text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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{"url":"https:\/\/cstheory.stackexchange.com\/questions\/52120\/unbounded-knapsack-instance-with-a-single-optimum-that-takes-each-item-once","text":"# Unbounded Knapsack Instance with a Single Optimum that takes each Item Once?\n\nConsider the Unbounded Knapsack Problem (UKP): We are given a set of $$n$$ items $$I = \\{1,\\ldots,n\\}$$ of integral weights $$w_1, \\ldots, w_n \\in \\mathbb{N}$$, integral profits $$p_1, \\ldots, p_n \\in \\mathbb{N}$$, and a budget $$B$$. The goal is to find a tuple $$(x_1, \\ldots, x_n) \\in \\mathbb{N}^n$$ which maximizes the total profit $$\\sum_{i \\in I} x_i \\cdot p_i$$ such that $$\\sum_{i \\in I} x_i \\cdot w_i \\leq B$$. In other words, in comparison to the classic knapsack, each item $$\ud835\udc56$$ can be taken any number of times.\n\nQuestion: Suppose that the profits are all polynomial in $$n$$; that is, $$\\forall i \\in I: p_i \\leq poly(n)$$. Now, for arbitrary parameter $$n$$, is there any UKP instance where the optimum must take each item exactly once? (profits being polynomial and weights can be defined arbitrarily) Stated alternatively, the profit of any feasible solution which differs from taking each item once has a strictly smaller profit.\n\nIf the answer to the above question is negative: If we construct an instance that maximizes the number of distinct items that must be taken for the optimum (w.r.t. some $$n$$ and again polynomial profits), what would this number be?\n\n\u2022 This seems like a nice homework exercise. Can you explain the context in which the problem arises, and what you know so far (relevant literature, and what you have tried that hasn't resolved the question)? Nov 7 at 15:52","date":"2022-12-06 07:55:05","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\": 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\": 13, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9003085494041443, \"perplexity\": 321.2163527362027}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446711074.68\/warc\/CC-MAIN-20221206060908-20221206090908-00625.warc.gz\"}"} | null | null |
{"url":"https:\/\/judge.mcpt.ca\/problem\/lcc18c2j3","text":"## LCC '18 Contest 2 J3 - Wrong Dere(c)k!\n\nView as PDF\n\nPoints: 7\nTime limit: 1.5s\nMemory limit: 64M\n\nAuthor:\nProblem type\n\nDereck is an avid Java programmer while Derek is a C++ programmer. Whenever someone asks them for help, they tend to mix up their names, frustrating them as they don't know any other languages other than the ones they program in. Being the good friend you are, you decide to intervene and tell people whether they have mixed up their names or not.\n\n\u2022 A statement about C++ is defined as a sentence that contains the word segmentation and\/or fault.\n\u2022 A statement about Java is defined as a sentence that contains the word biginteger and\/or apics (pronounced as AP ICS).\n\u2022 You will know when the person is asking Dereck or Derek if the sentence has a permutation of his name.\n\u2022 You are guaranteed that the sentence will either be a Java or C++ statement and not both.\n\u2022 You are guaranteed that the sentence will either ask for Dereck or Derek and not both.\n\n\u2022 e is interchangeable with 3\n\u2022 s is interchangeable with 5\n\u2022 a is interchangeable with @\n\u2022 t is interchangeable with 7\n\u2022 i is interchangeable with 1\n\nGiven a sentence, $$S$$, from Jason, the person who's asking Dere(c)k for help, can you politely tell them whether they're asking the wrong or right Dere(c)k?\n\n#### Input Specification\n\nThe first line will contain a string, $$S$$, with at most $$100\\ 000$$ characters, with all letters being lower-case.\n\n#### Output Specification\n\nIf $$S$$ was a Java statement towards Dereck or a C++ statement towards Derek, output Right Dere(c)k!. If it wasn't then output Wrong Dere(c)k!.\n\n$$S$$ will contain at most $$100$$ lower-case characters.\n\nNo further constraints.\n\n#### Sample Input\n\nhey dcr3ek, can you help me with my homework? i dont really understand b1g1nteger :p\n\n#### Sample Output\n\nRight Dere(c)k!\n\n#### Explanation\n\ndcr3ek can be rearranged as d3reck and since e is interchangeable with 3, d3reck becomes dereck. Following the last step, b1g1nteger becomes biginteger since i is interchangeable with 1. This makes the sentence a Java sentence that asks Dereck for help, so the output is Right Dere(c)k!","date":"2019-03-23 13:17:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.2638412415981293, \"perplexity\": 3459.170299177908}, \"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-2019-13\/segments\/1552912202804.80\/warc\/CC-MAIN-20190323121241-20190323143241-00231.warc.gz\"}"} | null | null |
all: test_elf_reader pie
pie:
$(MAKE) -C ../simplest_pie all
cp ../simplest_pie/simplest_pie ./pie.elf
test_elf_reader: ../../src/elf_reader.h ../../src/elf_reader.c test_elf_reader.cc
gcc ../../src/elf_reader.c -o elf_reader.o -c -std=c11
g++ test_elf_reader.cc -o test_elf_reader.o -c -std=c++11
g++ test_elf_reader.o elf_reader.o -o test_elf_reader
clean:
-rm test_elf_reader test_elf_reader.o elf_reader.o pie.elf
run: all
./test_elf_reader | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,263 |
Q: Depletion Mosfet as current source to power load I came acros the following application note for a Depletion Mosfet (https://www.infineon.com/dgdl/Infineon-Application_Note_Applications_for_Depletion_MOSFETs-AN-v01_00-EN.pdf) and i got intrigued.
In the above image, the depletion mosfet is being used as a current source to power a load with a constant current (the best it can, since this type of current source as some oscilations in the output current - from what i read).
My question is, how can you calculate the power that is being dissipated in the depletion mosfet (couldn't find the answer from my search)? It's Vds*Ids?
The objective would be to use the depletion mosfet + a power resistor to dissipate the energy from a set of capacitors (constant current discharge). The objective is that the depletion mosfet dissipates the less possible and that the resistor (load) dissipates the energy.
Best regards
A: The short answer is yes, the power dissipated in the MOSFET is Vds * Ids. Assuming that it behaves as a current limiter, the voltage on the resistor would be limited, so limiting the resistor dissipation. At higher voltages than this, the MOSFET would dissipate more power.
| {
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{"url":"http:\/\/www.numdam.org\/item\/CM_1969__21_3_253_0\/","text":"Natural covers\nCompositio Mathematica, Volume 21 (1969) no. 3, pp. 253-261.\n@article{CM_1969__21_3_253_0,\nauthor = {Franklin, S. P.},\ntitle = {Natural covers},\njournal = {Compositio Mathematica},\npages = {253--261},\npublisher = {Wolters-Noordhoff Publishing},\nvolume = {21},\nnumber = {3},\nyear = {1969},\nzbl = {0188.27901},\nmrnumber = {250252},\nlanguage = {en},\nurl = {http:\/\/www.numdam.org\/item\/CM_1969__21_3_253_0\/}\n}\nTY - JOUR\nAU - Franklin, S. P.\nTI - Natural covers\nJO - Compositio Mathematica\nPY - 1969\nDA - 1969\/\/\/\nSP - 253\nEP - 261\nVL - 21\nIS - 3\nPB - Wolters-Noordhoff Publishing\nUR - http:\/\/www.numdam.org\/item\/CM_1969__21_3_253_0\/\nUR - https:\/\/zbmath.org\/?q=an%3A0188.27901\nUR - https:\/\/www.ams.org\/mathscinet-getitem?mr=250252\nLA - en\nID - CM_1969__21_3_253_0\nER - \n%0 Journal Article\n%A Franklin, S. P.\n%T Natural covers\n%J Compositio Mathematica\n%D 1969\n%P 253-261\n%V 21\n%N 3\n%I Wolters-Noordhoff Publishing\n%G en\n%F CM_1969__21_3_253_0\nFranklin, S. P. Natural covers. Compositio Mathematica, Volume 21 (1969) no. 3, pp. 253-261. http:\/\/www.numdam.org\/item\/CM_1969__21_3_253_0\/\n\nA.B. Arhangel'Skii [1] Bicompact sets and the topology of spaces, Dokl. Akad. Nauk, SSSR, 150 (1963) 9. | MR | Zbl\n\nA.B. Arhangel'Skii [2] Some types of factor mappings and the relation between classes of topological spaces, Soviet Math. Dokl. 4 (1963), 1726-9. | Zbl\n\nA.B. Arhangel'Skii and S.P. Franklin [3] Ordinal invariants for topological spaces, Mich. Math. J. 15 (1968) 313-20. | Zbl\n\nC.E. Aull [4] Sequences in topological spaces, Not. Amer. Math. Soc. 12 (1965) 65T- 79.\n\nR.W. Bagley and J.S. Yang [5] On k-spaces and function spaces, Proc. Amer. Math. Soc. 17 (1966) 703-5. | Zbl\n\nS. Baron [6] The coreflective subcategory of sequential spaces, Canadian Math. Bul. 2 (1968) 603-4. | MR | Zbl\n\nT.K. Boehme [7] Linear s-spaces, Proceedings of the Symposium on Convergence Structures, University of Oklahoma, 1965.\n\nR. Brown [8] Ten topologies for X \u00d7 Y, Quart. J. Math. Oxford (2) 14 (1963), 303-19. | MR | Zbl\n\nD.E. Cohen [9] Spaces with weak topology, Quart. J. Math. Oxford (2) 5 (1954) 77-80. | Zbl\n\nE. Duda [10] Reflexive compact mappings, Proc. Amer. Math. Soc. 112 (966) 688-93. | MR | Zbl\n\nR.M. Dudley [11] On sequential convergence, Trans. Amer. Math. Soc. 112 (1964) 483-507. | Zbl\n\nI. Fleisher and S.P. Franklin [12] On compactness and projections, Contributions to Extension Theory of Topological Structures, Berlin 1969, 77-9. | Zbl\n\nS.P. Franklin [13] Spaces in which sequences suffice, Fund. Math. 57 (1965) 107-16. | Zbl\n\nS.P. Franklin [14] Spaces in which sequences suffice II, Fund. Math., 61 (1967), 51-65. | MR | Zbl\n\nD. Gale [15] Compact sets of functions and function rings, Proc. Amer. Math. Soc. 1 (1950) 303-8. | MR | Zbl\n\nJ.F. Kennison [16] Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303-15. | MR | Zbl\n\nJ. Kisynski [17] Convergence du type L, Coll. Math. 7 (1959) 205-11. | MR | Zbl\n\nE. Michael [18] Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. no. 11 (1952). | MR | Zbl\n\nK. Morita [19] On decomposition spaces of locally compact spaces, Proc. Japan. Acad. 32 (1956) 544-8. | MR | Zbl\n\nJ.H.C. Whitehead [20] Combinitory homotopy, Bull. Amer. Math. Soc. 55 (1949), 213-45. | Zbl\n\nG.T. Whyburn [21] Directed families of sets and closedness of functions, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 688-92. | MR | Zbl\n\nP. Gabriel and M. Zisman [22] Calculus of Fractions and Homotopy Theory, Springer, New York, 1967. | MR | Zbl\n\nN.E. Steenrod [23] A convenient catogory of topological spaces, Michigan Math. J. 14 (1967), 133-152. | MR | Zbl\n\nW.A. Luxemburg and L.C. Moore, Jr. [24] Archimedian quotient Riesz spaces, Duke Math. J. 34 (1967), 725-740. | Zbl","date":"2022-11-28 02:08:44","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\": 0.5399431586265564, \"perplexity\": 8001.485706339013}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710462.59\/warc\/CC-MAIN-20221128002256-20221128032256-00575.warc.gz\"}"} | null | null |
r"""
Solow growth model with Cobb-Douglas aggregate production:
.. math::
F(K, AL) = K^{\alpha}(AL)^{1 - \alpha}
where :math:`0 < \alpha < 1`.
"""
from __future__ import division
import numpy as np
import sympy as sym
from . import model
# declare key variables for the model
t, X = sym.symbols('t'), sym.DeferredVector('X')
A, k, K, L = sym.symbols('A, k, K, L')
# declare required model parameters
g, n, s, alpha, delta = sym.symbols('g, n, s, alpha, delta')
class CobbDouglasModel(model.Model):
_required_params = ['g', 'n', 's', 'alpha', 'delta', 'A0', 'L0']
def __init__(self, params):
"""
Create an instance of the Solow growth model with Cobb-Douglas
aggregate production.
Parameters
----------
params : dict
Dictionary of model parameters.
"""
cobb_douglas_output = K**alpha * (A * L)**(1 - alpha)
super(CobbDouglasModel, self).__init__(cobb_douglas_output, params)
@property
def steady_state(self):
r"""
Steady state value of capital stock (per unit effective labor).
:getter: Return the current steady state value.
:type: float
Notes
-----
The steady state value of capital stock (per unit effective labor)
with Cobb-Douglas production is defined as
.. math::
k^* = \bigg(\frac{s}{g + n + \delta}\bigg)^\frac{1}{1-\alpha}
where `s` is the savings rate, :math:`g + n + \delta` is the effective
depreciation rate, and :math:`\alpha` is the elasticity of output with
respect to capital (i.e., capital's share).
"""
s = self.params['s']
alpha = self.params['alpha']
return (s / self.effective_depreciation_rate)**(1 / (1 - alpha))
def _validate_params(self, params):
"""Validate the model parameters."""
params = super(CobbDouglasModel, self)._validate_params(params)
if params['alpha'] <= 0.0 or params['alpha'] >= 1.0:
raise AttributeError('Output elasticity must be in (0, 1).')
else:
return params
def analytic_solution(self, t, k0):
"""
Compute the analytic solution for the Solow model with Cobb-Douglas
production technology.
Parameters
----------
t : `numpy.ndarray`
Array of points at which the solution is desired.
k0 : (float)
Initial condition for capital stock (per unit of effective labor)
Returns
-------
analytic_traj : `numpy.ndarray` (shape=t.size, 2)
Array representing the analytic solution trajectory.
"""
s = self.params['s']
alpha = self.params['alpha']
# lambda governs the speed of convergence
lmbda = self.effective_depreciation_rate * (1 - alpha)
# analytic solution for Solow model at time t
k_t = (((s / (self.effective_depreciation_rate)) * (1 - np.exp(-lmbda * t)) +
k0**(1 - alpha) * np.exp(-lmbda * t))**(1 / (1 - alpha)))
# combine into a (T, 2) array
analytic_traj = np.hstack((t[:, np.newaxis], k_t[:, np.newaxis]))
return analytic_traj
| {
"redpajama_set_name": "RedPajamaGithub"
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package sobrecarga;
public class SubBase extends Base {
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,485 |
\section{Introduction}
A wide variety of interesting theories in physics which range, for
example,
from the standard model of strong, weak and electromagnetic interactions, to
Einstein general relativity and even to more speculative ideas like string
theories, can be understood and unified under the generic label of
constrained
systems. All such gauge theories
are characterized by the existence of relations (
constraints) among the original phase space variables, together with the
appearance of arbitrary functions
in the solutions of the equations of motion. The quantum mechanical
description
of such systems
deviates from the standard prescriptions, like the canonical or path integral
quantization for
unconstrained systems. A systematic procedure for dealing with the
quantization
of constrained systems was proposed some time ago by Dirac \cite{dirac} and
recently the method has been extended to the BRST-BFV prescription
\cite{fradkin} and also to the antifield method of Batalin-Vilkovisky
\cite{batalin},
both in the context of the path integral and operator
approach to quantization. These methods have been successfully applied to
many different problems such as supergravity \cite{kal} , topological field
theories \cite{bir} and superstrings \cite{hat}, just to mention a few
interesting cases.
Nevertheless, in the literature
we can find alternative methods of quantization, among which the Schwinger
action principle
\cite{schw} constitutes a very important case. This action principle can be
applied to
arbitrary quantum systems and starts from an operator formulation
of the action from the very
beginning. The general validity of this principle has recently motivated its
application to the case of constrained
systems. For example, in reference \cite{das} it is shown that when the
Schwinger action principle is applied to a system with only second class
constraints, it leads to (anti)commutations relations
corresponding precisely
to the Dirac bracket prescription. Another application of this
action principle
has been the calculation of the
quantum-mechanical BRST-invariant matrix elements
of the evolution operator in the cases of the spinless and the spining
relativistic free particle
\cite{rabello}, which were previously obtained
using the
BRST-BFV path integral formulation in Refs. \cite{henneaux},\cite{batlle}.
Unfortunately, the calculation in Ref. \cite{rabello} makes use of an
incorrect
(i.e. non-BRST invariant) basis for the physical states at the initial and
final times.
The Schwinger action principle can be viewed as a generalization
of the Weiss action principle in classical mechanics to the
quantum case . The Weiss principle states that if we make
an arbitrary
variation of the action
\begin{equation}
S=\int^{t''}_{t'}L(\dot q, q, t)\, dt,
\end{equation}
the Euler-Lagrange equations follows from the requirement
\begin{equation}
\delta S= G(t'')-G(t'),
\end{equation}
where the $G$'s are boundary terms \cite{sudarshan} . This means that such
variation
must not depend upon the trajectory that connects the
end-points, thus leading to the Euler-Lagrange equations of motion.
The explicit form of the
boundary terms
depends upon the dynamical variables which are kept fixed at boundaries.
For example, if we fix the coordinates $q$ at the boundaries $t''$ and $t'$,
then
\begin{equation}
G(t)=(p\delta q- H\delta t)|_{t },
\end{equation}
where $H$ is the corresponding Hamiltonian function and the notation is
$p\delta q=
p_i \delta q^i$, with the summation being over all the degrees of freedom
of the system. The notation of deleting the indices will be frequently
used in the sequel, in the cases where no confusion arises.
At the quantum level, the Weiss action principle is replaced by the
Schw\-in\-ger
action principle which states that
the arbitrary variation of the matrix
elements of the
evolution operator $<a''| U(t'',t') |b'>
\equiv \langle a'' t''|b' t'\rangle$ is given by
\begin{equation}
\delta \langle a'' t''|b' t'\rangle=i\langle a'' t''|\delta\bigg(
\int^{t''}_{t'}L(\dot{{\hat q}}, {{\hat q}}, t)\, dt\bigg)|b' t'\rangle. \label{delamp}
\end{equation}
Moreover, the variation of the hermitian action operator
${\hat S}=\int^{t''}_{t'}L(\dot {\hat q}, {\hat q}, t) dt$
must depend only
upon the
end point operators and times, in such a way that
\begin{equation}
\delta\bigg(\int^{t''}_{t'}L(\dot {\hat q}, {\hat q}, t)\, dt\bigg)=G({\hat A}'',
t'')-G({\hat B}', t'), \label{delL}
\end{equation}
where ${\hat A}''$ denotes a complete set of commuting operators at the time $t''$
with corresponding eigenvalues $a''$ and analogously for the operators ${\hat B}'$
at $t'$.
That is to say, the variation of the propagator is given by the corresponding
matrix elements of the variation of a single
quantum mechanical operator:
the action operator.
A convenient choice for the quantum Lagrangian is the first order form ${\hat L}=
{1 \over 2}\left( {\hat p} \dot {\hat q} + \dot {\hat q} {\hat p} \right)- H( {\hat q}, {\hat p}, t ) $,
where
$H({\hat q}, {\hat p}, t ) $ is the hermitian Hamiltonian operator constructed in the
usual way
starting from the definition ${\hat p}={\partial {\hat L} \over \partial \dot {\hat q}}$.
The resulting equations of motion are the standard Hamilton equations for the
quantum operators
\begin{equation}
\dot {\hat q}={\partial {\hat H} \over \partial {\hat p}}, \qquad \dot {\hat p}=-{\partial {\hat H}
\over \partial {\hat q}}\label{hei}
\end{equation}
and one can identify the corresponding end-point generators as
\begin{equation}
G(\hat q, \hat p) ={\hat p} \delta {\hat q} -{\hat H} \delta t \equiv G_{{\delta }_{{\hat q}}} +
G_{{\delta}_{t}}.
\end{equation}
At this stage it is also necessary to specify the operator character of
the
variations $\delta {\hat q}, \delta {\hat p}$
which imply the above results. When dealing with
bosonic (fermionic) operators, called operators of the first (second)
kind in Schwinger's notation, the corresponding variations satisfy the
standard commutation (anticommutation) rules of even (odd) elements
in a Grassmann algebra. The standard notation is that bosonic(fermionic)
objects have even(odd) Grassmann parity in the underlying Grassmann algebra.
By considering a canonical transformation which interchanges the roles of
${\hat q}$
and ${\hat p}$, it is possible to identify the generator of infinitesimal
transformations in ${\hat p}$ as $G_{{\delta}_{ {\hat p}}}= -{\hat q} \delta {\hat p}$. The above
expressions for the generators of the corresponding transformations, together
with the quantum mechanical interpretation of them as
producing infinitesimal unitary
transformations, leads to the general commutator
\begin{equation}
\left[ \hat A, \ {\hat G}_{{\delta }_{{\hat b}}} \right]=i
\delta_{\hat b}(\hat A).\label{cr1}
\end{equation}
{}From this expression we obtain the basic (anti)commutation relations for
the phase space
variables, after taking into account the (anti)commutation properties
of the parameters associated to the above transformations.
{}From Eqs. (\ref{delamp}) and (\ref{delL}), the final expression for arbitrary
variations of the
propagator is then given by
\begin{equation}
\delta\langle a'' t''|b' t'\rangle=i \langle a'' t''|G(A'', t'')-G(B', t')|b'
t'\rangle.\label{acp}
\end{equation}
In order to use the above expression as a
practical computational tool,
we must be able to solve the operator Heisenberg equations of motion
for the system in terms of the operators $A'', B' $ whose eigenvalues are
kept fixed at
the end-points. In this way, we will be able to calculate the corresponding
matrix elements in (\ref{acp}),
which provide a set of partial differential equations for the propagator, that
must be subsequently integrated.
In other words, we need to choose a complete set of (anti)commuting
operators at the initial and final times, together with a well
defined inner product in the Hilbert space of physical states,
in order to specify the quantum numbers at
the end-points which, of course, must be compatible with the
dynamics.
In this paper we introduce an operator BRST-BFV action for arbitrary systems
with first-class
constraints, which is inspired in Schwinger action principle. This action is
defined with
appropriate BRST-invariant boundary conditions.
As an application of this quantum action and as
an alternative procedure to the standard path-integral approach, we carefully
calculate the
propagators corresponding to the non-relativistic particle,
the relativistic spinless particle and the relativistic
spining particle. The corresponding calculations using the BRST-BFV
path integral approach can be found in Refs.\cite{henneaux}, \cite{batlle},
\cite{gomis2}.
The results presented in our work are based on a consistent choice of
end-points conditions and thus allows to clarify some incorrect points that
arise in Ref. \cite{rabello}.
The paper is organized as follows: section 2 contains our general prescription
to construct
the quantum BRST-BFV action, from which we subsequently calculate the
corresponding propagators using the Schwinger action principle. The
next sections, 3, 4 and 5, contain
the corresponding calculations for the following particular cases : the
parametrized non-relativistic particle, the relativistic free particle and the
spining relativistic free particle, respectively.
\section{The quantum BRST- BFV action}
Since the action principle does not provide a quantum action to start with,
we follow the usual procedure of defining the
quantum action as a consistent extension of
the classical action associated to the problem.
For a system with constraints, one of the most successful prescriptions to
construct a
classical gauge independent action is the BRST-BFV method \cite{libro}. The
resulting action has the
advantage of being invariant under BRST transformations and since
the remaining symmetry is only global, all the variations of the
canonical variables are independent.
We start from a classical
system described by canonical coordinates $q^i, p_i \ \\
(i=1,\dots,n)$,
having only first-class constraints $G_a(p,q) \ (a=1,\dots , m)$, and with a
first-class canonical Hamiltonian $H_0(q,p)$
\begin{equation}
G_a(q,p)\approx 0
\end{equation}
\begin{equation}
\{G_a, G_b\}_{PB} = C_{ab}^{\ \ c} (q,p) G_c, \quad
\{G_a, H_0\}_{PB} = D_{a}^{\ \ c} (q,p) G_c.
\end{equation}
We assume, for simplicity, that all second-class
constraints have been
eliminated, either by solving them or by transforming them into
first-class constraints, adding
new variables and
using, for example, the Batalin-Tyutin conversional method \cite{baty}.
Consider the variational principle in the class of paths
$q^i(\tau)$, $p_i(\tau)$, $\lambda^a(\tau)$, where $\lambda^a(\tau)$
are Lagrange multipliers associated to the constraints, with
prescribed values
at the
endpoints $\tau'$ and $\tau''$,
\begin{equation}
Q_i(q(\tau'),\ p(\tau'), \tau')={Q'}_i, \qquad
Q_i(q(\tau''),\ p(\tau''), \tau'')={Q''}_i, \label{boun}
\end{equation}
of a complete set of commuting variables $Q_i(q,p,\tau)$
\begin{equation}
\{Q_i , Q_j\}_{PB} =0, \ \ \hbox{(at equal times)}.
\end{equation}
The action for this variational principle is
\begin{equation}
S[q^i(\tau),p_i(\tau),\lambda^a(\tau)]=
\int_{\tau'}^{\tau''} (\dot q^i p_i - H_0 -\lambda^a G_a) d\tau -
B(\tau'') + B(\tau'), \label{classac}
\end{equation}
(for paths obeying (\ref{boun})), where the phase space function
$B(q,p,\tau)$ is such that
\begin{equation}
p_i \delta q^i =- P^i \delta Q_i + \delta B,
\end{equation}
for fixed $\tau$ \cite{hd}. Here, the $P^i$ are the momenta canonically
conjugated to the
$Q_j$,
\begin{equation}
\{P^i , P^j\}_{PB} =0, \ \ \ \ \{Q_i , P^j\}_{PB}=\delta_i^j.
\end{equation}
We assume that (\ref{classac}) is the final action of the
system arising after we have completed the Dirac procedure of generating all
possible secondary constraints and after we have eliminated all second-class
constraints. This means that we have already enforced the consistency
conditions $\dot G_a \approx 0$.
In order to construct the BRST-BFV effective action according to Ref.
\cite{libro}, we start from a configuration space where all degrees of freedom,
which can have either even or odd Grassmann parity,
are real. Also, we choose the Lagrangian to be real and even. If some
coordinate $\theta$ is fermionic ( odd Grassmann parity), the corresponding
momentum $p_\theta$ is imaginary and odd in such a way that
${\dot\theta} p_\theta$ is real an even. We assume also that
all the constraints are real. They can have either odd or even Grassmann
parity. In the later
case $\lambda^a$ is imaginary and odd, so that $\lambda^aG_a$ is both real
and even. Next we
promote the Lagrange multipliers to the status of
dynamical variables by introducing their corresponding canonically conjugated
momenta $\pi_a$ and we demand that $\pi_a \approx 0$, in such a
way that we have now $2n$ first-class constraints $G_A=(\pi_a, G_a)\approx 0$.
The Grassmann parity $\epsilon$ of the new variables is such that
$\epsilon(\pi_a)=\epsilon(\lambda^a)
=\epsilon (G_a)\equiv \epsilon_a$. The next step is to introduce the
ghost variables $ \eta^A$ together with the corresponding anti-ghost
variables $ {\cal P}_A$, in such a way that
$ \epsilon(\eta^A)= \epsilon({\cal P}_A)= \epsilon_a +1.$ Following the
standard convention we consider the splitting
\begin{equation}
\eta^A=(-(i)^{\epsilon_a+1}{\cal P}^a,{\cal C}^a),
\quad {\cal P}_A=((i)^{\epsilon_a+1}{\bar {\cal C}}_a,{\bar
{\cal
P}}_a).
\end{equation}
The classical effective BRST-BFV action turns out to be
\begin{equation}
S_{BRST}=\int_{\tau'}^{\tau''}\left({\dot q}^ip_i-
\lambda^a{\dot\pi}_a +
{\dot{\bar {\cal C}}}_a{\cal P}^a+{\dot{\cal C}}^a{\bar {\cal
P}}_a - H_{BRST} \right)d\tau - [B]_{\tau'}^{\tau''}, \label{effac1}
\end{equation}
where the integral is extended over the paths which obey the boundary
conditions
$$
Q_i(q(\tau'),\ p(\tau'), \tau')=Q'_i, \qquad
Q_i(q(\tau''),\ p(\tau''), \tau'')=Q''_i.
$$
\begin{equation}
{\cal C}^a(\tau') = {\cal C}^a(\tau'') =0, \qquad
{\bar {\cal C}}_a(\tau') = {\bar {\cal C}}_a(\tau'') =0, \label{bc1}
\end{equation}
$$
{\pi}_a(\tau') = {\pi}_a(\tau'') =0.
$$
In Eq.(\ref{effac1}), $H_{BRST}=H_c-\{\Psi,\Omega\}_{PB}$, $H_c$ is
the canonical Hamiltonian, $\Psi$ is the so
called
fermionic gauge-fixing term and
$\Omega$ is the nilpotent BRST-charge, which has odd Grassmann parity and
satisfies
$ \{ \Omega, \ \Omega \}_{PB}=0 $. The general form of the BRST charge is
$\Omega= -(i)^{\epsilon_a +1} {\cal P}^a \pi_a + {\cal C}^a G_a +$
``more'' , where ``more'' stands for terms at least quadratic in the
ghosts. A systematic algorithm for
this construction can be found in Ref. \cite{libro}.
In all the applications that we will consider in this work, we
choose the classical fermionic gauge to be
\begin{equation}
\Psi={\bar {\cal P}}_a \lambda^a, \label{FG1}
\end{equation}
which has odd Grassmann parity.
Let us observe that we can read out directly from the action (\ref{effac1})
the classical Poisson brackets for the fundamental variables
$$\{p_i,q^j\}_{PB}=-\delta^j_i=(-)^{\epsilon(q^j)+1}\{q^j,p_i\}_{PB} \ ,$$
$$\{\pi_a,\lambda^b\}_{PB}=-\delta^b_a=(-)^{\epsilon_a+1}
\{\lambda^b,\pi_a\}_{PB} \ ,$$
$$\{{\cal P}^a,{\bar{\cal C}}_b\}_{PB}=-\delta^a_b=(-)^{\epsilon_a}
\{{\bar{\cal C}}_b,{\cal P}^a\}_{PB} \ ,$$
$$\{{\bar{\cal P}}_a,{{\cal C}}^b\}_{PB}=-\delta_a^b=(-)^{\epsilon_a}
\{{{\cal C}}^b,{\bar{\cal P}}_a\}_{PB} \ .$$
The above action (\ref{effac1}) has two important
properties: (i) all canonical variables involved are unconstrained.
This feature is reflected in the choice of the associated
measure in
the path integral formulation of the method,
as the corresponding Liouville measure.
(ii) the remaining symmetry of the action
(\ref{effac1}) is a global supersymmetry generated by the
BRST charge $\Omega$, which imposes the choice of BRST-invariant end-point
conditions.
The classical
effective action (\ref{effac1}) is our starting point to construct
the quantum version of the BRST-BFV
method.
First, we promote all (imaginary)real phase space variables $A$, including the
ghosts, to
(antihermitian)her\-mitian operators ${\hat A}$.
Since the quantum action must be hermitian in order to preserve unitarity,
we also adopt the standard replacement for extending real classical products
of
real variables into hermitian products of hermitian quantum operators
\begin{equation}
(i)^{\epsilon(A)\epsilon(B)}AB\rightarrow{1\over2}(i)^{\epsilon(A)
\epsilon(B)}({\hat A}{\hat B} + (-1)^{\epsilon(A)\epsilon(B)}{\hat B}{\hat
A})
\equiv <<{\hat A}{\hat B}>>.\label{simm}
\end{equation}
Let us observe that the operator properties assumed for the variations
$\delta
{\hat A}, \delta{\hat B}$ precisely
guarantee that $ \delta <<{\hat A}{\hat B}>>=(\delta {\hat A}){\hat B}+ {\hat
A} (\delta
{\hat B})$. In particular,
the above prescription has to be applied both to the kinetic term and to the
boundary
term in the action. The quantum expression for the
latter will be discussed in each separate situation
and the specific form
will be dictated by the classical counterpart.
The interplay among the
variations of
both types of terms will allow the proper identification of the corresponding
quantum generators at the end points,
thus providing the basic (anti)commutation relations
for the dynamical variables directly from the action
principle.
According to the above prescription,
the quantum extension of the BRST charge
must lead to
an hermitian operator ${\hat \Omega}^\dagger ={\hat \Omega}$ such that $\{
{\hat \Omega}, \ {\hat \Omega} \} = 2 {\hat \Omega}^2= 0$,
with $\{ {\hat A}, \ {\hat B} \}={\hat A}{\hat B} + {\hat B} {\hat A}$
denoting the corresponding
anticommutator. Both, the canonical Hamiltonian together with the fermionic
gauge fixing term
are also promoted to the corresponding operators ${\hat H}_c$ (hermitian) and
${\hat \Psi}$ (antihermitian) respectively, while the effective Hamiltonian
operator is defined by
${\hat H}_{BRST}={\hat H}_c+ i\{ {\hat \Psi }, \ {\hat \Omega }\}$.
Besides,
the BRST charge must
be conserved i.e. $[{\hat \Omega}, \ {\hat H}_{BRST}]=0$, where
$[ {\hat A}, \ {\hat B}]={\hat A}{\hat B} - {\hat B} {\hat A}$
denotes the corresponding commutator.
In this way, the full quantum action turns out to be
\begin{equation}
{\hat S}_{BRST}=\int_{\tau'}^{\tau''}\left( <<{\dot{\hat q}}^i{\hat p}_i -
{{\hat \lambda}}^a{\dot {\hat \pi}}_a +
{\dot{\hat {\bar {\cal C}}}}_a{{\hat {\cal P}}}^a+{\dot{\hat{\cal
C}^a}}{\hat{\bar {\cal
P}}}_a >> - {\hat H}_{BRST} \right)d\tau -
[\hat{B}]^{\tau''}_{\tau'}. \label{qeffac}
\end{equation}
The basis vectors of the Hilbert space
at the initial time $\tau'$,
$| Q'_i, {\cal C}^{\prime
a}, \bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle$,
are labeled by the
corresponding fixed eigenvalues and satisfy
\begin{equation}
{\hat Q}_i | Q'_i, {\cal C}^{\prime a},
\bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle =
Q'_i
| Q'_i, {\cal C}^{\prime
a}, \bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle
\end{equation}
\begin{equation}
{\hat {\cal C}}^a | Q'_i, {\cal C}^{\prime a},
\bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle =
\hat {\bar {\cal C}}_a | Q'_i, {\cal C}^{\prime a},
\bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle =
{\hat {\pi}}_a | Q'_i, {\cal C}^{\prime a},
\bar {\cal C}^{\prime}_{ a}, {\pi}'_a \rangle =0,\label{cbc0}
\end{equation}
according to the classical boundary conditions (\ref{bc1}). Analogous
expressions are valid
for the basis vectors at the final time $\tau''$.
The invariance of the action under quantum BRST transformations
is stated in the
property
$ \delta_{\Omega} {\hat S}_{BRST}=i [{\hat \Omega}, \ {\hat S}_{BRST}]_{-}
=0 $.
The BRST invariance of the related transition amplitudes
$\langle a'' t'' | \hat S | b' t' \rangle$ is guaranteed
provided the end point states are also invariant under this
transformation, which means that ${\hat \Omega} | b' t' \rangle=0= {\hat
\Omega} | a'' t'' \rangle$.
\section{The parametrized non-relativistic particle}
The classical action for this system is
\begin{equation}
S=\int_{\tau'}^{\tau''} L d\tau= \frac{m}{2}\int_{\tau'}^{\tau''}\frac{{\dot
x}^2}{{\dot t}}\, d\tau.
\end{equation}
Next we define
$p_x = {\partial L \over \partial \dot x}$, $p_t={\partial L \over
\partial \dot t}$ as the momenta canonically conjugated to the coordinates
$x$ and $t$ respectively. Here the dot means the derivative with respect to
the parameter $\tau$. In this case, the canonical Hamiltonian $H_c$
is zero and the application of
the standard Dirac procedure leads to only one (first-class) constraint
\begin{equation}
G=H_0+p_t\approx 0, \label{cons1}
\end{equation}
where
\begin{equation}
H_0\equiv\frac{p_x^2}{2m}.
\end{equation}
Our application of the Schwinger action principle will start from the
effective action operator constructed according to the ideas of the previous
section. In this case, the subindex $a$ takes just one value, corresponding
to the only constraint of the problem . The
quantum effective action is
taken to be
\begin{eqnarray}
{\hat S}_{BRST}&=&\int_{\tau'}^{\tau''}\left( <<{\dot{\hat x}}{\hat p}_x
+{\dot{\hat t}}{\hat p}_t-
{{\hat \lambda}}{\dot {\hat \pi}} +
{\dot{\hat {\bar {\cal C}}}}{{\hat {\cal P}}}+{\dot{\hat{\cal
C}}}{\hat{\bar {\cal
P}}} >> - {\hat H}_{BRST} \right)d\tau \nonumber \\
& & + <<{\hat x}'{{\hat p}_x}'
+{\hat t}'{{\hat p}_t}'>>,
\label{qacfp0}
\end{eqnarray}
where
\begin{equation}
{\hat H}_{BRST}=i \{ {\hat \Psi }, \ {\hat \Omega } \},\quad
{\hat \Psi}= {\hat {\bar {\cal P}}}{\hat \lambda}, \quad
{\hat \Omega}=-i{\hat {\cal P}}{\hat \pi} + {\hat {\cal C}} \left(
\frac{{\hat p}_x^2}{2m}+{\hat p}_t \right). \label{addop1}
\end{equation}
In the sequel, all the canonical variables are considered to be
operators and we drop the hat on top of them in order to simplify
the notation.
The application of the action principle to the action (\ref{qacfp0}) leads
to the Heisenberg equations of motion, written in the general form of
Eqs.(\ref{hei})
in terms of the BRST-Hamiltonian,
together with the following identification of the generators
of transformations at the end-points
\begin{eqnarray}
\delta {\hat S}_{BRST}&=&\left( p_x''\delta x''+x'\delta p_x'
+p''_t\delta t''+t' \delta p_t' -\lambda''\delta\pi''
+\lambda'\delta \pi' -{\bar {{\cal P}''}} \delta {\cal C}'' \right.
\nonumber
\\
& & \left.+ {\bar {{\cal P}'}}
\delta {\cal C}'
-{\cal P}'' \delta {\bar {{\cal C}''}}+{\cal P}' \delta {\bar {{\cal C}'}}-
{H}''_{BRST}\delta \tau''
+{H}'_{BRST}\delta \tau' \right), \label{endpoint1}
\end{eqnarray}
where the superscript $'$ ($''$) denotes the evaluation of the
corresponding operator at $\tau=\tau' (\tau=\tau'')$ respectively.
According to the property (\ref{cr1}), the equation (\ref{endpoint1}) implies
the
following non-zero (anti)commutation
relations
at equal times
\begin{equation}
[x,p_x]=[t,p_t]= [\lambda,\pi]=i\qquad \{{\bar {\cal C}},{\cal P}\}=\{{\bar
{\cal P}},{\cal C}\}=-i.\label{com1}
\end{equation}
The equation (\ref{endpoint1}) also implies that the
eigenvalues which are kept fixed at the end points correspond
to the following operators
\begin{equation}
p_x(\tau'),\quad
p_t(\tau'),\quad\pi(\tau'),\quad{\cal C}(\tau'),\quad{\bar {\cal
C}}(\tau'),\label{BC11}
\end{equation}
\begin{equation}
x(\tau''),\quad t(\tau''),\quad
\pi(\tau''),\quad{\cal C}(\tau''),\quad{\bar {\cal C}}(\tau''),\label{BC12}
\end{equation}
which means that we are selecting the following basis for the Hilbert space
\begin{equation}
\left\{|p_x',p_t',
\pi',{\cal C}',{\bar {\cal C}}',\tau'\rangle \equiv |\tau' \rangle \right\},
\quad\quad \left\{\langle x'',t'',\pi'',{\cal C}'',{\bar {\cal C}}'',\tau''|
\equiv \langle \tau''|\right \},\label{basis1}
\end{equation}
at the initial and final end-points respectively.
The eigenvalues $\pi',\pi'',{\cal C}',{\cal C}'', $ ${\bar {\cal C}}',
{\bar {\cal C}}''$ are taken to be zero, according to Eq.(\ref{cbc0}).
Our notation is $A''\ (A')$ for the eigenvalues
of the operator $A(\tau'') \ (A(\tau'))$. However, in order to make the
notation not too cumbersome, we will denote with the same
letter, both the operator and its corresponding eigenvalue in the sequel,
expecting that no confusion arises.
{}From the (anti)commutation relations (\ref{com1}) we can show that the
BRST operator $\Omega$ constructed in (\ref{addop1}) is hermitian and
nilpotent.
Also,
the BRST-invariance of the above basis (\ref{basis1}) can be directly
verified.
The calculation of the effective Hamiltonian can now be performed, leading
to
\begin{equation}
H_{BRST}= i{\bar {\cal P}}{\cal
P}+\lambda G,\label{effham1}
\end{equation}
which is an hermitian operator satisfying
$ [ H_{BRST}, \Omega]= 0 $. The equations of motion
can be written in the following explicit form
\begin{eqnarray}
\dot p_x=0, & & \dot x -\frac{\lambda p_x}{m}=0,\quad
\dot p_t =0,\quad\dot t - \lambda=0,\quad
\dot\pi + G=0, \quad \dot\lambda=0, \nonumber \\
& & \dot{\cal P}=0,\quad \dot{\bar {\cal C}} -i{\bar {\cal P}}=0,\quad
\dot{\bar {\cal P}}=0,\quad \dot{\cal C}+i{\cal P}=0. \label{eqfp}
\end{eqnarray}
Next we consider the calculation of the propagator. The first step is
to solve the above operator equations. We obtain the general
solution
\begin{equation}
p_x=p'_x, \quad x(\tau)=x'+\frac{\lambda p_x}{m}(\tau-\tau'),\quad
p_t=p'_t, \quad t(\tau)=t'+\lambda(\tau-\tau'),\label{sol11}
\end{equation}
\begin{equation}
\pi(\tau)=\pi'-G (\tau-\tau'),\quad \lambda=\lambda',\label{sol12}
\end{equation}
\begin{equation}
{\cal P}={{\cal P}}', \quad{\bar {\cal C}}(\tau)={\bar {\cal C}}'+i{\bar {\cal
P}}(\tau-\tau'),\quad
{\bar {\cal P}}={{\bar {\cal P}}}', \quad {\cal C}(\tau)={\cal C}'-i{\cal
P}(\tau-\tau'),\label{sol13}
\end{equation}
where the superscript $'$ denotes the evaluation of the corresponding
operator at $\tau=\tau'$, which are used here to denote arbitrary operator
integration constants to be further specified according to the boundary
conditions (\ref{basis1}). A slightly rewritten expression
for the variation for the propagator, obtained from (\ref{endpoint1}), is
\begin{eqnarray}
\delta\langle\tau''|\tau'\rangle=i\langle\tau''|p_x'\delta x''+x'\delta p_x'
+p'_t\delta t''+t'\delta p_t' -\lambda '(\delta\pi''-\delta\pi')\nonumber\\
-{\bar {\cal P}'}(\delta{\cal C}'' -\delta{\cal C}')-{\cal P}'(\delta{\bar
{\cal
C}}''-\delta{\bar {\cal C}}')-{H_{BRST}}(\delta\tau''
-\delta\tau')|\tau'\rangle.\label{var1}
\end{eqnarray}
The next step is to calculate the corresponding matrix elements.
After we incorporate the chosen boundary conditions (\ref{basis1}) in the
above solutions
(\ref{sol11})-(\ref{sol13})
of the equations of motion, we can write $ H_{BRST}$
in terms of the end-points operators ${\cal C}',{\cal C}'',{\bar {\cal C}}',
{\bar {\cal C}}''$, together with the constant operators $\lambda$ and $G$.
The result is
\begin{equation}
H_{BRST}=\frac{i}{(\tau''-\tau')^2}\left({\bar {\cal C}}''{\cal C}''-{\bar
{\cal
C}}''{\cal C}'+{\cal C}''{\bar {\cal C}}'+{\bar {\cal C}}'{\cal C}'+
(\tau''-\tau')\right)+\lambda ' G \label{hef}
\end{equation}
where the {\em well-ordering} ( $''$ operators to the left and $' $ operators
to the right) has been achieved by using the anticommutator
\begin{equation}
\{{\bar {\cal C}}',{\cal C}''\}=-(\tau''-\tau'),\label{cbc}
\end{equation}
which is calculated from the solutions (\ref{sol11})-(\ref{sol13}),
together with the equal-time (anti)commutators (\ref{com1}).
The hermiticity of Eq. (\ref{hef})
can be verified explicitly by
using again the relation (\ref{cbc}).
All the terms whose matrix elements produce eigenvalues that
are fixed to zero at boundaries do not contribute to
the propagator, as it is the case of the ghosts and anti-ghosts.
Furthermore, reparametrization invariance demands that the
propagator be independent of the end-point values of the parameter
$\tau$. This is guaranteed provided that the matrix elements of $H_{BRST}$
are zero.
In order to show this, we need to
calculate the matrix elements for $\lambda= {\lambda}'$.
This can be done as follows:
multiply from the left the first Eq.(\ref{sol12}) by $\lambda$ and take
the appropriate
matrix elements on both sides of the resulting equation. Then, use the fact
that the eigenvalues of $\pi$ are fixed to zero at the boundaries,
together with the equal-time commutator of $\lambda$ and $\pi$. The result
is
\begin{equation}
(\tau''-\tau')\langle\tau''|\lambda|\tau'\rangle=-{i\langle\tau''|\tau'
\rangle\over({{p_x}'}^{\ 2}/2m)+{p_t}'},\label{EMML1}
\end{equation}
which immediately implies that
$\langle\tau''| H_{BRST} |\tau'\rangle=0 $.
As usual, we need to complete the rewriting of the variation (\ref{var1}) in
{\em well ordered form }.
In our case, this procedure has to be further applied to the operators
$x'$, ${p''}_t$ and $t'$. Using the corresponding
equations of motion we obtain
\begin{eqnarray}
\delta\langle\tau''|\tau'\rangle&=&i\langle\tau''| p_x'\delta x''+
(x''-\frac{\lambda' p_x'}{m}(\tau''-\tau'))\delta p_x'+p_t'\delta t''
\nonumber\\
&+&(t''-\lambda '(\tau''-\tau'))\delta p_t'|\tau'\rangle.
\end{eqnarray}
Finally, after substituting
the matrix elements of $\lambda$, we are able to integrate
the resulting system of partial differential equations, obtaining
\begin{equation}
\langle x'',t'',\tau'' |p_x',p_t',\tau'\rangle= \exp\{ip_x'x''+
ip_t't''\}/[({p_x}'^{\ 2}/2m)+{p_t}'],
\end{equation}
which is the correct propagator for the parametrized free particle.
An important point that we want to emphasize
is the
following :
suppose we have constructed a reparametrization invariant
version of an arbitrary theory defined through the Hamiltonian $H_0$, by
introducing
the parameter $\tau$ in complete analogy to the example considered in this
section. Under these
circumstances,
the extended Hamiltonian will be always proportional to the first-class
constraint
\begin{equation}
p_t+H_0(q,p)\approx 0,
\end{equation}
which arises as a consequence or the imposed reparametrization invariance.
The associated quantum condition upon the physical states is that
they must be annihilated by such constraint, which means that such states
can not depend on the parameter $\tau$ and, consequently, the
propagator must also be $\tau$ independent. In other words, the matrix
elements of the extended Hamiltonian between the physical states
must be zero.
The same argument is valid for the matrix elements of the BRST-Hamiltonian
between physical states, when we consider a
non-canonical fermionic gauge fixing $\Psi=\bar{\cal P}\lambda$, in the BRST
approach for a reparametrization-invariant theory.
The latter property, which we have explicitly verified in the case of the
parametrized non-relativistic free particle, is in contradiction with the
results presented in
Ref. \cite{rabello}.
\section{The relativistic particle}
Before considering this problem, let us emphasize two important points
which
can be directly inferred from the previous example : (i) in the case where the
dynamics of the ghost-antighost sector
of the theory decouples from the remaining variables,
the effective Hamiltonian has the same form as in Eq.(\ref{hef}), except that
$G$ is now replaced by the corresponding first-class constraint.
(ii) we can always calculate the matrix elements of the
Lagrange multiplier associated with the reparametrization-invariance
constraint, by imposing the condition that the matrix elements of the
BRST-Hamiltonian are zero.
With this ideas in mind we now consider the calculation of the propagator for
the relativistic free particle from the point of view of the BRST-BFV operator
formulation. We start from the classical action
\begin{equation}
S=\int_{\tau'}^{\tau''}d\tau \frac12 \left( {1 \over \lambda}{\dot x}^\mu
{\dot
x}_\mu-
\lambda m^2\right),
\end{equation}
which is reparametrization-invariant provided $\lambda$
transforms as a Lagrange multiplier. Here we are taking the standard
Minkowski metric $\eta^{\mu\nu}= \\ \mbox{diag}(-1,1,1,1)$.
The corresponding first-class constraint is now
\begin{equation}
\ G=p^\mu p_\mu + m^2\approx 0.
\end{equation}
Our starting point in the quantum problem is the operator effective action
\begin{eqnarray}
{S}_{BRST}&=&\int_{\tau'}^{\tau''}\left( <<{\dot{ x}}^\mu {p}_\mu -
{{ \lambda}}{\dot { \pi}} +
{\dot{{\bar {\cal C}}}} { {\cal P}}+{\dot{{\cal
C}}}{\bar {\cal
P}} >> - { H}_{BRST} \right)d\tau \nonumber \\
& & + <<{ x'}^\mu{{ p'}_\mu}>>,
\label{qacfp1}
\end{eqnarray}
with
\begin{equation}
{ H}_{BRST}=i \{ { \Psi }, \ { \Omega } \},\quad
{\Psi}= { {\bar {\cal P}}}{ \lambda}, \quad
{\Omega}=-i{{\cal P}}{ \pi} + {{\cal C}}\left (p^\mu p_\mu + m^2
\right),\label{addop}
\end{equation}
where the BRST-charge
has the same structure as in Eq.(\ref{addop1}) except for the
explicit form of the constraint $G$.
Here we are dropping the hats over the operators from the very beginning, in
order to simplify the notation. Starting from the action principle, in a
manner
completely analogous to the previous section, we obtain the following
non-zero
commutation relations
\begin{equation}
[x^\mu,p_\nu]=i\delta^\mu_\nu,\qquad [\lambda, \pi]=i,
\end{equation}
while the ghosts satisfy those anticommutators given in Eq.(\ref{com1}). The
(anti)\\ commutator algebra allows for the calculation of the
BRST-Hamiltonian
\begin{equation}
H_{BRST} = i{\bar {\cal
P}}{\cal P}+\lambda (p^2+m^2),
\end{equation}
together with the explicit form of the equations of motion
\begin{equation}
\dot p_\mu=0,\quad \dot{x^\mu} -2\lambda p^\mu=0,\quad
\dot \pi +G=0,\quad \dot\lambda=0,
\end{equation}
\begin{equation}
\dot{\cal P}=0,\quad \dot{\bar {\cal C}} -i{\bar {\cal P}}=0,\quad
\dot{\bar {\cal P}}=0,\quad \dot{\cal C}+i{\cal P}=0.
\end{equation}
The solution of the above equations is
\begin{equation}
p_\mu={p_\mu}' ,\quad {x^\mu}(\tau)={x^\mu}'+2\lambda p_\mu (\tau-\tau'),
\label{sol21}
\end{equation}
\begin{equation}
\pi(\tau)=\pi'-G(\tau-\tau'),\quad \lambda=\lambda',\label{sol22}
\end{equation}
\begin{equation}
{\bar {\cal P}}={{\bar {\cal P}}}', \quad {\bar {\cal C}}(\tau)={\bar {\cal
C}}'+i{\bar {\cal P}}(\tau-\tau'),\quad
{\cal P}={{\cal P}}', \quad {\cal C}(\tau)={\cal C}'-i{\cal
P}(\tau-\tau'),\label{sol23}
\end{equation}
where the primed operators denote integrations constants to be determined
according to the
choice of the end-point conditions. The BRST-invariant boundary conditions are
chosen in complete analogy with
the previous section by fixing the operators
\begin{equation}
p_\mu(\tau'),\quad \pi(\tau'),\quad {\cal C}(\tau'), \quad {\bar {\cal
C}}(\tau'),\label{BC21}
\end{equation}
\begin{equation}
x^\mu(\tau''),\quad \pi(\tau''),\quad {\cal C}(\tau''),\quad {\bar {\cal
C}}(\tau''),
\label{BC22}
\end{equation}
at the end-points.
This choice implies that the corresponding basis of the Hilbert space
are
\begin{equation}
\left\{|{p_\mu}',{\pi}',{\cal C}',{\bar {\cal
C}}',\tau'\rangle\right\}, \quad
\quad \left\{\langle {x^\mu}'',{\pi}'',{\cal C}'',{\bar {\cal
C}}'',\tau''|\right\},
\end{equation}
respectively. Again, the eigenvalues
$\pi', \pi'', {\cal C}', {\cal C}'', {\bar {\cal C}}', {\bar {\cal C}}''$ are
taken to be zero in order to enforce the BRST-invariance.
Since the effective Hamiltonian for this theory has the same structure
as in Eq.(\ref{hef}), we calculate the matrix elements for $\lambda$ by
demanding a null result for the matrix elements of $H_{BRST}$. The
answer is
\begin{equation}
(\tau''-\tau')\langle\tau''|\lambda|\tau'\rangle=-i{\langle\tau''|\tau'\rangle
\over p'^{\ 2}+m^2},
\end{equation}
which is analogous to that of Eq.(\ref{EMML1}).
Next we calculate the propagator. Its variation is given by
\begin{eqnarray}
\delta\langle\tau''|\tau'\rangle=i\langle\tau''|{p_\mu}'\delta {x^\mu}''+
{x^\mu}'\delta {p_\mu}' -\lambda'(\delta {\pi}''-\delta
{\pi}')\nonumber\\
-{\bar {\cal P}}'(\delta{\cal C}''-\delta{\cal C}') -{\cal P}'
(\delta{\bar {\cal C}}'' -
\delta{\bar {\cal C}}')-{H_{BRST}}(\delta\tau''-
\delta\tau')|\tau'\rangle.
\end{eqnarray}
Using the solutions given in Eqs. (\ref{sol21})-(\ref{sol23})
written in terms of the operators fixed at the end-points, we obtain
\begin{equation}
\delta\langle\tau''|\tau'\rangle=i\langle\tau''| {p_\mu}'\delta {x^\mu}''+
({x^\mu}''-2\lambda p_\mu'(\tau''-\tau'))\delta {p_\mu}'|\tau'\rangle,
\end{equation}
in a manner completely similar to the previous case.
Finally, introducing the matrix elements of $\lambda$ and integrating with
respect to the end point eigenvalues, we get the result
\begin{equation}
\langle {x^\mu}'',\tau'' |{p_\mu}',\tau'\rangle= \exp\{{ip_\mu}'{x^\mu}''\}
/[p'^{\ 2}+ m^2],
\end{equation}
which gives the propagator for the free relativistic particle.
\section{The spinning relativistic free particle}
As our final example we consider the spinning relativistic free particle.
To this end let us start from the following classical action
\begin{equation}
S=\int_{\tau'}^{\tau''}d\tau (\dot{x^\mu}p_\mu +\frac{i}{2}(\dot{\theta^\mu}
\theta_\mu+ \dot{\theta_5}\theta_5)-
N{\cal H} -M {\cal Q}_0)-\frac{i}{2}\theta(\tau'')\cdot\theta(\tau')
-[B]^{\tau''}_{\tau'},\label{action3}
\end{equation}
where the variables $x^\mu, p_\mu, N, {\cal H}$ are real-even
Gras\-smann-valued,
while $\theta^\mu, \theta_5,\ { {\cal Q}_0}$ are correspondingly real-odd and
$M$ is imaginary-odd, in accordance with our general conventions.
The first class constraints ${\cal H}$ and ${ {\cal Q}_0}$ are
\begin{equation}
{\cal H}=p^\mu p_\mu+m^2,\quad { {\cal Q}_0}=p_\mu\theta^\mu + m\theta_5.
\end{equation}
The explicitly written boundary term $-\frac{i}{2}\theta(\tau'')
\cdot\theta(\tau')=-{i\over2}(\theta^\mu(\tau'')
\theta_\mu(\tau')+\theta_5(\tau'')\theta_5(\tau')) $ provides
the correct end-point conditions for the fermionic coordinates $\theta^\mu,
\theta_5$
leading to the fixing of the following combinations \cite{henneaux}
\begin{equation}
\frac12(\theta^\mu(\tau')+\theta^\mu(\tau''))\equiv\xi^\mu, \quad
\frac12(\theta_5(\tau')+\theta_5(\tau''))\equiv\xi_5, \label {FBC}
\end{equation}
which provide unique solutions to the corresponding first-order
equations of motion. There could still be additional boundary terms in the
action (\ref{action3}), related to the choice of the end points conditions
for the remaining
variables, which are contained in $B$.
Next we go through the classical BRST formalism. Let us introduce
the
vector
\begin{equation}
G_A=(\pi_b, G_b)=(\pi_M,\pi_N,{ {\cal Q}_0},{\cal H}),\quad b=1,2,
\end{equation}
where the new variables $\pi_M$ and $\pi_N$ are the momenta canonically
conjugated to the Lagrange multipliers $M$ and $N$.
Here $\epsilon_1=1, \epsilon_2=0$. The ghosts and
anti-ghosts
are taken to be \begin{equation}
\eta^A=(-{\cal P}^1,-i{\cal P}^2,{\cal C}^1,{\cal C}^2), \qquad
{\cal P}_A=({\bar {\cal C}}_1, i{\bar {\cal C}}_2,{\bar {\cal P}}_1,{\bar
{\cal P}}_2),
\end{equation}
where $({\cal P}^1,{\bar {\cal C}}_1), ({\cal C}^1,{\bar {\cal P}}_1)$ are
even canonically-conjugated
ghost-antighost variables while $({\cal P}^2,{\bar {\cal C}}_2), ({\cal
C}^2,{\bar {\cal P}}_2)$ are correspondingly
odd .
With these ingredients we now construct the classical BRST charge.
The general expression for the case under consideration is
\begin{equation}
\Omega=\eta^AG_A-\frac{1}{2}(-1)^{\epsilon_B}\eta^B\eta^CC_{CB}^A{\cal P}_A,
\label{OM}
\end{equation}
where $\epsilon_B$ is the Grassmann parity of the constraint
associated with the
variable $b$
and $C_{CB}^A$ are
the structure functions of the algebra of constraints, which in this case is
given by
\begin{equation}
\{{ {\cal Q}_0},{ {\cal Q}_0}\}_{PB}=i{\cal H}, \qquad \{{ {\cal Q}_0},{\cal
H}\}_{PB}=0.
\end{equation}
Accordingly,
the only structure function different from zero is
$C_{11}^2=i$. Taking this into account and making the required
substitutions in Eq.(\ref{OM}) we get
\begin{equation}
\Omega=-{\cal P}^1\pi_M-i{\cal P}^2\pi_N+{\cal C}^1{ {\cal Q}_0}+{\cal
C}^2{\cal
H}+i({\cal C}^1)^2{\bar {\cal P}}_2,
\end{equation}
for the classical BRST charge.
The theory considered in this section is also reparametrization
invariant and thus the canonical Hamiltonian is zero.
Now we promote all dynamical variables to operators with the following reality
properties:
$x_\mu,
p^\mu, N$, $\pi_N, {\bar {\cal P}}_1$, ${\cal C}^1, {\cal P}^1, {\bar {\cal
C}}_1$ are hermitian-even
operators, ${\cal P}^2, {\bar {\cal P}}_2, M$ are antihermitian-odd operators
and
${\bar {\cal C}}_2,{\cal C}^2, \theta^\mu, \theta_5, \pi_M$ are hermitian-odd
operators. The quantum effective action that we start from is
\begin{eqnarray}
S_{BRST}&=&\int^{\tau''}_{\tau'} d\tau \left( << \dot{x^\mu}{p_\mu}
+\frac{i}{2}(\dot{\theta^\mu}
\theta_\mu+\dot{\theta_5}\theta_5)- N{\dot\pi}_N-
M{\dot\pi}_M \right. \nonumber \\
& & + \left. {\dot { \bar {\cal C}}}_1{\cal P}^1 +\dot {{\cal C}^1} {\bar
{\cal P}}_1
+{\dot {\bar {\cal C}}}_2{\cal P}^2 +\dot {{\cal C}^2} {\bar {\cal P}}_2 >>
-H_{BRST} \right) \nonumber \\
& & + <<- \frac{i}{2}\theta(\tau'')
\cdot\theta(\tau') +{x^\mu}' {p_\mu}'>>, \label{VP}
\end{eqnarray}
where
\begin{eqnarray}
& & { H}_{BRST}=i \{ { \Psi }, \ { \Omega } \},\quad
{\Psi}= <<{\bar {\cal P}}_1M+{\bar {\cal P}}_2N>>, \nonumber \\
& & \Omega=<<-{\cal P}^1\pi_M-i{\cal P}^2\pi_N+{\cal C}^1{ {\cal Q}_0}+{\cal
C}^2{\cal
H}+i({\cal C}^1)^2{\bar {\cal P}}_2>>.
\end{eqnarray}
The (anti)commutation relations arising from the action principle are
\begin{equation}
[x_\mu,p_\nu]=i\eta_{\mu\nu} \quad
\{\theta^\mu,\theta^\nu\}=-\eta^{\mu\nu}\quad
\{\theta_5,\theta_5\}=-1,\label{7}\\
\end{equation}
\begin{equation}
\{M,\pi_M\}=-i\quad [N,\pi_N]=i,\nonumber\\
\end{equation}
\begin{equation}
[{\bar {\cal P}}_1,{\cal C}^1]=-[{\cal C}^1,{\bar {\cal P}}_1]=[{\cal
P}^1,{\bar {\cal C}}_1]=-[{\bar {\cal C}}_1,{\cal P}^1]=-i,\nonumber\\
\end{equation}
\begin{equation}
\{{\bar {\cal P}}_2,{\cal C}^2\}=\{{\cal C}^2,{\bar {\cal P}}_2\}=\{{\bar
{\cal
C}}_2,{\cal P}^2\}=\{{\cal P}^2,{\bar {\cal C}}_2\}=-i. \label{CR}
\end{equation}
The calculation of the fermionic anticommutators in Eq.(\ref{7}) is a
particular case of the work in Ref.\cite{das}.
Using the above results one can directly verify
the anticommutator $\{ \Omega, \ \Omega
\}=0 $ and also we can calculate the BRST- Hamiltonian
\begin{equation}
H_{BRST}=-
{\bar {\cal P}}_1{\cal P}^1+M{ {\cal Q}_0}+2iM{\cal C}^1{\bar {\cal
P}}_2+i{\bar {\cal P}}_2{\cal P}^2+N{\cal H}, \label{hsrp}
\end{equation}
which leads to the following explicit form for the quantum effective action
\begin{eqnarray}
S_{BRST}&=& \int^{\tau''}_{\tau'} d\tau \left( << \dot{x^\mu}{p_\mu}
+\frac{i}{2}(\dot{\theta^\mu}
\theta_\mu+\dot{\theta_5}\theta_5)- N{\dot\pi}_N-
M{\dot\pi}_M \right. \nonumber\\
& & \left. +{\dot{\bar {\cal C}}}_1{\cal P}^1+\dot{{\cal
C}^1}{\bar {\cal P}}_1
+{\dot{\bar {\cal C}}}_2 {\cal P}^2+\dot{{\cal C}^2}{\bar {\cal P}}_2 >>
+{\bar {\cal P}}_1{\cal P}^1-M{ {\cal Q}_0} \right. \nonumber \\
& & \left. -2iM{\cal C}^1{\bar
{\cal P}}_2-i{\bar {\cal P}}_2{\cal P}^2-N{\cal H} \right) \nonumber \\
& & << -
\frac{i}{2}\theta(\tau'')
\cdot\theta(\tau') +{x^\mu}' {p_\mu}'>>.
\end{eqnarray}
The reality properties of the remaining operators are:
${\cal H}, H_{BRST}$ are hermitian-even, ${ {\cal Q}_0}, \Omega$ are
hermitian-odd, while $\Psi$ is antihermitian-odd.
