viewed the defense of the border as utmost in importance and would not protect human property rights of British slaveholders on Michigan soil. Black men in Michigan Territory were presumed free unless an American owner from the slave states made a claim. Despite this deference to U.S. slaveholders regarding fugitive slaves that meant the continued, legalized threat to black people in the Northwest, the committee's response was an avowed rejection of slavery as an assumptive state for all black men. These legislators affirmed Michigan's fledgling political identity as a free American territory and lauded black men as responsible and even patriotic. No other city, state, or territory within the nation had yet made such a bold defense of black men's collective honor. It happened first in Detroit.
But also central to this story is _why_ it happened in Detroit, an environment characterized by frontier conflict and borderland contingencies. The violent threat of Indians was assumed to be so great that black men not legally freed should be armed to fight against them. While their recognition of the talents of African American men might be viewed as progressive, if self-serving, William Hull and the territorial committee at the same time reinforced an oppositional ideology of "Americans" versus "Indians." Indigenous people were perceived as bogeymen in the wilderness, a terrifying, outsized threat requiring radical containment. At least these militiamen of color were not prone to taking scalps, territorial leaders may have thought, in a slanted view of reality that failed to recognize Euro-American brutalities against Native people. Here, in this circumscribed imaginative space of the colonial psyche, black men had an advantage. They could be viewed as co-combatants rather than age-old enemies. A conceptual line was now being drawn between Native Americans and African Americans that favored blacks in the pre–War of 1812 years. Black men had one thing the Michigan Territory needed more than almost anything else: the willingness and strength to defend Detroit and America's borders. But the effective difference between being "black" versus being "red" was far from clear cut in every interaction or circumstance. Members of each group were still enslaved in Detroit, sometimes within the same households. And the racialized categories ("negro," "black," "mulatto," and "panis") used to serve as shorthand for their naturalized subjugation were sometimes viewed as overlapping or interchangeable by officials. In 1808 John Askin recorded his contract of indenture with Charlotte Moses, "a mulatto or pawnee Girl of Detroit," who signed her X mark to "truly observe and obey" him as "her Said Master." Another example of multiple or confused racial identifiers appears in a criminal case that wound through the Michigan courts in the summer of 1814. Monique, a woman charged with stealing a valuable bedspread from the shop of Andrew Elliott, was found guilty by a grand jury in the territorial supreme court. The district court record in Detroit, where Monique resided, describes her as "a certain Black woman," while the supreme court record describes her as "a Pawny Woman." Notably, both the district and supreme court sessions were held in Detroit where Monique was personally known. Perhaps Monique was mixed-race; perhaps her sliding racial identification signaled her enslaved status more than any concrete racial designation. Precisely recording her racial identification was clearly not essential to the case or a matter of importance to the court. Similarly, individuals of Native ancestry or of mixed-race Afro-Indian descent were very likely to have been present in the so-called Negro Militia.
Judge Woodward thought the risk of Indian attack was being exaggerated and said as much in his critique of Governor Hull. Colonel Grant on the British side of the river also expressed disbelief at William Hull's fired-up rhetoric: "They have picketed in the whole town of Detroit," Grant wrote. "Every military preparation is going forward there, and every violent declaration against this side . . . the Governor of Detroit declares, if an Indian fires a hostile shot in Detroit or in the Territory, he will treat the Canadians with the utmost severity. The apprehensions circulated at Detroit appear to me to proceed more from Policy to freighten the Inhabitants into labour without food or reward, than from any real sense of danger from Indians." Grant went on to disclose to his superior that any alliance between the British at Fort Malden and western tribes was unpredictable. "The Aid I should expect there from Indians and Militia is of a very precarious kind," he wrote. "Indians can never be brought to act within pickets."
Grant's canny analysis painted a picture in which Hull was using the fear of Indians to compel undercompensated military labors, and in which Native people hardly stood at the ready to passively take orders from the British regarding designs on Detroit. As progressive as William Hull's actions seem with regard to black militiamen, they were also strategic in a way that furthered the consolidation of American authority within the town and beyond. Hull could use the deep desire for freedom among men of color to entice them to work for little or no pay, even as he used the specter of a Native assault to pull French farmers into town from thirty miles distant. William Hull's stated terror of Indians may have included an element of cold calculation, but he was right on one score—Native people had not yet been contained and could not be controlled. Just as American and British relations were a seething cauldron of suspicions, American and indigenous relations were far from settled in the Northwest.
The black militia authorized by Governor Hull remained active in Detroit for years, prepared, according to the territorial committee, to defend "the country." But which country would those men favor as they considered their political allegiances? Did they subscribe to any national identity at all when both countries that warily met at the Detroit River border held blacks and Native people as slaves? Peter Denison, the sole member of the black militia whose story we can access through the documentary record, demonstrated loyalty to his family rather than to Michigan or the United States. He had agreed to lead William Hull's unconventional military unit in exchange for freedom. But in the summer of 1807 while his men drilled in plain sight at the fort in Detroit, Peter Denison's children were still being held as slaves by Catherine Tucker. Peter and his wife Hannah took the case to court that autumn with the aid of Peter's fellow militia leader, Elijah Brush. Judge Woodward, who had never approved of the black militia, issued the writ of _habeas corpus_ as Brush requested but refused to free the children of the militia's well-known leader. Peter Denison must have felt that his trust had been betrayed—by the town of Detroit, the territory of Michigan, and perhaps Governor Hull himself. But he did not settle for this theft of his family's natural rights, any more than the Native peoples who continued to live around Detroit settled for the theft of their land base. Peter knew the rough terrain of the border; he had already crisscrossed the river in order to gather his men. In the fall of 1807, he abandoned Detroit's black militia, and likely his formal protection of freedom issued by the governor, to flee with his family to Canada.
The Denisons had held, and lost, a legitimate route to freedom. Now they were on the run as fugitive slaves. But Peter Denison had won a partner in Elijah Brush, not resulting from Brush's sympathy or guilt, or even an antislavery stance adopted by the attorney. These men had spent months as comrades in arms, serving in segregated units of the Michigan militia. Peter Denison and his wife had lived with Elijah and Adelaide Brush, in the intimate quarters of the couple's urban farm. Although Elijah could not have felt the anger, fear, and humiliation experienced by Peter Denison, whose children were counted as chattel, he could have shared Peter's sense of moral outrage. Hadn't Peter been willing to risk his life for Detroit, the capital of Michigan Territory? And yet the court of that territory refused to protect his children as full-fledged persons. When Peter Denison rowed the river with Hannah, his daughter Lisette, and his sons James, Sip, and Peter Junior, he was not without friends. A note in the Michigan Supreme Court record indicates, in just one line, that Denison family members "took refuge with Mr. Askin." Elijah Brush came through for the daring Denison family, convincing his father-in-law, once among British Detroit's largest slaveholders, to extend a hand.
Red-Lining Detroit Lands
Immediately following the series of territorial supreme court suits that tested the limits of slavery in Michigan, Governor Hull set his mind to the problem of Indians and land. Local white property holders had been complaining about Native Americans living too close to town and had expressed worry about a lack of formal federal recognition of their preexisting land claims. The loss of more than three hundred buildings to fire and the unsettled issue of how to reapportion lots within the town pickets raised the stakes of land competition all the more. And the shadow of possible war with the British placed a continuous pressure on the military readiness of Detroit, which, in the view of U.S. officials, entailed managing where Indians were on the landscape and what actions they engaged in.
In his dual capacity as governor and superintendent of Indian affairs for Michigan Territory (a conflict of interest when considered from the indigenous standpoint), William Hull started on the difficult task of reorganizing Detroit area lands by wresting more ground from Native people on the direct order of President Thomas Jefferson. Jefferson had been desirous of extending America's hold at Detroit beyond the immediate fort town. He informed the senate that "the posts of Detroit and Mackinac" had been designed as "mere depots for commerce with the Indians" by "the government which established and held them." Jefferson, in contrast, wanted to extend the land base around these forts for military purposes. Hence, he "thought it would be important to obtain from the Indians, such a cession in the neighborhood of these posts as might maintain a militia proportioned to this object." Already a veteran of the Louisiana Purchase with a keen understanding of the power of holding contiguous terrain for settlement and economic advancement, Jefferson had in mind acquiring lands in Michigan "so as to consolidate the new with the present settled country."
In December of 1807, Jefferson's secretary of war, Henry Dearborn, conveyed the order to William Hull to "hold a treaty with the chiefs of such Indian tribes or nations as are actually interested in the lands hereafter described." While Dearborn pointed out that it would be "difficult" for Hull "to ascertain, with any tolerable degree of certainty, the quantity of acres," Hull should expect to net in the ballpark of six hundred thousand acres, for which he was "not, on any condition, to exceed two cents per acre" and should endeavor to find it unnecessary to "exceed one cent per acre." Hull was convinced of the soundness of this aim and began to plan the treaty council. "I probably shall not hold the treaty until about the first of June," he wrote to Dearborn, "They are now on their hunting grounds, will soon be employed in making their Sugar, and in the month of May, will be engaged in their planting—In the meantime, I shall be making the preparatory arrangements." Hull's reply conveyed his own implicit awareness of Native people's wide-ranging use of their lands—for maple sugaring, hunting, and farming—necessities of cultural meaning and subsistence. Still, he expressed in his letter to Dearborn, in the interest of progress and economics, this land should be finagled for the United States at less than the cost Dearborn had set. "If the treaty can be effected," Hull penned, "and the lands can soon be opened for sale, it will be of vast advantage to this Country, and likewise to the United States—The more I see of the Country, the more valuable I consider it." Hull added in a postscript to his missive that he thought it advisable to extend the boundary "so as to include the islands" in the land cession.
Governor Hull called a meeting of Ottawa, Ojibwe, Wyandot, and Potawatomi leaders in the Wyandot village of Brownstown, south of Detroit, later that year. On November 7, representatives of the various tribes gathered and agreed to cede what is now all of southeastern Michigan and a sliver of northwestern Ohio. The payment for these lands was set at $10,000 in "money, goods, and implements of husbandry." Native people were to retain fishing and hunting rights and to receive "two blacksmiths," provided to the tribes as evidence of the U.S. government's "liberality." Several small portions of land, ranging from one to six miles square, were to be "reserved to the said Indian nations" for their villages and agricultural pursuits. William Hull reported to Thomas Jefferson in December of 1807 that all had gone smoothly, and that he had "heard of no complaint from a single individual of the Indians" regarding the treaty. He attested, too, with his jacketed chest puffed slightly out, that he "believe[d] a treaty was never made on fairer principles."
Governor Hull accomplished his objectives in this carefully orchestrated treaty council, and his description of the outcome may have faithfully reflected how he felt about the negotiations. But these treaty proceedings were not as pleasant as Hull's description implies. While the treaty itself details only land, monies, objects, and expertise to be exchanged, Hull's speech to the gathered Native leaders in advance of the treaty signing focused on an entirely different subject: warfare. When addressing representatives of the Ottawa, Ojibwe, Wyandot, and Potawatomi nations who held land and interests in Detroit, Hull highlighted themes of weapons, conflict, death, and danger. He addressed the gathered leaders as "My Children," and directed them to listen "with attention" for "the good of [their] women and children." Hull then offered his talk as a representation of the views of "Your father, the President of the United States" who "desires to recall to your minds the paternal policy pursued towards you by the United States." Referencing the mounting tensions between the United States and Great Britain, Hull explained that "a misunderstanding having arisen between the United States and the English, war may possibly ensue." In the event that war did break out, it was the president's wish that "the Indians should be quiet spectators." Hull's purpose in this speech, in addition to attaining land, was to keep Native people from fighting with the British against the Americans. He assured his listeners that if they did not express "intentions hostile to the United States," they would be left unmolested by the United States, and indeed, protected by the nation. But if they did harbor ill intentions, the United States would "lift the hatchet" and "never lay it down till that tribe is exterminated, or driven beyond the Mississippi." He warned them that if the Indians dared to challenge the U.S. militarily, they "will kill some of us; we shall destroy all of them." He then summarized these pertinent points by emphasizing "the interest your Great Father takes in your welfare; how anxious he is to promote your happiness; how desirous he is to prevent you from taking any measures, which will involve you in ruin." Hull concluded with the disclosure that this degree of candor was actually an act of kindness, "warning you of the fate of any tribe, who shall have the hardihood to raise the hatchet against us." He then advised the leaders to render "a plain and decided answer" on their political allegiances.
The content of Hull's speech, as submitted by him to Thomas Jefferson, did not dwell on the Detroit area land cession. It did not have to, when the threat of extermination and removal was implicitly leveraged as context for the treaty negotiations. How broadly would the U.S. president interpret "hostile intentions" on the part of the gathered nations? Would agreement to the requested land sale insulate the tribes from deadly accusations of hostility? Certainly the gathered Native leaders must have thought so; they proved themselves unwilling to take the chance for the sake of their families. One Ojibwe leader who signed the treaty, and whose name is recorded as Pooquiboad in the proceedings, stated: "Our solemn determination is, never to raise the hatchet against the United States. We too well know the fatal consequences of it." From the middle 1600s onward, indigenous people of the Great Lakes had fought valiantly and strategically for their homelands, autonomy, and relative positioning in a seemingly never-ending series of imperial wars. They knew the cost of losing in such battles, and many in the Ohio Valley had recently lost nearly all in the American revolutionary conflict and postwar campaigns of General Anthony Wayne. So William Hull was successful in achieving the Indian land cession desired by the president as well as propertied residents in Detroit. The negotiation that he viewed as utterly fair had been peppered with language steeped in threat.
The 1807 Treaty of Detroit is rarely mentioned in histories of Detroit, of Michigan, or of the Midwest, but it was critical to American officials' plan for defending against British and Native aggression on the northern U.S. border and to Michigan territorial leaders' hopes for fostering white settlement in the march toward statehood. This drawing of a broad boundary around the capital of Detroit and its environs set in place the pattern for the eventual relinquishment of most of what we now know as the state of Michigan by the early 1840s. The reduction of Native territorial sovereignty immediately around Detroit also had dire consequences for enslaved people who used indigenous spaces as routes of escape with the knowledge that slaveholders were unlikely to follow them there. The shrinkage of Native landholdings strengthened U.S. military positioning, flung the door wider for American settlement, and smoothed processes of surveillance and recapture for American slaveholders. A win for Governor Hull and U.S. settlers was a loss for Native people as well as for the enslaved.
William Hull found that in Detroit success and setbacks followed one another like the tumbling waves of the lakes. While Native leaders had consented to sell hundreds of thousands of acres in the deciduous lands of southeastern Michigan, French Detroiters were resistant to the reassignment of land lots via government auction. The great fire and mass exodus from the immediate town site had left the settlement in disarray and thrown the ownership of private land, much of it purchased from Native people or allocated in the French colonial period, into confusion. The nearly sixty homeowners who used to live within the town walls had been displaced; farmers outside of the walls along the river worried about whether the United States would view their eighteenth-century claims as legitimate. Augustus Woodward had crafted a plan for the redesign of the town that was approved by Congress in 1806 but disliked by local residents, who objected, in part, to Woodward's naming a main thoroughfare Woodward Avenue, after himself. (Woodward later denied this accusation, saying that he had named the street after the forests around Detroit. Only a portion of Woodward's design, between Grand Circus and the river, was ever realized.) Governor Hull and Judge Woodward established a Land Board to hear residents' claims and assign lots, then successively hired and lost three surveyors (then rehired the first) to plot out town lands. In addition to acreage within the town pickets that would be allotted to former residents who had lived there (at a small fee if lot sizes were larger than the originals), territorial leaders had gained permission from Congress to distribute by auction 10,000 acres north of the village to adult residents over the age of seventeen. Much of this new acreage had in the past been used as a commons by the townspeople, who shared the swath of cleared land surrounding the pickets for daily access and pasture land, and who likewise used the land of Hog Island (now Belle Isle Park) to let their livestock roam. U.S. officials in Washington saw this "quantity of vacant ground" around the walls as "valuable" federal land that could be sold. Detroiters complained in a formal memorial to Congress in 1808 and in a petition to the governor in 1811 about the loss of the public lands that had once been equitably shared by the community. Their petition specified that they wished to see the area "held by the inhabitants of the town forever as a commons." In valuing communal use of the land, the descendants of Detroit's oldest white settlers of the farming and working classes shared a view with Native people in the region diametrically opposed to the federal position that land should be sold for profit. The old settlers' vociferous protests, rendered in French and in English, yielded no change in policy, however; the land would be divided and "liberally" sold, making lots available to newcomers, to British residents who had not even sworn allegiance to the United States, and, remarkably, to the "wives and slaves" of some former in-town homeowners. Some residents were dismayed and even offended, feeling that struggling farm families and working-class laborers lost the use of the commons unless they could meet the "humiliating conditions" of paying for it.
George Winter, _Pottawattamie Indians Crooked Creek Indiana_ , 1837. Winter sketched this scene of a Potawatomi community near Logansport, Indiana, in August 1837, prior to the group's removal. Courtesy of Tippecanoe County Historical Association, Lafayette, Indiana.
The designation of land lots took decades to settle due to unceasing conflict. While American and British residents benefited from the new system, so too did individuals designated as their subordinates: current and former bondspeople. Among the recipients of deeds were several individuals described as "negro" or colored, including, Pomp ("a negro man"), Thomas Parker ("a negro . . . employed in the Hull family"), Pompey Abbott, Cato ("Dodemead's Negro"), Harry and Hannah ("Dodemead's negroes"), London and Mary (living at the Watsons'), Margrett (at the Voyers' home), Susan and Nell (at Mrs. Abbott's home), and Hannah ("Coate's Negro"). Joseph Cooper, "a negro," was noted as not having drawn a lot. This record of black land ownership demonstrates two interconnected, critically important facets of life for African American Detroiters in the early 1800s. They were eligible for in-town land and were hence treated as municipal residents on par with Anglo settlers. They were at the same time usually noted by first name only, designated by race, and attached by the use of possessive punctuation to white Detroiters. The Land Board record does not indicate whether these individuals were enslaved or free at the time. Some were certainly free by this period but particular individuals (like Pomp) appear as slaves in previous town records. Still others held an even more ambiguous status poised between slavery and freedom. Hannah, described as "Dodemead's Negro" in the land records, had evaded John Dodemead's claim to her in court in 1809. While John Dodemead had requested a writ of _habeas corpus_ to hold Hannah, a "black woman," and Thomas, a "Mulatto" boy (probably her son), several witnesses, including Elijah Brush and Solomon Sibley, testified that Dodemead had previously declared that the two "were not slaves of him or any other person." Perhaps Dodemead had been involved with Hannah, had a child with her, and intended to free them before changing his mind. Since prominent witnesses were aware of his past declaration of the woman and child's freedom, Dodemead was unable to retract it. Augustus Woodward decided in this case that Hannah and Thomas were "free persons" who must be "discharged out of the Custody of the Marshall of this territory and of Said John Dodemead." The appearance of Dodemead's name next to Hannah's in the land grant entry suggests that black land recipients depended upon a connection with or patronage from past or present white owners and employers, regardless of how tangled or contentious such relationships might be. Another black woman, also named Hannah, may have had a more constructive relationship with a patron, as she had the explicit help of Austin E. Wing, a Land Board official, in making her application. Significantly, Native people do not appear as designated by tribe or race in the Land Board lists. Mixed-race Native-French and Native-English town residents would be noted under their European surnames, and many other indigenous people had moved to different locations by the time these lots were assigned. The prominent Oneida woman trader, Sally (Sarah) Ainse, who had once owned a house and second lot in Detroit, had relocated to the Thames River in Upper Canada prior to the American assumption in 1787. And through the Treaty of 1807, most other free Native Detroiters had been red-lined, so to speak, outside the district through land cessions. While Governor Hull had made it a priority to build a stone Council House for trade and political meetings with the Indians in 1807, he did not wish to see those same Indians dwelling too near as neighbors.
Even as the Native population within the town proper was dwindling, by 1810, rates of enslavement had also dropped dramatically in Detroit due to a bundle of factors. A number of black and Native bondspeople had been transported across the river by retreating British owners. The liquid international border, crossable by boat, was encouraging escape attempts. The ban on slavery legalized by the Northwest Ordinance made it more difficult to buy and sell human beings. In accordance with Judge Augustus Woodward's decision in the Denison case, babies born to enslaved residents would now be free, and his decisions in the Pattinson and Elliott cases meant fugitives from Canada would also be treated as free people in Detroit. American Detroiters, such as the patrons in Richard Smyth's tavern, began to connect slavery with a previous British colonial administration and supported black runaways as a means of distinguishing themselves from the British. But whether enslaved or free (a phrase containing a vast magnitude of difference), most of the black people in town were working for, living with, and viewed as possessions of white residents. As a result of this mix of multiple causes, the 1810 census enumerated forty-three "free colored" residents in Detroit Town proper and only four "slaves." The tally for riverside suburbs totaled as follows: Cote du Nord-Est: six free colored; Cote de Poux: ten free colored and two slaves living within two slaveholding households; River Rouge: ten free colored and eight slaves living in two slaveholding households; Grand Marais: seven free colored and one slave; Grosse Pointe: three free colored and two slaves living in one slaveholding household. Several suburbs did not have residents listed in either of these categories. A tally of the census numbers indicates seventy-nine free people of color and seventeen enslaved people within a total population for the District of Detroit of 2,355. The 1810 census did not note the race of these enslaved individuals. The use of the term "Negro" so frequently in Land Board records suggests that most people within the categories of "free colored" and "slaves" were black or of mixed African descent. The population of enslaved Native Americans had dropped significantly since the 1790s, but several people categorized as "Panis" were still present into the first decades of the new century. The registry of Ste. Anne's Church (which had lost its original site due to the fire and Woodward's town plan that ran Jefferson Avenue straight through the burial ground) notes twenty-nine enslaved congregants between 1800 and 1810. Ten were black; fifteen were Native; one was "mulatto," and three had no racial identifier noted. The term "mulatto" could indicate a person of mixed African descent of either white or indigenous parentage, and any of the non-identified individuals could have been indigenous. Even as the practice of slaveholding faded in the second decade of the American era, unfree indigenous people still outnumbered unfree blacks in Detroit.
Enslaved and free black residents in the town saw their position improved through a land allotment process that included them. But longtime French inhabitants were vocal critics of the American attempt to rebuild the old town through a regularized layout, the grid that now characterizes much of the Midwest. It seemed to them that newer arrivals, namely influential Americans, were being awarded the choicest lots along the river and closest to town. Elijah Brush was a case in point; he had procured the first available farmland east of town in 1807. In February of 1808, Elijah and his wife Adelaide sold a prize parcel to William Hull, who made a series of personal purchases from previous settlers, many of them French, between 1808 and 1811. But even as Governor Hull increased his wealth through land ownership and commissioned the first brick house in Detroit for his family, he operated in a state of constant conflict. Hull withdrew his previous support of Woodward's newfangled town plan, and the two became political adversaries. Their argument over the black militia, which raged on from 1807 to 1811 and sparked Woodward's testy missives to Hull's superiors in Washington, contributed to the souring of their relationship. While Hull faced complaints from French residents and epistolary attacks from Woodward, he also contended with his wife's anxiety about political tensions in Detroit. During one of William Hull's trips to Washington in April of 1809, Sarah Hull wrote him a pointed letter that opened with the worrisome line: "My mind has been so agitated in thinking of the perplext situation you are placed in, that I find no relief but in writing. I shudder at the idea of you returning to Detroit, that never can be done with honour to yourself it is gone as much as if your commission was taken from you." Sarah knew her husband was trapped. Detroiters did not like him, and federal officials were using him for their own political ends. "You have experienced enough of the treatment of this people already," Sarah wrote of Detroit residents. And about government leaders in Washington, she warned: "the truth is they are the friends to Mr. Madison, not friend, to your character or interest." Sarah wanted to see her husband "nominated to the senate" and perhaps dreamed of a life in relatively genteel Washington City. She resented influential politicians for not putting her husband forward, despite his sacrifice in traveling "through the wilderness" of the West and "render[ing] services to his country." In large, dark lettering at the top of her final page, Sarah urged William to "Renounce all Politics Be Neuter." In cautioning her husband to avoid political entanglement through a tactic of neutrality, Sarah went so far as to advise emigration: "if you cannot do this in America flee to some other part of the world, at least till a government arises that can estimate your talents and reward your virtue." She concluded her sharp letter with the warm sentiment: "however disagreeable your situation is remember you have one friend that will devote her life to make you happy." Sarah Hull's missive was a Molotov cocktail of smart analysis and tough advice that recognized her husband's tenuous position. Within a few short years, William Hull would wish that he had followed Sarah's sage, if fiery, direction and left the leadership of Detroit to some luckier soul.
The Denisons on the Border
While Sarah and William Hull brooded over their unstable situation in Detroit, Hannah and Peter Denison had accomplished, by propulsion of unjust circumstances, just what Sarah Hull had recommended to her husband. The Denison family had moved to another country by crossing the river into Canada. In Sandwich, a town more modest than Detroit with "fifty log or frame houses built near the Old Huron Church, a small shipyard, two small wharves, and a small government warehouse," the Denisons made a new home. Several former Detroiters loyal to the British Crown had reconvened there, sometimes referring to Sandwich as "South Detroit." In Sandwich, the Denisons joined St. John's Anglican Church, where they participated in the social and religious rites of baptisms, weddings, and funerals. Choosing a Protestant denomination after having lived in a Catholic town, the Denison parents soon formalized their commitment to the faith. In October of 1808, nearly a year to the day after their failed freedom suit in the Michigan Supreme Court, "Peter and Hannah Donnison Adults, free Negroes" were baptized at St. John's. Elizabeth Denison, the couple's eldest child who went by the nickname "Lisette," served as sponsor for several Denison baptisms in the church. The merchant John Askin may have witnessed these baptisms, as he and other slaveholders who had recently moved from Detroit were also members of the congregation.
While the Denisons had full lives in the province of Upper Canada, they also became denizens of the border, expertly navigating the river that separated the United States from British Canada. They crossed and recrossed the strait by choice between 1807 and 1812, never once being caught and arrested as fugitive slaves. Catherine Tucker did not fight to retrieve the children, seeing, perhaps, a lost cause since the Denisons could readily run. Neither did William Hull dispatch men to find the black militia leader who had abruptly deserted his company. Hull may have felt, morally, that Peter's flight was just, or recognized, pragmatically, that the Denisons had influential friends on both sides of the border. Peter Denison found work as a "Negro servant" in the household of former Detroit slaveholder and lawyer Angus Mackintosh. Although life would never be for the Denison family what it was for a free white family there, and although the differences of race and class still structured their lives (as indicated by the limited work options available to Peter), the Denisons were integrated into a tight-knit network of Detroit River People: white and black, slave-owners and slaves, old settlers and new Americans.
In the years before the next conflict with Great Britain that Detroiters were anxiously anticipating, various members of the Denison family depended upon and renewed personal ties around Detroit steeped in a vexed history of slavery. In 1810, Elijah and Adelaide Brush were raising four boys in Detroit. Several people of color also resided with them, according to the Detroit town census. Six free "colored" people and one "slave" were listed by tally (with no names given) beside Elijah Brush's entry. There is no indication of that single enslaved person's identity, but precedent suggests this was an indigenous woman, a personal servant of Adelaide's dating back to the Askin family slaveholdings. The free people of color in the Brush household were the Denisons, who also appear in Detroit account ledgers in these same years. An anonymous merchant's sales ledger locates Peter Denison in town, describing him as "Peter Tucker's negroe man" in 1808. Over the next two years, Peter purchased "Sundries" and flour from this shopkeeper, regularly settling his account "in full." He also purchased 1¼ yards of "Humhum," a cotton textile used for lining coats. Peter's procurement of this fabric is a telltale sign that the Denison women were sewing for the family and perhaps for market. In 1809, the anonymous shopkeeper refers to Peter Denison as "Peter, Brush's black man," a shift indicative of the local acceptance of the Denisons' separation from the Tuckers two years after the pivotal freedom suit. The Denisons acted like and were treated as free people despite Judge Woodward's decision, benefiting from what legal historian Rebecca Scott has described as "the alchemy of creating status out of circumstances." But what had not changed in the time since the family fled to Canada and circled back to Detroit again was an insistence on the dependent attachment of black residents to white merchant elites. The use of possessive grammar and racial terminology to describe Peter in both ledger entries underscores the social hierarchy rooted in race and class that was still firmly in place in early 1800s Detroit. Looking for work, for respect, and for the best hope for their future, the Denison family spanned the border, living at times in Sandwich under the auspices of the Askins and living at times in Detroit with Elijah Brush. For this African American and Afro-Canadian family, Detroit was experienced on the ground as a place that bridged the river, regardless of differing national claims to lands on each side. In both locations, white patronage was a necessary element of the Denisons' personal security and livelihood. Their act of rebellion in taking Catherine Tucker to court and refusing to let the border box them in to slavery could only get the family so far in a larger society shaped by notions of racial difference and territorial conquest.
The Denisons returned to a place of compromised familiarity within the old town of Detroit, finding steady work with the Askin family, once among the largest slaveholders around. From 1808 to 1811, the Askin family ledger of credits and debits includes several mentions of the Denisons. Lisette (Elizabeth) is the most visible Denison family member in this record, followed by her next younger brother, James. Born in the mid-1780s, Lisette was in her twenties by this time. Her baby brother Scipio appears in the ledger too, as does her father, Peter. The absence of her mother's name suggests that Hannah worked from home at the Brush farm rather than crossing to the Askins' nearby property to provide domestic services. In the course of his accounting, John Askin carefully recorded the racial and caste status of the Denisons. In 1808, "James Dennison Negro Boy" is listed. In 1809, "Lisette negroes man & woman" appear, followed in that same year by an entry for "James and Lisette servants." In 1810, an entry for "Lissette & Jm. Denniston formerly slaves" simultaneously reveals John Askin's heightened awareness of the family's past state of bondage and his acceptance of their current status as free people. Despite Judge Augustus Woodward's legal affirmation of Catherine Tucker's right to the children in the 1807 court battle, his decision was not being applied on the ground where human relations played out in the nuanced exchanges of the everyday. The Denisons were treated like free people in Detroit, albeit free people of color with a lower standing than whites that upper-class community members took pains to inscribe in the cramped pages of their ledger books.
The Denison family, especially the children, did all manner of paid work for the Askins. Lisette Denison was compensated most often for spinning and sewing work; various entries noted items she produced with "thread," "purple cloth," and "gray coating," a fabric used for making coats. For a mixed variety of products, Lisette was paid in wages, sums for set purchases, as well as in bartered material goods. In June of 1809 she was due two months' worth of pay, a frustrating situation that may have influenced the care she took later in life with her finances. In August of that year the Askins gave Lisette "cash" to "buy shoes." In 1809 John Askin registered frustration with Lisette in a rare ledger entry composed in complete sentences rather than dry lists of services, credits, and debits. Lisette had managed to make herself unavailable to Askin, who complained that Lisette was: "Employed in the whole of the winter nights for herself & Brother without [permission] having refused to twist worsted saying she must mend her Brother's clothes which time must be [nearly] 3 Hours Every night in winter." Although John and Archange Askin wanted Lisette to spend time making the tightly twisted "worsted" yarn that the family could use or sell, they found that Lisette "has only spun or twisted yarn three times this winter though frequently desired to do so." During the cold winter months when days were short in the Great Lakes, Lisette was spending her evenings as she chose, helping her brother—or at least, that is what she told the Askins. Lisette possessed three quite valuable skills that she must have learned in apprenticeship to her mother, Hannah. She could spin; she could sew, and she could also bake. Recognizing that her specialized labor was prized enough that she would not be let go by the Askins even if they grew frustrated with her, Lisette controlled her own productivity. When it came to meeting her employer's intense demands, Lisette demonstrated a self-protective and even stubborn streak that would continue to characterize her personality into late adulthood and set her on a path to owning fine apparel of her own.
The Denisons provided essential services for the Askins. Under an 1810 ledger subheading titled "Lissette & Jm. Denniston formerly slaves," John Askin entered a note with a tally of the payments owed the Denison family: "James his credit for services with 4 [1/2] Bushells of corn . . . his father . . . & Lisette." James was performing agricultural labor on the Askin farm, and his father likely did the same. John Askin sometimes paid Peter in "bushelles of wheat," "whiskey," and "brandy." At times he paid Peter, as well as Lisette, by way of Elijah Brush. Twice he paid Lisette in "alms," church contributions that went to the pastor. Sometimes he paid in cash. John Askin regretted, though, that he was paying James more for fewer days of work than the slaveholder Captain McKee was paying "Geo" (George). The Denisons, as a family, were skilled and versatile laborers who knew how to drive hard bargains after years of experience with the Tuckers, not to mention the Brushes, the Askins, and even Governor Hull.
In addition to their exchanges with the Denisons, the Askins maintained a series of economic relationships with people and families they had once owned or who had been previously enslaved in Detroit. John Askin recorded trades for labor with "Mary," "Tom," and "George formerly my slave." Mary was paid an "allowance" and found herself in a similar situation as Lisette Denison when John Askin fell behind in paying her. In response, Mary, who was provided with leather supplies to make "shoe packs," "said she would work for nothing" during this period, suggesting that she occupied an ambiguous status between slavery, indentured servitude, and freedom, much like the Denisons. The Askins also continued to own enslaved people, though fewer than before, in these years. In 1810 John Askin recorded paying "4.8" in "expenses for Jim my negero." The Denisons and other liminal laborers in Detroit of black or Native ancestry and ambiguous or former slave status were intertwined within a web of community economic relationships that allowed them to make a living but continued to privilege the European and American elite. "Negro" workers and former "slaves" constructed, baked, fixed, and made all manner of things on Detroit farms, at Detroit shops, and inside Detroit households. They cut wood and planks, worked with ice and powered through snow, sewed textiles, and made durable shoes for the harsh weather conditions. Peter Denison likely resumed leading the black militia once he was back in the home of Elijah Brush. By 1809, Peter had purchased a muff, three blue handkerchiefs, more than thirty yards of blue flannel, and one pair of "worked mockasons" for which he paid in full. The bulk flannel order may have been for uniforms. Peter also bought "8 plain flat plates," butter, snuff and tobacco that year. Peter often paid cash for his items, and he accepted cash intended to go "to Hannah," and "to wife," for seamstress work. Peter's expenditures were recorded in the anonymous merchant's ledger among a mix of purchases made by diverse Detroiters. French old settlers like Pierre Chêne and Madame Macabe appeared in this record book, buying tobacco and calico, as did American professionals like Solomon Sibley, who purchased a lady's parasol for his wife and two pairs of "fine kid gloves." An indigenous man listed as "Na'auguaijigue Chief" paid for ten plugs of tobacco with "muskrats in full." And two African Americans besides the Denisons were listed in the ledger: a woman described as "Mary Ann Negroe Wench," who was paid for one month of "services" and a boy called "Jack the little Negro," who was paid for his "services" of delivering green tea and sugar. While procuring household goods as "Brush's black man," Peter Denison seems to have been ever mindful of his unstable status. In the winter of 1810, Elijah Brush wrote to John Askin, explaining that "Peter goes across to see if he can get any allowance from Lisette to assist in the purchase of his liberty if you should happen to owe him anything and wish it I will endeavor to furnish the money." That season, Elizabeth Denison borrowed £14 from Askin, which Askin passed along to Brush "on acct [account] of Lisette my letter." Peter and Hannah, aided by their industrious and effective daughter, moved out on their own, leaving Adelaide Brush to bemoan to her brother: "Peter and his wife [left] us this fall therefore, I have nobody to depend upon."
Formerly enslaved people—many of them now viewed as free people of color—were an integral part of the social and economic fabric that knit Detroit together in the years before the next war. The legal conditions of Detroit's location in Michigan Territory of the Northwest, together with the town's continued geographical isolation, meant that relationships had to be carefully negotiated. Such mediations provided a legally vulnerable family like the Denisons with the cover to live as free residents. At the same time, formerly enslaved people's need for cover created opportunity for merchants and landowners, who could contract work for delayed pay or no pay at all, lend money or withhold it, to continue exerting significant influence over disadvantaged people's lives. The Denisons met this overlay of obligation and control with a remarkable creativity and adroitness that simultaneously bespeaks their own aspirations as well as those of Detroit's liminal working class of color for whom detailed accounts do not survive.
The Black Militia and the War of 1812
Governor Hull first said no when asked to accept the position of brigadier general of the Northwestern Army. He repeated his refusal upon the second request from Secretary of War William Eustis. Hull was not eager to take the highest western military commission on the eve of America's second war with Great Britain. Perhaps age was an issue uppermost in his mind. A local hero of the Revolutionary War for his brave bayonet work, Hull was now fifty-nine years old and far less nimble. His wife Sarah's warning must also have rung in his head as he weighed this momentous decision. She had told him three years before to beware the manipulations of Washington insiders. Or maybe Hull was feeling miffed, as he had offered to serve in the military during the preceding winter and was told his service was not necessary. A final barrier to Hull's acquiescence was his reluctance to relinquish his gubernatorial post. But upon the third request of Secretary Eustis in the winter of 1812, and with the promise that he could hold both the civilian and military titles, Hull relented, agreeing to lead the forces of all federal troops in Michigan against a concerted British and Indian assault that was sure to come before long. War had not yet been declared, but tensions were rising feverishly in hot spots around the country. First the attack of the _Leopard_ upon the U.S.S. _Chesapeake_ off the coast of Virginia had dramatically symbolized the campaign of British impressments and the Crown's practice of bullying American ships and blockading American trade. Then the striking, Ohio-born Shawnee leader Tecumseh had gathered influence among several western and southern indigenous nations.
Tecumseh was organizing a coalition around the spiritual vision of his brother, Tenskwatawa, also known as the Prophet, in which indigenous people renewed their cultures, reclaimed their faiths, and took back their homelands. Tecumseh's aim, fed by Tenskwatawa's vision, was for Native independence won through a confederation of tribes, but he would ally with the British in order to achieve this goal. The Prophet had received permission from Potawatomi and Kickapoo residents to found a multi-tribal village of proponents on the Tippecanoe River in their territory of Indiana. A spiritual, intellectual, and organizational hub of the Native revolution, Prophet's Town was a bright red flag waving in the face of a bullish American government. As Prophet's Town drew adherents, Tecumseh, whose mother was Creek, traveled south into Cherokee and Creek territory sharing his two-pronged message of "prophetic nativism" and "intertribal unity." Watching the spread of Tecumseh's message and the political and spiritual gathering of nations in the western interior pushed the Americans to the offensive. In 1811 troops led by Indiana governor and future U.S. president William Henry Harrison had closed in on Prophet's Town, the source, Harrison believed, of a series of raids on Indiana settlers. Aware of Harrison's approach, the warriors struck first and were counterattacked by Harrison's men, who then burned the empty settlement to the ground, making Harrison into a frontier folk hero for segments of the American populace and inspiring the future pro-Harrison campaign rallying cry: "Tippecanoe and Tyler Too!" Tenskwatawa would not be deterred by American reprisals; he rebuilt Prophet's Town and grew its size to eight hundred warriors. Tecumseh, who had been traveling during the battle as an ambassador of the Native resistance, had survived to fight another dawn against the Americans.
Governor Hull had been keeping track of these dire developments from the capital in Detroit, as had been local residents. As Tecumseh and the Prophet's notoriety mushroomed with news of the Battle of Tippecanoe traveling across the forests and prairies, Detroiters were growing ever more fearful of an Indian attack on their town. In 1811, leading citizens drafted a memorial to the "president, senate, and house of representatives" in Washington, voicing their fears and urging "an increase in military force." The memorial writers described "dissatisfactions with the aboriginal inhabitants of these countries," which had "been kindled into an open flame." They begged the government not to allow "conflagration" to spread "along the whole line of the frontier," as "the Savage mind, once fully incensed, once diverted from the pursuit of their ordinary subsistence, once turned upon plunder, once inflamed by the loss of their kindred and friends, once satisfied with the taste of blood, is difficult to appease, and as terrible as subtle in vengeance. The horrors of savage belligerence description cannot paint. No picture can resemble the reality." But paint it these authors did, and with a self-focused, stereotyping brush that refused to see the legitimacy in Native people's defense of their original homelands and ways of life. This memorial, signed by Solomon Sibley, Augustus Woodward, George McDougall, Harris Hickman, and Richard Smyth, was the work of Anglo American professional and working-class men, who stressed the need for government "protection" in "their exposed and defenceless situation."
Governor Hull, who may not have exactly appreciated the pattern Detroiters had set of going over his head with their letters and memorials, agreed with the townspeople's diagnosis and prescription. The borderland northwest, Hull predicted, would be a front line of the international altercation to come. The British had already shown a willingness to abuse the power of the Royal Navy while carrying out their impressment policies. As a peninsula surrounded by coastline, Michigan was especially exposed to maritime attack, far more vulnerable than southern territories like Ohio, Indiana, and Illinois. A terrestrial threat also existed, deep inside the western woodlands. Although indigenous people had been pushed beyond a boundary in treaties at Greenville, Fort Wayne, and Detroit, they were inspired by spiritual renewal and outraged at the continual loss of land, and they were increasingly organizing across tribal lines. Hull, as historian Michael Witgen has put it, was "painfully aware that the United States, in stark contrast with the Canadians, had a troubled and violent history with the Native peoples living within the borders of the territory he claimed to govern . . . and assumed that the peoples of Anishinaabewaki [Ojibwe, Ottawa, and Potawatomi country] would turn against the United States." Back in 1807, a wary Governor Hull had ordered the Michigan militia to rebuild the pickets surrounding the town to a height of eighteen feet. Lately, he had been fixated on the notion that the government should immediately build a naval fleet to patrol the Great Lakes. In March of 1812, he wrote to Secretary of War Eustis recommending that "A force adequate to the defense of that vulnerable point [Detroit], would prevent war with the savages, and probably induce the enemy to abandon Upper Canada without opposition. The naval force of the Lakes would in that event fall into our possession." In April of 1812, Hull accepted his commission as brigadier general, but he never received the enhanced naval force he longed for.
The War of 1812: Indian Involvement 1811–1816. Map originally published in _Atlas of Great Lakes Indian History_ , edited by Helen Hornbeck Tanner. Copyright © 1987 by the University of Oklahoma Press, Norman. Reprinted by permission of the publisher. All rights reserved.
While Hull was lacking in full support from the federal government on the waterways, he did have at the ready Ohio militiamen, Michigan militiamen, and, one rare source suggests, the black militia of Detroit. Hull first had to gather his scattered troops from Ohio before preparing a defense of the northwestern border. According to a dispatch from New York written on July 18, Hull "arrived at Detroit, with 2,300 men, after a tedious march through the wilderness." In order to get there, Hull and his troops had been compelled to cut a trail through a portion of the thick and formidable marshland of northern Ohio's Black Swamp, watered by the Maumee River and greater than one hundred miles in length. Facing the acute challenge of traversing a difficult landscape weakened Hull's army before the war had officially begun. At the Miami River, Hull chartered a private boat, the schooner _Cuyahoga_ , to transport the wives and children of officers as well as trunks of records and medical supplies to Detroit. Because the War Department sent notice that the United States had formally declared war on Great Britain via the sluggish regular post, Hull found out the news days after British military leaders knew of it in Canada. Thus prepared to engage, officers at Fort Malden on the British side of the Detroit River dispatched a longboat, which captured the ship Hull had commissioned and commandeered Hull's supplies. Even as a Washington writer cheered Hull's arrival in Detroit, exclaiming Governor Hull "had arrived at Detroit on [July] the 5th, with his army amounting to nearly 2,500, all in good health and high spirits," Hull had been disadvantaged by geography and his own government and bested by the British command.
The fate of the _Cuyahoga_ foreshadowed the nature of this off-kilter conflict that tested, but in the end left in place, territorial boundaries established by the Revolutionary War. The War of 1812 was a series of odd engagements, missed opportunities, unfortunate accidents, and unanticipated atrocities, especially in Michigan Territory. Governor Hull, as well as the town of Detroit, would suffer from both mistakes and misfortune in a war that many Americans, especially Federalists in New England, were not even in favor of. But in the Great Lakes, from New York to Michigan Territory, fear of a Native alliance with the all too proximal British troops in Canada, fed a hawkish orientation. In New York, rumors circulated about the rise of an Indian force in league with the enemy. "Great exertions were making by the British at Fort Malden, to array the Indians against us," a letter writer exclaimed, "Previous to the declaration of war, a tomahawk, stained with blood, had been sent from Malden to all the neighboring tribes." The United States planned to forestall attack by launching an assertive invasion of Canada from Detroit. Directed by Secretary of War Eustis to prepare to wage an offensive war, Hull and his officers began to plot a frontal assault on British targets. Eustis commanded: "By my letter of the 18th inst. You were informed that war was declared against Great Britain. Herewith enclosed, you will receive a copy of that act, and of the President's proclamation, and you are authorized to commence offensive operations accordingly. Should the force under your command be equal to the enterprise, consistent with the safety of your own posts, you will take possession of Malden, and extend your conquests as circumstances may justify."
Hull and his men made an auspicious beginning for the American strategy by crossing the Detroit River and occupying the tiny town of Sandwich in July. Black militiamen may very well have been among this force. On July 20, 1812, an unsigned journalist's dispatch written in Ohio described the scene at Sandwich based on an eyewitness account: "We are further enabled to inform our readers, that we have since our last learned from a gentleman direct from Sandwich . . . that the army crossed the river without opposition; that the inhabitants generally fled, but on receiving the proclamation they returned to their houses, and resumed their businesses." After giving the account of the Sandwich campaign in which Hull had posted a proclamation inviting residents to join the American cause and assuring their protection, the writer of this piece made the following observation: "Previous to the army's leaving Detroit, a company of the black infantry associated and requested to accompany the army in support of America and freedom. Governor Hull accept[ed] the offer and gave commissions. The captain is said to be a very intelligent man, and the company perform well."
In a dispatch full of precise detail about troop movements, artillery pieces, and the eighty barrels of flour secured from the king's commissary at Sandwich, the black militia was entered into the written record of the War of 1812. The "intelligent captain" must have been Peter Denison, who had spent ample time in Sandwich but had resettled in Detroit with Elijah Brush, colonel of the First Regiment of the Michigan Volunteer Militia, before the war began. The reporter from Ohio noted in his commentary that these black men offered to fight for "America" and "freedom." However, the history of the Denison family, and of all enslaved people in the Detroit border zone, whether of black, indigenous, or Afro-Native ancestry, indicates a strategic lack of national allegiance. These were "revolutionary renegades," who fought for freedom, for independence, and for dignity of life, in ways that could sync with or diverge from the aims of any particular colonial or state power. As the first black military company on American soil authorized by a government official and commanded by black officers, the men of the black militia fought for the right of their families to be free from tyranny in any form.
Hull's taste of victory in the occupied Detroit River town did not last long. On July 17, the British along with Ojibwe and Ottawa allies captured the American fort on Mackinac Island. Hull heard this portentous news from two Ojibwe travelers whose route took them through Detroit. Judge Augustus Woodward wrote about the loss of the fort in the concluding lines of his July 28 letter to Secretary Eustis: "You will, no doubt, have received, through other channels, the information which has arrived here of the capture of Michilimackina by the enemy." It was in this same letter that Woodward complained about Hull issuing "three commissions to captain Denison, lieutenant Burgess, and ensign Bosset, black men." Would not these black soldiers have continued on through the next engagement of the war that unfolded in the town where they were stationed? In all likelihood, former slaves and men of color based in Detroit fought in the War of 1812.
On August 12, a British force led by Colonel Isaac Brock together with a Native force led by British Indian agent and slaveholder Matthew Elliott set sights on Detroit. At 1:00 p.m. on Saturday, August 15, Brock sent a message to Hull by way of a small vessel demanding Hull's relinquishment of the fort. "The force at my disposal authorizes me to require of you the immediate surrender of Detroit," Brock insisted, catching Hull by surprise. And then Brock's letter included a line meant to stoke the latent fears of Hull and his constituents. "It is far from my intention to join in a war of extermination," Brock wrote, "but you must be aware, that the numerous body of Indians who have attached themselves to my troops, will be beyond controul the moment the context commences." Hull stalled, hoping for reinforcements that never came from troops that he did not realize were located just miles outside of town. At 3:00 p.m., Hull rejected Brock's demand. By 4:00 p.m. the British were firing canons across the river. The Northwestern Army counterfired from artillery positioned in the heart of downtown Detroit. Hull directed Elijah Brush to guard the northern edge of the town, backing into the woodlands. If the black militia was activated, they were likely assigned a similar duty, positioning Peter Denison to coordinate with his colleague, Elijah Brush.
The British assault continued unabated into the night. Fitful residents who dared not sleep may have recalled stories of the siege of the village by the Ottawa warrior Pontiac two generations prior. The terrified occupants of Detroit Town desperately buried money and silver, or directed their slaves to do so. Women and children fled to the enclosed stockade at the fort as cannonball shots splintered the wooden walls, killing two soldiers. Lisette and Hannah Denison would have been among these women, clustered, perhaps, with Adelaide Askin and her children. Resourceful and independent, Lisette may have joined local women in nursing the wounded. Her brothers, James and Scipio, may have been defending the fort with her father, Peter, and other men of the black militia.
With ammunition running low, no reinforcements, and the threat of Indian reprisals against the civilian population that he was duty bound to protect as governor, Hull decided, in a fateful choice that military historians continue to analyze and debate, to surrender the town. Elijah Brush was among the four officers who drafted the statement of Detroit's capitulation, an American defeat that resounded across the country and brought harsh recriminations for Hull. Within forty-eight hours of the commencement of Colonel Brock's attack, old Fort Detroit was British once again. Imagine the fear of fugitive slaves who had escaped from Canada, the rage of Richard Smyth and the men who frequented his tavern. As the outlying farmhouses along the river were plundered by Native warriors, the disgraced Governor Hull moved into his former brick home, now occupied by his daughter and her family, where he was placed under armed British guard.
On the following Monday, August 17, Hull, his officers and staff, and members of the regular army were taken as prisoners of war to Quebec. Elijah Brush was among them. The military historian Gene Allen Smith has written that "Peter Denison was taken off with other white and black prisoners to Canada before being paroled." Although no apparent document directly points to this outcome, it is certainly plausible, as the British paraded nearly four hundred prisoners seized at Detroit. If Peter was taken to Quebec but released early, he died just days later. On August 27 of 1812, Reverend Richard Pollard of St. John's Church entered into the registry: "Peter Dennison . . . departed this life and was buried." The archival trail of Detroit's black militia ends here, with him.
But the war went on after the death of Peter Denison in 1812 and after the death of Elijah Brush in 1813. The families of these men lived through the British occupation of Detroit that lasted for more than a year, during which time Augustus Woodward intervened on behalf of the populace and won protections from the British commanding officer. In the winter of 1813, British troops and Tecumseh's warriors attacked French Town on the River Raisin in Michigan, a settlement that had formed when several French families migrated from Detroit in the 1780s. American troops were defeated, captured, and tortured there, a low point for American morale and a rallying point for demoralized U.S. soldiers who would take up the cry: "Remember the Raisin!" But by the next summer, U.S. forces were landing significant blows against the British. In 1813, after hanging his battle flag commemorating a quote by felled captain James Lawrence—"Don't give up the ship!"—naval commander Oliver Hazard Perry won a dramatic sea contest against vessels of the British navy on Lake Erie, a body of water where William Hull had first said an American force was needed. In 1814, General William Henry Harrison, who directed the Northwestern Army in Hull's wake, led troops to recapture Detroit for the United States. A series of clashes ensued in which British troops, Native forces, and American soldiers confronted one another but did not score victories decisive enough to tip the scales of war. In the Battle of New Orleans, which took place in January of 1815 just after American and British diplomats meeting in Belgium had signed the Treaty of Ghent in December, Commander Andrew Jackson amassed a multiracial force, including black and Choctaw soldiers, that prevented British troops from entering the city.
It was not until February of 1815 that Congress ratified the treaty and most Americans heard the good news that the war had formally ended. But neither the United States nor Great Britain had been victorious in the conflict. No territory had been gained or lost by either nation, though Canadians could take pride in having successfully fended off multiple American incursions. Native Americans in the region saw their influence severely reduced with the death of Tecumseh at the Battle of the Thames in 1813 and the reinstatement of American power at western forts at the war's end. The War of 1812 would be the last moment when indigenous forces allied across multiple tribal lines to challenge the United States militarily. In the northern reaches of Michigan, western reaches of Wisconsin and Minnesota, and great west of the high plains and Rocky Mountains, hundreds of Native populations still organized autonomous societies outside the reach of American colonialism. But in the Ohio Valley, the lower peninsula of Michigan, Illinois, Indiana, and the Southeast, the outcome of this war was "most ominous to the Indians."
While devastating for indigenous people, the conflict was a virtual "draw" for Great Britain and the United States, which has caused it to fade in memory for citizens of both these nations. But the War of 1812, often called the "forgotten" war of American history, marks a watershed moment for the story of slavery in Detroit. By the time war began, the number of enslaved people in the town and riverine suburbs had shrunk to a handful of individuals listed in the Ste. Anne's Church register. In 1812, a black woman named Nansey was described as the slave of Jacques Laselle, as was her son, Jean Baptiste Rémond, conceived with an "unknown father." Abraham Ford, a black man, was married to Marie Louise, a free Native woman of French and Native parentage, whose mother was "of the Sauteur nation" (Ojibwe); they had a child, Julie Ford, born in 1813. Abraham Ford is described in the register as "negro of Colonel Matthew Elliott." By the end of the war, slavery in Detroit had nearly met its demise. In 1820, no enslaved people were listed in the Ste. Anne's Church register or the Detroit census. The 1830 census noted one enslaved person within the borders of Michigan. Two years prior to Michigan statehood, in 1835, two enslaved people lived in Monroe and Cass Counties, Michigan.
Warfare, political struggle, and territorial laws had weakened the practice of slavery in Detroit during the late eighteenth and early nineteenth centuries, but enslaved people themselves dealt the final blows. Adopting a renegade politics, traversing the border in pursuit of freedom, and fighting against those who claimed to own them with legal as well as lethal weapons, enslaved people undermined the corrupt, fraying, suspect system until it snapped. They no doubt shared the view of fugitive slave J. Levy, who wrote a letter back to his master from Canada in 1852, boldly proclaiming that "liberty is ever watchful" and "security" to "self" "demanded the sacrifice."
During the War of 1812, hundreds of black men fought for the British as well as for the Americans, seeking freedom and respect for the priceless risk they took with their lives and futures. In the United States, African Americans sailed with Perry's troops on Lake Erie, spying Canada just across the waters. What these men learned about the secrets of the border, what enslaved Detroiters and black militia members had long known, became prized information for disparate black communities, especially after 1833 when Britain abolished slavery in its colonies and Canada became free soil. The stories shared by these revolutionary renegades traveled with military men of color and fugitives from slavery, adding a shimmering thread of hope to the collective consciousness held by African Americans and other oppressed peoples.
Conclusion:
The American City (1817 and Beyond)
The drama continues, but it does so with wrenching twists and turns, fervent disjuncture, and dizzying prospects.
_—June Manning Thomas and Henco Bekkering,_ Mapping Detroit, _2015_
After the dust in Detroit had settled following the War of 1812, Elizabeth Denison, known to her family by the nickname Lisette, continued on in the household of Adelaide Brush, widow of militiaman Elijah Brush. Lisette and her siblings lived as free residents of the city. But limitations that the Denison family and all free people of color had faced continued into mid-century; theirs was a hard-won and consistently compromised freedom. Lisette would spend the rest of her working life in the most common employment for free black women in the 1800s: as a domestic laborer in the homes of white Americans. In August of 1816, Lisette shared the joyful occasion of her brother Scipio's marriage to the seventeen-year-old Charlotte Paul in Detroit. In December of that year, Scipio and Charlotte had a daughter, Phoebe, who was baptized in 1817 across the river at St. John's Church in Sandwich. Lisette served as a sponsor for her baby niece's baptism, as she and the rest of the Denison family's younger generations continued their frequent crossings of the U.S.-Canadian border in what was, essentially, a transnational way of life. In 1819, a son named James was born to Scipio and Charlotte and baptized at St. John's, sponsored by his aunt Lisette, his uncle James, and his father Scipio. The absence of Hannah Denison's name in these church records of the 1810s suggests that she followed her husband, Peter Denison, into her final rest before these new grandbabies entered the world. If so, Hannah Denison missed Detroit's surge of growth in what one privileged Detroiter called an "auspicious era." Like Hannah and Peter Denison, and Elijah Brush, many of the most prominent figures in Detroit's slaveholding history had passed away or relocated by the 1820s. William Macomb, the town's largest slaveholder in the eighteenth century, had died before 1800. In 1817, his widow, Sarah Macomb, and son, David Macomb, were advertising nearly five thousand acres of land for sale, including plots in Upper Canada, "most excellent Land, on Grosse Isle," and an "elegant and pleasantly situated farm on the border of the Detroit River." The two other Macomb sons, William and John, had begun the process of selling their Detroit River and island lands in 1810, with John and his nephew William preferring to run a coffee plantation on the Caribbean island of Cuba where slavery was still patently legal. John Askin would pass away in 1818 at his home on the river, and James May would leave this life in 1829.
An Auspicious Era
As Lisette Denison searched the deep brown eyes of her baby nieces and nephews who just one generation ago would have been born into slavery, she may have cast her mind to the shadowed reality of that past, and then to the possibilities of a brighter future in Michigan. Certainly other talented Detroiters, especially those who enjoyed racial privilege, social position, and a reassuring measure of wealth, scanned the eastern horizon for signs of opportunity. In the newly launched _Detroit Gazette_ newspaper, established in July of 1817, tavern owner Richard Smyth was announcing a "meeting of the citizens of Detroit" to discuss "important matters relating to trade and the general prosperity." The Abbott family's merchant business, established in the 1770s and burgled back then by the company's slave woman and servant man, was still going strong in the fall of 1817, when James Abbott advertised blankets, sundry cloths, and "fine" flour for sale on credit in the _Gazette_. In the spring of 1817, John R. Williams, also a merchant in Detroit and descendant of the slaveholding Campaus on his mother's side, wrote to Samuel Abbott, a lawyer at Mackinac, to conduct business and share big news. Williams's letter bridged the old and new character of the city—the Detroit of colonial and Revolutionary War times that relied on systems of unfree labor and the post–War of 1812 Detroit that was increasingly modernizing and expanding its economy. In his missive, Williams solicited "Panis" labor and at the same time sounded a ring of ebullient optimism about industrial development and growth. Williams opened by disclosing his "difficulty of procuring servants" in Detroit and telling Abbott: "I am informed they can be procured at Mackinac, of the Panis Nation of both sexes." Specifically, Williams "would be glad to have a boy and girl from 12 to 18 years of age, Bound under indentures to serve for a limited number of years, say to the age of 30." If Abbott would do Williams the service of sending him a "boy and girl . . . of good moral habits and tractable disposition," Williams would clear the account on Abbott's "draft at sight." John Williams's request bespoke his close association of Native people with servitude, such that he believed the French term for an Indian slave, "Panis," designated a particular tribe of people. In the 1810s, Williams's entreaty smacked of old patterns. Many an indigenous person defined as property had been ordered from the straits of Mackinac by Detroit merchants in the century past. While Williams did not propose to buy these children outright, and could not have done so under Michigan law, he could pay Abbott a sizable fee in the form of debts eliminated for procuring their indentures such that they would be bound to him until mid-adulthood. Williams made no mention of indigenous parents or tribal leaders in his letter. A complacent consumer of Native labor, he fully expected these children to be easily plucked from their families and offered up for his use.
After dispensing with the prosaic business of getting hold of "Panis" servants, Williams turned readily to the "news." He informed Abbott that "The President of the U.S. has signified his determination to visit us this summer. I look upon the event as an auspicious aera in the prospective improvement of this country, and anticipate more alteration within the next five years than the country has undergone since its first settlement. The projected canal to connect the waters of Lake Erie with those of the Huron, will no doubt greatly acclimate the population & prosperity of this country." John Williams, who would become the first formally elected mayor of Detroit seven years after writing this letter, had the keen eye of a futurist. The Erie Canal, completed in 1825, would indeed open the floodgates of Euro-American settlement in Michigan and set Detroit on the path to becoming "a truly American city." For Williams, this modern version of Detroit would, and should, coincide with an older colonial order in which "tractable," or readily managed, indigenous children could be ordered like items in a catalogue. When President James Monroe visited the city for five days that August, "a period of great glorification for the small city," he might have witnessed the enduring imprint of this colonial history inscribed in the menial class status of Detroit's residents of color.
Beyond the growth of the white population and support of trade through federal infrastructure, residents of John Williams's ilk looked toward higher education as a means of uplifting Michigan Territory to the level of existing states. Citizens began rallying for the formation of a local university and launched into avid fundraising. Leading men stepped immediately forward in a "rapid and liberal manner," according to the _Gazette_. On the first day that subscriptions were collected, more than £1,000 of funding had been pledged for the cause that all upheld as worthy. Judge Augustus Woodward, who had always been fond of serious interdisciplinary study, and who, according to two nineteenth-century chroniclers, still kept one "pawnee" servant as "one of the last slaves in Detroit," introduced a bill to establish the school and delved into the development of a "System of Universal Science" to organize areas of study for the university. James May, the merchant whose wrecked ship in 1801 had killed a man he owned, made a payment of $5, the initial installment toward an overall pledge "to be paid in money." According to the record of the university treasurer, May agreed to pay this amount each year over five years in "the aid of the University of Michigan." James Abbott, also a slaveholder, pledged $315.32. Attorney Solomon Sibley, whose son would later own slaves and rise to political prominence in Minnesota, promised $625.67. The Detroit freemasons, in which slaveholder Joseph Campau served as treasurer, contributed an undisclosed major gift to the school. The university also drew support from a public relief fund dating back to the fire of 1805 that had not been fully exhausted. Hybrid from the outset, the school's financial foundation was sourced from both private and public wealth. Tuition was set at "a small sum," but "certified" students unable to pay would be supported by the territorial treasury. Members of Detroit's old slaveholding network were among those who contributed the earliest designated contributions, making public education in Michigan possible. The original list of trustees for the school included surnames of some of Detroit's earliest and largest slaveholding families: the Campaus, the Abbotts, and the Macombs. Organized as a "Primary School" linked to a "Classical Academy" with training through the high school level, the University of Michigania (also known as The Catholepistemiad) was formally established by territorial Governor Lewis Cass with the Reverend John Monteith serving as president and Father Gabriel Richard serving as vice president. Augustus Woodward, the main mover behind the ambitious initiative, laid the first cornerstone for the inaugural campus building in September of 1817. Two decades later, in 1837, the institution would spread its wings, gliding southwest to the forested hamlet of Ann Arbor.
This relocation to Ann Arbor, and the university's institutional and intellectual maturation there in the second half of the nineteenth century, depended on a large swath of land acquired through an unexpected chain of transactions. An agreement known as the Treaty of 1817 had cemented a transfer of approximately 4.2 million acres of land from indigenous to Euro-American hands in the aftermath of the War of 1812. The story was by then a familiar one in the Detroit River region and Ohio Valley: land speculation and government pressure pushed indigenous peoples to treat or sell, lest they be smothered by incoming settlers or driven out following violent battles with militiamen and military officers. But in the negotiations of this particular treaty, leaders of the Ojibwe, Ottawa, and Potawatomi nations specified that they wanted a portion of their land to be directed toward a certain purpose. They granted territory along the River Raisin in southeastern Michigan to the state, to be used or sold in order to support educational opportunities for their children. These Native leaders wished to see an extension of Ste. Anne's Church in Detroit and the "corporation of the college of Detroit" (Michigania) in order to better prepare their own children in a moment when territorial administrators had their minds set on statehood and a citizenry defined mainly as white. Michigan officials would later trade a portion of this original 1817 land grant on the River Raisin for acreage in Ann Arbor near the Huron River. Here, the college was relocated from its original site in downtown Detroit and expanded to offer advanced courses of classical study.
An iconic Midwestern and American educational institution, the University of Michigan was born of a compromise made by Native people in the context of a century of colonial warfare and land dispossession in the Great Lakes. Built on ill-gotten lands and funded, in part, by family wealth derived from slave labor, the University of Michigan system now shines as a cultural star of the state. In 1976, the Michigan State Legislature adopted Public Act 174, a law authorizing tuition waivers for tribally enrolled Native Americans who reside in Michigan and have been admitted to any of the state's public universities. This redistribution of public resources to citizens of indigenous nations is an ethical response to troubled historical relationships. Tuition for Native people has been, in the words of an undergraduate student at the University of Michigan from the Grand Traverse Band of Ottawa Indians in northern Michigan, "prepaid in land and blood."
The Mammon of Unrighteousness
Lisette Denison may have wondered, as talk of a university bolstered town pride, whether her nieces and nephews would ever study there. Records indicate they would not. The first African American student, Samuel Codes Watson, was admitted to the University of Michigan medical school in 1853; the first African American woman, Mary Henrietta Graham, was admitted to the college of literature in 1876. In the 1810s and 1820s, the livelihoods of Lisette and her family members still depended upon domestic labor and close connections with prominent white Detroiters. But Lisette had shown in her dealings with John Askin, when refusing to twist worsted yarn for hours on end, that she was capable of shaping the terms of such domestic employment. In the early 1820s, Lisette left the household of Adelaide Askin and began working for the family of prominent attorney Solomon Sibley. Lisette cooked for the Sibleys and provided care for their children. When Solomon Sibley's daughter, Catherine, left Detroit to attend Emma Willard's finishing school for girls in New York, she wrote back to her mother: "Tell Lisette I often wish I could visit her cookie jar." The Sibleys appreciated Elizabeth Denison's finely honed skills in the kitchen. And Lisette, by all appearances of what transpired over the next decade, appreciated Solomon Sibley's facility with the law.
Elizabeth Denison had grown up enslaved on a farm in the Detroit River hinterlands. She had no formal education and never learned to read or write. She had come of age during the era of Detroit's transformation into an American town and watched as Detroit area lands were extracted from indigenous people, divided up into lots, and sold for government profit. With the growing influx of eastern and southern settlers, Lisette saw Detroit transform into a small city with three thousand residents by 1817. She recognized the value of land and, like many white citizens around her, sought to acquire it for herself, even though moral title, she might have realized in her heart, belonged to the Native peoples who increasingly lived on small parcels of reservation lands north of Detroit near the Saginaw River, at the straits of Mackinac, and toward the western banks of Lake Michigan. As she matured, Lisette managed to redefine herself as a financially savvy urbanite at the dawn of Detroit's industrial metamorphosis. Beginning in 1825, Solomon Sibley's papers show a series of land purchases made by Lisette Denison and facilitated by Sibley. She bought 48.5 acres (four lots) in the town of Pontiac, due north of Detroit, from Sibley's business associate Stephen Mack, becoming the first black landowner in the city. She then leased these lands to her brother Scipio. Scipio and Charlotte Denison soon had another daughter, who was baptized in Pontiac. When their family needed a loan of $5, Scipio turned to his sister Lisette, who had herself married by then, in 1827, to a man who shared her brother's first name: Scipio Forth.
Lisette's marriage was short-lived. Her husband vanished from the historical record and, presumably, from her life soon thereafter. The mystery of her husband's disappearance was likely a source of sadness for Lisette, but she rebounded, taking a job in 1831 in the home of the president of Farmers and Mechanics Bank, former Detroit mayor, and War of 1812 veteran John Biddle. Lisette grew and diversified her investments throughout the 1830s. After her brother vacated the Pontiac land, Lisette rented it out. She then bought stock in the steamboat _Michigan_ and shares in Farmers and Mechanics Bank. In the spring of 1837, Lisette acquired land in downtown Detroit from Solomon Sibley's son, Ebenezer Sibley. She paid her mortgage off in full in 1842. Like her father before her, Elizabeth Denison had a knack for bartering desired skills that brought her support from prominent whites and then pushing that support to access new and sometimes radical opportunities. A notable cook and seamstress, Lisette had channeled the goodwill and connections of her influential patrons to become a woman of invested wealth. Whether to continue the benefit of these key relationships, to procure liquid assets in the form of cash payments, or to maintain caregiving responsibilities for children she had helped to raise, Lisette continued to work for John and Eliza Biddle as a cook, nanny, and housekeeper into the 1850s. But Lisette did not make her long-term domestic employment with the Biddles easy for the prominent couple. Recognizing her importance to the family, she continued to negotiate her own labor terms. In 1839, a visitor to the Biddle's elegant new home in Wyandotte, Michigan (fifteen miles south of Detroit), commented that she "[did] not know how [Mrs. Biddle] would get on but for Lisette who, notwithstanding her frequent threats of leaving, seems as firmly established as ever."
Fifteen years after this observation was made by a guest in her home, Eliza Biddle was still dependent on Lisette in what was an interdependent, often strained relationship. In 1855, Lisette accompanied Eliza on a trip to Paris in order to "keep house" for her employer. According to Eliza, who mentioned Lisette's cooking and penchant for fine gloves frequently in her letters to relatives and friends, Lisette created buckwheat concoctions that astonished and delighted Parisian high society. Almost forty years before Quaker Oats marketed Aunt Jemima pancake mix, making the stereotyped image of black women's domestic servitude a nostalgic American sensation, Biddle wrote the following about Lisette's cakes: "Lisette is making us quite celebrated in Paris by her buckwheat cakes and I expect some of these days to be invited to come to the Tuileries [Palace] and bring my black cook & her griddle that the Empress may enjoy the American luxury." Eliza Biddle proudly reported that the "Ambassador" himself requested Lisette's cakes. Rather than sending a parcel containing the treats, Eliza Biddle sent Lisette, who startled the "indignant" French chef "when she produced a fire in the furnace and produced her griddle." Eliza Biddle did not forget Elizabeth Denison's race, or shed her sense that a formerly enslaved African American woman could be viewed as a personal possession to be sent around town like a package. Lisette was too sharp to have been unaware of these racially biased attitudes on the part of her employer, or of Parisians' view of her as a folksy relic of America's quixotic slaveholding past. She even allowed her resentment to slip to the surface so that Biddle could glimpse her feelings. Eliza Biddle wrote about Lisette: "She thinks when she is sent for by the Emperor she will not return to our modest ménage but remain at court & perhaps have a carriage of her own." Eliza Biddle recognized Elizabeth Denison's ambition to do something greater than cooking for the Biddles, but she quickly squelched any critical introspection that such recognition might have raised for her. The next line of her letter celebrated the fame of Lisette's cakes while erasing Lisette's name as the creator of the delicacies: "Wherever we go we hear of these famous buckwheat cakes and of course when we invite company it is to sit round the table & enjoy them."
Elizabeth Denison made her griddle cakes, accepted her pay, and saved her Paris earnings. She kept close watch on her house in Detroit with the help of the Biddles and their associate, Mr. Campau, checking on whether the house was rented and if the rent was equal to the value. Eliza Biddle found Lisette's careful habit of saving money to be excessive; she wanted Lisette to hand over control of her earnings to the Biddles and accept a yearly allowance of $25 instead. Eliza Biddle's stated reason for this change was that Lisette was living too frugally and, worse, embarrassing the Biddles by "asking charity when she has really more than she can spend if she were to live till she is a hundred & no one she cares for to leave it to when she dies." Revealing the fissures in her relationship with her "black cook," Eliza complained that Lisette was telling people that she had been "badly used by everybody." The resentment Lisette felt after years of laboring as a domestic and being treated like a mere functionary showed even more in her elder age. Eliza Biddle tried to have her son William, Lisette's favorite among the Biddle children, "cheat" Lisette (Biddle's own choice of words) in order to gain control of her finances. Instead of receiving the Biddle's money in the paid allowance as she would be led to believe, Lisette would be receiving and spending down her own funds. But Eliza Biddle's financial scheme did not work. Lisette Denison maintained her savings and, contrary to Biddle's condescending expectation, made a plan for her bequest that included those she cared for.
Elizabeth Denison Forth. Photo courtesy of Saint James Episcopal Church, Grosse Ile, Michigan.
Mrs. John Biddle (Eliza Falconer Bradish). By Thomas Sully, Metropolitan Museum of Art, New York, New York. Available at www.metmuseum.org.
One year after the close of the Civil War in 1866, Elizabeth Denison's life ended in Detroit. Her file in the historic Elmwood Cemetery record indicates that she died on August 7, 1866, and was buried in the "Stranger's Ground." She had composed a will (and revision) with Solomon Sibley's assistance and selected William Biddle, who had completed his law degree at Harvard and was then working as an attorney in Detroit, to serve as executor of her estate. In her will dated January 1860, Lisette Denison acknowledged that she was "unable to read and write." She left various sums of money (between $50 and $100) to all of her living relatives: at that point only nieces and nephews, as she had lost her siblings and in-laws and never had children of her own. Finally, she authorized her trustee, William Biddle, to devote the remainder of her estate toward "the erection of a fine chapel for the use of the Protestant Episcopal Church." This chapel was to be a remedy for "the poor in our house of worship . . . humble followers of the lowly Jesus . . . excluded from those courts . . . shut out from those holy services by the mammon of unrighteousness." When Lisette dictated her intentions to Solomon Sibley, she spoke from experience. Lisette had been force-fed "the mammon," or riches, of "unrighteousness." She knew the bitter taste of poverty and the withering touch of slavery. A free woman who had stolen her own life with the loving aid of her family, she now wished to help others who suffered in want. Lisette signed this will, the only surviving document generated by an enslaved resident of Detroit, with her X mark.
In the modern city fashioned by American consolidation and expansion, Elizabeth Denison became a landowner and a shareholder before the onset of the Civil War. Her family's story is the most documentable case of slavery in the city of Detroit. Her will is a rare record of the consciousness and intentions of a member of that long-forgotten group. But even as Elizabeth Denison charted new paths for formerly enslaved residents of Detroit as well as for African American women, she negotiated the circumstances of her life in an environment shaped and colored by a history of slavery and indigenous land dispossession. Despite her noteworthy earnings, Lisette had been unable to prevent the indenture of her own nephew, Eastman Denison, aged eleven, to the son of Elijah Brush, Charles R. Brush, in 1834. She had not been able to avoid patronizing treatment on the part of her employers, or to break through the barriers of race, gender, class, and station that steered her into service as a "black cook" instead of earning her living as the brilliant businesswoman that she might have been a century later. And it is essential to this story that Lisette derived much of her wealth later in life from investments in land that Michigan governors William Hull and Lewis Cass had wrested from the families of the Wyandot, Ottawa, Potawatomi, and Ojibwe nations.
For all the limitations of her choices, of her times, and of her community, Elizabeth Denison's will reflects one clear value, one ethical commitment to be upheld even in death. She believed that it was paramount to tackle poverty, to welcome and tend to the poor who were excluded even in houses of worship. And so she dedicated the bulk of her wealth to the founding of a church that would respect and care for all people. William Biddle, Lisette's trustee, selected Grosse Ile for the site of the church. This was the island vacation spot preferred by his family, where Lisette had once worked as their housekeeper. Saint James Chapel on the island was established as a result of Elizabeth Denison's generosity, which was then enlarged by other contributors. The only existing original portrait of Lisette still hangs today in that house of worship, though Lisette herself had attended Mariners' Church on Jefferson Avenue in downtown Detroit in the last years of her life.
Is it ironic that a church made possible by a woman once enslaved in Detroit was built on Indian land illegally purchased by Detroit's largest slaveholder? Is it unexpected that two of the cities where Lisette Denison labored as a servant and invested as a landlord—Pontiac and Wyandotte—bear the names of an historic Ottawa figure and a tribe removed by the state of Michigan? At the conclusion of this patchwork quilt of an historical chronicle, perhaps not. These apparent contradictions reflect the difficult compromises as well as the unsettling outcomes that abound in the history of slavery in Detroit. While slavery was never the driving force behind Detroit's economy (based on animal pelts and land speculation), enslaved people's labor proved critical to domestic, business, and social functions, even as challenges to slavery were formative for some Detroiters' identity as Americans. A particular kind of society with slaves in early America, Detroit was a remarkable place where a northwestern frontier environment led to flexibility and creativity, even as the town's location along a liquid international border made it more porous than many other slaveholding spaces. As a region where indigenous enslavement was a long and continuous practice, Detroit produced an unusual cross-section of African American and Native American experiences of slavery, revealing slavery's adaptability to various natural and cultural environments and the interwoven processes of black and red racialization. At the same time, the trajectory of the narrative in these pages—from French colonial enslavement of mostly indigenous people to the life of a free black woman on the eve of the Civil War—suggests that even while Native slavery was always more prevalent in Detroit, black slavery emerged as more prominent in the documentary record. As black freed-people like Lisette Denison made their way in the nineteenth-century city, and as free Native Americans such as members of the Saginaw Chippewa Tribe at Mt. Pleasant (in mid-Michigan) and members of the Ottawa Grand Traverse Bay and Little Traverse Bay Bands (in northern Michigan) fought to maintain their tribal identities and reservations, those indigenous people who were held as slaves faded from historical records but continued to live and "make generations," hidden in "plain view," in and around the City of the Straits.
The Bouquet of Roses
Along the central riverfront, the footprint of colonial Detroit is snug as a vintage pin cushion. Here, where silver spires pierce the powder blue of sky, shiny high-rise office buildings reflecting the cool shades of water, it is difficult to imagine a prior world of French shingled homes and fruit orchards, of canoes and bateaux plying the waters, of Red Coats marching down the roads, of human slavery and beaver frenzy. But these are the same streets, now paved and more densely populated, where an enslaved indigenous woman was forced to give birth in a prison cell, where an enslaved black woman joined with an indentured white man to rob her master's storehouse, where the black family owned by a local merchant mourned the death of a father at sea, where Peter and Hannah Denison were purchased and later fought in the courts for their children's freedom. These striking individuals and their stories have long been erased from the collective consciousness of the city. The physical markers of colonial Detroit, which might have aided in memory, have all but faded from the surface of the landscape. The Macomb farm has disappeared. The home of the Brushes is gone now, too, with only a sign for Brush Street and the square of Brush Park keeping silent vigil. The earliest surviving home in the city, built for Charles Trowbridge and his bride, Catherine Sibley, only dates back to 1826. Lisette Denison would have visited there, as Catherine was the same Sibley daughter who missed Lisette's cookies while off at school in New York, and Charles Trowbridge helped to steward Lisette's papers late in her life. But Lisette's own house in Detroit has now vanished. In its place stands an empty lot, forlorn and riddled with glass shards.
There is currently no historical marker acknowledging slavery in Detroit—revealing that people were bought, sold, and held as property there. And yet, for more than a century spanning French, British, and American rule, Detroit was a place that saw unconscionable bondage, elicited inventive bids for freedom, and shaped lives not devoid of heroism. Where the human-made buildings and memorial plaques have long gone or never existed, the river that first called to Native hunters and French adventurers remains. The waters still flow between the lakes, narrowing at the earthen bend where Detroit City rises into the clear and open atmosphere. The strait stood as witness to all that transpired in this place. We can rely on that river now as a road to history, even as residents in the past rowed across it to survive.
These were the thoughts ice-skating across my mind as I toured Detroit with my friend and colleague, the legal historian Martha Jones, and other scholars invited by Martha to take her informal but much lauded tour of the city in the winter of 2013. It was a frigid day, snow packed and dazzling white, with sun rays gleaming off the blanketed sidewalks and skyscrapers. As I thought these wandering thoughts about rivers and histories, I walked across Hart Plaza to the windy riverbank, where a riveting sculpture now stands in bronze and granite. Built in 2011 for the occasion of Detroit's three hundredth birthday, the International Underground Railroad Memorial, sculpted by Ed Dwight, has a sister sculpture across the river in Windsor, Ontario. Each work of art represents a cluster of figures. On the Detroit side, African American freedom-seekers and underground activist George DeBaptiste gaze across the waterway to freedom; on the Windsor side, a family who has accomplished the crossing stares into each other's eyes and toward the heavens. As I walked a slow circle around the Detroit monument, breaking from the tour group, I came across the statue of a woman at the side of the ensemble. She wore a scarf on a head tilted downward as if weary from the journey that had brought her this far; she grasped a small boy lovingly about the shoulders, and from her hand dangled a sculpted basket woven of bronze. The artist had shaped the basket as an empty vessel, perhaps symbolic of want and need, but on this day the bronze container overflowed. A stranger, another admirer of this moving, metal piece, had left behind a dried bouquet of red and white roses. Already touched by the artwork itself, the faces and forms of those silent figures, I was affected upon seeing the petals, gleaming blush and glowing pearl in a coating of snow and winter sunlight. Some visitor to the city or, more likely, a resident, had left a bouquet for a monument. Those roses transformed the sculpture into beautiful still life: Freedom-Seekers with Flowers. I imagined this bouquet was a gift not only for those we remember—the thousands who crossed this river in the celebrated Underground Railroad—but also for those we forget, the hundreds who were enslaved right here, on the streets of old Detroit, and the countless unseen victims of human trafficking at the border today. The disjuncture and even discomfort of the fact of slavery in this place made the gesture of the roses all the more magical. Human connection blooms in the toughest of circumstances. Communities persevere. Resilience triumphs over ruin. In this way, as in many others, Detroit is signpost, symbol, and story—for its denizens, a region, a nation, a world.
_Gateway to Freedom_ , International Underground Railroad Memorial, author photos.
A Note on Historical Conversations and Concepts
Every project has more than a single origin story. This one has several, all shaped by a number of influences stemming from my experience as a resident of Michigan and professor at the University of Michigan in Ann Arbor for nearly fifteen years. Teaching a capstone senior seminar for the Department of Afroamerican and African Studies on representations of slavery that included an Underground Railroad tour presented by the African American Cultural and Historical Museum of Washtenaw County led me to discover, along with my students, the rich local history of southeastern Michigan abolitionism. It was delving further into this local history in an investigation of Adrian, Michigan, abolitionist Laura Smith Haviland that led me to review Michigan's 1855 personal liberty law. This protection for Michigan residents who were runaways from the slave states undermined the national Fugitive Slave Act of 1850. Reading it set me on a quest to find earlier laws, opening my eyes to loopholes in the Northwest Ordinance that left legal room for slavery and indentured servitude to exist in Michigan. Intrigued and also disappointed by this latter fact that was at odds with my own ideas about the state, I wanted to pursue the subject focusing on Detroit, where Michigan's practice of slavery was the most concentrated. Serendipitously, an interdisciplinary group of faculty members and graduate students at the University of Michigan began meeting to jointly explore the notion of introducing a new field of scholarly enquiry called the Detroit School of Urban Studies, in line with the Chicago and LA schools coined in previous decades. Our Department of Afroamerican and African Studies was centrally involved in this activity along with faculty in Social Work, Sociology, Urban Planning, and the Residential College, so I sat in on these discussions with urban planners, sociologists of the city, and twentieth-century urban historians, which heightened and sharpened my interest in Detroit. Although my peers were discussing postindustrial society, food deserts, green spaces, mass incarceration, and the pitfalls of gentrification, I could see links between this modern (and postmodern) Detroit and the Detroit of the colonial and early American eras when slavery was practiced. I began to visit Detroit museums and historic sites in southeastern Michigan to try to feel the outlines of a story I might tell even as my imagination was captured by a quotation by a colleague involved in the Detroit School discussions, the historian Charles Bright, who had written the following about Detroit history in an article in the _Journal of American History_ :
The dominant historical discourse [on Detroit] is one of rise and fall, spiked by an immense nostalgia for the city that once (briefly) was. The recent past is often deployed as a cautionary tale about what goes wrong with urban spaces when racism, white flight, and industrial evacuation undercut a city's viability. Such a historical construction places Detroit in a past that is now lost and irretrievable and leaves current residents . . . dangling at the end of history with little hope and no agency.
Bright's passage prompted a number of questions for me. Was Detroit's history really lost and irretrievable? What did it mean to be "dangling at the end of history"? And what kind of historical evidence or narrative would provide the impetus for those dangling on the end to pull themselves back up, into a fuller knowledge of history, community, place, and power relations? It so happened that my considering of these questions coincided temporally with the War of 1812 bicentennial and the Civil War sesquicentennial. There were a number of related events taking place in the Detroit area, and what I observed at the ones I attended indicated to me that the historical thread about slavery and Detroit that the public wanted to hold on to was a story of Detroit's role in the Underground Railroad. I sat in on sessions in which speakers extolled the bravery of their UGRR conductor ancestors and freedom-seeker ancestors, and sessions in which performers dramatically reenacted the feats of locally famous Michigan abolitionists. I also visited a new exhibit unveiled at the Detroit Historical Museum that celebrated the valiant organizers of the Detroit Underground and proclaimed the Northwest Territory to be a free space dating back to its founding in 1787. All of this interest in local history was exciting and even contagious, but there was something missing. Detroit was not only a place that fostered freedom bids as part of the Underground Railroad; it was also a place that fostered slavery throughout the second half of its colonial history and well into the American period. I wanted, then, to explore and share the stories of those who were enslaved in Detroit and to trace the form of slavery that took shape in a northern interior locale with a significant Native American presence. I wanted to understand how slavery and race intersected in early Detroit, how conditions of bondage and the extraction of unpaid labor intersected with gender roles and women's experiences, how enslaved people undermined their condition of unfreedom, and whether remnants of Detroit's history of slavery still existed in the city's landscape.
After beginning research on this project in the spring of 2011, I was stunned to learn just how few scholarly works had been written on the subject of slavery in Detroit. The sum total of dedicated secondary source materials that I uncovered with the help of my talented student research assistants consisted of a 1938 master's thesis completed by Therese Kneip at the University of Detroit, a 1970 article titled "Black Slavery in Michigan" published by David Katzman in the journal _American Studies_ , a chapter on "Black Slavery in Detroit" by Jorge Castellanos in the 1981 edited book _Detroit Perspectives_ , and an article titled "The Fluid Frontier" published by Afua Cooper in the _Canadian Review of American Studies_ in 2000. Cooper's work in particular emphasized the importance of both natural and political borders along the Detroit River and put forward the notion of "the border as a significant unit of analysis" for Canadian-American transnational black history. "One discovers," Cooper asserted about the border, "that Blacks who lived at its edges consciously manipulated it in their 'search for place.'" Cooper's insights about the material and metaphorical role of the border have influenced multiple studies, including my own. But in the year 2000, Afua Cooper's approach was rare; few other works were picking up on the important themes and questions she presented, especially on the U.S. side of the border.
More than a decade later, in 2012, Detroit journalist Bill McGraw released a well-researched newspaper story provocatively titled "Slavery Is Detroit's Big, Bad Secret." I had begun my research just a year earlier and wondered if McGraw had been drawn toward this topic, as I had been, by the groundswell of local talk about the Underground Railroad in Detroit's history during public events marking anniversaries of the Civil War and the War of 1812. Two of these gatherings took place at the Detroit Historical Museum and were the result of a long-term collaboration between scholars based at the museum and at Wayne State University. The historians Denver Brunsman and Joel Stone were central to these endeavors and published edited books in 2009 and 2012 featuring the work of graduate students and linked to museum-based symposia. These detailed edited collections on Detroit during the Revolutionary Era and War of 1812 years touched on the dynamics of slavery and contributed to the small body of existing literature. In addition, David Lee Poremba's scrupulously annotated chronology of Detroit completed for the city's tercentennial in 2001 includes a wealth of detail about key events that contributes to the reconstruction of the context in which slavery unfolded. In fact, the three hundredth anniversary of the city's founding was an important moment that inspired the production of a wider range of Detroit histories and chronicles than had been published since the early and mid-1900s; most of these anniversary works were geared toward popular audiences and fostered an energetic local public awareness of Detroit's long and fascinating history.
During the early stages of my research, I found, as well, that scholarship on African American history in Detroit during the colonial and early national periods was nearly as slim as the literature on slavery in the city. A University of Michigan doctoral dissertation and later articles by Norman McRae on "Blacks in Detroit" (1982), as well as books by David Katzman (1975) and Reginald Larrie (1981), included chapters on the pre-nineteenth-century era of black history in the city. Isabella Swan and Mark McPherson, both local Michigan historians, had written brief (in the case of Swan) and exploratory (in the case of McPherson) biographies of Elizabeth Denison Forth that were essential to this subject matter; both included crucial primary source transcriptions at the end of their books. But overall, as the colonial historian Christian Crouch has concurred in her nuanced papers on Detroit as "the Black City," it was as though blacks were imagined as having just appeared on the Detroit scene during the Great Migration of African Americans from the South and were associated only with Motor City manufacturing, the Motown musical sound, and mid-twentieth-century peaks of social unrest, otherwise known as the riots of 1943 and 1967. While I was in the midst of developing this project, a pivotal edited collection, years in the making, was released by Wayne State University Press. That book, _A Fluid Frontier_ , edited by Canadian historian Karolyn Smardz Frost and American literary scholar Veta Smith Tucker, focused on the valiant history of the Underground Railroad in Detroit but also wrestled with the unpleasant fact of slaveholding in the Detroit River region, particularly in the introduction and a chapter focused on the Denison family. In 2011, the Canadian historian Gregory Wigmore published his article "Before the Railroad: From Slavery to Freedom in the Canadian-American Borderland" in a _Journal of American History_ special issue on borderlands. A significant piece heralding and indeed modeling a broader discussion that recognizes the northern border as equal in historical importance and social texture as the southern border (with Mexico), Wigmore's work, like earlier publications by McRae and Cooper, emphasized the role of the Detroit River as a permeable border that enslaved people crossed in dual directions. Wigmore skillfully used the theme of river traffic to indicate a pre-history of slave escapes "before the [underground] railroad" as well as a broader context of international political machinations. There is, perhaps, a subtle sticking point between historians such as Wigmore and interdisciplinary scholars such as Veta Tucker over how to carbon-date the activities of the Underground Railroad. Tucker suggests in her opening chapter to _A Fluid Frontier_ that every escape in the region can be counted within Underground Railroad history, while Wigmore sets up a strict before-after structure in the language of his piece. It should be noted that the National Park Service's essential and admirable Network to Freedom program also takes a liberal view when determining what to count within the Underground Railroad framework and when to start counting. The historian Manisha Sinha, in her recent sweeping interracial study of the transnational abolition movement, asserts that the history of abolition begins when the first person resisted slavery. This argument is resoundingly convincing; however, the history of abolition (the multifaceted struggle to end enslavement across the Atlantic world) and the history of the Underground Railroad or Railway (organized networks of activists committed to aiding enslaved people's passage to freedom in the United States and Canada) do not fully overlap. On this question, I lean toward the view implicitly advanced by scholars Eric Foner and Stephen Kantrowitz, who describe the concerted organization of antislavery networks as a marker of the formation of the movement in the late 1820s and 1830s. It is relevant, though, as well as revealing for Underground Railroad scholarship, that research on Detroit indicates the existence of such networks in the very early 1800s in references to connected individuals who encouraged escapes as well as to the presence of Negro Town as a base camp for resisters.
Alongside the small but now steadily growing number of publications on slavery and early black history in Detroit, there have been several dissertations, manuscripts in progress, and new books produced by a generation of historical thinkers who are exposing the economic importance, political ambiguity, and cultural complexity of Detroit as a place situated betwixt and between colonial France and Great Britain, Great Britain and the United States, and multiple indigenous nations. In 2001, map historian and curator Brian Leigh Dunnigan released an extensive cartographical study, _Frontier Metropolis_ , which reproduced and contextualized maps and images to reconstruct the city's past and serves as a major reference guide for current studies. Dunnigan's interpretation emphasized the international and urban character of this remote frontier settlement across one and a half centuries. Catherine Cangany's _Frontier Seaport_ (2014), in implicit conversation with Dunnigan's interpretive graphic collection, emphasizes Detroit's port town character. Cangany's is the first in a series of full-length New Detroit History monographs that seek to move historical literature on the city beyond the scholarship of early twentieth-century antiquarian historians and political historians such as Silas Farmer and Clarence Burton, whose chief interests were in collecting data about the city in order to champion its progress in a rising industrial age. Cangany brings an enlightening Atlantic studies perspective to her analysis of early American Detroit, which she describes as a maritime trading town with economic and cultural ties to urban centers on the East Coast as well as in Europe. Cangany's focus on economic exchange and local politics leads her to notice the presence of enslaved people. Forthcoming histories by Karen Marrero, Andrew Sturtevant, and Kyle Mays will frame Detroit as an explicitly indigenous location where Native American and mixed-race Indian people lived in a nuanced set of relations with European and American settlers and, to a certain extent, African Americans. What I hope this book, _The Dawn of Detroit_ , adds to the mix is an explicit and concentrated focus on enslaved people's lives that necessitates seeing African American and Native American history in Detroit as interrelated rather than separate streams of experience.
My work joins with all of these aforementioned texts, and surely others, in the collaborative intellectual project of picturing early Detroit in a way that draws on the conceptual revelations of ethnic studies, women's and gender studies, and studies of the Atlantic world, the movement of trade and capital, and the intermingling of cultures. Somehow, as the reading public has internalized narratives about American national and regional pasts, we have forgotten that Detroit is ancient, that Detroit is indigenous, and that Detroit has a long-standing black presence. We have misplaced the knowledge that most of the Midwest was French, and we attribute anything fascinating in Francophone-American history to New Orleans, or maybe to St. Louis. We have never deeply considered the impact of the reality that slavery existed even in the Midwest and, as Afua Cooper so boldly stated it nearly two decades ago, in Canada where a "mythology" of a black "haven" holds sway. Scholars, while aware of these nuances, have only begun to probe them and to actively present them for public consideration. In our current transnational world where all entrenched human dilemmas are simultaneously local and global, a renewal of studies of Detroit and the U.S.-Canadian borderlands helps return us to a sense of the critical importance of the Great Lakes region to North American histories of extractive and settler colonialism, slavery, racial formation, cultural complexity, and the refusal of subjugated peoples to readily submit to domination.
Remembering the Black Militia
In the small number of studies that assess slavery in Detroit, or early black history in the city, the story of the black militia often rises to the fore. This book has been no exception, for that saga holds within it an explanatory power that captures the unstable racial dynamics produced by Detroit's borderland character. Today Detroit's black militia is commemorated on a plaque in the Detroit Historical Museum that details the biography of its leader, Peter Denison, as well as in literature produced by Ranger Shawna Mazur of the River Raisin National Battlefield in Monroe (the present-day location of French Town) and through historical reenactment at the Battlefield. These are necessary and enlightening interventions into local histories and memories that all too often overlook African American contributions to the state's early past. But even as we remember the historic occurrence of black men forming and leading an American military unit at the dawn of the nineteenth century, we must take care to recall and question the reasons why this special unit was authorized by Michigan authorities in the first place. William Hull imagined the black militia as a defensive force, positioned to fight primarily against Native Americans on whose lands Michigan Territory was located. Black men's seeming willingness to protect the United States raised their esteem in the view of some territorial officials and potentially set them at odds with indigenous people.
In addition to coming away with a lopsided interpretation that valorizes black agency and leaves in place a notion of Native Americans as enemies of the state, it is easy to part historical tracks at this juncture of the story of the black militia, to see Native American history moving in one direction that positions Indian people outside the United States, while seeing African American history moving in an opposing direction that positions black people as (co-opted) insiders. But the picture of what life looked like in early Detroit—what survival for subjugated groups looked like—was never so clearly divided along these kinds of racial lines. People of indigenous and African descent were enslaved both in that town and along each bank of the river. They ran away together, as in the case of Jenney (a mixed-race black woman) and Joseph Quinn (a young Native man) in 1807. They formed families together, as in the case of Abraham and Marie Louise Ford, an enslaved black man and his free Ojibwe-French wife, whose daughter was born in the midst of war in 1813. African Americans and Native Americans may even have been members of the black militia together, given the nature of slavery in the region, the tendency for Afro-Native people to be defined as "negro" in historical records, and the unit's makeup of runaway slaves from Canada. Of course, in addition to forming close connections, Native Americans and African Americans also faced off, across domestic spaces in which one was the owner, the other owned, and across lines of battle in the Revolutionary War and War of 1812. One thing these populations always shared with one another, as well as with settlers of the young American nation that sought but failed to define as well as confine them, was a fierce love of the dignity and autonomy embedded in the principle of freedom.
Borderlands and Frontiers
I have never quite imagined myself as a borderlands scholar, but as a place that birthed surprising events shaped by its location on multiple lines of differentiation and difference, Detroit compels its students to think in these expansive interpretive terms. In framing the parameters of this book in the introduction, I describe Detroit as a "frontier-borderland" environment. With the use of this language, I am calling on at least two streams of historical study: Native American histories of the Great Lakes and Middle West and African American histories of slavery. Histories of the Great Lakes, particularly those that focus on Native people in the region, engage with the notion of borderlands as spaces of cultural encounter. The classic example of this scholarship is Richard White's _The Middle Ground: Indians, Empires, and Republics in the Great Lakes Region_ , which captured the multilayered complexities of cross-cultural accommodation. White's concept of a "middle ground," defined as a "place in between: in between cultures, peoples, and in between empires and the nonstate world of villages," was an arena where indigenous peoples and Europeans encountered and negotiated with one another by necessity. He argued that a social and political middle ground, a "mutually intelligible world," formed through a series of misunderstandings between Indians and Europeans who were struggling to compromise through the end of the War of 1812. White's interpretation of inter-group dynamics in the Great Lakes influenced numerous studies to follow, some of which critiqued his argument, all of which built on his work. While I appreciate White's concept, I am inspired by the notion of "the Coast of the Strait" (described in the introduction of this book) to perceive these social relations differently.
Rather than seeing a _ground_ that various historical actors traversed to eventually meet in the middle in a place like Detroit, a metaphor that suggests terra firma beneath all of the historical actors' feet, I imagine Detroiters moving across more than one type of surface as they warily encountered one another: water as well as land. If free Europeans can be said to occupy one kind of cultural ground, and free Native Americans can be said to occupy an alternative kind of cultural ground, where do we place people who fit into neither of these categories? Where do we locate the enslaved? I will suggest that the unfree occupy a precarious position more akin to a shoreline, with one foot on water, the other on land. Located on an unpredictable metaphorical coast where the water and land converged, enslaved people encountered free people of various ethnic backgrounds from a differential position of insecurity. Instead of the "middle ground," a Midwestern landscape peopled by those who were free, we can imagine a coastline dominating early Detroit. This coast was a waterscape in the Great Lakes interior where enslaved people—Native Americans as well as Afro-Americans—strove to negotiate from a groundless position of material and legal instability.
I suppose I differ from many other historians of Native America in the social groups that I hold in view as I scan the Midwestern terrain. I want to insist on the visibility of an overlooked world—a black and indigenous world of bondspeople—shaped by their daily strategies of survival as well as the cultural heritages of their various homelands. This world of the unfree that surely formed in servant's quarters of merchant homes, in farm fields and fur trade shops, on riverbanks and riverboats, was not devised strictly along the lines of race, clan, or tribe; it was a shared social space of the struggling subjugated. With great care, colonial and early Americanists who study the Midwest are beginning to map this world. Jennifer Stinson offers a moving and analytically penetrating study of lead mining districts in Wisconsin and Illinois in the 1820s and 1830s that connects black slavery with Native land dispossession and an expanding culture of white masculinity and gentility that was supported by both. Christian Crouch is tracing the history of black Detroit through successive imperial regimes and analyzing black men's adaptations of indigenous terrain and strategies in the Midwest and Northeast. And in his forthcoming second study of indigenous peoples in the Great Lakes, Michael Witgen is endeavoring to formulate a capacious and exacting theoretical frame that historicizes the racialization of Indians in the age of U.S. expansion and interprets what he calls the "political economy of plunder" that links black and Native trajectories.
In addition to charting complex cultural and political relations between European colonies and indigenous communities, historians of Native America have wrestled with connotations of the term "frontier," rightly contesting the customary meaning of the word derived from historian Frederick Jackson Turner's 1894 thesis of westward expansion. In Turner's work and in American culture more generally, the word "frontier" has long suggested a line of difference between advancing white "civilization" and Native American "savagery," where cross-cultural confrontation ultimately gives way to the perfection of the American character and expansion of the colonial enterprise captured by the idea of "manifest destiny." However, in studies of the history of slavery, particularly work by Ira Berlin, frontier locations have been described as places on the edge of slavery's westward movement. These are locations where populations were relatively sparse, where lands were not fully settled by whites, and where practices of plantation slavery had not yet been systematized and fixed into social and legal practice. As legal historian Lea VanderVelde has so clearly described it: "Frontier slaves were sought for the needs of westward expansion," as "lands were available for settlement in great supply, but labor could not be hired." Because of the need for slave-owners to rely on their bondspeople differently in these rugged locations, frontier environments often left greater room for slaves to negotiate their relationships with masters. The frontier farm in 1820s Missouri, for instance, is a spot where one might expect to see an enslaved man clearing a field alongside his owner. Detroit was just such a place, and hence I have retained the language of "frontier" throughout this book, though with a degree of restraint.
Some historians of Native America and the West also see a utility in the use of the contested term "frontier." William Cronon employs this word sparingly in his environmental history of Chicago because of its ability to convey a macro-level historical relationship between cities and rural areas understood as frontiers in the nineteenth century. In his article on ethnic mixing in the Missouri River region titled "More Motley Than Mackinaw," John Mack Faragher employs the notions of "frontiers of inclusion" and "frontiers of exclusion." He argues that prior to the surge in Anglo-American population numbers and prior to Missouri statehood in 1821, French and Native American residents lived and worked together there, cooperating across lines of difference. With an increased American presence came greater racial differentiation and less political support for Indian land claims. Faragher sees the texture of frontier relations as shifting over time and degrading with an increased Anglo-American influence. While Faragher's emphasis is on change over time, I see an application for his analysis across time as well as across social spaces in the locale of Detroit. Similarly to what transpired in Missouri, free Native people saw their standing in Detroit decline with the diminishment of French power and the imposition of British and then American authority. For free indigenous people, Detroit moved from being something like a "frontier of inclusion" in the French period to becoming a "frontier of exclusion" in the British and American periods. But at the same time, there were always frontiers of inclusion and exclusion operating simultaneously in Detroit. While free Indians were included in French community and social life in noteworthy ways, unfree Indians—Native bondspeople—were excluded. The notion of frontiers of inclusion and exclusion, when viewed in place as well as across time, helps to illuminate social relations in Detroit in a way that keeps the presence of enslaved people of color visible.
Seeing early Detroit through a lens that includes Native Americans and African Americans within the same frame, together with their Euro-American captors and, at times, collaborators, highlights a related set of open and difficult questions that scholars are beginning to fruitfully engage. How can we further explore and understand the attitudes and activities of Native American slaveholders in the North? Did they have practices in common with familiar groups (Cherokees, Choctaws, Chickasaws, Creeks, Seminoles) that are categorized as the slaveholding tribes of the Southeast and Indian Territory? How did varieties of indigenous political organization in the eighteenth and nineteenth centuries shape slave trading and slaveholding practices in the North as compared to the South, in the woodlands as compared to the plains, and so on? How did earlier patterns of indigenous captive taking and slave labor usage (for instance, in the Fort Ancient and Mississippian archaeological periods and into the sixteenth and seventeenth centuries) affect later practices of slavery in Native communities? What do we do with the knowledge that so many Native women were first held captive by indigenous peoples in the Great Lakes? How do issues of gender, enslavement, and the racialization of Indians as "Panis" complicate notions of indigenous alliance, negotiation, and as it has lately been termed, "mastery" in interior Great Lakes areas where indigenous groups retained staying power well into the late nineteenth century? Does the language of "mastery" (meant to indicate prowess in imperial dynamics in a way that restores Native groups to a place of rightful recognition in international affairs) take on different connotations when we recognize that some of these "masters" actually possessed human beings as slaves?
And in what might be deemed a flip side of the tarnished coin of colonial influences, we must continue to ask the critical question of how we should understand the role of people of African descent within analyses of colonialism in Native American studies and African diaspora studies. Should black people be considered "settlers," a rhetorical move that groups them together with the Europeans who sometimes enslaved them but that also recognizes how black communities do indeed benefit from the dispossession of indigenous lands? The U.S. slavery historian Max Grivno offers a sharp take on this question, noting that in the "Northwest Frontier," blacks found a "liberating potential" due to a number of factors, including a diverse population, slavery's "unimportant role" in local economies, legal challenges to slavery like the Northwest Ordinance, and a high need for labor that increased laborers' bargaining potential. In this context, Grivno argues, "the frontiers' free black[s] and slaves were often most comfortable with white settlers, with whom they shared a language and a similar cultural heritage." While my study of enslaved people in Detroit has led me to see this site in a contrasting way that leans toward commonalities between blacks and Native Americans, I would not deny the fitness of Grivno's argument, especially in places farther west, such as Minnesota, where Euro-American labor and social systems developed later than in Detroit. Canadian indigenous studies scholars Zainab Amadahy and Bonita Lawrence have wrestled with the question of black settlement in material as well as ethical terms, landing uncomfortably on a notion of "ambiguous settlers" to account for black people's "desperate need to survive after slavery" while acknowledging that black writers on both sides of the border often fail to acknowledge Native land loss. "Black struggles for freedom," the co-authors assert, "have required (and continue to require) ongoing colonization of Indigenous land." In the United States, Native American studies scholars are also starting to think through the ways in which African American relationships to settler colonialism were similar to or distinct from those of Euro-Americans. Jodi Byrd, a Chickasaw literary scholar and colonial studies theorist who has acknowledged her own tribal nation's role in holding black bondspeople, determined that a separate word, "arrivants," is needed to capture the difference between black dwellers and white "settlers" on Native lands. In the domain of western history, public historian Crystal Alegria and Métis/Cree/Ojibwe doctoral student Jill Mackin are working with the term "refugee" in their development of a narrative that describes the experience of Lizzie Williams, a black woman who moved from Kentucky to Montana out of "desperation" following the Civil War. They seized on this language in rejection of the more common term "pioneer" and in the understanding that "refugee" conveys: "one that flees; _especially_ : a person who flees to a foreign country or power to escape danger or persecution."
The aspirational language of "ambiguous settlers," "arrivants," and "refugees" strives for a fair and sensitive means of articulating the compromises and complicities of various populations in a painful past. But, as Amadahy and Lawrence suggest, there is perhaps one space in the American-Canadian borderlands in which a radical alterity to colonial and racialized complicity existed: Native communities that accepted blacks via the Underground Railway (or "Railroad" in U.S. parlance). Putting forward Tuscarora "guides" as their primary example (but alas, offering no citation), Amadahy and Lawrence point to those who "risked their lives at a time when Indigenous people could have been enslaved, killed, or dispossessed of their land for helping runaways."
And so it seems we have come full circle. I took up this book project in part because I saw the public commemorations of Underground Railroad history in Detroit as too simplistic and celebratory, as too evacuative of an earlier and more ornery past complicit with racial slavery, but I also concede at this parting moment that the Underground Railroad motif does have the potential to do productive cultural work. The cognitive leap required to see that any operations of the famed Underground Railroad had to take place on current or former indigenous lands compels a respect for first peoples, their land holdings, and their political systems, even within a framework of feel-good popular mythology that obscures the wrongs of the United States, Canada, and the citizens of these nations. If scholars and writers can commit to the serious archival and intellectual project that must accompany such a leap, we can perhaps make progress in urging the publics of which we are part to challenge the intersecting systems and ongoing imprints of slavery and colonialism. The Great Lakes, as the historian Heidi Bohaker has so beautifully put it, was a place of "spiritually charged waterscapes," for humans as well as other-than-human beings. Perhaps here, in this ancient land of glassy waters, anything was, and still is, possible.