The corresponding equations of motion are
$$
\dot{p^\mu}=0,\quad \dot{x^\mu}-M\theta^\mu-2Np^\mu=0,\quad
\dot{\theta^\mu}+iMp^\mu=0,\quad \dot{\theta_5}+iMm=0,
$$
$$
\dot{\pi}_M+{ {\cal Q}_0}+2i{\cal C}^1{\bar {\cal P}}_2=0,\quad \dot M=0,\quad
\dot{\pi_N}+{\cal H}=0,\quad\dot N=0,
$$
$$
\dot{{\cal P}^1}=0,\quad\dot{{\bar {\cal C}}_1}+{\bar {\cal P}}_1=0,\quad
\dot{{\cal C}^1}+{\cal P}^1=0,\quad \dot{{\bar {\cal P}}_1}+2iM{\bar {\cal
P}}_2=0,
$$
$$
\dot{{\cal P}^2}=0,\quad\dot{{\bar {\cal C}}_2}-i{\bar {\cal P}}_2=0,\quad
\dot{{\bar {\cal P}}_2}=0,\quad \dot{{\cal C}^2}-2iM{\cal C}^1+i{\cal P}^2=0.
$$
The general solution of the above system is
\begin{equation}
p_\mu={p_\mu}' \ ,{\cal P}^1={{\cal P}^1}' \ ,M=M' \ ,N=N' \ ,{\cal
P}^2={{\cal
P}^2}', \ {\bar {\cal P}}_2=
{{\bar {\cal P}}_2}',
\end{equation}
\begin{equation}
x^\mu(\tau)=x'^\mu+(M\xi^\mu+2Np^\mu)(\tau-\tau'),
\end{equation}
\begin{equation}
\theta^\mu(\tau)=-iMp^\mu\tau+\xi^\mu+\frac{i}{2}Mp^\mu(\tau''+\tau'), \label
{TMU}
\end{equation}
\begin{equation}
\theta_5(\tau)=-iMm\tau+\xi_5+\frac{i}{2}Mm(\tau''+\tau'),
\end{equation}
\begin{equation}
{\cal C}^1(\tau)={\cal C}'^1-{\cal P}^1(\tau-\tau'),
\end{equation}
\begin{equation}
{\bar {\cal P}}_1(\tau)={\bar {\cal P}}'_1-2iM{\bar {\cal P}}_2(\tau-\tau'),
\end{equation}
\begin{equation}
{\bar {\cal C}}_1(\tau)={\bar {\cal C}}'_1-({\bar {\cal P}}'_1-iM{\bar {\cal
P}}_2(\tau-\tau'))(\tau-\tau'),
\end{equation}
\begin{equation}
{\bar {\cal C}}_2(\tau)={\bar {\cal C}}'_2+i{\bar {\cal P}}_2(\tau-\tau'),
\end{equation}
\begin{equation}
{\cal C}^2(\tau)={\cal C}'^2+iM(2{\cal C}'^1-{\cal
P}^1(\tau-\tau'))(\tau-\tau')-i
{\cal P}^2(\tau-\tau'),
\end{equation}
\begin{equation}
\pi_N(\tau)=\pi'_N-{\cal H}(\tau-\tau'),\label{PIN}
\end{equation}
\begin{equation}
\pi_M(\tau)=\pi'_M-({ {\cal Q}_0}+i(2{\cal C}'^1-{\cal P}^1(\tau-\tau')){\bar
{\cal P}}_2)
(\tau-\tau').\label{PIM}
\end{equation}
The notation is the same as in the previous sections.
The boundary conditions that we take are completely
similar to our previous cases.
The only novelty that we encounter here is related to the fermionic
degrees of freedom described by the $\theta$-variables. In order to
clearly elucidate this point, let us consider for a moment the
contribution of the fermionic degrees of freedom
$\theta^\mu$ to the change of the effective action
\begin{eqnarray}
\delta_{\theta_\mu} {S_{BRST}} & =
&\int_{\tau'}^{\tau''}d\tau(\frac{i}{2}\dot{\theta^\mu}
\delta\theta_\mu +\frac{i}{2}\delta\dot{\theta^\mu}\theta_\mu-M\delta
\theta_\mu p^\mu) \nonumber \\ & -
&\frac{i}{2}(\delta\theta^\mu(\tau'')\theta_\mu(\tau')+
\theta^\mu(\tau'')\delta\theta_\mu(\tau'))\nonumber\\
& = &\int_{\tau'}^{\tau''}d\tau((i\dot{\theta^\mu}-Mp^\mu)\delta\theta_\mu)+
\frac{i}{2}\delta(\theta^\mu(\tau')+\theta^\mu(\tau''))(\theta_\mu(\tau'')-
\theta_\mu(\tau')).\nonumber \\
\end{eqnarray}
Substituting the solution of the equations of motion for $\theta_\mu$
(\ref{TMU}),
together with the definition (\ref{FBC}) of the variable $\xi^\mu$
we obtain
\begin{equation}
\delta_{\theta_\mu} {S_{BRST}}=\delta\xi^\mu M p_\mu (\tau''-\tau').
\end{equation}
The same analysis can be applied to $\theta_5$.
The end-point operators are chosen in such a way that the
fixed eigenvalues are
\begin{equation}
p_\mu(\tau')={p_\mu}',\qquad x^\mu(\tau'')={x^\mu}''
\end{equation}
\begin{equation}
\frac12(\theta^\mu(\tau')+\theta^\mu(\tau''))=\xi^\mu,\quad
\frac12(\theta_5(\tau')+\theta_5(\tau''))=\xi_5,
\end{equation}
\begin{equation}
\pi_N(\tau')=\pi_N(\tau'')={\cal C}^i(\tau')={\cal C}^i(\tau'')={\bar {\cal
C}}_i(\tau')=
{\bar {\cal C}}_i(\tau'')=0, \quad i=1,2,
\end{equation}
together with the corresponding BRST-invariant basis
\begin{equation}
\{ \langle {x^\mu}'',{\pi_N}'',{\pi_M}'', {\theta''}^\mu(\xi^\mu),
{\theta''}_5(\xi_5),
{{\cal C}^i}'',{{\bar {\cal C}}_i}'',\tau''| \},$$
$$ \{ |{p_\mu}',{\pi_N}', {\pi_M}',{\theta'}^\mu(\xi^\mu),
{\theta'}_5(\xi_5),
{{\cal C}^i}',{{\bar {\cal C}}_i}',\tau'\rangle\}.
\end{equation}
Before going to the calculation of the propagator, let us rewrite the
effective Hamiltonian (\ref{hsrp}) in well ordered form. To this end, we use
the
equations of motion
together with the following (anti)commutation relations at different times
\begin{equation}
[{\bar {\cal C}}_1',{{\cal C}^1}'']=-i(\tau''-\tau'),
\quad \{{\bar {\cal C}}_2',{{\cal C}^2}''\}=-(\tau''-\tau').
\end{equation}
The result is
\begin{eqnarray}
H_{BRST}&=&\frac{1}{(\tau''-\tau')^2}[-({\bar {\cal C}}_1''{{\cal
C}^1}''-{\bar {\cal C}}_1''
{{\cal C}^1}'-{{\cal C}^1}''{\bar {\cal C}}_1'+{\bar {\cal
C}}_1'{{\cal C}^1}')\nonumber\\
&+&i({\bar {\cal C}}_2''{{\cal C}^2}''-{\bar {\cal C}}_2''{{\cal
C}^2}'+{{\cal C}^2}''{\bar {\cal C}}_2'+
{\bar {\cal C}}_2'{{\cal C}^2}')]\nonumber\\
&+&M(\xi^\mu p'_\mu+m\xi_5)+N(p'^2+m^2),
\end{eqnarray}
Again, it is a
direct matter to verify that $H_{BRST}$ is hermitian.
Before going to the calculation of the propagator it is necessary
to establish the following results
\begin{equation}
(\tau''-\tau')\langle\tau''|N|\tau'\rangle{\cal
H}'=-i\langle\tau''|\tau'\rangle,\quad
(\tau''-\tau')\langle\tau''|M|\tau'\rangle{ {\cal Q}'_0}=
i\langle\tau''|\tau'\rangle,
\end{equation}
where ${\cal H}'=(p'^2+m^2)$ and ${\cal Q}'_0=\xi^\mu p'_\mu+m\xi_5$.
These matrix elements
are calculated from Eqs.(\ref{PIN}) and (\ref{PIM}) respectively
and again imply the condition that the matrix
elements of the BRST-Hamiltonian between physical states
must be zero.
The general variation of the propagator is
\begin{equation}
\delta\langle\tau''|\tau'\rangle=i\langle\tau''|p'_\mu\delta {x^\mu}''+
{x^\mu}'\delta {p_\mu}' +\delta\xi^\mu Mp'^\mu(\tau''-\tau') +
\delta\xi_5 Mm(\tau''-\tau')
|\tau'\rangle.
\end{equation}
After substituting the solution of the equations of motion
for $x'^\mu$ in terms of the boundary operators and after performing the
necessary integrations,
we obtain the required propagator
\begin{equation}
\langle \tau''|\tau'\rangle=\exp[ip'x'']{(p'_\mu\xi^\mu + m\xi_5)\over
(p'^2+m^2 ) }.
\end{equation}
In conclusion, starting from the quantized version of the BRST-BFV effective
action given in Eq.(\ref{qeffac}),
together with the use of the Schwinger action principle and the
imposition of correct BRST-invariant
boundary conditions, we have obtained the
propagators of the parametrized non-relativistic free particle and of the
relativistic free particle, in the spinless and spining cases.
\section{ Acknowledgements}
LFU, JDV and JAG were partially supported by the grant UNAM-DAGAPA-IN100694.
LFU and JDV also ac\-knowledge support from the grant
CO\-NA\-CyT-400200-5-3544E. JAG is supported by the CONACyT graduate
fellowship \# 86226.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,785 |
{"url":"http:\/\/icpc.njust.edu.cn\/Problem\/Zju\/1007\/","text":"# Numerical Summation of a Series\n\nTime Limit: Java: 10000 ms \/ Others: 10000 ms\n\nMemory Limit: Java: 32768 KB \/ Others: 32768 KB\n\n## Description\n\nProduce a table of the values of the series\n\nEquation 1\n\nfor the 2001 values of x, x= 0.000, 0.001, 0.002, ..., 2.000.All entries of thetable must have an absolute error less than 0.5e-12 (12 digits ofprecision). This problem is based on a problem from Hamming (1962), whenmainframes were very slow by today's microcomputer standards.\n\n## Input\n\nThis problem has no input.\n\n## Output\n\nThe output is to beformatted as two columns with the values of x andy(x)printed as in the C printf or the Pascal writeln.printf(\"%5.3f %16.12f\\n\", x, psix ) writeln(x:5:3, psix:16:12) As an example, here are 4 acceptable lines out of 2001.0.000 1.644934066848...0.500 1.227411277760...1.000 1.000000000000...2.000 0.750000000000 The values of x should start at 0.000 and increase by 0.001 until the linewith x=2.000 is output.\n\n## Sample Input\n\nNone\n\n## Sample Output\n\nNone\n\n## Hint\n\nThe problem with summing the sequence in equation 1 is that too many terms may be required to complete the summation in the given time. Additionally, if enough terms were to be summed, roundoff would render any typical double precision computation useless for the desired precision. To improve the convergence of the summation process note that\nEquation 2\nwhich implies y(1)=1.0. One can then produce a series for y(x) - y(1) which converges faster than the original series. This series not only converges much faster, it also reduces roundoff loss. This process of finding a faster converging series may be repeated to produce sequences which converge more and more rapidly than the previous ones. The following inequality is helpful in determining how may items are required in summing the series above.\nEquation 3\n\n## Source\n\nZhejiang University Local Contest 2001","date":"2019-07-24 02:40:46","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\": 0.8623265027999878, \"perplexity\": 2257.146344889112}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-30\/segments\/1563195530250.98\/warc\/CC-MAIN-20190724020454-20190724042454-00215.warc.gz\"}"} | null | null |
Ellen Thunell is a native Floridian. She attended the University of Central Florida for her undergraduate and graduate degrees in Education. After teaching for over 13 years, Ellen decided to pursue a sales career and sold billboard advertising in the Midwest. When the billboard company sold, she continued in a sales career and followed in her father's footsteps with getting her real estate license. The decision of going with Watson Realty was not difficult at all. Ellen started in the Maitland office, was promoted and became the Sales Manager at the Kissimmee office, was promoted again and became the Broker-Manager of the Orlando South office, then was asked to be the Broker-Manager of the Wekiva office, and is now currently the Broker-Manager of the ChampionsGate office in Davenport. Ellen has been fortunate to work with such wonderful professionals in the company and is looking to add to the dynamic group of agents at the ChampionsGate office. In addition, we are always looking for buyers and sellers to help them with any of their real estate needs. Please feel free to contact Ellen at any time!
Ellen assisted us with the purchase of a short-term rental in the Disney area. She provided superior service in a sometimes difficult closing process and gave valuable advice on all aspects of the transaction. Ellen was a true personal advocate and always worked for our best interests. Her knowledge and experience helped us with the intricacies of the Florida and Orange County tax applications and she kept a very close eye on the timing and progress of our purchase. I highly recommend Ellen to anyone seeking the highest levels of customer service.
I am an agent at Watson Realty Corp in Championsgate Davenport. I have been at this office for over 4 years. The continuous training and the continued support, encouragement, advice, help and nurturing I have had during this time has been amazing and it is all because of our professional and knowledgeable broker Ellen Thunell. Ellen is always there when you need her, she always answers her phone, whether you want to ask advice or just need her to listen or need her to help. Her professionalism and work ethic are a credit to her. Thank you Ellen.
We first began working with Ellen in October of 2018 after moving from New York to Florida. We had sold a home that we loved in New York and inquired about a home that we fell in love with equally as much as the house in New York. It had everything we wanted which was a beautiful house, a pool, and plenty of room for our family. There were a few hiccups along the way with the purchase of the home, but Ellen tackled everyone of them with ease and we were able to close in 45 days from when the sellers accepted our offer. We were so blessed to have Ellen on this journey with us and found a home that we can settle down in and call our own. We are forever grateful for everything that Ellen and Watson Realty did for us. You made our dreams come true!
I have known Ellen now for the last 6 years. Over those years we have bought and sold a few million dollars worth of real estate. I can not think of anyone, who like Ellen, will do whatever it takes to make sure the job gets done and gets done correctly. Ellen brings ethics and accountability to an industry that I have found is sometimes lacking for. She works around the clock to get the job done, and continues to work on bettering herself. She has even gone above and beyond to help me find real estate out of the Central Florida area. Ellen is the best, there is no doubt in my mind, and I look forward to working with her on our next deal.
Ellen was responsive and professional every step of the way. She offered sound advice and was extremely gracious. We will definitely recommend her to our friends.
Our experience with Watson Realty Corp and Ellen Thunell was amazing! She was extremely knowledgeable, patient, and caring during our entire process. She made all efforts to keep lines of communication open, and was available at our schedule for home viewings, inspections, walk-throughs, and follow-ups. We were so grateful to have such a kind person, with a wealth of knowledge to share her experience with first time home buyers! We will be recommending her to all parties whom we come across interested in purchasing/selling their homes. We would not have found our dream home without her! | {
"redpajama_set_name": "RedPajamaC4"
} | 4,012 |
{"url":"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/dcdss.2009.2.697","text":"# American Institute of Mathematical Sciences\n\nSeptember\u00a0 2009,\u00a02(3):\u00a0697-722. doi:\u00a010.3934\/dcdss.2009.2.697\n\n## On shallow shell equations\n\n 1 Key Laboratory of Control and Systems, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China\n\nReceived\u00a0 April 2008 Revised\u00a0 October 2008 Published\u00a0 June 2009\n\nWe present explicit formulas for the shallow shell model consisting of a couple of a wave equation and a plate equation, where the middle surface is viewed as a natural manifold with the induced metric from the classical Euclidean space of three dimensions. The Green formula for the shallow is given by the displacement field which expresses the relationship between the interior and the boundary. Next, the ellipticity of the strain energy for the shallow shell is studied under some curvature assumptions on the middle surface. Finally, the motion equations for shallow shells are obtained in terms of the displacement field as an unknown. The new ingredients in these formulas are that they take a form which is not described by a coordinate patch to provide the shell theory with the modern geometry.\nCitation: Peng-Fei Yao. On shallow shell equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 697-722. doi: 10.3934\/dcdss.2009.2.697\n [1] Gamaliel Bl\u00e9, Carlos Cabrera. A generalization of Douady's formula. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6183-6188. doi: 10.3934\/dcds.2017267 [2] Francisco Brito, Maria Luiza Leite, Vicente de Souza Neto. Liouville's formula under the viewpoint of minimal surfaces. Communications on Pure & Applied Analysis, 2004, 3 (1) : 41-51. doi: 10.3934\/cpaa.2004.3.41 [3] Marius Mitrea. On Bojarski's index formula for nonsmooth interfaces. Electronic Research Announcements, 1999, 5: 40-46. [4] Wenxiang Sun, Xueting Tian. Dominated splitting and Pesin's entropy formula. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1421-1434. doi: 10.3934\/dcds.2012.32.1421 [5] Xiaojun Huang, Jinsong Liu, Changrong Zhu. The Katok's entropy formula for amenable group actions. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4467-4482. doi: 10.3934\/dcds.2018195 [6] Mario Roy. A new variation of Bowen's formula for graph directed Markov systems. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2533-2551. doi: 10.3934\/dcds.2012.32.2533 [7] Xijun Hu, Penghui Wang. Hill-type formula and Krein-type trace formula for $S$-periodic solutions in ODEs. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 763-784. doi: 10.3934\/dcds.2016.36.763 [8] Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 367-380. doi: 10.3934\/dcds.2009.23.367 [9] Zhiming Li, Lin Shu. The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4123-4155. doi: 10.3934\/dcds.2013.33.4123 [10] Jon Johnsen. Well-posed final value problems and Duhamel's formula for coercive Lax\u2013Milgram operators. Electronic Research Archive, 2019, 27: 20-36. doi: 10.3934\/era.2019008 [11] Dirk Pauly. On Maxwell's and Poincar\u00e9's constants. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 607-618. doi: 10.3934\/dcdss.2015.8.607 [12] Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Enrico Valdinoci. Asymptotics of the $s$-perimeter as $s\\searrow 0$. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2777-2790. doi: 10.3934\/dcds.2013.33.2777 [13] Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. Optimality of (s, S) policies with nonlinear processes. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 161-185. doi: 10.3934\/dcdsb.2017008 [14] Uri Shapira. On a generalization of Littlewood's conjecture. Journal of Modern Dynamics, 2009, 3 (3) : 457-477. doi: 10.3934\/jmd.2009.3.457 [15] David Mumford, Peter W. Michor. On Euler's equation and 'EPDiff'. Journal of Geometric Mechanics, 2013, 5 (3) : 319-344. doi: 10.3934\/jgm.2013.5.319 [16] Rabah Amir, Igor V. Evstigneev. On Zermelo's theorem. Journal of Dynamics & Games, 2017, 4 (3) : 191-194. doi: 10.3934\/jdg.2017011 [17] John Hubbard, Yulij Ilyashenko. A proof of Kolmogorov's theorem. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 367-385. doi: 10.3934\/dcds.2004.10.367 [18] Azniv Kasparian, Ivan Marinov. Duursma's reduced polynomial. Advances in Mathematics of Communications, 2017, 11 (4) : 647-669. doi: 10.3934\/amc.2017048 [19] Alicia Cordero, Jos\u00e9 Mart\u00ednez Alfaro, Pura Vindel. Bott integrable Hamiltonian systems on $S^{2}\\times S^{1}$. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 587-604. doi: 10.3934\/dcds.2008.22.587 [20] Hong Fu, Mingwu Liu, Bo Chen. Supplier's investment in manufacturer's quality improvement with equity holding. Journal of Industrial & Management Optimization, 2019\u00a0 doi: 10.3934\/jimo.2019127\n\n2019\u00a0Impact Factor:\u00a01.233","date":"2020-07-14 14:31:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.6029711961746216, \"perplexity\": 4908.85481364398}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-29\/segments\/1593655880665.3\/warc\/CC-MAIN-20200714114524-20200714144524-00313.warc.gz\"}"} | null | null |
Keydomar Vallenilla (La Guaira, Venezuela, 10 de agosto de 1999) es un deportista olímpico venezolano que compite en halterofilia, que consiguió la medalla de plata en los Juegos Olímpicos de Tokio 2020 en la categoría de 96kg al levantar 387 kgs.
Obtuvo una medalla de bronce en los Juegos Panamericanos de 2019 en la categoría de 96 kg.
Palmarés internacional
Campeón en la categoría de 96 kg Mundial de halterofilia 2021
Referencias
Halterófilos de Venezuela
Deportistas de Venezuela en los Juegos Panamericanos de 2019
Medallistas olímpicos de plata de Tokio 2020
Medallistas olímpicos | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,785 |
package stores
import (
"fmt"
"time"
"github.com/nats-io/nats-streaming-server/util"
)
// Used for display of limits
const (
limitCount = iota
limitBytes
limitDuration
)
// Clone returns a copy of the store limits
func (sl *StoreLimits) Clone() *StoreLimits {
cloned := *sl
cloned.PerChannel = sl.ClonePerChannelMap()
return &cloned
}
// ClonePerChannelMap returns a deep copy of the StoreLimits's PerChannel map
func (sl *StoreLimits) ClonePerChannelMap() map[string]*ChannelLimits {
if sl.PerChannel == nil {
return nil
}
clone := make(map[string]*ChannelLimits, len(sl.PerChannel))
for k, v := range sl.PerChannel {
copyVal := *v
clone[k] = ©Val
}
return clone
}
// AddPerChannel stores limits for the given channel `name` in the StoreLimits.
// Inheritance (that is, specifying 0 for a limit means that the global limit
// should be used) is not applied in this call. This is done in StoreLimits.Build
// along with some validation.
func (sl *StoreLimits) AddPerChannel(name string, cl *ChannelLimits) {
if sl.PerChannel == nil {
sl.PerChannel = make(map[string]*ChannelLimits)
}
sl.PerChannel[name] = cl
}
type channelLimitInfo struct {
name string
limits *ChannelLimits
isLiteral bool
isProcessed bool
}
// Build sets the global limits into per-channel limits that are set
// to zero. This call also validates the limits. An error is returned if:
// * any global limit is set to a negative value.
// * the number of per-channel is higher than StoreLimits.MaxChannels.
// * a per-channel name is invalid
func (sl *StoreLimits) Build() error {
// Check that there is no negative value
if err := sl.checkGlobalLimits(); err != nil {
return err
}
// If there is no per-channel, we are done.
if len(sl.PerChannel) == 0 {
return nil
}
literals := 0
sublist := util.NewSublist()
for cn, cl := range sl.PerChannel {
if !util.IsChannelNameValid(cn, true) {
return fmt.Errorf("invalid channel name %q", cn)
}
isLiteral := util.IsChannelNameLiteral(cn)
if isLiteral {
literals++
if sl.MaxChannels > 0 && literals > sl.MaxChannels {
return fmt.Errorf("too many channels defined (%v). The max channels limit is set to %v",
literals, sl.MaxChannels)
}
}
cli := &channelLimitInfo{
name: cn,
limits: cl,
isLiteral: isLiteral,
}
sublist.Insert(cn, cli)
}
// If we are here, it means that there was no error,
// so we now apply inheritance.
sl.applyInheritance(sublist)
return nil
}
func (sl *StoreLimits) applyInheritance(sublist *util.Sublist) {
// Get the subjects from the sublist. This ensure that they are ordered
// from the widest to the narrowest of subjects.
channels := sublist.Subjects()
for _, cn := range channels {
r := sublist.Match(cn)
// There has to be at least 1 match (the current channel name we
// are trying to match).
channel := r[0].(*channelLimitInfo)
if channel.isLiteral && channel.isProcessed {
continue
}
if !channel.isProcessed {
sl.inheritLimits(channel, &sl.ChannelLimits)
}
prev := channel
for i := 1; i < len(r); i++ {
channel = r[i].(*channelLimitInfo)
if !channel.isProcessed {
sl.inheritLimits(channel, prev.limits)
}
prev = channel
}
}
}
func (sl *StoreLimits) inheritLimits(channel *channelLimitInfo, parentLimits *ChannelLimits) {
cl := channel.limits
if cl.MaxSubscriptions < 0 {
cl.MaxSubscriptions = 0
} else if cl.MaxSubscriptions == 0 {
cl.MaxSubscriptions = parentLimits.MaxSubscriptions
}
if cl.MaxMsgs < 0 {
cl.MaxMsgs = 0
} else if cl.MaxMsgs == 0 {
cl.MaxMsgs = parentLimits.MaxMsgs
}
if cl.MaxBytes < 0 {
cl.MaxBytes = 0
} else if cl.MaxBytes == 0 {
cl.MaxBytes = parentLimits.MaxBytes
}
if cl.MaxAge < 0 {
cl.MaxAge = 0
} else if cl.MaxAge == 0 {
cl.MaxAge = parentLimits.MaxAge
}
if cl.MaxInactivity < 0 {
cl.MaxInactivity = 0
} else if cl.MaxInactivity == 0 {
cl.MaxInactivity = parentLimits.MaxInactivity
}
channel.isProcessed = true
}
func (sl *StoreLimits) checkGlobalLimits() error {
if sl.MaxChannels < 0 {
return fmt.Errorf("max channels limit cannot be negative (%v)", sl.MaxChannels)
}
if sl.MaxSubscriptions < 0 {
return fmt.Errorf("max subscriptions limit cannot be negative (%v)", sl.MaxSubscriptions)
}
if sl.MaxMsgs < 0 {
return fmt.Errorf("max messages limit cannot be negative (%v)", sl.MaxMsgs)
}
if sl.MaxBytes < 0 {
return fmt.Errorf("max bytes limit cannot be negative (%v)", sl.MaxBytes)
}
if sl.MaxAge < 0 {
return fmt.Errorf("max age limit cannot be negative (%v)", sl.MaxAge)
}
if sl.MaxInactivity < 0 {
return fmt.Errorf("max inactivity limit cannot be negative (%v)", sl.MaxInactivity)
}
return nil
}
// Print returns an array of strings suitable for printing the store limits.
func (sl *StoreLimits) Print() []string {
sublist := util.NewSublist()
for cn, cl := range sl.PerChannel {
sublist.Insert(cn, &channelLimitInfo{
name: cn,
limits: cl,
isLiteral: util.IsChannelNameLiteral(cn),
})
}
maxLevels := sublist.NumLevels()
txt := []string{}
title := "---------- Store Limits ----------"
txt = append(txt, title)
txt = append(txt, fmt.Sprintf("Channels: %s",
getLimitStr(true, int64(sl.MaxChannels),
int64(DefaultStoreLimits.MaxChannels),
limitCount)))
maxLen := len(title)
txt = append(txt, "--------- Channels Limits --------")
txt = append(txt, getGlobalLimitsPrintLines(&sl.ChannelLimits)...)
if len(sl.PerChannel) > 0 {
channels := sublist.Subjects()
channelLines := []string{}
for _, cn := range channels {
r := sublist.Match(cn)
var prev *channelLimitInfo
for i := 0; i < len(r); i++ {
channel := r[i].(*channelLimitInfo)
if channel.name == cn {
var parentLimits *ChannelLimits
if prev == nil {
parentLimits = &sl.ChannelLimits
} else {
parentLimits = prev.limits
}
channelLines = append(channelLines,
getChannelLimitsPrintLines(i, maxLevels, &maxLen, channel.name, channel.limits, parentLimits)...)
break
}
prev = channel
}
}
title := " List of Channels "
numberDashesLeft := (maxLen - len(title)) / 2
numberDashesRight := maxLen - len(title) - numberDashesLeft
title = fmt.Sprintf("%s%s%s",
repeatChar("-", numberDashesLeft),
title,
repeatChar("-", numberDashesRight))
txt = append(txt, title)
txt = append(txt, channelLines...)
}
txt = append(txt, repeatChar("-", maxLen))
return txt
}
func getLimitStr(isGlobal bool, val, parentVal int64, limitType int) string {
valStr := ""
inherited := ""
if !isGlobal && (val == parentVal) {
return ""
}
if val == parentVal {
inherited = " *"
}
if val == 0 {
valStr = "unlimited"
} else {
switch limitType {
case limitBytes:
valStr = util.FriendlyBytes(val)
case limitDuration:
valStr = fmt.Sprintf("%v", time.Duration(val))
default:
valStr = fmt.Sprintf("%v", val)
}
}
return fmt.Sprintf("%13s%s", valStr, inherited)
}
func getGlobalLimitsPrintLines(limits *ChannelLimits) []string {
defaultLimits := &DefaultStoreLimits
defMaxSubs := int64(defaultLimits.MaxSubscriptions)
defMaxMsgs := int64(defaultLimits.MaxMsgs)
defMaxBytes := defaultLimits.MaxBytes
defMaxAge := defaultLimits.MaxAge
defMaxInactivity := defaultLimits.MaxInactivity
txt := []string{}
txt = append(txt, fmt.Sprintf(" Subscriptions: %s", getLimitStr(true, int64(limits.MaxSubscriptions), defMaxSubs, limitCount)))
txt = append(txt, fmt.Sprintf(" Messages : %s", getLimitStr(true, int64(limits.MaxMsgs), defMaxMsgs, limitCount)))
txt = append(txt, fmt.Sprintf(" Bytes : %s", getLimitStr(true, limits.MaxBytes, defMaxBytes, limitBytes)))
txt = append(txt, fmt.Sprintf(" Age : %s", getLimitStr(true, int64(limits.MaxAge), int64(defMaxAge), limitDuration)))
txt = append(txt, fmt.Sprintf(" Inactivity : %s", getLimitStr(true, int64(limits.MaxInactivity), int64(defMaxInactivity), limitDuration)))
return txt
}
func getChannelLimitsPrintLines(level, maxLevels int, maxLen *int, channelName string, limits, parentLimits *ChannelLimits) []string {
plMaxSubs := int64(parentLimits.MaxSubscriptions)
plMaxMsgs := int64(parentLimits.MaxMsgs)
plMaxBytes := parentLimits.MaxBytes
plMaxAge := parentLimits.MaxAge
plMaxInactivity := parentLimits.MaxInactivity
maxSubsOverride := getLimitStr(false, int64(limits.MaxSubscriptions), plMaxSubs, limitCount)
maxMsgsOverride := getLimitStr(false, int64(limits.MaxMsgs), plMaxMsgs, limitCount)
maxBytesOverride := getLimitStr(false, limits.MaxBytes, plMaxBytes, limitBytes)
maxAgeOverride := getLimitStr(false, int64(limits.MaxAge), int64(plMaxAge), limitDuration)
MaxInactivityOverride := getLimitStr(false, int64(limits.MaxInactivity), int64(plMaxInactivity), limitDuration)
paddingLeft := repeatChar(" ", level)
paddingRight := repeatChar(" ", maxLevels-level)
txt := []string{}
txt = append(txt, fmt.Sprintf("%s%s", paddingLeft, channelName))
if maxSubsOverride != "" {
txt = append(txt, fmt.Sprintf("%s |-> Subscriptions %s%s", paddingLeft, paddingRight, maxSubsOverride))
}
if maxMsgsOverride != "" {
txt = append(txt, fmt.Sprintf("%s |-> Messages %s%s", paddingLeft, paddingRight, maxMsgsOverride))
}
if maxBytesOverride != "" {
txt = append(txt, fmt.Sprintf("%s |-> Bytes %s%s", paddingLeft, paddingRight, maxBytesOverride))
}
if maxAgeOverride != "" {
txt = append(txt, fmt.Sprintf("%s |-> Age %s%s", paddingLeft, paddingRight, maxAgeOverride))
}
if MaxInactivityOverride != "" {
txt = append(txt, fmt.Sprintf("%s |-> Inactivity %s%s", paddingLeft, paddingRight, MaxInactivityOverride))
}
for _, l := range txt {
if len(l) > *maxLen {
*maxLen = len(l)
}
}
return txt
}
func repeatChar(char string, len int) string {
res := ""
for i := 0; i < len; i++ {
res += char
}
return res
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,888 |
/*
* Boot support
*/
#include <common.h>
#include <command.h>
#include <s_record.h>
#include <net.h>
#include <ata.h>
#include <asm/io.h>
#include <part.h>
#include <fat.h>
#include <fs.h>
int do_fat_fsload (cmd_tbl_t *cmdtp, int flag, int argc, char * const argv[])
{
return do_load(cmdtp, flag, argc, argv, FS_TYPE_FAT);
}
U_BOOT_CMD(
fatload, 7, 0, do_fat_fsload,
"load binary file from a dos filesystem",
"<interface> [<dev[:part]>] <addr> <filename> [bytes [pos]]\n"
" - Load binary file 'filename' from 'dev' on 'interface'\n"
" to address 'addr' from dos filesystem.\n"
" 'pos' gives the file position to start loading from.\n"
" If 'pos' is omitted, 0 is used. 'pos' requires 'bytes'.\n"
" 'bytes' gives the size to load. If 'bytes' is 0 or omitted,\n"
" the load stops on end of file.\n"
" If either 'pos' or 'bytes' are not aligned to\n"
" ARCH_DMA_MINALIGN then a misaligned buffer warning will\n"
" be printed and performance will suffer for the load."
);
static int do_fat_ls(cmd_tbl_t *cmdtp, int flag, int argc, char * const argv[])
{
return do_ls(cmdtp, flag, argc, argv, FS_TYPE_FAT);
}
U_BOOT_CMD(
fatls, 4, 1, do_fat_ls,
"list files in a directory (default /)",
"<interface> [<dev[:part]>] [directory]\n"
" - list files from 'dev' on 'interface' in a 'directory'"
);
static int do_fat_fsinfo(cmd_tbl_t *cmdtp, int flag, int argc,
char * const argv[])
{
int dev, part;
block_dev_desc_t *dev_desc;
disk_partition_t info;
if (argc < 2) {
printf("usage: fatinfo <interface> [<dev[:part]>]\n");
return 0;
}
part = get_device_and_partition(argv[1], argv[2], &dev_desc, &info, 1);
if (part < 0)
return 1;
dev = dev_desc->dev;
if (fat_set_blk_dev(dev_desc, &info) != 0) {
printf("\n** Unable to use %s %d:%d for fatinfo **\n",
argv[1], dev, part);
return 1;
}
return file_fat_detectfs();
}
U_BOOT_CMD(
fatinfo, 3, 1, do_fat_fsinfo,
"print information about filesystem",
"<interface> [<dev[:part]>]\n"
" - print information about filesystem from 'dev' on 'interface'"
);
#ifdef CONFIG_FAT_WRITE
static int do_fat_fswrite(cmd_tbl_t *cmdtp, int flag,
int argc, char * const argv[])
{
long size;
unsigned long addr;
unsigned long count;
block_dev_desc_t *dev_desc = NULL;
disk_partition_t info;
int dev = 0;
int part = 1;
void *buf;
if (argc < 5)
return cmd_usage(cmdtp);
part = get_device_and_partition(argv[1], argv[2], &dev_desc, &info, 1);
if (part < 0)
return 1;
dev = dev_desc->dev;
if (fat_set_blk_dev(dev_desc, &info) != 0) {
printf("\n** Unable to use %s %d:%d for fatwrite **\n",
argv[1], dev, part);
return 1;
}
addr = simple_strtoul(argv[3], NULL, 16);
count = simple_strtoul(argv[5], NULL, 16);
buf = map_sysmem(addr, count);
size = file_fat_write(argv[4], buf, count);
unmap_sysmem(buf);
if (size == -1) {
printf("\n** Unable to write \"%s\" from %s %d:%d **\n",
argv[4], argv[1], dev, part);
return 1;
}
printf("%ld bytes written\n", size);
return 0;
}
U_BOOT_CMD(
fatwrite, 6, 0, do_fat_fswrite,
"write file into a dos filesystem",
"<interface> <dev[:part]> <addr> <filename> <bytes>\n"
" - write file 'filename' from the address 'addr' in RAM\n"
" to 'dev' on 'interface'"
);
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,392 |
The Newport, Tennessee junior guard averaged 24.0 points, 7.0 rebounds, 2.5 assists and 1.5 steals per game as the Mountaineers posted a 2-0 record last week versus USA South competition. In a 72-69, overtime, win over Maryville, Williams notched a double-double of 21 points and 11 rebounds to go along with two assists. In a 76-49 victory over Piedmont, Williams totaled 27 points, three rebounds, three assists and three steals. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,767 |
<?xml version="1.0" encoding="utf-8"?>
<!--
~ Copyright 2017 Wultra s.r.o.
~
~ Licensed under the Apache License, Version 2.0 (the "License");
~ you may not use this file except in compliance with the License.
~ You may obtain a copy of the License at
~
~ http://www.apache.org/licenses/LICENSE-2.0
~
~ Unless required by applicable law or agreed to in writing, software
~ distributed under the License is distributed on an "AS IS" BASIS,
~ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
~ See the License for the specific language governing permissions and
~ limitations under the License.
-->
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="match_parent"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:paddingBottom="@dimen/dialog_fingerprint_padding_small"
android:paddingEnd="@dimen/dialog_fingerprint_padding_default"
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,657 |
Sharon Durmaskin founded Durmaskin Communications in 2008. An experienced advertising, radio, audiotext, social media and Web specialist, Sharon brings more than 30 years of experience to Durmaskin Communications. She provides blogging, social media management, Web site content, newsletters, writing and proofreading for small to medium-sized businesses – especially those that might not have the budget to hire a large advertising agency. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,897 |
> Vermont
Vermont State Compliant No Smoking Signs
Browse our selection of Vermont No Smoking Signs. Our signs are made to meet state guidelines. If you don't see the sign you want, feel free design a custom sign with our online wizard.
Vermont's three laws that deal with smoking restrictions protect the public from secondhand tobacco smoke, which can result in eye and throat irritation and increase the risk of lung cancer and respiratory diseases. Vermont's 'Smoking in the Workplace' law protects employers and employees by restricting smoking in the workplace. Vermont's 'Tobacco on the School Grounds' law protects students, teachers and the public by prohibiting the use of tobacco on public school gounds. Vermont's 'Smoking in Public Places' law (also known as the Clean Indoor Air Act) protects public health by prohibiting the possession of lighted tobacco products in most places to which the general public has access.
Mandatory No Smoking Signs for Vermont
Recommended No Smoking Signs for Vermont
Law Excerpt
§ 1422. Smoking policy
Each employer who operates a workplace shall establish, or shall negotiate through the collective bargaining process, a written smoking policy. The policy shall prohibit smoking throughout the workplace or restrict smoking to designated enclosed smoking areas. For purposes of determining smoking policy for schools with school boards, the employer shall be the school board. (Added 1987, No. 69, § 2, eff. July 1, 1988; amended 1987, No. 162 (Adj. Sess.), § 3.) | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,604 |
\chapter{Secular Evolution in Disk Galaxies}
\abstract
Self-gravitating systems evolve toward the most tightly bound configuration that is
reachable via the evolution processes that are available to them. They do this by
spreading -- the inner parts shrink while the outer parts expand -- provided that
some physical process efficiently transports energy or angular momentum outward.
The reason is that self-gravitating systems have negative specific heats. As a result,
the evolution of stars, star clusters, protostellar and protoplanetary disks,
black hole accretion disks and galaxy disks are fundamentally similar.~How
evolution proceeds then depends~on~the evolution processes that are available to
each kind of self-gravitating system. These processes and their consequences for
galaxy disks are the subjects of my lectures and of this Canary Islands Winter School. \vskip 8pt} \def\vss{\vskip 6pt} \def\vsss{\vskip 2pt
I begin with a review of the formation, growth and death of bars. Then
\hbox{I review the slow (``secular'') rearrangement of energy, angular momentum,}
\noindent} \def\nnnhi{\noindent \hangindent=10pt and mass that results from interactions between stars or gas clouds and
collective phenomena such as bars, oval disks, spiral structure and triaxial dark halos.
The ``existence-proof'' phase of this work is largely over:~we~have a good heuristic understanding
of how nonaxisymmetric structures rearrange disk gas into outer rings, inner rings and stuff
dumped onto the center. The results of simulations correspond closely to the morphology of
barred and oval galaxies. Gas that is transported to small radii reaches high densities.
Observations confirm that many barred and oval galaxies have dense central concentrations
of gas and star formation. The result is to grow, on timescales of a few Gyr, dense central
components that are frequently mistaken for classical (elliptical-galaxy-like) bulges but
that were grown slowly out of the disk (not made rapidly by major mergers). The resulting
picture of secular galaxy evolution accounts for the richness observed in galaxy structure.
\special{psfile=./footnote.ps hoffset=-65 voffset=-60 hscale=90 vscale=90}
We can distinguish between classical and pseudo bulges because the latter retain
a ``memory'' of their disky origin. That is, they have one or more characteristics of disks:
(1) flatter shapes than those of classical bulges,
(2) correspondingly large ratios of ordered to random velocities,
(3) small velocity dispersions $\sigma$ with respect to the Faber-Jackson correlation between
$\sigma$ and bulge luminosity,
(4) spiral structure or nuclear bars in the ``bulge'' part of the light profile,
(5) nearly exponential brightness profiles and
(6) starbursts.
So the cleanest examples of pseudobulges are recognizable. However, pseudo and classical bulges can coexist in the same galaxy.
\vskip 4pt
I review two important implications of secular evolution:
\vskip -17pt
\phantom{Invisible text to fix line spacing so that the abstract fits on 2 pages}
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[(1)]{The existence of pseudobulges highlights a problem with our theory of galaxy
formation by hierarchical clustering. We cannot explain galaxies that are completely bulgeless.
Galaxy mergers are expected to happen often enough so that every giant galaxy should have a classical bulge.
But we observe that bulgleless giant galaxies are common in field environments. We now realize that
many dense centers of galaxies that we used to think are bulges were not made by mergers; they were
grown out of disks. So the challenge gets more difficult.
This is the biggest problem faced by our theory of galaxy formation.} \vskip 4pt
\item[(2)]{Pseudobulges are observed to contain supermassive black holes (BHs), but they do not
show the well known, tight correlations between BH mass and the mass and velocity dispersion of
the host bulge. This leads to the suggestion that there are two
fundamentally different BH feeding processes. Rapid global inward gas transport in galaxy mergers leads
to giant BHs that correlate with host ellipticals and classical bulges, whereas local and more stochastic
feeding of small BHs in largely bulgeless galaxies evidently involves too little energy feedback to result
in BH-host coevolution. It is an important success of the secular evolution picture that morphological
differences can be used to divide bulges into two types that correlate differently with their BHs.}
\end{enumerate}
\phantom{Invisible text to fix line spacing so that the abstract fits on 2 pages}
\vskip -17pt
I review environmental secular evolution{\thinspace}--{\thinspace}the transformation of gas-rich, star-forming
spiral and irregular galaxies into gas-poor, ``red and dead'' S0 and spheroidal (``Sph'') galaxies.
I show that Sph galaxies such as NGC\ts205 and Draco are not the low-luminosity end of the
structural sequence (the ``fundamental plane'') of elliptical galaxies. Instead, Sph galaxies have
structural parameters like those of low-luminosity~S$+$Im~galaxies. Spheroidals are continuous
in their structural parameters~with~the disks of S0 galaxies. They are bulgeless S0s.
\hbox{S$+$Im\thinspace$\rightarrow${\thinspace}S0$+$Sph}
transformation involves a variety of internal (supernova-driven baryon ejection) and environmental processes
(e.{\thinspace}g., ram-pressure gas stripping, harassment, and starvation).
\vskip 4pt
Finally, I summarize how hierarchical clustering and secular processes can be combined into a
consistent and comprehensive picture of galaxy evolution.
\vfill\eject
\def1{1}
\section{Introduction}
These lectures review the slow (``secular'') evolution~of~disk galaxies, both internally and environmentally driven.
As a heuristic introduction at a 2011 winter school, they emphasize a qualitative and intuitive understanding of physical processes.
This provides a useful complement to Kormendy \& Kennicutt (2004), which is a more complete review of technical details and
the literature. Since this is a school, my lectures will be as self-contained as possible.
There will therefore be some overlap with the above review~and with
Kormendy (1981, 1982b, 1993b, 2008a,{\thinspace}b);
Kormendy \& Cornell (2004);
Kormendy \& Fisher (2005, 2008) and
Kormendy \& Bender (2012).
\subsection{Outline}
The secular evolution of disk galaxies has deep similarities to the evolution of all other kinds of
self-gravitating systems. I begin by emphasizing these similarities. In particular, the growth of pseudobulges
in galaxy disks is as fundamental as the growth of stars in protostellar disks, the growth of black holes in black hole
accretion disks and the growth of proto-white-dwarf cores in red giant stars. A big-picture understanding of these
similarities is conceptually very important. The associated physics allows us to understand what kinds of galaxies
evolve secularly and what kinds do not. This review discusses only disk galaxies; secular evolution of ellipticals
is also important but is less thoroughly studied.
Galaxy bars are important as ``engines'' that drive secular evolution, so I~provide a heuristic
introduction to how bars grow and how they die. Then I review in some detail the evolution processes that are driven
by bars and by oval disks and the formation of the various kinds of structures that are built by these processes.
I particularly emphasize the growth and properties of pseudobulges. Based on this, I summarize how we recognize
pseudobulges and connect them up with our overall picture of galaxy formation.
Two consequences (among many) of secular evolution are particularly important. I review the problem of
understanding pure-disk galaxies. These are galaxies that do not contain classical bulges. We infer that they
have not experienced a major merger since the first substantial star formation. Many have barely experienced
secular evolution. We do not know how these galaxies are formed. Second, I review evidence that classical bulges
coevolve with their supermassive black holes but pseudobulges do not.
Next, I discuss secular evolution that is environmentally driven. Here, I
concentrate on the evidence that gas-rich, star forming spiral and irregular galaxies are transformed into gas-poor, ``red and
dead'' S0 and spheroidal galaxies. I particular emphasize the properties of spheroidals -- that is, tiny dwarfs such as Fornax,
Draco and UMi and larger systems such as NGC~147, NGC~185 and NGC~205. These are, in essence, bulgeless
S0 galaxies. And I review the various transformation processes that may make these objects.
Finally, I tie together our picture of galaxy formation by hierarchical clustering and galaxy merging
(lectures by Isaac{\thinspace}Shlosman, Nick{\thinspace}Scoville and Daniela{\thinspace}Calzetti)
and the secular evolution that is the theme of this School.
\subsection{Fast versus slow processes of galaxy evolution}
Kormendy \& Kennicutt (2004) emphasize that the Universe is in transition from early times when galaxy
evolution was dominated by fast processes -- hierarchical clustering and galaxy merging -- to a future
when merging will largely be over and evolution will be dominated by slow processes (Fig.~1.1).
\vfill
\begin{figure}[h]
\special{psfile=./KR2004-Figure1lo.eps hoffset=-11 voffset=-15 hscale=62 vscale=62}
\caption{\lineskip=0pt \lineskiplimit=0pt
Processes of galaxy evolution updated from Kormendy (1982b) and from Kormendy
\& Kennicutt (2004). Processes are divided vertically into fast (top) and slow (bottom).
Fast evolution happens on a free-fall (``dynamical'') timescale, $t_{\rm dyn} \sim (G \rho)^{-1/2}$, where
$\rho$ is the density of the object produced and $G$ is the gravitational constant. Slow means many
galaxy rotation periods. Processes are divided horizontally into ones that happen internally
in one galaxy (left) and ones that are driven by environmental effects (right). The processes at center
are aspects of all types~of~galaxy evolution. My lectures are about slow processes, both internal
(Sections 1.2{\thinspace\ts}--{\thinspace}1.6) and environmentally driven (Section 1.7).
}
\end{figure}
\eject
We have a well developed picture of galaxy formation that mostly involves the processes in the upper-right
corner of Fig.~1.1. Quantum density fluctuations in non-baryonic, dynamically cold dark matter form immediately
after the Big Bang and then get stretched by the expansion of the Universe. Gravity drives hierarchical clustering
that causes these fluctuations to grow, separate out from the expansion of the Universe, collapse and form galaxy halos.
The baryons first go along for the ride and later cool inside the halos to form stars and visible galaxies. Spiral galaxies
form when halos quiescently accrete gas that dissipates~and~forms~disks. Ellipticals form when galaxies collide and merge;
then dynamical violence scrambles disks into ellipsoidal ellipticals. It is a convincing story, developed in
Toomre (1977a);
White \& Rees (1978);
Kauffmann {\it et al.\ } (1993);
Steinmetz \& Navarro (2002, 2003),
and many other papers. Quoting Binney (2004),
``Cold Dark Matter theory has now reached the point at which it should be admitted as a Candidate Member to the Academy of
Established Theories, so that it can sit alongside the established theories of Maxwell, Einstein, and Heisenberg.''
Now we are making a transition to a time in the far future when the Universe will have expanded so much that most mergers that
ever will happen will already have happened. Even now, major mergers -- defined as ones in which the less-massive progenitor is within a
factor of (say) \hbox{5\thinspace--\ts10} of the mass of the bigger progenitor -- are uncommon. Minor mergers remain common now but will also get
less common in the future. As this happens, more and more galaxies spend more and more of their time not undergoing fast and violent
evolution events. And between such events -- that is, between galaxy collisions and mergers -- galaxies in isolation do not just sit
and age their stars. Instead, galaxies evolve on slow timescales; that is, timescales that are much longer than the crossing time
or the collapse time. We call such slow processes ``secular''. At present, both fast and slow processes are important. It is easy
to find (especially in cluster environments) good examples of galaxies whose histories have been dominated by fast processes. They are
the ellipticals and the classical bulges of disk galaxies. Elsewhere (particularly in field environments), it is easy to find galaxies
whose evolution has almost entirely been secular. Both of these types of galaxies are relatively easy to recognize. But it is also
important to understand that both kinds of processes can be important in a single galaxy, and in particular, that a galaxy can contain
both a classical (merger-built) bulge and a pseudo (secularly built) bulge. Recognizing this is difficult and indeed not always
possible. We will spend some considerable effort on understanding how to differentiate classical and pseudo bulges.
Beginning with the seminal paper of Toomre (1977a), most work on galaxy formation over the last 35 years has
concentrated on hierarchical clustering. The idea of secular evolution got its start at almost the same time; some of the earliest
papers on the subject are Kormendy (1979a, 1979b, 1981) and Combes \& Sanders (1981). But research on this subject remained for many
years a series of largely isolated ``cottage industries'' that did not penetrate the astronomical folklore. This changed very
rapidly~in~the~last~decade. In particular, Kormendy \& Kennicutt (2004) aimed to combine the cottage industries into a general
and well articulate paradigm on secular evolution that complements hierarchical clustering. Now, this subject has become a major
industry. Whole meetings have been devoted to it. This is the motivation that underlies the present Canary Islands Winter School.
\subsection{A comment about the name ``pseudobulges''}
As in Kormendy \& Kennicutt (2004), I use the name ``pseudobulge'' for all high-density, distinct central components of
galaxies that are grown slowly out of disks and not rapidly by galaxy mergers. They divide themselves into at least three
subtypes that involve different formation processes. Boxy bulges in edge-on galaxies are
bars seen side-on (Combes \& Sanders 1981). Bars are disk phenomena. I will call these ``boxy pseudobulges''.
Second, dense central components are grown out of disks when nonaxisymmetries transport gas toward the center where it feeds
starbursts. Often, these are recognizably more disky than merger-built bulges. But they are not guaranteed to be flat.
Still, it is often useful to refer to them as ``disky pseudobulges'' when we need to differentiate them from boxy pseudobulges.
Third, nuclear bars are a recognizably distinct subset of disky pseudobulges. What problem am I trying to solve by calling
all of these ``pseudobulges''?
Astronomers have a long history of inventing awkward names for things. For historical reasons, we have two different names
for the products of major galaxy mergers. If a merger remnant does not have a disk around it, we call it an ``elliptical''. But if
an elliptical subsequently accretes cold gas and grows a new disk (e.{\thinspace}g., Steinmetz \& Navarro 2002), then we call it a ``bulge''.
In particular, I will call it a ``classical bulge''. This is inconvenient when one wants to refer to all elliptical-galaxy-like
merger remnants without prejudice as to whether they have associated disks. Some authors call these ``spheroidal galaxies''.
This is exceedingly misleading, because the same name is used for dwarf galaxies such as Draco and Fornax that are essentially
bulgeless S0s (see Section 1.7 here). Another
alternative is to call them ``hot stellar systems''. This is misleading, because some ellipticals have lower velocity
dispersions than some pseudobulges and indeed also than some lenses (which certainly are disk components). I could {\it define\/}
the term ``ellipsoidals'' to mean both classical bulges and ellipticals. But this name has no constituency. So I will explicitly
say ``bulges and ellipticals'' when I need to refer to both at once.
I do not want the same problem to happen with pseudobulges.
\section{Self-gravitating systems evolve by spreading}
This is the most fundamental section of this review. I want to give~you~a heuristic, intuitive understanding
of why secular evolution happens in disk galaxies. And I want to show you how the evolution of essentially all self-gravitating
systems is fundamentally similar. The theme of this Winter School is the disk-galaxy version of that more general evolution.
I made this point in Kormendy \& Fisher (2008) and in Kormendy (2008a). However, it is important enough --
especially at a school -- that I repeat it here in detail. The following is a slightly expanded and paraphrased
version of the discussion in Kormendy (2008a).
The general principle that drives the evolution of self-gravitating systems is this: {\it it is energetically favorable
to spread}. That is, as energy or angular momentum is transported outward, the inner parts shrink and grow
denser, while the outer parts expand, grow more diffuse, and, in some cases, escape the system. How to see this depends
on whether the system is dominated by rotation or by random motions.
\subsection{If dynamical support is by random motions}
\def\thinspace{\thinspace}
For systems that are dominated by velocity dispersion, the argument is
given by Lynden-Bell \& Wood (1968) and by Binney \& Tremaine (1987). The essential
point is that {\it the specific heat of a self-gravitating system is negative.}
Consider an equilibrium system of $N$ particles of mass $m$, radius~$r$ and
three-dimensional velocity dispersion~$v$. The virial theorem tells us that
2{\thinspace}KE + PE = 0, where the kinetic energy is KE = $Nmv^2/2$ and the potential energy
is PE = $-G(Nm)^2/r$. \hbox{The total energy $E \equiv$ KE $+$ PE = $-$KE is negative.}
This is what it means to be a bound system. But the temperature of the system is
measured by $v^2$: $mv^2/2 = 3kT/2$. So the specific heat
$C \equiv dE/dT \propto d(-Nmv^2/2)/d(v^2)$ is also negative. In the above, $G$ is
the gravitational constant and $k$ is Boltzmann's~constant.
The system is supported by heat, so evolution is by heat transport.
If the center of the system gets hotter than the periphery, then heat tends to flow
outward. The inner parts shrink and get still hotter. This promotes further
heat flow. The outer parts receive heat; they expand and cool. Whether the
system evolves on an interesting timescale depends on whether there is an
efficient heat-transport mechanism. For example, many globular clusters evolve
quickly by two-body relaxation and undergo core collapse. Giant
elliptical galaxies -- which otherwise would evolve similarly -- cannot do so
because their relaxation times are much longer than the age of the Universe.
\subsection{If dynamical support is by rotation}
Tremaine (1989) provides a transparent summary of an argument due to
Lynden-Bell \& Kalnajs (1972) and to Lynden-Bell \& Pringle (1974). A disk is
supported by rotation, so evolution is by angular momentum transport. The
``goal'' is to minimize the total energy at fixed total angular momentum.
A rotationally supported ring at radius $r$ in a fixed potential $\Phi(r)$ has
specific energy $E(r)$ and specific angular momentum $L(r)$ given by
$$
E(r) = {r\over2}{d\Phi \over dr} + \Phi~~{\rm and}~~
L(r) = \biggl(r^3 \thinspace{d\Phi \over dr}\biggr)^{1/2}~. \eqno{(1.1)}
$$
Then $dE/dL = \Omega(r)$, where $\Omega = (r^{-1} d\Phi/dr)^{1/2}$ is the
angular speed of rotation. Disks spread when a unit mass at radius $r_2$
moves outward by gaining angular momentum $dL$ from a unit mass at
radius $r_1 < r_2$. This is energetically favorable: the change in energy,
$$
dE = dE_1 + dE_2 = \biggl[- \biggl({dE \over dL}\biggr)_1
+ \biggl({dE \over dL}\biggr)_2\thinspace\biggr]dL
= \thinspace[-\Omega(r_1) + \Omega(r_2)]\thinspace dL\thinspace, \eqno{(1.2)}
$$
is negative because $\Omega(r)$ usually decreases outward. ``Thus disk
spreading leads to a lower energy~state. In general, disk spreading,
outward angular momentum flow, and energy dissipation accompany one another
in astrophysical disks'' (Tremaine 1989).
\subsection{Spreading in various kinds of self-gravitating systems}
The consequences are very general. All of the evolution summarized in Fig.~1.2
happens because of the above physics.
Globular clusters, open clusters and the compact nuclear star clusters in galaxies
are supported by random motions. Absent any gas infall, they
spread in three dimensions by outward energy transport. The mechanism is
two-body relaxation, and the consequences are core collapse and the evaporation
of the outer parts.
\begin{figure*}
\vspace{3.6 truein}
\special{psfile=./spreadinglo.eps hoffset=-10.5 voffset=-15 hscale=62 vscale=62}
\caption{\lineskip=0pt \lineskiplimit=0pt
Powerpoint slide that emphasizes the underlying similarity in evolutionary processes
that shape various kinds of self-gravitating systems. The secular evolution of galaxy
disks (top row) is the subject of my lectures.
}
\end{figure*}
Stars are spherical systems supported by pressure. They spread in three
dimensions by outward energy transport. The mechanisms are radiation or
convection mediated by opacity. Punctuated by phases of stability when nuclear
reactions replace the energy that is lost, stellar evolution consists of a
series of core contractions and envelope expansions. One result is red
(super)giants containing cores that will become white dwarfs, neutron stars,
or stellar mass black holes.
Protoplanetary disks are supported by rotation; they spread in two dimensions by outward angular momentum transport.
The tendency toward energy equipartition between low-mass and high-mass objects has the consequence that big planets sink
by flinging smaller planets outward. If the evolution results from the interaction of a big planet with a collective
phenomenon such as a spiral density wave in gas or rubble, then the effect is the same. The results are hot Jupiters and
colder Neptunes or rubble.
Protostars are spherical systems coupled to circumstellar disks by
magnetic fields that wind up because of differential rotation. This drives
jets that look one-dimensional but that really are three-dimensional; they
carry away angular momentum and allow the inner circumstellar disk to shrink
and accrete onto the star (Shu {\it et al.\ } 1994, 1995).
An accretion disk around a black hole is supported by rotation, so it evolves by angular
momentum transport. The evolution happens because of magnetic coupling between various parts
of the accretion disk. The details are complicated, but the net effect is that some material flows outward
as part of a jet and other material is accreted onto the black hole. Note again that pictures of this process --
whether observations of radio jets or artists' conceptions of the accretion process -- almost always show
narrow jets. But, as in the case of protostars, outward angular momentum transfer must be involved in order
for some of the material to accrete onto the black hole.
Galactic disks are supported by rotation. They spread in two dimensions by outward angular momentum transport.
Efficient engines are provided by bars and by oval disks. Like all of the above, \hbox{the evolution
is secular -- slow} compared to the collapse time or crossing time of the disk. {\it The growth of a pseudobulge
in a galactic disk is as natural as the growth of a star in a protostellar disk and as the growth of a black hole
in a black hole accretion disk.} Only the processes that transport angular momentum are different.
This secular evolution is the subject of my paper and this Winter School.
\begin{figure*}
\vspace{5.2truein}
\special{psfile=./KN79-Vlo.eps hoffset=-7 voffset=149 hscale=29 vscale=29}
\special{psfile=./Corbelli-M33-rotcurve-cleanlo.eps hoffset=160 voffset=193 hscale=35 vscale=35}
\special{psfile=./N4736-SDSS-croplo2.eps hoffset=-5 voffset=-9 hscale=33 vscale=33}
\special{psfile=./N4736-THINGS-rotcurve-cleanlo.eps hoffset=190.5 voffset=-14 hscale=29.5 vscale=29.5}
\caption{\lineskip=0pt \lineskiplimit=0pt
Typical examples of spiral galaxies that do (NGC 4736, bottom) and do not (M{\thinspace}33, top) have mass distributions that
are conducive to secular evolution. The top-left plots (Kormendy \& Norman 1979) show a generic rotation curve~$V(r)$
and associated angular velocity curves $\Omega(r) \equiv V(r)/r$ and $\Omega -\kappa/2$, where $\kappa$ is
the epicyclic frequency. Where $V \propto r$, $\Omega =$ constant and secular evolution is not energetically favorable.
Even where $V(r)$ is turning downward from $V \propto r$ toward $V =$ constant, $\Omega$ decreases outward so slowly
that secular evolution is disfavored. This is the situation throughout a galaxy like M{\thinspace}33 (top-right rotation
curve and rotation curve decomposition, from Corbelli \& Salucci 2000). M{\thinspace}33 has neither a classical bulge nor a
significant pseudobulge. In contrast, NGC 4736 (image at bottom-left, from {\tt http://www.wikisky.org})
has a rotation curve that decreases outward with radius, as derived by de Blok {\it et al.\ } (2008; bottom-right panel here).
Disk spreading is energetically very favorable. Moreover,~NGC~4736~is a prototypical strongly oval galaxy,
so it has an engine for secular evolution. Not surprisingly, it is our best ``poster child'' for secular evolution --
an unbarred galaxy with a pseudobulge identified by five classification criteria (Section 1.5.3).
}
\end{figure*}
\subsection{What kinds of galaxy disks evolve secularly?}
For secular evolution to happen, a galaxy needs two things. It needs a driving mechanism such as a bar, a
globally oval disk (Section 1.3.3), or global spiral structure. And disk spreading must be energetically favorable.
Equation (1.2) tells us that it is more energetically favorable to transport angular momentum outward the more the angular
rotation velocity $\Omega(r)$ decreases outward. This lets us divide galaxies into three types, as follows.
Galaxies that lack driving agents should not show strong secular evolution. Examples are unbarred galaxies
with classical bulges and weak or no global spiral structure (e.{\thinspace}g., M{\thinspace}31, NGC 2841 and NGC 4594, the
Sombrero Galaxy). We will see that these objects generally do not show centrally concentrated molecular gas and star
formation. We take this as an sign that secular evolution largely is not happening.
For galaxies with engines, Fig.~1.3 shows how the tendency to evolve depends on the mass distribution as
revealed by the rotation curve $V(r)$. Where $V(r)$ increases proportional to $r$ (or even rather more slowly),
the angular rotation velocity $\Omega(r)$ is constant (or very slowly decreasing outward). This means that it is
not energetically favorable to evolve. This is the situation in an Scd galaxy like M{\thinspace}33, where we
find no pseudobulge.
The Corbelli \& Salucci (2000) decomposition of the M{\thinspace}33 rotation curve into contributions due to the stellar disk,
the gas disk and the dark matter halo reveals an additional reason why secular evolution is disfavored. The contribution of
the dark matter to $V(r)$ is everywhere comparable to or larger than that of the visible matter. But dark halos are
dynamically much hotter than disks. They do not participate in disk dynamics. The observation that the self-gravity of the
disk is ``diluted'' by the gravity of the much stiffer halo is a further sign that secular evolution is disfavored.
Kormendy \& McClure (1993) show that M{\thinspace}33 contains a nuclear star cluster (like a large globular cluster) but no
significant evidence for a pseudobulge.
In contrast, if a galaxy has a flat rotation curve, then $\Omega \propto 1/r$ and secular evolution is energetically
favorable (top-left panels of Fig.~1.3). Even more extreme are galaxies in which the rotation curve decreases outward.
De Blok {\it et al.\ } (2008) conclude that the rotation curve of NGC 4736 decreases outward (Fig.~1.3, bottom-right).\footnote{This
result depends on the assumption that the gas is on circular orbits everywhere in the galaxy and that asymmetries in the velocity
field and in the galaxy image (Fig.~1.3, bottom-left) are due to warps. These assumptions are not valid. NGC 4736 has
an oval disk (Bosma {\it et al.\ } 1977; Kormendy 1982b, 1993b; Kormendy \& Kennicutt 2004; Fig.~1.8 here). A suitable analysis of the velocity
field based on plausible axial ratios for the inner disk and outer ring has not been made. However, it is likely that the true rotation
curve decreases outward more slowly than Fig.~1.3 suggests. Nevertheless, disk secular evolution is more energetically favorable in
NGC 4736 than it is in most galaxies.} Under these circumstances, secular evolution should be especially important. In fact, NGC 4736
turns out to be our best ``poster child'' for secular evolution in an unbarred galaxy~(see~also~Fig.\ts1.6, Section 1.3.3., Fig.~1.8,
Fig.~1.28, Fig.~1.31, Fig.~1.35., Fig.~1.38, Table\ts1.3).
It will turn out that angular momentum redistribution and therefore radial mass transport happens mostly to gas. The
need for gas disfavors early-type galaxies and favors late-type galaxies.
Putting all this together, we can already foresee what the observational review in the rest of this paper will
reveal: {\it Secular evolution in galaxy~disks is, in the current Universe, happening mostly in intermediate-late-type
(e.{\thinspace}g.,~Sbc) galaxies. These are the galaxies in which pseudobulges turn out to be most prominent. Secular evolution
is too slow to be important in the latest-type galaxies, because the mass distribution is too ``fluffy'', and so it is not
energetically favorable to transport angular momentum outward. And secular processes no longer transport much gas in S0 and Sa
galaxies, because they no longer contain much gas. Nevertheless, (1) purely stellar secular processes are expected to happen in these
galaxies, and (2) secular evolution is believed to have been important in the past, because many S0 galaxies are observed
to contain disky pseudobulges.}
I turn next to a discussion of our motivation and where it will lead us.
\section{The study of galaxy evolution -- structural components}
An important goal of extragalactic astronomy is to understand the structure of galaxies as encoded, e.{\thinspace}g., in the
classification schemes of Hubble (1936), de Vaucouleurs (1959) and Sandage (1961, 1975). An updated version of Hubble classification
is shown in Fig.~1.4, and a perpendicular cut through de Vaucouleurs' classification volume at stage Sb is shown in Fig.~1.5.
For each kind of galaxy, we want to understand the present structure and the formation and evolution processes which created
that structure.