Acknowledgments
I could not have taken up this book project, or completed it within the span of six years, without the wonderful collaboration and assistance of many giving people. Tayana Hardin, once a graduate student in American culture and now a professor in her own right, began work on this project as my first research assistant in the spring of 2012. I then applied to a campus program that funds undergraduate work-study students to conduct research with faculty members, invited graduate students in history and American culture to participate, and formed a small research team on slavery in Detroit. Our group of seven worked over a two-year period to find, transcribe, interpret, and present primary sources. The members of this team, Michelle Cassidy, Emily Macgillivray, Paul Rodriguez, Sarah Khan, Kaisha Brezina, and Alexandra Passarelli, were indispensable to the project and a joy to work with. We created a website to share our findings (mappingdetroitslavery.com). I am grateful to our web designer, Ariela Steif, and to the generous scholars who read our website draft and made suggestions for improvement: Veta Tucker, Greg Wigmore, Brian Dunnigan, and Lucy Murphy. An additional bounty of thanks goes to Michelle Cassidy, who designed the website map and worked closely with the French records to translate church register entries and create tallies and graphs, to Michelle's husband, Alex Sin, for assisting her with the charts, and to Michelle and Emily Macgillivray, both, who aided me with this project with patience and prime research as well as translation skills for more than three years.
My brilliant colleagues at UM helped (and saved!) me at every turn, particularly Michael Witgen, who read three chapters of the manuscript; Brian Dunnigan, who shared his wealth of knowledge about Detroit history and images at various stages of the work and helped me fine tune military references; Greg Dowd, who offered clarifying, corrective, and encouraging feedback; and Martha Jones, my dear friend and toughest reader, who pushed me on the legal aspects of this history. Other generous readers whose feedback greatly improved the manuscript include Michael McDonnell, Jennifer Stinson, and my dear friend Paulina Alberto. Terry McDonald, director of the Bentley Library at UM, shared valuable sources and responded to the links between university history and slavery with absolute openness and a desire to document the facts. As former dean of the College of Liberal Arts & Sciences, Terry was one of the first to encourage me to forge ahead with my book on Michigan history, a subject beyond my past regional focus on the South. I benefited from hearing reactions to and feedback on this work in talks at Indiana University, the University of Minnesota, Pomona College, Harvard University, Northwestern University, the University of Chicago, the University of Cincinnati, Yale University, Johns Hopkins University, Stanford University, and the University of British Columbia. Scholars in the organization Historians Against Slavery helped me to connect past and present in my thinking. Many other people supported me through their input, interest, administrative expertise, inspiration, or quiet encouragement. They include: Stephen Ward, Beth James, Angela Dillard, Karen Marrero, Rebecca Scott, Jay Gitlin, David Blight, Walter Johnson, Christina Snyder, Jodi Byrd, Sherene Razack, Scott Morgensen, Kel Keller, Bill Hart, John Steckley, Andrew Sturtevant, Rachel Whitehead, Phil Deloria, Kristin Hass, Shawna Mazur, Roy Finkenbine, Carol Mull, Del Moyer, Robert Olender, Darryl Li, François Furstenberg, Angus Burgin, Philip Morgan, Liz Thornberry, Father Daniel Trapp, Mark Bodwen and the Burton Historical Collection staff, Lisa Brooks, Christine DeLucia, David Glassberg, Ned Blackhawk, Heather Thompson, Tim LeCain, Brett Walker, Mary Murphy, Susan Kollin, Lucy Murphy, Margaret Jacobs, Christopher Phillips, Nathan Marvin, Emily Albarillo, Wayne High, Judy Gray, Keaten North, Tammy Zill, Mark Simpson-Vos, Eric Crahan, Jesse Hoffnung-Garskof, David Roediger, Patricia Montemurri, Pat Majher, Krista Ewbank and Kate Sullivan of Saint James Chapel, Melba Boyd, Katie Barkel and Brian Short of LSA Communications, Rowena McClinton, Carl Ekberg, Sharon Person, Margery Fee, my co-instructor, Joel Howell, and all of the talented graduate students in the Literature of U.S. History seminar (winter 2016), Deborah Meadows and Shirley Vaughn of the African American Cultural & Historical Museum of Washtenaw County, Kevin Walsh, Pete Kalinski and Thomas Reed of Digging Detroit, Stephanie Wichmann for French lessons (however poor my performance was!), and surely others whose names I may have regrettably omitted. Thank you to my dedicated agent, Deirdre Mullane, who supports my crazy array of projects and found a fitting home for this one. Thank you, as well, to my editor at The New Press, Marc Favreau, who saw the possibilities for a historical project like this to speak to our present pressing social and environmental issues. I am deeply grateful to the Mellon Foundation, which sponsored part of the writing of this book through a New Directions in the Humanities Fellowship, and to the Eisenberg Institute for Historical Studies at UM, which secured for me a teaching release to research the Michigan abolitionist Laura Smith Haviland, an investigation that eventually led to this book.
As always, my family draws me away from the page to live in this beautiful physical world and makes everything I accomplish possible. I am forever grateful to: Joseph, Nali Azure, Noa Alice, and Sylvan David Gone; Patricia Miles King; Erin, Erik, Benny, and Montroue Miles; James and Sean King; Sharon Juelfs; Rakale Collins-Quarells; Steve McCullom, Tyrone McCullom, and Deborah Banks Johnson; Vanessa, Melvin, Amanda, and Alexis Walker; Maryanna Gone DuBois; Stephanie and Baylee Rain Iron Shooter; and Joseph Azure. Thank you also to Luna for being the one by my desk-side at all odd hours.
Bibliographic Abbreviations and Quotations
Because there are three archives and collections that I used repeatedly in researching this book, I have abbreviated references to them in the chapter citations.
BHC: Burton Historical Collections, Detroit Public Library, Detroit, MI.
BHL: Bentley Historical Library, University of Michigan, Ann Arbor, MI.
MPHC: This abbreviation, standing for Michigan Pioneer and Historical Collections, is commonly used in Michigan histories to indicate a massive set of compiled primary materials originally published under the separate titles of: _Pioneer Collections_ (1876–1886), _Historical Collections_ (1886–1912), and _Michigan Historical Collections_ (1915–1929).
Quotations in this book duplicate the original text of eighteenth- and nineteenth-century sources to the extent possible. This includes varied spellings for the same names or places and grammatical errors. I have tried to reduce usage of the indicator "[sic]" to denote an error in the original.
Notes
**Introduction: The Coast of the Strait**
. For a history of the use of the racial term "red" by Native Americans as well as Europeans, see Nancy Shoemaker, "How Indians Got to Be Red," _American Historical Review_ 102 (June 1997): 624–44.
. Michael Witgen, _An Infinity of Nations: How the Native New World Shaped Modern North America_ (Philadelphia: University of Pennsylvania Press, 2013), 11.
. Bkejwanong as an Anishinaabe settlement: Michael A. McDonnell, _Masters of Empire: Great Lakes Indians and the Making of America_ (New York: Hill and Wang, 2015), 47–48. The persistence of French culture: Jay Gitlin, _The Bourgeois Frontier: French Towns, French Traders, and American Expansion_ (New Haven: Yale University Press, 2010), 1, 11, 155. Detroit as a Canadian dependency: William Renwick Riddell, _Michigan Under British Rule: Law and Law Courts, 1760–1796_ (Lansing: Michigan Historical Society, 1926), 15. Wild-garlic place: William Cronon, _Nature's Metropolis: Chicago and the Great West_ (New York: W. W. Norton, 1991), 23.
. National Audubon Society, "Detroit River—Facts and Figures," <http://web4.audubon.org/bird/iba/michigan/Press/DetroitRiverFactSheet.pdf>. Accessed August 9, 2012. "Junction" quote: Jean-Claude Robert, "The St. Lawrence and Montreal's Spatial Development in the Seventeenth Through the Twentieth Century," in Stéphane Castonguay and Matthew Evenden, eds., _Urban Rivers: Remaking Rivers, Cities and Space in Europe and North America_ (Pittsburgh: University of Pittsburgh Press, 2012), 147.
. Jodi A. Byrd, _The Transit of Empire: Indigenous Critiques of Colonialism_ (Minneapolis: University of Minnesota Press, 2011). For illuminating analyses of indigenous Americans in the Atlantic world and parallels as well as differences between a "black" and "red" Atlantic, see Jace Weaver, _The Red Atlantic: American Indigenes and the Making of the Modern World, 1000–1927_ (Chapel Hill: University of North Carolina Press, 2014). For an astute articulation of the intimate and damaging ties between Europe, Africa, the Americas, and Asia, see Lisa Lowe, _The Intimacies of Four Continents_ (Durham, NC: Duke University Press, 2015). Lowe defines intimacies in this book as the "braided" nature of slavery, colonialism, empire, and the rise of liberal ideology across these geographical spaces as well as the close contacts between people originating from the various continents, 38, 34.
. Quoted in Brian Leigh Dunnigan, _Frontier Metropolis: Picturing Early Detroit, 1701–1838_ (Detroit: Wayne State University Press, 2001), 13. René-Robert Cavalier La Salle was the first European explorer to sail the Great Lakes. Father Hennepin accompanied La Salle on the 1679 voyage and recorded the earliest detailed description of Detroit. The ship was later lost and has yet to be uncovered. Dunnigan, _Frontier Metropolis_ , 13. greatlakesexploration.org/expedition.htm. Accessed December 15, 2014.
. Michelle Cassidy, Emily Macgillivray, and Tiya Miles, "Placing Indigenous Peoples in Early Detroit," in Linda Campbell, Andrew Newman, Sara Safranksy, and Timothy Stallmann, eds., _Detroit: A People's Atlas_ (Detroit: Wayne State University Press, forthcoming). Ottawa presence: Gregory Evans Dowd, _War Under Heaven: Pontiac, the Indian Nations, and the British Empire_ (Baltimore: Johns Hopkins University Press, 2002), 28. Location of Huron villages: Andrew Keith Sturtevant, "Jealous Neighbors: Rivalry and Alliance Among the Native Communities of Detroit, 1701–1766" (Ph.D. diss., William and Mary, 2011), 24. Detroit as native hunting ground: Karen L. Marrero, "Founding Families: Power and Authority of Mixed French and Native Lineages in Eighteenth Century Detroit" (Ph.D. diss., Yale, 2011), 134–37. Hurons and Wyandots: The development of the Wyandots as a western configuration of Huron people was an involved social and political process resulting from migration. Some Hurons (Hurons being one of the three branches of the Iroquoian Wendat people of the upper Great Lakes, including Hurons, Petuns, and Neutrals) migrated southwest in the mid-1600s in the aftermath of war with the Iroquois Confederacy. The Hurons who settled in northern Michigan near the straits of Mackinac in the 1670s and along the Detroit River in the early 1700s came to be called Wyandots in early U.S. treaties. These Wyandots also included some members of the Petun nation. John L. Steckley, _The Eighteenth-Century Wyandot: A Clan-Based Study_ (Waterloo, Ontario: Wilfrid Laurier University Press, 2014), 22–25. "Coast of the Strait" as a translated Huron name for Detroit appears in Silas Farmer, _History of Detroit and Wayne County and Early Michigan: A Chronological Cyclopedia of the Past and Present_ (1890; Detroit: Gale Research Company, 1969), 3. According to the Huron and Wyandot linguist John Steckley, the Huron word _Taochiarontkion_ does translate into French as "La côte du détroit," and in English as "the coast of the strait." Another Huron word for Detroit, _Karontaen_ , translates into English as "where a log lies." John Steckley, email exchange with Tiya Miles, November 17, 2016. Steckley cited the following reference for these early terms as recorded by the French: Pierre Potier, _Fifteenth Report of the Bureau of Archives for the Province of Ontario_ (Toronto: C. W. James, 1920).
. Richard Quinney, _Borderland: A Midwest Journal_ (Madison: University of Wisconsin Press, 2000), xiii–xiv.
. Gloria Anzaldúa, _Borderlands/La Frontera: The New Mestiza_ (San Francisco: Aunt Lute Books, 1987), 3.
. Edmund Morgan, "Slavery and Freedom: The American Paradox," _Journal of American History_ 59 (June 1972): 5–29; Edmund Morgan, _American Slavery, American Freedom: The Ordeal of Colonial Virginia_ (New York: W. W. Norton, 1975).
. I have borrowed this phrasing from the African American history scholar Robin Kelley. See Robin D. G. Kelley, _Freedom Dreams: The Black Radical Imagination_ (Boston: Beacon Press, 2002).
. Brian Leigh Dunnigan, "Charting the Shape of Early Detroit, 1701–1838," in June Manning Thomas and Henco Bekkering, eds., _Mapping Detroit: Land, Community, and Shaping a City_ (Detroit: Wayne State University Press, 2015), 18.
. Cadillac's dream quote: McDonnell, _Masters of Empire_ , 70.
. P. Nick Kardulias, "Negotiation and Incorporation on the Margins of World-Systems: Examples from Cyprus and North America," _Journal of World-Systems Research_ 13:1 (2007): 55–82, 68, 70.
. Anne F. Hyde, _Empires, Nations, and Families: A New History of the North American West, 1800–1860_ (Lincoln: University of Nebraska Press, 2011), 19.
. Richard White, _The Middle Ground: Indians, Empires, and Republics in the Great Lakes Region, 1650–1815_ (New York: Cambridge University Press, 1991), 116; Claudio Saunt, _West of the Revolution: An Uncommon History of 1776_ (New York: W. W. Norton, 2014), 145.
. Meaghan O'Neill, "50 Surprising Fashion and Beauty Products Made From Oil That You Probably Use Everyday (Even If You're Green)," www.treehugger.com/style/50-surprising-fashion-and-beauty-products-made-from-oil-that-you-probably-use-everyday-even-if-youre-green.html. Accessed July 26, 2016. Petroleum Services Association of Canada, "Clothing," www.oilandgasinfo.ca/oil-gas-you/products/clothing. Accessed July 26, 2016.
. Witgen, _Infinity of Nations_ , 215–16, 267, 270.
. Hyde, _Empires, Nations, and Families_ , 19.
. Christof Mauch and Thomas Zeller, "Rivers in History and Historiography: An Introduction," in Christof Mauch and Thomas Zeller, eds., _Rivers in History: Perspectives on Waterways in Europe and North America_ (Pittsburgh: University of Pittsburgh Press, 2008), 5. "Inland navigation": J. Disturnell, ed., _Sailing on the Great Lakes and Rivers of America_ (Philadelphia: J. Disturnell, 1874), iii.
. Dunnigan, "Charting the Shape of Early Detroit," 21. The stream behind the settlement, called Savoy Creek, lies beneath the city streets now.
. White, _Middle Ground_ , 117.
. To my knowledge, it has not been demonstrated through documentary evidence that slaves came to Detroit with Cadillac. Historian of Afro-Canada Afua Cooper asserts that they did without offering a primary source in Afua Cooper, _The Hanging of Angélique: The Untold Story of Canadian Slavery and the Burning of Old Montréal_ (Athens: University of Georgia Press, 2007), 74. The presence of slaves in Detroit in 1701 is certainly possible and even likely, since they were already in New France at the time and had been since 1628; Cooper 70, 72, 75. In addition, as Cadillac sought to bring representatives of various subsets of a varied labor force along with him, it would have made sense for him to include slaves. Cadillac's contingent: Brian Leigh Dunnigan, _Frontier Metropolis: Picturing Early Detroit, 1701–1838_ (Detroit: Wayne State University Press, 2001), 18–19.
. Guillaume Teasdale, "The French of Orchard Country: Territory, Landscape, and Ethnicity in the Detroit River Region, 1680s–1810s" (Ph.D. diss., York University, 2010), 214–15.
. French "northern style" architecture: Teasdale, "Orchard Country," 16–17.
. F. Clever Bald, _Detroit's First American Decade: 1796 to 1805_ (Ann Arbor: University of Michigan Press, 1948), 17, 25; Farmer, _History of Detroit_ , 489.
. Dunnigan, "Charting the Shape of Early Detroit," 22.
. White, _Middle Ground_ , 154–58.
. The stories of enslaved people surface sporadically in merchant, church, and legal records. A primary figure is Peter Denison, a black man who, together with his wife, Hannah Denison, sued in a court of law for their children's freedom. While the Denison family is described in a number of sources, many other slaves in Detroit can only be traced through the scattered fragments of truncated lists and notations. This is especially and poignantly true for the scores of unfree Native American women labeled " _Panis_ " in the records, a term derived in part from the name Pawnee, the horticultural and non-equestrian Missouri River Indians frequently taken in slave raids by Great Lakes indigenous peoples.
. Benjamin Drew, _A North-Side View of Slavery: The Refugee: Or, The Narratives of Fugitive Slaves in Canada, Related by Themselves_ (Boston: John P. Jewett and Company, 1856).
. Christopher P. Lehman, _Slavery in the Upper Mississippi Valley, 1787–1865_ (Jefferson, NC: McFarland & Company, 2011), 1–4, 26, 43, 45. Perhaps because slavery in Detroit and Michigan differed from slavery in other Northwest Territory states in focus, Michigan is often neglected in studies that address slavery in the Midwest. These studies tend to look most closely at the southern-leaning states of Indiana and Illinois as well as at Minnesota, perhaps because of the famous Supreme Court _Dred Scott_ decision rendered about a man held in slavery at Ft. Snelling, Minnesota. For more on slavery in the Midwest, see Leslie Schwalm, _Emancipation's Diaspora: Race and Reconstruction in the Upper Midwest_ (Chapel Hill, NC: University of North Carolina Press, 2009).
. For cultural analyses of ideas, rhetoric, and imagery of ruin in Detroit, see Colin Dickey, _Ghostland: An American History in Haunted Places_ (New York: Viking, 2016), 256–59; Dora Apel, _Beautiful Terrible Ruins: Detroit and the Anxiety of Decline_ (New Brunswick, NJ: Rutgers University Press, 2015); Kavita Ilona Nayar, "Reclaiming a Fallen Empire: Myth and Memory in the Battle Over Detroit's Ruins," (M.A. thesis, Temple University, 2012).
. Lea VanderVelde's specific description of slave labor on the fringes of westward expansion in St. Louis contributed to my development of a summary of slave labor in the different western location of Detroit; Lea VanderVelde, _Redemption Songs: Suing for Freedom before Dred Scott_ (New York: Oxford University Press, 2014), 16. Likewise, Jennifer Stinson's emphasis on the dirty work done by slaves near the Mississippi River contributed to my sense of what a wet and muddy location meant for the workloads of black women. Jennifer Kirsten Stinson, "Black Bondspeople, White Masters and Mistresses, and the Americanization of the Upper Mississippi River Valley Lead District," _Journal of Global Slavery_ 1:2 (October 2016) (unpublished version, cited by permission).
. VanderVelde, _Redemption Songs_ , 12. For a discussion of the use of the term "frontier" in this book that situates the word within Native American historical studies and African American slavery studies, please see the historiographical essay following the conclusion.
. In thinking about the unexpected nature of slavery in Detroit then and now, I have been influenced by my colleague Phil Deloria, whose book popularized the notion of "Indians in unexpected places" in Native American studies as well as American studies circles. See Philip J. Deloria, _Indians in Unexpected Places_ (Lawrence: University Press of Kansas, 2006). The Michigan Human Trafficking Unit was formed in 2011. AG Human Trafficking Cases, State of Michigan Attorney General Bill Schuette, www.michigan.gov. Accessed December 10, 2014. For more on the approximately 1,200-plus cases of murdered and missing indigenous women in Canada that have taken place over a period of more than thirty years, see Jessica Murphy, "Canada Launches Inquiry into Murdered and Missing Indigenous Women," _The Guardian_ , December 9, 2015. Audra Simpson, "The State Is a Man: Theresa Spence, Loretta Saunders and the Gendered Costs of Settler Sovereignty," _Theory & Event_ (forthcoming: Spring 2017). Sherene H. Razack, "Gendered Racial Violence and Spacialized Justice: The Murder of Pamela George," _Canadian Journal of Law and Society_ 15:2 (2000): 91–130. Lisa J. Ellwood, "MMIW: A Comprehensive Report," IndianCountryTodayMediaNetwork.com, February 2016. Accessed April 30, 2016. Toni L. Griffin and June Manning Thomas, "Epilogue: Detroit Future City," in June Manning Thomas and Henco Bekkering, eds., _Mapping Detroit: Land, Community, and Shaping a City_ (Detroit: Wayne State University Press, 2015), 211, 213.
**1: The Straits of Slavery (1760–1770)**
. Silas Farmer, _History of Detroit and Wayne County and Early Michigan: A Chronological Cyclopedia of the Past and Present_ (1890; reprint, Detroit: Gale Research Company, 1969), 221; Brian Leigh Dunnigan, _Frontier Metropolis: Picturing Early Detroit, 1701–1838_ (Detroit: Wayne State University Press, 2001), 24. David A. Armour and Keith R. Widder, _At the Crossroads: Michilimackinac During the American Revolution_ (Mackinac Island, MI: Mackinac Island State Park Commission, 1978), 3. While Farmer measures the stockade at ten feet high, and Dunnigan says it was made of oak, Armour and Widder describe it as fifteen feet high and cedar. The fort and pickets were reconfigured after Pontiac's siege, which likely accounts for this difference; Armour and Widder, _Crossroads_ , 48; Donald Lee, "Clark and Lernoult: Reduction by Expansion," in Denver Brunsman and Joel Stone, eds., _Revolutionary Detroit: Portraits in Political and Cultural Change, 1760–1805_ (Detroit: Detroit Historical Society, 2009), 73–77, 74.
. Farmer, _History_ , 367; David Lee Poremba, ed., _Detroit in Its World Setting: A Three Hundred Year Chronology, 1701–2001_ (Detroit: Wayne State University Press, 2001), 39.
. Poremba, _Detroit_ , 37. Jean Dilhet, _Beginnings of the Catholic Church in the United States_ , translated and annotated by Patrick W. Browne (Washington, D.C.: The Salve Regina Press, 1922), 114. Dunnigan, _Frontier_ , 38, 19. Brian Leigh Dunnigan, "Charting the Shape of Early Detroit, 1701–1838," in June Manning Thomas and Henco Bekkering, eds., _Mapping Detroit: Land, Community, and Shaping a City_ (Detroit: Wayne State University Press, 2015), 22.
. Quoted in Farmer, _History_ , 11. For a full description of Detroit by Cadillac, see "Report of Detroit," Letter of Cadillac to M. de Pontchartrain, September 25, 1802, MS/Cadillac A. deLam, Burton Historical Collection, Detroit Public Library, Detroit, MI.
. Farmer, _History_ , 4.
. Poremba, _Detroit_ , 40; Dunnigan, _Frontier_ , 46, 52, 53.
. Dilhet, _Beginnings_ , 114.
. Quoted in Marcel Trudel, _Canada's Forgotten Slaves: Two Hundred Years of Bondage_ , George Tombs, trans. (1960; reprint, Montréal: Véhicule Press, 2013), 30–31. Beavers have two layers of fur: a coarse, insulating outer layer of long strands and a soft inner layer of shorter strands. The strands of this inner layer readily twine together into a matted or felted texture when processed. Because furs worn by Native people as robes were partially pre-processed by human skin as well as the smoke-filled atmospheres of Native homes, worn furs commanded higher prices in the trade; Kardulias, "Negotiation and Incorporation on the Margins of World-Systems," 69, 70, 71. "Fat beaver" could be used to refer to a grade of fur more commonly called "coat beaver" (castor gras), meaning: "that which has contracted a certain gross and oily humour, from the sweat exhaled by the bodies of the Savages by whom it has been worn . . . used only in the making of hats"; _Encyclopedia Britannica or Dictionary of Arts, Sciences and General Literature_ , Seventh Edition (Adam and Charles Black, 1842), 478; "The Beaver and Other Pelts," Digital Collections, McGill Library; <http://digital.library.mcgill.ca/nwc/history/01.htm>. "Beaver Pelts," _Historical Encyclopedia of Canada_ (2013), <http://www.thecanadianencyclopedia.ca/en/article/beaver-pelts>. The term "fat beaver" was also used to refer to beaver harvested in winter when the pelts were thickest. For an engrossing analysis of the use of dress to signal identity in the context of colonization and racialization, see Sophie White, _Wild Frenchmen and Frenchified Indians: Material Culture and Race in Colonial Louisiana_ (Philadelphia: University of Pennsylvania Press, 2012).
. Jay Gitlin describes the swath of French territory in colonial North America as a corridor running from north to south; Gitlin, _Bourgeois Frontier_ , 2. Clarence M. Burton, ed., _The City of Detroit Michigan: 1701–1922_ (Detroit-Chicago: The S.J. Clarke Publishing Company, 1922), 719.
. Quoted in Trudel, _Canada's Forgotten_ , 57; Therese Agnes Kneip, "Slavery in Early Detroit" (Ph.D. diss., University of Detroit, 1938), 3.
. Donna Valley Russell, ed., _Michigan Censuses 1710–1830: Under the French, British, and Americans_ (Detroit: Detroit Society for Genealogical Research, Inc., 1982), 1762 Census, 19. Karen Marrero, "On the Edge of the West: The Roots and Routes of Detroit's Urban Eighteenth Century," in Jay Gitlin, Barbara Berglund, and Adam Arenson, eds., _Frontier Cities: Encounters at the Crossroads of Empire_ (Philadelphia: University of Pennsylvania Press, 2012), 66–86, 76. Early Detroit population numbers are difficult to pin down for several reasons. The size of the settlement was ambiguous because people lived on both sides of the river running for several miles; a ten-mile stretch on either side of the fort and across the river from the fort is assumed in the 1762 French census cited here. Many families had two residences: a home in the fort and a farm in the "country," which meant that people could be counted twice depending on where they were at the time of the name collection. Many individuals were transient, especially hunters and voyageurs, which meant they might not be counted at all. Importantly, the 1762 French census does not include women; an estimated number of women was added in the 1982 publication of Detroit censuses resulting in the number 1,100. Poremba gives the numbers 2,000 for the size of Detroit's population in 1760 and 300 for farms/homes, _Detroit_ , 39.
. Dunnigan, _Frontier_ , 50.
. David M. Katzman, "Black Slavery in Michigan," _American Studies_ 11:2 (Fall 1970) 56–66, 60.
. James Sterling Letter Book, 1761–1765, finding aid, biography, William L. Clements Library, University of Michigan, Ann Arbor, MI.
. James Sterling to [?], November 22, 1762, Sterling Letter Book; Sterling Letter Book, 1761–1765, finding aid, biography.
. To James Stirling, Detroit, August 23, 1760, Letterbooks of Phyn and Ellice, quoted in Farmer, _History of Detroit_ , 344.
. Isabella Graham to John Marshal, 1769, Divie Duffield Papers, MS/Duffield (D. B.) Burton Historical Collection, Detroit Public Library, Detroit, MI. Joanna Bethune, _The Life of Mrs. Isabella Graham_ (New York: John F. Taylor, 1839), 11–13. Graham is viewed as a philanthropist for her organizing on behalf of poor widows and orphans in New York.
. James Sterling to Captain Walter Rutherford, October 27, 1761, Sterling Letter Book; James Sterling to Mr. Collbeck, October 27, 1761, Sterling Letter Book, William L. Clements Library, University of Michigan, Ann Arbor, MI.
. James Sterling to Robert Holmes, April 20, 1762, Sterling Letter Book; James Sterling to John Sterling, June 12, 1762, Sterling Letter Book; James Sterling to Ensign J. Schlosser, June 12, 1762, Sterling Letter Book. Historian Christian Crouch expertly analyzes this escape in her paper: "The Black City: African and Indian Exchange in Pontiac's Detroit," revised version of Christian Crouch, "The Black City: Detroit and the Northeast Borderlands through African Eyes in the Era of 'Pontiac's War,'" The War Called Pontiac's Conference, April 5, 2013, Philadelphia, 20–21.
. The insight that Sterling might have predicted Pontiac's War comes from Jon William Parmenter, "Pontiac's War: Forging New Links in the Anglo-Iroquois Covenant Chain, 1758–1766," _Ethnohistory_ 44:4 (Autumn 1997): 617–54, 626; quoted in Parmenter, "Pontiac's War," 626.
. Sterling Letter Book, finding aid, biography.
. The classic treatment of this event is Francis Parkman, _The Conspiracy of Pontiac and the Indian Uprising of 1763_ (1851; Boston, 1898). On pageantry in the memory of Pontiac's rebellion, see Kyle Mays, "Pontiac's Ghost in Detroit: Constructing Race and Gender through Indigenous Masculinity at the Turn of the 20th Century Detroit," conference paper, American Society for Ethnohistory Annual Meeting, New Orleans, LA, September 14, 2013.
. Richard Middleton, _Pontiac's War: Its Causes, Course and Consequences_ (New York: Routledge, 2012), 66; Gregory Evans Dowd, _A Spirited Resistance: The North American Indian Struggle for Unity, 1745–1815_ (Baltimore: Johns Hopkins University Press, 1992), 36; Andrew Keith Sturtevant, "Jealous Neighbors: Rivalry and Alliance Among the Native Communities of Detroit, 1701–1766" (Ph.D. diss., The College of William and Mary, 2001), 246, 258, 266.
. Parmenter, "Pontiac's War," 618.
. Alan Taylor, _American Colonies: The Settling of North America_ (New York: Penguin, 2001), 92. McDonnell, _Masters of Empire_ , 26. For a clear and succinct breakdown of colonial systems, see Nancy Shoemaker, "A Typology of Colonialism," _Perspectives on History_ (October 2015), 29.
. John Mack Faragher, "'More Motley than Mackinaw': From Ethnic Mixing to Ethnic Cleansing on the Frontier of the Lower Missouri, 1783–1833," in Andrew R. L. Cayton and Fredrika Teute, eds., _Contact Points: American Frontiers from the Mohawk Valley to the Mississippi, 1750–1830_ (Chapel Hill: University of North Carolina Press, 1998), 304–326, 305.
. Middleton, _Pontiac's War_ , 65, 68; Dowd, _Spirited_ , 35.
. Middleton, _Pontiac's War_ , 65; Sturtevant, _Jealous_ , 254.
. Middleton, _Pontiac's War_ , 83.
. Middleton, _Pontiac's War_ , 70.
. Middleton, _Pontiac's War_ , 70, 72.
. John Porteous Diary, Volume 2: Journal Pontiac's Siege of Detroit, May 7–13, 1763, 17 (Wednesday, May 11, 1763), Burton Historical Collection, DPL. Middleton, _Pontiac's War_ , 72.
. Carl J. Eckberg, _Stealing Indian Women: Native Slavery in Illinois Country_ (Urbana: University of Illinois Press, 2010), 14; Trudel, _Canada's Forgotten_ , 97.
. Milo Milton Quaife, ed. _The Siege of Detroit in 1763: The Journal of Pontiac's Conspiracy, and John Rutherford's Narrative of Captivity_ (Chicago: R. R. Donnelley, 1958), 43–44, 139.
. Middleton, _Pontiac's War_ , 77.
. Middleton, _Pontiac's War_ , 71; Parmenter, "Pontiac's War," 630.
. James Sterling to Duncan & Co., July 24, 1763, Sterling Letter Book.
. Parmenter, "Pontiac's War," 628.
. James Sterling to John Sterling, October 6, 1763, Sterling Letter Book.
. Quoted from Parmenter, "Pontiac's War," 628.
. Dowd, _Spirited_ , 35.
. Parmenter, "Pontiac's War, 630, 631.
. Andrew J. Blackbird, _History of the Ottawa and Chippewa of Michigan; A Grammar of Their Language, And Personal and Family History of the Author_ (Ypsilanti, MI: Ypsilantian Job Printing House, 1887), 7.
. Parmenter, "Pontiac's War," 636–37; Quoted in Parmenter, "Pontiac's War," 635. After hearing a report about the peace conference that took place at Johnson Hall, the headquarters of Sir William Johnson in New York, Pontiac promised George Croghan, chief deputy to William Johnson, that he would not wage war again. Jon Parmenter argues that even as Pontiac agreed to peace, he did not admit guilt and used the opportunity to skillfully request gunpowder on credit from the British. Decades later, in 1769, Pontiac was killed by an Indian man near Cahokia, Illinois, in an incident unrelated to the war.
. Katz, "Black Slavery," 60.
. Emily Macgillivray and Tiya Miles, "'She Has Lived in Fashion': A Native Woman Trader's Household in the Detroit River Region," accepted for Karen Marrero and Andrew Sturtevant, eds., _A Place in Common: Telling Histories of Early Detroit_ (Lansing: Michigan State University Press, in progress).
. Afua Cooper, _The Hanging of Angélique: The Untold Story of Canadian Slavery and the Burning of Old Montréal_ (Athens: University of Georgia Press, 2007), 81.
. The foundational work of carefully recovering the history of slavery in New France was done by French Canadian historian Marcel Trudel in the 1960s, and by Afro-Canadian historian Afua Cooper (focusing on black slavery) and American historian Brett Rushforth (focusing on Indian slavery) in the early 2000s.
. Trudel, _Canada's Forgotten,_ 15; Cooper, _Hanging_ , 70.
. Trudel, _Canada's Forgotten_ , 65–70; Brett Rushforth, _Bonds of Alliance: Indigenous and Atlantic Slaveries in New France_ (Chapel Hill: University of North Carolina Press, 2012), 169.
. White, _Wild Frenchmen_ , 7, 12.
. Trudel, _Canada's Forgotten_ , 48.
. Trudel, _Canada's Forgotten_ , 37; Cooper, _Hanging_ , 72; Quoted in Cooper, _Hanging_ , 75.
. Marcel Trudel and his co-investigator, Micheline D'Allaire, conducted this count as part of a survey of French records. See Trudel, _Canada's Forgotten_ , 31, 34, 36, 41, 73, 61, 76, 83; for the research methods that resulted in these numbers, see 58–59.
. Spear, _Race_ , 59–63; While the Code Noir served as a guide for New France residents, it was not legally binding there according to Marcel Trudel, who argues that a new code would have had to be enacted to be legal, as in the case of Louisiana, Trudel, _Canada's Forgotten_ , 122; see 119–22 for a full summary of the provisions of the Code Noir.
. For detailed summaries of the provisions of the two Codes Noir, see Spear, _Race_ , 59–68; Rushforth, _Bonds_ , 123–31.
. Spear, _Race_ , 72; Ekberg, _Stealing_ , 89.
. Ekberg, _Stealing_ , 46.
. Ekberg, _Stealing_ , 13, 21. I am grateful to John Petoskey, the student who introduced me to Blackbird's diary as part of our work on his honors thesis. Petoskey's interpretation of the "Underground" people as Pawnees and as Ottawa captives spurred my use of this example; John Minode'e Petoskey, "Blood Quantum and Twenty-First Century Sovereignty in the Grand Traverse Band of Ottawa and Chippewa Indians," undergraduate honors thesis, University of Michigan, Ann Arbor, 2016, 47–48; Andrew J. Blackbird, _History of the Ottawa and Chippewa of Michigan; A Grammar of Their Language, And Personal and Family History of the Author_ (Ypsilanti, MI: Ypsilantian Job Printing House, 1887), 25–26; Martha Royce Blaine, "Pawnee," _Encyclopedia of North American Indians_ , Frederick E. Hoxie, ed. (Boston: Houghton-Mifflin, 1996), 472. Rushforth, _Bonds_ , 397.
. This confusion held sway in the colonial period and in modern-day scholarship until Brett Rushforth offered a close examination and detailed explanation in _Bonds_ , 169–73. For example, Marcel Trudel wrote in the first history of slavery in New France: "The Panis are the only Amerindian nation to appear each year in slave documents with such astounding regularity. There was a true Panis slave market, just as there was an ebony slave market." Trudel, _Canada's Forgotten_ , 65. For another example of "Panis" interpreted as the single nation "Pawnee," see Jorge Castellanos, "Black Slavery in Detroit," in Wilma Wood Henrickson, ed., _Detroit Perspectives: Crossroads and Turning Points_ (Detroit: Wayne State University Press, 1991), 85–93, 86.
. New France records in Canada that mention slaves do sometimes list the captive person's tribe of origin. This difference raises the question of whether French record keepers in the satellite post at Detroit, mainly priests, felt there was a greater need to suppress this information. Trudel, _Canada's Forgotten_ , 63–64.
. Quoted in Rushforth, _Bonds,_ 136, 393–95; Cooper, _Hanging_ , 76; Trudel, _Canada's Forgotten_ , 45–54).
. Trudel, _Canada's Forgotten_ , 46; Rushforth, _Bonds_ , 137.
. Cooper, _Hanging_ , 76, 137.
. Women dressing skins for trade: Karen L. Anderson, _Chain Her by One Foot: The Subjugation of Women in Seventeenth-Century New France_ (London: Routledge, 1991), 159. Moccasins: Catherine Cangany, "Fashioning Moccasins: Detroit, the Manufacturing Frontier, and the Empire of Consumption, 1701–1835," _The William and Mary Quarterly_ 69:2 (April 2012): 265–302, 266, 268, 286.
. Trudel, _Canada's Forgotten_ , 121; Jennifer M. Spear, _Race, Sex, and Sexual Order in Early New Orleans_ (Baltimore: Johns Hopkins University Press, 2009), 67.
. Dowd, _Spirited_ , 12; Brett Rushforth, "'A Little Flesh We Offer You': The Origins of Indian Slavery in New France," in Alan Gallay, ed., _Indian Slavery in Colonial America_ (Lincoln: University of Nebraska, 2009), 353–89, 366.
. Rushforth, _Bonds_ , 68.
. Rushforth, _Bonds_ , 66.
. For detailed histories and analyses of French-Indian marriages, European-Indian marriages, and metís families, see: Susan Sleeper-Smith, _Indian Women and French Men: Rethinking Cultural Encounter in the Western Great Lakes_ (Amherst: University of Massachusetts Press, 2001); Kathleen DuVal, "Indian Intermarriage and Métissage in Colonial Louisiana," _The William and Mary Quarterly_ , Third Series, 65:2 (April 2008): 267–304; Anne F. Hyde, _Empires, Nations, and Families: A New History of the North American West, 1800–1860_ (Lincoln: University of Nebraska Press, 2011); Lucy Eldersveld Murphy, _Great Lakes Creoles: A French-Indian Community on the Northern Borderlands, Prairie Du Chien, 1750–1860_ (New York: Cambridge University Press, 2014); Karen Marrero, "Founding Families: Power and Authority of Mixed French and Native Lineages in Eighteenth Century Detroit" (Ph.D. diss., Yale University, 2011).
. The French phrase _à la façon du pays_ meant "in the custom of the country"; Duval, "Indian Intermarriage," 267. Although many of these relationships are viewed by historians to have been consensual, there were risks involved for indigenous women who entered these cross-cultural marriages. They might gain access to trade goods and improve the status of their families through the creation of ties with influential traders, but they also became subject over time to French-Catholic understandings of hierarchical gender roles that emphasized men's dominance over women and the expectation that a proper woman should serve and obey her husband; Anderson, _Chain Her by One Foot_ , 55, 57, 226–27.
. Catherine J. Denial, _Making Marriage: Husbands, Wives, and the American State in Dakota & Dakota and Ojibwe Country_ (St. Paul: Minnesota Historical Society Press, 2013), 99–100; Sylvia Van Kirk, _Many Tender Ties: Women in Fur-Trade Society, 1670–1870_ (Norman: University of Oklahoma Press, 1980) 37–38.
. Spear, _Race_ , 18, 26, 37.
. For the association of Native women and land, as well as the notion of Native women's "rapeability," see Audra Simpson, "The State Is a Man: Theresa Spence, Loretta Saunders and the Gendered Costs of Settler Sovereignty," _Theory & Event_ (forthcoming: spring 2017). Also see Sherene H. Razack, "Gendered Racial Violence and Spacialized Justice: The Murder of Pamela George," _Canadian Journal of Law and Society_ 15:2 (2000): 91–130. The historian Margaret Newell has shown through her reading of indirect sources that in seventeenth- and eighteenth-century New England, indigenous women (and girl) captives were also victims of sexual assault. She notes that women from high-status Native families sometimes received better treatment from their New England owners. Margaret Ellen Newell, _Brethren by Nature: New England Indians, Colonists, and the Origins of American Slavery_ (Ithaca, NY: Cornell University Press, 2015), 82, 83, 126, 230, 63.
. French New Orleans colonist Tivas de Gourville quoted in Spear, _Race_ , 29; La Vente quoted in Spear, _Race_ 24; Cadillac and La Vente's views described in Spear, _Race_ , 23–4.
. DuVal, "Indian Intermarriage," 269, 271.
. Trudel, _Canada's Forgotten_ , 153; Rushforth, _Bonds_ , 265; E. A. S. Demers, "John Askin and Indian Slaves at Michilimackinac," in Alan Gallay, ed., _Indian Slavery in Colonial America_ (Lincoln: University of Nebraska, 2009), 392–416, 401. An examination of Ste. Anne's Church records from Detroit between 1760–1815 indicate that one slaveholder, Jean Baptiste, served as godparent to the infant of his Panis slave, Madelaine, and "an unknown father" in 1798. While this fact is not evidence of paternity, it does raise the question of whether a French father might use this religious kinship system to informally claim or create a link with an enslaved child. Ste. Anne Church Records, Bentley Historical Library, 86966mf 534c, 535c, 536c, University of Michigan, Ann Arbor, MI. Used by permission of the Detroit Catholic Diocese.
. DuVal, "Indian Intermarriage," 279.
. DuVal, "Indian Intermarriage," 279.
. Rev. David Bacon, a Protestant missionary from the Congregational Church Association of Connecticut, came to Detroit in 1800. Methodist minister Rev. Nathaniel Bangs came to Detroit in 1804. Poremba, _Detroit_ , 71, 89.
. Burton, _City_ , 704; Edward J. Hickey, _Ste. Anne's Parish: One Hundred Years of Detroit History_ , ed., Joe L. Norris (Detroit: Wayne State University Press, 1951), 18; Detroit Places Ste. Anne's Church, History, <http://historydetroit.com/places/ste_annes.php>. Accessed December 9, 2013.
. This list of tribes comes from a review of the Ste. Anne's Records, BHL, through 1819.
. The term "Sauteuse" here indicates Ojibwe. For more on the various names and subgroups of Anishinaabe people in the Great Lakes, see Michael Witgen, _An Infinity of Nations: How the Native New World Shaped Early North America_ (Philadelphia: University of Pennsylvania Press, 2012), 13.
. Trudel states that the Campeaus (sometimes spelled Campaus) in Montreal were a tight-knit family with fifty-seven slaves among them although they were only "small-scale fur traders" and not among the ultra-rich; Trudel, _Canada's Forgotten_ , 259.
. Judy Jacobson, _Detroit River Connections: Historiographical and Biographical Sketches of the Eastern Great Lakes Border Region_ (Baltimore: Clearfield Company, 1994); Russell, _Michigan Censuses_ , 1762 Census, 20. Campau family wealth in the 1800s: Gitlin, _Bourgeois Frontier_ , 141–143. The Campau family papers in Detroit do not reveal many details of their slave transactions. Only one document describes the transfer of an enslaved "Negro" woman named Nancy from Jean B. Romain to his daughters on September 4, 1790. A transnational study of this slaveholding family that closely examined records on both sides of the border would be a revealing approach for further research. Campau Family Papers, Burton Historical Collection, Detroit Public Library, Detroit, MI.
. Russell, _Michigan Censuses_ , 1762 Census, 21–25. There are nine head-of-household Campaus listed in the 1762 census. Louis Campau had no accompanying details beside his name in the census and is therefore not listed in my summary. Michel or Alex Campau (first name is uncertain in the record) had no notations for the latter part of the census categories by his name, suggesting either that the information was incomplete or that he had no girls, boys, slaves, or paid workers in his household; he is not listed in my summary.
. Ste. Anne's Church Records, Reel 1, VII, 1744–1780.
. James Sterling to Ensign J. S. Schlosser, June 12, 1762, Sterling Letter Book. I am grateful to Jonathan Quint for pointing out the reference to Native women in this letter.
. Dowry: Crouch, "Black City," 25; James Sterling to [?], February 26, 1765, Sterling Letter Book; quoted in Marrero, "Founding Families," 281; Marrero, "Founding," 282–83.
. Independent trade routes: Crouch, "Black City," 25.
. Crouch, "Black City," 1, 4; James Sterling to [?], Sept 29, 1765, Sterling Letter Book. Christian Crouch was the first to analyze Sterling's preference for black male laborers. In her paper, "The Black City," she carefully considers and leaves open the question of why Sterling preferred black male laborers, speculating that black men had a greater facility in travel because of a learned ability to get along with native people lacking in white men like Morrison.
. Marrero, "Founding Families," 276; quoted in Marrero, 282; quoted in Crouch, "Black City," 25. Karen Marrero first makes this argument that a black slave was a status symbol for Angelique Sterling in "Founding Families," 282.
. James Sterling to [?], November 12, 1764, Sterling Letter Book.
. To John Porteous, June 6, 1771, Letterbooks of Phyn and Ellice, merchants, at Schenectady, New York, 1767–1776 (Buffalo Historical Society-BHS Microfilm Publication No. 1), Vol. 1. For several other letters involving slave orders for Detroit, see Farmer, _History of Detroit_ , 344.
. For examples of freedom suits won on the basis of Native American ancestry (especially maternity), see: Lea VanderVelde, _Redemption Songs: Suing for Freedom before Dred Scott_ (New York: Oxford University Press, 2014), 7, 39–56; Ariela Julie Gross, _What Blood Won't Tell: A History of Race on Trial in America_ (Cambridge, MA: Harvard University Press, 2008), 22–27; Ariela Gross and Alejandro De La Fuente, "Slaves, Free Blacks, and Race in the Legal Regimes of Cuba, Louisiana, and Virginia: A Comparison," _North Carolina Law Review_ 91:5 (June 2013): 1699–1756, 1733; Tiya Miles, "The Narrative of Nancy, A Cherokee Woman," _Frontiers, A Journal of Women Studies_ , Special Issue: Intermarriage and North American Indians 29:2, 3 (Spring 2008): 59–80; Ekberg, _Stealing_ , 91, 93. In Spanish-influenced areas of the Caribbean, Florida, and Southwest, indigenous slavery persisted into the nineteenth century; see Andrés Reséndez, _The Other Slavery: The Uncovered Story of Indian Enslavement in America_ (Boston: Houghton Mifflin, 2016).
. Marrero, "Founding Families," 272.
. Marrero, "Founding Families," 272, 287, 310; Quaife, _Siege_ , 187.
. Ekberg, _Stealing_ , 68; Ste. Anne's Records, May 30, 1764.
. In his historical study of colonial French Illinois, Carl Ekberg describes this tendency by saying that Indian women were "reserved for white men"; _Stealing_ , 76.
. James Sterling to [?], January 10, 1762, Sterling Letter Book.
. Ste. Anne's Records, BHL. Our figure does not include enslaved babies listed as "mulatto" or with undesignated racial information, although some of these infants might well have been of indigenous descent. Carl Ekberg gives the number 167 for babies born to enslaved Indian mothers and white fathers in Detroit, citing Marcel Trudel; Ekberg, _Stealing_ , 28. Trudel states that 177 "illegitimate children" were born to Indian slaves in Detroit; Trudel, _Canada's Forgotten_ , 204. Trudel notes here, too, that Native enslaved women outnumbered men, and he implies that white men's attraction influenced this demographic imbalance.
. Ekberg, _Stealing_ , 75.
. Jacobson, _Detroit_ , 29. Cangany, "Fashioning Moccasins," 285–86.
. Demers, "John Askin," 397–98. Re: Mannette, Detroit Notorial Register, Vol. A, June 11, 1768, Burton Historical Collection, Detroit Public Library, pp. 68–69.
. Detroit Notorial Register, Vol. A, June 11, 1768, Burton Historical Collection, Detroit Public Library, pp. 68–69.
. Armour and Widder, _Crossroads_ , 36, 71. Jacobson, _Detroit River_ , 36.
. Detroit can be characterized as a "society with slaves" rather than as a "slave society" because the core feature of the economy (the fur trade) was not produced solely or mainly by slave labor, and other labor systems persisted alongside slavery here. Nevertheless, slavery was important to the stability and economy of the settlement. For a description of this distinction in places where slavery was practiced, see Ira Berlin, _Many Thousands Gone: The First Two Centuries of Slavery in North America_ (Cambridge, MA: Harvard University Press, 1998), 8–9.
. Ekberg discusses this blurred status of Indian slaves in French households; see _Stealing_ , 45.
. Trudel, _Canada's Forgotten_ , 140.
**2: The War for Liberty (1774–1783)**
. The name of Ann Wyley has been recorded a number of ways in primary and secondary sources. She has been called Ann and Anne, as well as Nancy. Her last name has been spelled Wyley or Wiley. Jean Contencineau's name has likewise been recorded with numerous spellings: Contancinau, Coutencineau. I am using the spelling from the Detroit trial record, March 1776. "Record of criminal trial in 1776, Detroit, ss," reprinted in Charles H. Lanman, _History of Michigan, Civil and Topographical in a Compendious Form: with a View of Surrounding Lakes_ (New York: E. French, 1839), 133–35. (Lanman offers as citation: "This record was found in the possession of Judge May. He knew the jury who tried the case.") This trial record is also reprinted in Detroit in the Revolution, File: 2, Box: Works Detroit History 1760, Burton Papers (MS/Burton C.M.), Burton Historical Collection, Detroit Public Library, 61–62.
. The Detroit River is often described as a "highway" of commerce in the region. See, for instance, Denver Brunsman, "Introduction," in Brunsman and Stone, eds., _Revolutionary Detroit_ , 3–22, 5.
. This by-decade breakdown of the enslaved population is the result of our (Tiya Miles and Michelle Cassidy's) analysis of the Ste. Anne's Church records in which notations about "Panis," "Negro," and "Mulatto" slaves consistently appear. Our numbers are approximate because the Ste. Anne records do not offer a comprehensive count of all slaves in Detroit, some of whom were not involved in the church. In addition, these records include a number of entries about slaves for whom no racial designation is given. We have noted these people in a category labeled "unknown" in our count. The racial "unknowns" for the 1760s totaled thirteen people; the "unknowns" in the 1700s totaled four people. More than likely, the majority of these individuals were "Panis." In the ratio for the 1760s to which this note corresponds, I have combined the number of blacks (three) with the number of "Mulattos" (two) to arrive at the total of five reported, even though the term "mulatto" could be used to designate persons of black and Indian ancestry as well as of black and white ancestry. Michelle Cassidy, a graduate student in the History Department at the University of Michigan, counted the number of entries in the Ste. Anne records and broke them down by decade, race, and gender. St. Anne Records, Bentley Historical Library, 86966mf 534c, 535c, 536c, University of Michigan, Ann Arbor, MI. Used by permission of the Detroit Catholic Diocese.
. "The Story of Jean Contancinau: Testimony," translated in Detroit in the Revolution, File 2, 57–58, Burton Papers, DPL. (Clarence Burton includes as citation: "The papers here collected are from the Haldimand collection, and Lanman's History of Michigan. The testimony, such as it is, is in French in the old Detroit registry," 56.
. Burton, "Detroit in the Revolution" (booklet), 25.
. Lanman, 134. "The Story of Jean Contancinau: Testimony," translated in Detroit in the Revolution, File 2, 58, Burton Papers, DPL. After the French and Indian War, Detroit operated under British martial law. The Quebec Act, passed in October 7, 1774 (the same year these thefts took place), brought civil rule to Michigan through a hybrid approach of French civil law and British criminal law. William Renwick Riddell, _Michigan Under British Rule: Law and Law Courts, 1760–1796_ (Lansing: Michigan Historical Society, 1926), 19–20. The stolen purse was green: "The Story of Jean Contancinau: Testimony," translated in Detroit in the Revolution, File 2, 59, Burton Papers, DPL.
. For an analysis of the role of clothing in colonial transculturation processes, see Sophie White, _Wild Frenchmen and Frenchified Indians: Material Culture and Race in Colonial Louisiana_ (Philadelphia: University of Pennsylvania Press, 2012). For a discussion of the use of clothing to challenge caste and assert creativity and adornment in slave communities, see Stephanie Camp, _Closer to Freedom: Enslaved Women and Everyday Resistance in the Plantation South_ (Chapel Hill: University of North Carolina Press, 2004). Barbara Heath describes enslaved people's use of material objects such as buttons and buckles to change the appearance of substandard clothing distributed by owners: Barbara Heath, "Materiality, Race, and Slavery: How Archaeology Contributes to Dialogues at Historic Sites," unpublished paper, National Council on Public History, Nashville, TN, April 2015.
. "Record of criminal trial in 1776, Detroit, ss," reprinted in Charles H. Lanman, _History of Michigan_ , 133.
. Besides establishing the boundaries of Canada and declaring the application of British law to the former French territory, the Quebec Act of 1774 protected the right of French settlers to maintain their property and the right of Catholics to practice their faith. Lanman, _History of Michigan_ , 132–33. The Quebec Act provided for the first civil government in Detroit, with the king slated to appoint "a governor, lieutenant-governor, or commander-in-chief, and a council." Farmer, _History of Detroit_ , 84. Of these possibilities, Lieutenant Governor Henry Hamilton, was the only official assigned. He became the supervisor of Philip Dejean, who was already serving as notary and justice of the peace in the town. Dejean had been appointed by military officers Captain Turnbull and Major Bayard, in 1767. In 1768 a public election (the structure of which is unclear) confirmed his role as "judge and justice of the district of Detroit." Burton, "Detroit in the Revolution" (booklet), 20.
. Detroit in the Revolution, File 2, 108, 48, Burton Papers, DPL; Burton, "Detroit in the Revolution" (booklet), 20.
. Lanman, _History of Michigan_ , 132.
. Ann is first called "Anne" in this testimony and then "Nancy."
. Second declaration of Prisoners, Detroit in the Revolution, File 2, 294, Burton Papers, DPL.
. Cenette, Chatelain and C Enfant did not appear in the 1768 or 1779 Detroit censuses; however, a Mrs. Chatlain is listed for 1779. A Joseph L'Enfant appears in the 1779 Detroit census as the owner of two slaves. Donna Valley Russell, ed., _Michigan Censuses 1710–1830: Under the French, British, and Americans_ (Detroit: Detroit Society for Genealogical Research, Inc., 1982), 42.
. "Record of criminal trial in 1776, Detroit, ss," reprinted in Charles H. Lanman, _History of Michigan,_ 133. "The Story of Jean Contancinau: The Verdict," Detroit in the Revolution, File 2, 60, 61, Burton Papers, DPL.
. "The Story of Jean Contancinau: The Judgment," Detroit in the Revolution, File 2, 62, Burton Papers, DPL.
. Presentment against Philip Dejean, Canadian Archives, Series B. Vol. 225, p. 501, reprinted in "Detroit in the Revolution," File 2, 69, Burton Papers, DPL. William Renwick Riddell, _The First Judge of Detroit and His Court_ (Ann Arbor: University of Michigan Press, 1915), 9.
. Secondary sources disagree about Wyley's ultimate fate, and primary sources exist only in piecemeal fashion. The Detroit legal historian and judge William Riddell states that she was not put to death; Riddell, _The First Judge of Detroit_ , 9. Detroit historian Clarence Burton also states that she was not executed in a description of the case that includes transcripts of the court record; see Clarence Burton, "Detroit in the Revolution" (booklet), File 2, 69, Burton Papers, DPL. Burton discusses the case similarly in: Clarence Burton "Building of Detroit-People," Works Detroit History 1701, MS/Burton, C.M., Burton Historical Collection, DPL, 10; also see Clarence Burton, "Detroit Under British Rule," Works Detroit History 1760, MS/Burton, C.M. Burton, Historical Collection, DPL, 26. In contrast, Detroit historian Silas Farmer states that Wyley was executed, see: Farmer, _History of Detroit_ , 173–174, 957. For other accounts of this case, see: Poremba, _Detroit_ , 50 (who calls this the first burglary in Detroit); Kneip, "Slavery in Early Detroit," 27–28; Errin T. Stegich, "Liberty Hangs at Detroit: The Trial and Execution of Jean Contencineau," in Denver Brunsman and Joel Stone, eds., _Revolutionary Detroit_ : 67–72.
. Rashauna Johnson, _Slavery's Metropolis: Unfree Labor in New Orleans During the Age of Revolutions_ (New York: Cambridge University Press, 2016), 147.
. Mr. Thomas William to P. Dejean, August 5, 1778, Detroit, William Papers, Burton Historical Collection, DPL.
. Tiya Miles, "Taking Leave, Making Lives: Creative Quests for Freedom in Early Black and Native America," in Gabrielle Tayac, ed., _IndiVisible: African-Native American Lives in the Americas_ (Washington, D.C.: Smithsonian Institution, 2009), 146–49. Leslie M. Harris, _In the Shadow of Slavery: African Americans in New York City, 1626–1863_ (Chicago: University of Chicago Press, 2003), 37.
. John Bell Moran, _The Moran Family: 200 Years in Detroit_ (Detroit: Alved of Detroit, 1949), 28.
. The Royal Proclamation (October 7, 1763): "established the Allegheny Mountains as a formal boundary line between American colonial settlements and the western Indians' hunting grounds and forbade all future private purchases of land from the Indians, reserving that privilege to the Crown." However, many settlers ultimately ignored the act, which was difficult to enforce from afar. Quoted from Jon William Parmenter, "Pontiac's War: Forging New Links in the Anglo-Iroquois Covenant Chain, 1758–1766," _Ethnohistory_ 44:4 (Autumn 1997): 617–54, 629. Colin G. Calloway, _The American Revolution in Indian Country: Crisis and Diversity in Native American Communities_ (New York: Cambridge University Press, 1995), 21.
. George L. Cornell, "American Indians at Wawiiatanong: An Early American History of Indigenous Peoples at Detroit," in John H. Hartig, _Honoring Our Detroit River: Caring for Our Home_ (Bloomfield Hills, MI: Cranbrook Institute of Science, 2003), 20.
. Ste. Anne's Records, BHL.
. Quoted in Brian Leigh Dunnigan, _Frontier Metropolis: Picturing Early Detroit, 1701–1838_ (Detroit: Wayne State University Press, 2001), 120; Farmer, _History of Detroit_ , 472–73.
. Farmer, _History of Detroit_ , 837.
. Quoted in David McCullough, _1776_ (New York: Simon & Schuster, 2005), 135; McCullough, 135–37.
. To Alex and William Macomb, June 22, 1775, Letterbooks of Phyn and Ellice, merchants, at Schenectady, New York, 1767–76 (Buffalo Historical Society-BHS Microfilm Publication No. 1), Vol. 3. David A. Armour and Keith R. Widder, _At the Crossroads: Michilimackinac During the American Revolution_ (Mackinac Island, MI: Mackinac Island State Park Commission, 1978), 1; Peter Silver, _Our Savage Neighbors: How Indian War Transformed Early America_ (New York: W. W. Norton & Co., 2008), 229.
. John H. Hartig, "Introduction," in Hartig, ed., _Honoring Our Detroit River_ , 1–8, 6.
. Quoted in Isabelle E. Swan, _The Deep Roots: A History of Gross Ile, Michigan to July 6, 1876_ (Grosse Ile, MI: Grosse Ile Historical Society, 1977), 20, 21.
. Swan, _Deep Roots_ , 14, 23.
. Harris, _Shadow of Slavery_ , 11.
. Phrasing by Karen Marrero, "On the Edge of the West: The Roots and Routes of Detroit's Urban Eighteenth Century," in Jay Gitlin and Adam Arenson, eds., _Frontier Cities: Encounters at the Crossroads of Empire_ (Philadelphia: University of Pennsylvania Press, 2012), 66–86.
. Catherine Cangany, _Frontier Seaport: Detroit's Transformation into an Atlantic Entrepot_ (Chicago: The University of Chicago Press, 2014), 3.
. Swan, _Deep Roots_ , 13–15, 23; Old Deed "Grosse Ile," LMS / Macomb Family Papers, July 6 1776, Detroit Public Library, Detroit, MI; A. Macomb quoted in Swan, _Deep Roots_ , 21; Macomb military account: Milo M. Quaife, "When Detroit Invaded Kentucky," _Filson Club History Quarterly_ 1:2 (January 1927): 53–67, 55.
. Swan, _Deep Roots_ , 14, 24–26. Size of farm: Record Book of Macomb Estate, Macomb Family Papers, R2:1796, BHC, DPL.
. Ste. Anne's Records, BHL. James May to Wm Macomb, Jan 12 1790, Alexander Fraser Papers, Detroit Public Library.
. David M. Katzman, "Black Slavery in Michigan," _American Studies_ 11:2 (Fall 1970), 60.
. Quoted in Swan, _Deep Roots_ , 17.
. Quoted in Armour and Widder, _Crossroads_ , 51. De Peyster kinship link: Armour and Widder, _Crossroads_ , 51.
. Calloway, _American Revolution_ , 29–32, 36, 39, 43–44, 46; Armour & Widder, _Crossroads_ , 51.
. Donald Lee, "Clark and Lernoult: Reduction by Expansion," in Brunsman and Stone, eds., _Revolutionary Detroit_ , 73–77, 75; Quaife, "When Detroit Invaded Kentucky," 1927.
. Lee, "Clark and Lernoult," in Brunsman and Stone, eds., _Revolutionary Detroit_ , 75; Thomas Jefferson to George Rogers Clark, Dec. 25, 1780, _The Papers of Thomas Jefferson_ , Julian P. Boyd. ed., Vol. 4 (Princeton, NJ: Princeton University Press, 1951), 234–37.
. Proclamation by George R. Clark, December 24, 1778, translated in Jerry Lewis, "Red and Black Slaves in the Illinois Territory," in Terry Straus and Grant P. Arndt, eds., _Native Chicago_ (Chicago: Albatross Publishers, 1998), 82–86.
. Americans were not the first to racialize Indians as Clark does in this example. British officers in Pontiac's war also used racial terms, such as "copperheaded" and "black," to indicate Native people.
. In her illuminating study of the racial term "red," Nancy Shoemaker shows how Native people in the East had their own meanings for color terms (such as red being associated with war) long before "red" came to be associated with Indianness. Both Europeans and American Indians began to adopt the racial term "red," in different ways and for different reasons, in the late 1700s and early 1800s. Clark's negative use of the term in the Illinois document, meant to emphasize slave caste, is not a usage that Native Americans would have willingly adopted. Nancy Shoemaker, "How Indians Got to Be Red," _The American Historical Review_ 102 (June 1997): 624–44. Frederick E. Hoxie, "Introduction," in Frederick E. Hoxie, Ronald Hoffman, and Peter J. Albert, eds., _Native Americans and the Early Republic_ (Charlottesville: University Press of Virginia, 1999), ix. James Sterling to John Sterling, October 6, 1763, Sterling Letter Book.
. Clark, Proclamation, in Lewis, trans., "Red and Black Slaves." Slave resistance during the war: Benjamin Quarles, "The Revolutionary War as a Black Declaration of Independence," in Ira Berlin and Ronald Hoffman, eds., _Slavery and Freedom in the Age of the American Revolution_ (Urbana: University of Illinois Press, 1983), 283, 290, 291; Manisha Sinha, _The Slave's Cause: A History of Abolition_ (New Haven, CT: Yale University Press, 2016), 51–52.
. Calloway, _American Revolution_ , 22.
. Quaife, "When Detroit Invaded Kentucky," 55.
. Captain Bird to Major Arent S. De Peyster, June 11, 1780, transcribed in Quaife, "When Detroit Invaded Kentucky," 62–63.
. Captain Bird to Wm Lee, a Negroe free, 1784, MS Bird Papers, Detroit Public Library.
. Silver, _Savage Neighbors_ , 250–51; Armour & Widder, _Crossroads_ , 94; Brunsman, "Introduction," in Brunsman and Stone, eds., _Revolutionary Detroit_ , 12. Brett Rushforth notes the importance of slaves as "tokens" of alliance between indigenous groups and the French; Rushforth, _Bonds of Alliance_ , 220–21.
. Judy Jacobson, _Detroit River Connections: Historiographical and Biographical Sketches of the Eastern Great Lakes Border Region_ (Baltimore: Clearfield Company, 1994), 17.
. Statement by Captain John Dunkin, quoted in Maude Ward Lafferty, "Destruction of Ruddle's and Martin's Forts in the Revolutionary War," _Register of the Kentucky Historical Society_ 54:189 (October 1956): 15; Lafferty, "Destruction," 26.
. "Petition of Agnes La Force," Haldimand Papers, MPHC, XIX, 494. Also quoted in Kneip, "Slavery in Early Detroit," 32–33.
. Quaife, "When Detroit Invaded Kentucky," 3, 4; Lafferty, "Destruction," 26; Kneip, "Slavery in Detroit," 32; "List of Slaves formerly the property of Mrs. Agnes Le Force now in possession of," transcribed in Quaife, 66–67. "Slave Captives at Ruddell's and Martin's Forts," www.frontierfolk.net/ramsha_research/captives3html; Accessed July 28, 2016. Jacques Duperon Baby: Riddell, _Michigan Under British Rule_ , 52–53.
. Calloway, _American Revolution_ , 54.
. Quoted in Clarence Burton, "Detroit in the Revolution" (Booklet—1906 Address to the Sons of the American Revolution) Works Printed Treaty of 1782 Miscellaneous Printed Material, Burton Papers, MS/Burton C. M., Burton Historical Collection, Detroit Public Library, 26; Clarence Burton, Detroit in the Revolution, File: 2, Box: Works Detroit History 1760, Burton Papers, MS/Burton, C. M., Burton Historical Collection, Detroit Public Library, p. 2 typescript/137 handwritten. Riddell, _Michigan Under British Rule_ , 50.
. Burton, Detroit in the Revolution, File 2, p. 3 typescript/110 handwritten.
. "Advertisement," transcribed in Burton, "Detroit in the Revolution," Booklet 22, BHC, DPL.
. To Sir from Most Humble Servant, Sept. 21, 1777, Quebec, transcribed in John Almon and Thomas Pownall, _The Remembrance of Impartial Repository of Public Events_ , Vol. 6 (London: J Almon, 1778), 188–89; also transcribed in Burton, Detroit in the Revolution, File 2, pp. 11–12 handwritten.
. Stegich, "Liberty Hangs," 68; Burton, Detroit in the Revolution, File 2, p. 1 typescript / 108 handwritten; Clarence Burton, "Building of Detroit-People," Works Detroit History 1701, MS/Burton, C. M., BHC, DPL, 10, 11; Clarence Burton, "Detroit Under British Rule," Works Detroit History 1760, MS/Burton, C. M., BHC, DPL, 26; Armour and Widder, _Crossroads_ , 94; William Renwick Riddell, _The First Judge at Detroit and His Court_ (Ann Arbor: University of Michigan Press, 1915), 30. Hair buying: Silver, _Savage Neighbors_ , 250–51; Burton, Detroit in the Revolution, File 2, p. 1 typescript / 108 handwritten.
. Gifts: Alan Taylor, _The Divided Ground: Indians, Settlers, and the Northern Borderland of the American Revolution_ (New York: Vintage, 2006), 102.
. Russell, ed., _Michigan Censuses_ , 1782 Census, 49–56; Katzman, "Black Slavery in Michigan," 60; Calloway, _American Revolution_ , 54, 61.
. Quoted in Armour and Widder, _Crossroads_ , 135, 136, 117, 135.
. _The John Askin Papers Volume I: 1747–1795_ , Milo M. Quaife., ed. (Detroit: Detroit Library Commission, 1928), 68.
. Askin Papers Vol. I, 94.
. Detroit move: Cangany, _Frontier Seaport_ , 31; Jacobson, _Detroit River_ , 32. Barthe lot: "Actual Survey of the Narrows betwixt the Lake Erie and Sinclair," by P. McNiff, reproduced in Dunnigan, _Frontier Metropolis_ , 62; Jacobson, _Detroit River_ , 34. Sterling as representative: Armour and Widder, _Crossroads_ , 75. Askin's setbacks: Jacobson, _Detroit River_ , 32.
. Charlotte: Armour & Widder, _Crossroads_ , 37. Pompey and Jupiter: "Sale of Negro Slaves," Askin Papers, Vol. I, 58–59. Toon: Askin Papers, Vol I, 55.
. John Askin to Jean Baptiste Barthe, June 8, 1778, Askin Papers, Vol. I, 118. Pomp and crew: John Askin to Jean Baptiste Barthe, May 18, 1778, Askin Papers, Vol. I, 91–94. Askin says about this crew, "I have given all three their provisions, and rum, up to June 1, and have paid them their wages for the same time." This line may indicate that Pomp received some pay for his work, although Askin owned him and any pay would have been less than what the others received. More likely, as the sentence syntactically separates "provisions, and rum" from "wages," it can be read as differentiating these categories in a way that would not include Pompey as a recipient of wages.
. Sale of Indian: John Askin to Jean Baptiste Barthe, June 8, 1778, Askin Papers, Vol. I, 119. Pretty Panis: John Askin to Mr. Beausoleil, May 18, 1778, Askin Papers, Vol. I, 97–98. Shoes and gown: John Askin to Todd and McGill at Montreal, May 28, 1778, Askin Papers, Vol. I, 101–102; Jacobson, _Detroit River_ , 31–32. Fancy girls: Edward E. Baptist, "'Cuffy,' 'Fancy Maids,' and 'One-Eyed Men': Rape, Commodification, and the Domestic Slave Trade in the United States," _American Historical Review_ 106:5 (December 2001): 1619–50. For more on fancy girls, see also Sharony Green, _Remember Me to Miss Louisa: Hidden Black-White Intimacies in Antebellum America_ (DeKalb: Northern Illinois University Press, 2015); Sharony Green, "'Mr. Ballard, I Am Compelled to Write Again': Beyond Bedrooms and Brothels, a Fancy Girl Speaks," _Black Women, Gender & Families_ 5:1 (Spring 2011): 17–40.
. Askin Papers, Vol. I, 135. Sherene H. Razack, "Gendered Racial Violence and Spatialized Justice: The Murder of Pamela George," _Canadian Journal of Law and Society_ 15:2 (2000): 91–130, 93.
. Melissa R. Luberti, "Caught in the Revolution: The Moravians in Detroit," in Brunsman and Stone, eds., _Revolutionary Detroit_ , 102–105, 102. Sympathy and complicity: Henry A. Ford, "History of the Moravian Settlement," also titled "The Old Moravian Mission at Mt. Clemens," Michigan Historical Collections, Vol. 10, 107–115, 110. Spies: Greg Dowd writes that the Moravians passed along information about an intended attack on Fort Laurens, Dowd, _Spirited_ , 84–85. Taciturn: quoted in Ford, "Moravian Settlement," 1. Flames: quoted in Dowd, _Spirited_ , 84. This insight about Zeisberger's reasoning comes from Greg Dowd's analysis. For more on the Moravians in the Midwest, see John Heckewelder, _A Narrative of the Mission of the United Brethren among the Delaware and Mohegan Indians_ (Philadelphia, PA: McCarty & Davis, 1820).
. Luberti, "Caught," 102–103. Mulatto: Moravian Diary, Oct 18, 1776, translation by Del Moyer.
. Rev. David Zeisberger quoted in Ford, Moravian Settlement," 110.
. The attack took place in March of 1782: Luberti, "Caught," 103; Calloway, _American Revolution_ , 39; Dowd, _Spirited_ , 86; Silver, _Savage Neighbors_ , 265–67. Treatment at Detroit: David Zeisberger, _Diary of David Zeisberger: A Moravian Missionary among the Indians of Ohio_ , Vol. I, Eugene F. Bliss, ed. (Cincinnati: Robert Clark & Co., 1885), 111–12.
. _Diary of Zeisberger_ , Vol. 1, May, June 1783, 146, 154.
**3: The Wild Northwest (1783–1803)**
. Benjamin Quarles, "The Revolutionary War as a Black Declaration of Independence," in Ira Berlin and Ronald Hoffman, eds., _Slavery and Freedom in the Age of the American Revolution_ (Urbana: University of Illinois Press, 1983), 283. Manisha Sinha, _The Slave's Cause: A History of Abolition_ (New Haven, CT: Yale University Press, 2016), 42–44, 51.
. Edward Countryman, _The American Revolution_ (1985; Revised Edition, New York: Hill and Wang, 2003), 228.
. Report, Mr. Jefferson, Mr. Chafe, Mr. Howell, Temporary Government of Western Country Delivered March [ ]1784, MS/Jefferson Papers, BHC, DPL. The ordinance of 1784, drafted by a committee led by Jefferson, was viewed to be inadequate in part because it gave too much political authority to settlers in the territorial period. Jefferson was out of the country in 1787 when the new ordinance was written. Denis Duffey, "The Northwest Ordinance as a Constitutional Document," _Columbia Law Review_ 95:4 (May 1995): 929–68, 935–37. Other members of Jefferson's 1784 committee included Samuel Chase and David Howell. In 1787, Peter Dane, a delegate from Massachusetts, introduced the slavery article for inclusion in the final text. Peter Onuf has argued that southerners could accept the slavery exception in the Northwest because they expected to benefit economically through commercial exchange with the region as it grew. Peter S. Onuf, _Statehood and Union: A History of the Northwest Ordinance_ (Bloomington: Indiana University Press, 1987), 46–49, 110–11.
. Northwest Ordinance (1787), www.ourdocuments.gov. Accessed May 5, 2015.
. Heather Ann Thompson, "Why Mass Incarceration Matters: Rethinking Crisis, Decline, and Transformation in Postwar American History," _Journal of American History_ (December 2010): 703–734, on prison labor see 717–23.
. David G. Chardavoyne, "The Northwest Ordinance and Michigan's Territorial Heritage," in Paul Finkelman and Martin J. Hershock, eds., _The History of Michigan Law_ (Athens: Ohio University Press, 2006), 20.
. Allison Mileo Gorsuch, "Midwest Territorial Courts and the Development of American Citizenship, 1810–1840" (Ph.D. diss., 2013), 40. Duffey, "Northwest Ordinance," 933–34.
. "Foundational document": Duffey, "Northwest Ordinance," 949. I am borrowing language from Lisa Lowe when I describe slavery and colonialism as "braided." Lowe points to "settler colonialism as the condition for African slavery in the Americas." Lisa Lowe, _The Intimacies of Four Continents_ (Durham, NC: Duke University Press, 2015), 37–38.
. Paul Finkelman, "Evading the Ordinance: The Persistence of Bondage in Indiana and Illinois," _Journal of the Early Republic_ 9:1 (Spring 1989): 21–51, 22.
. Jefferson to Clark, Dec. 25, 1780, Jefferson Papers, Vol. 4, 237.
. Proclamation by George R. Clark, December 24, 1778, translated in Jerry Lewis, "Red and Black Slaves in the Illinois Territory," in Terry Straus and Grant P. Arndt, eds., _Native Chicago_ (Chicago: Albatross Publishers, 1998), 82–86. The Paris Peace Treaty of September 30, 1783, The Avalon Project, Yale Law School, avalon.law.yale.edu. Accessed May 5, 2015. William Renwick Riddell, "Notes on Great Britain and Canada with Respect to the Negro," _Journal of Negro History_ 13:2 (April 1928): 185–98, 186.
. Russell, ed., _Michigan Censuses_ , 1782 Census, 49–56; Katzman, "Black Slavery in Michigan," 60. William Macomb re Sale of Two Negro Slaves, Macomb Family Papers, BHC, DPL.
. Heidi Bohaker, "Reading Anishinaabe Identities: Meaning and Metaphor in Nindoodem Pictographs," _Ethnohistory_ 57:1 (Winter 2010): 11–33, 18.
. Sale of Negro Man Pompey, Copy of Deed Furnished by W.W. Backus of Detroit, "Reports of Counties, Etc.," MPHC, Vol. VI, 417.
. James Mackelm to John Askin, September 4, 1801, Askin Correspondence, John Askin Papers, Folder 1800, BHC, DPL; James Mackelm to John Askin, September 20, 1801, Askin Correspondence, John Askin Papers, Folder 1800, BHC, DPL. Campau Family Papers, MS/Campau, 1715–1928 (delivery orders: Oct. 1791, Sept. 1792, Jan. 1796, Dec. 1797, Jan. 1804) BHC, DPL.
. Calloway, _American Revolution_ , 23.
. It can be convincingly argued that these lands were not Great Britain's to cede. For a critical discussion of British claims to possessing Native lands in the Canadian borderland region dating back to 1668, see Adam Gaudry, "Fantasies of Sovereignty: Deconstructing British and Canadian Claims to Ownership of the Historic-Northwest," _NAIS: Journal of the Native American and Indigenous Studies Association_ 3:1 (2016): 46–74. Gov. Arthur St. Clair as slaveholder: Lehman, _Slavery in the Upper Mississippi Valley_ , 12.
. David R. Farrell, "Askin (Erskine), John," _Dictionary of Canadian Biography Online_ , 2, <http://www.biographi.ca/009004-11901-ephp?id_nbr=2242>. Accessed Oct. 12, 2012. For more on Belle Isle see Janet Anderson, _Island in the City: Belle Isle, Detroit's Beautiful Island_ , Companion Book to an Exhibit at the Detroit Historical Museum, 2001, Bentley Historical Library, University of Michigan, Ann Arbor, MI; Michael Rodriguez and Thomas Featherstone, Detroit's Belle Isle: Island Park Gem (Chicago: Arcadia Publishing, 2003). Taylor, _Divided Ground_ , 10.
. Riddell, _Michigan Under British Rule_ , 22, 26.
. Farmer, _History of Detroit_ , 84; David Lee Poremba, ed., _Detroit in Its World Setting: A Three Hundred Year Chronology, 1701–2001_ (Detroit: Wayne State University Press, 2001), 61, 62, 63, 346. D W Smith to John Askin, June 25, 1793, Askin Papers, Vol. II, 476–77.
. Ste. Anne's Records. This marriage also linked Grant to John Askin, as it was Askin's sister-in-law who became Grant's wife. Farrell, "Askin," _Dictionary of Canadian Biography_ , 3.
. Bill of Sale Josiah Cutten, Askin Papers, Vol. I, 284–87, 410–411.
. Harrow Family File, "The King's Vessels," 29, 36 (1786), BHC, DPL.
. Alexander Harrow Papers, Journal and Letter Book, typescript, D5 1791–1800, MS/Harrow, BHC, DPL. Stinson argues astutely that slave labor shored up white masculinity and class status in westward settlements where the idealized gentility of white life was difficult to reproduce and maintain. Stinson, "Black Bondspeople," 17, 18 (unpublished version, cited by permission).
. John Askin Estate Inventory - Detroit 1787, Jan. 1, 1787, John Askin Papers, BHC, DPL. Pompey does not appear in this inventory.
. Ste. Anne's Records, 1785, BHL, UM.
. Alexander Coventry, _Memoirs of an Emigrant The Journal of Alexander Coventry, M.D.; in Scotland, the United States and Canada during the period 1783–1831_ , Vol. I (Albany: The Albany Institute of Art and History, 1978), 1797, p. 859; quoted in Emily Macgillivray and Tiya Miles, "'She Has Lived in Fashion': A Native Woman Trader's Household in the Detroit River Region," accepted for eds., Karen Marrero and Andrew Sturtevant, _A Place in Common: Telling Histories of Early Detroit_ (Lansing: Michigan State University Press, in progress); Ainse's household: Macgillivray and Miles, "'She Has Lived in Fashion.'" Ainse's spouse Montour and relocation to Detroit: Taylor, _Divided Ground_ , 397, 399. Emily Macgillivray, "Indigenous Trading Women of the Borderland Great Lakes, 1740–1845" (Ph.D. diss., University of Michigan, Ann Arbor, 2017).
. Askin Papers, Vol. I, 193.
. Margaret Paulee, captured by the Shawnee warrior White Bark, described Blue Jacket's Detroit home and slaves in two accounts; quoted in John Sugden, _Blue Jacket: Warrior of the Shawnees_ (Lincoln: University of Nebraska Press, 2003), 5; Blue Jacket's father-in-law was Jacques Baby, p. 53. For more on Paulee, see John H. Moore, "A Captive of the Shawnees, 1779–1784," _West Virginia History_ 23:4 (July 1962): 287–96.
. Excerpts from Fragments of an Account Book at the Fort Malden Museum Amherstburg, Ontario, May 27, 1784, cited in Macgillivray and Miles, "'She Has Lived in Fashion.'" Ainse's business in Detroit: Taylor, _Divided Ground_ , 399. Ainse's male partner in Detroit: Macgillivray, "Indigenous Trading Women."
. Macgillivray, "Indigenous Trading Women." Macgillivray and Miles, "'She Has Lived in Fashion'"; Emily Macgillivray generously shared her findings about Ainse's familial ties to Moravians in the Detroit area.
. Zeisberger Diary, Vol. 1, Sept. 1782, p. 111; Oct. 5, 1783, 166; Zeisberger Diary, Vol. 2, Sept. 27, 1796, p. 458; Zeisberger Diary, Vol. 1, June 14, 1784, pp. 194–95; 1782, p.106; 1784, p. 205; Nov. 16, 1785, p. 249.
. Zeisberger Diary, Vol. 1, 1782, p. 117; Feb. 26, 1784, p. 183; Ford "History of the Moravian Settlement" / "Old Moravian Mission," 110, 113; Zeisberger Diary, Vol. 1, Feb. 22, 1784, p. 183; Feb. 12, 1784, p. 182.
. Zeisberger Diary, Vol. 1, Feb. 13, 1784, p. 182.
. Taylor, _Divided Ground_ , 136. Harrow Papers, Journal and Letterbook, March 15, 1799, BHC, DPL.
. "Matthew Elliott Essex County," (Toronto: York University, Harriet Tubman Institute, 2012), 1, 3, 4. For more on Elliott's use of slave and indentured labor, see Reginald Horsman, _Matthew Elliott, British Indian Agent_ (Detroit: Wayne State University Press, 1964), 9, 29, 49.
. Zeisberger Diary, Vol. 2, 1791, p. 232. Diary of the Indian Congregation at Fairfield in Upper Canada, 1801, January 25, 1801, Moravian Archives, Bethlehem, PA, translated for Tiya Miles by Del-Louise Moyer. Diary of the Indian Congregation in Salem, Petquottink in Lake Erie, 1790–91, May 5, 1791, Moravian Archives, Bethlehem, PA, translated for Tiya Miles by Del-Louise Moyer, 2014.
. Meldrum: Cangany, _Frontier Seaport_ , 29. Land: "The Tucker Story," Highlights from the Harrison Township Historical Commission's First Educational Presentation: The Legacy of William Tucker," April 27, 1994. Land and Virginia slaves as the Denisons: Robert F. Eldredge, _Past and Present of Macomb County, Michigan_ (Chicago: S. J. Clarke Publishing Co., 1905), 626–27. Location on river: Zeisberger Diary, Vol. 1, Oct. 1, 1784, p. 203. Bride and slaves: "Tucker, William, House," MI State Historic Preservation Objects, www.mcgi.state.mi.us/hso/sites/9541.htm. Accessed January 16, 2013.
. Zeisberger Diary, Vol. 1, Aug. 9, 1783, p. 160; vol. 2, Sun July 29, 1791, p. 186, Sun Aug. 7, 1791, p. 206.
. _Denison et al v. Catherine Tucker_ , in William Wirt Blume, ed., _Transactions of the Supreme Court of the Territory of Michigan, 1805–1814_ , Vol. II (Ann Arbor: University of Michigan Press, 1935), 133–136. Isabella E. Swan, _Lisette_ (Grosse Ile, MI: Published by the Author, 1965), 4.
. Swan, _Lisette_ , 3.
. No record that I was able to identify indicates Hannah Denison's place of birth. Because she was moved through French and Indian circles, it seems likely that she was born in or obtained from Montreal or Quebec, where most slaves in northern New France were held. Within these two cities, Marcel Trudel found a fairly even number of black slaves, who made up 35.9 percent and 39.5 percent of the populations, respectively. Trudel, _Canada's Forgotten_ , 257.
. Swan, _Lisette_ , 4 note 6. Mark McPherson, "Lisette's Legacy of Slavery" (second of a five part series), _Michigan Chronicle_ , February 3, 1999. File B/Negroes—Forth, Elizabeth Denison, Reading Room, DPL. Elizabeth Denison Forth's Elmwood Cemetery record gives her birth place as Virginia. This is likely an error dating back to county histories that said William Tucker brought a slave family with him from Virginia. This cemetery record also states that Forth died at age 114, another likely error. R. C. Simpson, To Whom It May Concern, Elmwood Cemetery, File B/Negroes—Forth, Elizabeth Denison, Reading Room, DPL.
. "The Dennison DNA Project," <http://www.johnbrobb.com/JBR-DEN-1.htm>. Accessed September 13, 2016. "Denniston/Dennison/Denison Homepage," <http://freepages.genealogy.rootsweb.ancestry.com/~vadennison>. Accessed September 13, 2016.
. Mark McPherson, "Lisette's Legacy of Slavery," (second of a five part series) _Michigan Chronicle_ , February 3, 1999. File B/Negroes—Forth, Elizabeth Denison, Reading Room, DPL.
. Harrow Papers, Journal and Letter Book, June 24, 1798, BHC, DPL.
. Chippewa use and defense of land: Zeisberger Diary, Vol. 1, 1782, pp. 91, 122, 184; Nov. 1784, p. 207; Jan. 1785, p. 217; Jan. 1786, p. 256; Ford, "Moravian Settlement," 6.
. Winter and famine: Zeisberger Diary, Vol. 1, 1784, pp. 183, 203, 211; 1787, p. 353, 1788, p. 451; 1789, p. 47. Pestilence: Zeisberger Diary, Vol. 1, 1789, pp. 57–58.
. Zeisberger Diary, Vol. 2, 1791, p. 217; Nov. 1793, pp. 329–31.
. Dowd, _Spirited_ , 113.
. New era and empire creation quotations: Calloway, _American Revolution_ , xv.
. Quoted from title of Karl S. Hele, ed., _Lines Drawn upon the Water: First Nations and the Great Lakes Borders and Borderlands_ (Waterloo, Ontario: Wilfrid Laurier University Press, 2008).
. Zeisberger Diary, Vol. 2, 1796, p. 461.
. The Jay Treaty, November 19, 1794, The Avalon Project, Avalon.aw.yale.edu, Article 2.
. The Jay Treaty, November 19, 1794, The Avalon Project, Avalon.aw.yale.edu, Article 2. Gorsuch, "Midwest Territorial Courts," 15, 25, 34.
. Martha S. Jones, "Time, Space, and Jurisdiction in Atlantic World Slavery: The Volunbrun Household in Gradual Emancipation New York," _Law and History Review_ 29:4, Law, Slavery, and Justice: A Special Issue (November 2011): 1031–60, 1034.
. Christopher Phillips, _The Rivers Ran Backward: The Civil War and the Remaking of the American Middle Border_ (New York: Oxford University Press, 2016), 6, 10. Phillips locates his slaveholding ancestors in Kentucky.
. 1773 Detroit Census, September 22, 1773, _Michigan Pioneer and Historical Collection, 1876–1886_ , Vol. 9 (Lansing: Pioneer Society of the State of Michigan), 649; Russell, ed., _Michigan Censuses_ , 1782, 49–56, 1796, 59–67; Ste. Anne's Records, BHC.
. Christian Crouch establishes this point about the racial makeup of slaves changing in Detroit with the influx of Anglo settlers. Christian Crouch, "The Black City: African and Indian Exchange in Pontiac's Detroit," revision of Christian Crouch, "The Black City: Detroit and the Northeast Borderlands through African Eyes in the Era of 'Pontiac's War,'" paper presented at The War Called Pontiac's conference, Philadelphia, April 2013, cited by permission of the author, 2, 29. Marcel Trudel's sums for the number of slaves held in Detroit are larger than mine overall. In a chart that breaks down the number of slaves in the province of Quebec (the borders of which changed over time) by city, he lists for Detroit 523 Indian slaves and 127 black slaves for a total of 650 slaves; Trudel, _Canada's Forgotten_ , 83, 75. Unfortunately, his incredibly instructive chart does not indicate exactly which sources he drew from to arrive at these totals for Detroit. My highest total for the enslaved population in Detroit is closer to 300. I attribute this variance to a number of factors. First, Trudel looks at a time span of 1629–1834, Second, he includes a wide range of French Canadian archival documents that I did not review. He counted each mention of a slave in these documents to arrive at a total number of 4,200 slaves in Quebec and the subsequent town breakdown. Third, Detroit's general population numbers shift depending upon what boundaries are drawn (inside the fort walls, or inside as well as outside; on one side of the river, or on both sides), making stable and transparent enumeration a challenge. While I did keep a running count of the number of enslaved people who appeared in Detroit-based slaveholders' manuscript records, I did not add these numbers to my totals. I relied on Ste. Anne's Church records and census records as the main sources for my sums and used them to corroborate each other. The numbers on the Ste. Anne's register ran very close to the census numbers. Adding the church, census, and manuscript record numbers together would have brought me to an overall figure closer to Trudel's at 600, but I strove to avoid double counting in a situation in which many enslaved people went unnamed. Readers may therefore take my figures as conservative estimates. For additional sources that offer population figures for Detroit's enslaved, see David M. Katzman, "Black Slavery in Michigan," _Midcontinent American Studies Journal_ 11: 2 (fall 1970): 56–66, 62, 65. William Renwick Riddell, "The Slave in Upper Canada," _Journal of the American Institute of Criminal Law and Criminology_ 14:2 (August 1923): 249–278, 251, note 10.
. The outcome of Francois's case is not recorded. Askin Papers, Vol. I, 399–401. Ford, "Moravian Settlement" / "Old Moravian Mission," 114–15.
. Zeisberger Diary, Vol. 2, 1794, p. 380.
. Madelaine Askin to John Askin, March 4, 1798, Askin Papers, Vol. II, 132–33. Alexander Harrow Papers, Feb. 13, 1797, Feb. 14, 1797, Feb. 28, 1797, March 27, 1797, July 22, 1797, June 1, 1798, March 25, 1799, BHC, DPL.
. Kenneth W. Porter, "Negroes and the Fur Trade," _Minnesota History_ 15:4 (Dec. 1934) 421–33, 424. John Askin Estate Inventory - Detroit 1787, Jan. 1, 1787, "Debts due Me taken from . . . Book No. 11," John Askin Papers, Burton Historical Collection, DPL.
. Record Book of Macomb Estate, Macomb Family Papers, R2:1796, BHC, DPL. Bet and her sons do not seem to have ended up with Captain Harrow, who tried to buy them in the same year. F. Clever Bald, _Detroit's First American Decade, 1796 to 1805_ (Ann Arbor: University of Michigan Press, 1948), 31.
. Robert B. Ross, _The Early Bench and Bar of Detroit from 1805 to the End of 1850_ (Detroit: Published by Richard P. Joy and Clarence M. Burton, 1907), 137.
. As quoted in Ross, _Early Bench_ , 139.
. May ledger book, James May Papers, D3: 1792–98, BHC, DPL; May Daybook, D3: 1798–1804, BHC, DPL. This may have been a different Pompey than the man Askin bought in 1775.
. As quoted in Ross, _Early Bench_ , 139.
. John Askin Papers, Vol. II, 358.
. F. Clever Bald, _Detroit's First American Decade, 1796 to 1805_ (Ann Arbor: University of Michigan Press, 1948), 187, 134.
. Askin Papers, Vol. II, 358–59.
. Foot injury: Letterbooks of Phyn and Ellice, April 19, 1775, BHS. Toon's death: Askin Papers, diary, v. 1, 50–58. Clinging to rock, frozen to death: Moravian Diary, Thames River, Ontario, June 3, 1807, December 1, 1800, translated by Del-Louise Moyer. These last two references are to enslaved men owned by Matthew Elliott.
. Askin Papers, Vol. II, 563.
. Bald, _Detroit's First_ , 75, 106, 151.
. John Askin to Jam & McGill, May 15, 1800, Askin Papers, Vol. II, 293. Also quoted in Bald, _Detroit's First_ , 165–66.
. John McCall was the printer in Detroit in 1796. According to Clever Bald, citing Silas Farmer, McCall was likely using a printing press formerly owned by William Macomb. Bald, _Detroit's First_ , 93, fn 6.
. As quoted in Ross, _Early Bench_ , 138.
. Frederick A. Ogg, _The Old Northwest: A Chronicle of the Ohio Valley and Beyond_ (Toronto: Glasgow, Brook & Co.; Textbook Edition, Yale University Press, 1919), 99, 134–35. Brian Leigh Dunnigan, "The War of 1812 in The Old Northwest: An Introduction to the Bicentennial Edition, in Alec R. Gilpin, ed., _The War of 1812 in The Old Northwest_ (1958; reprint, East Lansing: Michigan State University Press, 2012), viii. Bald, _Detroit's First_ , 138, 132. R.W. Dick Phillips, _Arthur St. Clair II: The Invisible Patriot_ (Bloomington, IN: iUniverse LLC), 39.
. As quoted in Bald, _Detroit's First_ , 132; Bald, _Detroit's First_ , 139.
. Ogg, _The Old Northwest_ , 78.
. Michigan Censuses, 1796 Wayne County, 74. This figure is an undercount. Hundreds more residents lived in settlements stretching along the river for miles, making a total of 2,053. In addition, one hundred absent men were estimated by the census takers to have been missed.
. As quoted in Bald, _Detroit's First_ , 140.
. As quoted in Bald, _Detroit's First_ , 140. For a detailed account of the tobacco spitting incident and Bates's view of French women, see Gitlin, _Bourgeois Frontier_ , 147–148. For more on French elite adaptation to American expansion into former French territories, see Eberhard L. Faber, _Building on the Land of Dreams: New Orleans and the Transformation of Early America_ (Princeton, NJ: Princeton University Press, 2016).
. As quoted in Bald, _Detroit's First_ , 141.
. Bald, Detroit's First, 161, 169. Clarence M. Burton, _History of Detroit, 1780–1850, Financial and Commercial_ (Detroit, 1917), 43.
. Notices in French & English: Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 1802–1805 (Detroit: Printed under the authority of the Common Council of Detroit with an Introduction by C.M. Burton, Historiographer, Burton Historical Collection, 1922), 44. Mail and news: Bald, _Detroit's First_ , 92–93. Mail: Observations relative to Wayne County by Sol. Sibley, for the perusal of Capt W. H. Harrison, 1800, Solomon Sibley Papers, BHC, DPL; Geo Wallace to James Henry, October 1802, Sibley Papers, BHC, DPL. Sibley's views: Observations relative to Wayne County by Sol. Sibley, for the perusal of Capt W. H. Harrison, 1800, Solomon Sibley Papers, BHC, DPL.
. Bald, _Detroit's First_ , 189.
. Burton, _History of Detroit_ , 43.
. John Askin to Robert Hamilton, April 8, 1802, Askin Papers, vol. II, 372–74.
. Solomon Sibley to S. C. Vance, Aug. 20, 1803, Sibley Papers, BHC, DPL.
. Quoted in Finkelman, "Evading the Ordinance," 30. Onuf, _Statehood and Union_ , 117.
. Finkelman, "Evading the Ordinance," 22, 23, 24, 36. M. Scott Heerman, "In a State of Slavery: Black Servitude in Illinois, 1800–1830," _Early American Studies: An Interdisciplinary Journal_ 14:1 (Winter 2016): 114–39, 117, 118. Allison Mileo Gorsuch, "To Indent Oneself: Ownership, Contracts, and Consent in Antebellum Illinois," in Jean Allain, ed., _The Legal Understanding of Slavery: From the Historical to the Contemporary_ (New York: Oxford University Press, 2012), 134, 137. Kinds of labor: Finkelman, 42; Heerman, 127, 129, 130.
. Henry Hastings Sibley as slaveholder: Walt Bachman, _Northern Slave, Black Dakota: The Life and Times of Joseph Godfrey_ (Bloomington, MN: Pond Dakota Press, Pond Dakota Heritage Society, 2013), 19, 20, 59, 198 n. 41. For more on slavery in Minnesota, see Christopher P. Lehman, _Slavery in the Upper Mississippi Valley, 1787-1865_ (Jefferson, NC: McFarland & Company Inc., 2011), 114–141. "Governors of Minnesota," Minnesota Historical Society, <http://collections.mnhs.org/governors/index.php/10003986>. "House Divided," Dickinson College, <http://hd.housedivided.dickinson.edu/node/39873>. Both accessed July 29, 2016.
. Donna Valley Russell, ed., _Michigan Censuses 1710–1830_ , 1782 (Detroit: Detroit Society for Genealogical Research, Inc., 1982), 49–57.
. The Declaration of Independence, The Charters of Freedom, www.archives.gov/exhibits/charters/declaration_transcript.html. Accessed April 7, 2015.
. Macomb County is formally named for Alexander Macomb, son of Alexander Macomb (William Macomb's brother) and a War of 1812 veteran and Army commander in chief from 1828 to 1841. Macomb was born in 1782 in Detroit at the height of the city's slaveholding period. Like his uncle William, Alexander's father owned slaves and had seven enslaved people in his household the year the younger Alexander was born. Alexander Macomb likely inherited human property. Russell, ed., _Michigan Censuses_ (Detroit Census of 1782), 54. Governor Lewis Cass established the name for Michigan's third county in 1818. www.michmarkers.com/startup.asp?startpage=S0418.htm. Accessed May 30, 2016.
**4: The Winds of Change (1802–1807)**
. Riddell, _Michigan Under British Rule_ , 19–20. Northwest Ordinance, July 13, 1787; (National Archives Microfilm Publication M332, roll 9); Northwest Ordinance (1787), www.ourdocuments.gov. Accessed May 5, 2015. Miscellaneous Papers of the Continental Congress, 1774–89; Records of the Continental and Confederation Congresses and the Constitutional Convention, 1774–89, Record Group 360; National Archives; https://ourdocuments.gov/doc.php?flash=true&doc=8. Accessed June 2, 2016. Duffey, "Northwest Ordinance," 956.
. Adelaide's elder sisters were Thérèse, Ellen, and Archange. Archange Askin's husband was Captain David Meredith. Askin Papers, Vol. I, 13–16; Fashion: Cangany, _Frontier Seaport_ , 49; Education: Jennifer Dionne, "Franco-Ontariens avant la lettre? La correspendence de la famille Askin" (PhD. Diss., University of Ottawa, 2007), 46–47.
. Solomon Sibley to Samuel Vance October 1, 1802, Samuel C. Vance Papers, Manuscripts and Visual Collections Department, William Henry Smith Memorial Library, Indiana Historical Society, Indianapolis, IN.
. Wedding: Bald, _Detroit's First_ , 19. China: Elijah Brush to Hugh Martin, February 25, 1802, Sibley Papers, BHC, DPL; also quoted in Bald, _Detroit's First_ , 191. Silver: E Brush to Robinson and Martin, July 28, 1803; also quoted in Bald, _Detroit's First_ , 215. Elijah Brush to Martin & Robinson, July 11, 1802, Sibley Papers, BHC, DPL. Summer cloak, bonnet, shoes: E. Brush to Robinson & Martin, February 9, 1804, Sibley Papers, BHC, DBL, also quoted in Bald, _Detroit's First_ , 225. Men's clothing: Brush to Martin & Robinson, July 11, 1802, Sibley Papers, BHC, DPL; Beaver hat: Elijah Brush to Robinson & Martin, Sibley Papers Aug 7, 1802, BHC, DPL. Catherine Cangany first makes this point that the Brushes ordered items from New York while most Detroiters could not; Cangany, _Frontier Seaport_ , 45–46.
. Bald, _Detroit's First_ , 215, 225.
. John Askin to Alexander Henry, February 27, 1802, Askin Papers, Vol. II, 371.
. John Askin to Robert Hamilton, April 8, 1802, Askin Papers, Vol. II, 372–74.
. Askin to Hamilton, April 8, 1802, Askin Papers, Vol. II, 372–74.
. John Askin to Isaac Todd, April 8, 1802, Askin Papers, BHC, DPL.
. John Askin to Robert Hamilton, April 8, 1802, Askin Papers, Vol. II, 372–74; Bald, _Detroit's First_ , 197.
. Elijah Brush to John Askin, March 22, 1805, Askin Papers, Vol. II, 459–60.
. Bald, _Detroit's First_ , 197. Askin to James and McGill, April 8, 1802; Taxes in 1802, Bald, _Detroit's First_ , 193–94. Brush obtained title to the Askin farm in 1806. Sale of Brush Farm, Askin Papers, Vol. II, pp. 530–32; Jacobson, _Detroit River Connections_ , 60–61.
. John Askin Jr. to John Askin, November 11, 1807, Askin Papers Vol. II, pp. 583–84; Bald, _Detroit's First_ , 233.
. Afua Cooper, "The Fluid Frontier: Blacks and the Detroit River Region. A Focus on Henry Bibb," _Canadian Review of American Studies_ 30:2 (2000): 130, 133.
. As quoted in Reginald Horsman, _Matthew Elliott, British Indian Agent_ (Detroit: Wayne State University Press, 1964), 46; Shawnee wife: Horsman, 144; quoted in Horsman, 48.
. Quoted in "Matthew Elliott Essex County" (Toronto: York University, Harriet Tubman Institute, 2012), 4, 5; whipping and shackles: "Matthew Elliott," 5.
. William Henry Smith, ed., _The St. Clair Papers. The Life and Public Services of Arthur St. Clair_ , Vol. II (Cincinnati: Robert Clarke & Co., 1882), 318–19. For a critique of the Northwest Ordinance's effect on black and Native populations, see Sakina Mariam Hughes, "Under One Big Tent: American Indians, African Americans and the Circus World of Nineteenth-Century America" (Ph.D. diss., Michigan State University, 2012), 52–55.
. Martha S. Jones, "Time, Space, and Jurisdiction ln Atlantic World Slavery: The Volunbrun Household in Gradual Emancipation New York," _Law and History Review_ 29:4, Law, Slavery, and Justice: A Special Issue (November 2011): 1031–60, 1034.
. Askin Papers, Vol. II, 357–58. Simon Campaue Complaint, Sibley Papers, March 25, 1802, BHC, DPL. Jas. Henry to any or either Constables of the County of Wayne, July 3, 1802, Sibley Papers, BHC, DPL. In the Case of Toby, a Panis Man, in William Wirt Blume, ed., _Transactions of the Supreme Court of the Territory of Michigan, 1805–1814_ Vol. II (Ann Arbor: The University of Michigan Press, 1935), 404, 405. Mary Abbott, Complaint, June 1802, Sibley Papers, BHC, DPL.
. Elizabeth Audrain married to Robert Abbott: Burton, _History of Detroit_ , 20. Abbot v. Jones, September 28, 1807, in Blume, ed., _Supreme Court of Michigan_ Vol. II, 23–28.
. Abbot v. Jones, September 28, 1807, in Blume, ed., _Supreme Court of Michigan_ Vol. II, 23–28.
. For unfree people's negotiation of indenture contracts, see Heerman, "In a State of Slavery." For enslaved people's and free blacks' use of law, see Laura F. Edwards, "Status without Rights: African Americans and the Tangled History of Law and Governance in the Nineteenth-Century U.S. South," _American Historical Review_ 112:2 (2007): 365–93; Ariela Gross and Alejandro De La Fuente, "Slaves, Free Blacks, and Race in the Legal Regimes of Cuba, Louisiana, and Virginia: A Comparison," _North Carolina Law Review_ 91:5 (June 2013): 1769–56; Ariela J. Gross, _What Blood Won't Tell: A History of Race on Trial in America_ (Cambridge, MA: Harvard University Press, 2008); Martha S. Jones, _Birthright Citizens: A History of Race and Rights in Antebellum America_ (New York: Cambridge University Press, 2017).
. A.J. Hull to Jaques Lassell, June 5, 1805, Sibley Papers, BHC, DPL. Antoine and Anna Smith are also referred to as Anthony and Anne Smith in the records.
. A.J. Hull to Jaques Lassell, June 5, 1805, Sibley Papers, BHC, DPL.
. Ste. Anne Records, October 15, 1803, June 22, 1816. The record referencing Angelique's birth says she was born to an "unknown father." This may have been an oversight in the record, or Antoine may no longer have been with his family.
. Alexander Harrow to Robert Taylor his servant, conditional manumission of said Rob, July 2, 1802, Sibley Papers, BHC, DPL.
. Ransom to Grant, August 7, 1802, Sibley Papers, BHC, DPL. John Reed: August 13, 1803, August 19, 1803, Sibley Papers, BHC, DPL. James May was appointed U.S. marshal from August to November 1806; Farmer History of Detroit, 176.
. S. Sibley to Col. Grant, August 19, 1803, Sibley Papers, BHC, DPL.
. Christian Crouch makes a similar point, arguing that enslaved blacks may have learned the terrain and how to negotiate it politically from the example of native people. Christian Crouch, "The Black City: African and Indian Exchange in Pontiac's Detroit," revision of Christian Crouch, "The Black City: Detroit and the Northeast Borderlands through African Eyes in the Era of 'Pontiac's War,'" paper presented at The War Called Pontiac's conference, Philadelphia, April 2013, cited by permission of the author.
. Charles St. Bernard, Indenture, October 4, 1799, Berthelet Papers, Burton Historical Collection, Detroit Public Library.
. Heerman, "State of Slavery," 117. "Bob's Indenture," 1802, William Woodbridge Papers, 1763–1919, BHC, DPL. Preserved servitude contracts are few and far between in Detroit and most often identify poor whites and free Native American workers, but some of these records might be further evidence of the experience of enslaved people. For another Detroit indentured servant record, see Matt Henry, Justice of the Peace, July 31, 1803, Solomon Sibley Papers, BHC, DPL.
. David Maney to Eliabeth Burnett, September 17, 1802, Sibley Papers, BHC, DPL. James May Papers, D3, 1792–98, Pomp: September 6, 1795, Black Betty: August 3, 1797, BHC, DPL. May Papers, D3: 1798–1804 Daybook, Burnett: August 27, 1800, La Leavre: December 3, 1800, Black Patty: April 10, 1801, BHC, DPL. Black Betty and Black Patty's names are similar enough that they might have been the same person. May's daybook also includes a payment reference for 1793: "cash lent him to pay Baby's man," Vincent Laframboise: June 1793, May Papers BHC, DPL. Macomb Papers, Ledger, August 27, Sept 3, September 10 1804, January 6, 1805, April 9, 1805.
. Askin Papers, Vol. II, pp. 388–89.
. Diary of the Reconnoitering Trip Made by Brothers Luckenbach and Haven, Accompanied by the Indian Brother Andreas, at St. Mary's River, the Southern Arm of Miami, which Empties into Lake Erie, August 29, 1808 (B157F11 08-29-1808), Moravian Archives, Bethlehem, PA, translated for Tiya Miles by Del-Louise Moyer, 2015. Tanner, _Atlas of Great Lakes Indian History_ , Maps 17, 18 pp. 85–88. Joseph Badger, A Memoir of Rev. Joseph Badger (Hudson, OH: Sawyer, Ingersoll & Co., 1851; Niles, OH: Niles Historical Society, 1997, 100, 130–31. "The Journal of Benjamin Larkin, 1794–1820," in William Warren Sweet, ed., _Religion on the American Frontier, 1783–1840: The Methodists: A Collection of Source Materials_ , Vol. 4 (Chicago: University of Chicago Press, 1946), 241. Historian William Hart places the contemporary location of Negrotown at: "the intersections of County Routes 37, 29, and 40 just west of Belle Vernon, Ohio, and north of Upper Sandusky. Bill Hart, "Sources to 'Negrotown,' Ohio, 1800–1843," unpublished compilation, 2016.
. Diary of Fairfield Mission, Thames River, Ontario, Canada, 1792–1813, July 4 1797, Moravian Archives, Bethlehem, PA, translated for Tiya Miles by Del-Louise Moyer.
. Kenneth W. Porter, "Negroes and the Fur Trade," _Minnesota History_ 15:4 (Dec. 1934), 421–33, 424. Bill Hart, "Sources to 'Negrotown,' Ohio, 1800–1843," unpublished compilation, 2016.
. Bill Hart, "Sources to 'Negrotown,' Ohio, 1800–1843," unpublished compilation, 2016.
. Bill Hart, Conversation with Tiya Miles about Negro Town, June 7, 2016, Middlebury, VT. For more on black-Wyandot relations in Ohio, see Sakina M. Hughes, "The Community Became an Almost Civilized and Christian One: John Stewart's Mission to the Wyandots and Religious Colonialism as African American Racial Uplift," _NAIS: Journal of the Native American and Indigenous Studies Association_ 3:1 (2016): 24–45.
. Askin Papers, Vol. II, 561–63. Nobbin was recaptured and held at the Askin estate on May's behalf. May proclaimed that Nobbin was likely afraid of being whipped as punishment. In 1813, John Askin bemoaned the escape of his enslaved woman, Madelaine; Askin Papers, Vol. II, 772.
. Escapes seem to increase after 1796; however, record keeping improves as well at this moment due to the activity of the court. It is therefore possible that the number of escapes remained nearly constant but that evidence becomes more plentiful because of court recording.
. As quoted in Judy Jacobson, _Detroit River Connections: Historiographical and Biographical Sketches of the Eastern Great Lakes Border Region_ (Baltimore: Clearfield Company, 1994), 6.1
. Bald, _Detroit's First_ , 190; Bald, _Great Fire_ , 4–5.
. Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 1802–1805 (Detroit: Printed under the authority of the Common Council of Detroit with an Introduction by C.M. Burton, Historiographer, Burton Historical Collection, 1922), 41.
. An Act for the Relief and Settlement of the Poor, in _Laws of the Territory of Michigan: Laws Adopted by the Governor and Judges_ , Vol. 1 (Lansing: W. S. George & Co Printers to the State, 1871), 4 vols. University of Michigan Law Library, Source library: Yale Law Library, _The Making of Modern Law: Primary Sources_ , 602. An Act to Regulate Blacks and Mulattoes, and to Punish the Kidnapping of Such Persons, in _Laws of the Territory of Michigan_ , 634. The earliest law addressing indentured servitude in American Detroit was a Michigan Territory law passed in 1809: An Act for Support of the Poor stipulated that servants who had completed their contracts could become lawful settlers but that bringing "paupers" into the territory would be penalized. In 1827, a later territorial law, An Act for the Relief and Settlement of the Poor, stipulated that each town had to maintain its own poor and that individuals who had completed their indentures in the territory were legal settlers. Also in 1827, a more detailed Act Concerning Apprentices and Servants was passed, which assumed voluntary servitude for all servants, required parental or guardian approval for minors, set an age limit at twenty-one years for length of childhood indenture and noted that indentures might have varying specific durations, provided for the jailing of servants who reneged on their duties, and allowed for complaints to be made about mistreatment by masters. _Laws of the Territory of Michigan: Laws Adopted by the Governor and Judges_. Vol. 2. (Lansing: W. S. George & Co Printers to the State, 1874), pp. 40, 507–508, 595. None of these laws make mention of race. For more on Thornton and Lucie (also Rutha) Blackburn, see: Karolyn Smardz Frost, "Forging Transnational Networks for Freedom: From the War of 1812 to the Blackburn Riots of 1833," in Karolyn Smardz Frost and Veta Smith Tucker, eds., _A Fluid Frontier: Slavery, Resistance, and the Underground Railroad in the Detroit River Borderland_ (Detroit: Wayne State University Press, 2016), 43–66; Norman McRae, "Crossing the Detroit River to Find Freedom," _Michigan History_ Vol. 67, No. 2 (March/April 1983): 35–39.
. Bald, _Great Fire_ , 10–11. By adopting a comprehensive fire prevention system, Detroit was borrowing from cities like Philadelphia, which began adopting similar codes in the early 1700s. Arwen P. Mohun, _Risk: Negotiating Safety in American Society_ (Baltimore: Johns Hopkins University Press, 2013), 12, 17, 24.
. Bald, _Detroit's First_ , 197; Bald, _Great Fire_ , 10.
. Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 1802–1805 (Detroit: Printed under the authority of the Common Council of Detroit with an Introduction by C.M. Burton, Historiographer, Burton Historical Collection, 1922), 37–38, 59. Henry Berthelet applied for U.S. citizenship and took the oath in Detroit in 1807; In the Matter of the application of Henry Berthelet, in William Wirt Blume, ed., _Transactions of the Supreme Court of the Territory of Michigan, 1805–1814_ , Vol. I (Ann Arbor: The University of Michigan Press, 1935), 404.
. The United States vs. Margaret White, September 4, 1800, Woodbridge Papers, BHC, DPL. White pled not guilty. Rashauna Johnson, _Slavery's Metropolis: Unfree Labor in New Orleans During the Age of Revolutions_ (New York: Cambridge University Press, 2016), 115–26.
. Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 43.
. J. May meat and trash: Ross, _Early Bench_ , 139. Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 44.
. Corporation of the Town of Detroit: Act of Incorporation and Journal of the Board of Trustees, 37.
. Ste. Anne Church Records, BHL, UM.
. 1802 taxes: Bald, _Detroit's First_ , 194; the highest homes taxed in 1802 were owned by Richard Donovan and John Dodemead. 1805 taxes: Other high taxpayers included Solomon Sibley and father Gabriel Richard. R. N. Drake, "Sketch of Judge May: The Grandfather of Mrs. Seymour," From Drake Scrapbook in Possession of R.N. Drake, R.N. Drake, Seattle, WA, from Scrapbook of Drake loaned to C.M.B., James May Papers, Wallet 1, BHC, DPL. The grandson of an original French Detroit settler and slaveholder, Joseph Campau likely inherited slaves. Certainly, he owned at least two Native slaves, Jacques and Thomas, who both died in 1805. Ste. Anne Church Records, BHL, UM.
. Macomb Ledger, Macomb Estate Papers, BHC, DPL, 19–20.
. Bald, _Detroit's First_ , 235. Bald notes that the western boundary of Michigan Territory differed slightly from the previous boundary of Wayne County. Instead of extending to the western edge of Lake Michigan, Michigan Territory's border was drawn through the middle of the lake.
. Elijah Brush and Thomas Jones were appointed fire inspectors by the town trustees in 1805; Bald, _Detroit's First_ , 237. Brush was appointed lieutenant colonel of Legionary Corps in the Militia of the Territory of Michigan; William Hull, to all to whom these presents shall come, William Woodbridge Papers, September 12, 1805, BHC, DPL.
. E. Brush to Robison & Martin, October 6, 1803, Sibley Papers, BHC, DPL.
. Bald, _Detroit's First_ , 240.
. Robert Munro letter, June 14, 1805, as quoted in Farmer, _History of Detroit_ , 490.
. Robert Munro letter, June 14, 1805, as quoted in Farmer, _History of Detroit_ , 490–91.
. Bald, _Great Fire_ , 12–14; Bald, _Detroit's First_ , 239–40; Jean Dilhet, _Beginnings of the Catholic Church in the United States_ , translated and annotated by Patrick W. Browne (Washington, D.C.: The Salve Regina Press, 1922), 114; Robert Munro letter, June 14, 1805, as quoted in Farmer, _History of Detroit_ , 491.
. Munro to Harrison, June 14, 1805, Logan Esarey, ed., _Governors Messages and Letters: Messages and Letters of William Henry Harrison_ , Vol. 1, 1800–1811 (Indianapolis: Indiana Historical Commission, 1922), 136–37; also quoted in Farmer, _History of Detroit_ , 490.
. Bald, _Great Fire_ , 13–14.
. Munro to Harrison, June 14, 1805, Logan Esarey, ed., _Governors Messages_ , 136–37; also quoted in Farmer, _History of Detroit_ , 490.
. As quoted in Bald, _Great Fire_ , 14.
. Bald, _Detroit's First_ , 242. While Jefferson attempted to appoint three judges as stipulated in the plan for Michigan Territory, two men turned down the third open post, resulting in only Woodward and Bates being present after the fire. Bald, _Detroit's First_ , 242, footnote 5.
. Jefferson to John Woodward, Jefferson Papers, Series 1, Vol. 4, Library of Congress, Washington, D.C.
. Notes on My Visit to Mr. Jefferson, 1796, Augustus Brevoot Woodward Papers, BHC, DPL.
. Notes on My Visit to Mr. Jefferson, 1796, Augustus Brevoot Woodward Papers, BHC, DPL.
. "Essay on Habit," 1794, Box 1 Correspondence 1782–94, Augustus Brevoot Woodward Papers, BHC, DPL. Woodward's notes cite at least two cases involving blacks during his Washington years. In one case he played a role in taking depositions from a free black woman named Milly Smith who was married to an enslaved man and attempting to free her children; Augustus Woodward Papers, Box 2: 1795–1805, April 8, 1803, BHC, DPL. The other case involved an indentured "mulatto woman" named Celeste about whom Woodward had information requested by her employer; Pollock to Woodward, April 23, 1804, Correspondence with Oliver Pollock Folder, 1780–1813, BHC, DPL. Thomas Jefferson, _Notes on the State of Virginia_ (Philadelphia: Prichard and Hall, 1788).
. A.B. Woodward to Thomas Jefferson, October 20, 1803, Jefferson Papers, Series 2, vol. 88, Woodward Papers, BHC, DPL.
. Bald, _Detroit's First_ , 242. Woodward oath of fidelity, September 12, 1805, Woodward Papers, BHC, DPL.
. Woodward's was the strongest voice on the Supreme Court by far. Justice Frederick Bates resigned in 1806, leaving his seat vacant until 1808 when he was replaced by Justice James Witherell. Justice John Griffin, the third initial appointee, has been described as a fairly passive supporter of Woodward's leadership. Woodward served as chief justice from 1805 to 1823. Burton, "Augustus Brevoort Woodward," 638, 640, 646. Edward J. Littlejohn, "Slaves, Judge Woodward, and the Supreme Court of the Michigan Territory," _Michigan Bar Journal_ (July 2015): 22–25, 22, 23. The Woodward Code of Laws, created in 1805, was republished in _Laws of the Territory of Michigan: Laws Adopted by the Governor and Judges_. Vol. 1. Lansing, 1871. 4 vols. _The Making of Modern Law: Primary Sources_.
. Littlejohn, "Slaves," 22–25, 23.
. Bald, _Detroit's First_ , 241–42.
. Farmer, _History of Detroit_ , 490; Girardin, baker, as slaveholder: Ste. Anne Church Records, January 1, 1786.
. Bald, _Great Fire_ , 15; Bald, _Detroit's First_ , 242.
. William Hull to James Madison, August 3, 1805, as quoted in Farmer, _History of Detroit_ , 490.
. David Braithwaite, "Brigadier General William Hull: His Military and Political Story," _Hull Family Association Journal_ 15:1 (Autumn 2004): 96–99, 97.
. Mr. Gentle as quoted in Farmer, _History of Detroit_ , 491; Bald, _Detroit's First_ , 241.
. Bald, _Detroit's First_ , 243.
. See Naomi Klein, _The Shock Doctrine: The Rise of Disaster Capitalism_ (New York: Picador, 2007).
. Bald, _Great Fire_ , 12. Elijah Brush, James May, and John Anderson to the President of the United States, 1806, LMS/Alexander D. Fraser Papers, 1800–1816, BHC, DPL.
. Bald, _Great Fire_ , 16. Kenneth R. Fletcher, "A Brief History of Pierre L'Enfant and Washington D.C.," Smithsonian.com, April 30, 2008. Accessed May 13, 2016.
. Topica, August 16 & 17, 1792, Woodward Papers, BHC, DPL.
. Notes: Burke's Reflections on the French Revolution, May 24, 1794, Woodward Papers, BHC, DPL; To the President of the United States of America, July 4, 1798, Woodward Papers, BHC, DPL.
. Copy of Philip Freneau, "On the American and French Revolutions," January 1, 1790, Woodward Papers, BHC, DPL.
. "Between a Patriot & a British," July 29, 1796, Woodward Papers, BHC, DPL.
. May's home, located on the corner of Jefferson Ave. and Cass St. May's Creek, was later closed off and incorporated into the city's sewer system. Ross, _Early Bench_ , 140–42. Farmer, _History of Detroit_ , 481.
. Mr. Gentle, Statements, as quoted in Farmer, _History of Detroit_ , 491.
. William Tucker Probate, reel 1, Wayne County Probates, State Library of Michigan, Lansing, MI. In his decision of the _Denison v. Tucker_ case, Judge Woodward says British buying and selling of slaves is to be determined case by case.
. Tucker Probate, Wayne County Probates, State Library of Michigan.
. Denison et al v. Catherine Tucker, Writ of Habeas Corpus ad Subjiciendum, in William Wirt Blume, ed., _Transactions of the Supreme Court of the Territory of Michigan, 1805–1814_ , Vol. II (Ann Arbor: The University of Michigan Press, 1935), 133–36.
. _Denison v. Tucker_ , Blume, ed., _Supreme Court of Michigan_ Vol. II, 133–36.
. "The Brush Homestead in 1850," reproduced in Farmer, _History of Detroit_ , 378.
. Silas Farmer, _History of Detroit_ , 367, 374.
. Jacobson, _Detroit River_ , 60.
. Brush treasurer: Farmer, _History of Detroit_ , 89.
. Jacobson, _Detroit River_ , 60.
. While seamstresses did "piece work" sewing, dressmakers possessed a higher level of skill, and in a free labor economy, earned more pay; Angela P. Robbins, "Bridging the Old South and the New: Women in the Economic Transformation of the North Carolina Piedmont, 1865–1920" (Ph.D. diss., University of North Carolina Greensboro, 2010), p. 21. As quoted in Jacobson, _Detroit River_ , 61.
. VanderVelde, _Redemption Songs_ , 9. The records on this case do not include opinions or dissents by any other judge. The notes of Detroit archivist and historian Clarence Burton also indicate that Woodward was the sole decider in this case; Legal Notes, Clarence Burton Papers, DPL. Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, _Supreme Court of Michigan_ , ed., Blume, Vol. II, 216. Michigan's Dred Scott case quote: Reginald R. Larrie, _Makin' Free: African Americans in the Northwest Territory_ (Detroit: Blaine Ethridge Books, 1981), 6; a like phrase also quoted in Charlie Keller, "Detroit's First Black Militia," in Denver Brunsman, Joel Stone, and Douglas D. Fisher, eds., _Border Crossings: The Detroit River Region in the War of 1812_ (Detroit: Detroit Historical Society, 2012), 89. For more on the Dred and Harriet Scott case and an analysis that includes gender and the family, see Lea VanderVelde, _Mrs. Dred Scott: A Life on Slavery's Frontier_ (New York: Oxford University Press, 2009).
. As quoted in Littlejohn, "Slaves," 23.
. Littlejohn, "Slaves, 23; Charles Moore, "Augustus Brevoort Woodward—A Citizen of Two Cities," in The Committee on Publication and the Recording Secretary, Records of the Columbia Historical Society, vol. 4 (Washington D.C., 1901): 114–27, 126.
. Littlejohn, "Slaves," 22, 23; Moore, "Slave Law," 126; Burton, "Augustus Brevoort Woodward," MPHC, Vol. 29, 638–39.
. Quotations and mottos, Woodward Papers April 10, 1789 BHC, DPL.
. Woodward Papers April 10, 1789 BHC, DPL; Composition of 1793, On the qualities requisite for greatness, May 2 1793, Woodward Papers, BHC, DPL.
. _Laws of the Territory of Michigan: Laws Adopted by the Governor and Judges_ , Vol. 1. Lansing, 1871. 4 vols. _The Making of Modern Law: Primary Sources_ , 10.
. Paul D. Halliday, _Habeas Corpus: From England to Empire_ (Cambridge, MA: Harvard University Press, 2010), 1–2, 101, 120, 174. Anthony Gregory, _The Power of Habeas Corpus in America: From the King's Prerogative to the War on Terror_ (Cambridge: Cambridge University Press, 2013), 78–80. As Lea VanderVelde has detailed, the first freedom suit decided in the Northwest Territory was brought by black Revolutionary War veteran, Peter McNelly. McNelly petitioned for the freedom of himself and his wife, Queen, in Vincennes, Indiana, in 1794; their suit also employed the writ of habeas corpus. Although the judge found in their favor, power plays among prominent white men led to Peter McNelly's kidnapping and coerced indenture and to Queen's disappearance. VanderVelde, _Redemption Songs_ , 24–37.
. Wilbert E. Moore, "Slave Law and the Social Structure," _Journal of Negro History_ 26:2 (April 1941): 171–202, 188.
. _Denison v. Tucker_ , in Blume, ed., _Supreme Court of Michigan_ , Vol. II, 133–36.
. Journal, in Blume, ed., _Supreme Court of of Michigan_ , Vol. I, 381.
. Journal, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 381. Woodward decision: Journal, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 387.
. In the Matter of Elizabeth Denison, James Denison, Scipio Denison, and Peter Denison junior, detained by Catherine Tucker, August–October 14, 1807, Oct. 1, 1807, Woodward Papers, BHC, DPL.
. Reading List, Sept 6, 1792, Woodward Papers, BHC, DPL.
. James Wood to Augustus Woodward, Aug. 18, 1807, Sandwich, Harris Hickman Papers, BHC, DPL. "An ACT to enable persons held in slavery, to sue for their freedom," June 27, 1807, Laws of the Territory of Louisiana, Missouri Digital Heritage, Missouri State Archives. Petitioners held the burden of proof in demonstrating that they were actually free and being held by force. <https://www.sos.mo.gov/archives/education/aahi/beforedredscott/1807FreedomStatute>. <https://www.sos.mo.gov/archives/education/aahi/beforedredscott/history_freedomsuits>. Accessed March 30, 2017.
. Woodward decision: Journal, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 386. As quoted in Littlejohn, "Slaves," 25.
. Syllabi of Decisions and Opinions, In the Matter of Elizabeth Denison, Et Al, September 26, 1807, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 319.
. McRae, "Crossing," 36.
. Pattinson Petition for return of slave Jenney, Woodward Papers, F: 1805–1807, BHC, DPL; Case 76, Pattinson's Affidavit, in Blume, ed., _Supreme Court of Michigan_ , Vol. II, 156. Littlejohn, "Slaves," 24; Norman McRae, "Crossing the River to Find Freedom," _Michigan History_ 67:2 (March/April 1983): 35–39, 36. In the Case of Toby, a Panis Man, in _Supreme Court of Michigan_ , Vol. II, 404, 405.
. Calendar of Cases, Case 76 In the Matter of Richard Pattinson, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 99–100; Syllabi of Decisions and Opinions, No. 76 In the Matter of Richard Pattinson, October 23, 1807, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 321–22. Journal, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 414.
. Case 76, Pattinson's Affidavit, in Blume, ed., _Supreme Court of Michigan_ , Vol. II, 156; Case 76 In the Matter of Richard Pattinson, in Blume, ed., _Supreme Court of Michigan_ , Vol. I, 99. Pattinson Petition for return of slave Jenney, Oct. 19, 1807 Woodward Papers, June 14, 1811 F: 1805–1807 BHC, DPL.
. James Heward vs. Charles Curry, Affidavit In the Case of Matthew Elliott Esq., October 21, 1807, Selected Papers SC of Michigan, 155–56; James Heward Papers, File 29 (new No. 49), BHC, DPL. "Matthew Elliott Essex County," (Toronto: York University, Harriet Tubman Institute, 2012), 7.
. Calendar of Cases, Case 60 In the Matter of Elizabeth Denison, James Denison, Scipio Denison and Peter Denison, Jr., 1807, Habeas corpus, in Blume, ed., _Supreme Court of Michigan_ Vol. II, 86–87. Brush representing Elliott: Selected Papers, Case 90, Affidavit of Elijah Brush, 1807, in Blume, ed., _Supreme Court of Michigan_ , Vol. II, 215–16.
. Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, _Supreme Court of Michigan_ , ed., Blume, Vol. II, 216.
. As quoted in Littlejohn, "Slaves," 24.
. Veta Smith Tucker, "Uncertain Freedom in Frontier Detroit," in Karolyn Smardz Frost and Veta Smith Tucker, eds., _A Fluid Frontier: Slavery, Resistance, and the Underground Railroad in the Detroit River Borderland_ (Detroit: Wayne State University Press, 2016), 27–42. Veta Tucker gives a detailed account of the Denisons' time in Canada; see Tucker, "Uncertain Freedom," 35. Sandwich is now a historic neighborhood in the city of Windsor, Ontario.
**5: The Rise of the Renegades (1807–1815)**
. According to David Poremba, the Smyth tavern was located on present-day Woodward Ave., near the Woodbridge intersection. David Lee Poremba, _Detroit in Its World Setting_ , 90. Smyth as hatter: Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, _Supreme Court of Michigan_ , ed., Blume, Vol. II, 216.
. Augustus B. Woodward to James Madison, March 17, 1808, Ms/Woodward A. B., BHC, DPL. Translation by Michelle Cassidy, November 2016.
. Duffey, "Northwest Ordinance," 953–54.
. Braithwaite, "Military Record," 96–98, 97; quote from Braithwaite, 96. Anthony J. Yanik, _The Fall and Recapture of Detroit in the War of 1812_ (Detroit: Wayne State University Press, 2011), 13, 14. Hull children, Lake Erie winds, vanished town: "Introduction," MHPC Vol. XL, 30, 31.
. SH (Sarah Hull) to William Hull, April 10, 1809, William Hull Papers, BHC, DPL. Donna Valley Russell, ed., _Michigan Censuses 1710–1830: Under the French, British, and Americans_ (Detroit: Detroit Society for Genealogical Research, 1982), 1805 Lists, 82–86. Catherine Cangany captures this aspect of Detroit's insularity: Detroit's "insularity, its dogged preservation of social and political localisms, its disdain for things unwanted and external, and its refusal to stand on ceremony"; Cangany, _Frontier Seaport_ , 167–68. Quote about French residents: Augustus B. Woodward to James Madison, March 17, 1808, Ms/Woodward A. B., BHC, DPL. Quoted description of Detroit: Alec R. Gilpin, _The War of 1812 in The Old Northwest_ (2012; reprint, East Lansing: Michigan State University Press, 1958), 24–25. Braithwaite, "Military Record," 96–98, 96. Sarah and William married in 1781; Braithwaite, "Military Record," 96. Sarah Hull at Saratoga: "Biographical Sketch: Sarah Fuller Hull, Wife of General William Hull," _Hull Family Association Journal_ 15:3 (Autumn 2004): 99; reprint of Elizabeth F. Ellet, _The Eminent and Heroic Women of America_ (New York: Arno Press, 1974, repr. of 1783 ed.), 95–96.
. Alan Taylor, _The Civil War of 1812: American Citizens, British Subjects, Irish Rebels, & Indian Allies_ (New York: Vintage Books, 2010), 102–105. Hull route by boat: Yanik, _Fall and Recapture_ , 14.
. Impressment numbers: James Miller and John Thompson, _National Geographic Almanac of American History_ (Washington, D.C.: National Geographic, 2007), 124; ten thousand American men had been captured, with thousands gaining release and six thousand remaining in British custody by 1807; Taylor, _Civil War of 1812_ , 105. Jenkin Ratford: Taylor, _Civil War of 1812_ , 102.
. Embargo: Miller and Thompson, _Almanac of American History_ , 125. Indian fears and Fort Mackinac Letter: Yanik, _Fall and Recapture_ , 16–17.
. Yanik, _Fall and Recapture_ , 16. "Introduction," MPHC Vol. XL, 34–35.
. Lieutenant Colonel E. Brush Commission by William Hull, Sept. 12, 1805, William Woodbridge Papers, DPL. Brush resigned from this post in 1809.
. James Askin to Charles Askin, August 18, 1807, Askin Papers, Vol. II, 566. John Askin to Isaac Todd, September 4, 1807, _Askin Papers_ , Vol. II, 570; quoted in Keller, "Detroit's First Black Militia," 85.
. Lieut. Colonel Grant to Secretary Green, August 17, 1807, MPHC Vol. VI, 41–43.
. Case 60, In the Matter of Elizabeth Denison, James Denison, Scipio Denison and Peter Denison, Jr., Calender of Cases, Papers in File, _Supreme Court of Michigan_ , ed., Blume, Vol. I, 87. Examination of James Dodemead respecting the ill treatment said to have been received by James Heward, a subject of his Britannic Majesty, October 27, 1807, Heward Papers, DPL.
. Examination of James Dodemead respecting the ill treatment said to have been received by James Heward.
. Examination of James Dodemead respecting the ill treatment said to have been received by James Heward. Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, _Supreme Court of Michigan_ , ed., Blume, Vol. II, 216. Case 91, Affidavit of Harris H. Hickman, 218–19.
. Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, 217.
. Examination of James Dodemead respecting the ill treatment said to have been received by James Heward, a subject of his Britannic Majesty, October 27, 1807, Heward Papers, DPL. Affidavit of Elijah Brush, respecting ill treatment of Matthew Elliott, _Supreme Court of Michigan_ , ed., Blume, Vol. II, 216. Augustus B. Woodward to James Madison, March 17, 1808, Ms/Woodward A. B., BHC, DPL.
. Lieut. Colonel Grant to Secretary Green, August 17, 1807, MPHC Vol. VI, 41–43. Quarles, _The Negro in the American Revolution_ , 8, 68, 83. Blacks boarding ships: Taylor, _Civil War of 1812_ , 113. Starting with Virginia in 1639, American colonial governments banned the arming of people of African descent, but they rolled back these prohibitions at times when officials felt the need for extra military manpower, such as in the Yamasee War of 1715, during which South Carolina approved of arming Africans, including those who were enslaved, to fight Native combatants. This process did not include training or a formalization of black men's leadership or authority. Charles Johnson, Jr., _African American Soldiers in the National Guard: Recruitment and Deployment during Peacetime and War_ (Westport, CT: Greenwood Press, 1992), 1–2. The African American military historian Charles Johnson dates the formal beginning of African American militia groups to the late nineteenth century (1877) and notes that territorial policy sometimes deviated from national policy. This was, he states, the case with William Hull, who "formed a company composed entirely of Africans to assist in protecting the frontier against British invasion." Johnson, _African American Soldiers_ , 5. The force from Santo Domingo that fought with French troops in support of the American cause in Savannah during the American Revolution in 1779 was not American-born but Haitian; Quarles, _The Negro in the American Revolution_ , 82. In Massachusetts, an all-black company was led by Col. George Middleton during the Revolutionary War; Middleton was African American; Manisha Sinha, _The Slave's Cause: A History of Abolition_ (New Haven: Yale University Press, 2016), 49. Monuments to black soldiers in the Revolutionary War exist in Savannah as well as Washington, D.C.
. A.B. Woodward to William Eustis, Secretary of War, July 28, 1812, Clarence Edwin Carter, _Territorial Papers_ , Volume 10, 389–92.
. William Hull to Jaspar Grant, September 3, 1807, MPHC, Vol. 31, 600, quoted in Keller, "Detroit's First Black Militia," 91.
. "Black History Month: Remembering the First Black Militia," no date listed], [MonroeNews.com, Accessed March 19, 2012. Reconstructing the formation and engagements of the black militia of Detroit is a difficult task due to the piecemeal nature of the written record. Only a handful of primary sources have been found to date about the militia. Two of those sources, a journalistic report on the war from July 2012 and a letter by Augustus Woodward in June of 1811, are, to my knowledge, noted first here. A search for Peter Denison in the War of 1812 pension files achieved no new results. It is my hope that future historians of early Detroit will keep digging for records about this occurrence. Secondary accounts of the development of the militia have been offered in the black history month article cited above as well as by the following scholars. In some details of chronology and interpretation the descriptions by these scholars differ from my own. The lack of plentiful source material means that each scholar working on this topic has had to connect the dots, and they have done so in varying ways at the level of detail. I am indebted to all of the following individuals and projects for their published reconstructions of these events. Veta Tucker, "Uncertain Freedom," in Frost and Tucker, eds., _A Fluid Frontier_. Charlie Keller, "Detroit's First Black Militia," in Brunsman, Stone, and Fisher, eds., _Border Crossings_ , 85–100. Gene Allen Smith, _The Slaves' Gamble: Choosing Sides in the War of 1812_ (New York: Palgrave Macmillan, 2013), 33–34. Donald R. Hickey, _Don't Give Up the Ship: Myths of the War 1812_ (Urbana: University of Illinois Press, 2006), 191. Johnson, Jr., _African American Soldiers in the National Guard_ , _5_. "Peter Denison," Detroit African-American History Project, Wayne State University, www.daahp.wayne.edu/biographies. Accessed August 16, 2012. Veta Tucker's chapter, in particular, helped me to see that Peter Denison may have given up freedom to flee with his family. Charlie Keller's chapter is the most precise and best cited account in print.
. The 1805 law establishing the Michigan militia directed that each "company" should be assigned a captain, lieutenant, and ensign and should wear uniforms. _Laws of the Territory of Michigan_ , Vol. I, _The Making of Modern Law_ , Yale Law Library, 47, 48.
. Augustus B. Woodward to James Madison, July 18, 1807, Folder January–July, 1807, Box 1806–1808, Augustus Brevoort Woodward Papers, BHC; also transcribed in MPHC, 12: 511–18. Quoted in Charlie Keller, "Detroit's First Black Militia," in Brunsman, Stone, and Fisher, eds., _Border Crossings_ , 89.
. Judge Woodward's Resolution on Sundry Subjects, and the Report of the Committee on the Same, Dec. 31, 1806, MHPC, V. 12, 462–65, 463. Only the transcription has been found of this document, and the 1806 date appears to be an error. All other primary sources indicate that the black militia was formed in 1807, after the _Chesapeake_ incident. The introduction to the Michigan Historical Collections series that includes the transcription in question notes that Woodward delivered his document to the committee in the fall of 1808. "Introduction," MHPC Vol. XL, 41.
. Judge Woodward's Resolution on Sundry Subjects, and the Report of the Committee on the Same, Dec. 31, 1806, MHPC, V. 12, 462–65, 463.
. There was no independent or elected legislature in territorial Michigan. The governor and three judges governed the territory, with Hull and Woodward being the most prominent voices. Hull likely dictated or wrote much of the committee's response to Woodward's Resolutions, which was signed by Judge John Griffin; "Introduction," MPHC Vol. XL, 44. Charlie Keller also points out that Governor Hull probably steered the findings of this committee; Keller, "Detroit's First Black Militia," 91. Judge Woodward's Resolution, MHPC, V. 12, 462–65, 470, 472. Woodward to Leib, [Gesurel?], June 14, 1811 Woodward Papers, BHC, DPL.
. Indenture of Charlotte Moses, Askin Papers, Vol. II: 607–608.
. Case 432, Box 9, Supreme Court, Michigan Territorial Records, Archives of Michigan, Michigan Historical Center, Lansing, MI. Laura Edwards presents an illuminating analysis of why textiles were so sought after in the nineteenth century for both their use value and exchange value; she also shows the importance of enslaved women's assumed ability to own textiles as possessions. Laura F. Edwards, "Textiles, Popular Culture and the Law," _Buffalo Law Review_ 64 (2016): 193–214.
. Lieut. Colonel Grant to Secretary Green, August 17, 1807, MPHC Vol. VI, 41–43.
. Case 60, In the Matter of Elizabeth Denison, James Denison, Scipio Denison and Peter Denison, Jr., Calender of Cases, Papers in File, _Supreme Court of Michigan_ , ed., Blume, Vol. I, 87.
. Cangany, _Frontier Seaport_ , 139–40, 154–55.
. Treaty of Detroit and Related Treaties, _American State Papers: Documents, Legislative and Executive of the Congress of the United States_ , Part 2, Volume 1 (Gales and Seaton: 1832), digitized Pennsylvania State University, 745–48.
. Treaty of Detroit and Related Treaties, _American State Papers: Documents, Legislative and Executive of the Congress of the United States_ , Part 2, Volume 1 (Gales and Seaton: 1832), digitized Pennsylvania State University, 745–48.
. William Hull to Dearborn, February 20, 1807, MPHC Vol. XL, 1805–1813, 100–102.
. Treaty of Detroit and Related Treaties, _American State Papers: Documents, Legislative and Executive of the Congress of the United States_ , Part 2, Volume 1 (Gales and Seaton: 1832), digitized Pennsylvania State University, 745–48. Treaty of Detroit, 1807. <http://clarke.cimich.edu/resource_tab/native_americans_in_michigan/treaty_rights/text_of_michigan-related_treaties/detroit1807.html>. Accessed March 15, 2012. Poremba, _Detroit_ , 91. For an analysis of native political leadership in the region, see: Cary Miller, _Ogimaag: Anishinaabeg Leadership, 1760–1845_ (Lincoln: University of Nebraska Press, 2010).
. Treaty of Detroit and Related Treaties, _American State Papers: Documents, Legislative and Executive of the Congress of the United States_ , Part 2, Volume 1 (Gales and Seaton: 1832), digitized Pennsylvania State University, 745–48.
. Charles E. Cleland, _Rites of Conquest: The History and Culture of Michigan's Native Americans_ (Ann Arbor: University of Michigan Press, 1992), 218, 229. Poremba, _Detroit_ , 91.
. Walter Johnson makes the similar and instructive point that the development of lands for plantation enterprises in Louisiana reduced enslaved people's means of hiding and escaping in forested landscapes. Walter Johnson, _River of Dark Dreams: Slavery and Empire in the Cotton Kingdom_ (Cambridge, MA: Harvard University Press, 2013), 220–21.
. Cangany, _Frontier Seaport_ , 157, 158. Arthur Mullen, "Detroit through 300 Years—Physical Clues to Our Long History," www.cityscapedetroit.org/articles/Physical_clues.html. Accessed November 18, 2013.
. Cangany, _Frontier Seaport_ , 150, 152, 154, 155; Poremba, _Detroit_ , 90.
. Farmer, _History of Detroit_ , 24–25; Quoted in Farmer, _History of Detroit_ , 24; quoted in Farmer, _History of Detroit_ , 25; quoted in Farmer, _History of Detroit_ , 27–28. "Introduction," MHPC Vol. XL, 33.
. M. Agnes Burton., ed., _Governor and Judges Journal: Proceedings of the Land Board of Detroit_ (Detroit: 1915), 20, 44, 47, 116, 207, 230, 231. In the Matter of Hannah, A Negro Woman, _Supreme Court of Michigan_ , Vol. I, ed., Blume, 163, 486–87.
. Taylor, _Divided Ground_ , 399. Ainse encountered her own problems with land boards, finding that the Canadian government refused to fully recognize her land claims that were based on previous Indian deeds.
. Hull to Dearborn, February 20, 1807, MPHC Vol. XL, 96–97; "Introduction," MHPC Vol. XL, 39.
. Russell, ed., _Michigan Censuses_ , 87–91.
. Cangany, _Frontier Seaport_ , 152; Ste. Anne's Church Records.
. For a discussion of the flexibility and changeability of racial and color terms such as "mulatto" and "mustee," see Jack D. Forbes, _Africans and Native Americans: The Language of Race and the Evolution of Red-Black Peoples_ (Urbana: University of Illinois Press, 1993).
. Poremba, _Detroit_ , 91. Deed of Bargain and Sale from Elijah Brush, and wife; Deed of Mortgage from Governor Hull to Elijah Brush; deed Joseph Watts sells land to William Hull; Sarah, Alexander and Angus Makintosh lease land to William Hull; Indenture of lease between Pierre Toussaint Chesne and William Hull; Deed Joseph Mini and Javotte Mini to William Hull; Deed of Pierre Rivier, Relinquishment of dower Archange Rivard to William Hull; Deed, Pierre Toussaint _Cécile Thérèse Chêne_ to William Hull; Incomplete deed between Hull and Daniel Robinson; Watson of New York to William Hull mortgage 1¾ acres lots in Detroit, William Hull Papers, Folder L2: 1808–1810, Folder L2: 1811–25, BHC, DPL.
. SH (Sarah Hull) to William Hull, April 10, 1809, William Hull Papers, BHC, DPL.
. Gilpin, _War of 1812 in the Old Northwest_ , 66. "St. John's Anglican Church, Sandwich, Ontario, <http://essexanglican.awardspace.com>. Accessed June 25, 2016.
. Peter and Hannah baptism: quoted in Tucker, "Uncertain Freedom," 37. Family baptisms: Swan, _Lisette_ , 8; the church register includes several individual Denison names in baptism, birth and burial notes (such as James, Hannah, Scipio, Lisette/Elizabeth, Phoebe, Juliet, and Charlotte) between 1811 and 1819. Juliet is listed as a fourteen-year-old daughter of Peter and Hannah in 1816; Phoebe is listed as the daughter of Scipio and Charlotte Denison, so a grandchild of Peter and Hannah; St. John's, Anglican, 1802–1827, Register of baptisms, marriages and burials, 1802–1827, Sandwich, Ontario, Archives of Ontario, Toronto. A third generation was born, raised, and baptized in Canada, and some of these descendants stayed there. Slaveholders in the church: Tucker, "Uncertain Freedom," 35.
. Peter as "Negro Servt [servant] of Angus McIntosh [Mackintosh]" is noted upon Peter's death: St. John's Register, August 28, 1812. Also quoted in Tucker, "Uncertain Freedom, 37.
. Rebecca J. Scott, "Social Facts, Legal Fictions, and the Attribution of Slave Status: The Puzzle of Prescription," _Law and History Review_ (2017): 1–22, 10.
. Anonymous Ledger, MS/Anonymous, L4: 1806–15, BHC, DPL. Hum-Hum, a cotton fabric from Indian, was most popular in the mid- to late eighteenth century; Elisabeth McClellan, _Historic Dress in America, 1607–1800_ (Philadelphia: George W. Jacobs & Co, 1904), 388.
. The Askin Ledger, part of the John Askin Papers at the Detroit Public Library, is a lengthy fifty-page account in the original cursive script that employs financial shorthand. I was very fortunate to have the assistance of an undergraduate student, Paul Rodriguez, aided by a graduate student, Michelle Cassidy, who worked on an initial transcription of this ledger as well as the Macomb ledger over the course of two academic years. Even with this remarkable effort, the ledger is challenging to work with. I have summarized all references to the Denisons here and quoted only when I could be quite sure of my transcription, which drew from the original text and the students' transcription. The Askin ledger has its own page numbers in the top right hand corner, but these are difficult to read and not always present. We therefore renumbered the pages from 1 to 50. When possible, I give two page numbers for references to indicate our numbering and the original numbering. References to the Denisons appear on pp: 35/180, 36, 37, 38, 39/222, 41/235, 42, 43, 44, 47, and 50. Lisette working winter nights: 36. Many other early Detroiters also appear in this ledger, including Elijah and "Mrs." Brush. MS Askin, J. L4, 1806–1812, BHC, DPL.
. Askin Ledger, Askin Papers, BHC, DPL.
. Mary, Tom, George: 35, 33, 34, 37/205. Jim: 29. Jobs performed by people of color: 13, 24, 33/177. Askin Papers, BHC, DPL.
. Anonymous Ledger, MS/Anonymous, L4: 1806–15, BHC, DPL. Adelaide Brush to Charles Askin, July 27, 1810; Elijah Brush to John Askin, February 13, 1810 Askin family fonds [textual record], Correspondence with the Brush family, 1801-1850, MG 19 A 3 Volume 37, Library and Archives Canada, Ottawa, ON. These letters do not make clear who Peter Denison was buying himself from. The money may have gone to Catherine Tucker, who had indentured Peter and Hannah to Brush, or to William Hull or the town of Detroit due to Peter's abandonment of the black militia in 1807 to flee with his family to Canada. It is possible, but unlikely, that Elijah Brush paid himself to free Peter, since he promises to "furnish the money." I am grateful to Rachel Whitehead for leading me to these letters.
. Gilpin, _War of 1812 in the Old Northwest_ , 27, 28, 29; Yanik, _Fall and Recapture_ , 23.
. Gregory Evans Dowd, _A Spirited Resistance: The North American Indian Struggle for Unity, 1745–1815_ (Baltimore: Johns Hopkins University Press, 1993), 142, 144.
. Gilpin, _War of 1812 in the Old Northwest_ , 4, 6, 13, 16; Yanik, _Fall and Recapture_ , 20–21. For a detailed study of Tecumseh's revolution and broader native resistance campaigns, see Dowd, _A Spirited Resistance_.
. Yanik, _Fall and Recapture_ , 21–22. John Tyler was Harrison's vice presidential candidate in the 1840 presidential race.
. Memorial to Congress by Citizens of Michigan Territory, MHPC Vol. XL, 346–53.
. Witgen, _Infinity of Nations_ , 327.
. Yanik, _Fall and Recapture_ , 17; Gilpin, _War of 1812 in the Old Northwest_ , 28, 29; Hull quoted in Yanik, _Fall and Recapture_ , 22.
. The longevity of the black militia is a point of debate among the handful of historians who have written about it. Most state that the company was disbanded by 1811, before the start of the war. This argument is sound and based on the fact that Judge Augustus Woodward's references to the group conclude in this year and no primary sources from Michigan officials note a continuation of the force. One historian states that the militia continued past 1811, and its men served in the War of 1812, but the primary sources he cites do not actually show evidence for this claim. There is logic on the side of the argument for War of 1812 involvement. It seems unreasonable that Hull, having taken the risk to form the black militia and being supported in this by a territorial special committee, would not use this group during war preparations. My representation of the black militia's involvement in the very first months of the war is based on the uncovering of a new source by a reporter that is not full proof of the group's continuation (as the reporter's source could have passed on dated information) but is certainly evidentiary and highly suggestive. Report to readers on war developments, Zanesville, OH, July 20, 1812, _Document Transcriptions of The War of 1812 in the Northwest_ , Vol. IV, Anecdotes of the Lake Erie Area War of 1812, Transcribed from Original Sources by Richard C. Knopf (Columbus: Ohio Historical Society, 1957), 120–21.
. Letter from Detroit to New York, July 18, 1812, _Document Transcriptions of The War of 1812 in the Northwest_ , Knopf, trans., 110.
. Black Swamp: Harry L. Coles, _The War of 1812_ (Chicago: University of Chicago Press, 1965), 45–46; Gilpin, _War of 1812_ , 36, 51. Yanik, _Fall and Recapture_ , 48.
. We learn that letters have been received, _Document Transcriptions of The War of 1812 in the Northwest_ , July 25, 1812, Knopf, trans., 111.
. We learn that letters have been received, _Document Transcriptions of The War of 1812 in the Northwest_ , July 25, 1812, Knopf, trans., 111.
. Eustis quoted in Yanik, _Fall and Recapture_ , 50–51.
. Report to readers on war developments, Zanesville, OH, July 20, 1812, _Document Transcriptions of The War of 1812 in the Northwest_ , July 20, 1812, Knopf, trans., 120–21. Hull's Proclamation: Yanik, _Fall and Recapture_ , 56; Gilpin, _War of 1812 in the Old Northwest_ , 73–74.
. bell hooks, "Revolutionary 'Renegades': Native Americans, African Americans, and Black Indians," in _Black Looks: Race and Representation_ (Boston: South End Press, 1992).
. Fort Mackinac: Gilpin, _War of 1812 in the Old Northwest_ , 89; Yanik, _Fall and Recapture_ , 63. A. B. Woodward to William Eustis, Secretary of War, July 28, 1812, Clarence Edwin Carter, Territorial Papers, Volume 10, 389–92. While not conclusive for the argument that the black militia was active at the start of the war, Woodward's complaint does not foreclose this likelihood. He makes no mention of the militia having been disbanded, which would seem relevant in a letter about Hull's misdeeds and the war's development in real time.
. Yanik _Fall and Recapture_ , 91, 92; location of artillery on present-day Jefferson Ave., Yanik 89; Brock quoted in Yanik, 88.
. Yanik, _Fall and Recapture_ , 88, 94.
. Yanik, _Fall and Recapture_ , 94–96, 100.
. Denison in Quebec quote: Smith, _Slaves' Gamble_ , 34. Number of Detroit prisoners: Taylor, _Civil War of 1812_ , 175.
. Hull was released from the British on parole in October of 1812. He returned to Massachusetts before being court-martialed by the U.S. government in 1813 for the charges of treason, cowardice and neglect of duty. Although Hull was found guilty of the second two charges and sentenced to death, President Madison commuted this sentence. Negative representations of Hull both at the time and in histories of the war have led to debate and the historian Anthony Yanik's recent book, subtitled "In Defense of William Hull." Yanik and others argue that Hull was a scapegoat for Madison, Hull's officers, and the Republican Party for larger failures of the war. Gilpin, _War of 1812 in the Old Northwest_ , 232. Yanik, _Fall and Recapture_ , 125–27. Elijah Brush was apparently released by February of 1813; Jacobson, _Detroit River Connections_ , 62. Denison's death: St. John's Register, August 28, 1812. Also quoted in Tucker, "Uncertain Freedom, 37.
. Treaty of Ghent, Primary Documents in American History, Library of Congress, <https://www.loc.gov/rr/program/bib/ourdocs/Ghent.html>. Accessed July 29, 2016. For more on the reduction of Native negotiating influence after the War of 1812, see White, _Middle Ground_ , 516–17, 523, For more on Native persistence, population, and strength in the Great Lakes beyond the War of 1812, see Witgen, _Infinity of Nations_ , 27, 325–27; McDonnell, _Masters of Empire_ , 318–19.
. French Town: Ralph Naveaux, _Invaded on all Sides: The Story of Michigan's Greatest Battlefield, Scene of the Engagements at French Town and the River Raisin in the War of 1812_ (Marceline, MO: Walsworth Publishing Co., 2008), 17. For more on the battle at the River Raisin, see Naveaux, _Invaded on All Sides._ Brush's death: Swan, _Lisette_ , 8; Jacobson, _Detroit River Connections_ , 61–63. Gilpin, _War of 1812 in the Old Northwest_ , 126; Yanik, _Fall and Recapture_ , 162. Taylor, _Civil War of 1812_ , 243. Ominous quote: Taylor, _Civil War of 1812_ , 439.
. "Forgotten war": Donald R. Hickey, _The War of 1812: A Forgotten Conflict_ (1989; reprint, Urbana: University of Illinois Press, Bicentennial Edition, 2012); Taylor, _Civil War of 1812_ , 10.
. Coles, _War of 1812_ , 255. Taylor, _Civil War of 1812_ , 10. Ste. Anne's Church Records: Marie Louise baptism, February 3, 1799; Jean Baptiste Rémond, baptism, July 5, 1812; Julie Ford, baptism, August 11, 1813. Ste. Anne's Church Records; Russell, ed., _Michigan Censuses_ , 101–147; Katzman, "Black Slavery in Michigan," 62. R. G. Dunlop, W. L. Mackenzie, John H. Dunn, Adolphus Judah, W. R. Abbott, David Hollin, Malcolm Cameron, and J. Levy, "Records Illustrating the Condition of Refugees from Slavery in Upper Canada before 1860," _Journal of Negro History_ 13:2 (April 1928): 199–207, 205.
. Taylor, _Civil War of 1812_ , 327.
. Fergus Bordewich is the first scholar I know of to offer this supposition that black men's involvement in the War of 1812 informed a larger black population about the liberatory possibilities of Canada. Fergus M. Bordewich, _The Underground Railroad and the War for the Soul of America_ (New York: Harper Collins, 2005), 114.
**Conclusion: The American City (1817 and Beyond)**
. Swan, _Lisette_ , 8. St. St. John's, Anglican, 1802–1827, Register of baptisms, marriages and burials, 1802–1827, Sandwich, Ontario, Archives of Ontario, Toronto. Marriage Certificate of Scipio Dennison and Charlotte Paul, Zd4-Denison Family, Solomon Sibley Papers, DPL.
. George McDougall, attorney for Sarah Macomb, _Detroit Gazette_ , September 17, 1817, p. 4; George McDougall, agent for David B. Macomb, _Detroit Gazette_ , September 17, 1817, p. 4. Clarence Burton, _History of Detroit, 1780–1850, Financial and Commercial_ (Detroit: 1917), 58–61. Jacobson, _Detroit River Connections_ , 25, 129.
. "Notice. A Meeting," _Detroit Gazette_ , September 19, 1817, p. 3. "Commission Store," _Detroit Gazette_ , September 19, 1817, p. 3. John Williams to Samuel Abbott, May 1817, John R. Williams Papers, BHC, DPL. Monroe: MPHC, Vol. 38, p. 446. John R. Williams was the son of Cecile Campau; his father, Thomas Williams, hailed from Albany, NY; Gitlin, _Bourgeois Frontier_ , 144–145.
. John Williams to Samuel Abbott, May 1817, John R. Williams Papers, BHC, DPL. William was elected mayor in 1824; Poremba, _Detroit_ , 76, 104. "American city": F. Clever Bald, _Detroit's First American Decade_ , 1948; "Subscription List," _Detroit Gazette_ , September 19, 1817, p. 1; "Statutes of the University of Michigania," _Detroit Gazette_ , September 19, 1817, p. 2; "Subscription List," _Detroit Gazette,_ October 10, 1817, p. 3; Poremba, _Detroit_ , 98, 99.
. "Subscription List," _Detroit Gazette_ , September 19, 1817, p. 1; "Statutes of the University of Michigania," _Detroit Gazette_ , September 19, 1817, p. 2; "Subscription List," _Detroit Gazette,_ October 10, 1817, p. 3. The subscription lists printed in the newspaper name thirty-five people but are incomplete. The newspaper does not include some names (such as James May, Augustus Woodward, and Barnabas Campau) that are listed as donors in other sources. Augustus Woodward also kept a subscription list for $150 donors that may have been independent of the university treasurer's list. Woodward's list reference: Campau Papers, MS/Campau Family, 1817 May–December, BHC, DPL. Terrence McDonald, director of the Bentley Library at the University of Michigan, calculated that "the total amount of subscriptions was $5100. The two newspaper lists total $4086 . . . we are missing the names of those who together contributed about $1000. The subscriptions were raised between Sept. 19 and Oct. 10 1817." Terrence McDonald to Tiya Miles, email correspondence, July 31, 2016.
. C.M. Burton, "Augustus Brevoort Woodward," MPHC Vol. 29, p. 658.
. Burton, "Augustus Brevoort Woodward," MPHC Vol. 29, pp. 658–659.
. May donation: R.N. Drake, "Sketch of Judge May: Grandfather of Mrs. Seymour," Drake Scrapbook in Possession of R. N. Drake, Seattle, Washington, From SB of Drake loaned to C.M.B., James May Papers, Wallet 1, BHC, DPL, 8. Silas Farmer, _History of Detroit and Wayne County_ , 729. Drake gives a figure of $100 for May's contribution. Farmer gives a figure of $25. Both authors provide transcribed or quoted copies of these pledge documents; however, the originals have not been found in the University of Michigan archives at the Bentley Library or in papers at the Detroit Public Library. Records of other contributions: Barnabas Campau: Campau Papers, MS/Campau, Barnabas, Folder 1819–21, BHC, DPL; "the Lodge": Campau Papers, MS/Campau Family, 1817 May–December, BHC, DPL; use of city fire fund: Campau Papers, MS/Campau Family, 1817 May–December, BHC, DPL. Woodward's slave: Robert B. Ross and George B. Catlin, _Landmarks of Detroit: A History of the City_ (Detroit: Evening News Association, 1898), 416. Burton, _History of Detroit, 1780–1850_ , 73. Michelle Cassidy, "The Origins of Article 16 and the University of Michigan," paper written for the University of Michigan Bicentennial Committee, Ann Arbor, MI, 2015. Joseph Campau was a member of the Ancient Free and Accepted Masons, Zion Lodge, Number 10; Gitlin, _Bourgeois Frontier_ , 54–55. He reportedly died as the richest man in Michigan; Jacobson, _Detroit River Connections_ , 85.
. Cassidy, "The Origins of Article 16 and the University of Michigan," University of Michigan Bicentennial Committee. _An Act to Establish the Catholepistemiad, or university of Michigania_ (August 26, 1817), Frank Egelston Robbins, ed., _University of Michigan Early Records, 1817–1837_ (Ann Arbor: The University of Michigan, 1935), 3–5.
. Quote by John Petoskey, University of Michigan College of Literature, Science & the Arts (2016) and School of Law (currently enrolled); used by permission of John Petoskey, June 21, 2016. To be eligible for the tuition waiver, applicants must be enrolled in a United States federally recognized tribal community, of one-quarter blood quantum, with established Michigan residency of at least twelve months. The waiver is defined as a benefit stemming from political relations between government entities (such as the state of Michigan and tribes) rather than race or ethnicity. Michigan Indian Tuition Waiver Frequently Asked Questions, Michigan.Gov, <https://www.michigan.gov/documents/mdcr/faqsmitw_329746_7.pdf>. Michigan Indian Tuition Waiver, Michigan Department of Civil Rights, <http://www.michigan.gov/mdcr/0,1607,7-138--240889--,00.html>. Accessed June 20, 1016.
. First Minority Graduates and Attendees, Bentley Historical Library, UM, <http://bentley.umich.edu/legacy-support/umtimeline/minfirsts.php>. Accessed July 1, 2016.
. Catherine Sibley quoted in Swan, _Lisette_ , 9.
. MPHC, Vol. 38, p. 446.
. Swan, _Lisette_ , 9, 13. Deed, Stephen Mack to Elizabeth Dennison; Lease of lots in Pontiac, Scipio and Elizabeth Forth to Scipio Dennison; Lease of lots in Pontiac, Scipio and Elizabeth to Scipio; Promissory note, Scipio Dennison to Elizabeth; Letter, Scipio Dennison to Solomon Sibley; Zd4-Denison Family, Solomon Sibley Papers, DPL. A Michigan state historical marker in Pontiac recognizes Elizabeth Denison Forth's biography and land purchase. <http://www.michmarkers.com/startup.asp?startpage=L1860.htm>. Accessed July 23, 2016.
. Swan, _Lisette_ , 10, 14, 16, 17; Visitor Elizabeth Campbell quoted in Swan, _Lisette_ , 18. Biddle served as mayor from 1827 to 1828; Poremba, _Detroit_ , 106. Sibley family: Sibley House Detroit, <http://sibleyhousedetroit.com/the-sibley-family>; Accessed July 13, 2016.
. Maurice M. Manring, _Slave in a Box: The Strange Career of Aunt Jemima_ (Charlottesville: University Press of Virginia, 1998), 61–65, 74–75. Eliza Biddle to Aaron Ogden, January 15, 1855, Gershom Mott Williams Papers, BHC, DPL, transcribed in McPherson, _Looking for Lisette_ , 440. The set of documents that Mark McPherson calls the "Lisette Letters" in his Appendix B refers to twelve letters in the Biddles' correspondences that mention Elizabeth Denison.
. Swan, _Lisette_ , 8, 9, 14, 21. Eliza Biddle to Susan Biddle, June 28, 1859, transcribed in McPherson, _Looking for Lisette_ , 445–46.
. Elmwood Cemetery internment record, B/Negroes-Forth, Elizabeth Denison, Reading Room, DPL. This record is not wholly accurate. It states that Elizabeth Denison Forth was 114 years old at the time of her death in 1866 and that she was born in Virginia. All other records indicate that she was born a slave in the 1780s in Detroit, which means that she died close to the age of 90. Lisette Denison's grave location is given as Strangers Ground 45–194 in the Elmwood record.
. Draft of Elizabeth Dennison's Will, Zd4-Denison Family, Solomon Sibley Papers, DPL. Elizabeth Denison Forth Will, Folder B/Negroes-Forth, Elizabeth Denison, Reading Room, DPL.
. Swan, _Lisette_ , 15; Indenture of service between Scipio and Eastman Dennison and Charles E. Brush in Green Bay, 1834, Zd4-Denison Family, Solomon Sibley Papers, DPL.
. Swan, _Lisette_ , 49. Saint James Church has produced a historical pamphlet that covers the history of Elizabeth Denison as its "founder." This pamphlet is informative and engaging, but my account here differs from it in some respects, especially regarding the relationship between Lisette Denison and Eliza Biddle. The pamphlet states that the two women "shared a strong bond" and made a "vow" to found a church together on Grosse Ile. I have not seen evidence for this claim. I am grateful, though, to the church for sharing their version of the history so generously; "Saint James Story of the Chapel," Saint James Church, Grosse Ile, MI.
. Histories of American Indian enslavement retain the idea that the practice died out by the middle 1700s and that Indian slaves after that time were likely to be mixed Afro-Native or lost to the designation "Negro" in plantation records. Studying slavery in Detroit shows the continuation of a clear practice of Indians being kept as slaves well into the nineteenth century.
. The novelist Gayl Jones includes a haunting refrain of the call to "make generations" in her classic story of generations of black women sexually abused in slavery; Gayl Jones, _Corregidora_ (Boston: Beacon, 1975), 10, 60, 90, 101. The historian Susan Sleeper Smith developed this concept of Midwestern Indians using a hiding-in-plain-sight strategy of survival, with a focus on Indiana. Susan Sleeper Smith, _Indian Women and French Men: Rethinking Cultural Encounter in the Western Great Lakes_ (Amherst: University of Massachusetts Press, 2001), 115, 116; see Chapter Seven.
. Swan, _Lisette_ , 49. Sibley House Detroit, <http://sibleyhousedetroit.com/the-sibley-family/>. The Charles C. Trowbridge House is located at 1380 East Jefferson in downtown Detroit, Detroit 1701, <http://detroit1701.org/Trowbridge_Hist.htm>. Accessed July 13, 2016.
. Frost and Tucker, "Introduction," in Frost and Tucker, eds., _A Fluid Frontier_ , 2–4. EdDwight.com, <http://www.eddwight.com/memorial-public-art/international-underground-railroad-memorial-detroit-mi-windsor-canada>; Accessed July 13, 2016. Detroit 1701, <http://detroit1701.org/UndergroundRailroad.htm>; Accessed July 13, 2016.
**A Note on Historical Conversations and Concepts**
. Charles Bright, "'It Was As If We Were Never There': Recovering Detroit's Past for History and Theater," _Journal of American History_ (March 2002).
. Therese A. Kneip, "Slavery in Early Detroit," MA Thesis, University of Detroit, 1938. David M. Katzman, "Black Slavery in Michigan," _American Studies_ 11:2 (fall 1970): 56–66. Cooper, "The Fluid Frontier," 129–49.
. Bill McGraw, "Slavery Is Detroit's Big, Bad Secret. Why Don't We Know Anything About It?" _Deadline Detroit_ , www.deadlinedetroit.com, August 27, 2012. Accessed August 28, 2012. In 2005 a senior honors thesis addressed the topic of Midwestern slavery with particular attention to Michigan: Daniel Rhoades, "There Were No Innocents: Slavery in the Old Northwest 1700–1860," Senior Honors Thesis, Eastern Michigan University, Ypsilanti, 2005. Brunsman and Stone, eds., _Revolutionary Detroit_. Brunsman, Stone, and Fisher, eds., _Border Crossings_. David Lee Poremba, ed., _Detroit in Its World Setting: A Three Hundred Year Chronology, 1701–2001_ (Detroit: Wayne State University Press, 2001).
. David M. Katzman, _Before the Ghetto: Black Detroit in the Nineteenth Century_ (Urbana: University of Illinois Press, 1973). Reginald R. Larrie, _Makin' Free: African-Americans in the Northwest Territory_ (Detroit: Blaine Ethridge Books, 1981). Norman McRae, "Blacks in Detroit, 1736–1833: The Search for Freedom and Community and Its Implications for Educators" (Ph.D. diss., The University of Michigan, Ann Arbor, 1982). Swan, _Lisette_. Swan is also the author of a lengthy local history of Grosse Ile: Swan, _Deep Roots_. Mark F. McPherson, _Looking for Lisette: In Quest of an American Original_ (Dexter, MI: Mage Press, 2001). Christian Crouch, "The Black City: African and Indian Exchange in Pontiac's Detroit," revised version of Christian Crouch, "The Black City: Detroit and the Northeast Borderlands through African Eyes in the Era of 'Pontiac's War,'" The War Called Pontiac's Conference, April 5, 2013, Philadelphia, PA, 1–2.
. Frost and Tucker, eds., _A Fluid Frontier_. Gregory Wigmore, "Before the Railroad: From Slavery to Freedom in the Canadian-American Borderland," _Journal of American History_ 98:2 (2011): 437–54.
. Eric Foner, _Gateway to Freedom: The Hidden History of the Underground Railroad_ (New York: W. W. Norton, 2015). Stephen Kantrowitz, _More Than Freedom: Fighting for Black Citizenship in a White Republic, 1829–1889_ (New York: Penguin, 2012). Manisha Sinha, _The Slave's Cause: A History of Abolition_ (New Haven: Yale University Press, 2016), 9.
. Brian Leigh Dunnigan, _Frontier Metropolis: Picturing Early Detroit, 1701–1838_ (Detroit: Wayne State University Press, 2001). Cangany, _Frontier Seaport_. The three-hundred-year chronology by David Lee Poremba has also been central to the reimagining of Detroit as a diverse and complex settlement. David Lee Poremba, ed., _Detroit in Its World Setting: A Three Hundred Year Chronology, 1701–2001_ (Detroit: Wayne State University Press, 2001). Silas Farmer, _History of Detroit and Wayne County and Early Michigan: A Chronological Cyclopedia of the Past and Present_ (1890; reprint, Detroit: Gale Research Company, 1969). Clarence M. Burton, ed., _The City of Detroit Michigan: 1701–1922_ (Detroit-Chicago: The S.J. Clarke Publishing Company, 1922).
. Cooper, "The Fluid Frontier," 130.
. In my use of the term "refusal" here and elsewhere in this book I am drawing mainly from the theoretical work of anthropologist Audra Simpson, who has interrogated the U.S.-Canada border as it has shaped the political and familial lives of Mohawk people in the community of Kahnawake. A key concept that I draw from Simpson is that even while taking into account the many costs and compromises, indigenous people have refused to be defined in static ways by settler states; therefore, the meaning and future of Euro-American and Euro-Canadian political borders on present and former indigenous lands are far from settled. Simpson calls a stance that rejects state "recognition" a politics of "refusal." Audra Simpson, _Mohawk Interruptus: Political Life Across the Border of Settler States_ (Durham, NC: Duke University Press, 2014); see especially pp. 7, 11–12, chapter 4. I am also drawing from the work of Beth Piatote, a literary scholar who examines reactions to forced domesticities and competing nationalisms in the work of Pauline Johnson and others during the "assimilation" policy period. Beth H. Piatote, _Domestic Subjects: Gender, Citizenship, and Law in Native American Literature_ (New Haven, CT: Yale University Press, 2013), 17, 26.
. Visit the Detroit Historical Museum at <http://detroithistorical.org/detroit-historical-museum/plan-your-visit/general-information>. The Detroit Historical Museum is run by the Detroit Historical Society: <http://detroithistorical.org>. Shawna Mazur, a ranger at the River Raisin Battlefield, has researched and published on the black militia and shared her work with the public, park staff, and visitors. In 2009, reenactor Xavier Allen portrayed a black militia member at the River Raisin Battlefield Commemoration. His photo is featured and captioned in Shawna Mazur's essays. Shawna Mazur, "In Support of America and Freedom: The Establishment of the First Black Militia," _Monroe Evening News_ (February 2010); Shawna Mazur, "Slavery and the Black Militia," _River Raisin News & Dispatch_, Newsletter of the Monroe County Historical Museum, Monroe County Historical Commission & Monroe County Historical Society (July/August/September 2009). Visit the River Raisin Battlefield at: <https://www.nps.gov/rira/index.htm>.
. Richard White, _The Middle Ground: Indians, Empires, and Republics in the Great Lakes Region, 1650–1815_ (New York: Cambridge University Press, 1991), x. For more studies that focus on Native history in the Great Lakes and Midwest as a borderland, see Michael Witgen, _An Infinity of Nations: How the Native New World Shaped Modern North America_ (Philadelphia: University of Pennsylvania Press, 2013); John P. Bowes, _Exiles and Pioneers: Eastern Indians in the Trans-Mississippi West_ (Cambridge: Cambridge University Press, 2007); Alan Taylor, _The Divided Ground: Indians, Settlers, and the Northern Borderland of the American Revolution_ (New York: Vintage, 2006); Daniel P. Barr, ed. _The Boundaries Between Us: Natives and Newcomers along the Frontiers of the Old Northwest Territory, 1750–1850_ (Kent, OH: Kent State University Press, 2006); Karl S. Hele, ed., _Lines Drawn Upon the Water: First Nations and The Great Lakes Borders and Borderlands_ (Waterloo, Ontario: Wilfrid Laurier University Press, 2008). For work that treats the Detroit River as a borderland region, see Wigmore, "Before the Railroad," 437–54; Lisa Philips Valentine and Allan K. McDougall, "Imposing the Border: The Detroit River from 1786 to 1807," _Journal of Borderlands Studies_ , Special Issue: The Canadian-American Border: Toward a Transparent Border? 19:1 (2004): 13–22. For work that sees the Midwest as a borderland for African American history, see Matthew Salafia, "Searching for Slavery: Fugitive Slaves in the Ohio River Valley Borderland, 1830–1860," _Ohio Valley History_ 8:4 (Winter 2008): 38–63; Gary Knepp's _Freedom's Struggle: A Response to Slavery from Ohio's Borderlands_ (Milford, OH: Little Miami Publishing Co., 2008). For treatments of social exchange and development in the Midwest borderlands, also see Elizabeth A. Perkins, _Border Life: Experience and Memory in the Revolutionary Ohio Valley_ (Chapel Hill: University of North Carolina Press, 1998); James Z. Schwartz's, _Conflict on the Michigan Frontier: Yankee and Borderland Cultures, 1815–1840_ (DeKalb, IL: Northern Illinois University Press, 2009).
. White raises and then critiques an aquatic metaphor in his introduction to _The Middle Ground_. He suggests that the story of white-Indian relations has often been told as a story of the sea (representative of Europeans) repeatedly smashing into a rock (representative of American Indians) like a relentless, inevitable storm. White explains that this is a simplistic metaphor of European advancement and Native assimilation (or, in more progressive histories, Native persistence) that he will strive to avoid; White, _Middle Ground_ , ix.
. Heidi Bohaker closely examines pictographs representing Anishinaabe clans (often used as signatures on treaties) to build an argument that troubles Richard White's representation of the Great Lakes. Bohaker shows that Native people were accustomed to a mobile lifestyle and maintained a clan system and out-marriage structure that meant they had relatives across the region. These groups, she argues, could therefore not be "refugees" with nowhere to go after conflicts and wars. In addition, she asserts that a focus on the "middle ground" fixes our attention on cultural exchange rather than on indigenous cultural formations and practices; Heidi Bohaker, "'Nindoodemag': The Significance of Algonquian Kinship Networks in the Eastern Great Lakes Region, 1600–1701," _The William and Mary Quarterly_ , Third Series, 63:1 (January 2006): 23–52. In his broad study of Ottawa influence in and on the Great Lakes, Michael McDonnell chooses to limit his use of the middle ground frame to military forts, making the point that beyond these dispersed spaces of European or American influence, Native people controlled the terms of interaction. McDonnell also offers a strong overarching dissent from Richard White's characterization of the Great Lakes region, taking issue with White's assessment that the inhabitants were "shattered" groupings of indigenous people in the aftermath of trade wars. McDonnell, _Masters of Empire_ , 14, 333, note 6. Andrew Lipman takes a humorous approach to situating and unseating White's argument through a review of several works; Andrew Lipman, "No More Middle Grounds?" _Reviews in American History_ 44:1 (March 2016): 24–30.
. In the use of the term "groundless," I have borrowed from my colleague Greg Dowd, who plays rhetorically with the slate of Native American history text titles that implicitly reflect on Richard White's phrase, "middle ground." Gregory Evans Dowd, _Groundless: Rumors, Legends and Hoaxes on the Early American Frontier_ (Baltimore: Johns Hopkins University Press, 2015).
. White, _Middle Ground_ , ix. In her sweeping study of French and Indian families engaged in the western fur trade, Anne Hyde captures the influence and longevity of mixed-race networks. She describes these mixed-race families as making up one of "three worlds" or "three streams" next to the white and Native worlds identified by Richard White. Although she does illuminate people often rendered invisible, like White, Hyde does not explore a black world, or even a world of enslaved Indians. Elite mixed-race families make for compelling objects of study, but, as Hyde notes, they were also people of privilege who owned others as slaves. Her work is an indication that even when we turn to the rubric of "family" as a means of powerfully illuminating the histories of marginalized people—particularly women—we can miss other groups who were oppressed by the very subpopulations that our work unearths. Building on White's and Hyde's formulation of European, Native, and mixed-race Euro-Indian worlds, I point to a world of the unfree on which these other worlds relied for strength and standing. Hyde, _Empires_ , 1, 3. Brett Rushforth's broad and insightful study of slavery in New France focuses almost wholly on Native American slaves. Brett Rushforth, _Bonds of Alliance: Indigenous and Atlantic Slaveries in New France_ (Chapel Hill: University of North Carolina Press, 2012). As I worked toward this picture of the shared world of bondspeople, I found conversation partners in studies on New England slavery; see, Daniel R. Mandell, "The Saga of Sarah Muckamugg: Indian and African American Intermarriage in Colonial New England," in Martha Hodes, ed., _Sex, Love, Race: Crossing Boundaries in North American History_ (New York: New York University Press, 1999), 72–90; Margaret Newell, _Brethren by Nature: New England Indians, Colonists, and the Origins of American Slavery_ (Ithaca: Cornell University Press, 2015); Wendy Warren, _New England Bound: Slavery and Colonization in Early America_ (New York: W. W. Norton, 2016).
. Jennifer Kirsten Stinson, "Black Bondspeople, White Masters and Mistresses, and the Americanization of the Upper Mississippi River Valley Lead District," _Journal of Global Slavery_ 1:2 (October 2016), pp. 165–195. Christian Crouch, "The Black City: African and Indian Exchange in Pontiac's Detroit," revised version of Christian Crouch, "The Black City: Detroit and the Northeast Borderlands through African Eyes in the Era of 'Pontiac's War,'" The War Called Pontiac's Conference, April 5, 2013, Philadelphia, PA, 20–21. Michael Witgen, book manuscript in progress, "Native Sons: Indigenous Land, Black Lives, and the Political Economy of Plunder in North America."
. Frederick Jackson Turner, _The Significance of the Frontier in American History_ (Madison: State Historical Society of Wisconsin, 1894).
. Ira Berlin, _Generations of Captivity: A History of African American Slaves_ (Cambridge, MA: Harvard University Press, 2003), 153, 154, 182, 188, 192, 198.
. Lea VanderVelde, _Redemption Songs: Suing for Freedom before Dred Scott_ (New York: Oxford University Press, 2014), 16.
. William Cronon, _Nature's Metropolis: Chicago and the Great West_ (New York: W.W. Norton, 1991), xviii–xix.
. John Mack Faragher, "'More Motley than Mackinaw': From Ethnic Mixing to Ethnic Cleansing on the Frontier of the Lower Missouri, 1783–1833, in Andrew R. L. Cayton and Fredrika Teute, eds., _Contact Points: American Frontiers from the Mohawk Valley to the Mississippi, 1750–1830_ (Chapel Hill: University of North Carolina Press, 1998), 304–326, 305. Faragher borrows the notion of "frontiers of inclusion" from geographer Marvin W. Mikesell. For more on cross-cultural relations in the Old Northwest, see Daniel P. Barr, ed., _The Boundaries Between Us: Natives and Newcomers along the Frontiers of the Old Northwest Territory, 1750–1850_ (Kent, OH: Kent State University Press, 2006).
. A slate of field-changing twenty-first century works that can be categorized as a new incarnation of the "New Indian History," or, as the University of Michigan doctoral student Harold Walker Elliott has termed it, the "Power School" of Indian history, has explored Native empire, power, and influence in the seventeenth, eighteenth, and nineteenth centuries. See, for instance, McDonnell, _Masters of Empire_ ; Kathleen DuVal, _The Native Ground: Indians and Colonists at the Heart of the Continent_ (Philadelphia: University of Pennsylvania Press, 2006); Pekka Hämäläinen, _The Comanche Empire_ (New Haven, CT: Yale University Press, 2008); Witgen, _Infinity of Nations_.
. Max L. Grivno, "'Black Frenchmen' and 'White Settlers': Race, Slavery, and the Creation of African-American Identities along the Northwest Frontier, 1790–1840," _Slavery and Abolition_ 21:3 (December 2000): 75–93, 76, 78, 85. Grivno cites examples from Minnesota and Wisconsin where black men claimed a "white" self-identification and were defined as white for a time by territorial organizers, "Black Frenchmen," 85, 89; Michael Witgen explores this dynamic in Minnesota at length in his manuscript in progress, _Native Sons_. In Detroit over the time period of my study, I found no examples of black residents stating that they were "white" or wishing to be seen as such. Zainab Amadahy and Bonita Lawrence, "Indigenous Peoples and Black People in Canada: Settlers or Allies?" In Arlo Kempf, ed., _Breaching the Colonial Contract: Anti-Colonialism in the US and Canada_ (New York: Springer, 2009), 121, 120. Jodi A. Byrd, _The Transit of Empire: Indigenous Critiques of Colonialism_ (Minneapolis, MN: University of Minnesota Press, 2011), xxx. Byrd credits the Caribbean (Barbadian) poet Kamau Brathwaite with the origination of this term, xix.
. Tiya Miles, email correspondence with Jill Mackin (doctoral candidate, Montana State University) and Crystal Alegria (co-director, The Extreme History Project), March 17 and 18, 2017. Quoted material is taken from Alegria's email, March 18, 2017. Prominent historian of the Black West Quintard Taylor also uses the term "refugee," but more often attached to wartime experience and without an explicit critique of Native land dispossession. Taylor frequently uses "pioneers" and "settlers" to describe black migrants. It is important to note that his work predates the currently common critical discussions of settler colonialism in Native American and indigenous studies. Quintard Taylor, _In Search of the Racial Frontier: African Americans in the American West, 1528–1990_ (New York: W.W. Norton, 1998). For an illuminating analysis of comparative racialization and settler colonialism, see Patrick Wolfe, "Land, Labor, and Difference: Elementary Structures of Race," _The American Historical Review_ 106:3 (June 2001): 866–905. For an innovative use of "refugee" reflective of current events, see David Blight, "Frederick Douglass, Refugee," _The Atlantic_ , February 7, 2017.
. Amadahy and Lawrence, "Indigenous Peoples and Black People in Canada," 120.
. The historian Roy Finkenbine of the University of Detroit Mercy has compiled a three-page list of primary and secondary sources related to Indians and the Underground Railroad in the Midwest. He is working on a chapter based on his findings, which will appear in the edited collection-in-progress: Damian Pargas, ed., _Fugitive Slaves in North America_ (University Press of Florida). For a slave narrative that features Native collaboration, see especially Josiah Henson, _The Life of Josiah Henson, Formerly a Slave_ (Boston: Arthur D. Phelps, 1849). Manuscripts and dissertations related to this topic are underway by Natalie Joy, at Northern Illinois University, who is working on a book titled "Abolitionists and Indians in the Antebellum Era," and by Darryl Omar Freeman at Washington State University, who is working on a dissertation titled "The First Freedom Line." I have made short forays into this area; see Tiya Miles, "Of Waterways and Runaways: Reflections on the Great Lakes in Underground Railroad History," _Michigan Quarterly Review_ (Summer 2011); Tiya Miles, "'Shall Woman's Voice Be Hushed?' Laura Smith Haviland in Abolitionist Women's History," _Michigan Historical Review_ (Winter 2013). Bohaker, "'Nindoodemag," 52.
Index
"In this digital publication the page numbers have been removed from the index. Please use the search function of your e-Reading device to locate the terms listed."
Abbott, Elizabeth Audrain
Abbott, James
Abbott, Mary
Abbott, Robert
Abbott, Samuel
Abbott & Finchley
Abbott family
Adams, John
African Americans, free. _See_ free blacks
African American servants
African American soldiers. _See also_ black militia
African and African American slaves; Ann Wyley; Blue Jacket and; Clark view; family separation; fire of 1805; French and Indian War; Indian intermarriage; James May ownership; John Askin ownership; New France; Northwest Ordinance; Raudot proclamation; relations with Indian slaves; revolts; Revolutionary War; Ste. Anne's Church records; William Tucker ownership; Woodbridge ownership. _See also_ black militia; _Denison v. Tucker_
agriculture; Elliott; famine; farmers' market; John Askin; Moravian missionaries; ribbon farms; slaves and; William Macomb
Ainse, Sally
Albany, New York
alcohol
Alegria, Crystal
Amadahy, Zainab
American Revolution. _See_ Revolutionary War
Amherstberg, Ontario; maps. _See also_ Fort Malden
Anderson, John
Anishinaabeg. _Seealso_ Ojibwes; Ottawas; Potawatomies
Ann Arbor
Anzaldúa, Gloria
Askin, Adelaide (Alice). _See_ Brush, Adelaide Askin
Askin, Archange (1775–ca. 1866)
Askin, Catherine (Kitty)
Askin, James
Askin, John; Alexander Grant relations; on black militiamen; death; Denisons and; on Detroit's incorporation; on Elijah Brush; fire code offender; fire of 1805; French language use; justice of the peace; land speculation; Macomb estate purchases; Moravian missionary relations; move across river; ribbon farm; St. John's Church; Sally Ainse relations; slaves and servants
Askin, John, Jr.
Askin, Madelaine
Askin, Marie-Archange Barthe (1747–1820)
Baby, Jacques Duperon
Bacon, David
Bald, Clever
Bangs, Nathaniel
banks
Barron, James
Barthe, Jean Baptiste
Barthe, Marie-Archange. _See_ Askin, Marie-Archange Barthe
Barthe family
Bates, Frederick
Battle of Fallen Timbers
Battle of New Orleans
Battle of the Thames
Beaubien, Antoine
Beaubien family
beavers. _See also_ fur trade
Belle Isle. _See_ Hog Island (Belle Isle)
Berthelet, Henry
Biddle, Eliza
Biddle, John
Biddle, William
Billettes, Francis
Bird, Henry
Blackbird, Andrew
Blackburn, Lucie
Blackburn, Thornton
black code (1827)
Black Code (French slavery). _See_ Code Noir
black militia; historiography
black servants. _See_ African American servants
black soldiers. _See_ African American soldiers
Blue Jacket
board of trustees
Bohaker, Heidi
Boone, Daniel
Boston
Bradstreet, John
Bright, Charles
British loyalists; James May and; Sandwich
British navy
Brock, Isaac
Brunsman, Denver
Brush, Adelaide Askin; home; War of 1812
Brush, Charles R.
Brush, Edmund
Brush, Elijah; black militia; death; Denisons and; Elliott case; home; letter to Jefferson; militia leader; post-fire land allotment and sales; slaves and servants; town trustee; War of 1812
Burnett, William
Byrd, Jodi
Cadillac, Antoine Laumet de La Mothe, Sieur de
Cahokia, Illinois
Campau, Joseph
Campau, Simon
Campau (Campeau) family; Belle Isle
Campbell, Donald
_Canada's Forgotten Slaves_ (Trudel)
Cangany, Catherine: _Frontier Seaport_
canoes
capital punishment
Capitulation of Montreal
captives, Native American. _See_ Native American captives and captive-taking
Caribbean, French. _See_ French Caribbean
Cass, Lewis
Catholic Church. _See also_ Ste. Anne's Catholic Church
censuses
Chardavoyne, David
Chatham, Ontario
Chêne, Pierre
Cherokees
_Chesapeake-Leopard_ affair
Chicago
Chillicothe, Ohio
Chippewas. _See_ Ojibwes
Choctaws
Cicotte (Chicoste) family
Cincinnati
Clark, George Rogers
class consciousness
Clinton River. _See_ Huron River (Clinton River)
Code Noir
colleges and universities
commons
Congo, Louis
Congress, U.S. _See_ U.S. Congress
Continental Congress
Constitutional Convention
Contencineau, Jean
cooks and cooking
Cooper, Afua
Cooper, Joseph
Cotteral, George
Council House
Countryman, Edward
Creeks
Crees
criminal justice
Croghan, George
Cronon, William
Crouch, Christian
Cuba
Cuillerier, Marie Angelique. _See_ Sterling, Angelique
Curry, Peter
Cutten, Josiah (Joseph Cotton)
_Cuyahoga_
Dailey, William
Dakotas
Dane, Peter
d'Auteuil, Ruette
Dearborn, Henry
death sentence
DeBaptiste, George
Dejean, Philip
Delawares; massacres; midwives; Pontiac's War; Revolutionary War; Shawnee relations; Wayne and
Denison, Charlotte Paul
Denison, Eastman
Denison, Elizabeth (Lisette); death; historiography; land purchases; portrait; War of 1812
Denison, Hannah; birth; death; War of 1812
Denison, James
Denison, Peter; death; commemorative plaques; militia officer; War of 1812
Denison, Peter, Jr.
Denison, Scipio (Sip)
_Denison v. Tucker_
De Peyster, Arent Schuyler
"Détroit" (name)
Detroit fire of 1805. _See_ fire of 1805
_Detroit Gazette_
Detroit Historical Museum
Detroit Land Board. _See_ Land Board of Detroit
Detroit ordinances. _See_ ordinances, municipal
Detroit River; in art; Brush farm; ferries; historiography; international border; ribbon farms; winter travel on
Detroit School of Urban Studies
Detroit Treaty. _See_ Treaty of Detroit (1807)
Dilhet, Jean
disease
District of Hesse. _See_ Hesse
Dodemead, James
Dodemead, John
Dolson, Matthew
Donnelson, James
Duggan, Thomas
Duncan, John
Dunnigan, Brian Leigh: _Frontier Metropolis_
Du Sable, Jean Baptiste Pointe
Duval, Kathleen
Dwight, Ed
Edwards, Laura
Elliott, Andrew
Elliott, Matthew; lawsuit; slaves; War of 1812
Erie Canal
escaped slaves; court cases; Denisons; Elliott case; habeas corpus and; indenture and; indigenous spaces and; James Sterling and; legislation and ordinances; Levy; militias; Pattinson case; Quinn; Richard Smyth and. _See also_ Underground Railroad
Eustis, William
Fairfield on the Thames
Fallen Timbers, Battle of. _See_ Battle of Fallen Timbers
"fancy trade"
Faragher, John Mack
Farmers and Mechanics Bank
farming. _See_ agriculture
"fat beaver"
fear of Indian attacks
fire of 1805; rebuilding
fire prevention
Flower, Jacob
_A Fluid Frontier_ (Frost and Tucker)
Ford, Abraham
Ford, Mary Louise
Fort Detroit site and plan; early buildings
Forth, Elizabeth Denison. _See_ Denison, Elizabeth (Lisette)
Forth, Scipio
fortifications
Fort Lernoult (Fort Shelby)
Fort Mackinac
Fort Malden; War of 1812
Fort Michilimackinac; Askin; Detroit fire of 1805; Mitchell; Sally Ainse
Fort Niagara; maps
Fort Sackville
Fort Shelby. _See_ Fort Lernoult (Fort Shelby)
Fort Wayne; maps
Foxes
Fox War
free blacks; kidnapping of. _See also_ Dennison, Elizabeth (Lisette); escaped slaves
freemasons
free people of color ( _gens de couleur libre_ ). _See also_ free blacks
French and Indian War
French Caribbean
French language; Hannah Denison; Sibley on; Woodward
French servants
French Town
"frontier" (word)
_Frontier Metropolis_ (Dunnigan)
_Frontier Seaport_ (Cangany)
Frost, Karolyn Smardz
Fugitive Slave Act
fugitive slaves. _See_ escaped slaves
fur trade; African American men; Askin; British and; decline; Detroit as hub; intermarriage in; Macomb family; power couples. _See also_ Abbott & Finchley
Gage, Thomas
Geel, Abraham
_gens de couleur libre_. _See_ free people of color ( _gens de couleur libre_ )
gift giving; captives in
Girardin, Jacques
Gladwin, Henry
godparents
Gouin (Gouen) family
Graham, Isabella
Graham, Mary Henrietta
Grant, Alexander
Grant, Colonel (Kentucky slaveholder)
Grant, Jaspar
"Great Father"
Great Peace of Montreal
Green, James
Griffin, John
Griswold, Stanley
Grivno, Max
Grosse Ile
habeas corpus
Haldimand, Frederick
Hamilton, Henry
Hands, William
Harrison, William Henry
Harrow, Alexander
Harvey, John
Haudenosaunee (Iroquois). _See also_ Mohawks; Oneidas; Senecas
Heath, Barbara
Hecker, Joseph
Heckewelder, John
Hennepin, Louis
Henry, Patrick
Hesse District
Heward, James
Hickman, Harris
historiography
Hog Island (Belle Isle)
House, Michael
Hull, A.J.
Hull, Sarah
Hull, William; black militia; court-martial and death sentence; fear of Indian attack; Indian relations; Land Board; land purchases; War of 1812; Woodward relations
hunting
Huron River (Clinton River)
Hurons (Wyandots); African intermarriage; captive-taking; land cessions; Pontiac's War; Revolutionary War; Ste. Anne's Church
Hyde, Anne
Illinois; dispossession of Native lands; War of 1812. _See also_ Cahokia, Illinois; Chicago
Illinois people
impressment
incorporation, municipal
indenture; Denisons; laws
Indiana; dispossession of Native lands; maps; Prophet's Town; War of 1812. _See also_ Vincennes, Indiana
Indian agents. _See also_ Elliott, Matthew
Indian attacks, fear of. _See_ fear of Indian attacks
Indian captives and captive-taking. _See_ Native American captives and captive-taking
Indian reservations
Indian slaves. _See_ Native American slaves
inheritance of slaves
intermarriage; Afro-Indian; British-French; slaves
interracial sex. _See also_ mixed-race people; sexual slavery and concubinage
Iroquois. _See_ Haudenosaunee (Iroquois)
Jackson, Andrew
Jay, John
Jay Treaty
Jefferson, Thomas; appointees; _Chesapeake-Leopard_ affair; Indian relations; Michigan Territory; _Notes on the State of Virginia_ ; Woodward relations
Johnson, Charles
Johnson, William
Jones, Martha
Jones, Thomas
_Jones v. Abbott_
Kaskaskia
Kentucky
Kickapoo people
King Louis XIV. _See_ Louis XIV, King of France
King Louis XV. _See_ Louis XV, King of France
LaForce, Agnes
Lake Erie; Erie Canal; War of 1812
Lake Huron; maps
Lake Ontario; maps
Lake St. Clair
Langdon, Austin
Larkin, Benjamin
La Leavre, Charles
Land Board of Detroit
land grabs
language, French. _See_ French language
languages, Native American. _See_ Native American languages
Landry, Charles
Lassalle, Jacques
La Vente, Henri Roulleaux
Lawrence, Bonita
lawsuits
leather goods
Lee, William
L'Enfant, Pierre Charles
_Leopard-Chesapeake_ affair. See _Chesapeake-Leopard_ affair
Lernoult, Richard
Levy, J.
liquor. _See_ alcohol
Louis XIV, King of France
Louis XV, King of France
loyalists. _See_ British loyalists
Mack, Stephen
Mackelm, James
Mackin, Jill
Mackinac. _See_ Fort Mackinac
Mackintosh, Angus
Macomb, Alexander (1748–1831)
Macomb, Alexander (1782–1841)
Macomb, David
Macomb, Edgar & Macomb
Macomb, John Gordon
Macomb, John W.
Macomb, Sarah Jane Dring
Macomb, William; account book; death; Moravian missionary relations; ribbon farm; Sally Ainse relations; slaves
Macomb, William, Jr.
Macomb County
Madison, James
Maney, David
maps
marriage, mixed. _See_ intermarriage
marriage "in the custom of the country"
Marietta, Ohio
Mascouten people
Masonville, Alexis
Massachusetts. _See also_ Boston
massacres
May, James; code violator; death; fire of 1805; letter to Jefferson; slaves; taxpayer; University of Michigan; U.S. marshal; Woodward relations
May, Joseph
Mazur, Shawna
McDonald, James
McDonnell, Michael
McDougall, George
McDougall, Robert
McGraw, Bill
McKee, Alexander
McLean, Hector
McNelly, Peter
Meldrum, George
Meldrum and Park
memorial sculptures
merchants (retailers). _See also_ Abbott & Finchley; Phyn and Ellice; Macomb, Edgar & Macomb
Miami River
Miamis: captive-taking; Pontiac's War; Revolutionary War; Ste. Anne's Church; Wayne and
Michigan militia. _See also_ black militia
Michigan state legislature
Michigan Supreme Court
Michigan Territory; courts; higher education; laws; officials
Michilimackinac. _See_ Fort Michilimackinac
_The Middle Ground: Indians, Empires, and Republics in the Great Lakes Region_ (White)
Middleton, George
midwives
militias
Minnesota
missionaries, Protestant. _See_ Protestant missionaries
Missouri. _See also_ St. Louis
Mitchell, David
Mitchell, Sedrick
mixed-race people; African-Native; Askin family; black code; Hyde views; inherited slavery; Ste. Anne's Church; in sex slavery; as slaveholders
moccasin-making
Mohawks
Monroe, James
Monteith, John
Montour, Andrew
Montour family
Montreal; Campaus; Dejean and Hamilton; LaForce; maps; slaves; trade; treaties
Moravian missionaries
Morrison, Charles
Moses, Charlotte
municipal incorporation. _See_ incorporation, municipal
municipal ordinances. _See_ ordinances, municipal
Munro, Robert
Muscogees. _See_ Creeks
National Park Service
Native American attacks, fear of. _See_ fear of Indian attacks
Native American captives and captive-taking
Native languages
Native American reservations. _See_ Indian reservations
Native American servants
Native American slaves; African relations; Clark views; fire of 1805; John Askin ownership; John May ownership; Northwest Ordinance; Pontiac's War; Raudot proclamation; runaways; Ste. Anne's Church records; sexual service; theft by. _See also_ "Panis" (word)
naval battles
navy, British. _See_ British navy
Navarre, Catherine
Navarre, Robert
Negro Militia. _See_ black militia
Negro Town, Ohio; map
Nelson, Jonathan
Neolin
New England; Elijah Brush roots; Hull roots. _See also_ Massachusetts; New York
New Orleans; War of 1812
newspapers
New York; law model; shopping; slave revolts; War of 1812; Woodward roots. _See also_ Albany, New York; Niagara, New York; Schenectady, New York
Niagara, New York. _See also_ Fort Niagara
Northwestern Army
Northwest Ordinance; Article 6; _Denison v. Tucker_ and; habeas corpus and
Northwest Territory; courts; legislature; indenture; maps; officials; seat
_Notes on the State of Virginia_ (Jefferson)
Ohio; cattle; dispossession of Native lands; runaway slaves; Sibley; statehood; supreme court model; War of 1812
Ojibwes; captives and captive-taking; land cessions; Moravian missionary relations; Pontiac lineage; Pontiac's War; Revolutionary War; War of 1812; Wayne and
Oneidas
Onuf, Peter
ordinances, municipal
Ottawas; captives and captive-taking; land cessions; Pontiac lineage; Pontiac's War; Revolutionary War; Ste. Anne's Church; War of 1812; Wayne and
Panis. _See_ Native American slaves
"Panis" (word)
Paris. _See also_ Treaty of Paris
Parker, Thomas
Parmenter, Jon
Patterson, Charles
Pattinson, Richard
Pawnees
Pennsylvania
Perry, Oliver Hazard
Phillips, Christopher
Phyn and Ellice Company
Pollard, Richard
polygamy
Pontchartrain, Jérome Phélypeaux, Comte de
Pontiac (Ottawa leader)
Pontiac, Michigan
Pontiac's War
Pooquiboad
Poremba, David Lee
Porteous, John
Potawatomies; captive-taking; du Sable and; Grosse Ile; land cessions; Pontiac's War; Prophet's Town; Revolutionary War; Ste. Anne's Church; Wayne and
press. _See_ newspapers
Proclamation of 1763. _See_ Royal Proclamation of 1763
Prophet's Town
prostitution
Protestant churches
Protestant missionaries. _See also_ Moravian missionaries
public land. _See_ commons
punishment of slaves
Quebec; city; District of Hesse; James Hull; slaves; War of 1812. _See also_ Upper Canada
Quebec Act
Quinn, Joseph
racialization; of black slaves; of Indians
Raisin River. _See_ River Raisin
Ransom, Daniel
rape
Ratford, Jenkin
Raudot, Jacques
"red" (racial term)
Reed, John
Rémond, Jean Baptiste
reservations. _See_ Indian reservations
retailers. _See_ merchants (retailers)
revolts, slave. _See_ slave revolts
Revolutionary War; black soldiers; Sarah Hull; William Hull. _See also_ Treaty of Paris
Richard, Gabriel
Richard, Marie Suzanne
River Raisin
Robertson, Samuel
Robertson, William
Romain, Jean B.
Roman Catholic Church. _See_ Catholic Church
Royal Navy. _See_ British navy
Royal Proclamation of 1763
Rushforth, Brett
St. Bernard, Charles
St. Clair, Arthur
St. Clair, Arthur, II
St. Clair, William
St. Cosme, Rose
Ste. Anne's Catholic Church; fire of 1805; James Sterling; Smiths; tobacco chewing in; Treaty of 1817; William Macomb
Ste. Anne's Street
Saint James Church, Grosse Ile
St. John's Anglican Church, Sandwich, Ontario
St. Louis
Sandwich, Ontario. _See also_ St. John's Anglican Church, Sandwich, Ontario
Sault Ste. Marie
Saunt, Claudio
Schenectady, New York. _See also_ Phyn and Ellice Company
Schindler, Jonas
Schuyler, Philip
Scott, Rebecca
sculptures, memorial. _See_ memorial sculptures
Senecas
servants, African American. _See_ African American servants
servants, French. _See_ French servants
servants, Native American. _See_ Native American servants
servitude, indentured. _See_ indenture
Seven Years' War. _See_ French and Indian War
sexual assault. _See_ rape
sexual slavery and concubinage
Shawnees: Blue Jacket; Pontiac's War; Revolutionary War; Sally Ainse; Tecumseh and Tenskwatawa; Wayne and
ships. See also _Chesapeake-Leopard_ affair
Shoemaker, Nancy
Sibley, Catherine
Sibley, Ebenezer
Sibley, Henry
Sibley, Sarah Sproat
Sibley, Solomon; co-mayor; Elijah Brush relations; fear of Indian attack; _Jones v. Abbott_ ; Lisette Denison relations; prosecutor; purchases; University of Michigan
Sibley family
Simcoe, John Graves
Sinclair, Patrick
Sinha, Manisha
Sioux. _See also_ Dakotas
slave raiding; Henry Bird; Pawnees and
slave revolts
slaves, African and African American. _See_ African and African American slaves
slaves, escaped. _See_ escaped slaves
slaves, inheritance of. _See_ inheritance of slaves
slaves, Native American. _See_ Native American slaves
slaves, punishment of. _See_ punishment of slaves
Smith, Anna
Smith, Antoine
Smith, David William
Smith, Gene Allen
Smith, Milly
Smyth, Richard
Sterling, Angelique Cuillerier
Sterling, James; alcohol control committee; marriage; Ste. Anne's Church
Stinson, Jennifer
Stockwell, John
Stone, Joel
Supreme Court of Michigan. _See_ Michigan Supreme Court
Swan, Isabella
tanners and tanning
tarring and feathering
taxation
Taylor, Alan
Taylor, Quintard
Taylor, Robert
Tecumseh
Tenskwatawa (Prophet)
Thames River (Canada). _See also_ Fairfield on the Thames
Tippecanoe River
town codes. _See_ ordinances, municipal
town commons. _See_ commons
Three-Fifths Clause (U.S. Constitution)
Treaty of Detroit (1807)
Treaty of 1817
Treaty of Ghent
Treaty of Greenville
Treaty of Paris
Trowbridge, Charles
Trudel, Marcel; _Canada's Forgotten Slaves_
Tucker, Catherine. _See alsoDenison v. Tucker_
Tucker, Veta Smith
Tucker, William
Turner, Frederick Jackson
Underground Railroad
uniforms
University of Michigan
Upper Canada; Askin family; Denisons; District of Hesse; Elliott; Eustis view; executions; Fairfield; laws and ordinances; Macomb family; Simcoe. _See also_ black militia; Sandwich, Ontario
U.S. Congress; Detroit redesign; Treaty of Ghent
U.S. Constitution. _See also_ Three-Fifths Clause (U.S. Constitution)
U.S.S. _Chesapeake_. See _Chesapeake-Leopard_ affair
VanderVelde, Lea
Vincennes, Indiana
Virginia
Wallace, George
War of 1812; map; run-up
Washington, George
Washington City (Washington, D.C.)
Watson, Samuel Codes
Watson, William
Wayne, Anthony
Wayne County; censuses and tax lists
Wendat people. _See_ Hurons
wheat
White, Margaret
White, Richard: _Middle Ground_
Williams, Joel
Williams, John R.
Williams, Lizzie
Williamsburg, Virginia
Wilson, John
Wilson, Stephen
Windsor, Ontario; maps
Wing, Austin E.
Winter, George
Wisconsin
Witgen, Michael
Witherell, James
women, sexual slavery of. _See_ sexual slavery and concubinage
Wood, James
Woodbridge, Dudley
Woodward, Augustus; British occupation and; _Denison v. Tucker_ ; Elliott case; fear of Indian attack; Pattinson case; town redesign; University of Michigan; view of black militia; War of 1812
working class
Wyandots. _See_ Hurons (Wyandots)
Wyandotte, Michigan
Wyley, Ann
Yack, John Michel
Yamasee War
Zeisberger, David
About the Author
**Tiya Miles** is the recipient of a 2011 MacArthur Foundation "genius grant" and is the Elsa Barkley Brown Collegiate Professor and the Mary Henrietta Graham Distinguished University Professor at the University of Michigan in the departments of American culture, Afroamerican and African studies, history, and women's studies and in the Native American Studies Program. She lives in Ann Arbor.
Celebrating 25 Years of Independent Publishing
Thank you for reading this book published by The New Press. The New Press is a nonprofit, public interest publisher celebrating its twenty-fifth anniversary in 2017. New Press books and authors play a crucial role in sparking conversations about the key political and social issues of our day.
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Table of Contents
1. Cover
2. Title Page
3. Copyright
4. Dedication
5. Contents
6. Introduction: The Coast of the Strait
7. 1. The Straits of Slavery (1760-1770)
8. 2. The War for Liberty (1774-1783)
9. 3. The Wild Northwest (1783-1803)
10. 4. The Winds of Change (1802-1807)
11. 5. The Rise of the Renegades (1807-1815)
12. Conclusion: The American City (1817 and Beyond)
13. A Note on Historical Conversations and Concepts
14. Acknowledgments
15. Bibliographic Abbreviations and Quotations
16. Notes
17. Index
18. About the Author
# Guide
1. Cover
2. Contents
3. Title Page
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{"url":"http:\/\/im.ufrj.br\/index.php\/pt\/noticias-e-eventos\/ciclos-de-palestras-e-seminarios-do-im\/colga-coloquio-de-geometria-e-aritmetica","text":"\u00c9 um prazer convid\u00e1-los para mais uma edi\u00e7\u00e3o do nosso\u00a0Col\u00f3quio de Geometria e Aritm\u00e9tica do Rio de Janeiro.\u00a0As palestras ser\u00e3o realizadas na pr\u00f3xima sexta 25 de outubro,\u00a0na Uff - Audit\u00f3rio do Bloco G - Campus Grogoat\u00e1.\n\n#### A programa\u00e7\u00e3o ser\u00e1 a seguinte:\n\n10:30: Luca Scala (UFRJ)\n\nT\u00edtulo: Singularities of the Isospectral Hilbert Scheme\n\nResumo: The Isospectral Hilbert Scheme of Points over a surface was defined by Haiman as the blow-up of the product variety X^n of a complex algebraic surface X along the scheme-theoretic union of its pairwise diagonals; it realizes one of the parametrizations of configurations of n points over the surface X taking into account the order of the points in the configuration. It is in general a singular variety: its singularities are related on one hand to the singularities of the boundary of the (standard) Hilbert scheme of points and on the other hand to those of the union of the pairwise diagonals in the product X^n: the latter, in case of the affine plane, coincide with a subspace arrangement. Haiman himself showed that the Isospectral Hilbert scheme is normal and Gorenstein, but lots of questions about the singularities of this variety remain unanswered; we state three conjectures on this point. We prove that the singularities of B^n are canonical if n \u22645, log-canonical if 6 \u2264n\u22647 and that they are definitely not log-canonical if n\u22659. We also give two explicit resolutions of B^3, one crepant and one S_3-equivariant.\n\n11:30: caf\u00e9.\n\n12:00: Andr\u00e9 Contiero (UFMG)\n\nT\u00edtulo: On the strata in the moduli of pointed curves given by Weierstrass gaps\n\nResumo: We will present a new lower bound for the dimension of the moduli space of pointed curves with prescribed Weierstrass semigroup at the marked point. This new lower bound is derived from Pinkham's equivariant deformation theory and improves all the previous ones that we are aware. Few results of a working in progress on the rationality of these moduli spaces will also be presented.\n\nAs palestras do Col\u00f3quio de Geometria e Aritm\u00e9tica (COLGA) do Rio de Janeiro ser\u00e3o realizadas em\u00a030 de agosto (sexta-feira),\u00a0no Instituto de Matem\u00e1tica, UFRJ - CT sala C116 \u2013 Ilha do Fund\u00e3o.\n\nPrograma\u00e7\u00e3o:\n\n09:30 \u00e0s 10:30:\u00a0Applications of curves over finite fields to polynomial problems, Daniele Bartoli (Universit\u00e0 degli Studi di Perugia - It\u00e1lia).\n\nResumo: Algebraic curves over finite fields are not only interesting objects from a theoretical point of view, but they also have deep connections with different areas of mathematics and combinatorics.\u00a0In fact, they are important tools when dealing with, for instance, permutation polynomials, APN functions, planar functions, exceptional polynomials, scattered polynomials, Moore-like matrices.\u00a0In this talk I will present some applications of algebraic curves to the above mentioned objects.\n\n10:30 \u00e0s 11:00: Pausa para o caf\u00e9.\n\n11:00 \u00e0s 12:00:\u00a0Inflection of linear series on hyperelliptic curves over arbitrary fields (joint with I. Biswas, I. Darago, C. Han and C. Garay L\u00f3pez), Ethan Cotterill (UFF).\n\nResumo: According to Plucker's formula, the total inflection of a linear series (L,V) on a complex algebraic curve C is fixed by numerical data, namely the degree of L and the dimension of V.\u00a0The problem of describing the k-rational inflectionary locus of a Gal(k-bar\/k)-linear series (L,V) when k is a non-algebraically closed field is significantly more subtle.\u00a0For example, the topology of the real inflectionary locus of a real linear series depends in a nontrivial way on the topology of the real locus of C. I will describe joint work with Biswas and Garay L\u00f3pez in which we study this dependency when C is hyperelliptic and (L,V) is a complete series. Our main tool is a nonarchimedean degeneration, which allows us to relate the (real) inflection of complete series to the (real) inflection of incomplete series on elliptic curves.\u00a0I will also describe work in progress with Darago and Han in which we compute k-rational inflectionary loci valued in the Grothendieck--Witt group GW of an arbitrary field k. To do so, we apply the A^1 homotopy theory of Morel, Voevodsky, Levine, Kass and Wickelgren.\n\nAs palestras ser\u00e3o realizadas na pr\u00f3xima sexta-feira,\u00a028 de Junho,\u00a0na UFRJ - Instituto de Matem\u00e1tica, UFRJ - CT, Sala C208 \u2013 Ilha do Fund\u00e3o.\n\nPrograma\u00e7\u00e3o:\n\n09:30 \u00e0s 10:30:\u00a0The Hurwitz curve over a finite fielde and its Weierstrass points for the morphism of lines, Herivelto Borges (USP - S\u00e3o Carlos).\n\nResumo:\u00a0Let \u00a0$\\mathcal{X}$\u00a0be an irreducible algebraic curve defined over an algebraically closed \u00a0field \u00a0$\\mathbb{K}$\u00a0\u00a0 of characteristc \u00a0$p\\geq 0$.\u00a0The genus of\u00a0$\\mathcal{X}$\u00a0\u00a0is certainly the most famous \u00a0birational invariant of \u00a0$\\mathcal{X}$. If \u00a0$\\mathbb{K}(\\mathcal{X})$\u00a0denotes the function field \u00a0of\u00a0$\\mathcal{X}$,\u00a0the group all \u00a0$\\mathbb{K}$-automorphisms \u00a0of\u00a0$\\mathbb{K}(\\mathcal{X})$\u00a0is called \u00a0{\\it automorphism group} of\u00a0$\\mathcal{X}$, and it is denoted by Aut$(\\mathcal{X})$.\u00a0Such group is another birational invariant of \u00a0$\\mathcal{X}$, and the study of Aut\u00a0$(\\mathcal{X})$\u00a0has \u00a0become a central problem within the theory of algebraic curves.\u00a0In this talk, we will consider smooth Hurwitz curves\n\n$\\mathcal{H}_n: \\, XY^n+YZ^n+X^nZ=0,$\n\nover the finite field\u00a0$\\mathbb{F}_{p}$\u00a0and \u00a0provide \u00a0an \u00a0explict \u00a0description of \u00a0its Weierstrass points for the \u00a0morphism of lines. That is, we will completely charaterize the special set \u00a0of points $P\\in \\mathcal{H}_n$\u00a0for which the intersection multiplicity \u00a0$I(P,\\mathcal{H}_n \\cap T_{P}\\mathcal{H}_n)$\u00a0is somewhat large. As a consequence, the full automorphism \u00a0group Aut$(\\mathcal{H}_n)$, as well as the genera of all Galois subcovers \u00a0of\u00a0$\\mathcal{H}_n$\u00a0will be presented. 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Q: Unable to connect to a .mdf database file in Windows application from client machine I am creating a Windows application to maintain the School Students information. I am using a LocalDB database and I do have the copies of <DBName>.MDF and <DBName>_Log.LDF. As Visual Studio along with MSSQLLocalDB already installed in my laptop, I am able to connect to the database and application is just working fine.
I just copied the build files along with DB files in my client machine and tried opening the windows application. But the app returning below errors when it is trying access the database:
The Underlying Provided Failed to Open".