Our picture of galaxy formation by hierarchical clustering and our School's subject of secular evolution are
both important in creating the structures in Figs.~1.4 and 1.5. Ellipticals and classical (elliptical-galaxy-like) bulges
of disk galaxies form by hierarchical clustering and major mergers.~I review this in Section 1.8, and Isaac Shlosman
discusses it in his lectures. Bulges are usually classical in S0\thinspace--{\thinspace}Sb galaxies.~Secularly~built
pseudobulges are not distinguished in Hubble classification, but they are already important in some S0s,
and they become the usual central component at type Sbc and in later types (Kormendy \& Kennicutt 2004). Unlike these permanent components,
spiral density waves are temporary features of disks that mostly last only as long as they have driving engines (Toomre 1977b, 1981).
\vfill
\setcounter{figure}{3}
\begin{figure}[h]
\special{psfile=./tuningforkcolorlo.eps hoffset=-14 voffset=-16 hscale=68 vscale=68}
\caption{Revised Hubble classification (Kormendy \& Bender 1996) recognizing the difference (the ``E{\thinspace}--{\thinspace}E dichotomy'')
between boxy, slowly rotating ellipticals that have cores and disky-distorted, more rapidly rotating and coreless ellipticals that are
continuous in their properties with S0s. Ellipticals are understood to form via rapid processes; i.{\thinspace}e., by major mergers
and violent relaxation. These are reviewed in Section 1.8, where I discuss galaxy formation by hierarchical clustering.
S0 and spheroidal galaxies (not included in Hubble types)
form~--~I~suggest~--~at least mostly by environmental secular evolution (Section 1.7). Spiral galaxies evolve partly by rapid processes
(mergers make classical bulges, shown orange~in~the~figure). However, the evolution of many spirals has been dominated by
secular processes, including the formation of pseudobulges (also shown in orange, because Hubble classes do not distinguish between
classical and pseudo bulges).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{Inner rings ``(r)'' and outer rings ``(R)''}
Figure 1.4 omits several regular features in galaxy structure that we need to understand.
The most important of these are encoded in de Vaucouleurs' (1959) more detailed classification,
illustrated here in Fig.~1.5. Rotate the ``tuning fork'' diagram in Fig.~1.4 about the E\thinspace--{\thinspace}S0 axis.
In the plane of the page, de Vaucouleurs retains the distinction between unbarred (``SA'') and barred (``SB'') galaxies.
The new, third dimension above and below the page is used for the distinction between galaxies that do or
do not contain inner rings. Fig.~1.5 is a perpendicular cut through this classification~volume.
\vfill
\begin{figure}[hb]
\special{psfile=./deV-cross-section-Sblo.eps hoffset=-9 voffset=-20 hscale=62 vscale=62}
\caption{Perpendicular cut at type Sb through the galaxy classification volume as defined by
de Vaucouleurs (1959).
I am grateful to Ron Buta for this version from the {\it de Vaucouleurs Atlas of Galaxies} (Buta {\it et al.\ } 2007).
}
\end{figure}
\eject
Figure\ts1.6 (top) illustrates the distinction (bottom half of Fig.~1.5) between
SB(s) galaxies in which two global spiral arms begin at the ends of the bar and SB(r) galaxies
in which there is a ring of stars and gas surrounding the ends of the bar and the spiral arms start
somewhere on this ring. In Figures 1.5 and 1.6, there is a prominent, nearly straight
dust lane on the rotationally leading side of the bar in SB(s) galaxies. Notwithstanding Fig.~1.5,
there is generally no such dust lane in SB(r)~bars~(Sandage~1975). Note in NGC 2523 that the inner
ring is patchy and blue and contains young stars, like the outer disk but unlike the relatively ``red
and dead'' bar and (pseudo)bulge. This is a common property of inner rings.
\vfill
\begin{figure}[hb]
\special{psfile=./N1300-2523-1291-4736-2000x1572lo.eps hoffset=-12 voffset=-15 hscale=65 vscale=65}
\caption{(top) Contrast SB(s) and SB(r) structure: (left) SB(s)bc galaxy NGC~1300 has two global spiral
arms that begin at the ends of the bar. (right) The SB(r)bc galaxy NGC 2523 has a somewhat more
multi-armed but still global spiral pattern with arms that begin from the inner ring, not necessarily at the end of
the bar.
(bottom) Galaxies with outer rings: (left) the (R)SB(lens)0/a galaxy NGC 1291 and (right) the (R)SA(lens)ab galaxy
NGC 4736. The latter is a prototypical oval galaxy. It contains a pseudobulge that is identified by no less than
five classification criteria from Section 1.5.3.
NGC 2523 is a Hubble Heritage image; NGC 2523 is from Adam Block (NOAO/AURA/NSF); NGC 1291 and NGC 4736 are from Kormendy
\& Kennicutt (2004).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Figure 1.6 (bottom) shows another feature that is recognized by de Vaucouleurs and Sandage although
it is not given a separate classification~bin in diagrams like Fig.~1.5. Both barred and unbarred galaxies
can contain outer rings ``(R)'' at approximately twice the radius of the inner disk.
The properties of inner and outer rings are discussed (for example) in
Kormendy (1979b, 1981, 1982b),
Buta (1990, 1995, 2011, 2012),
Buta \& Crocker (1991),
Buta \& Combes (1996) and
Buta {\it et al.\ } (2007).
I particularly use the following.
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{Inner rings essentially always encircle the end of the bar.}
\item{Outer rings typically have radii $\sim 1.2$ times the radius of the bar.
There is no overlap in the distribution of radii of inner and outer rings.}
\item{Both inner and outer rings typically contain H{\thinspace}{\sc i} gas and star formation.}
\item{Inner rings typically have intrinsic axial ratios of $\sim 0.85 \pm 0.10$ with the long
axis parallel to the bar (Buta 1995).}
\item{Outer rings typically have intrinsic axial ratios of $\sim 0.87 \pm 0.14$. In most galaxies,
the long axis is perpendicular to the bar (as seen face-on), but a few outer rings are
elongated parallel to the bar (Kormendy 1979b; Buta 1995).}
\item{Figure 1.5 contains one mistake. There is no continuity between the inner rings in unbarred and barred
galaxies. Instead, SA inner rings are similar to nuclear star-forming rings in SB galaxies (see
Fig.~1.31 in Section 1.5.1).
Nuclear rings are always much smaller than inner rings (Comer\'on {\it et al.\ } 2010).}
\end{enumerate}
All of the above structural properties are natural products of the secular evolution that I review
in these lectures.
\subsection{Lens Components ``(lens)''}
Lenses are the final morphological component that we need to recognize observationally and to understand within our
picture of galaxy evolution. There is much confusion in the literature about lenses. It is unfortunate that de Vaucouleurs
chose to use the name ``lenticular'' for S0 galaxies. I empathize: a bulge-dominated, edge-on S0 such as NGC~3115~or~NGC~5866
is indeed shaped rather like an edge-on glass lens. But this is due to the combination of a thick bulge and a thin disk;
it does not happen because these S0s contain lens components. In fact, most unbarred S0s do not
contain lens components, whereas some Sa and Sb galaxies -- particularly barred ones -- do contain lens components. We need
to overcome the confusion that results from use of the misleading name ``lenticular galaxy''. In all of my papers including
this one, I avoid use of the name ``lenticular galaxy'' and always call these objects ``S0 galaxies''. And I try to identify
lens components strictly using the following definition.
\vskip 8pt} \def\vss{\vskip 6pt} \def\vsss{\vskip 2pt
\begin{figure*}
\vskip 2.4truein
\special{psfile=./2MASS_NGC_1553_JHKlo.eps hoffset=-5 voffset=-8 hscale=30 vscale=30}
\special{psfile=./n1553profilelo.eps hoffset=173 voffset=2 hscale=33 vscale=33}
\caption{(left) Color $JHK$ image of the SA(lens)0 galaxy NGC 1553 from the 2MASS Large Galaxy Atlas (Jarrett {\it et al.\ } 2003;
image from NED). The lens is the elliptical shelf in the brightness distribution interior to the outer, exponential
disk. It is best seen in the $V$-band, major-axis brightness profile shown in the right panel (Freeman 1975).
The straight line is an exponential fit to the disk profile.
}
\end{figure*}
A lens component is an elliptical ``shelf'' in the brightness distribution of a disk galaxy. That is, it has a shallow
brightness gradient interior~to~a sharp outer edge. Typical face-on lenses have axial ratios of $\sim$\ts0.85\thinspace--\ts0.9.
Lenses occur most commonly in barred galaxies; then the bar almost always fills the lens in one dimension. NGC 1291 in
Fig.~1.6 is an (R)SB(lens)0/a example of this configuration. Lenses can also occur in unbarred galaxies; the prototypical
example is the SA(lens)0 galaxy NGC 1553 (Fig.~1.7). It is important to note that there is no overlap in the intrinsic
ellipticity distributions of bars and lenses.~Bars always have much smaller (pole-on) axial ratios of \lapprox \thinspace$1/4$.
So bars and lenses are clearly different, even though both occur only in disk galaxies. A lens and an inner ring of the
same size can occur together (e.{\thinspace}g., NGC 3081). The properties of lenses
are established in
Kormendy (1979b) and in
Buta (2011, 2012);
Buta {\it et al.\ } (1996, 2007).
I will argue in Sections 1.4.3.4{\thinspace}--{\thinspace}1.4.3.6 that lenses are defunct bars. That is, following
Kormendy (1979b, 1981, 1982b), I suggest that bars evolve away into lenses when the secular evolution that
they drive increases the central mass concentration so much that the elongated bar orbits can no longer
precess together at the same bar pattern speed $\Omega_p$.
I use the notation SA(lens) and SB(lens), respectively, for unbarred and barred galaxies with lenses.
Buta {\it et al.\ } (2007) uses the letter ``el''; I do not do this only because it is difficult to distinguish
``el'' from the number~1.
\vfill\eject
It will turn out that lenses, outer rings, inner rings and pseudobulges are~like~the~more
familiar classical bulges, bars and disks in the sense that they are distinct components in the structure of galaxies that
retain their essential character over many galaxy rotations. They are different from spiral arms, which are
density waves in the disk that last -- more or less -- only as long as the ``engine'' that
drives them. Still,
there are many ways in which the above components can be combined into a galaxy. This
results in de Vaucouleurs classifications that may be as complicated as (R)SB(r)bc
or (R)SB(lens)0/a (NGC 1291 in Fig.~1.6). This complication makes many people
uneasy. However, I emphasize: {\it Every letter in such a complicated galaxy classification
now has a physical explanation within our picture of secular galaxy evolution.} It is a
resounding testament to the educated ``eyes'' of classifiers such as Allan Sandage and
Gerard de Vaucouleurs that they could pick out regularities in galaxy structure that
ultimately were understandable in terms of galaxy physics.
\subsection{Oval Disks}
Fundamental to our understanding of the engines that drive secular evolution is the observation that many
unbarred galaxies nevertheless are not globally axisymmetric. The inner disks of these galaxies typically
have intrinsic axial ratios of $\sim$\ts0.85. Bars are more elongated (typical axial ratio $\sim$\ts0.2),
but a much smaller fraction (typically \lapprox \ts1/3) of the disk participates. Observations indicate that
oval disks are approximately as effective in driving secular evolution as are bars.
Oval galaxies can be recognized independently by photometric criteria
(Kormendy \& Norman 1979;
Kormendy 1982b)
and by kinematic criteria
(Bosma 1981a, b). They are illustrated schematically and with observations of prototypical galaxies in
Fig.~1.8. The photometric criteria are:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{The disk consists of two nested ovals, each with a shallow brightness gradient interior to a sharp outer edge.}
\item{The outer oval has a much lower surface brightness than the inner oval. It can consist of a featureless disk
(e.{\thinspace}g., in an S0 galaxy) or spiral arms that make a pseudo ($\equiv$ not quite closed) outer ring or a
complete outer ring.}
\item{The nested ovals generally have different axial ratios and position angles, so they must be oval if
they are coplanar. But the flatness of edge-on galaxies at these fairly high surface brightnesses shows that
these disks are oval.}
\end{enumerate}
NGC 4736 and NGC 4151 are outer ring and outer spiral arm versions of oval galaxies (Fig.~1.8). I use the notation
SA(oval) or SB(oval) -- exactly analogous to SA(lens) or SB(lens) -- for galaxies with oval disks.
\vfill\eject
\centerline{\null}
\vfill
\begin{figure}[ht]
\vskip 1truein
\special{psfile=./ovallo.eps hoffset=-34 voffset=340 hscale=68 vscale=68}
\special{psfile=./N4736-image-V3lo.eps hoffset=-12 voffset=126 hscale=63.0 vscale=63.0}
\special{psfile=./N4151-image-Vlo.eps hoffset=-12 voffset=-11 hscale=63.0 vscale=63.0}
\caption{Criteria for recognizing unbarred oval galaxies shown schematically (top) and with observations
of NGC 4736 and NGC 4151 (adapted from Fig.~9 in Kormendy \& Kennicutt 2004). The image of NGC 4736 is from
my IIIa-J plate taken with the 1.9 m Palomar Schmidt telescope. The image of NGC 4151 is from
{\tt http://www.wikisky.org}.
The H{\thinspace}{\sc i} velocity contours of NGC 4736 and NGC 4151 are from
Bosma {\it et al.\ } (1977a)
and from
Bosma {\it et al.\ } (1977b), respectively.
}
\end{figure}
\eject
The kinematic criteria for recognizing ovals are that the velocity field is symmetric and regular, but:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{the kinematic major axis twists with radius;}
\item{the optical and kinematic major axes are different; and}
\item{the kinematic major and minor axes are not perpendicular.}
\end{enumerate}
Here observation (a) is equally consistent with a warp. But (b) and (c) point uniquely to an
oval velocity field that is seen at a skew orientation. Given this conclusion, observation (a) then means that the
intrinsic orientations of the outer and inner ovals are different. Usually, the outer oval is elongated perpendicular
to the inner one, as seen face-on. My favorite poster child for secular evolution, NGC 4736, shows all of these
effects.~The~classical~Seyfert\ts1 galaxy NGC 4151 shows them even more clearly (Fig.~1.8).
Figure 1.9 shows four more oval galaxies. I use it to emphasize four points.
\vskip -18pt
\phantom{Invisible text to improve line spacing.}
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[(1)]{Oval galaxies are
very recognizable and very common.~It is curious that they have not better penetrated the astronomical folklore.
Kormendy \& Kennicutt (2004) show that they are important engines for secular evolution.}
\end{enumerate}
\vfill
\begin{figure}[hb]
\special{psfile=./N2859-3504-3368-1068lo.eps hoffset=-10 voffset=-17 hscale=62 vscale=62}
\caption{Sequence of outer-ring galaxies that are structurally similar except that a bar embedded in the lens or
inner oval structure ranges from strong at upper-left to invisible at lower-right. All images are from
{\tt http://www.wikisky.org}.
}
\end{figure}
\eject
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[(2)]{There is a complete structural continuity in outer ring galaxies from (R)SB objects that have strong bars
to (R)SA objects that are completely barless.\footnote{The (R)SA(oval)ab galaxy NGC 4736
(Figs.~1.3,
1.6,
1.8,
1.28,
1.31,
1.35,
1.38)
contains a nuclear bar but no main bar. The nuclear bar provides a ``connection'' to barred galaxies that is relevant
in Section 1.5.2.8. But it is much too small to affect the overall evolution of the galaxy. NGC 4736 is therefore
completely unbarred for the purposes of the present discussion. Similarly, NGC 1068 (Fig.~1.9) also has a nuclear
bar but no main bar. I suggest that the connection between these two nuclear bars and their host oval disks is not
an accident -- that, in fact, oval disks are the late-type analogs of lenses and thus were once barred (see point 3).
The hint is that some nuclear bars can survive even after the main bar has evolved away.} NGC 2859 is one of the best
examples of an (R)SB(lens)0 galaxy in which the bar fills the lens in one dimension. Another excellent example is
NGC 3945
(Kormendy 1979b;
Fig.~1.17 and
Fig.~1.24 here). NGC 3504 and NGC 3368 are two examples among many of galaxies that have
well defined oval disks and extremely weak bars. I have typed them as (r,oval) and (s,oval) because there is a
bright blue rim of star formation around the outside of the inner oval, exactly as in many (r,lens) galaxies.
I am not aware of any measurements of the bar strength that take into account the oval structure. But the bars
that are revealed by the 2MASS survey at $K^\prime$ band must be only a few percent of the disk light.
NGC 1068 is classified as unbarred by Sandage (1961) and by Buta {\it et al.\ } (2007); there is a hint of a
bar in the 2MASS image (Jarrett {\it et al.\ } 2003). NGC 4736 is a purely unbarred, oval galaxy.$\dagger$}
\item[(3)]{Albert Bosma has advocated for many years that (lens) and (oval) components are the early-Hubble-type
and later-Hubble-type versions of the same kind of structure. For many years, I was unsure about whether or
not to believe this. I am now convinced that Albert is exactly correct. The reasons are discussed in
Sections 1.4.3.4{\thinspace}--{\thinspace}1.4.3.6.
Here, I juxtapose (R)SB(lens) and (R)SAB(oval) galaxies in Fig.~1.9 to emphasize their similarity. I will
continue to use this notation throughout this review, but I want to make it clear that \hbox{\it I believe that (lens)
and (oval) structures are fundamentally the same.}}
\item[(4)]{There also is a continuity from complete outer rings (R) such as the one in NGC 2859 through spiral arms that
are distorted until they almost closed to form what is called a ``pseudoring'' (R$^\prime$) as in NGC 3504 through
to spiral arms that are less -- but similarly -- distorted as in NGC 4151 (Fig.~1.8 here) and NGC 1300
(compare Fig.~1.6 here with Fig.~13 in Kormendy 1979b). See de Vaucouleurs (1959); de Vaucouleurs {\it et al.\ } (1991:~RC3)
and Buta (2011, 2012) for further discussion.}
\end{enumerate}
\phantom{gronk}
\vskip -13pt
All of these continuities prove to have important physical interpretations within our developing picture
of disk-galaxy secular evolution. Most of them are reviewed in the following sections. The stellar dynamics of
(R)S(r) galaxies are discussed in Lia Athanassoula's (2012) third lecture.
Further examples of the above structures are shown in Ron Buta's (2012)
lectures and in the {\it de Vaucouleurs Atlas of Galaxies\/} (Buta {\it et al.\ } 2007).
\vfill\eject
\subsection{Classical versus physical morphology of galaxies}
At the start of a new science, it is common to classify the objects under study into ``natural groups''
(Morgan 1951) whose members share observed characteristics that are judged to be important. The success of the
taxonomy depends on how well the natural groups -- the classification bins -- prove to correlate~with~physics.
The galaxy classification scheme of Hubble (1936) and Sandage (1961) as augmented by de Vaucouleurs (1959) won
a Darwinian struggle between taxonomic systems because it succeeded best in ordering galaxies by properties that
helped us to understand galaxy formation and evolution. Ron Buta (2012) reviews this subject in his lectures
at this School.
It is important -- and fundamental to the aims of this paper -- to contrast morphological galaxy classification as
practiced in the early days of extragalactic research with what becomes necessary as the subject matures. Sandage and Bedke (1994)
emphasize the importance early on of not being led astray by preconceptions:
``The extreme empiricist claims that no whiff of theory may be allowed into the {\it initial} classification procedures, decisions,
and actions.'' Nevertheless, every classifier chooses which features to consider as important and which to view as secondary.
Hubble succeeded because he chose properties that became important to our understanding. Sandage recognizes this:
``Hubble correctly guessed that the presence or absence of a disk, the openness of the spiral-arm pattern, and the degree of
resolution of the arms into stars, would be highly relevant." Hubble based his classification on choices
made with future interpretation in mind. \vsss
In contrast (Kormendy 2004a): ``At the level of detail that we nowadays try to understand, the time has passed when we can
make effective progress by defining morphological bins with no guidance from a theory. [Breaking] down the wall between morphology
and interpretation successfully has always been a sign of the maturity of a subject. For example, without guidance from a theory,
how would one ever conceive of the complicated measurements required to see solar oscillations or use them to study the interior
structure of the Sun? In the same way, we need the guidance of a theory to make sense of the bewildering variety of phenomena
associated with galaxies and to recognize what is fundamental and what is not. This motivates a `physical morphology' [Kormendy 1979a,{\thinspace}b,
1981, 1982b; Kormendy \& Kennicutt 2004], not as a replacement for classical morphology -- which remains vitally important~-- but as
a step beyond it. Physical morphology is an iteration in detail that is analogous to de Vaucouleurs's iteration beyond the
Hubble tuning fork diagram.''
One purpose of this review is to bring this process up to date. Our aim is to engineer the best one-to-one correspondence that
we currently can between recognized types of galaxies or galactic building blocks and physical processes of galaxy formation.
It is reasonable to expect that an improved understanding of galaxies will show that an initial classification
missed some physics. Also, some features of galaxies could not, early on, be observed well enough to be included
in the classification. Two substantial additions and one small tweak to classical morphology are needed here. The small
tweak is to recognize~that nuclear star-forming rings are distinct from and often occur together with inner rings (r)
in barred galaxies. This was point (f) in Section 1.3.1. The first major correction is to recognize and differentiate between
real and counterfeit ellipticals (Section 1.7). The second is to recognize and differentiate between real and counterfeit bulges.
The latter are ``pseudobulges'' (Section 1.5).
An essential aspect of physical morphology is to treat galaxies as being composed of a small number of building blocks,
the distinct components in the mass distribution. The problem that this solves and the benefits that it provides were described
as long ago as Kormendy (1979a):
``[Classical morphology] assigns a classification cell to each list of galaxy characteristics. As we look at galaxies
more and more closely, the list of observed characteristics becomes alarmingly large. Thus the revised morphological types of
de Vaucouleurs already require `about one hundred cells' (de Vaucouleurs 1963) and still do not recognize features such as lenses.
It is difficult to attach dynamical significance to the bewildering variety of forms that the system describes.''
In physical morphology, ``we aim to identify as distinct components groups of stars or gas whose structure, dynamics, and
origin can profitably be thought of as distinct from the dynamics and origin of the rest of the galaxy. \dots~~The large number
of cells in classical morphology is now thought of as the many ways that components and their secondary behavior [such as spiral
structure] can be combined to make a galaxy. The strength of this approach is twofold. It breaks up the complicated problem of
galaxy structure into smaller and more manageable pieces to which it is easier to attach dynamical interpretations. Secondly,
{\it investigations of correlations and interactions between components are very efficient in suggesting previously unrecognized
dynamical processes} [emphasis added]. Thus the component approach provides an efficient framework for studies of galaxy dynamics.''
Throughout this review, my aim is to tweak the distinctions between galaxy components (and hence their names) until they
are both correct descriptions and uniquely tied to physical processes of galaxy formation.
\section{A Heuristic introduction to bars and spiral structure}
Bars are the most important drivers for secular evolution in galactic disks; we will see them again and again throughout
this School. For this reason, I now want to give you a heuristic introduction to bar dynamics and evolution. Lia Athanassoula
(2012) will talk about this subject in more detail. Here, I concentrate on a simple version of the essential
physics that you need to understand in order to have an intuitive feel for how bars form, grow and die. Bars are density
waves in the disk. That is, the bar pattern rotates more-or-less rigidly at a single pattern angular velocity $\Omega_p$,
whereas the angular velocity $\Omega(r)$ of material in the disk varies with radius. This is even more true of spiral structure:
over most of a global spiral pattern, the stars and gas have $\Omega > \Omega_p$; they catch up to the spiral arms from behind, move
through them in the rotation direction (lingering in the arms to give them their density enhancement) and then move on in the
rotation direction toward the next arm. Since bars and spirals have some similarities, I briefly discuss spiral structure, too.
\subsection{Orbital resonances in a galactic disk}
Orbital resonances are the key to understanding bars and spirals. The main resonances -- inner Lindblad resonance, corotation,
and outer Lindblad resonance -- will recur in many of the lectures at this school. I therefore need to introduce them in some detail.
The general orbit of a star in a galactic disk is an unclosed rosette, because the potential is not Keplerian
(that is, the galaxy mass is distributed in radius and not all in one central point as in, for example, the Solar System).
Figure 1.10 shows disk orbits as seen in a frame of reference that rotates clockwise (orange arrow) at the
pattern speed $\Omega_p$ of some coherent structure. In this figure, I show a spiral arm (red), because spirals almost
always trail in the rotation direction (that is, the arm is convex in the direction of rotation). Thus it is easy to remember
the rotation direction at a glance.~I work in the epicyclic approximation (Mihalas \& Routly 1968; Binney \&
Tremaine 1987) in which radial excursions are small. Then, at the radius where the stars and the pattern corotate, i.{\thinspace}e.,
where $\Omega_p = \Omega$ (green), a stellar orbit is a small elliptical epicycle around the mean radius.
The motion around the ellipse is counterclockwise, because the forward velocity is higher when the star is closer to the center
than average. In the epicyclic approximation, the motion around the ellipse is simple harmonic. Corotation is the most
important resonance in the galaxy, because the mean position of the star with respect to the global pattern never changes
as long as $\Omega_p$ is fixed.
\begin{figure*}
\vskip 5.5truein
\special{psfile=./resonanceslo.eps hoffset=-10 voffset=-18 hscale=71 vscale=71}
\caption{Schematic illustration of galactic orbits as seen in a frame of reference that rotates clockwise
(orange arrow) at the pattern angular velocity $\Omega_p$ of some coherent structure such as a spiral
arm (red). The pattern stays fixed as we view it, whereas stars drift with respect to the pattern
forward (clockwise) inside corotation and backward (counterclockwise) outside corotation.
At the corotation resonance (green: $\Omega_p = \Omega$), a star with a small component of random
velocity added to $\Omega$ executes simple harmonic motion counterclockwise around a closed~ellipse (the
``epicyclic approximation''). At the inner Lindblad resonance (blue: $\Omega_p = \Omega - \kappa/2$, where
$\kappa$ is the epicyclic frequency), the stellar orbit is closed and the star executes two radial
excursions for every revolution forward around the center. At the outer Lindblad resonance (red: $\Omega_p = \Omega
+ \kappa/2$), the orbit is closed and the star executes two radial excursions for every revolution backward around
the center in the rotating frame. At other radii, several of which are shown, the stellar orbits are unclosed.
}
\end{figure*}
\eject
We will need the ``epicyclic frequency'' $\kappa$ of the small radial and azimuthal excursions around
the mean motion,
$$
\kappa^2 = {{2V}\over{r}}\biggl({V \over r} + {{dV}\over{dr}}\biggr)~, \eqno{(1.3)}
$$
where $V(r)$ is the rotation velocity as a function of radius $r$.
If we move slightly inward from corotation toward the galactic center, then a star
oscillates around almost-closed ellipses while drifting forward with respect to the global pattern (leftmost
orbit illustrated in Fig.~1.10).
Contining toward smaller radii (next three orbits inward in Fig.~1.10), the forward drift gets
faster until the backward loop disappears and we end up with an unclosed rosette orbit that involves somewhat
more than two radial excursions for every revolution forward in the rotation direction around the center. It is
clear that, as we move farther inward and the forward drift rate continues to increase, the orbit again becomes
almost closed, now with almost exactly two radial excursions for every revolution (this is the second-innermost
orbit shown in the figure).
Continuing toward still-smaller $r$, we arrive at ``inner Lindblad resonance'' (ILR) where the (blue) orbit
is closed and the star executes exactly two radial excursions while it drifts forward with respect to the global
pattern by one complete revolution around the center. This happens where $\Omega_p = \Omega - \kappa/2$.
ILR is again an important resonance, because the star repeatedly has the {\it same phase} in its radial oscillation
when it has the {\it same position} with respect to the global pattern. So the star interacts more strongly
with the pattern near ILR than it does elsewhere in the disk. Moreover, ILR gives us a first-order understanding of
bar dynamics, as discussed in the next section.
Starting at corotation and moving outward, stars drift backward with respect to the global pattern
as seen in our rotating frame.~At~some~large~$r$, the orbit is closed as the star makes
two radial oscillations for every revolution backward around the center (the orbit is not illustrated). This is ``outer Lindblad resonance''
(OLR), and it happens where $\Omega_p = \Omega + \kappa/2$.
The generic rotation curve $V(r)$ and frequencies $\Omega(r)$ and $\Omega(r) - \kappa(r)/2$ are
shown in Fig.~1.3. Where $V \propto r$, $\kappa = 2\thinspace\Omega$ and $\Omega - \kappa/2 = 0$. Where \hbox{$V =$ constant,}
$\kappa = \sqrt{2}\thinspace\Omega$ and $\Omega - \kappa/2 = (1 - 1/\sqrt{2})\thinspace\Omega$ decreases proportional to $\Omega$.
In between, $\Omega - \kappa/2$ first rises and then falls with increasing $r$ as the rotation curve turns downward from
$V \propto r$ to $V \simeq$ constant. {\it The radial range over which $\Omega - \kappa/2$ varies little with radius
turns out to be crucial to the formation of bars and spiral arms. The evolving height and radial extent of the $\Omega - \kappa/2$
maximum proves to control the fate of bars. And the natural pattern speed for bars proves to be $\Omega_p \simeq
\Omega - \kappa/2$.} As follows:
\subsection{Bars and spirals as almost-kinematic density waves}
The essential insight into the dynamics of bars and global spirals is due to Lindblad (1956) and Kalnajs (1973;
see Toomre 1977b for a lucid review). It is illustrated in Fig.~1.11. Especially for outward-rising rotation curves (M{\thinspace}33)
and even for nearly constant or falling rotation curves (M{\thinspace}81), the angular precession rate $\Omega - \kappa/2$ of
ILR orbits is small and nearly constant over much of the galaxy.~\hbox{Suppose that $\Omega$\thinspace$-$\thinspace$\kappa/2$ is
{\it exactly\/} constant~with~$r$.} Then:~{\it If closed ILR orbits are arranged to produce a trailing spiral enhancement in density
(top left) or a straight bar (top right), the orbits will precess together at exactly the same $\Omega - \kappa/2$ and so will
preserve the spiral or bar shape. These are purely kinematic density waves.}
\begin{figure}[hb]
\vskip 3.7truein
\special{psfile=./kinematic-bar-SSlo.eps hoffset=8 voffset=-19 hscale=57 vscale=57}
\caption{(bottom) Frequencies $\Omega$, $\kappa$ and
$\Omega \pm \kappa/2$ for almost-circular~orbits~in~M{\thinspace}33 (Shu {\it et al.\ } 1971) and M{\thinspace}81
(Visser 1980). Both galaxies have large radial ranges in which $\Omega - \kappa/2 \simeq$
constant and ILR orbits precess almost together.
(top left) From Kalnajs (1973), elliptical ILR orbits aligned to produce a spiral density wave.
\hbox{(top right)} From Englmaier \& Gerhard (1997), examples of principal orbit families for a bar
oriented at $-45^{\circ}$. The elongated orbits parallel to the bar are the $x_1$ family out of
which the bar is constructed. If $\Omega - \kappa/2 =$ constant with radius over the extent
of the $x_1$ orbits, they precess together and preserve the bar shape.
Interior to ILR, the $x_2$ orbits are perpendicular to the bar. (The almost-square orbit has four
radial oscillations for each revolution; it is a 4:1 ultraharmonic resonance orbit.)
}
\end{figure}
\eject
In practice, $\Omega - \kappa/2$ is not quite constant. To make real bars~or
spirals, {\it it is the job of self-gravity to keep the orbits precessing exactly together.}
This discussion is a heuristic argument for another important conclusion. {\it The natural
pattern speed of a bar or global spiral is $\Omega_p \simeq \Omega - \kappa/2$.} Note in Fig.~1.11 that this
is much slower than $\Omega$ over most of the galaxy. That is, stars and gas revolve around the galactic center
more quickly than the pattern rotates; they catch up to the pattern from behind, participate in it for a time --
lingering in the pattern and thereby enhancing its density (Toomre 1981) -- and then continue onward in the forward
rotation direction. For bars, corotation happens
near the end of the bar or slightly beyond it (see Sellwood \& Wilkinson 1993 for a review).
Some barred galaxies that have substantial (pseudo)bulges also have nuclear bars $\sim$ one-tenth of the
radius of the main bar (Section 1.5.2.8). When the galaxy mass distribution is very centrally concentrated, $\Omega - \kappa/2$
has~a high maximum at small radii (frequency curves for M{\thinspace}81 in Fig.~1.11).
{\it The natural pattern speed of a nuclear bar is roughly equal to the local value of $\Omega - \kappa/2$
and is therefore much higher than the pattern speed of the main~bar.} This is seen in numerical simulations
(Debattista \& Shen 2007; Shen \& Debattista 2009) and in real galaxies (Corsini {\it et al.\ } 2003).
The $x_1$ family of closed bar orbits shown in Fig.~1.11 and the similar, non-periodic orbits that are
trapped around them by the bar's self-gravity involve large perturbations from circular orbits. Strong bars are nonlinear.
Then the approximations that we have made are not accurate. In particular, the true pattern speed is rather larger than
the local value of $\Omega - \kappa/2$ (e.{\thinspace}g., Shen \& Debattista 2009).
Nevertheless, the epicyclic approximation still captures the essence of the physics (Ceverino \& Klypin 2007).
In particular, for any realistic $\Omega_p \sim \Omega - \kappa/2$, there must be an inner Lindblad resonance
in a centrally concentrated galaxy such as M{\thinspace}81, but there cannot be an ILR in a pure-disk galaxy such as M{\thinspace}33.
Inside ILR, the closed ``$x_2$ orbits'' are elongated perpendicular to the bar (Fig.~1.11). So they cannot
be used to construct the bar and to maintain its self-gravity. We will see in Section 1.5 that the secular evolution of a barred galaxy
is in part to transport gas toward the center and thereby to build a pseudobulge. {\it As
secular evolution increases the central concentration of a barred galaxy, the inner maximum in $\Omega - \kappa/2$ gets
higher and wider~in~radius. Therefore it gets more difficult for self-gravity to keep the decreasing number of $x_1$ orbits
precessing together.~Also, the number of (damaging) $x_2$ orbits increases.~The bar gets weaker. Thus, bars naturally commit suicide
by the secular evolution that they drive. This happens preferentially in early-type galaxies, not in galaxies such as M{\thinspace}33.}
All of these heuristic predictions prove to be accurate.
\vfill\eject
\subsection{The growth, structural evolution and death of bars}
This section is an overview of the life histories of bars -- from rapid growth through secular evolution in ``middle age''
through eventual death -- at the level that we need in this Winter School. I concentrate in this section on the bars themselves;
the effects of bars on the other components in their galaxies will be the subject of later sections. I will not cover the rich dynamics
of bars in their nonlinear phases. For this work, the best review is Sellwood \& Wilkinson (1993).~Contact between the complicated
nonlinear dynamics that is reviewed there and the simplified story that I tell~here~is~not~always~good. That's where the frontier
in this subject lies. Here, I will summarize the most important bar evolution processes based on a series of seminal papers.
Sellwood \& Wilkinson (1993, hereafter SW93) provide more references, and Athanassoula (2012) reviews -- and, indeed,
advances -- some of these subjects in her lectures at this School.
My orientation is a little different from that of SW93. They take -- as much as possible,
in this complicated subject -- a formal approach rooted in the rigorous mathematics of galaxy dynamics. I take an observer's
approach. That is, I try to benefit as much as possible from the insight gained from analytical and $n$-body studies,
but I also put equal emphasis~on~letting~the observations suggest (or, in some cases, prove) which processes are at work.
Sometimes observations hint that a process (e.{\thinspace}g., evolution of bars~to~lenses) takes place even when the theory of
such a process is not well formulated. But asking the right question is the efficient road to progress. So this observational
guidance is very useful. One key is to remember which ideas are hypotheses and which are proven. And it is especially
important not to overinterpret the temptingly rich array of possibilities that are inherent in this subject. I will try to be clear
about the confidence with which various ideas are suggested. And I will emphasize what I believe are the most important
remaining problems.
\subsubsection{Bar instability}
Massive, cold, rotating disks are famously unstable to the formation of bars (e.{\thinspace}g.,
Ostriker \& Peebles 1973;
Toomre 1977b, 1981;
SW93).
Many $n$-body studies start with a stellar disk that is highly unstable and then follow the evolution
of the bar that results. Most results that are derived in this way are probably realistic, modulo (important!)~the neglect
of gas and dark matter. However, it is important to realize that bar evolution almost certainly does not start this way.
It is unrealistic to think that a disk grows axisymmetrically to a high mass, meanwhile using up its gas to make stars, and
only then discovers (``Oh, my God!'') that it is bar-unstable.
In a paper entitled ``Most Real Bars are Not Made by the Bar Instability'', Sellwood (2000) expresses a related worry.
Most barred galaxies have enough central mass concentration so {\it the bar essentially must have an ILR.} That~is,
$\Omega - \kappa/2$ is similar to the curve for M{\thinspace{81} in Fig.~1.11. Our heuristic arguments in \S\ts1.4.2 then
make plausible the result that also emerges from more detailed studies (e.{\thinspace}g., Toomre 1981), namely that a bar instability
never gets started when the resulting bar would have a strong ILR. Sellwood acknowledges and dismisses the possibility that the
disk might not originally have allowed an ILR, i.{\thinspace}e., that the central concentration was manufactured by the bar only after it formed.
One piece of supporting evidence was a conclusion (Abraham {\it et al.\ } 1999) that strongly barred galaxies were rare at $z > 0.5$;
this is now known to be incorrect (Jogee {\it et al.\ } 2004). More immediate was the concern that building up the central concentration
weakens~the~bar. I will suggest below that bar suicide happens, and it happens at a measurable (pseudo)bulge-to-disk
ratio. But I, too, have worried about why strong bars can coexist with strong ILRs.~The evidence will suggest that, when the central
mass grows slowly {\it while the bar has a strong angular momentum~sink,} a nonlinear bar can -- for a while -- continue to grow
even when it already has an ILR. But the more important point for the present section is this: {\it present\/} disk conditions
do not favor the growth of bars by a simple instability. \vskip 8pt} \def\vss{\vskip 6pt} \def\vsss{\vskip 2pt
Possible implications:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{Bar formation may be a threshold process that begins and then proceeds slowly and perhaps episodically
(Sellwood 2000) as the disk grows massive enough with respect to its dark halo (see also Mihos {\it et al.\ } 1997).}
\item{The formation of the stars that now make up the bars in early-type galaxies happened long
ago in progenitor galaxies about which we know very little.~~E.{\thinspace}g., the
boxy bulge $\equiv$ almost-end-on bar of our Galaxy is made of stars that are very old and enhanced
in $\alpha$ elements (see Renzini 1999 for a review).
So its stars formed over a period of \lapprox1~Gyr.
Gas fractions were much higher then than they are now (Genzel~et~al.~2006).
Gas may be centrally important to bar formation. Observations of high-redshift disks that are nevertheless
younger than our Galaxy's bulge stars show surprises such as $\sim 10^8$-$M_\odot$ clumps
and high velocity dispersions (Genzel {\it et al.\ } 2006; F\"orster~Schreiber~et~al.~2009). The clumps are
believed to form by violent instabilities, and they eventually merge to form at least some
classical bulges (Elmegreen {\it et al.\ } 2008; Section 1.8.1 here). None of this sounds like the typical initial conditions
assumed in $n$-body simulations of bar formation. We have no reason to be confident that we
know how to start those simulations with realistic initial conditions.}
\item{Contrariwise, a bar may form long after star formation makes the stellar disk. One way is thought
to be through tidal tickling by neighboring galaxies (e.{\thinspace}g.,
Noguchi 1987, 1988; 1996, which also discusses gas infall;
Gerin {\it et al.\ } 1990;
Barnes {\it et al.\ } 1991;
Mihos {\it et al.\ } 1997).
It is difficult to test this (for example) by looking for an excess of barred galaxies in dense environments such as the Coma cluster.
The reason is that any extra tendency to form bars where there are many galaxy encounters must compete with and may lose out to the
stabilizing effects of disk heating (Marinova {\it et al.\ } 2012; see Kormendy \& Bender 2012 for evidence that disk heating happens even in
the Virgo cluster).}
\item{Occam's razor is a dangerous weapon.~Answers are not guaranteed~to~be~simple. All the above -- i.{\thinspace}e.,~a series of episodic,
encounter-driven growth spurts that punctuate a steady, slower growth by outward angular momentum transport as envisaged
by Sellwood (2000) -- may happen. {\it It is important to understand that global spiral structure connected with a bar or inner
ring is a signature of outward angular momentum transport and therefore a sign that the bar is growing stronger.}}
\end{enumerate}
In the next sections, I review the life histories of bars and the evolution that they drive in their host galaxies,
keeping the above issues in mind. As needed, I emphasize where simulations do not yet include important~physics.
Limitations include
(1) that many simulations do not include gas, and gas physics is variously but always importantly simplified,
(2) that continued infall of gas and small galaxies is not included,
(3) that feedback from hot young stars, from supernovae and from active galactic nuclei is generally not included and may be important,
and especially
(4) that simulated galaxies are usually not as multicomponent as real galaxies.
Two-body relaxation is uninterestingly slow in galaxy disks.
Evolution is driven by the interactions of stars and gas with collective phenomena.
Physical morphology (\S\ts1.3.4) invites us to investigate the interactions of different nonaxisymmetric components in galaxies.
This is where the action is.
\subsubsection{$N$-body simulations:\\Rapid bar growth via instability\\followed by secular growth via angular momentum transport}
Among the many published $n$-body studies of bar formation (SW93), I focus on Sparke \& Sellwood (1987), because they analyze
their simulation in ways that tell us what we need to know. The initial condition~is~an~axisymmetric galaxy with a bulge-to-total
ratio of 0.3.~The bulge is a rigid Plummer\thinspace(1911) sphere with size $\sim$\thinspace$1/5$ that of the disk. A rigid potential is a
limitation:~the bulge gives the galaxy an ILR, and it is interesting to see the (surprising lack of) consequences, but the bar and
bulge~cannot~interact. The disk is a Kuz'min (1956)\thinspace--{\thinspace}Toomre (1963) model, density $\propto 1/(a^2 + r^2)^{3/2}$, where $r$
is radius and $a$ measures the scale length of the density falloff. With a Toomre (1964) {\it axisymmetric\/} stability parameter of
$Q = 1$, the initial disk was very unstable. The disk contained 50,{\kern 0.4pt}000 particles whose gravity was softened on a length
scale of $0.1{\thinspace}a$. Other limitations are that the model contains no gas and no ``live'' dark matter halo of simulated particles;
both of these limit the extent to which the bar sees a sink for angular momentum that allows it to grow. More detailed simulations
can now be run, but this subject does not get the attention that it deserves, and in particular, analyses are not usually as physically
motivated and compelling as the one in Sparke \& Sellwood (1987). There is much to be learned from this simulation, as follows.
Figure 1.12 shows the evolution of the disk density, and Fig.~1.13 shows the growth in amplitude of the bar and
the evolution of the pattern speed of the bar and its associated spiral structure. Time is measured in natural units
(discussed in Sparke \& Sellwood 1987). Beginning immediately and extending to time 50, the disk rapidly grows a two-armed
instability that is bar-shaped near the center and a global, two-armed~spiral~farther~out. The bar rapidly grows stronger:~more stars
participate, the axial ratio of the bar decreases, the bar grows longer and its pattern speed decreases.
Figure 1.13 dramatically reveals the important result that {\it the pattern speed of the bar is larger than the pattern speed
of the spiral at all times.} This is consistent with our heuristic argument: the bulge creates a near-central maximum in
$\Omega - \kappa/2$, and the pattern speeds of the bar at relatively small radii and the spiral at relatively larger radii are
comparable to \hbox{but slightly larger than the local value~of~$\Omega - \kappa/2$.}~(Note:~in Fig.~1.13, frequency\thinspace$=$\thinspace$2\Omega_p$,
because the pattern is bisymmetric.) {\it Because $\Omega_p$ is smaller for
the spiral than for the bar, the spiral continually shears away from the bar.~It is no surprise that spiral arms do not
necessarily start at the end of the bar, especially in galaxies such as NGC 2523, which have well developed inner rings and which
therefore are dynamically mature.}
Figure 1.13 makes it clear that the rapid, instability-driven initial growth of the bar is followed by a distinct later
phase of secular growth, when the bar amplitude increases and $\Omega_p$ decreases more slowly than in the early, rapid phase.
In this collisionless model, the outer disk has been heated so much that the spiral structure is weak during the secular phase
(Fig.~1.12). In real galaxies, there are two reasons why the later growth is more dramatic. First, galaxies contain gas;
(1) its response is stronger than that of the stars and, in fact, dissipative, and (2) gas also keeps the stellar disk cooler
and more responsive, because the stars that form from it are formed with low velocity dispersions. Second, the dark halo in a
real galaxy provides an additional sink for the disk angular momentum.
\vfill\eject
The bar ends roughly at corotation. Therefore, stars stream through the bar density wave in the forward direction.
Analysis of the orbital structure of the late-stage model shows that -- as expected -- the bar is made almost exclusively of
orbits trapped around the $x_1$ family of closed orbits that align with the bar. Despite the presence of an IRL,, there are
almost no orbits analogous to the $x_2$ family (the model has only 50,{\kern 0.4pt}000 particles, and not all orbits were checked.)
Additional details of the orbit structure are discussed in Sparke \& Sellwood (1987).
\begin{figure}[hb]
\vskip 5.3truein
\special{psfile=./sparke-sellwood-fig1lo2.eps hoffset=24 voffset=-15 hscale=53 vscale=53}
\caption{Bar formation in the $n$-body simulation of Sparke \& Sellwood (1987, Fig.~1). Times are in natural
units that are discussed in their paper. Only one particle in ten is included, and the bulge component is not shown.
}
\end{figure}
\eject
\cl{\null} \vfill
\begin{figure}[hb]
\vskip 10pt
\special{psfile=./sparke-sellwood-fig3lo.eps hoffset=8 voffset=-15 hscale=57 vscale=57}
\caption{Evolution of the bar in the $n$-body model of Sparke \& Sellwood (1987). Panels (a) and (b) show the
amplitude and phase of the bar as a function of time. A straight line is fitted to the phases at late times.
It shows that the pattern speed decreases quickly during the early, rapid growth of the bar and then more slowly
during the later, secular growth. The bottom panels show contours of the square root of the power in the bar
or spiral perturbation as a function of frequency $=$ $2\Omega_p$ and radius. Panel (c) is for the early part of the rapid growth
(up to time 31) and panel (d) is for the slow growth phase at times 40 to 103. A very important conclusion is that
the bar has a higher pattern speed than the spiral structure. Also, note that the pattern speeds of both the bar
and the spiral arms decrease with time, as shown for the bar in panel (b). The smooth curves show $2 \Omega$
(solid curve) and $2 \Omega \pm \kappa$ (dashed curves) for the initial, axisymmetric model. They apply only
approximately during the later, nonlinear phases. Nevertheless, it is clear that both the bar and the spiral
have pattern speeds that are similar to but slightly larger than the local values of $\Omega - \kappa/2$. Also
note that the bar develops despite the fact that it has an ILR. These are Figs.~2 and 3 from Sparke \& Sellwood (1987).
Similar results are illustrated in Bournaud \& Combes (2002).
}
\end{figure}
\eject
\begin{figure*}
\vskip 2.8truein
\special{psfile=./sparke-sellwood-fig6lo.eps hoffset=-12 voffset=-19 hscale=63 vscale=63}
\caption{Comparison of the $n$-body bar model of Sparke \& Sellwood (1987: isodensity contours at right) with
the SB0 galaxy NGC 936 (Kormendy 1983: isophote map at left). This is Fig.~6 from Sparke \& Sellwood (1987).
}
\end{figure*}
Comparison to real SB0 galaxies shows that the $n$-body bar model of Sparke \& Sellwood (1987) is realistic
in many respects. It has the shallow density gradient and sharp outer edge of real bars in early-type galaxies.
It has the rectangular shape observed, e.{\thinspace}g., in NGC 936 (Fig.~1.14). And it shows qualitatively similar
non-circular streaming motions. At the end of the simulation, the disk is too hot to allow
much spiral structure; therefore, the bar has no ``live'' component with which it can effectively interact, and
as a result, it is very robust. The situation in NGC 936 is similar: the Toomre (1964) stability parameter in
the outer disk is $Q \simeq 3$ to 4, so essentially no small-scale structure is possible (Kormendy 1984b). Not
surprisingly, the purely stellar-dynamical $n$-body model of Sparke \& Sellwood (1987) is a realistic simulation
of an SB0 galaxy but not of a gas-rich barred spiral.
Shortcomings of the model are easily linked to limitations in the physics:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{The model is two-dimensional and therefore cannot include orbital
complexity (including chaos) that is fundamentally three-dimensional. In particular, the bar cannot
buckle and hence thicken in the axial direction (Section 1.4.3.3).}
\item{The lack of gas means that the model can simulate SB0 but not spiral galaxies.}
\item{The bar cannot grow very much at late times because the disk gets too hot. The same problem is well known
in the context of understanding spiral structure. Quoting Toomre (1990): ``The gravitational forces involved
in [spiral structure] have the unwelcome side effect that they tend to increase the mean epicyclic motions
of any stars \dots~which take part. Typically, in just a few revolutions, these would-be participants become
simply too `hot' to contribute appreciably to any more fun. In other words, the vigor of these apparent
`spiral instabilities' was quickly recognized to doom any hopes for their longevity -- unless one adds some
form of cooling \dots~such as might be natural in a gas but surely not in a disk of stars.'' Toomre concluded that
``It really seems
as if we typically need at least to double the known amounts of reasonably active mass in the disks of Sc galaxies --
beyond the gas amounts that they are known to possess~-- in order that such galaxies appear about as few-armed
as they often are. {\it And from where can they have obtained \dots~such relatively cool additional disk material
if not from recent infall\thinspace}'' (emphasis added). So another limitation of the Sparke \& Sellwood
model -- and of other $n$-body simulations~-- is the lack of continued cosmological infall of
cold gas (Combes 2008a; Bournaud \& Combes 2002).}
\item{Lacking gas, the bar cannot commit suicide by transporting gas to the center and building a pseudobulge that makes it more
difficult for $x_1$ orbits to precess together. I believe that $n$-body studies overestimate the robustness of bars
when they give them no opportunity to increase the central mass concentration.}
\item{Concurrently, the bar cannot continue to grow stronger if the model does not include a ``live halo'' of particles
that can act as an angular momentum sink.}
\end{enumerate}
\vskip -5pt
These comments are not meant to be critical of Sparke~\&~Sellwood~(1987). Sellwood \& Carlberg (1984) recognize
the importance of gas infall to the maintenance of spiral structure. Sparke \& Sellwood (1987)
is a clean study with the machinery that was available at the time. It focuses on fundamentals that we need to understand.
Many $n$-body studies both before and since have led to similar
conclusion and have further extended our understanding of bar evolution (e.{\thinspace}g., Athanassoula 2003, 2005, 2012).
My remarks are meant to highlight how much this subject presents opportunities to students now.~There is a danger
that we may miss important physics because we do not yet observe the early stages of bar formation. This is
an opportunity for observers of high-$z$ galaxies. Modulo this uncertainty:
{\it I suggest that bars grow secularly via an ongoing competition between outward angular momentum transport that
strengthens the bar and the buildup of pseudobulges that weaken the bar.} This competition allows some barred galaxies
to have both strong bars and high-mass (pseudo)bulges that create (otherwise destructive) ILRs near the center.
Both the disk and the dark halo are angular momentum sinks. For the halo, this conclusion is based mostly on
$n$-body simulations (e.{\thinspace}g.,
Sellwood 1980, 2006, 2008;
Athanassoula 2003, 2005;
Athanassoula \& Misiriotis 2002),
but note that Valenzuela \& Klypin (2003) conclude that the effect is often overestimated.
For the disk, global spiral structure is the visible sign that the process is ongoing.
Cold gas is important to the evolution for many reasons. It makes the disk more responsive, both via
its small velocity dispersion and by making new stars that keep the disk cold. Radial redistribution of
gas is one product of angular momentum transport. And especially important is the conclusion reviewed in the next
sections that gas driven inward to the center builds substantial pseudobulges in many galaxies.
The natural frequencies at which ILR orbits want to precess therefore become less constant with radius.
When this effect wins the above competition, the bar is weakened or destroyed. Continued cosmological infall
of cold gas is central to all of these processes.
I argue in the rest of this review that many aspects of the above story are well understood but
that many opportunities remain to be explored.
\subsubsection{Vertical buckling of bars and the formation of box-shaped bulges}
The vertical thickening of bars into ``box-shaped bulges'' is reviewed from a theoretical perspective in SW93
and from an observational perspective in Kormendy \& Kennicutt (2004). My review here is brief.
$N$-body simulations show that strong bars thicken in the axial direction until they look peanut-shaped when
viewed side-on and box-shaped when viewed at the most common orientations between side-on and end-on. The first
paper to show this -- Combes \& Sanders (1981) -- was one of the earliest papers on galaxy secular evolution. Two
distinct processes are responsible.
Figure 1.15 shows the evolution of an $n$-body bar that, seen side-on, turns into a ``box-shaped bulge''
via a buckling instability in the axial direction (Raha {\it et al.\ } 1991). The instability happens after the bar
is well formed, and \phantom{0000000000}
\vfill
\begin{figure}[hb]
\vskip 1truein
\special{psfile=./Raha12lo.eps hoffset=0 voffset=-21 hscale=64 vscale=64}
\caption{Face-on (left) and edge-on (right) views of the vertical buckling of an $n$-body bar
and the formation of a ``box-shaped bulge'' (Figs.~1 and 2 from Raha {\it et al.\ } 1991). The rotation
period at the end of the bar is $\Delta T \simeq 200$ time units.
}
\end{figure}
\eject
\noindent its growth is about as rapid as that of the original bar instability. Two bar rotations later,
the bar has weakend considerably, grown more centrally concentrated, and \hbox{become box- or peanut-shaped as seen
side-on.} \hbox{The resemblance to box-shaped bulges in edge-on galaxies (Section\ts1.5.2.9),} already noted by Combes \&
Sanders (1981) is compelling. Many other \hbox{$n$-body} studies reach similar results (e.{\thinspace}g.,
Athanassoula \& Misiriotis 2002;
Athanassoula 2003, 2005;
Athanassoula {\it et al.\ } 2005;
Shen {\it et al.\ } 2010).
A second mechanism by which bars may thicken in the axial direction is via resonances between the rotation
of the bar and the vertical oscillations of disk stars (e.{\thinspace}g.,
Pfenniger 1984, 1985;
Combes {\it et al.\ } 1990;
Pfenniger \& Norman 1990, 1991;
Pfenniger \& Friedli 1991;
Hasan {\it et al.\ } 1993).
When the vertical oscillation of stars is in resonance with the azimuthal rotation of a bar, each star repeatedly
encounters the bar at a similar phase~in~its~orbit. This pumps up the vertical velocity dispersion of disk stars
and gives the center a boxy appearance when viewed edge-on. Unlike bar buckling, resonant heating is
inherently a secular process.
The relative importance of these two processes in making the observed ``box-shaped bulges'' is not known.
However, the most important conclusion appears robust regardless of the answer: when we see a boxy bulge in an edge-on
galaxy, it is part of the bar and not a merger remnant. We therefore call these features ``box-shaped pseudobulges''.
I return to them in Section 1.5, when I discuss the evolution that bars drive in their galaxies.
\subsubsection{Bar suicide and the origin of lens components.\\I.~$N$-body simulations}
Early $n$-body simulations suggested that bars are very robust (see SW93). The reason is
now clear: those simulations contained no gas and so could not engineer big changes in the
central concentration of the mass distribution. More recent simulations which allow the galaxy to grow a central mass
-- either ``by fiat'' or more naturally by rearranging the disk gas -- show that {\it bars tend
to commit suicide by the secular evolution that they drive.} In particular, they force disk
gas to fall toward the center, where it builds up a high-central-concentration pseudobulge, and this causes
the bar to weaken. Pseudobulge growth is covered in later sections. The death of bars and their evolution --
I suggest -- into lens components is discussed here.
The earliest simulations of this process were motivated by the observation that most galaxies contain central
supermassive black holes (Kormendy \& Richstone 1995). The earliest paper that I know, Norman \& Hasan (1990),
already got essentially the modern answer:~``It is estimated~that~a~black~hole with mass equal to 17\thinspace\% the total mass
is required to destroy the [$x_1$] family of orbits and hence the bar.'' No galaxy is known to have such a big black hole
(Kormendy \& Ho 2013), but we now know that a centrally concentrated pseudobulge -- although less effective than a
point mass -- has a similar effect. Hasan \& Norman (1990) is a detailed followup. Pfenniger \& Norman (1990)
concentrated on pseudobulge building by a combination of inward radial gas flow and resonant vertical heating, and
they reached similar conclusions about bars destruction. Subsequent discussion has centered on the question of
how much central mass is needed to affect a particular degree of bar weakening. Apparent disagreements between
papers mainly result from the fact that fluffier central mass concentrations are less damaging to bars.
Why central mass concentrations are destructive is easy to see using Fig.~1.11 and was summarized in Section 1.4.2. As the
central mass increases, the central maximum in $\Omega - \kappa/2$ becomes higher and broader in radius (see the panel for
M{\thinspace}81). This shrinks the radius range in which $\Omega$\thinspace$-$\thinspace$\kappa/2$ varies slowly with radius and in which~it~is
possible to have $\Omega_p$\thinspace$\sim$\thinspace$\Omega$\thinspace$-$\thinspace$\kappa/2$. To put it differently, the radius range between ILR and
corotation in which $x_1$ orbits align with the bar gets smaller. Recall that $x_2$ orbits interior to ILR align perpendicular
to the bar. So, as the central concentration increases, there are fewer bar-supporting $x_1$ orbits, and they
have a harder time all precessing at the same rate $\Omega_p \sim \Omega - \kappa/2$. As the bar potential weakens,
self-gravity becomes less able to keep all the orbits precessing together. Once an orbit ``escapes'' from its alignment
with the bar, it phase-mixes azimuthally in a short time. Even if there is no big change in orbital eccentricities,
the long, thin shelf in surface brightness that makes up the bar will, \hbox{I suggest (Kormendy 1979b), tend to phase-mix}
azimuthally into a lower-surface-brightness and more axially symmetric shelf in surface brightness that has the same sharp
outer edge that the bar had. This is precisely a description of a lens component. It is part of the reason why I suggest
that, as strong bars weaken, the stars that escape from them grow a lens. I suggest further that we see galaxies at
all phases of this evolution: some have bars and no lenses; many have bars embedded in lenses of the same major-axis size,
and some have lenses with no bars.
The rest of this section reviews further papers on bar suicide and observational evidence that lenses are defunct bars.
Combes (2008b,\ts2010,\ts2011) gives brief theoretical \hbox{reviews of bar-to-lens} evolution.~She also
reviews an additional important aspect of bar dissolution. When gas loses angular momentum and flows
toward the center, the stellar bar receives that angular momentum that is lost by the gas. This makes the orbits
rounder and the bar weaker. Papers that emphasize this effect include Bournaud \& Combes (2002) and Bournaud {\it et al.\ } (2005).
\vfill\eject
\cl{\null}\vfill
\begin{figure}[hb]
\vskip 5.truein
\special{psfile=./NormanBarDeathlo.eps hoffset=36 voffset=-18 hscale=56 vscale=56}
\caption{Death of an $n$-body bar as the central mass concentration is increased (adapted from Figs.~1, 2 and 3 of
Norman {\it et al.\ } 1996). An initial axisymmetric disk was evolved to time 100, by which time a stable bar had developed (leftmost
configuration shown in each of the three rows of particle distributions~at~the~top). The top three rows show the time
evolution as a point mass is grown at the center. Its mass shrinks from bulge size to zero size between $t = 100$ to $t = 150$.
At the end, it makes up 0\thinspace\%, 3\thinspace\% and 7\thinspace\% of the mass of the disk (top row to bottom~row). In the absence of a
central point mass, the bar is stable (top). The bar is weakened progressively more as the central mass increases.
The bar amplitude is shown in the middle panel. The bottom panel shows the $t = 200$ amplitude as a
function of the final central point pass. Note that, whereas higher point masses more thoroughly destroy the bar, its
amplitude is non-zero even for a 7\thinspace\% central point mass.
}
\end{figure}
\cl{\null}\vskip -27pt
\eject
\cleardoublepage
My lectures included an example from Norman {\it et al.\ } (1996) of an $n$-body simulation of the weakening of a bar by a
growing central mass. This is illustrated in Fig.~1.16. A Kuz'min -- Toomre disk that contains 75\thinspace\% of the mass is
the only component modeled with (50,{\kern 0.4 pt}000) ``live'' particles. The rest of the mass is in a rigid bulge. This
is modeled as the sum of two Plummer spheres, initially of the same size; the aim was to let one of them shrink in radius
once the bar was well established. The disk was initially given a Toomre stability parameter of $Q = 1$ ensuring that a bar
would~form. This already guarantees that the initial bar will coexist with a bulge whose $B/T$ ratio
is typical of observed galaxies. Figure 1.16 shows that the inner part of the disk formed a bar by time 50; if nothing
further was done to the model (top row of particle distributions and ``no central mass'' amplitude line in the middle panel),
the bar remained stable in amplitude to time 200.
Between time 100 and time 150 (about four bar tumbling periods), the lower-mass ``bulge'' Plummer sphere was shrunk
by a factor of 50 in radius. Note that this turns it effectively into a point mass, not a pseudobulge with a realistic
scale length. No mass was added, so the overall equilibrium of the disk was essentially unaffected. But the amplitude of
the bar decreased as the central point mass was shrunk.~Even a 3\thinspace\% central point mass reduced the bar amplitude substantially.
A 7\thinspace\% point mass killed it almost completely.
Norman {\it et al.\ } (1996) explored the mechanism whereby the bar is destroyed in some detail, both in the above,
two-dimensional simulation and in three-dimensional simulations that give similar results. In essence, moving some
mass to the center shrinks the phase space (e.{\thinspace}g., radial range) of the $x_1$ orbits. As ILR moves
outward, some $x_2$ orbits appear, and these do not support the bar. Some orbits become chaotic. At some point (time
$\sim$\thinspace$140 \pm 5$ in Fig.~1.16), the bar coherence quickly breaks down and the disk becomes more axisymmetric. Note
that the bar is not destroyed completely.
Norman and collaborators acknowledge that these are ``highly idealized calculations intended to study just one aspect
of the rich secular evolution of barred galaxies. The contraction of a rigid mass component is, of course, highly artificial,''
and more to the point, the pseudobulges that weaken real bars have length scales $\sim 1/10$ those of their associated disks;
they are not point masses. With Norman {\it et al.\ } (1996), we emphasize that the model is constructed so a relatively large
bulge coexists comfortably~with~the~bar. Figure 1.16 should be taken as a ``proof of concept'' of bar suicide, not
as a definitive measurement of how much central mass concentration is required to achieve it. I use Norman {\it et al.\ } (1996)
and not more detailed simulations as my example here because my purpose is primarily pedagogical,~and~I~don't want the
essential theme to get lost in the details of orbit analysis.
The real world is substantially more complicated in ways that make it difficult to predict via simulations how much
central mass concentration a bar can tolerate. No available simulation realistically follows the competition between (1) the
bar growth that results from allowing the disk and dark halo to be angular momentum sinks, with the disk kept cold and continually
replenished with cosmologically infalling gas, and (2) the secular evolution that builds up the central mass concentration and
that thereby fights the growth of the bar. While the pseudobulge grows both through gas infall and star formation and
(e.{\thinspace}g., Norman {\it et al.\ } 1996) by the redistribution of stars, resonances such as (but not limited to) ILR sweep through the central
regions and continually keep a fresh supply of material responsive to resonant interactions with the bar.
So it is no surprise that some papers suggest that central mass concentrations as small as a few percent of the disk mass
are enough to destroy bars
(e.{\thinspace}g., Berentzen {\it et al.\ } 1998;
Sellwood \& Moore 1999;
Hozumi \& Hernquist 1999, 2005;
Bournaud {\it et al.\ } 2002, 2005;
Hozumi~2012)
whereas others (e.{\thinspace}g.,
Friedli \& Benz 1993;
Norman {\it et al.\ } 1996;
Athanassoula {\it et al.\ } 2005)
find that larger masses are necessary. These apparent disagreements are largely resolved by a fundamental conclusion
due to Shen \& Sellwood (2004): ``{\it For a given [central] mass, dense objects cause the greatest reduction in bar amplitude,
while significantly more diffuse objects have a lesser effect\/}'' (emphasis added).
The culprit in bar suicide is certainly not the central supermassive black hole (Shen \& Sellwood 2004) or even a
nuclear star cluster, since these typically have masses of $\sim$ 0.2\thinspace\% of the mass of a classical bulge and a smaller
fraction of the mass of a pseudobulge or disk (see Kormendy \& Ho 2013 for a review).
The results of Shen \& Sellwood (2004) suggest that pseudobulges mainly are responsible for destroying bars. For a ``soft''
central mass whose size is comparable to that of a pseudobulge, Shen and Sellwood find that a 5\thinspace\% central mass decreases the bar strength
to $\sim$\ts60\thinspace\% of its undamaged value, whereas a 10\thinspace\% mass decreases the bar strength to $\sim$\ts1/3 of its undamaged value.
Orbital analysis reveals that the bar dies because the phase space of $x_1$ orbits shrinks, and many $x_1$ orbits become chaotic as the
bar decays. In most of these models, the dark matter halo was a rigid potential and therefore not an angular momentum sink. Test runs
with a live halo show that the bar is then slightly harder to destroy. Similarly, the disk is dissipationless and does not accrete cold
gas from the cosmological web, so it is not as good an angular momentum sink as the disk in a real spiral galaxy. Nevertheless, these results
provide a realistic picture of what it takes to destroy a bar, at least as judged by a comparison with real galaxies (Section 1.4.3.5).