Inner expectation: Server not accessible or not available
I am pretty much sure that my client machine doesn't have any SQL client tools installed, so it quite possible that failing to connect the .MDF database file.
Now my questions are:
*
*Is it really possible to connect to a .mdf database file from Windows application in client machine without installing any big tools? As my client doesn't want to install any big tools on their system
*If my 1st question answer is Yes, How we can achieve this? Any changes required in my code or config file?
*If this required any small tools to install in client application, what are they?
*If .MDF database file not at all going to work on client machine, are there any alternatives? Please suggest.
My connection string:
<connectionStrings>
<add name="SchoolDBEntities"
connectionString="metadata=res://*/DBModel.csdl|res://*/DBModel.ssdl|res://*/DBModel.msl;provider=System.Data.SqlClient;provider connection string="data source=(LocalDB)\MSSQLLocalDB;attachdbfilename=|DataDirectory|\SchoolDB.mdf;integrated security=True;connect timeout=30;MultipleActiveResultSets=True;App=EntityFramework""
providerName="System.Data.EntityClient" />
</connectionStrings>
A: @Chetan Ranpariya is almost correct. If you are using MS SQL Server - any version - you must have SQL Server installed on the machine where the mdf/ldf files live or at least where they can be accessed by the SQL Server program.
If I read your question correctly, you have MSSQL Installed on your laptop and that is why it works there. You do not have MSSQL installed on the client's computer or network so your calls to the DB fail.
As to what else to use, that question is far too broad. It depends on a lot of factors.
John
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\section{Introduction}
The atomic nucleus, which at energies in the range of mega-electron volts can be viewed as a quantum system of strongly interacting protons and neutrons \cite{scidac,furnstahl,nuclei}, is a very fascinating object. One of the most intriguing challenges is the description of its time evolution. Indeed the nucleus can be naturally found in quantum states that decay by emitting photons, electrons or even nucleons and heavier particles.
This endeavor becomes even more necessary in the rise of new experiments that probe new modes of radioactivity which will need theoretical justification \cite{mona}.
One way is to solve the time-dependent Schr\"{o}dinger equation by means of time discretization techniques \cite{Bulgac10062011,volya,oishi}. A different approach lies in the solution of the time-independent Schr\"{o}dinger equation in the complex energy or momentum space. The time dependence is then absorbed by the complex nature of the solution, whose imaginary part is associated with the decay time. Metastable nuclear states and resonances could then be described in a time-independent formalism \cite{Gamow,Berggren,Romo,phil_trans}.
Formulating the structure and reaction problem in the complex energy plane \cite{cs_real1,cs_real2,gaute_michel,Fossez, Laza,Laza2,Deltuva,Deltuva2,kruppa_scatcs,Myo20141,kikuchi}, provides with an alternative step towards the unification of structure (bound states) and reaction (resonances) aspects in nuclear physics, which will lead in a more controlled and model independent evaluation of observables. Noted that there
already exists vivid progress on the \textit{ab-initio} description of structure and reactions on the real-axis by Lawrence Livermore and TRIUMF groups \cite{rgm1,rgm2,rgm3},
by Los Alamos/Argonne groups \cite{nollett_react} and also on the lattice by \cite{dean_lee,briceno}.
\section{The NC(GSM) formalism}
One of the ways to obtain complex energy solutions of a physical system is by turning the Schr\"{o}dinger equation into an eigenvalue problem and diagonalizing the complex Hamiltonian matrix.
The basic code that has been employed for the description of resonances, by diagonalizing a very large non-Hermitian complex symmetric Hamiltonian matrix, is the Gamow Shell Model (GSM) code \cite{michel_2002,NM2,review_GSM,ncgsm,eff_inter}. The orthonormal underlying basis, upon which the Hamiltonian matrix is diagonalized, is known as Berggren basis \cite{Berggren} which provides a symmetric description of bound states, resonances and scattering states. The Hamiltonian matrix is non-Hermitian and complex symmetric with complex eigenvalues. The matrix is sparse and a relatively small number of eigenvectors and eigenvalues is of interest. At this point there is no conceptual difference between GSM with a core and the NCGSM besides the underlying Hamiltonian. Indeed, in the GSM case
the Hamiltonian consists of the one-body kinetic energy, the one-body mean-field (either schematic or Hartree-Fock) and the residual NN interaction, whereas in the NCGSM case the one-body mean field is not present in the A-body Hamiltonian \cite{ncgsm}. The nucleon-nucleon interaction is expressed in the Berggren basis using the potential separable expansion (PSE) \cite{gyar_kruppa} in a HO basis method \cite{hagen_morten_michel,gsm_radii,ncgsm}. In this way, matrix elements between scattering and/or resonant states never diverge, due to the Gaussian fall-off of the HO radial form factor, and in addition one can conveniently transform matrix elements from the
relative frame to the lab frame. For matrix elements of other operators, such as electromagnetic transition operators, the renormalization of integrals relies on the method of external complex scaling (ECS).
We note here though that the PSE method has also been employed for the calculation of the recoil matrix elements of the intrinsic Hamiltonian, since in this case the ECS technique does not provide converged
results.
For the diagonalization of the large complex symmetric matrix we have used
a complex extension of the Lanczos algorithm \cite{review_GSM}.
The largest matrix that has been diagonalized has a dimension of $\sim$ 10$^6$. This number materializes to about A=4,5 for \textit{ab-initio} no-core calculations in the Berggren basis and to 7-8 active valence particles when assuming a frozen configuration (also known as ``core") but allowing only a portion of the particles occupying the continuum (Berggren) orbitals (particle-hole truncations).
The second alternative is the Davidson method \cite{review_GSM} (see also a recent application on the description of tunneling for a two-body atomic system \cite{Forssen}).
We would like to highlight a unique feature of the GSM diagonalization. Both the Lanczos and the Davidson methods calculate the ground state of the system as the lowest eigenvalue. In the GSM where the Hamiltonian matrix is non-Hermitian, the lowest eigenvalue is not guaranteed to coincide with the ground state and it may as well be a scattering state. A criterion is established which separates the state of interest from the wealth of scattering states; that is the overlap method \cite{review_GSM}.
In the overlap method a smaller diagonalization takes place first, in a space spanned by
\begin{table}[h!]
\caption{Comparisons \cite{Pap_Maris} between the NCGSM and the computer program MFDn. N$_{\rm{shell}}$ = 2n+$\ell$ and $\hbar$$\omega$ = 20 MeV. }
\centering
\begin{tabular}{c c c c}
\hline\hline
Nucleus & MFDn & NCGSM & Difference \\ [0.5ex]
\hline
$^2$H 1$^+$ (N$_{\rm{shell}}$ = 4) & -1.6284 & -1.6284 & $\leq$ 0.1 keV \\
$^2$H 1$^+$ (N$_{\rm{shell}}$ = 8) & -2.1419 & -2.1419 & $\leq$ 0.1 keV \\
$^3$H 1/2$^+$ (N$_{\rm{shell}}$ = 4) & -7.6016 & -7.6016 & $\leq$ 0.1 keV \\
$^3$H 1/2$^+$ (N$_{\rm{shell}}$ = 8) & -8.3203 & -8.3203 & $\leq$ 0.1 keV \\
$^3$He 1/2$^+$(N$_{\rm{shell}}$ = 8) & -7.6084 & -7.6084 & $\leq$ 0.1 keV\\
$^4$He 0$^+$ (N$_{\rm{shell}}$ = 4) & -27.3685 & -27.3684 & 0.1 keV \\
$^6$Li 1$^+$ (N$_{\rm{shell}}$ = 4) & -24.9778 & -24.9776 & 0.2 keV \\ [1ex]
$^6$Li 3$^+$ (N$_{\rm{shell}}$ = 4) & -22.4959 & -22.4957 & 0.2 keV \\ [1ex]
\hline
\end{tabular}
\label{tab:1}
\end{table}
a few states (usually single particle bound states and resonances). This smaller space sometimes is also called the ``pole approximation". The solution is the reference eigenvector.
At a second step a diagonalization in the full space (bound states+resonances+scattering states) takes place and the solution is the one that maximizes the overlap with the reference eigenvector.
Together with the GSM, another algorithm known as the Density Matrix Renormalization Group (DMRG) has also been used \cite{White,Papenbrock_dmrg,Pittel,Rotureau_2006,ncgsm}. The method is a truncation algorithm which aims in reducing the sizes of the matrices to be diagonalized, while keeping the same accuracy as in the full calculation. DMRG is an iterative method for which at each step the space is increased by adding basis states one-by-one and the truncation is dictated by
the density matrix which is constructed in each step. At each step a complex symmetric non-Hermitian matrix is diagonalized via the Lanczos method and the matrix is smaller than the typical matrix of a full-fledged GSM calculation. Several diagonalizations of such smaller matrices are performed until a convergence criterion is reached. A recent variant of the DMRG method \cite{Legeza:2015fja} has shown that very large model spaces can be reached and many ``sweeps" can be performed in a timely manner, making it tempting to use such a variant also in Berggren basis DMRG based calculations.
\section{Applications of the NCGSM approach}
\subsection{Benchmarks}
Aiming at a predictive theory it becomes increasingly important to complete a quality control on the solvers which are employed for the solution of
the many-body problem, a task that implies validation and cross-checks (benchmarks) of existing codes \cite{witek_jacek_stat}.
To test the NCGSM algorithm we have performed benchmark
calculations, in which we compared the NCGSM results with
results obtained using the NCSM \cite{Barrett2013131} Many-Fermion Dynamics nuclear (MFDn) computer program \cite{mfdn,mfdn2},
and in Table (\ref{tab:1}) we present applications for systems up to $^6$Li. For this benchmark we employed a Harmonic Oscillator (HO) basis
in a Full Configuration Interaction (FCI) truncation and
the JISP16 realistic interaction \cite{jisp16}. Nevertheless, chiral interactions were also tested successfully \cite{Pap_Maris}. This agreement reassures that the calculations are
not contaminated with unintentional errors or flaws. It should be noted that there has also been two other successful works that benchmarked the GSM algorithm, using central interactions and a $\alpha$-core,
against the complex scaling technique \cite{kruppa_george,masui}.
\subsection{ANCs and widths}
In its current implementation the NCGSM is not ready to provide scattering observables on the real-axis, such as cross-sections, even though such
a goal is not far from reach after the combination of the GSM with the Resonating Group Method \cite{rgm_book} using phenomenological interactions/optical potentials \cite{yannen,Fossez}.
\begin{figure}[h!]
\centering
\includegraphics[width=100mm]{overlap_5He_Hankels}
\caption[T]{\label{Fig1}
(Color online) Overlap function and tail fit with a Hankel function. C$_{lj}$ stands for the ANC. Figure is from \cite{ncgsm}.}
\end{figure}
We are able however to compute overlaps between nuclear states and access information associated with the ``tail" of the overlap.
The relevant quantity in the study of asymptotic properties of the nuclear wavefunction or actually its projection onto cluster (sub-cluster) states \cite{nollett_2011}
is the Asymptotic Normalization Coefficient (ANC). Recently there is a collective effort in nuclear theory to compute asymptotic quantities and
we are witnessing an abandonment of quantities such as spectroscopic factors in favor of ANCs and widths or partial widths.
The basic argument behind this endeavor, besides the physics interest (e.g. relevance to astrophysical processes for both resonance widths and ANCs),
is the fact that asymptotic quantities are less model dependent and closer to the notion of an observable quantity \cite{kadyrov,furn_achim}. At the same time ANCs can serve as an internal consistency test between many-body methods since
calculations at distances far away from the nuclear interaction range always pose challenges and difficulties (see e.g. discussion at \cite{nollett_2012} for some of the \textit{ab-initio} methods).
The GSM or the NCGSM which are formulated on a basis that has a correct asymptotic behavior and captures the relevant long range physics, become
appropriate for the calculation of asymptotic quantities. For a detailed review of the progress that has been made in the calculation of ANCs and also the experimental
situation we refer the reader to \cite{nollett_2012} and also \cite{okolowicz} for ANCs calculations within the GSM.
In this contribution we present calculations that were published in \cite{ncgsm} of ANCs within the NCGSM using realistic interactions.
The model space of the calculation, as it was described in \cite{ncgsm}, includes single particle (s.p.) partial waves with angular momentum up to $\ell$ = 4 (g-waves).
For $^5$He, being particle unstable in its ground state, we employed a complex GHF basis consisting of the s.p. 0p$_{3/2}$ resonant state and non-resonant p$_{3/2}$
states along the complex contour which encloses the s.p. resonant state, a necessary condition for the s.p. Berggren completeness to be satisfied.
In order to obtain the many-body solution and calculate the overlap for the reaction: $^4\rm{He}_{0_+}$ + n $\to$ $^5\rm{He}_{3/2^-}$ we used the Davidson diagonalization \cite{review_GSM} method and limited our selves to continuum configurations that allowed up to four particles occupying continuum orbits (4p-4h truncation). In the future it will be important to assess the importance of the configurations involving many particles in continuum orbits and also try to
accompany the results with a truncation error associated with the missing configurations. It should also be noted that the creation operator for the calculation of the overlap does not only
create on a single state,
but there is a sum over all continuum states; a fundamental difference between NC(GSM) and traditional configuration interaction calculations in a HO basis \cite{gsm_SF}.
We present our results in Fig.\ref{Fig1} which was taken from \cite{ncgsm} for the effective V$_{low\, k}$ \cite{Bogner20031,HjorthJensen1995125,cens} $\Lambda$ = 1.9fm$^{-1}$ chiral N$^3$LO NN interaction \cite{EM_pot}.
We see that the overlap exhibits both real and imaginary parts reflecting the complex nature of the Berggren basis. After fitting the asymptotic part of the overlap
with a complex Hankel function we extract an ANC with a real part of 0.197 fm$^{-1/2}$. Now knowing the ANC we are able to obtain the width of $^5$He using the formula:
%
\begin{equation}
\label{anc_width}
C = \sqrt{ \frac{\Gamma \mu}{\hbar^2 \Re(k)} }
\end{equation}
%
that relates the width and the ANC \cite{okolowicz}, where $\mu$ is the reduced mass, $k$ is the real part of the complex linear momentum that corresponds to the
neutron-separation energy of $^5$He and $C$ stands for the ANC. The result for the width is $\Gamma$ = 311 keV.
Within the 4p-4h truncation, the complex Davidson
diagonalization provided for the S$_{1n}$ the value of -1.561 MeV and a width $\Gamma$ of 370 keV. The small difference between the width obtained from the ANC
formula and the one obtained from the diagonalization stems from an approximation that was made on the proof of formula \eqref{anc_width}. The approximation is that
the real part of the linear momentum has to be considered. It has been shown in \cite{ncgsm} that this approximation implies the condition $\frac{\Gamma}{2S_{1n}} \to $ 0,
namely, formula \eqref{anc_width} will work for states that have
widths much smaller as compared to two-times the separation energy. In our case $\frac{\Gamma}{2S_{1n}}$ = 11.8 $\%$,
which explains the deviation from the exact diagonalization result.
\subsection{NCGSM results for $^{4}$H and $^4$Li}
\begin{figure}[h!]
\centering
\includegraphics[width=100mm]{4H_4Li_spec}
\caption[T]{\label{Fig2}
(Color online) Ground state and first excited state spectra of $^4$H and $^4$Li. Gray scale denotes the continuum/scattering regime which is described by adopting a complex Beggren basis.}
\end{figure}
Next we are presenting calculations for $^4$H and $^4$Li. These systems have also been computed in approaches with realistic interactions,
in \cite{scat_benchm} for a scattering benchmark calculation within several few body methods and in \cite{horiuchi} within the complex scaling method.
Especially for hydrogen isotopes there exists a recent experimental interest since measurements
claim to observe a relatively narrow $^7$H resonance \cite{caamano}. In addition, it is believed that the triplet of isotopes $^{5,6,7}$H resemble the Helium isotopic chain ($^{6,7,8}$He). Namely
$^7$H resembling $^8$He is the most ``bound" member of the triplet having a relatively small width, $^6$H resembling $^7$He is ``unbound" reflecting its extremely large width while $^5$H is just a broad resonance (broader than $^7$H), resembling in this case $^6$He which is less bound than $^8$He. The theoretical investigation of the shell structure and the pairing correlations in the continuum
will be a decisive factor in the understanding of the binding mechanism in this area of the chart and it
will also be a challenging task.
In this work we are using a phenomenological WS potential for the generation of the basis. For $^4$H and $^4$Li the
WS basis is created for the $^3$H + n or $^3$He + p systems respectively.
Namely for $^4$H a neutron 0$p_{3/2}$ s.p. resonant state is considered
whereas for $^4$Li a proton 0$p_{3/2}$ s.p. resonant state. The long-range Coulomb interaction in the case of $^4$Li is treated in the same way as in \cite{ncgsm,michel_coul,coul_isosp}.
Besides the complex neutron and proton resonances and the associated complex continua, we consider s.p. partial waves up to h-waves ($\ell$=5) as HO basis states characterized by a frequency of $\hbar \omega$ = 20 MeV. In particular, for $^4$H and for the neutron space we used a basis that consisted of 15p$_{3/2}$ complex s.p. states and 7s$_{1/2}$, 7p$_{1/2}$, 2d, 2f, 2g, 1h real HO s.p. states, while for the proton space all basis states are HO states with 7s$_{1/2}$, 7p$_{1/2}$, 2d, 2f, 2g, 1h.
Noted that we are using a different truncation scheme that departs from the typical N$_{max}$ or N$_{shell}$ HO truncation. Here, and also in other NCGSM calculations, we choose to use more radial nodes for specific $\ell$ states. Here states with $\ell$=0,1 have been chosen to have more nodes since
we noticed that they contribute more energy to the system. Further calculations that investigate this behavior are in progress.
The same basis was used for $^4$Li but instead of a neutron s.p. resonant state we considered a proton s.p. resonant state.
Our results for the g.s and first excited states of $^4$H and $^4$Li are shown on Fig.\ref{Fig2}. The energies are with respect to the one-neutron and one-proton particle thresholds.
For the thresholds, the g.s. energies of $^3$H and $^3$He are found to be -7.92 MeV and -7.12 MeV respectively, for an effective V$_{low\, k}$ $\Lambda$ = 2.0fm$^{-1}$ N$^3$LO Chiral EFT interaction.
Overall we observe a good agreement with experimental measurements \cite{tunl} and especially the small gap between the 1$^-$ and 2$^-$ states that has been observed is also predicted in our calculation.
Even though the calculations for the widths show stability, the widths are very large, so we are not dealing with typical resonances that would have an appreciable impact on cross-sections.
In the calculation presented here we restricted the occupation of continuum orbits to a maximum of three particles (3p-3h).
In our future work we will provide results without truncations and also with investigations on the impact of missing excitations on energies and widths.
\section{Conclusions and outlook}
In conclusion, we presented applications of the NCGSM for the calculation of energies, widths and asymptotic quantities such as ANCs of unbound nuclei. At the same
time we benchmarked our algorithm against another commonly used solver.
Our immediate goals are to continue working on applications of the NCGSM for light unbound nuclear systems in the neutron and proton rich side of the nuclear chart.
The success of the NCGSM is tied with advances in computer algorithms and the formulation of efficient complex symmetric diagonalization solvers. On the physics side, even
when the most efficient solver will be at hand, a full calculation in the Berggren basis (no p-h truncations) for a system such as $^{11}$Li will be very demanding. Hence, one of our goals is
to quantify at first the impact of missing truncations (we already know that the weight of many particles in continuum orbits is small). Also we aim at a construction of a realistic effective interaction, i.e. an interaction in the NCGSM nuclear medium \footnote{NCGSM medium here should be seen as the model space that the A-nucleons evolve, but in addition, scattering to continuum orbits will be allowed through the Berggren basis} that
would stem from a realistic free-space interaction, which we will then utilize for NCGSM calculations (see e.g. \cite{gsm_eff_gaute} for a Lee-Suzuki transformation for interactions in the complex energy plane and a multireference perturbation theory approach).
Finally, we would like to contribute to the effort of bridging the gap between Lattice-QCD and low energy physics and a possible way was shown in \cite{bira_lat}. This could be achieved once NCGSM will be utilized to handle NNN interactions. Then we could naturally compute resonant features of finite nuclei at any pion mass
that is available at that time.
\subsection{Acknowledgments}
This work was supported by the US DOE under grants No. DESC0008485 (SciDAC/NUCLEI). This work was also supported in part by the FUSTIPEN (French-U.S. Theory
Institute for Physics with Exotic Nuclei) under U.S. DOE grant No. DE-FG02-10ER41700.
We would like to thanks H. M. Aktulga, W. Nazarewicz, J. P. Vary, C. Yang, E. G. Ng and G. I. Fann for fruitful discussions on complex energy diagonalization solvers
and P. Maris for his help with the benchmark calculations of Table I.
\bibliographystyle{apsrev4-1}
| {
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{"url":"https:\/\/socratic.org\/questions\/how-do-you-determine-the-mass-of-5-20-moles-of-c-6h-12-gram-formula-mass-84-2-gr","text":"# How do you determine the mass of 5.20 moles of C_6H_12 (gram-formula mass = 84.2 grams\/mole)?\n\nMar 26, 2018\n\nThe mass of $\\text{5.20 mol C\"_6\"H\"_12}$ is $\\text{438 g C\"_6\"H\"_12}$.\n\nRefer to the explanation for the process.\n\n#### Explanation:\n\nDivide the given moles by the molar mass of the compound. I prefer to do this by multiplying by the inverse of the molar mass, since it is a fraction. I believe it's easier to see what happens with the units.\n\n5.20color(red)cancel(color(black)(\"mol C\"_6\"H\"_12))xx(84.2\"g C\"_6\"H\"_12)\/(1color(red)cancel(color(black)(\"mol C\"_6\"H\"_12)))=\"438 g C\"_6\"H\"_12\" (rounded to two significant figures)\n\nThe mass of $\\text{5.20 mol C\"_6\"H\"_12}$ is $\\text{438 g C\"_6\"H\"_12}$.","date":"2020-06-06 09:10:05","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 5, \"mathjax_inline_tex\": 1, \"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\": 0.7076046466827393, \"perplexity\": 828.8071379410068}, \"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-2020-24\/segments\/1590348511950.89\/warc\/CC-MAIN-20200606062649-20200606092649-00075.warc.gz\"}"} | null | null |
Michael Howard Wolf Law Firm, the well-established law firm in Fort Lauderdale, Florida, has the renowned attorney Michael Howard Wolf leading the pack. He is one of the Florida's finest and most experienced attorneys and has recorded tremendous success within his 41-year career.
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YOUNG, STERN, AND TANNENBAUM, P.A. | {
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Until It Sleeps — сингл американской группы Metallica, с шестого студийного альбома Load.
Список композиций
Музыкальное видео
Клип на песню был снят в окрестностях Лос-Анджелеса, в мае 1996 года под руководством режиссёра Сэмюэля Бейера.
Премьера видеоклипа состоялась 23 мая 1996 года.Вдохновением для видео стал триптих Иеронима Босха «Сад земных наслаждений».
В 1996 году клип выиграл в номинации лучшее хард-рок видео по версии MTV.
Участники записи
Джеймс Хэтфилд — ритм-гитара, вокал
Кирк Хэмметт — соло-гитара
Джейсон Ньюстед — бас-гитара
Ларс Ульрих — ударные
Чарты
Сертификации
Примечания
Ссылки
Until It Sleeps на Metallica.com
Until It Sleeps (Official Music Video) на YouTube
Песни Metallica
Синглы 1996 года
Песни 1996 года
Синглы Elektra Records
Песни о болезнях и расстройствах
Синглы, возглавлявшие UK Rock Chart | {
"redpajama_set_name": "RedPajamaWikipedia"
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Q: Understand quadratic divergence in first-order correction to 2-point green's function in $\phi^4$ theory Concerning only scalar QED here and momentum configuration for Feynman's diagrams. For 2-point green's function of $\phi^4$ theory$$G(x_1,x_2)=\langle\Omega|T(\phi(x_1)\phi(x_2)\exp\left(\frac{-i\lambda}{4!}\int d^4y~\phi^4(y)\right)|\Omega\rangle.$$
As with perturbation theory, we have $$G(x_1,x_2)=\langle\Omega|T\{\phi(x_1)\phi(x_2)\}|\Omega\rangle+\langle\Omega|T\left\{\phi(x_1)\phi(x_2)\int~d^4y~\frac{-i\lambda}{4!}\phi^4(y)\right\}|\Omega\rangle+o(\lambda^2)$$ which we evaluate order by order using Wick's theorem. In particular, for the order $\lambda$ term, we have
$$\langle\Omega|T\left\{\phi(x_1)\phi(x_2)\int~d^4y~\frac{-i\lambda}{4!}\phi^4(y)\right\}|\Omega\rangle=\int d^4y(-i\lambda)\frac{1}{4!}\langle\Omega|4\cdot 3\cdot\mathcal{C}(\phi(x_1)\phi(y))\mathcal{C}(\phi(x_2)\phi(y))\mathcal{C}(\phi(y)\phi(y))|\Omega\rangle$$
having excluded disconnected graphs, where I hope you will excuse me for using $\mathcal{C}(\phi(x_1)\phi(y))$ to denote the contraction between $\phi(x_1)\phi(y)$ as I have no idea how to LaTeX wick contraction without simplerwick package, i.e. $$\mathcal{C}(\phi(x_1)\phi(y)):=\lim_{\epsilon\to 0^+}\int\frac{d^4k_1}{(2\pi)^4}\frac{i}{k^2_1-m^2+i\epsilon}e^{-ik_1\cdot(x_1-y)}.$$
Consider the Fourier Transform of the $\lambda$ order term (denoted $G_\lambda$) I wrote above\begin{align}\mathcal{F}(G_\lambda)(p_1,p_2)&=\int~d^4 x_1d^4 x_2 G_\lambda(x_1,x_2)e^{-ip_1x_1-ip_2x_2}\\&=\frac{1}{2}(2\pi)^4\delta^4(p_1+p_2)\frac{i}{p_1^2-m^2}\frac{i}{p_2^2-m^2}\lim_{\epsilon\to 0^+}\int~\frac{d^4k}{(2\pi)^4}\frac{i}{k^2-m^2+i\epsilon}.\end{align}
I am trying to understand the divergence of the integral
$$\int d^4k\frac{i}{k^2-m^2+i\epsilon}.$$
The technique given to me was that (btw we are in flat spacetime with mostly minus metric) we should do a substitution with $ik_E^0=k^0$, $\vec{k}_E=\vec{k}$ so the integral becomes$$I=\int^{iT_f}_{iT_i}dk^0_E\int^\infty_{-\infty}d^3\vec{k}_E\frac{1}{k_E^2+m^2}$$ where $k^2_E:=(k^0_E)^2+(\vec{k}_E)^2$.
Question 1
In calculating $S$-matrix elements, we have $T_f\to\infty$ and $T_i\to-\infty$. In this case should not the integration range go from $i\infty$ to $-i\infty$ or is there no difference to just write $\int^\infty_\infty~dk^0_E$?
Question 2
When estimating the value of the above integral, why is it the case that when $|k_E|\to \alpha$ for large real positive valued $\alpha$, the integral goes to $$I\sim\int^\alpha\frac{|k_E|^3}{|k_E|^2}d|k_E|$$ I certainly understand that $m$ contribution can be neglected, but I fail to make much sense on how we go from $d^4k_E$ to $d|k_E|$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,670 |
An application of a gradient relaxation method to noisy infrared images.
Image segmentation is an essential preliminary step in automatic pictorial pattern recognition and scene analysis problems. The objective of segmentation techniques is to partition an image into regions or components. The purpose of this thesis is to analyze a segmentation technique called gradient relaxation. The gradient relaxation method is a viable method in segmenting objects within an image. The gradient relaxation technique is applicable to images having unimodal distributions. This method is applied to noisy infrared images in an attempt to detect and classify the target. The method allows for an easy selection of a threshold value which may be required for other types of image processing on the image. The main issue is to examine the effectiveness of this technique applied to noisy infrared images from uncooled focal plane array sensor having unimodal distributions. The technique was able to extract the target in the image, producing a homogeneous and uniform region for most of the cases studied. A target which was fragmented into several parts because of the noise is not detectable. The technique could be implemented in hardware and applied to the inputs of a classification system for detectable objects in noisy infrared images. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,358 |
""" Tests for YATSM scripts
"""
import os
import shutil
import unittest
from utils_mapping import TestMaps
class Test_YATSMMap(TestMaps):
def setUp(self):
""" Setup test data filenames and load known truth dataset """
self.script = 'yatsm_map.py'
# Test data
self.root = os.path.join(
os.path.dirname(os.path.abspath(__file__)), 'data')
self.result_dir = os.path.join(self.root, 'YATSM')
self.robust_result_dir = os.path.join(self.root, 'YATSM_ROBUST')
self.data_cache = os.path.join(self.root, 'cache')
self.example_img = os.path.join(self.root, 'example_img')
self.outdir = os.path.join(self.root, 'outdir')
# Answers
self.answers = os.path.join(self.root, 'answers')
if not os.path.isdir(self.outdir):
os.makedirs(self.outdir)
def tearDown(self):
""" Deletes answer directory """
if os.path.isdir(self.outdir):
shutil.rmtree(self.outdir)
# Test coefficients
def test_coef(self):
""" Test creating coefficient map """
output = os.path.join(self.outdir, 'coef_all.gtif')
args = '--root {r} coef 2000-06-01 {o}'.format(
r=self.root,
o=output).split(' ')
msg, retcode = self._run(self.script, args)
self.assertEqual(retcode, 0)
# Test output
self._compare_maps(os.path.join(self.outdir, output),
os.path.join(self.answers, output))
def test_coef_robust(self):
""" Test creating robust coefficient map """
output = 'coef_all_robust.gtif'
# Test robust coefficients
args = '--root {r} --result {rr} --robust coef 2000-06-01 {o}'.format(
r=self.root,
rr=self.robust_result_dir,
o=os.path.join(self.outdir, output)).split(' ')
msg, retcode = self._run(self.script, args)
self.assertEqual(retcode, 0)
# Test robust coefficients, expecting error
args = '--root {r} --robust coef 2000-06-01 {o}'.format(
r=self.root,
o=os.path.join(self.outdir, output)).split(' ')
msg, retcode = self._run(self.script, args)
self.assertEqual(retcode, 1)
# Test output
self._compare_maps(os.path.join(self.outdir, output),
os.path.join(self.answers, output))
def test_coef_bands(self):
""" Test if correct bands are output """
# Test bands outputs
# Test coefficient outputs
pass
def test_coef_before_after(self):
""" Test use of --before and --after flags """
pass
# Test prediction
# Test classification
# Test optional arguments
def test_ndv(self):
""" Test output file NoDataValue """
pass
def test_output_format(self):
""" Test output GDAL file format """
pass
def test_date_format(self):
""" Test input date format type """
pass
class Test_YATSMChangeMap(TestMaps):
def setUp(self):
""" Setup test data filenames and load known truth dataset """
self.script = 'yatsm_changemap.py'
# Test data
self.root = os.path.join(
os.path.dirname(os.path.abspath(__file__)), 'data')
self.result_dir = os.path.join(self.root, 'YATSM')
self.robust_result_dir = os.path.join(self.root, 'YATSM_ROBUST')
self.data_cache = os.path.join(self.root, 'cache')
self.example_img = os.path.join(self.root, 'example_img')
self.outdir = os.path.join(self.root, 'outdir')
# Answers
self.answers = os.path.join(self.root, 'answers')
if not os.path.isdir(self.outdir):
os.makedirs(self.outdir)
def tearDown(self):
""" Deletes answer directory """
if os.path.isdir(self.outdir):
shutil.rmtree(self.outdir)
def test_numchange(self):
pass
if __name__ == '__main__':
unittest.main()
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,518 |
From the French names Aubrey and Aubry; derived ultimately from the Germanic name Alberic, from Proto-Germanic *Albirīks, from *albiz ("elf, fairy") + *rīks ("king, ruler"). Possibly influenced by Gaulish Albiorīx (literally "ruler of the world"). Cognates include German Alberich and Italian Alberico.
IPA(key): /ˈɔːbɹi/
An English patronymic surname.
A male given name from the Germanic languages or transferred from the surname.
1595, William Shakespeare, King Henry VI, Part 3, Act III,Scene III:
Call him my king, by whose injurious doom / My elder brother, the Lord Aubrey Vere, / Was done to death?
A female given name transferred from the surname, of 1970s and later American usage.
Retrieved from "https://en.wiktionary.org/w/index.php?title=Aubrey&oldid=60335600"
English terms derived from French
English proper nouns
English given names
English male given names
English male given names from Germanic languages
English male given names from surnames
English female given names
English female given names from surnames
English surnames from given names
English unisex given names
etyl cleanup/en/fr
Proto-Germanic redlinks
Proto-Germanic redlinks/m | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,710 |
Q: Angular Routing callback path and auth0 BACKGROUND:
I am trying my hand at an angular application and I'm having a huge issue with wrapping my head around routing.
I have 2 questions that I need to figure out that I have been struggling with for a few days now and at this point, I am just wasting time going in circles.
DETAILS:
I have a routes tree defined in my root app module like this:
export const ROUTES: Routes = [
{
path: "callback",
component: CallbackComponent
},
{
path: "secure",
loadChildren: "./secure/secure.module#SecureModule",
canActivate: [AuthGuard]
},
{
path: "public",
loadChildren: "./public/public.module#PublicModule"
},
{
path: "",
redirectTo: "public",
pathMatch: "full"
},
{ path: "**", component: PageNotFoundComponent }
];
@NgModule({
declarations: [AppComponent, PageNotFoundComponent],
imports: [
AuthModule,
BrowserModule,
BrowserAnimationsModule,
HttpClientModule,
RouterModule.forRoot(ROUTES, {enableTracing: (environment.production === false)}),
StoreModule.forRoot(reducers, { metaReducers }), //sets the entire app up to use ngrx store and applies the metaReducers class as a parent to all reducers used throughout the system. this helps with the debug tools
EffectsModule.forRoot(effects),
StoreRouterConnectingModule,
environment.production === false ? StoreDevtoolsModule.instrument() : [],
],
providers: [
{ provide: ErrorHandler, useClass: AppServices.RollbarErrorHandler },
{
provide: AppServices.RollbarService,
useFactory: AppServices.rollbarFactory
}
],
exports: [AppComponent, PageNotFoundComponent]
})
When I first load my app with the URL localhost:4200, the public path gets loaded. That makes sense to me because the URL pattern matches the "" path so it gets redirected to the "public" path and loads that. This works fine as my public path gets loaded correctly.
The issue I am having comes up when I am authenticating against Auth0 which calls a callback URL defined as localhost:4200/callback after the user has been authenticated. I would think that this URL matches the "callback" route and should load the CallbackComponent. Unfortunately, it doesn't and it loads the public path again.
My CallbackComponent is defined in my AuthModule (where it also exported) which is obviously a separate module. In my experimenting, there is no issue with loading the component in the AppModule pages so I don't think this component being in another module is an issue but figured I'd mention it in case it is.
QUESTIONS
1) Why the heck is the "callback" path not loading when the URL is localhost:4200/callback?
2) Auth0 will pass token information and any errors back to that same URL in the querystring after a hash (eg localhost:4200/callback#error=... or, on success, localhost:4200/callback#access_token=...). Will that have an effect on the path matching? If so, what do I update my path to in order to handle that? If not, I believe that part of the URL will be considered a fragment, so I just get that information off the activatedRoute or is there some other way I am missing to handle fragments in routes?
Thanks in advance for any help.
UPDATE
I'm attaching the Router tracing blocks to show what exactly I'm seeing:
First is the navigation events when I navigate to the root URL
Navigated to http://localhost:4200/
platform-browser.js:380 Router Event: NavigationStart
platform-browser.js:367 NavigationStart(id: 1, url: '/')
platform-browser.js:367 NavigationStart {id: 1, url: "/"}
platform-browser.js:380 Router Event: RouteConfigLoadStart
platform-browser.js:367 RouteConfigLoadStart(path: public)
platform-browser.js:367 RouteConfigLoadStart {route: {…}}
core.js:3675 Angular is running in the development mode. Call enableProdMode() to enable the production mode.
platform-browser.js:380 Router Event: RouteConfigLoadEnd
platform-browser.js:367 RouteConfigLoadEnd(path: public)
platform-browser.js:367 RouteConfigLoadEnd {route: {…}}
platform-browser.js:380 Router Event: RoutesRecognized
platform-browser.js:367 RoutesRecognized(id: 1, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 RoutesRecognized {id: 1, url: "/", urlAfterRedirects: "/public", state: RouterStateSnapshot}
platform-browser.js:380 Router Event: NavigationCancel
platform-browser.js:367 NavigationCancel(id: 1, url: '/')
platform-browser.js:367 NavigationCancel {id: 1, url: "/", reason: ""}
platform-browser.js:380 Router Event: NavigationStart
platform-browser.js:367 NavigationStart(id: 2, url: '/')
platform-browser.js:367 NavigationStart {id: 2, url: "/"}
platform-browser.js:380 Router Event: RoutesRecognized
platform-browser.js:367 RoutesRecognized(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 RoutesRecognized {id: 2, url: "/", urlAfterRedirects: "/public", state: RouterStateSnapshot}
platform-browser.js:380 Router Event: GuardsCheckStart
platform-browser.js:367 GuardsCheckStart(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 GuardsCheckStart {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: '')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: 'public')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: 'public')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: '')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: '')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: '')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: GuardsCheckEnd
platform-browser.js:367 GuardsCheckEnd(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } , shouldActivate: true)
platform-browser.js:367 GuardsCheckEnd {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot, shouldActivate: true}
platform-browser.js:380 Router Event: ResolveStart
platform-browser.js:367 ResolveStart(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 ResolveStart {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ResolveEnd
platform-browser.js:367 ResolveEnd(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 ResolveEnd {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: '')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: '')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: '')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: 'public')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: 'public')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: '')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: NavigationEnd
platform-browser.js:367 NavigationEnd(id: 2, url: '/', urlAfterRedirects: '/public')
platform-browser.js:367 NavigationEnd {id: 2, url: "/", urlAfterRedirects: "/public"}
This is the router tracing when I go straight to the callback url:
Navigated to http://localhost:4200/callback
platform-browser.js:380 Router Event: NavigationStart
platform-browser.js:367 NavigationStart(id: 1, url: '/')
platform-browser.js:367 NavigationStart {id: 1, url: "/"}
platform-browser.js:380 Router Event: RouteConfigLoadStart
platform-browser.js:367 RouteConfigLoadStart(path: public)
platform-browser.js:367 RouteConfigLoadStart {route: {…}}
core.js:3675 Angular is running in the development mode. Call enableProdMode() to enable the production mode.
platform-browser.js:380 Router Event: RouteConfigLoadEnd
platform-browser.js:367 RouteConfigLoadEnd(path: public)
platform-browser.js:367 RouteConfigLoadEnd {route: {…}}
platform-browser.js:380 Router Event: RoutesRecognized
platform-browser.js:367 RoutesRecognized(id: 1, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 RoutesRecognized {id: 1, url: "/", urlAfterRedirects: "/public", state: RouterStateSnapshot}
platform-browser.js:380 Router Event: NavigationCancel
platform-browser.js:367 NavigationCancel(id: 1, url: '/')
platform-browser.js:367 NavigationCancel {id: 1, url: "/", reason: ""}
platform-browser.js:380 Router Event: NavigationStart
platform-browser.js:367 NavigationStart(id: 2, url: '/')
platform-browser.js:367 NavigationStart {id: 2, url: "/"}
platform-browser.js:380 Router Event: RoutesRecognized
platform-browser.js:367 RoutesRecognized(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 RoutesRecognized {id: 2, url: "/", urlAfterRedirects: "/public", state: RouterStateSnapshot}
platform-browser.js:380 Router Event: GuardsCheckStart
platform-browser.js:367 GuardsCheckStart(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 GuardsCheckStart {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: '')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: 'public')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: 'public')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: '')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationStart
platform-browser.js:367 ChildActivationStart(path: '')
platform-browser.js:367 ChildActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationStart
platform-browser.js:367 ActivationStart(path: '')
platform-browser.js:367 ActivationStart {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: GuardsCheckEnd
platform-browser.js:367 GuardsCheckEnd(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } , shouldActivate: true)
platform-browser.js:367 GuardsCheckEnd {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot, shouldActivate: true}
platform-browser.js:380 Router Event: ResolveStart
platform-browser.js:367 ResolveStart(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 ResolveStart {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ResolveEnd
platform-browser.js:367 ResolveEnd(id: 2, url: '/', urlAfterRedirects: '/public', state: Route(url:'', path:'') { Route(url:'public', path:'public') { Route(url:'', path:'') { Route(url:'', path:'') } } } )
platform-browser.js:367 ResolveEnd {id: 2, url: "/", urlAfterRedirects: UrlTree, state: RouterStateSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: '')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: '')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: '')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: 'public')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ActivationEnd
platform-browser.js:367 ActivationEnd(path: 'public')
platform-browser.js:367 ActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: ChildActivationEnd
platform-browser.js:367 ChildActivationEnd(path: '')
platform-browser.js:367 ChildActivationEnd {snapshot: ActivatedRouteSnapshot}
platform-browser.js:380 Router Event: NavigationEnd
platform-browser.js:367 NavigationEnd(id: 2, url: '/', urlAfterRedirects: '/public')
platform-browser.js:367 NavigationEnd {id: 2, url: "/", urlAfterRedirects: "/public"}
It's essentially exactly the same except for the initial Navigated to value.
A: From what I've seen couple of things might be the problem.
You should use ' ' instead of "".
Make sure you have in index.html
Also the order of paths matters. I think you got that right.
I'm not sure how important it is, but you are exporting the ROUTES instead of routemodule.
Try to create routemodule something looking like this:
const routes: Routes = [
{ path: 'callback', component: CallbackComponent },
{ path: 'secure', loadChildren: './public/public.module#SecureModule' },
{ path: 'public', loadChildren: './public/public.module#PublicModule' },
{ path: '', redirectTo: '/dashboard', pathMatch: 'full' },
{ path: '**' , component: PageNotFoundComponent }
];
@NgModule({
imports: [RouterModule.forRoot(routes)],
exports: [RouterModule]
})
export class AppRoutingModule { }
and import it in your app module. Im also not sure why you exporting appComponent, I though there should be appmodule there.
import { AppRoutingModule } from "./app-router.module";
@NgModule({
declarations: [AppComponent, PageNotFoundComponent],
imports: [
AuthModule,
BrowserModule,
BrowserAnimationsModule,
HttpClientModule,
AppRoutingModule,
StoreModule.forRoot(reducers, { metaReducers }), //sets the entire app up to use ngrx store and applies the metaReducers class as a parent to all reducers used throughout the system. this helps with the debug tools
EffectsModule.forRoot(effects),
StoreRouterConnectingModule,
environment.production === false ? StoreDevtoolsModule.instrument() : [],
],
providers: [
{ provide: ErrorHandler, useClass: AppServices.RollbarErrorHandler },
{
provide: AppServices.RollbarService,
useFactory: AppServices.rollbarFactory
}
],
exports: [AppComponent, PageNotFoundComponent]
})
The problem is somewhere here
In both of you routerTracing you are getting
platform-browser.js:367 NavigationStart(id: 1, url: '/')
platform-browser.js:367 NavigationStart {id: 1, url: "/"}
In second one you should be getting
platform-browser.js:367 NavigationStart(id: 1, url: '/callback')
platform-browser.js:367 NavigationStart {id: 1, url: "/callback"}
For your second question I think you need to implement 'callback:tocken' in path. Check Angular main guide and how they implement ids for heroes. But that might be different for tockens.
That's All I got so far. Good luck! I'll try to help more if you post updates.
A: Only to extend the otherwise valid Vato's answer:
Your main app module should export itself and not its component like this:
import { whatever } from "anywhere";
@NgModule({
declarations: [...],
imports: [...],
providers: [...],
exports: [...] // exporting no AppComponent here
})
export class AppModule {} // exports self class after all
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,427 |
{"url":"https:\/\/direct.mit.edu\/view-large\/967705","text":"Table 1:\nSummary of the Equations for Our Discrete and Rhythmic Model Equations.\nDiscreteRhythmic\nTransformation system:\u00a0\u00a0Transformation system:\nEquation 2.1\u00a0\u00a0Equation 2.1\n\nCanonical system:\u00a0\u00a0Canonical system:\nEquation 2.2\u00a0\u00a0Equation 2.5\nForcing term:\u00a0\u00a0Forcing term:\nEquation 2.3\u00a0\u00a0Equation 2.6\n\nOptional terms:\u00a0\u00a0Optional terms:\nEquation 2.15\u00a0\u00a0Equation 2.15\nEquation 2.20\n\nhi= equal spacing in \u00a0\u00a0hi= equal spacing in\n\nDiscreteRhythmic\nTransformation system:\u00a0\u00a0Transformation system:\nEquation 2.1\u00a0\u00a0Equation 2.1\n\nCanonical system:\u00a0\u00a0Canonical system:\nEquation 2.2\u00a0\u00a0Equation 2.5\nForcing term:\u00a0\u00a0Forcing term:\nEquation 2.3\u00a0\u00a0Equation 2.6\n\nOptional terms:\u00a0\u00a0Optional terms:\nEquation 2.15\u00a0\u00a0Equation 2.15\nEquation 2.20\n\nhi= equal spacing in \u00a0\u00a0hi= equal spacing in\n\nNotes: The high-level design parameters of the discrete system are , the temporal scaling factor, and g, the goal position. The design parameters of the rhythmic system are g, the baseline of the oscillation; , the period divided by ; and r, the amplitude of oscillations. The terms Ct and Cc are coupling terms that are application dependent and explained in section 3.2. The parameters wi are fitted to a demonstrated trajectory using locally weighted learning. The parameters , and ci are positive constants. Unless stated otherwise, the values at the bottom of the table are used in this letter.\n\nClose Modal","date":"2021-06-23 16:55:07","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\": 0.8932539224624634, \"perplexity\": 5131.290226956491}, \"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-2021-25\/segments\/1623488539764.83\/warc\/CC-MAIN-20210623165014-20210623195014-00346.warc.gz\"}"} | null | null |
Hortense Rouvier has specialized over the course of the past 17 years in merger & acquisition work and in corporate restructuring and reorganizations. Hortense's practice focuses on venture capital and expansion capital investment and divestment transactions and LBOs.
She honed her skills working for international law firms (Gide Loyrette Nouel, Paul Hastings Janofsky & Walker LLP), and for the Private Equity department of a leading French investment bank (Société Générale Asset Management, now Amundi PEF). Her dual approach to legal issues enables her to provide pragmatic solutions tailored to the specific needs of her clients, who are French and international groups across different sectors of the service industry, investment funds and private investors, as well as managers of high added value innovative projects, such as in the field of new technologies.
Hortense joined Lawways in September 2009 to set up Lawways Corporate. Hortense is licensed to practice by the Paris Bar (CAPA exam, Paris Bar Professional Training School – 1998), and holds a DEA post-graduate degree in Business Law (Panthéon Assas University, Paris II – 1997). | {
"redpajama_set_name": "RedPajamaC4"
} | 1,217 |
Frank Koester, born Franz Köster (28 August 1876, Sterkrade, Germany - 5 October 1927, New York City) was a German-American engineer and author.
Biography
He received ten years of theoretical training, with practical engineering and municipal experience in Germany, including four years of shop and field practice. After winning a gold medal for electrical engineering at the Exposition Universelle (1900), he came to the United States in 1902 and became a naturalized citizen in 1911. He was connected with the construction of the New York City subway system and other large engineering undertakings in the United States, South America, Alaska and the Philippines. Among his employers were the Guggenheim Exploration Company and the American Smelting and Refining Company A considerable part of his practice has been devoted to the design, construction and operation of power stations.
Recognizing the great potential in city planning, he made a special study of modern methods in this field, taking city planning courses at Charlottenburg College in Germany. He was a delegate to the City Planning Congress at Düsseldorf, Germany, in 1912, and to the International Congress of City Planning and City Maintenance held at Ghent, Belgium, in 1913, where he made an address; "Cooperation of Engineer and Architect in City Planning". He also did contract work in civil engineering, street lighting and urban planning. Among his clients were the Pennsylvania cities of Allentown, Bethlehem and Scranton.
Works
Steam Electric Power Plants (New York and London, 1908)
Hydro-electric Developments and Engineering (New York and London, 1909)
The Price of Inefficiency (New York, 1913)
Electricity for the Farm and Home (New York, 1913)
Modern City Planning and Maintenance (New York and London, 1914)
Secrets of German Progress (New York, 1915)
Under the Desert Stars (speculative fiction) (New York, 1923)
Sources
Biographical introduction and an electronic version of Koester's article
1876 births
1927 deaths
American engineers
American urban planners
American male writers
German emigrants to the United States | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,852 |
namespace s {
class Www {
public:
struct Session {};
struct Request {
boost::beast::http::request<boost::beast::http::string_body> message;
std::string toString() const;
};
struct Response {
boost::beast::http::response<boost::beast::http::string_body> message;
};
class Server : public Process {
public:
class IHandler {
public:
virtual ~IHandler() = default;
virtual MethodTask<Response> getResponse(Process*, Request const&) = 0;
virtual GenTask<Buffer> getChunked(Process*, Request const&) = 0;
static std::unique_ptr<IHandler> makeSimple(
std::function<MethodTask<Response>(Process*, Request const&)> f);
};
Server(ProcessArgs i, std::shared_ptr<IHandler> handler,
Tcp::ListenerOptions options)
: Process(std::move(i)), handler_(std::move(handler)),
options_(std::move(options)) {}
ProcessTask run();
private:
std::shared_ptr<IHandler> handler_;
Tcp::ListenerOptions options_;
};
};
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 5,050 |
Q: Calculate YEAR of a past date without YEAR in PHP I extract dates from a log file which doesn't include the year.
The only known fact is that the date is in the past. Could be 1 second ago, but not longer than 365 days ago.
I like to calculate the year.
logfile date format is
date('m-d H:i:s');
If the current date would be '1 April 2018',
log file '1 Jan' would be '1 Jan 2018'.
However when the log file date reads
'20 Dec' I need '20 Dec 2017'
'2 Apr' I need '2 Apr 2017' (as 2 Apr 2018 would be in the future)
'1 Apr' I need '1 Apr 2018' (that's today)
A: I would suggest to use this snippet as a starting point :
$today = date('m-d H:i:s');
$dates = array(
'04-20 15:00:00',
'02-03 15:00:00',
'05-12 15:00:00',
'01-14 15:00:00',
'02-15 15:00:00',
);
echo $today.'<br>';
foreach($dates as &$date) {
$exploded = explode(' ',$date);
if($date > $today) {
$date = $exploded[0].'-2017 '.$exploded[1];
echo $date . '<br>';
} else {
$date = $exploded[0].'-2018 '.$exploded[1];
echo $date . '<br>';
}
}
it should output something like this :
03-26 11:49:33
04-20-2017 15:00:00
02-03-2018 15:00:00
05-12-2017 15:00:00
01-14-2018 15:00:00
02-15-2018 15:00:00
A: you can try something like this
function convertMonthStringToInt($strMonth) {
$month = array(
'Jan' => 0,
'Feb' => 1,
'Mar' => 2,
'Apr' => 3,
'May' => 4,
'Jun' => 5,
'Jul' => 6,
'Aug' => 7,
'Sep' => 8,
'Oct' => 9,
'Nov' => 10,
'Dec' => 11,
);
return $month[$strMonth];
}
function findYear($monthLog) {
$currentYear = date('Y');
$currentMonth = date('M');
if(convertMonthStringToInt($monthLog) > convertMonthStringToInt($currentMonth)) {
return $currentYear - 1;
}
else {
return $currentYear;
}
}
then you can use findYear function to find the correct year
findYear('Nov'); // 2017
findYear('Jan'); // 2018
findYear('Mar'); //2018
findYear('Aug'); // 2017
etc...
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,580 |
package com.hauldata.dbpa.task;
import com.hauldata.dbpa.expression.Expression;
import com.hauldata.dbpa.process.Context;
import com.hauldata.dbpa.process.NestedTaskSet;
public class DoTask extends Task implements TaskSetParent {
private Expression<Boolean> whileCondition;
private NestedTaskSet taskSet;
public DoTask(
Prologue prologue,
Expression<Boolean> whileCondition) {
super(prologue);
this.whileCondition = whileCondition;
}
@Override
public Task setTaskSet(NestedTaskSet taskSet) {
this.taskSet = taskSet;
return this;
}
@Override
public NestedTaskSet getTaskSet() {
return taskSet;
}
@Override
protected void execute(Context context) throws Exception {
Context nestedContext = context.makeNestedContext(getName());
try {
if (whileCondition == null) {
taskSet.run(nestedContext);
}
else {
while (whileCondition.evaluate()) {
taskSet.run(nestedContext);
}
}
}
catch (BreakingException ex) {
// Not an error
}
finally {
nestedContext.close();
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,189 |
{"url":"http:\/\/mathoverflow.net\/questions\/14860\/regarding-the-gerstenhaber-bracket-on-hochschild-cohomology-and-morita-equivalenc","text":"# Regarding the Gerstenhaber bracket on Hochschild cohomology and Morita equivalence\n\nAssociated to any $A_\\infty$ $k$-algebra $A$ the Hochschild cochain complex $CH^*(A)$ has the structure of a dg-Lie algebra and a dg-algebra which are compatible enough that the cohomology is a Gerstenhaber algebra.\n\nIf two $A_\\infty$ algebras are Morita equivalent, are their Hochschild cochain complexes isomorphic in (i) the category of $k$-dg-algebras and (ii) the category of $k$-dg-Lie algebras, both up to quasi-isomorphism? Are they isomorphic in some category that feels both structures together?\n\nNow suppose that $\\mathcal{C}$ is a dg-category over a field $k$. We say that the $k$-dg-algebra $CH^*(\\mathcal{C}) = End(id_\\mathcal{C})$ is the Hochschild cochain complex. Does $CH^*(\\mathcal{C})$ have a bracket that generalizes the known one in the case that $\\mathcal{C}$ is a (derived) category of modules? If two dg-categories are quasi-equivalent are their Hochschild cochain complexes quasi-isomorphic?\n\nIs there a point of view that clarifies these issues?\n\n-\nI can't contribute anything solid, but I think the operations you're doing are very similar to taking the E[2]-center of an E[1] algebra in a symmetric category. Lurie has a long paper on the arxiv about E[k] algebras. \u2013\u00a0 S. Carnahan Feb 10 '10 at 7:58\nI'm not entirely sure I understand the question, but perhaps Keller's paper people.math.jussieu.fr\/~keller\/publ\/dih.pdf is what you are looking for. \u2013\u00a0 Aaron Bergman Feb 12 '10 at 3:51\nKeller's result tells us that if $A$ and $B$ are ($A_\\infty$-)quasi-isomorphic then $CH(A)$ and $CH(B)$ are quasi-isomorphic (prehaps even in the $L_\\infty$ sens, not only as complexes). But what do you mean by two $A_\\infty$-algebras to be Morita equivalent. For a genuine algebra $A$, the Hochschild complex is (I think) the deformation DGLA for the representation category $A-mod$. So it seems that Morita equivalent algebras will have quasi-isomorphic Hochschild DGLAs. \u2013\u00a0 DamienC Jul 26 '10 at 14:59\nThe paper in A. Bergman's comment contains the answer to my question. Indeed, the Hochschild cochain complex of a small dg category has a B-infinity structure, which is a structure that lies between the structure of a Gerstenhaber algebra and a strong homotopy Gerstenhaber algebra. According to Keller's paper, if two small dg-categories are Morita equivalent, then their Hochschild cochain complexes are isomorphic in the homotopy category of B-infinity algebras. This implies that their Hochschild cohomologies are isomorphic as Gerstenhaber algebras. \u2013\u00a0 Ian Shipman Aug 31 '10 at 15:25\nIt is well-known the Hochschild cohomology of a graded commutative algebra has the Gerstenhaber algebra structure. But generally $A_\\infty$ algebra is not commuative, is there any reference for the $A_\\infty$ case? By the way, what is the product or cup structure to take for $A_\\infty$ algebra? Thanks! \u2013\u00a0 Jay Oct 9 '13 at 9:17","date":"2015-02-27 15:25:05","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\": 0.8957480192184448, \"perplexity\": 544.0430728970284}, \"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-2015-11\/segments\/1424936461332.16\/warc\/CC-MAIN-20150226074101-00180-ip-10-28-5-156.ec2.internal.warc.gz\"}"} | null | null |
import { envOverride } from "../utils";
import { Constants } from "../emulator/constants";
/**
* Get base URL for RealtimeDatabase. Preference order: emulator host env override, realtime URL env override, and then specified host.
* @param options command options.
*/
export function realtimeOriginOrEmulatorOrCustomUrl(host: string): string {
return envOverride(
Constants.FIREBASE_DATABASE_EMULATOR_HOST,
envOverride("FIREBASE_REALTIME_URL", host),
addHttpIfRequired
);
}
/**
* Get base URL for RealtimeDatabase. Preference order: realtime URL env override, and then the specified host.
* @param options command options.
*/
export function realtimeOriginOrCustomUrl(host: string): string {
return envOverride("FIREBASE_REALTIME_URL", host);
}
function addHttpIfRequired(val: string) {
if (val.startsWith("http")) {
return val;
}
return `http://${val}`;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,048 |
{"url":"https:\/\/www.tensorflow.org\/versions\/r1.8\/api_docs\/python\/tf\/contrib\/layers\/xavier_initializer","text":"# tf.contrib.layers.xavier_initializer\n\n### Aliases:\n\n\u2022 tf.contrib.layers.xavier_initializer\n\u2022 tf.contrib.layers.xavier_initializer_conv2d\ntf.contrib.layers.xavier_initializer(\nuniform=True,\nseed=None,\ndtype=tf.float32\n)\n\n\nSee the guide: Layers (contrib) > Initializers\n\nReturns an initializer performing \"Xavier\" initialization for weights.\n\nThis function implements the weight initialization from:\n\nThis initializer is designed to keep the scale of the gradients roughly the same in all layers. In uniform distribution this ends up being the range: x = sqrt(6. \/ (in + out)); [-x, x] and for normal distribution a standard deviation of sqrt(2. \/ (in + out)) is used.\n\n#### Args:\n\n\u2022 uniform: Whether to use uniform or normal distributed random initialization.\n\u2022 seed: A Python integer. Used to create random seeds. See tf.set_random_seed for behavior.\n\u2022 dtype: The data type. Only floating point types are supported.\n\n#### Returns:\n\nAn initializer for a weight matrix.","date":"2018-08-16 00:09:13","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\": 0.26063022017478943, \"perplexity\": 9342.690190211079}, \"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-2018-34\/segments\/1534221210387.7\/warc\/CC-MAIN-20180815235729-20180816015729-00551.warc.gz\"}"} | null | null |
\section{Introduction}
The idea that we and all standard matter live on a brane embedded in
a higher dimensional bulk has attracted a lot of attention[1-3]. In
this view point, extra dimensions are accessible only for graviton
and possibly non-standard matter. The setup of Randall and Sundrum
(RSII) considers the observable universe as a $3$-brane with
positive tension embedded in five dimensional anti-de sitter bulk.
In the low energy limit, the $5D$ graviton is localized on the brane
due to the warped geometry of the bulk. The notion of AdS/CFT
correspondence help us to understand this property since the
$4D$ gravity is coupled to a conformal field in the RS model [4,5].\\
The effect of the bulk on the brane can be determined by the
effective mass $\mathcal{M}$ of the bulk fluid that is measured by a
bulk observer at the brane. For spherically symmetric brane, this
mass can be considered as effective gravitational mass of the bulk.
This mass depends on the brane scale factor and the proper time on
the brane. In the case that the bulk observer is comoving with the
bulk fluid, the mass is assumed to be comoving. However, for matter
components such as a bulk radiation fluid, there is no comoving
observer[6,7].
On the other hand, the model proposed by Dvali, Gabadadze and
Porrati (DGP) is a radiative correction, the bulk is a flat
Minkowski spacetime, but a reduced gravity term appears on the brane
without tension. This model is different in this respect that it
predicts deviations from the standard $4$-dimensional gravity over
large distances. In this scenario, the transition between four and
higher-dimensional gravitational potentials arises due to the
presence of both the brane and bulk Einstein terms in the action.
Existence of a higher dimensional embedding space allows for the
existence of bulk or brane matter which can certainly influence the
cosmological evolution on the brane. This model has a rich
phenomenology discussed in [8]. Maeda, Mizuno and Torii have
constructed a braneworld scenario which combines the Randall-Sundrum
II ( RSII) model and DGP model[9]. In this combination, an induced
curvature term appears on the brane in the RSII model. This model
has been called {\it warped DGP braneworld} in literature[10]. The
existence of induced gravity term leads to a self-accelerating
branch in the brane evolution[11,12].\\ Braneworld model with scalar
field minimally or non-minimally coupled to gravity have been
studied extensively(see[13] and references therein). The
introduction of non-minimal coupling (NMC) is not just a matter of
taste; it is forced upon us in many situations of physical and
cosmological interests. For instance, NMC arises at the quantum
level when quantum corrections to the scalar field theory are
considered. Even if for the classical, unperturbed theory this NMC
vanishes, it is necessary for the renormalizability of the scalar
field theory in curved space. In most theories used to describe
inflationary scenarios, it turns out that a non-vanishing value of
the coupling constant cannot be avoided. In general relativity, and
in all other metric theories of gravity in which the scalar field is
not part of the gravitational sector, the coupling constant
necessarily assumes the value of \, $\frac{1}{6}$\,. The study of
the asymptotically free theories in an external gravitational field
with a Gauss-Bonnet term shows a scale dependent coupling parameter.
Asymptotically free grand unified theories have a non-minimal
coupling depending on a renormalization group parameter that
converges to the value of $\frac{1}{6}$ or to any other initial
conditions depending on the gauge group and on the matter content of
the theory. An exact renormalization group study of the
$\lambda\phi^4$ theory shows that NMC$=\frac{1}{6}$ is a stable
infrared fixed point. Also in the large $N$ limit of the
Nambu-Jona-Lasinio model, we have NMC$=\frac{1}{6}$. In the $O(N)$-
symmetric model with $V =\lambda\phi^4$, NMC is generally nonzero
and depends on the coupling constants of the individual bosonic
components. Higgs fields in the standard model have NMC$=0$ or
$\frac{1}{6}$. Only a few investigations produce zero value(for a
more complete discussion of these issues we refer to papers by V.
Faraoni, specially Ref. [14] and references therein). In view of the
above results, it is then natural to incorporate an explicit NMC
between scalar field and induced Ricci scalar on the brane.
On the other hand, in a braneworld scenario, the radiative
corrections in the bulk lead to higher curvature terms. At high
energies, the Einstein-Hilbert action will acquire quantum
corrections. The Gauss-Bonnet (GB) combination arises as the leading
bulk correction in the case of the heterotic string theory [15].
This term leads to second-order gravitational field equations linear
in the second derivatives in the bulk metric which is ghost free
[16-18], the property of curvature invariant of the Gauss-Bonnet
term.\\
Inclusion of Gauss-Bonnet term in the action results in a variety of
novel phenomena which certainly affects the cosmological
consequences of these generalized braneworld setup, although these
corrections are smaller than the usual Einstein-Hilbert terms
[19-21]. Moreover, the zero mode of graviton has been localized in
the GB model [22]. The cosmological evolution corresponding to RS
model in the presence of a bulk GB term has been considered in
[17,23-28] see also [29]. Also the case of minimally coupled scalar
field with
GB gravity has been discussed extensively[30-33].\\
In the presence of GB term with induced gravity, there are different
cosmological scenarios, even if there isn't any matter in the
bulk[34]. In this paper, we generalize the previous studies to the
case that a scalar field non-minimally coupled to induced curvature
is present on the brane in the presence of radiative corrections. We
first review briefly the setup of
Brown-Maartens-Papantonopoulos-Zamarias(BMPZ)[35]. Then we
generalize this setup to the more general framework of scalar-tensor
theories. We show that relative to BMPZ scenario, there are several
interesting features which affect certainly the cosmological
dynamics on the brane. Since Gauss-Bonnet and induced gravity
effects are related to two extremes of the scenario (UV and IR
limits), inclusion of sringy effects via Gauss-Bonnet term leads to
a finite density big bang[35]. This interesting feature has been
explained in a fascinating manner by $T$-duality of string
theory[36]. On the other hand, non-minimal coupling itself accounts
for a non-singular soft big bang scenario[37]. In our setup,
existence of non-minimal coupling of scalar field and induced
gravity on the brane, controls the initial density of this finite
big bang scenario. In other words, in this framework, non-minimal
coupling with its special fine-tuning ( see [38] and references
therein), plays the role of a parameter that can control density of
matter fields at the beginning of the universe. As we will show,
incorporation of both GB and non-minimal coupling effects will
enhance special characters of BMPZ scenario.
\section{DGP Inspired Scalar-Tensor Theories}
The action of the DGP scenario in the presence of a non-minimally
coupled scalar field on the brane can be written as follows [39]
$$S=\frac{1}{2\kappa_{5}^{2}}\int d^{5}x\sqrt{-g^{(5)}}\Big[
R^{(5)}-2\Lambda_{5}\Big]$$
\begin{equation}
+\Bigg[\frac{r}{2\kappa_{5}^{2}}\int
d^{4}x\sqrt{-g}\bigg(\alpha(\phi) R -2\kappa_{4}^{2} g^{\mu\nu}
\nabla_{\mu}\phi\nabla_{\nu}\phi -4\kappa_{4}^{2}V(\phi) -4
\kappa_{4}^{2}\lambda\bigg)\Bigg]_{y=0},
\end{equation}
where we have included a general non-minimal coupling $\alpha(\phi)$
in the brane part of the action. $y$ is coordinate of the fifth
dimension and we assume the brane is located at $y=0$.\,
$g^{(5)}_{AB}$ is five dimensional bulk metric with Ricci scalar
${R^{(5)}}$, while $g_{\mu\nu}$ is induced metric on the brane with
induced Ricci scalar $R$.\, $g_{AB}$ and $g_{\mu\nu}$ are related
via $g_{\mu\nu}={\delta_{\mu}}^{A}{\delta_{\nu}}^{B}g_{AB}$.
$\lambda$ is the brane tension (constant energy density) and $r$ is
the cross-over scale that is defined as follows
\begin{equation}
r=\frac{\kappa_{5}^{2}}{2 \kappa_{4}^{2}}=\frac{M_{4}^{2}}{2
M_{5}^{3}}.
\end{equation}
The generalized cosmological dynamics of this setup is given by the
following Friedmann equation [34,40]
\begin{equation}
\varepsilon\sqrt{H^{2}-\frac{
\Upsilon}{a^{4}}-\frac{\Lambda_{5}}{6}+\frac{K}{a^{2}}}=r
\alpha(\phi)\Big(H^{2}+\frac{K}{a^{2}}\Big)-
\frac{\kappa_{5}^{2}}{6}(\rho+ \rho_{\phi}+\lambda).
\end{equation}
where $\varepsilon=\pm 1$ is corresponding to two possible branches
of DGP cosmology and $\Upsilon$ is the bulk black hole mass which is
related to the bulk Weyl tensor. This mass, as generalized dark
radiation, induces mirage effects in the evolution and the
gravitational effect of the bulk matter on the brane evolution can
be described in terms of this mass as measured by a bulk observer at
the location of the brane (the DGP limit has a Minkowski bulk
$\Lambda_{5}=0$ with $\Upsilon=0$). A part of the effects of
non-minimal coupling of scalar field $\phi$ with gravity is hidden
in the definition of the effective energy density. Assuming the
following line element
$$ds^{2}=q_{\mu\nu}dx^{\mu}dx^{\nu}+b^{2}(y,t)dy^{2}=-n^{2}(y,t)dt^{2}+
a^{2}(y,t)\gamma_{ij}dx^{i}dx^{j}+b^{2}(y,t)dy^{2},$$ where
$\gamma_{ij}$ is a maximally symmetric 3-dimensional metric defined
as $\gamma_{ij}=\delta_{ij}+k\frac{x_{i}x_{j}}{1-kr^{2}}$, the
energy density of non-minimally coupled scalar field on the brane is
given as follows [39,41]
\begin{equation}
\rho_{\phi}=\left[\frac{1}{2}\dot{\phi}^{2}+n^{2}V(\phi)-6\alpha'H\dot{\phi}\right]_{y=0},
\end{equation}
where \,$H=\frac{\dot{a}}{a}$\, is Hubble parameter,\,
$\alpha'=\frac{d\alpha}{d\phi}$ and $\dot{\phi}=\frac{d\phi}{dt}$.
If we consider a flat brane (K=0) with $\lambda=0$ and also a
Minkowski bulk ($\Lambda_{5}=0$, $\Upsilon=0$), then we can write
equation (3) as follows
\begin{equation}
H^{2}=\pm \frac{H}{r
\alpha(\phi)}+\frac{\kappa_{4}^{2}}{3\alpha(\phi)}(\rho
+\rho_{0\phi}-6\alpha'H\dot{\phi}).
\end{equation}
where
$\rho_{0\phi}=\left[\frac{1}{2}\dot{\phi}^{2}+n^{2}V(\phi)\right]_{y=0}$.
The DGP model has two branches, i.e \, $\varepsilon=\pm 1$
corresponding to two different embedding of the brane in the bulk.
The behavior of two branches at high energies and low energies are
summarized as follows: \\
In the high energy limit we find
\begin{equation}
\hspace{1.5
cm}DGP(\pm):\,\,\,\,\,\,\,\,H^{2}=\frac{\kappa_{4}^{2}}{3\alpha(\phi)}(\rho
+\rho_{\phi}),
\end{equation}
while in low energy limit we have \\
$$ DGP(+):\,\,\,\,\,\,\,\,H\longrightarrow \frac{1}{r
\alpha(\phi)}-2\frac{\kappa_{4}^{2}\alpha'\dot{\phi}}{\alpha(\phi)}$$
\begin{equation}
DGP(-):\,\,\,\,\,\,\,\,H=0.
\end{equation}
In terms of dimensionless variables introduced in [35]
\begin{equation}
h=Hr,\,\,\,\mu=\frac{r\kappa_{5}^{2}}{6}\rho,\,\,\,\,
\mu'=\frac{r\kappa_{5}^{2}}{6}\rho_{0\phi},\,\,\,\,\sigma=\frac{r\kappa_{5}^{2}}{6}\lambda
,\,\,\,\,\tau=\frac{t}{r},
\end{equation}
we find
\begin{equation}
h^{2}=\pm \frac{h}{
\alpha(\phi)}+\frac{(\mu+\mu')}{\alpha(\phi)}-\frac{2 h
\kappa_{4}^{2}}{\alpha(\phi)}\frac{d \alpha}{d \tau}.
\end{equation}
The solutions of this equation for $h$ are as follows
\begin{equation}
h=\pm\frac{1}{2\alpha(\phi)}-\frac{\kappa_{4}^{2}}{\alpha(\phi)}\frac{d
\alpha}{d \tau}+\frac{\sqrt{1\mp 4\kappa_{4}^{2}\frac{d \alpha}{d
\tau}+4(\kappa_{4}^{2}\frac{d \alpha}{d
\tau})^{2}+4\alpha(\phi)(\mu+\mu')}}{2\alpha(\phi)}.
\end{equation}
Here the negative root is not suitable since in the limit of \, $\mu
+\mu'\longrightarrow 0$, with this sign one cannot recover the low
energy limit of the model highlighted in (7).
\begin{figure}[htp]
\begin{center}
\special{psfile=1.eps angle=0 hscale=60 vscale=60 hoffset= 25
voffset=-325}
\end{center}
\vspace{7 cm}
\caption{\small { Two possible branches of DGP-inspired non-minimal model. The non-minimal
coupling of scalar field is assumed to be positive and the brane is considered to be tensionless, $\sigma=0$.}}
\end{figure}
\begin{figure}[htp]
\begin{center}
\special{psfile=2.eps angle=0 hscale=60 vscale=60 hoffset= 25
voffset=-280}
\end{center}
\vspace{5 cm}
\caption{\small { Two possible branches of DGP-inspired non-minimal model. The non-minimal
coupling of scalar field is assumed to be negative and the brane is considered to be tensionless, $\sigma=0$.}}
\end{figure}
Figure $1$ shows the behavior of these solutions with some specific
values of non-minimal coupling\footnote{To plot all of the figures
in this paper, equation (41) acts as a condition on the values that
$\alpha$ can attains. The possible values of $\gamma$ extracted from
observational data are shown in table (1). Using SNIa+LSS+H(z) test,
we obtain $\alpha\geq 0.01$ and $\alpha\leq -0.01$ approximately.
For simplicity in drawing figures we have assumed that scalar field
has no dynamics, i.e. $\frac{d\phi}{d\tau}=0$. The time dependent
non-minimal coupling will be discussed at the end of the paper. }.
The upper sign in relation (10) is related to DGP(+) and lower sign
for DGP(-). It is seen that there is a late-time self-acceleration
in the DGP(+) branch similar to the minimal case, however, in
minimal case when $\mu\longrightarrow0$ then $h\longrightarrow1$,
whereas in the non-minimal case, in this limit i.e \,
$\mu+\mu'\longrightarrow0$, we have
$h\longrightarrow\frac{1}{\alpha(\phi)}-2\frac{\kappa_{4}^{2}}{\alpha(\phi)}\frac{d
\alpha}{d \tau}$. In DGP(+) branch, the endpoint is a vacuum de
Sitter state and Anti de Sitter state for positive and negative
non-minimal coupling respectively whereas in the DGP(-) branch, the
endpoint is a Minkowski state. The effect of non-minimal coupling in
this case is to shift the end point of DGP(+) branch. Depending on
the value that $\alpha(\phi)$ can attain [38], the late-time
acceleration of the universe can be fine-tuned properly.
Now for $\lambda\neq0$, the solutions of dimensionless Friedmann
equation are as follows
\begin{equation}
h=\pm\frac{1}{2\alpha(\phi)}-\frac{\kappa_{4}^{2}}{\alpha(\phi)}\frac{d
\alpha}{d \tau}+\frac{\sqrt{1\mp 4\kappa_{4}^{2}\frac{d \alpha}{d
\tau}+4(\kappa_{4}^{2}\frac{d \alpha}{d
\tau})^{2}+4\alpha(\phi)(\mu+\mu'+\sigma)}}{2\alpha(\phi)}.
\end{equation}
These solutions are shown in figures $3$ and $4$ with $\sigma\neq
0$. For negative tension in DGP(+) branch, the endpoint is a vacuum
de Sitter state and there is a self-acceleration whereas in DGP(-)
branch the solutions terminate at finite density (fig.3). For
positive tension, both of the solutions $(DGP(\pm))$ have
self-acceleration and the
endpoints are vacuum de Sitter state (fig.4).\\
The existence of the energy density $(\lambda)$ on the brane gives
rise to a shift of the solutions. Moreover, existence of
$\alpha(\phi)$ leads to further shift of these solutions.\\
\begin{figure}[htp]
\begin{center}
\special{psfile=3.eps hscale=60 vscale=60 hoffset= 25
voffset=-320}
\end{center}
\vspace{6 cm}
\caption{\small { Two possible branches of DGP inspired non-minimal model with negative tension
brane and positive non-minimal coupling. We have set $\alpha(\phi)=0.01, 0.02$ and $\sigma=-4$.}}
\end{figure}
\begin{figure}[htp]
\begin{center}
\special{psfile=4.eps hscale=60 vscale=60 hoffset= 25
voffset=-250}
\end{center}
\vspace{5 cm}
\caption{\small { Two possible branches of DGP inspired non-minimal model with positive
brane tension and positive non-minimal coupling. We have set $\alpha(\phi)=0.01, 0.02$ and $\sigma=10$.}}
\end{figure}\\
DGP model is an IR modification of general relativity. In the UV
limit, stringy effects will play important role. In this viewpoint,
to discuss both UV and IR limit of the scenario simultaneously, the
DGP model is not sufficient and we should incorporate stringy
effects via inclusion of the Gauss-Bonnet terms.
\section{Gauss-Bonnet Braneworlds}
The Gauss-Bonnet term with coupling constant $\beta$ is written as
follows
$$L_{GB}=R^{(5)2}-4R_{ab}^{(5)}R^{(5)ab}+R_{abcd}^{(5)}R^{(5)abcd}$$
where $R^{(5)}$ is the curvature scalar of the 5-dimensional bulk
spacetime. These corrections have origin on stringy effects and the
most general action should involve both Gauss-Bonnet and the
Einstein-Hilbert term in 5D theory. The GB term is present only in
the bulk action
\begin{equation}
S_{bulk}=\frac{1}{2\kappa_{5}^{2}}\int d^{5}x\sqrt{-g^{(5)}}\Bigg[
R^{(5)}-2\Lambda_{5}+\beta\Big(R^{(5)2}-4R_{ab}^{(5)}R^{(5)ab}+R_{abcd}^{(5)}R^{(5)abcd}\Big)\Bigg],
\end{equation}
where $\beta$ is the Gauss-Bonnet coupling which can be positive or
negative in the classical GB theory. If $\beta$ is negative, it has
been seen in [42] that this braneworld model leads to antigravity or
tachyon modes on the brane. However, in the presence of a bulk
scalar field, these effects are not present even with negative
$\beta$.\\
The Friedmann equation in the presence of Gauss-Bonnet effects is as
follows [43]
\begin{equation}
H^{2}=\frac{C_{+}+C_{-}-2}{8 \beta}-\frac{K}{a^{2}},
\end{equation}
where
\begin{equation}
C_{\pm}=\Bigg[\sqrt{\Big(1+\frac{4}{3}\beta
\Lambda_{5}+8\beta\frac{\Upsilon}{a^{4}}\Big)^{\frac{3}{2}}+\frac{\beta
\kappa_{5}^{4}(\rho+\lambda)^{2}}{2}}\pm\kappa_{5}^{4}(\rho+\lambda)\sqrt{\frac{\beta}{2}}\Bigg]^{\frac{2}{3}}.
\end{equation}
This equation is a cubic equation with three possible roots. For
$\rho>0$ there is only one real root.\\
The behavior of GB model at high and low energies are as follows
[35]
\begin{equation}
\hspace{1.5 cm}H\gg\alpha^{-\frac{1}{2}}\rightarrow
H^{2}\propto\rho^{\frac{2}{3}},\hspace{2 cm}high\,\, energy\,\,
limit
\end{equation}
and
\begin{equation}
\hspace{1.1 cm}H\ll\alpha^{-\frac{1}{2}}\rightarrow
H^{2}\propto\rho^{2}\hspace{2 cm}low\,\, energy\,\, limit.
\end{equation}
\section{Gauss-Bonnet Induced Gravity with Non-Minimally Coupled Scalar Field on the Brane }
As we have explained, Gauss-Bonnet effect is a high energy stringy
effect. On the other hand, non-minimal coupling of scalar field and
induced gravity on the brane is forced upon us from several
compelling reasons. Some of these reasons have their origin on pure
quantum field theoretical considerations[14]. Then it is natural to
incorporate both Gauss-Bonnet and non-minimal coupling effects to
have a more reliable framework for treating cosmological dynamics.
The action of the GBIG (Gauss-Bonnet term in the bulk and the
Induced Gravity term on the brane) scenario in the presence of a
non-minimally coupled scalar field on the brane can be written as
follows
$$S=\frac{1}{2\kappa_{5}^{2}}\int d^{5}x\sqrt{-g^{(5)}}\Bigg[
R^{(5)}-2\Lambda_{5}+\beta\Big(R^{(5)2}-4R_{ab}^{(5)}R^{(5)ab}+R_{abcd}^{(5)}R^{(5)abcd}\Big)\Bigg]$$
\begin{equation}
+\Bigg[\frac{r}{2\kappa_{5}^{2}}\int
d^{4}x\sqrt{-g}\bigg(\alpha(\phi) R -2\kappa_{4}^{2} g^{\mu\nu}
\nabla_{\mu}\phi\nabla_{\nu}\phi -4\kappa_{4}^{2}V(\phi) -4
\kappa_{4}^{2}\lambda\bigg)\Bigg]_{y=0},
\end{equation}
where $\beta$ and $r$ are the GB coupling constant and IG cross-over
scale respectively. The relation for energy conservation on the
brane is as follows
\begin{equation}
\dot{\rho}+\dot{\rho}_{\phi}+3H(1+\omega)(\rho+\rho_{\phi})=6\alpha'\dot\phi
\Big(H^2+\frac{K}{a^2}\Big).
\end{equation}
where $\omega=\frac{p+p_{\phi}}{\rho+\rho_{\phi}}$\, with $p$ and
$\rho$ pressure and density of ordinary matter. Since for ordinary
matter, $\dot{\rho}+3H(\rho+P)=0$, the non-minimal coupling of the
scalar field and induced curvature on the brane leads to the
non-conservation of the scalar field effective energy
density[41].\\
The cosmological dynamics of the model is given by the following
generalized Friedmann equation
\begin{equation}
\Bigg[1+\frac{8}{3}\beta
\Big(H^{2}+\frac{\Psi}{2}+\frac{K}{a^2}\Big)\Bigg]^{2}\Big(H^2-\Psi+\frac{K}{a^2}\Big)=\Bigg[r
\alpha(\phi)H^{2}+r
\alpha(\phi)\frac{K}{a^2}-\frac{\kappa_{5}^{2}}{6}(\rho+\rho_{\phi}+\lambda)
\Bigg]^{2}.
\end{equation}
This equation describes the cosmological evolution on the brane with
tension and a non-minimally coupled scalar field on the brane. The
bulk contains a black hole mass and a cosmological constant. $\Psi$
is defined as follows
\begin{equation}
\Psi+2 \beta
\Psi^{2}=\frac{\Lambda_{5}}{6}+\frac{\Upsilon}{a^{4}}.
\end{equation}
If $\beta=0$, the model reduces to DGP model, while for $r=0$ we
recover the Gauss-Bonnet model. Here we restrict our study to the
case where bulk black hole mass vanishes, ($\Upsilon=0$) and
therefore $\Psi+2 \beta \Psi^{2}=\frac{\Lambda_{5}}{6}$. The bulk
cosmological constant in the presence of GB term is given by
$\Lambda_{5}=-\frac{6}{l^{2}}+\frac{12\beta}{l^{4}}$, where $l$ is
the bulk curvature. For a spatially flat brane ($K=0$), the
Friedmann equation is given by
\begin{equation}
\Bigg[1+\frac{8}{3}\beta
\Big(H^{2}+\frac{\Psi}{2}\Big)\Bigg]^{2}\Big(H^2-\Psi\Big)=\Bigg[r
\alpha(\phi)H^{2}-\frac{\kappa_{5}^{2}}{6}(\rho+\rho_{\phi}+\lambda)
\Bigg]^{2}.
\end{equation}
We define the following dimensionless quantities
\begin{equation}
\gamma=\frac{8\beta}{3r^{2}},\hspace{1cm}\chi=\frac{r^{2}}{l^{2}},\hspace{1cm}\psi=\Psi
r^{2},
\end{equation}
where the dimensionless Friedmann equation takes the following form
\begin{equation}
\Bigg[1+\gamma
\Big(h^{2}+\frac{\psi}{2}\Big)\Bigg]^{2}\Big(h^2-\psi\Big)=\Bigg[
\alpha(\phi)h^{2}-\Big(\mu+ \mu'+\sigma
-2\frac{d\alpha(\phi)}{d\tau}h \kappa_{4}^{2}\Big) \Bigg]^{2}.
\end{equation}
To find cosmological dynamics of our model, we should solve this
equation in an appropriate parameter space. In which follows, we
consider Minkowski and AdS bulk and investigate their cosmological
consequences.
\subsection{Minkowski Bulk($\psi=0$) with Tensionless Brane($\sigma=0$)}
In this case, the non-minimal GBIG Friedmann equation takes the
following form
\begin{equation}
\Big(1+\gamma h^{2}\Big)^{2} h^{2}=\Bigg[
\alpha(\phi)h^{2}-\Big(\mu+ \mu' -2\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}\Big) \Bigg]^{2}.
\end{equation}
It is straightforward to show that in this case
$$\frac{d(\mu+\mu')}{d(h^2)}=-\frac{(1+\gamma h^{2})(3\gamma
h^{2}+1)}{2\Big(\alpha(\phi)h^{2}-(\mu+\mu')+2\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}\Big)}\hspace{5cm}$$
\begin{equation}
+\frac{2\Bigg[\alpha(\phi)^{2}h^{2}+3\alpha(\phi)\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}-(\mu+\mu')\Big(\alpha(\phi)+\frac{1}{h}\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\Big)+2(\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2})^{2}\Bigg]}{2\Big(\alpha(\phi)h^{2}-(\mu+\mu')+2\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}\Big)}.
\end{equation}
The initial Hubble rate and density are given by substituting the
result of $\frac{d(\mu+\mu')}{d(h^2)}=0$ in to equation (24). This
leads us to the following relations
\begin{equation}
h_{i}=\frac{\alpha(\phi)+\sqrt{\alpha(\phi)^{2}-3\gamma+6\gamma\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}}}{3\gamma},
\end{equation}
\begin{equation}
(\mu+\mu')_{i}=\frac{2\alpha(\phi)^{3}-9\alpha(\phi)\gamma+18\alpha(\phi)\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\gamma+2\Big(\alpha(\phi)^{2}-3\gamma+6\gamma\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\Big)^{\frac{3}{2}}}{27\gamma^{2}}.\hspace{7 cm}
\end{equation}
Before proceeding further, we should stress on two important points
here: firstly, the presence of GB term removes the big bang
singularity in this setup, and the universe starts with an initial
finite density. Gauss-Bonnet effect is essentially a string-inspired
effect in the bulk which its combination with pure DGP scenario
leads to a finite big bang proposal on the brane. A consequence of
string inspired field theories is the existence of minimal
observable length of the order of Planck length[44-46]. One cannot
probe distances smaller than this fundamental length. In fact a
string cannot live on the scale smaller than its length. This
feature leads us to generalize the standard Heisnberg uncertainty
relation to incorporate this Planck scale effect[47,48]. The
existence of this minimal observable length essentially removes
spacetime singularity and acts as a UV cutoff of the corresponding
field theory( see for instance [49] which discusses inflation with
minimum length cutoff. See also [50]). So, in principle existence of
a finite density big bang is supported at least in this
viewpoint[51], see also [52]. Secondly, non-minimal coupling of
scalar field with induced gravity on the brane controls the value of
the initial density. This is not the only importance of non-minimal
coupling of scalar field and induced gravity. In fact non-minimal
coupling provides a mechanism for generating spontaneous symmetry
breaking at Planck scale on the brane[53]. In this respect and based
on the arguments presented at the introduction on the importance of
the non-minimal coupling, non-minimal coupling of scalar field and
induced gravity on the brane itself is a high energy correction of
the theory and it is natural to expect that this effect couples with
stringy effects in Planck scale. In fact in this setup, we encounter
a smoother behavior due to Gauss-Bonnet term ( a finite density big
bang) and the late-time effects of non-minimally coupled scalar
field component. These effects together provide a more reliable
cosmological scenario.
The behavior of $h$ with respect to $\mu+\mu'$ is shown in figure
$5$. This figure shows also that the GBIG1 and GBIG2 branches have
self-acceleration for some positive values of non-minimal coupling
in the same manner as the DGP(+) branch, whereas GBIG3 branch
similar to DGP(-) has no self-acceleration. This is similar to pure
DGP or GB model alone where there is a big bang singularity. The
self-accelerating GBIG2 branch is not a physical solution since it
is accelerating throughout its evolution. For negative values of
non-minimal coupling, the GBIG3 and GBIG2 have self-acceleration
while GBIG1 has not such a property. Now it is easy to show that
$$(\mu+\mu')\rightarrow\infty :\hspace{1cm}\gamma\rightarrow0 \hspace{2.5cm}$$
$$(\mu+\mu')\rightarrow 0 :\hspace{1cm}\gamma\rightarrow \frac{\alpha(\phi)^{2}}{4(1-2\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}.$$ In the minimal case, the maximum value of
$\gamma$ leads to a minimum value of $h_{i}$. Here, in the presence
of non-minimal coupling of scalar field and induced gravity with
$\gamma_{max}= \frac{\alpha(\phi)^{2}}{4(1-2\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}$\,, we cannot conclude that this leads to a
minimum value for $h$. Using equation (26), the value of $h_{i}$ for
$\gamma_{max}$ is given as follows
\begin{equation}
h_{i}=\frac{2(1-2\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\alpha(\phi)}.
\end{equation}
When $\gamma=\gamma_{max}$ and $(\mu+\mu')= 0$, there is a vacuum
brane with de Sitter expansion. The $h$ asymptotic value is
obtained when $\mu+\mu'\rightarrow 0$ in equation (24)
\begin{equation}
h_{\infty}^{6}+\frac{(2\gamma-\alpha^{2})}{\gamma^{2}}h_{\infty}^{4}-\frac{(4\alpha
\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\gamma^{2}}h_{\infty}^{3}+\frac{\Big[1
-4(\frac{d \alpha}{d
\tau}\kappa_{4}^{2})^{2}\Big]}{\gamma^{2}}h_{\infty}^{2}=0.
\end{equation}
This equation has four non-zero roots that two of them are
negative and unacceptable. When $\gamma\rightarrow 0$, we should
have the non-minimal DGP model.
\begin{figure}[htp]
\begin{center}
\special{psfile=5.eps hscale=50 vscale=50 hoffset= -65
voffset=-270} \vspace{5cm}\special{psfile=5b.eps angle =0
hscale=50 vscale=50 hoffset=190 voffset=-128}
\end{center}
\caption{\small { Solutions of the Friedmann equation for a tensionless brane in a Minkowski
bulk. For clarification, we have plotted the figure in two different scales to highlight intermediate
points. Also we have set $\gamma=0.003$ and $\alpha(\phi)=0.2, -0.2$.}}
\end{figure}\\
From equation (24) one can deduce
\begin{equation}
(\mu+\mu')=\alpha(\phi)h^{2}-h(\gamma h^{2}+1)+2\frac{d \alpha}{d
\tau}\kappa_{4}^{2}h,
\end{equation}
where $h_{\infty}\leq h<h_{i}$. Since $(\mu+\mu')_{\infty}$=0, from
equation (30) it follows that
\begin{equation}
\gamma=\frac{\alpha(\phi)h_{\infty}-1+2\frac{d \alpha}{d
\tau}\kappa_{4}^{2}}{h_{\infty}^{2}}.
\end{equation}
By expanding $\mu+\mu'$ to first order in $h^{2}-h_{\infty}^{2}$,
we find
\begin{equation}
h^{2}=h_{\infty}^{2}+\frac{2\Big(\alpha(\phi)h_{\infty}^{2}+2\frac{d
\alpha}{d
\tau}\kappa_{4}^{2}h_{\infty}\Big)}{\alpha(\phi)h_{\infty}\Big(2-6\frac{d
\alpha}{d
\tau}\kappa_{4}^{2}-\alpha(\phi)h_{\infty}\Big)-8(\frac{d
\alpha}{d \tau}\kappa_{4}^{2})^{2}+4\frac{d \alpha}{d
\tau}\kappa_{4}^{2}}(\mu+\mu').
\end{equation}
In comparison with equation (5), we find the following effective
4-dimensional Newton's constant
\begin{equation}
G=\Bigg[\frac{\Big(\alpha(\phi)h_{\infty}^{2}+2\frac{d \alpha}{d
\tau}\kappa_{4}^{2}h_{\infty}\Big)}{\alpha(\phi)h_{\infty}\Big(2-6\frac{d
\alpha}{d
\tau}\kappa_{4}^{2}-\alpha(\phi)h_{\infty}\Big)-8(\frac{d
\alpha}{d \tau}\kappa_{4}^{2})^{2}+4\frac{d \alpha}{d
\tau}\kappa_{4}^{2}}\Bigg]\frac{\alpha(\phi)G_{5}}{r},
\end{equation}
where $G_{5}=\frac{\kappa_{5}^{2}}{8\pi}$ and
$G=\frac{\kappa_{4}^{2}}{8\pi}$ are five and four dimensional
gravitational constant respectively. From equation (33) we obtain
a relation between $M_{5}^{3}$ and $M_{p}^{2}$ as follows
\begin{equation}
M_{5}^{3}\simeq \Bigg[\frac{\Big(\alpha(\phi)r^{2}H_{0}^{2}+2\frac{d
\alpha}{d\tau}\kappa_{4}^{2}rH_{0}\Big)}{\alpha(\phi)rH_{0}\Big(2-6\frac{d
\alpha}{d \tau}\kappa_{4}^{2}-\alpha(\phi)rH_{0}\Big)-8(\frac{d
\alpha}{d \tau}\kappa_{4}^{2})^{2}+4\frac{d \alpha}{d
\tau}\kappa_{4}^{2}}\Bigg]\frac{\alpha(\phi)M_{p}^{2}}{r}.
\end{equation}
Here $H_{\infty}\sim H_{0}$, and we see the important role played by
non-minimal coupling in this setup. In principle, one can fine tune
the value of the non-minimal coupling such that fundamental scale of
the bulk be reduced to values in the range accessible for next
generation of accelerators. To compare with DGP(+) limit, when
$\mu+\mu'\rightarrow0$, that is at late-time, we have
$rH_{0}\longrightarrow\frac{1}{\alpha(\phi)}-2\frac{\kappa_{4}^{2}}{\alpha(\phi)}\frac{d
\alpha}{d \tau}$, therefore this equation in this limit reduces to
$M_{5}^{3}\simeq \frac{M_{p}^{2}}{r}$. This is an interesting result
since there is no effect of non-minimal coupling in the non-minimal
DGP(+) limit at late-time and the relation between $M_{5}^{3}$ and
$M_{p}^{2}$ is the same as minimal case. This is not surprising
since essentially a part of motivation for inclusion of non-minimal
coupling has its origin on the quantum field theoretical
considerations( the renormalizability of quantum field theory in
curved background and quantum corrections to the scalar field
theory). In this view point, non-minimal coupling shows its
importance mainly in the high energy UV sector of the theory while
apparently DGP(+) gives IR sector of the theory free of stringy and
strong quantum field theoretical effects. We should stress that
non-minimal coupling of scalar field and induced gravity on DGP
brane modifies cross over scale[39]. The above argument is
restricted to the limit $\mu+\mu'\rightarrow0$ which is related to
the late time stage of evolution. In equation (34), when
$\alpha(\phi)$ attains different values, $M_{5}$ increases or
decreases relative to its value in DGP limit. When
$rH_{0}\rightarrow\frac{2(1-2\frac{d
\alpha}{d\tau}\kappa_{4}^{2})}{\alpha(\phi)}$, $M_{5}$ increases. We
should stress that these results are sensitive to the sign of the
non-minimal coupling explicitly.
\subsection{Minkowski Bulk ($\psi=0$) with Brane Tension($\sigma\neq0$)}
In this case the Friedmann equation is as follows
\begin{equation}
(1+\gamma h^{2})^{2}h^2=\Bigg[ \alpha(\phi)h^{2}-\Big(\mu+
\mu'+\sigma -2\frac{d\alpha(\phi)}{d\tau}h \kappa_{4}^{2}\Big)
\Bigg]^{2}.
\end{equation}
The effect of brane tension is similar to considering a cosmological
constant on the brane. In this case, there are three possible
solutions (GBIG\,1-3). To find initial and final Hubble rates and
density, we set $\frac{d(\mu+\mu')}{d(h^{2})}=0$. The initial and
final Hubble rates denoted by $h_{i}$ and $h_{e}$ respectively, are
given by
\begin{equation}
h_{i,\,e}=\frac{\alpha(\phi)\pm\sqrt{\alpha(\phi)^{2}-3\gamma+6\gamma\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}}}{3\gamma},
\end{equation}
and the initial and final density are calculated as follows
\begin{equation}
(\mu+\mu')_{i,\,e}=\frac{2\alpha(\phi)^{3}-9\alpha(\phi)\gamma+18\alpha(\phi)\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\gamma\pm2\Big(\alpha(\phi)^{2}-3\gamma+6\gamma\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\Big)^{\frac{3}{2}}}{27\gamma^{2}}-\sigma,\hspace{7
cm}
\end{equation}
where the plus sign is for initial state and minus sign shows the
final state. These points have $h'=0$. The point $h=0$ is the place
which GBIG3 loiters, that it is given by
\begin{equation}
(\mu+\mu')_{l}=-\sigma.
\end{equation}
and $h_{\infty}$ is given by
$$h_{\infty}^{6}+\frac{(2\gamma-\alpha^{2})}{\gamma^{2}}h_{\infty}^{4}-\frac{(4\alpha
\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\gamma^{2}}h_{\infty}^{3}+\frac{\Big[1+2\alpha\sigma
-4(\frac{d \alpha}{d
\tau}\kappa_{4}^{2})^{2}\Big]}{\gamma^{2}}h_{\infty}^{2}$$
\begin{equation}
+\frac{(4\sigma \frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\gamma^{2}}h_{\infty}-\frac{\sigma^{2}}
{\gamma^{2}}=0.
\end{equation}
to obtain this relation we have set $\mu+\mu'=0$ in equation (35).\\
The relation between $h$ and $\mu+\mu'$ is shown in figure $6$ for a
negative tension brane. In this figure for positive non-minimal
coupling, the GBIG1 and GBIG2 branches start with an initial Hubble
rate and density $\Big(h_{i},(\mu+\mu')_{i}\Big)$ whereas the GBIG3
branch doesn't remove the big bang singularity. GBIG1 and GBIG3
terminate at a finite Hubble rate and density
$\Big(h_{e},(\mu+\mu')_{e}\Big)$, whereas GBIG2 terminates in a
vacuum de Sitter state. On the other hand, for negative non-minimal
coupling, the GBIG2 branch has a big bang singularity and this is a
self-accelerating solution. GBIG1 and GBIG3 start without big bang
singularity $\Big(h_{i},(\mu+\mu')_{i}\Big)$ and both of them have
self-acceleration but GBIG3 throughout evolution loiters and then
evolves. A universe which undergoes a period of loitering is an
attractive alternative to standard cosmologies. Generally a
loitering universe is an expanding Friedmann universe that undergoes
a phase of slow expansion with redshift of $(z \sim 3 - 5)$. It is
believed that the large scale structure of the universe is formed
during this semi-static phase[54].
\begin{figure}[htp]
\begin{center}
\special{psfile=6.eps hscale=50 vscale=50 hoffset= -55
voffset=-260} \vspace{5cm}\special{psfile=6b.eps angle =0 hscale=50
vscale=50 hoffset=180 voffset=-118}
\end{center}
\caption{\small { Solutions of the Friedmann equation with a negative tension brane in a Minkowski
bulk. We have assumed
$\gamma=0.003$, $\sigma=-4$, $\psi=0$, $\alpha(\phi)=0.2$ and $-0.2$ for solid and dot curves
respectively. The figures are plotted with different scale to highlight important features.}}
\end{figure}
\newpage
Figure $7$ is the result for a positive tension brane. Here with
positive non-minimal coupling, the three solutions have
self-acceleration. There are a finite density for GBIG1 and GBIG2
but GBIG3 has big bang singularity. For negative non-minimal
coupling, these solutions are not physically reliable since for all
of them the density is negative.\\
\begin{figure}[htp]
\begin{center}
\special{psfile=7.eps hscale=70 vscale=60 hoffset= 25
voffset=-310}
\end{center}
\vspace{6 cm}
\caption{\small { Solutions of the Friedmann equation with a positive tension brane in a Minkowski bulk.
$\gamma=0.003$, $\sigma=10$, $\psi=0$, $\alpha(\phi)=0.2$ and $-0.2$ for dot and solid curves respectively.}}
\end{figure}
Note also that $\sigma_{i,\,e}$ and $\sigma_{l}$ are quantities
for which $\mu_{i,\,e}=0$ and $\mu_{l}=0$ respectively. From
equation (37), $\sigma_{i,\,e}$ are given in terms of $\gamma$ and
$\alpha(\phi)$ by
\begin{equation}
\sigma_{i,\,e}=\frac{2\alpha^{3}(\phi)-9\alpha(\phi)\gamma+18\alpha(\phi)\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\gamma\pm2\Big(\alpha^{2}(\phi)-3\gamma+6\gamma\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\Big)^{\frac{3}{2}}}{27\gamma^{2}},
\end{equation}
and from equation (38), $\sigma_{l}=0$. In the non-minimal case,
the maximum value of $\gamma$ is
$\gamma_{max}=\frac{\alpha^{2}(\phi)}{3-6\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}}$. For
$\gamma=\frac{\alpha^{2}(\phi)}{3-6\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}}$, GBIG1 branch disappears, since $h_{i}=h_{e}$ at
$\gamma_{max}$. Actually the point $h_{i}=h_{e}$ is now a point of
inflection. The requirement to have real value for the square root
in equation (36) and (37) leads us to the following relation
\begin{equation}
\gamma\leq\frac{\alpha^{2}(\phi)}{3-6\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}}.
\end{equation}
Based on this relation, the range of variation of $\gamma$ depends
on the non-minimal coupling coefficient directly. The latest
observational constraints on the values of $\gamma$ are listed in
table $1$ [55]. In this framework, we can constraint non-minimal
coupling of scalar field and induced Ricci scalar using
observational data. Considering a conformal coupling of the scalar
field and induced gravity on the brane defined as
$\alpha(\phi)=(1-\xi \phi^{2})$, we can constraint $\xi$ based on
the constraints imposed on $\gamma$ presented in table $1$. A
detailed study of constraints on non-minimal coupling of scalar
field and gravity based on various observational data and
theoretical techniques are summarized in reference [38]( see also
[56-64] for more details). For a time-independent scalar field,
$\alpha(\phi)$ will be time-independent also. Using the result of
SNIa+LSS+H(z)( the third line of table $1$) for $\gamma$ and
relation (41), we obtain $\alpha\geq0.01$ and $\alpha\leq -0.01$.
Since $\alpha(\phi)=(1-\xi \phi^{2})$, we find
$$-\sqrt{\frac{0.99}{\xi}}\leq\phi\leq\sqrt{\frac{0.99}{\xi}},$$ for $\alpha\geq0.01$ and
$$\phi\geq\sqrt{\frac{1.01}{\xi}}\,\,\,\,\,\,\, and\,\,\,\,\,\,\,
\phi\leq-\sqrt{\frac{1.01}{\xi}},$$ for $\alpha\leq -0.01$
respectively. The values of $\xi$ are constraint to be in the range
of $\xi\leq 0.99\phi^{-2}$ and $\xi\geq 1.01\phi^{-2}$. As we see
these constraints are dependent on the scalar field and this is
reasonable since dynamics of scalar field essentially affects its
coupling to gravity. In this viewpoint, variation of gravitational
coupling as a field in scalar-tensor gravity can be attributed to
variation of non-minimal coupling.
\begin{table*}
\begin{center}
\caption{The values of $\gamma$ in the different test.} \label{t1}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\hline
Test& $\gamma$ \\
\hline
SNIa &$0.0278_{-0.0278}^{+0.0033}$ \\
SNIa+LSS& $0.000_{-0.000}^{+0.005}$ \\
SNIa+LSS+H(z)& $0.000_{-0.000}^{+0.003}$ \\
\hline
\hline
\end{tabular}
\end{center}
\end{table*}
\subsection{AdS Bulk ($\psi\neq0$) with Brane Tension($\sigma\neq0$)}
For $\psi\neq0$, the bulk is AdS since $\Lambda_{5}\neq0$. We
should solve equation (23) for this case. The condition $h=0$
gives two solutions
\begin{equation}
\mu_{b,c}=\mp\sqrt{-\psi}(1+\frac{\psi}{2})-\sigma,
\end{equation}
where $\mu_{c}$ is the density at the point that GBIG3 collapses
(corresponding to plus sign), while $\mu_{b}$ is the density of the
new bouncing point for GBIG4 (corresponding to minus sign). In the
previous subsection (Minkowski bulk) there is a loitering point.
Here this point separates into bouncing and collapsing points. It is
interesting that when $\psi=-5$, the GBIG4 branch disappears.
Although the exact value of $\psi$ for disappearance of this branch
is not important and depends on the choice of parameters, the fact
that in principle this branch can be disappeared in a suitable
parameter space is an important result. To obtain turning points of
the branches, we calculate $\frac{d(\mu+\mu')}{d(h^2)}$ as follows
$$\frac{d(\mu+\mu')}{d(h^2)}=-\frac{\Big[1+\gamma (h^{2}+\frac{\psi}{2})\Big]\Big[3\gamma
(h^{2}-\frac{\psi}{2})+1\Big]}{2\Big(\alpha(\phi)h^{2}-(\mu+\mu'+\sigma)+2\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}\Big)}\hspace{5cm}$$
\begin{equation}
+\frac{2\Bigg[\alpha(\phi)^{2}h^{2}+3\alpha(\phi)\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}-(\mu+\mu'+\sigma)\Big(\alpha(\phi)+\frac{1}{h}\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2}\Big)+2(\frac{d\alpha(\phi)}{d\tau}
\kappa_{4}^{2})^{2}\Bigg]}{2\Big(\alpha(\phi)h^{2}-(\mu+\mu'+\sigma)+2\frac{d\alpha(\phi)}{d\tau}h
\kappa_{4}^{2}\Big)}.
\end{equation}
By substituting $\frac{d(\mu+\mu')}{d(h^2)}=0$, these points can be
obtained by solving the equation
\begin{equation} \frac{3}{2}\gamma
h^{3}+(\frac{1}{2}-\frac{3}{4}\gamma \psi) h-\alpha
h\sqrt{h^{2}-\psi}-\frac{d \alpha}{d
\tau}\kappa_{4}^{2}\sqrt{h^{2}-\psi}=0.
\end{equation}
There are three roots (which are presented in Appendix A ) two of
which are complex. Using equation (23), $h_{\infty}$ for AdS bulk
satisfies the following equation
$$h_{\infty}^{6}+\frac{(2\gamma-\alpha^{2})}{\gamma^{2}}h_{\infty}^{4}-\frac{(4\alpha
\frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\gamma^{2}}h_{\infty}^{3}+\frac{\Big[1+2\alpha\sigma-\psi\gamma(1+\frac{3}{4}\psi\gamma)
-4(\frac{d \alpha}{d
\tau}\kappa_{4}^{2})^{2}\Big]}{\gamma^{2}}h_{\infty}^{2}$$
\begin{equation}
+\frac{(4\sigma \frac{d \alpha}{d
\tau}\kappa_{4}^{2})}{\gamma^{2}}h_{\infty}-\frac{\Big[\psi(1+\frac{\psi\gamma}{2})^{2}+\sigma^{2}\Big]}
{\gamma^{2}}=0.
\end{equation}
In comparison with the minimal case [35], the behavior of the
branches are changed considerably. To see these differences, we
obtain numerical solutions of the above equation for different
values of $\psi$. The results of this calculations are shown in
figures $8$, $9$ and $10$ respectively.
\begin{figure}[htp]
\begin{center}
\special{psfile=8.eps hscale=60 vscale=60 hoffset= 25
voffset=-330}
\end{center}
\vspace{7 cm}
\caption{\small { The solutions of the Friedmann equation with a positive brane tension in AdS bulk.
We have chosen $\gamma=0.003$, $\sigma=10$, $\psi=-5$, $\alpha(\phi)=0.2,\, 0.3$.}}
\end{figure}
\begin{figure}[htp]
\begin{center}
\special{psfile=9.eps hscale=50 vscale=50 hoffset= -65
voffset=-242} \vspace{5cm}\special{psfile=9b.eps angle =0 hscale=50
vscale=50 hoffset=190 voffset=-100}
\end{center}
\caption{\small { The solutions of the Friedmann equation with a negative brane tension in AdS bulk and in two different scales.
We have set $\gamma=0.003$, $\sigma=-4$, $\psi=-1$, $\alpha(\phi)=0.2,\, 0.3$.}}
\end{figure}
\begin{figure}[htp]
\begin{center}
\special{psfile=10.eps hscale=50 vscale=50 hoffset= -65
voffset=-242} \vspace{5cm}\special{psfile=10b.eps angle =0
hscale=50 vscale=50 hoffset=190 voffset=-100}
\end{center}
\caption{\small { The solutions of the Friedmann equation with a negative brane tension in AdS bulk and in two different scales.
$\gamma=0.003$, $\sigma=-4$, $\psi=-1$, $\alpha(\phi)=1$ i.e. minimal case.}}
\end{figure}
As these figures show, $\alpha(\phi)$ as non-minimal coupling of the
scalar field and induced gravity on the brane, controls the initial
density and the age of the universe in this sense that these
quantities are sensitive to the proposed value of the non-minimal
coupling. For large values of $\alpha(\phi)$, the universe age and
its initial density are higher than the case with a small value of
$\alpha(\phi)$. Moreover, by increasing $\alpha(\phi)$, one of the
solutions, that is, GBIG4 disappears from the set of the solutions
(note that these results are obtained for constant values of $\psi$
and $\sigma$ while $\alpha(\phi)$ is variable). The GBIG4 branch
gives a bouncing cosmological solution. A bouncing universe goes
from an era of accelerated collapse to an expanding phase without
displaying any singularity. In the bouncing universe, the equation
of state parameter of the matter content, $\omega$, must transit
from $\omega<-1$ to $\omega>-1$ [65]. However, current observational
data show that the equation of state parameter $\omega$ was larger
than $-1$ in the past and is less than $-1$ today [66,67]. In our
framework, we have seen that in a suitable domain of parameters
space, by increasing $\alpha(\phi)$ values the GBIG4 branch
containing a bouncing cosmology will disappear. Even for a constant
$\alpha(\phi)$ there is no bouncing solution for any values of
$\psi$. For example with $\psi=-5$, this branch disappear
completely. These arguments show that inclusion of non-minimal
coupling of scalar field and induced gravity on the brane can be
used to fine-tune braneworld cosmological models in the favor of
observational data.
\section{Time Evolution of the Branches }
In this section we discuss more general case of a time-dependent
non-minimal coupling. All arguments presented in the preceding
sections can be reconsidered in this time-dependent framework. We
focus on Minkowski bulk ($\psi=0$) with brane tension($\sigma\neq0$)
for instance. Starting with Friedmann equation (35), we try the
following ansatz
\begin{equation}
\phi(t)\propto t^{-\nu}
\end{equation}
in order to investigate the late-time behavior of this scenario. As
has been mentioned at the end of the subsection $4.2$, the values of
$\xi$ are constraint to be in the range of $\xi\leq 0.99 \phi^{2}$
and $\xi\geq 1.01 \phi^{2}$. By adapting these conditions and
choosing $\alpha(\phi)=1-\xi \phi^{2}$, equation (35) can be
rewritten as follows
\begin{equation}
(1+\gamma h^{2})^{2}h^2=\Bigg[ (1-\xi t^{-2\nu})h^{2}-\Big(\mu+
\mu'+\sigma -2\kappa_{5}^{2} \nu \xi t^{(-2\nu-1)}h\Big) \Bigg]^{2}.
\end{equation}
where proportionality constant in (46) has been set equal to unity.
The constraints on $\xi$ are now time-dependent as $\xi\geq 0.99
t^{-2\nu}$ and $\xi \leq 1.01 t^{-2\nu}$. The results of numerical
solution of this equation are shown in figures $11$ and $12$ for
different values of $\xi$. Note that three graphs of figure $11$ (
and also figure $12$ with a different value of non-minimal coupling
coefficient $\xi$) are corresponding to three branches of figure
$6$, but now with time variation of non-minimal coupling. These
solutions are various possibilities of GBIG scenario with a time
varying non-minimally coupled scalar field on the brane. For
instance, figures $11a$ and $12a$ are corresponding to GBIG2 branch
of the scenario. On the other hand, figures $11b$ and $12b$ are
corresponding to GBIG1 branch and finally, $11c$ and $12c$ are
corresponding to GBIG3 branch. The main point to stress here is the
fact that in the presence of explicit time evolution of scalar
field, these branches show more or less the same late-time behavior
as discussed in previous sections.
\newpage
\begin{figure}[htp]
\begin{center}
\special{psfile=11.eps hscale=50 vscale=50 hoffset= -55
voffset=-260} \vspace{5cm}\special{psfile=11b.eps angle =0
hscale=50 vscale=50 hoffset=180
voffset=-118}\vspace{5cm}\special{psfile=11c.eps angle =0
hscale=60 vscale=60 hoffset=50 voffset=-210}
\end{center}
\vspace{2.5cm}
\caption{\small { Solutions of the Friedmann equation with a negative tension brane in a Minkowski
bulk. We have assumed
$\gamma=0.003$, $\sigma=-4$, $\psi=0$, $\nu=0.9$, $\kappa_{5}^{2}=1$, $\xi=0.99 \phi^{2}$.}}
\end{figure}
\begin{figure}[htp]
\begin{center}
\special{psfile=12.eps hscale=60 vscale=60 hoffset= -70
voffset=-220} \vspace{5cm}\special{psfile=12b.eps angle =0
hscale=60 vscale=60 hoffset=170
voffset=-78}\vspace{5cm}\special{psfile=12c.eps angle =0
hscale=60 vscale=60 hoffset=40 voffset=-140}
\end{center}
\caption{\small { Solutions of the Friedmann equation with a negative tension brane in a Minkowski
bulk. We have assumed
$\gamma=0.003$, $\sigma=-4$, $\psi=0$, $\nu=0.9$, $\kappa_{5}^{2}=1$, $\xi=2 \phi^{2}$.}}
\end{figure}
\newpage
Finally the issue of stability of the self-accelerated solutions
should be stressed here. It has been shown that the
self-accelerating branch of the DGP model contains a ghost at the
linearized level [68]. The ghost carries negative energy density and
it leads to the instability of the spacetime. The presence of the
ghost can be related to the infinite volume of the extra-dimension
in DGP setup. When there are ghosts instabilities in
self-accelerating branch, it is natural to ask what are the results
of solutions decay. One possible answer to this question is as
follows: since the normal branch solutions are ghost-free, one can
think that the self-accelerating solutions may decay into the normal
branch solutions. In fact for a given brane tension, the Hubble
parameter in the self-accelerating universe is larger than that of
the normal branch solutions. Then it is possible to have nucleation
of bubbles of the normal branch in the environment of the
self-accelerating branch solution. This is similar to the false
vacuum decay in de Sitter space. However, there are arguments
against this kind of reasoning which suggest that the
self-accelerating branch does not decay into the normal branch by
forming normal branch bubbles [68]. It was also shown that the
introduction of Gauss-Bonnet term in the bulk does not help to
overcome this problem [69]. In fact, it is still unclear what is the
end state of the ghost instability in self-accelerated branch of DGP
inspired setups (for more details see [68]). On the other hand,
non-minimal coupling of scalar field and induced gravity provides a
new degree of freedom which requires special fine tuning and this my
provide a suitable basis to treat ghost instability. As we have
shown, non-minimal coupling of scalar field and induced gravity has
the capability to remove bouncing solutions. It seems that this
additional degree of freedom has also the capability to provide the
background for a more reliable solution to ghost instability. This
issue deserves as a new research program.
\section{Summary and Conclusions}
DGP model modifies the IR sector of general relativity. In the UV
limit of a reliable theory, stringy effects should play important
role. In this viewpoint, to discuss both UV and IR limit of the
scenario simultaneously, the DGP model is not sufficient alone and
we should incorporate stringy effects via inclusion of the
Gauss-Bonnet terms. The presence of GB term removes the big bang
singularity, and the universe starts with an initial finite density.
Non-minimal coupling of scalar field and induced gravity on the
brane which is motivated from several compelling reasons, controls
the value of the initial density in a finite big bang cosmology on
the brane. This is not the only importance of non-minimal coupling
of scalar field and induced gravity; non-minimal coupling provides a
mechanism for generating spontaneous symmetry breaking at Planck
scale on the brane. In this respect, non-minimal coupling of scalar
field and induced gravity on the brane itself is a high energy
correction of the theory and it is natural to expect that this
effect couples with stringy effects in Planck scale. Investigation
of the late-time behavior of DGP scenario with GB and non-minimal
coupling effects provides a framework for constraining non-minimal
coupling using recent observational data. In our model, the values
of non-minimal coupling are constraint so that the values that $\xi$
can attain are constraint to be in the range of $\xi\leq
0.99\phi^{-2}$ and $\xi\geq 1.01\phi^{-2}$. In our setup, these
constraints are dependent on the scalar field dynamics and this is
reasonable since essentially dynamics of scalar field affects its
coupling to gravity. One of the main outcome of our analysis is the
implication of non-minimal coupling on bouncing cosmologies. In the
bouncing universe, the equation of state parameter of the matter
content, $\omega$, must transit from $\omega<-1$ to $\omega>-1$.
However, current observational data show that the equation of state
parameter $\omega$ was larger than $-1$ in the past and is less than
$-1$ today. In our framework, we have seen that with a suitable
parameter space, by increasing $\alpha(\phi)$ values, the GBIG4
branch containing a bouncing cosmology will disappear. Even for a
constant $\alpha(\phi)$ there is no bouncing solution for any values
of $\psi$. These arguments show that inclusion of non-minimal
coupling of scalar field and induced gravity on the brane can be
used to fine-tune braneworld cosmological models in the favor of
observational data. Although most of the arguments in the paper are
based on a time independent non-minimal coupling, but as we have
shown, inclusion of an explicit time dependence of non-minimal
coupling will not change the physical nature of the solutions.
Finally we have discussed the issue of ghost instabilities in
self-accelerated solutions and possible impacts of Gauss-Bonnet term
and non-minimal coupling on this issue.
{\bf Acknowledgment}\\
This work has been supported partially by Research Institute for
Astronomy and Astrophysics of Maragha, Iran.\\
{\bf APPENDIX A: Three Roots of Equation (44)}
$$h_{1}=\frac{A}{3(3\gamma-\alpha)}-\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)/$$
$$\Bigg[3\times 2^{\frac{2}{3}}(3\gamma-\alpha) \Bigg(-216\gamma
A-1620 \gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A+16 A^{3}+$$
$$\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16
A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}\Bigg]+\frac{1}{6\times
2^{\frac{1}{3}}(3\gamma-\alpha)}\Bigg(-216\gamma A-1620
\gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16 A^{3}+\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha A$$
$$-144\psi\alpha^{2} A+16A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}$$
$$h_{2}=\frac{A}{3(3\gamma-\alpha)}-\Bigg(\Big(1+i\sqrt{3}\Big)\Big(6(3\gamma-\alpha)
(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)\Bigg)/$$
$$\Bigg[6\times 2^{\frac{2}{3}}(3\gamma-\alpha) \Bigg(-216\gamma
A-1620 \gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A+16 A^{3}+$$
$$\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16 A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}\Bigg]-\frac{\Big(1-i\sqrt{3}\Big)}{12\times
2^{\frac{1}{3}}(3\gamma-\alpha)}\Bigg(-216\gamma A-1620
\gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16 A^{3}+\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha A$$
$$-144\psi\alpha^{2} A+16 A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}$$
$$h_{3}=\frac{A}{3(3\gamma-\alpha)}-\Bigg(\Big(1-i\sqrt{3}\Big)\Big(6(3\gamma-\alpha)
(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)\Bigg)/$$
$$\Bigg[6\times 2^{\frac{2}{3}}(3\gamma-\alpha) \Bigg(-216\gamma
A-1620 \gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A+16 A^{3}+$$
$$\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16 A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}\Bigg]-\frac{\Big(1+i\sqrt{3}\Big)}{12\times
2^{\frac{1}{3}}(3\gamma-\alpha)}\Bigg(-216\gamma A-1620
\gamma^{2}\psi A+ 72\alpha A+ 972\gamma\psi\alpha
A-144\psi\alpha^{2} A$$
$$+16 A^{3}+\Big[4\Big(6(3\gamma-\alpha)(2-3\gamma\psi+2\alpha\psi)-4A^{2}\Big)^{3}+(-216\gamma
A-1620 \gamma^{2}\psi A+72\alpha A+972\gamma\psi\alpha A$$
$$-144\psi\alpha^{2} A+16
A^{3})^{2}\Big]^{\frac{1}{2}}\Bigg)^{\frac{1}{3}}$$\\
where $A=\frac{d \alpha}{d \tau}\kappa_{4}^{2}$.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,365 |
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} | 4,533 |
Added properties:
```csharp
public SKRectI Rect { get; }
public SKSizeI Size { get; }
```
#### Type Changed: SkiaSharp.GRGlBackendTextureDesc
Added properties:
```csharp
public SKRectI Rect { get; }
public SKSizeI Size { get; }
```
#### Type Changed: SkiaSharp.GRGlTextureInfo
Added constructor:
```csharp
public GRGlTextureInfo (uint target, uint id);
```
#### Type Changed: SkiaSharp.SKBitmap
Added methods:
```csharp
public static SKBitmap Decode (System.ReadOnlySpan<byte> buffer);
public static SKBitmap Decode (System.ReadOnlySpan<byte> buffer, SKImageInfo bitmapInfo);
public static SKImageInfo DecodeBounds (System.ReadOnlySpan<byte> buffer);
public SKData Encode (SKEncodedImageFormat format, int quality);
public bool Encode (System.IO.Stream dst, SKEncodedImageFormat format, int quality);
public SKBitmap Resize (SKSizeI size, SKFilterQuality quality);
public SKShader ToShader ();
public SKShader ToShader (SKShaderTileMode tmx, SKShaderTileMode tmy);
public SKShader ToShader (SKShaderTileMode tmx, SKShaderTileMode tmy, SKMatrix localMatrix);
```
#### Type Changed: SkiaSharp.SKCanvas
Added properties:
```csharp
public bool IsClipEmpty { get; }
public bool IsClipRect { get; }
```
Added methods:
```csharp
public void DrawArc (SKRect oval, float startAngle, float sweepAngle, bool useCenter, SKPaint paint);
public void DrawAtlas (SKImage atlas, SKRect[] sprites, SKRotationScaleMatrix[] transforms, SKPaint paint);
public void DrawAtlas (SKImage atlas, SKRect[] sprites, SKRotationScaleMatrix[] transforms, SKColor[] colors, SKBlendMode mode, SKPaint paint);
public void DrawAtlas (SKImage atlas, SKRect[] sprites, SKRotationScaleMatrix[] transforms, SKColor[] colors, SKBlendMode mode, SKRect cullRect, SKPaint paint);
public void DrawPatch (SKPoint[] cubics, SKColor[] colors, SKPoint[] texCoords, SKPaint paint);
public void DrawPatch (SKPoint[] cubics, SKColor[] colors, SKPoint[] texCoords, SKBlendMode mode, SKPaint paint);
public void DrawRoundRectDifference (SKRoundRect outer, SKRoundRect inner, SKPaint paint);
public int SaveLayer ();
```
#### Type Changed: SkiaSharp.SKColorSpacePrimaries
Added field:
```csharp
public static SKColorSpacePrimaries Empty;
```
#### Type Changed: SkiaSharp.SKColorSpaceTransferFn
Added field:
```csharp
public static SKColorSpaceTransferFn Empty;
```
#### Type Changed: SkiaSharp.SKDynamicMemoryWStream
Added methods:
```csharp
public bool CopyTo (System.IO.Stream dst);
public void CopyTo (System.Span<byte> data);
```
#### Type Changed: SkiaSharp.SKFontManager
Added method:
```csharp
public SKTypeface MatchFamily (string familyName);
```
#### Type Changed: SkiaSharp.SKImage
Obsoleted methods:
```diff
[Obsolete ("Use FromPixels (SKImageInfo, SKData, int) instead.")]
public static SKImage FromPixelData (SKImageInfo info, SKData data, int rowBytes);
```
Added methods:
```csharp
public static SKImage FromPixels (SKImageInfo info, SKData data);
public bool IsValid (GRContext context);
public bool ReadPixels (SKPixmap pixmap);
public bool ReadPixels (SKImageInfo dstInfo, IntPtr dstPixels);
public bool ReadPixels (SKImageInfo dstInfo, IntPtr dstPixels, int dstRowBytes);
public SKImage ToRasterImage (bool ensurePixelData);
public SKShader ToShader ();
public SKImage ToTextureImage (GRContext context);
public SKImage ToTextureImage (GRContext context, SKColorSpace colorspace);
```
#### Type Changed: SkiaSharp.SKImageInfo
Added methods:
```csharp
public SKImageInfo WithSize (SKSizeI size);
```
#### Type Changed: SkiaSharp.SKMask
Added methods:
```csharp
public static SKMask Create (System.ReadOnlySpan<byte> image, SKRectI bounds, uint rowBytes, SKMaskFormat format);
public System.Span<byte> GetImageSpan ();
```
#### Type Changed: SkiaSharp.SKMatrix
Added constructor:
```csharp
public SKMatrix (float[] values);
```
Added fields:
```csharp
public static SKMatrix Empty;
public static SKMatrix Identity;
```
Added properties:
```csharp
public bool IsIdentity { get; }
public bool IsInvertible { get; }
```
Obsoleted methods:
```diff
[Obsolete ("Use MapRect(SKRect) instead.")]
public static void MapRect (ref SKMatrix matrix, out SKRect dest, ref SKRect source);
[Obsolete ("Use PostConcat(SKMatrix) instead.")]
public static void PostConcat (ref SKMatrix target, SKMatrix matrix);
[Obsolete ("Use PostConcat(SKMatrix) instead.")]
public static void PostConcat (ref SKMatrix target, ref SKMatrix matrix);
[Obsolete ("Use PreConcat(SKMatrix) instead.")]
public static void PreConcat (ref SKMatrix target, SKMatrix matrix);
[Obsolete ("Use PreConcat(SKMatrix) instead.")]
public static void PreConcat (ref SKMatrix target, ref SKMatrix matrix);
[Obsolete ("Use CreateRotation(float) instead.")]
public static void Rotate (ref SKMatrix matrix, float radians);
[Obsolete ("Use CreateRotation(float, float, float) instead.")]
public static void Rotate (ref SKMatrix matrix, float radians, float pivotx, float pivoty);
[Obsolete ("Use CreateRotationDegrees(float) instead.")]
public static void RotateDegrees (ref SKMatrix matrix, float degrees);
[Obsolete ("Use CreateRotationDegrees(float, float, float) instead.")]
public static void RotateDegrees (ref SKMatrix matrix, float degrees, float pivotx, float pivoty);
[Obsolete ()]
public void SetScaleTranslate (float sx, float sy, float tx, float ty);
```
Added methods:
```csharp
public static SKMatrix Concat (SKMatrix first, SKMatrix second);
public static SKMatrix CreateIdentity ();
public static SKMatrix CreateRotation (float radians);
public static SKMatrix CreateRotation (float radians, float pivotX, float pivotY);
public static SKMatrix CreateRotationDegrees (float degrees);
public static SKMatrix CreateRotationDegrees (float degrees, float pivotX, float pivotY);
public static SKMatrix CreateScale (float x, float y);
public static SKMatrix CreateScale (float x, float y, float pivotX, float pivotY);
public static SKMatrix CreateSkew (float x, float y);
public static SKMatrix CreateTranslation (float x, float y);
public SKMatrix Invert ();
public SKPoint MapVector (SKPoint vector);
public SKMatrix PostConcat (SKMatrix matrix);
public SKMatrix PreConcat (SKMatrix matrix);
```
#### Type Changed: SkiaSharp.SKMatrix44
Added property:
```csharp
public bool IsInvertible { get; }
```
Added methods:
```csharp
public static SKMatrix44 CreateTranslation (float x, float y, float z);
public void Set3x3ColumnMajor (float[] src);
public void Set3x3RowMajor (float[] src);
public static SKMatrix44 op_Implicit (SKMatrix matrix);
```
#### Type Changed: SkiaSharp.SKPath
Added method:
```csharp
public void Transform (SKMatrix matrix, SKPath destination);
```
#### Type Changed: SkiaSharp.SKPathMeasure
Added methods:
```csharp
public SKMatrix GetMatrix (float distance, SKPathMeasureMatrixFlags flags);
public SKPoint GetPosition (float distance);
public SKPath GetSegment (float start, float stop, bool startWithMoveTo);
public SKPoint GetTangent (float distance);
public void SetPath (SKPath path);
```
#### Type Changed: SkiaSharp.SKPicture
Added methods:
```csharp
public SKShader ToShader ();
public SKShader ToShader (SKShaderTileMode tmx, SKShaderTileMode tmy);
public SKShader ToShader (SKShaderTileMode tmx, SKShaderTileMode tmy, SKRect tile);
public SKShader ToShader (SKShaderTileMode tmx, SKShaderTileMode tmy, SKMatrix localMatrix, SKRect tile);
```
#### Type Changed: SkiaSharp.SKPixmap
Obsoleted methods:
```diff
[Obsolete ("Use Encode(SKWStream, SKJpegEncoderOptions) instead.")]
public static bool Encode (SKWStream dst, SKPixmap src, SKJpegEncoderOptions options);
[Obsolete ("Use Encode(SKWStream, SKPngEncoderOptions) instead.")]
public static bool Encode (SKWStream dst, SKPixmap src, SKPngEncoderOptions options);
[Obsolete ("Use Encode(SKWStream, SKWebpEncoderOptions) instead.")]
public static bool Encode (SKWStream dst, SKPixmap src, SKWebpEncoderOptions options);
[Obsolete ("Use Encode(SKWStream, SKEncodedImageFormat, int) instead.")]
public static bool Encode (SKWStream dst, SKBitmap src, SKEncodedImageFormat format, int quality);
[Obsolete ("Use Encode(SKWStream, SKEncodedImageFormat, int) instead.")]
public static bool Encode (SKWStream dst, SKPixmap src, SKEncodedImageFormat encoder, int quality);
```
Added methods:
```csharp
public bool Encode (System.IO.Stream dst, SKJpegEncoderOptions options);
public bool Encode (System.IO.Stream dst, SKPngEncoderOptions options);
public bool Encode (System.IO.Stream dst, SKWebpEncoderOptions options);
public bool Encode (System.IO.Stream dst, SKEncodedImageFormat encoder, int quality);
public bool Erase (SKColorF color);
public bool Erase (SKColorF color, SKRectI subset);
public System.Span<T> GetPixelSpan<T> ();
```
#### Type Changed: SkiaSharp.SKRegion
Added properties:
```csharp
public bool IsComplex { get; }
public bool IsEmpty { get; }
public bool IsRect { get; }
```
Added methods:
```csharp
public bool Contains (SKPath path);
public bool Contains (SKRectI rect);
public SKRegion.ClipIterator CreateClipIterator (SKRectI clip);
public SKRegion.RectIterator CreateRectIterator ();
public SKRegion.SpanIterator CreateSpanIterator (int y, int left, int right);
public SKPath GetBoundaryPath ();
public bool QuickContains (SKRectI rect);
public bool QuickReject (SKPath path);
public bool QuickReject (SKRectI rect);
public bool QuickReject (SKRegion region);
public void SetEmpty ();
public bool SetRects (SKRectI[] rects);
public void Translate (int x, int y);
```
#### Type Changed: SkiaSharp.SKRoundRect
Added constructor:
```csharp
public SKRoundRect (SKRect rect, float radius);
```
#### Type Changed: SkiaSharp.SKShader
Added methods:
```csharp
public static SKShader CreateBitmap (SKBitmap src);
public static SKShader CreateColor (SKColorF color, SKColorSpace colorspace);
public static SKShader CreateImage (SKImage src);
public static SKShader CreateImage (SKImage src, SKShaderTileMode tmx, SKShaderTileMode tmy);
public static SKShader CreateImage (SKImage src, SKShaderTileMode tmx, SKShaderTileMode tmy, SKMatrix localMatrix);
public static SKShader CreateLinearGradient (SKPoint start, SKPoint end, SKColorF[] colors, SKColorSpace colorspace, SKShaderTileMode mode);
public static SKShader CreateLinearGradient (SKPoint start, SKPoint end, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode);
public static SKShader CreateLinearGradient (SKPoint start, SKPoint end, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode, SKMatrix localMatrix);
public static SKShader CreatePerlinNoiseFractalNoise (float baseFrequencyX, float baseFrequencyY, int numOctaves, float seed, SKSizeI tileSize);
public static SKShader CreatePerlinNoiseImprovedNoise (float baseFrequencyX, float baseFrequencyY, int numOctaves, float z);
public static SKShader CreatePerlinNoiseTurbulence (float baseFrequencyX, float baseFrequencyY, int numOctaves, float seed, SKSizeI tileSize);
public static SKShader CreatePicture (SKPicture src);
public static SKShader CreateRadialGradient (SKPoint center, float radius, SKColorF[] colors, SKColorSpace colorspace, SKShaderTileMode mode);
public static SKShader CreateRadialGradient (SKPoint center, float radius, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode);
public static SKShader CreateRadialGradient (SKPoint center, float radius, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode, SKMatrix localMatrix);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKMatrix localMatrix);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace, SKShaderTileMode tileMode, float startAngle, float endAngle);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode tileMode, float startAngle, float endAngle);
public static SKShader CreateSweepGradient (SKPoint center, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode tileMode, float startAngle, float endAngle, SKMatrix localMatrix);
public static SKShader CreateTwoPointConicalGradient (SKPoint start, float startRadius, SKPoint end, float endRadius, SKColorF[] colors, SKColorSpace colorspace, SKShaderTileMode mode);
public static SKShader CreateTwoPointConicalGradient (SKPoint start, float startRadius, SKPoint end, float endRadius, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode);
public static SKShader CreateTwoPointConicalGradient (SKPoint start, float startRadius, SKPoint end, float endRadius, SKColorF[] colors, SKColorSpace colorspace, float[] colorPos, SKShaderTileMode mode, SKMatrix localMatrix);
public SKShader WithColorFilter (SKColorFilter filter);
public SKShader WithLocalMatrix (SKMatrix localMatrix);
```
#### Type Changed: SkiaSharp.SKSvgCanvas
Obsoleted methods:
```diff
[Obsolete ("Use Create(SKRect, Stream) instead.")]
public static SKCanvas Create (SKRect bounds, SKXmlWriter writer);
```
Added methods:
```csharp
public static SKCanvas Create (SKRect bounds, SKWStream stream);
public static SKCanvas Create (SKRect bounds, System.IO.Stream stream);
```
#### Type Changed: SkiaSharp.SKSwizzle
Added method:
```csharp
public static void SwapRedBlue (System.Span<byte> pixels);
```
#### Type Changed: SkiaSharp.SKTypeface
Added property:
```csharp
public int GlyphCount { get; }
```
Obsoleted methods:
```diff
[Obsolete ("Use CountGlyphs(byte[], SKTextEncoding) instead.")]
public int CountGlyphs (byte[] str, SKEncoding encoding);
[Obsolete ("Use CountGlyphs(ReadOnlySpan<byte>, SKTextEncoding) instead.")]
public int CountGlyphs (System.ReadOnlySpan<byte> str, SKEncoding encoding);
[Obsolete ("Use CountGlyphs(string) instead.")]
public int CountGlyphs (string str, SKEncoding encoding);
[Obsolete ("Use CountGlyphs(ReadOnlySpan<byte>, SKTextEncoding) instead.")]
public int CountGlyphs (IntPtr str, int strLen, SKEncoding encoding);
[Obsolete ("Use GetGlyphs(ReadOnlySpan<byte>, SKTextEncoding) instead.")]
public ushort[] GetGlyphs (byte[] text, SKEncoding encoding);
[Obsolete ("Use GetGlyphs(ReadOnlySpan<byte>, SKTextEncoding) instead.")]
public ushort[] GetGlyphs (System.ReadOnlySpan<byte> text, SKEncoding encoding);
[Obsolete ("Use GetGlyphs(string) instead.")]
public ushort[] GetGlyphs (string text, SKEncoding encoding);
[Obsolete ("Use GetGlyphs(string) instead.")]
public int GetGlyphs (string text, out ushort[] glyphs);
[Obsolete ("Use GetGlyphs(byte[], SKTextEncoding) instead.")]
public int GetGlyphs (byte[] text, SKEncoding encoding, out ushort[] glyphs);
[Obsolete ("Use GetGlyphs(IntPtr, int, SKTextEncoding) instead.")]
public ushort[] GetGlyphs (IntPtr text, int length, SKEncoding encoding);
[Obsolete ("Use GetGlyphs(ReadOnlySpan<byte>, SKTextEncoding) instead.")]
public int GetGlyphs (System.ReadOnlySpan<byte> text, SKEncoding encoding, out ushort[] glyphs);
[Obsolete ("Use GetGlyphs(string) instead.")]
public int GetGlyphs (string text, SKEncoding encoding, out ushort[] glyphs);
[Obsolete ("Use GetGlyphs(IntPtr, int, SKTextEncoding) instead.")]
public int GetGlyphs (IntPtr text, int length, SKEncoding encoding, out ushort[] glyphs);
```
Added methods:
```csharp
public bool ContainsGlyphs (System.ReadOnlySpan<char> text);
public bool ContainsGlyphs (string text);
public bool ContainsGlyphs (System.ReadOnlySpan<byte> text, SKTextEncoding encoding);
public bool ContainsGlyphs (IntPtr text, int length, SKTextEncoding encoding);
public int CountGlyphs (System.ReadOnlySpan<char> str);
public int CountGlyphs (byte[] str, SKTextEncoding encoding);
public int CountGlyphs (System.ReadOnlySpan<byte> str, SKTextEncoding encoding);
public int CountGlyphs (IntPtr str, int strLen, SKTextEncoding encoding);
public ushort[] GetGlyphs (System.ReadOnlySpan<char> text);
public ushort[] GetGlyphs (System.ReadOnlySpan<byte> text, SKTextEncoding encoding);
public ushort[] GetGlyphs (IntPtr text, int length, SKTextEncoding encoding);
public int[] GetKerningPairAdjustments (System.ReadOnlySpan<ushort> glyphs);
```
#### Type Changed: SkiaSharp.SkiaExtensions
Added methods:
```csharp
public static SKAlphaType GetAlphaType (this SKColorType colorType, SKAlphaType alphaType);
public static int GetBytesPerPixel (this SKColorType colorType);
public static SKTextEncoding ToTextEncoding (this SKEncoding encoding);
```
#### Type Changed: SkiaSharp.StringUtilities
Obsoleted methods:
```diff
[Obsolete ("Use GetEncodedText(string, SKTextEncoding) instead.")]
public static byte[] GetEncodedText (string text, SKEncoding encoding);
```
Added methods:
```csharp
public static byte[] GetEncodedText (System.ReadOnlySpan<char> text, SKTextEncoding encoding);
public static string GetString (System.ReadOnlySpan<byte> data, SKTextEncoding encoding);
public static string GetString (System.ReadOnlySpan<byte> data, int index, int count, SKTextEncoding encoding);
```
#### New Type: SkiaSharp.SKColorF
```csharp
public struct SKColorF {
// constructors
public SKColorF (float red, float green, float blue);
public SKColorF (float red, float green, float blue, float alpha);
// fields
public static SKColorF Empty;
// properties
public float Alpha { get; }
public float Blue { get; }
public float Green { get; }
public float Hue { get; }
public float Red { get; }
// methods
public SKColorF Clamp ();
public static SKColorF FromHsl (float h, float s, float l, float a);
public static SKColorF FromHsv (float h, float s, float v, float a);
public void ToHsl (out float h, out float s, out float l);
public void ToHsv (out float h, out float s, out float v);
public SKColorF WithAlpha (float alpha);
public SKColorF WithBlue (float blue);
public SKColorF WithGreen (float green);
public SKColorF WithRed (float red);
public static SKColor op_Explicit (SKColorF color);
public static SKColorF op_Implicit (SKColor color);
}
```
#### New Type: SkiaSharp.SKRotationScaleMatrix
```csharp
public struct SKRotationScaleMatrix {
// constructors
public SKRotationScaleMatrix (float scos, float ssin, float tx, float ty);
// fields
public static SKRotationScaleMatrix Empty;
public static SKRotationScaleMatrix Identity;
// properties
public float SCos { get; set; }
public float SSin { get; set; }
public float TX { get; set; }
public float TY { get; set; }
// methods
public static SKRotationScaleMatrix Create (float scale, float radians, float tx, float ty, float anchorX, float anchorY);
public static SKRotationScaleMatrix CreateDegrees (float scale, float degrees, float tx, float ty, float anchorX, float anchorY);
public static SKRotationScaleMatrix CreateIdentity ();
public static SKRotationScaleMatrix CreateRotation (float radians, float anchorX, float anchorY);
public static SKRotationScaleMatrix CreateRotationDegrees (float degrees, float anchorX, float anchorY);
public static SKRotationScaleMatrix CreateScale (float s);
public static SKRotationScaleMatrix CreateTranslation (float x, float y);
public SKMatrix ToMatrix ();
}
```
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,372 |
Calls / Announcements
About JSSE
1-2019 National Holidays and other Socio-Political Rituals in Schools /
Featured Topic
The Phenomenon of Banished Soldiers in Polish Schools as an Example of the Politics of Memory
Ewa Bacia Technische Universität Berlin
DOI: https://doi.org/10.4119/jsse-887
Purpose: The article intends to analyse the manner in which banished soldiers are presented in the new history curriculum at schools in Poland as an example of the politics of memory.
Design/methodology/approach: The analyses performed included the following issues: the history of banished soldiers, the core history curriculum after the education reform in Poland, its objectives and goals (with particular emphasis on banished soldiers), the manner of presenting the banished soldiers in educational, public and social environments in Poland today, the impact of new historical politics on the Polish society and democracy.
Findings: The manner of presenting the issue of banished soldiers in the core curriculum for teaching history in Polish schools exemplifies the efforts to introduce a new political paradigm into the educational context. The primary purposes of teaching history at schools have become to stir up patriotic emotions and strengthen bonds with the Polish nation. These goals are to be reached by promoting distinguished figures in the country. However, any controversies related to the "heroes" are deliberately ignored, which is especially evident in the case of banished soldiers. Patriotism is identified with a black and white vision of history that emphasizes the good acts of "Poles" and the cruel acts of "others". The simplified vision of history, which expressly ignores controversies and is reluctant to discuss dilemmas, is a real threat to the future of Polish democracy.
Ewa Bacia, Technische Universität Berlin
Ph.D., Research Assistant, Technische Universität Berlin, Institute of Education, Department of Educational Psychology
1-2019 National Holidays and other Socio-Political Rituals in Schools
Journal of Social Science Education – ISSN: 1618-5293
Faculty of Sociology
Postbox 100 131 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,351 |
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\section{Introduction}
In a helical flow both energy and helicity are inviscid invariants which are
cascaded from the integral scale to the dissipation scale \cite{Lesieur}. If these scales for
the helicity are separated there will be an inertial range in which an
equivalent of the four-fifth law for helicity transfer holds. This is a
scaling relation for a third order structure function with a different
tensorial structure from the structure function associated with the flux of energy.
For helicity flux this is,
$\langle \delta {\bf v}_\|(l)\cdot[{\bf v}_\bot(r)\times {\bf v}_\bot(r+l)]\rangle
= (2/15) \overline{\delta}l^2$, where $\overline{\delta}$ is the mean dissipation
of helicity. This relation is called the 'two-fifteenth
law' due to the numerical prefactor \cite{Procaccia,russian}.
The inertial ranges for helicity cascade and for energy cascade are different
because the dissipation of helicity scales as
$D_H(k) \sim k D_E(k)$, thus the helicity will be dissipated within
the inertial range for energy cascade. From balancing the helicity flux
and the helicity dissipation a Kolmogorov scale $\xi=K_H^{-1}$ for helicity dissipation
can be defined \cite{D&G},
\begin{equation}
\xi \sim (\nu^3 \overline{\varepsilon}^2/\overline{\delta}^3)^{1/7},
\label{KH}
\end{equation}
where $\nu$ is the kinematic viscosity, $\overline{\varepsilon}$ is
the mean energy dissipation per unit mass and $\overline{\delta}$ is the mean
helicity dissipation per unit mass.
This scale is larger than the usual Kolmogorov scale
$\eta=K_E^{-1}\sim (\nu^3/\overline{\varepsilon})^{1/4}$.
The physical
picture for fully developed helical turbulence is shown schematically in
figure 1. The mean dissipations
$\overline{\delta}$ and $\overline{\varepsilon}$ are solely determined by
the forcing in the integral scale. There will then be an inertial range with
coexisting cascades of energy and helicity with third order structure functions
determined by the four-fifth -- and the two-fifteenth laws. This is followed
by an inertial range between $K_H$ and $K_E$ corresponding to non-helical turbulence,
where the dissipation of positive and negative helicity vortices balance and
the two-fifteenth law is not applicable.
\begin{figure}[htb]
\epsfxsize=13.5cm
\epsffile{paladin1.eps}
\caption[]{The inertial range for helicity cascade is smaller than the inertial
range for energy cascade. In the range $K_H<k<K_E$ the dissipation
of positive and negative helicity balance.}
\end{figure}
\section{The anomalous scaling exponents}
There is now experimental evidence that the K41 scaling
relations are not exact. There are corrections for moments different
from 3, expressed through anomalous scaling exponents, $\langle \delta
v(l)^p \rangle \sim l^{\zeta(p)}$ where $\zeta(p)\ne p/3$.
Understanding and quantitatively determining the anomalous scaling exponents is
one of the most intriguing and unsolved problems in turbulence.
The intermittency corrections to the K41 scaling could depend on the transfer of
helicity, maybe similar to the way the different
sectors in anisotropic turbulence might give rise to sub-leading corrections
of scaling exponents \cite{Arad}.
Furthermore,
the helicity cascade
itself leads to a set of anomalous scaling exponents related to moments
of the third order correlator of the two-fifteenth law.
There is at present no experimental measurements from helical turbulence of the
scaling exponents associated with the two-fifteenth law.
It was recently shown numerically
by Biferale et al. \cite{Biferale} that in the case of a shell model the anomalous
scaling exponents for the helicity transfer has a strong difference
between odd and even powers such that the scaling exponent $\zeta^H(p)$ is not a convex
function.
Biferale et al. used a shell model consisting of two coupled GOY shell models. We
will show here that the results obtained holds for the standard GOY shell
model as well.
Shell models are
toy-models of turbulence which by construction have second order inviscid
invariants similar to energy and helicity in 3D turbulence.
Shell models
can be investigated numerically for high Reynolds numbers,
in contrast to the Navier-Stokes equation, so that high order statistics
and anomalous scaling exponents are easily accessible.
Shell models lack any spatial structures so
we stress that only certain aspects of the turbulent cascades have
meaningful analogies in the shell models. This should especially
be kept in mind when studying helicity which is intimately linked
to spatial structures, and the dissipation of helicity to reconnection of
vortex tubes \cite{Levich}. The following thus only concerns the spectral aspects
of the helicity and energy cascades.
The GOY model \cite{GOY,Kadanoff,jpv} is the most well studied shell model.
It is defined from the governing equation,
\begin{equation}
\dot{u_n}=i k_n (u_{n+2}u_{n+1}-\frac{\epsilon}{\lambda}u_{n+1}u_{n-1}+
\frac{\epsilon-1}{\lambda^2}u_{n-1}u_{n-2})^* -\nu k_n^2 u_n + f_n
\label{1}
\end{equation}
with $n=1, ..., N$ where the $u_n$'s are the complex shell velocities. The
wave numbers are defined as $k_n = \lambda^n$, where $\lambda$ is the shell
spacing. The second and third terms are dissipation and forcing. The model
has two inviscid invariants, energy, $E=\sum_n E_n =\sum_n |u_n|^2$,
and 'helicity', $H=\sum_nH_n=\sum_n (\epsilon -1)^{-n}|u_n|^2$. The
model has two free parameters, $\lambda$ and $\epsilon$. The 'helicity'
only has the correct dimension of helicity if $|\epsilon -1|^{-n}=k_n
\Rightarrow 1/(1-\epsilon)=\lambda$.
In
this work we use the standard parameters $(\epsilon,\lambda)=(1/2,2)$
for the GOY model.
A natural way to define the structure functions of moment $p$ is through the
transfer rates of the inviscid invariants,
\begin{eqnarray}
S^E_p(k_n)= \langle(\Pi^E_n)^{p/3}\rangle k_n^{-p/3}\sim k_n^{-\zeta^E(p)} \label{s3e} \\
S^H_p(k_n)= \langle(\Pi^H_n)^{p/3}\rangle k_n^{-2p/3}\sim k_n^{-\zeta^H(p)}
\label{s3h}
\end{eqnarray}
The energy flux is defined in the usual
way as $\Pi^E_n = d/dt|_{n.l.}(\sum_{m=1}^{n} E_m) $ where
$d/dt|_{n.l.}$ is the time rate of change due to the non-linear term in
(\ref{1}). The helicity flux $\Pi^H_n$ is defined similarly. By a simple algebra we have
the following expression for the fluxes,
\begin{eqnarray}
\langle \Pi^E_n \rangle= (1-\epsilon) \Delta_n + \Delta_{n+1} =\overline{\varepsilon}\label{pie} \\
\langle \Pi^H_n \rangle= (-1)^n k_n(\Delta_{n+1}-\Delta_n)=\overline{\delta}
\label{pih}
\end{eqnarray}
where $\Delta_n = k_{n-1}Im \langle u_{n-1}u_nu_{n+1}\rangle$,
$\overline{\varepsilon}$ and $\overline{\delta}$ are the mean dissipations of
energy and helicity respectively. The first equalities hold without averaging
as well.
These equations are the shell model equivalents of
the four-fifth -- and the two-fifteenth law.
In the definition (\ref{s3e}), (\ref{s3h}) of the structure functions there is a slight
ambiguity in the definition of
$x^{p/3}$ for negative $x$ and $p$ not a multiplum of 3.
The complex roots for
$(-1)^{1/3}$ are $(-1, 1/2 \pm i \sqrt{3}/2)$ and for $(-1)^{2/3}$ they are $(1,- 1/2 \pm i \sqrt{3}/2)$. The common way of circumventing the ambiguity
is by defining
$x^{p/3}= sgn(x)|x|^{p/3}$, which neglects the imaginary
roots\footnote{This can not
always be done. Had we defined the structure functions from some, say,
sixth order correlator, we are in trouble since
$z=(-1)^{1/6}$ has no real roots.}.
With this
definition we have,
\begin{eqnarray}
S_p(k_n) = \int_0^{\infty}[\psi_n(x)+\psi_n(-x)]x^{p/3}dx \equiv \int_0^{\infty}\psi_n^+(x)x^{p/3}dx \, \,
&(p\, \mbox{ even}) \label{pdf1} \\
S_p(k_n) = \int_0^{\infty}[\psi_n(x)-\psi_n(-x)]x^{p/3}dx \equiv
\int_0^{\infty}\psi_n^-(x) x^{p/3}dx \, \,
&(p\, \mbox{ odd}) \label{pdf2}
\end{eqnarray}
where $\psi_n(x)$ is the probability density function (pdf) for $\Pi_n$.
$\psi_n^+(x)$ is (twice) the symmetric part of the pdf and $\psi_n^-(x)$
is (twice) the anti-symmetric part. Note that $\psi_n^+(x)$ is itself
a pdf while $\psi_n^-(x)$ is not. $\psi_n^-(x)$ is, except for a normalization, a pdf only if $\psi_n(x)>\psi_n(-x)$ for
all positive $x$.
\begin{figure}[htb]
\epsfxsize=13.5cm
\epsffile{paladin2.eps}
\caption[]{The anomalous scaling exponents, $\zeta^E(p)$ (dashed
curve) and $\zeta^H(p)$. The two full curves for even and odd moments
for the helicity are calculated according to (\ref{pdf1}) and (\ref{pdf2})
respectively. The error bars on the $\zeta^E(p)$ curve are
within the triangles, so we see a deviation between
$\zeta^E(2p)$ and $\zeta^H(2p)$.
The error bars for the odd moments of $\zeta^H(p)$ are
large because they are determined by the scaling of the anti-symmetric part of the probability
density functions. The dashed-dotted line is the K41 scaling.}
\end{figure}
The scaling exponents are determined from the scaling of the pdf's through,
\begin{equation}
\int_{-\infty}^{\infty}x^{p/3}\psi_{\lambda k}(x)dx=\lambda^{-\zeta(p)}
\int_{-\infty}^{\infty}x^{p/3}\psi_k(x)dx,
\end{equation}
so the scaling exponents for $p$ even is related to the scaling of $\psi_n^+$
while for $p$ odd they are related to the scaling of $\psi_n^-$.
We have performed a simulation of the standard GOY model with
$(\epsilon, \lambda, \nu, N)=(1/2, 2, 10^{-9}, 26)$ and a forcing
of the form $f_n = 0.01 \delta_{2,n}/u_2^*$, corresponding to a constant
energy input. The simulation was about $5000$ large eddy turnover times.
Figure 2 shows the anomalous scaling exponents, $\zeta^E(p), \zeta^H(p)$
for the energy and the
helicity calculated according to (\ref{pdf1}) and (\ref{pdf2}).
Using (\ref{pdf1}) the
scaling exponent $\zeta^H(p)$ can be defined for any real positive $p$, which
from the H\"{o}lder inequality is a convex curve. Similarly using (\ref{pdf2})
assuming $\phi_n^-(x)$ to be a positive function we can define a continuous
curve $\tilde{\zeta}^H(p)$ which is also from the H\"{o}lder inequality
a convex curve.
The scaling exponent $\zeta^H(p)$ defined for integer $p$ jumps between the two curves shown in figure 2.
The scaling exponents differs from the ones found by
Biferale et al. for the two-component GOY model. We find that
$\zeta^H(2p)$ is slightly larger than $\zeta^E(2p)$.
The scaling regime in
which $\zeta^H(p)$ is calculated is $K_{\mbox{I}}<k<K_H$ while for the
energy $K_{\mbox{I}}<k<K_E$.
The negative part of the probability density is negligible in the
case of energy transfer, $\psi_n(x)\approx \psi_n^+(x)\approx \psi_n^-(x)$ for
$x>0$, but for helicity transfer the negative tail is big which gives
the strong even-odd oscillations between the two curves. Note that $\zeta^E(3)=1$ and $\zeta^H(3)=2$
are just the four-fifth -- and the two-fifteenth law.
\begin{figure}[htb]
\epsfxsize=13.5cm
\epsffile{paladin3.eps}
\caption[]{The left hand panels show probability density
functions $\psi(x)$ of the
helicity flux for shells 3 and 6. The
right hand panels show the probability distribution functions $\Psi(x)$ for $x > 0$,
the dashed curves are $1-\Psi(-x)$ which for a symmetric distribution is identical
to $\Psi(x)$. The scaling exponents for the even moments depends on the scaling
with $n$ of the symmetric part of the pdf which corresponds to the mean curve between the full and
dashed curves. The scaling exponents for the odd moments depends on the scaling of
the anti-symmetric part of the pdf corresponding to the gap betwwen the full and dashed curves.
}
\end{figure}
Figure 3 shows the probability distribution function (PDF) for helicity flux,
defined by $\Psi(x)=\int_{-\infty}^x \psi(y)dy$ for shell numbers $n=3$ and
$n=6$ both
in the inertial range for helicity flux.
The negative tail is plotted as $1-\Psi(-x)$ which for a symmetric pdf gives
two overlapping curves. We can similarly define the PDF $\Psi_n^\pm(x)\equiv
\int_0^x\psi_n^\pm(y)dy$. A simple algebra gives $\Psi_n^+(x)=\Psi_n(x)+(1-\Psi_n(-x))-1$
and $\Psi_n^-(x)=\Psi_n(x)-(1-\Psi_n(-x))+(1-2\Psi(0))$. So we see that
the scaling of $\Psi_n^+(x)$ is related to the scaling of the mean of the
two curves in the right panels in figure 3, while the scaling of $\Psi_n^-(x)$
is related to the gap between the two curves.
\section{Conclusion}
Coexisting cascades of energy and helicity are possible in the GOY
shell model. The scaling of the odd order moments of the helicity
transfer depends on the scaling of the anti-symmetric part of the probability
density function for the helicity flux. This defines a convex
anomalous scaling curve through the point $\zeta^H(3)=2$ which is
the two-fifteenth law. The even order moments of the helicity
flux has anomalous scaling exponents
close to the ones found for the energy flux. In the simulation
a scale break at $K_H$ is not observed. This implies that the anomalous
scaling exponents for the energy flux are not influenced
by the cascade of helicity.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 303 |
Q: postgresql one to many as json result, how to filter? I have a simple db structure with a one to many relationship
CREATE TABLE customer (
id SERIAL PRIMARY KEY,
email TEXT,
first_name TEXT,
last_name TEXT
);
CREATE TABLE customer_address (
id SERIAL PRIMARY KEY,
customer_id INTEGER NOT NULL,
street_name TEXT NOT NULL,
street_number TEXT NOT NULL,
zip_code TEXT NOT NULL,
city TEXT NOT NULL
);
For my application I want to return each customer with all its addresses as one row, whereby I encapsulate all the addresses in a json array. This is done like this:
SELECT customer.*,
addresses
FROM customer
left join (SELECT
Array_to_json(Array_agg(
Json_build_object('id', address.id, 'street_name', address.street_name, 'street_number', address.street_number, 'zip_code', address.zip_code, 'city', address.city))) AS addresses,
address.customer_id
AS customer_id
FROM customer_address AS address
GROUP BY address.customer_id) addresses
ON addresses.customer_id = customer.id
join customer_address
ON customer_address.customer_id = customer.id
This works fine and gives me a resultset with for each result an element called addresses containing a JSON array of all the customer's addresses.
Now I would like to select all customers (with all of their addresses) whose street_name is like a certain search term. And I can't get it to work. How can I select full records including all addresses inlined when one address has a street name containing a certain value (matched with an ILIKE) ?
I tried adding: WHERE customer_address.street_name LIKE 'Ro', and while this works, if I replace this where statement with something completely different such as WHERE customer.id > 0 I get doubles in the result set
Here is an sql Fiddle to play around in:
http://sqlfiddle.com/#!17/0e818/4
A: This join condition looks wrong:
JOIN customer_address ON customer_address.id = customer.id
Shouldn't it be
JOIN customer_address ON customer_address.customer_id = customer.id
Here is the fiddle:
http://sqlfiddle.com/#!17/2fff0/6
Following the discussions on the original answer, here is the final solution that addresses the raised issues:
http://sqlfiddle.com/#!17/2fff0/25
A: Does this cover your expected result?
SELECT customer.*,addresses
FROM customer
LEFT JOIN (SELECT array_to_json(array_agg(json_build_object('id',address.id,'street_name',address.street_name,'street_number',address.street_number,'zip_code',address.zip_code,'city',address.city))) AS addresses,address.customer_id AS customer_id
FROM customer_address AS address
GROUP BY address.customer_id) addresses
ON addresses.customer_id = customer.id
JOIN customer_address ON customer_address.id = customer.id
WHERE customer_address.street_name LIKE 'Ro%'
id | email | first_name | last_name | addresses
-: | :------------ | :--------- | :-------- | :-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 | john@test.com | John | Doe | [{"id" : 1, "street_name" : "Route", "street_number" : "222", "zip_code" : "9000", "city" : "NY"},{"id" : 2, "street_name" : "Ro", "street_number" : "444", "zip_code" : "9000", "city" : "LA"}]
dbfiddle here
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,081 |
Q: Php how to correctly use return function? Hello I have a problem with this function I want to show the result of the function to put in a variable and send it to the database but it does not show me anything you can see in the example in the Second Block when I added echo its show me but I don't know how to get that result out I did use return but it gave a different result
$fullname = "Ayoub Chafik" ;
function orderID($data){
$AKK = "AK". date('YmdHis');
$string = strtoupper($data);
$strs=explode(" ",$string);
foreach($strs as $str)
$str[0];
}
// I want to see resulte here of this function
echo orderID($fullname) ;
?>
This is the second Block
<?php
$fullname = "Ayoub Chafik" ;
function orderID($data){
echo $AKK = "AK". date('YmdHis');
$string = strtoupper($data);
$strs=explode(" ",$string);
foreach($strs as $str)
echo $str[0];
}
echo orderID($fullname) ;
?>
A: As I explained in comment you store it in a variable and return it. Check below example. Also it is a good practice to open the {} even its only one line for more readability.
$fullname = "Ayoub Chafik" ;
function orderID($data) {
$string = strtoupper($data);
$strs = explode(" ", $string);
$results = '';
foreach($strs as $str) {
$results .= $str[0];
}
return $results;
}
echo orderID($fullname) ;
A: Some examples varying output based on your code sample.
$fullname = "Ayoub Chafik";
function orderID($data){
$string = strtoupper($data);
$strs=explode(" ",$string);
foreach($strs as $str) {
return $str;
}
}
echo orderID($fullname) ;
// output "AYOUB"
function _orderID($data){
$return = false;
$string = strtoupper($data);
$strs=explode(" ",$string);
foreach($strs as $str) {
$return = $str;
}
return $return;
}
echo _orderID($fullname) ;
// output "CHAFIK"
function _orderID_($data){
$return = [];
$string = strtoupper($data);
$strs=explode(" ",$string);
foreach($strs as $str) {
array_push($return,$str);
}
return json_encode($return);
}
echo _orderID_($fullname) ;
// output ["AYOUB","CHAFIK"]
check the above examples on PHP SandBox
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,619 |
package org.apache.kylin;
import org.apache.kylin.common.KylinConfig;
import org.apache.kylin.common.util.LocalFileMetadataTestCase;
import org.apache.kylin.metadata.realization.RealizationRegistry;
import org.apache.kylin.metadata.realization.RealizationType;
import org.junit.After;
import org.junit.Before;
import org.junit.Test;
import java.util.Set;
import static org.junit.Assert.assertEquals;
/**
*/
public class RealizationRegistryTest extends LocalFileMetadataTestCase {
@Before
public void setup() throws Exception {
createTestMetadata();
}
@After
public void after() throws Exception {
cleanupTestMetadata();
}
@Test
public void test() throws Exception {
final RealizationRegistry registry = RealizationRegistry.getInstance(KylinConfig.getInstanceFromEnv());
final Set<RealizationType> realizationTypes = registry.getRealizationTypes();
assertEquals(RealizationType.values().length - 1, realizationTypes.size());
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,772 |
Патентно-інформаційна служба (, ; ) – комплекс установ і заходів, які здійснюють інформаційне забезпечення винахідницької діяльності. Усі винаходи для забезпечення оперативного пошуку згідно з [Міжнародною патентною класифікацією] поділені на вісім розділів.
Розділ А –Потреби людини
Розділ В – Різні технологічні процеси, транспортування.
Розділ С – Хімія, металургія.
Розділ Е – Будівництво, гірнича справа.
Розділ F – Механіка, освітлення, опалювання, двигуни і насоси, зброя, вибухові роботи, боєприпаси.
Розділ G – Фізика.
Розділ Н – Електрика.
Така будова МПК дозволяє використати її як ефективний пошуковий інструмент і полегшує орієнтування у величезному потоці патентної інформації, яка зберігається в патентних фондах. В розділі Е є тематичні рубрики: буріння, видобуток нафти, газу, води, розчинних або плавких речовин з бурових свердловин; експлуатація шахт і кар'єрів; шахтні стовбури; тунелі; виробки, засоби техніки безпеки, транспорт; закладення виробленого простору; обладнання для рятувальних робіт; вентиляція та дренаж рудників або тунелів. Розділи В та С містять багато інформації про способи і засоби (процеси) збагачення корисних копалин.
Див. також
Патент
Патентна класифікація
Література
Патентна справа | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,914 |
Meet Our Majors Director and Info about Major's Division
We are here to provide you and your family with the best baseball experience possible! Please take a moment to read about our director and about the Majors Program.
Mike Hackett
Director of Majors
Phone: xxx-xxx-xxxxx
About Mike Hackett: Mike has been involved with WNLL going on his 5 year. He has coached several teams from AA up to Majors including Fall Ball and All Stars. Mike is truly dedicated to the development of the Majors program.
About Majors:
The Majors division is the most advanced level of the Little League program and is open to players of league age 10 - 12. Players must attend try-outs and be evaluated on their abilities. Following try-outs, managers will draft players based upon skill assessment. Players not drafted to a Major division team will be automatically placed in the AAA division draft. Players at this level are taught advanced techniques in hitting, fielding, throwing and pitching. More complex strategies and plays are also introduced and explained. Teams in this division usually practice at least two times per week on non-game days. The Majors division follows Little League pitching rules and games are officiated by qualified umpires. The level of play is competitive and game scores, player statistics and win/loss records are maintained. All Major division teams participate in a post-season tournament. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,604 |
\section{Introduction}
Let $X$ be a time-homogeneous Markov process. Hunt's hypothesis
(H) says that ``every semipolar set of $X$ is polar". This
hypothesis plays a crucial role in the potential theory of (dual)
Markov processes. To illustrate its importance, let us recall some
potential-theoretic principles.
Suppose that $E$ is a locally compact space with a countable base.
Let $(X, P^x)$ and $(\hat{X},\hat P^x)$ be a pair of dual standard
Markov processes on $E$ as described in Blumenthal and Getoor \cite[VI]{BG68}. Denote by
${\cal B}^n$ the family of all nearly Borel measurable subsets of
$E$. For $D\subset E$, we define the first hitting time of $D$ by
$$
\sigma_D:=\inf\{t>0:X_t\in D\}.
$$
A set $D\subset E$ is called polar (respectively, essentially
polar) if there exists a set $C\in {\cal B}^n$ such that $D\subset
C$ and $P^x(\sigma_C<\infty)=0$ for every $x\in E$ (respectively,
almost every $x\in E$ with respect to the reference measure). $D$
is called a thin set if there exists a set $C\in {\cal B}^n$ such
that $D\subset C$ and {$P^x(\sigma_C=0)=0$} for every $x\in E$.
$D$ is called semipolar if $D\subset\bigcup_{n=1}^{\infty}D_n$ for
some thin sets $\{D_n\}_{n=1}^{\infty}$.
Denote by $E^x$ the expectation with respect to $P^x$. Let $\alpha>0$. A finite $\alpha$-excessive function $f$ on $E$ is called a regular potential provided that
$E^x\{e^{-\alpha T_n}f(X_{T_n})\}\rightarrow E^x\{e^{-\alpha
T}f(X_{T})\}$ for $x\in E$ whenever $\{T_n\}$ is an increasing
sequence of stopping times with limit $T$. Denote by
$(U^{\alpha})_{\alpha>0}$ the resolvent operators for $X$.
\begin{itemize}
\item {\bf Bounded positivity principle $(P^*_{\alpha})$}: If $\nu$ is a finite signed measure
such that $U^{\alpha}\nu$ is bounded, then $\nu U^{\alpha}\nu\geq 0$, where $\nu U^{\alpha}\nu:=\int_EU^{\alpha}\nu(x)\nu(dx)$.
\item {\bf Bounded energy principle $(E^*_{\alpha})$}: If $\nu$ is a finite measure with compact support
such that $U^{\alpha}\nu$ is bounded, then $\nu$ does not charge
semipolar sets.
\item {\bf Bounded maximum principle $(M^*_{\alpha})$}: If $\nu$ is a finite measure
with compact support $K$ such that $U^{\alpha}\nu$ is bounded, then
$\sup\{U^{\alpha}\nu(x):x\in E\}=\sup\{U^{\alpha}\nu(x):x\in K\}$.
\item {\bf Bounded regularity principle $(R^*_{\alpha})$}: If $\nu$ is a finite measure
with compact support such that $U^{\alpha}\nu$ is bounded, then
$U^{\alpha}\nu$ is regular.
\item {\bf Polarity principle} ({\bf Hunt's hypothesis (H)}): Every semipolar set is polar.
\end{itemize}
\begin{pro}\label{thm1}
Assume that all 1-excessive (equivalently, all $\alpha$-excessive, $\alpha>0$) functions are lower
semicontinuous. Then
$$(P^*_{\alpha})\Leftrightarrow (E^*_{\alpha})
\Leftrightarrow(M^*_{\alpha})\Leftrightarrow(R^*_{\alpha})\Leftrightarrow ({\rm H}).
$$
\end{pro}
{\bf Proof.} $(R^*_{\alpha})\Leftrightarrow ({\rm H})$ is proved in Blumenthal and Getoor \cite{BG68} and $(M^*_{\alpha})\Leftrightarrow ({\rm H})$ is proved in Blumenthal and Getoor \cite{BG70}.
$(P^*_{\alpha})\Rightarrow (M^*_{\alpha})$ is proved in Rao \cite{R77} and
$(M^*_{\alpha})\Rightarrow (P^*_{\alpha})$ is proved in Fitzsimmons \cite{Fi90}.
By \cite[Propsition (2.1)]{BG70}, $(E^*_{\alpha})
\Rightarrow (M^*_{\alpha})$. By \cite[Proposition (5.1)]{BG70} and the equivalence of $(M^*_{\alpha})$ and $({\rm H})$, $(M^*_{\alpha})
\Rightarrow (E^*_{\alpha})$.\hfill\fbox
Hunt's hypothesis (H) is also equivalent to some other important
properties of Markov processes. For example, Blumenthal and Getoor
\cite[Proposition (4.1)]{BG70} and Glover \cite[Theorem
(2.2)]{G83} showed that (H) holds if and only if the fine and
cofine topologies differ by polar sets; Fitzsimmons and Kanda
\cite{FK} showed that (H) is equivalent to the dichotomy of
capacity.
In spite of its importance, (H) has been verified only in some
special situations. Some forty years ago, Getoor conjectured that
essentially all L\'{e}vy processes satisfy (H).
From now on we let $(\Omega,{\cal F},P)$ be a probability space
and $X=(X_t)_{t\ge 0}$ be an $\mathbf{R}^n$-valued L\'{e}vy
process on $(\Omega,{\cal F},P)$ with L\'{e}vy-Khintchine exponent
$\psi$, i.e.,
\begin{eqnarray*}
E[\exp\{i\langle z,X_t\rangle\}]=\exp\{-t\psi(z)\},\ z\in
\mathbf{R}^n,t\ge 0,
\end{eqnarray*}
where $E$ denotes the expectation {with respect to} $P$ and $\langle\cdot,\cdot\rangle$ denotes the Euclidean inner product of $\mathbf{R}^n$. The classical L\'{e}vy-Khintchine formula tells us that
\begin{eqnarray*}
\psi(z)=i\langle a,z\rangle+\frac{1}{2}\langle
z,Qz\rangle+\int_{\mathbf{R}^n} \left(1-e^{i\langle
z,x\rangle}+i\langle z,x\rangle 1_{\{|x|<1\}}\right)\mu(dx),
\end{eqnarray*}
where $a\in \mathbf{R}^n,Q$ is a symmetric nonnegative definite
$n\times n$ matrix, and $\mu$ is a measure (called the L\'evy
measure) on $\mathbf{R}^n\backslash\{0\}$ satisfying
$\int_{\mathbf{R}^n\backslash\{0\}} (1\wedge
|x|^2)\mu(dx)<\infty$. Hereafter, we use Re$(\psi)$ and Im$(\psi)$
to denote the real and imaginary parts of $\psi$, respectively,
and use $(a,Q,\mu)$ to denote $\psi$.
Let us recall some important results obtained so far for Getoor's
conjecture. When $n=1$, Kesten \cite{Ke69} {(cf. also Bretagnolle
\cite{Br71}) showed that if $X$ is not a compound Poisson
process, then every $\{x\}$ is non-polar} if and only if
\begin{eqnarray*}\label{Ke69-a}
\int_0^{\infty}\mbox{Re}([1+\psi(z)]^{-1})dz<\infty.
\end{eqnarray*}
Port and Stone \cite{PS69} proved that for the asymmetric
Cauchy process on the line every $x$ is regular for $\{x\}$, and thus (H) holds in this case. Further, Blumenthal and Getoor
\cite{BG70} showed that all stable processes with index
$\alpha\in (0,2)$ on the line satisfy (H).
Kanda \cite{Ka76} and Forst \cite{F75} proved that (H)
holds if $X$ has bounded continuous transition densities (with respect to the Lebesgue measure $dx$) and
the L\'{e}vy-Khintchine exponent $\psi$ satisfies $|\mbox{Im} (\psi)|\leq
M(1+\mbox{Re}(\psi))$ for some positive constant $M$.
Rao \cite{R77} gave a short proof of the Kanda-Forst theorem under the weaker condition that $X$ has resolvent densities.
In particular, for $n\ge 1$, all
stable processes with index $\alpha\neq 1$ satisfy (H). Kanda
\cite{Ka78} proved that (H) holds for stable processes on
$\mathbf{R}^n$ with index $\alpha= 1$ if we assume that the linear
term vanishes. Silverstein {\cite{Si77} extended the Kanda-Forst
condition to the non-symmetric Dirichlet forms setting,
Fitzsimmons \cite{Fi01} extended it to the semi-Dirichlet forms
setting and Han et al. \cite{HMS11} extended it to the
positivity-preserving forms setting. Glover and Rao \cite{GR86}
proved that $\alpha$-subordinates of general Hunt processes
satisfy (H) (cf. Theorem \ref{GR} below).
{Rao \cite{R88} proved that if all 1-excessive functions of $X$ are
lower semicontinuous and $|{\rm Im}(\psi)|\leq (1+{\rm
Re}(\psi))f(1+{\rm Re}(\psi))$, where $f$ is an increasing function
on $[1,\infty)$ such that $\int_N^{\infty}(\lambda f(\lambda))^{-1}d\lambda=\infty$ for
every $N\geq 1$, then $X$ satisfies (H).}
Let $X$ be a L\'{e}vy process on $\mathbf{R}^n$ with
L\'{e}vy-Khintchine exponent $(a,Q,\mu)$. In \cite{HS11}, we showed that if $Q$ is non-degenerate then $X$ satisfies (H); if $Q$ is degenerate then, under the assumption that $\mu({\mathbf{R}^n\backslash
\sqrt{Q}\mathbf{R}^n})<\infty$, $X$ satisfies (H) if
and only if the equation
$$
\sqrt{Q}y=-a-\int_{\{x\in {\mathbf{R}^n\backslash
\sqrt{Q}\mathbf{R}^n}:\,|x|<1\}}x\mu(dx)
$$
has at least one solution $y\in \mathbf{R}^n$. We also showed that if $X$ is a
subordinator and satisfies (H) then its drift coefficient must be 0.
In this paper, we will continue to explore (H) for L\'{e}vy
processes. The rest of the paper is organized as follows. In
Section 2, we present a comparison result on L\'{e}vy processes
which shows that big jumps have no effect on the validity of (H)
in some sense. Based on this result and the Kanda-Forst-Rao
theorem, in Section 3, we give examples of subordinators
satisfying (H). In Section 4, we give a new necessary and
sufficient condition for (H) and obtain an extended
Kanda-Forst-Rao theorem. By virtue of this theorem, we give a new
class of L\'{e}vy processes satisfying (H). In section 5, we
construct a type of subordinators that does not satisfy Rao's
condition. To the best of our knowledge, no existing criteria can
be applied to this example. It suggests that maybe new ideas and
methods are needed in order to completely solve Getoor's
conjecture even for the case of subordinators.
\section{A comparison result on L\'{e}vy processes}\setcounter{equation}{0}
In this section, we prove a comparison result on L\'{e}vy
processes which implies that big jumps have no effect on the
validity of (H) in some sense.
Let $X$ be a L\'{e}vy process on $\mathbf{R}^n$ with
L\'{e}vy-Khintchine exponent $(a,Q,\mu)$. Suppose that $\mu_1$
is a finite measure on $\mathbf{R}^n\backslash\{0\}$ such that
$\mu_1\leq \mu$. Denote $\mu_2:=\mu-\mu_1$ and let $X'$ be a
L\'{e}vy process on $\mathbf{R}^n$ with L\'{e}vy-Khintchine
exponent $(a',Q,\mu_2)$, where
\begin{eqnarray*}
a':=a+\int_{\{|x|<1\}}x\mu_1(dx).
\end{eqnarray*}
\begin{thm}\label{thm2.1}
Let $X$ and $X'$ be L\'{e}vy processes defined as above.
Then
\noindent (i) they have same semipolar sets.
\noindent (ii) they have same essentially polar sets.
\noindent (iii) if both $X$ and $X'$ have resolvent densities, then $X$
satisfies (H) if and only if $X'$ satisfies (H).
\end{thm}
{\bf Proof.} Denote by $\psi$ and $\psi'$ the L\'{e}vy-Khintchine
exponents of $X$ and $X'$, respectively. Then,
\begin{eqnarray}\label{thm2.1-a}
\psi'(z)&=&i\langle a',z\rangle+\frac{1}{2}\langle
z,Qz\rangle+\int_{\mathbf{R}^n} \left(1-e^{i\langle
z,x\rangle}+i\langle z,x\rangle
1_{\{|x|<1\}}\right)\mu_2(dx),\nonumber\\
\psi(z)&=&i\langle a,z\rangle+\frac{1}{2}\langle
z,Qz\rangle+\int_{\mathbf{R}^n} \left(1-e^{i\langle
z,x\rangle}+i\langle z,x\rangle
1_{\{|x|<1\}}\right)\mu(dx)\nonumber\\
&=&\psi'(z)+\int_{\mathbf{R}^n}\left(1-e^{i\langle
z,x\rangle}\right)\mu_1(dx).
\end{eqnarray}
(i) Suppose that $Y$ is a compound Poisson process with L\'{e}vy
measure $\mu_1$ and is independent of $X'$. By (\ref{thm2.1-a}),
$X$ has the same law as that of $X'+Y$. Let $T_1$ be the first
jumping time of $Y$. Then $T_1$ possesses an exponential
distribution and thus $P(T_1>0)=1$. Hence, for any set $A$ and any
point $x\in \mathbf{R}^n$, $x$ is a regular point of $A$ relative
to $X$ if and only if it is a regular point of $A$ relative to
$X'$. Therefore $X$ and $X'$ have same semipolar sets.
(ii) Set $C:=\mu_1(\mathbf{R}^n\backslash\{0\})$. By
(\ref{thm2.1-a}), we get
\begin{eqnarray}\label{sec2-3}
\mbox{Re}\psi'(z)\leq \mbox{Re}\psi(z)\leq
\mbox{Re}\psi'(z)+C
\end{eqnarray}
and
\begin{eqnarray}\label{sec2-4}
|\mbox{Im}\psi(z)|\leq |\mbox{Im}\psi'(z)|+C,\ \
|\mbox{Im}\psi'(z)|\leq |\mbox{Im}\psi(z)|+C.
\end{eqnarray}
For $\lambda>0$, we have
\begin{eqnarray}
\mbox{Re}\left(\frac{1}{\lambda+\psi(z)}\right)
&=&\frac{\lambda+\mbox{Re}\psi(z)}{(\lambda+\mbox{Re}\psi(z))^2+(\mbox{Im}\psi(z))^2},\label{sec2-5}\\
\mbox{Re}\left(\frac{1}{\lambda+\psi'(z)}\right)
&=&\frac{\lambda+\mbox{Re}\psi'(z)}{(\lambda+\mbox{Re}\psi'(z))^2+
(\mbox{Im}\psi'(z))^2}.\label{sec2-6}
\end{eqnarray}
By (\ref{sec2-3}) and (\ref{sec2-4}), we find that if $\lambda\geq
\sqrt{2}C$ then
\begin{eqnarray}\label{sec2-7}
\frac{\lambda+\mbox{Re}\psi(z)}{(\lambda+\mbox{Re}\psi(z))^2+(\mbox{Im}\psi(z))^2}
&\geq&
\frac{\lambda+\mbox{Re}\psi'(z)}{(\lambda+\mbox{Re}\psi'(z)+C)^2+
(|\mbox{Im}\psi'(z)|+C)^2}\nonumber\\
&\geq&\frac{\lambda+\mbox{Re}\psi'(z)}
{2[(\lambda+\mbox{Re}\psi'(z))^2+2C^2+(\mbox{Im}\psi'(z)^2]}\nonumber\\
&\geq&\frac{1}{4}\frac{\lambda+\mbox{Re}\psi'(z)}
{(\lambda+\mbox{Re}\psi'(z))^2+(\mbox{Im}\psi'(z))^2}.
\end{eqnarray}
Similar to (\ref{sec2-7}), we find that if $\lambda\geq 2C$ then
\begin{eqnarray}\label{sec2-8}
\frac{\lambda+\mbox{Re}\psi'(z)}{(\lambda+\mbox{Re}\psi'(z))^2+(\mbox{Im}\psi'(z))^2}
&\geq&
\frac{\lambda+\mbox{Re}\psi(z)-C}{(\lambda+\mbox{Re}\psi(z))^2+
(|\mbox{Im}\psi(z)|+C)^2}\nonumber\\
&\geq&\frac{\frac{1}{2}\lambda+\mbox{Re}\psi(z)}{(\lambda+\mbox{Re}\psi(z))^2+2C^2+
2(\mbox{Im}\psi(z))^2}\nonumber\\
&\geq&\frac{1}{4}\frac{\lambda+\mbox{Re}\psi(z)}{(\lambda+\mbox{Re}\psi(z))^2+(\mbox{Im}\psi(z))^2}.
\end{eqnarray}
By (\ref{sec2-5})-(\ref{sec2-8}), we obtain that if $\lambda\geq
2C$ then for any $z\in \mathbf{R}^n$,
\begin{eqnarray}\label{sec2-9}
\frac{1}{4}\ \mbox{Re}\left(\frac{1}{\lambda+\psi'(z)}\right)\leq
\mbox{Re}\left(\frac{1}{\lambda+\psi(z)}\right)\leq 4\
\mbox{Re}\left(\frac{1}{\lambda+\psi'(z)}\right).
\end{eqnarray}
By (\ref{sec2-9}) and Hawkes \cite[Theorem 3.3]{Ha79}, we obtain that a
set is essentially polar for $X$ if and only if it is essentially
polar for $X'$.
(iii) This is a direct consequence of (i), (ii) and \cite[Theorem 2.1]{Ha79}.\hfill\fbox
For $\delta>0$, we define
$$
B_{\delta}:=\{x\in\mathbf{R}^n:0<|x|<
\delta\}.
$$
\begin{cor}\label{cor2.2}
Let $X_{\delta}$ be a L\'{e}vy process on $\mathbf{R}^n$
with L\'{e}vy-Khintchine exponent
$(a_{\delta},Q,\mu|_{B_{\delta}})$, where
\begin{eqnarray*}
a_{\delta}:=\left\{
\begin{array}{ll}
a+\int_{\{\delta\leq |x|<1\}}x\mu(dx),&\ \mbox{if}\ \ 0<\delta<1,\\
a,&\ \mbox{if}\ \ \delta\geq 1.
\end{array}
\right.
\end{eqnarray*}
Then, all the assertions of Theorem \ref{thm2.1} hold with $X'$ replaced by
$X_{\delta}$.
\end{cor}
\begin{rem}\label{rem2.3}
If $\int_{|x|\leq 1}|x|\mu(dx)<\infty$, then $\psi$ can be
expressed by
$$\psi(z)=i\langle
d,z\rangle+\frac{1}{2}\langle z,Qz\rangle+\int_{\mathbf{R}^n}
\left(1-e^{i\langle z,x\rangle}\right)\mu(dx),
$$
where $-d$ is called the drift of $X$. In this case, we call $(d,
Q,\mu)$ the L\'{e}vy-Khintchine exponent of $X$. For $\delta>0$,
we define $B_{\delta}$ and $X_{\delta}$ as above. Let
$X_{\delta}'$ be a L\'{e}vy process on $\mathbf{R}^n$ with
L\'{e}vy-Khintchine exponent $(d, Q,\mu|_{B_{\delta}})$. We claim
that $X_{\delta}$ and $X_{\delta}'$ have the same law and then all
the assertions of Theorem \ref{thm2.1} hold with $X'$ replaced by
$X_{\delta}'$. In fact, we have
\begin{eqnarray}\label{rem2.2-a}
d=a+\int_{\{|x|<1\}}x\mu(dx).
\end{eqnarray}
If $0<\delta<1$, then
\begin{eqnarray}\label{rem2.2-b}
a_{\delta}+\int_{\{|x|<1\}}x\mu|_{B_{\delta}}(dx)=\left(a+\int_{\{\delta\leq
|x|<1\}}\mu(dx)\right)+\int_{\{|x|<\delta\}}x\mu(dx)=d;
\end{eqnarray}
if $\delta\geq 1$, then
\begin{eqnarray}\label{rem2.2-c}
a_{\delta}+\int_{\{|x|<1\}}x\mu|_{B_{\delta}}(dx)=a+\int_{\{|x|<1\}}x\mu(dx)=d.
\end{eqnarray}
By (\ref{rem2.2-a})-(\ref{rem2.2-c}), we know that $X_{\delta}$
and $X_{\delta}'$ have the same L\'{e}vy-Khintchine exponent $(d,
Q,\mu|_{B_{\delta}})$ and thus have the same law.
\end{rem}
\section{Examples of subordinators satisfying (H)}\setcounter{equation}{0}
In this section, we will present new examples of subordinators
satisfying (H) by virtue of the comparison result given in Section
2 and the Kanda-Forst-Rao theorem. To the best of our knowledge,
which subordinators satisfy (H) is unknown in general. To
appreciate the importance of the validity of (H) for
subordinators, let us recall the following remarkable result of
Glover and Rao.
\begin{thm}\label{GR} {\rm (Glover and Rao \cite{GR86})} Let $(X_t)_{t\ge 0}$ be a standard process on a locally compact space with a
countable base and $(T_t)_{t\ge 0}$ be an independent subordinator
satisfying Hunt's hypothesis (H). Then $(X_{T_t})_{t\ge 0}$
satisfies (H).
\end{thm}
Let $X$ be a subordinator. Then, its L\'{e}vy-Khintchine exponent
$\psi$ can be expressed by
$$\label{1-a}
\psi(z)=-idz+\int_{(0,\infty)}{\left(1-e^{izx}\right)}\mu(dx),\
z\in \mathbf{R},
$$
where $d\geq 0$ (called the drift coefficient) and $\mu$ satisfies
$\int_{(0,\infty)}(1\wedge x)\mu(dx)<\infty$. In \cite{HS11}, we
have proved the following result.
\begin{pro}\label{pro4.1}
If $X$ is a subordinator and satisfies (H), then $d=0$.
\end{pro}
By Proposition \ref{pro4.1}, when we consider (H) for
subordinators, we may concentrate on the case that $d=0$.
Hereafter we use $c_1, c_2,\dots$ to denote constants whose values
can change from one appearance to another.
\subsection{Special subordinators}
Let $X$ be a subordinator. Recall that the potential measure $U$
of $X$ is defined by
$$
U(A)=E\left[\int_0^{\infty}1_{\{X_t\in A\}}dt\right],\ A\subset
[0,\infty).
$$
For $\alpha>0$, the $\alpha$-potential measure $U^{\alpha}$ of $X$
is defined by
$$
U^{\alpha}(A)=E\left[\int_0^{\infty}e^{-\alpha t}1_{\{X_t\in
A\}}dt\right],\ A\subset [0,\infty).
$$
$X$ is called a {\it special subordinator} if $U|_{(0,\infty)}$
has a decreasing density with respect to the Lebesgue measure.
\begin{thm}\label{thm4.2}
Let $X$ be a special subordinator. Then $X$ satisfies (H) if and
only if $d=0$.
\end{thm}
{\bf Proof.} By Proposition \ref{pro4.1}, we need only prove the
sufficiency. Suppose that $d=0$. If $\mu$ is a finite measure,
then $X$ is a compound Poisson process and thus satisfies (H).
Now we consider the case that $\mu$ is an infinite measure. By
Bretagnolle \cite[Theorem 8]{Br71}, $X$ does not hit points, i.e., any single
point set $\{x\}$ is a polar set of $X$, which together with the
assumption that $U|_{(0,\infty)}$ has a decreasing density with
respect to the Lebesgue measure, implies that $U|_{[0,\infty)}$
has a density with respect to the Lebesgue measure. Since for any
$\alpha>0$, $U^{\alpha}(\cdot)\leq U(\cdot)$, we obtain that for
any $\alpha\geq 0$, $U^{\alpha}$ is absolutely continuous with
respect to the Lebesgue measure. Then by Hawkes \cite[theorem 2.1]{Ha79},
we know that for any $\alpha\geq 0$, all $\alpha$-excessive
functions are lower semicontinuous. Therefore, by the fact that
$X$ does not hit points and Blumenthal and Getoor \cite[Proposition (5.1), Theorem
(5.3)]{BG70}, following the same argument for stable subordinators
\cite[page 140]{BG70}, we obtain that $X$ satisfies
(H).\hfill\fbox
\subsection{Locally quasi-stable subordinators}
Let $S$ be a stable subordinator of index
$\alpha$, $0<\alpha<1$. Then, its L\'{e}vy-Khintchine exponent
$\psi_S$ has the form
$$\label{3.1}
\psi_S(z)=c|z|^{\alpha}(1-i\,\mbox{sgn}(z)\tan(\pi\alpha/2)),\
z\in (-\infty,\infty),
$$
where $c>0$. Its L\'{e}vy measure $\mu_S$ is absolutely continuous
with respect to the Lebesgue measure $dx$ and can be expressed by
\begin{eqnarray}\label{add001}
\mu_S(dx)=\left\{ \begin{array}{ll} c^+x^{-\alpha-1}dx,&\mbox{if}\
x>0,\\
0,&\mbox{if}\ x\le 0,
\end{array}
\right.
\end{eqnarray}
where $c^+>0$.
\begin{defi}\label{defi4.3}
Let $X$ be a subordinator with drift $0$ and L\'{e}vy measure
$\mu$. We call $X$ a {locally quasi-stable subordinator} if there
exist a stable subordinator $S$ with L\'{e}vy measure $\mu_S$,
positive constants $c_1,c_2,\delta$, and finite measures $\mu_1$
and $\mu_2$ on $(0,\delta)$ such that
$$c_1\mu_S-\mu_1\le
\mu\le c_2\mu_S+\mu_2\ \ {\rm on}\ (0,\delta). $$
\end{defi}
\begin{pro}\label{pro4.4}
Any locally quasi-stable subordinator satisfies (H).
\end{pro}
{\bf Proof.} Let $X,S,\mu_1$, $\mu_2$ and $\delta$ be as in
Definition \ref{defi4.3}. By Theorem \ref{thm2.1} and Remark
\ref{rem2.3}, we assume without loss of generality that
$\mu|_{[\delta,\infty)}=0$ and $\mu_1=0$. Denote by $\psi$ and
$\psi_S$ the L\'{e}vy-Khintchine exponents of $X$ and $S$,
respectively. Let $\mu_S$ be as in (\ref{add001}). Then
\begin{eqnarray}\label{pro5.4-a}
{\rm Re}\psi(z)&=&\int_0^{\infty}(1-\cos(zx))\mu(dx)\nonumber\\
&\ge&c_1\int_0^{\delta}(1-\cos(zx))\mu_S(dx)\nonumber\\
&=&c_1\left(\int_0^{\infty}(1-\cos(zx))\mu_S(dx)-\int_{\delta}^{\infty}(1-\cos(zx))\mu_S(dx)\right)\nonumber\\
&=&c_1{\rm Re}\psi_S(z)-K_1\nonumber\\
&=&c'|z|^{\alpha}-K_1,
\end{eqnarray}
where $c_1,c',K_1$ are positive constants.
\begin{eqnarray}\label{pro5.4-b}
|{\rm Im}\psi(z)|&\le&\int_0^{\infty}|\sin(zx)|\mu(dx)\nonumber\\
&\le&c_2\int_0^{\delta}|\sin(zx)|\mu_S(dx)\nonumber\\
&=&c_2\int_0^{\infty}|\sin(zx)|\mu_S(dx)-
c_2\int_{\delta}^{\infty}|\sin(zx)|\mu_S(dx)\nonumber\\
&\le&c_2c\left\{\int_0^{1/|z|}|\sin(zx)|x^{-1-\alpha}dx+
\int_{1/|z|}^{\infty}|\sin(zx)|x^{-1-\alpha}dx\right\}+K_2\nonumber\\
&\le&c_2c\left\{|z|\int_0^{1/|z|}x^{-\alpha}dx+\int_{1/|z|}^{\infty}x^{-1-\alpha}dx\right\}+K_2\nonumber\\
&=&c''|z|^{\alpha}+K_2,
\end{eqnarray}
where $c_2,c'',K_2$ are positive constants. By (\ref{pro5.4-a})
and (\ref{pro5.4-b}) we know that the Kanda-Forst condition holds
for $\psi$. By (\ref{pro5.4-a}) and Hartman and Wintner \cite{HW42}, we know that $X$
has bounded continuous transition densities. Therefore, $X$ satisfies (H) by the Kanda-Forst theorem.\hfill\fbox
\begin{cor}\label{cor4.5}
Let $\varphi$ be a L\'{e}vy-Khintchine exponent and $\mu$ be a
L\'{e}vy measure of some special subordinator with drift 0 or some
locally quasi-stable subordinator. Then, the L\'{e}vy process with
L\'{e}vy-Khintchine exponent
\begin{eqnarray}\label{cor3.5-a}
\Phi(z):=\int_{(0,\infty)}\left(1-e^{-\varphi(z)x}\right) \mu(dx)
\end{eqnarray}
satisfies (H).
\end{cor}
{\bf Proof.} Let $X$ be a L\'{e}vy process with
L\'{e}vy-Khintchine exponent $\varphi$ and $(T_t)_{t\ge 0}$ be a
subordinator with drift 0 and L\'{e}vy measure $\mu$, which is
independent of $X$. Then $Y_t:=X_{T_t}$ has the L\'{e}vy exponent
$\Phi$ defined by (\ref{cor3.5-a}). Therefore, by Theorem
\ref{GR}, Theorem \ref{thm4.2} and Proposition \ref{pro4.4}, we
obtain that $Y$ satisfies (H).\hfill\fbox
\subsection{Further examples}
In this subsection, we give further examples of subordinators
satisfying (H) by virtue of the comparison result given in
Section 2 and the following theorem of Rao.
\begin{thm}\label{R2} {\rm (Rao \cite{R88})} Let $X$ be a L\'evy process such that all 1-excessive functions are lower semicontinuous. Suppose there is an increasing function $f$ on $[1,\infty)$ such that
$ \int_N^{\infty}(\lambda f(\lambda))^{-1}d\lambda=\infty $ for
any $N\ge 1$ and $|1+\psi|\le (1+{\rm Re}(\psi))f(1+{\rm
Re}(\psi))$. Then (H) holds.
\end{thm}
Let $0<\alpha<1$ and $0<\delta<1$. We define
$$
\mu_T(dx):=\frac{1}{-\log(x)x^{1+\alpha}}dx,\ \ 0<x<\delta
$$
and
$$
\mu_V(dx)=\frac{-\log(x)}{x^{1+\alpha}}dx,\ \ 0<x<\delta.
$$
Let $X$ be a subordinator with drift 0 and L\'{e}vy measure
$\mu$.
\noindent (i) If $c_1\mu_T-\mu_1\le \mu\le c_2\mu_S+\mu_2$ on
$(0,\delta)$ for some positive constants $c_1,c_2$ and finite
measures $\mu_1,\mu_2$ on $(0,\delta)$, then $X$ satisfies (H).
In fact, by Theorem \ref{thm2.1} and Remark \ref{rem2.3}, we may
assume without loss of generality that $\mu|_{[\delta,\infty)}=0$
and $\mu_1=0$. For any $z\in \mathbf{R}$ with $|z|>1$, we have
\begin{eqnarray}\label{exm-1-a}
{\rm Re}\psi(z)&=&\int_0^{\infty}(1-\cos(zx))\mu(dx)\nonumber\\
&\ge&c_1\int_0^{\delta}(1-\cos(zx))\mu_T(dx)\nonumber\\
&=&c_1\int_0^{\infty}(1-\cos(zx))\mu_T(dx)-c_1\int_{\delta}^{\infty}(1-\cos(zx))\mu_T(dx)\nonumber\\
&\ge&c_1\int_{1/2|z|}^{1/|z|}(1-\cos(zx))\frac{1}{-\log(x)x^{1+\alpha}}dx-K_3\nonumber\\
&\ge&c_1'z^2\int_{1/2|z|}^{1/|z|}\frac{x^2}{-\log(x)x^{1+\alpha}}dx-K_3\nonumber\\
&\ge&c_1'\frac{z^2}{\log(2|z|)}\int_{1/2|z|}^{1/|z|}\frac{x^2}{x^{1+\alpha}}dx-K_3\nonumber\\
&=&c_1{''}\frac{|z|^{\alpha}}{\log(2|z|)}-K_3,
\end{eqnarray}
where $c_1',c_2'',K_3$ are positive constants. By (\ref{pro5.4-b})
and (\ref{exm-1-a}), we obtain that $|{\rm Im}\psi(z)|\le
c^*(1+{\rm Re}\psi(z))\log(1+{\rm Re}\psi(z))$ for some positive
constant $c^*$. By Hartman and Wintner \cite{HW42} and (\ref{exm-1-a}), we know that
$X$
has bounded continuous transition densities. Therefore, $X$ satisfies (H) by Theorem \ref{R2}.
\bigskip
\noindent (ii) If $c_1\mu_S-\mu_1\le \mu\le c_2\mu_V+\mu_2$ on
$(0,\delta)$ for some positive constants $c_1,c_2$ and finite
measures $\mu_1,\mu_2$ on $(0,\delta)$, then $X$ satisfies (H).
In fact, by Theorem \ref{thm2.1} and Remark \ref{rem2.3}, we may
assume without loss of generality that $\mu|_{[\delta,\infty)}=0$
and $\mu_1=0$. For any $z\in \mathbf{R}$ with $|z|>1/\delta$, we
have
\begin{eqnarray}\label{exm-2-a}
|{\rm
Im}\psi(z)|&\le&\int_0^{\infty}|\sin(zx)|\mu(dx)\nonumber\\
&\le& c_2\int_0^{\delta}|\sin(zx)|\mu_V(dx)
+K_4\nonumber\\
&\le&c_2\left\{\int_0^{1/|z|}|\sin(zx)|\frac{-\log(x)}{x^{1+\alpha}}dx+
\int_{1/|z|}^{\delta}|\sin(zx)|\frac{-\log(x)}{x^{1+\alpha}}dx\right\}+K_4\nonumber\\
&\le&c_2'\left\{|z|\int_0^{1/|z|}{\frac{-\log(x)}{x^{\alpha}}}dx+\log(|z|)
\int_{1/|z|}^{\infty}x^{-1-\alpha}dx\right\}+K_4\nonumber\\
&\le&c_2^{''}\left\{|z|\int_0^{1/|z|}{\frac{-(1-\alpha)\log(x)-1}
{x^{\alpha}}}dx+|z|^{\alpha}\log(|z|)\right\}+K_4\nonumber\\
&=&2c_2^{''}|z|^{\alpha}\log(|z|)+K_4,
\end{eqnarray}
where $c_2',c_2'',K_4$ are positive constants. By (\ref{pro5.4-a})
and (\ref{exm-2-a}), we obtain that
$|{\rm Im}\psi(z)|\le c^{**}{\rm Re}\psi(z)$ $\log({\rm
Re}\psi(z))$ for some positive constant $c^{**}$. By
(\ref{pro5.4-a}) and Hartman and Wintner \cite{HW42}, we know that $X$
has bounded continuous transition densities. Therefore, $X$ satisfies (H) by Theorem \ref{R2}.
\section{A new necessary and sufficient condition for (H) and an extended Kanda-Forst-Rao theorem}\setcounter{equation}{0}
Let $X$ be a L\'{e}vy process on $\mathbf{R}^n$. From now on we
assume that all 1-excessive functions are lower semicontinuous,
equivalently, $X$ has resolvent densities. Define
$$
A:=1+{\rm Re}(\psi),\ \ B:=|1+\psi|.
$$
\begin{thm}\label{thm112} {\rm (Rao \cite{R88})} Let $\nu$ be a finite measure of finite 1-energy, i.e.,
$$\int_{\mathbf{R}^n} B^{-2}(z)A(z)|\hat \nu(z)|^2dz<\infty.$$ Then
\begin{equation}\label{H1}
\lim_{\lambda\rightarrow\infty}\int_{\mathbf{R}^n}|\hat\nu(z)|^2(\lambda+{\rm Re}\psi(z))|\lambda+\psi(z)|^{-2}dz
\end{equation}
exists. The limit is zero if and only if $U^1\nu$ is regular.
\end{thm}
Based on Theorems \ref{thm112} and \ref{R2}, we can prove the
following result.
\begin{lem}\label{Thm33} Let
$\nu$ be a finite measure of finite 1-energy and $f$ be an
increasing function on $[1,\infty)$ such that $
\int_N^{\infty}(\lambda f(\lambda))^{-1}d\lambda=\infty $ for some
$N\ge 1$. Then $U^1\nu$ is regular if and only if
$$
\lim_{\lambda\rightarrow\infty}\sum_{k=1}^{\infty}\int_{\{B(z)>A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{\lambda}{\lambda^2+({\rm Im}\psi(z))^2}|\hat \nu(z)|^2dz=0.
$$
\end{lem}
\noindent {\bf Proof.} Since $f$ is an increasing function on
$[1,\infty)$, $ \int_N^{\infty}(\lambda
f(\lambda))^{-1}d\lambda=\infty $ for some $N\ge 1$ if and only if
$ \int_N^{\infty}(\lambda f(\lambda))^{-1}d\lambda=\infty $ for
any $N\ge 1$. From the proof of Theorem \ref{R2} (see Rao \cite{R88}),
we know that the limit
\begin{equation}\label{gap2}
\lim_{\lambda\rightarrow\infty}\int_{A(z)\le\lambda}\frac{\lambda}{\lambda^2+B^2(z)}|\hat \nu(z)|^2dz
\end{equation}
exists and equals the limit in (\ref{H1}). We now show that the limit in (\ref{gap2}) equals 0 if and only if
\begin{equation}\label{H21}
\lim_{\lambda\rightarrow\infty}\int_{\{A(z)\le\lambda,\,B(z)>A(z)f(A(z))\}}\frac{\lambda}{\lambda^2+B^2(z)}|\hat \nu(z)|^2dz=0.
\end{equation}
To this end, we need only show that (\ref{H21}) implies that
\begin{equation}\label{gap}
\lim_{\lambda\rightarrow\infty}\int_{A(z)\le\lambda}\frac{\lambda}{\lambda^2+B^2(z)}|\hat \nu(z)|^2dz=0.
\end{equation}
Suppose that (\ref{H21}) holds. Then, the limit
$$
\lim_{\lambda\rightarrow\infty}\int_{\{A(z)\le\lambda,\,B(z)\le A(z)f(A(z))\}}\frac{\lambda}{\lambda^2+B^2(z)}|\hat \nu(z)|^2dz
$$
exists since the limit in (\ref{gap2}) always exists. Note that
\begin{eqnarray*}
& &\int_1^{\infty}\lambda^{-1}f(\lambda)^{-1}d\lambda\int_{\{A(z)\le\lambda,\,B(z)\le A(z)f(A(z))\}}\lambda(\lambda^2+B^2(z))^{-1}|\hat \nu(z)|^2dz\\
&=&\int_{\{B(z)\le A(z)f(A(z))\}}|\hat \nu(z)|^2dz\int_{A(z)}^{\infty}[f(\lambda)(\lambda^2+B^2(z))]^{-1}d\lambda\\
&\le&\frac{\pi}{2}\int_{\{B(z)\le A(z)f(A(z))\}}[B(z)f(A(z))]^{-1}|\hat \nu(z)|^2dz\\
&\le&\frac{\pi}{2}\int_{\mathbb{R}^d}B^{-2}(z)A(z)|\hat \nu(z)|^2dz\\
&<&\infty.
\end{eqnarray*}
Since $\int_1^{\infty}\lambda^{-1}f(\lambda)^{-1}d\lambda=\infty$,
$$\lim_{\lambda\rightarrow\infty}\int_{\{A(z)\le\lambda,\,B(z)\le A(z)f(A(z))\}}\frac{\lambda}{\lambda^2+B^2(z)}|\hat \nu(z)|^2dz=0.$$
Therefore, (\ref{gap}) holds by (\ref{H21}).
For each $k\in \mathbf{N}$, we have
\begin{eqnarray}\label{kljh1}
&&1_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,\lambda\ge (k+1)|{\rm Im}\psi(z)|\}}\frac{\lambda}{\lambda^2+({\rm Im}\psi(z))^2}|\hat \nu(z)|^2\nonumber\\
&\le&1_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,\lambda\ge (k+1)|{\rm Im}\psi(z)|\}}\frac{1}{\lambda}|\hat \nu(z)|^2\nonumber\\
&\le&\frac{1}{k+1}1_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1\}}\frac{|\hat \nu(z)|^2}{|{\rm Im}\psi(z)|}.
\end{eqnarray}
We assume without loss of generality that $f(1)=\sqrt{2}$. Note that $B(z)>A(z)f(A(z))$ implies that $B(z)\le\sqrt{2}|{\rm Im}\psi(z)|$. Then, we obtain by $\int_{\mathbf{R}^n} B^{-2}(z)A(z)|\hat \nu(z)|^2dz<\infty$ that
\begin{equation}\label{kljh2}
\sum_{k=1}^{\infty}\frac{1}{2(k+1)}\int_{\{B(z)>A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1\}} \frac{|\hat \nu(z)|^2}{|{\rm Im}\psi(z)|}dz<\infty.
\end{equation}
By (\ref{kljh1}), (\ref{kljh2}) and the dominated convergence theorem, we get
$$
\lim_{\lambda\rightarrow\infty}\sum_{k=1}^{\infty}\int_{\{B(z)>A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,\lambda\ge (k+1)|{\rm Im}\psi(z)|\}}\frac{\lambda}{\lambda^2+({\rm Im}\psi(z))^2}|\hat \nu(z)|^2dz=0.
$$
Therefore, the proof is complete by noting (\ref{H21}).\hfill\fbox
Note that if $\nu$ is a finite measure such that $U^1\nu$ is bounded then $\nu$ has finite 1-energy (cf. Rao \cite[page 622]{R88}). By Lemma \ref{Thm33} and Proposition \ref{thm1}, we obtain the following necessary and sufficient condition for (H).
\begin{thm}\label{thmnb} Let $f$ be an increasing
function on $[1,\infty)$ such that $ \int_N^{\infty}(\lambda
f(\lambda))^{-1}d\lambda=\infty $ for some $N\ge 1$. Then (H)
holds if and only if
\begin{eqnarray}\label{thm2.4-1}
\lim_{\lambda\rightarrow\infty}\sum_{k=1}^{\infty}\int_{\{B(z)>A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{\lambda}{\lambda^2+({\rm Im}\psi(z))^2}|\hat \nu(z)|^2dz=0
\end{eqnarray}
for any finite measure $\nu$ with compact support such that $U^1\nu$ is bounded.
\end{thm}
\begin{rem}
Theorem \ref{thmnb} indicates that the validity of (H) is closely
related to the behavior of $\psi(z)$ where ${\rm Im}(\psi(z))$ is
not well controlled by ${\rm Re}(\psi(z))$, which is possible and
can be seen from the uniform motion on $\mathbf{R}$ and the
example given in Section 5.\end{rem}
By virtue of Theorem \ref{thmnb}, we obtain the following result extending the Kanda-Forst-Rao theorem on (H).
\begin{thm}\label{cor11}
(H) holds if the following extended Kanda-Forst-Rao condition ((EKFR) for short) holds:\\
(EKFR) There are two measurable functions $\psi_1$ and $\psi_2$ on $\mathbf{R}^n$ such that $\rm{Im}(\psi)=\psi_1+\psi_2$,
and
\begin{eqnarray}\label{vbn1}
&&\quad\quad\quad |\psi_1|\leq Af(A),\nonumber\\
&&\int_{{\mathbf{R}^n}}\frac{|\psi_2(z)|}{(1+{\rm Re}\psi(z))^2+({\rm Im}\psi(z))^2}dz<\infty,
\end{eqnarray}
where $f$ is an increasing function on $[1,\infty)$ such that $
\int_N^{\infty}(\lambda f(\lambda))^{-1}d\lambda=\infty $ for some
$N\ge 1$.
\end{thm}
\begin{rem}
If $\psi_2=0$, then the (EKFR) condition is just Rao's condition.
In particular, if $f=1$, then it is just the Kanda-Forst
condition. An integrability condition similar to (\ref{vbn1}) has
been used in Glover \cite[Theorem 3.1]{Gl81}.
\end{rem}
\noindent {\bf Proof of Theorem \ref{cor11}.}
By Theorem \ref{thmnb}, we need only show that the limit in (\ref{thm2.4-1}) equals 0. We assume without loss of generality that $f(1)=1/3$. Note that $B(z)>3\sqrt{2}A(z)f(A(z))$ implies that $|{\rm Im}\psi(z)|> A(z)$ and $|{\rm Im}\psi(z)|> B(z)/\sqrt{2}$, and $|\psi_2(z)|>2A(z)f(A(z))$ implies that $|\psi_2(z)|>|{\rm Im}\psi(z)|/2$. Then, by (\ref{vbn1}), the fact that $A(z)\leq c(1+|z|^2)$ for some positive constant $c$ and the dominated convergence theorem, we obtain that
\begin{eqnarray*}
&&\sum_{k=1}^{\infty}\int_{\{B(z)>3\sqrt{2}A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{\lambda}{\lambda^2+({\rm Im}\psi(z))^2}|\hat \nu(z)|^2dz\\
&\le&\sum_{k=1}^{\infty}\int_{\{|{\rm Im}\psi(z)|>3A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{1}{2|{\rm Im}\psi(z)|}|\hat \nu(z)|^2dz\\
&\le&\sum_{k=1}^{\infty}\int_{\{|\psi_2(z)|>2A(z)f(A(z)),\,k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{|\psi_2(z)|}{|{\rm Im}\psi(z)|^2}| \hat \nu(z)|^2dz\\
&\le&\sum_{k=1}^{\infty}\int_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,A(z)\le\lambda<(k+1)|{\rm Im}\psi(z)|\}}\frac{2|\psi_2(z)|}{B^2(z)}|\hat \nu(z)|^2dz\\
&\le&\sum_{k=1}^{\infty}\int_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,\lambda<(k+1)^2A(z)\}}\frac{2|\psi_2(z)|}{B^2(z)}|\hat \nu(z)|^2dz\\
&\le&\sum_{k=1}^{\infty}\int_{\{k\le \frac{|{\rm Im}\psi(z)|}{A(z)}<k+1,\,\lambda<c(k+1)^2(1+|z|^2)\}}\frac{2|\psi_2(z)|}{B^2(z)}|\hat \nu(z)|^2dz\\
&\rightarrow&0\ \ {\rm as}\ \lambda\rightarrow\infty.
\end{eqnarray*}
The proof is complete.\hfill\fbox
In the following, we give an application of Theorem \ref{cor11}.
\begin{thm}\label{new111} Let $\gamma>0$ and $X$ be
a L\'evy process on $ \mathbf{R}$ satisfying
\begin{equation}\label{new090}
\liminf_{|z|\rightarrow\infty}\frac{{\rm
Re}\psi(z)}{|z|\log^{\gamma}(|z|)}>0.
\end{equation}
Then $X$ satisfies (H).
\end{thm}
{\bf Proof.} By (\ref{new090}), we get
$$
\lim_{|z|\to\infty}\frac{{\rm Re}\psi(z)}{\log(1+|z|)}=\infty.
$$
Hence $X$ has bounded continuous transition densities by
Hartman and Wintner \cite{HW42}. Let $f(\lambda)=\log(\lambda)$ for $\lambda\in
[1,\infty)$ and set $\psi_1(z):=1_{\{|{\rm Im}\psi(z)|\le
A(z)f(A(z))\}}{\rm Im}\psi(z)$, $\psi_2(z):=1_{\{|{\rm
Im}\psi(z)|> A(z)f(A(z))\}}{\rm Im}\psi(z)$ for $z\in \mathbf{R}$.
Condition (\ref{new090}) implies that there exists a constant
$c>0$ such that
$$|\psi_2(z)|\ge c1_{\{|\psi(z)|>
A(z)f(A(z))\}}|z|\log^{1+\gamma}(|z|)$$ when $|z|$ is sufficiently
large. Therefore, (\ref{vbn1}) holds and the proof is complete by
Theorem \ref{cor11}.\hfill\fbox
\begin{exa} By Theorem \ref{new111}, Theorem \ref{thm2.1} and Corollary \ref{cor2.2}, we obtain a new class of 1-dimensional L\'{e}vy processes satisfying (H). Let $X$ be a L\'{e}vy process on $\mathbf{R}$ with
L\'{e}vy-Khintchine exponent $(a,Q,\mu)$. Suppose that there exist
constants $\gamma>0$, $0<\delta<1$, $c>0$, and a finite measure
$\mu'$ on $\{x\in \mathbf{R}^n: 0<|x|<\delta\}$ such that
$$
d\mu\geq \frac{c(-\log(|x|))^{\gamma}}{x^2}dx-d\mu' \ \ {\rm on}\
\{x\in \mathbf{R}: 0<|x|<\delta\}.$$ Similar to (\ref{exm-1-a}),
we can show that (\ref{new090}) holds. Then, $X$ satisfies (H).
Note that in this example it does not matter if $a$ or $Q$ equals
0.
Let $Y$ be another 1-dimensional L\'{e}vy process which is
independent of $X$. Theorem \ref{new111} implies that the
perturbed process $Y+X$ also satisfies (H).
\end{exa}
\begin{rem}
Blumenthal and Getoor introduced in \cite{BG61} the following
index $\beta''$ defined by
\begin{equation}\label{mnb}
\beta''=\sup\left\{\tau\geq 0:\frac{{\rm
Re}\psi(z)}{|z|^{\tau}}\to \infty\ \mbox{as}\ |z|\to
\infty\right\}.
\end{equation}
Let $X$ be a L\'evy process on $ \mathbf{R}$. Then, Theorem
\ref{new111} implies that (H) holds when $\beta''>1$. This result
is also a direct consequence of the following proposition.
\begin{pro}\label{pro-1} Let $X$ be
a L\'evy process on $ \mathbf{R}$. Suppose that
\begin{equation}\label{zxcv}
\liminf_{|z|\to \infty}\frac{|\psi(z)|}{|z|\log^{1+\gamma}|z|}>0
\end{equation}
for some constant $\gamma>0$. Then (H) holds.