\eject
\vfill\eject
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./BarLens-6Panel-Annotlo.eps hoffset=-10 voffset=-14 hscale=62 vscale=62}
\caption{Typical galaxies in which a bar fills a lens component in one dimension. This figure shows a sequence from a strong bar
with essentially no lens (NGC 4643) through galaxies that have both bars and lenses (NGC 2950, NGC 4340, NGC 3945) to NGC 3081,
which has an exceedingly weak bar embedded in a bright lens with a very bright, star-forming inner ring around the rim of the lens.~The
{\it HST\/} image~at right is an enlargement of the inner ring, lens, bar and pseudobulge.~In NGC 3081, the pseudobulge replicates the
main B(r,lens) structure with a nuclear~bar. All images are from {\tt http://www.wikisky.org} except those of NGC 3801, which
are from the {\it de Vaucouleurs Atlas of Galaxies} (Buta {\it et al.\ } 2007: left image) and {\it HST} (Buta {\it et al.\ } 2004: right image).
Similar galaxies are shown in earlier figures.
In Fig.~1.6, NGC 1291 is an (R)SB(lens)0/a galaxy similar to NGC 3945 here.
In Fig.~1.9, NGC 2859 is an (R)SB(lens)0 galaxy similar to NGC 3945. The other galaxies in that figure are
later-Hubble-type versions of the sequence shown here.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Bar suicide and the origin of lens components. II. Observations}
Long before we knew of a process that could destroy bars, Kormendy~(1979b, 1981, 1982b) suggested that bars weaken
with time and evolve into lenses. Observations on which this suggestion was based include the following.
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{Lens components are very common in barred galaxies; in the sample of 121 SB galaxies studied by Kormendy (1979b),
54\thinspace\% of SB0$^-$ to SBa galaxies have lenses. The relative light contribution of the bar
and lens varies widely from ${\rm bar}/\kern 0.5pt{\rm lens} \gg 1$ to ${\rm bar}/\kern 0.5pt{\rm lens} \ll 1$. Figure 1.17 shows
such a sequence. I illustrate many B(lens) structures in these lectures to emphasize how common they are.}
\item{Lens components occur but are rare in unbarred S0\thinspace--{\thinspace}Sa galaxies. Examples are shown in
Figs.~1.7 and 1.18. It is likely that the inner ``oval disks'' in later-type (typically Sb) galaxies
are lenses, too. If B $\rightarrow$ lens evolution occurs, this suggests that it goes nearly to completion
(i.{\thinspace}e., ${\rm bar}/{\rm total}$ light $\rightarrow$ 0)
rarely in early-type galaxies and more commonly in mid-Hubble-type galaxies.}
\item{Lens components and bars in early-type galaxies have similar radial brightness profiles; i.{\thinspace}e., shallow
surface brightness gradients interior to a sharp outer edge. The brightness profiles of the lenses measured in
Kormendy \& Bender (2012) are well fitted by S\'ersic (1968) functions with $n \simeq 0.5$ (i.{\thinspace}e., Gaussians).}
\item{When bars and lenses occur together, the bar almost always fills the lens in one dimension
(Kormendy 1979b,
Buta {\it et al.\ } 2007;
Buta 2011, 2012;
Fig.~1.17 and references there).
Points (c) and (d) imply that, to make a lens, it is sufficient to azimuthally phase-mix bar orbits.
Points (a) and (b) hint that such a process occurs in many barred galaxies but that bars are completely destroyed
only rarely. This is consistent with Section 1.4.3.4: moderate ``soft'' mass concentrations weaken bars but do not
necessarily destroy them.}
\end{enumerate}
\vfill
\vskip 1.3truein
\begin{figure}[hb]
\special{psfile=./N2784-N3245-Annotlo.eps hoffset=-7 voffset=-15 hscale=61 vscale=61}
\caption{{\kern -1.5pt}The prototypical unbarred S0 galaxy with a lens is NGC\ts1553~(Fig.~1.7). This figure shows two more examples.
NGC 2784 is from the {\it de Vaucouleurs Atlas} and NGC 3245 (rotated so north is at left) is from {\tt http://www.wikisky.org}. The lenses
are the elliptical shelves in surface brightness just outside the (pseudo)bulges.
Several earlier figures show barless, late-type analogs which probably also are lenses
(NGC 4736 in Figs.~1.3, 1.6 and 1.8; NGC 4151 in Fig.~1.8).
}
\end{figure}
\cl{\null}
\vskip -28pt
\cl{\null}
\vskip -30pt
\begin{enumerate}[e]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[(e){\kern -5pt}]{~Figure 1.19 shows a compelling observation that supports B $\rightarrow$ lens evolution. The top panels show
rotation velocity $V$ and velocity dispersion~$\sigma$ along the major axes of the barred S0(lens) galaxy
NGC\ts3945 (Fig.~1.17) and the unbarred S0(lens) galaxy NGC 1553 (Fig.~1.7). The NGC 3945 bar is oriented along
the minor axis, so the major-axis observations in Fig.~1.19 really measure the lens. The bottom panel shows $V/\sigma$ for these
two galaxies plus NGC 2784 (Fig.~1.18) and two more SB0 galaxies. I conclude: (1) {\it The inner part of each lens is hotter than
its corresponding pseudobulge. That is, $\sigma$ is higher and $V$ is smaller in the lens than in the pseudobulge.}
(2) {\it This behavior and the $V/\sigma$ radial profiles are the same in barred and unbarred lenses.}
(3) {\it And $V/\sigma$ in these lenses is similar to $V/\sigma$ along the ridge line of the strong bar
in NGC 936} (Kormendy 1983).}
\end{enumerate}
\vfill
\vskip 1.3truein
\begin{figure}[hb]
\special{psfile=./LensSigmalo.eps hoffset=17 voffset=-19 hscale=53.5 vscale=53.5}
\caption{(top) Major-axis rotation velocity $V$ and velocity dispersion $\sigma$ data in NGC 3945 [SB(lens)0] and in NGG 1553
[SA(lens)0]. The lens radius is 51$^{\prime\prime}$ in NGC 3945 and 36$^{\prime\prime}$ in NGC 1553. The instrumental dispersion
is $\sim$\ts100 km s$^{-1}$ for NGC 3945 and $\sim$\ts65 km s$^{-1}$ for NGC 1553. (bottom) Local ratio of
rotation velocity to azimuthal velocity dispersion in lenses of barred and unbarred galaxies. Radii are normalized to the
radius of the lens for galaxies and to the corotation radius for the n-body models. Horizontal ``error bars'' show the
range in radii over which data were averaged. Open symbols refer to measurements contaminated by bulge light. This figure is
taken from Kormendy (1981, 1982b, 1984a).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\begin{enumerate}[e]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[\phantom{(e)}]{Thus the relative importance of ordered motions (rotation) and random motions is similar in lenses and bars,
both observed and $n$-body-simulated. In particular, at about 40\thinspace\% of the radius $r_{\rm lens}$ of the lens,
$V/\sigma \sim 0.8$.
Also, $\sigma$ is the line-of-sight velocity dispersion, so the total velocity dispersion is likely
to be at least a factor of $\sqrt{2}$ larger. This means that the ratio of rotational kinetic energy
to random kinetic energy is $\sim 1/3$ in the inner parts of both bars and lenses. That is, stellar orbits
are similarly far from circular. Lenses are parts of disks (Freeman~1975), and yet they are
hotter than their associated (pseudo)bulges. The close similarity of $V^2/\sigma^2$ in bars and lenses
(cf.~Bosma {\it et al.\ } 2010) means that it is relatively easy for bars to evolve into lenses -- it is enough if $x_1$ orbits
escape the persuasion to precess together that is supplied by bar self-gravity; it is not necessary to
change their energies and angular momenta drastically.
}
\item[(f){\kern -5pt}]{~The fact that we see arbitrarily weak bars embedded in strong lenses is a powerful argument that these bars were once
stronger (Kormendy 2004b). NGC 3081 in Fig.~1.17 is the best example. It contains an exceedingly faint bar,
but almost all of the inner light is in the lens -- which is {\it much\/} rounder~--~and~the pseudobulge. {\it Can we really
imagine that one or two percent of the stars~in~a~disk discover that they are bar-unstable, that they make a nice,
highly elongated bar, and that most of the disk meanwhile stays just slightly oval? This is not what happens in $n$-body
simulations of bar formation. There, essentially all of the disk participates in the instability, and most disk stars that
live interior to the final radius of the bar participate in the bar.} That's why $n$-body bars buckle in the axial direction --
they are self-gravitating structures. Lenses, on the other hand, appear to be flat (e.{\thinspace}g., Kormendy 1982b and
Kormendy \& Bender 2012). Thus the observation (Figs.~1.17 and 1.18) that there is a complete continuity from
${\rm bar}/{\rm lens} \gg 1$ to ${\rm bar}/{\rm lens} \ll 1$ to ${\rm bar}/{\rm lens} = 0$, together with the above results,
strongly suggests that bars evolve into lenses.
The fact that barless lenses are rare at early Hubble types implies that any evolution is relatively slow or that it stops
when a galaxy gets transformed into an S0. The observation of barless ovals that appear to be equivalent to lenses in galaxies
such as NGC 4736 and NGC 1068 implies that the evolution goes to completion more readily in galaxies that contain gas.}
\end{enumerate}
\phantom{More invisible text to fix line spacing}
\vskip -20pt
All of these suggestions are comfortably consistent with -- and arguably could have been predicted from -- our picture that bars drive
secular evolution that builds up the central density by forming pseudobulges that are harmful to the survival of the bar.
I do not want to argue too forcefully for this picture. I especially do not want to suggest that
bar $\rightarrow$ lens evolution is the only thing~that~happens. But the most economical suggestion that is consistent with
observations and simulations is that bars evolve away as they increase the central concentration of the galaxy.~One result is lens
components that~have~the same radii, shallow brightness gradients, and sharp outer edges as their parent bars. Some tests of this idea
are suggested in Section 1.4.3.7.
\vfill
\subsubsection{Bar suicide and the origin of lens components.\\III.~What pseudobulge mass is required to destroy bars?}
\vskip -5pt
We get a preliminary idea of what $PB/T$ ratio divides SA and SB galaxies by examining values for intermediate-Hubble-type
oval galaxies that are illustrated in this paper. Two more such galaxies are shown in Fig.~1.20.
Table 1.1 shows~the~results. The sample is small.
Also, $PB/T$ ratios of SAB galaxies vary widely, perhaps because the central concentrations of pseudobulges
vary widely. Nevertheless, we derive a clean result, as follows.
{\it Table 1 suggests that realistic pseudobulges with $PB/T \simeq 0.34 \pm 0.02$ are massive enough to destroy bars
essentially completely and to convert them into lenses. This is a preliminary result, reported here for the first time.}
\cl{\null} \vskip -60pt \cl{\null}
\begin{table}[h]
\caption{Pseudobulge-to-total luminosity ratios for \phantom{0000000}barred~and~unbarred~oval~galaxies}
\begin{tabular}{c|lcl}
\hline \hline
{Galaxy} & {~~~~Type} & {$PB/T$} & Source\\
\hline
NGC 2273 & \phantom{(R$^{\prime}$)}SBa & $0.19 \pm 0.02$ & Kormendy \& Bender (2013) \\
NGC 3393 & (R$^{\prime}$)SBab & $0.27 \pm 0.06$ & Kormendy \& Bender (2013) \\
\hline
NGC 3081 & \phantom{(R$^{\prime}$)}SAB0/a& $0.11\phantom{\pm 0.000}$ & Laurikainen {\it et al.\ } (2010) \\
NGC 3368 & \phantom{(R$^{\prime}$)}SABab & $0.25\phantom{\pm 0.000}$ & Kormendy \& Bender (2013) \\
NGC 4151 & (R$^{\prime}$)SABab & \phantom{0}$0.327\phantom{\pm 0.000}$ & Gadotti (2008) \\
\hline
UGC 3789 & (R)SAab & $0.32 \pm 0.03$ & Kormendy \& Bender (2013) \\
NGC 1068 & (R)SAb & $0.35 \pm 0.05$ & Kormendy \& Bender (2013) \\
NGC 4736 & (R)SAab & $0.36 \pm 0.01$ & Kormendy \& Bender (2013) \\
\hline \hline
\end{tabular}
\label{sample-table}
\end{table}
\vskip 1.truein
\begin{figure}[hb]
\special{psfile=./N3393-U3789lo.eps hoffset=30 voffset=-16 hscale=49.5 vscale=49.5}
\caption{Oval galaxies that bracket the $PB/T$ value which divides galaxies that do and do not have bars.
The barred galaxy NGC 3393 has $PB/T = 0.27 \pm 0.06$;
the unbarred galaxy UGC 3789 has $PB/T = 0.32 \pm 0.03$.
This figure from Kormendy \& Ho (2013) is based on Digital Sky Survey images from {\tt http://www.wikisky.org}.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Remaining puzzles and suggestions for further work}
Our understanding of the lives and deaths of bars is now reasonably well developed. A few particularly
obvious problems and suggestions about how to address them are outlined below.
\begin{enumerate}[a]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{How do bars form? Despite the long history of seeing violent instabilities when $n$-body systems
are given small Toomre $Q$ by {\it fiat\/}, and despite convincing hints that tidal tickling helps,
we understand bar formation less well than we think. We need to investigate bar growth both observationally
by observing distant galaxies and by using simulations. Closely related and very important are (b)~and~(c).} \vskip 2pt
\item{We need to study bar evolution via the competition between angular momentum sinks
(the outer disk and dark halo), which make the bar grow stronger, and the increasing importance
of ILR as the bar moves material inward, which makes the bar grow weaker. This is a complicated
modeling job. But the great richness of possible interactions between nonaxisymmetric components is lost when
the relevant components either are not included or are turned into fixed potentials. I do not criticize
published papers for trying to distill clean subsets of the physics that we want to study. But there are
effects that we cannot find if component interactions are switched off. In particular,
it is likely that a bar can coexist with a more massive (pseudo)bulge if it grew in the context of the above
competition.} \vskip 2pt
\item{Including gas is critically important in studying bar evolution. Gas dissipation is essential for the inward
flow of the material that builds pseudobulges. Whether recycled, not yet used up, or accreted from outside, gas
helps to keep the disk cold enough to be responsive. Without it, $n$-body disks get so hot that
spiral structure switches off and the disk gets less effective at absorbing angular momentum. Cosmological
accretion of cold gas may be essential~for~realistic~bar~evolution.} \vskip 2pt
\item{On the observational front, we need to measure the luminosity and mass functions of elliptical galaxies, classical bulges,
pseudobulges and disks as a function of environmental density. Early observations demonstrate that the answers are
different in clusters and in the field (Sandage {\it et al.\ } {\kern -1pt}1985a; Kormendy{\thinspace}{\it et{\thinspace}al.\/}{\thinspace}2010).
But we need more quantitative measures of the relative importance of secular evolution and hierarchical clustering
and merging as a function of environment.} \vskip 2pt
\item{The idea that bars evolve into lenses needs to be tested further. Note how many
relevant observations and theoretical hypotheses date from the 1980s. This is an opportunity
for today's students. We need absorption-line kinematic measurements of bars and lenses. We need
photometry and component decomposition to see, e.{\thinspace}g.,~whether the bar/lens luminosity
ratio tends to be smaller as the (pseudo)bulge is more massive or more centrally concentrated. Caution:~many
decomposition codes use the assumption
that each component has a flattening that is independent of radius. This is certainly wrong and commonly leads to
unphysical conclusions (e.{\thinspace}g., about numbers of components). And we need mass models to determine halo properties.
There is much work to be done.}
\end{enumerate}
\vfill\eject
\section{Secular evolution and the growth of pseudobulges}
This section reviews the processes of secular evolution in disk galaxies and the structures that they produce.
I begin with bar-driven evolution but also discuss why evolution happens in more than just barred galaxies. Much
emphasis will be on the high-density central parts of galaxies that in the past were confused with merger-built bulges.
As explained in Section 1.1.3, I call such components ``pseudobulges'' if -- to the best of our knowledge -- they were not
made by mergers but rather were grown out of the disk.
The essential qualitative results of secular evolution were known more than 30 years ago at the time of my Saas-Fee
lectures (Kormendy 1982b). From that review, Table 1.2 here lists the major structural components in galaxies and what we then
thought we knew about their origin.~All of the suggested formation mechanisms are strongly supported by more recent~work and
form the main subjects of these lectures. The only change that I have made in reproducing Table 1.2 is to remove a suggestion
that the transition~from \phantom{000000000}
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./Saas-Fee-Table1-corrlo.eps hoffset=25 voffset=-25 hscale=50 vscale=50}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent ellipticals and bulges to thick and thin disks is continuous. The only change in emphasis that I would make
in reformulating the table now would be to emphasize major mergers as the origin of classical bulges and ellipticals
and note that dissipation and starbursts occur naturally in wet mergers.
To bring this story up to date, let's start by revisiting the definition of a classical bulge. The clearest
statement that captures the intention~of morphologists such as Sandage and de Vaucouleurs is by Alvio Renzini (1999):
``A bulge is nothing more nor less than an elliptical galaxy that happens to live in the middle of a disk.'' There is a world
of information hidden in this beguilingly simple defintion:
First, what is an elliptical? Formally, this subject is beyond~the~scope of these lectures.~We understand that ellipticals
form by major~galaxy~mergers and not by secular processes. Still, we cannot understand pseudobulges without knowing something about
classical bulges and ellipticals. Moreover, some lecturers at this school (notably Isaac Shlosman and Nick Scoville) focus
on our standard picture of the evolution of structure by hierarchical clustering and galaxy mergers. I try to connect this story with
our picture of secular evolution in Section\ts1.8. Some properties of elliptical galaxies and classical bulges are compared in
Section 1.7. Here, I list the properties that we need in the present section. Classical bulges and elliptical galaxies
\begin{enumerate}[a]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{have smooth, nearly elliptical isophotes;}
\item{have S\'ersic (1968) function $\log{I(r)} \propto r^{-1/n}$ brightness profiles that fall steeply toward larger radii $r$
with 2 \lapprox\thinspace$n$ \lapprox \ts4 for most bulges (e.{\thinspace}g., Fisher \& Drory 2008);}
\item{satisfy the same ``fundamental plane'' correlations (Djorgovski \& Davis 1987; Faber {\it et al.\ } 1987; Djorgovski {\it et al.\ } 1988;
Bender {\it et al.\ } 1992) between the ``effective radius'' $r_e$ that contains half of the total light, the ``effective surface
brightness'' $\mu_e$ at $r_e$ and the total absolute magnitude $M_V$ (Fisher \&{\thinspace}Drory~2008; Kormendy \& Bender 2012)
as illustrated here in Fig.~1.68 and}
\item{generally rotate approximately as rapidly as oblate spheroidal stellar systems that have isotropic velocity dispersions
and that are flattened mainly by rotation (e.{\thinspace}g., Kormendy \& Illingworth 1982).}
\end{enumerate}
\noindent Point (c) is the most important, because some of (a), (b) and (d) are shared by other kinds of ellipsoidal stellar
systems called ``spheroidals'' (Section\ts1.7).
I adopt the Renzini definition, because it embodies the idea that I want to emphasize,
namely that the definition of a component should be made in terms of its formation physics as well as its observed properties.
\begin{figure*}
\vskip 1.44truein
\special{psfile=./M87-N4594-N1353lo.eps hoffset=-11 voffset=-14 hscale=62.7 vscale=62.7}
\caption{Illustrating the surrogate definitions of a bulge: M{\thinspace}87 is a giant elliptical,
and NGC 4594 is a classical-bulge-dominated Sa galaxy seen almost edge-on. These are Hubble Heritage
images. The right panel shows the surface brightness profile along the major axis of the Sb galaxy
NGC 1353; we use it again in Fig.~1.33. It is decomposed into an outer exponential disk profile and
an inner (it will turn out: pseudobulge) profile with a S\'ersic index of $n = 1.3 \pm 0.3$.}
\end{figure*}
The problem with our definition is that it is difficult to apply, especially to galaxies that are not seen edge-on.
Therefore it is common to use one of two surrogate definitions as illustrated in Fig.~1.21. When a galaxy disk is seen
nearly edge-on (e.{\thinspace}g., NGC 4594, at center), then the part of the galaxy that is like an elliptical (e.{\thinspace}g., M{\thinspace}87, at left)
is the high-surface-brightness, centrally concentrated component that is thicker than the disk. When the galaxy is seen nearly face-on,
we cannot see such a central thickening. But we know from galaxies like NGC 4594 that the brightness profile of the bulge is
much steeper than that of the disk and extends, near the center, to much higher surface brightnesses than those of the disk.
NGC 1353 in Fig.\ts1.21 shows a clear separation between the high-surface-brightness central (pseudo)bulge and the outer
exponential disk. It also illustrates how we decompose the surface brightness profile of a face-on galaxy into bulge and disk parts
that add up to the observed profile. Bulge-disk decomposition is discussed in Section 1.7.4.1. Here, I note the surrogate definition
of a bulge that is used when a galaxy is seen nearly face-on: it is the central part of the galaxy that is defined by the extra light
above the inward extrapolation of the outer, exponential or S\'ersic disk profile. That is, the bulge-dominated part of NGC 1353
is the part at $r$ \lapprox \ts10$^{\prime\prime}$. It happens to be a pseudobulge rather than a classical bulge, but this does
not affect the surrogate definition.
The good news is that classifying bulges by using the surrogate definitions is easy. The bad news is that we don't know what
they are physically. That is, there is no guarantee that the surrogate definitions always identify central components that originate
via the same formation physics. In fact, I will try to convince you in this section that the surrogate definitions often
identify high-surface-brightness central components that are nothing like ellipticals, especially in late-type galaxies.
\vfill\eject
Therefore, I adopt a different approach that is more physically motivated but also more hazardous (Kormendy \& Kennicutt 2004).
I define classical bulges to be elliptical galaxies that happen to live in the middle of a disk. For this to make
sense physically, we need to check that there exist central components of disk galaxies that have essentially all of the properties
of comparable-luminosity elliptical galaxies. This check has been made; it is discussed in Sections 1.7.4.4 and 1.8.1.
The intention is that classical bulges, like ellipticals, form via major galaxy mergers. In contrast, I define a pseudobulge as the
dense central part of a galaxy -- either a thick component that bulges above and below an edge-on disk or the extra light at small
radii above the inward extrapolation of the outer disk profile -- that was constructed from the disk by (mostly) secular processes.
For this definition to make sense, we need to see convincing evidence that secular disk evolution happens and that it
makes pseudobulges that we know how to identify. We have such evidence; the classification criteria are listed in Section 1.5.3.
There turn out to be three generic kinds of pseudobulges (Fig.~1.22).
These definitions involve different practical problems. We always know what we are talking about physically. But it may be
difficult to apply the classification criteria. I prefer this problem to the ones above that are inherent in a descriptive classification.
My job in the rest of this section is to present the case for a physically motivated definition of pseudobulges.
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./Pseudobulge-3kindslo.eps hoffset=21 voffset=-14 hscale=52 vscale=52}
\caption{Powerpoint slide illustrating three kinds of pseudobulges. Section 1.5.2.9 discusses boxy pseudobulges
as vertically buckled bars. Construction of disky pseudobulges is discussed here. For nuclear bars, see
Section 1.5.2.8.}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\def{\it et al.\ }{{\it et al.\ }}
\subsection{The response of gas to a rotating bar:\\Construction of outer rings, inner rings and pseudobulges}
Figure 1.23 shows the fundamental results of bar-driven secular evolution. The disk spreads (Section 1.2).
Gas at large radii gains angular momentum; it moves to still larger radii and is shepherded into an outer ring near OLR.
This is identified with the outer rings in (R)SB galaxies (Fig.~1.24). Gas at small radii gives up some
of its angular momentum and falls to the center. High-density gas likes to make stars; we see starbursts
in \hbox{Figs.~1.29\thinspace\ts--\ts1.31}. We identify the result as a pseudobulge. In between, gas is focused into
a ring around the end of the bar, the inner ring seen in SB(r) galaxies~(Fig.\ts1.24).
\vfill
\begin{figure}[hb]
\special{psfile=./Simkin-Su-Schwarzlo.eps hoffset=-7 voffset=-18 hscale=61 vscale=61}
\caption{Gas particle distributions in a ``sticky particle'' simulation of the response
of cold gas to a rotating bar. The bar is not shown but, in each panel, is horizontal and has a diameter equal to
that of the inner ring in the last panel. The panels show the gas response after 2, 3, 5 and 7 bar rotations
(numbers at upper-right in each panel). The arrows in the first and last panels indicate the position of the inner
Lindblad resonance (ILR), the corotation resonance (CR) and the outer Lindblad resonance (OLR). From Simkin {\it et al.\ } (1980).}
\end{figure}
\eject
Figure\ts1.24 shows the close correspondence between the features produced in the Simkin {\it et al.\ } (1980)
simulation and the morphology of barred galaxies. More sophisticated hydrodynamic calculations clarify
the physics (Fig.~1.26), but it is remarkable that just letting gas particles stick together when they
collide is enough to reach the most basic conclusions.
\vfill
\begin{figure}[hb]
\vspace{4.45 truein}
\special{psfile=./ESO4262-N2217-N3945-N3081lo.eps hoffset=-2 voffset=-15 hscale=59.5 vscale=59.5}
\caption{Examples of galaxies which show the morphological features that were produced in the sticky particle
simulation of Simkin {\it et al.\ } (1980). NGC 3945 is from a photographic plate that I took with the Mount
Wilson 100-inch telescope; the others are from the {\it de Vaucouleurs Atlas of Galaxies} (Buta {\it et al.\ } 2007).
All four galaxies have complete or almost complete outer rings (R). ESO 426-2 and NGC 3081 have both
an outer ring and an inner ring (r); such galaxies are rare. NGC 2217 contains a lens component that
is filled by the bar in one dimension. NGC 3945 and NGC 3081 are also illustrated in Fig.~1.17.
Additional galaxies with similar morphology are shown in Figs.~1.3, 1.6, 1.8, 1.9, 1.17, 1.36, 1.37 and 1.45.}
\end{figure}
\eject
Figure 1.25 explores the difference between SB(r) and SB(s) galaxies. Sanders \& Tubbs (1980) investigated how the
response of gas to a bar varies with bar pattern speed and strength. Fast bars have small corotation radii; e.{\thinspace}g.,
$r_{\rm cor}$/(disk scale length) = 0.7 in the bottom-left model panel. They drive SB(s) structure like that in NGC 1300.
Slower bars end near corotation ($r_{\rm cor}/a = 1.1$) and drive SB(r) structure like that in NGC 2523. Since bars slow
down as they evolve (Fig.~1.13) and since it takes time to collect gas into an inner ring,
we conclude that SB(s) galaxies are dynamically young and that SB(r) galaxies are dynamically mature.
\vfill
\begin{figure}[hb]
\vfill
\special{psfile=./SandersTubbs346N1300N2523kylo.eps hoffset=50 voffset=-13 hscale=43.5 vscale=43.5}
\caption{Contours of steady-state gas density in response to a bar (adapted
from Sanders \& Tubbs 1980, who also show intermediate cases). The bar is horizontal and has a length equal to four
axis tick marks. The top row explores the effect of varying the ratio $M_B/M_D$ of bar mass to disk mass.
The second row varies the bar axial ratio $b/a$. The third row varies the bar pattern speed, parametrized by the
ratio $r_{\rm cor}/a$ of the corotation radius to the disk scale length. The middle column is the same standard model
in each row; it resembles the SB(r) galaxy NGC 2523. The left panels resemble the SB(s) galaxy NGC 1300.
The right panels take the parameters to unrealistic extremes; they do not resemble real galaxies.
}
\end{figure}
\cl{\null} \vskip -30pt
\eject
Consistent with this conclusion is the observation (Sandage 1975) that dust lanes on the rotationally
leading sides of bars are common in SB(s) galaxies but rare in SB(r) galaxies (cf.~Figs.~1.6, 1.24, 1.25).~The
gas between the inner ring and the pseudobulge has largely been depleted in SB(r) galaxies (see
Kormendy \& Barentine 2010:~Fig.~1.46 here and Barentine \& Kormendy 2012 for examples).
Sanders \& Tubbs (1980) also investigated the effects of varying the strength of the imposed bar potential,
measured both by the ratio of bar mass to disk mass $M_B/M_D$ (top row of simulation results in Fig.~1.25) and by the
axial ratio $b/a$ of the bar (middle row of simulation results). Very weak bars ($M_B/M_D = 0.13$) or bars that
are not very elongated ($b/a = 1/2$, more like an oval disk than like a bar) produced weak SB(s) structure that
does not resemble well developed SB(s) galaxies such as NGC 1300. Parameters that are more realistic in matching
strongly barred galaxies ($M_B/M_D = 0.53$, $b/a = 1.4$, and $r_{\rm cor}/a = 1.1$; i.{\thinspace}e., the standard model
shown in the middle column of model results) provided the best match to an SB(r) galaxy. This model shows a linear
maximum in gas density that is parallel to the bar and offset from it in the forward rotation direction like the straight
dust lanes in SB(s) galaxies. But the bar potential and gas content are imposed by the initial conditions; they are
not self-consistently evolved from more axisymmetric initial conditions. This accounts for the (rarely observed)
coexistence of the offset gas density maximum in the bar and the (r) structure. Finally, note that,
when the bar is much stronger than bars in real galaxies ($M_B/M_D = 2.7$) or much slower than in real galaxies
($r_{\rm cor}/a = 3$), the gas response fails to resemble that in observed galaxies.
Better simulations generally confirm and expand on the above conclusions (e.{\thinspace}g.,
Salo {\it et al.\ } 1999;
Rautiainen \& Salo 2000;
Rautiainen {\it et al.\ } 2005;
Treuthardt {\it et al.\ } 2009;
see Kormendy \& Kennicutt 2004 for further review).
In particular, detailed hydrodynamic models of the gas response in the region of the bar confirm the offset density
maximum seen in the Sanders \& Tubbs (1980) model and greatly clarify the nature of bar-driven secular evolution.
The most illuminating simulations are by Athanassoula (1992), shown here in Fig.~1.26. She explored
the response of inviscid gas to an imposed bar, concentrating on the production of gas shocks and their relation
to dust lanes. If the mass distribution is sufficiently centrally concentrated to result in an ILR, then she
found that straight gas shocks~-- which we identify with dust lanes -- are produced that are offset in the forward
(rotation) direction from the ridge line of the bar. The ``$x_2$ orbits'' that align perpendicular to the bar inside
ILR push the offset to be largest near the center. This is seen in Fig.~1.26 and Fig.~1.27 as well as in Fig.~1.5 and Fig.~1.6.
\vfill\eject
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./Athanassoula-N1365-Vlo.eps hoffset=5 voffset=-14 hscale=59 vscale=59}
\caption{Comparison of the gas response to a bar (Athanassoula 1992 model 1) with NGC 1365.
The galaxy image is from the VLT and is reproduced courtesy of ESO. In the models, the bar
potential is oriented at $-45^{\circ}$ to the vertical, parallel to the lowest-density (dark)
part of the gas density grayscale distribution at upper-left. The bar axial ratio is 0.4 and its
length is approximately half of the box diagonal. The top-right panel shows the velocity field;
arrow lengths are proportional to flow velocities. Discontinuities in gas velocity indicate
shocks at the narrow ridge lines of high gas density in the upper-left panel. High gas
densities are identified with dust lanes in real galaxies. The model correctly reproduces the
observations that dust lanes are offset in the forward rotation direction from the ridge line of
the bar, that they are offset by larger amounts nearer the center, and that very near the center,
they curve and become nearly azimuthal. The bottom-right panel shows the H{\thinspace}{\sc i} velocity
field of NGC 1365 from Lindblad {\it et al.\ } (1996). The contour interval is 20 km s$^{-1}$. The
velocity contours crowd strongly in the dust lanes shown at lower-left (the scales of the two
panels are slightly different). This supports the interpretation that the dust lanes
are signatures of shocks in the gas velocity field. Shocks are signs that the gas
loses energy. It must fall toward the center. In fact, NGC 1365 has high gas densities and
active star formation in its bright center (Lindblad 1999; Curran {\it et al.\ } 2001a, b).
Adapted from Fig.~7 of Kormendy \& Kennicutt (2004).}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The consequence of shocks is that they inevitably imply that gas flows toward the center.
Because the shocks are nearly radial, gas impacts them at a steep angle. Therefore the velocity that is
lost in the shock is mainly rotational. This robs the gas of energy and forces it to fall toward the center.
Important confirmation of these results is provided by the observation that H{\thinspace}{\sc i}
gas velocity contours crowd closely just where we observe dust lanes in optical images (e.{\thinspace}g., NGC 1365
in Fig.~1.26 and NGC 1530 in Fig.~1.27). The H{\thinspace}{\sc i} observations do not have high enough spatial resolution
to prove that a shock must be present, but the rapid change in the velocity field coincident with the dust
lane strongly supports the above evolution picture.
It is easy to get a heuristic understanding of the gas velocity field shown in Fig.~1.26.
Gravitational torques produced by the bar accelerate the gas as it approaches the bar. As a result,
it climbs to larger radii as it crosses the ridge line of the bar. Then, as it leaves the bar, the bar
potential minimum is behind the gas and decelerates it. Incoming gas overshoots a little before it plows
into the departing gas, so the shocks are nearly radial but offset from the ridge line of the bar in the
rotationally forward direction.
\vfill
\begin{figure}[hb]
\special{psfile=./N1530-Image-Vlo.eps hoffset=-7 voffset=-15 hscale=61 vscale=61}
\caption{NGC 1530 is another excellent example of the crowding of H{\thinspace}{\sc i} velocity contours at the
position of the dust lane in an SBb galaxy. The image is from
{\tt http://www.caelumobservatory.com/gallery/n1530.shtml} courtesy of Adam Block.
The velocity field is from Regan {\it et al.\ } (1997) courtesy of Michael Regan.}
\end{figure}
\eject
Do observations show central concentrations of gas in barred galaxies and in other galaxies (e.{\thinspace}g.,
oval disks) in which the above secular evolution is expected to happen? And do they {\it not\/} show such
central gas concentrations in the {\it absence\/} of engines for secular evolution? Figure 1.28 provides six
examples of the general result that the answer is ``yes''.
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./BIMA-labelslo.eps hoffset=-8 voffset=-19 hscale=62 vscale=62}
\caption{Radial profiles of CO gas and stellar $K$-band surface brightness from the BIMA SONG (Fig.~20 from Kormendy \&
Kennicutt 2004, adapted from Regan {\it et al.\ } 2001). CO surface brightness is in magnitudes of Jy km s$^{-1}$ arcsec$^{-2}$
with zeropoint at 1000 Jy km s$^{-1}$ arcsec$^{-2}$. The stellar surface brightness profiles have been shifted
vertically to the CO profiles. Morphological types are from the RC3 (de Vaucouleurs {\it et al.\ } 1991) and oval disks are
identified in Kormendy \& Kennicutt (2004). NGC 4736 is a prototypical pseudobulge also illustrated in
Figs.~1.3, 1.6 and 1.8.
All galaxies in this figure except NGC 7331 have structures that are expected to cause gas to flow toward the center.
NGC 7331 is included to show the very different CO profile in a galaxy with a probable classical bulge (cf.~Fig.~1.29).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
What happens to the infalling gas? Concentrated into a small volume, it gets very dense.
Crunching gas likes to make stars. The Schmidt~(1959)~-- Kennicutt (1989, 1998a, 1998b) law that star formation
rates increase faster than linearly with gas density makes this explicit (Fig.~1.32 here). Confirming our
expectations, observations point to enhanced star formation, often in spectacular starbursts, near the centers of barred
and oval galaxies. In particular, {\it Spitzer Space Telescope\/} mid-infrared observations in the 24 $\mu$m bandpass
are sensitive to warm dust that reradiates light from hot young stars (Fig.~1.29). Survey results by Fisher (2006) and
Fisher {\it et al.\ } (2009) show ubiquitous central star formation in medium- and late-type barred and oval galaxies but not
in galaxies with classical bulges (Fig.~1.29).
\cl{\null}
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./SpitzerMIPS-SFRlo.eps hoffset=-15 voffset=-19 hscale=63.6 vscale=63.6}
\caption{Powerpoint slide showing typical high central star formation rates (SFRs) in galaxies
that contain driving agents for secular evolution (bars and oval disks) but not in galaxies
that contain no driving agent (NGC 3521).~A schematic galaxy spectrum (top right, from
Kennicutt 2003) shows the separate, roughly black body spectra of stellar populations in galaxies
(``stars'') and of warm dust (``dust''). The {\it Spitzer Space Telescope} MIPS 24 $\mu$m bandpass
is sensitive to dust that reradiates light from young stars. Thus SFRs are high where galaxies are bright at
24 $\mu$m. The upper row of images from the {\it Carnegie Atlas of Galaxies}
(Sandage \& Bedke 1994) show typical galaxies in $B$ band. The bottom row of {\it Spitzer\/}
24 $\mu$m images show high central SFRs in the pseudobulges of NGC 1566 and NGC 3351 but not in
the classical bulge of NGC 3521. This figure appears courtesy of David B.~Fisher.}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
More detailed views of this star formation are shown in Figs.~1.30~and~1.31. Figure 1.30 shows NGC 5236, a particularly close
and well known example. The dust lanes on the rotationally trailing sides of the spiral arms are believed to have the same cause
as the ones on the leading sides~of~the~bar: they trace shocks where the gas enters the spiral arms. Star formation is triggered
there by gas compression. Since $\Omega > \Omega_p$, the gas moves forward, beyond the shock, during the time that it takes
stars to form. As a result, the ridge line of bright young stars and H{\thinspace}{\sc ii} regions that ``are strung out like pearls along the arms''
(Baade 1963) is offset forward of the dust lanes. Our picture of how spiral density waves stimulate star formation and hence are traced by
young stars is discussed in
Roberts (1969);
Dixon (1971);
Shu {\it et al.\ } (1973) and
Roberts {\it et al.\ } (1975) and is reviewed in
Toomre (1977b).
Returning to bar-driven inward gas transport and its consequences, the central regions of NGC 5236 are dominated by
intense star formation
(Harris {\it et al.\ } 2001;
Knapen {\it et al.\ } 2010).
Similarly, the whole of the central region of NGC 1365 (Fig.~1.26) is undergoing a starburst
(Kristen {\it et al.\ } 1997;
Galliano {\it et al.\ } 2008;
Elmegreen {\it et al.\ } 2009)
A less intense but still prototypical example is NGC 1300 (Fig.~1.6; Knapen {\it et al.\ } 2006; Comer\'on {\it et al.\ } 2010).
Spiral galaxies in which there is no significant ILR and in which the spiral structure extends to the center
can also have central starbursts (for example, NGC 4321,
Knapen et al.~1995a, b;
Sakamoto et al.~1995).
\vfill
\begin{figure}[hb]
\special{psfile=./M83-VLT-HSTlo.eps hoffset=-10 voffset=-17 hscale=62 vscale=62}
\caption{M{\thinspace}83 = NGC 5236 is a prototypical face-on SAB(s)c galaxy with dust lanes on the trailing sides of the
spiral arms and the leading sides of the bar. The center is undergoing
a spectacular starburst. The left image is from
the ESO VLT ({\tt http://www.eso.org/public/images/eso9949a/} with color balance tweaked
to better match the enlargement at right, which is a Hubble Heritage image).
\omit{({\tt http://heritage.stsci.edu/2009/29/index.html}).}
}
\end{figure}
\eject
Nuclear starburst rings are particularly compelling examples of the star formation that -- we suggest -- results
from inward transport~of~disk~gas. Figure 1.31 shows examples. Three of these galaxies are barred, but NGC~4736
is in my prototypical unbarred, oval galaxy (Figs.~1.3, 1.6, 1.8). It emphasizes again that numerical simulations
and observations both imply that oval galaxies evolve secularly in the same way that barred galaxies do.
\vfill
\begin{figure}[hb]
\vspace{4.45 truein}
\special{psfile=./SB-NuclearStarForm-rev-4736lo.eps hoffset=-2 voffset=-18 hscale=59.5 vscale=59.5}
\caption{Nuclear star-forming rings in barred and oval galaxies (update of Fig.~8 in Kormendy \& Kennicutt 2004).
Sources: NGC 4314 -- Benedict {\it et al.\ } (2002);
NGC 1326 -- Buta {\it et al.\ } (2000) and Zolt Levay (STScI);
NGC 1512 -- Maoz {\it et al.\ } (2001);
NGC 4736 -- Zolt Levay (STScI).
The NGC 4736 panel was made from nonoverlapping images in the bandpasses indicated by the colors used in
these RGB renditions.~All colors are available in only two places around the ring, but they make it clear
that this star-forming ring in a prototypical oval galaxy (see Figs.~1.3, 1.6 and 1.8)
is closely similar to the other nuclear rings, which occur in barred galaxies. Note that these
nuclear rings are distinct from and always smaller than the inner rings that encircle bars (see
point (f) in Section 1.3.1).
}
\end{figure}
\eject
The star formation discussed in this section is not associated with galaxy mergers and instead is closely
connected with probable engines for secular evolution and with observed features (such as radial dust lanes
in bars) which suggest that such evolution is in progress. We conclude with some confidence that it is building
pseudobulges. Are the gas supplies and star formation rates (SFRs) consistent with reasonable growth times for
pseudobulges of the observed masses?
Kormendy \& Kennicutt (2004) address this for nuclear star-forming rings (Fig.~1.32). The rings have larger
SFR densities $\Sigma_{\rm SFR}$ and total gas densities $\Sigma_{\rm gas}$ than do spiral galaxies in general,
defining a Schmidt-Kennicutt relation similar to the well known $\Sigma_{\rm SFR} \propto \Sigma_{\rm gas}^{1.4}$.
Absent continued gas infall, the \phantom{00000000000000000}
\vfill
\begin{figure}[hb]
\special{psfile=./SFR-GasDensitylo.eps hoffset=18 voffset=-20 hscale=52 vscale=52}
\caption{Correlation between SFR surface density and total gas surface density for circumnuclear star-forming rings
(filled squares) compared to disk-averaged values for spiral galaxies (filled circles) and the
centers of these galaxies (open circles). The nuclear ring data are compiled in Kormendy \& Kennicutt (2004, from
which this figure is taken); the other data are from Kennicutt (1998b). Diagonal lines show
gas consumption timescales if no additional gas is supplied to the central region.
}
\end{figure}
\eject
\noindent currently available gas would be consumed in $\sim$\ts0.2\thinspace--\ts2 Gyr. However, I have argued that the
central gas is continually replenished. Thus the observed SFRs of
0.1\thinspace--\ts10 $M_\odot$ yr$^{-1}$ are consistent with the formation of pseudobulges with masses $\sim$\thinspace$10^8$\thinspace--\thinspace$10^{10}$
$M_\odot$ over several Gyr. These values are reasonable.
Fisher {\it et al.\ } (2009) and Fisher \& Drory (2010) use the {\it Spitzer Space Telescope\/} to study SFRs and star formation
histories in classical and pseudo bulges in detail. They conclude (2009) that ``All bulges are found to be forming
stars irrespective of bulge type (pseudobulge or classical bulge). [However,] classical bulges have the lowest specific SFR
[SFR per unit stellar mass], implying growth times that are longer than a Hubble time, thus the present-day SFR does not
likely play a major role in the evolution of classical bulges. [In contrast,] at present-day SFRs, the median pseudobulge
could have grown the present-day stellar mass in 8 Gyr. In almost all galaxies in our sample, the specific SFR of the bulge
is higher than that of the outer disk.
This suggests that almost all galaxies are increasing their $B/T$ through internal star formation. The SFRs in pseudobulges
correlate with their structure. More massive pseudobulges have higher SFR density, this is consistent with the stellar
mass being formed by moderate, extended star formation. Bulges in late-type galaxies have similar SFRs as pseudobulges in
intermediate-type galaxies and are similar in radial size. However, they [have lower masses]; thus, they have much shorter
growth times, $\sim$\ts2 Gyr. Our results are consistent with a scenario in which bulge growth via internal star formation
is a natural and near ubiquitous phenomenon in disk galaxies.''
I want to emphasize the contrast between star formation in major mergers and star formation during secular evolution
(Kormendy \& Kennicutt 2004). Merger starbursts last \lapprox ~{\kern -1pt}a few hundred million years. Most classical
bulges and ellipticals are seen long after the assembly events that constructed them. Therefore, they are mostly seen
to contain old stars. In contrast, secular
evolution is inherently long-term. Except in S0 pseudobulges, we usually see star formation in action.
{\it If star formation is ubiquitous, it must be secular.}
As a result, ongoing star formation that is not observed to be associated with morphological indicators of a merger in progress
(such as tidal tails) is the first pseudobulge classification criterion listed in Section 1.5.3.
{\it We have a detailed picture of internal secular evolution in galaxy disks. Central molecular gas concentrations
and starbursts are closely associated with bars and oval disks that act as evolution engines. They are not generally
found in classical bulges. They are also closely associated with dust lanes and H{\thinspace}I velocity crowding in bars that are
signatures of secular evolution. These correlations argue in favor of internal secular evolution and against the
idea that these features could be produced by large numbers of minor mergers.}
\subsection{The observed properties of pseudobulges}
Quoting Kormendy \& Kennicutt (2004): ``How can we tell whether a (pseudo)bulge is like an elliptical or
whether it formed secularly? The answer and the theme of this section is that pseudobulges retain enough
memory of their disky origin so that the best examples are easily recognizable.'' As we move from ``proof of concept''
into work on large samples of galaxies, we will have to face the difficulty that classification gets difficult when --
as we must expect -- both a classical bulge and a subsequently grown pseudobulge are present. In such cases, bulge-pseudobulge
decomposition is necessary (e.{\thinspace}g., Erwin {\it et al.\ } 2003). In this
section, I discuss the properties of more prototypical, pure pseudobulges to show how they differ from classical bulges
and ellipticals. Section 1.5.3 then lists the classification criteria, numbered according to the subsections in the following
discussion.
\subsubsection{Pseudobulges of spiral galaxies show ongoing star formation}
As noted in the previous section, ongoing {\it central\/} star formation in relatively normal spiral galaxies that show
no signs of a merger in progress is a strong pseudobulge indicator. The work by Fisher {\it et al.\ } (2009, 2010) shows that such
star formation is generally present in morphologically classified pseudo but not classical bulges. If star formation
is ubiquitous, it must be secular.
\subsubsection{Pseudobulges are flatter than classical bulges}
This is a two-part criterion. First, when the galaxy is highly inclined and the ellipticity profile
$\epsilon(r)$ tells us the relative flattening of various components, pseudobulges are often (not always)~seen to be flatter
than classical bulges. Commonly a part of them is as flat as the associated outer disks. Second,
pseudobulges in spiral (but not S0) galaxies usually show spiral structure all the way to the center of the galaxy. Classical bulges,
like ellipticals, are essentially never flatter than $\epsilon = 0.6$ . They cannot show spiral structure.
This classification criterion can be applied even to face-on galaxies.
The connection between pseudobulge flatness and secular evolution has been made since the earliest papers on this subject.
Kormendy (1993b) describes the prototypical pseudobulge in NGC 4736 like this: ``The central brightness profile
is an $r^{1/4}$ law that reaches the high central brightness characteristic of a bulge (Boroson 1981). However, the $r^{1/4}$-law
component shows a nuclear bar and spiral structure to within a few arcsec of the center. Bars are disk phenomena. More
importantly, it is not possible to make spiral structure in a bulge. Thus the morphology already shows that the $r^{1/4}$-law
profile belongs to a disk. This is shown more quantitatively by [rapid rotation]'', which is discussed here in Section 1.5.2.3.
The importance of spiral structure is further emphasized by Courteau {\it et al.\ } (1996): ``Many of these [late-type] galaxies
[in their sample] show spiral structure continuing into the central regions. \dots~We invoke secular dynamical evolution and
gas inflow via angular momentum transfer and viscous transport'' as the interpretation of the disky central structure.
Spectacular examples of disky pseudobulges often with spiral structure emerge from {\it HST} imaging surveys.
The best known of these is by Carollo and collaborators
(Carollo {\it et al.\ } 1997, 1998;
Carollo \& Stiavelli 1998;
Carollo 1999;
Carollo {\it et al.\ } 1999, 2002;
Seigar {\it et al.\ } 2002).
They refer to bulges that are structurally unlike ellipticals as ``irregular bulges'' and note that:
``The widespread presence of star formation in the irregular bulges support scenarios in which a fraction of bulges
form relatively late, in dissipative accretion events driven by the disk.'' Figures 1.33 and 1.34 show examples.
\cl{\null}
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./N1353lo.eps hoffset=-12 voffset=-19 hscale=62 vscale=62}
\caption{NGC 1353 pseudobulge: the images show (left to right and top to bottom)
the 2MASS $JHK$ image with a field of view of 4\md4 $\times$ 4\md4 (Jarrett {\it et al.\ } 2003),
an {\it HST\/} WFPC2 F606W image (Carollo {\it et al.\ } 1998), and
an 18$^{\prime\prime}$ $\times$ 18$^{\prime\prime}$ zoom of the F606W image.
The plots show surface photometry with the {\it HST\/} profile shifted to the $K$ band;
$\mu$ is surface brightness, $\epsilon$ is ellipticity and PA is position~angle.
A bulge-disk decomposition of the major-axis profile into a S\'ersic function plus an exponential disk
(curves) shows that a ``bulge'' dominates at radii $r$ \lapprox \ts10$^{\prime\prime}$.
This component is identified as a pseudobulge
(1) because it has the same apparent flattening as the disk (compare the 18$^{\prime\prime}$ and large-field views),
(2) because it shows small-scale spiral structure that can only be sustained in a disk,
(3) because patchiness indicates the presence of dust and star formation and
(4) because its S\'ersic index $n = 1.3 \pm 0.3$ is less than 2. From Kormendy \& Kennicutt (2004) which shows
more examples.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Figure 1.34 shows {\it HST\/} images of the central parts of Sa\thinspace--{\thinspace}Sbc galaxies. All show flat shapes, spiral structure, of
patchy star formation. These are the central regions that, by the surrogate definitions, would be identified as the
galaxies' bulges. It seems safe to conclude that no one who saw these images would define bulges as mini-ellipticals that live
at the centers of disks.
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./CarolloMosaic-log-textlo.eps hoffset=29 voffset=-16 hscale=56.5 vscale=56.5}
\caption{Sa -- Sbc galaxies whose ``bulges'' have disk-like properties. Each panel shows an 18$^{\prime\prime}$ $\times$
18$^{\prime\prime}$ region around the galaxy center extracted from {\it HST\/} WFPC2 F606W images taken and kindly provided
by Carollo {\it et al.\ } (1998). North is up and east is at left. Intensity is proportional to the logarithm of the galaxy surface
brightness. From Kormendy \& Kennicutt (2004).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Pseudobulges are more rotation-dominated than classical bulges}
Pseudobulges were first recognized because rotation is more important with \hbox{respect to random motions than it is in classical
bulges. Via~the~\hbox{$V_{\rm max}/\sigma$\thinspace--\thinspace$\epsilon$}} diagram (Fig.\ts1.35) for galaxies such as NGC\ts3945 and NGC\ts4736,
Kormendy (1982a,{\thinspace}b) concluded that some ``SB bulges are more disklike than SA bulges'' and: ``{\it a significant
fraction of the bulge in many SB galaxies may consist of disk gas which has been transported to the center by the bar.~As the gas accumulates,
it forms stars and builds up a centrally concentrated stellar distribution which is photometrically like a bulge but dynamically like a disk.}''
Again, the fundamental ideas about secular evolution have been with us for a long time. These results are brought up to date with more
recent long-slit spectroscopy in Fig.\ts1.35. The result is that $V_{\max}/\sigma$ is larger at a given $\epsilon$ in pseudobulges
(most filled symbols) than in classical bulges (open symbols) or in ellipticals (crosses).
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./vose-iau153-rome-BWlo.eps hoffset=30 voffset=-18 hscale=49 vscale=49}
\caption{Relative importance of rotation and random velocity as a function
of ellipticity $\epsilon$ = (1\thinspace$-${\thinspace}axial ratio) for various kinds of
stellar systems. Here $V_{\rm max}/\sigma$ is the ratio of the maximum rotation
velocity to the mean velocity dispersion interior to $r_e$. The
``Oblate'' line describes oblate-spheroidal systems that have
isotropic velocity dispersions and that are flattened by rotation;
it is a consequence of the tensor virial theorem (Binney \& Tremaine 1987).
From Kormendy \& Fisher (2008).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The disky dynamics of pseudobulges are beautifully illustrated by the SAURON team's integral-field
spectroscopy. This result is particularly important, so Figs.~1.36 and 1.37 show three examples in detail.
In Fig.~1.36, the surface brightness profile tells us the part of NGC 4274 that the surrogate definitions
would identify as the bulge. It dominates at $r$ \lapprox \ts10$^{\prime\prime}$. The two-dimensional
kinematic and line-strength maps then show that, compared to the rest of the inner parts of the galaxy,
the component at $r$ \lapprox \thinspace\ts10$^{\prime\prime}$ rotates more rapidly, has a lower velocity dispersion,
and has stronger H{\thinspace}$\beta$ absorption lines. The latter result means that the central disky structure
is made of younger stars than the rest of the galaxy. As Falc\'on-Barroso {\it et al.\ } (2006) and Peletier {\it et al.\ }
(2007a, b; 2008) note, all this is very consistent with our picture of bar-driven secular evolution.
Figure 1.37 shows closely similar results for the SB galaxies NGC~3623~and NGC 5689. It is
remarkable how clearly the central component is a rapidly rotating, cold disk in all three
galaxies. The younger ages of the pseudobulges also supports our evolution picture. Note again that
all three galaxies are barred.
\vfill
\vskip 2.truein
\begin{figure}[hb]
\special{psfile=./NGC4274-Peletier-IAU245-2lo.eps hoffset=-13 voffset=-18 hscale=66 vscale=66}
\caption{SAURON integral-field spectroscopy of the disky pseudobulge of the Sa
galaxy NGC 4274. The galaxy is barred, but the bar is foreshortened, because it is
oriented nearly along the minor axis. It fills an inner ring, as is normal in
SB(r) galaxies (Kormendy 1979b).~The brightness profile (upper-right)
is decomposed into a S\'ersic (1968) function plus an exponential disk. The
S\'ersic function has $n = 1.3$, i.{\thinspace}e., $n < 2$, as in other pseudobulges
(Section 1.5.2.6). The pseudobulge dominates the light at radii $r$~\lapprox
\thinspace10$^{\prime\prime}$. The kinematic maps (Falc\'on-Barroso et al.~2006)
show that this light comes from a disky component that is more rapidly rotating (center),
lower in velocity dispersion (right), and stronger in H$\beta$ line strength (left,
from Peletier et al.~2007a) and hence younger than the rest of the inner galaxy.
From Kormendy \& Fisher (2008) as adapted from Peletier {\it et al.\ } (2007b, 2008).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
\begin{figure}[ht]
\vskip 4.79truein
\special{psfile=./N3623lo.eps hoffset=-10 voffset=-18 hscale=62 vscale=62}
\special{psfile=./N5689lo.eps hoffset=-10 voffset=174 hscale=62 vscale=62}
\caption{SAURON integral-field spectroscopy of the disky pseudobulges of the SB0
galaxy NGC 5689 and the SABa galaxy NGC 3623 (adapted from Falc\'on-Barroso {\it et al.\ } 2006).
Again, both bars are oriented nearly along the minor axis. As in NGC 4274, the bar
in NGC 3623 fills an inner ring. Also as in NGC 4274, the kinematic maps show that
both galaxies contain pseudobulges that are prominently disky and more rapidly rotating (center),
lower in velocity dispersion (right), and stronger in H$\beta$ line strength (left) and
hence younger than the rest of the inner galaxy. It is important to emphasize that
pseudobulges generally show more than one (here: three) of the classification criteria
listed in Section 1.5.3).
}
\end{figure}
\cl{\null}
\vskip -40pt
\cl{\null}
\subsubsection{Pseudobulges have small velocity dispersions for their luminosities}
Pseudobulges have smaller $\sigma$ than do classical bulges of the same $M_B$
(e.{\thinspace}g., Kormendy \& Illingworth 1983;
Kormendy \& Kennicutt 2004;
Gadotti \& Kauffmann 2009;
cf.~Falc\'on-Barroso {\it et al.\ } 2006;
Peletier {\it et al.\ } 2007a).~This could partly be due to low $M/L_B$ ratios resulting from young stars.
\clearpage
\subsubsection{Almost all pseudobulges have bulge-to-total ratios $PB/T$ \lapprox \ts1/3.\\
Bulges with $B/T$ $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \ts1.2 are classical.}
Fisher\thinspace\&{\thinspace}Drory (2008) study the properties of \hbox{(pseudo)bulges~in~79, S0\thinspace--{\thinspace}Sc} galaxies to clarify our
classification criteria. They show that, in general, different classification criteria agree in distinguishing pseudobulges
from classical bulges. To do this work, they need first to classify bulges using purely morphological criteria (Fig.~1.38).
This has the disadvantage that morphology alone cannot always identify pseudobulges in S0 galaxies.
But it lets them study a large sample, and it allows a fair test of (for example) the already strong hint (see
Kormendy \& Kennicutt 2004) that the S\'ersic indices of pseudobulges are smaller than those of classical bulges.
\vfill
\begin{figure}[hb]
\special{psfile=./Fisher2008-BulgeImageslo.eps hoffset=36 voffset=-14 hscale=49 vscale=49}
\caption{Morphological features used by Fisher \& Drory (2008; 2010) to classify bulges as classical or pseudo.
Classical bulges have smooth, nearly featureless and nearly elliptical isophotes as do elliptical galaxies
(NGC 3998, NGC~3031~=~M{\thinspace}81). Pseudobulges show one or more of the following:
nuclear bars,
spiral structure, or
patchy star formation (bottom four galaxies).
From Fisher \& Drory (2010).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Fisher \& Drory (2008) measure surface brightness profiles of their galaxies using {\it Hubble Space Telescope\/}
({\it HST\/}) archival images, their own large-field images from the McDonald Observatory 0.9 m telescope and images
from archives such as the Sloan Digital Sky Survey (SDSS). Combining data from many sources provides accurate
profiles over wide dynamic~ranges. They decompose the brightness profiles into disk components with exponential
profiles and (pseudo)bulge components with S\'ersic (1968) function profiles. Figure 1.39 is an example.
This work further confirms the pseudobulge properties discussed in previous sections and provides
several new results:
About half of early-type galaxies contain pseudobulges; almost all Sbc galaxies contain pseudobulges, and
as far as we know, no Sc or later-type galaxy has a classical bulge (see Fig.~1.40). This is in excellent agreement
with results discussed in Kormendy \& Kennicutt (2004).
Pseudobulges are often as flat as their associated disks; classical bulges are thicker
than their associated disks. NGC 3031\thinspace={\thinspace}M{\thinspace}81 and NGC 3169 in Fig.~1.39 are examples.
\vfill
\begin{figure}[hb]
\special{psfile=./Fisher-Decomp1lo.eps hoffset=-12 voffset=-20 hscale=63 vscale=63}
\caption{Photometric decompositions of a galaxy with a classical
bulge (M81,{\thinspace}left) and one with a pseudobulge (NGC 3169). Classification is
carried out as in Fig.~1.38. In the bottom panels, the filled circles are
the major-axis profiles and the solid curves are the S\'ersic function (pseudo)bulge,
the exponential disk and their sum, which is almost invisible atop the data points.
The fit is made between the vertical dashes; note that both galaxies contain
nuclear star clusters (``nuclei'') in addition to their bulges.
The S\'ersic index and the fit RMS are given in the key. The middle panel shows the
deviations of the fit from the data in more detail. The top panel shows the
total ellipticity profile. From Fisher \& Drory (2008).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
\begin{figure*}
\vskip 3.3truein
\special{psfile=./BoverT-Hubble-Fisher-Drorylo.eps hoffset=28 voffset=-17 hscale=52 vscale=52}
\caption{Logarithm of (pseudo)bulge-to-total luminosity ratio $B/T$ versus
Hubble type. Bulges are classified as in Fig.~1.38. Black squares show how the average $B/T$
for pseudobulges and classical bulges together correlates with Hubble type as
expected from its use as a Hubble classification criterion (Sandage 1961). Note: some
pseudobulges have log $B/T$\thinspace$<$\thinspace$-1.6$. From Fisher \& Drory (2008).
}
\end{figure*}
\cl{\null}
\vskip -28pt
Pseudobulge-to-total luminosity ratios are almost always $PB/T$ \lapprox \ts0.35 (Fig.~1.40),
consistent with the expectation that one cannot secularly convert {\it almost all\/} of a disk into a bulge
(Kormendy \& Kennicutt 2004). Small bulge-to-total luminosity ratios $B/T$ do not guarantee that a
bulge is pseudo, but large $B/T$ $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \ts0.5 guarantee that it is classical.
\subsubsection{Most pseudobulges have S\'ersic $n < 2$. Classical bulges have $n \geq 2$.}
Figures 1.33 and 1.36 show that the pseudobulges in NGC 1353 and NGC 4274 have S\'ersic indices
$n = 1.3 \pm 0.3$; i.{\thinspace}e., almost-exponential brightness profiles. The pseudobulge in NGC 3169
(Fig.~1.39) has $n = 1.45 \pm 0.24$, which is still close to exponential. In contrast, the classical
bulge of M{\thinspace}81 has $n = 3.79 \pm 0.39$. This difference turns out to be a general result.
Kormendy \& Kennicutt (2004) review the history of this result.~The~idea that bulges in
late-type galaxies have nearly exponential (not $r^{1/4}$-law) brightness profiles dates back to
work by Andredakis \& Sanders (1994) and Andredakis {\it et al.\ } (1995). At first, no connection was made
to pseudobulges; the result was just that $n$ is smaller in bulges of later-Hubble-type galaxies.
\eject
Then Courteau {\it et al.\ } (1996) carried out bulge-disk decompositions for $>$\ts300 galaxies
and concluded that $>$ 2/3 of them -- especially at late Hubble types -- are best fitted by
double exponentials, one for the bulge and one for the disk. As a diagnostic of formation processes,
Courteau {\it et al.\ } (1996) went on to examine the ratio $h_b/h_d$ of the scale lengths of the inner and outer
exponentials. They found that $h_b/h_d = 0.08 \pm 0.05$ and concluded that: ``Our measurements of exponential
stellar density profiles [in bulges] as well as a restricted range of [bulge-to-disk] scale lengths
provide strong observational support for secular evolution models.
Self-consistent numerical simulations of disk galaxies evolve toward a double
exponential profile with a typical ratio between bulge and disk scale lengths
near 0.1 (D.~Friedli 1995, private communication) in excellent agreement with
our measured values''.
Fisher \& Drory (2008) find closely similar results. The effective radii $r_e$ of pseudobulges and the
scale lengths $h_d$ of their associated disks are coupled, whereas the same is not true for classical
bulges. Specifically, the mean ratio is ${<}r_e/h_d{>} = 0.21 \pm 0.10$ for 53 pseudobulges
but ${<}r_e/h_d{>} = 0.45 \pm 0.28$ for 26 classical bulges. Since $r_e = 1.678{\thinspace}h_b$ for an
exponential, the above result for pseudobulges corresponds approximately to
${<}h_b/h_d{>} = 0.13 \pm 0.06$ (the conversion is approximate because the pseudobulges
are not exactly exponentials). This confirms the results by Courteau {\it et al.\ } (1996) and
similar results by MacArthur {\it et al.\ } (2003). Courteau and MacArthur did not calculate $h_b/h_d$
separately for classical and pseudo bulges and therefore found a correlation with Hubble type
rather than different distributions of $h_b/h_d$ for the two types of bulges. But Courteau and MacArthur,
like Fisher and Drory, interpreted the connection between bulge and disk properties as a sign
that secular evolution and pseudobulge formation become more important at later Hubble
types.
As a result of this and other work (see especially Weinzirl {\it et al.\ } 2009), the connection between pseudobulges and
small S\'ersic indices is by now well established. Classical bulges, on the other hand, have S\'ersic indices like
those of elliptical galaxies, which have $n$ $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \ts2 (e.{\thinspace}g., Kormendy {\it et al.\ } 2009, hereafter KFCB). Moreover,
the S\'ersic indices $n \simeq 2$ to 3 of ellipticals are well understood as natural results of their formation by major
galaxy mergers (e.{\thinspace}g., Hopkins {\it et al.\ } 2009a, c; see Kormendy {\it et al.\ } 2009 for a review). So the connection between
the $n$ $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \thinspace\ts2 S\'ersic indices of classical bulges with their formation by major mergers is also well established.
Therefore, even though we do not fully understand how disk secular evolution determines the resulting
pseudobulge S\'ersic indices, we see strong enough correlations between $n$ and other pseudobulge properties
so that we can use the S\'eersic index as a classification criterion (Figs.~1.41, 1.42).
\vfill\eject
\cl{\null}
\begin{figure*}
\vskip 4.38truein
\special{psfile=./FisherDrory-2008lo.eps hoffset=-9 voffset=-18 hscale=43 vscale=43}
\special{psfile=./FisherDrory-2010lo.eps hoffset=177 voffset=-7 hscale=41.28 vscale=41.28}
\caption{Correlations with (pseudo)bulge S\'ersic index $n_b$ of (top to bottom) bulge absolute magnitude,
effective brightness at (left) or averaged interior to (right) the half-light radius $r_e$ and effective
radius $r_e$. The $V$-band date in the left plots are from Fisher \& Drory (2008); the 3.6 $\mu$m-band
{\it Spitzer Space Telescope} data in the right plots are from Fisher \& Drory (2010). In all panels,
the central components are classified morphologically as in Fig.~1.38.