\end{pro}
{\bf Proof.} Let $f\equiv 1$ and set $\psi_1(z):=1_{\{|{\rm
Im}\psi(z)|\le A(z)f(A(z))\}}{\rm Im}\psi(z)$,
$\psi_2(z):=1_{\{|{\rm Im}\psi(z)|> A(z)f(A(z))\}}{\rm Im}\psi(z)$
for $z\in \mathbf{R}$. Condition (\ref{zxcv}) implies that
\begin{eqnarray*}
\limsup_{|z|\to \infty}\left\{\frac{|\psi_2(z)|}{(1+{\rm
Re}\psi(z))^2+({\rm
Im}\psi(z))^2}\cdot|z|\log^{1+\gamma}|z|\right\}<\infty.
\end{eqnarray*}
Therefore, (\ref{vbn1}) holds and the proof is complete by Theorem
\ref{cor11}.\hfill\fbox
We remark that Proposition \ref{pro-1} can also be proved by
Theorem \ref{thm112}. In fact, the limit in (\ref{H1}) equals the
limit in (\ref{gap2}) and hence equals 0 by (\ref{zxcv}) and the
dominated convergence theorem.
\end{rem}
\section{A type of subordinators that does not satisfy Rao's condition}\setcounter{equation}{0}
As pointed out in Rao \cite{R88}, from the proof of Theorem \ref{R2}
it seems that the condition $B\le Af(A)$ is not far from being
necessary. In this section, however, we will construct a type of
subordinators that does not satisfy Rao's condition.
\subsection{Construction of the example}
We fix an $\alpha$ such that $\frac{1}{2}<\alpha<1$. In the
sequel, we define a function $\rho$ on $\mathbf{R}$ which will be
used as the density function of a L\'evy measure $\mu$.
First, we set $n_1=2$. Define a function $\rho_1$ on $\mathbf{R}$
as follows.
$$
\rho_1(x)=\frac{1}{x^{1+\alpha}},\ \ {\rm if}\ \frac{1}{2n^2_1}<x<\frac{1}{n^2_1};\ \ 0,\ {\rm otherwise}.
$$
We define $\mu_1(dx)=\rho_1(x)dx$ and denote by $\psi_1$ the
L\'evy-Khintchine exponent of $\mu_1$. Then, for $z\in
[\frac{n_1}{2}, 2n_1]$, we have
\begin{eqnarray}\label{jkl1}
{\rm Re}\psi_1(z)&=&\int_0^1(1-\cos(zx))\mu_1(dx)\nonumber\\
&\le&\frac{1}{2}\int_{1/2n_1^2}^{1/n_1^2}z^2x^2\frac{1}{x^{1+\alpha}}dx\nonumber\\
&\le&\frac{2n_1^{2\alpha-2}}{2-\alpha}\nonumber\\
&\le&2
\end{eqnarray}
and
\begin{eqnarray}\label{jkl2}
{\rm Im}\psi_1(z)&=&\int_0^1\sin(zx)\mu_1(dx)\nonumber\\
&=&\int_{1/2n_1^2}^{1/n_1^2}\sin(zx)\mu_1(dx)\nonumber\\
&\ge&\int_{1/2n_1^2}^{1/n_1^2}\frac{zx}{2x^{1+\alpha}}dx\nonumber\\
&\ge&\frac{1}{8}n_1^{2\alpha-1}.
\end{eqnarray}
We increase $n_1$ so that
$\frac{1}{8}n_1^{2\alpha-1}>\frac{6}{1-\alpha}$.
For any $z\in \mathbf{R}$, we have
\begin{equation}\label{21}
{\rm Re}\psi_1(z)=\int_0^1(1-\cos(zx))\mu_1(dx)\le
\int_{1/2n_1^2}^1\frac{1}{x^{1+\alpha}}dx\le
\frac{2^{\alpha}n_1^{2\alpha}}{\alpha}\le 4n_1^{2\alpha}
\end{equation}
and
\begin{equation}\label{22}
|{\rm Im}\psi_1(z)|\le\int_0^1|\sin(zx)|\mu_1(dx)\le
\int_{1/2n_1^2}^1\frac{1}{x^{1+\alpha}}dx\le
\frac{2^{\alpha}n_1^{2\alpha}}{\alpha}\le 4n_1^{2\alpha}.
\end{equation}
\vskip 0.3cm We choose an $n_2\in \mathbf{N}$ such that
$n^2_2>2n_1^2$. We define a function $\rho_2$ on $\mathbf{R}$ as
follows.
$$
\rho_2(x)=\frac{1}{x^{1+\alpha}},\ \ \mbox{if}\ \frac{1}{2n^2_2}<x<\frac{1}{n^2_2};\ \ 0,\ {\rm otherwise}.
$$
Note that there is no overlap between $\rho_1$ and $\rho_2$. We
define $\mu_2(dx)=\rho_2(x)dx$ and denote by $\psi_2$ the
L\'evy-Khintchine exponent of $\mu_2$. Then, similar to the
above, we can show that for $z\in [\frac{n_2}{2}, 2n_2]$
\begin{equation}\label{1}
{\rm Re}\psi_2(z)\le 2\ \ {\rm and}\ \ {\rm Im}\psi_2(z)\ge
\frac{1}{8}n_2^{2\alpha-1}\left(>\frac{6}{1-\alpha}\right).
\end{equation}
Note that for $z\in [\frac{n_1}{2}, 2n_1]$ we have
\begin{eqnarray}\label{p1}
{\rm Re}\psi_2(z)&=&\int_0^1(1-\cos(zx))\mu_2(dx)\nonumber\\
&\le&\frac{1}{2}\int_{1/2n_2^2}^{1/n_2^2}z^2x^2\frac{1}{x^{1+\alpha}}dx\nonumber\\
&\le&\frac{2n_1^2n_2^{2\alpha-4}}{2-\alpha}
\end{eqnarray}
and
\begin{eqnarray}\label{p2}
|{\rm Im}\psi_2(z)|&\le&\int_0^1|\sin(zx)|\mu_2(dx)\nonumber\\
&\le&\int_{1/2n_2^2}^{1/n_2^2}|\sin(zx)|\frac{1}{x^{1+\alpha}}dx\nonumber\\
&\le&\int_{1/2n_2^2}^{1/n_2^2}2n_1x\frac{1}{x^{1+\alpha}}dx\nonumber\\
&\le&\frac{2n_1n_2^{2\alpha-2}}{1-\alpha}.
\end{eqnarray}
We increase $n_2$ (with $n_1$ fixed) so that $n_2\ge
n_1^{5/(2-2\alpha)}$. By (\ref{p1}) and (\ref{p2}), we get
\begin{equation}\label{az1}
{\rm Re}\psi_2(z)\le\frac{2}{(1-\alpha)n_1^4},\ \ |{\rm
Im}\psi_2(z)|\le\frac{2}{(1-\alpha)n_1^4},\ \ z\in
\left[\frac{n_1}{2}, 2n_1\right].
\end{equation}
Then, by (\ref{jkl1}), (\ref{jkl2}) and (\ref{az1}), we obtain
that for $z\in [\frac{n_1}{2}, 2n_1]$,
\begin{equation}\label{r1}
{\rm Re}\psi_1(z)+{\rm Re}\psi_2(z)\le 2+\frac{2}{(1-\alpha)n_1^4}
\end{equation}
and
\begin{equation}\label{r2}
{\rm Im}\psi_1(z)+{\rm Im}\psi_2(z)\ge
\frac{1}{8}n_1^{2\alpha-1}-\frac{2}{(1-\alpha)n_1^4}.
\end{equation}
We further increase $n_2$ so that $n_2\ge
(96)^{1/(2\alpha-1)}n_1^{(4+2\alpha)/(2\alpha-1)}$ which ensures
that for any $z\in \mathbf{R}$ (cf. (\ref{21}), (\ref{22}) and
(\ref{1})),
\begin{equation}\label{az2}
{\rm Re}\psi_1(z)\le \frac{1}{3n_1^4}{\rm
Im}\psi_2\left(\frac{n_2}{2}\right),\ \ |{\rm Im}\psi_1(z)|\le
\frac{1}{3n_1^4}{\rm Im}\psi_2\left(\frac{n_2}{2}\right).
\end{equation}
By (\ref{1}) and (\ref{az2}), we obtain that for $z\in
[\frac{n_2}{2}, 2n_2]$,
\begin{equation}\label{q1}
{\rm Re}\psi_1(z)+{\rm Re}\psi_2(z)\le \frac{1}{3n_1^4}{\rm
Im}\psi_2\left(\frac{n_2}{2}\right)+2
\end{equation}
and
\begin{equation}\label{q2}
{\rm Im}\psi_1(z)+{\rm Im}\psi_2(z)\ge
\left(1-\frac{1}{3n_1^4}\right){\rm
Im}\psi_2\left(\frac{n_2}{2}\right).
\end{equation}
Define
\begin{equation}\label{q20}\vartheta:=\max\left\{\frac{5}{2-2\alpha},
\frac{4+2\alpha}{2\alpha-1}\right\}.\end{equation} We can set
$n_2$ to be $cn_1^{\vartheta}$, for some positive constant $c$
depending only on $\alpha$, such that (\ref{r1}), (\ref{r2}),
(\ref{q1}) and (\ref{q2}) hold.
For any $z\in \mathbf{R}$, we have
\begin{equation}\label{31}
{\rm Re}\psi_2(z)=\int_0^1(1-\cos(zx))\mu_2(dx)\le
\int_{1/2n_2^2}^1\frac{1}{x^{1+\alpha}}dx\le
\frac{2^{\alpha}n_2^{2\alpha}}{\alpha}\le4n_2^{2\alpha}
\end{equation}
and
\begin{equation}\label{32}
|{\rm Im}\psi_2(z)|\le\int_0^1|\sin(zx)|\mu_2(dx)\le
\int_{1/2n_2^2}^1\frac{1}{x^{1+\alpha}}dx\le
\frac{2^{\alpha}n_2^{2\alpha}}{\alpha}\le4n_2^{2\alpha}.
\end{equation}
\vskip 0.3cm We choose an $n_3\in \mathbf{N}$ such that
$n^3_2>2n_2^2$. We define a function $\rho_3$ on $\mathbf{R}$ as
follows.
$$
\rho_3(x)=\frac{1}{x^{1+\alpha}},\ \ \mbox{if}\ \frac{1}{2n^2_3}<x<\frac{1}{n^2_3};\ \ 0,\ {\rm otherwise}.
$$
Note that there is no overlap among $\rho_1$, $\rho_2$ and
$\rho_3$. We define $\mu_3(dx)=\rho_3(x)dx$ and denote by
$\psi_3$ the L\'evy-Khintchine exponent of $\mu_3$. Then, similar
to the above, we can show that for $z\in [\frac{n_3}{2}, 2n_3]$,
\begin{equation}\label{41}
{\rm Re}\psi_3(z)\le 2\ \ {\rm and}\ \ {\rm Im}\psi_3(z)\ge
\frac{1}{8}n_3^{2\alpha-1}
\end{equation}
and for any $z\in \mathbf{R}$,
$$
{\rm Re}\psi_3(z)\le4n_3^{2\alpha},\ \ |{\rm Im}\psi_3(z)|\le
4n_3^{2\alpha}.
$$
Similar to (\ref{p1}) and (\ref{p2}), we obtain that for $z\in
[\frac{n_1}{2}, 2n_1]$,
\begin{equation}\label{v1}
{\rm Re}\psi_3(z)\le\frac{2n_1^2n_3^{2\alpha-4}}{2-\alpha},\ \
|{\rm Im}\psi_3(z)|\le\frac{2n_1n_3^{2\alpha-2}}{1-\alpha}
\end{equation}
and for $z\in [\frac{n_2}{2}, 2n_2]$,
\begin{equation}\label{v2}
{\rm Re}\psi_3(z)\le\frac{2n_2^2n_3^{2\alpha-4}}{2-\alpha},\ \
|{\rm Im}\psi_3(z)|\le\frac{2n_2n_3^{2\alpha-2}}{1-\alpha}.
\end{equation}
We increase $n_3$ (with $n_1,n_2$ fixed) so that $n_3\ge
n_2^{5/(2-2\alpha)}$. By (\ref{v1}) and (\ref{v2}), we get
\begin{equation}\label{az22}
{\rm Re}\psi_3(z)\le\frac{2}{(1-\alpha)n_2^4},\ \ |{\rm
Im}\psi_3(z)|\le\frac{2}{(1-\alpha)n_2^4},\ \ z\in
\left[\frac{n_1}{2}, 2n_1\right]\bigcup\left[\frac{n_2}{2},
2n_2\right].
\end{equation}
Hence, by (\ref{r1}), (\ref{r2}) and (\ref{az22}), we obtain that
for $z\in [\frac{n_1}{2}, 2n_1]$,
\begin{equation}\label{rr1}
{\rm Re}\psi_1(z)+{\rm Re}\psi_2(z)+{\rm Re}\psi_3(z)\le
2+\frac{2}{(1-\alpha)n_1^4}+\frac{2}{(1-\alpha)n_2^4}
\end{equation}
and
\begin{equation}\label{rr2}
{\rm Im}\psi_1(z)+{\rm Im}\psi_2(z)+{\rm Im}\psi_3(z)\ge
\frac{1}{8}n_1^{2\alpha-1}-\frac{2}{(1-\alpha)n_1^4}-\frac{2}{(1-\alpha)n_2^4}.
\end{equation}
By (\ref{q1}), (\ref{q2}), (\ref{az22}) and (\ref{1}), we obtain
that for $z\in [\frac{n_2}{2}, 2n_2]$,
\begin{equation}\label{qq1}
{\rm Re}\psi_1(z)+{\rm Re}\psi_2(z)+{\rm Re}\psi_3(z)\le
\frac{2}{3n_1^4}{\rm
Im}\psi_2\left(\frac{n_2}{2}\right)+2+\frac{2}{(1-\alpha)n_2^4}
\end{equation}
and
\begin{equation}\label{qq2}
{\rm Im}\psi_1(z)+{\rm Im}\psi_2(z)+{\rm Im}\psi_3(z)\ge
\left(1-\frac{1}{3n_1^4}-\frac{1}{3n_2^4}\right){\rm
Im}\psi_2\left(\frac{n_2}{2}\right).
\end{equation}
We further increase $n_3$ so that $n_3\ge
(192)^{1/(2\alpha-1)}n_2^{(4+2\alpha)/(2\alpha-1)}$ which ensures
that for any $z\in \mathbf{R}$ (cf. (\ref{21}), (\ref{22}),
(\ref{31}), (\ref{32}) and (\ref{41})),
\begin{equation}\label{az2223}
{\rm Re}\psi_1(z),{\rm Re}\psi_2(z),|{\rm Im}\psi_1(z)|,|{\rm
Im}\psi_2(z)|\le \frac{1}{6n_2^4}{\rm
Im}\psi_2\left(\frac{n_3}{2}\right).
\end{equation}
Therefore, we obtain by (\ref{41}) and (\ref{az2223}) that for
$z\in [\frac{n_3}{2}, 2n_3]$,
\begin{equation}\label{cq1}
{\rm Re}\psi_1(z)+{\rm Re}\psi_2(z)+{\rm Re}\psi_3(z)\le
\frac{1}{3n_2^4}{\rm Im}\psi_3\left(\frac{n_3}{2}\right)+2
\end{equation}
and
\begin{equation}\label{cq2}
{\rm Im}\psi_1(z)+{\rm Im}\psi_2(z)+{\rm Im}\psi_3(z)\ge
\left(1-\frac{1}{3n_1^4}-\frac{1}{3n_2^4}\right){\rm
Im}\psi_3\left(\frac{n_3}{2}\right).
\end{equation}
We set $n_3$ to be $ 2^{1/(2\alpha-1)}cn_2^{\vartheta}$, where
$\vartheta$ and $c$ are as the same as above.
\vskip 0.3cm Continue in this way, we define $\rho_4,\rho_5,\dots$
All of these functions have no overlap and we have estimates
similar to (\ref{rr1})-(\ref{qq2}), (\ref{cq1}) and (\ref{cq2}).
Now we define
$$
\rho=\sum_{i=1}^{\infty}\rho_i.
$$
One finds that $\mu(dx)=\rho(x)dx$ is the L\'evy measure of a
subordinator $X$ with the L\'evy-Khintchine exponent
$$
\psi=\sum_{i=1}^{\infty}\psi_i.
$$
Moreover, we have that for $k\ge 2$,
\begin{equation}\label{hgf}
n_k=(k-1)^{1/(2\alpha-1)}cn_{k-1}^{\vartheta},
\end{equation} and for $z\in [\frac{n_k}{2},2n_k]$,
\begin{equation}\label{hgf7}
{\rm Im}\psi_k(z)\ge\frac{1}{8}n_k^{2\alpha-1},
\end{equation}
\begin{equation}\label{general1}
{\rm Re}\psi(z)\le \frac{1}{3n_{k-1}^4}{\rm
Im}\psi_k\left(\frac{n_k}{2}\right)+2+\frac{2}{1-\alpha}\sum_{k=1}^{\infty}\frac{1}{n_k^4},
\end{equation}
and
\begin{equation}\label{general2}
{\rm Im}\psi(z)\ge
\left(1-\frac{1}{3}\sum_{k=1}^{\infty}\frac{1}{n_k^4}\right){\rm
Im}\psi_k\left(\frac{n_k}{2}\right).
\end{equation}
\subsection{Discussions}
In this subsection, we make discussion about the subordinators
constructed in Subsection 5.1. Below we use $c_1, c_2,\dots$ to
denote positive constants depending only on $\alpha$.
\noindent \textbf{1.} By the estimates (\ref{general1}) and
(\ref{general2}), we can show that Rao's condition does not hold
for the subordinators. In fact, by (\ref{hgf}), there exists a
constant $c_1> 1$ such that
\begin{equation}\label{explain}
n_k>c_1^{c_1^k}, \ \ k\in \mathbf{N}. \end{equation}
By (\ref{hgf7}),
(\ref{general1}) and (\ref{general2}), we find that there exist
constants $c_2,c_3,c_4>0$ such that for any $k\ge2$,
\begin{equation}\label{add345}
\frac{{\rm Im}\psi(z)}{1+{\rm Re}\psi(z)}\ge c_2n_{k-1}^4\ge
c_3n_k^{3/\vartheta}\ge
c_3\left(\frac{z}{2}\right)^{3/\vartheta},\ \ \forall z\in[n_k/2,
2n_k].
\end{equation}
\begin{equation}\label{break1}
{\rm Re}\psi(z)\le c_4n_{k-1}^{\alpha\vartheta-3},\ \ \forall
z\in[n_k/2, 2n_k].
\end{equation}
The estimates (\ref{add345}) and (\ref{break1}) imply that there
does not exist an increasing function $f$ on $[1,\infty)$
satisfying $ \int_N^{\infty}(\lambda
f(\lambda))^{-1}d\lambda=\infty $ for some $N\ge 1$ and
$|1+\psi|\le (1+{\rm Re}(\psi))f(1+{\rm Re}(\psi))$. That is,
Rao's condition does not hold for the subordinators constructed in
Subsection 5.1.
By Theorem \ref{thm2.1}, we can modify the L\'evy measure $\mu$
defined in Subsection 5.1 by a finite measure and hence obtain a
subordinator which does not satisfy Rao's condition and whose
L\'evy measure $\mu$ has a smooth density $\rho$ with respect to
the Lebesgue measure on $(0,\infty)$.
\vskip 0.3cm \noindent \textbf{2.} Besides the index $\beta''$
(see (\ref{mnb})), Blumenthal and Getoor introduced also in
\cite{BG61} the indexes $\beta$ and $\sigma$ defined by
$$
\beta=\inf\left\{\tau>0:
\int_{\{|x|<1\}}|x|^{\tau}\mu(dx)<\infty\right\}
$$
and
$$
\sigma=\sup\left\{\tau\le 1:
\int_1^{\infty}\frac{x^{\tau-1}}{\int_0^{\infty}(1-e^{-xy})\mu(dy)}dx<\infty\right\}.
$$
From the construction of the subordinators given in Subsection
5.1, we obtain by \cite[Theorem 6.1]{BG61} that
$$
\sigma=\beta=\alpha.
$$
By (\ref{hgf}) and (\ref{general1}) (cf. (\ref{pro5.4-b})), we
get
$$
\beta''\le \alpha-\frac{4}{\vartheta}.
$$
\vskip 0.1cm \noindent \textbf{3.} Take $\alpha=3/4$. For the
subordinators constructed in Subsection 5.1, we claim that there
exists a finite signed measure $d\nu=g_1dx-g_2dx$ with $g_1,g_2\in
L^1_+(\mathbb{R};dx)$ such that
\begin{equation}\label{pop11}\int_{\mathbf{R}}
B^{-2}(z)A(z)|{\hat\nu}(z)|^2dz<\infty\end{equation}
but
\begin{equation}\label{pop12}
\lim_{\lambda\rightarrow\infty}\int_{\mathbf{R}}|{\hat{\nu}}(z)|^2(\lambda+{\rm
Re}\psi(z))|\lambda+\psi(z)|^{-2}dz=\infty.\end{equation}
Let $\omega$ be a sufficiently large number. We define
$$
\zeta_{\omega}(x):=\left\{1-\frac{1-1/({\omega})^{0.1}}{{\omega}}\cdot|x|\right\},
\ \ {\rm if}\ |x|\le\omega;\ \ \frac{1}{|x|^{0.1}},\ {\rm
otherwise},
$$
and
$$
\eta_{\omega}(x):=\left\{1-\frac{1-1/({\omega})^{0.1}}{{\omega}}\cdot|x|\right\}\vee
0, \ \ x\in \mathbb{R}.
$$
By Polya's theorem (cf. Lukacs \cite[Theorem 4.3.1]{Luka}), both
$\zeta_{\omega}$ and $\eta_{\omega}$ are characteristic functions
of absolutely continuous symmetric distributions. Define
$\varsigma_{\omega}:=\eta_{\omega}-\zeta_{\omega}$. Then, $
\varsigma_{\omega}(x)=0$ if $|x|\le{\omega}$; $
\varsigma_{\omega}(x)=1/|x|^{0.1}$ if $|x|\ge (1.1){\omega}$; and
$0\le \varsigma_{\omega}(x)\le 1/|x|^{0.1}$ otherwise.
Let $k_0\in \mathbf{N}$ be a sufficiently large number. For $k\ge
k_0$, we define
$\xi_k:=\varsigma_{\frac{n_k}{2}}-\varsigma_{\frac{2n_k}{1.1}}$.
We find that $\xi_k$ is a characteristic function of the
difference of two functions $g^k_1,g^k_2\in L^1_+(\mathbb{R};dx)$
with $\|g_1^k\|_{L^1},\|g_2^k\|_{L^1}\le 2$. Define
$g_1:=\sum_{k=1}^{\infty}g^k_1/2^k$,
$g_2:=\sum_{k=1}^{\infty}g^k_2/2^k$ and $d\nu:=g_1dx-g_2dx$. By
applying (\ref{q20}), (\ref{hgf}), (\ref{explain}) and the first
inequality of (\ref{add345}) to $B(z)/A(z)$ and applying
(\ref{hgf7}), (\ref{general2}) to $B(z)$, we find that there
exists a constant $c_5>0$ such that
\begin{eqnarray*}
\int_{\mathbf{R}}
B^{-2}(z)A(z)|{\hat\nu}(z)|^2dz
&=&\int_{\mathbf{R}}
\frac{1}{\frac{B(z)}{A(z)}\cdot B(z)}|{\hat\nu}(z)|^2dz\\
&\le&c_{5}\sum_{k=1}^{\infty}\frac{1}{n_k^{\frac{4}{\vartheta}-\frac{1}{22}}\cdot
n_k^{2\alpha-1}\cdot
2^{2k}}\int_{n_k/2}^{2n_k}\frac{1}{z^{0.2}}dz\\
&=&c_{5}\sum_{k=1}^{\infty}\frac{1}{n_k^{9/11}\cdot
2^{2k}}\int_{n_k/2}^{2n_k}\frac{1}{z^{0.2}}dz\\
&<&\infty.\end{eqnarray*}
However, there exists a constant $c_6>0$
such that (cf. ({\ref{pro5.4-b} and (\ref{explain}))
\begin{eqnarray*}
\int_{\mathbf{R}}
|{\hat\nu}(z)|^2\frac{n_k^{\alpha}}{(n_k^{\alpha})^2+({\rm
Im}\psi(z))^2}dz&\ge&c_{6}\frac{1}{n_k^{\frac{3}{4}}\cdot 2^{2k}}\int_{(0.55)n_k}^{\frac{2n_k}{1.1}}\frac{1}{z^{0.2}}dz\\
&\rightarrow&\infty\ \ {\rm as}\
k\rightarrow\infty,\end{eqnarray*} which implies (\ref{pop12}).
By (\ref{pop11}) and (\ref{pop12}) we can also conclude that Rao's
condition does not hold for the subordinators constructed in
Subsection 5.1. In fact, from the proof of Theorem \ref{R2} (see
Rao \cite{R88}), we can see that under Rao's condition, $$
\lim_{\lambda\rightarrow\infty}\int_{\mathbf{R}}|{\hat{\nu}}(z)|^2(\lambda+{\rm
Re}\psi(z))|\lambda+\psi(z)|^{-2}dz=0
$$
holds for any finite signed measure of finite 1-energy.
It is interesting to
compare (\ref{pop11}) and (\ref{pop12}) with the following result,
which is a consequence of Theorem \ref{thm112}.
\begin{thm}\label{slight} Let $X$ be a L\'evy process on $\mathbf{R}^n$ such that all 1-excessive functions are lower
semicontinuous. Then (H) holds if and only if
\begin{equation}\label{sx}
\lim_{\lambda\rightarrow\infty}\int_{\mathbf{R}^n}|\hat\nu(z)|^2(\lambda+{\rm
Re}\psi(z))|\lambda+\psi(z)|^{-2}dz=0
\end{equation}
for any finite measure $\nu$ of finite 1-energy.
\end{thm}
{\bf Proof.} By Theorem \ref{thm112}, Rao \cite[Remark, page 622]{R88}
and Blumenthal and Getoor \cite[VI. (4.8)]{BG68}, we need only prove the necessity.
Suppose that (H) holds for $X$. Let $\nu$ be a finite measure of
finite 1-energy and $\kappa$ be the standard Gaussian measure on
$\mathbf{R}^n$. Then, $\nu+\kappa$ has finite 1-energy, which
implies that
\begin{equation}\label{pop13}
\int_{\mathbf{R}^n}U^1(\nu+\kappa)d(\nu+\kappa)<\infty.
\end{equation}
By (\ref{pop13}), $\kappa(\{x:U^1(\nu+\kappa)(x)=\infty\})=0$.
Hence $U^1(\nu+\kappa)$ is locally integrable (with respect to the
Lebesgue measure $dx$) by \cite[VI. (2.3)]{BG68}. By (H) and
\cite[VI. (4.9)]{BG68}, we find that $U^1(\nu+\kappa)$ is regular.
Therefore, (\ref{sx}) holds by Theorem \ref{thm112} and the proof
is complete.\hfill\fbox
So far we have not been able to
prove or disprove that (H) holds for the subordinators constructed
in Subsection 5.1. This example suggests that maybe completely new
ideas and methods are needed for resolving Getoor's conjecture.
\bigskip
{ \noindent {\bf\large Acknowledgments} \vskip 0.1cm \noindent We
thank Professor Fengyu Wang for helpful comments that improved a
previous version of the paper. We are grateful to the support of
NNSFC, Jiangsu Province Basic Research Program (Natural Science
Foundation) (Grant No. BK2012720), and NSERC.}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,727 |
NSSE survey still available for Washburn students
Richard Kelly
There has been a large push for particular students to take the National Survey of Student Engagement at Washburn.
However, as of April 21, the push hasn't convinced over half of the eligible population, with 56 percent of the eligible students unaccounted for.
According to Sandra Selden, research analyst for institutional research, completing the NSSE provides crucial data to the university.
"Completing the NSSE provides Washburn with valuable information that will help guide changes in policies, curriculum, and resources," said Selden via e-mail.
She also went on to say that as a result of Washburn's past student responses to NSSE, for example, all general-purpose classrooms are now mediated and Wi-Fi was expanded across campus.
The 2011 NSSE survey is available to 2,451 freshman and senior students through early June.
"To access the survey, the student should click on the link provided in one of the many email reminders that were sent to them in February and March of this year," said Selden via e-mail. "If they cannot locate an email with the link, they can go directly to https://www.nssesurvey.org. However, this will require them to request a login ID using their @washburn.edu e-mail address." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,527 |
\section{Introduction}
According to the National Curricular Parameters (\textit{Par\^ametros Curriculares Nacionais}) \cite{PCN} of Brazil, the student's formation must have, as the main objective, the getting and comprehension of basic concepts, as well as the scientific preparation and the capacity to use different technologies related to the different actuation areas. In the secondary level, it is proposed a most general formation, opposite to that specific one. It is also proposed the development of the capacity to research, analyse and select informations. Furthermore, education must aim develop the capacity to learn, create and formulate, instead of memorization exercise.
In this way, one can not restrict education to the scholar context, once it can happen in several places, from which we can cite scientific disseminate centers and museums \cite{Tran-Tesis,Ash-Book}. Moreover, it is known that the student's knowledge is gotten not only in experiences occurring inside the classroom, but also from their experiences in the everyday life and didactic activities, which can be proposed, for example, by the teacher. Thus, the scientific dissemination centers, the electronic media and the science museums are important tools in the learning process \cite{museuselet}. According to Langhi \textit{et al} \cite{langhi}, learning may happen in several environments, and these ones can be classified as formal, informal and non-formal settings. Furthermore, we can cite, as learning activity, the activities known as scientific popularization.
Langui \textit{et al} \cite{langhi} define formal education as that one occurring in the scholar environment and others teaching establishments, with own structure and planning, whose objective is to work, didactically, the systematized knowledge. The non-formal education is that one having collective character and involving educative practicals which does not occur in the scholar environment and has not legal requirement. During these activities, the student experiments the freedom to choose the concepts to be learned. Among the examples offering non-formal settings, one can cite: museums, media, training agencies for specific social groups and non-conventional teaching institutions, which organize events such as free courses, science fairs and scientific meetings \cite{langhi}. It is important to say that, in spite it does not occur in a scholar environment, the non-formal education is not free of a certain degree of intentionality and systematization.
In this context, museums and science centers, which can be classified as non-formal education settings \cite{langhi}, can favour the conceptual expansion and refinement in an environment which can bring emotions, becoming coupled with the cognitive process, doted of an intrinsic motivation for the learning of science \cite{emo8}. Furthermore, non-formal settings are places providing the appreciation and the understanding of sciences by voluntary and individual actions, popularizing the scientific and technological knowledges \cite{cient9}. And still, nowadays, it is increasing the concern with both, affective and emotional impacts and with the production of meaning and knowledge construction \cite{marandino}.
Given the importance of non-formal settings for the student's learning, there are several works dedicated to research the influence of museums for the science education (see, for example Refs. \cite{Ash-Book,Tran-Tesis,cient9,solinf,park}). Nevertheless, the presence of museums and science centers are not a reality in the most of Northeast of Brazil. Thus, to visit one of these non-formal spaces must be a tiring, stressful and expensive activity, due the distances among several cities located in this region and the nearest scientific centers. In this case, in order to provide different learning environments for the students, the teacher can propose accessible activities in his living region and to arouse the enthusiasm of the student for scientific knowledge.
When we think in hydrodynamics teaching, several works have investigated about the learning process and new forms to address concepts on this issue. For example, one can cite some elaborated experiments destined to teach fluid dynamics \cite{turblam,airjets}. Furthermore, Arellano \textit{et al} have proposed the injection of particles or bubbles in order to simplify the complex task of teaching the hydrodynamics of a swimmer's propulsion to undergraduate students of Physical Education, once, with this technique, the students have the opportunity to see how the water is actively moving when the body is propelled through the water \cite{Swimming}. In addition, from the analysis of 15 original simulations, created with GeoGebra software, Romero \textit{et al} \cite{romero-EJP} have applied a questionnaire on the interest of using simulations to teach fluid mechanics to simulation-taught students and compare the answers to that given by students taught without use of simulations. At the examination, the average grade and the percentage of passed students were higher in group 1 than in group 2, however, the author recognises that additional strategies need to be adopted aiming to help students develop the skills required to succeed in physics course. An apparent paradox in communicating vessels systems is discussed in the work of Miranda \cite{Miranda}, in which the author shows that, for a liquid in any connected vessel system, it is not possible to realize simultaneously Pascal's principle, mass and energy conservation. In addition, there are propositions of hydrostatic teaching from experimental activities using low cost materials, e.g., plastic bottles \cite{Pet} and water cup \cite{dinner}. Finally, the transport of water from the roots to the crown of trees is discussed for two conduit architectures is considered in the work of \cite{TreeHyd} and it is proposed to be exposed to undergraduate students, in order to get an interdisciplinar communication with Biology. In this work, the author considers the subject of broad interest because it provides a naturally-occurring example of an unusual metastable state of matter.
In this Paper, we report the proposition to study basic concepts of hydrodynamics from the visit to a river lock, which consists in a work of hydraulic engineering that allows boats ascend or descend the rivers and seas in places where there are gaps (dam or waterfalls). In our case, we have chosen to visit the Sobradinho's river lock, once it is the nearest structure of this kind to Senhor do Bonfim - BA, Brazil. Furthermore, we show the proposition to construct a model of a river lock, in order to study the operation of this system, in more details. We also discuss the opportunity that must be given to the students, to discuss and couple knowledge of different contents of other disciplines, such as Geography and History, to Physics, seeing the science as a human activity and understanding about social, economic and politic impacts brought from the construction of a dam.
This work is divided as follows: in section 2, we present the Sobradinho's river lock and talk about its operation and economic importance; section 3 brings a discussion on some hydrodynamic concepts that can be addressed from the operation of a river lock; in section 4, we present the proposition to construct a model of a river lock in order to study, in more details, the river lock's operation; finally, in section 5, the conclusions are presented.
\section{The Sobradinho's dam and hydrodynamic of river locks}
The artificial lake formed from the Sobradinho's dam has length of 320 km \cite{ashfra} (from municipality of Sobradinho to the municipality of Pilão Arcado) and a water surface area of 4,214 km$^2$. Its storage capacity is around 34.1 million of liters, being the second largest artificial lake in the world. It ensures, through a depletion of up to 12 m, together with the Tr\^es Marias Reservoir, a regulated flow of 2,060 m$^3$/s during the dry season, allowing operation of all hydroelectric plants of the \textit{Companhia Hidroel\'etrica do Vale do S\~ao Francisco} (CHESF), situated along the S\~ao Francisco River.
This dam incorporates a river lock, owned by \textit{Companhia Docas do Estado da Bahia} (CODEBA), whose camera has 120 m of length and 17 m width, allowing the boats to overcome the gap created by the dam, around 32.5 meters, with maximum filling time of 16 minutes. This river lock ensures the continuity of traditional navigation between the stretch of the São Francisco River between the cities of Pirapora-MG and Juazeiro-BA/Petrolina-PE (1,371 km navigable) favouring the waterway transport and therefore, the commercial navigation in the Old Chico (form with which the river is known in the region). In Figure \ref{sobr}, one can see a highlighted view of the river lock under discussion. In this same figure, we show a map locating the Sobradinho's dam in the state of Bahia-Brazil.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.9]{mapaeclusa.eps}\end{center}
\caption{Location of the Sobradinho's dam. Featured, we have a view of the river lock in that dam. The vessel is raised to the highest level by opening a gate, which releases the entry of water coming from the dam in the region of the lock.}\label{sobr}
\end{figure}
River locks function as stairs or elevators for ships or boats, in which there are two gates separating the two river (or sea) levels. In the Fig. \ref{pontos}, we show a schematic view representing, in a very simplified form, the operation of a river lock. When the boat ups the river, it enters in the lock at the downstream side (marked in the figure as C) and remains in the chamber (region B). The downstream is then closed and the chamber filled with water, causing the boat to rise until it reaches the level of the upper reservoir. Thereafter, the gate 1 can be opened and the boat leaves the lock, going to the dam, marked in the Figure as the region A. When the boat downs the river, it enters in the chamber at the upstream side of the lock and the gate is closed, emptying the chamber gradually until it reaches the level of the lower reservoir. Finally, the gate 2 is opened and the boat leaves of the river lock. The operations of filling and emptying the chamber are usually made by gravity with the help of small gates and valves. An animation showing the operation of the Sobradinho's river lock can be found on the website cited in Ref. \cite{ashfra}.
\begin{figure}[h]\begin{center}
\includegraphics[scale=0.4]{esquema1.eps}\end{center}\caption{Schematic view of the operation of a river lock. Once, in statical conditions, the pressure must be the same for points situated in the same height, if we open the link between A and B, there will be a water flow from the region A to the region B, until the water level is equal in the two sides. The same argument must be used when we open the link between B and C. In this case, when the board comes from C, going to A, the link between B and C must be opened in order to decreases the water level in B. The gate is opened and the boat can go to B. Now, the link between A and B is opened and the water level in B rises. The gate 1 is opened and the boat can pass to A.}\label{pontos}
\end{figure}
\subsection{Static}
In order to study the hydrodynamical principle of the operation of a river lock, we will simplify it to a communicating vessels system, whose dynamical properties can be well defined from the Euler equation \cite{landau,faber}:
\begin{equation}
\frac{\partial \mathbf{v}}{\partial t}+(\mathbf{v}\cdot\nabla)\mathbf{v}=-\frac{\nabla p}{\rho}+g\mathbf{\hat{z}},
\end{equation}
where $\mathbf{v}$ is the fluid velocity, $\rho$ is its density, $p$ the pressure of the fluid and $g$, the gravity acceleration. For a fluid in rest, we have:
\begin{equation}\label{static}
\nabla p=\rho g\mathbf{\hat{z}}.
\end{equation}
If the fluid density is considered constant along its volume and the $z$ axis is taken as vertical, the Eq. (\ref{static}) can be integrated to give:
\begin{equation}
\frac{\partial p}{\partial x}=\frac{\partial p}{\partial y}=0,\hspace{1cm}\frac{\partial p}{\partial z}=-\rho g.
\end{equation}
Thereby,
\begin{equation}\label{hidro}
p=-\rho g z + \text{constante}.
\end{equation}
If the fluid has a free surface, in the height $h$, for which an external pressure $p_0$, at all points, is applied, this surface must be a horizontal plane $z=h$. From the condition $p=p_0$ when $z=h$, we have that the constant, in the Eq. (\ref{hidro}), is given by $p_0+\rho g h$, such that:
\begin{equation}\label{equil}
p=p_0+\rho g (h-z).
\end{equation}
In this way, given a point in a fluid, the pressure on this point will depend only on the height of the liquid. In this case, from observing the Fig. \ref{pontos}, we can conclude that, from the opening of the gate 2, a point situated in the region C will be subject, initially, to a pressure lower than the pressure on a point, at the same height, situated in the region B. From the Eq. (\ref{equil}), if the regions are linked, the pressure must be equal in the two points, thus, there will be a transference of fluid from the region B to C, when connecting valve between these two regions is opened. The region C does not rise its level because the water goes to the river, and, in the case of Sobradinho's dam, it goes to the cities of Petrolina/Juazeiro. Then, there is a reduction on the water height in the region B, until it reaches the level of the river (region C).
From the same principle, when the region B is in the level of the river (C), there will be a flux of water from the region A to the region B, filling this region and rising the water height.
\subsection{Dynamics}
Now, we will analyse the rising velocity of the liquid column inside the river lock in function of the water flow released by the connection valve between the regions A and B. Obviously, if we maintain a constant flow $\mathcal{Q}$, given by $\mathcal{Q}=\frac{d V}{dt}$, where $V$ is the volume of water that pass from the region A to the region B, a boat will be rise until the upper of the river lock with a constant velocity, given by:
\begin{equation}
v(t)=\frac{\mathcal{Q}}{S_B},
\end{equation}
where $S_B$ is the surface's area of the region B. In this case, the height will be a linear function of the time, given by:
\begin{equation}\label{MRU}
z(t)=\frac{\mathcal{Q}}{S_B}t,
\end{equation}
where we have done $z(0)=0$.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.4]{comunic.eps}\end{center}
\caption{Simple model to analyse the rising velocity of the liquid column in a river lock. Here, we have considered that the water flow is a function of the height $z$, inside the region B represented in the Fig. \ref{pontos}. Once the pressure in the opening linking the regions A and B increases with $z$, the velocity of exit of water in this opening diminishes, thus, the liquid column rises with a decreasing velocity.}\label{novesq}
\end{figure}
Now, we will study what occurs when the water flow is variable with the time, which can be obtained, for example, by maintaining the opening of the valve linking A and B with a constant area $S_P$, as it is shown in Fig. \ref{novesq}. In this case, when the valve is opened, the water level in the region B rises, increasing the pressure of the water on the exit $S_P$. Thereby, if we maintain the valve opened with a constant area, the water flow will not be constant, once the increasing of pressure in the region B will diminish the water flow through the opening that separates the two regions.
As it has been said, when the link between A and B is opened, there will be a water flow from the region A, with area $S_A$, to the region B, with area $S_B$, passing through the opening with area $S_P$. In order to determine the velocity of the water when it passes through the opening, we will use the Bernoulli's equation \cite{landau}:
\begin{equation}
\frac{1}{2}\rho v^2+\rho gz+p=\kappa,
\end{equation}
where $\kappa$ is a constant. In this case, the fluid's velocity through the opening with area $S_P$ is given by:
\begin{equation}\label{continuidade}
\frac{1}{2}\rho v_P^2+\rho gz_P+p_P=\frac{1}{2}\rho v_S^2+\rho gz_A+p_A,
\end{equation}
in which the subscript indices $P$ and $A$ are representing the surfaces with area $S_P$ and $S_A$, respectively. $z_{P}\equiv z(t)$ is the height of water column when it pass to the region with area $S_B$. From the Fig. \ref{novesq}, we have that $z_A=h$, $z_P=0$, $p_A=p_0$, $p_P=p_0+\rho g z_B(t)$. Furthermore, we will consider $S_A\gg S_P$, then the lowering velocity of the water in the region A is $v_A=0$. Thus, from Eq. (\ref{continuidade}), the velocity of the water through the valve linking the regions A and B will be given by:
\begin{equation}
v_P(t)=\sqrt{2g[h-z_B(t)]}.
\end{equation}
In this way, defining $z_B(t)\equiv z(t)$, we have that the water flow $\mathcal{Q}(t)$ through the region with area $S_P$ is:
\begin{equation}
\mathcal{Q}(t)=S_P\sqrt{2g[h-z(t)]}.
\end{equation}
And, in this case, the rising velocity of the water at the river lock (region B) will be:
\begin{equation}\label{vel}
v_B(t)=\frac{\mathcal{Q}(t)}{S_B}=\frac{S_P}{S_B}\sqrt{2g[h-z(t)]}.
\end{equation}
Once $z(0)=0$, we have that the velocities of the water through the valve, $v_P(t)$ and in the river lock region, $v_B(t)$, in the instant $t=0$ are given by $v_P(0)=\sqrt{2gh}$ and $v_B(0)=\frac{S_P}{S_B}\sqrt{2gh}$. Furthermore, they decrease their values when the height of the water column rises, in such way that these velocities will vanish when $z(t)=h$.
Finally, aiming to determine the function, $z(t)$, for which the height of the water rises in the region B, we start from the velocity definition $v\equiv\frac{dz}{dt}$. One can note that:
\begin{equation}
\int\frac{dz}{\sqrt{2g[h-z(t)]}}=\frac{S_P}{S_B}t.
\end{equation}
This integral is evaluated to give:
\begin{equation}
z(t)=h+\left(\kappa\frac{S_P}{S_B}\right)t-\frac{1}{2}g\left(\frac{S_P}{S_B}\right)^2t^2 -\frac{\kappa^2}{2g},
\end{equation}
where $\kappa$ is a constant of integration. Taking the initial boundary condition $z(0)=0$, we obtain $\kappa=\sqrt{2gh}$, and so:
\begin{equation}\label{MRUV}
z(t)=\sqrt{2gh}\left(\frac{S_P}{S_B}\right)t-\frac{1}{2}g\left(\frac{S_P}{S_B}\right)^2t^2.
\end{equation}
One can note that the rising of the water level in the river lock is well represented by a uniformly variable rectilinear motion function, in which the water, and consequently the boat, begin its upward movement with initial velocity $v_B(0)=\frac{S_P}{S_B}\sqrt{2gh}$, decreasing its value with a constant acceleration given by $a=\left(\frac{S_P}{S_B}\right)^2 g$. In this way, the needed time to the boat reaches the highest point of the river lock, $z(t)=h$, and continue its flux, is:
\begin{equation}
t_\text{up}=\frac{S_B}{S_P}\sqrt{\frac{2h}{g}}.
\end{equation}
As expected, the rising time of the boat is directly proportional to the river lock surface area, $S_B$, and decreases with the increasing of the height of the river lock.
\section{Constructing a river lock's model}
The visit to the river lock has been important because, in this ambient, the students can have contact with several devices that could not be viewed in a formal space (classroom). Furthermore, they have the opportunity to hear and discuss the theoretical and practical aspects about the operation of a river lock with a professional having experience with the possible problems coming from the operation of these structures. Other advantage of this visit comes from the opportunity to observe probable social and environmental impacts caused by the construction of a dam.
After the visit to the Sobradinho's dam, as a part of a multidisciplinary activity involving several areas of knowledge, as Physics, History, Geography and Portuguese, we have constructed a model of a river lock (See Fig. \ref{fotomaq}), in order to evaluate the learning process and systematize the acquired knowledge. The model was constructed according the schema of the Fig. \ref{pontos}. In order to avoid water waste, when it pass from the region B to the region C, we have put a vessel receiving the water exiting from the model. A water pump returned the water from the vessel to the region A.
In the Fig. \ref{fotomaq}, we present a photograph of the constructed model. In that, one can note highlighted, the regions A, B and C. The valves linking the regions has been done through pipes and taps (Link AB and Link BC), which release water passage, when opened. When the link AB is opened, we release the water flow from region A to the region B. In this case, the liquid column height in B rises. In this model, in order to ensure the constant height of the region A, we have filled the vessel while the water have flowed to the region B. This procedure will ensure that the rising of the water in the region B obeys the Eq. (\ref{MRUV}), that is, the liquid column is rising in an uniformly variable rectilinear motion. Obviously, by closing the link AB and opening the link BC, the water flows from B to C, however, once the height at the region C does not rise, the passage of the water from B to C must obey the Eq. (\ref{MRU}), once the flow must be considered constant.
\begin{figure}[h]\begin{center}
\includegraphics[scale=0.8]{maquetef1.eps}\end{center}\caption{Photograph of the model constructed in order to observe, inside the classroom, the operation of a river lock. Here, we highlight the regions A, B and C, represented in the schema of the Fig. \ref{novesq}.}\label{fotomaq}
\end{figure}
Aiming to test the validity of the Eq. \ref{MRUV}, we performed some measurements with the constructed model. The model's parameters are $h=34.5$ cm, $S_P=\pi$ cm$^2$ and $S_B=847.9$ cm$^2$. To predict the needed time to fill the place B, we used $g=9.81$ m/s$^2$, obtaining $t_{\text{up}}\approx 71.58$ s. Besides to measure the filling time, we determined the height of the water column for $t=30$ s and $t=60$ s. The predicted values are $z(30\text{ s})\approx22.86$ cm and $z(60\text{ s})\approx33.60$ cm. The obtained experimental values were obtained after ten measurements an they were $z(30\text{ s})=21.5\pm1.4$ cm, $z(60\text{ s})=31.8\pm1.3$ cm and the filling time was $t_{up}=69.72\pm0.7$ s. The disagree among the theoretical and experimental values is associated with errors due to sealing problems in the gates, which made it possible that there was a water flow slightly higher than expected from the A to B region. In addition, there may be variations due to the actual value for the local gravity acceleration.
\section{Conclusions}
We have proposed the visit to a river lock as a non-formal setting for teaching hydrodynamics. In particular, we have visited the Sobradinho's dam, situated in the S\~ao Francisco river, 150 km away from Senhor do Bonfim. This travel had, as main objective, to show the operation of a hydroelectric plant and, in special, a river lock.
With this activity, we believe that it can be enabled the integration among the propaedeutic contents, learned in the classroom, and practical applications of these ones. In the local, we have realized a discussion on the physical principles based on the operation of a river lock, as well as its economic importance, in such way that students might realize that physics is not a subject disconnected from reality, having important links with other areas of knowledge. Thus, the students realized that the economic development is linked to the scientific development of a country. When we return to the formal space (classroom), we have constructed a model to show, in a more detailed form, the operation of a river lock for the students.
The visit to the river lock, with the participation of students and teachers, allowed a greater integration among stakeholders and the contextualization of contents relevant to each discipline. As a consequence, it was accomplished with a interdisciplinarity among Physics, History and Geography, where it has been possible to discuss on problems such as siltation, transportation, economy, water use for irrigation and electricity generation, as well as social, economical and environmental impacts due the construction of a dam. Furthermore, the History teacher could explain the evolution of the economy and culture of the communities located in places affected by the Sobradinho's dam.
Finally, besides the river lock, the presence of a hydroelectric plant at Sobradinho gave us the opportunity to discuss other physical concepts with the students, e.g., the processes of electric power generation, hydropower, alternative forms for energy generation and electromagnetic induction. We could review the energy conservation principle.
\section*{Acknowledgements}
The authors thank CNPq (grant number 562867/2010-4) and PROPES of IFBaiano for financial support. We thank also the employees of the Sobradinho's river lock for the receptivity and hospitality. We are also in debit with Antonio S Silva, Maisa F S Martins and Amanda A Melo for helping with the river lock model operation.
\thebibliography{99}
\bibitem{PCN}
http://portal.mec.gov.br/seb/arquivos/pdf/CienciasNatureza.pdf (In Portuguese).
\bibitem{Tran-Tesis}
Tran L U 2002 \textit{The roles and goals of educators teaching science in non-formal settings}, thesis submitted to the Graduate Faculty of North Carolina State University. Available in http://repository.lib.ncsu.edu/ir/bitstream/1840.16/830/1/etd.pdf. Accessed in May 13, 2013.
\bibitem{Ash-Book}
Ash D and Wells G 2006 \textit{Dialogic Inquiry in Classroom and Museum}, In \textit{Learning in places: the informal education reader} edited by Zvi B, Burbules N C, Silberman-Keller D 2006, p. 35. Peter Lang Publishing Inc. New York.
\bibitem{museuselet}
Falk J H 2001 {\it Free-Choice Science Learning: Framing the discussion} (New York: Teachers College Press).
\bibitem{langhi}
Langhi R and Nardi R 2009 \textit{Rev Bras Ens F\'is} {\bf 31} 4402 (In Portuguese).
\bibitem{emo8}
Queiroz G, Krapas S, Valente M E, David E, Damas E and Freire F 2002 \textit{Rev Bras Pesq Ens Ci\^enc} {\bf 2} 2 (In Portuguese)
\bibitem{cient9}
Pereira G R and Coutinho-Silva R 2010 \textit{Rev Bras Ens F\'is} {\bf 32} 3402 (In Portuguese)
\bibitem{marandino}
Marandino M 2006 {\it A Pesquisa em Ensino de Ci\^encias no Brasil e suas Metodologias} (Editora da Uniju\'i, ́Iju\'i) (In Portuguese)
\bibitem{solinf}
Aroca S C and Silva C C 2011 \textit{Rev Bras Ens F\'is} {\bf 33} 1402 (In Portuguese)
\bibitem{park}
Moll R F 2010 \textit{Phys Educ} {\bf 45}, 362
\bibitem{turblam}
Riveros H G and Riveros-Rosas D 2010 \textit{Phys Educ} {\bf 45} 288
\bibitem{airjets}
L\'opez-Arias T, Gratton L M, Zendri G and Oss S 2011 \textit{Phys Educ} {\bf 46} 373
\bibitem{Swimming}
Arellano R and Pardillo S 2001 \textit{Teaching Hydrodynamic Concepts Related to Swimming Propulsion Using Flow Visualization Techniques in the Pool}. Available in http://www.ugr.es/~swimsci/SwimmingScience/page4/page16/page38/files/2001ArellanoNSTBS.pdf
Accessed in April 10, 2013.
\bibitem{romero-EJP}
Romero C and Mart\'inez E 2013 \textit{Eur. Journ Phys.} \textbf{34} 873
\bibitem{Miranda}
Miranda E N 2009 \textit{Eur J Phys} \textbf{30} L55
\bibitem{Pet}
Jesus V B L and Macedo-Junior M A V 2011 \textit{Rev Bras Ens F\'is} {\bf 33} 1507 (In Portuguese)
\bibitem{dinner}
Marshall R 2013 \textit{Phys Educ} \textbf{48} 390
\bibitem{TreeHyd}
Denny M 2012 \textit{Eur J Phys} \textbf{33} 43
\bibitem{ashfra}
AHSFRA 2011 {\it Administra\c c\~ao da Hidrovia do S\~ao Francisco}. Available in \underline{www.ahsfra.gov.br} (In Portuguese) Acessed in March 13, 2013
\bibitem{landau}
Landau L D and Lifshitz E M 1986 \textit{Fluid Mechanics}, 2$^{nd}$ edition, (Pergamon Books Ltd, Moscow)
\bibitem{faber}
Faber T E 1995 \textit{Fluid Dynamics for Physicists} (Cambridge University Press, Cambridge)
\end{document} | {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,623 |
\section{Introduction}
Width parameters play an important role in algorithmic graph theory, as evidenced by various surveys~\cite{DJP19,Gu17,HOSG08,KLM09,Ou17}.
A graph class ${\cal G}$ has {\it bounded} width, for some width parameter, if there exists a constant~$c$ such that every graph in ${\cal G}$ has width at most~$c$.
Mim-width is a relatively young width parameter that was introduced by Vatshelle~\cite{Va12}.
It is defined as follows. A \textit{branch decomposition} for a graph~$G$ is a pair $(T, \delta)$, where $T$ is a subcubic tree and $\delta$ is a bijection from~$V(G)$ to the leaves of $T$.
Every edge $e \in E(T)$ partitions the leaves of $T$ into two classes, $L_e$ and $\overline{L_e}$, depending on which component of $T-e$ they belong to.
Hence, $e$ induces a partition $(A_e, \overline{A_e})$ of $V(G)$, where $\delta(A_e) = L_e$ and $\delta(\overline{A_e}) = \overline{L_e}$.
We let $G[A_e,\overline{A_e}]$ be the bipartite subgraph of $G$ induced by the edges with one end-vertex in $A_e$ and the other in $\overline{A_e}$.
A matching $F \subseteq E(G)$ of $G$ is {\it induced} if there is no edge in $G$ between vertices of different edges of $F$.
We let $\mathrm{cutmim}_{G}(A_{e}, \overline{A_{e}})$ be the size of a maximum induced matching in $G[A_{e}, \overline{A_{e}}]$.
The \emph{mim-width} $\mathrm{mimw}_{G}(T, \delta)$ of $(T, \delta)$ is the maximum value of $\mathrm{cutmim}_{G}(A_{e}, \overline{A_{e}})$ over all edges $e\in E(T)$. The \emph{mim-width} $\mathrm{mimw}(G)$ of $G$ is the minimum value of $\mathrm{mimw}_{G}(T, \delta)$ over all branch decompositions $(T, \delta)$ for $G$.
Vatshelle~\cite{Va12} proved that every class of bounded clique-width, or equivalently, bounded boolean-width, module-width, NLC-width or rank-width, has bounded mim-width, and that the converse is not true. That is, he proved that there exist graph classes of bounded mim-width that have unbounded clique-width.
This means that proving that a problem is polynomial-time solvable for graph classes of bounded mim-width (see~\cite{BV13,BK19,BPT19,BTV13,GMR20,JKST19,JKT,JKT19} for examples of such problems) yields more tractable graph
classes than doing this for clique-width. Hence, mim-width has greater {\it modeling power} than clique-width.
However, the {\it trade-off} is that fewer problems admit such an algorithm, as we explain below by means of a relevant example, namely the classical {\sc Colouring} problem.
Moreover, computing mim-width is {\sf NP}-hard~\cite{SV16} and, in contrast to the situation of clique-width~\cite{OS06}, it remains a challenging open problem to develop a polynomial-time algorithm for approximating the mim-width of a graph (doing this within a constant factor of the optimal is not possible unless $\mathsf{NP} = \mathsf{ZPP}$~\cite{SV16}).
This has the following implication. For a class of graphs~${\cal G}$ with bounded mim-width, we need an explicit polynomial-time algorithm for computing a branch decomposition whose mim-width is bounded by a constant. When this is possible, we say that the mim-width of ${\cal G}$ is {\it quickly computable}. We can then develop a polynomial-time algorithm for the problem of interest via dynamic programming over the computed branch decomposition; see~\cite{BHMPP,BTV13,KKST17} for some examples.
A {\em colouring} of a graph $G=(V,E)$ is a mapping $c\colon V\rightarrow\{1,2,\ldots \}$ that gives each vertex~$u\in V$ a {\it colour} $c(u)$ in such a way that, for every two adjacent vertices $u$ and $v$, we have that $c(u)\neq c(v)$. If for every $u\in V$ we have $c(u)\in \{1,\ldots,k\}$, then we say that $c$ is a {\it $k$-colouring} of $G$.
The {\sc Colouring} problem is to decide whether a given graph $G$ has a $k$-colouring for some given integer $k\geq 1$. If $k$ is fixed, that is, not part of the input, we call this the $k$-{\sc Colouring} problem. A classical result of Lov\'asz~\cite{Lo73} states that $k$-{\sc Colouring} is {\sf NP}-complete even if $k=3$.
The {\sc Colouring} problem is an example of a problem that distinguishes between classes of bounded mim-width and bounded clique-width: it is polynomial-time solvable for every graph class of bounded clique-width~\cite{KR03} but {\sf NP}-complete for circular-arc graphs~\cite{GJMP80}, which form a class whose mim-width is bounded and quickly computable~\cite{BV13}. When we fix $k$, we no longer have this distinction, as
$k$-{\sc Colouring}, for every fixed integer $k\geq 1$, is polynomial-time solvable for a graph class whose mim-width is bounded and quickly computable~\cite{BTV13}.
Kwon~\cite{Kw20} observed that an instance of the more general {\sc List $k$-Colouring} problem (defined below) can be reduced to an instance of {\sc $k$-Colouring} while only increasing the mim-width of the input graph by at most $k$ (see also~\cite{BHP}).
Hence, the {\sc List $k$-Colouring} problem is also polynomial-time solvable for a graph class whose mim-width is bounded and quickly computable.
For an integer $k\geq 1$, a {\it $k$-list assignment} of a graph
$G=(V,E)$ is a function $L$ that assigns each vertex $u\in V$ a {\it list} $L(u)\subseteq \{1,2,\ldots,k\}$ of {\it admissible} colours for $u$. A colouring $c$ of $G$ {\it respects} $L$ if $c(u)\in L(u)$ for every $u\in V$. For a fixed integer~$k\geq 1$, the {\sc List $k$-Colouring} problem is to decide whether a given graph~$G$ with a $k$-list assignment $L$ admits a colouring that respects $L$.
Note that for $k_1\leq k_2$, {\sc List $k_1$-Colouring} is a special case of {\sc List $k_2$-Colouring}.
\begin{theorem}[\cite{Kw20}]\label{t-lc}
For every $k\geq 1$, {\sc List $k$-Colouring} is polynomial-time solvable for a graph class whose mim-width is bounded and quickly computable.
\end{theorem}
\noindent
In this note, we continue previous work~\cite{BHP} and
show that known polynomial-time results for {\sc List $k$-Colouring} on special graph classes can be obtained, and strengthened, by applying Theorem~\ref{t-lc}.
\subsection*{Related Work}
A graph is {\it $H$-free}, for some graph $H$, if it contains no induced subgraph isomorphic to $H$. For a set of graphs $\{H_1,\ldots,H_p\}$, a graph is {\it $(H_1,\ldots,H_p)$-free} if it is $H_i$-free for every $i\in \{1,\ldots,p\}$.
We denote the {\it disjoint union} of two graphs $G_1$ and $G_2$ by $G_1+G_2=(V(G_1)\cup V(G_2), E(G_1)\cup E(G_2))$. We let $P_r$ and $K_r$ denote the path and complete graph on $r$ vertices, respectively.
The complexity of {\sc Colouring} for $H$-free graphs has been settled for every graph $H$~\cite{KKTW01}, but there are still
infinitely many open cases for {\sc $k$-Colouring} restricted to $H$-free graphs when $H$ is a {\it linear forest}, that is,
a disjoint union of paths. We refer to~\cite{GJPS17} for a survey and to~\cite{CHSZ18,CSZ,KMMNPS18} for updated summaries.
In particular, Ho\`ang et al.~\cite{HKLSS10} proved that for every integer $k\geq 1$, {\sc $k$-Colouring} is polynomial-time solvable for $P_5$-free graphs. This result was generalized by Couturier et al.~\cite{CGKP15} as follows:
\begin{theorem}[\cite{CGKP15}]\label{t-known}
For every $k\geq 1$ and $s\geq 0$, {\sc List $k$-Colouring} is polynomial-time solvable for $(sP_1+P_5)$-free graphs.
\end{theorem}
\noindent
We may assume without loss of generality that an instance of {\sc List $k$-Colouring} is $K_{k+1}$-free, for otherwise it is a no-instance. Hence, Theorem~\ref{t-known} also immediately follows from combining Theorem~\ref{t-lc} with the following recent result.
\begin{theorem}[\cite{BHP}]\label{t-known2}
For every $r\geq 1$ and $s\geq 0$, the mim-width of the class of $(K_r,sP_1+P_5)$-free graphs is bounded and quickly computable.
\end{theorem}
\noindent
Theorem~\ref{t-known2}
is part of a recent study~\cite{BHP,BHMPP} on the boundedness of mim-width for hereditary graph classes~${\cal G}$ characterized by a small set ${\cal F}_{\cal G}$ of forbidden induced subgraphs. If ${\cal F}_{\cal G}=\{H\}$, then ${\cal G}$ has bounded mim-width if and only if ${\cal G}$ has bounded clique-width~\cite{BHMPP}. On the other hand, this equivalence does not always hold when ${\cal F}_{\cal G}=\{H_1,H_2\}$~\cite{BHMPP}.
For $r\geq 1$ and $s\geq 1$, we let $K_{r,s}$ denote the complete bipartite graph with partition classes of size $r$ and $s$. The graph $K_{1,s}$ is also known as the $(s+1)$-vertex star.
The {\it $1$-subdivision} of a graph $G$ is the graph obtained from $G$ by subdividing each edge of $G$ exactly once. We denote the $1$-subdivision of a star~$K_{1,s}$ by $K_{1,s}^1$;
in particular $K_{1,2}^1=P_5$.
Even more recently than~\cite{BHP}, Chudnovsky, Spirkl and Zhong proved the following result.
\begin{theorem}[\cite{CSZ}]\label{t-known3}
For every $k\geq 1$, $s\geq 1$ and $t\geq 1$, {\sc List $3$-Colouring} is polynomial-time solvable for $(K_{1,s}^1,P_t)$-free graphs.
\end{theorem}
For every $s\geq 1$ and $t\geq 2s+5$, the class of $(K_{1,{s+2}}^1,P_t)$-free graphs contains the class of $(sP_1+P_5)$-free graphs. Hence, Theorem~\ref{t-known3} generalizes Theorem~\ref{t-known} for the case where $k=3$.
As $K_{1,s}$ is an induced subgraph of $K_{1,s}^1$,
Theorem~\ref{t-known3} also generalizes the following result for the case where $r=1$.
\begin{theorem}[\cite{GPS14b}]\label{t-known4}
For every $k\geq 1$, $r\geq 1$, $s\geq 1$ and $t\geq 1$, {\sc List $k$-Colouring} is polynomial-time solvable for $(K_{r,s},P_t)$-free graphs.
\end{theorem}
\subsection*{Our Result}
In this note we generalize Theorem~\ref{t-known2}.
\begin{theorem}\label{t-new}
For every $r\geq 1$, $s\geq 1$ and $t\geq 1$, the mim-width of the class of $(K_r,K_{1,s}^1,P_t)$-free graphs is bounded and quickly computable.
\end{theorem}
\noindent
Recall that an instance of {\sc List $k$-Colouring} may be assumed to be $K_{k+1}$-free. Combining Theorem~\ref{t-new} with Theorem~\ref{t-lc} enables us to generalize
both Theorems~\ref{t-known} and~\ref{t-known3}.
\begin{corollary}\label{c-new}
For every $k\geq 1$, $s\geq 1$ and $t\geq 1$, {\sc List $k$-Colouring} is polynomial-time solvable for $(K_{1,s}^1,P_t)$-free graphs.
\end{corollary}
\noindent
Corollary~\ref{c-new} is tight in the following sense. Let $L_{1,s}$ denote the subgraph obtained from $K_{1,s}^1$ by subdividing one edge exactly once; in particular $L_{1,2}=P_6$.
Then, as {\sc List $4$-Colouring} is {\sf NP}-complete for $P_6$-free graphs~\cite{GPS14}, we cannot generalize Corollary~\ref{c-new} to $(L_{1,s},P_t)$-free graphs for $k \ge 4$, $s\geq 2$ and $t\geq 6$.
Moreover, the mim-width of $(K_4,P_6)$-free graphs is unbounded~\cite{BHMPP} and so we cannot extend Theorem~\ref{t-new} to $(K_r,L_{1,s},P_t)$-free graphs,
for $r\geq 4$, $s\geq 2$ and $t\geq 6$, either.
The {\sc List $3$-Colouring} problem is polynomial-time solvable for $P_7$-free graphs~\cite{BCMSSZ18}, but the computational complexities of {\sc $3$-Colouring} and {\sc List $3$-Colouring} is open for $P_t$-free graphs if $t\geq 8$. In particular, we do not know any integer $t$ such that {\sc $3$-Colouring} or {\sc List $3$-Colouring} are {\sf NP}-complete for $P_t$-free graphs. Hence, an extension of Corollary~\ref{c-new} might still be possible for $k=3$, and we leave this for future work. This requires more research into the structure of $P_t$-free graphs.
Theorem~\ref{t-new} has other applications as well. For a graph $G$, let $\omega(G)$ denote the size of a maximum clique in $G$.
Chudnovsky et al.~\cite{CKPR20} gave for the class of $(K_{1,3}^1,P_6)$-free graphs, an $n^{O(\omega(G)^3)}$-time algorithm for \textsc{Max Partial $H$-Colouring}, a problem equivalent to {\sc Independent Set} if $H=P_1$ and to {\sc Odd Cycle Transversal} if $H=P_2$. In other words, \textsc{Max Partial $H$-Colouring} is polynomial-time solvable for $(K_{1,3}^1,P_6)$-free graphs with bounded clique number.
Chudnovsky et al.~\cite{CKPR20} noted that \textsc{Max Partial $H$-Colouring} is polynomial-time solvable for graph classes whose mim-width is bounded and quickly computable. Hence, Theorem~\ref{t-new} generalizes their result for \textsc{Max Partial $H$-Colouring} to $(K_{1,s}^1,P_t)$-free graphs with bounded clique number, for any $s\geq 1$ and $t\geq 1$.
However, the running time of the corresponding algorithm is worse than $n^{O(\omega(G)^3)}$ (see~\cite{CKPR20} for details).
\smallskip
\noindent
It remains to prove Theorem~\ref{t-new}, which we do in the next section.
\section{The Proof of Theorem~\ref{t-new}}\label{s-new}
We first state two lemmas. The first lemma shows that given a partition of the vertex set of a graph $G$, we can bound the mim-width of $G$ in terms of the mim-width of the graphs induced by each part and the mim-width between any two of the parts.
\begin{lemma}[\cite{BHP}]\label{mimmultijoin}
Let $G$ be a graph, and let $(X_1,\dotsc,X_p)$ be a partition of $V(G)$ such that $\mathrm{cutmim}_G(X_i,X_j) \le c$ for all distinct $i,j \in \{1,\dotsc,p\}$, and $p \ge 2$. Then \[\mathrm{mimw}(G) \le \max\left\{c\left\lfloor\left(\frac{p}{2}\right)^2\right\rfloor,\max_{i \in \{1,\dotsc,p\}}\{\mathrm{mimw}(G[X_i])\} + c(p-1)\right\}.\]
Moreover, if $(T_i,\delta_i)$ is a branch decomposition of $G[X_i]$ for each $i$, then we can construct, in $O(1)$ time, a branch decomposition $(T,\delta)$ of $G$ with $\mathrm{mimw}(T,\delta) \le \max\{c\lfloor(\frac{p}{2})^2\rfloor,\max_{i \in \{1,\dotsc,p\}}\{\mathrm{mimw}(T_i,\delta_i)\} + c(p-1)\}$.
\end{lemma}
A {\it clique} in a graph is a set of pairwise adjacent vertices. An {\it independent set} is a set of pairwise non-adjacent vertices.
A {\it dominating set} is a set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$.
For the second lemma we need Ramsey's Theorem. This theorem states that for every two positive integers $k$ and $\ell$, there exists an integer $R(k,\ell)$ such that every graph on at least $R(k,\ell)$ vertices contains a clique of size~$k$ or an independent set of size~$\ell$.
For $r\geq 3$ and $s,t\geq 1$, let $M(r,s,t)=(1+R(r+1,R(r+1,s)))^t$.
The next lemma generalizes a result of Chudnovsky, Spirkl and Zhong~\cite{CSZ} for the case where $r=3$ to $r\geq 1$. The proof of this generalization is analogous to the proof in~\cite{CSZ} for the case where $r=3$ (replace each occurrence of ``$4$'' in the proofs of Lemma~11 and~13 in~\cite{CSZ} by ``$r+1$'').
\begin{lemma}\label{l-dom}
For every $r\geq 1$, $s\geq 1$ and $t\geq 1$, a connected
$(K_{r+1},K_{1,s}^1,P_t)$-free
graph contains a dominating set of size at most $M(r,s,t)$.
\end{lemma}
\noindent
We are now ready to prove Theorem~\ref{t-new}, which we restate below. Its proof closely resembles the proof of Theorem~\ref{t-known2}.
Note that the constant bound depends on $r$, $s$ and $t$.
\medskip
\noindent
{\bf Theorem~\ref{t-new} (restated).}
{\it For every $r\geq 1$, $s\geq 1$ and $t\geq 1$, the mim-width of the class of $(K_r,K_{1,s}^1,P_t)$-free graphs is bounded and quickly computable.}
\begin{proof}
Let $G=(V,E)$ be a $(K_r,K_{1,s}^1,P_t)$-free graph for some $r\geq 1$, $s\geq 1$ and $t\geq 1$.
We may assume without loss of generality that $G$ is connected.
We use induction on $r$. If $r\leq 2$, then the statement of the theorem holds trivially.
Suppose that $r\geq 3$.
By Lemma~\ref{l-dom}, we find that $G$ has a dominating set $D$ of size at most
$M(r-1,s,t)$,
which is a constant, as $s$ and $t$ are fixed. Moreover,
we can find $D$ in polynomial time by brute force (or we can apply the $O(tn^2)$-time algorithm of~\cite{CSZ}). We let $p=|D|$.
We will partition the vertex set of $G$ with respect to $D$ as follows.
We first fix an arbitrary ordering $d_1,\ldots,d_p$ on the vertices of $D$.
Let $X_1$ be the set of vertices in $V\setminus D$ adjacent to $d_1$.
For $i\in \{2,\ldots,p\}$, let $X_i$ be the set of vertices in $V\setminus D$
adjacent to $d_i$, but non-adjacent to any $d_h$ with $h\leq i-1$.
Then $D$ and the sets $X_1,\ldots,X_p$ partition $V$ (some of the sets $X_i$ might be empty).
By construction, $d_i$ is adjacent to every vertex of $X_i$ for each $i\in \{1,\ldots,p\}$. As $G$ is $K_r$-free, this implies that
each $X_i$ induces a $(K_{r-1},K_{1,s}^1,P_t)$-free subgraph of $G$. We denote this subgraph by $G_i$. By the induction hypothesis, the mim-width of $G_i$ is bounded and quickly computable for every $i\in \{1,\ldots,p\}$.
Consider two sets $X_i$ and $X_j$ with $i<j$.
We claim that $\mathrm{cutmim}_G(X_i,X_j) < c=R(r-1,R(r-1,s))$.
Towards a contradiction, suppose that $\mathrm{cutmim}_G(X_i,X_j) \geq c$.
Then, by definition, there exist two sets $A= \{a_1,a_2,\dotsc,a_c\} \subseteq X_i$ and $B =
\{b_1,b_2,\dotsc,b_c\} \subseteq X_j$, each of size $c$, such that $\{a_1b_1,\ldots,a_cb_c\}$ is a set of $c$ edges with the property that $G$ does not contain any edges $a_ib_j$ for $i\neq j$ (note that edges $a_ia_j$ and $b_ib_j$ may exist in $G$).
As $G[X_i]$ is
$K_{r-1}$-free, Ramsey's Theorem tells us that the subgraph of $G$ induced by $A$ contains an
independent set $A'$ of size $c'=R(r-1,s)$. Assume without loss of generality that $A'=\{a_1,\ldots,a_{c'}\}$. Let $B'=\{b_1,\ldots,b_{c'}\}$. As $G[X_j]$ is $K_{r-1}$-free, the subgraph of $G$ induced by $B'$ contains an independent set $B''$ of size~$s$. Assume without loss of generality that $B''=\{b_1,\ldots,b_s\}$.
By construction, $d_i$ is adjacent to every vertex of $\{a_1,\ldots,a_s\}\subseteq X_i$ and non-adjacent to every vertex of $\{b_1,\ldots,b_s\}\subseteq X_j$.
Hence, $\{a_1,\ldots,a_s,b_1,\ldots,b_s,d_i\}$ induces a $K_{1,s}^1$ in $G$, a contradiction.
We conclude that $\mathrm{cutmim}_G(X_i,X_j) < c$.
We now apply Lemma~\ref{mimmultijoin} to find that the mim-width of $G-D$ is bounded and quickly computable.
Let $(T,\delta)$ be a branch decomposition for $G-D$ with mim-width~$k$.
We can readily extend $(T,\delta)$ to a branch decomposition $(T^*,\delta^*)$ for $G$ with mim-width at most $k + |D|= k + p$. Namely, we can obtain $T^*$ from $T$ by identifying one leaf of $T$ with a leaf of an arbitrary subcubic tree with $p+2$ leaves.
Recall that we found the set $D$ in polynomial time. We conclude that the mim-width of $G$ is bounded and quickly computable.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,701 |
Abstract: Previous studies have demonstrated that sheet formability is governed by the interlacing effect of pure stretch forming and pure deep drawing. In this paper, knitted fabric reinforced thermoplastic composite sheets, which exhibit excellent stretchability and drapeability, are investigated for their formability. Initially a new parameter, X, which describes the amount of stretching relative to drawing during forming is introduced. It is shown that sheet forming processes, specified by the use of various combinations of forming conditions, can be characterized by the parameter X. Finally, the overall formability of knitted fabric composite sheet is discussed with reference to the X-factor. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,213 |
Opening tomorrow, Wednesday, April 1, at 1:00 pm slt, is an exhibition entitled Line by Giovanna Cerise. Installed through the sim Otium (created by Franz Markstein, and about which I've written here), the objects and artworks appear in a variety of environments: in a traditional gallery space, in urban environments (along pathways, through corridors and so on, often blending in seamlessly with their surroundings), on the beach, hidden in the woods, and elsewhere. All the works are available for purchase.
As the title suggests, Giovanna explores the line, perhaps that simplest but most important of artistic gestures, and she demonstrates her remarkable ability to create convincing works in diverse media. Giovanna says of the installation, "Creation of a path-research on the infinite freedom hidden in two-dimensional and three-dimensional size. The line, with its lightness incisive, inspired the transposition of the complexity of the solid structures of some of my work in new areas, expression of pure essentiality."
Giovanna offers supplemental destinations to guide visitors through the sim, and given how much artwork is installed and how many places there are to explore — it's easy to miss things — I would recommend making use of them: Music, Dice, Otium, Sirene and Beach. But you'll certainly also want to wander about, discovering works here and there. Line will remain open indefinitely. While you're visiting, you might find the sim itself highly enjoyable, and, if so, please consider leaving a contribution for its continued support.
Posted by Ziki Questi at 11:32 PM No comments:
City Inside Out
Opening today, Thursday, March 26 at 1:00 pm slt, is City Inside Out, a major sim-wide installation by Haveit Neox. Focused on the struggles faced by those who are homeless in our major urban centers, the build is dazzling in its complexity, although, with its clear layout, not what one would call bewildering or confusing. "To someone without a home living on the streets, the bustling city becomes one united exterior," explains Haveit in his notes. "City Inside Out explores a world that lacks interiors. Entering any doorway opens onto yet another exterior." To the homeless, living on the streets is their never ending experience; their perception of life is from the outside, never able to enter or be accepted into interior spaces.
Towering hundreds of meters into the sky, City Inside Out unfolds on three levels: underground (be sure to walk through a narrow doorway to reach the larger space), on the surface, and in the air. "The eroding exteriors infuse themselves into the air space of the sky, onto the land of perpetual traffic, and below the land, completing the dominance of the harsh realities into every possible corner," adds the artist. (For today's opening, the landing point is here, up in the sky, but otherwise visitors should start at the ground level. "The LEA kiosk is on the ground, where I prefer people to start," says Haveit. "I'd like them to see ground levels first, then walk up to the sky level.") Visitors might discover a number of "hidden" places, such as the one in the photo immediately above, which Haveit calls The Dry Fields: "There is no life there. It's barren of opportunities."
Although Haveit's work often focuses on issues of social inequality, the initial inspiration for this build came from another source entirely. "I had recently seen pictures of the most ancient city in civilization called Catal Huyuk, in Turkey," he told me. "There were no streets, but only holes in the roofs for people to climb down. The rooftops were the streets. And this got me to thinking...why didn't people have roads? Were there dangers on ground level? Such as carnivorous beasts? That idea of not having doors or windows was really interesting to me. But the dangers in the 'streets' is what lead me to thinking about the homeless, who face this daily."
The windlight setting preferred by Haveit, Phototools- July Light 02, is seen here, and provides a beautifully foggy and misty experience. (Unfortunately, some bloggers and photographers who may have taken images before today depicted a black sky background, which is not at all what Haveit intended. The large megaprims surrounding the build were set on full bright and were affected by this ALM bug — I noticed the problem and alerted Haveit, who has now switched off full bright.) While City Inside Out is finished for now, there's more to come. "I set up a notecard at the landings to encourage people to participate their observations of the homeless," Haveit explains. "I would like to build one or two scenes from their texts, and post others on boards to share with visitors for phase 2. So there will be a few more additions to the city." The installation will remain on display through June 30.
Posted by Ziki Questi at 9:51 AM No comments:
Frisland to Close
Today, Charlie Namiboo, Frislanda Ferraris and Anabell Barzane announced that they will be closing Frisland (about which I originally wrote here when in opened a year ago), one of Second Life's most popular photogenic sims, in the coming weeks. Real life circumstances and the rise of the dollar against the Euro have simply brought about the necessity. But there's still time to enjoy Frisland — Charlie, Anna and Fris say it will probably be around mid-May before the sim packs up and disappears. Thanks to all three of them for having shared this tranquil, lovely space.
Posted by Ziki Questi at 6:41 PM No comments:
L'Arc en Ciel Revisited
It's been many months since I wrote about L'Arc en Ciel (read here from last July), the beautiful sim by Asa Vordun, and thanks to Ronin Undercroft I returned yesterday to explore it anew. Now embracing an entirely new design, the sim is even more striking than before — magnificently impressive and varied, with new things to see at every turn, beckoning both adventurers and photographers. (Click on any image to zoom in — these show the sim's default custom windlight setting.)
Asa's extraordinary skill at design is such that the sim contains woodlands, urban grittiness, farmland and more, all somehow merging seamlessly into a whole: here, it seems to make sense that we move from a bucolic pasture scene with horses grazing in a paddock to a string of city row houses with abandoned vehicles littering the associated street. All the while, beautiful shooting stars anoint the sky with long flashes of light. Somehow, L'Arc en Ciel seems far larger than a single sim, perhaps because visitors must walk about (no flying, but you would want to walk anyway), and because of the long geographic arc that one must travel to see the entire region.
The many small buildings on sim are exquisitely decorated, so that interiors (although none are pictured here) are just as splendid as the landscape, and small touches everywhere are delightful — I smiled as I encountered, near the end of the traveled path, a cat standing on two legs, looking up in wonder at the shooting stars. Given Asa's way of working, parts of the sim might have transformed even by the time you read this: "I keep on changing it all the time," she explains, adding that she prefers to keep the sim open even while revisions are underway. If you enjoy your visit, please consider leaving a contribution to help support the sim, and a guestbook awaits along the path.
Posted by Ziki Questi at 11:52 AM No comments:
For Relay for Life in 2014, artist Beq Janus created the installation Metamorphosis, inspired by the work of artist M. C. Escher, whose mathematically influenced works in various mediums featured transformations, logical puzzles and impossible situations. Although the build disappeared with the end of Relay for Life 2014, the artist was invited by the Quarry Hill School of Mines & Industries at New Babbage to reconstruct it in the sky — teleport here to visit. Working almost exclusively in white, black and gray, Beq's build unmistakably captures the feel of Escher's work, down to the feel of the woodcuts and his playful interlocking lizards. (Click on any image to zoom in.)
"My sim," explains Beq in the installation notes, "was inspired directly by a section of the 1939 woodcut Metamorphosis II — though the scene appears both in the earlier Metamorphosis I and the final Metamorphosis III, created towards the end of his career. Metamorphosis is itself a journey and the artwork 'morphs' from one tessellated shape to another from a simple chequered grid through lizards and hexagons into bees and fish then birds, capturing many of the themes of his early paintings. It then morphs back into blocks before becoming the view of Atrani [on the Amalfi coast]." The build covers the better part of the sim, so it's important to turn your draw distance up to fully capture the view, and to play with windlight settings — and be sure to peek into the telescope to see the artist's signature. Do take time to teleport below to explore Quarry Hill and other part of New Babbage, which are always worth a visit. (Thanks to Cat Horatio for a flickr post that drew my attention to Metamorphosis.)
Burnstein's Travels
Now open at the Flossify Gallery is an exhibition of photography by Jamisson Burnstein entitled Burnstein's Travels....Voyages in Second Life, primarily depicting landscapes but with a other subject matter as well, covering Jamie's visits to an extensive number of sims. And it's large exhibition, filling three spacious rooms as well as some additional areas; all images are available for purchase. (Personally, I found the gallery's proclivity to use fuschia and pink a little distracting.) The show continues through the end of March.
Misty Second Life
Now open at the SonderBar is an exhibition of photography by WuWai Chun entitled Misty Second Life. The beautiful, etherial images are indeed shrouded in mist, depicting, with a few exceptions, landscapes, waterscapes and cityscapes, captured with the photographer's keen sense of composition and distance. It's a small space, and WuWai has made the most of it, with images not only covering every nook and cranny of wall space, but also the ceiling. All the works are on sale, and proceeds benefit Feed a Smile, a non-governmental organization that helps feed children in Kenya. (If you don't arrive directly at the gallery on your first teleport, trying the landmark a second time or head upstairs and look for the gallery, and know too (if it is of any concern) that the SonderBar is an adult destination that caters to the BDSM lifestyle.)
Moon [ Imagination ]
The moon does indeed loom large at ARNICAR India's new sim, Moon [ Imagination ], hovering over the eastern horizon. Like ARNICAR's previous builds, it's a sim that mixes beauty and fantasy, landscape and detail into a delightful whole. The ground level, where one arrives, is built just off the water, with a walkway extending most of the length of the sim, connecting visitors with little vignettes or scenes — a wrecked roller coaster, a funny encounter with paparazzi, the gnarled tree at the base of the moon, and others. It's important to set your draw distance up as far as it can go, because you'll want to be able to see the entire landscape at a glance, including elements that are set in the sky, including a biplane navigating through a field of airborne boulders.
But there's more than first meets the eye. Click on the front of the time travel device near the landing point (you might need to be close), which serves as a teleporter. From there, you have a choice of three additional destinations: Earth, House and Planet Station. You can spot the house far overhead in the air — a quirky home on a huge boulder (bottom image). And earth is, quite charmingly, contained inside a terrestrial globe, where a streetcar and other items are reflected in empty space (image immediately below). At the planet station (not pictured), we're off in the heavens, surrounded by planets and the constellations.
In all of the four areas of the sim, opportunities for photography abounds (these images show the sim's default windlight setting, but others work well too), and there are plenty of cozy spots for couples to relax or pose — even a horse you can ride together around the ground level. ARNICAR opened the sim about three weeks ago, and told me this morning that she's not certain how long it will stay around, so be sure to visit soon, and please consider offering a contribution at one of the various tip jars.
Lobby cam Preview
Today, Bryn Oh announced the opening date of her forthcoming sim-wide installation at Immersiva, Lobby cam, which will be revealed on Sunday, March 29. Bryn has often incorporated small glimpses of her "real life" artwork in her builds, but in this video they're front and center for the first two minutes, showing us the vivid connections between her artwork in real and virtual mediums.
The Trace Reopens
Kylie Jaxxon shared this afternoon that she has reopened The Trace, a much beloved sim that has been one of the most visited and photographed by explorers, couples and seekers of solitude. It's a sim that changes with the seasons — with a complete redesign, not just a change of color — and Kylie was just taking the wraps off an autumn version a few months ago when she suddenly announced that exceptional real life circumstances would necessitate an immediate closure.
Happily the sim is now back, and warm temperatures have arrived — "a little reminiscent of the previous summer," says Kylie, but distinctively its own. The beach scene isn't the sort of beach that one sees frequently in Second Life — the common surfing or tropical scenes — but is rather a flat wetlands with marshy areas, where the waves quietly drift in to shore, giving the entire build a calm, meditative look. There are pervasive and haunting cries in the air from the gulls that lazily swoop about, and birds nest in large numbers on the shore.
The center of the island comprises a quaint row of beach houses and cottages; a couple of the inhabitants are out fishing on The Trace's northeast corner. If you're searching for tranquility, this just might fit the bill. Please consider leaving a contribution at the tip jar located near the landing point.
"I'm smiling already and I only just got here!" remarked Maya Paris as she and I converged on Sparkys, an installation by Romy Nayar that opened yesterday at MetaLES. And it's fabulously engaging — along with Maya, I have had a delightful time there today with Honour McMillan, Cica Ghost, Giovanna Cerise and Romy herself, just playing and having fun. One arrives at a world that appears to be only white, black and gray — but it seems that the residents have discovered something new: color, which they harvest from odd little flying animals, the sparkies (or sparkys). To get around, visitors need to follow a pre-established path through the city-on-stilts by clicking on elevators, balloons and other modes of transport. (If you reach a platform that doesn't seem to have a way to leave, just wait, and something will show up to offer you a ride.)
"The story is," Romy explained to me (slightly edited for translation), "that a doctor has invented a new substance that makes color — because everything was white — and he can produce the colors from the sparkys that you will meet in the forest. And everybody in the city is trying to give color to the city — but they have a great deal of work, so you can help if you want." And indeed, you'll spot many of the city's inhabitants working with colors — or at least trying to figure out what to do with them. The lady in the image above distributes the paint, so be sure to connect with her during your visit. (The forest, by the way, is the area with the curious dark trees, and you'll spot the sparkies there, being tended by a watcher — you can get a glimpse of it in the first image at the uppermost center.)
To help paint, wear the object you'll receive, click on it to set your parameters, and then go into mouselook to color things. (Update: You have to join the MetaLES group in order to paint.) Nothing's permanent — the paint washes away after a few minutes, so you can keep busy for a long time. (By the way, the paint is prim-based, so if there's too much coloring going on the sim can reach its object limit. Just wait a minute or two to continue.) This is simply one of the best art installations to open in a while — playful, imaginative, and beautifully constructed. Sparkys will remain on display at MetaLES through the month of April.
Posted by Ziki Questi at 3:49 PM 11 comments:
A few days ago, Torley teleported me to Everwinter, a post-apocalyptic theme park created by Lauren Bentham that replaces the previous build on Elven Mist, historic Bentham Forest. And quite a transformation it is: obscured by mist and fog and a sort of sepia-toned atmospheric haze, the theme park has seen better days. Littered with broken rides, broken glass, and, well, broken everything, the build features plenty of places to hang out (dilapidated sofas, a tire swing, rusty ride seats and so on). A few creepy children are out playing, slipping in circles or just eerily standing, many wearing gas masks (and bringing to mind "The Empty Child" episode of Doctor Who, even if coincidental).
Lauren made use of materials from a number of creators, especially some new designs by Jaimy Hancroft — "I wanted to do a build like this for a long time, and when I saw her theme park bits I couldn't resist," she explained — and Jaimy's works happen to be available at the current manifestation of The Arcade. The photogenic Everwinter won't disappear anytime soon: "It's permanent," Lauren assured me. You'll receive some sim rules as you arrive (no face lights, please), and a few tip jars are available in case you'd like to lend support.
Posted by Ziki Questi at 4:41 PM 1 comment:
When life gives you apples...run!
Now open at LEA6 as the final installment of the Linden Endowment for the Arts Full Sim Art Series (the sim, no worries, will continue to offer other artistic opportunities) is Rebeca Bashly's When life gives you apples...run! "Looking at various myths, legends and fairy tales, apples seem to be pretty misfortunate for women," Rebeca says in her exhibition notes. "When an apple appears in a story, you know that something will go bad. From Eve through Greek mythology to Snow White, there was always a catch with an apple. It is beautiful, delicious, tempting, seductive. A perfect disguise for all bad that can come. I use it as a symbol for the monstrosities that woman too often don't recognize as such in its early stages. This installation is about domestic violence and eating disorders — on first sight two very different things, but violence against someone and violence against oneself are the same thing, a violence."
And an eaten apple is precisely where we find ourselves as we arrive, although you might not realize it unless you zoom way out. (I've had repeated problems with the mesh of the apple not rezzing on arrival, so try right-clicking the general area, which should force it to appear.) About 95 meters high from its base to the tip of its stem, the apple is an extraordinary piece of mesh sculpture that brings to mind Rebeca's Colossus of Rhodes, created for Fashion for Life in 2013. As visitors wind their way upwards and through it, worm-like (just follow the path), they encounter two points at which they teleport away to second scenes: No Place Like Home, with an emphasis on domestic violence (image above, with a heart bursting apart a house over a highway); and Doll House, which focuses on anorexia nervosa and bulimia nervosa (lowest image). At each location, a brief story awaits. Positioned in the center of the apple between the two story locations is a prominent sculpture, Seed2 (image below), featuring two women, naked and intertwined.
When you make it the top of the apple (there are a couple spots where I fell through the floor — just keep going), you'll step out at the pinnacle, where a tremendous view of the apple awaits. This is a poignant work, heartfelt and personal, and a fitting end to the Full Sim Art Series, which has been administered by the University of Western Australia (UWA) in partnership with the LEA. When life gives you apples...run! will remain on display through March.
Opening tomorrow, Monday, March 9, at 12 pm slt, is a new sim-wide build, Ruins, by Cica Ghost. (As I write this, though, Cica has just opened the sim, so it's possible to visit for an unofficial advance peek.) Only the blackbirds and wildflowers remain to inhabit the ruins of the once active city, its brick edifices having collapsed to reveal the deserted worlds within. While we can easily discern where some buildings stood — a few still have a floor or two intact — many columns stand alone or in groups, only vaguely suggesting some former structure.
To my mind, the brick ruins evoke a nineteenth-century city, perhaps a gritty industrial revolution town, built long before modern steel and glass, but of course Cica intended no such deliberate connection. Perhaps the iron cables strung between some of the columns have helped keep them steady and erect over the decades. Trees grow inside what were houses; flowers — now shriveled and dead — populate a bathtub. But perhaps we do see some signs of life: the weathered wooden planks between buildings suggest that someone has been here — at least since things fell to ruin — and, in a kitchen, water is running, and a pot of pasulj — Serbian white bean stew — is on the stove, an orange balloon floating languidly overhead.
If you're not running a viewer that automatically changes your environmental settings, you're likely to miss out Cica's custom windlight, shown here. The ruins are sure to be a favorite location for photographers and will probably remain on display for about a month. Please consider leaving a contribution near the landing point to support this and future work, or visit Cica's shop (there's a landmark giver on the sim) to pick up copies of some of her other artworks.
Posted by Ziki Questi at 4:52 PM 2 comments:
FreeWee's Laboratory v.8.0: Music, Myth, Magic, Light, Shadows, Physics
The title of FreeWee Ling's installation at LEA27 says it all: FreeWee's Laboratory v.8.0: Music, Myth, Magic, Light, Shadows, Physics. Over the years, her artwork has touched on all those areas and more — she creates with remarkable versatility and prolific creativity, to the point where her work might not be immediately recognizable as her own. She's also been an ardent champion of the virtual arts in general, having worked extensively with the University of Western Australia, where she's now enjoying a fellowship in real life. The presentation at LEA27 is almost like a retrospective, taking us through much of FreeWee's oeuvre — and it's likely to change over time as she continues to add and refine material.
Much of her art is interactive — often playful or humorous — and invites physical exploration. In the image above, we're inside the Nanotech Platform, where a linear accelerator tube (on the right) fires a volley of ten nanoprims, and detectors down the line inform us as to whether or not they were seen. I'm standing at the large nano rezzer sphere, which rezzes a single nano. Nearby, in another building, is the Theatrum Instrumentorum, containing sonic works, including an array of musical instruments (some playable) and creations developed in collaboration with Oriscus "Oz" Zauberflote, with whom FreeWee works as Kithara Associates.
And then there are works that place avatars into poses, sometimes capturing the camera. In the image immediately above (zoom in to see me in a box), I'm in one of the stops in A Time Away — other locations, to which we're transported automatically and dropped into place, include a sports car ride through a tunnel, a swim in a pond, a ski slope, some sort of egg capsule, and a ride on a space shuttle. As FreeWee says, it's "a kind of amusement park ride. Imagine a roller coaster that suddenly turns into a carousel or bumper cars or a sideshow magic act. That's basically how my mind works."
But to my mind, FreeWee's most interesting endeavors investigate light. Be sure to spend lots of time in the Shadow Lab (image below), where you're going to need to have advanced lighting turned on, with sun/moon and projector shadows as well. The image doesn't capture the experience, as the projected light is in motion, creating fascinating effects that handsomely show off Second Life's capabilities. In the image immediately above at the gladiatrix projection model, texture-less prims are brought to life by projected light. And there's much more, enough to keep you busy for a long time, or for return trips. The Laboratory will remain on display through the end of June.
FreeWee's Laboratory v.8.0: Music, Myth, Magic, Li...
Elle Ellsmere at LEA5
Hills Gallery
Spring in Frisland | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,875 |
{"url":"https:\/\/www.semanticscholar.org\/paper\/On-the-Hilbert-eigenvariety-at-exotic-and-CM-weight-Betina-Deo\/d67ccb7fc654f7c63d38f17f2c98331997c8800b","text":"# On the Hilbert eigenvariety at exotic and CM classical weight 1 points\n\n@article{Betina2018OnTH,\ntitle={On the Hilbert eigenvariety at exotic and CM classical weight 1 points},\nauthor={Adel Betina and Shaunak V. Deo and Francesc Fit'e},\njournal={arXiv: Number Theory},\nyear={2018}\n}\n\u2022 Published 29 June 2018\n\u2022 Mathematics\n\u2022 arXiv: Number Theory\nLet $F$ be a totally real number field and let $f$ be a classical cuspidal $p$-regular Hilbert modular eigenform over $F$ of parallel weight $1$. Let $x$ be the point on the $p$-adic Hilbert eigenvariety $\\mathcal E$ corresponding to an ordinary $p$-stabilization of $f$. We show that if the $p$-adic Schanuel Conjecture is true, then $\\mathcal E$ is smooth at $x$ if $f$ has CM. If we additionally assume that $F\/\\mathbb Q$ is Galois, we show that the weight map is \\'etale at $x$ if $f$ has either\u2026\u00a0Expand\n1 Citations\nOn generalized Iwasawa main conjectures and $p$-adic Stark conjectures for Artin motives\nWe formulate a cyclotomic main conjecture and an extra zeros conjecture for general p-stabilized Artin representations, which are shown to imply the p-part of the Tamagawa number conjecture for ArtinExpand\n\n#### References\n\nSHOWING 1-10 OF 42 REFERENCES\nOn the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve\n\u2022 Mathematics\n\u2022 2018\nWe prove that the cuspidal $p$-adic eigencurve $C_{cusp}$ is etale over the weight space at any classical weight $1$ Eisenstein point $f$. Further we show that $C_{cusp}$ meets transversely at $f$Expand\nGeometry of the eigencurve at CM points and trivial zeros of Katz p-adic L-functions\n\u2022 Mathematics\n\u2022 2019\nThe primary goal of this paper is to study the geometry of the p-adic eigencurve at a point f corresponding to a weight one theta series irregular at p. We show that f belongs to exactly three orExpand\nSTARK POINTS AND $p$-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE\n\u2022 Mathematics\n\u2022 Forum of Mathematics, Pi\n\u2022 2015\nLet $E$ be an elliptic curve over $\\mathbb{Q}$, and let ${\\it\\varrho}_{\\flat }$ and ${\\it\\varrho}_{\\sharp }$ be odd two-dimensional Artin representations for which ${\\it\\varrho}_{\\flat }\\otimesExpand On the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image We show that the p-adic eigenvariety constructed by AndreattaIovita-Pilloni, parameterizing cuspidal Hilbert modular eigenforms defined over a totally real field F , is smooth at certain classicalExpand On Nearly Ordinary Hecke Algebras for$GL(2)$over Totally Real Fields Since this work is a continuation of our previous paper [8], we shall suppose the familiarity on the reader's part with the result and the notation in [8]. Especially we fix a rational prime p and aExpand Iwasawa Theory for Artin Representations, I \u2022 Mathematics \u2022 2018 This article is the first of a pair of articles dealing with the Iwasawa theory of modular forms of weight 1 and, more generally, of Artin representations satisfying certain conditions. The mainExpand Les Vari\\'et\\'es de Hecke-Hilbert aux points classiques de poids$1$We show that the Eigenvariety attached to Hilbert modular forms over a totally real field$F$is smooth at the points corresponding to certain classical weight one theta series and we give a preciseExpand On Galois representations associated to Hilbert modular forms. In this paper, we prove that, to any Hilbert cuspidal eigenform, one may attach a compatible system of Galois representations. This result extends the analogous results of Deligne and Deligne\u2013SerreExpand Overconvergent Hilbert modular forms \u2022 Mathematics \u2022 2005 <abstract abstract-type=\"TeX\"><p>We generalize the construction of the eigencurve by Coleman-Mazur to the setting of totally real fields, and show that a finite slope Hilbert modular eigenform can beExpand Anti-cyclotomic Katz$p$-adic$L\\$-functions and congruence modules\n\u2022 Mathematics\n\u2022 1993\n\u2014 The purpose of this paper is to prove the divisibility of the characteristic power series of the congruence module of a Hida \/?-adic family of theta series coming from a CM-field (with fixedExpand","date":"2021-11-29 05:53:38","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\": 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\": 0.891411542892456, \"perplexity\": 796.7298555227746}, \"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-2021-49\/segments\/1637964358688.35\/warc\/CC-MAIN-20211129044311-20211129074311-00468.warc.gz\"}"} | null | null |
\section*{Introduction}
Let $X$ be a complex contact manifold. By Darboux theorem, a local
model of $X$ is an open subset of the projective cotangent bundle $P^*M$
of a complex manifold $M$. Let $\she_{P^*M}$ be the sheaf of
microdifferential operators on $P^*M$. A microdifferential algebra ($\she$-algebra, for short)
on
$X$ is a sheaf of $\C$-algebras locally isomorphic to $\she_{P^*M}$.
In the strict sense, to quantize $X$ means to endow it with an
$\she$-algebra. This might not be possible in
general. However, Kashiwara~\cite{Kas96} proved that $X$ is endowed
with a canonical $\she$-algebroid $\stke_X$. This means the
following.
To an algebra $A$ one associates the linear category with one object
and elements of $A$ as its endomorphisms. Similarly, to a sheaf of algebras on $X$
one associates a linear stack.
An $\she$-algebroid on $X$ is a $\C$-linear stack locally equivalent to one associated with an
$\she$-algebra.
Having to deal with an algebroid instead of an algebra is not very
limiting. For example, one can consider the stack of modules $\stkMod(\stke_X)$
and in particular regular holonomic modules attached to Lagrangian
subvarieties (see \cite{Kas96,DS07} and~\cite{DP05} for the involutive case).
The algebroid $\stke_X$ is endowed with an anti-involution,
corresponding to the formal adjoint of microdifferential operators.
Moreover, the graded algebroid associated to its order filtration is trivial.
It is shown in~\cite{Pol07} that $\stke_X$ is unique among such $\she$-algebroids.
In this paper, we consider $\she$-algebroids with no extra structures, hence
including twisted quantizations of $X$, i.e.~filtered $\she$-algebroids whose associated
graded algebroid is non trivial (see~\cite{Pol11}).
In fact, even more generally, we consider stacks of twisted $\she$-modules, i.e.~stacks locally equivalent to a stack of modules over an $\she$-algebra.
In Theorems~\ref{thm:Emoritatrivial} and~\ref{thm:class}, and Corollary~\ref{cor:class}, we prove the following classification results, giving an explicit geometric realization of the isomorphisms in (iii) and (iv) below.
\begin{itemize}
\item[(i)]
Two $\she$-algebroids are equivalent if and only
if they are Morita equivalent, i.e.~their stacks of modules are equivalent.
\item[(ii)]
Any stack of twisted $\she$-modules is globally equivalent to the stack of modules
over an $\she$-algebroid.
\item[(iii)]
The set of equivalence classes (resp. Morita classes) of $\she$-algebroids is canonically isomorphic to $H^2(Y;\C^\times_Y)$, for $Y$ the symplectification of $X$.
\item[(iv)]
The group of invertible $\she$-bimodules is isomorphic to $H^1(Y;\C^\times_Y)$.
\end{itemize}
To obtain our results, we use techniques of microlocal calculus, non commutative cohomology and Morita theory for linear stacks.
\smallskip
In Section~\ref{se:nonab} we collect, without proofs, the main facts of non commutative cohomology we need to prove our results. Note that cohomology with values in non commutative groups was already used in~\cite{Bou99} to classify $\she$-algebras, and cohomology with values in 2-groups is used in~\cite{Pol08,Pol11} for the classification of algebroids.
In Section~\ref{se:alg} we give the basics of the theory of algebroids. The existence of a canonical deformation quantization algebroid on a complex symplectic manifold is proved in~\cite{PS04} (see also~\cite{Kon01}). The general theory of deformation quantization modules for Poisson manifolds is developed in~\cite{KS10}.
In Section~\ref{se:Mor}, we detail Morita theory for linear stacks. In particular, the notion of Picard good stacks allows us to recover results of~\cite{Low08}. Morita theory for linear categories is developed in~\cite{Mit65,Mit85}. The case of stacks of modules over sheaves of algebras is discussed in~\cite{KS06} (see also~\cite{DP03}).
In Section~\ref{se:mic} we recall some results from the theory of microdifferential operators. In particular, we detail the proof of Theorem~\ref{thm:Eeloc}, due to Kashiwara, on the structure of invertible bimodules. This allows us to prove the key Theorem~\ref{thm:localEPicardGood}.
In Section~\ref{se:results} we prove our main results. For symplectic manifolds, or more generally for Poisson manifolds, some results related to ours appeared in the literature: on a complex symplectic manifold, deformation quantization algebroids with anti-involution and trivial graded have been classified up to equivalence in~\cite{Pol08} (see also \cite{BGNT07,BGNT11} for the possibly twisted case), whereas Morita-type results for deformation quantization algebras are obtained in~\cite{Bur02,BW04,BDW09} for real Poisson manifolds, and in~\cite{Yek10} in the algebraic setting.
In Appendix~\ref{se:coc} we recall the cocycle description of algebroids and functors between them.
\subsection*{Convention} In this text, when dealing with categories and stacks, we will
not mention any smallness condition (with respect to a given universe), leaving to the
reader the task to make it precise when necessary.
\subsection*{Acknowledgments}
We express our gratitude to Masaki Kashiwara for useful discussions and
for communicating us Theorem~\ref{thm:Eeloc}.
\section{Non commutative cohomology}\label{se:nonab}
We are interested in classifying
$\she$-algebroids and stacks of $\she$-modules.
Thanks to the existence of a canonical $\she$-algebroid,
this amounts to classify stacks locally
equivalent to a given one. To this end, we recall here some
techniques of cohomology with values in a stack of
$2$-groups. References are made to~\cite{Bre94} (and to the references therein), and
to \cite[\S1.4]{Del73} for the strictly commutative case (see also~\cite{AN09} for an explicit
description in terms of crossed modules). We follow the presentation of~\cite{Pol08}.
\medskip
Let $X$ be a topological space (or a site).
\subsection{Stacks}\label{se:linearstacks}
A prestack $\stkc$ on $X$ is a lax presheaf of categories.
Lax in the sense that for a chain of three open
subsets $W\subset V\subset U$ the restriction functor $\cdot |_W \colon \stkc(U)\to \stkc(W)$
coincides with the composition $\stkc(U)\to[\cdot |_V] \stkc(V)\to[\cdot |_W] \stkc(W)$ only up to
an invertible transformation (such transformations satisfying a natural cocycle
condition for chains of four open subsets).
For $\objc,\objc'\in\stkc(U)$, denote by $\shHom[\stkc](\objc,\objc')$
the presheaf on $U$ given by $U \supset V\mapsto
\Hom[\stkc(V)](\objc|_V,\objc'|_V)$.
One says that $\stkc$ is a separated prestack if $\shHom[\stkc](\objc,\objc')$
is a sheaf for any $\objc,\objc'$.
A stack on $X$ is a separated prestack satisfying a natural descent
condition, analogue to that for sheaves.
Given a stack $\stkc$, we denote by $\pi_0(\stkc)$ the sheaf associated to the presheaf
$X \supset U\mapsto \{\text{isomorphism classes of objects in }\stkc(U)\}$.
Let $\varphi\colon Y \to X$ be a continuous map (or a morphism of sites). For $\stkd$ a stack
on $Y$ and $\stkc$ a stack on $X$, we denote by $\oim \varphi \stkd$ and $\opb \varphi \stkc$ the
stack-theoretical direct and inverse image, respectively.
Recall that $\opb \varphi \stkc$ is the stack on $Y$ associated to the separated prestack
$\varphi^{+}\stkc$, defined on an open subset $V \subset Y$ by the category
\begin{align*}
\operatorname{Ob}(\varphi^{+}\stkc (V)) &= \DUnion_{U\supset \varphi(V) \atop U \text{
open} }\operatorname{Ob}(\stkc (U)),\\
\Hom[\varphi^{+}\stkc (V)](\objc_{U},\objc_{U'}) &= \Gamma(V,
\opb \varphi \shHom[\stkc](\objc_U|_{U \cap U'},\objc_{U'}|_{U \cap U'})).
\end{align*}
One checks that there is a natural equivalence (in fact, a $2$-adjunction)
\begin{equation}\label{eq:2adj}
\oim \varphi \stkFun(\opb \varphi \stkc,\stkd) \equi[]
\stkFun(\stkc,\oim \varphi \stkd).
\end{equation}
Hence there are adjunction functors
$$
\stkc \to \oim \varphi \opb \varphi \stkc, \qquad \opb \varphi \oim \varphi \stkd \to \stkd.
$$
By using the left-hand side functor, one gets an isomorphsim of sheaves
\begin{equation}\label{eq:inv-pi_0}
\opb \varphi \pi_0(\catc)\isoto \pi_0(\opb \varphi\catc).
\end{equation}
\subsection{Stacks of $2$-groups}
Let $\stkc$ be stack on $X$.
Denote by $\stkAut(\stkc)$ the stack
whose objects are auto-equivalences, and whose
morphisms are {\em invertible} transformations.
Proposition~\ref{pr:patch} for
$\stkc_i=\stkc'_i=\stkc|_{U_i}$ describes how to patch objects and morphisms
of $\stkAut(\stkc)$.
For $\shu=\{U_{i}\}_{i\in I}$ an open cover of $X$, set
\[
U_{ij} = U_{i} \cap U_{j},\quad U_{ijk} = U_{i} \cap U_{j} \cap
U_{k},\quad\text{etc.}
\]
With notations as in~Proposition~\ref{pr:patch}, let $H^1(\shu;
\stkAut(\stkc))$ be the pointed set of equivalence classes of pairs
$\pair{\functf_{ij}}{\transfa_{ijk}}{ijk\in I}$ satisfying the cocycle
condition \eqref{eq:alpha}, modulo the coboundary relation described by
\eqref{eq:alpha2}. One sets
\begin{equation}\label{eq:cohAutA}
H^1(X; \stkAut(\stkc)) = \ilim[\shu]H^1(\shu; \stkAut(\stkc)).
\end{equation}
By Proposition~\ref{pr:patch}, it follows
\begin{corollary}\label{cor:h1aut}
The pointed set $H^1(X; \stkAut(\stkc))$ is in bijection with the
pointed set of equivalence classes of stacks locally equivalent to $\stkc$.
\end{corollary}
Let us recall how to make the construction \eqref{eq:cohAutA}
functorial.
\medskip
A $2$-group is a category endowed with a group structure both on objects and
on morphisms. More precisely, a category $\catg$ is a $2$-group if it is a
groupoid (i.e.~all morphisms are invertible) and it has a structure
$(\stkg,\otimes,\mathbf{1})$ of monoidal category (i.e.~endowed
with the categorical analogue of a unital product) which is rigid (i.e.~each
object admits the categorical analogue of an inverse with respect to
$\otimes$). Functors of $2$-groups and transformations between them are
monoidal functors and monoidal transformations.
A stack of $2$-groups is a stack $\stkg$ whose sections $\stkg(U)$ are
$2$-groups, whose restrictions are functors of $2$-groups and whose
transformations between restriction functors are monoidal. Functors of stacks
of $2$-groups are functors of monoidal stacks.
Recall that one sets $\pi_1(\stkg) = \shHom[\stkg](\mathbf{1},\mathbf{1})$. This and
$\pi_0(\stkg)$ are sheaves of groups, the former being necessarily commutative.
Any functor of stacks of $2$-groups induces a group morphism at the level of $\pi_1$ and $\pi_0$.
\begin{example}\label{exa:g01}
For $\shg$ a sheaf of groups, denote by $\shg[0]$ the stack obtained by
enriching $\shg$ with identity arrows, and by $\shg[1]$ the stack of right
$\shg$-torsors. Then $\shg[0]$ is a stack of $2$-groups, and $\shg[1]$ is a
stack of $2$-groups if and only if $\shg$ is commutative.
\end{example}
Another example of stack of $2$-groups is given by $\stkAut(\stkc)$ for
$\stkc$ a stack.
Let $\stkg$ be a stack of $2$-groups and $\shu$ an open cover of $X$.
One can extend as follows the construction~\eqref{eq:cohAutA}, where one should
read ``$\otimes$'' instead of ``$\circ$'' in all diagrams in Appendix~\ref{se:cocy}.
A $1$-cocycle with values in $\stkg$ is a pair $\pair{\functf_{ij}}{\transfa_{ijk}}{ijk\in I}$ with
$\functf_{ij}\in\stkg(U_{ij})$ and $\transfa_{ijk}\in
\Hom[\stkg](\functf_{ik},\functf_{ij}\tens\functf_{jk})$ satisfying
\eqref{eq:alpha}. Two such 1-cocycles $\pair{\functf_{ij}}{\transfa_{ijk}}{ijk\in
I}$ and $\pair{\functf'_{ij}}{\transfa'_{ijk}}{ijk\in I}$ are cohomologous if
there is a pair \,
$\pair{\functg_i}{\transfb_{ij}}{ij\in I}$ with
$\functg_i\in\stkg(U_i)$ and $\transfb_{ij}\in
\Hom[\stkg](\functf'_{ij}\tens\functg_{j}, \functg_{i}\tens\functf_{ij})$
satisfying \eqref{eq:alpha2}.
The first cohomology pointed set of $\stkg$ on $X$ is given by
\[
H^1(X; \stkg) = \ilim[\shu]H^1(\shu; \stkg),
\]
where $H^1(\shu; \stkg)$ denotes the pointed set of equivalence classes of
$1$-cocycles on $\shu$, modulo the relation of being cohomologous.
One can also define cohomology in degree 0 and $-1$.
This construction is functorial in the sense that short exact
sequences of 2-groups induce long exact cohomology sequences (in a sense to be made
precise). In
particular, equivalent 2-groups have isomorphic cohomologies.
With the notations as in Example~\ref{exa:g01} one has
\begin{equation}\label{eq:HiG}
H^1(X; \shg[i]) \simeq H^{1+i}(X; \shg)
\quad\text{for }i=0,1,
\end{equation}
where the pointed set $H^1(X; \shg)$ is defined by Cech cohomology and $H^2(X;
\shg)$ is considered only for $\shg$ abelian.
\subsection{Crossed modules}
A crossed module is the data
\[
\shg^\bullet = (\shg^{-1} \to[d] \shg^0,\ \delta)
\]
of a complex of sheaves of groups and of a left action $\delta$ of $\shg^0$ on
$\shg^{-1}$ such that for any $f\in\shg^0$ and $a\in\shg^{-1}$
\[
d \circ \delta(f) =\ad(f) \circ d, \qquad
\delta\bigl(d(a)\bigr)=\ad(a),
\]
where $\ad(a)(b) = a b a^{-1}$. A morphism of crossed modules is a morphism
of complexes of sheaves of groups compatible with the left actions.
There is a functorial way of associating to a crossed module a stack of
$2$-groups as follows. For $\shg^\bullet$ a crossed module one denotes by $[\shg^\bullet]$ the
stack of $2$-groups associated to the separated prestack whose objects on $U\subset X$
are sections $f\in\shg^{0}(U)$ and whose morphisms $f\to f'$ are sections
$a\in \shg^{-1}(U)$ satisfying $f' = d(a) f$. Then $[\shg^\bullet]$ is a stack of
$2$-groups, with monoidal structure given by $f\tens g=fg$ at the level of
objects and by $a\tens b = a\delta(f)(b)$ at the level of morphisms, for
$a\colon f\to f'$ and $b\colon g\to g'$.
One checks that there are isomorphisms of groups
$$
\pi_i([\shg^\bullet])\simeq H^{-i}(\shg^\bullet), \qquad i=0,\,1
$$
and, with the notations and conventions as in Example~\ref{exa:g01}, equivalences
of stacks of 2-groups
\[
\bigl[\shg[i]\bigr]\equi[]\shg[i], \qquad i=0,\,1.
\]
\subsection{Strictly abelian crossed modules}
Denote by $\catd^{[-1,0]}(\Z_X)$ the full subcategory of the
derived category of sheaves of abelian groups whose
objects have cohomology concentrated in degree $[-1,0]$. Consider a complex of
abelian groups $\shf^\bullet \in \catc^{[-1,0]}(\Z_X)$ as a crossed module with
trivial left action. Then the functor $\shf^\bullet \mapsto [\shf^\bullet]$
factorizes through $\catd^{[-1,0]}(\Z_X)$ and one has
\begin{equation}\label{eq:h1commcross}
H^1(X;\shf^\bullet) = H^1(X;[\shf^\bullet]).
\end{equation}
Let $\psi\colon X \to Y$ be a continuous map (or a morphism of sites).
The inverse and direct image of stacks of $2$-groups are again stacks of $2$-groups, and one has
\begin{equation}\label{eq:roim}
\opb\psi[\shg^\bullet] \equi[] [\opb\psi\shg^\bullet] \qquad
\oim\psi[\shf^\bullet] \equi[] [\tau_{\leq 0}\roim\psi\shf^\bullet],
\end{equation}
where $\tau_{\leq 0}$ is the truncation functor. In particular, for a commutative sheaf of groups
$\shf$, one gets
\begin{equation}\label{eq:pi-roim}
\pi_i(\oim\psi (\shf[1]))\simeq R^{1-i}\oim\psi\shf, \qquad i=0,\,1.
\end{equation}
\section{Algebroids}\label{se:alg}
Mitchell~\cite{Mit72} showed how algebras can be replaced by linear categories.
Similarly, sheaves of algebras can be replaced by linear stacks.
An algebroid is a linear stack locally equivalent to an algebra.
This notion, already implicit in~\cite{Kas96}, was introduced in~\cite{Kon01}
and developed in~\cite{DP05} (see also \cite[\S2.1]{KS10} and \cite{DK11}).
It is the linear analogue of the notion of gerbe from~\cite{Gir71}: an
algebroid is to a gerbe as an algebra is to a group.
\medskip
Let $X$ be a topological space (or a site), and $\shr$ a sheaf of commutative
rings on $X$.
\subsection{Linear stacks}\label{sse:linearstacks}
A stack $\stkc$ on $X$ is called $\shr$-linear ($\shr$-stack, for short) if for any
$\objc,\objc'\in\stkc(U)$ the sheaf $\shHom[\stkc](\objc,\objc')$ is endowed with an
$\shr|_U$-module structure compatible with composition. In particular,
$\shEnd[\stkc](\objc)$ has an $\shr|_U$-algebra structure with product given
by composition. A functor between $\shr$-linear stacks is called $\shr$-linear
($\shr$-functor, for short) if it is $\shr$-linear at the level of morphisms, while no
linearity conditions are required on transformations.
One says that two $\shr$-stacks are equivalent if they
are equivalent through an $\shr$-functor. This implies that the
quasi-inverse is also an $\shr$-functor. We denote by $\equi$ this
equivalence relation.
The center $Z(\stkc)$ of an $\shr$-stack $\stkc$ is the sheaf
of endo-transformations of
the identity functor $\id_\stkc$. It has a natural structure of sheaf of commutative
$\shr$-algebras. Note that a stack $\stkc$ is $\shr$-linear if and only if it is $\Z$-linear and its
center is an $\shr$-algebra.
If $\stkc$ is an $\shr$-stack, then its opposite stack $\stkc^\op$ is again an $\shr$-linear.
For $\stkd$ another $\shr$-stack, denote by
$\stkFun[\shr](\stkc,\stkd)$ the $\shr$-stack whose objects are
$\shr$-functors and whose morphisms are transformations. The tensor product
$\stkc\tens[\shr]\stkd$ is the $\shr$-stack associated with the prestack
$U\mapsto \stkc(U)\tens[\shr(U)]\stkd(U)$ whose objects are pairs in
$\stkc(U)\times\stkd(U)$, with morphisms
\[
\Hom[{\stkc(U)\tens[\shr(U)]\stkd(U)}]((\objc,\objd),(\objc',\objd'))
= \Hom[\stkc(U)](\objc,\objc')
\tens[\shr(U)]
\Hom[\stkd(U)](\objd,\objd').
\]
\begin{lemma}\label{lem:stktensadj}
If $\shr$ is an $\shs$-algebra and $\stke$ an $\shs$-stack, then
\[
\stkFun[\shs](\stkc\tens[\shr]\stkd,\stke) \equi
\stkFun[\shr](\stkc,\stkFun[\shs](\stkd,\stke)).
\]
(This is in fact a $2$-adjunction.)
\end{lemma}
Let $\varphi\colon Y \to X$ be a continuous map (or a morphism of sites). Then
$\opb \varphi\stkc$ is $\opb \varphi \shr$-linear and there is a $\opb \varphi \shr$-equivalence
$$
\opb \varphi (\stkc\tens[\shr]\stkd)\equi[] \opb \varphi \stkc\tens[\opb \varphi\shr]\opb \varphi\stkd.
$$
If $\stke$ is a $\opb \varphi \shr$-stack, then $\oim \varphi \stke$ is $\shr$-linear and there is an $\shr$-functor
\begin{equation}
\label{eq:dir-im}
\oim \varphi \stke\tens[\shr]\oim \varphi \stkf \to \oim \varphi (\stke\tens[ \opb \varphi \shr]\stkf).
\end{equation}
\subsection{Modules over a linear stack}
Denote by $\Mod(\shr)$ the category $\shr$-modules and by
$\stkMod(\shr)$ the corresponding $\shr$-stack given by $U\mapsto
\Mod(\shr|_U)$
For $\stkc$ an $\shr$-stack, the
stack of $\stkc$-modules is defined by
\begin{equation}
\label{eq:Mod}
\stkMod(\stkc) = \stkFun[\shr](\stkc,\stkMod(\shr)).
\end{equation}
(It follows from Lemma~\ref{lem:ModR} that this definition does not
depend on the base ring.
See also Lemma~\ref{lem:ZMod}.)
The contravariant $2$-functor $\stkMod(\dummy)$ is defined as follows.
On objects, it is given by \eqref{eq:Mod}.
Consider the diagram
\[
\xymatrix@C=3em{ \stkc \ar@/_.8em/[r]_{\functf'}
\ar@/^.8em/[r]_{\Downarrow\, \transfd}^{\functf} &
\stkd \ar[r]^-{\shn} & \stkMod(\shr)}.
\]
To an $\shr$-functor $\functf\colon \stkc\to\stkd$ one
associates the $\shr$-functor
\[
\stkMod(\functf)\colon \stkMod(\stkd)\to\stkMod(\stkc), \qquad
\shn \mapsto \shn \circ \functf,
\]
and to a transformation $\transfd\colon \functf\Rightarrow\functf'$ one associates the
transformation,
\[
\stkMod(\transfd)\colon\stkMod(\functf)\Rightarrow\stkMod(\functf'),
\]
such that $\stkMod(\transfd)(\shn) = \id_\shn \mathop\bullet \transfd$
is the morphism associated to $\shn\in\stkMod(\stkd)$,
where $\bullet$ denotes the horizontal composition of transformations. In
other words, for $\objc\in\stkc$ one has
$\stkMod(\transfd)(\shn)(\objc) = \shn(\transfd(\objc))$ as morphisms from
$\shn(\functf(\objc))$ to $\shn(\functf'(\objc))$ in $\stkMod(\shr)$. We use
the notations
\begin{equation}\label{eq:2mod}
{}_\functf(\dummy) = \stkMod(\functf),\quad
\transfd = \stkMod(\transfd).
\end{equation}
\subsection{Algebras as stacks}
Let $\sha$ be a sheaf of $\shr$-algebras.
Denote by $\sha^\op$ the opposite algebra and by $\stkMod(\sha)$ the
$\shr$-stack of left $\sha$-modules.
Denote by $\astk\sha$ the full substack of $\stkMod(\sha^\op)$
whose objects are locally free right $\sha$-modules of rank one. For any
$\shn\in\astk\sha(U)$ there is an $\shr|_U$-algebra isomorphism
$\shEnd[\astk \sha](\shn) \simeq \sha|_U$.
Note that the stack $\astk\sha$ has a canonical global object given by $\sha$ itself with its
structure of right $\sha$-module. In particular, the sheaf $\pi_0(\astk \sha)$ is a singleton.
For $f\colon\sha\to\shb$ an $\shr$-algebra morphism, denote by
$\astk f\colon \astk\sha\to\astk\shb$ the
$\shr$-functor induced by the extension of scalars $(\dummy)\tens[\sha]\shb$.
We thus have a functor between the stack of $\shr$-algebras and that of
$\shr$-stacks
\begin{equation*}
\astk{(\dummy)} \colon \shr\text-\stack{Alg}_X \to \shr\text-\stack{Stk}_X.
\end{equation*}
\begin{remark}\label{rm:aprstk}
Let $\aprstk\sha$ be the separated prestack $U\mapsto \astk{\sha(U)}$, where $ \astk{\sha(U)}$ denotes the $\shr(U)$-category with one object and sections of $\sha(U)$ as its endomorphisms.
By Yoneda lemma (see \S\ref{sse:Y}), the stack associated to $\aprstk\sha$ is $\shr$-equivalent to $\astk\sha$.
\end{remark}
The stack $\shr\text-\stack{Stk}_X$ is naturally upgraded to a 2-stack
by considering transformations of functors.
By enriching
$\shr\text-\stack{Alg}_X$ with identity transformations,
the functor
$\astk{(\dummy)}$ upgrades to a 2-functor.
With the terminology of 2-stacks, one has
\begin{lemma}\label{le:+locfull}
The 2-functor $\astk{(\dummy)}$ is faithful and locally full.
\end{lemma}
Here, locally full means that
for any two $\shr$-algebras $\sha$ and $\shb$ on $U\subset X$ and any
$\shr$-functor $\functf\colon\astk\sha\to\astk\shb$ there exist a cover
$\shu=\{U_{i}\}_{i\in I}$ of $U$ and morphisms of $\shr$-algebras $f_i\colon
\sha|_{U_i}\to\shb|_{U_i}$ such that $\functf|_{U_i} \simeq \astk f_i$.
\begin{proof}
By Remark~\ref{rm:aprstk}, the 2-functor $\astk{(\dummy)}$ is the composition of the 2-functor
$\aprstk{(\dummy)}$, which is full and faithful, and of the "associated stack" 2-functor $\asso{(\dummy)}$, which is faithful and locally full when restricted to separated prestacks.
\end{proof}
\begin{definition}
One says that an $\shr$-stack $\stkc$ is equivalent to an $\shr$-algebra $\sha$ if
$\stkc\equi\astk\sha$.
\end{definition}
In Proposition~\ref{pro:AequiB} we characterize the condition of
equivalence between algebras.
Recall that a stack $\stkc$ is non empty if it has at least one global object, and it is locally connected by isomorphisms if any two objects $\objc,\objc'\in\stkc(U)$ are locally isomorphic.
If $\stkc$ is $\shr$-linear, this amounts to ask that the sheaf
$\shHom[\stkc](\objc,\objc')$ is a locally free $\shEnd[\stkc](\objc')$-module of rank one.
\begin{lemma}\label{lem:a+}
An $\shr$-stack $\stkc$ is equivalent to an $\shr$-algebra if and only if it
is non empty and locally connected by isomorphisms
\end{lemma}
\begin{proof}
One implication is clear. Suppose that $\stkc$ is non empty and let $\objc\in\stkc(X)$. Then the fully faithful functor $\astk{\shEnd[\stkc](\objc)}\to\stkc$ is an equivalence if and only if $\stkc$ is locally connected
by isomorphisms.
\end{proof}
Let $\stkc$ be an $\shr$-stack. For $\shn\in \astk \shr$ and $\objc\in \stkc$, one defines
$\shn \tens[\shr] \objc\in \stkc$ as the representative of $\shn \tens[\shr] \hom[\stkc](\cdot,\objc)\in \stkMod(\stkc^\op)$. Then one has $\shr$-equivalences
\begin{align*}
\astk\shr \tens[\shr] \stkc \equi \stkc, & \qquad (\shn, \objc) \mapsto \shn \tens[\shr] \objc,\\
\stkc \equi \stkFun[\shr](\astk\shr,\stkc), & \qquad \objc \mapsto (\dummy) \tens[\shr] \objc.
\end{align*}
\begin{lemma}
\label{lem:ModR}
The definition \eqref{eq:Mod} of stack of $\stkc$-modules does not
depend on the base ring $\shr$.
\end{lemma}
\begin{proof}
Let $\shr$ be an $\shs$-algebra. It follows from Lemma~\ref{lem:stktensadj} for $\stkd = \astk\shr$
and $\stke = \stkMod(\shs)$ that
\[
\stkFun[\shs](\stkc,\stkMod(\shs))
\equi \stkFun[\shr](\stkc,\stkMod(\shr)),
\]
where we use the equivalence
$
\stkFun[\shs](\astk\shr,\stkMod(\shs)) \equi \stkMod(\shr).
$
\end{proof}
\subsection{Compatibility}
Let $\sha$ and $\shb$ be two $\shr$-algebras, and $\varphi\colon Y \to X$ a continuous map
(or a morphism of sites). There are an $\shr$-algebra isomorphism
\[
Z(\sha) \isoto Z(\astk \sha), \qquad
a \mapsto (\shn \to \shn \colon n \mapsto an),
\]
and $\shr$-equivalences
\begin{align*}
(\astk\sha)^\op &\equi \astk{(\sha^\op)}, \qquad
\shn \mapsto \shHom[\sha^\op](\shn, \sha), \\
\stkMod(\sha) &\equi \stkMod(\astk\sha), \qquad
\shm \mapsto (\dummy) \tens[\sha] \shm, \\
\astk\sha \tens[\shr] \astk\shb &\equi \astk{(\sha \tens[\shr] \shb)}, \qquad
(\shn , \shq) \mapsto \shn\tens[\shr]\shq\\
\opb \varphi \astk\sha &\equi \astk{(\opb \varphi \sha)}, \qquad
\shn \mapsto \opb\varphi \shn.
\end{align*}
For $f,f'\colon \sha\to \shb$ two $\shr$-algebra morphisms, the sections on $U\subset X$
of the sheaf $\hom[{\stkFun[\shr](\astk \sha,\astk \shb)}]( \astk f , \astk {f'} )$ are given by
\begin{equation}
\label{eq:shbfunct}
\{ b\in \shb(U) \colon b f(a) = f'(a) b \, \text{ for each } a\in
\sha(V) \text{ and } V\subset U\},
\end{equation}
with composition of transformations given by the product in $\shb$.
For $\shn$ a left $\shb$-module, denote by ${}_{f}\shn$ the associated
left $\sha$-module.
With notations \eqref{eq:2mod}, one has
\begin{equation}
\label{eq:2modalg}
{}_{\astk f}\shn = {}_{f}\shn, \qquad b(\shn)\colon
{}_{f}\shn \to {}_{f'}\shn\colon n\mapsto bn.
\end{equation}
\subsection{Algebroids}\label{sse:algebroid}
Recall from Lemma~\ref{lem:a+} that an $\shr$-stack is equivalent to
an $\shr$-algebra if and only if it is non empty and is locally connected
by isomorphisms.
\begin{definition}\label{def:algebroid}
An $\shr$-algebroid is an $\shr$-stack which is locally non empty and
locally connected by isomorphisms.
\end{definition}
In other words, an $\shr$-algebroid is an $\shr$-stack $\stka$ which is locally equivalent
to an algebra. It is globally an algebra if and only if it has a global object\footnote{If the category
$\stka(U)$ has a zero objects for $U\subset X$, then $\stka|_U\equi[]\astk 0$, where $0$ denotes the ring with $1=0$. In particular, except for the case $\astk 0$, algebroids are not stacks of additive categories.}.
The stack $\stkMod(\stka)$ is an example of stack of twisted sheaves, i.e.~it is
a stack locally equivalent to a stack of modules over an algebra (see~\cite{KS06,DP03}).
A cocyclic description of algebroids and of their modules is recalled in
Appendix~\ref{se:acocy} and~\ref{se:mcocy}.
Note that the existence of an $\shr$-functor
$\astk\shr\to\stka$ is equivalent to the existence of a global object
for $\stka$. In this case there is a forgetful functor
\[
\stkMod(\stka) \to \stkMod(\shr).
\]
\begin{lemma}
An $\shr$-stack $\stkc$ is an algebroid if and only if $\pi_0(\stkc)$ is a singleton.
\end{lemma}
It follows from~\eqref{eq:inv-pi_0} that inverse images of algebroids are algebroids.
Let $\stkc$ be an $\shr$-stack. Then for any $\shr$-algebroid $\stka$ one has
$$
\pi_0(\stka\tens[\shr]\stkc)\simeq\pi_0(\stkc).
$$
In particular, the tensor product of algebroids is an algebroid.
\begin{definition}
\begin{itemize}
\item[(i)]
Let $\sha$ be an $\shr$-algebra. An $\shr$-twisted form of $\sha$ is
an $\shr$-algebroid locally $\shr$-equivalent to $\sha$.
\item[(ii)]
An invertible $\shr$-algebroid is an $\shr$-twisted form of $\shr$.
\end{itemize}
\end{definition}
Note that any $\shr$-functor between invertible $\shr$-algebroids is an equivalence,
since it is locally isomorphic to the identity of $\astk\shr$.
If $\stkc$ is an invertible $\shr$-algebroid, then $\shr\isoto Z(\stkc)$ and for any $\shr$-stack $\stkd$
there is an $\shr$-equivalence
$$
\stkc^\op\tens_\shr\stkd \equi \stkFun[\shr](\stkc,\stkd), \quad (\gamma,\delta)\mapsto \hom[\stkc](\gamma,\cdot) \tens[\shr] \delta.
$$
In particular, the set of $\shr$-equivalence classes of invertible $\shr$-algebroids
is a group, with multiplication given by $\tens[\shr]$ and inverse given by $(\cdot)^\op$.
By Corollary~\ref{cor:h1aut}, the cohomology $H^1(X;\stkAut[\shr](\astk\sha))$ classifies
$\shr$-equivalence classes of $\shr$-twisted forms of $\sha$.
In terms of crossed modules, one has
\[
\stkAut[\shr](\astk\sha) \equi[] [(\sha^\times\to[\ad]
\shAut[\shr\text-\stack{Alg}_X](\sha),\ \delta)],
\]
where $\delta(f)(a) = f(a)$.
In particular,
$\stkAut[\shr](\astk\shr) \equi[] \shr^\times[1]$ and~\eqref{eq:HiG} implies
\begin{lemma}
\label{lem:tors}
The group of $\shr$-equivalence classes of
invertible $\shr$-alge\-broids is isomorphic to $H^2(X;\shr^\times)$.
\end{lemma}
\subsection{Inner forms}
Let $\sha$ be a central $\shr$-algebra, i.e.~$Z(\sha)=\shr$.
(If $\sha$ is not central, the following discussion still holds by replacing $\shr$ with $Z(\sha)$.)
Denote by $\inn(\sha)$ the sheaf of inner automorphisms of $\sha$,
i.e.~automorphisms locally of the form $\ad(a)$ for some $a\in\sha^\times$.
Recall that an $\shr$-algebra $\shb$ is called an inner form of $\sha$ if
there exists an open cover $\{U_i\}_{i\in I}$ of $X$ and ring isomorphisms
$f_i\colon \sha|_{U_i} \to \shb|_{U_i}$ such that $f_j^{-1}f_i \in
\inn(\sha|_{U_{ij}})$.
Examples of inner forms are given by Azumaya algebras
and rings of twisted differential operators (see for example~\cite{DP03} for more details).
Let $\shb$ be an $\shr$-algebra. Denote by $\stke_{\sha,\shb}\subset \stkFun[\shr](\astk\sha,\astk\shb)$ the full substack of $\shr$-equivalences. Note that
$\stke_{\sha,\shb}^\op\equi\stke_{\shb,\sha}$.
\begin{lemma}\label{le:AinnerB}
$\shb$ is an inner form of $\sha$ if and only if $\stke_{\sha,\shb}$ is an $\shr$-algebroid.
\end{lemma}
\begin{proof}
Since $\shr$-equivalences $\astk\sha\equito\astk\shb$ are locally given by $\shr$-algebra isomorphisms $\sha\isoto\shb$, it follows that $\stke_{\sha,\shb}$ is locally non empty if and only if $\shb$ is locally isomorphic to $\sha$.
Let $f, f '\colon\sha\to\shb$ be $\shr$-algebra
isomorphisms. Setting $a=f^{-1}(b)$ in~\eqref{eq:shbfunct}, the invertible transformations from $\astk f$ to $\astk {f'}$ are given by
$$
\{ a\in \sha^\times \colon f^{-1}f' = \ad(a) \},
$$
hence $\stke_{\sha,\shb}$ is an $\shr$-algebroid if and only if $\shb$ is an inner form of $\sha$.
\end{proof}
Since $\shEnd[\stke_{\sha,\shb}](\astk f)= \shr$, if $\shb$ is an inner form of $\sha$ it follows that
$\stke_{\sha,\shb}$ is an invertible $\shr$-algebroid and $\stke_{\sha,\shb}\tens[\shr]\astk\sha \equi\astk\shb$. In particular, one gets an equivalence of stacks of 2-groups $\stkAut[\shr](\astk \sha)\equi[] \stkAut[\shr](\astk \shb)$.
Consider the non abelian exact sequence
\[
H^1(X; \sha^\times) \to[b] H^1(X; \inn(\sha)) \to[c] H^2(X;\shr^\times)
\]
induced by the short exact sequence
\[
1\to \shr^\times \to \sha^\times \to[\ad] \inn(\sha) \to 1.
\]
For $\shb$ an inner form of $\sha$ and $\shp$ a locally free $\sha^\op$-module of rank one, denote by $[\shb]$ and $[\shp]$ the associated cohomology classes
in $H^1(X;\inn(\sha))$ and $H^1(X; \sha^\times)$ respectively.
Then $b[\shp]=[\shEnd[\sha^\op](\shp)]$ and $c([\shb])=[\stke_{\sha,\shb}]$.
\begin{proposition}
\label{pro:AequiB}
The following conditions are equivalent.
\begin{itemize}
\item[(i)]
The stacks $\astk\sha$ and $\astk\shb$ are $\shr$-equivalent.
\item[(ii)]
There exists a locally free $\sha^\op$-module $\shp$ of rank one
such that $\shb\simeq\shEnd[\sha^\op](\shp)$.
\item[(iii)]
$\shb$ is an inner form of $\sha$ and $c([\shb])=1$.
\end{itemize}
\end{proposition}
\begin{proof}
(i)$\Rightarrow$(ii)\footnote{The equivalence between (i) and (ii) can also be deduced
from Corollary~\ref{cor:AutInv}.}
Let $\functg\colon\astk\shb\to\astk\sha$ be an $\shr$-equivalence.
Recall that $\astk\shb \subset \stkMod(\shb^\op)$ is the substack of
locally free modules of rank one.
Let $\objb$ be the canonical global object of $\astk\shb$, and set $\shp =
\functg(\objb)$. Then $\shb$ is isomorphic to $\shEnd[\sha^\op](\shp)$.
\smallskip\noindent
(ii)$\Rightarrow$(iii)
$\shb$ is clearly an inner form of $\sha$ and $\shp$ has a structure of $\sha^\op\tens[\shr]\shb$-module by the isomorphism $\shb\isoto\shEnd[\sha^\op](\shp)$. Then $(\cdot)\tens[\shb]\shp$ gives a global object of $\stke_{\shb,\sha}$ and $c([\shb])=[\stke_{\shb,\sha}^\op]=1$.
\smallskip\noindent
(i)$\Leftarrow$(iii)
By Lemma~\ref{le:AinnerB} follows that $c([\shb])=1$ if and only if $\stke_{\sha,\shb}$ has a global object.
\smallskip\noindent
\end{proof}
\section{Morita theory for linear stacks}\label{se:Mor}
Morita theory classically deals with modules over algebras.
It is extended to modules over linear categories in~\cite{Mit65,Mit85}
and to stacks of modules over sheaves of algebras
in~\cite[Chapter~19]{KS06} (see also \cite{DP03}).
Here, we summarize these extensions by considering stacks of modules over linear
stacks, and in particular over algebroids.
\medskip
Let $X$ be a topological space (or a site), and $\shr$ a sheaf of
commutative rings on $X$.
\subsection{Yoneda embedding}\label{sse:Y}
Recall that a category is called (co)complete if it admits small (co)limits. A
prestack $\stkc$ on $X$ is called (co)complete if the categories $\stkc(U)$
are (co)complete for each $U\subset X$, and the restriction functors commute
with (co)limits.
A prestack $\stkc$ on $X$ is called a proper stack (see~\cite{KS01,Pre07}) if
it is separated, cocomplete, and if for each inclusion of open subsets
$v\colon V \hookrightarrow U$, the restriction functors $\stkc(v) = (\cdot)|_V$ admits a
fully faithful left adjoint
\[
\eim v \colon \stkc(V) \to \stkc(U),
\]
called zero-extension, such that for a diagram of open inclusions
\[
\xymatrix@=1em{ V\cap W \ar[r]^-{v'} \ar[d]_{w'} & W \ar[d]^-w \\ V
\ar[r]^v & U, }
\]
the natural transformation $\eim{v'} \circ \stkc(w') \to \stkc(w) \circ \eim
v$ is an isomorphism.
\begin{lemma}
\label{eq:vpropersheaf}
For $\objc\in\stkc(V)$ and $\objc'\in\stkc(U)$
there is an isomorphism of $\shr|_U$-modules
\[
\oim v\hom[\stkc|_V](\objc,\objc'|_V) \simeq
\hom[\stkc|_U](\eim v\objc,\objc').
\]
\end{lemma}
Recall that proper stacks are stacks.
\begin{lemma}\label{lem:modproper}
For any $\shr$-stack $\stkc$, the $\shr$-stack $\stkMod(\stkc)$ is proper and complete.
\end{lemma}
\begin{proof}
Recall first that $\stkMod(\shr)$ is complete and cocomplete. It is also
proper. In fact, for $v\colon V \hookrightarrow U$ an open inclusion, the
restriction functor of $\stkMod(\shr)$ coincides with the sheaf-theoretical
pull-back $\opb v$. This admits the direct image functor $\oim v$ as left
adjoint, and the zero-extension functor $\eim v$ as a right adjoint.
The statement follows, as $\stkMod(\stkc) =
\stkFun[\shr](\stkc,\stkMod(\shr))$ inherits the properties and structures of
$\stkMod(\shr)$. For example, for $v\colon V\hookrightarrow U$ an inclusion of
open subsets, the functor $\eim v \colon\catMod(\stkc|_V) \to
\catMod(\stkc|_U)$ is given by $(\eim v\shm)(\objc) = \eim u(\shm(\objc
|_{V\cap W}))$, where $\shm\colon \stkc|_V\to\stkMod(\shr|_V)$ is a
$\stkc|_V$-module, $W\subset U$ is an open subset, $\objc\in\stkc(W)$, and
$u\colon V\cap W \to U$ is the embedding.
\end{proof}
Let $\stkc$ be an $\shr$-stack.
The (linear) Yoneda embedding
is the full and faithful $\shr$-functor
\begin{equation}
\label{eq:stkyoneda}
\yoneda\stkc \colon \stkc^\op \to \stkMod(\stkc), \quad
\objc\mapsto \shHom[\stkc](\objc, \dummy)
\end{equation}
whose essential image are the functors $\stkc\to\stkMod(\shr)$ which are
representable.
In analogy with the case $\stkc=\astk\sha$ for $\sha$ and $\shr$-algebra,
a module $\shm\in\stkMod(\stkc)$ which is representable is called locally free of rank one.
As in the classical case, the full faithfulness of \eqref{eq:stkyoneda} follows from
\begin{lemma}\label{lem:Yoneda}
For $\shm\in\catMod(\stkc)(U)$ there is an isomorphism of $\stkc|_U$-modules
\begin{equation}
\label{eq:prstkYonedaLemma}
\shm(\dummy) \simeq \hom[\stkMod(\stkc)](\yoneda \stkc(\dummy), \shm).
\end{equation}
\end{lemma}
Denote by $\stkc/X$ the fibered category associated with $\stkc$. Recall that
objects of $\stkc/X$ are pairs $(u,\objc)$ with $u\colon U\hookrightarrow X$
an open inclusion, and $\objc\in\stkc(U)$. Morphisms $\transfa\colon (u,\objc)
\to (u',\objc')$ are defined only if $U'\subset U$, and in that case are given
by morphisms $\objc\vert_{U'}\to \objc'$ in $\stkc(U')$. For $\transfa'\colon
(u',\objc') \to (u'',\objc'')$ another morphism, the composition\footnote{Here we
denote for short by $\transfa|_{U''}$ the composite $\objc|_{U''} \isofrom
\objc|_{U'}|_{U''} \to[\transfa|_{U''}] \objc'|_{U''}$.}
is given by $\transfa' \circ \transfa|_{U''}$. A functor of stacks
$\functf\colon\stkc\to\stkd$ naturally induces a functor
$\functf/X\colon\stkc/X\to\stkd/X$.
For $\shm\colon\stkc\to\stkMod(\shr)$ an object in $\catMod(\stkc)$, denote
for short by $\stkc^\op_\shm$ the comma category $(\stkc/X^\op)_{\shm/X}$
By~\eqref{eq:prstkYonedaLemma}, objects of $\stkc^\op_\shm$ are triples $(u,
\objc,m)$ with $u\colon U\hookrightarrow X$ an open inclusion,
$\objc\in\stkc^\op(U)$, and $m\in\sect(U;\shm(\objc))$.
\begin{lemma}
\label{le:stkfunlim}
For $\shm,\shn\in\catMod(\stkc)$ there is an isomorphism in $\catMod(\shr)$
\[
\hom[\stkMod(\stkc)](\shm, \shn)
\simeq \plim[(u, \objc,m)\in \stkc^\op_\shm] \oim u \shn(\objc).
\]
\end{lemma}
\begin{proof}
For any open subset $V\subset X$, one has the isomorphism
\[
\Hom[\stkMod(\stkc|_V)](\shm|_V, \shn|_V)
\isoto \plim[(u, \objc,m)\in (\stkc|_V^\op)_{\shm|_V}] \sect(U; \shn(\objc)),
\]
associating to $\functf\colon \shm|_V\to \shn|_V$ the family
$\{\functf(\objc)(m))\}_{(u,\objc,m)}$.
\end{proof}
\begin{lemma}
\label{pr:YMprstk}
For $\shm\in\catMod(\stkc)$ there is an isomorphism in $\catMod(\stkc)$
\[
\shm \simeq \ilim[(u, \objc,m)\in \stkc^\op_\shm] \eim u \yoneda
\stkc(\objc).
\]
\end{lemma}
\begin{proof}
This follows from the fact that for any $\shn\in\catMod(\stkc)$ there are
$\shr$-module isomorphisms
\begin{align*}
\hom[\stkMod(\stkc)](\shm, \shn)
&\simeq \plim[(u, \objc,m)\in \stkc^\op_\shm] \oim u \shn(\objc) \\
&\simeq \plim[(u, \objc,m)\in \stkc^\op_\shm] \oim u
\hom[\stkMod(\stkc|_U)]( \yoneda \stkc(\objc), \shn|_U) \\
&\simeq \plim[(u, \objc,m)\in
\stkc^\op_\shm] \hom[\stkMod(\stkc)]( \eim u \yoneda \stkc(\objc), \shn) \\
&\simeq \hom[\stkMod(\stkc)]( \ilim[(u, \objc,m)\in \stkc^\op_\shm] \eim u
\yoneda \stkc(\objc), \shn) .
\end{align*}
Here, the first isomorphism follows from Lemma~\ref{le:stkfunlim}, the second
isomorphism follows from \eqref{eq:prstkYonedaLemma}, and the third
isomorphism follows from Lemma~\ref{eq:vpropersheaf}.
\end{proof}
\begin{lemma}\label{lem:ZMod}
For $\stkc$ an $\shr$-stack, there is a natural isomorphism of $\shr$-algebras
$Z(\stkMod(\stkc)) \simeq Z(\stkc)$.
\end{lemma}
\begin{proof}
The Yoneda embedding induces by adjunction a morphism of $\shr$-algebras
$Z(\stkMod(\stkc)) \to Z(\stkc^\op)$. Its inverse associates to $\transfc\in
Z(\stkc^\op)$ the endo-transformation $\tilde\transfc$ of
$\id_{\stkMod(\stkc)}$ given by $\tilde\transfc(\shm) = \ilim[(u,\objc,m)\in
\stkc_\shm^\op] \yoneda \stkc(\transfc(\objc))$.
\end{proof}
\subsection{Operations via Kan extensions}
For non linear categories, the following result is known as Kan extension
(see for example~\cite[pag.~106]{Mit65} or \cite[Prop.~2.7.1]{KS06}).
\begin{theorem}
\label{th:kan}
For $\shn\in\stkMod(\stkc)$ consider the diagram
\[
\xymatrix@R=1em@C=3em{ \stkMod(\stkc^\op) \ar@{.>}[dr]_-{\functt_\shn} &
\stkc \ar[d]_-\shn \ar@{_(->}[l]_-{\yoneda{\stkc^\op}}
\ar@{^(->}[r]^-{\yoneda \stkc^\op} & \stkMod(\stkc)^\op
\ar@{.>}[dl]^-{\functh_\shn} \\ & \stkMod(\shr) . }
\]
\begin{itemize}
\item[(i)]
There exists a unique $\shr$-functor $\functt_\shn$ (up to unique isomorphism)
commuting with colimits and zero-extensions, and making the left hand side of
the diagram (quasi)-commute.
\item[(ii)]
The functor $\functh_\shn =\hom[\stkMod(\stkc)](\dummy,\shn)$ is the only
$\shr$-functor (up to unique isomorphism) commuting with limits and making the
right hand side of the diagram (quasi)-commute.
\end{itemize}
\end{theorem}
\begin{proof}[Sketch of proof]
(i) For $\shp\in\stkMod(\stkc^\op)$ one has
\begin{multline*}
\functt_\shn(\shp) \simeq \functt_\shn( \ilim[(u,\objc,p)\in \stkc_\shp] \eim
u\yoneda{\stkc^\op}(\objc) ) \\
\simeq \ilim[(u,\objc,p)\in \stkc_\shp] \eim
u\functt_\shn( \yoneda{\stkc^\op}(\objc) ) \simeq \ilim[(u,\objc,p)\in
\stkc_\shp] \eim u\shn(\objc) .
\end{multline*}
(ii) Similarly, for $\shm\in\stkMod(\stkc)$ one has
\begin{multline*}
\functh_\shn(\shm) \simeq \functh_\shn( \ilim[(u,\objc,m)\in \stkc_\shm^\op]
\eim u\yoneda{\stkc}(\objc) ) \\
\simeq \plim[(u,\objc,m)\in \stkc_\shm^\op] \oim
u \functh_\shn(\yoneda{\stkc}(\objc) ) \simeq \plim[(u,\objc,m)\in
\stkc_\shm^\op] \oim v\shn(\objc),
\end{multline*}
so that $\functh_\shn =\hom[\stkMod(\stkc)](\dummy,\shn)$ by
Lemma~\ref{le:stkfunlim}.
\end{proof}
As for modules over a ring, we will often use the short hand notation
$$
\hom[\stkc](\cdot,\cdot) = \hom[\stkMod(\stkc)](\cdot,\cdot).
$$
\begin{notation}
\label{not:tens}
We denote by
\begin{align*}
\hom[\stkc] &\colon \stkMod(\stkc\tens_\shr\stkd^\op)^\op \tens_\shr
\stkMod(\stkc\tens_\shr\stke) \to \stkMod(\stkd\tens_\shr\stke), \\
\tens_\stkc & \colon \stkMod(\stkc^\op\tens_\shr\stkd) \tens_\shr
\stkMod(\stkc\tens_\shr\stke) \to \stkMod(\stkd\tens_\shr\stke)
\end{align*}
the $\shr$-functors obtained by picking up operators from the $\shr$-functors
\begin{align*}
\hom[\stkc] &\colon \stkMod(\stkc)^\op \tens_\shr \stkMod(\stkc)
\to \stkMod(\shr), \\ \functt &\colon \stkMod(\stkc^\op) \tens_\shr
\stkMod(\stkc) \to \stkMod(\shr), \quad (\shp,\shn)\mapsto \functt_\shn(\shp).
\end{align*}
\end{notation}
For $\sha$, $\shb$, $\shc$ three $\shr$-algebra, and $\stkc=\astk
\sha$, $\stkd=\astk \shb$, $\stke=\astk \shc$, the functor $\tens[\astk \sha]$
is isomorphic to the usual tensor product of modules $\tens[\sha]$. For
example, for $\shn\in\stkMod(\sha)$ and $\shp\in\stkMod(\sha^\op)$, the
isomorphism
\[
\shp\tens_\sha \shn = \functt_\shn(\shp) \simeq \ilim[u\colon U\subset X,\ p\in \shp(U)] \shn,
\]
amounts to present $\shp\tens_\sha \shn$ as a quotient of $\DSum_{u\colon U
\subset X,\ p\in \shp(U)}\eim u(\shn|_U)$.
Most of the formulas concerning the usual hom-functor and tensor product hold.
For example,
\begin{lemma}
\label{le:tenshomadj}
For $\shm\in\stkMod(\stkc^\op\tens_\shr\stkd)$,
$\shn\in\stkMod(\stkc\tens_\shr\stke)$, and
$\shp\in\stkMod(\stkd\tens_\shr\stkf)$, there is an isomorphism
in $\stkMod(\stke^\op\tens_\shr\stkf)$
\[
\hom[\stkd](\shm\tens_\stkc \shn, \shp) \simeq
\hom[\stkc](\shn, \hom[\stkd](\shm,\shp)).
\]
\end{lemma}
\begin{proof}
One checks that in $\stkMod(\stke\tens[\shr]\stkd)$
\[
\shm\tens_\stkc \shn \simeq \ilim[{(u,\functf,n)\in
\stkFun[\shr](\stke,\stkc^\op)_\shn}] \eim u\shm\circ\functf ,
\]
where the comma category is defined via the functor
$\stkFun[\shr](\stke,\yoneda \stkc)$. Then, both terms in the statement are
isomorphic to
\[
\plim[{(u,\functf,n)\in \stkFun[\shr](\stke,\stkc^\op)_\shn}]
\oim u\hom[\stkd](\shm\circ\functf, \shp|_U).
\]
\end{proof}
\subsection{Morita equivalence}
Let us discuss how classical Morita theory extends to linear
stacks.
\begin{lemma}
\label{le:radjilim}
An $\shr$-functor $\functh\colon\stkMod(\stkc)\to\stkMod(\stkd)$ commutes with
colimits and zero-extensions (resp.~limits and extensions) if and only if it
admits a right (resp.~left) adjoint.
\end{lemma}
\begin{proof}
Assume that $\functh$ commutes with colimits and zero-extensions. Set
$\shp=\functh \circ \yoneda\stkc \in\stkMod(\stkc^\op\tens_\shr\stkd)$. For
$\shm\in\stkMod(\stkc)$ one has
\[
\functh(\shm) \simeq \functh\bigl(\ilim[(u,\objc,m)\in \stkc_\shm^\op] \eim u\yoneda
\stkc(\objc)\bigr) \simeq \ilim[(u,\objc,m)\in \stkc_\shm^\op] \eim u\shp(\objc) \simeq \shp\tens_\stkc \shm.
\]
Hence $\functh\simeq \shp\tens_\stkc(\dummy)$ admits
$\hom[\stkd](\shp,\dummy)$ as a right adjoint by Lemma~\ref{le:tenshomadj}.
The converse implication is obvious, and the dual statement is similar.
\end{proof}
Denote by $\stkFun[\shr]^r(\stkMod(\stkc),\stkMod(\stkd))$ the stack of
$\shr$-functors admitting a right adjoint.
\begin{theorem}
\label{th:premorita}
\begin{itemize}
\item[(i)]
The functor
\[
\stkMod(\stkc^\op\tens_\shr\stkd) \to
\stkFun[\shr]^r(\stkMod(\stkc),\stkMod(\stkd)), \quad \shp \mapsto
\shp\tens_\stkc(\dummy),
\]
is an $\shr$-equivalence.
\item[(ii)]
For $\shp\in\stkMod(\stkc^\op\tens_\shr\stkd)$ and
$\shq\in\stkMod(\stkd^\op\tens_\shr\stke)$ one has
\[
(\shq\tens[\stkd]\shp) \tens[\stkc] (\cdot) \simeq (\shq \tens[\stkd]
(\cdot)) \circ (\shp \tens[\stkc] (\cdot)).
\]
\end{itemize}
\end{theorem}
\begin{proof}
(i) By uniqueness of the Kan extension, a quasi-inverse is given by
$\functh\mapsto \functh \circ \yoneda{\stkc}$.
(ii) also follows from uniqueness of Kan extension.
\end{proof}
\begin{remark}
Denoting by $\stkFun[\shr]^l(\stkMod(\stkc),\stkMod(\stkd))$ the stack of
$\shr$-functors admitting a left adjoint, one similarly gets an
$\shr$-equivalence
\[
\stkMod(\stkc^\op\tens_\shr\stkd) \to
\stkFun[\shr]^l(\stkMod(\stkd),\stkMod(\stkc))^\op, \quad \shp\mapsto
\hom[\stkd](\shp,\dummy),
\]
and the corresponding commutative diagram as in
Theorem~\ref{th:premorita}~(ii). These constructions are interchanged by
the $\shr$-equivalence
\begin{equation*}
\stkFun[\shr]^r(\stkMod(\stkc),\stkMod(\stkd)) \equi
\stkFun[\shr]^l(\stkMod(\stkd),\stkMod(\stkc))^\op
\end{equation*}
sending a functor to its adjoint.
\end{remark}
We use the notation
\begin{equation}
\label{eq:bimod}
\bimod\stkc \in \stkMod(\stkc^\op\tens_\shr\stkc)
\end{equation}
for the canonical object $\hom[\stkc](\cdot,\cdot)$.
This corresponds to the Yoneda embedding $\yoneda \stkc$
via the equivalence induced by Lemma~\ref{lem:stktensadj}
\[
\stkFun[\shr](\stkc^\op\tens_\shr\stkc,\stkMod(\shr)) \equi
\stkFun[\shr](\stkc^\op,\stkMod(\stkc)).
\]
If $\stkc=\astk\sha$, the object
$\astk\sha\in\stkMod(\sha^\op\tens[\shr]\sha)$ coincides with
$\sha$, considered as a bimodule over itself.
If $\stkc$ is an invertible $\shr$-algebroid, then $\stkc^\op\tens_\shr\stkc\equi[\shr] \astk \shr$
and $\stkc$ is isomorphic to $\shr$ as a bimodule over itself.
Note that, by Lemma~\ref{lem:Yoneda} the functor $\hom[\stkc] (\bimod\stkc,\dummy)$, and hence
$\bimod\stkc\tens_\stkc (\dummy)$, is isomorphic to the identity.
\begin{definition}
\label{def:inv}
\begin{itemize}
\item[(i)]
One says that $\shq\in\stkMod(\stkd^\op\tens_\shr\stkc)$ is an inverse of
$\shp\in\stkMod(\stkc^\op\tens_\shr\stkd)$ if there are isomorphisms of
$\stkc\tens_\shr\stkc^\op$- and $\stkd\tens_\shr\stkd^\op$-modules, respectively,
\[
\shq\tens_\stkd \shp \simeq \bimod\stkc, \quad
\shp\tens_\stkc \shq \simeq \bimod\stkd.
\]
\item[(ii)]
An object $\shp\in\stkMod(\stkc^\op\tens_\shr\stkd)$ is called invertible if
it has an inverse.
\end{itemize}
\end{definition}
One proves (see e.g.~\cite[\S19.5]{KS06}) that $\shp$ is invertible if and
only if one of the following equivalent conditions is satisfied
\begin{itemize}
\item [(i)]
$\hom[\stkc^\op](\shp,\bimod\stkc)$ is an inverse of $\shp$;
\item [(ii)]
the functor $\shp\tens[\stkc](\dummy) \colon \stkMod(\stkc) \to
\stkMod(\stkd)$ is an $\shr$-equivalence.
\item [(iii)]
the functor $\hom[\stkc^\op](\shp,\dummy) \colon \stkMod(\stkc^\op) \to
\stkMod(\stkd^\op)$ is an $\shr$-equiva\-lence.
\end{itemize}
For any $\shr$-functor $\functf\colon \stkc \to \stkc'$, denote by $\stkEndo[\stkc](\functf)$ the
$\shr$-stack associated to the separated prestack whose objects on $U\subset X$ are those
of $\stkc(U)$ and $\Hom(\gamma,\gamma')=\Hom[\stkc'(U)](\functf(\gamma),\functf(\gamma'))$.
Then, considering $\stkc\in\stkMod(\stkc^\op\tens_\shr\stkc)$ as a functor $\stkc^\op \to \stkMod(\stkc)$, one has $\stkc\equi\stkEndo[\stkc^\op](\stkc)$ by~\eqref{eq:stkyoneda}.
Moreover, considering $\shp\in\stkMod(\stkc^\op\tens_\shr\stkd)$ as a functor $\stkc^\op \to \stkMod(\stkd)$, the condition of $\shp$ being invertible is further equivalent to
\begin{itemize}
\item [(iv)] \label{pgv}
$\shp$ is a faithfully flat\footnote{$\shp$ is a faithfully flat $\stkc^\op$-module if the functor $\shp\tens[\stkc](\dummy)$ is faithful and exact.} $\stkc^\op$-module locally of finite presentation\footnote{$\shp$ is a $\stkc^\op$-module of finite presentation if the functor $\hom[\stkc^\op](\shp,\dummy)$ commutes with small filtrant colimits.}
and $\stkd\equi \stkEndo[\stkc^\op](\shp)$;
\item [(v)]
$\shp$ is $\stkc^\op$-progenerator\footnote{$\shp$ is $\stkc^\op$-progenerator if the functor $\hom[\stkc^\op](\shp,\dummy)$ is faithful and exact.} locally of finite type and $\stkd\equi \stkEndo[\stkc^\op](\shp)$.
\end{itemize}
By reversing the role of $\stkc$ and $\stkd$, one gets dual equivalent conditions.
Given an $\shr$-functor $\functh\colon \stkMod(\stkc) \to \stkMod(\stkd)$, we will use the same
notation $\functh$ for the induced $\shr$-functor, obtained by picking up operators,
$$
\stkMod(\stkc^\op\tens[\shr]\stkc) \to \stkMod(\stkc^\op\tens[\shr]\stkd).
$$
\begin{corollary}[Morita]\label{cor:morita}
An $\shr$-functor $\functh\colon \stkMod(\stkc) \to \stkMod(\stkd)$ is an
equivalence if and only if
$\shp = \functh(\stkc)$ is an invertible $(\stkc^\op\tens_\shr\stkd)$-module. Moreover, one has
$\functh \simeq \shp\tens_\stkc(\dummy)$.
\end{corollary}
\begin{definition}
Two stacks $\stkc$ and $\stkd$ are Morita $\shr$-equivalent if their
stacks of modules $\stkMod(\stkc)$ and $\stkMod(\stkd)$ are $\shr$-equivalent.
\end{definition}
Hence $\stkc$ and $\stkd$ are Morita $\shr$-equivalent if and only if there exists an invertible
$(\stkc^\op\tens_\shr\stkd)$-module.
Let us say that $\shp\in\stkMod(\stkc^\op\tens[\shr]\stkd)$
is locally free of rank one over $\stkc^\op$ if for any $\objd\in\stkd$ the $\stkc^\op$-module
$\shp(\objd)$ is locally free of rank one, that is to say, the functor $\shp(\objd) \colon
\stkc^\op \to\stkMod(\shr)$ is representable.
Recall from~\eqref{eq:2mod} that
${}_\functf(\dummy)\colon \stkMod(\stkc)\to\stkMod(\stkd)$ denotes
the functor associated to an $\shr$-functor $\functf\colon \stkd\to\stkc$.
\begin{proposition}\label{pro:AutInv}
The $\shr$-functor
\begin{equation}\label{eq:FctMod}
\stkFun[\shr](\stkd,\stkc) \to
\stkMod(\stkc^\op\tens[\shr]\stkd),
\quad \functf\mapsto {}_\functf\bimod\stkc
\end{equation}
is fully faithful and induces an equivalence with the full substack of
locally free modules of rank one over $\stkc^\op$.
\end{proposition}
\begin{proof}
(i) The functor in the statement equals $\yoneda {\stkc^\op}\circ \cdot$.
This is fully faithful, since $\yoneda {\stkc^\op}$ is fully faithful.
(ii) Assume that $\shp\in\stkMod(\stkc^\op\tens[\shr]\stkd)$ is a locally
free module of rank one over $\stkc^\op$. Then $\shp \simeq
{}_\functf\bimod\stkc$, where $\functf\colon \stkd \to\stkc$ is the
functor associating to $\objd\in\stkd$ the representative of $\shp(\objd)$.
\end{proof}
\begin{corollary}\label{cor:AutInv}
Two stacks $\stkc$ and $\stkd$ are $\shr$-equivalent if and
only if there exists $\shp \in \stkMod(\stkc^\op\tens[\shr]\stkd)$
which is invertible and locally free of rank one over $\stkc^\op$.
\end{corollary}
In particular, two algebroids $\stka$ and $\stkb$ are $\shr$-equivalent if and only if there exists an
invertible $(\stka^\op\tens[\shr]\stkb)$-module $\shp$ which is locally free of
rank one over $\stka^\op$. These conditions on $\shp$ are equivalent
to the condition that $\shp$ is bi-invertible in the sense of
\cite[Corollary 2.1.10]{KS10}.
\begin{remark}\label{rem:LocFreeBim}
If $\stkc\equi\astk\sha$ and $\stkd\equi\astk\shb$, the functor $\astk\shb \to\astk\sha$
associated to an $\sha^\op\tens[\shr]\shb$-module $\shp$ locally free of rank one
over $\sha^\op$ is $\functf = (\cdot)\tens[\shb]\shp$.
Note that any local isomorphism $h\colon \sha \isoto \shp$ of right $\sha$-modules defines
a local $\shr$-algebra morphism (isomorphism if $\shp$ invertible)
\begin{equation}\label{eq:LocFreeBim}
f\colon \shb\to \shEnd[\sha^\op](\shp) \to[\ad(\opb h)] \shEnd[\sha^\op](\sha)\simeq \sha,
\end{equation}
(the first arrow is induced by the $\shb$-module structure of $\shp$), for which
$h\colon {}_f\sha \isoto \shp$ is an isomorphism of $\sha^\op\tens[\shr]\shb$-modules and
$\functf \simeq \astk f$. If $h$ is given by $a \mapsto ua$ for a local generator $u$ of the right $\sha$-modules $\shp$, then $f(b) = a$ for $a$ such that $ua=bu$.
\end{remark}
\subsection{Picard good stacks}
We will use the notation
\[
\stkc^e = \stkc^\op\tens_\shr\stkc.
\]
Denote by $\stkInv(\stkc^e)$ the substack of $\stkMod(\stkc^e)$ whose objects
are invertible $\stkc^e$-modules and whose morphisms are only those morphisms which
are invertible. Then $\tens[\stkc]$ induces on $\stkInv(\stkc^e)$ a natural structure of stack
of $2$-groups, and~\eqref{eq:FctMod} gives a fully faithful functor of
stacks of $2$-groups
\begin{equation}\label{eq:AutInv}
\stkAut[\shr](\stkc)_\op \hookrightarrow \stkInv(\stkc^e),
\quad \functf\mapsto {}_\functf\stkc.
\end{equation}
Here, for $\stkg$ a stack of $2$-groups, $\stkg_\op$ denotes the stack of
$2$-groups with the same groupoid structure as $\stkg$ and with reversed
monoidal structure.
\begin{definition}
\label{def:Picgood}
An $\shr$-stack $\stkc$ is Picard good if \eqref{eq:AutInv} is an
equivalence.
\end{definition}
By Proposition~\ref{pro:AutInv}, it follows that $\stkc$ is Picard good
if and only if all invertible $\stkc^e$-modules are locally free of rank one over $\stkc^\op$.
An $\shr$-algebra $\sha$ is Picard good if it is so as an $\shr$-stack, hence if and only if all invertible $\sha^e$-modules are locally free as right (or, equivalently, left) $\sha$-modules. Since invertible bimodules are projective as right (or left) modules, it follows that examples of Picard good rings are projective-free rings, and in particular local rings. Note however that Picard-good does not imply projective-free (see Remark~\ref{rem:tf}).
Since the condition of being Picard good is local, an algebroid is Picard good if and only if so are the algebras that locally represent it.
By Corollary~\ref{cor:morita}, there is an
equivalence of stacks of $2$-groups
$$
\stkInv(\stkc^e) \equito \stkAut[\shr](\stkMod(\stkc)), \quad
\shp\mapsto \shp\tens[\stkc](\cdot).
$$
We thus have a (quasi-)commutative diagram
\begin{equation}\label{eq:m}
\xymatrix@C=0em@R=2em{
\stkInv(\stkc^e) \ar[rr]^-{\equi[]} &&
\stkAut[\shr](\stkMod(\stkc)) \\
& \stkAut[\shr](\stkc)_\op ,
\ar@{_(->}[ul] \ar@{^(->}_m[ur],}
\end{equation}
where $m$ is induced by the functor $\stkMod(\dummy)$.
It follows that $\stkc$ is Picard good if and only if $m$ is an equivalence.
\begin{proposition}\label{pro:picgood}
Let $\stkc$ be a Picard good $\shr$-stack.
\begin{itemize}
\item[(i)]
Let $\stkd$ be an $\shr$-stack locally equivalent to
$\stkc$. Then $\stkc$ and
$\stkd$ are Morita $\shr$-equivalent if and only if they are
$\shr$-equivalent.
\item[(ii)]
Let $\stkm$ be an $\shr$-stack locally $\shr$-equivalent to $\stkMod(\stkc).$
Then $\stkm\equi\stkMod(\stkd)$ for an $\shr$-stack $\stkd$ locally
$\shr$-equivalent to $\stkc$.
\end{itemize}
\end{proposition}
\begin{proof}
(i) Let $\stkEquiv[\shr](\cdot,\cdot)$ denote the stack of $\shr$-equivalences, with invertible transformations as morphisms. Consider the functor
$$
\stkEquiv[\shr](\stkc,\stkd) \to
\stkEquiv[\shr](\stkMod(\stkd),\stkMod(\stkc))
$$
induced by the 2-functor $\stkMod(\dummy)$. Since $\stkd$ is locally equivalent to $\stkc$,
this locally reduces to the functor $m$ as in~\eqref{eq:m}. It follows that this is locally, hence globally, an equivalence.
\smallskip\noindent (ii)
Let $\stke \subset \stkm$ be the full substack of objects $\shp$ with the property that for any local $\shr$-equivalence $\functh\colon \stkm \equito \stkMod(\stkc)$, the $\stkc$-module
$\functh(\shp)$ is locally free of rank one.
Since $\stkc$ is Picard good, the $\shr$-stack $\stke$ is well defined and locally $\shr$-equivalent to $\stkc^\op$.
Set $\stkd=\stke^\op$. Then the $\shr$-functor
$$\stkm \to \stkMod(\stkd), \quad \shn \mapsto \hom[\stkm](\cdot,\shn)$$
is locally, hence globally, an equivalence.
\end{proof}
If $\stkc$ is an invertible $\shr$-algebroid, then it is Picard good if and only if $\shr$ is, and one has equivalences of stacks of 2-groups
\begin{equation}\label{eq:TorsInv}
\shr^\times[1] \equito \stkInv(\shr)\equi[] \stkInv(\stkc^e),
\quad \shp \mapsto \shr \times_{\shr^\times} \shp.
\end{equation}
(Recall that $\shr^\times[1]$ denotes the stack of $\shr^\times$-torsors.)
Moreover, in this situation the stack $\stkd$ in $(ii)$ above is $\shr$-equivalent to the full substack of $\stkFun[\shr](\stkm,\stkMod(\shr))$ whose objects are equivalences.
Examples of stacks as in Proposition \ref{pro:picgood} (ii) arise from deformations of categories of modules as discussed in~\cite{LVdB06}.
In particular, Proposition \ref{pro:picgood} applies when $\stkc$ is (equivalent to) the structure sheaf of a ringed space. We thus recover results of \cite{Low08}.
\section{Microdifferential operators}\label{se:mic}
We collect here some results from the theory of microdifferential operators of
\cite{S-K-K} (see also \cite{Kas86,Kas03}). The statements about the automorphisms of the sheaf of microdifferential operators are well known. Since we lack a reference for the proofs, we give them here.
\subsection{Microdifferential operators}
Let $M$ be an $n$-dimensional complex manifold, $T^*M$ its cotangent bundle
and $\dTM \subset T^*M$ the open subset obtained by removing the zero-section.
Denote by $\she_{\dTM}$ the sheaf of microdifferential operators on
$\dTM$ (see \cite{S-K-K,Kas03}). Recall that $\she_{\dTM}$ is a sheaf of central $\C$-algebras
endowed with a $\Z$-filtration by the order of the operators, and one has
$$\gr\she_{\dTM}\simeq \DSum_{m\in\Z}\sho_{\dTM}(m),$$
where $\sho_{\dTM}(m)$ is the subsheaf of $\sho_{\dTM}$ of holomorphic functions
homogeneous of degree $m$.
For $\lambda\in\C$, denote by $\she_\dTM(\lambda)$ the sheaf of microdifferential
operators of order at most $\lambda$, and set
\[
\she_\dTM^{[\lambda]} = \Union_{n\in\Z}\she_\dTM(\lambda+n),
\]
where $[\lambda]$ is the class of $\lambda$ in $\C/\Z$. Note that
$\she_\dTM^{[\lambda]}$ is a bimodule over $\she_\dTM = \she_\dTM^{[0]}$.
In a local coordinate system $(x)$ on $M$, with associated symplectic
coordinates $(x;\xi)$ on $\dTM$, a section $P\in\sect(V;\she_\dTM(\lambda))$
is determined by its total symbol, which is a formal series
\[
\tot(P)=\sum_{j=0}^{+\infty} p_{\lambda - j}(x,\xi)
\]
with $p_{\lambda - j}\in\sho_\dTM(V)$ homogeneous of degree ${\lambda - j}$,
satisfying suitable growth conditions in $j$. If $Q$
is a section of $\she_\dTM(\mu)$, then $PQ\in \she_\dTM(\lambda + \mu)$ has
total symbol given by the Leibniz formula
\[
\tot(P Q)=
\sum_{\alpha\in \N^n} \frac{1}{\alpha !}
\partial^{\alpha}_\xi\tot(P)
\partial^{\alpha}_x\tot(Q).
\]
Denote by
\[
\sigma_\lambda\colon\she_\dTM(\lambda)\to\sho_\dTM(\lambda) \quad\text{and}\quad
\sigma\colon\she_\dTM^{[\lambda]}\to\sho_\dTM
\]
the symbol of order $\lambda$ and the principal symbol, respectively, where
$\sigma(P)=\sigma_\lambda(P)$ for
$P\in\she_\dTM(\lambda)\setminus\she_\dTM(\lambda-1)$.
Note that for any $P\in \she_\dTM(\lambda)$ and $Q\in \she_\dTM(\mu)$ one has
$$
\sigma_{\lambda +\mu}(PQ)=\sigma_\lambda(P)\sigma_\mu(Q).
$$
Recall that a microdifferential operator is invertible at $p\in\dTM$ if and only if its
principal symbol does not vanish at $p$.
\subsection{Endomorphisms of $\she_\dTM$}
\begin{lemma}\label{lem:ffilt}
Any $\C$-algebra automorphism of $\she_\dTM$ is filtered and symbol
preserving.
\end{lemma}
\begin{proof}
Let $f$ be a $\C$-algebra automorphism of $\she_\dTM$.
Define the spectrum of $P\in\she_\dTM(V)$ as
\begin{align*}
\Sigma(P)\colon V &\to \mathcal P(\C)\\
p &\mapsto \{a\in\C \colon a-P \text{ is not invertible at }p\},
\end{align*}
where $\mathcal P(\C)$ denotes the set of subsets of $\C$.
Note that $\Sigma(P) = \Sigma(f(P))$.
Set for short
\[
\she_m = \she_\dTM(m)\setminus\she_\dTM(m-1).
\]
Recall that $P$ is invertible if and only if its principal symbol does not vanish.
\smallskip\noindent(i)
If $P\in\she_0$ and its principal symbol is not locally constant,
then $\Sigma(P)(p) = \{\sigma(P)(p)\}$.
Since $\Sigma(P) = \Sigma(f(P))$, it follows that $f(P)\in\she_0$
and $\sigma(P) = \sigma(f(P))$.
\smallskip\noindent(ii)
Let $P\in\she_0$ have locally constant principal symbol.
For any
$Q\in\she_\dTM(0)\setminus\opb{\sigma_0}(\C_\dTM)$ one has
\[
\begin{split}
\sigma_0(P)\sigma_0(Q)
= \sigma_0(PQ)
= \sigma_0(f(PQ))
= \sigma(f(P))\sigma_0(f(Q))
= \sigma(f(P))\sigma_0(Q)
\end{split}
\]
where the second equality follows from (i).
One deduces $\sigma(f(P)) = \sigma_0(P)$, so that in particular $f(P)\in\she_0$.
\smallskip\noindent(iii)
Pick an operator $D\in \she_1$ invertible at $p$, and let $d$ be the degree of
$f(D)$. Then $f(D)^m$ is an invertible operator of order $d m$ and one has
\[
f(\she_m)
= f (D^m \she_0 )
= f(D)^m f(\she_0)
= f(D)^m \she_0
= \she_{d m}.
\]
Since $f$ is an automorphism of $\she_\dTM \setminus \{0\} =
\DUnion\nolimits_{m\in\Z } \she_m$, it follows that $d=\pm 1$. Thus $f$ either
preserves or reverses the order. Note that if an operator $P$ satisfies
$\sigma(P)(p)=0$, then $\Sigma(P)(p)=\C$ if and only if $P$ has
positive order. Hence $f$ preserves the order.
\smallskip\noindent(iv)
We have proved that $f$ is filtered and preserves the symbol of operators in
$\she_0$. As $\she_m = D^m \she_0$, to show that $f$ is symbol preserving it is enough
to check that
$\sigma_1(D) = \sigma_1 (f(D)).$
Let $(x;\xi)$ be a local system of symplectic coordinates at $p$. Identifying
$x_i$ with the operator in $\she_0$ whose total symbol is $x_i$, one has
\[
\begin{split}
\partial_{\xi_i}\sigma_1(D)
&= \{x_i, \sigma_1(D)\}
= \{\sigma_0(x_i), \sigma_1(D)\}
= \sigma_0([x_i,D]) \\
&= \sigma_0(f([x_i,D]))
= \sigma_0([f(x_i),f(D)])
= \{ \sigma_0(f(x_i)), \sigma_1(f(D))\} \\
&= \{ x_i, \sigma_1(f(D))\} =
\partial_{\xi_i}\sigma_1f((D)),
\quad\text{for }i=1,\dots,n,
\end{split}
\]
so that
\[
\sigma_1(D) = \sigma_1 (f(D)) + \varphi(x),
\]
and one takes the homogeneous component of degree $1$.
\end{proof}
\begin{proposition}\label{pro:fadp}
Any $\C$-algebra automorphism of $\she_\dTM$ is locally of the form $\ad(P)$
for some $\lambda\in \C$ and some invertible $P\in \she_\dTM(\lambda)$.
\end{proposition}
\begin{proof}
Identify $\dTM\times\dTM$ to an open subset of $T^*(M\times M)$.
Let $(x)$ be a system of local coordinates on $M$, and denote by $(x,y)$ the
coordinates on $M\times M$. For $Q\in\she_\dTM$, denote by $Q_x$ and $Q_y$ its
pull-back to $\she_{\dTM\times \dTM}$ by the first and second projection,
respectively.
Let $f\colon \she_\dTM \to \she_\dTM$ be a $\C$-algebra automorphism.
By Lemma~\ref{lem:ffilt}, $f$ is filtered and symbol preserving.
Denote by $\shl$ the $\she_{\dTM\times \dTM}$-module with one generator $u$ and relations
\[
\big(x_i-f(y_i) \big) \,u= \big(\partial_{x_i} - f(\partial_{y_i}) \big) \,u =0,
\quad\text{for }i=1,\dots,n.
\]
Then the image $f(Q)$ of $Q\in\she_\dTM$ is characterized by the relation
\begin{equation}\label{eq:fQ}
f(Q)_y\, u = Q^*_x \, u
\quad\text{in }\shl,
\end{equation}
where $Q^*$ denotes the adjoint operator, and
$(\shl,u)$ is a simple module along the conormal bundle of the diagonal
$\Delta$ in $T^*(M\times M)$ (see~\cite{Kas03}).
Denote by $\shc_\Delta$ the sheaf of complex microfunctions along the conormal bundle to
$\Delta$. By \cite[Theorem~8.21]{Kas03}, there exists $\lambda\in\C$ and an
isomorphism
\[
\varphi\colon \she_{\dTM\times\dTM}^{[\lambda]} \tens[\she_{\dTM\times\dTM}] \shc_\Delta \isoto \shl,
\]
so that $\varphi(P_y\tens\delta_\Delta) =u$ for some invertible $P\in
\she_\dTM(\lambda)$. One then has
\[
\begin{split}
P_yQ_yP^{-1}_yu
&=P_yQ_yP^{-1}_y\varphi(P_y\tens\delta_\Delta)
=\varphi(P_yQ_y\tens\delta_\Delta)
=\varphi(Q^*_xP^*_x\tens\delta_\Delta) \\
&=Q^*_x\varphi(P^*_x\tens\delta_\Delta)
=Q^*_x\varphi(P_y\tens\delta_\Delta)
= Q^*_xu.
\end{split}
\]
It follows by \eqref{eq:fQ} that one has $f = \ad(P)$.
\end{proof}
\subsection{Invertible $\she$-bimodules}
Denote by $P^*M$ the projective cotangent bundle of $M$ and by $\gamma\colon \dTM \to P^*M$ the projection. Set
$$
\she_{P^*M} = \oim\gamma\she_{\dTM}.
$$
This is a sheaf of $\C$-algebras endowed with a $\Z$-filtration such that
$\gr\she_{P^*M}\simeq \DSum_{m\in\Z}\sho_{P^*M}(m)$, where one sets
$\sho_{P^*M}(m)=\oim\gamma\sho_{\dTM}(m)$. Note that $\she_{\dTM}$ is constant along
the fibers of $\gamma$. Since these are connected, the adjunction morphism gives an isomorphism
$$
\opb \gamma \she_{P^*M} \isoto \she_{\dTM}.
$$
\begin{lemma}\label{lem:extE}
Let $Z\subset \dTM$ be a closed conic analytic subset. Then
$$
H^j\rsect_Z\she_\dTM = 0 \qquad \text{for $j<\codim_\dTM Z$.}
$$
\end{lemma}
\begin{proof}
Setting $W=\gamma(Z)$, we have $\rsect_Z\she_\dTM \simeq
\opb\gamma\rsect_W\she_\PM$.
We thus have to show that $H^j\rsect_W\she_\PM = 0$ for
$j<\codim_\PM W$. Identify $\she_\PM$ with the sheaf $\shc_\Delta$ of
complex microfunctions along the conormal bundle of the diagonal in $P^*=P^*(M\times M)$.
By quantized contact transformations, $\shc_\Delta$ can further be identified
with the sheaf of complex microfunctions $\shc_S$ along the conormal bundle to
a hypersurface $S\subset P^*$. One has $\shc_S \simeq
\sho_S\dsum H^1_{[S]}\sho_{P^*} \simeq \sho_S^{\oplus\Z}$. Hence $H^j\rsect_W\shc_S
= 0$ for $j<\codim_SW$.
\end{proof}
\begin{proposition}
\label{pr:M**}
Let $\shm$ be a coherent torsion-free $\she_\dTM$-module. Then $\shm$ is locally
free outside a closed conic analytic $2$-codimensional subset.
\end{proposition}
\begin{proof}
We will reduce to the analogue statement for $\sho$-modules, which is well-known
(see \cite[Corollary 5.15]{Kob87}).
Set for short $\she=\she_\dTM$, $\she(0)=\she_\dTM(0)$ and $\sho(0)=\sho_\dTM(0)$.
A coherent $\she(0)$-submodule $\shl\subset\shm$ such that $\she\shl=\shm$ is called a lattice.
(a) $\shm$ has a torsion-free lattice $\shl$. In fact, let $\shf$ be a lattice
in $\shm^* = \shHom[\she](\shm,\she)$. Then $\shf^* =
\shHom[\she(0)](\shf,\she(0))\subset \shHom[\she](\shm^*,\she) = \shm^{**}$ and
$\she\shf^*=\shm^{**}$, i.e.~$\shf^*$ is a lattice in $\shm^{**}$. Then
$\shl=\shf^*\cap\shm$ is a lattice in $\shm$. Since $\shf^{*}$ is reflexive (that is, $\shf^{*} \to (\shf^*)^{**}$ is an isomorphism), $\shf^*$ is torsion free, and so is its submodule $\shl$.
(b) The coherent $\sho(0)$-module $\overline\shl = \shl/\shl(-1)$ is torsion-free. In fact,
consider the exact sequence
\[
0 \to \she(-1) \to \she(0) \to[\sigma_0] \sho(0) \to 0.
\]
Then $\sho(0) \tens[\she(0)] \shl \simeq \overline\shl$. Hence $(\overline\shl)^{*} =
\shHom[\sho(0)](\overline\shl,\sho(0)) \simeq \shHom[\sho(0)](\sho(0) \tens[\she(0)] \shl,\sho(0)) \simeq
\shHom[\she(0)](\shl,\sho(0))$. The exact sequence
\[
0 \to \shHom[\she(0)](\shl,\she(-1) ) \to \shHom[\she(0)](\shl,\she(0) ) \to
\shHom[\she(0)](\shl,\sho(0))
\]
thus reads
\[
0 \to \shl^*(-1) \to \shl^* \to (\overline\shl)^{*}.
\]
Hence $\overline{\shl^*} \subset (\overline\shl)^{*}$. Then
$\overline\shl\subset\overline{\shl^{**}}\subset (\overline{\shl^*})^* \isoto
(\overline{\shl^*})^{***}$, so that $\overline\shl$ is torsion-free.
(c) Since $\overline\shl$ is torsion-free, it is locally free outside a
closed conic analytic $2$-codimensional subset $S$. Hence the same holds true for $\shl$ by Nakayama
lemma. Thus $\shm=\she\shl$ is also locally free outside $S$.
\end{proof}
\begin{remark}
\label{rem:tf}
Since projective $\she_\dTM$-modules are torsion-free, it follows that $\she_\dTM$ is (coherent)
projective-free if $\dim M = 1$. This is no more true if $\dim M > 1$.
\end{remark}
Set
\[
\she_\dTM^e = \she_\dTM^\op\tens[\C]\she_\dTM.
\]
Note that, for $[\lambda],[\mu]\in\C/\Z$ the morphism of $\she_\dTM^e$-modules
$$
\she_\dTM^{[\lambda]}\tens[\she_\dTM]\she_\dTM^{[\mu]} \to \she_\dTM^{[\lambda + \mu]}, \quad
P\tens Q \mapsto PQ
$$
is an isomorphism. In particular, $\she_\dTM^{[\lambda]}$ is an invertible $\she_\dTM^e$-module.
Moreover, if $P\in\she_\dTM(\lambda)$ has non vanishing symbol on $V\subset \dTM$,
there is an isomorphism of $\she_V^e$-modules
\begin{equation}
\label{eq:Elloc}
{}_{\ad(\opb P)}(\she_V) \isoto \she_V^{[\lambda]}, \quad
Q \mapsto PQ.
\end{equation}
\begin{lemma}\label{lem:Elm}
For $[\lambda],[\mu]\in\C/\Z$, one has
\[
\shHom[\she_\dTM^e](\she_\dTM^{[\lambda]},\she_\dTM^{[\mu]}) =
\begin{cases}
\C_\dTM &\text{for }[\lambda] = [\mu], \\
0 &\text{otherwise}.
\end{cases}
\]
\end{lemma}
\begin{proof}
The problem is local and we take a system $(x) = (x_1,\dots,x_n)$ of
local coordinates in $V\subset \dTM$ such that $\partial_1$ is invertible in $V$.
By~\eqref{eq:Elloc}
\begin{align*}
\shHom[\she_{V}^e](\she_{V}^{[\lambda]},\she_{V}^{[\mu]})
&\simeq \shHom[\she_{V}^e]({}_{\ad(\partial_1^{-\lambda})}(\she_{V}),
{}_{\ad(\partial_1^{-\mu})} (\she_{V})) \\
&\simeq \{ P\in\she_{V} \colon P \partial_1^{-\lambda} Q \partial_1^{\lambda} =
\partial_1^{-\mu} Q \partial_1^{\mu} P,\ \forall Q\in\she_{V} \}.
\end{align*}
Assume that there exists $P\neq 0$ as above.
Taking for $Q$ the operators $\partial_1$, $x_i$ and $\partial_i$,
respectively, we deduce that $[P,\partial_1] = [P,x_i] = [P,\partial_i] = 0$
for $i=2,\dots,n$. It follows that $P$ only depends on $\partial_1$. Noting
that $[\partial_1^\lambda,x_1] = \lambda\partial_1^{\lambda-1}$ and taking
$Q=x_1$, we get
\[
[x_1,P] = (\mu - \lambda) P \partial_1^{-1}.
\]
Write $P = \sum_{j\leq m}c_j
\partial_1^j$ with $c_i\in\C$ and $c_m\neq 0$. Then the above equality gives $m=\mu -
\lambda$ and $c_j=0$ for $j<m$.
\end{proof}
The following result was communicated to us by Masaki Kashiwara (refer to \cite{KV10} for related results).
\begin{theorem}\label{thm:Eeloc}
Any invertible $\she_\dTM^e$-module is isomorphic to
$L\tens[\C]\she_\dTM^{[\lambda]}$, for some local system of rank one $L$ and some locally constant $\C/\Z$-valued function $[\lambda]$.
\end{theorem}
\begin{proof}
Set for short $\she=\she_\dTM$. Let $\shp$ be an invertible $\she^e$-module.
It is enough to show that $\shp$ is locally isomorphic to
$\she^{[\lambda]}$ for some locally constant function $[\lambda]$.
In fact, it will follow from Lemma~\ref{lem:Elm} that
$L = \shHom[\she^e](\she^{[\lambda]},\shp)$ is a local system of rank one and
$L\tens[\C]\she^{[\lambda]} \isoto \shp$.
(a) Since $\shp$ is invertible, the underlying $\she$-module ${}_{\bullet}\shp$ is projective locally of finite presentation by (iv) and (v) on page~\pageref{pgv}, and hence coherent torsion-free. By Proposition~\ref{pr:M**}, ${}_{\bullet}\shp$ is locally free outside a closed analytic $2$-codimensional subset $Z$. As $\shp$ is invertible, its rank is one.
(b) Suppose that ${}_{\bullet}\shp$ is free of rank one. Then there exists
$[\lambda]$ such that $\shp^{[-\lambda]} = \shp \tens[\she^e] \she^{[-\lambda]}$ admits a regular generator, i.e.~a generator $u$ of ${}_{\bullet}\shp^{[-\lambda]}$ such that $Pu = uP$ for any $P\in\she$. Indeed, let $t$ be a generator of ${}_{\bullet}\shp$ and let $f\colon\she\isoto \she$,
be the $\C$-algebra isomorphism as in ~\eqref{eq:LocFreeBim}: $f(P) = Q$ for $Q$ such that $tP=Qt$.
By Proposition~\ref{pro:fadp}, $f$ is locally of the form $\ad(P)$ for some $\lambda\in \C$ and
$P\in \she(\lambda)$ with never vanishing symbol. Then $u=t\opb P$ is a regular generator of $\shp^{[-\lambda]}$.
Let $V$ be a contractible open neighborhood of a point in $Z$.
We are left to show that if ${}_{\bullet}\shp$ is locally free of rank one on
$V\setminus Z$, then ${}_{\bullet}\shp^{[-\lambda]}$ has a regular generator on $V$.
It will follow that $\shp|_{V}\simeq \she^{[\lambda]}_{V}$.
(c) Since local regular generators $u$ of $\shp^{[-\lambda]}$ are unique up to multiplicative
constants, $\C u \subset \shp^{[-\lambda]}$ defines a local system of rank one on $V\setminus Z$.
As $V\setminus Z$ is simply connected, such local system is constant.
Thus $\shp^{[-\lambda]}$ has a regular generator $u$ on $V\setminus Z$.
Consider the distinguished triangle
$$
\rsect_Z \shp^{[-\lambda]} \to \shp^{[-\lambda]} \to \rsect_{V\setminus Z}\shp^{[-\lambda]} \to[+1]
$$
Since $\shp^{[-\lambda]}$ is invertible, then ${}_{\bullet}\shp^{[-\lambda]}$ is flat by (iv) on page~\pageref{pgv}, so that
$$\rsect_Z(V;\shp^{[-\lambda]}) \simeq \rsect(V;\rsect_Z\she\tens[\she]\shp^{[-\lambda]}).$$
By Lemma~\ref{lem:extE} one gets $H^j\rsect_Z(V;\shp^{[-\lambda]}) = 0$ for $j=0,1$.
It follows that $\Gamma(V;\shp^{[-\lambda]})\isoto\Gamma(V\setminus Z;\shp^{[-\lambda]})$, hence the generator $u$ of ${}_{\bullet}\shp^{[-\lambda]}$ on $V\setminus Z$ extends uniquely to $V$.
\end{proof}
In particular, since any $\she_\dTM^{[\lambda]}$ is a locally free right
$\she_\dTM$-module of rank one by~\eqref{eq:Elloc}, it follows that the $\C$-algebra $\she_\dTM$ is Picard good.
Recall that the projection $\gamma\colon \dTM \to P^*M$ is a principal $\C^\times$-bundle.
\begin{theorem}\label{thm:localEPicardGood}
The $\C$-algebra $\she_{P^*M}$ is Picard good.
\end{theorem}
\begin{proof}
Let us prove that any invertible $\she_{P^*M}^e$-module $\shp$
is locally free of rank one as right $\she_{P^*M}$-module.
Since this is a local problem, we may restrict to a simply connected open subset $U\subset P^*M$, so that $\opb\gamma(U) \simeq U\times\C^\times$. The $\she_{\opb\gamma(U)}^e$-module $\opb \gamma \shp$ being invertible, by Theorem~\ref{thm:Eeloc} one gets
\[
\shp \isoto \oim\gamma\opb\gamma\shp \simeq \oim\gamma(L\tens[\C] \she_{\opb\gamma(U)}^{[\lambda]})
\]
for some $[\lambda]\in\C/\Z$ and some local system of rank one $L$ on $\opb\gamma(U)$ with monodromy $e^{-2 \pi i \lambda}$ on $\C^\times$.
By restricting to $U'\subset U$, we may assume that there exists an invertible operator $D$ of order 1. This defines an isomorphism of right $\she_{U'}$-modules
$$
\she_{U'} \isoto \oim\gamma(L\tens[\C]
\she_{\opb\gamma(U')}^{[\lambda]}) \quad
Q \mapsto D^\lambda Q.
$$
\end{proof}
Note that, given a local system of rank one $L$ and $[\lambda]\in\C/\Z$, one has
$\oim \gamma (L \tens[\C] \she_\dTM^{[\lambda]})\neq 0$ if and only if the monodromy of $L$
along the fiber of $\gamma$ is given by $e^{-2 \pi i\lambda}$.
In particular, $\oim \gamma \she_{\dTM}^{[\lambda]}= 0$ for any $[\lambda]\neq 0$.
\section{Microdifferential algebroids}\label{se:results}
Here we state and prove our results on classification of
$\she$-algebroids on a contact manifold.
\subsection{Contact manifolds}
Let $X$ be a complex manifold of odd dimension, say $2n-1$.
Denote by $\sho_X$ the sheaf of
holomorphic functions and by $\Omega^1_X$ the sheaf of holomorphic $1$-forms.
A structure of
(complex) contact manifold on $X$ is the assignment of a holomorphic principal
$\C^\times$-bundle $\gamma\colon Y\to X$, called symplectification, and of a
holomorphic one-form $\alpha \in \sect(Y;\Omega^1_Y)$, called contact form,
such that $\omega = d \alpha$ is symplectic (i.e.~$\omega^n$ vanishes nowhere)
and
$i_\theta \alpha = 0$,
$L_\theta \alpha = \alpha$.
Here, $\theta$ denotes the infinitesimal generator of the action of
$\C^\times$ on $Y$, $i_\theta$ the inner product and $L_\theta$ the Lie
derivative.
One may consider $\alpha$ as a global section of
$\Omega^1_X\tens[\sho_X]\sho_X(1)$, where $\sho_X(1)$ denotes the dual
of the sheaf of sections of the line bundle $\C\times_{\C^\times}Y$.
Let $M$ be a complex manifold of dimension $n$.
Then $P^*M$ has a natural contact structure given by the Liouville one-form on
$\dTM$ and by the projection $\gamma\colon \dTM \to P^*M$.
By Darboux theorem, $P^*M$ is a local model for a contact manifold $X$, meaning that
there are an open cover $\{U_i\}_{i\in I}$ of $X$ and
contact embeddings (i.e.~embeddings preserving the contact forms) $j_i\colon
U_i \hookrightarrow P^*M$ for any $i\in I$.
A fundamental result by~\cite{S-K-K} asserts
that contact transformations (i.e.~biholomorphisms
preserving the contact forms) can be locally quantized. This means the
following. Let $N$ be another complex manifold of dimension $n$, $U\subset
P^*M$ and $V\subset P^*N$ open subsets and $\chi\colon U\to V$ a contact
transformation. Then any $x\in U$ has an open neighborhood $U'$ such that
there is a $\C$-algebra isomorphism $\opb \chi (\she_{P^*N}|_{\chi (U')}) \isoto
\she_{P^*M}|_{U'}$.
\begin{definition}\label{def:mical}
An $\she$-algebra on a contact manifold $X$ is a sheaf
$\sha$ of $\C$-algebras such that there are an open cover $\{U_i\}_{i\in I}$
of $X$, contact embeddings $j_i\colon U_i \hookrightarrow P^*M$ and
$\C$-algebra isomorphisms $\sha|_{U_i} \simeq \opb j_i\she_{P^*M}$ for any
$i\in I$.
\end{definition}
Given an $\she$-algebra $\sha$, the $\C$-algebra $\opb \gamma \sha$ on $Y$
satisfies $\opb \gamma \sha|_{\opb \gamma(U_i)} \simeq \opb {\tilde j_i}\she_{\dTM}$ for $\tilde j_i$ a lifting of $j_i\colon U_i \hookrightarrow P^*M$.
Note that, from Proposition~\ref{pro:fadp} it follows that for $[\lambda]\in \C/\Z$ the invertible
$\opb \gamma \sha^e$-module $(\opb \gamma \sha)^{[\lambda]}$ is well-defined.
In the strict sense, to quantize $X$ means to endow it with an
$\she$-algebra (see~\cite{Bou99}). This might not be possible in
general. However, as we now recall, Kashiwara~\cite{Kas96} proved that
$X$ is endowed with a canonical $\she$-algebroid.
\subsection{Microdifferential algebroids}
\begin{definition}\label{def:microalg}
\begin{itemize}
\item[(i)]
An $\she$-algebroid on $X$ is a $\C$-algebroid $\stka$
such that for every open subset $U\subset X$ and any object
$\obja\in\stka(U)$, the $\C$-algebra $\shEnd[\stka](\obja)$ is an
$\she$-algebra on $U$.
\item[(ii)]
A stack of twisted $\she$-modules on $X$ is a $\C$-stack $\stkm$ such that
there are an open cover $\{U_i\}_{i\in I}$ of $X$, $\she$-algebras
$\she_i$ on $U_i$ and equivalences $\stkm|_{U_i} \equi[\C] \stkMod(\she_i)$
for any $i\in I$.
\end{itemize}
\end{definition}
Note that a $\C$-stack $\stka$ is an $\she$-algebroid if and
only if there are an open cover $\{U_i\}_{i\in I}$ of $X$, $\she$-algebras
$\she_i$ on $U_i$ and equivalences $\stka|_{U_i}\equi[\C]\astk{\she_i}$ for any $i\in I$.
In particular, $\stkMod(\stka)$ is a stack of twisted $\she$-modules.
Kashiwara's construction of the canonical $\she$-algebroid on $X$ was performed by patching data as explained in
Appendix~\ref{se:acocy} (see~\cite{DK11} for a more intrinsic
construction).
More precisely, he proved in~\cite{Kas96} the
existence of an open cover $\shu = \{U_i\}_{i\in I}$ of $X$, of
$\she$-algebras $\she_i$ on $U_i$, of
isomorphisms of $\C$-algebras $f_{ij}\colon \she_j\to\she_i$
on $U_{ij}$ and of sections
$a_{ijk}\in\sect(U_{ijk};\she_i(0)^\times)$, satisfying the cocycle condition
\begin{equation}
\label{eq:KasCoc}
\begin{cases}
f_{ij}f_{jk} = \ad(a_{ijk})f_{ik},\\
a_{ijk} a_{ikl} = f_{ij}(a_{jkl}) a_{ijl}.
\end{cases}
\end{equation}
By Proposition~\ref{pr:glue}~(i), this implies
\begin{theorem}[\cite{Kas96}]
Any complex contact manifold $X$ is endowed with a canonical
$\she$-algebroid $\stke_X$.
\end{theorem}
It follows that a $\C$-stack on $X$ is an
$\she$-algebroid (resp.~a stack of twisted $\she$-modules) if and only if it
is locally $\C$-equivalent to $\stke_X$ (resp.~to $\stkMod(\stke_X)$). In particular, if
$X=P^*M$ then $\stke_{P^*M}$ is $\C$-equivalent to $\she_{P^*M}$, and $\she$-algebroids
are $\C$-twisted forms of $\she_{P^*M}$.
Recall that an algebroid is Picard good if and only if so are the algebras
that locally represent it. Hence, by Theorem~\ref{thm:localEPicardGood} one gets
that any $\she$-algebroid, and in particular $\stke_X$, is Picard good.
>From Proposition~\ref{pro:picgood}, we thus deduce the following
\begin{theorem}\label{thm:Emoritatrivial}
\begin{itemize}
\item[(i)]
Two $\she$-algebroids are $\C$-equivalent if and only
if they are Morita equivalent.
\item[(ii)]
Any stack of twisted $\she$-modules is $\C$-equivalent to the stack of modules
over an $\she$-algebroid.
\end{itemize}
\end{theorem}
To classify $\she$-algebroids, we thus need to compute the first cohomology
with value in the stack of 2-groups $\stkAut[\C](\stke_X)\equi[]\stkInv(\stke_X^e)_\op$,
where we set $\stke_X^e = \stke_X^\op\tens[\C]\stke_X$.
\subsection{Geometry of $\gamma\colon Y\to X$}\label{se:gamma}
\begin{lemma}\label{lem:roimgamma}
For $M$ an abelian group, there is a distinguished triangle
$$
M_X \to \roim\gamma M_Y \to M_X[-1] \to[+1]
$$
\end{lemma}
\begin{proof}
As the complex $\roim\gamma M_Y$ is concentrated in degrees $[0,1]$, by
truncation it is enough to prove the isomorphisms
\begin{equation}\label{eq:roimgammatemp}
H^i\roim\gamma M_Y \simeq M_X,\quad\text{for } i=0,1.
\end{equation}
For $i=0$ it is induced by the adjunction morphism $M_X \to
\roim\gamma M_Y$.
Set $SY=Y/\R_{>0}$ and consider $\gamma$ as the composite of $p\colon Y \to
SY$ and $q\colon SY\to X$, which are principal bundle for the groups $\R_{>0}$
and $S^1$, respectively. Note that $\roim p M_Y \simeq M_{SY}$, so that
$\roim\gamma M_Y \simeq \roim q M_{SY} \simeq \reim q M_{SY}$. The
infinitesimal generator $\theta$ of the action of $\C^\times$ on $Y$ induces a
trivialization of the relative orientation sheaf $or_{SY/X}$. Hence $\epb q
M_X \simeq M_{SY}[1]$. Then the isomorphism \eqref{eq:roimgammatemp} for $i=1$
is induced by the adjunction morphism $\reim q M_{SY} \simeq \reim q \epb q
M_X[-1] \to M_X[-1]$.
\end{proof}
Let $M=\C^\times$. The induced long exact cohomology sequence is
\[
H^1(Y;\C^\times) \to[\mu_1] H^0(X;\C^\times) \to[\delta]
H^2(X;\C^\times) \to[\gamma^\#] H^2(Y;\C^\times) \to[\mu_2] H^1(X;\C^\times) .
\]
Let us describe the above sequence (see also~\cite[Chapitre V \S 3.1, 3.2]{Gir71}), were we use the notation $[\cdot]$ both for isomorphism and $\C$-equivalence classes.
For $L$ a local systems of rank one on $Y$, $\mu_1([L])$ is the locally constant function on $X$ giving the monodromy of $L$ along the fibers of $\gamma$.
\begin{lemma}\label{lem:pi_0}
\begin{itemize}
\item[(i)]
There is a group isomorphism $\pi_0(\oim\gamma\astk{\C_Y})\simeq\C_X^\times$, where the group structure on the left-hand side is induced by $\tens_\C$.
\item[(ii)]
For any $\C$-stack $\stkd$ on $Y$, the sheaf $\pi_0(\oim \gamma \stkd)$ is endowed with a $\C_X^\times$-action.
\end{itemize}
\end{lemma}
\begin{proof}
(i) Recall that $\astk{\C_Y}$ is the stack of local systems of rank one on $Y$ and $\C^\times_Y[1]$ that of $\C_Y^\times$-torsors. Then the functor
\[
\C_Y^\times[1] \to\astk{\C_Y},
\quad \shp \mapsto \C \times_{\C^\times} \shp
\]
defines a group isomorphism $\pi_0(\oim\gamma\astk{\C_Y})\simeq \pi_0(\oim\gamma(\C_Y[1]))$.
By~\eqref{eq:pi-roim}, the latter is isomorphic to $R^1\oim \gamma \C_Y^\times$, hence to $\C_X^\times$ by Lemma~\ref{lem:roimgamma}.
\smallskip\noindent
(ii) By using~\eqref{eq:dir-im}, one gets a $\C$-functor
$$
\oim\gamma\astk{\C_Y}\tens[\C] \oim\gamma\stkd \to \oim\gamma\stkd, \quad (L,\delta) \mapsto L\tens[\C]\delta.
$$
This defines an action of $\pi_0(\oim\gamma\astk{\C_Y})\simeq\C_X^\times$ on $\pi_0(\oim\gamma\stkd)$.
\end{proof}
\begin{notation}\label{nt:subAlg}
Let $\stkc$ be a $\C$-stack. For $s$ a global section of $\pi_0(\stkc)$, we denote by $\stkc^s$ the full substack of $\stkc$ whose objects have isomorphism class $s$ in $\pi_0(\stkc)$.
\end{notation}
Note that $\stkc^s$ is a $\C$-algebroid, since $\pi_0(\stkc^s)=\{s\}$. It is locally $\C$-equivalent to the algebra $\shEnd[\stkc](\objc)$ for any local representative $\objc$ of $s$.
\medskip
By Lemma~\ref{lem:tors}, the cohomology group $H^2(X;\C^\times)$ classifies equivalence classes of invertible $\C_X$-algebroids. Then, for $m \in H^0(X;\C^\times) \simeq \sect(X,\pi_0(\oim\gamma\astk{\C_Y}))$, one has
$$\delta(m) = [(\oim\gamma\astk{\C_Y})^m].$$
Here $(\oim\gamma\astk{\C_Y})^m$ is identified with the $\C_X$-algebroid of local systems $L\in\oim\gamma\astk{\C_Y}$ with $\mu_1([L]) = m$. In particular,
$\astk{\C_X}$ is equivalent to $(\oim\gamma\astk{\C_Y})^1$ via the adjunction functor $\astk{\C_X} \to \oim \gamma \astk{\C_Y}$ and one has a decomposition $\oim\gamma\astk{\C_Y} \equi[\C]
\coprod\nolimits_{m\in\C_X^\times} (\oim\gamma\astk{\C_Y})^m$.
For $\stks$ an invertible $\C_X$-algebroid, $\gamma^\#([\stks]) =[\opb\gamma\stks]$.
\begin{proposition}
For $\stkt$ an invertible $\C_Y$-algebroid, $\mu_2([\stkt])$ is the class of the local systems of rank one $\C \times_{\C^\times} \pi_0(\oim\gamma\stkt)$.
\end{proposition}
\begin{proof}
By Lemma~\ref{lem:pi_0}, there is an action of $\pi_0(\oim\gamma\astk{\C_Y})\simeq\C_X^\times$ on
$\pi_0(\oim\gamma\stkt)$. Since $R^2\oim \gamma \C_Y^\times = 0$, the stack $\oim\gamma\stkt$ is locally $\C$-equivalent to $\oim\gamma\astk{\C_Y}$, hence $\pi_0(\oim\gamma\stkt)$
is a $\C_X^\times$-torsor.
It follows that $\C \times_{\C^\times} \pi_0(\oim\gamma\stkt)$ is a local system of rank one on $X$.
Choose an open covering $\{U_i\}$ of $X$ in such a way that $\stkt$ is described, by means of the Proposition~\ref{pr:patch} (i), by the data
$(\astk \C_{V_i}, (\cdot)\tens[\C]M_{ji}, \transfa_{ijk})$, where $V_i=\opb \gamma (U_i)$ and
$M_{ji}$ are local sistem of rank one on $V_{ij}$. Then $\C \times_{\C^\times} \pi_0(\oim\gamma\stkt)$
is represented by the 1-cocycle $\{\mu_1(M_{ji})\}$ with values in $\C^\times$, which
gives a Cech representative of the class $\mu_2([\stkt])$.
\end{proof}
\subsection{Classification results}
Set
\[
\stke_Y = \opb\gamma\stke_X.
\]
This can be described by patching the $\C$-algebras $\opb\gamma\she_i$ along the pull back
on $Y$ of the data~\eqref{eq:KasCoc}.
Let $\stke_Y^e = \stke_Y^\op\tens[\C]\stke_Y$. For $[\lambda]\in\C/\Z$, the algebroid version of the invertible bimodule $\she_\dTM^{[\lambda]}$ is the $\stke_Y^e$-module $\stke_Y^{[\lambda]}$ defined by
$$
(\alpha,\beta) \mapsto \shendo[\stke_Y](\beta)^{[\lambda/2]} \tens[{\shendo[\stke_Y](\beta)}] \hom[\stke_Y](\alpha,\beta)\tens[{\shendo[\stke_Y](\alpha)}] \shendo[\stke_Y](\alpha)^{[\lambda/2]}.
$$
It is invertible, as being invertible is a local property.
Consider the direct image functor
\[
\oim\gamma \colon \oim \gamma\stkMod(\stke_Y^e) \to \stkMod(\stke_X^e)
\]
and recall the morphism
$H^1(Y;\C^\times) \to[\mu_1] H^0(X;\C^\times)\simeq H^0(X;\C/\Z)$ from \S\ref{se:gamma}.
\begin{theorem}\label{thm:gammainv}
The functor
\begin{equation}
\label{eq:E-inv}
\oim\gamma\stkInv(\C_Y) \to \stkInv(\stke_X^e),
\qquad L \mapsto \oim\gamma(L \tens[\C] \stke_Y^{\mu_1(L^*)})
\end{equation}is an equivalence of stacks of 2-groups.
\end{theorem}
\begin{proof}
(a) A priori, $\oim\gamma(L \tens[\C] \stke_Y^{\mu_1(L^*)})$ is an object of
$\stkMod(\stke_X^e)$. This is locally, hence globally, invertible with inverse given by $\oim\gamma(L^* \tens[\C] \stke_Y^{\mu_1(L)})$.
(b) The sheaf $\C_Y$ is sent to $\stke_X$, since $\oim\gamma(\stke_Y)\simeq\stke_X$ as $\stke_X^e$-modules. Moreover, the natural morphism
$$
\oim\gamma(L \tens[\C] \stke_Y^{\mu_1(L^*)}) \tens[\stke_X] \oim\gamma(L'
\tens[\C] \stke_Y^{\mu_1(L'^*)}) \to \oim\gamma(L \tens[\C] L'^* \tens[\C] \stke_Y^{\mu_1(L^*) + \mu_1(L'^*)})
$$
is locally, hence globally, an isomorphism. Hence~\eqref{eq:E-inv} is monoidal.
(c) For an invertible $\stke_X^e$-module $\shp$, define its exponential as the unique locally
constant $\C/\Z$-valued function $\epsilon(\shp)$ on $X$ such that $\opb \gamma \shp$ is locally isomorphic to $\stke_Y^{\epsilon(\shp)}$ (this is well-defined by Theorem~\ref{thm:Eeloc}.). Then $\epsilon(\oim\gamma(L\tens[\C] \stke_Y^{\mu_1(L^*)}))=\mu_1(L^*)$, and by using the Lemma~\ref{lem:Elm} one gets that the functor
$$
\shp\mapsto \hom[\stke_Y^e](\stke_Y^{\epsilon(\shp)}, \opb \gamma \shp)
$$
is a quasi-inverse of~\eqref{eq:E-inv}.
\end{proof}
Let $\mathrm{Pic}(\stke_X^e)$ denote the set of isomorphism class of invertible
$\stke_X^e$-modules, endowed with the group structure induced by $\tens[\stke_X]$.
\begin{corollary}\label{cor:class} There is a group isomorphism
$\mathrm{Pic}(\stke_X^e)\simeq H^1(Y; \C_Y^\times).$
\end{corollary}
\begin{theorem}\label{thm:class}
The set of $\C$-equivalence classes (resp. Morita classes) of $\she$-algebroids is canonically isomorphic, as a pointed set, to $H^2(Y;\C^\times_Y)$.
\end{theorem}
\begin{proof}
Since $\stke_X$ is Picard good, by Theorem~\ref{thm:gammainv} there is
an equivalence of stacks of 2-groups
$$
\stkAut[\C](\stke_X) \equi[] \oim\gamma\stkInv(\C_Y)_\op.
$$
The right-hand term is equivalent to $\oim\gamma\stkInv(\C_Y)$ by the functor $L\mapsto L^*$.
Since $\C_Y$ is Picard good, from~\eqref{eq:TorsInv} and by using~\eqref{eq:roim} one gets an equivalence of stacks of 2-groups
\[
\oim\gamma\stkInv(\C_Y) \equi[] [\roim\gamma\C_Y^\times[1]].
\]
It then follows from \eqref{eq:h1commcross} that
\begin{equation}
\label{eq:MoritaClass}
H^1(X; \stkAut[\C](\stke_X)) \simeq H^2(Y; \C_Y^\times).
\end{equation}
\end{proof}
We end by giving a geometric realization of the isomorphism~\eqref{eq:MoritaClass}.