}
\end{figure*}
\cl{\null}
\vskip -35pt
Therefore classical bulges have S\'ersic $n \geq 2$, whereas pseudobulges usually
have $n < 2$. Note in Fig.~1.41 and in the earlier discussion of NGC 4736 that some pseudobulges
do have S\'ersic indices as big as $n \simeq 4$. Therefore it is always important to apply as many
classification criteria as possible.
\subsubsection{Fundamental plane parameter correlations}
Figure 1.41 provides an introduction to the correlations between effective radius $r_e$, effective brightness
$\mu_e$ at $r_e$, velocity dispersion $\sigma$ and bulge absolute magnitude $M_V$ (the ``fundamental plane'').
Classical bulges satisfy the fundamental plane correlations of elliptical galaxies.
Some pseudobulges do so, too. But many have larger $r_e$ and fainter $\mu_e$ than do classical bulges.
\vfill\eject
\cl{\null}
Figure 1.68 updates the observation that classical bulges and ellipticals have the same correlations.
Simulations of major galaxy mergers reproduce these correlations (e.{\thinspace}g.,
Robertson {\it et al.\ } 2006;
Hopkins {\it et al.\ } 2008, 2009b).
Earlier versions that emphasize pseudobulges are shown in Figs.~1.42 and 1.43. Many pseudobulges
satisfy the correlations for bulges and ellipticals, but in general, they show substantially larger scatter.
\vfill
\begin{figure}[hb]
\special{psfile=./K-Fisher-2008-correlationslo.eps hoffset=10 voffset=-23 hscale=64 vscale=64}
\caption{Structural parameter correlations for pseudobulges (blue), classical bulges (brown), ellipticals (red),
and spheroidal galaxies (green). Pseudobulge data and most bulge points are from Fisher \& Drory (2008).
The ellipticals, five bulge points and the green squares are from Kormendy {\it et al.\ } (2009: KFCB). Green
triangles show all spheroidals from Ferrarese {\it et al.\ } (2006) that are not in KFCB. Crosses show all
spheroidals from Gavazzi {\it et al.\ } (2005) that are not in KFCB or in Ferrarese {\it et al.\ } (2006). Open squares
are Local Group spheroidals (Mateo 1998; McConnachie \& Irwin 2006). The bottom panels show major-axis
S\'ersic index $n$ and effective surface brightness $\mu_e$ versus galaxy or bulge absolute magnitude.
The top panel shows $\mu_e$ versus effective radius $r_e$ (the Kormendy 1977b relation, which shows the
fundamental plane almost edge-on). From Kormendy \& Fisher (2008).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Figure 1.43 shows the $\mu_e$\thinspace--\thinspace$r_e$ correlation from Carollo (1999). I emphasize this version because
it shows more extreme pseudobulges together with spheroidal galaxies, galactic nuclear star clusters and globular clusters.
Spheroidals form a sequence perpendicular to the correlation for ellipticals (Figs.~1.42, 1.61). Globular clusters are
different from both ellipticals and spheroidals (Kormendy 1985, 1987). The comparison that is important here is the one
between bulges plus ellipticals, pseudobulges and galactic nuclei.
Figures 1.42 and 1.43 show that some pseudobulges satisfy the parameter correlations for classical bulges and
ellipticals, but many deviate by having brighter $\mu_e$ (Kormendy \& Bender 2012) or fainter $\mu_e$ (see also
Falc\'on-Barroso {\it et al.\ } 2002;
Kormendy \& Fisher 2008;
Gadotti 2009).
All available data suggest that {\it pseudobulges fade out by becoming low in surface brightness, not by becoming like
nuclear star clusters. Nuclear star clusters are not faint versions of pseudobulges. Indeed, tiny pseudobulges and
normal nuclei coexist in Scd galaxies like M{\thinspace}101 and NGC 6946 (Kormendy {\it et al.\ } 2010).}
The fundamental plane is only secondarily useful for bulge classification. Many pseudobulges satisfy
the correlations for classical bulges, so use of the correlations as the only classification method (Gadotti 2009;
Gadotti \& Kauffmann 2009) is not feasible. Extreme pseudobulges can be identified because their parameters deviate from the E
correlations in Fig.~1.42, but these objects can usually be robustly classified using other criteria anyway.
\vfill
\begin{figure}[hb]
\special{psfile=./Carollo-1999-fig2a-Romelo.eps hoffset=45 voffset=-20 hscale=41.5 vscale=41.5}
\caption{Effective surface brightness versus effective radius for various kinds of stellar
systems (Carollo 1999; this version is from Kormendy \& Fisher 2008).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Nuclear bars}
Figure 1.44 shows examples of nuclear bars at the centers of barred and oval galaxies. Nuclear bars are well known
phenomena (de Vaucouleurs 1959; Sandage 1961; Kormendy 1981, 1982b; Buta {\it et al.\ } 2007; Buta~2011,~2012). They are always
much smaller than the main bars in which they are embedded.~Observations are consistent with the suggestion that their physics
is essentially the same as that of main bars. How they form is not known in detail, but it is reasonable to expect that the
growth of stellar disky pseudobulges out of inflowing cold gas can result in a bar instability.
Pattern speeds $\Omega_p$ of nuclear bars are well predicted by Section 1.4.2. They live at small radii where stellar
densities are high and where $\Omega - \kappa/2$~is~large. So $\Omega_p \sim \Omega - \kappa/2$ should be larger
for nuclear bars than it is for main bars. This is seen in $n$-body models
(Debattista \& Shen 2007;
Shen \& Debattista 2009).
Direct measurement of $\Omega_p$ is difficult, but Corsini {\it et al.\ } (2009) use the Tremaine \& Weinberg (1984) method on
NGC 2950 and conclude that the main and nuclear bars have different pattern speeds.
For present purposes, different $\Omega_p$ is sufficiently well established by the observation that nuclear bars
have random orientations with respect to their main bars (Fig.~1.44).
Bars are disk phenomena.~A nuclear bar therefore identifies a pseudobulge.
\vfill
\begin{figure}[hb]
\special{psfile=./NuclearBarslo.eps hoffset=-10 voffset=-20 hscale=60.5 vscale=60.5}
\caption{Bars within bars. The main bar is rotated until it is horizontal. Contour levels are close together in intensity
at large radii and widely spaced in intensity in the nuclear bars. NGC 3081 and NGC 1433 have inner rings.
NGC 1291 is also shown in Fig.~1.6.
NGC 3081 and NGC 3945 are shown in Figs.~1.17 and 1.24.
The images are courtesy Ron Buta; this figure is from Kormendy \& Kennicutt (2004).
The nuclear bar in NGC 2950 (see above discussion) is illustrated in Fig.~1.17.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Boxy pseudobulges are edge-on bars.}
Section 1.4.3.3 reviews how bars buckle and thicken in the vertical
direction and consequently look like ``box-shaped bulges'' when seen edge-on. These are parts of
disks, so I call them ``boxy pseudobulges''. The one in our Galaxy is particularly clearcut, because we are
close enough to it so that, from our perspective, the near side looks taller than the far side (Fig.~1.45).
\vfill
\begin{figure}[hb]
\special{psfile=./MW-COBE-ShenModel-xlo.eps hoffset=-11.5 voffset=-19 hscale=62.5 vscale=62.5}
\caption{The boxy pseudobulge = almost-end-on bar of our Galaxy in (bottom: from~{\tt
http://www.nasaimages.org/luna/servlet/detail/nasaNAS$\sim$5$\sim$5$\sim$24223}
{\tt $\sim$127634:COBE-s-View-of-the-Milky-Way})
a COBE infrared view
and (top) an $n$-body model from Shen {\it et al.\ } (2010). The top three model panels show the face-on
and side-on views as projected and seen from far away. Seen almost side-on (top), the bar looks
peanut-shaped. Seen almost end-on from the direction of our Sun (right-hand view), it looks boxy
when seen from far away.~Viewed instead~from within our
Galaxy at the position of the Sun (bottom model panel), the near side of the bar is significantly closer
than the far side. Therefore the near side looks taller than the far side,
exactly as in the COBE image (Blitz \& Spergel 1991).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Observations which further show that boxy bulges are edge-on bars are reviewed in Kormendy
\& Kennicutt (2004). The well known example of NGC 4565 (Fig.~1.46, from Kormendy \& Barentine 2010) turns out
to be an SB(r) galaxy with a second, tiny pseudobulge at its center that is distinct from the boxy bar (Fig.~1.47).
\vfill
\begin{figure}[hb]
\special{psfile=./N4565-KB2010lo.eps hoffset=77 voffset=-15 hscale=46.5 vscale=46.5}
\caption{(a) Optical and (b,{\thinspace}c) {\it Spitzer} 3.6 $\mu$m negative images of NGC 4565 shown at
different stretches to emphasize (b) the boxy bar and (c) an inner ring and pseudobulge. The newly
detected pseudobulge is the central bright dot. (d) {\it Spitzer} IRAC 8 $\mu$m negative image
showing PAH emission and therefore star formation from the inner ring and outer disk. Because the inner ring is
dark inside at 8\thinspace$\mu$m, we conclude that the dark inside seen at 3.6 $\mu$m is not caused by dust absorption.
Rather, the ring really is dark inside. Therefore NGC 4565 is an SB(r)b galaxy, i.{\thinspace}e., an almost-edge-on
analog of NGC 2523 (bottom panel). The NGC 2523 image has been scaled so the inner ring has the same apparent
radius as in NGC 4565 and rotated to the apparent bar position angle inferred for NGC 4565. We suggest that
NGC 2523, if oriented as in the bottom panel and inclined still more until we observed it almost edge-on, would
show the features seen in the NGC 4565 images.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Finding the tiny pseudobulge hidden inside the boxy bar of NGC 4565 solves a long-standing puzzle and
cements an important implication for the statistics of $(P)B/T$ luminosity ratios. Compare NGC 4565 with any
more face-on barred galaxy, such as NGC 2523 in Fig.~1.46. Face-on galaxies show a (pseudo)bulge, a bar,
and an outer disk; i.{\thinspace}e., three or more components. The edge-on galaxy NGC 4565
shows only a ``boxy bulge'' and a disk. As long as we thought that boxy distortions were minor features of bulges,
this was no problem -- many unbarred Sb galaxies have just a bulge and a disk. But if the box
in NGC 4565 is an edge-on bar, then the galaxy contains a bar and a disk; i.{\thinspace}e., only two components.~This
is not seen in face-on galaxies except at very late Hubble types. Where is the ``bulge'' in NGC 4565?
Figures 1.46 and 1.47 show the answer. The minor-axis profile of the boxy structure is exponential.
Inside this structure,
there is a clearly distinct, tiny central component that has $n = 1.33 \pm 0.12$ and that therefore is a second,
``disky'' pseudobulge. The important implication is that $PB/T = 0.06 \pm 0.01$ is {\it much smaller\/} than
the value $B/T \simeq 0.4$ (Simien \& de Vaucouleurs 1986) for the box. Closely similar results are found for
the edge-on ``boxy bulge'' galaxy NGC 5746 (Barentine \& Kormendy 2012). Not counting boxy bulges because
they are bars, {\it $(P)B/T$ ratios are much smaller than we have thought for essentially all edge-on galaxies with
boxy bulges. In particular, the {\it classical\/}-bulge-to-total ratio in our Galaxy is $\sim 0$} (Shen {\it et al.\ } 2010).
\vfill
\begin{figure}[hb]
\special{psfile=./f3.eps hoffset=-30 voffset=-94 hscale=61 vscale=61}
\caption{Minor-axis profile of NGC 4565 from Kormendy \& Barentine (2010).
The dashed lines show a decomposition of the profile into components in order of increasing radius:
a Seyfert nucleus (Ho {\it et al.\ } 1997) or nuclear star cluster that is not included in the fit, the
pseudobulge (S\'{e}rsic), box-shaped bar (S\'{e}rsic) and outer halo (exponential). The solid line is the sum of the components.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{Pseudobulges classification criteria}
The bulge-pseudobulge classification criteria updated from Kormendy \& Kennicutt (2004) are listed here for convenience.
They are identified by the number $m$ in the Section 1.5.2.$m$ in which they were discussed.
\begin{enumerate}[e]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[(1){\kern -3pt}]{If the center of the galaxy is dominated by Population I material (young stars, gas and dust),
but there is no sign of a merger in progress, then the bulge is at least {\it mostly\/} pseudo. }
\item[(2){\kern -3pt}]{Pseudobulges often have disky morphology; e.{\thinspace}g., their apparent flattening
is similar to that of the outer disk, or they contain spiral structure all the way in to
the center of the galaxy. Classical bulges are much rounder than their disks
unless the galaxy is almost face-on, and they cannot have spiral structure.}
\item[(3){\kern -3pt}]{Pseudobulges are more rotation-dominated than classical bulges
in the \hbox{$V_{\rm max}/\sigma$\thinspace--\thinspace$\epsilon$} diagram.
Integral-field spectroscopy often shows that the central surface brightness excess over the inward
extrapolation of the outer disk profile is a flat central component that rotates rapidly and that has a
small velocity dispersion.}
\item[(4){\kern -3pt}]{Many pseudobulges are low-$\sigma$ outliers in the Faber-Jackson (1976) correlation between (pseudo)bulge
luminosity and velocity dispersion. A similar signature is that $\sigma$ {\it decreases} from the disk into
the pseudobulge.}
\item[(5){\kern -3pt}]{Small bulge-to-total luminosity ratios do not guarantee that a bulge
is pseudo,~but almost all pseudobulges have $PB/T$ \lapprox \ts0.35.~If $B/T$ $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \ts0.5, the bulge is classical.}
\item[(6){\kern -3pt}]{Most pseudobulges have S\'ersic index $n < 2$, whereas almost all classical
bulges have $n \geq 2$. The processes that determine the small S\'ersic indices of
pseudobulges are not understood, but the correlation of small $n$ with other
pseudobulge indicators is so good that this has become a convenient classification
criterion. Note, however, that some pseudobulges do have S\'ersic indices as big as 4.}
\item[(7){\kern -3pt}]{Classical bulges fit the fundamental plane correlations for elliptical
galaxies. Some pseudobulges do, too, and then these correlations are not helpful for
classification. But more extreme pseudobulges are fluffier than classical bulges;
they have larger $r_e$ and fainter surface brightnesses $\mu_e$ at $r_e$. These
can easily be identified using fundamental plane correlations.}
\item[(8){\kern -3pt}]{In face-on galaxies, the presence of a nuclear bar shows that a pseudobulge dominates the central light.
Bars are disk phenomena. Triaxiality in giant ellipticals involves completely different physics --
slow (not rapid) rotation and box (not $x_1$ tube) orbits. }
\item[(9){\kern -3pt}]{In edge-on galaxies, boxy bulges are edge-on bars; seeing one is sufficient to identify a pseudobulge.
The boxy-nonrotating-core side of the ``E{\thinspace}--{\thinspace}E dichotomy'' of elliptical galaxies into two kinds
(Kormendy {\it et al.\ } 2009) cannot be confused with boxy, edge-on bars because boxy ellipticals -- even if they
occur in disk galaxies (and we do not know of an example) -- are so luminous that we would measure
$B/T > 0.5$. Then point (5) would tell us that this ``bulge'' is classical.}
\end{enumerate}
It is important always to apply as many classification criteria~as~possible.
\vfill\eject
\subsection{Secular evolution and hierarchical clustering}
We now have a well articulated paradigm of secular evolution in galaxy disks that complements our
standard picture of hierarchical clustering. There is no competition between these two galaxy formation pictures --
both are valid, and their relative importance depends on cosmological lookback time and on environment. I have emphasized
that the Universe is in transition from early times when the rapid processes of hierarchical clustering
were most important in controlling galaxy evolution to future times when galaxy merging will largely have finished and
slow, internal processes will dominate.
In the present Universe, the mass in bulges (including ellipticals) and that in disks are roughtly equal
(Schechter \& Dressler 1987;
Driver~{\it et al.}~2007;
Gadotti 2009;
Tasca \& White 2011).
Uncertainties are large, with estimated ratios of the mass in bulges to that in disks as large as
$\sim$\ts2 (Fukugita {\it et al.\ } 1998). One reason is that the relative numbers of disks and merger remnants
is a strong function of environment:~disks predominate in the field, whereas most giant ellipticals live in galaxy clusters (Section\ts1.6.1).
The ratio of mass in classical bulges to that in pseudobulges has not yet been determined for large and unbiased
galaxy samples. It is reasonable to expect that the {\it ratio of masses\/} is not large.
In contrast, the {\it ratio of numbers\/} of pseudobulges to numbers of classical bulges could easily be $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ 1.
Kormendy \& Kennicutt (2004) estimated that most Sa galaxies contain classical bulges, that in Sb galaxies, classical and
pseudo bulges are comparably common and that most Sbc galaxies contain pseudobulges. Recent work suggests that there are
more pseudobulges at early Hubble types than Kormendy \& Kennicutt thought
(Fisher \& Drory 2008;
Weinzirl {\it et al.\ } 2009).
S0 galaxies contain pseudobulges more often than Sa galaxies, consistent with parallel-sequence galaxy classifications in which
S0s form a sequence in $(P)B/T$ that parallels the sequence of spirals (Section 1.7). At late Hubble types, Sc\thinspace--{\thinspace}Im
galaxies appear never to contain classical bulges.~Many Scd\thinspace--{\thinspace}Sm galaxies do not contain pseudobulges, either;
M{\thinspace}33 is an example, and the main reason is that $\Omega(r)$ depends little enough on radius so that it is not energetically
profitable to transport angular momentum outward (Section 1.2.4).
I conclude with a point of perspective from Kormendy \& Kennicutt (2004). In the early 1970s, when I was a
graduate student, Hubble classification was in active use, but we also knew about many regular features in galaxy disks,
such as lens components, nuclear, inner and outer rings, nuclear bars and boxy bulges, that we did not understand and that
often were not even included in the classification. We also knew many peculiar galaxies, no two of which look alike; they did
not fit comfortably into Hubble classification, and we did not understand them, either. Now both the peculiar galaxies and the
structural regularities are becoming well understood within two paradigms of galaxy evolution that got their start in the late 1970s.
The peculiar galaxies were once normal but now are undergoing tidal interactions or are galaxy mergers in progress (Section 1.8.1).
And structures such as rings and lenses that are seen in many galaxies are products of the secular evolution of relatively isolated
galaxy disks. Between collisions, galaxies do not just sit quietly and age their stellar populations. Galaxies represent snapshots
of moments in time during dynamical evolution that goes on today and that will contine to go on for many billions of years to come.
\section{Astrophysical implications of pseudobulges}
The general implications of pseudobulges for galaxy formation are the main subject of this Winter School.~Here, I focus on two
additional astrophysical implications that came -- at least to me -- as a surprise. First is the challenge that classical-bulge-less
galaxies (even ones that contain pseudobulges) present for our picture of galaxy formation by hierarchical clustering and merging.
Second is the lack of any tight correlation between the masses of supermassive black holes and the properties of pseudobulges.
\omit{Some parts of these lecture writeups also overlap my past reviews of this subject (Kormendy 1979a, 1979b, 1981, 1982, 1993, 2008;
Kormendy \& Kennicutt 2004; Kormendy \& Cornell 2004; Kormendy \& Fisher 2005, 2008).}
\subsection{A challenge for our theory of galaxy formation\\by hierarchical clustering and merging:\\Why are there so many pure-disk galaxies?}
Look at any movie of a numerical simulation of hierarchical clustering in action. Your overwhelmingly strong impression
will be that the lives of dark matter halos are violent. They continually collide with and accrete smaller halos,
which -- by and large -- approach from random directions. And virtually no halo grows large\footnote{In this review, as in
Kormendy {\it et al.\ } (2010), I will adopt the sufficient and practical definition that a ``large'' galaxy is one in which the circular orbit rotation
velocities of massless test particles at large radii are $V_{\rm circ} \geq 150$ km s$^{-1}$.} without undergoing at least a few major
mergers between progenitors of comparable mass.
{\it Given this merger violence, how can there be so many bulgeless galaxies? The puzzle has two parts.
How does hierarchical clustering prevent the formation of classical bulges that are the scrambled-up remnants of
the progenitor stars that predate the merger? And how does the merger assembly of galaxy halos prevent the
destruction of large but very flat disks, at least some of which are made in part of old stars. Bulgeless disks are
not rare.}
\vfill\eject
Figure\ts1.48 shows the purest examples of this problem, the iconic \hbox{late-type} galaxies whose edge-on
orientations make it clear that they have no classical bulges and no signs of pseudobulges. Such~galaxies~are~common
(Karachentsev {\it et al.\ } 1993; Kautsch {\it et al.\ } 2006). UGC 7321 is studied~by Matthews {\it et al.\ } (1999a); Matthews (2000);
Banerjee {\it et al.\ } (2010). IC\ts5249 is studied by van der Kruit {\it et al.\ } (2001). Matthews {\it et al.\ } (1999b), Kautsch (2009) and
van der Kruit \& Freeman (2011) review superthin galaxies.
It is a challenge to explain these galaxies. It helps that they~are~not~large: Hyperleda lists rotation
velocities of $V_{\rm circ} = 95$, 79, 97 and 92 km s$^{-1}$ for UGC 7321, IC 2233, IC 5249 and UGC 711, respectively.
This is smaller than $V_{\rm circ}$\thinspace=\thinspace$135 \pm 10$ km s$^{-1}$ in M{\thinspace}33 (Corbelli\thinspace\&{\thinspace}Salucci 2000; Corbelli 2003). \phantom{00000}
\vfill
\begin{figure}[hb]
\special{psfile=./4-Pure-Diskslo.eps hoffset=-10 voffset=-16 hscale=62 vscale=62}
\caption{Edge-on, completely bulgeless, pure-disk galaxies. All images are from {\tt http://www.wikisky.org}; the top
galaxies are from the SDSS and the bottom ones are from DSS. The DSS images have a bluer color balance
than the SDSS.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent Explaining bulgeless disks is least difficult for dwarf galaxies. They suffer fewer mergers and tend to accrete
gas in cold streams or as gas-rich dwarfs
(Maller {\it et al.\ } 2006;
Dekel \& Birnboim 2006;
Koda {\it et al.\ } 2009;
Brooks {\it et al.\ } 2009;
Hopkins {\it et al.\ } 2009d, 2010).
Energy feedback from supernovae counteracts gravity most effectively in dwarf galaxies
(Dekel \& Silk 1986;
Robertson {\it et al.\ } 2004;
D'Onghia {\it et al.\ } 2006;
Dutton 2009;
Governato {\it et al.\ } 2010).
Attempts to explain pure disks have come closest to success in explaining dwarf galaxies
(Robertson {\it et al.\ } 2004;
Governato {\it et al.\ } 2010).
Kormendy {\it et al.\ } (2010) conclude that the highest-mass, pure-disk galaxies are the ones that most constrain our formation picture.
They inventory all giant galaxies ($V_{\rm circ} \geq 150$ km s$^{-1}$) at distances $D \leq 8$ Mpc within which we can resolve small
enough radii to find or exclude even the smallest~bulges. Table 1.3 documents the $B/T$ and $PB/T$ luminosity ratios for these
galaxies. Giant, bulgeless galaxies are not rare. Figure 1.49 shows the most extreme galaxies in which $B/T = 0$ rigorously.
Kormendy {\it et al.\ } (2010) emphasize \phantom{00000}
\vfill
\begin{figure}[hb]
\special{psfile=./M101-N6946-I342-N4945lo.eps hoffset=-10 voffset=-17 hscale=62.5 vscale=62.5}
\caption{Face-on, completely bulgeless, pure-disk galaxies. All four galaxies have bulge-to-total luminosity ratios
of $B/T = 0$. They have the smallest pseudobulges in the local sample of giant galaxies (outer rotation
velocities~$V_{\rm circ}$\thinspace$>$\ts150~km~s$^{-1}$; for these galaxies,~174--210 km s$^{-1}$) in Table 1.3.~The
pseudobulge-to-total luminosity ratios $PB/T$ are given in the figure. Unless otherwise noted, the images are from
{\tt http://www.wikisky.org} or Kormendy {\it et al.\ } (2010).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent that {\it ``we do not have the freedom to postulate classical bulges which have arbitrary properties (such as low surface brightnesses)
that make them easy to hide. Classical bulges and ellipticals satisfy well-defined fundamental plane correlations} (Fig.~1.68).
{\it Objects that satisfy these correlations cannot be hidden in the above galaxies.
So $B/T = 0$ in 4/19 of the giant galaxies in our sample.''} Seven more galaxies contain pseudobulges; since we believe that these are grown
secularly out of disks and not made via mergers, these are pure-disk galaxies from the hierarchical clustering point of view. Four more
galaxies contain classical bulges smaller than any that are made in hierarchical clustering simulations. Only M{\thinspace}31 and M{\thinspace}81 have
classical bulges with $B/T \simeq 1/3$, and only two more galaxies are ellipticals with $B/T = 1$
Fisher \& Drory (2011) derive similar statistics in the $D \leq 11$ Mpc volume.
\vfill
\special{psfile=./table1.3.ps hoffset=-115 voffset=-174 hscale=98 vscale=98}
\cl{\null}
\vskip -28pt
\eject
Kormendy {\it et al.\ } (2010) conclude that {\it giant bulgeless galaxies do not form the rare tail of a distribution of formation histories
that include~a~few fortuitously mergerless galaxies. In the field, the problem of forming giant, pure-disk galaxies by
hierarchical clustering is acute. In contrast, in the Virgo cluster, $_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ \ts2/3 of the stellar mass is in merger
remnants. Therefore the problem of explaining pure-disk galaxies is a strong function of environment.}
This is a sign that AGN feedback, the physics popularly used to address the problem, is not the answer. The effectiveness of
energy feedback depends on galaxy mass. In contrast, galaxies tell us that environment is the controlling factor. Giant,
pure-disk galaxies (Fig.~1.49) are more massive than small ellipticals. And the thin disk of our Galaxy{\thinspace}--{\thinspace}which,
given its boxy bar, is a giant pure-disk galaxy{\thinspace}--{\thinspace}contains stars as old as 10 Gyr (Oswalt {\it et al.\ } 1996; Winget \& Kepler 2008). So I
suggest that the solution to the pure-disk problem is not to use energy feedback to delay disk star formation in order to give the halo
time to grow without forming a classical bulge. I believe that a viable solution must use the environmental dependence of the
pure-disk galaxy problem in an essential way (e.{\thinspace}g., Peebles \& Nusser 2010).
\vskip -24.1pt
\cl{\null}
\subsection{\hbox{Supermassive black holes do not correlate with pseudobulges}}
Kormendy \& Ho (2013) review a modest revolution that is in progress in studies of supermassive black holes
(BHs) in galaxy centers. For~more~than a decade, observed BH demographics have suggested a simple picture
in which BH masses $M_\bullet$ show a single correlation each with many properties of their host galaxies (Fig.\ts1.50).
Most influential was the discovery of a tight correlation between $M_\bullet$ and the velocity dispersion $\sigma$
of the host bulge~at radii where stars mainly feel each other and~not~the~BH
(Ferrarese \& Merritt 2000;
Gebhardt {\it et al.\ } 2000;
Tremaine {\it et al.\ } 2002;
G\"ultekin {\it et al.\ } 2009).
Correlations are also observed between $M_\bullet$ and bulge luminosity
(Kormendy 1993a;
Kormendy \& Richstone 1995;
Magorrian {\it et al.\ } 1998),
bulge mass
(Dressler 1989;
McLure \& Dunlop 2002;
Marconi \& Hunt 2003;
H\"aring \& Rix 2004;);
core parameters of elliptical galaxies
(Milosavljevi\'c {\it et al.\ } 2002;
Ravindranath {\it et al.\ } 2002;
Graham 2004;
Ferrarese {\it et al.\ } 2006;
Merritt 2006;
Lauer {\it et al.\ } 2007;
Kormendy \& Bender 2009),
and globular cluster content
(Burkert \& Tremaine 2010;
Harris \& Harris 2011).
These have led to the belief that BHs and bulges coevolve and regulate each other's growth (e.{\thinspace}g.,
Silk \& Rees 1998;
Richstone {\it et al.\ } 1998;
Granato {\it et al.\ } 2004;
Di Matteo {\it et al.\ } 2005;
Springel {\it et al.\ } 2005;
Hopkins {\it et al.\ } 2006;
Somerville {\it et al.\ } 2008).
This simple picture is now evolving into a richer and more plausible story in which BHs correlate
differently with different kinds of galaxy components. BHs do not correlate at all with galaxy disks
(Kormendy \& Gebhardt 2001;
\vfill\eject
\noindent Kormendy {\it et al.\ } 2011; Kormendy \& Ho 2013), although some pure-disk galaxies contain BHs (see
Ho 2008 for a review).
And despite contrary~views,
(Ferrarese 2002;
Baes {\it et al.\ } 2003;
Volonteri {\it et al.\ } 2011),
it is clear that BHs do not correlate tightly enough with dark matter halos to imply any special relationship
between them beyond the fact that dark matter controls most of the gravity that makes hierarchical clustering happen
(Ho 2007;
Kormendy \& Bender 2011;
Kormendy \& Ho 2013). So BHs coevolve only with bulges.
What about pseudobulges? They are closely connected with disks, but some contain BHs.
The best example is our Galaxy (Genzel {\it et al.\ } 2010).
Hu (2008) finds, for a small sample, that BHs in pseudobulges have smaller $M_\bullet$ than BHs in classical bulges
and ellipticals of the same $\sigma$. Graham (2008) reports the possibly related result that barred galaxies also deviate from the
$M_\bullet$\thinspace--\thinspace$\sigma$ relation in having small $M_\bullet$, but interpretation is complicated by the fact that some
of his barred galaxies contain classical bulges (e.{\thinspace}g., NGC 1023, NGC 4258), some contain pseudobulges (e.{\thinspace}g.,
NGC 3384, our Galaxy) and some contain both (NGC 2787). More definitively, results similar to Hu's are found by
Nowak {\it et al.\ } (2010) and by
Greene {\it et al.\ } (2010).
Kormendy {\it et al.\ } (2011) and Kormendy \& Ho (2013) now show for larger samples that pseudobulges correlate little enough
with $M_\bullet$ so coevolution is not implied (Fig.~1.50). This simplifies the problem of coevolution by focusing
our attention on galaxy mergers. It is a substantial success of the secular evolution picture that a morphological
classification of bulges separates them into two kinds that correlate differently with BHs.
\vfill
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=pseudobulges.ps hoffset=-81 voffset=-342 hscale=76 vscale=76}
\caption{Correlation of dynamically measured BH mass $M_\bullet$ with (left) \hbox{$K$-band} bulge absolute magnitude
and (right) velocity dispersion averaged inside $r_e$.
Pseudobulges with dynamical BH detections are shown with blue filled circles and those with $M_\bullet$ upper limits
are shown with blue open circles.
NGC 2787 may have both a small classical and a large pseudo bulge (Erwin {\it et al.\ } 2003); its blue symbol has a red center.
Classical bulges and ellipticals are shown in ghostly light colors to
facilitate comparison. This is a preliminary figure from Kormendy \& Ho (2013).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\section{Environmental secular evolution:\\The structure and formation of S0 and spheroidal galaxies}
Research on internal secular evolution is now a major industry,~but~work~on environmental secular evolution
still is a series of important but disconnected cottage industries. We need to make the subject an integral
part of our standard picture of galaxy evolution. This section reviews
environmental secular evolution, following Kormendy \& Bender (2012).
Our theme is that dwarf spheroidal (dSph) galaxies such as Draco and UMi and higher-luminosity Sph galaxies such as
NGC 205 are transformed, `\hbox{`red and dead''} spiral and irregular galaxies and that many S0 galaxies similarly are transformed
earlier-type spirals. That is, Sph galaxies are bulgeless S0s. The easiest way to introduce this theme is using Fig.~1.51.
This is one of the best-known extragalactic images, but it is not widely realized that it includes an easy way to form a
mental picture of the difference between elliptical and spheroidal galaxies. In doing so, it speaks directly to the
fundamental question: What is an elliptical galaxy (Fig.~1.52)?
\vfill
\begin{figure}[hb]
\special{psfile=./m31-wiki-dss2croplo.eps hoffset=-9 voffset=-18 hscale=61.5 vscale=61.5}
\caption{M{\thinspace}31 (Sb, center), M{\thinspace}32 (E, lower companion) and NGC 205 (Sph, upper companion)
from the Digital Sky Survey via {\tt http://www.wikisky.org}.}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{What is (and what is not) an elliptical galaxy?}
In Fig.~1.51, M{\thinspace}31 is an Sb spiral with a classical bulge;~\hbox{$B/T = 0.34 \pm 0.03$}
(Kormendy {\it et al.\ } 2010). Absent the~disk, the
bulge is indistinguishable from a smallish elliptical. M{\thinspace}32~is~one~of~the tinest true ellipticals, with a
$V$-band absolute magnitude of $M_V \simeq -16.7$ (Kormendy {\it et al.\ } 2009). It is small and dense and
commonly called a ``compact elliptical'' (cE). But compactness is not a disease; it is mandated by the
physics that makes the Fundamental Plane (Figs.~1.57, 1.68). In fact, M{\thinspace}32 is an entirely
normal example of a tiny elliptical (Kormendy~{\it et~al.}~2009). In contrast, NGC 205 is the most
luminous example in the Local Group of a galaxy that satisfies the morphological definition of an
elliptical but that differs quantitatively from ellipticals (as a result, it is typed ``E5 pec'').
\hbox{{\it NGC~205 has the same luminosity as M{\thinspace}32,}} $M_V \simeq -16.6$ (Mateo 1998). It looks
different because it is larger, lower in surface brightness and shallower in surface brightness gradient.
Measured quantitatively, these differences put NGC 205 near the bright end of a sequence of elliptical-looking
galaxies that is disjoint from{\thinspace}--{\thinspace}in fact, almost perpendicular to{\thinspace}--{\thinspace}the sequence of ellipticals
and classical bulges in Figs.\ts1.43, 1.57, 1.68{\thinspace}--{\thinspace}1.69 and 1.71. {\it This means that NGC 205 is not an elliptical.}
\vfill
\begin{figure}[hb]
\special{psfile=./Sph-ne-Elo.eps hoffset=11 voffset=-15 hscale=55 vscale=55}
\caption{What is an elliptical galaxy? Morphologically, the dwarf galaxy Leo~I (top-middle panel)
resembles the dwarf irregulars Leo{\thinspace}A and GR{\thinspace}8 in its low surface brightness and shallow
brightness gradient.~But it resembles the giant elliptical~M{\thinspace}87 in having elliptical isophotes
and no cold gas. Since only the latter characteristics morphologically define
ellipticals, Leo I is often called a ``dwarf elliptical''. However,
purely morphological criteria prove unable to distinguish objects that have
different formation~histories.\thinspace~Leo I turns out to be related to dI galaxies,
not to ellipticals.\thinspace~So I do not call it a dwarf elliptical; rather, I call it
a dwarf spheroidal (dSph)~galaxy.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent Finding gas and young stars in it supports this conclusion. We call such objects ``spheroidal galaxies'' (Sphs),
adapting a name (``dwarf spheroidal'') that is in common use for smaller examples. The fact that NGC 205 has surface
brightnesses similar to those of the disk of M{\thinspace}31 is not an accident.
A variety of evidence leads to the conclusion that Sph galaxies are defunct late-type galaxies whereas classical
bulges and ellipticals are the remnants of major galaxy mergers. This story is the subject of the present section.
Recall (Section 1.3.4) how classical morphologists attach no interpretation to descriptions, whereas physical morphologists
try to construct a system in which classification bins uniquely separate objects that have different origin and evolution.
I emphasized there that, even though classical morphologists try to avoid interpretation, they nevertheless makes choices about
which features to view as important and which to view as secondary. Figure\ts1.52 illustrates how this results in a problem
for classifying elliptical galaxies. In its {\it isophote shape\/}, Leo I resembles the elliptical galaxy M{\thinspace}87. However,
in its {\it surface brightness}, it resembles the irregular galaxies Leo{\thinspace}A and Gr\ts8. Hubble classification is based mainly
on isophote shape, so it has been common to call galaxies like Leo I and NGC 205 ``dwarf ellipticals'' (e.{\thinspace}g., Sandage\ts1961).
{\it But there has never been any guarantee that structural morphology identifies physically different kinds of objects.}
Figure 1.53 makes this point concrete.
\vfill
\begin{figure}[hb]
\special{psfile=./WhoDoesNotBelonglo.eps hoffset=-5.5 voffset=-15 hscale=60 vscale=60 }
\caption{The danger of classifying using only morphology. Who does not belong?
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
\begin{figure*}
\vskip 3.6truein
\special{psfile=./Dolphin-Cowlo.eps hoffset=-9 voffset=-17 hscale=61.5 vscale=61.5}
\caption{Dolphins are Mammals. Convergent evolution happens. It happens to galaxies
as well as to creatures on Earth, and elliptical and spheroidal galaxies prove
to be examples. They look morphologically similar but have different formation histories.
I warmly thank Douglas Martin ({\tt http://www.dolphinandcow.com}) for permission to use this figure.
}
\end{figure*}
\cl{\null}
\vskip -37pt
Who does not belong in Fig.~1.53? The answer is of course well known (Fig.~1.54). Dolphins (Fig.~1.53, top right) are mammals,
even though they are morphologically similar to sharks (Fig.~1.53, top left). To make a living, both need to be well streamlined,
strong swimmers. Convergent evolution made them that way. In contrast, a leafy seadragon (Fig.~1.53, bottom right:
{\tt http://picasaweb.google.com/lh/photo/cEq5cwlB2\_cmufKXlOKJcg}) is a kind of seahorse whose main need is good camouflage
to avoid predators. So, even though it is a fish, its morphology has evolved to be very different from that of a shark.
A ``Hubble classification'' of sea animals that was superficially based on visible structural characteristics could mistakenly
combine sharks and dolphins into the same or closely related classification bins and could miss the more subtle (but more important)
differences that distinguish sharks and sea dragons from dolphins and cows. Which parameters best distinguish the physical differences
that are most important to us is not necessarily obvious without detailed study.
Convergent evolution happens to galaxies, too.
\vfill
\eject
\subsection{The E -- Sph dichotomy}
Why did we ever think that Leo{\thinspace}I and NGC\ts205 are ellipticals?~The~answer is that
research on galaxies began with descriptive classical morphology (e.{\thinspace}g.,
Hubble 1936;
de Vaucouleurs 1959;
Sandage 1961),
and then the above galaxies satisfy the definition of an elliptical. However, {\it we will see in
Fig.~1.59 that Sandage et al.\thinspace(1985b) had no trouble in distinguishing between E and dE galaxies of the
same luminosity.} If this sounds surpassingly strange to you, you have the right reaction.
I will come back to this point below.
Astronomers are conservative people -- this is often healthy -- and most people clung to the idea
that galaxies like Leo I and NGC 205 are ellipticals even after hints to the contrary started to appear.
Figure 1.55 shows an example. Ellipticals (filled circles) have higher surface brightness at lower
galaxy luminosities, whereas ``dwarf ellipticals'' (open~circles~and~crosses) have lower surface
brightnesses at lower luminosities. M{\thinspace}32 is consistent with the extrapolation of the E sequence.
However, at that time, we thought that M{\thinspace}32 is compact because it has been tidally
truncated by M{\thinspace}31 (King 1962; Faber 1973). Bingelli {\it et al.\ } (1984) therefore concluded that E and dE galaxies form
a continuous but not monotonic sequence in surface brightness as a function of luminosity. Meanwhile,
one could wonder whether the two sequences in Fig.~1.55 already hint at different formation physics.
\vfill
\begin{figure}[hb]
\special{psfile=./BST1984lo.eps hoffset=-8 voffset=-20 hscale=59 vscale=59}
\caption{Parameter correlations for elliptical and ``dwarf elliptical'' galaxies from
Bingelli {\it et al.\ } (1984). These authors suggested that giant and dwarf ellipticals
form a continuous but not monotonic sequence in mean surface brightness as a function
of absolute magnitude $M_{\rm BT}$ and that M{\thinspace}32 -- which deviates prominently
from this sequence -- is pathological.
}
\end{figure}
\cl{\null}
\vskip -30pt
\eject
\cl{\null}
\begin{figure*}
\vskip 2.0truein
\special{psfile=./WirthGallagher-LF.eps hoffset=23 voffset=-17 hscale=49 vscale=49}
\caption{Luminosity functions of (top) normal elliptical galaxies roughly from M{\thinspace}32 to M{\thinspace}87 and
(bottom) spheroidal galaxies roughly from Draco and UMi to galaxies such as NGC{\thinspace}205 (Wirth
\& Gallagher 1984). At that time, ``spheroidals'' were commonly called ``dwarf ellipticals''.
This figure then shows that the smallest non-dwarf ellipticals have lower luminosity than the biggest
dwarf ellipticals.
}
\end{figure*}
\cl{\null}
\vskip -45pt
Wirth \& Gallagher (1984) were the first to suggest that M{\thinspace}32-like compact ellipticals and not the more diffuse
galaxies like Draco and Leo{\thinspace}I and NGC\ts205 form the faint end of the luminosity sequence of elliptical galaxies.
This was based on a successful search for {\it relatively isolated\/} dwarf compact ellipticals which resemble
M{\thinspace}32. The new compact ellipticals and the well known ones that are companions to larger galaxies were found
to lie along the extrapolation to lower luminosity of the correlations for {\it normal\/} ellipticals
of parameters such as effective radius and velocity dispersion. With respect to this family of normal ellipticals,
``the diffuse ellipticals are a distinct structural family of spheroids whose properties begin to diverge from those
of the classical ellipticals at an absolute magnitude of $M_B \sim -18$. At $M_V = -15$, these two families differ in
mean surface brightness by nearly two orders of magnitude. The key point to note for this discussion is that, in
the range \hbox{$-18$ \lapprox \thinspace$M_B$ \lapprox \thinspace$-15$,} {\it both} structural classes of elliptical galaxies coexist''
(Wirth \& Gallagher 1984). This implies that the luminosity functions of elliptical and spheroidal
galaxies differ as shown in Fig.~1.56.
The Wirth \& Gallagher (1984) paper was largely based on four newly found, free-flying compact ellipticals.
The competing idea (Faber 1973) that compact ellipticals are tidally truncated was largely based on three galaxies,
M{\thinspace}32, NGC 4486B and NGC 5846A; then the diffuse dwarfs would be the faint extension of the E sequence.
With both conclusions based on small numbers of galaxies, it was not clear which picture is correct.
The rest of this section reviews the now very strong evidence that Wirth \& Gallagher (1984) were presciently close
to correct in almost every detail, including Fig.~1.56.
\eject
As a graduate student at Caltech in the early 1970s, I was brought up on the picture that ellipticals
form a continuous, non-monotonic sequence in their structural parameters from the brightest to the faintest galaxies~known.
Then, in the 1980s, I gained access to two important technical advances. The first was CCD detectors that are linear in
sensitivity over large dynamic ranges. The second was the Canada-France-Hawaii telescope (CFHT), which had the best ``seeing''
then available on any optical telescope. These allowed me to study the central structure of galaxies in unprecedented detail.
The results revolutionized my picture of
ellipticals. They confirmed and extended Wirth \& Gallagher (1984), whose ideas I was not aware of until the end of my work.
The story is instructive for students, so I describe it here in detail, abstracted from a popular article in {\it Stardate\/}
magazine (Kormendy 2008b).
My CFHT surface photometry showed an unexpected result (Fig.~1.57). Ellipticals define the sequence of red points:~less
luminous ones are smaller and higher in surface brightness from M{\thinspace}87 to M{\thinspace}32.~This much was expected; for bright galaxies,
it is the correlation shown by the filled~circles~in~Fig.~1.55. Importantly, the high-resolution CFHT photometry helps to fill
in the gap between M{\thinspace}32 and the other ellipticals.\thinspace~This makes M{\thinspace}32 look less peculiar. \phantom{000000}
\vfill
\begin{figure}[hb]
\special{psfile=./Kormendy1985-Correlationslo.eps hoffset=72 voffset=-12 hscale=35.5 vscale=35.5}
\caption{Kormendy (1985, 1987) showed with much larger samples that E and Sph
galaxies form disjoint sequences in parameter space (cf.~Wirth \& Gallagher 1984).
Sphs (yellow) are not faint ellipticals (red). Instead, their parameter
correlations are almost identical to those of dwarf spiral and irregular
galaxies (blue). This figure shows approximate central surface brightness
and King (1966) core radius, both corrected as well as possible for PSF blurring,
versus $B$-band absolute magnitude.
}
\end{figure}
\cl{\null}
\vskip -45pt
\eject
\noindent The surprise was the behavior of the ``dwarf ellipticals'', shown in Fig.~1.57 by yellow points. Using near-central
parameters rather than parameters measured within the effective radii $r_e$ as in Fig.~1.55, it is clear that dwarf ellipticals
do not satisfy the correlations for elliptical galaxies. Less luminous dwarf ellipticals are lower -- not higher -- in surface brightness.
A gap has appeared between ordinary and dwarf ellipticals. Wirth \& Gallagher's (1984) conclusions are confirmed with a much larger sample.
Size and density are diagnostic of galaxy formation, so I realized at this point that dwarf ellipticals are not ellipticals at all.
As one point after another got plotted and intermediate cases failed to show up, my previous picture of elliptical galaxies fell apart.
Kuhn (1970) captures exactly what happens in a scientist's mind when his understanding of a subject falls apart. Quoting Kormendy (2008b):
``The first reaction was consternation. What have I screwed up? I checked my data reduction. I considered whether my galaxy sample
could be biased. Nothing seemed wrong. Better data just led in an unexpected direction. I had to accept the new result: dwarf ellipticals
are not ellipticals. But then we should not call them ``dwarf ellipticals''. The smallest such companions to our Milky Way had
sometimes been called dwarf spheroidals. So, to minimize the departure from tradition, I called all such objects ``spheroidals''.
The biggest ones in Virgo are only as luminous as an average elliptical, but they are giant spheroidals.''
``If spheroidals are not ellipticals, what are they? Kuhn describes what happens next. Deprived of the guidance of any previous
understanding of a subject, a scientist in the midst of a scientific revolution does not know what to do next. In turmoil and in desperation,
wild ideas get tried out, most of them wrong. I plotted in my diagrams all the other kinds of stellar systems that I knew about.
I plotted globular clusters of stars [green points], spiral galaxy disks [two large blue plus signs, each an average for several galaxies
from Freeman 1970], and irregular galaxies [blue plus signs]. The globulars were unconnected with ellipticals and
spheroidals. But the irregulars and spirals were a surprise. They showed exactly the same correlations as the spheroidals. Aha! A new
picture was emerging. Maybe spheroidals are related to spirals and irregulars. They have almost the same structure. They don't
contain gas and young stars, which are common in spirals and irregulars. And they have smoother structure. But I realized that, if
the gas were removed or converted into stars, dynamical evolution of the now-gasless spheroidal would smooth out its formerly patchy
structure within a few galactic rotations. We knew that the dwarf spheroidal companions of the Milky Way had varied star formation
histories. A few contain only old stars, as ellipticals do, but most experienced several bursts of star formation, and the most recent
burst was a few billion or even as little as a few hundred million years ago. What are galaxies that have not yet had their last burst of
star formation and that therefore still must contain gas? This is not a controversial question [Kormendy \& Bender 1994]. They are irregulars.
I realized: if we looked at the Milky Way's dwarf spheroidals when the Universe was half of its present age, about half of them would
still be irregulars. Irregulars have been turning into Sphs gradually over most of the history of the Universe. In the Virgo cluster,
lots of processes can make this happen. The most obvious is ram-pressure stripping: as an irregular galaxy falls into Virgo
for the first time, it rams into the million-degree gas that fills the cluster, and its cold gas gets swept away. It started to look
like no accident that the irregulars in Virgo live around the outside of the cluster, while the center is inhabited by spheroidals
[Binggeli {\it et al.\ } 1987].''
``Within a few days, I had a new picture.~Spheroidals are defunct~spiral and irregular galaxies converted by their environment
to look like ellipticals. This helped our picture of galaxy formation, because we already knew that ellipticals form by galaxy mergers,
whereas, quoting Tremaine (1981), `Dwarf elliptical satellite galaxies cannot form by mergers with other satellites since their relative
velocities are too high.' We were in trouble when we had to find a single formation process that could explain NGC 4472, one of
the biggest galaxies in the nearby Universe, and dwarf spheroidals that are a million times less luminous and that look like fragile,
gossamer clouds of stars [Fig.~1.58 here]. But they look like the smallest irregulars, minus gas and young stars [Fig.~1.52 here].
So this problem was solved. I~reported these results [at a workshop in Rehovot, Israel], and they were~well received.''
The result that E and Sph galaxies are different is called the E{\thinspace}--{\thinspace}Sph dichotomy.
\vfill
\begin{figure}[hb]
\special{psfile=./Fornax-Sculptor-Draco-RGBlo.eps hoffset=-11.5 voffset=-17 hscale=62.5 vscale=62.5}
\caption{Luminosity sequence of dSph satellites of our Galaxy.~Fornax,~Sculptor and Draco have absolute magnitudes of
\hbox{$M_V = -13.2$, $-11.1$ and $-8.8$,} respectively (Mateo 1998), and correspondingly decreasing surface brightnesses
(see Fig.~1.57). Draco is the cloud of faint stars in the right panel; the bright stars with the
instrumentally-produced red halos are foreground stars in our Galaxy. Contrast M{\thinspace}87 in Fig.~1.52. Could M{\thinspace}87
and Draco really have similar formation histories, with different results only because
changing the mass tweaks the formation physics? The results reviewed here imply that the answer is ``no''.
We now believe that M{\thinspace}87 is a remnant of the dynamical violence of galaxy mergers, whereas Draco formed
quescently as a dwarf irregular that lost its gas long ago. From Kormendy (2008b).
}
\end{figure}
\cl{\null}
\vskip -45pt
\eject
\subsection{Mixed reactions to the E -- Sph dichotomy}
Scientific research is a quintessentially human enterprise, as reactions to the above result illustrate:
The essential theoretical understanding of why Sph and S$+$Im galaxies have lower stellar densities at lower galaxy
masses followed immediately. Dekel \& Silk (1986) ``suggest that {\it both the dI's and the dE's} [here:~dSphs]
{\it have lost most of their mass\/} in [supernova-driven] winds after the first burst of star formation, and that this process determined
their final structural relations. The dI's somehow managed to retain a small fraction of their original gas, while the dE's either have
lost all of their gas at the first burst of star formation or passed through a dI stage before they lost the rest of the gas and turned dE.''
Our story here adds detail on dI\thinspace$\rightarrow${\thinspace}dSph transformation processes but otherwise is based on exactly the above picture.
Reactions among observers have been more mixed. The reasons are many and revealing and occasionally entertaining; they range from
innate conservatism to specific scientific arguments to turf wars. I will concentrate on the part of this history that is most instructive
for students.
I already noted that many astronomers are conservative:~they~do~not~easily discard a picture that they believed in for many years.
This is healthy~-- imagine what would happen if we chased, willy-nilly, after every outrageous idea that got proposed. It
is prudent to treat new ideas with respect, but in a mature subject, it is uncommon for a long-held, well-supported picture to be completely
wrong. The situation is more tricky when subjects are young and not yet well developed. This proved to be such a case. Nevertheless,
it is understandable that people who had long been involved in research on dwarf galaxies reacted to the above developments with some ambivalence.
In particular, the group of Sandage, Binggeli, Tammann and Tarenghi wrote a series of papers on the Virgo cluster in the mid-1980s, some before
and some after the Wirth \& Gallagher (1984) and Kormendy (1985, 1987) papers. Struggles with the new ideas were evident in some of the later
papers. The nature of these struggles reveals how seeds of the new ideas could have been recognized in the older results. I belabor this
point because the conceptual blindness that results when we embrace a paradigm of how nature works always threatens our ability to see something
new. {\it As you do your research, it is healthy to be careful and conservative but also prudent to ask yourself: Am I missing something because
of paradigm-induced conceptual blindness?} Kuhn (1970) provides a perceptive discussion of this subject.
Figure 1.55 already illustrated how one hint -- the opposite slopes of the surface-brightness--luminosity correlations -- was contained
in previous work.
\eject
\cl{\null}
\begin{figure*}
\vskip 2.8truein
\special{psfile=./VirgoLF3lo.eps hoffset=-12 voffset=-17 hscale=65 vscale=65 }
\caption{Luminosity functions of elliptical and spheroidal galaxies in the Virgo cluster.
This figure is adapted from Sandage {\it et al.\ } (1985b), who used the traditional name ``dE'' for
spheroidals. I have updated the Hubble constant from $H_0 = 50$ to 70 km s$^{-1}$ Mpc$^{-1}$.
Magnitudes are in $B$ band. From Kormendy \& Bender (2012).
}
\end{figure*}
\phantom{gronk}
\vskip -40pt
Figure 1.59 is a better illustration (Sandage {\it et al.\ } 1985b). It shows with data on Virgo galaxies the result that is shown
schematically~in~Fig.~1.56. {\it The luminosity function of ellipticals is bounded at high and low $L$}. M{\thinspace}32 has normal properties
for its low luminosity, but such tiny ellipticals are rare. In contrast, spheroidal galaxies (which Sandage {\it et al.\ } 1985b~call~``dEs'')
never are very bright, but they get rapidly more common at lower luminosities until they are lost in the detection noise.
The steep faint-end slope of the luminosity function had been recognized
for a long time (Zwicky 1942, 1951, 1957) and is built into the well known Schechter (1976) analytic luminosity function.
But, to the best of my knowledge, Sandage {\it et al.\ } (1985a, b) and Binggeli {\it et al.\ } (1988) were the first to measure luminosity functions separately
for different morphological types of galaxies and to show that only Sph galaxies have luminosity functions that continue to rise with
decreasing luminosity to the detection limit of the data. This is the solid result in Fig.~1.59. Here is the incongruity:
{\it Sandage et al.~(1985b) distinguish between elliptical and dwarf elliptical galaxies of the same luminosity.}
Quoting Kormendy \& Bender (2012): ``A dwarf version of a creature is one that, when mature, is smaller than the normal sizes of
non-dwarf versions of that creature. \dots~And yet, [Fig.~1.59] invites us to imagine that the smallest non-dwarf ellipticals are
20 times less luminous than the brightest `dwarf ellipticals'.''
Sandage and collaborators recognized and struggled with this incongruity. Quoting Sandage \& Binggeli (1984):~``The distinction
between E and dE types is made on morphological grounds alone, using surface brightness
as the criterion. Normal E galaxies have a steep radial profle (generally following an $r^{1/4}$ law)
with high central brightness.~The~typical~dE~has~a {\it nearly flat} radial profile, following
either a King [1966] model with a small concentration index or equally well an exponential law.
The morphological transition from E to dE is roughly at $M_B \simeq -18$, but there is overlap.''
Recognition of this difference dates back at least to Baade (1944):
``NGC\ts147 and NGC\ts185 are elliptical nebulae of very low luminosity. In structure, they deviate
considerably from what is considered the typical E-type nebula. In both objects the density gradient
is abnormally low.''
Binggeli {\it et al.\ } (1985) also recognized the quantitative similarity beween spheroidals~and~irregulars;
their Virgo ``membership criteria applied are: (1) dE and Im members have low surface brightness. \dots''.
Soon afterward, Sandage {\it et al.\ } (1985b) admit that ``We are not
certain if this [E{\thinspace}--{\thinspace}dE dichotomy] is totally a tautology due merely to the arbitrary classification criteria
that separate E from dE types \dots~or if the faint cutoff in the [E luminosity function] has physical
meaning related to the properties of E and dE types. In the first case, the problem would be only one
of definition.~In the~second, the fundamental difference in the forms of the luminosity functions of E and
dE types\thinspace\dots{\thinspace}would suggest that two separate physical families may, in fact, exist with {\it no\/}
continuity between them (cf.~Kormendy 1985 for a similar conclusion).'' Revising a long-held picture can
be uncomfortable.
Within a few more years, Binggeli {\it et al.\ } (1988) recognized that ``The distinction
[between] Es and dEs must almost certainly mean that the two classes are of different origin [Kormendy 1985, Dekel \& Silk 1986].
This is also supported by the fact that the luminosity functions of Virgo Es and dEs [are different].'' And Binggeli
\& Cameron (1991) concluded that ``there are no true intermediate types between E and dE. The [E{\thinspace}--{\thinspace}dE] dichotomy
is {\it model-independent\/}'' (emphasis in the original).
But psychology did not lose its hold on people. Binggeli changed~his~mind: in a section entitled ``The E--dE dichotomy
and how it disappears'', Jerjen \& Binggeli (1997) emphasize the observation that, in a plot of brightness profile S\'ersic
index {\it versus} $M_{BT}$, E and dE galaxies show a continuous correlation. They conclude that compact ellipticals like M{\thinspace}32 and its
analogs in Virgo are ``special'' and that dEs form the extension of the ellipticals to low $L$. However, this is not the only
relevant correlation. The observations which suggest the dichotomy had not disappeared. And the fact that one can find parameters
of galaxies that are insensitive to the differences between two types does not prove that the two types are the same. Many
parameters are continuous between ellipticals and spheroidals. E.{\thinspace}g., the content of heavy elements is not only a continuous
function of luminosity for ellipticals and spheroidals, it is essentially the same continuous function for spirals and irregulars, too
(e.{\thinspace}g., Mateo 1998). If we looked only at element abundances, we would be blind to all structural differences encoded in Hubble types.
More recent criticisms of the E -- Sph dichotomy are reviewed in Kormendy {\it et al.\ } (2009) and in Kormendy \& Bender (2012).
The arguments involve technical details such as sample size and profile analysis techniques. These are of less immediate
interest, and any discussion of them quickly gets long. I~therefore refer readers to the above papers for our answers
to the criticisms. A few are relevant here and will be discussed below. But the best way to address uncertainty about
the E -- Sph dichotomy is to observe larger samples of galaxies and to address more general scientific questions, as follows.
\vskip -30pt
\phantom{000000000000}
\subsection{\hbox{Confirming the E--Sph dichotomy with large galaxy samples}}
Kormendy {\it et al.\ } (2009: KFCB) extend the sample size of the parameter correlations in Fig.~1.57 by measuring
brightness profiles for all known ellipticals in the Virgo cluster and combining these with data on $\sim$\ts275 Sph galaxies.
Examples are shown in Fig.~1.60. Data from many sources were combined to construct composite profiles over large dynamic ranges.
S\'ersic functions fit most of the galaxy light to remarkable precision:~over the fit ranges (vertical dashes in Fig.~1.60),
the average RMS deviation = 0.040 mag arcsec$^{-2}$ for the whole KFCB sample. Kormendy (2009) further added ellipticals
from Bender {\it et al.\ } (1992) and Sphs from Chiboucas {\it et al.\ } (2009). The updated Fig.~1.57 is shown in Fig.~1.61.
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./n4486mu.ps hoffset=-52 voffset=-50 hscale=31 vscale=31}
\special{psfile=./n4458mu.ps hoffset=67 voffset=-50 hscale=31 vscale=31}
\special{psfile=./v1185mu.ps hoffset=188 voffset=-50 hscale=31 vscale=31}
\caption{Surface brightness profiles of 3 galaxies from KFCB.~NGC\ts4486~(M{\thinspace}87) is an elliptical galaxy with a central
``core''; i.{\thinspace}e., central ``missing light'' with respect to the inward extrapolation of the outer S\'ersic function fit
(black curve). NGC 4458 is an elliptical galaxy with central ``extra light'' above the inward extrapolation of the outer
S\'ersic fit. VCC 1185 is a Sph galaxy with a nuclear star cluster (type Sph,N) in addition to its S\'ersic-function
main body. This figure illustrates the robust profiles that are derived by using many images that provide
data in overlapping ranges of radii (e.{\thinspace}g.,{\it HST} data near the center; large-field CFHT data at large $r$).
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\vfill\eject
Figure 1.61 strongly confirms the dichotomy between E and Sph galaxies as found in Kormendy (1985, 1987),
Binggeli \& Cameron (1991) and
Bender {\it et al.\ } (1992, 1993).
Note that the Sph sequence approaches the E sequence near its middle, not near its faint end.
\vfill
\begin{figure}[hb]
\special{psfile=./fig_spiral_disks_e_canary.ps hoffset=-84 voffset=-178 hscale=85 vscale=85}
\caption{Global parameter correlations from KFCB and Kormendy (2009) with Sph galaxies in the Local
and M{\thinspace}81 groups updated from Kormendy \& Bender (2012). This figure shows 90 ellipticals and 295
spheroidals. One elliptical plots in the Sph sequence when effective parameters are
used; difficult cases such as this one were classified in KFCB using parameters measured at the radius that
contains 10\thinspace\% of the total light. Reason: the E{\thinspace}--{\thinspace}Sph dichotomy is most pronounced when
near-central parameters are used (contrast Fig.~1.57 with this figure).
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The small-$r_e$, bright-$\mu_e$ end of the sequence of ellipticals is defined in part
by galaxies like M{\thinspace}32 that are sometimes called ``compact ellipticals''. As noted above, {\it compact
ellipticals are not a special class.} They are continuously connected to brighter ellipticals in essentially all
parameters. Moreover, M{\thinspace}32 is no longer unique, as it appeared to be in Fig.~1.57. We now know
of a number of M{\thinspace}32 analogs
(Binggeli {\it et al.\ } 1985;
Lauer {\it et al.\ } 1995;
Faber {\it et al.\ } 1997;
KFCB).
Figure 1.61 illustrates and KFCB reviews evidence that M{\thinspace}32 is normal for its low $L$.
However, it is often suggested that these galaxies are compact only because they have been tidally stripped
by much larger companions (e.{\thinspace}g.,
Faber 1973;
Ferrarese {\it et al.\ } 2006;
Bekki {\it et al.\ } 2001;
Chen {\it et al.\ } 2010).
Kormendy \& Bender (2012) review why it is not plausible that this is the explanation for why small Es are compact.
This issue is important, so I enumerate the arguments here:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{Compact ellipticals are not always companions of brighter galaxies (Wirth \& Gallagher 1984).
Some are so isolated that no tidal encounter with a big galaxy is likely ever to have happened (e.{\thinspace}g.,
VCC 1871: Kormendy \& Bender 2012).}
\item{Compact Es do not have small S\'ersic indices suggestive of tidal truncation. In fact,
they have the same range of S\'ersic indices $n \sim 2$ to 3.5 as isolated coreless ellipticals.
For example, M{\thinspace}32 has $n \simeq 2.9$, larger than the median value for coreless ellipticals.
Numerical simulations show that major mergers of gas-poor galaxies like the ones in
the nearby Universe make remnants that have exactly the above range of S\'ersic indices (Hopkins {\it et al.\ } 2009a).}
\item{Many Sph galaxies also are companions of bright galaxies, but we do not argue that they have been truncated amd
thereby made abnormally compact. An example is NGC~205, which is shown by the open square at $M_{VT} = -16.6$
in Fig.~1.61. It is much fluffier than M{\thinspace}32.}
\item{Figure 1.68 below will show that the compact end of the E sequence is also defined by tiny bulges.
Classical bulges and ellipticals have closely similar parameter correlations. Most classical
bulges that appear in our correlation diagrams do not have bright companion galaxies.}
\item{In Fig.~1.61, the ellipticals from M{\thinspace}32 to cD galaxies define projections of the ``fundamental plane'' correlations
(Djorgovski \& Davis 1987; \hbox{Faber {\it et al.\ } 1987;} Djorgovski {\it et al.\ } 1988; Bender {\it et al.\ } 1992). Its interpretation is
well~known: galaxy parameters are controlled by the Virial theorem modified by small nonhomologies. N-body simulations
of major galaxy mergers reproduce the E-galaxy fundamental plane, not the Sph parameter sequence that is almost
perpendicular to it (Robertson {\it et al.\ } 2006; Hopkins {\it et al.\ } 2008, 2009b).}
\end{enumerate}
\noindent Kormendy and Bender conclude: ``some compact Es may~have~been~pruned slightly, but tidal
truncation is not the reason why the E sequence extends to the left of where it is approached by the
Sph sequence in [Fig.\ts1.61].''
\subsubsection{Classical bulges and ellipticals satisfy the same fundamental plane parameter correlations.~I.~Bulge-disk decomposition}
Point (d) above anticipates the result of this subsection:~classical bulges are essentially indistinguishable
from elliptical galaxies of the same luminosity. This in turn was further anticipated when I defined classical bulges
to be elliptical galaxies that happen to live in the middle of a disk. Here, the time has come to ante up
the evidence by adding classical bulges to Fig.~1.61.
Figure 1.62 emphasizes the most important requirement for this analysis. For each disk galaxy, it is necessary
to decompose the observed brightness distribution into (pseudo)bulge and disk parts. This is a fundamental
part of the classification of the central component as classical or pseudo. It provides {\it separately\/} the parameters
of the bulge and the disk, both of which we need. For some applications, a kinematic decomposition is also needed.