\medskip
First, let us explain how to twist $\stke_Y$ by a local system of rank one $L$ on $X$, obtaining a $\C$-algebroid $\stke_Y^L$ on $Y$ locally $\C$-equivalent to $\stke_Y$.
Choose an open covering $\{U_i\}$ of $X$ in such a way that $L$ is represented by a 1-cocycle
$\{[\lambda_{ij}]\}$ with values in $\C/\Z$. Set $V_i=\opb \gamma (U_i)$ and consider the data
$(\stke_{V_i}, (\cdot)\tens[\stke_{V_{ij}}]\stke_{V_{ij}}^{[\lambda_{ij}]}, \transfm_{ijk})$, where
$\transfm_{ijk}$ denotes the invertible transformation induced by the canonical isomorphism of
$\stke_{V_{ijk}}^e$-modules
$$
\stke_{V_{ijk}}^{[\lambda_{ij}]} \tens[\stke_{V_{ijk}}]\stke_{V_{ijk}}^{[\lambda_{jk}]}\isoto \stke_{V_{ijk}}^{[\lambda_{ik}]}.
$$
Then $\stke_Y^L$ is the $\C$-stack on $Y$ obtained from these data by Proposition~\ref{pr:patch} (i).
Note that $(\stke_Y^L)^\op\equi[\C]\stke_Y^{L^*}$ and $\stke_Y^L\equi[\C]\stke_Y$ if $L$ is trivial.
Recall from Lemma~\ref{lem:pi_0} that $\pi_0(\oim \gamma \stke_Y^L)$ is endowed with a $\C_X^\times$-action, and denote by $L^\times$ the $\C^\times$-torsor associated to $L$.
\begin{lemma}\label{lem:iso-pi_0L}
$\pi_0(\oim \gamma \stke_Y^L)\simeq L^\times \times_{\C^\times}\pi_0(\oim \gamma\stke_Y)$ as $\C^\times$-sheaves.
\end{lemma}
\begin{proof}
Let $\{[\lambda_{ij}]\}$ be a 1-cocycle with values in $\C/\Z$ representing $L$ on an open
covering $\{U_i\}$ of $X$. Then $\oim \gamma \stke_Y^L|_{U_i}\equi[\C]\oim \gamma \stke_Y|_{U_i}$ and the associated glueing $\C$-equivalences $\oim \gamma \stke_Y|_{U_{ij}}\to\oim \gamma \stke_Y|_{U_{ij}}$ are given by $(\cdot)\tens[\stke_{V_{ij}}]\stke_{V_{ij}}^{[\lambda_{ij}]}$, where $V_i=\opb \gamma(U_i)$. We thus get isomorphisms of $\C^\times$-sheaves $\pi_0(\oim \gamma \stke_Y^L)|_{U_i}\simeq \pi_0(\oim \gamma\stke_Y)|_{U_i}$, with associated glueing automorphisms of
$\pi_0(\oim \gamma \stke_Y)|_{U_{ij}}$
given by multiplication by $e^{2\pi i \lambda_{ij}}$.
This follows from the commutative diagram of stacks of 2-groups
$$
\xymatrix{ \C/\Z_X[0] \ar[d] \ar[r]^-{\simeq} & \C^\times_X [0] \ar[d] \\
\oim\gamma\stkAut[\C](\stke_Y) \ar[r]^-{\pi_0} & \shAut(\pi_0(\oim \gamma \stke_Y))[0],}$$
where the left-hand vertical arrow is the functor $[\lambda]\mapsto (\cdot)\tens[\stke_Y] \stke_Y^{[\lambda]}$ and the right-hand one is the $\C^\times$-action.
Hence $\pi_0(\oim \gamma \stke_Y^L)$ is isomorphic to $\pi_0(\oim \gamma \stke_Y)$ twisted by the
$\C^\times$-torsor $L^\times$.
\end{proof}
Let $\stkt$ be an invertible $\C_Y$-algebroid. Recall that we denote by $\mu_2(\stkt)$ the local system of rank one on $X$ associated to the $\C^\times$-torsor $\pi_0(\oim\gamma\stkt)$.
\begin{lemma}\label{lem:iso-pi_0T}
$\pi_0(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))\simeq\pi_0(\oim \gamma\stke_Y)$
as $\C^\times$-sheaves.
\end{lemma}
\begin{proof}
By using the functor~\eqref{eq:dir-im}, one gets a morphism
$$
\pi_0(\oim \gamma\stkt) \times \pi_0(\oim\gamma \stke_Y^{\mu_2(\stkt^\op)})\to
\pi_0(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))
$$
which is $\C^\times$-equivariant on each term. Hence it factors through $\pi_0(\oim \gamma\stkt) \times_{\C^\times} \pi_0(\oim\gamma \stke_Y^{\mu_2(\stkt^\op)})$. By Lemma~\ref{lem:iso-pi_0T}, this is isomorphic to $\pi_0(\oim \gamma\stke_Y)$, since $\pi_0(\oim \gamma\stkt^\op)$ is isomorphic to the $\C^\times$-torsor opposite to $\pi_0(\oim \gamma\stkt)$. It follows that we have a morphism
$$
\pi_0(\oim \gamma\stke_Y)\to \pi_0(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))
$$
of $\C^\times$-sheaves, which is locally, hence globally, an isomorphism.
\end{proof}
\begin{corollary}
$\pi_0(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))$ has a canonical global section.
\end{corollary}
\begin{proof}
The adjunction functor $\stke_X \to \oim \gamma \stke_Y$ defines a morphism
$\pi_0(\stke_X) \to \pi_0(\oim \gamma \stke_Y)$. Since $\pi_0(\stke_X)$ is a singleton, this gives
a global section of $\pi_0(\oim \gamma \stke_Y)$, hence of $\pi_0(\oim \gamma(\stkt
\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))$ by Lemma~\ref{lem:iso-pi_0T}.
\end{proof}
Denote by $can$ the canonical global section of $\pi_0(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))$. Then the inverse of the isomorphism~\eqref{eq:MoritaClass} is realized as
\[
[\stkt] \mapsto [(\oim \gamma(\stkt\tens[\C]\stke_Y^{\mu_2(\stkt^\op)}))^{can}],
\]
where $[\cdot]$ denotes the $\C$-equivalence class and we use the Notation~\ref{nt:subAlg}.
If $\stks$ be an invertible $\C_X$-algebroid, then $\mu_2(\opb\gamma\stks^\op)$
is trivial and the above isomorphism reduces to
\[
[\opb\gamma\stks] \mapsto [(\oim \gamma \opb\gamma(\stks\tens[\C]\stke_X))^{can}] = [\stks\tens[\C]\stke_X].
\]
\begin{remark} Replacing $\stke_X$ by an $\she$-algebroid in the previous construction, one gets an action of $H^2(Y;\C^\times_Y)$ on the set of $\C$-equivalence classes (resp. Morita classes) of $\she$-algebroids. In such a way, the latter becomes an
$H^2(Y;\C^\times_Y)$-torsor and the canonical isomorphism~\eqref{eq:MoritaClass} is obtained by choosing the $\C$-equivalence class of $\stke_X$ as base point.
\end{remark}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,444 |
{"url":"http:\/\/www.worldcat.org\/identities\/viaf-242099474\/","text":"# Chang, Richard\n\nOverview\nWorks: 28 works in 41 publications in 1 language and 518 library holdings History\u00a0 Interviews Actor HV8138, 364\nPublication Timeline\n1960 | |2020\nKey\nPublications about Richard Chang\nPublications by Richard Chang\nMost widely held works by Richard Chang\nState-of-the-art-reactor consequence analysis (SOARCA) report : draft report for comment ( )\n4 editions published in 2012 in English and held by 157 WorldCat member libraries worldwide\nContemporary criminal justice by Harry W More ( Book )\n2 editions published in 1974 in English and held by 148 WorldCat member libraries worldwide\nState-of-the-art-reactor consequence analyses (SOARCA) report by Richard Chang ( )\n2 editions published in 2012 in English and held by 147 WorldCat member libraries worldwide\nHistorians and Meiji statesmen by Richard Chang ( Book )\n1 edition published in 1978 in English and held by 7 WorldCat member libraries worldwide\nHistorians and Taisho statesmen by Richard Chang ( Book )\n1 edition published in 1978 in English and held by 6 WorldCat member libraries worldwide\nOn the structure of NP computations under Boolean operators by Richard Chang ( Book )\n2 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide\nA central theme of this thesis is the development of the hard\/easy argument which shows intricate connections between the Boolean Hierarchy and the Polynomial Hierarchy. The hard\/easy argument shows that the Boolean Hierarchy cannot collapse unless the Polynomial Hierarchy also collapses. The results shown in this regard are improvements over those previously shown by Kadin. Furthermore, it is shown that the hard\/easy argument can be adapted for Boolean hierarchies over incomplete NP languages. That is, under the assumption that certain incomplete languages exist, the Boolean hierarchies over those languages must be proper (infinite) hierarchies. Finally, this thesis gives an application of the hard\/easy argument to resolve the complexity of a natural problem - the unique satisfiability problem. This last refinement of the hard\/easy argument also points out some long-ignored issues in the definition of randomized reductions\nThe Boolean hierarchy and the polynomial hierarchy : a closer connection by Richard Chang ( Book )\n2 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"We show that if the Boolean hierarchy collapses to its k[superscript th] level, then the polynomial hierarchy collapses to the k[superscript th] level of the difference hierarchy of [formula] languages.\"\nA relationship between difference hierarchies and relativized polynomial hierarchies by Richard Beigel ( Book )\n2 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide\nChang and Kadin have shown that if the difference hierarchy over NP collapses to level $k$, then the polynomial hierarchy (PH) is equal to the $k$th level of the difference hierarchy over $\\Sigma_{2}[superscript]{p}$. We simplify their proof and obtain a slightly stronger conclusion: If the difference hierarchy over NP collapses to level $k$, then PH = $\\left(P_{(k-1)-tt}[superscript]{NP}\\right)[supers cript]{NP}$. We also extend the result to classes other than NP: For any class $C$ that has $\\leq_{m}[superscript]{p}$-complete sets and is closed under $\\leq_{conj}[superscript]{p}$- and $\\leq_{m}[superscript]{NP}$-reductions, if the difference hierarchy over $C$ collapses to level $k$, then $PH[superscript]{C} =$\\left(P_{(k-1)-tt}[superscript]{NP}\\right)[supers cript]{C}$. Then we show that the exact counting class$C_{=}P$is closed under$\\leq_{disj}[superscript]{p}$- and$\\leq_{m}[superscript]{co-NP}$-reductions. Consequently, if the difference hierarchy over$C_{=}P$collapses to level$k$then$PH[superscript]{PP}$is equal to$\\left(P_{(k-1)-tt}[superscript]{NP}\\right)[supers cript]{PP}\\$. In contrast, the difference hierarchy over the closely related class PP is known to collapse\nAn example of a theorem that has contradictory relativizations and a diagonalization proof by Richard Chang ( Book )\n2 editions published in 1989 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"We construct a computable space bound S(n), with n\u00b2 [less than] S(n) [less than] n\u00b3 and show by diagonalization that DSPACE[S(n)] = DSPACE[S(n) log n]. Moreover, we show that there exists an oracle A such that DSPACE[superscript A][S(n)] [is not equal to] DSPACE[superscript A][S(n) log n]. This is a counterexample to the belief that if a theorem has contradictory relativizations, then it connot be proved using standard techniques like diagonalization [7]\nOn computing Boolean connectives of characteristic functions by Richard Chang ( Book )\n1 edition published in 1990 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"We study the existence of polynomial time Boolean connective functions for languages. A language L has an AND function if there is a polynomial time f such that [formula]. L has an OR function if there is a polynomial time g such that [formula]. While all NP-complete sets have these functions, we show that Graph Isomorphism, which is probably not complete, also has them. We characterize the complete sets for the classes D[superscript P] and [formula] in terms of AND and OR, and we relate these functions to the structure of the Boolean hierarchy and the query hierarchies\nRandom reductions in the Boolean hierarchy are not robust by Richard Chang ( Book )\n2 editions published in 1990 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"We investigate random reductions from complete sets in the Boolean Hierarchy to their complements. We show that under the assumption that the Polynomial Hierarchy is infinite, the error probability of such reductions cannot be significantly lower than a constant. This constant depends on the classes in question. Thus, random reductions in the Boolean Hierarchy are not robust. We also show that the trivial random reductions between classes at the second level of the Boolean Hierarchy are optimal.\"\nOn the structure of bounded queries to arbitrary NP sets by Richard Chang ( Book )\n2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"In [Kad87b], Kadin showed that if the Polynomial Hierarchy (PH) has infinitely many levels, then for all k, [formula]. In this paper, we extend Kadin's technique to show that a proper query hierarchy is not an exclusive property of SAT. In fact, for any A [formula], if PH is infinite, then [formula]. Moreover, for the case of parallel queries, we show that P[formula] is not contained in P[formula]. We claim that having a proper query hierarchy is a consequence of the oracle access mechanism and not a result of the 'hardness' of a set. To support this claim, we show that assuming PH is infinite, one can construct an intermediate set B [formula] so that [formula]. That is, the query hierarchy for B grows as 'tall' as the query hierarchy for SAT\nOn the structure of uniquely satisfiable formulas by Richard Chang ( Book )\n1 edition published in 1990 in English and held by 4 WorldCat member libraries worldwide\nAbstract: \"This paper presents some new results on the computational complexity of the set of uniquely satisfiable Boolean formulas (USAT). Valiant and Vazirani showed that USAT is complete for the class D[superscript P] under randomized reductions. In spite of the fact that the probability bound of this reduction is low, we show that USAT captures many properties possessed by D[superscript P] many-one complete sets. We show that the structure of USAT can affect the structure of D[superscript P] and the entire Polynomial Hierarchy (PH) as well. That is, 1. if USAT [formula], then D[superscript P] = co-D[superscript P] and PH collapses\nHistorians and the Taisho Statesmen by Richard T Chang ( )\n2 editions published in 1984 in No Linguistic content and English and held by 2 WorldCat member libraries worldwide\nThis data collection contains data from questionnaire sent to 68 historians in Japan for their assessments of 18 statesmen active during the Taisho period in Japan (1912-1926). The data include biographical information on the respondents, such as birthplace, year of birth, Marxist or non-Marxist affiliation, university of graduation, status (e.g., professor, assistant professor, or doctoral candidate), faculty (discipline), and academic specialization. The file also includes the historians' assessments of the Taisho statesmen on an interval scale of five, from most important, most influential to least important, least influential. For a related data collection, see HISTORIANS AND THE MEIJI STATESMEN (ICPSR 7653)\nOptimizing customer value ( Visual )\n1 edition published in 1997 in English and held by 2 WorldCat member libraries worldwide\nExplains ways you organization can enhance its quality to service customers better, and increase the perceived value of your products and services\nThe church at the millennium : eight bishops respond ( Visual )\n1 edition published in 2000 in English and held by 2 WorldCat member libraries worldwide\nThe Passion plan putting your passion to work ( Visual )\n1 edition published in 2001 in English and held by 2 WorldCat member libraries worldwide\nDesigned to increase one's self-awareness of their true passion in life, and to illustrate how cultivating this passion opens doors to both personal and professional success. Provides guidelines for developing one's own Passion Plan and vignettes throughout highlight individuals as they progress through the Passion Plan seven-step process\nHistorians and the Meiji Statesmen by Richard Chang ( )\n2 editions published in 1984 in No Linguistic content and English and held by 2 WorldCat member libraries worldwide\nThis data collection contains survey information for 127 historians in Japan and 14 historians in England and the United States on their assessments of 40 Meiji statesmen active in the Meiji period in Japan (1868-1912). Part 1 contains data collected from the Japanese respondents, including their rankings of the statesmen on a five-point interval scale (from most important, most influential, to least important, least influential) and a cumulative ranking on a ten-point interval scale. Part 1 also includes biographical information about the interview respondents, i.e., birthplace, year of birth, university of graduation, and field of study. Part 2 contains data collected from the English and American respondents, including their rankings of the Meiji statesmen on the five-point interval scale. For a list of the 40 Meiji statesmen, details of the five ranks, and a description of the criteria for the ten-point interval scale, see Appendices C and D, and Table 16 in Chang, Richard. HISTORIANS AND MEIJI STATESMEN. Gainesville, FL: University of Florida Press, 1970. For a related data collection, see HISTORIANS AND THE TAISHO STATESMEN (ICPSR 7608)\nOn the superelastic response of nickel-titanium-alloy archwires in flexure by Richard Chang ( Book )\n1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide\nNear speed-of-light on-chip electrical interconnects by Richard Chang ( Book )\n1 edition published in 2002 in English and held by 1 WorldCat member library worldwide\n\nmore\nfewer\nAudience Level\n 0 1 Kids General Special\n\nRelated Identities\nLanguages\nEnglish (31)","date":"2014-09-18 20:24:00","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\": 0.35845139622688293, \"perplexity\": 3185.5736690426093}, \"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-2014-41\/segments\/1410657129229.10\/warc\/CC-MAIN-20140914011209-00050-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
Q: Merge multiple database results into one I am unsure as to what to call this question. I have been thinking a lot about it, and I do not think that what I've chosen covers it adequately, but it was the best I could manage. Forgive me if it is very misleading or incorrect.
I am creating a small CMS for personal use, but I have stumbled upon trouble.
The information is stored in a MySQL database, and the table has three columns: cid, page and cont.
The cid is the identifier of a certain piece of content. If a page has multiple pieces of content, such as a main area of text and a sub area of text, the cid on these rows would be different, but the page would be the same, seeing as the content is on the same page.
On the index page of the CMS I am then displaying all the different pages that exist in the database, as links. The user then clicks the link to the page on which he'd want to change the content.
Now, here is my issue:
When displaying the data from the database, rows that have the same page, but different cid is, logically, displayed as separate links.
That sounded confusing. I'll say it differently:
What I need is that if a result has the same page as another result, these two are merged together into one link, and not displayed as two separate links.
This is how the database looks:
+------------+----------+-----------------------------------------+
| cid | page | cont |
+-----------------------------------------------------------------+
| page1-main | page1 | This is the first page on this website! |
| page2-main | page2 | This is the second page! |
| page2-sub | page2 | This is sub-content! |
+------------+----------+-----------------------------------------+
As I said, what I want is to have any rows that have the same page be merged into one result in my while loop, because what happens now is that they are separated into two different results. This is my loop and query:
$query = mysqli_query("SELECT * FROM content");
while($row = mysqli_fetch_array($query))
{
?>
<a href="edit.php?p=<?php echo $row['page'];?>">Link!</a>
<?php
}
That will, of course, display two results, even though they have the same page. I am unsure as to whether it is some PHP I will have to do, or it is in the MySQL query. I am a good bit unexperienced in SQL, but fairly experienced in PHP.
I've been thinking about some ifs. Like, storing every new result that is displayed in a variable and then comparing them, and if one that has occurred before occurs again, then it is not displayed, or something. But I don't know.
It would be wonderful if anyone could help me out here.
A: > what I want is to have any rows that have the same page
> be merged into one result
You can use GROUP BY to merge them:
$query = mysqli_query("SELECT * FROM content GROUP BY page");
A: These queries will return an equivalent result:
SELECT page FROM content GROUP BY page;
SELECT DISTINCT page FROM content ORDER BY page;
If you don't need to return columns other than page, then replace the * in your query (which is shorthand for "all columns", and instead reference just the columns that you actually need returned.)
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{"url":"https:\/\/labs.tib.eu\/arxiv\/?author=Z.%20Krahn","text":"\u2022 We report results from the first search for $\\nu_\\mu\\to\\nu_e$ transitions by the NOvA experiment. In an exposure equivalent to $2.74\\times10^{20}$ protons-on-target in the upgraded NuMI beam at Fermilab, we observe 6 events in the Far Detector, compared to a background expectation of $0.99\\pm0.11$ (syst.) events based on the Near Detector measurement. A secondary analysis observes 11 events with a background of $1.07\\pm0.14$ (syst.). The $3.3\\sigma$ excess of events observed in the primary analysis disfavors $0.1\\pi < \\delta_{CP} < 0.5\\pi$ in the inverted mass hierarchy at the 90% C.L.\n\u2022 This paper reports the first measurement using the NOvA detectors of $\\nu_\\mu$ disappearance in a $\\nu_\\mu$ beam. The analysis uses a 14 kton-equivalent exposure of $2.74 \\times 10^{20}$ protons-on-target from the Fermilab NuMI beam. Assuming the normal neutrino mass hierarchy, we measure $\\Delta m^{2}_{32}=(2.52^{+0.20}_{-0.18})\\times 10^{-3}$ eV$^{2}$ and $\\sin^2\\theta_{23}$ in the range 0.38-0.65, both at the 68% confidence level, with two statistically-degenerate best fit points at $\\sin^2\\theta_{23} =$ 0.43 and 0.60. Results for the inverted mass hierarchy are also presented.\n\u2022 A Search for Lorentz Invariance and CPT Violation with the MINOS Far Detector(1007.2791)\n\nJuly 16, 2010 hep-ph, hep-ex\nWe searched for a sidereal modulation in the MINOS far detector neutrino rate. Such a signal would be a consequence of Lorentz and CPT violation as described by the Standard-Model Extension framework. It also would be the first detection of a perturbative effect to conventional neutrino mass oscillations. We found no evidence for this sidereal signature and the upper limits placed on the magnitudes of the Lorentz and CPT violating coefficients describing the theory are an improvement by factors of $20-510$ over the current best limits found using the MINOS near detector.\n\u2022 Differential cross sections for the reactions gamma p-> p eta and gamma p -> p eta-prime(0909.0616)\n\nOct. 19, 2009 nucl-ex\nHigh-statistics differential cross sections for the reactions gamma p -> p eta and gamma p -> p eta-prime have been measured using the CLAS at Jefferson Lab for center-of-mass energies from near threshold up to 2.84 GeV. The eta-prime results are the most precise to date and provide the largest energy and angular coverage. The eta measurements extend the energy range of the world's large-angle results by approximately 300 MeV. These new data, in particular the eta-prime measurements, are likely to help constrain the analyses being performed to search for new baryon resonance states.","date":"2021-01-19 20:37:33","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\": 0.6654638648033142, \"perplexity\": 1676.0736067875168}, \"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-2021-04\/segments\/1610703519784.35\/warc\/CC-MAIN-20210119201033-20210119231033-00453.warc.gz\"}"} | null | null |
{"url":"https:\/\/stuartwheaton.com\/blog\/2020-05-25-mortgage-npv\/","text":"## Mortgage Decision Woes\n\nI bought my house almost 2 years ago now, and one of the big lessons I learned is that there\u2019s always another lesson to be learned. Totally , but it\u2019s true. I first smacked into this once we finally chose a house and had our offer accepted. I\u2019m done with spreadsheets, pro\/con lists, and cost analyses, right? WRONG! The process of paying for the house presented almost as many questions and decision points as finding the house. How does a coder deal with this? Python of course.\n\n## Mortgage 101\n\nLet\u2019s start out slow. Skip ahead if you know the basics.\n\n### Variables\n\nThere are a number of variables to consider with a mortgage, that either vary by loan or chosen home. These include enough quantity and quality to facilitate discussion in the rest of this post, but by no means serve as a complete picture of the mortgage-related terms that will pop up.\n\n#### Loan Variables\n\nInterest Rate\nThe percentage of the loan amount that will be owed as interest per year.\nPoints\nOne \u201cpoint\u201d is one percentage point of the loan amount, which can be paid upfront in exchange for \u201cbuying down\u201d a lower interest rate.\nPMI\nPrivate Mortgage Insurance - insurance you may be required to pay for, which gives the lender money if you default on the mortgage loan. Read: you buy this for the lender and get no benefit out of it whatsoever. Until your equity in the house exceeds 20% of the loan amount, PMI is mandatory. The lender may offer to pay this monthly cost, but it will cost you points or a higher interest rate.\nLoan Term\nThe number of years you have to pay back the loan. Typically 15 or 30 years, the latter being most common.\n\n#### Home Variables\n\nPrincipal\nThe amount of money loaned by the lender; equal to the home price minus down payment.\nDown Payment\nThe amount of money paid upfront towards the loan, not including closing costs. Paying a larger down payment shows lenders greater financial means and accountability, leading to lower interest rates and access to a wider range of loan products. It\u2019s possible to pay 0% down, but typically 3% of the house price is the minimum. 20% is the amount you\u2019ve probably heard before because it\u2019s what banks like - that\u2019s the minimum to get out of paying private mortgage insurance (PMI).\nClosing Costs\nAdditional fees that are paid at the time of sale, in addition to the down payment. For the buyer this typically includes taxes and fees going to local\/state governments and title companies, among other things. Traditionally the real estate agents are paid by the seller.\nEscrow Payments\nMonthly payments towards property taxes, home insurance, HOA fees, and other official liabilities that are facilitated by the lender. Often this means you don\u2019t have to worry about paying these directly, but as always it\u2019s not about you! There\u2019s a large backlog of these payments built up into an \u201cescrow\u201d account to make sure that even if you default on the loan, the government still gets their tax money!\nLoan Type\nMortgage loans come in many different flavors but we\u2019ll focus on fixed interest rate loans here, where the interest rate stays the same throughout the loan term. Variable rate loans allow the interest rate to change with the going rate of the market (for both good and bad), and so is obviously both more complicated and harder to simulate.\n\n### Monthly Payment\n\nA mortgage loan accrues simple interest, and does not compound. This is because the amount paid is pre-calculated over the life of the loan in what\u2019s called the amortization schedule. At the beginning, most of your monthly payment will go towards interest and not paying down the principal. Over time, this flips as the principal goes down and so interest also goes down. But the monthly payment is always the same, and can be calculated with this equation:\n\n P Principal I Interest Rate (Monthly) N Loan Term (Months) M Monthly Payment for Interest and Principal\n$M=P*I\\frac{(1+I)^N}{(1+I)^N-1}$\n\n## Algorithmic Evaluation\n\nSo how can we evaluate different loans given all these different variables? Is a .5% interest rate cut worth paying a point up front? Should I pay 10% down and deal with PMI for a few years? How does this change if I want to sell the house at 5 years vs. 10 years? To answer these, I decided to take a page from the business class book and look at net present value.\n\n### Net Present Value (NPV)\n\nThe premise of NPV is that paying money a year from now is better - to a calculable degree - than paying that same amount of money now; in an ideal world, you\u2019d invest the sum in the market and keep the earned interest when you have to pay out in a year. Inflation also plays a role, too, as $100 next year will very likely be worth (relatively) slightly less than$100 today. Inflation and the market average market rage can be combined using the Fisher Equation, then exponentially compounded monthly to get a discount factor. By reducing the cost of the year-from-now payment by the discount factor, we get its value in today\u2019s dollars, or Present Value (PV). By summing up all of the PVs for all payments and incomes, we arrive at the Net Present Value (NPV). Assuming a simple discount factor of 1.12 per year (1.02 per month), the PV of the $100 payment, discounted monthly, would be -$78.85, meaning that paying $100 a year from now is functionally equivalent to paying only$78.85 today.\n\n$\\begin{eqnarray} PV & = & \\frac{-100}{1.02^{12}} \\\\ & = & -78.85 \\end{eqnarray}$\n\n### NPV Applied\n\nApplying this concept to a mortgage loan, we can calculate the NPV of each loan to be able to directly compare them. While technically you own equity in the house beginning from the down payment, it shouldn\u2019t be counted as a positive asset until the house is actually sold. For every year, we can simulate what the NPV would be if we were to sell the house at the end of that year. The table below shows the various PV-related events that can happen in a given month.\n\nMonth \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Present-Value Event\nMonth 0 Add down payment and closing costs as a negative\nMonth 1-N Add discounted monthly payment as a negative\nMonth X PMI is removed from total payment (if applicable) once equity reaches 20%\nMonth N \u201cSell\u201d the house and add inflated equity, discounted, as a positive\n\n### How a Nerd Buys a House\n\nSo the answer to \u2018how a nerd buys a house\u2019 is write a Python script! Check it out on the linked GitHub repo - it\u2019s super easy to get running and the parameters are self-descriptive. It only works for fixed-rate mortgages right now; I tried modeling more complicated loan types, but it proved to be not particularly useful given the large assumptions required. Below are the sample parameters provided and the corresponding output. With a target year of year 10, the loans are presented in order of greatest (least negative) NPV given a sale at year 10. All other years are listed as well in tabular form.\n\n### Loans\n\n1. Loan1-minDown: A 4.5% interest rate, 30-year term loan where we make the minimum (typically) down payment of 3%. No points and \\$200 of PMI per month.\n\n2. Loan1-maxDown: The same loan except we pay 20% down payment, which allows us to forego PMI payments.\n\n3. Loan2: The same loan except we pay down 1 point to earn a 0.5% cut in interest rate - down to 4.0%.\n\n#### Sample Parameters\n\n{\n\"market\": {\n\"avgInflation\": 2.0,\n\"marketInt\": 7.0,\n\"agentRate\": 6.0\n},\n\"houseDetails\":\n{\n\"price\": 322000,\n\"annualPropTax\": 3500,\n\"annualHoaFee\": 90,\n\"annualInsurance\": 900,\n\"targetYear\": 10\n},\n\"loans\":\n[\n{\n\"name\": \"Loan1-minDown\",\n\"type\": \"fixed\",\n\"intRate\": 4.5,\n\"points\": 0.0,\n\"downPayment\": 3.0,\n\"pmi\": 200,\n\"closingCosts\": 10000,\n\"term\": 30\n},\n{\n\"name\": \"Loan1-maxDown\",\n\"type\": \"fixed\",\n\"intRate\": 4.5,\n\"points\": 0.0,\n\"downPayment\": 20.0,\n\"pmi\": 0,\n\"closingCosts\": 10000,\n\"term\": 30\n},\n{\n\"name\": \"Loan2\",\n\"type\": \"fixed\",\n\"intRate\": 4.0,\n\"points\": 1.0,\n\"downPayment\": 3.0,\n\"pmi\": 200,\n\"closingCosts\": 10000,\n\"term\": 30\n}\n]\n}\n\n\n#### Sample Output\n\nNew monthly payment (no PMI) for Loan1-minDown at month 109 :1956.75\nNew monthly payment (no PMI) for Loan2 at month 103 :1865.33\n=== Initial Monthly Payments ===\nLoan1-maxDown Loan2 Loan1-minDown\n--------------- ------- ---------------\n1679.39 2065.33 2156.75\n\n=== Net Present Value ===\nLoan1-maxDown Loan2 Loan1-minDown\n-- --------------- --------- ---------------\n0 -23783.4 -78863 -24123\n1 -51270.2 -52037.8 -53085.8\n2 -67561.2 -68770.9 -70699.2\n3 -82457.7 -84116.1 -86777.6\n4 -96087.4 -98195.3 -101461\n5 -108567 -111119 -114878\n6 -120001 -122990 -127144\n7 -130487 -133898 -138364\n8 -140110 -143929 -148634\n9 -148410 -153159 -158041\n10 -155531 -161658 -165656\n11 -162092 -169489 -172647\n12 -168146 -176711 -179071\n13 -173738 -183375 -184979\n14 -178910 -189532 -190419\n15 -183701 -195223 -195434\n16 -188145 -200490 -200063\n17 -192274 -205369 -204341\n18 -196115 -209892 -208301\n19 -199695 -214091 -211970\n20 -203037 -217992 -215376\n21 -206161 -221621 -218542\n22 -209087 -225002 -221490\n23 -211832 -228154 -224240\n24 -214412 -231096 -226809\n25 -216841 -233847 -229212\n26 -219131 -236422 -231466\n27 -221294 -238836 -233582\n28 -223341 -241101 -235574\n29 -225282 -243229 -237451\n30 -227123 -245232 -239223\n\n\n#### Discussion\n\nIn this example, Loan1-maxDown provides the best NPV at year 10 due to a much lower monthly cost, despite the higher upfront investment in down payment. Because the points payment is sunk at the outset when it\u2019s the most costly (in NPV terms), Loan2 never ends up coming out ahead of the others. This goes to show why many people think that points are rarely worth it, especially if you don\u2019t plan to stick out the term of the loan or never refinance. I found this tool to be incredibly useful when comparing multiple mortgages with varying terms and parameters, and I hope you do too.\n\n#### Assumptions\n\n\u2022 The housing market will not deviate from the average inflation. Obviously not a good assumption since housing depends on location and other factors, but unless one can forecast the sale price of the house, simply applying inflation to the current price is the most reasonable course of action.\n\n\u2022 The average inflation and market growth rate will be constant. Again obviously this cannot be the case, but it\u2019s a reasonable assumption given that the future is unknowable.\n\n\u2022 You will not get out of PMI early (if applicable) through an assessed home price increase. This is possible but most people won\u2019t do it.\n\n\u2022 Default market parameters:\n\n\u2022 Default inflation value of 2%. In the US, this is the stated inflation target, so it\u2019s a fair assumption.\n\u2022 Default market growth rate of 7%, which is considered the average (minus inflation) in modern times.\n\u2022 Default agent fee of 6% (buyer and seller 3% each), paid at the time of sale. It\u2019s a scam for sure, but unless you go rogue, you\u2019re stuck with it.\n\nDisclaimer: I am not a lawyer, financial advisor, or mortgage expert, just a lowly software developer who learned some things through the home-buying process. Use this tool at your own risk.","date":"2021-01-22 02:48:13","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\": 2, \"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\": 0.2181490808725357, \"perplexity\": 3222.9419259329543}, \"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-2021-04\/segments\/1610703529080.43\/warc\/CC-MAIN-20210122020254-20210122050254-00017.warc.gz\"}"} | null | null |
Pattern Services and Revisions
If you are an Annie's customer and have a question about the instructions on a pattern you have purchased, please visit:
http://www.anniescatalog.com/pages/customer_care/pattern_services.html
Contents
Introduction
General Directions
Classic Cables Scarf
Fairamay Shawl
Jamie's Mitts
Adestan Slipper Socks
Felted Backpack
Aran Throw
Cables Purse
Gon Earflap Hat
Baby Sweater
General Information
Introduction
Cables are classic elements found in many knitwear designs. They add beauty, fluidity and a touch of class to a simple design. Knitting cables on a knitting loom requires the manipulation of stitches, which is easily done by using a cable needle. Work the cables on a background of reverse stockinette stitches to make your cables pop even more!
The designs included in this booklet will introduce you to a few cabling techniques. Master the cabling techniques at the front of the book, and you can design your own projects too!
Cables work best when worked with yarns that have some inherent elasticity; for this reason, yarns with wool content are a good choice. The yarns used in this booklet were selected because of their elasticity/bounce. When selecting your yarns, stretch them out and test their bounce.
Have fun knitting these classic designs!
General Directions
Begin with the following materials to get started knitting cables on circle looms.
Materials
• Knifty Knitter™ circle- and long-loom series from Provo Craft*
• Knitting tool included with loom
• Cable needle
• Crochet hook (for casting on)
• 2 size 5 (3.75mm) double-pointed knitting needles (for holding stitches)
• Yarn needle
• Split-ring stitch markers
• Scissors
• Measuring tape/gauge checker
• Blocking wires (optional)
_*Samples were knit on Provo Craft Knifty Knitter series looms; however, patterns can be knit on other knitting looms. Be sure to check for gauge and peg count when substituting knitting looms._
Pattern Note
All of the patterns are worked in a clockwise direction around the knitting loom (where the first row starts from right to left).
Basic Techniques
Chain Cast On
To cast on, move your loom from left to right. Working yarn should end up on the right side to begin the first row (in order to have the first row start from right to left).
Make a slip knot and place it on the peg. Take the working yarn towards the inside of the loom.
**Step 1:** Insert crochet hook through the slip knot. Hook working yarn, forming a chain.
**Step 2:** Place chain on next empty peg to the right.
**Step 3:** Insert crochet hook through chain just made. Hook working yarn forming a chain.
**Step 4:** Place chain on next empty peg to the right (Photo A).
**Step 5:** Repeat Steps 3 and 4 until desired number of stitches have been cast on. Each peg will have 1 loop.
Knit Stitch (k)
The knit stitch is a smooth V-shaped stitch; it is identical to the knit stitch created with knitting needles.
**Step 1:** Place working yarn in front of the peg and above the loop on the peg.
**Step 2:** Insert knitting tool from bottom up and catch the working yarn with the tool, thus forming a loop.
**Step 3:** Hold the newly formed loop (from Step 2) with the knitting tool (Photo B).
**Step 4:** Pull up on the loop on the tool to take the loop that was originally on the peg, off the peg.
**Step 5:** Place the loop you are holding (from Step 3) on the peg. Pull on the working yarn to tighten the stitch.
Twisted Knit Stitch (also known as single stitch)
In needle knitting, this stitch is known as the twisted knit stitch or a stitch knit through the back loop.
**Step 1:** Take the working yarn (yarn coming from the ball of yarn) to the inside of the knitting loom.
**Step 2:** Moving in a clockwise direction around the knitting loom, encircle the peg counter clockwise with the yarn to form e-wrap (Photo C).
**Step 3:** Continue to e-wrap all the pegs. Each peg should have 2 loops on it.
**Step 4:** Using your knitting tool, lift the bottommost loop off the peg, let it fall towards the inside of the knitting loom.
Purl Stitch (p)
The purl stitch is the opposite of the knit stitch. Instead of a smooth V, you will see bumpy fabric.
**Step 1:** Place working yarn in front of peg and below the loop on the peg.
**Step 2:** Insert knitting tool from the top down and hook the working yarn with the tool (Photo D).
**Step 3:** Pull the loop caught with the tool, up through the stitch.
**Step 4:** Continue to pull up on loop to remove the original loop from the peg.
**Step 5:** Place the loop you are holding (from Step 3) on the peg. Gently tug on the working yarn to tighten the stitch.
Stockinette Stitch
The stockinette stitch is created by knitting every row.
Garter Stitch
The garter stitch is formed by 2 rows.
**Row 1:** Knit.
**Row 2:** Purl.
The combination of these 2 rows creates 1 garter-stitch row and 1 garter-stitch ridge.
Adding Another Skein
To attach a new skein of yarn at beginning of the next row, join the 2 ends of yarn with a slip knot. Knit the first 3 stitches of the row with both yarns together. Drop the old strand and continue knitting with the new strand.
Basic Bind Off (also called flat removal method)
**Step 1:** Knit the item until you have only 1 loop on each peg. The working yarn is coming from the last peg. Knit the first 2 loops. Move the loop from the 2nd peg over to the first peg. Lift the bottom loop over the top loop and off the peg to bind off first stitch (Photo E). Move the loop from the first peg over to the vacated 2nd peg.
**Step 2:** Knit the next loop. Move this loop over to the previous peg. Lift bottom loop over and off the peg (2nd stitch bound off).
**Step 3:** Repeat Step 2 until all stitches have been bound off.
**Step 4:** When you reach the last peg, cut the working yarn leaving a 5-inch tail. Knit the loop. Remove the stitch from the peg. Pull the yarn tail end through the loop.
Shaping Techniques
Decreases
There are 2 decrease techniques used in this book, the terms used are the same as used in needle knitting.
These decreases take place on 2 pegs. Peg 1 is on the right and Peg 2 is on the left.
**K2tog (knit 2 together—slants to the right)**
**Step 1:** Take the loop from Peg 1 and place it on Peg 2.
**Step 2:** Knit all the pegs as you normally would. When you reach the peg with 2 loops, treat the 2 loops as 1 and knit them together.
**Ssk (slip, slip, knit—slants to the left)**
**Step 1:** Take the loop off Peg 1 and hold it. Take loop off Peg 2 and hold it. Place the loop from Peg 1 on Peg 2. Place the loop that was on Peg 2 back on Peg 2. Peg 1 is empty, Peg 2 has 2 loops.
**Step 2:** Knit all the pegs as you normally would. When you reach the peg with 2 loops, treat the 2 loops as 1 and knit them together.
Increases
**M1 (Make 1)**
**Step 1:** Create an empty peg where you need to increase a stitch by moving the loops to the outer pegs.
**Step 2:** With knitting tool, reach for the ladder that runs from 1 peg to the next, pick it up, twist it and place it on the empty peg.
**Step 3:** Knit on the knitting loom as usual, when you reach this peg, treat it just as any other peg and work it as per directions in pattern.
**Yo (yarn over)**
The yo increase is used in conjunction with the k2tog and the ssk decrease techniques.
**Step 1:** To create a yo, take the yarn towards the inside of the knitting loom.
**Step 2:** Go around the peg in a counterclockwise direction (e-wrap the peg).
Wrap & Turn Short Rows
When working a sock, the heel is created in 2 parts—a decreasing part and an increasing part.
The decreasing section requires the knowledge of a technique known as **Wrap and Turn (W &T).** The increasing section requires the knitter to knit over the wrap and the loop together.
Decreasing section
**Short row:** The term "short row" means that a row is not knit to the end; instead, knit to a certain point and stop. Then turn and knit back in the opposite direction. To avoid creating a hole, use W&T.
**To work W &T short row**
**Step 1:** Knit to the designated turning point. Take the next loop off the peg.
**Step 2:** Take the working yarn towards the inside of the knitting loom and wrap around the peg, bring the yarn towards the front of the loom.
**Step 3:** Place loop back on the peg. The peg now has 1 wrap and the knit stitch.
**Step 4:** Pick up working yarn and knit back in the other direction.
Be sure to leave the peg with the wrap untouched.
Increasing section
In the increasing section, the wrap and the loop are treated as 1 and knit together.
Cable Techniques
Cables over 2 stitches
**LT (Left Twist)**
**Step 1:** Skip Peg 1, knit Peg 2 (Photo F).
**Step 2:** Place loop from Peg 2 on cable needle.
**Step 3:** Move loop from Peg 1 to Peg 2.
**Step 4:** Place loop from cable needle on Peg 1.
**Step 5:** Knit loop on Peg 2.
**RT (Right Twist)**
**Step 1:** Place loop from Peg 1 on cable needle and hold to the center of the knitting loom (Photo G).
**Step 2:** Knit loop on Peg 2 and move to Peg 1.
**Step 3:** Place loop from cable needle on Peg 2.
**Step 4:** Knit loop on Peg 2.
Cables over 3 stitches
**RC (Right Cross)**
**Step 1:** Place loop from Peg 1 on cable needle and hold to center of knitting loom.
**Step 2:** Move loops from Peg 2 and Peg 3 to Peg 1 and Peg 2 (Photo H).
**Step 3:** Place loop from cable needle on Peg 3.
**Step 4:** Knit all three Pegs.
**LC (Left Cross)**
**Step 1:** Skip Peg 1 and Peg 2. Knit Peg 3 (Photo I).
**Step 2:** Place loop from Peg 3 on cable needle.
**Step 3:** Knit Peg 1 and Peg 2. Move loop from Peg 2 to Peg 3 and loop from Peg 1 to Peg 2.
**Step 4:** Place loop from cable needle on Peg 1.
_**Note:** The following 3-stitch cables are worked in the same manner as the Right Cross and Left Cross except the crossing stitch is purled rather than knitted._
**RPC (Right Purl Cross)**
**Step 1:** Place loop from Peg 1 on cable needle and hold to center of the knitting loom.
**Step 2:** Knit Peg 2 and Peg 3. Move loop from Peg 2 to Peg 1 and loop from Peg 3 to Peg 2.
**Step 3:** Take loop from cable needle and place it on Peg 3.
**Step 4:** Purl loop on Peg 3.
**LPC (Left Purl Cross)**
**Step 1:** Skip Peg 1 and Peg 2. Purl Peg 3.
**Step 2:** Place loop from Peg 3 on cable needle.
**Step 3:** Knit skipped pegs. Move loop from Peg 2 to Peg 3 and loop from Peg 1 to Peg 2.
**Step 4:** Place loop from cable needle on Peg 1.
Cables over 4 stitches
**4-st LC (4-stitch Left Cross—work over 4 stitches, on Pegs 1–4)**
**Step 1:** Skip Peg 1 and Peg 2 (Photo J).
**Step 2:** Knit stitches on Peg 3 and Peg 4, place these loops on cable needle and hold to the center of knitting loom.
**Step 3:** Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4.
**Step 4:** Place loops from the cable needle and on Peg 1 and Peg 2.
**Step 5:** Gently pull loop on Peg 3 and then the loop on Peg 4 to tighten the stitches.
**4-st RC (4-stitch Right Cross—work over 4 stitches, on Pegs 1–4)**
**Step 1:** Place loops from Peg 1 and Peg 2 on cable needle (Photo K).
**Step 2:** Knit Peg 3. Place it on Peg 1.
**Step 3:** Knit Peg 4. Place it on Peg 2.
**Step 4:** Take Loop 1 from cable needle and place it on Peg 3. Knit it.
**Step 5:** Take Loop 2 from cable needle and place it on Peg 4. Knit it.
Cables over 6 stitches
_**Note:** Work in same manner as 4-stitch cables, except cross 3 stitches instead of 2._
**6-st LC (6-stitch Left Cross—work over 6 stitches, on Pegs 1–6)**
**Step 1:** Skip Peg 1, Peg 2 and Peg 3.
**Step 2:** Knit loops on Peg 4, Peg 5 and Peg 6, place these 3 stitches on cable needle and hold to center of knitting loom.
**Step 3:** Knit skipped loops. Place loop from Peg 1 on Peg 4, loop from Peg 2 on Peg 5 and loop from Peg 3 on Peg 6.
**Step 4:** Place loops from the cable needle on Peg 1, Peg 2 and Peg 3.
**Step 5:** Gently pull loop on Peg 4, loop on Peg 5, then Peg 6 to tighten the stitches.
**6-st RC (6-stitch Right Cross—work over 6 stitches, on Pegs 1–6)**
**Step 1:** Place loops from Peg 1, Peg 2 and Peg 3 on cable needle.
**Step 2:** Knit Peg 4 and place it on Peg 1.
**Step 3:** Knit Peg 5 and place it on Peg 2.
**Step 4:** Knit Peg 6 and place it on Peg 3.
**Step 5:** Take Loop 1 from cable needle and place it on Peg 4. Knit it.
**Step 6:** Take Loop 2 from cable needle and place it on Peg 5. Knit it.
**Step 7:** Take Loop 3 from cable needle and place it on Peg 6. Knit it.
Finishing Techniques
Mattress Stitch
Lay the pieces side by side, with right sides facing up.
Start the seam at the bottom edge. First join the cast-on rows, inserting the yarn needle between the first and 2nd stitch in from the edge, underneath 1 of the "bars" of yarn that run between the stitches. Then, working with the other piece, do the same.
Pull gently on the yarn to close the stitches.
Grafting/Kitchener Stitch
Place stitches onto knitting needles as indicated in pattern, making sure that the stitches are set up on the needles correctly.
Insert the yarn needle into the first stitch on the needle closest from right to left, pull needle through, leaving stitch on the needle. Insert the needle into the first stitch on the back needle from the left, leave the stitch on the needle. Pull the yarn through.
Needles are set for grafting, following the next 4 steps:
**Step 1:** Insert the tapestry needle into the first stitch on the front needle from the left. Slip stitch off the needle.
**Step 2:** Insert the needle into the next stitch on the front needle from the right. Leave stitch on the needle. Gently pull on the working yarn to tighten stitch. Do not pull too much.
**Step 3:** Insert the needle into the first stitch on the back needle as if to right, and slip it off the needle.
**Step 4:** Insert the needle into the next stitch on the back needle as if to left. Leave this stitch on the needle. Snug up the yarn by pulling gently on the working yarn.
Repeat Steps 1–4. At the end, the needles will have 2 stitches remaining. Repeat Step 1 and then repeat Step 3.
Weave in the ends to the wrong side of piece.
I-cord
I-cords are used in this book as drawstrings.
3-stitch I-cord
**Step 1:** Cast on 3 stitches.
**Step 2:** Knit to end of row.
**Step 3:** Take working yarn to the back of the pegs and run the yarn behind the pegs to the front of Peg 1 (Photo L).
**Step 4:** Knit to the end of row.
Repeat Steps 3 and 4 until I-cord reaches desired length.
Bind off.
Pull on the I-cord to set the stitches.
2-stitch I-cord
**Step 1:** Cast on 2 stitches.
**Step 2:** Form a figure 8 with yarn on both pegs (Photo M).
**Step 3:** Lift the bottommost loop off the peg.
Repeat Steps 2 and 3 until I-cord reaches desired length.
Bind off.
Pompom
Cut 2 doughnut-shape pieces out of cardboard, about 1 inch bigger than the desired size of pompom.
Cut a small square out 1 of the sides to create a small opening.
Sandwich a piece of yarn in between the 2 cardboards, tie a temporary knot.
Grab working yarn and wrap it around the 2 pieces of cardboard. Start at the left and move towards the right.
When the cardboard is completely full, find the temporary knot and hold on to it. With scissors slip in between the 2 pieces of cardboards and begin cutting around the circle. When you are finished cutting, tighten the knot securely.
Trim pompom to desired size.
Felting Instructions
Set the washer to the smallest setting, regular cycle and hot water. Add 1 tablespoon of Eucalan Woolwash or shampoo.
_**Designer Note:** Eucalan Woolwash saves rinsing the item by hand and makes the wet wool smell better._
Place the item to be felted in a zippered pillowcase; put it in the washer. Add 2 pairs of jeans to aid in agitation. It is not recommended to use towels, as these may leave fuzz in felted items. Start the washer.
Check the felted items frequently. Stop the machine completely before placing your hand inside. If additional felting is required, reset the washer and continue the felting process. Check the progress closely and shape item as the felting process continues by pulling at the corners. Item is felted when it feels firm, and the stitches are indistinguishable. Keep felting the bag until you are completely satisfied. It may take a few cycles. Do not let the machine go into the rinse-and-spin cycle, as this will create creases that are very difficult to remove.
When the item reaches the desired look, remove it from the zippered pillowcase, place it between towels and squeeze out as much water as possible. Shape again by stretching damp item over a suitable-sized form. If nothing that resembles the shape is available, use plastic bags inside to give it its form. The felted item should fit over the fitted form snuggly. Shape all the corners. Make sure that everything looks the way you want it to look. Feel free to pull at it. Do not let it dry until you are completely satisfied with the way it looks. Once it looks the way you desire, let it dry completely, away from sunlight and from any heating vents. It may take up to 2 full days to dry completely. Keep shaping it during the drying process, if you so desire.
Classic Cables Scarf
Skill Level
Finished Size
4½ x 70 inches
_**Note:** Instructions are given for an adult-length scarf. A shorter scarf can be made by working fewer cable repeats._
Materials
• Lion Brand Jiffy bulky weight yarn (3 oz/135 yds/85g per skein): 2 skeins camel #124
• Blue Knifty Knitter round loom (24 pegs)
• Knitting tool
• Tapestry needle
• Cable needle
Gauge
16 stitches and 14 rows = 4 inches/10cm
Special Abbreviations
**4-st RC (4-stitch Right Cross):** Place loops from Peg 1 and Peg 2 on cable needle. Knit Peg 3 and place loop on Peg 1. Knit Peg 4 and place loop on Peg 2. Place Loop 1 from cable needle on Peg 3 and knit it. Place Loop 2 from cable needle on Peg 4 and knit it.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place stitches from cable needle on Peg 1 and Peg 2. Gently pull on the loop on Peg 3 and then on the loop on Peg 4 to tighten the stitches.
Pattern Note
Wrap the row before cable crossing loosely.
Instructions
Cast on 18 stitches.
Border
**Rows 1, 3 and 5:** K2, p2, k4, p2, k4, p2, k2.
**Rows 2, 4 and 6:** P2, p2, k4, p2, k4, p2, p2.
Body
**Row 1:** K2, p2, 4-st RC, p2, 4-st LC, p2, k2.
**Row 2:** P2, p2, k4, p2, k4, p2, p2.
**Row 3:** K2, p2, k4, p2, k4, p2, k2.
**Row 4:** P2, p2, k4, p2, k4, p2, p2.
Repeat Rows 1–4 until piece measures about 2 inches less than desired length.
Border
**Rows 1, 3 and 5:** K2, p2, k4, p2, k4, p2, k2.
**Rows 2, 4 and 6:** P2, p2, k4, p2, k4, p2, p2.
Bind off and weave in ends.
Block to measurements.
Fairamay Shawl
Skill Level
Finished Size
18 x 65 inches
Materials
• Lion Brand Lion Cashmere Blend medium weight yarn (1.5 oz/84 yds/40g per skein): 8 skeins silver #150
• Long Blue Knifty Knitter Long loom series (62 pegs)
• Knitting tool
• Cable needle
• Tapestry needle
Gauge
13 stitches and 18 rows = 4 inches/10cm
Special Abbreviations
**Yo, sl 1, k1, psso (yarn over, slip 1, knit 1, pass slipped stitch over):** Take loop off Peg 1 and place on cable needle. E-wrap Peg 1. Knit Peg 2. Take loop off Peg 2 and hold it with knitting tool or fingers. Place loop from cable needle on Peg 2. Replace loop from Peg 2 on top of loop. Lift over the bottommost loop, leaving only 1 loop on the peg.
**K2tog, yo (knit 2 together, yarn over):** Move loop from Peg 1 to Peg 2. Knit both loops together. Move remaining loop from Peg 2 to Peg 1 to leave Peg 2 empty for the yo. E-wrap (see page 3) Peg 2 to create a yo.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place stitches from cable needle on Peg 1 and Peg 2. Gently pull on the loop on Peg 3 and then on the loop on Peg 4 to tighten the stitches.
Pattern Note
Work your stitches with a loose tension making it easier to move the stitches.
**Instructions**
Cast on 62 stitches.
**Row 1:** Knit.
**Row 2:** Purl.
**Row 3:** Knit.
**Row 4:** Purl.
**Row 5:** *P2, k2tog, yo, p2, k4; repeat from * to last 2 stitches, p2.
**Row 6:** P2, *k4, p2, k2, p2; repeat from * to end of row.
**Row 7:** *P2, yo, sl 1, k1, psso, p2, 4-st LC; repeat from * to last 2 stitches, p2.
**Row 8:** P2, *k4, p2, k2, p2; repeat from * to end of row.
**Row 9:** *P2, k2tog, yo, p2, k4; repeat from * to last 2 stitches, p2.
**Row 10:** P2, *k4, p2, k2, p2; repeat from * to end of row.
**Row 11:** *P2, yo, sl 1, k1, psso, p2, k4; repeat from * to last 2 stitches, p2.
**Row 12:** P2, *k4, p2, k2, p2; repeat from * to end of row.
Repeat Rows 5–12 until piece measures 64 inches.
Repeat Rows 5–9.
**Next row:** Purl.
**Next row:** Knit.
**Next row:** Purl. Bind off.
**Finishing**
Wet block as follows by immersing shawl in warm, soapy water for about 20 minutes. Squeeze out as much water by using a towel, do not wring. Block to dimensions given. Designer recommends blocking wires to block shawl.
Jamie's Mitts
Skill Level
Size
Adult
Materials
• Lion Brand Wool-Ease Thick & Quick super bulky weight yarn (6 oz/106 yds/170g per skein): 1 skein grass #131
• Blue Knifty Knitter round loom (24 pegs)
• Knitting tool
• Cable needle
• Stitch marker
• Tapestry needle
Gauge
11 stitches and 19 rows = 4 inches/10cm
Special Abbreviations
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place stitches from cable needle on Peg 1 and Peg 2. Gently pull loop on Peg 3 and then on loop on Peg 4 to tighten the stitches.
**4-st RC (4-stitch Right Cross):** Place loops from Peg 1 and Peg 2 on cable needle. Knit Peg 3 and place loop on Peg 1. Knit Peg 4 and place loop on Peg 2. Place Loop 1 from cable needle on Peg 3 and knit it. Place Loop 2 from cable needle on Peg 4 and knit it.
Pattern Stitch
**Rib Stitch**
**Round 1:** *K2, p2; repeat from * to the end of round. Repeat Round 1 for pattern.
**Instructions**
Left Hand
Cuff
Cast on 21 stitches.
**Rows 1, 3 and 5:** *K2, p2; repeat from * to last stitch, k1.
**Rows 2, 4 and 6:** K1, *p2, k2; repeat from * to end of row.
Body
**Row 1:** K3, p2, k4, p2, k10.
**Row 2:** K10, p2, k4, p2, k3.
**Row 3:** K3, p2, 4-st LC, p2, k10.
**Row 4:** K10, p2, k4, p2, k3.
[Repeat Rows 1–4] 5 times.
Shape thumb
Place stitch marker on Peg 14.
Move stitches outwards to leave an empty peg at Peg 14.
_**Note:** See page 4 for instructions on M1 increase._
**Next row:** K3, p2, k4, p2, k to marker, m1, k to end.
**Next row:** K11, p2, k4, p2, k3. Move stitches outwards to leave an empty peg at Peg 14.
**Next row:** K3, p2, 4-st LC, p2, k to marker, m1, k to end.
**Next row:** K12, p2, k4, p2, k3. Move stitches outwards to leave an empty peg at Peg 14.
**Next row:** K3, p2, k4, p2, k to marker, m1, k to end.
Join to work in the round.
Work 3 rounds in Rib Stitch pattern.
Bind off and weave in ends.
Block lightly.
Seam below thumb opening.
Right Hand
Cuff
Cast on 21 stitches.
**Rows 1, 3 and 5:** K1, *p2, k2; repeat from * to end of row.
**Rows 2, 4 and 6:** *K2, p2; repeat from * to the last stitch, k1.
Body
**Row 1:** K10, p2, k4, p2, k3.
**Row 2:** K3, p2, k4, p2, k10.
**Row 3:** K10, p2, 4-st RC, p2, k3.
**Row 4:** K3, p2, k4, p2, k10. [Repeat Rows 1–4] 5 times.
Shape thumb
Place stitch marker on Peg 8.
Move stitches outwards to leave an empty peg at Peg 8.
_**Note:** See page 4 for instructions on M1 increase._
**Next row:** K8, M1, k2, p2, k4, p2, k3.
**Next row:** K3, p2, k4, p2, k11. Move stitches outwards to leave an empty peg at Peg 8.
**Next row:** K9, M1, k2, p2, 4-st RC, p2, k3.
**Next row:** K3, p2, k4, p2, k12. Move stitches outwards to leave an empty peg at Peg 8.
**Next row:** K10, M1, k2, p2, k4, p2, k3.
Join to work in the round.
Work 3 rounds in Rib Stitch pattern.
Bind off and weave in ends.
Block lightly.
Seam below thumb opening.
Adestan Slipper Socks
Skill Level
Size
Adult
Materials
• Patons Shetland Chunky Tweeds bulky weight yarn (3 oz/123 yds/85g per skein): 4 skeins biscuit tweeds #67024
• Blue Knifty Knitter round loom (24 pegs)
• Knitting tool
• Cable needle
• Stitch markers
• Tapestry needle
• 2 size 8 double-pointed needles (for holding stitches to graft the toe area)
Gauge
13 sts and 18 rows = 4 inches/10cm
Special Abbreviations
**LT (Left Twist):** Skip Peg 1, knit Peg 2. Place loop from Peg 2 on cable needle. Move loop from Peg 1 to Peg 2. Place loop from cable needle on Peg 1. Knit loop on Peg 2.
**W &T (Wrap and Turn):** Knit to turning point. Take next loop off peg. Take working yarn to the inside of loom and wrap the peg, bringing yarn toward front of loom. Place loop back on peg. Pick up working yarn and knit back in other direction. Leave peg with wrap untouched.
Pattern Stitch
**Rib Stitch**
**Round 1:** *K2, p2; repeat from * to the end of round. Repeat Round 1 for pattern.
Pattern Note
For more information on creating a heel and toe using short-row shaping see page 5.
**Instructions**
Leg
Cast on all pegs in the round.
Work 4 rounds of Rib Stitch pattern.
**Round 5:** P1, k8, p1, k2, p1, k8, p1, k2.
**Round 6:** P1, k8, p1, k2, p1, k8, p1, k2.
**Round 7:** P1, k8, p1, LT, p1, k8, p1, LT.
Repeat Rounds 5–7 until leg measures 7½ inches or desired length.
Heel
Place stitch marker at Peg 24; from this point on, this peg will be Peg 1. Count 11 pegs to the left, place a stitch marker on the 11th peg; there should be a stitch marker on Peg 1 and Peg 12. The heel is worked as a flat panel on these 12 pegs. The cup for the heel is formed by knitting short rows. Remember to wrap each of the turning pegs.
**Row 1:** K11 (from Pegs 1–11), W&T Peg 12.
**Row 2:** K10 (from Pegs 11–2), W&T Peg 1.
**Row 3:** K9 (from Pegs 2–10), W&T Peg 11.
**Row 4:** K8 (from Pegs 10–3), W&T Peg 2.
**Row 5:** K7 (from Pegs 3–9), W&T Peg 10.
**Row 6:** K6 (from Pegs 9–4), W&T Peg 3.
**Row 7:** K5 (from Pegs 4–8), W&T Peg 9.
**Row 8:** K4 (from Pegs 8–5), W&T Peg 4.
**Row 9:** K5 (from Pegs 5–9). Make sure to knit 2 over 1 on Peg 9.
**Row 10:** K6 (from Pegs 9–4). Make sure to knit 2 over 1 on Peg 4.
**Row 11:** K7 (from Pegs 4–10). Make sure to knit 2 over 1 on Peg 10.
**Row 12:** K8 (from Pegs 10–3). Make sure to knit 2 over 1 on Peg 3.
**Row 13:** K9 (from Pegs 3–11). Make sure to knit 2 over 1 on Peg 11.
**Row 14:** K10 (from Pegs 11–2). Make sure to knit 2 over 1 on Peg 2.
**Row 15:** K11 (from Pegs 2–12). Make sure to knit 2 over 1 on Peg 12.
**Row 16:** K12 (from Pegs 12–1). Make sure to knit 2 over 1 on Peg 1.
Foot
_**Note:** The foot is worked in the round._
**Round 1:** K8, p1, k2, p1, k8, p1, k2, p1.
**Round 2:** K8, p1, k2, p1, k8, p1, k2, p1.
**Round 3:** K8, p1, LT, p1, k8, p1, LT, p1.
**Next rounds:** Repeat Rounds 1–3 until foot measures 2 inches less than desired length.
Shape toe
**Next 2 rounds:** Knit.
_**Note:** The toe is worked as a flat panel using the same instructions from the heel._
Work Rows 1–16 of Heel instructions.
**Finishing**
In preparation for closing the toe, take the stitches off the knitting loom and place them on the size 8 knitting needles.
Take stitches from Pegs 24–11 and place them on 1 knitting needle. Take stitches from Pegs 12–23 and place them on the 2nd knitting needle.
Graft front and back stitches together using the Kitchener stitch (page 8).
Weave in all ends.
Block lightly.
Felted Backpack
Skill Level
Size
**Pre-felted:** 14 inches tall x 12½ inches wide x 5 inches deep
Finished Measurements
**Felted:** 11 inches tall x 10 inches wide x 4 inches deep
Materials
• Lion Brand Lion Wool medium weight yarn (3 oz/158 yds/85g per skein): 6 skeins goldenrod #187
• Yellow Knifty Knitter Loom (40 pegs)
• Knitting tool
• Tapestry needle
• Cable needle
• ¾-inch magnetic snap closure (optional)
Gauge
11 stitches and 14½ rows = 4 inches/10cm with 2 strands of yarn
Special Abbreviations
**Yo (yarn over):** Take yarn towards the inside of knitting loom and go around the peg in a counterclockwise direction.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place stitches from cable needle on Peg 1 and Peg 2. Gently pull loop on Peg 3 and then loop on Peg 4 to tighten the stitches.
**K2tog (knit 2 stitches together):** Place loop from Peg 1 on Peg 2. Treat the 2 loops as 1 and knit them together.
Pattern Stitch
**Garter Stitch**
**Row 1:** Knit.
**Row 2:** Purl.
Rows 1 and 2 make 1 garter-stitch ridge.
Pattern Note
Use 2 strands of yarn held together throughout.
**Instructions**
Front Top Band
Cast on 40 stitches.
Work 12 rows in Garter Stitch pattern. (6 garter-stitch ridges)
**Next row (eyelet row):** *K4, bind off 2 stitches; repeat from * to last 4 stitches, k4.
**Next row:** *K4, [yo] twice; repeat from * to last 4 stitches, k4.
Body
**Rows 1 and 2:** K5, p2, k4, p2, k1, p12, k1, p2, k4, p2, k5.
**Row 3:** K5, p2, 4-st LC, p2, k14, p2, 4-st LC, p2, k5.
**Row 4:** K5, p2, k4, p2, k14, p2, k4, p2, k5.
Repeat Rows 1–4 until body measures 14 inches.
Bottom
Work 20 rows Garter Stitch pattern. (10 garter-stitch ridges)
Back
Work in stockinette stitch for 10 inches.
**Next row (eyelet row):** *K4, bind off 2 stitches; repeat from * to last 4 stitches, k4.
**Next row:** *K4, [yo] twice; repeat from * to last 4 stitches, k4.
Work 12 rows in Garter Stitch pattern. (6 garter-stitch ridges)
Flap
**Rows 1 and 2:** K5, p2, k4, p2, k1, p12, k1, p2, k4, p2, k5.
**Row 3:** K5, p2, 4-st LC, p2, k14, p2, 4-st LC, p2, k5.
**Row 4:** K5, p2, k4, p2, k14, p2, k4, p2, k5.
[Repeat Rows 1–4] 7 times.
**Next row:** K2tog, k3, p2, k4, p2, k1, p12, k1, p2, k4, p2, k3, k2tog. (38 stitches)
**Next row:** K2tog, k2, p2, k4, p2, k1, p12, k1, p2, k4, p2, k2, k2tog. (36 stitches)
**Next row:** K2tog, k1, p2, 4-st LC, p2, k14, p2, 4-st LC, p2, k1, k2tog. (34 stitches)
**Next row:** K2tog, p2, k4, p2, k14, p2, k4, p2, k2tog. (32 stitches)
**Next row:** K2tog, p1, k4, p2, k1, p12, k1, p2, k4, p1, k2tog. (30 stitches)
**Next row:** K2tog, k4, p2, k1, p12, k1, p2, k4, k2tog. (28 stitches)
Bind off all stitches.
Sides
**Make 2 alike**
Cast on 12 stitches.
Work in Garter Stitch pattern until piece measures 10 inches from cast-on edge.
**Next row:** K2, bind off 2 stitches, k4, bind off 2 stitches, k2.
**Next row:** K2, [yo] twice, k4, [yo] twice, k2.
Work in Garter Stitch pattern until piece measures 14 inches from cast-on edge.
Bind off.
Sew sides to body of bag.
Straps
Cast on 6 stitches.
Work in Garter Stitch pattern until piece measures 25 inches.
Bind off.
I-cord
Cast on 3 stitches.
Following instructions for 3-stitch I-cord on page 8, work a 40-inch length of I-cord.
Bind off.
**Finishing**
Felt as per felting instructions on page 9.
Referring to photo for placement, sew straps securely to back of bag.
Thread the I-cord through the eyelets.
If desired, attach magnetic snap closure to hold flap in place.
Aran Throw
Skill Level
Finished Size
51 x 56 inches
Materials
• Lion Brand Wool-Ease Thick & Quick super bulky weight yarn (6 oz/106 yds/170g per skein): 12 skeins fisherman #099
• Yellow Knifty Knitter Loom (40 pegs)
• Knitting tool
• Cable needle
• Tapestry needle
Gauge
9½ stitches and 14 rows = 4 inches/10cm
Special Abbreviations
**3-st RC (3-stitch Right Cross):** Place loop from Peg 1 on cable needle and hold to center of knitting loom, knit Peg 2 and Peg 3 and move loops to Peg 1 and Peg 2. Place loop from cable needle on Peg 3. Knit loop on Peg 3.
**3-st LC (3-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit Peg 3. Place loop from Peg 3 on cable needle. Knit Peg 1 and Peg 2. Move loop from Peg 2 to Peg 3, and loop from Peg 1 to Peg 2. Place loop from cable needle on Peg 1.
**3-st RPC (3-stitch Right Purl Cross):** Place loop from Peg 1 on cable needle and hold to center of knitting loom. Knit Peg 2 and Peg 3. Move loop from Peg 2 to Peg 1 and loop from Peg 3 to Peg 2. Take loop from cable needle and place it on Peg 3. Purl loop on Peg 3.
**3-st LPC (3-stitch Left Purl Cross):** Skip Peg 1 and Peg 2. Purl Peg 3 and place loop on cable needle. Knit skipped pegs. Move loop from Peg 2 to Peg 3 and loop from Peg 1 to Peg 2. Place loop from cable needle on Peg 1.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these loops on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place loops from cable needle on Peg 1 and Peg 2. Gently pull on the loop on Peg 3 and then the loop on Peg 4 to tighten the stitches.
Pattern Stitches
**A. Garter Stitch**
**Row 1:** Knit.
**Row 2:** Purl.
Rows 1 and 2 make 1 garter-stitch ridge.
**B. Medallion Stitch**
**Row 1:** P2, k10, p6, k4, p6, k10, p2.
**Row 2:** P2, k2, p6, k2, p6, k4, p6, k2, p6, k2, p2.
**Row 3:** P2, k10, p6, 4-st LC, p6, k10, p2.
**Row 4:** P2, k2, p6, k2, p6, k4, p6, k2, p6, k2, p2.
**Row 5:** P2, k10, p5, 3-st RC, 3-st LC, p5, k10, p2.
**Row 6:** P2, k2, p6, k2, p5, k2, p2, k2, p5, k2, p6, k2, p2.
**Row 7:** P2, k10, p4, 3-st RC, k2, 3-st LC, p4, k10, p2.
**Row 8:** P2, k2, p6, k2, p4, k2, p4, k2, p4, k2, p6, k2, p2.
**Row 9:** P2, k10, p3, 3-st RC, k4, 3-st LC, p3, k10, p2.
**Row 10:** P2, k2, p6, k2, p3, k2, p6, k2, p3, k2, p6, k2, p2.
**Row 11:** P2, k10, p3, k10, p3, k10, p2.
**Row 12:** P2, k2, p6, k2, p3, k2, p6, k2, p3, k2, p6, k2, p2.
**Row 13:** P2, 3-st LPC, k4, 3-st RPC, p3, k10, p3, 3-st LPC, k4, 3-st RPC, p2.
**Row 14:** P3, k2, p4, k2, p4, k2, p6, k2, p4, k2, p4, k2, p3.
**Row 15:** P3, 3-st LPC, k2, 3-st RPC, p4, k10, p4, 3-st LPC, k2, 3-st RPC, p3.
**Row 16:** P4, k2, p2, k2, p5, k2, p6, k2, p5, k2, p2, k2, p4.
**Row 17:** P4, 3-st LPC, 3-st RPC, p5, k10, p5, 3-st LPC, 3-st RPC, p4.
**Row 18:** P5, k4, p6, k2, p6, k2, p6, k4, p5.
**Row 19:** P5, 4-st LC, p6, k10, p6, 4-st LC, p5.
**Row 20:** P5, k4, p6, k2, p6, k2, p6, k4, p5.
**Row 21:** P5, k4, p6, k10, p6, k4, p5.
**Row 22:** P5, k4, p6, k2, p6, k2, p6, k4, p5.
**Row 23:** P5, 4-st LC, p6, k10, p6, 4-st LC, p5.
**Row 24:** P5, k4, p6, k2, p6, k2, p6, k4, p5.
**Row 25:** P4, 3-st RC, 3-st LC, p5, k10, p5, 3-st RC, 3-st LC, p4.
**Row 26:** P4, k2, p2, k2, p5, k2, p6, k2, p5, k2, p2, k2, p4.
**Row 27:** P3, 3-st RC, k2, 3-st LC, p4, k10, p4, 3-st RC, k2, 3-st LC, p3.
**Row 28:** P3, k2, p4, k2, p4, k2, p6, k2, p4, k2, p4, k2, p3.
**Row 29:** P2, 3-st RC, k4, 3-st LC, p3, k10, p3, 3-st RC, k4, 3-st LC, p2.
**Row 30:** P2, k2, p6, k2, p3, k2, p6, k2, p3, k2, p6, k2, p2.
**Row 31:** P2, k10, p3, k10, p3, k10, p2.
**Row 32:** P2, k2, p6, k2, p3, k2, p6, k2, p3, k2, p6, k2, p2.
**Row 33:** P2, k10, p3, 3-st LPC, k4, 3-st RPC, p3, k10, p2.
**Row 34:** P2, k2, p6, k2, p4, k2, p4, k2, p4, k2, p6, k2, p2.
**Row 35:** P2, k10, p4, 3-st LPC, k2, 3-st RPC, p4, k10, p2.
**Row 36:** P2, k2, p6, k2, p5, k2, p2, k2, p5, k2, p6, k2, p2.
**Row 37:** P2, k10, p5, 3-st LPC, 3-st RPC, p5, k10, p2.
**Row 38:** P2, k2, p6, k2, p6, k4, p6, k2, p6, k2, p2.
**Row 39:** P2, k10, p6, 4-st LC, p6, k10, p2.
**Row 40:** P2, k2, p6, k2, p6, k4, p6, k2, p6, k2, p2.
**Instructions**
Panel 1
Cast on 40 stitches.
Work 208 rows in Garter Stitch pattern (total of 104 garter-stitch ridges), or until panel measures 56 inches from cast-on edge.
Bind off.
Panel 2
**Make 2**
Cast on 40 stitches.
Lower Border
Work 4 rows in Garter Stitch pattern. (2 garter-stitch ridges)
Body
Work [Rows 1–40 of Medallion Stitch pattern] 5 times. (200 rows)
Upper Border
Work 4 rows in Garter Stitch pattern. (2 garter-stitch ridges)
Bind off.
**Assembly**
Place a Panel 2 on each side of Panel 1. Sew seams.
Block to size.
Cables Purse
Skill Level
Finished Size
7½ x 9 inches, not including handles
Materials
• Caron Simply Soft Quick super bulky weight yarn (3 oz/50 yds/85g per skein): 2 skeins bone #0003
• Yellow Knifty Knitter round loom (41 pegs)
• Knitting tool
• Cable needle
• Tapestry needle
• 2 purse handles with 5-inch-wide opening
Gauge
12 stitches and 15 rows = 4 inches/10cm
Special Abbreviations
**6-st LC (6-stitch Left Cross):** Skip Peg 1, Peg 2 and Peg 3. Knit loop on Peg 4, Peg 5 and Peg 6, place these 3 stitches on cable needle and hold to center of knitting loom. Knit loops on Peg 1, Peg 2 and Peg 3. Place loop from Peg 1 on Peg 4, loop from Peg 2 on Peg 5 and loop from Peg 4 on Peg 6. Place stitches from cable needle on Peg 1, Peg 2 and Peg 3. Gently pull loop on Peg 4, then loop on Peg 5 and then loop on Peg 6 to tighten the stitches.
**6-st RC (6-stitch Right Cross):** Place loops from Peg 1, Peg 2 and Peg 3 on cable needle. Knit Peg 4 and place loop on Peg 1. Knit Peg 5 and place loop on Peg 2. Knit Peg 6 and place loop on Peg 3. Take Loop 1 from cable needle and place it on Peg 4. Take Loop 2 from cable needle and place it on Peg 5. Take Loop 3 from cable needle and place it on Peg 6.
Pattern Notes
Leave a long tail at cast-on edge and bind-off edge to be used for seaming the handles in place.
Wrap the row before crossing for cables loosely.
**Instructions**
Handle casing
Cast on 20 stitches.
**Rows 1–14:** Knit.
Cast on 4 sts at beginning of next 2 rows. (28 stitches)
Body
**Rows 1–4:** P3, k6, p3, k4, p3, k6, p3.
**Row 5:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
**Rows 6–10:** P3, k6, p3, k4, p3, k6, p3.
**Row 11:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
**Rows 12–16:** P3, k6, p3, k4, p3, k6, p3.
**Row 17:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
**Rows 18–30:** P3, k6, p3, k4, p3, k6, p3.
**Row 31:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
**Rows 32–36:** P3, k6, p3, k4, p3, k6, p3.
**Row 37:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
**Rows 38–42:** P3, k6, p3, k4, p3, k6, p3.
**Row 43:** P3, 6-st LC, p3, k4, p3, 6-st RC, p3.
Bind off 4 stitches at beginning of next 2 rows. (20 stitches)
Handle casing
**Rows 1–14:** Knit.
Bind off using the basic bind off on page 4 and weave in all ends.
Finishing
Block lightly. If necessary, adjust the stitches on the cable-crossing rows.
Place piece right side down on a table. *Place 1 of the handles on either the cast-on or bound-off edge. Pass the stockinette portion of the bag through the handle, fold over the stockinette fabric so it covers the entire lower portion of the handle.
Sew the edge (on the wrong side of the fabric) to secure the handle in place.
Repeat from * with the other handle.
Sew sides of the bag with mattress stitch (page 8).
Cion Earflap Hat
Skill Level
Sizes
Child (adult) Instructions are given for smaller size, with larger size in parentheses. When only 1 number is given, it applies to both sizes.
Finished Measurement
**Circumference:** 22 (25) inches, slightly stretched
Materials
• Lion Brand Wool-Ease Thick & Quick super bulky weight yarn (6 oz/106 yds/170g per skein): 1 skein sky blue #106 or raspberry #112
• Red Knifty Knitter round loom (31 pegs)
• Knitting tool
• Tapestry needle, cable needle, 2 stitch (peg) markers
• Cable needle
Gauge
9½ stitches and 17½ rows = 4 inches/10cm
Special Abbreviations
**4-st RC (4-stitch Right Cross):** Place loops from Peg 1 and Peg 2 on cable needle. Knit Peg 3 and place loop on Peg 1. Knit Peg 4 and place loop on Peg 2. Place Loop 1 from cable needle on Peg 3 and knit it. Place Loop 2 from cable needle on Peg 4 and knit it.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place stitches from cable needle on Peg 1 and Peg 2. Gently pull on the loop on Peg 3 and then loop on Peg 4 to tighten the stitches.
**Instructions**
Front/Back Panel
**Make 2 alike**
_**Note:** See page 4 for instructions on ssk and k2tog decreases._
Cast on 14 (16) stitches.
**Row 1:** Purl.
**Row 2:** Knit.
**Row 3:** Purl.
**Row 4:** Knit.
**Rows 5–24:** Knit.
**Row 25:** Ssk, knit to last 2 stitches, k2tog. (12, 14 stitches)
**Row 26:** Knit.
**Rows 27–36 (38):** Repeat rows 25 and 26. (2 stitches remain)
Place remaining stitches on waste yarn.
Block lightly and weave in ends.
Side panel
**Make 2 alike**
I-cord tie
Cast on 2 stitches.
Work 2-st I-cord (see page 8) for 12 (18) inches.
Cable earflap
_**Note:** See page 4 for instructions on M1 increase._
**Row 1:** K1, M1, k1, M1. (4 stitches)
**Row 2:** Knit.
**Row 3:** K1, M1, k2, M1, k1. (6 stitches)
**Row 4:** Knit.
**Row 5:** K1, M1, k4, M1, k1. (8 stitches)
**Row 6:** Knit.
**Row 7:** K1, M1, k2, 4-st RC, M1, k1. (10 stitches)
**Row 8:** K1, p1, k6, p1, k1.
**Row 9:** K1, M1, p1, 4-st LC, k2, p1, M1, k1. (12 stitches)
**Row 10:** K2, p1, k6, p1, k2.
**Row 11:** K1, M1, k1, p1, k2, 4-st RC, p1, k1, M1, k1. (14 stitches)
**Row 12:** K3, p1, k6, p1, k3. Continue with body below.
**For large size only**
**Row 13:** K1, M1, k2, p1, 4-st LC, k2, p1, k2, M1, k1. (16 stitches)
**Row 14:** K4, p1, k6, p1, k4.
Continue with body below.
Body
**For small size only**
**Row 1:** K3, p1, 4-st LC, k2, p1, k3.
**Row 2:** K3, p1, k6, p1, k3.
**Row 3:** K3, p1, k2, 4-st RC, p1, k3.
**Row 4:** K3, p1, k6, p1, k3.
Repeat [Rows 1–4] 6 times.
**For large size only**
**Row 1:** K4, p1, k2, 4-st RC, p1, k4.
**Row 2:** K4, p1, k6, p1, k4.
**Row 3:** K4, p1, 4-st LC, k2, p1, k4.
**Row 4:** K4, p1, k6, p1, k4.
Repeat [Rows 1–4] 6 times.
Crown
**For both sizes**
Continue in pattern as established, decreasing 1 stitch at each end by using ssk on the right side, and k2tog on the left side, every other row until 8 stitches remain.
Work in stockinette stitch and continue decreasing as before until 2 stitches remain.
Place 2 stitches on waste yarn.
**Finishing**
Weave in ends.
Block lightly.
Sew all pieces together.
Thread yarn end through tapestry and weave through 8 stitches at top to close.
**Pompom**
Following instructions on page 8, make 2 pompoms. Referring to photo for placement, attach 1 pompom to each end of the I-cord.
Baby Sweater
Skill Level
Sizes
12 (18, 24) months Instructions are given for smallest size, with larger sizes in parentheses. When only 1 number is given, it applies to all sizes.
Finished Measurement
**Chest:** 21¾ (23¼, 24¾) inches Fits snuggly.
Materials
• Caron Simply Soft Quick super bulky weight yarn (3 oz/50 yds/85g per skein): 4 (4, 5) skeins berry blue #0015
• Yellow Knifty knitter (40 pegs)
• Knitting tool
• Cable needle
• Tapestry needle
Gauge
11 stitches and 15 rows = 4 inches/10cm
Special Abbreviations
**4-st RC (4-stitch Right Cross):** Place loops from Peg 1 and Peg 2 on cable needle. Knit Peg 3 and place loop on Peg 1. Knit Peg 4 and place loop on Peg 2. Place Loop 1 from cable needle on Peg 3 and knit it. Place Loop 2 from cable needle on Peg 4 and knit it.
**4-st LC (4-stitch Left Cross):** Skip Peg 1 and Peg 2. Knit loops on Peg 3 and Peg 4, place these stitches on cable needle and hold to center of knitting loom. Knit skipped loops on Peg 1 and Peg 2. Place loop from Peg 1 on Peg 3 and loop from Peg 2 on Peg 4. Place loops from cable needle on Peg 1 and Peg 2. Gently pull loop on Peg 3 and then loop on Peg 4 to tighten the stitches.
Pattern Stitches
**A. Garter Stitch**
**Row 1:** Knit.
**Row 2:** Purl.
Rows 1 and 2 make 1 garter-stitch ridge.
**B. Braid Cable**
(worked over 10 stitches)
**Row 1:** P2, 4-st RC, k2, p2.
**Row 2:** P2, k6, p2.
**Row 3:** P2, k2, 4-st LC, p2.
**Row 4:** P2, k6, p2.
**Instructions**
Back
Cast on 30 (32, 34) stitches.
Work 4 rows in Garter Stitch pattern. (2 garter-stitch ridges)
Work in stockinette stitch until piece measures 7½ (8, 9) inches from cast-on edge, or desired length to underarm.
**Shape raglan**
Bind off 2 (2, 3) sts at beginning of next 2 rows.
Decrease 1 stitch at each end [every other row] 8 (9, 9) times.
Bind off rem 10 stitches.
Front
Cast on 30 (32, 34) stitches.
Work 4 rows in Garter Stitch pattern. (2 garter-stitch ridges)
**Next row:** K10 (11, 12) stitches, work Row 1 of Braid Cable pattern over next 10 stitches, knit rem sts.
Continue to work in patterns as established, working center 10 stitches in Braid Cable pattern and remaining stitches in stockinette stitch until piece measures 7½ (8, 9) inches from cast-on edge, or desired length to underarm. Discontinue Braid Cable pattern.
Divide the stitches on loom into 2 groups of 15 (16, 17) stitches each.
Join a skein of yarn at Peg 16 (17, 18). From this point on, you will work each side with a different ball of yarn.
Shape neck & raglan
**Next row:** Bind off 2 (2, 3) stitches, knit to center 3 stitches, p3; for 2nd half, with other skein, p3, knit remaining stitches.
**Next row:** Bind off 2 (2, 3) stitches, knit across both sides.
Continue in pattern following Raglan Shaping decreases as for Back at the outside edges and 3-stitch Garter Stitch edging on V-neck opening until piece measures same as Back.
Bind off remaining 5 stitches from each side.
Sleeves
Cast on 14 stitches.
Work 4 rows of Garter Stitch pattern. (2 garter-stitch ridges)
Work in stockinette stitch, increasing 1 stitch at each end [every 5th row] 5 (5, 6) times. (24, 24, 26 stitches)
Work even until piece measures 8 (9, 10) inches from cast-on edge or desired sleeve length.
Shape raglan
Bind off 2 (2, 3) stitches at beginning of next 2 rows.
Decrease 1 stitch at each end [every other row] 6 (7, 7) times, then [every 3rd row] once.
Bind off remaining 6 (4, 4) stitches.
**Finishing**
Block all pieces.
Sew sleeves to front and back along raglan edges. Sew side and underarm seams.
General Information
Skill Levels
Beginner projects for first-time knitters using basic stitches. Minimal shaping.
Easy projects using basic stitches, repetitive stitch patterns, simple color changes and simple shaping and finishing.
Intermediate projects with a variety of stitches, mid-level shaping and finishing.
Experienced projects using advanced techniques and stitches, detailed shaping and refined finishing.
Standard Yarn Weight System
Categories of yarn, gauge ranges, and recommended needle sizes
Knit Abbreviations & Symbols
**approx** | approximately
---|---
**beg** | begin/beginning
**CC** | contrasting color
**ch** | chain stitch
**cm** | centimeter(s)
**cn** | cable needle
**dec** | decrease/decreases/decreasing
**dpn(s)** | double-pointed needle(s)
**g** | gram
**inc** | increase/increases/increasing
**k** | knit
**k2tog** | knit 2 stitches together
**LH** | left hand
**lp(s)** | loop(s)
**m** | meter(s)
**M1** | make one stitch
**MC** | main color
**mm** | millimeter(s)
**oz** | ounce(s)
**p** | purl
**pat(s)** | pattern(s)
**p2tog** | purl 2 stitches together
**psso** | pass slipped stitch over
**p2sso** | pass 2 slipped stitches over
**rem** | remain/remaining
**rep** | repeat(s)
**rev St sto** | reverse stockinette stitch
**RH** | right hand
**rnd(s)** | rounds
**RS** | right side
**skp** | slip, knit, pass stitch over—one stitch decreased
**sk2p** | slip 1, knit 2 together, pass slip stitch over, then knit 2 together—2 stitches have been decreased
**sl** | slip
**sl 1k** | slip 1 knitwise
**sl 1p** | slip 1 purlwise
**sl st** | slip stitch(es)
**ssk** | slip, slip, knit these 2 stitches together—a decrease
**st(s)** | stitch(es)
**St st** | stockinette stitch/stocking stitch
**tbl** | through back loop(s)
**tog** | together
**WS** | wrong side
**wyib** | with yarn in back
**wyif** | with yarn in front
**yd(s)** | yard(s)
**yfwd** | yarn forward
**yo(s)** | yarn over(s)
|
---|---
[ ] | work instructions within brackets as many times as directed
( ) | work instructions within parentheses in the place directed
** | repeat instructions following the asterisks as directed
* | repeat instructions following the single asterisk as directed
" | inch(es)
Inches Into Millimeters & Centimeters
All measurements are rounded off slightly.
Knitting Needle Conversion Chart
We wish to thank ProvoCraft for providing the Kniffty Knitter looms used in this book.
**Learn to Knit Cables on Looms** is published by DRG, 306 East Parr Road, Berne, IN 46711. Printed in USA. Copyright © 2007 DRG. All rights reserved. This publication may not be reproduced in part or in whole without written permission from the publisher.
**RETAIL STORES:** If you would like to carry this pattern book or any other DRG publications, visit DRGwholesale.com
Every effort has been made to ensure that the instructions in this publication are complete and accurate. We cannot, however, take responsibility for human error, typographical mistakes or variations in individual work. Please visit AnniesCustomerCare.com to check for pattern updates.
ISBN: 978-1-59012-218-1 | 7 8 9 10
---|---
| {
"redpajama_set_name": "RedPajamaBook"
} | 376 |
//---------------------------------------------------------------------
// <copyright file="ODataNavigationLinkExpandedItemObjectModelAnnotation.cs" company="Microsoft">
// Copyright (C) Microsoft Corporation. All rights reserved. See License.txt in the project root for license information.
// </copyright>
//---------------------------------------------------------------------
namespace Microsoft.Test.Taupo.OData.Common
{
#region Namespaces
using Microsoft.OData.Core;
#endregion Namespaces
/// <summary>
/// An OData object model annotation for navigation link to capture its expanded value.
/// </summary>
/// <remarks>Non expanded links don't have this annotation at all.</remarks>
public sealed class ODataNavigationLinkExpandedItemObjectModelAnnotation
{
/// <summary>
/// The expanded item.
/// This can be either:
/// - ODataFeed - for expanded feed
/// - ODataEntry - for expanded entry
/// - null - for null expanded entry
/// - ODataEntityReferenceLink - for entity reference link in requests
/// - List of ODataItem - for deep bindings in request, the list may contain ODataEntityReferenceLink or ODataFeed instances.
/// </summary>
public object ExpandedItem { get; set; }
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,689 |
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National Air and Space Museum. Office of the Director
0.25 cu. ft. (1 half document box)
This accession consists of records documenting a lecture given by General John R. Dailey, Director, at the Royal Aeronautical Society on the occasion of the 25th anniversary of the opening of the National Air and Space Museum. Materials include the published text of the lecture, presenter's notes, and slides. | {
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35. Mistrzostwa Świata w Kolarstwie Przełajowym 1984 odbyły się w holenderskim mieście Oss, w dniach 18 - 19 lutego 1984 roku. Rozegrano wyścigi mężczyzn w kategoriach zawodowców, amatorów i juniorów.
Medaliści
Szczegóły
Zawodowcy
Amatorzy
Reprezentant Belgii, Ivan Messelis zajął czwarte miejsce, jednak został zdyskwalifikowany za stosowanie dopingu.
Juniorzy
Tabela medalowa
Linki zewnętrzne
1984 w kolarstwie
Kolarstwo w Holandii
Mistrzostwa świata w kolarstwie przełajowym | {
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Mayor McCallion says she was 'joking' about enforcing idling bylaws at drive-thrus
Posted May 8, 2014 6:13 am EST
Cars line up at a Tim Hortons drive-thru in Fort McMurray, Alta. THE CANADIAN PRESS/Larry MacDougal
Mississauga Mayor Hazel McCallion was serious when she urged people to avoid drive-thrus at a city council meeting Wednesday, noting the harmful emissions that are spewed by idling cars.
But she later said was 'joking' about having the city's three-minute ban on idling enforced while drivers sit waiting for their double doubles and Big Macs.
"I was really joking," she said. "There's no way that we can monitor the idling at drive-thrus. We don't have the staff to do it."
Under existing bylaws, idlers could face a $150 fine, but bylaw officers have typically been issuing warnings rather than fines.
It's not just the pollution that irritates McCallion, it's also the traffic jams caused by long lines at rush hour, she told city council.
McCallion would prefer an outright ban on drive-thrus, but she admits that would be a tough sell to council.
Her comments were spawned from a staff report about how Mississauga is coping with the effects of climate change.
City of Toronto bylaws cap idling at one minute and expects employees to follow a "10-second rule" for idling.
According to the Ministry of Natural Resources, idling for longer than 10 seconds wastes more gas and produces more carbon emissions than restarting the engine.
Click here for the the Ministry of Natural Resources website on idling, including interactive idling impact calculators.
[View the story "YOUR REACTION: Idling in drive-thrus" on Storify]
Have you ever been ticketed in a drive-thru line?
bylaws|drive-thrus|idling|Mississauga | {
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In Greek mythology, Penelope or Penelopeia ( ; , Pēnelópeia, or , Pēnelópē) was a dryad, the daughter of Dryops. She resides on mount Kyllene in Arcadia and is the mother of the god Pan or of Nomios by Hermes.
This particular Penelope is sometimes confused with her namesake, Penelope, the wife and queen of Odysseus, in stories in which she is said to be the mother of Pan.
Notes
References
Apollodorus, The Library with an English Translation by Sir James George Frazer, F.B.A., F.R.S. in 2 Volumes, Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1921. ISBN 0-674-99135-4. Online version at the Perseus Digital Library. Greek text available from the same website.
Gaius Julius Hyginus, Fabulae from The Myths of Hyginus translated and edited by Mary Grant. University of Kansas Publications in Humanistic Studies. Online version at the Topos Text Project.
The Homeric Hymns and Homerica with an English Translation by Hugh G. Evelyn-White. Homeric Hymns. Cambridge, MA.,Harvard University Press; London, William Heinemann Ltd. 1914. Online version at the Perseus Digital Library. Greek text available from the same website.
Nonnus of Panopolis, Dionysiaca translated by William Henry Denham Rouse (1863-1950), from the Loeb Classical Library, Cambridge, MA, Harvard University Press, 1940. Online version at the Topos Text Project.
Nonnus of Panopolis, Dionysiaca. 3 Vols. W.H.D. Rouse. Cambridge, MA., Harvard University Press; London, William Heinemann, Ltd. 1940-1942. Greek text available at the Perseus Digital Library.
Dryads
Women in Greek mythology | {
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Progress Together: Becoming Data Driven
Thursday Jul 11, 2019 03:00 pm EDT
1100 First St NE #1200, Washington, DC 20002
Date: Thursday, July 11, 2019, 3:00 to 4:30 p.m. (EDT)
The promise of using data to make more informed decisions seems simple. Consumers make data-driven decisions every day when buying household goods, booking hotels, or choosing where to eat. Businesses use data every day to determine the ads we see, the best location for expansion, or the cost of their services. But using data to drive decisions about social programs continues to remain out of reach for many policymakers and program administrators at all levels.
The stakes are high. The data are messy. The systems are old. But the pressure is on. Civil servants and community organizations are being asked to do more with less and, often, just keeping things running is hard enough. Many conversations about the promise of using data to drive decisions lead with new steps, new requirements, new staff, and new expectations that are simply out of reach for too many.
Join Mathematica on July 11, 2019, from 3:00 to 4:30 p.m. (EDT) at our Washington, DC, offices or online as we bring together leaders from a variety of sectors to discuss the challenges of becoming data driven and offer action-oriented, accessible advice on how organizations can take their first steps, or their next steps, to progress together. This is the first in a series of in-person and online conversations throughout 2019 dedicated to data-driven progress. All in-person guests are encouraged to attend a networking reception following the discussion.
Christina Becker is a health policy and program associate at the American Public Human Services Association (APHSA), where she is deeply involved in the National Collaborative for Integration of Health and Human Services and serves as chair of the collaborative's Analytics Committee. Becker is also the policy liaison for the IT Solutions Management for Human Services affinity group. Before joining APHSA, she worked in the judges' chambers of the Fairfax County General District Court.
Paul Decker is the president and CEO of Mathematica and a nationally recognized expert in policy research, data analytics, education, and labor policy. Decker has led the expansion and diversification of Mathematica's work into new and evolving areas while maintaining its long-standing commitment to rigorous and objective analysis. He is a past president of the Association for Public Policy Analysis & Management, currently serves as a trustee of the Committee for Economic Development, and chairs the Government Relations Committee of CEO Connection.
Connor Norwood is the chief data officer for the Indiana Family and Social Services Administration, which administers the state's Medicaid and social service programs. He oversees the agency's enterprise data warehouse, which houses the data required to support the reporting, business intelligence, and advanced analytics for Indiana's health and human services programs. He also holds an adjunct faculty appointment at Indiana University's Richard M. Fairbanks School of Public Health and teaches in the Healthcare Innovation Leadership Institute.
Veronica Olazabal is the director of measurement, evaluation, and organizational performance at the Rockefeller Foundation. She is an award-winning data and analytics enthusiast with a professional portfolio encompassing 15 years, four continents, and numerous domestic and international agencies, including the Mastercard Foundation and Nuru International. In addition to serving on a number of funding and advisory boards, Olazabal serves on the American Evaluation Association's Board of Directors.
Clarence Wardell is the director of city solutions at Results for America, supporting Bloomberg Philanthropies' What Works Cities Initiative to help mid-size cities use data and evidence to guide programming and investment decisions. He is a former member of the U.S. Digital Service and co-led the White House Police Data Initiative, aimed at using open data to increase trust and engagement among law enforcement and the communities they serve. Wardell also served as a presidential innovation fellow from 2014–2015.
Mathematica Policy Research | {
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{"url":"https:\/\/web2.0calc.com\/questions\/please-help_75419","text":"+0\n\n0\n491\n3\n\nWe have a standard deck of 52 cards, with 4 cards in each of 13 ranks. We call a 5-card poker hand a full house if the hand has 3 cards of one rank and 2 cards of another rank (such as 33355 or AAAKK). What is the probability that five cards chosen at random form a full house?\n\nSep 9, 2021\n\n#1\n0\n\nYou choose a rank for the three cards, then choose a rank for the two cards.\u00a0 There are C(52,5) ways of choosing 5 cards, so the probability is\n\n$\\frac{\\binom{13}{2} \\binom{4}{2} \\binom{4}{3}}{\\binom{52}{5}} = \\frac{3}{4165}.$\n\nSep 9, 2021\n#2\n+631\n0\n\nI'm actually not to familiar with statistics but would be very happy to learn where you learned this, do you think you'd be able to point me to a resource?\n\nhelperid1839321 \u00a0Sep 9, 2021\n#3\n+2388\n0\n\nGuest\u2019s answer is wrong. So it appears he didn\u2019t learn it.\n\nThere are numerous examples of online poker-hand probability\u00a0texts and examples. Google is a good starting point ...Bing is too.... so is Yahoo.... and Dogpile....\n\nSolution for this question:\n\nChoose the rank for the triple nCr(13,1)\n\nChoose three suits for the triple nCr(4,3)\n\nChoose a different rank for the pair nCr(12,1)\n\nChoose two suits for the pair nCr(4,2)\n\nThen\n\nDivide this by the total number of five-card hands. nCr(52,5)\n\n$$\\hspace {7cm} \\large \\text{ } \\dfrac{\\dbinom {13}{1}\\dbinom {4}{3}\\dbinom {12}{1}\\dbinom {4}{2}}{\\dbinom {52}{5}} = \\dfrac{6}{4165} \\approx 0.144\\%$$\n\nGA\n\nSep 10, 2021\nedited by Guest \u00a0Sep 10, 2021","date":"2022-08-14 10:04:22","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\": 0.7445282340049744, \"perplexity\": 751.1789479978888}, \"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-2022-33\/segments\/1659882572021.17\/warc\/CC-MAIN-20220814083156-20220814113156-00554.warc.gz\"}"} | null | null |
The Color Before the Sun è l'ottavo album in studio del gruppo musicale statunitense Coheed and Cambria, pubblicato il 9 ottobre 2015 dalla 300 Entertainment.
Tracce
Formazione
Gruppo
Claudio Sanchez – voce, chitarra
Travis Stever – chitarra, cori
Josh Eppard – batteria, percussioni, cori
Zach Cooper – basso, cori
Altri musicisti
Roy Agee – ottoni
Mike Haynes – ottoni
Jennifer Kummer – ottoni
Avery Bright – strumenti ad arco
Melodie Morris – strumenti ad arco
Eleonore Denig – strumenti ad arco
Jay Joyce – piano Rhodes
Chondra Marie Sanchez – cori
The Prize Fighter Inferno – effetti
Collegamenti esterni | {
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The President & Family
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2018-0263-F: Emails Processed in Response to Blumenthal v. NARA FOIA Litigation
Emails responsive to this request are being released on a rolling basis in segments. Please check this page for updates. The materials in FOIA 2018-0263-F are a selective, not necessarily all inclusive, body of documents responsive to the topic of the FOIA. Researchers should consult the archivist about related materials.
Official records of George W. Bush's presidency are housed at the George W. Bush Presidential Library and Museum and administered by the National Archives and Records Administration under the provisions of the Presidential Records Act.
For information about the electronic records at the George W. Bush Presidential Library, please see the Electronic Records Guide.
Segment 1 - published online on February 11, 2019
2018-0263-F[1]: Emails Sent to Brett Kavanaugh, Jason Lundell, and Manuel Miranda in December 2003
FOIA 2018-0263-F[1] requested emails on which Brett Kavanaugh, Jason Lundell, and Manuel Miranda were all included, either as senders or recipients, during December 2003.
This FOIA consists of four emails that contain a December 3, 2003 news article by Jeff Gannon of Talon News. There are two unique emails from different senders, with a duplicate of each email included.
2018-0263-F[1]
Segment 2 - published online on March 12, 2019
2018-0263-F[2]: Emails From, To, CC, or BCC Manuel Miranda and Brett Kavanaugh between July 2003 - April 2004 and Emails From, To, CC, or BCC Brett Kavanaugh Containing the Terms "Manny" or "Ledeen" between November 2003 - February 2004
FOIA 2018-0263-F[2] requested materials related to emails between Manuel Miranda and Brett Kavanaugh between July 2003 - April 2004 and emails sent or received by Brett Kavanaugh containing the terms "Manny" or "Ledeen" between November 2003 - April 2004.
This FOIA primarily contains speech drafts, news articles, and op-eds, as well as talking points regarding Brett Kavanaugh's nomination to the United States Court of Appeals - DC Circuit and administrative emails regarding facts pertaining to the status of George W. Bush administration judicial nominees.
Segment 3 - published online on April 4, 2019
2018-0263-F[3]: Emails From, To, CC, or BCC Brett Kavanaugh Containing the Terms "dem staff," mole, spy*, spies, Ledeen, Willett, and Lundell between July 2003 - April 2004 That Have Not Already Been Processed
FOIA 2018-0263-F[3] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh containing the terms "dem staff," mole, spy*, spies, Ledeen, Willett, and Lundell between July 2003 - April 2004.
This FOIA primarily contains emails containing news articles, press releases regarding state legislative actions, announcements of George W. Bush Administration nominees and scheduling of their hearings as well as a briefing for the Radio and Television Correspondents Dinner and various scheduling emails.
Segment 4 - published online on April 23, 2019
2018-0263-F[4]: Emails From, To, CC, or BCC Brett Kavanaugh Containing the Terms Manuel, Manny, or Miranda between July 2003 - April 2004 That Have Not Already Been Processed
FOIA 2018-0263-F[4] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh containing the terms Manuel, Manny, or Miranda between July 2003 - April 2004.
This FOIA primarily contains emails containing news articles, public opinion polls, excerpts from the Congressional Record, as well as announcements of personnel changes and judicial nominations from the George W. Bush Administration. Additional material for release includes routine scheduling emails, briefing papers for public presidential events, correspondence from members of Congress, as well as drafts of the acknowledgements portions of President George W. Bush's remarks and statements.
Segment 5 - published online on September 9, 2019
2018-0263-F[5]: Emails From, To, CC, or BCC Brett Kavanaugh Containing the Term Pryor between July 2003-May 2006 That Have Not Already Been Processed
FOIA 2018-0263-F[5] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh containing the term Pryor between July 2003 and May 2006.
This FOIA primarily contains talking points, press releases, fact sheets, transcripts, newsletters and information from outside organizations, news articles, routine emails regarding statistical information, information concerning the recess appointment of William H. Pryor Jr. on February 20, 2004, and information related to the nomination of Brett M. Kavanaugh to the U.S. Court of Appeals for the District of Columbia Circuit. Transcripts include Senate Judiciary Committee confirmation hearing transcripts and Senate Judiciary Committee business meeting transcripts. Also included is a memorandum of understanding from the Senate regarding judicial nominations. Records regarding Pryor's appointment include biographical data sheets, administrative emails, draft and final routine memorandum to President George W. Bush to approve the recess appointment, a statement by President George W. Bush, and emails coordinating the sending of a congratulatory letter. Records related to Kavanaugh's appointment include emails that mention Kavanaugh's involvement with the Pryor appointment such as news articles, excerpts from blog posts, and transcripts.
Segment 6 - published online on October 8, 2019
2018-0263-F[6]: Emails From, To, CC, or BCC Brett Kavanaugh Containing the Term Pickering between July 2003-May 2006 That Have Not Already Been Processed
FOIA 2018-0263-F[6] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh containing the term Pickering between July 2003 and May 2006.
This FOIA primarily contains legislative correspondence reports, judicial nomination statistics, press gaggles, a guest list for a Congressional Ball, draft and final versions of the acknowledgements for a speech given by President George W. Bush, questions regarding Judge Charles Pickering Sr.'s attendance at an event, published writings such as op-eds, articles, and blog posts, newsletters from organizations such as the Federalist Society and the Heritage Foundation, a letter from Representative Charles Pickering Jr. recommending the awarding of the Congressional Medal of Freedom to G.V. "Sonny" Montgomery, and a response to that letter from White House staffer David Hobbs.
Segment 7 - published online on November 14, 2019
2018-0263-F[7]: Emails From, To, CC, or BCC Brett Kavanaugh Referencing William Haynes or Priscilla Owen between July 2003-May 2006 that have not already been processed
FOIA 2018-0263-F[7] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh referencing William Haynes or Priscilla Owen between July 2003 and May 2006.
This FOIA primarily contains news articles, Google Alert messages, and an email regarding William J. Haynes' entry into the White House. Records related to Priscilla Owen include news articles, a congratulatory message from Owen to Brett Kavanaugh, a list of judges for a column to be written by George Will, and background materials on Miguel Estrada, Carolyn Kuhl, and Owen dated between July 2003 and September 2003.
Segment 8 - published online on December 11, 2019
2018-0263-F[8]: Emails From, To, CC, or BCC Brett Kavanaugh Referencing Priscilla Owen between July 2003-May 2006 that have not already been processed
FOIA 2018-0263-F[8] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh referencing Priscilla Owen between July 2003 and May 2006.
This FOIA primarily contains a "myth vs. fact" fact sheet regarding Kavanaugh's suitability for appointment to the U.S. Court of Appeals, news articles and opinion pieces, emails regarding the plans for Owen's appearance at the White House upon her confirmation, a final draft of both a statement and talking points regarding Owen's confirmation, and additional administrative and routine emails.
Segment 9 - published online on January 9, 2020
2018-0263-F[9]: Emails From, To, CC, or BCC Brett Kavanaugh Referencing Priscilla Owen or Carolyn Kuhl between July 2003-May 2006 that have not already been processed
FOIA 2018-0263-F[9] requested previously unprocessed materials related to emails sent or received by Brett Kavanaugh referencing Priscilla Owen or Carolyn Kuhl between July 2003 and
This FOIA primarily contains articles, talking points, lists of questions asked by Senators during judicial confirmation hearings, event photo status spreadsheets, and copies of letters sent to Senators Feinstein and Schumer. Also included are administrative emails regarding Owen's confirmation, appointment, and investiture.
PDF files require the free Adobe Reader.
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Learn more about the George W. Bush Presidential Library and Museum - the facility, staff, important partnerships, contact information, how to support or volunteer, applicable laws and regulations, and the National Archives and Records Administration.
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Work 2943 SMU Boulevard, Dallas, TX 75205 | {
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