Photometric decomposition is the crucial requirement that allows us to ask whether classical bulges satisfy the parameter
correlations for ellipticals. Absent such a decomposition, even the distinction between ellipticals and spheroidals is
blurred. This is part of the reason why Ferrarese {\it et al.\ } (2006); Chen {\it et al.\ } (2010), and Glass {\it et al.\ } (2011) do not see the E{\thinspace}--{\thinspace}Sph
dichotomy. If bulges and disks are combined in various proportions and then measured as one-component galaxies,
it is inevitable that the resulting parameters will be intermediate between those of bulges and disks and that including
them will blur the distinction between the bulge and Sph\thinspace$\approx${\thinspace}disk sequences in Fig.~1.61 (see Figs.~76 and 77 in KFCB
and Figs.~1.63 and 1.64 here).
\vfill
\begin{figure}[hb]
\special{psfile=./N4594-HST.eps hoffset=3 voffset=-6 hscale=34.2 vscale=34.2}
\special{psfile=./NGC_4762_gri.eps hoffset=181 voffset=-6 hscale=34.2 vscale=34.2}
\caption{(left) Sombrero Galaxy and (right) NGC 4762, the second-brightest S0 galaxy
in the Virgo cluster. These galaxies illustrate why bulge-disk decomposition is necessary.
NGC 4594 is an Sa galaxy with $B/T = 0.93 \pm 0.02$ (Kormendy 2011b). Without
photometric decomposition, we measure essentially only the bulge. We learn nothing about the
disk. If an S0 version of this galaxy (e.{\thinspace}g., NGC 3115) were viewed face-on, it would
be difficult even to discover the disk (Hamabe 1982). In contrast, NGC 4762 is an edge-on S0
with a tiny bulge; $B/T = 0.13 \pm 0.02$ (Fig.~1.63). Without photometric decomposition,
we measure essentially only the disk. We learn nothing about the bulge.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The need for bulge-disk decomposition can best be understood using an analogy. Imagine studying a population
of people, horses and people who ride on horses. Knowing nothing about them, one might measure parameters and
plot parameter correlations (linear size, mass, \dots) to look for different physical populations and regularities within each
population that might drive interpretation. We need to be careful, because some parameters (volume mass density within this
analogy; mass-to-light ratio for galaxies) prove to be insensitive to structural differences.~Still, careful parameter~study
is promising. But the biggest people are bigger than the smallest horses. If random people are paired with random horses
and the resulting population of people+horses, together with some pure people and some pure horses, are analyzed as
one-component systems, it is inevitable that a complete continuity will be found between people and horses. But it would
be wrong to conclude that people are the same as horses. Rather, if one decomposes people and horses when they occur
together and measures their parameters separately, it will be found that some parameter correlations clearly separate
people of various sizes from horses of various sizes, even though their size distributions overlap. Further study will also
show that certain special parameters (semi-trivially:~number of arms versus number of legs in this analogy; near-central parameters in
the cases of galaxies) are especially helpful in distinguishing the physically different populations that are under study.
The one elliptical galaxy (red point) that lies within the sequence of Sphs (green points) in some panels of Fig.~1.61 was
classified using central parameters (Fig.~34 in KFCB).
It feels strange to ``beat this dead horse'' (I'm sorry -- I could not resist): the need for component
decomposition has been understood for more than 30 years. It quickly became standard analysis
(Kormendy 1977a;
Burstein 1979;
Kent~1985).
It is still so now
(Peng et al. 2002;
Knapen {\it et al.\ } 2003;
de Souza {\it et al.\ } 2004;
Laurikainen {\it et al.\ } 2004, 2005, 2007;
Courteau {\it et al.\ } 2007;
M\'endez-Abreu {\it et al.\ } 2008;
Weinzirl {\it et al.\ } 2009).
The structure (this section) and formation physics (Section 1.8) of bulges and disks are very different, and it blurs
our vision of both to analyze them as single-component systems.
\subsubsection{Small-bulge S0 galaxies and the transition from S0 to Sph galaxies}
Kormendy \& Bender (2012:~KB2012) collect bulge and disk parameters from a variety of sources for or do photometry
and bulge-disk decomposition of all S0 galaxies from the {\it HST} ACS Virgo Cluster survey (C\^ot\'e {\it et al.\ } 2004;
Ferrarese {\it et al.\ } 2006). This section reviews the results. Classical bulges are added to the parameter correlation diagrams
in Fig.~1.68. But another and -- it will turn out -- especially interesting result will be to extend the Sph sequence to higher
luminosities. Kormendy \& Bender (2012) conclude that {\it Sph galaxies and S0 disks (but not bulges) are continuous in their
parameter correlations. That is, Sph galaxies are bulgeless S0s.}
Three galaxies serve here to illustrate the transition from S0 galaxies with large classical bulges and flat disks
to Sph galaxies with no bulges and with structure that can be vertically disky or thick.\thinspace~We start with NGC\ts4762.
Figure 1.62 shows that it differs from our canonical picture of Hubble classification (Sandage 1961) in which S0 galaxies are transition
objects between elliptical and Sa galaxies. The bulge-to-total luminosity ratio $B/T$ is a classification parameter; $B/T \equiv 1$ for
ellipticals, and $B/T$ is intended to decrease along the sequence E\thinspace--{\thinspace}S0\thinspace--{\thinspace}Sa{\thinspace}--{\thinspace}Sb\thinspace--{\thinspace}Sc. With some
noise, this is observed (Simien \& de Vaucouleurs 1986). But Sidney van den Bergh (1976) already recognized
that some S0 galaxies such as NGC\ts4762 have small bulges and, except for their cold gas content and spiral structure, are more similar
in their overall structure to Sbc galaxies than they are to Sa galaxies. As an alternative to the Hubble (1936) ``tuning-fork diagram'',
he proposed a ``parallel sequence classification'' in which S0 galaxies form a sequence \hbox{S0a{\thinspace}--{\thinspace}S0b{\thinspace}--{\thinspace}S0c} with decreasing
$B/T$ that parallels the sequence \hbox{Sa{\thinspace}--{\thinspace}Sb{\thinspace}--{\thinspace}Sc} of spiral galaxies with similar, decreasing $B/T$ ratios. Van den Bergh
suggested that late-type S0 galaxies with small bulges are defunct late-type spiral galaxies that were transformed by environmental processes
such as ram-pressure stripping of cold gas by hot gas in clusters. The KB2012 bulge-disk decompositions of NGC 4762
and similar galaxies quantitatively confirm van den Bergh's picture, as follows.
The brightness profile of NGC 4762 measured along the major axis of the disk is shown in Fig.~1.63 (left).
It shows a central bright and relatively round bulge and, at larger radii, three shelves in a very flat \hbox{edge-on}~disk.
The inner shelf is somewhat subtle, but the steep decrease in surface brightness between the middle and outer shelves is obvious
in Fig.~1.62. What is this complicated structure? This may seem like a tricky problem, but in fact, it is easy. Relatively face-on
galaxies that have two or three shelves in their brightness distributions are very common. The ones with two shelves are the oval-disk
galaxies discussed in Section 1.3.3. To get a third shelf, it is just necessary to add an early-type bar -- these have shallow
radial brightness gradients interior to a sharp outer end. Now, the bar normally fills its attendant lens in one dimension (Section 1.4.3.4
and Fig.~1.17). But consider a non-edge-on SB(lens)0 galaxy such as NGC 2859 (Fig.~1.9) or NGC 2950 (Fig.~1.17) in which the bar has a
skew orientation (not along either the apparent major or apparent minor axis). If we rotated either of these galaxies about a horizontal line
through the center in the corresponding figure until the galaxy was seen edge-on, its disk would show three shelves in its major-axis
profile. Exterior to the bulge, the innermost shelf would be the bar, the next would be the lens, and the third would be
the outer disk. This is how Kormendy \& Bender interpret Fig.~1.63 (left). Thus NGC 4762 is an
edge-on SB(lens)0 galaxy. Bars and lenses have shallow brightness gradients at small $r$, so profile decomposition~is~easy.
The bulge S\'ersic index $n = 2.29 \pm 0.05$ and round shape identify it as classical. Importantly,
$B/T = 0.13 \pm 0.02$ is very small. So Kormendy \& Bender (2012) classify NGC 4762 as SB(lens)0bc. Note in Fig.~1.63 (right)
how measuring NGC 4762 as a single-component system (green point with brown center) mixes parameters of the classical bulge (brown point)
and disk (green cross). Only after bulge-disk decomposition do we see that the tiny classical bulge of NGC 4762 helps to define the compact
extension of the E{\thinspace}--{\thinspace}bulge parameter sequence.
\vfill
\begin{figure}[hb]
\special{psfile=./n4762AAA.ps angle=0 hoffset=-58 voffset=-73 hscale=44 vscale=44}
\special{psfile=./fig_n4762.ps hoffset=120 voffset=-108 hscale=50 vscale=50}
\caption{(left) Ellipticity and surface brightness along the major axis of NGC\ts4762
measured by fitting elliptses to the isophotes in the ACS and SDSS $g$-band images. The dashed curves
show a decomposition of the profile inside the fit range (vertical dashes). The bulge, bar, lens and disk
are represented by S\'ersic functions with indices $n$ given in the figure. Their sum
(solid curve) fits the data with an RMS of 0.033 V mag arcsec$^{-2}$.
(right) Parameter correlations showing the results of the bulge-disk
decomposition. The green filled circles with the brown centers show the
total parameters measured by Ferrarese {\it et al.\ } (2006) for the bulge and disk together. They are connected
by straight lines to the parameters of the bulge (dark brown filled circles) and disk
(dark green crosses). From KB2012.
}
\end{figure}
\eject
NGC 4452 is closely similar to NGC 4762 but is even more extreme. Figure 1.64 (left) shows that it, too, is an
edge-on SB(lens)0 galaxy. The decomposition robustly shows that NGC 4452 has only a very tiny pseudobulge with $n \simeq 1.06 \pm 0.14$
(recall classification criterion (6) in Section 1.5.3) and $PB/T = 0.017 \pm 0.004$. This is an SB(lens)0c galaxy.
\vfill
\begin{figure}[hb]
\special{psfile=./N4452-WIKI-SDSSx.eps hoffset=0.3 voffset=195 hscale=35.5 vscale=35.5}
\special{psfile=./n4452AAA.ps angle=0 hoffset=-58 voffset=-71 hscale=44 vscale=44}
\special{psfile=./fig_n4452.ps hoffset=120 voffset=-105.7 hscale=50 vscale=50}
\caption{(top left) SB(lens)0 galaxy NGC\ts4452. The tiny pseudobulge is almost invisible. The inner disk
is edge-on and very flat; it again consists of two
shelves in surface~brightness. Including the outer, thicker disk, these three shelves are
signatures of a bar, lens and disk. (bottom left) Ellipticity $\epsilon$ and
surface brightness $\mu_V$ along the major axis of NGC 4452. The five dashed curves show a decomposition of
the profile inside the fit range (vertical dashes). The nucleus,
bulge, bar, lens and disk are represented by S\'ersic functions with indices $n$ given in
the figure. Their sum (solid curve) fits the data with RMS = 0.044 V mag arcsec$^{-2}$.
(bottom right) Parameter correlations showing the results of the bulge-disk
decomposition. The green filled circles with the blue centers show the
total parameters measured by Ferrarese {\it et al.\ } (2006) for the bulge and disk together. These points are connected
by straight lines to the parameters of the pseudobulge (blue filled circles) and disk (dark green crosses).
From KB2012.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The parameter correlations in Figs.~1.63 and 1.64 serve to emphasize how bulge-disk decomposition improves our understanding
of the E sequence. The small black filled dots show the parameters measured by Ferrarese {\it et al.\ } (2006) for the ACS Virgo
cluster survey S0s. They do not violate the E sequence. But they do combine bulge and disk properties
into one set of parameters, so they fail to show something that is very important. In each of these two galaxies,
the bulge is tiny, comparable in luminosity to the smallest ellipticals. The classical bulge of NGC 4762 helps to
define the extension of the E sequence toward objects that are more compact than any spheroidal. Even the tiny pseudobulge
of NGC\ts4452 lies~near~the compact end of the E$+$bulge sequence (cf.~Figs.~1.42 and 1.43, which show other, similarly
compact and tiny pseudobulges). Figures 1.68 and 1.69 will summarize the parameter correlations for classical bulges
and S0 disks, respectively. Here, I want to emphasize two things. First, there exist S0 galaxies with
classical-bulge-to-total luminosity ratios $B/T$ that range from almost 1 to essentially zero. The pseudobulge
in NGC 4452 is so small that one cannot hide a significant classical bulge in that galaxy. Second, both NGC 4762
and NGC 4552 have vertically thickened and warped outer disks. Both galaxies have nearby companions. Kormendy \&
Bender (2012) interpret these results as indicating that the outer disks are tidally warped and being heated dynamically
in the vertical direction. They present evidence that many other S0 and Sph galaxies in the Virgo
cluster are dynamically heated, too. Thus NGC 4762 and NGC 4552 are ``missing links'' that have some properties of
S0 galaxies and some properties of the brightest Sph galaxies.
NGC 4638 is even more spectacularly an S0 -- Sph transition object. Figure 1.65 shows (bottom) the large-scale structure
and (top) an embedded, edge-on disk and bulge in an enlargement from {\it HST\/} images. When we wrote KB2012, this
structure was, to our knowledge, unique. Figure 1.65 (bottom) suggests that NGC 4638 is an edge-on
S0 whose bulge happens to be very boxy. This would be interesting but not unique; boxy bulges are discussed in Section 1.5.2.9.
But already in the bottom panel of Fig.~1.65, the structure looks suspiciously unusual: the brightness gradient in the boxy
structure is very shallow, like that in its companion, the normal Sph,N galaxy NGC 4637. The top panel of Fig.~1.65 shows an
almost-round, small bulge in NGC 4638 with a normal, steep brightness gradient. To our surprise, {\it the brightness profile robustly shows\/}
(Fig.~1.66) {\it that the outer boxy structure has a S\'ersic brightness profile with $n = 1.11 \pm 0.12$ characteristic of the
main body of a Sph galaxy. This profile is not concave-upward, as it would be if the bulge and the boxy structure where part of
the same component with $n \gg 4$.}
\vfill\eject
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./N4638ACSrgb3.eps hoffset=62 voffset=221 hscale=33 vscale=33}
\special{psfile=./vcc1938wiki.eps hoffset=0 voffset=-4 hscale=35.3 vscale=35.3}
\caption{(top) Color image of NGC 4638 = VCC 1938 made from the {\it HST} ACS $g$, mean of $g$ and $z$, and $z$ images.
This image shows the edge-on disk and central bulge. Brightness is proportional to the square root of intensity,
so the brightness gradient in the bulge is much steeper than that in the boxy halo. The very red foreground star
near the NE side of the disk is also evident in the bottom image.
(bottom) Color image of NGC 4638 = VCC 1938 from {\tt WIKISKY}. The brightness ``stretch'' emphasizes
faint features, i.{\thinspace}e., the extremely boxy, low-surface-brightness halo in which the S0 disk and bulge are
embedded. The elongated dwarf to the west of NGC 4638 is the Sph,N galaxy NGC 4637. Like many other spheroidals,
NGC~4637 is flatter than any elliptical. Note also that VCC 2048 (not illustrated) is another ``missing link''
galaxy with both S0 and Sph properties: like NGC 4637, it is flatter than any elliptical; its main body is clearly a Sph,
but it contains an embedded, tiny S0 disk (see KB2012, from which the above images are taken).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
Kormendy \& Bender (2012) therefore conclude that {\it NGC 4638 contains three structural components, and edge-on
S0 galaxy that consists of an $n = 3.6 \pm 1.4$ classical bulge plus an $n = 0.5 \pm 0.1$ Gaussian disk embedded in
a normal Sph galaxy with $n = 1.11 \pm 0.12$. I.{\thinspace}e., NGC 4638 has the properties of both an S0 and a Sph galaxy.}
VCC 2048 is similar (Fig.~1.65 caption).
It is instructive to compare the parameters of the three components of NGC 4638 with their counterparts in pure
S0 and Sph galaxies (Fig.~1.67). The classical bulge helps to define the compact end of the normal E{\thinspace}--{\thinspace}Sph
parameter sequence. It is within a factor or $\sim$\ts2 as compact as M{\thinspace}32. The disk proves to have the highest
effective brightness of any S0 disk shown in Fig.~1.69. The reasons are (1) that it is edge-on, so the path length
through it is large, and (2) that its profile is Gaussian rather than exponential; the strong outer truncation
results in small $r_e$ and hence bright $\mu_e$. The boxy component is consistent with the extrapolation of the
Sph sequence; it is the brightest Sph galaxy known in the Virgo cluster.
\vfill
\begin{figure}[hb]
\special{psfile=./v1938AAA.ps angle=0 hoffset=-16 voffset=-87 hscale=55 vscale=55}
\caption{Ellipticity $\epsilon$ and surface brightness $\mu_V$ along the major axis of NGC 4638 as measured
on the {\it HST} ACS and SDSS $g$ images. Dashed curves show a three-S\'ersic-function decomposition of
the profile inside the fit range (vertical dashes). The bulge is small, but it is classical.
The disk has a Gaussian profile, as do many other S0s discussed in KB2012. Remarkably, the outer, boxy halo
is clearly distinct from the bulge and disk and has a S\'ersic index $n = 1.11 \pm 0.12$.
The sum of the components (solid curve) fits the data with an RMS of 0.054 V mag arcsec$^{-2}$. From KB2012.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
NGC 4638 lives in a high-density part of the Virgo cluster where strong dynamical heating is plausible.
Kormendy \& Bender interpret the boxy Sph part of the galaxy as the dynamically heated remnant of the outer disk.
Because these stars are no longer part of a disk, the disk that remains has a strongly truncated, i.{\thinspace}e., Gaussian
profile.
KB2012 discusses additional evidence that higher-luminosity Sphs are, by and large, more disky.
This is consistent with the suggestion that dynamical heating is one of the S\thinspace$\rightarrow${\thinspace}Sph transformation
processes and that this heating has the smallest effect on the biggest, most robust galaxies.
\vfill
\begin{figure}[hb]
\special{psfile=./f16.eps hoffset=-50 voffset=-156 hscale=75 vscale=75}
\caption{Parameter relations showing results of the bulge-disk-Sph decomposition of NGC 4638. The green circles
with the brown centers show the total parameters measured by Ferrarese {\it et al.\ } (2006) for all components together. These points
are connected by lines to the parameters of the classical bulge (brown circles), the disk (green crosses),
and the Sph halo (green square). From KB2012.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsubsection{Interim summary and road map}
In Section 1.7.4.2, our discussion of the E{\thinspace}--{\thinspace}Sph dichotomy branched out in a new direction --
the close relationship between Sphs and S0 galaxy disks. Section 1.7.5 pursues this.~Meanwhile, it is useful to summarize
where~we~are.
Section 1.7 is about environmental secular evolution. The ``bottom line'' will be that a
variety of environmental processes appear to have transformed some intermediate-Hubble-type spiral galaxies
into S0s and some late-type spiral and Magellanic irregular (Im) galaxies into Sphs. Sph galaxies will prove to be bulgeless
S0s. ``Missing link'' galaxies that have some S0 and some Sph properties are the new subject that entered
the above discussion.
Recall that we were in the process of investigating the E{\thinspace}--{\thinspace}Sph dichotomy. That is, even though they
{\it look\/} similar, elliptical and spheroidal galaxies have quantitatively different structural parameters
and parameter correlations. This imples that they have different formation histories -- histories that we are
in the process of deciphering. I reviewed the history of the above discovery,
concentrating on how improved measurements and enlarged galaxy samples have strengthened the evidence for the
dichotomy. Originally not recognized (Fig.~1.55), it was first found using small galaxy samples (Fig.~1.57) and
since has been confirmed using 90 ellipticals and 295 spheroidals (Fig.~1.61).
Our next aim has been to add classical bulges, to increase the sample size and to further show that tiny
ellipticals are not compact because they are tidally stripped. This led us into a discussion of bulge-disk
decomposition and a description of three example galaxies, two of which have classical bulges that are substantially
as compact as the smallest ellipticals. In our standard picture of bulge formation by major mergers, these
bulges would have formed before their attendant disks. It is implausible that such bulges are compact because they
were tidally stripped.
The bulge parameters measured and collected in KB2012 now allow us to
``pay the piper'' in confirming our definition of bulges as (essentially) ellipticals that live in the middle of a
disk. This is the subject of Section 1.7.4.4. I then return to Sph and S0 galaxies in Section 1.7.5.
\subsubsection{Classical bulges and ellipticals satisfy the same fundamental plane parameter correlations.~II.~Results}
Figure 1.68 shows the parameter correlations from Fig.~1.61 with 57 bulges added. Of these, 35 are known to be
classical via their parameters and the discussion in the source papers (see the key). I also add 22 bulges from
Baggett {\it et al.\ } (1998); they are shown with open circles, because we cannot be certain that they are classical. I examined
all of these galaxies and ensured as well as possible (using Section 1.5.3) that their bulges are classical.
\vfill\eject
Figure 1.68 confirms the assumptions that underlie our definition of classical bulges:~they satisfy the same
parameter correlations as do ellipticals. Given the uncertainties in bulge-disk decomposition, there is no
evidence that the scatter for classical bulges is different from that for ellipticals. This is an update of a result
that has been found previously, e.{\thinspace}g., by Fisher \& Drory (2008, 2010:~Fig.~1.41 here). Pseudobulges can satisfy
these relations, but they have much larger scatter, and they fade out by becoming low in surface brightness, not by becoming compact
(Figs.~1.42 and 1.43).
\vfill
\begin{figure}[hb]
\special{psfile=./fig_spiral_disks_bulge_canary.ps hoffset=-70 voffset=-166 hscale=80 vscale=80}
\caption{Global parameter correlations from KFCB, from Kormendy (2009), and from Fig.~1.61 here including the sample of
bulges from KB2012. All ACS VCS S0s are included, three as Sphs and 23 as bulges. For simplicity,
points in further figures encode bulge type but not the source of the data.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{Sph galaxies are bulgeless S0 galaxies}
Figure 1.69 shows Fig.~1.68 with the disks of S0 galaxies added. Kormendy \& Bender (2012)
conclude that spheroidals are continuous in their parameter correlations with the disks (but not the bulges) of S0
galaxies. People~call a galaxy an S0 if it has smooth, nearly elliptical isophotes and {\it two components\/},
a bulge and a disk. If it has no bulge and only one, shallow-surface-brightness-gradient component,
we give it a different name -- a spheroidal.
\vfill
\begin{figure}[hb]
\special{psfile=./fig_spiral_disks_s0disks_canary.ps hoffset=-58 voffset=-158 hscale=77 vscale=77}
\caption{Parameter correlations for ellipticals, bulges and Sphs with disks of 126 S0s added
(green points outlined in black). Bulges and disks of S0 galaxies are plotted
separately. The middle panel shows the Freeman (1970) result that disks
of big galaxies tend to have the same central surface brightness $\mu_0 = \mu_e - 1.822$
mag arcsec$^{-2}$ for an exponential.
\omit{Here, $\mu_e \simeq 22.0$ $V$ mag arcsec$^{-2}$ corresponds to $\mu_0 = \mu_e - 1.82 \simeq
20.2$ $V$ mag arcsec$^{-2}$ or about 21.1 $B$ mag arcsec$^{-2}$. This is slightly brighter
than the Freeman value of 21.65 $B$ mag arcsec$^{-2}$ because many of the disk parameters are
not corrected to face-on orientation. } We conclude that Sphs are continuous with the disks
but not the bulges of S0 galaxies. Updated from KB2012.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
\begin{figure*}
\vskip 2.75truein
\special{psfile=./figure70.ps hoffset=27 voffset=-111 hscale=44 vscale=44}
\caption{Maximum rotation velocity of the bulge $V_{\rm circ,bulge}$ (red points)
and disk $V_{\rm circ,disk}$ (black points) derived in bulge-disk-halo decompositions of the
rotation curves of galaxies whose outer, dark matter rotation velocities are $V_{\rm circ}$.
Equality of the visible and dark matter rotation velocities is shown by the dotted~line.
Every red point has a corresponding black point, but many galaxies are bulgeless and then
only a disk was included in the decomposition.
This figure illustrates the well known rotation~curve~conspiracy,
$V_{\rm circ,bulge} \simeq V_{\rm circ,disk} \simeq V_{\rm circ}$ for~the~halo
(Bahcall \& Casertano 1985; van Albada \& Sancisi 1986; Sancisi \& van Albada~1987).
It shows that the conspiracy happens mostly for galaxies with $V_{\rm circ} \sim 200$~km~s$^{-1}$.
The lines are least-squares fits with variables symmetrized around 200 km s$^{-1}$.
The bulge correlation is steeper than that for disks;
bulges disappear at $V_{\rm circ} \simeq 104 \pm 16$ km s$^{-1}$.
From Kormendy \& Bender (2011) and Kormendy \& Freeman (2013).
\pretolerance=15000 \tolerance=15000
}
\end{figure*}
\phantom{00000000}
\vskip -39pt
That bulges disappear where Fig.\ts1.69 suggests is shown~in~Fig.\ts1.70. Rotation curve
decompositions confirm what our experience tells us: bulges disappear at $V_{\rm circ} \sim 100$
km s$^{-1}$ or $M_{\rm V,{\thinspace}disk} \sim -18$ (Tully \& Fisher 1977). There is noise; e.{\thinspace}g.,
M{\thinspace}33 has $M_{\rm V,{\thinspace}disk} = -19.0$ and $V_{\rm circ} \simeq 135 \pm 10${\thinspace}km{\thinspace}s$^{-1}$
(Corbelli 2003) and no bulge (Kormendy \& McClure 1993). But of course, we also
expect that disks fade when they are transformed from S$+$Im~to~S0. Figure 1.70 is an important observational
``target'' for future work: the formation physics that underlies it is largely unknown. But there
is ample evidence that bulges disappear approximately where the Sph and S0 disk sequences meet
in Fig.~1.69. This is enough to explain the different names.
Kormendy \& Bender (2012) suggest that the kink in the $\mu_e${\thinspace}--{\thinspace}$M_V$ correlation that
happens roughly at the transition from S0 disk to Sph tells us where the correlation turns into a sequence of
decreasing baryon retention at lower galaxy luminosity. It is not an accident that this happens roughly where
the bulge contribution to the gravitational potential well disappears.
\vfill \eject
\subsection{Spiral and irregular galaxies have the same structural correlations as S0 galaxy disks and Sph galaxies}
Kormendy's (1985, 1987) conclusion that Sph galaxies are defunct dS$+$Im galaxies depended critically on the
observation (Fig.\ts1.57) that they~all~have the same structural parameter correlations.~That result was based~on~a~small
number of galaxies and has never been checked. KB2012 updates and extends this test with 407 galaxies
that cover the complete luminosity range from the tiniest dwarf irregulars to the brightest Sc disks. Figure 1.71 shows
that S$+$Im galaxies do indeed have the same parameter correlations as S0 disks and spheroidals.\thinspace~Therefore they
are closely related.
\vfill
\begin{figure}[hb]
\special{psfile=./fig_spiral_disks_spiral_canary.ps hoffset=-56 voffset=-160 hscale=76.5 vscale=76.5}
\caption{Fig.~1.69 correlations with disks of Sa{\thinspace}--{\thinspace}Im galaxies added
(blue points for 407 galaxes from 14 sources listed in the keys).
When bulge-disk decomposition is needed, the components are plotted separately.
From KB2012.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{A revised parallel-sequence classification of galaxies}
Figure 1.72 shows our proposed revision of Sidney van den Bergh's (1976) morphological classification scheme based on the foregoing
observations.
Van den Bergh put S0 galaxies in a sequence that parallels the spirals; the classification parameter that
determines the stage along either sequence is the (pseudo)bulge-to-total luminosity ratio, $(P)B/T$. Pseudo~and~classical
bulges are not distinguished; in a classification based on small-scale~images, this is the only practical strategy. Only $(P)B/T$
and not parameters such as spiral arm pitch angle determine the stage, so van den Bergh's classification of spirals
is not quite the same as Sandage's or de Vaucouleurs's.~We do not address this issue. Figure 1.72 adopts van den Bergh's
theme of placing S0s and spirals in parallel sequences based only on $(P)B/T$.
Kormendy \& Bender extend ven den Bergh's discussion in two ways. \vskip -18pt \phantom{0000000000000000}
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{They resolve the uneasy aspect of van den Bergh's paper that he listed~no~S0c or later-type S0 galaxies. Based on a
comparison of $(P)B/T$ ratios of S0s with spirals of known Hubble type, they find several
of the ``missing'' late-type S0s; e.{\thinspace}g., the S0bc galaxy NGC 4762; the S0c galaxy NGC 4452 (Section 1.7.4.2).
NGC 4452 is also singled out as an S0c by Cappellari {\it et al.\ } (2011), who independently propose a parallel-sequence
classification based on kinematic maps. A few other S0cs are known (Laurikainen {\it et al.\ } 2011; Buta 2012). }
\item{They place Sph galaxies in parallel with Im galaxies. They note that, in a more detailed classification that includes
Sd and Sm galaxies, some Sphs (e.{\thinspace}g., ones with nuclear star clusters) would be placed in parallel with late-type
(especially Sm) spirals, and others (e.{\thinspace}g., ones without nuclei) would be put in parallel with Ims.
Adding Sph galaxies at the late-type end of the S0 sequence for the first time finds a natural home for them in a
morphological classification scheme.}
\end{enumerate}
\vfill
\begin{figure}[hb]
\special{psfile=./TuningFork-S0-ss.eps hoffset=0 voffset=-4 hscale=31 vscale=31}
\caption{Revised parallel-sequence morphological classification of galaxies.
The E types are from Kormendy \& Bender (1996). Transition objects between
spirals and S0s (van den Bergh's anemic galaxies) exist but are not illustrated.
Bulge-to-total ratios decrease toward the right; Sc and S0c galaxies have tiny or no
pseudobulges. Sph and Im galaxies are bulgeless. From KB2012.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
It is important to understand which observations lead to Fig.~1.72\footnote{Allan Sandage (2004)
accused Sidney van den Bergh of hermeneutical circularity in setting up his parallel-sequence
classification, which -- he thought -- involved too much interpretation. A prosaic but sufficient
paraphrase is ``circular reasoning''. The basic idea is this: a morphological classification of galaxies should be
set up based only on observations and not on interpretation (see Section 1.3.4). The aim is that regularities revealed by the
classification will later aid interpretation. However, if some interpretation is used in setting up the classification,
then the ``aid'' that the classification can provide is foreordained. This is circular reasoning. In practice, science
is not as ``black and white'' as Sandage suggests. Even the greatest scientists (Sandage explicitly picked Hubble as one
of these) set up classifications with future interpretation~in~mind. They make decisions about which observations to
treat as relevant and which ones to treat as secondary. Van den Bergh did this faithfully; Sandage was just uneasy about
how important those decisions were. It should be clear from these remarks that I respect both sides of the argument.
In the end, further advances reviewed here have, I claim, vindicated van den Bergh's decisions. For a classification
to be successful, it must ultimately motivate a clearcut paradigm of interpretation. Van den
Bergh's parallel-sequence classification has done this.}.
They involve quantitative parameter measurements, but they do not involve interpretation. First, the
observations that establish E{\thinspace}--{\thinspace}S0{\thinspace}--{\thinspace}Sph continuity:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{Galaxies with smooth, nearly elliptical isophotes, little cold gas and little star formation range in bulge-to-total
luminosity ratio from $B/T = 1$ to $B/T = 0$. Here, the existence of a bulge component and the measurement of $B/T$
are based on quantitative surface photometry, on nonparametric measurements of structural parameters for elliptical and Sph
galaxies by integrating the observed isophotes, on parametric (S\'ersic-function-based) bulge-disk decomposition for
disk galaxies, and on the resulting structural parameter correlations (Figs.~1.68, 1.69). When $B/T = 1$, we call
the object an elliptical; when $1 > B/T > 0$, we call the central component a bulge and the outer component -- if flat\footnote{This
is to prevent confusion with cD galaxies, which have cluster-sized debris halos, not disks.}~--
a disk, and when $B/T = 0$, we call the galaxy a spheroidal.}
\item{In the structural correlations between effective radius $r_e$, effective brightness $\mu_e \equiv \mu(r_e)$ and total
absolute magnitude, Sph galaxies define a sequence that is continuous with the disks but not the bulges of S0 galaxies.
There is some overlap in luminosity between Sphs and S0 disks.}
\item{NGC\ts4762, NGC\ts4452, NGC\ts4638 and VCC\ts2048 are galaxies that have both~S0 and Sph properties. We know this
because all four galaxies are seen edge-on. All contain flat disks. Three contain a tiny (pseudo)bulge
(VCC 2048 contains only a nuclear star cluster). The thick outer components of all four galaxies have parameters --
including S\'ersic indices $n \sim 1$ -- that are indistinguishable from those of Sphs. That is, these galaxies consist of
S0 central parts embedded in Sph or Sph-like outer halos. This helps to establish S0{\thinspace}--{\thinspace}Sph continuity.}
\item{Bigger Sph galaxies tend to be dynamically more S0-disk-like:~they have larger ratios of rotation
velocity to velocity dispersion (van Zee {\it et al.\ } 2004). Note: at all $L$, some Sphs rotate slowly
(see KB2012 for a review).
}
\end{enumerate}
\noindent These observations justify our conclusion that Sph galaxies are continuous in their properties with S0 disks,
which in turn motivates our juxtaposition of Sph galaxies with S0cs. In essence, Sph galaxies are bulgeless S0s.
\vfill\eject
\noindent ~~Observations that suggest parallel sequences of S$+$Im and S0$+$Sph galaxies:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{For every $B/T$ ratio that is observed in an S0 or Sph galaxy, there are S or Im galaxies that have
corresponding, similar $B/T$ ratios. We see a continuous transition from S0 to E as
$B/T \rightarrow 0$. We do not know whether Sas also have a continuous
transition $B/T \rightarrow 0$. The Sombrero galaxy (NGC 4594) has one of the largest bulge-to-total ratios known,
$B/T = 0.93 \pm 0.01$ (Kormendy \& Bender 2013). I know no Sa with larger $B/T$. Thus it is prudent to retain a
classification S0(0) that is intermediate between elliptical and both~Sa~and~S0a.}
\item{Except for details such as spiral structure, the {\it global\/} structure of spirals and S0s is similar.
For any generic Sa, Sb, or Sc galaxy, there are similar S0a, S0b, or S0c galaxies. In particular,
the bulges of spiral and S0 galaxies both satisfy the E parameter correlations. The fractions of classical
and pseudo bulges are similar at similar stages along the tuning fork (Kormendy \& Kennicutt 2004). And the disks
of S$+$Im galaxies have almost the same parameter correlations as Sph galaxies and S0 disks (Fig.~1.71).}
\item{Some Sph galaxies contain low-contrast spiral structure; therefore they contain embedded disks
(Jerjen {\it et al.\ } 2000, 2001;
Barazza {\it et al.\ } 2002;
De Rijcke {\it et al.\ } 2003;
Graham {\it et al.\ } 2003;
Ferrarese {\it et al.\ } 2006;
Lisker {\it et al.\ } 2006, 2007, 2009).}
\item{Many dSph companions of our Galaxy contain intermediate-age stellar populations
(Da Costa 1994;
Mateo 1998:~Fig.~1.73 here;
Tolstoy {\it et al.\ } 2009).
Both among the Galaxy's satellites and in the larger {\it HST} ACS Nearby Galaxy Treasury Survey
(Weisz {\it et al.\ } 2011a, b), {\it dS, dIm and dSph galaxies have similar, heterogeneous star formation
histories except that the star formation rate in dSph galaxies is currently zero.}~This is a matter of
definition{\thinspace}--{\thinspace}if~a~dwarf contains gas and star formation, it is called dSph/dIm or
dIm. The Virgo cluster contains several examples (Ferrarese {\it et al.\ } 2006; KB2012).}
\vfill
\begin{figure}[hb]
\special{psfile=./mateo-sfr-dSph-dIlo.eps hoffset=-6 voffset=-19 hscale=60.5 vscale=60.5}
\caption{Star formation histories of dSph and dIm galaxies from Mateo (1998).
Relative star formation rates are shown as a function of time since the Big Bang.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\item{Similarly, some spiral galaxies in clusters contain gas only near their centers, and some S0s
contain near-central gas and small amounts of star formation. This is discussed in Section 1.7.9.
Here, it again means that some S0 galaxies are less different from some spiral galaxies than optical
images would suggest.}
\item{Van den Bergh's (1976) ``anemic galaxies'' are omitted from Fig.~1.72 for simplicity,
but they are galaxies that are intermediate in properties between spiral and S0 galaxies.
Their contain only low-amplitude spiral structure star formation. The transition from
S to anemic to S0 looks continuous.}
\end{enumerate}
\noindent Thus a substantial collection of morphological and structural parameter observations
motivate our suggested parallel-sequence galaxy classification. We revise it to place
Sph galaxies at the end of the S0 sequence, juxtaposed with the latest-type spirals and irregulars.
It is important to note three things. We do not intend to imply that the luminosity function of
galaxies is the same at all stages of the tuning fork. Indeed, we already know that
Im and Sph galaxies tend to have lower luminosities than earlier-type S and S0 galaxies. Second,
we do not mean to imply that galaxies are equally abundant at every stage of either the S$+$Im
or the S0$+$Sph sequence. Indeed, it is clear that S0c galaxies are much rarer than
Sphs or earlier-type S0s. This provides a hint for interpretation. But it is not a reason to
change the classification. And third, we do not intend~to~fix~what~isn't~broken. Our suggestion
of a parallel-sequence classification is not meant to replace Hubble classes. We propose
Fig.~1.72 as a complement to Hubble classification, useful because it encodes a different collection
of observations that are relevant to a different collection of questions about formation physics.
\vskip -24pt
\phantom{000000000000000000000000}
\subsection{Parallel-sequence classification and\\bimodality in the galaxy color-magnitude relation}
Work on galaxy formation nowadays concentrates on the history of star formation in the Universe
and on understanding stellar populations. The iconic observation that current work tries to explain is the
color bimodality of galaxies in the color-magnitude relation as revealed by the Sloan Digital Sky Survey (SDSS)
at low redshifts
(Strateva {\it et al.\ } 2001;
Bernardi {\it et al.}~2003;
Kauffmann {\it et al.\ } 2003a, b;
Hogg {\it et al.\ } 2002, 2004;
Blanton {\it et al.\ } 2003, 2005;
Baldry {\it et al.\ } 2004)
and by HST studies of galaxies at high redshifts.
Figure 1.74 shows this result and illustrates how the E{\thinspace}--{\thinspace}S0{\thinspace}--{\thinspace}Sph arm of the parallel-sequence
tuning fork relates to it. The bright end of the prominent and thin red sequence consists of ellipticals, S0s,
and some early-type spirals. But their luminosity functions are bounded at low $L$. When the red
sequence is extended fainter, it must become dominated by Sphs at $M_V \ll -18$. The deepest surveys
detect this (Blanton {\it et al.\ } 2005; Drory {\it et al.\ } 2009).
\vfill\eject
\cl{\null}
\begin{figure*}
\vskip 2.75truein
\special{psfile=./CattaneoFig-ablo.eps hoffset=72 voffset=-14 hscale=31 vscale=31}
\caption{Correspondence between our parallel-sequence classification and the color bimodality of galaxies
in the SDSS color-magnitude relation. The top panel shows contours of galaxy number density in the correlation
between SDSS $u - r$ color and galaxy baryonic mass $M/M_\odot$ (Baldry {\it et al.\ } 2004). The narrow
``red sequence'' of mostly-non-star-forming galaxies and the broader ``blue cloud'' of star-forming galaxies
are well known. The bottom panel shows the morphological types from Fig.~1.72 that dominate in various parts of the top panel.
The rapidly rising luminosity function of spheroidals at the low-mass limit of the diagram may account for
the contour in the top panel at (9.0, 2.2). The ``take-home point'' is that the bright end of the red sequence
consists of ellipticals, S0s and early-type spirals, but the faint end is dominated by Sph galaxies.
Adapted from KB2012.
\pretolerance=15000 \tolerance=15000
}
\end{figure*}
\phantom{Bloody random text to fix CUP's vertical spacing quirks.}
\vskip -70pt
\phantom{Bloody random text to fix CUP's vertical spacing quirks.}
\subsection{S+Im $\rightarrow$ S0+Sph galaxy transformation processes}
The natural interpretation of the observations discussed in this section is that S0 and Sph galaxies
are defunct, ``red and dead'' versions of spiral and irregular galaxies that have been transformed by physical processes~to
be discovered. Most of these turn out to be environmentally driven~and~slow.
The relative ordering and positioning of galaxies in the parallel-sequence classification is justified
on purely observational grounds based on choices of which results to use in the classification and which
to regard -- for present purposes -- as secondary. However, it would be disingenuous to pretend that I and many
others have not been thinking about the underlying formation and evolution processes for a long time. This is
inevitable in a world where no observational curiosity goes uninterpreted for long. In fact, there are many
candidate processes. Astronomers frequently argue about which of many compelling theories are correct.
My experience is that these arguments go on longest when everybody is correct. This is one of those occasions.
Candidate S+Im $\rightarrow$ S0+Sph galaxy transformation processes are reviewed in KB2012.
Here, I list them briefly including only the most important supporting observations:
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item{The main {\it internal\/} evolution process was already mentioned in Section 1.7.3. Below a fiducial mass that
corresponds to $V_{\rm circ} \simeq 100$ km s$^{-1}$, i.{\thinspace}e., just where bulges disappear (Fig.~1.70) and
therefore galaxy names get changed from S0 to Sph (Fig.~1.69), supernova-driven winds are expected to
expell a larger fraction of a galaxy's baryons from lower-mass objects regardless of whether they now are irregular or spheroidal
(e.{\thinspace}g., Larson 1974;
Saito 1979;
Dekel \& Silk 1986;
Vader 1986;
Schaeffer \& Silk 1988; see
Hensler {\it et al.\ } 2004;
Stinson {\it et al.\ } 2007
for two among many more recent discussions). This is why I suggested that the decreasing surface brightnesses of Sph and Im galaxies
at lower luminosities (Fig.~1.71) is a baryon retention sequence.} \vskip 6pt
\item{The most thoroughly studied {\it external\/} transformation process is ram-pressure stripping of cold gas by
hot gas in clusters and perhaps groups of galaxies.
Suggested by Gunn \& Gott (1972), the idea has varied in popularity. It has never gained
widespread acceptance, perhaps in part because Dressler~(1980) argued that it was {\it not\/} the main cause of the
morphology-density relation that spiral galaxies get less abundant whereas S0 galaxies get more abundant
at higher galaxy densities in clusters. Dressler argued that this result does not strongly depend on cluster richness.
However, examination of his \hbox{Fig.~8{\thinspace}--{\thinspace}10}~(see~Fig.\ts25
in KB2012) shows that the ratio of S0 to S galaxies increases from low-concentration clusters to
high-concentration clusters to \hbox{X-ray-emitting clusters}. An alternative hypothesis
is that ram-pressure stripping happens more easily in clusters of all richness than simple energy arguments suggest.
More recent results bear this out:} \vskip 6pt
\item[\phantom{(a)}]{Compelling evidence for ongoing ram-pressure stripping is provided by H$\alpha$ and H{\thinspace}{\sc i} observations of
spiral galaxies in the Virgo cluster
(Chung {\it et al.\ } 2007;
Kenney {\it et al.\ } 2004, 2008).
Figure 1.75 shows some of these results. Many spiral galaxies embedded in the X-ray gas that fills the cluster
center show remarkable H{\thinspace}{\sc i} tails. The above authors interpret them as cold gas that trails behind the galaxy
after having been stripped from the galaxy by the hot gas in the cluster. The spectacular H$\alpha$ filaments that point
from the tidally disturbed NGC 4438 toward the hot-gas-rich NGC 4406 (top panel in Fig.~1.75) are similarly interpreted as
ram-pressure stripped. Also, many spirals near the center of the cluster are
much smaller and more depleted in H{\thinspace}{\sc i} than are galaxies in the cluster outskirts
(Cayatte {\it et al.\ } 1990;
Chung {\it et al.\ } 2009).
Kormendy \& Bender (2012) note that ``the three most depleted galaxies illustrated in Fig.~8 of Chung {\it et al.\ } (2009) are
NGC 4402, NGC 4405 and NGC 4064. They have a mean absolute magnitude $M_V = -19.4 \pm 0.2$. Virtually all Sphs are fainter
than this.~~~If even the deep gravitational potential wells of still-spiral galaxies
}
\end{enumerate}
\eject
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./RamVirgolo.eps hoffset=8 voffset=-20 hscale=61 vscale=61}
\caption{The large panel shows 0.5 -- 2.0 keV X-ray brightness contours in the Virgo cluster as measured with {\it ROSAT}
by B\"ohringer {\it et al.\ } (1994). Superposed are grayscale images of galaxies with H{\thinspace}{\sc i} tails indicative of
ongoing ram-pressure gas stripping (white or black contours). The H{\thinspace}{\sc i} images are from Chung {\it et al.\ } (2007);
Kenney {\it et al.\ } (2004); Abramson {\it et al.\ } (2011). The color inset image and large image at top show the
H$\alpha$ emission filaments that extend from NGC 4438 to NGC 4406 (Kenney {\it et al.\ } 2008). Each small inset image shows
the galaxy centered on its position in the cluster, but the panels are magnified.
This figure is adapted from Fig.~4 in Chung {\it et al.\ } (2007) and is reproduced from KB2012.
\pretolerance=15000 \tolerance=15000
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\begin{enumerate}[(a)]\listsize
\renewcommand{\theenumi}{(\alph{enumi})}
\item[\phantom{(a)}]{suffer H{\thinspace}{\sc i} stripping,
then the shallow potential wells of dS$+$Im galaxies are more likely to be stripped.'' Substantial additional
evidence also suggests that ram-pressure stripping is more effective than we thought (see KB2012 and
van Gorkom \& Kenney 2013 for reviews).}\vskip 7pt
\item[\phantom{(a)}]{Can ram-pressure stripping still happen in the Local Group's much shallower gravitational
potential well? Compelling observations which indirectly suggest that the answer is ``yes'' are shown
in Fig.~1.76. Close companions of our Galaxy, of M{\thinspace}31, and of other nearby giant galaxies are almost all spheroidals;
distant companions are irregulars; Sph/Im transition galaxies tend to live at intermediate distances, and larger irregulars
``survive'' at closer distances to their giant companions
(Einasto {\it et al.\ } 1974;
van den Bergh 1994a,{\thinspace}b,{\thinspace}2007;
Mateo 1998;
Skillman {\it et al.\ } 2003;
Bouchard {\it et al.\ } 2009;
McConnachie 2012).
Hints of similar effects in larger satellites are seen in the Zurich Environmental Study (ZENS:~Cibinel {\it et al.\ } 2012).~Like
previous authors, Kormendy \& Bender suggest that ``ram-pressure stripping can happen even in environments that
are gentler than cluster centers. It may be indirect evidence for a pervasive warm-hot intergalactic medium
(WHIM: Dav\'e {\it et al.\ } 2001) that is difficult to detect directly but that may be enough to convert dwarf irregulars into
spheroidals.''
}\vskip 7pt
\item[\phantom{(a)}]{All this evidence suggests that ram-pressure stripping is one of the processes that transforms late-type,
gas-rich and star-forming galaxies into red and dead S0 and Sph galaxies.}
\vfill
\begin{figure}[hb]
\special{psfile=./Mateo-2008-Fig5lo.eps hoffset=20 voffset=-19 hscale=53 vscale=53}
\caption{From Mateo (2008), the ages of the youngest stellar populations in dwarf galaxy companions
versus Galactocentric or M31centric distance $R$. Except for the Magellanic Clouds, all close companions
of our Galaxy and of M{\thinspace}31 are spheroidals. Distant companions are irregulars except for three
free-flying dSphs (pink points). The Sph/Im transition galaxies mostly lie at intermediate distances.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\item[(c)]{Galaxy harassment is a dynamical process that should operate wherever objects orbit repeatedly through
rapidly varying gravitational potential fields, especially in virialized clusters of galaxies with velocity
dispersions that are much larger than the internal velocities of galaxies. It is the cumulative effect of
many encounters with other galaxies and with the cluster potential. Simulations show that it
strips outer mass, heats disks and promotes gas inflow toward the center that presumably feeds star formation
(Moore\thinspace{\it et{\thinspace}el.}\ts1996, 1998;
Lake {\it et al.\ } 1998).
A variant is tidal stirring of dwarf galaxies on elliptical orbits around our Galaxy or M{\thinspace}31
(Mayer {\it et al.\ } 2001a,{\thinspace}b, 2006).
Kormendy \& Bender concur with the above authors in suggesting that harassment converts late-type disks into spheroidals
and more robust, earlier-type spirals into hotter systems that resemble S0s. A benefit of this picture is that
inflowing gas can feed star formation; this helps to explain why S0 disks and spheroidals -- which must fade substantially
after star formations stops -- do not have much lower surface brightnesses than current versions of S$+$Im progenitors
(see Ferguson \& Binggeli 1994 for a review of this problem). Gravity is not negotiable. Its effects are clean.
It is encouraging how many observations can be tied together into a coherent picture if harassment is one of the galaxy
transformation processes:} \vskip 6pt
\item[\phantom{(a)}]{(1) Dynamical heating plausibly explains why faint spheroidals are not flat, why many bright
spheroidals contain disks (either observed directly when seen edge-on or inferred from their spiral structure), and
why the outer parts of our ``rosetta stone'' galaxies NGC 4762, NGC 4552, NGC 4638 and VCC 2048 are vertically thick
whereas their more robust inner parts are flat.} \vskip 7pt
\item[\phantom{(a)}]{2) Sph and Im galaxies have similar distributions of axial ratios
(Ferguson \& Sandage 1989;
Binggeli \& Popescu 1995).
The latter authors conclude that ``there is no evidence for a difference between the flattening distributions of {\it nucleated\/}
dE,N and classical (giant) Es''.~However, in my experience, many~Sph,N galaxies are flatter than any elliptical.
NGC~4637 in Fig.~1.65 and VCC~2048 in Fig.~10 of KB2012 are examples. Ferguson \& Sandage note that
``The similarity of flattenings of dE (bright, no N) and Im types removes one of the previous objections to the
hypothesis that some dwarf ellipticals could be stripped dI's''. The exact engineering needs further study,
but dynamical heating added to the fact that the smallest galaxies are not flat anyway provides a promising
way to explain the flattening observations.} \vskip 6pt
\item[\phantom{(a)}]{3) Intracluster light is believed to consist of stars that have been stripped by harassment from
individual galaxies. In the Virgo cluster, it is irregular~and still in the early stages of formation
(Mihos {\it et al.\ } 2005, 2009;
Arnaboldi {\it et al.\ } 1996, 2002, 2004;
Castro-Rodrigu\'ez {\it et al.\ } 2009;
Arnaboldi \& Gerhard 2010).
In rich clusters, it is widely observed
(Thuan \& Kormendy 1977;
Adami~{\it et~al.} 2005;
Krick \& Bernstein 2007;
Gonzalez {\it et al.\ } 2007;
Okamura 2011).
When intracluster light is very bright, it is called a ``cD halo''
(Morgan \& Lesh 1965;
Oemler 1976;
Schombert 1988).
These halos are robustly understood to consist of tidally liberated stars and disrupted galaxies
(Richstone 1976;
Dressler 1979;
Kelson {\it et al.\ } 2002).
If gravitational harassment can produce all these effects, it is difficult to see how the mere heating of
smaller galaxies could be avoided.} \vskip 5pt
\item[\phantom{(a)}]{4) Kormendy \& Bender (2012) suggest that the ``new class of dwarfs that are of huge size (10000 pc in diameter
in the extreme) and of very low surface brightness of about 25 B mag arcsec$^{-2}$ at the center'' discovered by Sandage
\& Binggeli (1984) are ``spheroidals that have been harassed almost to death''.} \vskip 5pt
\item[\phantom{(a)}]{5) Anisotropic dynamical heating is a natural way to try to explain triaxial and slowly rotating Sphs (e.{\thinspace}g.,
Bender \& Nieto 1990).
This idea is consistent with the observation that the brightest Sphs are in many cases the most disky and rapidly rotating
ones. However, unusually violent encounter histories can allow a small number of Sphs to be anisotropic even at
the highest masses.} \vskip 5pt
\item[\phantom{(a)}]{6) Carefully engineered encounter histories can make Sph galaxies that have kinematically decoupled
subsystems, even counterrotation of the harassed outer parts with respect to the inner galaxy
(De Rijcke {\it et al.\ } 2004;
Gonz\'alez-Garc\'\i a {\it et al.\ } 2005).~Counterrotating systems are seen in VCC\ts510 (Thomas {\it et al.\ } 2006).} \vskip 5pt
\item[(d)]{Starvation of continued infall of cold gas from the cosmological structure hierarchy is frequently discussed as
an S$+$Im $\rightarrow$ S0$+$Sph transformation process (e.{\thinspace}g.,
Larson {\it et al.\ } 1980;
Balogh {\it et al.\ } 2000;
Bekki {\it et al.\ } 2002;
Boselli {\it et al.\ } 2009).
Absent such infall, star formation at currently observed rates generally uses up the available gas in a few Gyr
(Larson {\it et al.\ } 1980;
Boselli {\it et al.\ } 2009).
Given the observation that the center of the Virgo cluster and {\it a fortiori\/} the centers of rich clusters
of galaxies are dominated by hot gas (e.{\thinspace}g., Fig.~1.75), it is difficult to see how starvation can be avoided.
These are not environments where low-density cold gas can survive to feed continued accretion onto galaxies for
billions of years after the cluster acquires a large velocity dispersion.}
\end{enumerate}
Thus many processes
(1) may explain the growing dark matter dominance (i.{\thinspace}e., baryon deficiency) of lower-mass dwarf galaxies and
(2) can potentially transfrom S$+$Im galaxies into S0$+$Sph galaxies.
Kormendy \& Bender (2012) emphasize that ``the relevant question is not `Which one of these mechanisms is correct?' It is
`How can you stop any of them from happening?' It seems likely to us that all of the above processes matter.''
In this regard, I conclude by emphasizing the following points.
Most papers (Boselli {\it et al.\ } 2009 is an exception) investigate one process; when they get into trouble
explaining some particular observation, they conclude that this process is not the answer.~If all above processes
happen, then there is more potential to understand all of the diagnostic observations. Theorists like to ask clean
questions, investigating one process at a time. There are good reasons for this. But Nature does everything~together.
Eventually, we will have to do likewise if we expect to understand galaxy evolution. The hellishly complicated interplay of
different processes is a feature, not a bug. We cannot avoid this problem forever.
Second, one observation that is frequently cited to disfavor ram-pressure stripping and strangulation is that bulges
are systematically bigger in S0s than in spirals (e.{\thinspace}g., Dressler 1980). But (i) small pseudobulges in late-type spirals
skew the distribution of S-galaxy bulges to smaller luminosities; if such galaxies are transformed before secular evolution
has time to make pseudobulges, the result is a Sph, not an S0. Then it will not be counted among the S0s. Also, (ii) the
distribution of S0 bulges is skewed toward high luminosity by the frequent misclassification of the highest ellipticals as S0s
(KFCB). This happens because their high S\'ersic indices $n \gg 4$ give them a ``core-halo'' appearance that persuades
classifiers to call~them~S0s. An example is the elliptical galaxy NGC 4406, which is classified S0 by Sandage \& Tammann (1981).
Similarly, giant ellipticals~are~commonly~classified~S0$_3$ when they contain nuclear dust disks; e.{\thinspace}g., the elliptical
NGC\ts4459 (KFCB). (iii) When accurate bulge-disk decompositions are carried out, the folklore that S0 galaxies mostly have
large bulges is not confirmed. Among~S0s discussed in KFCB and in KB2012, about half have $(P)B/T < 0.5$ and
six have $(P)B/T$ \lapprox \ts1/3, the value for the Sb~galaxy~M{\thinspace}31.
Finally, (iv) the distribution of $B/T$ in the progenitor galaxies of any transformation process is a strong
function of environment -- bulgeless disks are preferentially made in the field, and merger remnants are preferentially made
in clusters such as Virgo (Kormendy {\it et al.\ } 2010). So field spirals do not fairly sample the potential progenitors of
S0 galaxies in clusters.
Another observation that is frequently cited to disfavor ram-pressure stripping and strangulation is that
S0s have higher surface brightnesses than spirals. Disk fading that follows the shutdown of star formation might lead
us to expect the opposite effect. But Fig.~1.71 shows little sign of such an effect. Note that the surface brightnesses
of both S0 and spiral disks are not corrected for inclination, so they are treated in the same way. However, internal absorption
is important in spirals and not in S0s. So internal-absorption-corrected surface brightnesses of spiral galaxy disks would be brighter
than those of S0 disks. Also, harassment -- like any effect that rearranges angular momentum -- persuades some gas to fall
toward the center and should increase the surface brightness there via star formation.
Finally, Kormendy \& Bender (2012) point out that S $\rightarrow$ S0 transformation does not require the removal
of all gas nor the quenching of all star formation. Some S0s still contain gas, especially molecular gas near their
centers (e.{\thinspace}g.,
Welch \& Sage 2003;
Sage \& Wrobel 1989;
Thronson {\it et al.\ } 1989;
Devereux \& Young 1991;
Young {\it et al.\ } 1995).
These S0s form stars. The Virgo spirals whose outer H{\thinspace}{\sc i} distributions are truncated
have normal central molecular gas content (Kenney \& Young 1986). We do not need to solve
the problem of removing all gas from the deepest parts of galaxy potential wells.
It is clear that much work -- much {\it complicated\/} work -- is still needed on the messy baryonic physics of
galaxy evolution. But I am encouraged to think that the still unknown details of the various transformation processes
do not threaten our overall picture that at least some S0s and likely all Sph galaxies are defunct spiral and irregular galaxies.
\vskip -30pt
\phantom{"Gobble gobble gobble" invisibly to fix CUP section spacing}
\subsection{Environmental secular evolution --\\``An Idea Whose Time Has Come''}
Morphological observations such as those encoded in the parallel-sequence classification of Fig.~1.72 lead to the
robust conclusion that many S0s are closely related to spiral galaxies and that essentially all Sph galaxies are closely
related to the latest-type spirals and irregulars. Figure 1.72 does not directly tell us what that relationship is.
However, in recent years, rapidly improving observations of transformation processes in action, including
H{\thinspace}{\sc i} and H$\alpha$ tails,
relatively recent star formation in dSph galaxies,
vertically thick outer disks in interacting S0s and
``rosetta stone'' galaxies with both S0 and Sph properties,
strongly imply that some or all of a collection of environmental processes transform spiral and irregular
galaxies into red and dead S0 and spheroidal galaxies. This happens especially in rich clusters, but small
galaxies can suffer transformation even in relatively quiescent environments such as the Local Group.
Kormendy \& Bender (2012) suggest that ``environmental secular evolution is An Idea Whose Time Has Come.''
\vskip -30pt
\phantom{"Gobble gobble gobble" invisibly to fix CUP section spacing}
\section{Toward a Comprehensive Picture of Galaxy Formation}
This section ties together our standard picture of galaxy formation by hierarchical clustering
(lectures by Shlosman,{\thinspace}Scoville,{\thinspace}Calzetti)
with our School's subject of secular evolution
(lectures by Athanassoula, Binney, Buta, Peletier, van Gorkom and me).
For pedagogical reasons, it is useful to introduce this standard picture here. Shlosman (2012) provides more detail.
What is at stake for future work? We have a formation paradigm: quantum density fluctuations
in non-baryonic dark matter form immediately after the Big Bang and then get stretched by the expansion of the Universe; gravity drives
hierarchical clustering that causes the fluctuations to grow, separate, collapse and form galaxy halos; the baryons cool inside
the halos to form stars and visible galaxies. Spirals form when halos accrete gas that dissipates and forms disks. Ellipticals
form when galaxies collide and merge; then dynamical violence scrambles disks into ellipsoidal Es. This picture is well supported
by theory and observations. What are the remaining puzzles{\thinspace}--{\thinspace}the cracks in the paradigm?~They are short-cuts to progress.
First, what is understood? Hierarchical clustering of dark matter initial density fluctuations is nowadays calculated in
exquisite detail (Fig.~1.77). Results are in excellent agreement with observations of large-scale structure.
Our job is illustrated in Fig.~1.78. Hierarchical clustering of dark matter is well understood
(background image).~More tricky is the physics of baryonic galaxy formation within dark halos.~It is possible
that all remaining problems with our formation picture on galaxy scales are problems of baryonic physics.
\vfill
\begin{figure}[hb]
\special{psfile=./millenniumlo.eps hoffset=35 voffset=-15 hscale=48.5 vscale=48.5}
\caption{The Millennium Simulation (Springel {\it et al.\ } 2005) is the iconic example of an $n$-body calculation of the formation of large-scale and
galaxy-sized structures via hierarchical clustering of primordial quantum density fluctuations that have been
stretched by the expansion of the Universe and increased in contrast by self-gravity.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
The good news is that ellipticals are fairly well understood. Simulations of the hierarchical growth of galaxies
suggest that they change back and forth between spiral and elliptical, depending on whether their recent history was dominated
by a major merger or by cold gas dissipation (Fig.~1.79). Today's students did not live through the revolution in our understanding
that resulted from Toomre's (1977a) introduction of mergers to our lexicon of galaxy formation. I therefore review this subject briefly.
The first bad news is that we do not know how to form bulgeless galaxies. Continued bulge growth is inherent to the story in Fig.~1.79.
Once you have a bulge, you cannot get rid of it.~This problem was reviewed in Section 1.6.1.
The other bad news is that galaxy formation by hierarchical clustering of cold dark matter still has problems on the size scales
of individual galaxies. Reviews of the subject run the gamut from very optimistic (Primack 2004) to sober (Silk \& Mamon 2012) to very
pessimistic (Kroupa 2012). This is a sign of a subject in flux{\thinspace}--{\thinspace}of~cracks in the paradigm. These are opportunities.
The comfortable news is that we have a growing understanding of secular evolution in disk galaxies. It happens now in low-
and intermediate-density environments. But finding pseudobulges in Virgo S0s shows that it had time to happen
even in the progenitor environments of some present-day clusters.
\vfill
\begin{figure}[hb]
\special{psfile=./ComprehensivePicturelo.eps hoffset=31 voffset=-15.5 hscale=50 vscale=50}
\caption{Theme of building a comprehensive picture of galaxy formation by studying the physics of baryonic galaxies as
embedded in the dark matter hierarchy represented here by the Millennium Simulation.
High-density environments are dominated by merger remnants{\thinspace}--{\thinspace}giant ellipticals in rich clusters.
We understand them fairly well. Low-density environments are dominated by pure-disk galaxies such as M{\thinspace}101;
we do not understand how they form.~Bulge-dominated spirals~like the Sombrero live in intermediate environments.
Barred and other galaxies that undergo secular evolution also tend to live in intermediate-density environments.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./SteinmetzNavarroAnnotLiteLo.eps hoffset=10 voffset=-16 hscale=56 vscale=56}
\caption{Example of the evolution of a single galaxy by hierarchical clustering (Steinmetz \& Navarro 2002, 2003).
Colors denote old stars, young stars $<$\ts200 Myr old and cold gas (see keys). Scale bars are 5 kpc in all panels.
Panel (a) shows the most massive progenitor at $z = 4$; it already contains both old stars and a gas disk. In panel (b),
a classical bulge forms in a major merger at $z \simeq 3$ and then regrows a disk by later infall of cold gas.
Panel (c): at $z = 1.8$, the galaxy looks like an early-type spiral with a dense bulge surrounded by a young disk.
Panel (d): At $z \simeq 1.6$, tidal forcing by a companion shown in the $z = 1.2$ image triggers a bar.
The satellite is accreted at $z = 1.18$, but the bar prominent in the young component survives
for several more Gyr. Panel (e): At $z = 0.7$, the galaxy merges with another galaxy
that has about half of its mass. The result is an elliptical galaxy at $z = 0.27$. This could accrete more
gas and form a Sombrero-galaxy-like system, but it cannot get rid of its large bulge.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{Formation of ellipticals by major galaxy mergers}
It is hard to describe to today's students what a revelation it was when Alar Toomre (1977a) presented his
hypothesis that all ellipticals are created from progenitor disk galaxies by the dynamical violence of
galaxy collisions and mergers. The feeling had been that stars are too small to collide, so interacting
galaxies merely pass through each other. We missed two points. First, tidal effects are easily
strong enough to scramble cold, rotating disks into dynamically hot ellipticals. Doing this work takes
energy out of the orbits and soon causes the galaxies to merge.~Second, large and massive
halos of dark matter surround visible galaxies and give them much bigger collision cross sections than we
thought when we saw only the visible stars. It is no accident that the merger picture became established
soon after~we~realized that dark matter is real (Faber \& Gallagher 1979). Mergers-in-progress turn out to
explain a whole zoo of previously mysterious peculiar galaxies~(e.{\thinspace}g., Figs.\ts1.80{\thinspace}--{\thinspace}1.82).
Toomre's suggestion that mergers make all ellipticals~is, as far as we know, exactly correct.~And Toomre's
(1980) additional hypothesis that mergers make classical bulges robustly looks to be exactly correct,~too.
\vfill
\begin{figure}[hb]
\special{psfile=./Mice+BarnesModello.eps hoffset=30 voffset=-14.5 hscale=50 vscale=50}
\caption{Formation of peculiar galaxies such as NGC\ts4676 (``the mice'') by ongoing gravitational
encounters. Such encounters explain most objects in
(e.{\thinspace}g.)~Arp's (1966) {\it Atlas of Peculiar Galaxies\/}. (top) Hubble Heritage image.
(bottom left) Our view of the initial conditions and (bottom right) the moment when the
configuration matches the galaxies for an $n$-body simulation
(Barnes 1998, 2004) of two infinitely thin disks (blue particles) embedded in
spherical dark halos (red particles).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
I was in the audience for Toomre's (1977a) talk; we all remember it~as~a historic moment.
But not everyone was immediately captured by the new ideas, and I confess that I was a partial agnostic for longer
than most. Kormendy (1989) was a late paper that tried to keep merger enthusiasm from getting out of control.
Its point is still correct~-- the sequence of increasing density in smaller ellipticals (Fig.~1.68) is a
sequence of increasing dissipation with accompanying starbursts during formation. As emphasized all along by Toomre,
merger progenitors generally contain gas; crunching gas likes to make stars, and so star formation is an integral
part of spiral-spiral mergers.
By $\sim$\ts1990, we understood that ultraluminous {\it IRAS\/} galaxies (``ULIRGS'') are prototypical
dissipative mergers in progress
(Joseph \& Wright 1985;
Sanders {\it et al.\ } 1988a, b;
Sanders \& Mirabel 1996;
Rigopoulou {\it et al.\ } 1999;
Dasyra {\it et al.\ } 2006a, b;
see Dasyra {\it et al.\ } 2006c and KFCB Section 12.3.2 for reviews). Figure 1.81 shows the most famous example. Dust-shrouded starbursts generally
dominate the far-infrared luminosity $L > 10^{12}$ $L_\odot$ (see Joseph 1999 and KFCB for reviews). Their structural
parameters are consistent with the E fundamental plane
(Kormendy \& Sanders 1992;
Doyon {\it et al.\ } 1994;
Genzel {\it et al.\ } 2001;
Tacconi {\it et al.\ } 2002;
Veilleux {\it et al.\ } 2006;
Dasyra {\it et al.\ } 2006a, b).
Stellar velocity dispersions $\sigma \simeq 100$ to 230 km s$^{-1}$ show that local ULIRGs are making moderate-luminosity
ellipticals; i.{\thinspace}e.,
the disky-coreless side of the E{\thinspace}--{\thinspace}E dichotomy in Figs.~1.4 and 1.60
(Genzel {\it et al.\ } 2001;
Tacconi {\it et al.\ } 2002;
Dasyra {\it et al.\ } 2006a, b; c).
\vfill
\begin{figure}[hb]
\special{psfile=./Arp220-HH-HSTnicmoslo.eps hoffset=20 voffset=-16 hscale=52.5 vscale=52.5}
\caption{Arp 220, the prototypical Ultraluminous Infrared Galaxy,
an elliptical galaxy being formed by a dissipative merger accompanied by
a dust-shrouded starburst. At left is a Hubble Heritage image. The {\it HST\/} NICMOS
$JHK$ image at right reveals two remnant nuclei separated by 0\sd98 $\simeq$ 360 pc (Scoville {\it et al.\ } 1998).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent
Central to the rapid acceptance of the merger picture was the extensive observational evidence for mergers in progress
that was published by Fran\c cois Schweizer (e.{\thinspace}g., 1978, 1980, 1982, 1987, 1996). Figure 1.82 shows the particularly
convincing example if NGC 7252 (the ``atoms for peace'' galaxy). It has both diagnostic tidal tails and ``ripples'' or
``shells'' in the light distribution that trace edge-on caustics of wrapped~former~disks. Shells, too, became standard
merger diagnostics~(Malin~\&~Carter 1980, 1983; Schweizer \& Seitzer 1988). Shells are seen in absorption as well as in
stars; an example of the explanation of a previously mysterious peculiar galaxy as an S0 that contains an accreted and now
phase-wrapped dust disk is NGC 4753 (Steiman-Cameron {\it et al.\ } 1992). The correlation that stronger fine structure
such as shells is seen in ellipticals with younger~stellar~populations~(bluer colors and stronger
H$\beta$ absorption lines) further~supported~the~merger picture and filled in the evolution time sequence between
mergers in progress and old, completely relaxed and phase-mixed ellipticals
(Carter {\it et al.\ } 1988; \phantom{00000000}
\vfill
\begin{figure}[hb]
\special{psfile=./N7252-ESOxlo.eps hoffset=5 voffset=-17 hscale=57.8 vscale=57.8}
\caption{NGC 7252 is another prototypical merger-in progress that is making an elliptical galaxy (Schweizer 1982).
Two tidal tails that point in roughly opposite directions and that have opposite velocity differences with
respect to the systemic velocity are the simplest diagnostic signature of a merger in progress (see~the~seminal
paper by Toomre \& Toomre 1972). The essential point is that dynamical clocks run most slowly at the largest
radii, so remnant tidal tails persist long after the main bodies of interacting galaxies have merged. For H{\thinspace}{\sc i}
observations and $n$-body models of NGC 7252, see Hibbard {\it et al.\ } (1994, 1995, 1996).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\noindent Schweizer {\it et al.\ } 1990;
Schweizer \& Seitzer 1992).
Compelling further support was provided both by detailed H{\thinspace}{\sc i} observations (e.{\thinspace}g.,
Hibbard {\it et al.\ } 1994, 1995, 1996, 2001a,{\thinspace}b -- see {\tt http://www.nrao.edu/astrores/HIrogues}) and especially by $n$-body simulations
(the master of the art is Josh Barnes 1988, 1989, 1992).
Simulations further confirmed that mergers dump huge amounts of gas to galaxy centers, thereby feeding starbursts (e.{\thinspace}g.,
Barnes \& Hernquist 1991, 1992, 1996;
Mihos \& Hernquist 1994;
Hopkins {\it et al.\ } 2009a).
By the time of the reviews of
Schweizer (1990, 1998);
Barnes \& Hernquist (1992),
Kennicutt (1998c) and
Barnes (1998),
the merger revolution in our understanding of elliptical galaxies was a ``done deal''.
A variant of the merger picture involves the observation that many~\hbox{high-$z$} galaxies are dominated by
$10^8$\thinspace--\thinspace$10^9$ $M_\odot$, kpc-size star forming clumps (e.{\thinspace}g.,
Elmegreen {\it et al.\ } 2005, 2007, 2008a, 2009a,{\thinspace}b;
Bournaud {\it et al.\ } 2007;
Genzel {\it et al.\ } 2008;
F\"orster Schreiber {\it et al.\ } 2009;
Tacconi {\it et al.\ } 2010).
Bournaud's galaxy UDF\ts1668 (Fig.~1.83) is remarkably similar to the initial conditions used by van Albada (1982)
to simulate the collapse of lumpy initial conditions. He showed (Fig.~1.83 here) that relatively gentle collapses
produce S\'ersic-function profiles with \hbox{$n \simeq 2${\thinspace}--{\thinspace}4} like those in real classical bulges
(e.{\thinspace}g., Fisher \& Drory 2008). This is confirmed in modern $n$-body merger simulations (e.{\thinspace}g., Hopkins {\it et al.\ } 2009a).
\vfill
\begin{figure}[hb]
\special{psfile=./vanAlbada-Bournaudlo.eps hoffset=-10 voffset=-18 hscale=62.5 vscale=62.5}
\caption{Mergers of two galaxies that consist mostly of stars make S\'ersic (1968)
function remnants with indices $n \sim 2${\thinspace}--{\thinspace}4.~An early illustration of this~is~van
Albada (1982), whose initial conditions look remarkably similar to the
clumpy high-$z$ galaxy UDF 1666 studied by Bournaud {\it et al.\ } (2007). It is
an example~of~the clump instability picture discussed by Elmegreen {\it et al.\ } (2008b).
Van Albada's initial conditions were parameterized by the ratio
of twice the total kinetic energy~to the negative of the potential energy.~In virial
equilibrium, $2T/W = 1$.~For~smaller values, van Albada found that
gentle collapses ($2T/W = 0.5$) make S\'ersic profiles with~$n < 4$, whereas
violent collapses ($2T/W$\thinspace\lapprox\ts0.2) make $n$\thinspace$_>\atop{^\sim}$} \def\lapprox{$_<\atop{^\sim}$ 4.~This
is a sign that the clumps discussed by Elmegreen {\it et al.\ } (2008b) merge to make classical bulges.
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\cl{\null}
Elmegreen {\it et al.\ } (2008b) model gas-rich galaxy disks in the early Universe and find that they
violently form clumps like those observed (Fig.~1.84). The clumps quickly merge and make
a high-S\'ersic-index bulge. It rotates slowly. Rotation velocities decrease with
increasing distance from~the~disk plane.~So these are classical bulges, and this is a variant on
the merger picture. From many colorful conversations with Allan Sandage, I suspect that he would
have welcomed this ``ELS with lumps'' picture (ELS = Eggen {\it et al.\ } 1962).
\vfill
\begin{figure}[hb]
\special{psfile=./ElmegreenClumpMergerlo.eps hoffset=29 voffset=-14 hscale=53.5 vscale=53.5}
\caption{A variant of the merger picture involves high-$z$ disks that are
unstable to the formation of large clumps which quickly merge to form a classical bulge.
It has ellipsoidal (not cylindrical) rotation (bottom). From Elmegreen {\it et al.\ } (2008b).
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
\subsection{Mergers and secular evolution both happen in a hierarchically clustering Universe}
``It is impossible to remove the problem of galaxy formation from its cosmological context of
hierarchical clustering'' (Jones 1992). Begun in papers like White \& Rees (1978), our picture of
hierarchical clustering has reached a remarkable level of sophistication. The Millenniumm Simulation
is one example from a vast literature. I want to emphasize again that the merger formation of elliptical
galaxies that was discussed in Section\ts1.8.1, the secular evolution of disk galaxies that was discussed
in Sections \hbox{1.2{\thinspace}--{\thinspace}1.6}, and the environmental secular evolution that was discussed in
Section\ts1.7 all happen within the cosmological context of hierarchical clustering. Much work remains to
be done in connecting the story of galaxy formation on the kpc scales of most studies of individual
galaxies with the Mpc scales where \hbox{$n$-body} dark matter simulations are at their best.
Current work is dominated by the complicated physics of baryons, including the effects of
reionization, dissipation, star formation, energy feedback and active galactic nuclei. We like to
think that galaxies are mature objects and that our job is to study galaxy evolution to see how they
got that way. {\it But $\sim$\ts2/3 of the baryons in the Universe do not yet live in galaxies or have not
yet cooled and formed stars} (e.{\thinspace}g.,
Fukugita {\it et al.\ } 1998;
Dav\'e {\it et al.\ } 2001;
Read \& Trentham 2005).
{\it Galaxy formation is much less ``finished'' than we like to think!} Our job is far from finished, too.
For all of us students of galaxies, this~is~good~news.
\omit{
\cl{\null}
\vfill
\begin{figure}[hb]
\special{psfile=./DM-VM-Spectrum.eps hoffset=28 voffset=-4 hscale=40 vscale=40}
\caption{From Read \& Trentham (2005): the field galaxy baryonic mass function (black
data points and spline fits) compared with the dark matter halo masss spectrum
from Weller {\it et al.\ } (2005). The shortfall of visible galaxies at low masses is
usually interpreted to be caused by the ejection of baryons by supernova-driven
energy feedback. The shortfall at high masses is conventionally interpreted as
due to energy feedback from active galactic nuclei (AGNs) that keeps the gas
halos of galaxies and of clusters of galaxies too hot to cool and form stars.
Heating can also be provided by continued gas infall from the surrounding structure
hierarchy (Dekel \& Silk 2005, 2008). An additional important effect is that some
large halos are occupied by groups and clusters of galaxies and not by individual
galaxies. Finally, even at intermediate masses, there is a significant shortfall
in baryonic galaxies compared to expectations based on the canonical cosmological
baryon fraction. This is interpreted to be due to the fact that many baryons
still reside in a ``warm-hot intergalactic medium'' (WHIM) that surrounds even
galaxies such as the Milky Way (Dave {\it et al.\ } 2001). The ``take-home message'' is
this: We like to think that galaxies are mature objects and that our job is to
study galaxy evolution to see how they got that way. But about 2/3 of the baryons
in the Universe do not yet live in galaxies or have not yet cooled and formed
stars. Galaxy formation is much less ``finished'' than we like to think!
}
\end{figure}
\cl{\null}
\vskip -28pt
\eject
}
\section*{Acknowledgments}
It is a great pleasure to thank Jes\'us F\'alcon-Barroso and Johan Knapen for organizing
this 2011 workshop, for inviting me to give the introductory and closing lectures, and
for meticulously editing this book.
I am also grateful to J\'esus for his untiring efforts to make our visit to the
Canary Islands such a pleasure. I also especially want to thank IAC students
Judit Bakos,
Javier Blasco Herrera,
Santiago Erroz,
Adriana de Lorenzo-C\'aceres,
Mireia Montes,
Agnieszka Ry\'s,
Jos\'e Ram\'on S\'anchez-Gallego and
Marja Seidel
for their help with the workshop and for their kindness to Mary and to me. And finally,
I would like to thank all of the above and all of the students for making this an
extraordinarily pleasureable and productive experience. It was a pleasure to meet you all,
and I hope to see you again often. Warmest best wishes from Mary and from me for successful and
fulfilling careers.
Mary and I very much enjoyed our interactions with the other lecturers,
Lia{\thinspace}Athanassoula,
James{\thinspace}Binney,
Albert{\thinspace}Bosma,
Ron{\thinspace}Buta,
Daniela{\thinspace}Calzetti,
Reynier Peletier,
Nick Scoville,
Isaac Shlosman and
Jacqueline van Gorkom.
These lectures were prepared, delivered and in large part written up during two visits
to the Max-Planck-Institut f\"ur Extraterrestrische Physik, Garching-bei-M\"unchen, Germany and the
Observatory of the Ludwig-Maximilians-Universit\"at, Munich, Germany. It is a great pleasure~to~thank
Managing Director Ralf Bender and the staff of both institutes for their wonderful hospitality
and financial support. I also warmly thank Christa Ingram and Bettina Niebisch of the
Max-Planck-Institut f\"ur Extraterrestrische Physik for transcribing my oral lectures.
And I sincerely thank the many people who allowed me to reproduce figures (see captions).
As with all my papers, I owe a huge debt of gratitude to Mary Kormendy for her editorial help
and for her patience and understanding during the preparation of this review.
This work makes extensive use of data products from the digital image database
of the Sloan Digital Sky Survey (SDSS). Funding for
SDSS and SDSS-II was provided by the Alfred P.~Sloan Foundation, the Participating Institutions,
the National Science Foundation, the US Dept.~of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher
Education Funding Council for England. The SDSS is managed by the Astrophysical Research
Consortium for the Participating Institutions.~They are the
American Museum of Natural History, Astrophysical Institute~Potsdam, University of Basel,
University of Cambridge, Case Western Reserve University, University of Chicago, Drexel
University, Fermilab, the Institute for Advanced Study, the Japan Participation Group,
Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli
Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the
Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the
Max-Planck-Institute for Astronomy, the Max-Planck-Institute for Astrophysics,
New Mexico State University, Ohio State University, University of Pittsburgh,
University of Portsmouth, Princeton University, United States Naval Observatory
and the University of Washington.
This research depended critically on extensive use of NASA's Astrophysics Data System
bibliographic services.
I also made extensive use of the NASA/IPAC Extragalactic~Database~(NED),
which is operated by the Jet Propulsion Laboratory and the California Institute of Technology
under contract with NASA.
And I used the HyperLeda electronic database (Paturel {\it et al.\ } 2003) at
{\tt http://leda.univ-lyon1.fr} and the image display tool SAOImage DS9 developed by the Smithsonian
Astrophysical Observatory.
My work on secular evolution is supported by NSF grant AST-0607490 and by the
Curtis T.~Vaughan, Jr.~Centennial Chair in Astronomy.
Note added November 2013: This review was finished and submitted in mid-June 2012. The astro{\kern 1pt}-ph
version is essentially identical to the published paper except for differences in spelling (British
there and American here) and for improvements here in a few figures. The present version remains
up to date except for one important new paper by Sellwood (2013). This is a broad
review of the theory of ``Secular Evolution in Disk Galaxies'' that overlaps some of the present
subjects but that also discusses many additional fundamental topics.
It is an important complement to the present paper and to Kormendy \& Kennicutt (2004).
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\end{document}
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\section{1. DETAILS OF THE DENSITY FUNCTIONAL THEORY CALCULATIONS}
We used the WIEN2K~\cite{wien2k} implementation of the full potential linearized augmented plane wave (LAPW) method with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional~\cite{perdew_1996}. For the simulation we took the space group 227: Fd-3m and the lattice constant a = 10.26 Bohr of Si from Ref.~\cite{tobbens2001}. To capture the single Ti impurity influence, three different supercells were used corresponding to the sizes of the 1 $\times$ 1 $\times$ 1, 2 $\times$ 2 $\times$ 2, 3 $\times$ 3 $\times$ 3 Si$_8$ supercell (see Fig. \ref{fig:X1}). Following the conclusion of Ref.~\cite{K_Sanchez_2009_supp} the Ti is located at the tetrahedral interstitial site (Fig.~\ref{fig:X1}). We use a k-point mesh of 11 $\times$ 11 $\times$ 11 for the undoped normal cell and of 3 $\times$ 3 $\times$ 3 for the supercells. The basis set sizes were determined by $RK_{max}=6$. To better describe the experimental band-gap of Si we apply the LDA+U approximation~\cite{anisimov_1993}, or to be more precise the PBE+U approximation, with U=-5.1 eV for Si-$p$. As shown in Fig.~\ref{fig:X2} our PBE+U results compare accurately with the results obtained from the modified Becke-Johnson potential~\cite{tran_09_supp}, especially for the Density of States (DOS) close to the gap. For the results shown in Sec. 7
the internal forces were relaxed to less than 2mRy/Bohr. For all other results in the supplement and the manuscript we did not relax the atomic positions.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.7\columnwidth,clip=true]{figS1.eps}
\caption{Three supercells used to capture the single Ti impurity influence. For TiSi$_8$ the Ti-Si bonds outside the supercell are shown to illustrate the tetrahedral coordination of the Ti interstitial. The table shows the coordinates of the non-relaxed Ti and Si positions expressed in the supercell lattice vectors. }
\label{fig:X1}
\end{figure}
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.7\columnwidth,clip=true]{figS2.eps}
\caption{Comparison of Density of States (DOS) of TiSi$_{64}$ obtained from PBE+U (black) and the modified Becke-Johnson potential (mBJ) (red). (a) in a large frequency range, (b) around the impurity band region.}
\label{fig:X2}
\end{figure}
\clearpage
\section{2. DETAILS OF THE WANNIER FUNCTION CALCULATIONS}
To derive the Wannier function based tight binding Hamiltonians from the DFT calculations we perform a projected Wannier function transformation~\cite{w_ku_02_supp}. Specifically we project the Ti-$d$, Si-$s$ and Si-$p$ orbitals onto the bands within [-12.5,11] eV. Fig.~\ref{fig:X3} shows the comparison of the Wannier and DFT bandstructures for pure Si and the TiSi$_{64}$ supercell.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.9\columnwidth,clip=true]{figS3.eps}
\caption{Comparison of Wannier and DFT bandstructure for Si (left) and TiSi$_{64}$ (right).}
\label{fig:X3}
\end{figure}
\section{3. Full DOS spectrum}
The DOS spectrum obtained from DCA~\cite{jarrell_2001} for the undoped case and the Ti concentration $x=0.2\%$ are shown in Fig.~\ref{fig:dos_comp}. We note that the impurity band is located inside the band gap for the doped case.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS4.eps}
\caption{DOS of Si(Ti) with Ti concentration of $x=0.2\%$ (calculated with DCA) compared with the DOS of pure Si.}
\label{fig:dos_comp}
\end{figure}
\clearpage
\section{4. Convergence of DOS and TDOS with cluster size}
We check the convergence of the DCA and the TMDCA with cluster size N$_c$ and find that the DOS converges up to cluster size N$_c$=64 and the TDOS converges up to cluster size N$_c$=128 as shown in Fig.~\ref{fig:dos_tdos_Nc}. We use these cluster sizes throughout the manuscript and the supplement.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS5.eps}
\caption{The DOS (upper panel) and TDOS (lower panel) of Si(Ti) with $x=0.2\%$ and $x=1\%$ for various cluster sizes. }
\label{fig:dos_tdos_Nc}
\end{figure}
\section{5. Convergence of DOS and TDOS with $k_{mesh}$ in the Brillouin Zone}
We check the convergence of DCA and TMDCA against the
size of the mesh in momentum space ($k_{mesh}$), and find that both DOS and TDOS are well converged with $k_{mesh}=5 \times 10^5$ k-points in the Brillouin zone as shown in Fig.~\ref{fig:dos_tdos_kmesh}. We use this number of k-points throughout the manuscript and the supplement.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS6.eps}
\caption{DOS (left) and TDOS (right) for Ti concentration $x=1\%$ and three different values of $k_{mesh}$. kmesh1$=1.08\times 10^5$ k-points, kmesh2$=2.56 \times 10^5$ k-points, kmesh3$=5 \times 10^5$ k-points in BZ. }
\label{fig:dos_tdos_kmesh}
\end{figure}
\clearpage
\section{6. Convergence of DOS and TDOS with R$_{mt}$*K$_{max}$}
We check the convergence of DOS and TDOS against the number of LAPW basis functions used in the DFT, which is controlled by the parameter R$_{mt}$*K$_{max}$. Specifically we perform DFT calculations of pure Si and TiSi$_{216}$ supercell for various values of R$_{mt}$*K$_{max}$ and derive the impurity potential for each of them. We find that both DOS and TDOS are well converged for R$_{mt}$*K$_{max}$=6 as shown in Fig.~\ref{fig:dos_rkmax}.
We use this value throughout the manuscript and the supplement.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS7.eps}
\caption{DOS (N$_c$=64) and TDOS (N$_c$=128) with Ti concentration $x=1\%$ for various values of R$_{mt}$*K$_{max}$. }
\label{fig:dos_rkmax}
\end{figure}
\clearpage
\section{7. Effect of lattice relaxation on DOS and TDOS}\label{sec:relax}
We derive the impurity potential from the TiSi$_{216}$ supercell using lattice relaxed atomic positions and use it for the DCA and TMDCA calculation. We compare our results with the case without lattice relaxation. The change in DOS and TDOS is negligible as shown in Fig.~\ref{fig:dos_relax}. The critical Ti concentration determined using this impurity potential still lies between 0.1\% and 0.2\% as shown in Fig.~\ref{fig:dos_tdos_<_x_np_relax}.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS8.eps}
\caption{DOS and TDOS with Ti concentration $x=1\%$ based on the impurity potential derived with and without lattice relaxation. }
\label{fig:dos_relax}
\end{figure}
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS9.eps}
\caption{DOS and TDOS of Ti doped Si based on the impurity potential derived using lattice relaxation for
various Ti concentrations: $x=$1\%, 0.4\%, 0.2\%, 0.1\%. The chemical potential is represented by the dashed line.}
\label{fig:dos_tdos_<_x_np_relax}
\end{figure}
\clearpage
\pagebreak
\section{8. Effect of spin-polarization on DOS and TDOS}
We derive the impurity potential from the TiSi$_{216}$ supercell using spin-polarized DFT and use it for the DCA and TMDCA calculation. As shown in Fig.~\ref{fig:dos_tdos_x_sp} for Ti concentrations $x<0.4\%$, the spin majority part of the impurity band is fully filled and energetically separated from the partially filled spin minority impurity band. Therefore electrons from the valence band can only be promoted to the spin-minority impurity band and we need focus our study of localization on those spin minority states around the chemical potential. Fig.~\ref{fig:dos_tdos_x_sp} shows that the DOS and TDOS of the spin-minority impurity band follows the same trend as those of the non spin-polarized impurity band presented in Fig. 2 of the manuscript. In particular the critical Ti concentration still lies between 0.1\% and 0.2\%.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS10.eps}
\caption{DOS and TDOS of spin-polarized Ti doped Si for
various Ti concentrations: $x=$1\%, 0.4\%, 0.2\%, 0.1\%. Results for both spin species are plotted. The chemical potential is represented by the dashed line. }
\label{fig:dos_tdos_x_sp}
\end{figure}
\clearpage
\section{9. Comparing DOS and TDOS for TiSi$_{64}$ and TiSi$_{216}$ derived impurity potentials}
Fig.~\ref{fig:dos_tdos_64_216} shows that DOS and TDOS change little when the impurity potential is derived from the TiSi$_{64}$ supercell instead of the TiSi$_{216}$.
\begin{figure}[h!]
\includegraphics[trim = 0mm 0mm 0mm 0mm,width=0.5\columnwidth,clip=true]{figS11.eps}
\caption{DOS and TDOS of Ti doped Si based on the impurity potential derived from the supercells TiSi$_{64}$ and TiSi$_{216}$, and various Ti concentrations: $x=$1\%, 0.4\%, 0.2\%, 0.1\%. VB, CB, and IB correspond to the valence, conduction and intermediate band, respectively. The chemical potential is represented by the dashed line. }
\label{fig:dos_tdos_64_216}
\end{figure}
| {
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Shmuel Fledel (58) has been named the CEO of the Solar Thermal Energy Business Unit in the Solar & Hydro Division of Siemens Energy. Fledel is an aeronautical engineer and has vast experience in production process improvement. He has profound knowledge of engineering, finance and marketing, which he gained in various high-level management positions during his career.
�Shmuel Fledel will lead us forward as we optimize our processes and strategy, strengthen our business, and implement the utilization of ecofriendly solar thermal technology in existing and new applications. Here, research and development will play a key role,� said Ted Scheidegger, CEO of the Solar & Hydro Division of Siemens Energy.
Until 2005, Fledel was President & CEO of Cyclone Aviation Products Ltd., a company specialized in aircraft structures production and helicopter maintenance and services. Between 2005 and 2008, Fledel as company executive vice president was responsible for maintenance and engineering for the El Al Airlines. Since 2008, Fledel was President & CEO of TAT Technologies Group, a company whose production, maintenance and overhaul portfolio includes heat exchanger systems and components, electromotive systems, auxiliary power units, landing gear and air conditioning systems. | {
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Template support
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templates: "my_templates"
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{"url":"http:\/\/www.findstat.org\/SemistandardTableaux","text":"Possible database queries for semistandard tableaux: search your data \/ browse all statistics \/ browse all maps\n\n# 1. Definition & Example\n\n\u2022 A semistandard (Young) tableau of a partition $\\lambda \\vdash n$ is a map from the cells of the Young diagram of $\\lambda$ to $\\{1,2,\\dots,r\\}$ for some $r$, such that rows are weakly and columns are strictly increasing.\n\n\u2022 The set of semistandard tableaux of shape $\\lambda \\vdash n$ with maximal possible entry $r$ is denoted by $\\mathcal{SSYT}_{\\lambda,r}$, and $$\\mathcal{SSYT}_{n,r} = \\bigcup_{\\lambda \\vdash n}\\mathcal{SSYT}_{\\lambda,r}$$ denotes the set of semistandard tableaux of size $n$.\n\n The four semistandard tableaux of size 2 and maximal entry 2 [[1,1]] [[1,2]] [[2,2]] [[1],[2]]\n\u2022 Semistandard tableaux are graphically represented by filling the cells of the Young diagram in English notation.\n\n# 2. FindStat representation and coverage\n\n\u2022 A semistandard tableau is uniquely represented as a list of lists giving the fillings of the cells row by row.\n\u2022 Semistandard tableaux are graded by $n$ where $n$ is both the size and the maximal possible entry.\n\n\u2022 The database contains all semistandard tableaux of size\/maximal possible entry at most 6.\n\n## 3.1. Properties\n\n\u2022 The number of semistandard tableaux of a partition $\\lambda$ with all entries in $\\{1,\\ldots,r\\}$ is given by the hook-content formula $$\\big|\\mathcal{SST}_\\lambda\\big| = \\prod_{(i,j)}\\frac{r+i-j}{hook(i,j)},$$ where the product ranges over all boxes $(i,j)$ in the Young diagram of $\\lambda$, and where $hook(i,j)$ is the hook length of the box$(i,j)$ in $\\lambda$.\n\n## 3.2. Remarks\n\n\u2022 Semistandard tableaux are in bijection with Gelfand-Tsetlin patterns.\n\n\u2022 Skew Tableaux come from taking the set difference of two partitions of different sizes. If the resulting boxes are filled with numbers such that the columns are increasing and the rows are weakly increasing, then it is called a semistandard skew tableaux.\n\n\u2022 The number of semistandard tableaux of shape $\\lambda$ and content $\\mu$ is equal to the Kostka number $K_{\\lambda\\mu}$. The hook length formula is a special case when $\\mu = (1,1,1,...,1)$, since that corresponds to a standard tableau. However, there is no general formula for the Kostka numbers.","date":"2018-05-25 12:47:26","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\": 0.8366551995277405, \"perplexity\": 293.84820193826755}, \"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-2018-22\/segments\/1526794867092.48\/warc\/CC-MAIN-20180525121739-20180525141739-00453.warc.gz\"}"} | null | null |
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Critics' Corner »
Time reviews
Author Topic: Time reviews (Read 1066 times)
Time review: This gripping, gruelling portrait of life in prison is essential viewing
Sean Bean and Stephen Graham lead a brilliant cast in a three-part series from Jimmy McGovern
When Mark Cobden enters prison in the first moments of Jimmy McGovern's new drama, he soon learns that the question "What are you doing?" has another meaning. His fellow inmates aren't asking him what he's up to (it's not like there's much to do, anyway). They want to find out the length of his sentence, how much time he's doing - and in discovering that, to get the measure of what kind of man he is, whether he is a threat, an ally, or someone to push around.
A former teacher consumed by guilt over his crime, Mark (a melancholy Sean Bean) falls into that latter category ("Do one, granddad," one prisoner hisses back when Mark tries to remonstrate with him like he's negotiating with a Year Nine who hasn't done their homework). It seems he couldn't be worse equipped for life inside, where sugar and boiling water aren't just component parts for a nice cup of tea (you may want to avert your eyes during the most viscerally unpleasant scene involving a kettle since Line of Duty's rogue prison guards roughed up Lindsay Denton), officers burst into cells wearing riot gear, and most of the inmates should, as one character points out, be in psychiatric care, not jail.
His personal support officer is Eric McNally, played by Stephen Graham, a scrupulous, decent guard with an unblemished record; he couldn't be further from an Orange Is The New Black-style villain, getting off on abuses of power. When an inmate seeks to exploit a family secret, though, he finds himself forced to choose between his principles and the safety of those closest to him.
Mark and his fellow prisoners move through a world drained of colour: this institution seems to exist almost entirely in greyscale, punctuated only by dashes of light blue (the washed-out shade of the striped shirts worn for family visits) and burgundy (the colour of their work scrubs). One inmate receives "a black and white photocopy of a colouring in" from his young daughter - the original gets destroyed, in case it's laced with spice.
It's bleak stuff, and there's a sense of grim, almost tragic inevitability to many of the stories that unfurl over the course of three episodes, especially Eric's (made all the more wrenching by Graham's measured performance). Yet amid all this grey, moments of unbearable sadness sometimes make way for glimmers of redemption. These flashes of hope in the gloom, along with the carefully handled, humanising glimpses into the back stories of a handful of other inmates, make this classic McGovern. There's a certain didacticism to it, of course, but it never gets in the way of a powerful narrative.
It's the second time that Bean and Graham have worked together, having previously starred alongside one another in an episode of McGovern's 2010 anthology series Accused, and their scenes together are powerfully understated. This is much more than a two-hander, though, and it'd be remiss to overlook the quietly heartbreaking performances of the supporting cast, from Hannah Walters, married to Graham in real life, as Eric's wife Sonia, to Jack McMullen as Mark's young cellmate Daniel, whose lengthy sentence stretches out hopelessly in front of him, to the reliably brilliant Siobhan Finneran as the prison's chaplin.
Their work, in tandem with McGovern's devastating story-telling and striking direction from Lewis Arnold (who previously worked on shows such as Des and the third series of Broadchurch), ensures that these three hour-long episodes are difficult but essential viewing. It's both deeply damning and touchingly hopeful, at once a searing indictment of a system where for the most part, as one of Mark's cellmates puts it, "you come in bad and you go out worse" and a testament to our capacity to change.
Time is on BBC One on June 6 at 9pm. The full series will be available on BBC iPlayer after episode one has aired.
https://www.standard.co.uk/culture/tvfilm/time-bbc-one-review-stephen-graham-sean-bean-jimmy-mcgovern-b938221.html
Time—a tense and claustrophobic prison drama
The BBC is making a big deal of this new three-part prison drama—and not just because of its big name actors.
Sean Bean is Mark Cobden, a teacher who finds himself in prison, consumed by guilt and out of his depth.
His story intertwines with prison guard Eric McNally, played by Stephen Graham, who is forced into a dangerous situation after a threat from a prisoner.
Bean and Graham contribute a lot to the series' strength. Bean is more Roy Cropper than Ned Stark here—but is utterly convincing as a quiet man who just wants to keep his head down. Graham's role is more familiar for him, but he does look and speak like a prison guard.
More than that, the claustrophobic, noisy, stressful atmosphere of prison is pervasive. Close camera angles, constant background noise, but quiet, understated yet shocking violence in the foreground.
If there's a message—delivered in some at times blunt exposition—it's that crowding vulnerable and troubled people into prison is a dangerous idea.
Often this still seems to rest on the idea that the prisoners are the real danger.
But it is an absorbing and troubling drama.
https://socialistworker.co.uk/art/51895/Time+a+tense+and+claustrophobic+prison+drama
Re: Time reviews
Time review – Is the BBC's Stephen Graham prison drama worth a watch?
Time episodes 1-3 were made available for review.
Stick Stephen Graham in anything (heck just hold up a camera to him doing his weekly shop) and we'd watch on in awe.
The man never fails to treat each and every frame like an acting masterclass – as previously seen in Channel 4's haunting drama The Virtues as well as Shane Meadows' superb movie-turned-anthology This Is England.
And BBC One's Time, by Jimmy McGovern, is no different.
Starring opposite Sean Bean (Game of Thrones, Snowpiercer), the two lead characters are on opposite sides of the law and, as such, are tracing completely different paths. And yet, as more pieces of each of their stories start to unfold, it becomes clear that their individual struggles cross over in more ways than you might expect.
Graham takes on the role of Eric McNally, an experienced and dedicated prison officer who values the safety and wellbeing of those in his charge. Think Gandalf or Ted Hastings (season five excluded); whenever McNally arrives on screen, there's a sudden sense that everything is going to be okay.
Bean plays Mark Cobden, a former schoolteacher and first-time offender who is haunted by what placed him behind bars. Under the watchful eye of McNally, Cobden is navigating a terrifying new world with a whole set of unwritten rules.
It is through his often-naive eyes that the audience too is engulfed by the unforgiving and relentless daily grind of being a prison inmate. Like Cobden, viewers cannot escape or look away (unless, of course, it gets too much and they reach for the remote) which adds to the claustrophobic feeling that builds across the series.
Set against the backdrop of a men's prison in Liverpool, Time is a visceral and brutally violent depiction of life on the inside. What seems to begin as a character study and exploration into the minds of these two central men, soon transcends into a commentary on the painful injustice of the system that they are both a part of.
If you are expecting a Line of Duty-like, high-octane drama that's packed with big set pieces and unpredictable (if not a little ridiculous) plot twists, then Time might not be for you. Although a fictional story, it's very much grounded in realism.
Without giving away any specific plot points (because, spoilers!) Time also intricately explores themes of male mental health and internalised toxic masculinity – although some scenes should almost certainly carry a content warning, if they should even be shown at all.
Despite its heaviness, the three-part series does not feel like a slog to watch – and that is mostly down to its emotive writing, which builds rapport with its audience, and the talent of the two leading actors themselves. Neither Graham or Bean steal the limelight from the other, each an equal and complimenting part to every scene that they share.
Time is worth watching for their performances alone, but you'll find it impossible not to also have some moral and ethical takeaways too. All-in-all, it's a frustrating watch – but that seems to be entirely the point.
https://www.digitalspy.com/tv/a36569492/time-review-bbc-stephen-graham/
Sean Bean is arresting as a prison inmate in gripping BBC drama Time
Right from the disorienting start of Jimmy McGovern's intense three-parter, protagonist Mark Cobden and the viewer are thrown into a frightening, unpredictable world. Trembling in the back of a prison van, Mark, a quiet, unassuming teacher, is on the way to begin his sentence at (fictional) HMP Craigmore, already unsettled by the seething menace all around him. He's taken, bewildered, through all the rituals of induction, including "pants down and squat", and spends his first night alone, before being taken to cell 39, shared with another prisoner. Mark has a lot to learn, for starters that he must address prison officers as "Boss", and when someone says "What are you doing?" the correct answer isn't "Having a cuppa" or "Nothing", but "Four years".
Gentle Mark (Sean Bean) is an easy target for the bullies, his claim that "I killed someone" merely eliciting barks of incredulous laughter. But his first problem is highly strung Bernard (Aneurin Barnard) who thinks Mark may be a spy sent from above. "Shtum from now on!" his wild-eyed cellmate insists, then breaks his own rule with a paranoid rant about the prison system. However disconnected from reality Bernard seems, somewhere within his fulminations we can detect a trace of McGovern's own reforming zeal. It comes out more strongly later on when officer Eric McNally (Stephen Graham) bursts out: "They should all be in mental hospitals, not in this nick, but there's no room for them
As grey day succeeds grey day, a numbing repetition of ambling around, lying on bunks or queueing for the same daily choice of "chicken or cheese?", it seems as though this is to be a strictly realistic depiction of the plotless limbo of prison. Mark is a timid soul (Bean playing excellently against type) who flees from confrontation until he realises that in prison there is no place to flee. The prison chaplain, Sister Marie-Louise (Siobhan Finneran), becomes an ally, her response to a disbelief in God being a cheery "You don't know what you're missing!" Considering that his stony face only alters by tiny degrees, Graham brings a vivid humanity to the screw who is as secretly kind as he is hard-boiled. Director Lewis Arnold piles on the claustrophobic menace, crowding the frame until it feels as if the violence could spill out of the screen.
From being two men quietly negotiating their corner of hell on different terms, Mark and McNally are abruptly pushed beyond their limits into parallel narratives of coercion and duress. The governing themes — no easy dividing line between good and evil, all are fallible, there but for the grace of God go I — may be clichés, but they combine to make a drama to grip your vitals.
https://www.ft.com/content/138bc565-c59b-4612-ac53-fb67f9b9fd8e
Time, BBC One review ★★★★★
You can tell within seconds of Time – Jimmy McGovern's new three-parter – that the timid schoolteacher Mark (Sean Bean) doesn't belong in prison.
When he rides in a prisoner transport vehicle (like a jail on wheels), the other convicts scream and shout. Mark stays silent and afraid. After taking residence in HMP Craigmore, he shrinks and flinches from violent bullies who steal his sandwiches and his phone calls. He has a near-pacifistic demeanour, which barely benefits in this depressing, grey-and-white container. Its terrifying testosterone seeps through the bland walls and heavy doors.
But unlike Andy Dufresne in The Shawshank Redemption, which Time rarely but inevitably imitates, Mark admits to his crime. He did it, that's for sure, and he's been sentenced to four years. And yet, despite the punishment suiting the offence, Mark still doesn't belong there. It's a riveting, upsetting paradox.
A concurrently armoured and fragile Stephen Graham (The Virtues, The Irishman) also stars, playing the lead police officer Eric. The series follows both him and Mark in parallel, crossing only occasionally.
Eric is caught in an impossible situation. A few inmates under his charge, through a corruptive set of circumstances, find out his son is locked up in another prison. That hold on Eric – organised by the shady, croaky and frightening prisoner Jackson (Brian McCardie, who played Tommy Hunter in Line of Duty) – is a bit elaborate, but provides a gruelling insight into the politics of prison life.
McGovern provides no easy answers to the dense, ethical questions he brings up. For a time, the series shows that prison shapes these criminals into worse people. The stories of Mark's cell-mates confirm this. It is telling when, in one scene, Eric describes that half his prisoners deserve to be in mental institutions but 'there's no room for em'.
On the other side, Mark has a desperate need to atone without the chance of forgiveness. He is being punished, after all, and his guilt is excruciating. Bean's hard and weathered performance is a genuine marvel, and you immediately forget his credits in Hollywood.
McGovern's point, it seems, is that these arguments aren't clear-cut; they're horrendously messy and often chaotic. Mark is constantly at risk of betraying his morality to survive and Eric, a caring and considerate officer, is threatened into forsaking his own principles to protect his son.
The series also drifts into the personal stories of the other prisoners, the reasons ranging from gambling issues to simply 'saving face'. They reveal these motivations either to families of the victims or to school kids, the latter set up by the ineffably nice prison chaplain Marie-Louise (Siobhan Finneran).
Although these intense examinations avoid the more antagonistic convicts, they're extremely sympathetic vignettes of men who went the wrong way. You feel for every one of them, despite the sometimes horrific reasons for their imprisonment.
These quandaries exist in a place so oppressive and brutal and restricted that you feel the hurt of time lost. Similar to Shawshank, that sense of time starts as a slow hurdle before hundreds of days pile on top of each other. Time is certainly bleak, but doesn't linger too long in the trauma of it all. The series is even morbidly addictive in its deep questions and detailed character work. McGovern has made another winner.
https://www.culturewhisper.com/r/tv/time_bbc_drama_sean_bean_review_stephen_graham/16381
Time review: BBC One prison drama is brutal, must-watch television
The bleak three-part series is a must-see, both as a lesson on the British prison system, and a masterclass in acting.
At a recent press event, actor Stephen Graham described his hard-hitting new series, BBC One prison drama Time, as "difficult to watch". He went on to theorise that the reason the three-parter is such difficult viewing is because it makes the audience think: about the British penal system; about the justice system; and about how many inmates should be in mental health units, not prisons.
All of this is true, but the series would not be nearly as brutal viewing if it wasn't for the two visceral central performances: from Graham himself, and Sean Bean.
Creator Jimmy McGovern recently revealed that Time was written with Sean Bean and Stephen Graham in mind. "They've got faces you'd die for, you know?" he said. "Full of life; full of compassion and humanity. I think if you're going to write about a prison, that's the kind of thing you need, isn't it? Compassion, humanity, experience – all in the lines of those faces."
Under the gaze of director Lewis Arnold (Des), every line, every flicker of emotion on those two famous faces is pushed to the fore. We follow their characters closely, as each man takes on his own personal battles, their respective lives and struggles intersecting.
Bean plays Mark, a former teacher who faces four years in prison. He's soft-spoken, and when he arrives, we discover he's much older than the other new inmates in his cohort. One even dubs him "grandad," his tone verging on cruel.
The bleak visuals of the series are intentional: the disused prison where Time was filmed was specially painted grey, to make the location feel more "miserable". 'Hopeless' is also an accurate description.
Mark is woefully ill-equipped for the harsh realities of prison life. He acts as a stand-in for the viewer during the first episode's more shocking moments, including a harrowing scene involving a boiled kettle and packet of sugar.
This is a contrast to Stephen Graham's character Eric, a prison guard who has seen it all before. Eric, who is also a personal support officer to Mark, isn't a bully or villain – in fact none of the guards we meet in episode one are. Eric is a decent, family man, but his principles are challenged over the course of the series when he crosses paths with one of the prison's most dangerous inmates.
Graham is given ample time to showcase his acting skills over the course of the series, but this first episode belongs to Bean. Mark's quiet terror during his first few days in prison is painful to watch, as are the ways other, hardened inmates take advantage of his gentle nature. The playground bullying he endures – his lunch stolen, his precious calls home interrupted – strips him of his dignity, hour by hour.
Stephen Graham is right when he calls the series "difficult to watch," but it's also a must-see, both as a lesson on the British prison system, and a masterclass in acting
https://www.radiotimes.com/tv/drama/time-review-bbc/
CHRISTOPHER STEVENS reviews the weekend's TV: Prison drama that turns tough guy Sean Bean into Mr Softie
Sean Bean's face is so lined, it looks like a child has drawn eyes on an inky thumbprint. He's more wrinkly than a tramp's boot that's been left under a sunlamp, and twice as tough.
Compared with Sean, action hero Jack Reacher is as soft and snooty as Jacob Rees-Mogg. So it's hard to understand why other inmates, in the prison drama Time (BBC1), take one look and decide he's a pushover.
He's Sharpe, he's Boromir in Lord Of The Rings, he's Ned Stark from Game Of Thrones for heaven's sake. He doesn't get these roles because he's the diffident type.
Even Sean Bean playing a timid teacher called Mark, in jail for the first time in his life after a drunken car accident, looks like he's carved from weathered granite and boiled in vinegar.
But bullying Johnno (James Nelson-Joyce) swans into Mark's cell and nicks his sugar. Then he barges him out of the queue for the payphones, and punches him on the nose.
Mark trudges sheepishly away. A fellow inmate warns him that he should have punched back: 'Your life won't be worth living now.'
You'd expect a bloke who has spent his life in classrooms to be more confident about dealing with bullies. And for all his swagger, Johnno looks like he's made from twigs. Sean could knock him over with a sneeze.
The distractions of casting aside, Time is a visceral and violently scary drama. Writer Jimmy McGovern's script conveys how dehumanising the experience of prison is, from the moment the first iron door slams.
'Are you suicidal?' asks one prison officer in the dull voice of somebody asking for a shoe size. 'Have you ever suffered depression?' inquires another and, when Mark starts to say something about his youth, she snaps: 'Yes or no?'
Stephen Graham cuts a menacing figure as Mr McNally, a Scouse version of Mr Mackay from Porridge — short temper, narrow eyes, not noted for his forgiving nature.
He expects inmates to call him 'Boss' and seems to hanker for the American prisons of movies like Cool Hand Luke. Boss McNally would like to carry a shotgun and send his convicts out to work on chain gangs.
But he's being bullied, too: the prisoners have heard McNally's own son is serving a sentence in another jail. If the Boss doesn't start doing people favours, Junior might come to harm.
Loaded with scenes of self-harm and vicious assaults, Time has echoes of the Ray Winstone 1979 classic, Scum.
https://www.dailymail.co.uk/tvshowbiz/article-9658669/CHRISTOPHER-STEVENS-Prison-drama-turns-tough-guy-Sean-Bean-Mr-Softie.html
Time review – Sean Bean and Stephen Graham astound in enraging prison drama
The performances of Bean and Graham are, even though we have come to expect brilliance from them both, astonishing. So, too, are those from everyone in smaller roles, none of which is underwritten or sketchy, and who thicken the drama into something more profoundly moving and enraging at every turn. Time well spent.
https://www.theguardian.com/tv-and-radio/2021/jun/06/time-review-sean-bean-and-stephen-graham-astound-in-enraging-prison-drama
Time review: An avant-garde experiment in what prison with Sean Bean would be like
As far as is discernible from the first episode, the plot of Time, Jimmy McGovern's new prison drama, goes something like this: Mark Cobden (Sean Bean) is off to jail. He ran someone over when he was drunk. His estranged wife doesn't want to let his son talk to him. We don't yet know why. On the other side of the prison divide, Eric McNally (Stephen Graham) is a decent screw, civil with his charges but cursed with a temper. He also has a son, himself in prison, which makes him a blackmail target for well-connected gangsters.
Story-wise, that's your lot. In other respects, Time seems to be an avant-garde experiment in replicating what it would be like to do time with Sean Bean. As one of his earlier characters might have said, one does not simply walk into the slammer. In the opening minutes, we see the lapsed catholic Cobden progress through all the holy stations of the prison-drama. There's Sean in the noisy van, Sean in the first-night holding cell, Sean crouching to have his bum checked, Sean in his new tracksuit, moping into his cell, Sean having his lunch nicked, Sean sitting in the exercise ground, Sean navigating his psychopath self-harming cellmate Bernard (Aneurin Barnard) and the yobs across the hallway. He's a gentle soul, Cobden, a teacher on the outside, a model of stoicism inside, but he's going to have to learn to handle himself. Sean is basically your dad in prison, except your mum still wants to sleep with him.
To be fair to her, being locked up with Sean is not without its consolations. The granite-grey palette in which everything is saturated suits his craggy face. The part is less expansive than those he sometimes takes on, giving him chance to brood and mull. Cobden is a glacier rather than a box of fireworks. Guilt weighs heavily on him as he shuffles around his new home.
https://www.independent.co.uk/arts-entertainment/tv/reviews/time-review-sean-bean-stephen-graham-b1859556.html
Time is a hard to watch prison-based drama from the BBC but it's worth every minute
Each performance is incredibly powerful and, even though the programme is fictional, it is very much grounded in realism. Time is a necessary lesson on the British prison system and a masterclass in acting.
Bean and Graham work so beautifully together and really bring the story to life. You can instantly tell McGovern had them in mind as he was writing the piece.
https://futuretechtrends.co.uk/2021/06/06/time-is-a-hard-to-watch-prison-based-drama-from-the-bbc-but-its-worth-every-minute/
Time viewers dub Sean Bean and Stephen Graham drama "almost unwatchable" — in the best way
https://www.digitalspy.com/tv/a36641801/time-bbc-one-reactions-sean-bean-stephen-graham/
Time viewers stunned by 'grim' BBC crime drama 'can't stop watching'
https://www.express.co.uk/showbiz/tv-radio/1446327/Time-viewers-grim-Stephen-Graham-Sean-Bean-Jimmy-McGovern-drama-BBC-video
Time, BBC1, evaluation: Sean Bean and Stephen Graham are painful in this heartbreaking, fearless jail dramatization
https://technotrenz.com/news/time-bbc1-evaluation-sean-bean-and-stephen-graham-are-painful-in-this-heartbreaking-fearless-jail-dramatization-937911.html
Time, BBC1, review: Sean Bean and Stephen Graham are harrowing in this heartbreaking, fearless prison drama
https://inews.co.uk/culture/time-bbc1-review-sean-bean-and-stephen-graham-are-harrowing-in-this-heartbreaking-fearless-prison-drama-1035690
Time: Sean Bean, Stephen Graham combine for a shocking, compelling prison drama
I have two words of advice for anything contemplating diving into the BBC's latest prison drama: steel yourself.
Time (which begins screening on Prime at 9.30pm, tonight, Saturday, with episodes available on demand on Sky Go the same evening) assails you from the opening scene and doesn't let up until the credits roll.
Thank goodness it's only a three-parter, because the assault on the senses might not be sustainable.
But we're not talking mere shock value here, this is a brilliantly executed look at two men on either side of the cell door of the prison system. One that welcomes back a beloved screenwriter – Cracker, Moving On, Hillsborough's Jimmy McGovern – to prime time and showcases the talents of two of Britain's most under-rated actors in Sean Bean and Stephen Graham.
It wouldn't all quite be so powerful though, if it wasn't for former Lord of the Rings' star Bean and ubiquitous "everyman" Graham (The Irishman, Boardwalk Empire). These aren't histrionic turns, just nuanced, sensitive and compelling performances that draw the audience into their characters' lives and troubles.
Stunning, at times breathtaking and rage-inducing drama, you might need a cup of tea and a lie down after watching Time, but you'll also already be counting the hours until the next episode drops.
Time begins screening on Prime at 9.30pm on Saturdays from June 12. Each episode will also be available to stream on Sky Go the same evening.
https://www.stuff.co.nz/entertainment/stuff-to-watch/300330823/time-sean-bean-stephen-graham-combine-for-a-shocking-compelling-prison-drama
Jimmy McGovern's new prison drama Time is full of captivating performances
Sean Bean and Stephen Graham are utterly sensational in portraying two men trapped inside.
I can't say that I've ever been the number one fan of the screenwriter Jimmy McGovern. I loved Robbie Coltrane in Cracker, of course, and I liked The Lakes, starring John Simm as a badly behaved kitchen porter (or at any rate, I was completely startled by The Lakes, which seemed very naughty indeed to anyone who spent their childhood holidays by Ullswater, all those buttocks bobbing up and down in poor old Patterdale). But after that, the shows seemed to grow ever more sentimental and preachy. And there were so many of them! Somewhere along the way, the factories and the terraced houses, the Catholic priests and the shop stewards, all began to blur. In life, redemption is a magnificent thing. Forgiveness! I want a lot more of that. But on telly, an excess of it makes your teeth ache, as if you've been eating too many sweets.
Imagine my surprise, then, when just as the first episode of his new series, Time (6 June, 9pm), was about to end, I found myself wondering if I should watch the second before bed. Imagine, too, my further amazement as, that very same night, I immediately lined up the third (all three are on iPlayer). What was happening to me?
It wasn't even as if I was enjoying myself. I cried through most of the last episode, quietly at first, and then uncontrollably (though not, I fear, cathartically). In this drama, McGovern labours a somewhat basic point, which is that prison mostly doesn't work (or not in this country). But my God, the way he does it. Very little happens and yet, everything does, the worlds of its two principal characters turning and turning again, in ways that are unfathomable to both of them, even as they've only themselves to blame.
Not that McGovern can take all the credit. I can't think that Sean Bean and Stephen Graham have ever been better, each of them deploying only the tiniest muscles in their faces in the cause of stabbing the audience in the heart. Bean is Mark, a former school teacher, who is beginning a sentence for manslaughter, having killed a man while drunk behind the wheel. Graham is Eric, a prison officer of 30 years' standing who works on Mark's wing.
Picture a set of scales (I'm quite sure McGovern did, as he wrote). When the series starts, the two of them are unevenly balanced, one a criminal and the other squeaky clean. But things are about to change. While Mark is determined to atone for what he has done, Eric is about to dip his toe in the murk into which he has hitherto only peered from the sidelines. His son, it turns out, is serving a prison sentence elsewhere, word of which has got out among the lags. If he wants his boy to be safe, he's going to have to start bringing in stuff (drugs, knives) for the men in his charge.
Time is wonderfully attentive to detail. It feels well-researched. Snooker balls inserted into a sock become a cosh. Sugar and boiling water is the punishment meted out to snitches. A man who cuts himself, or bangs his head against the wall until it cracks, is extracted from his cell by screws who use plastic riot shields to press him into a corner, like coffee in a cafetiere.
So many petty rules and regulations, and yet, everywhere, such chaos. The noise – the absolute din – is constant and overwhelming. Allies are bought, not made. Enmities, on the other hand, are formed in a split second: a single glance can do it.
In the midst of all this, and the performances of so many good actors (Siobhan Finneran as a Catholic nun, Aneurin Barnard as Mark's disturbed cell mate), Bean is utterly sensational: a still, trembling point who embodies not only fear, shame, utter bewilderment and (for a while) loss of self, but also stoicism, kindness and, yes, remorse.
Contrition is a hard thing to make felt, even in real life. That an actor can impress it on us, his sincerity almost warm to touch, seems to me to be a truly remarkable thing. I had not expected it of him, nor of this script, and now I am a penitent, too. I come, in my sackcloth and my ashes, to bear witness to a Sunday night miracle.
https://www.newstatesman.com/culture/tv-radio/2021/06/jimmy-mcgoverns-new-prison-drama-time-full-captivating-performances
'Exhausted and blown away by brilliance of BBC's Time with Sean Bean and Stephen Graham'
Rarely does a TV drama have such an impact that I sit shell-shocked , silently sobbing on the sofa long after the final credits have rolled.
I watched the entire three hours of BBC1's gritty prison series Time in one hit, and it left me exhausted, emotional and blown away by the sheer brilliance of it.
For one thing, there's Sean Bean's craggy face, which I could stare at all day. He's one of those actors who doesn't even need to speak to get your attention.
Then, of course, there's Stephen Graham – another heavy hitter who commands every scene.
In the Jimmy McGovern drama, Bean plays Mark Cobden, a drunk-driver sent to jail for four years after knocking over and killing a cyclist.
Graham is prison guard Eric McNally, who has his own problems protecting his son David, an inmate in another jail.
From the moment Mark, an ordinary man and former teacher, arrived at HMP Craigmore, the scenes were shocking
and uncomfortable, but felt tragically, devastatingly authentic.
Prison is a place where violence can erupt at any moment, where most people are mad, bad or just downright miserable. No one is left unscathed.
An inmate chucked boiling water over someone they'd branded a grass, and laced it with salt and sugar "to make it stick".
Bullies spotted Mark's vulnerability and stole his food and cut off his precious phone calls to home.
It makes you wonder: What would you do? How would you survive?
Mark's cellmate (an excellent Aneurin Barnard) was wide-eyed and overwhelmed with mental health problems.
He shouldn't have been there.
And in a neat plot device, an outreach group for troubled kids enabled us to hear more tragic stories from prisoners full of regret about pasts
A thought-provoking comment on the prison system, with focus on one man's guilt and desperation to atone, and a good-hearted guard dragged down by a ruthless system he can't beat.
It was nothing but grim, to be honest, but powerful performances from every cast member made it one of the most absorbing shows I've seen in ages – from Siobhan Finneran as the kind Catholic chaplain, to Sue Johnston as Mark's bewildered mum, and Brian McCardie as a quietly terrifying prison kingpin.
A brutal series about remorse, guilt and survival with nightmarish flashbacks and harrowing confrontations.
But there were also odd moments of friendship and humanity, just enough to keep us hopeful.
Go and lock yourself away for three hours and watch it immediately. It will be time well spent.
https://www.mirror.co.uk/tv/tv-reviews/exhausted-blown-away-brilliance-bbcs-24305019
'There's nothing here I did not see inside' – a former HMP inmate on Time
Jimmy McGovern's hard-hitting drama is a brutally honest portrayal of a failed public service and gets everything right about prison life – minus the tedium
Time is a compelling, honest portrayal of a failed public service; a service that fails those it incarcerates, as well as the public who pay for it and suffer the consequences of that failure, not least in the obscenely high reoffending rates. McGovern has, again, lived up to his reputation.
https://www.theguardian.com/tv-and-radio/2021/jun/18/time-former-hmp-inmate-jimmy-mcgovern-sean-bean-stephen-graham
Time review: Sean Bean and Stephen Graham in extraordinary prison drama
Spanning only three episodes, this British miniseries starring Sean Bean is gritty, nuanced and powerful.
"I would love to, but I don't have the time." Judging by that all-too-common refrain, time is the one commodity everyone wished they had more of.
Unless, of course, you're in prison. Then time is all you have, the elastic perception of it stretching for eons as you try to stay sane and stay alive, really putting emphasis on the "serving" part of serving time.
Starring the powerhouse pair of Sean Bean and Stephen Graham and written by Jimmy McGovern, Time is a probing three-episode British miniseries set in a prison in northern England. Gritty, nuanced and understated, it's a series that encapsulates show and not tell.
It may be harrowing at times, it may even be hard to watch, but Time trades in flashy filmmaking techniques for an immersive storytelling experience that varies between dramatic moments and mundane, banal scenes.
It adds up to a cohesive whole, a TV show that captures the lives of those within an imperfect system of justice, where there is brutality but also decency.
We meet Mark Cobden (Bean) as he's transferred to prison to start his four-year sentence for killing a man while drink-driving. On the outside, Mark was a schoolteacher and his soft hands are immediately commented on.
The fact everyone he meets on that first day asks if it's his first time in prison condemns the cycle of recidivism that inmates are trapped in. Another incident in which one of Mark's cellmates partake in illegal drugs and comments that it's something he never did before incarceration is equally damning.
Guilt-ridden for his crime, Mark is haunted by images of his victim but finds purpose in aiding the prison chaplain Marie-Louise (Siobhan Finneran).
A lesser series would've charted out Mark's redemptive arc, but Time does the harder work of asking the question if atonement is even possible. That a series centred on crime and punishment dives deep into that thorny idea is another indicator of its thoughtfulness.
Graham's character is Eric, a senior prison officer. But he's not the other side of the equation because in many ways, he's on the same side. Eric is good at his job. He enforces the rules but he's fair, and he certainly doesn't have the sadistic streak that so many archetypal TV officers do.
Eric jeopardises his career and his principles when an inmate approaches him with an impossible proposition. This isn't set up as a great moral dilemma but rather a very human choice.
Time doesn't judge the people within the system, whether they're on the inmate side or the staff side. There are supporting characters including other inmates played by Jack McMullen, Aneurin Barnard and Kevin Harvey.
They don't have a lot of screentime but they're all distinct. It's the sort of deft world-building and nimble writing that's comparable to The Wire's David Simon.
Time presents these characters and their choices as almost ordinary. That's the power of this extraordinary series, to challenge us about our own choices, about how we spend our time.
The first episode of Time is streaming on Foxtel Now* and Fetch with new episodes broadcast on BBC First on Sundays at 8.30pm
https://www.news.com.au/entertainment/tv/streaming/time-review-sean-bean-and-stephen-graham-in-extraordinary-prison-drama/news-story/f31442bff1e1faab771f6aef9d915c95
Streaming reviews: Sean Bean and Stephen Graham shine bright in bleak English crime drama Time
PRISONS have always made for intriguing drama. Wentworth, Prison Break, Orange Is The New Black, the list goes on.
Partly it's because jail represents a kind of hell on earth, but also we all naturally imagine how we'd survive in such a brutal environment. English crime drama, Time, explores the latter.
Actors Sean Bean and Stephen Graham could turn a Home & Away script into compelling television. So it's little surprise they both deliver brilliant performances.
Bean, best known for playing physically-imposing roles in Lord Of The Rings and Game Of Thrones, exposes his vulnerable side as a 50-something teacher Mark Cobden, who is incarcerated in a northern England prison.
Guilt-ridden and unaccustomed to the harsh realities of prison life, the polite and meek Cobden soon finds himself at the mercy of the more sinister inmates.
Bean plays the role in a wonderfully under-stated manner, allowing his wrinkled forehead and jowls to convey the sadness and fear he's experiencing in the frightfully foreign situation that involves a cell mate self-harming and later overdosing.
Meanwhile, Graham (Snatch, This Is England) plays jail warden Eric McNally, who faces the task of protecting Cobden, while also juggling to shield his own family and maintain his principles.
Fresh off his mesmerising performance as a tortured alcoholic in the series, The Virtues, Graham again delivers.
Liverpool-bred screenwriter Jimmy McGovern has perfectly captured the bleakness and fear of prison life and the dangerous culture at its heart.
It once seemed impossible that Bean could surpass his performance as the noble, yet tragically flawed, Ned Stark in season one of Game Of Thrones, but Mark Cobden could be the finest role of his career.
https://www.canberratimes.com.au/story/7341091/timely-performance-from-sean-bean-ignites-gritty-jail-drama/?cs=14257 | {
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} | 3,777 |
\section{A: Generalization to higher dimensions}
\noindent The scheme can be used more generally to reduce a dataset of $d$-dimensional qudits to $n$-dimensional qunits, as illustrated in Fig.\ \ref{fig:SF}(a). At the output of the $(d\times d)$-dimensional encoding unitary $U$, the first $n$ modes are retained as the modes of the encoded states, while the last $(d-n)$ modes constitute the junk modes. \color{black} The unitary $U$ contains $\left[ d(d-1)/2 - n(n-1)/2 \right]$ two-mode unitaries, each of which entails two free parameters to be optimized. This amounts to fewer free parameters than for a general $d$-dimensional unitary \cite{Reck1994,Laing2011,Martin-Lopez2014}, since the single-mode phase shifters and $ \left[ n(n-1)/2\right]$ two-mode unitaries that act within the subspace of the first $n$ modes are unnecessary. \color{black} Denoting the occupation probability of the $k$-th junk mode for the $m$-th training state by $P^m_{\mathrm{j}k}$, \color{black} and letting $m_\mathrm{max}$ be the number of training states, \color{black} the cost function for training the unitary transformation can be defined as \color{black} $C=\sum_{m=1}^{m_\mathrm{max}} \sum_{k=1}^{d-n} P^m_{\mathrm{j}k}/m_\mathrm{max}$ \color{black} (other definitions are also possible).
After encoding quantum states from the dataset with a trained unitary $U$, they can be decoded by acting with $U^{\dagger}$ on the encoded states, after augmenting them with $(d-n)$ vacuum inputs modes (see Fig.\ \ref{fig:SF}(b)).
\begin{figure}[h]
\centering
\includegraphics[width=16.5cm]{SupplementalFigure.pdf}
\caption{(a) Training of an autoencoder that reduces qudits to qunits. The cost function is calculated based on the occupation probabilities of the $(d-n)$ junk modes. (b) The encoding-decoding sequence for the autoencoder. Ideally, the decoded state $|\Psi_f\rangle$ is equal to the input state $|\Psi_i\rangle$ for any member of the dataset. (c) Relationship between different quantum states in the encoding-decoding sequence. $|\Psi_{\mathrm{i}}\rangle$ is an input state of the autoencoder; $|\Psi_{\mathrm{eo}}\rangle$ is the output of the encoding unitary $U$; $|\Psi_{\mathrm{di}}\rangle$ is the result of discarding the junk modes and replacing them with vacuum, post-selected on the photon being in the first $n$ modes after the encoding unitary; $|\Psi_{\mathrm{f}}\rangle$ is the output of the decoding transformation $U^{\dagger}$.}
\label{fig:SF}
\end{figure}
\section{B: Quantifying the device performance}
\noindent In our device, two types of error need be minimized for any given input state: (i) the probability that the photon gets discarded due to it occupying the junk modes, in which case the autoencoder fails to produce an output photon, and (ii) the difference between the original input, $|\Psi_{\mathrm{i}}\rangle$, and the output after an encoding-decoding sequence, $|\Psi_{\mathrm{f}}\rangle$. We use the probability that the photon occupies one of the junk modes, $P_{\mathrm{j}}= \sum_{k=1}^{d-n} P_{\mathrm{j}k}$, as a measure of both types of error.
Clearly, the probability that the photon gets discarded due to it occupying the junk modes is simply $P_{\mathrm{j}}$. In other words, the success probability of the autoencoder producing an output is $1-P_{\mathrm{j}}$.
Given that an output is produced, the fidelity of the input and output of the encoding-decoding sequence is also determined by $P_{\mathrm{j}}$. This can be seen as follows: Let $\{\alpha_{n_1} |~ n_1\in \{1,2,...,n \}\}$ be the complex amplitudes of the first $n$ modes of $|\Psi_{\mathrm{eo}}\rangle$ and $\{\beta_{n_2} | ~n_2\in \{1,2,...,d-n \}\}$ the amplitudes of the junk modes, such that $|\Psi_{\mathrm{eo}}\rangle=(\alpha_1, ..., \alpha_{n},\beta_1, ..., \beta_{d-n})^T$. Then $|\Psi_{\mathrm{di}}\rangle=(1-P_{\mathrm{j}})^{-1/2}(\alpha_1, ..., \alpha_{n},0, ..., 0)^T$, and
\begin{eqnarray}
|\langle \Psi_{\mathrm{i}}|\Psi_{\mathrm{f}} \rangle|^2&=&|\langle \Psi_{\mathrm{eo}}|\Psi_{\mathrm{di}} \rangle|^2\nonumber \\
&=&|(1-P_{\mathrm{j}})^{-1/2}(\alpha_{1}^*\alpha_{1}+...+\alpha_{n}^*\alpha_{n})|^2\nonumber \\
&=&1-P_{\mathrm{j}}.
\end{eqnarray}
\color{black}
\section{C: Training algorithm}
\noindent The gradient descent algorithm we use for training the autoencoder is an iterative procedure that aims to find a minimum of the cost function $C(\mathbf{x})$, which depends on the four motorized wave plate angles in the autoencoder, $\mathbf{x}=\left( x_1,x_2,x_3,x_4\right) $. At the start of the training procedure, the angles are initialized randomly. Each iteration consists of the two stages described below: 1.\ a probing stage and 2.\ a movement stage.
\begin{enumerate}
\item The purpose of the probing stage is to estimate an approximate gradient, $\nabla C|_{\mathbf{x_\mathrm{cur}}}$, at the current wave plate settings $\mathbf{x}=\mathbf{x_\mathrm{cur}}$ through discretization. In order to estimate the partial derivative with respect to the $n$-th variable, the $n$-th wave plate is individually rotated by an adjustment value, $s_a$, resulting in a configuration $\mathbf{x}_{\mathrm{p}n}$. There, the cost function is measured, which requires a sequential preparation of the different training states, before returning the wave plate to its previous orientation. The partial derivative with respect to the $n$-th wave plate angle is then estimated as the slope of the secant line $ \left. \frac{\partial C}{\partial x_n}\right|_{\mathbf{x_\mathrm{cur}}}=\left[ C(\mathbf{x}_{\mathrm{p}n})-C(\mathbf{x_{\mathrm{cur}}})\right]/ s_a $.
\item In the movement stage, a simultaneous rotation of all four wave plates with a step size proportional to $s_a$ is made in the opposite direction of the gradient: $\mathbf{x_\mathrm{cur}} \rightarrow \mathbf{x_\mathrm{cur}}-s_a \nabla C|_{\mathbf{x_\mathrm{cur}}}$.
\end{enumerate}
\noindent Two different adjustment values, a coarse value and a fine value, are used at different times of the training procedure. The coarse adjustment value of $s_a= 12^{\circ}$ is used to quickly approach a minimum at the beginning of the training procedure. Once the cost function crosses a threshold value of 0.1, a smaller value of $s_a= 5^{\circ}$ is used for increased precision. Note that although we use $s_a$ from stage 1 again in stage 2, in general, a different proportionality coefficient for the step size (learning rate) could also have been used in stage 2.
In addition to the above, a deliberate disturbance is incorporated if a specific condition occurs: If the device is unable to achieve a cost function below 0.1 within 50 steps, each wave plate is rotated by 25°. The purpose of this is to bump the device out of poor optimizations and allow the reconfiguration to more desirable values. The conditional disturbance was added based on earlier observations of the training procedure, where for some of the training runs the cost function plateaued at values of 0.15±0.05. This extra feature serves to ensure a reliable device performance.
\color{black}
\color{black}
\section{D: Example transformations}
\noindent Here, we provide the three unitary transformations which the autoencoder learned in the training runs depicted in Fig.\ \ref{fig:drift}. The unitaries are calculated based on a model of the setup and the experimental configuration of the wave plates at the end of the training runs. We denote the transformation learned in the control run as $U_1$, and the two transformations learned under perturbations as $U_2$ and $U_3$. The transformations are
\[
U_1
=
\begin{bmatrix}
-0.373 - 0.037 i & -0.927 + 0.015 i & 0 \\
0.008 + 0.213 i & -0.013 - 0.085 i & -0.003 - 0.973 i \\
-0.017 + 0.902 i & -0.035 - 0.363 i & -0.012 + 0.230 i
\end{bmatrix},
\]
\[
U_2
=
\begin{bmatrix}
0.054 - 0.610 i & -0.790 - 0.042 i & 0 \\
-0.090 + 0.094 i & -0.075 - 0.067 i & 0.014 - 0.986 i \\
0.052 + 0.778 i & -0.601 + 0.062 i & 0.120 + 0.112 i
\end{bmatrix},
\]
\[
U_3
=
\begin{bmatrix}
0.495 + 0.298 i & -0.795 + 0.185 i & 0 \\
-0.172 + 0.228 i & 0.025 + 0.200 i & 0.048 - 0.936 i \\
-0.135 + 0.753 i & 0.303 + 0.449 i & 0.142 + 0.319 i
\end{bmatrix}.
\]
\noindent Note that the $(1,3)$ element of each unitary is 0 because the autoencoder does not comprise, or require, a fully general unitary transformation between the three modes. Our autoencoder can omit one of the $2\times 2$ transformations of a general decomposition \cite{Reck1994,Laing2011,Martin-Lopez2014}, namely the one in the encoded output subspace, without affecting the cost function or the ability to learn how to compress any compressible set of qutrits.
\color{black}
\end{document} | {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,301 |
Buying or Starting a Business? Why Read This Blog? | Buying or Starting a Business?
First, thank you for giving us a try!
This blog is intended to be a series of published posts, and is being started for several reasons. Our biggest motivation is that we have become extremely and increasingly alarmed at the number of people who walk around with their heads in the clouds, spending tons of their hard-earned money in an effort to buy or start up a business, without really knowing what they were spending their money on. And failing! Some – not all of this wasted money – but some of it is because they are simply given wrong information by people that have their own agendas, and it is in their best interest to misrepresent opportunities, thereby giving business buyers and startup people incorrect information, from the beginning.
Who would have the motivation to spread misinformation? Everybody that can make a buck from your deal! This includes Business Owners/Sellers, Business Brokers, Franchise Companies, Loan Brokers, and even Accountants and Attorneys. Yes, even Accountants and Attorneys!
The moral is that you are the only person that you can trust. And you cannot trust yourself unless you are a knowledgeable Buyer. Starting up or buying a business in any other way, is like sending a soldier off to battle with a shiny new rifle, but no ammunition.
And just to set the record straight, we are not the kind of Brokers that use that old cliché, that all Attorneys are deal breakers. Our relationships with Attorneys are terrific, and we actually get a large number of referrals from Lawyers. The same with Accountants. We ALWAYS encourage both Buyers and Sellers to seek out advice from their Attorneys and Accountants the the strongest, possible way, even to the point of suggesting candidates for such posts, if necessary. Normally, in such extremely rare instances where an Attorney or an Accountant kills one of our deals, it is for very good reasons. But as in with any profession, there are always a couple of bad apples. (Believe it or not, there are actually some bad Business Brokers out there, as well!) Your protection is your own knowledge. You need to know what questions to ask, and when the answers are given, you have to have enough knowledge to determine whether that information is reasonable.
By becoming proficient at the research, you can reduce your chances of failure. But if you do fail, you will also have the tools to get up, brush yourself off and get back into the game.
Failure is not to be taken lightly. But it is not a sin; it is not something to be ashamed of; it does not make you less of a person. Some of the most famous and wealthy business people have actually experienced mammoth failures and even bankruptcies, before becoming successful. Failure because you took the risk too lightly and made a decision without doing the proper research is a bit insane.
This is not a blog about telling you or encouraging you to buy or start a business. It is about working hard enough at investigating your dream to determine whether it is worth having, and worth the risk. It is about establishing realistic goals, based on realistic expectations. Some of what you will read over the next weeks is fairly technical; much more can be classified as organized, common sense.
A huge number of people who want to be in business have no real idea what they are in for. Many years ago, I personally did speaking engagements in tandem with Nurse/Author Marlene Kramer, who wrote a book called, "Reality Shock: Why Nurses Leave Nursing". Reality Shock, according to Ms. Kramer, described the bombshell that Nurses receive when they realize how different the daily activities they encounter in the profession are from what they expected or were led to believe, while in nursing school. And it causes Nurses to bail out of their profession in alarming numbers. I never forgot her lectures, and the concept is incredibly fitting, here.
As Brokers, there have been any number of instances where a Business Owner called us to sell his/her business, after only owning it for a year or so. One woman, we vividly recall – and we are not picking on women; she happens to be one that we remember, almost word-for-word – said she had given up her job and bought a business so that she could have more time with her children. She imagined that by owning a business, she could create her own schedule.
That is a great concept. Except that you have to go into it knowing that when you have a staff to rely on, the ones that call in sick, the ones that quit without notice, the ones that are most difficult to replace are invariably going to be the evening, night and weekend workers. And who will fill the void they left behind? In the vast number of instances, it is YOU! The Business Owner! That was her unfortunate realization, after she bought her business: She was not only assuming her own, planned responsibilities, but filling in for others, for any variety of absences.
"I want to be my own boss!" is a reason many people state, for wanting their own business. WRONG!!! Every Client, every potential Customer, any of the people you depend on to operate or supply your business is, one way or another, your boss.
We could argue about some of those people, but Customers are not something you can dispute, as to whether they are your "boss". Don't do what they want, don't give them what they feel they are due and you will hear it from them, just the way you would from your old boss, Mr. Scrooge.
Many people feel that e-Commerce business insulates them from this experience, and that is one of the allures of people wanting that kind of opportunity. In fact, e-Commerce can be even more problematic in this area. The Internet means that when your Customer/Boss feels that you have screwed up, frequently you will see you and your business targets of complaints that are both vicious and impossible to fight. And e-Commerce Customers are more attuned to using the Net, so that kind of business is even more apt to be skewered, electronically. "Flamed", is the appropriate term. People will make critical comments on the Net with such extraordinary exaggeration and savagery, that they would never, ever say in any other way.
Never thought of these things? This is all part of Reality Shock. (Thank you, Marlene Kramer. It has been close to thirty years since we last spoke and you would undoubtedly never remember me, but your lessons were well learned!) And it is absolutely crucial that you do everything you can to avoid that ugly kind of surprise, when you own your own business.
This blog does not suggest it is the only way to understand these issues. The opinions represented here are frequently our own, based on a dozen (and counting) years of Business Brokerage, (our Web Site is www.bafgroup.com,) and more than twenty years of startup and troubleshooting for a variety of companies, (from Mom and Pops, to Franchises to FORTUNE 500 subsidiaries,) before that. There will always be one Reader who will disagree, saying, "But I know a guy who…" Great! Understood! Go in peace!
However, realize that what is being expressed here is not the opinion of just one person; it is also from information gained from a huge number of transactional experiences, from discussions with other Buyers, Sellers, Brokers, Attorneys, Bankers, Accountants, Taxi Drivers…okay, maybe not Taxi Drivers, unless they have bought or sold their businesses. The Reader that knows ONE GUY that did it differently may be on to something new or novel; but he could also be dealing with one guy that succeeded by mistake; or one guy who fell into a fortunate series of situations through pure dumb luck, which cannot be replicated; or one guy who bragged and lied about it!
Many people who freely offer their advice on the Internet, we have found, actually have no tangible experience in the area in which they are offering such advice. They are specifically people who know a guy, who told them about a brother-in-law who knew a guy… Is that the kind of information you want to use as the basis for making the biggest investment in your life?
Some of the topics represented here will be painfully brief; some will be tediously long, all depending on the variables involved with the topics, themselves.
Some of you will want more detail about specific information. We welcome such questions; however, realize that not every question can be answered, or in the kind of detail that you might wish. We will make every effort to comply with questions, if you choose to post them.
Thanks, in advance, for being with us. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,203 |
Q: Braintree: Creating a new subscription after the user has canceled I am trying to decide how to handle the situation where a user has subscribed through the month, lets says 6/1 they are subscribed through until 6/31. Midway through the month they decide to cancel their subscription (6/15), but then on 6/20, they decide to restart their subscription again. How is this handled in Braintree, if at all? Is there an advised route for handling this situation?
My current thought:
I'll be keeping track of their canceled subscription and checking how far they are paid through and stop providing them service once that period ends. I was considering putting the new subscription on a trial period for the difference in days between their canceled subscription paid through date (in this case 10 days). The implication here is that I have to check now if they are in a trial period on top of the paid through date if for some reason they do this n times within the month. I saw some advice to consider the implications of trial periods on the Braintree documentation and so I wanted to make sure this was the best route to go.
In relation to the 'n' repetitions, does the trial-duration decrease with each day? So trial period starts on 6/20 with ten days remaining, does the trial-duration go down to 9 on 6/21? There seems to be no indication on the documentation on what the specific case is.
A: Thanks to the Braintree Support team:
The main reason we advise you to take extra care with trial periods is that there are risk and liability issues around making sure your customer knows when they're going to be charged. However, it can get difficult to keep track of start dates when using trial periods. What I'd recommend doing, actually, is setting a first billing date instead when you create a new subscription. This allows you to specify a particular date (rather than just a day of the month or a time period into the future) to first charge your customer.
All you'd have to do is keep track of the date each subscription was paid through (which you could do via our API.) Then, if a customer canceled their subscription and created a new one before that date occurred, just create a new subscription with a first billing date of the day after the paid-through date. You then wouldn't have to do any trial period checking if the customer kept canceling and re-signing up—the only thing you'd need to keep track of was the paid-through date of the original subscription.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,390 |
{"url":"http:\/\/math.stackexchange.com\/questions\/151585\/how-to-prove-the-pullback-lemma?answertab=votes","text":"# How to prove the pullback lemma\n\nI am new in category theory. I am trying to prove the well known fact that if you have a commutative diagram of the form \u25a1\u25a1, where each square is a pullback, then the whole diagram is a pullback too, and hence deduce that the pullback of a pullback square is a pullback. Every book I have looked at has this as an exercise, but I (embarrasingly, I know) cannot see the solution. I have tried using the universality property of the two pullbacks but i am lost in calculations. If someone could help, I would really appreciate it.\n\n-\nCrossposted: mathoverflow.net\/questions\/98378\/\u2026 \u2013\u00a0Rasmus May 30 '12 at 13:49\nYou might also try posting your work up to the point where you get lost in calculations; then someone might help you find your way out again. \u2013\u00a0MJD May 30 '12 at 14:18\n\nThanks for a citeable reference for this proof! Trivial nitpick: $m = m' = n' \\circ f$ on page 2 should be $m = m' = f \\circ n'$. \u2013\u00a0darij grinberg Jun 30 '15 at 12:56","date":"2016-05-04 20:16:09","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\": 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\": 0.9198704957962036, \"perplexity\": 185.28337260287307}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-18\/segments\/1461860123845.65\/warc\/CC-MAIN-20160428161523-00031-ip-10-239-7-51.ec2.internal.warc.gz\"}"} | null | null |
Q: Restart read required when migrating existing application from PostgreSQL to YugabyteDB [Question posted by a user on YugabyteDB Community Slack]
I am trying to migrate an existing application from PostgreSQL to YugabyteDB using a cluster with 3 nodes.
The smoke tests run fine but I received the following error as soon as I use more than one concurrent user:
com.yugabyte.util.PSQLException: ERROR: Query error: Restart read required at: { read: { physical: 1648067607419747 } local_limit: { physical: 1648067607419747 } global_limit: <min> in_txn_limit: <max> serial_no: 0 }
at com.yugabyte.core.v3.QueryExecutorImpl.receiveErrorResponse(QueryExecutorImpl.java:2675)
at com.yugabyte.core.v3.QueryExecutorImpl.processResults(QueryExecutorImpl.java:2365)
at com.yugabyte.core.v3.QueryExecutorImpl.execute(QueryExecutorImpl.java:355)
at com.yugabyte.jdbc.PgStatement.executeInternal(PgStatement.java:490)
at com.yugabyte.jdbc.PgStatement.execute(PgStatement.java:408)
at com.yugabyte.jdbc.PgPreparedStatement.executeWithFlags(PgPreparedStatement.java:162)
at com.yugabyte.jdbc.PgPreparedStatement.execute(PgPreparedStatement.java:151)
at com.zaxxer.hikari.pool.ProxyPreparedStatement.execute(ProxyPreparedStatement.java:44)
at com.zaxxer.hikari.pool.HikariProxyPreparedStatement.execute(HikariProxyPreparedStatement.java)
at org.jooq.tools.jdbc.DefaultPreparedStatement.execute(DefaultPreparedStatement.java:219)
at org.jooq.impl.Tools.executeStatementAndGetFirstResultSet(Tools.java:4354)
at org.jooq.impl.AbstractResultQuery.execute(AbstractResultQuery.java:230)
at org.jooq.impl.AbstractQuery.execute(AbstractQuery.java:340)
at org.jooq.impl.AbstractResultQuery.fetch(AbstractResultQuery.java:284)
at org.jooq.impl.SelectImpl.fetch(SelectImpl.java:2843)
at org.jooq.impl.DefaultDSLContext.fetch(DefaultDSLContext.java:4749)
I am using the version 11.2-YB-2.13.0.1-b0
It is a clinical data repository implemented using Spring Boot and JOOQ. The application exposes a REST API to store and query clinical documents inside the database.
I try to execute a JMeter test plan that creates and queries random documents using 10 concurrent users during a fixed period (5min).
Until now, we were using PostgreSQL which seems to have Read Committed as the default isolation level. So, I assume that I have to change the isolation at the application level as Spring uses the one defined by the database by default.
A: Please note that the default isolation level of PostgreSQL and YugabyteDB is not the same.
Read Committed Isolation is supported only if the gflag yb_enable_read_committed_isolation is set to true. By default this gflag is false and in this case the Read Committed isolation level of Yugabyte's transactional layer falls back to the stricter Snapshot Isolation (in which case READ COMMITTED and READ UNCOMMITTED of YSQL also in turn use Snapshot Isolation).
Can you change the isolation level as above for YugabyteDB? Please refer to this doc link for more details - https://docs.yugabyte.com/latest/explore/transactions/isolation-levels/
It should work much better after the change.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,682 |
Q: Check if a (String) variable is well defined - use preprocessor? I am currently developing an Arduino based project involving a password check.
The password is provided as a global variable in the source code. However, the password should only allow certain characters (basically only letters, numbers and just a few special characters).
I want to ensure that no other characters are used - otherwise the code shouldn't compile.
Is there a way (possibly using the preprocessor) to check a String variable for the characters it contains and abort compilation if "illegal" characters are used?
Example code snipplet (probably not necessary, however...):
const String password1 = "test"; // should compile
const String password2 = "%$§~^"; // should NOT compile
A: No, I do not believe this is possible at the preprocessor level. The C preprocessor cannot inspect strings.
If you were to abandon the Arduino IDE and use a Makefile or shell script, you could do it there.
Something along the lines of:
PASSWORD="test"
if [ echo $PASSWORD | grep -e <magic regexp for invalid chars> ]
then
gcc ... -DPASSWORD="$(PASSWORD)"
else
exit 1
fi
Another way might be:
typedef enum
{
MY_A 'a',
MY_B 'b',
MY_C 'c',
// etc. for all allowed characters
} my_charset;
const my_charset *password = {MY_P, MY_A, MY_S, MY_S, MY_W, MY_O, MY_R, MY_D};
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,472 |
Q: This program doesn't print syslogs anywhere? I am using fc19, just now I have installed syslog-ng. Looks like syslog is no more available for fc19. I started the syslog-ng service. The status of syslog-ng is running. This is my program. I don't where is it logging the output.
#include<iostream>
#include<ctime>
#include<syslog.h>
#include <unistd.h>
using namespace std;
class my_syslog
{
private:
int m_sys;
public:
my_syslog(int init);
void get_time();
};
my_syslog::my_syslog(int init):m_sys(init)
{
cout<<"Constructor called"<<endl;
}
void my_syslog::get_time()
{
time_t now = time(0);
tm* localtm = localtime(&now);
//cout << "SJ:The local date and time is: " << asctime(localtm) << endl;
// Convert now to tm struct for UTC
//tm* gmtm = gmtime(&now);
//if (gmtm != NULL) {
//cout << "The UTC date and time is: " << asctime(gmtm) << endl;
//}
syslog (LOG_INFO, "SJ:The local date and time is: %s",asctime(localtm));
}
int main(int argc, char **argv)
{
my_syslog instant(100);
for(int i = 0; i<=10;i++)
{
instant.get_time();
sleep(10);
}
cout<<"Program End"<<endl;
return 0;
}
The /etc/syslog-ng/syslog-ng.conf is the following.
@version:3.3
# syslog-ng configuration file.
#
# This should behave pretty much like the original syslog on RedHat. But
# it could be configured a lot smarter.
#
# See syslog-ng(8) and syslog-ng.conf(5) for more information.
#
# Note: it also sources additional configuration files (*.conf)
# located in /etc/syslog-ng/conf.d/
options {
flush_lines (0);
time_reopen (10);
log_fifo_size (1000);
chain_hostnames (off);
use_dns (no);
use_fqdn (no);
create_dirs (no);
keep_hostname (yes);
};
source s_sys {
file ("/proc/kmsg" program_override("kernel") flags(kernel));
unix-dgram ("/dev/log");
internal();
# udp(ip(0.0.0.0) port(514));
};
destination d_cons { file("/dev/console"); };
destination d_mesg { file("/var/log/messages"); };
destination d_auth { file("/var/log/secure"); };
destination d_mail { file("/var/log/maillog" flush_lines(10)); };
destination d_spol { file("/var/log/spooler"); };
destination d_boot { file("/var/log/boot.log"); };
destination d_cron { file("/var/log/cron"); };
destination d_kern { file("/var/log/kern"); };
destination d_mlal { usertty("*"); };
filter f_kernel { facility(kern); };
filter f_default { level(info..emerg) and
not (facility(mail)
or facility(authpriv)
or facility(cron)); };
filter f_auth { facility(authpriv); };
filter f_mail { facility(mail); };
filter f_emergency { level(emerg); };
filter f_news { facility(uucp) or
(facility(news)
and level(crit..emerg)); };
filter f_boot { facility(local7); };
filter f_cron { facility(cron); };
#log { source(s_sys); filter(f_kernel); destination(d_cons); };
log { source(s_sys); filter(f_kernel); destination(d_kern); };
log { source(s_sys); filter(f_default); destination(d_mesg); };
log { source(s_sys); filter(f_auth); destination(d_auth); };
log { source(s_sys); filter(f_mail); destination(d_mail); };
log { source(s_sys); filter(f_emergency); destination(d_mlal); };
log { source(s_sys); filter(f_news); destination(d_spol); };
log { source(s_sys); filter(f_boot); destination(d_boot); };
log { source(s_sys); filter(f_cron); destination(d_cron); };
# Source additional configuration files (.conf extension only)
@include "/etc/syslog-ng/conf.d/*.conf"
# vim:ft=syslog-ng:ai:si:ts=4:sw=4:et:
Please help with what is going wrong here.
A: Before you can use syslog() you need to openlog().
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"redpajama_set_name": "RedPajamaStackExchange"
} | 8,108 |
{"url":"http:\/\/www.crcg.de\/wiki\/Joachim_Hilgert:_Asymptotic_K-Support_and_Restrictions_of_Representations","text":"# Joachim Hilgert: Asymptotic K-Support and Restrictions of Representations\n\nIn the late nineties T. Kobayashi wrote a series of papers in which he established a criterion for the discrete decomposablity of restrictions of unitary representations of reductive Lie groups to reductive subgroups. A key tool in the proof of sufficiency of his criterion was the use of the theory of hyperfunctions to study the microlocal behavior of characters of restrictions to compact subgroups. In this paper we show how to replace this tool by microlocal analysis in the $LaTeX: C^\\infty$ category.","date":"2013-05-23 21:53:56","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\": 1, \"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\": 0.7319298386573792, \"perplexity\": 414.5712150526397}, \"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-2013-20\/segments\/1368703830643\/warc\/CC-MAIN-20130516113030-00080-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
Q: How to use mail function in codeIgniter? $query = $this->db->insert('table_name',$data);
if($query==true)
{
$to = $this->input->post('email');
$subject = "Activation Link";
$message = "<p>Welcome: ".$this->input->post('email')."</p>
<p>Thank you for join InSquareFeet. To activate your account please <a href=".base_url()."thankyou/".$confirm_id."></a></p>";
$headers = "MIME-Version: 1.0" . "\r\n";
$headers .= "Content-type:text/html;charset=UTF-8" . "\r\n";
$headers .= "From: ayush@gmail.com";
mail($to,$subject,$message,$headers);
echo '<p>Thank you for connecting with us. We have sent you an activation link on your email id.</p>';
}
else
{
echo '<p>Error!</p>';
}
In this code, I have created a mail function where I insert the form value into the database which is work perfectly but I also want to send the confirmation mail to the candidate which is not working. I don't know why? Where I am doing wrong? Please help me.
Thank You
A: Codeigniter has provided some inbuilt libraries with examples. I think you guys are not even searching anything and just asking questions How to use. Even if you search How to use email in Codeigniter in google you will get many tutorials about codeigniter libraries and its uses.
Here are some examples for your reference.. Instead of using mail() function use inbuilt libraries which allows you to set smtp config.
How to use email function in codeigniter
How to set configuration for email in codeingiter
Sending email with google smtp configuration in codeigniter
another example about setting config in codeigniter email
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 259 |
\section{Introduction}
Since the advent of Witten's reformulation of the Jones polynomial
using $\mathrm{SU}(2)$ Chern-Simons theory \cite{witten1989},
there have been fruitful interplays between
3-dimensional quantum field theories (3D QFTs) and mathematics of 3-manifolds and knots.
In the interplays, mathematicians provide rigorous approaches to topological quantum field theories while physicists suggest new topological invariants and conjectures which seem to be unexpected to mathematicians.
Recently, 3D-3D correspondence \cite{Terashima:2011qi,Dimofte:2011ju} accelerates the interplays drastically as it allows us to study various supersymmetric quantities in 3D supersymmetric QFTs in terms of mathematical quantities of 3-manifolds.
In this paper, we study 3D $\mathcal{N}=2$ supersymmetric QFTs $\mathcal{T}_{N=2}[\mathcal{M},\mathcal{K}]$ labeled by a closed 3-manifold $\mathcal{M}$ and a knot $\mathcal{K}\subset \mathcal{M}$.
Under mild assumptions, we propose concrete conjectures on the knot exterior $M=\mathcal{M}\backslash \nu(\mathcal{K})$ deduced from the twisted indices, the partition functions of $\mathcal{T}_{N=2}[\mathcal{M},\mathcal{K}]$ placed on curved backgrounds $\Sigma_g \times S^1$.
Here $\nu(\mathcal{K})$ denotes a tubular neighborhood of $\mathcal{K}$ and $\Sigma_g$ is a Riemann surface of genus $g$.
We give a particular focus on the conjecture for $g=0$ (see Conjecture \ref{conj:intro} below) which is most unexpected in the mathematical viewpoint.
\begin{conjecture} \label{conj:intro} Let $M$ be a compact 3-manifold with a torus boundary whose interior admits a hyperbolic structure. Let $X^\mathrm{irr}(M)$ be the character variety of irreducible $\mathrm{SL}_2(\mathbb{C})$-representations.
Suppose that every irreducible component of $X^\mathrm{irr}(M)$ is of dimension 1. Then for any slope $\gamma \in H_1(\partial M; \mathbb{Z})$ we have
\[\sum_{[\rho] \in \mathrm{tr}_\gamma^{-1}(z)} \frac{1} {\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma) } =0\]
for generic $z \in \mathbb{C}$. Here $\mathrm{tr}_\gamma : X^\mathrm{irr}(M)\rightarrow \mathbb{C}$ is the trace function of $\gamma$ and $\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)$ is the adjoint Reidemeister torsion with respect to $\rho$ and $\gamma$.
\end{conjecture}
We observe that Conjecture \ref{conj:intro} is deeply related to global residue theorem. In particular, we give a rigorous proof of Conjecture \ref{conj:intro} for the figure-eight knot exterior.
Note that this gives an infinite family of $\mathcal{T}_{N=2}[\mathcal{M},\mathcal{K}]$ (obtained by varying a slope $\gamma$) where our physical arguments used to derive the conjecture are mathematically supported.
We also present numerical verification to provide non-trivial consistency checks for the assumptions in Conjecture \ref{conj:intro}.
In particular, we emphasize
that all irreducible components of $X^\mathrm{irr}(M)$ (not just the geometric component) should be taken into account in the 3D-3D relation. Otherwise, the twisted index at $g=0$ may not be even an integer (see Section \ref{sec:knot74} and Remark \ref{rmk:allcomponent}).
The paper is organized as follows.
In Section \ref{sec:3D-3D}, we give a general survey on 3D-3D correspondence.
In Section \ref{sec: conjecture from physics}, we focus on the 3D-3D relation for the twisted indices which leads Conjecture \ref{conj:intro}.
In Section \ref{sec:def}, we recall some definitions and properties of adjoint Reidemeister torsion.
In Section \ref{sec:proof}, we prove the conjecture for the figure-eight knot exterior.
We discuss some further directions in Section \ref{sec:further}.
\section{A brief survey on 3D-3D correspondence} \label{sec:3D-3D}
The 3D-3D correspondence relates 3D suppersymmetric quantum field theories (SQFTs) and mathematcis of 3-manifolds.
The correspondence can be understood from the physics of M5-branes, 6-dimensional extended objects in M-theory.
Precisely, we consider the low-energy world-volume theory of multiple $N$ M5-branes called the 6D $A_{N-1}$ $(2,0)$ theory.
\begin{align}
\begin{split}
&(\textrm{6D $A_{N-1}$ (2,0) theory})
\\
&=(\textrm{low-energy world-volume theory of coincident $N$ M5-branes}).
\end{split}
\nonumber
\end{align}
Through a twisted compactification of the 6D theory along a closed 3-manifold $\mathcal{M}$ with a defect along a knot $\mathcal{K} \subset \mathcal{M}$, we can geometrically engineer a 3D SQFT $\mathcal{T}_N[\mathcal{M},\mathcal{K}]$ labeled by a pair $(\mathcal{M},\mathcal{K})$ and $N\geq2$.
\begin{align}
\begin{split}
\mathcal{T}_N[\mathcal{M},\mathcal{K}]&:= (\textrm{3D theory obtained from a twisted compactification of }
\\
&\textrm{6D $A_{N-1}$ (2,0) theory along $\mathcal{M}$ with a regular maximal defect along $\mathcal{K}$}).
\end{split}
\nonumber
\end{align}
To preserve some supersymmetries, we perform a partial topological twisting using the usual $SO(3)$ subgroup of $SO(5)$ R-symmetry of the 6D theory.
Then the resulting 3D theory $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$ has 3D $\mathcal{N}=2$ superconformal symmetry with $su(N)$ flavor symmetry associated to the maximal regular defect. An explicit field-theoretic construction of $\mathcal{T}_N[\mathcal{M},\mathcal{K}]$ was proposed in \cite{Dimofte:2011ju,Dimofte:2013iv} using an ideal triangulation of the knot complement.
One interesting aspect of the construction is that partition functions (ptns) of $\mathcal{T}_N[\mathcal{M},\mathcal{K}]$ on supersymmetric (SUSY) curved backgrounds $\mathbb{B}$ give topological invariants of $(\mathcal{M}, \mathcal{K})$.
\begin{align}
\begin{split}
\textrm{3D-3D relation : } &(\textrm{SUSY ptns of $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$ on $\mathbb{B}$})
\\
&= (\textrm{topological invariants $\mathcal{I}_N (\mathcal{M}, \mathcal{K},\mathbb{B})$}).
\end{split}
\nonumber
\end{align}
During the last decades, physicists have studied various supersymmetric backgrounds $\mathbb{B}$ and developed techniques for computing the SUSY ptn on $\mathbb{B}$ using so-called localization technique (see \cite{Willett:2016adv} for a review). For $\mathbb{B} = S^2\times_q S^1$ the corresponding SUSY ptn is called a superconformal index \cite{Kim:2009wb} where $q$ denotes the Omega-deformation parameter on $S^2\times S^1$.
For $\mathbb{B} = S^3_b/\mathbb{Z}_k$ the corresponding SUSY ptn is called a squashed Lens space partition function \cite{Hama:2011ea} where $b$ denotes the squashing (Omega-deformation) parameter. For the above cases, the 3D-3D relation is known as follows.
\begin{align}
\begin{split}
&(\textrm{$S^3_b/\mathbb{Z}_k$ partition function of $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$})
\\
& \qquad = (\textrm{State-integral model of $\mathrm{SL}_N(\mathbb{C})$ theory of level $k$ \cite{Dimofte:2014zga}});
\\
&(\textrm{Superconformal index of $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$})
\\
& \qquad = (\textrm{3D index \cite{Dimofte:2011py,Garoufalidis:2016ckn,Dimofte:2013iv}} ).
\end{split}
\nonumber
\end{align}
Another interesting SUSY partition function which has not been explored seriously in the context of 3D-3D correspondence until quite recent days is a twisted index \cite{Benini:2015noa,Benini:2016hjo,Closset:2016arn,Gukov:2015sna,Gukov:2016gkn}, the SUSY ptn on $ \mathbb{B}=\Sigma_g\times S^1$. Here $\Sigma_g$ is a closed Riemann surface of genus $g$. Let
\begin{align}
\mathcal{I}_N (\vec{x};\mathcal{M}, \mathcal{K}, g )= (\textrm{Twisted index of $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$ on $\Sigma_g \times S^1$}) \label{twistedindex}
\end{align}
where $\vec{x} = \{ x_i\}_{i=1}^{N-1}$ are fugacities for $(N-1)$ Cartan generators of the $su(N)$ flavor symmetry.
When $N=2$, the precise 3D-3D relation for the twisted index is given as follow \cite{Gang:2018hjd,Gang:2019uay}:
\begin{align}
\mathcal{I}_{N=2}(x;\mathcal{M},\mathcal{K},g) = \mkern-20mu \sum_{[\rho] \in\mathrm{tr}_\gamma^{-1}(x+x^{-1}) } \mkern-30mu \left( d_\gamma \cdot \textrm{Tor}(M;\mathfrak{g}_\rho, \gamma) \right)^{g-1}
\label{3d-3d relation}
\end{align}
for generic $x \in \mathbb{C}^\times$ where
\begin{align}
\begin{split}
&\bullet \textrm{$M$ is the knot exterior $\mathcal{M} \backslash \nu(\mathcal{K})$;}
\\
&\bullet\textrm{$\gamma \in H_1(\partial M;\mathbb{Z})$ is a cycle representing a meridian of $\mathcal{K}$;}
\\
&\bullet\textrm{$\mathrm{tr}_\gamma : X^\mathrm{irr}(M) \rightarrow \mathbb{C},\ [\rho] \mapsto \mathrm{tr}(\rho(\gamma))$ is the trace function of $\gamma$;}
\\
&\bullet\textrm{$d_\gamma = \begin{cases}
1 \quad \textrm{if $\gamma \in \textrm{Ker}(i_\ast : H_1 (\partial M;\mathbb{Z}) \rightarrow H_1 (M;\mathbb{Z}/2\mathbb{Z})) $} \\ 2 \quad \textrm{otherwise}.
\end{cases}$}
\end{split}
\label{eqn:notation}
\end{align}
Here $\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)$ is the adjoint Reidemeister torsion with respect to $\rho$ and $\gamma$. We refer to Section \ref{sec:def} for the precise definition.
An interesting point is that there is no other topological quantity appeared in the relation \eqref{3d-3d relation} except the adjoint Reidemeister torsion, which is nothing but the 1-loop perturbative invariant of $\mathrm{SL}_2(\mathbb{C})$ Chern-Simons theory.
\section{Ground state counting of wrapped M5-branes} \label{sec: conjecture from physics}
The 3D twisted index \eqref{twistedindex} can be also viewed as the Witten index \cite{Witten:1982df} for the 1D supersymmetric quantum mechanics (SQM)
\begin{align*}
\begin{split}
&\mathcal{T}_N[\mathcal{M}\times \Sigma_g,\mathcal{K}]:= (\textrm{1D SQM obtained from a twisted compactification of}
\\
&\qquad \textrm{the 6D $A_{N-1}$ (2,0) theory along $\mathcal{M}\times \Sigma_g$ with a regular defect along $\mathcal{K}\times \Sigma_g$}). \end{split}
\end{align*}
We hereafter restrict our attention to $N=2$ and omit the subscript $N$ for simplicity.
The symmetries of $\mathcal{T}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$ are
\begin{align}
\label{symmetries}
\begin{split}
&\bullet \textrm{Time translation},
\\
&\bullet\textrm{2 supercharges $Q$s : $16$ $Q$s are broken to 2 $Q$s by topological twisting},
\\
&\bullet\textrm{$SO(2)$ R-symmetry : $SO(5)$ is broken to $SO(2)$ by topological twisting},
\\
&\bullet\textrm{$su(2)$ symmetry : flavor symmetry associated to the knot $\mathcal{K} \subset \mathcal{M}$}.
\end{split}
\end{align}
Here the symbol $su(2)$ could be either $SO(3)$ or $SU(2)$. The global structure of the $su(2)$ symmetry of $\mathcal{T}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$ is determined by the following criterion \cite{Gang:2018wek}.
\begin{align*}
su(2) = \begin{cases} SU(2) \quad \textrm{if $\gamma \in \textrm{Ker}\: i_* $} \\ SO(3) \quad \textrm{otherwise.}
\end{cases}
\end{align*}
The Witten index \cite{Witten:1982df} of $\mathcal{T}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$ is given by
\begin{align}\label{eqn:witten}
\mathcal{I}(x;\mathcal{M}, \mathcal{K}, g):= \textrm{Tr}_{\mathcal{H} [\mathcal{M}\times \Sigma_g;\mathcal{K}]}\; e^{- \beta \hat{H}}(-1)^{\hat{R}} x^{\hat{T}}.
\end{align}
Here the trace is taken over an infinite dimensional vector space
\begin{align*}
\mathcal{H} [\mathcal{M}\times \Sigma_g;\mathcal{K}]\;: \; \textrm{Hilbert-space of $\mathcal{T}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$}
\end{align*}
and the Noether charge operators $\hat{H}, \hat{R}$, and $\hat{T}$ associated to the symmetries in \eqref{symmetries} act on $\mathcal{H} [\mathcal{M}\times \Sigma_g;\mathcal{K}]$ as mutually commuting self-adjoint operators.
\begin{align*}
\begin{split}
&\bullet \hat{H} \;: \; \textrm{Energy}
\\
&\bullet \hat{R}\; :\; \textrm{$SO(2)=U(1)$ R-symmetry charge}
\\
&\bullet \hat{T} \;:\; \textrm{A cartan of $su(2)$ flavor symmetry}
\end{split}
\end{align*}
We choose a normalization of Cartan generators $R$ and $T$ of $U(1)$ and $su(2)$ respectively as follows.
\begin{align*}
\begin{split}
&i R = i \; {\rm Id}_{1\times 1} \in {\mathfrak u}(1)
\\
& i T = i \begin{pmatrix}
1 & 0 \\
0 & -1
\end{pmatrix} \in \mathfrak{su}(2)
\end{split}
\end{align*}
Note that the operators $\hat{R}$ and $\hat{T}$ act linearly and their eigenvalues are
%
\begin{align}
\begin{split}
&(\textrm{Eigenvalues of $\hat{H}$}) \in \mathbb{R}_{\geq 0}, \quad (\textrm{Eigenvalues of $\hat{R}$}) \in \mathbb{Z},\\
& (\textrm{Eigenvalues of $\hat{T}$}) \in \begin{cases} \mathbb{Z} & \textrm{if $\gamma \in \textrm{Ker}\: i_* $}\quad \\ 2 \mathbb{Z} & \textrm{otherwise.}
\end{cases}
\end{split} \label{Spectrum of Noether charges}
\end{align}
On the Hilbert-space $\mathcal{H}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$, there are also Grassmannian odd supercharge operators, $\hat{Q}$ and its adjoint $\hat{Q}^\dagger$, satisfying the (anti)-commutation relations:
\begin{align*}
\begin{split}
&\hat{Q} \hat{Q}^\dagger + \hat{Q}^\dagger \hat{Q} = 2\hat{H}\;, \quad [\hat{Q},\hat{T}] = [\hat{Q}^\dagger, \hat{T}] = \hat{Q}^2 = 0\;,
\\
& [\hat{R},\hat{Q}] = \hat{Q}\;, \quad [\hat{R}, \hat{Q}^\dagger] = - \hat{Q}^\dagger\;.
\end{split}
\end{align*}
As the usual, the index \eqref{eqn:witten} does not depend on $\beta$, since there is no contribution other than supersymmetric ground states $(\hat{H}=0)$.
More precisely, this is due to the cancellation between two states
\begin{align*}
|E, R,T \rangle \quad \textrm{and } \quad \sqrt{\frac{2}{E}}\hat{Q}|E,R,T\rangle
\end{align*}
for $E\neq 0$ where $|E,R,T\rangle$ is a normalized simultaneous eigenstate of $(\hat{H},\hat{R},\hat{T})$ with eigenvalues $(E,R,T)$ respectively. The second state is also a normalized simultaneous eigenstate with eigenvalues $(E,R+1,T)$.
Therefore, the index \eqref{eqn:witten} counts the ground states of $\mathcal{T}[\mathcal{M}\times \Sigma_g;\mathcal{K}]$ with signs, i.e.
\begin{align}
\mathcal{I}(x;\mathcal{M}, \mathcal{K} , g):= \textrm{Tr}_{\mathcal{H}^{E=0} [\mathcal{M}\times \Sigma_g;\mathcal{K}]}\; (-1)^{\hat{R}} x^{\hat{T}}
\label{eqn:ground}
\end{align}
where
\begin{align*}
\mathcal{H}^{E=0} [\mathcal{M}\times \Sigma_g;\mathcal{K}] := \left\{|\psi \rangle \in \mathcal{H} [\mathcal{M}\times \Sigma_g;\mathcal{K}] \;: \; \hat{H}|\psi \rangle =0 \right\}.
\end{align*}
Note that the condition $\hat{H}|\psi \rangle =0$ is equivalent to $\hat{Q}|\psi \rangle=0$.
Under the assumption that every irreducible component of $X^\mathrm{irr}(M)$ is of dimension 1, we expect that the number of ground states (= \textrm{dim} $\mathcal{H}^{E=0} [\mathcal{M}\times \Sigma_g;\mathcal{K}]$) is finite. It follows that (using the fact \eqref{Spectrum of Noether charges})
\begin{align}
\mathcal{I}(x;\mathcal{M}, \mathcal{K},g) \in \begin{cases} \mathbb{Z}[x+x^{-1}] &\textrm{if $\gamma \in \textrm{Ker}\;i_* $} \\ \mathbb{Z}[x^2+x^{-2}] & \textrm{otherwise}.
\end{cases} \label{3d Index as Laurent series}
\end{align}
Combining the above with the 3D-3D relation \eqref{3d-3d relation}, we obtain a non-trivial
prediction: (for simplicity we substitute $x+x^{-1}$ by $z$)
\begin{conjecture} Let $M$ be a compact 3-manifold with a torus boundary. Suppose that every irreducible component of $X^\mathrm{irr}(M)$ is of dimension 1. Then for any slope $\gamma \in H_1(\partial M; \mathbb{Z})$ we have
\[
\sum_{[\rho] \in \mathrm{tr}_\gamma^{-1}(z)} \mkern-10mu\left( d_\gamma \cdot \textrm{Tor}(M;\mathfrak{g}_\rho, \gamma) \right)^{g-1} \in \begin{cases} \mathbb{Z}[z] & \textrm{if $\gamma \in\textrm{Ker}\;i_* $} \\ \mathbb{Z}[z^2] & \textrm{otherwise}
\end{cases}\]
for generic $z \in \mathbb{C}$. See the notation \eqref{eqn:notation}.
\end{conjecture}
\begin{remark}
The geometrical choice of $(\mathcal{M},\mathcal{K})$ determines and is determined by the other pair $(M, \gamma)$ via Dehn filling and drilling out.
In Sections \ref{sec:def} and \ref{sec:proof},
we use the latter pair in order to follow mathematical conventions.
\end{remark}
\subsection{Conjecture for $g=0$ : no SUSY ground state } \label{sec : no ground state}
We claim that if the knot complement $\mathcal{M}\backslash\mathcal{K}$ (or equivalently the interior of $M$) admits a hyperbolic structure, then
\begin{align} \label{eqn:empty}
\begin{split}
&\mathcal{H}^{E=0}[\mathcal{M}\times \Sigma_g;\mathcal{K}] =(\textrm{empty}) \quad \textrm{for } g=0.
\end{split}
\end{align}
As a consequence, we obtain Conjecture \ref{conj:intro} from the relations \eqref{3d-3d relation} and \eqref{eqn:ground}.
A physical argument for the claim \eqref{eqn:empty} is given as follows. We may consider general $N \geq 2$.
The Hilbert-space describes supersymmetric ground states of the 1D quantum mechanical system obtained from a twisted compactification of 6D $A_{N-1}$ theory on $\mathcal{M}\times \Sigma_g$ with a maximal regular defect along $\mathcal{K} \subset \mathcal{M}$. The 3D-3D relation was derived by studying the twisted index on $\Sigma_g$ of the 3D theory $\mathcal{T}_{N}[\mathcal{M},\mathcal{K}]$. Alternatively, the ptn can be considered as the twisted index on $M$ of the 4D theory $\mathcal{T}_N[\Sigma_g]$ \cite{Gaiotto:2008cd}. The 4D theory is defined as the low energy effective theory of the twisted compactification of 6D $A_{N-1}$ theory on $\Sigma_g$. The classical vacuum moduli space of the 4D theory is given as the solutions of generalized $\mathrm{SL}_N(\mathbb{C})$ Hitchin's equations coupled to a real adjoint scalar $\sigma$ on $\Sigma_g$ \cite{Yonekura:2013mya}. When $g=0$, there is only the trivial flat connection on $\Sigma_g = S^2$ and the Hitchin moduli space is a point. On the point, there is $(N-1)$-dimensional vacuum moduli (say reducible branch) space parameterized by the real scalar field $\sigma$. Physically, the moduli describes the dynamics of totally separated $N$ M5-branes. As argued in \cite{Gang:2018wek}, the reducible branch is separated from the other branch (say irreducible branch) of vacuum moduli space in the compactification of the 6D theory on the hyperbolic 3-manifold $M$. The 3D-3D relation \eqref{3d-3d relation} was derived for the 3D theory sitting on the irreducible branch. After siting on the irreducible branch, the reducible vacua disappear and there is no remaining classical vacua for $g=0$. This implies the claim \eqref{eqn:empty}.
\section{The Reidemeister torsion for a knot exterior} \label{sec:def}
\def\mathbb{Z}{\mathbb{Z}}
\def\mathbb{F}{\mathbb{F}}
\def\mathbb{R}{\mathbb{R}}
\def\mathbb{C}{\mathbb{C}}
We devote this section to briefly recall basic definitions and known results for the sign-refined Reidemeister torsion. We mainly follow \cite{porti1997torsion, yamaguchi2008relationship,turaev2012torsions}.
\subsection{Definitions}
\subsubsection{Torsion of a chain complex} \label{sec:chaincplx}
Let $\mathbb{F}$ be a field.
For an $\mathbb{F}$-vector space with two (ordered) bases $c$ and $c'$ we denote by $[c'/c] \in \mathbb{F}^\times$ the determinant of the transition matrix taking $c$ to $c'$.
Let $(0 \rightarrow C_n \rightarrow \cdots \rightarrow C_0\rightarrow 0)$ be a chain complex of $\mathbb{F}$-vector spaces with boundary maps $\partial_i : C_i \rightarrow C_{i-1}$.
Let $c_i$ be a basis of $C_i$ and $h_i$ be a basis of the $i$-th homology $H_i(C_\ast)$.
We choose $b_i \subset C_i$ such that $\partial_i b_i$ is a basis of $\mathrm{Im} \mkern1mu \partial_{i} \subset C_{i-1}$ and choose a representative $\widetilde{h}_i$ of $h_i$ in $\mathrm{Ker}\mkern1mu \partial_i \subset C_i$.
It follows from the short exact sequences
\begin{equation*}
0\rightarrow \mathrm{Ker}\mkern1mu \partial_i \rightarrow C_i \overset{\partial_i}{\rightarrow} \mathrm{Im}\mkern1mu \partial_i \rightarrow 0 \quad \textrm{and}\quad
0 \rightarrow \mathrm{Im}\mkern1mu \partial_{i+1} \rightarrow \mathrm{Ker}\mkern1mu \partial_i\rightarrow H_i(C_\ast)\rightarrow 0
\end{equation*}
that the collection $\partial_{i+1} b_{i+1} \sqcup \widetilde{h}_i \sqcup b_i$ is a basis of $C_i$.
The \emph{sign-refined Reidemeister torsion} (\cite{turaev1986reidemeister}) is defined by
\begin{equation}\label{eqn:torsion}
\mathrm{Tor}(C_\ast,c_\ast, h_\ast) = (-1)^{|C_\ast|}\prod_{i=0}^n \left[ (\partial_{i+1} b_{i+1} \sqcup \widetilde{h_i} \sqcup b_i)/c_i \right]^{(-1)^i} \in \mathbb{F}^\times
\end{equation}
where the symbol $|C_\ast|= \sum_{i=0}^n \big(\sum_{j=0}^i \dim C_j\big) \cdot \big(\sum_{j=0}^i \dim H_j(C_\ast)\big) $.
It is known (see e.g. \cite{turaev1986reidemeister,turaev2012torsions}) that $\mathrm{Tor}(C_\ast,c_\ast,h_\ast)$ does not depend on the auxiliaries choices of $b_\ast$ and $\widetilde{h}_\ast$.
\subsubsection{Torsion of a CW-complex} \label{sec:cw}
Let $W$ be a finite CW-complex with a \emph{homology orientation} $\mathfrak{o}$, an orientation of the $\mathbb{R}$-vector space $H_\ast(W;\mathbb{R})$.
We enumerate the cells of $W$ by $c_i$ ($1 \leq i \leq m)$
and fix an orientation of each $c_i$ so that
the cells $c_\ast$ form a basis of $C_\ast(W;\mathbb{R})$.
We choose a basis $h_\ast$ of $H_\ast(W;\mathbb{R})$ respecting the orientation $\mathfrak{o}$ and let
\begin{equation}\label{eqn:tau}
\tau=\mathrm{sgn} \left( \mathrm{Tor}(C_\ast(W;\mathbb{R}),c_\ast,h_\ast)\right) \in \{\pm1\}.
\end{equation}
The sign $\tau$ clearly depends on the orientation $\mathfrak{o}$, but not on a precise choice of the basis $h_\ast$.
Let $G=\mathrm{SL}_2(\mathbb{C})$ and $\mathfrak{g}$ be its Lie algebra.
A representation $\rho:\pi_1(W)\rightarrow G$ endows $\mathfrak{g}$ with
a right $\mathbb{Z}[\pi_1 (W)]$-module structure: $v \cdot g = \mathrm{Ad}_{\rho(g^{-1})} (v)$ for $v \in \mathfrak{g}$ and $g \in \pi_1(W)$.
We consider the chain complex
\[ C_*(W;\mathfrak{g}_\rho) = \mathfrak{g} \otimes_{\mathbb{Z}[\pi_1 W]} C_*(\widetilde{W};\mathbb{Z})\]
where $\widetilde{W}$ is the universal cover of $W$ with the induced CW-structure, and denote by $H_\ast(W;\mathfrak{g}_\rho)$ its homology.
For each cell $c_i$ of $W$ we choose a lift $\widetilde{c}_i$ to $\widetilde{W}$ arbitrarily so that the set
\begin{equation*}
\mathcal{B} =\{ h \otimes \widetilde{c}_1, e \otimes \widetilde{c}_1, f \otimes \widetilde{c}_1, \cdots, \ h \otimes \widetilde{c}_m, e \otimes \widetilde{c}_m, f \otimes \widetilde{c}_m \}
\end{equation*}
is a basis of $C_\ast (W;\mathfrak{g}_\rho)$.
Here $\{h,e,f\}$ is the usual basis of $\mathfrak{g}$ (see Remark \ref{rmk:basis_ind}). Letting $\boldsymbol{h}_\ast$ be a basis of $H_\ast(W;\mathfrak{g}_\rho)$, we define
\begin{equation*}
\mathrm{Tor}(W;\mathfrak{g}_\rho, \boldsymbol{h}_\ast, \mathfrak{o}) :=\tau \cdot \mathrm{Tor}(C_\ast(W;\mathfrak{g}_\rho), \mathcal{B}, \boldsymbol{h}_\ast) \in \mathbb{C}^\times.
\end{equation*}
The torsion $\mathrm{Tor}(W;\mathfrak{g}_\rho, \boldsymbol{h}_\ast, \mathfrak{o})$ does not depend on the choice of the order and orientations of the cells $c_\ast$ (as they appear both in $\tau$ and $\mathcal{B}$) and the lifts $\widetilde{c}_i$ (as we are working on $\mathrm{SL}$).
It is also known that $\mathrm{Tor}(W;\mathfrak{g}_\rho,\boldsymbol{h}_\ast,\mathfrak{o})$ is invariant under conjugating $\rho$ and subdividing $W$; the sign $(-1)^{|C_\ast|}$ in the equation \eqref{eqn:torsion} is needed to ensure such invariance.
We refer to \cite{turaev2001introduction} for details.
\begin{remark} \label{rmk:basis_ind} It is known that if the Euler characteristic of $W$ is zero, the torsion
$\mathrm{Tor}(W;\mathfrak{g}_\rho,\boldsymbol{h}_\ast,\mathfrak{o})$ does not depend on the choice of the basis of $\mathfrak{g}$. We hereafter only consider knot exterior in $S^3$, so the basis of $\mathfrak{g}$ would not be essential.
\end{remark}
\subsubsection{Torsion of a knot exterior} \label{sec:knotexterior}
Let $K$ be an oriented hyperbolic knot in $S^3$ and $M$ be the knot exterior $S^3 \backslash \nu(K)$ with a fixed triangulation. We orient a meridian $\mu$ of $K$ by the right-hand screw rule and let a homology orientation $\mathfrak{o}$ of $M$ be the one induced from the basis
$\{[\mathrm{pt}], [\mu]\} \subset H_\ast(M;\mathbb{R})=H_0(M;\mathbb{R}) \oplus H_1(M;\mathbb{R})$. Here $\mathrm{pt}$ denotes a point in $M$.
A \emph{slope} $\gamma$ is an oriented simple closed curve in $\partial M$ with non-trivial class in $H_1(\partial M;\mathbb{Z})$. An irreducible representation $\rho :\pi_1(M)\rightarrow G$ is called \emph{$\gamma$-regular} (\cite{porti1997torsion,yamaguchi2008relationship}) if:
\begin{itemize}
\item $\dim H_1(M;\mathfrak{g}_\rho)=1$;
\item the inclusion $\gamma \hookrightarrow M$ induces an epimorphism $H_1(\gamma;\mathfrak{g}_\rho) \rightarrow H_1(M;\mathfrak{g}_\rho)$;
\item if $\mathrm{tr} \left(\rho(\pi_1(\partial M)) \right) \subset \{ \pm 2\}$, then $\rho(\gamma) \neq \pm\mathrm{Id}$.
\end{itemize}
The orientation of $\gamma$ is not necessary here but is required in the construction below. Note that the notion of $\gamma$-regularity is invariant under conjugation, so the notion of an irreducible $\gamma$-regular character is well-defined.
For an irreducible $\gamma$-regular representation $\rho$ it is known that $\dim H_i(M;\mathfrak{g}_\rho)=1$ for $i= 1,2$, and $\dim H_i(M;\mathfrak{g}_\rho)=0$ for $i\neq 1,2$.
We fix a basis $\boldsymbol{h}_\ast=\{\boldsymbol{h}_1,\boldsymbol{h}_2\}$ of $H_\ast(M;\mathfrak{g}_\rho)$
by $\boldsymbol{h}_1 = v \otimes \widetilde{\gamma}$ and $\boldsymbol{h}_2 = v \otimes \widetilde{\partial M}$
where $v\in\mathfrak{g}$ is a non-zero vector such that $\mathrm{Ad}_{\rho(g)}(v)=v$ for all $g \in \pi_1(\partial M)$.
Note that (i) such a vector $v$ is unique up to scaling, since $\rho(\pi_1(\partial M)) \not \subset \{\pm \mathrm{Id}\}$;
(ii) the tilde symbols $\widetilde{\gamma}$ and $\widetilde{\partial M}$ are used for lifts of $\gamma$ and $\partial M$ to the universal cover;
(iii) the boundary $\partial M$ is oriented by the convention ``the inward normal vector in the last position''.
With above choices, we define
\[ \mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma) := \mathrm{Tor}\left(M;\mathfrak{g}_\rho,\boldsymbol{h}_\ast, \mathfrak{o}\right) \in \mathbb{C}^\times.\]
The torsion $\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)$ does not depend on the choice of a triangulation of $M$ (as the torsion is invariant under subdivision) and a scaling of the vector $v$ (as it appears in both $\boldsymbol{h}_1$ and $\boldsymbol{h}_2$).
We refer to \cite[\S 3]{porti1997torsion} and \cite{yamaguchi2008relationship} for details.
\subsubsection{Changing a slope} \label{sec:changing}
Suppose that an irreducible representation $\rho :\pi_1(M)\rightarrow G$ is both $\gamma$- and $\delta$-regular for slopes $\gamma$ and $\delta$.
It is known (see \cite[\S 3]{porti1997torsion}) that its character $[\rho]$ is contained in an 1-dimensional irreducible component, say $X$, of the algebraic set $X^\mathrm{irr}(M)=\{\pi_1(M)\rightarrow G : \mathrm{irreducible}\}/_{\mathrm{Conj}}$.
Let $u_\gamma$ and $u_\delta : X \rightarrow \mathbb{C}$ be functions satisfying up to conjugation
\begin{equation} \label{eqn:fcnu}
\rho'(\gamma) = \begin{pmatrix} e^{u_\gamma([\rho'])} & \ast \\ 0 & e^{-u_\gamma([\rho'])} \end{pmatrix}
\quad \mathrm{and} \quad
\rho'(\delta) = \begin{pmatrix} e^{u_\delta([\rho'])} & \ast \\ 0 & e^{-u_\delta([\rho'])} \end{pmatrix}
\end{equation}
for all characters $[\rho']\in X$.
Under the assumption that both $u_\gamma$ and $u_\delta$ are holomorphic and non-singular at $[\rho]$, which is often the case, ``slope changing rule'' follows from \cite[Proposition 4.7]{porti1997torsion}:
\begin{equation}\label{eqn:basischange}
\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma) = \dfrac{\partial u_\gamma}{\partial u_\delta} \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\delta)
\end{equation}
where the derivative is evaluated at $[\rho]$.
\subsection{Formulas for computing the torsion}
The torsion of a knot exterior is often computed by using the torsion polynomial (see e.g. \cite{yamaguchi2008relationship,dubois2009non,tran2014twisted}). It is computationally convenient as the torsion polynomial is obtained from a chain complex with trivial homology.
\subsubsection{Torsion polynomial}
Let $K\subset S^3$ be an oriented hyperbolic knot and $M=S^3 \backslash \nu(K)$.
Let $\rho:\pi_1(M)\rightarrow G$ be an irreducible representation and $\alpha : \pi_1(M)\rightarrow \mathbb{Z}$ be the abelianization map, counting the signed linking number with $K$.
We endow $\mathfrak{g}(t)=\mathbb{C}(t)\otimes \mathfrak{g}$ with a right $\mathbb{Z}[\pi_1(M)]$-module structure:
\[(p \otimes v)\cdot g = t^{\alpha(g)}p\otimes \mathrm{Ad}_{\rho(g^{-1})}(v)\]for $p \otimes v \in \mathfrak{g}(t)$ and $g \in \pi_1(M)$. Here $\mathbb{C}(t)$ denotes the field of rational functions in one variable $t$.
Let $\lambda$ be the canonical longitude of $K$ with the orientation same as $K$, and assume that $\rho$ is $\lambda$-regular. It is known (see \cite[Proposition 3.1.1]{yamaguchi2008relationship}) that the chain complex
\[C_\ast(M;\mathfrak{g}(t)_\rho)=\mathfrak{g}(t) \otimes_{\mathbb{Z}[\pi_1 M]} C_\ast(\widetilde{M};\mathbb{Z})\]
of $\mathbb{C}(t)$-vector spaces is acyclic, i.e., its holomogy is trivial.
The \emph{torsion polynomial} is given by
\[\mathrm{Tor}(M;\mathfrak{g}(t)_\rho) := \tau \cdot \mathrm{Tor}(C_\ast(M;\mathfrak{g}(t)_\rho), 1 \otimes \mathcal{B}, \emptyset) \in \mathbb{C}(t)^\times.\]
We refer to Section \ref{sec:cw} for definitions of the sign $\tau$ and basis $\mathcal{B}$.
Note that the torsion polynomial is defined up to $t^n (n\in\mathbb{Z})$ due to the $\pi_1(M)$-action on $\mathbb{C}(t)$.
In \cite{yamaguchi2008relationship} Yamaguchi proved that the torsion polynomial determines $\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)$ as follows.
\begin{theorem}[\cite{yamaguchi2008relationship}] \label{thm:yamaguchi} The torsion polynomial $\mathrm{Tor}(M;\mathfrak{g}(t)_\rho)$ has a simple zero at $t=1$ and
\begin{equation} \label{eqn:yamaguchi} \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)=-\left. \dfrac{d}{dt}\right|_{t=1} \mathrm{Tor}(M;\mathfrak{g}(t)_\rho).
\end{equation}
Note that the indeterminacy of $\mathrm{Tor}(M;\mathfrak{g}(t)_\rho)$ does not affect the equation \eqref{eqn:yamaguchi}.
\end{theorem}
\subsubsection{Fox calculus} In \cite{kitano1996twisted} Kitano proved that the torsion polynomial agrees with the twisted Alexander invariant of $K$ with respect to $\mathrm{Ad}_\rho$. In particular, it can be computed in terms of the Fox differential calculus.
We first choose a finite group presentation of $\pi_1(M)$ of deficiency 1 (for instance, the Wirtinger presentation)
\[\pi_1(M) = \langle g_1,\cdots,g_n | r_1,\cdots,r_{n-1} \rangle.\]
Let $W$ be the 2-dimensional CW-complex corresponding to the presentation.
Recall that $W$ has one 0-cell, $n$ 1-cells, and $(n-1)$ 2-cells.
Identifying the chain complex $C_\ast(W;\mathfrak{g}(t)_\rho)$ with
\[
0 \rightarrow \mathfrak{g}(t)^{n-1} \overset{\partial_2}{\longrightarrow} \mathfrak{g}(t)^{n} \overset{\partial_1}{\longrightarrow} \mathfrak{g}(t) \rightarrow 0,
\]
the boundary maps $\partial_1$ and $\partial_2$ are given by (see e.g. \cite{kitano1996twisted}, \cite[\S 3.4]{yamaguchi2008relationship})
\begin{align*}
\partial_1 &= \left( \Phi(g_1 -1), \cdots ,\Phi(g_n-1)\right) \in M_{1,n}(M_{3,3}(\mathbb{C}(t))) \\
\partial_2 &= \left( \Phi\left(\dfrac{ \partial r_i}{\partial g_j}\right)\right)_{1 \leq i \leq n-1,\ 1\leq j \leq n} \in M_{n,n-1}(M_{3,3}(\mathbb{C}(t))).
\end{align*}
Here $\partial/\partial g$ denotes the Fox calculus, $M_{i,j}$ denotes the set of $i\times j$ matrices, and the map $\Phi : \mathbb{Z}[\pi_1(M)] \rightarrow M_{3,3}(\mathbb{C}(t))$ is given by \[\Phi \left(\sum_{i} n_i g_i\right)=\sum_{i} n_i t^{\alpha(g_i)} \mathrm{Ad}_{\rho(g_i)} \in M_{3,3}(\mathbb{C}(t))\]
for $n_i \in\mathbb{Z}$ and $g_i \in \pi_1(M)$.
From the fact that $W$ is simple homotopic to the knot exterior $M$, we have
\begin{equation} \label{eqn:foxtor}
\mathrm{Tor}(M;\mathfrak{g}(t)_\rho) = \epsilon \cdot \dfrac{\det \left( \partial_{2;\widehat{j}} \right)}{\det \left(\Phi(g_{j}-1)\right)}
\end{equation}
for some $1 \leq j \leq n$ and $\epsilon \in \{ \pm1\}$. Here $\partial_{2;\widehat{j}}$ is the square matrix obtained from $\partial_2$ by deleting the $j$-th row, and the index $j$ can be chosen freely among those satisfying $\det (\Phi(g_j-1)) \neq 0$. The existence of such an index $j$ follows from \cite[Lemma 2]{wada1994twisted}.
\begin{remark} \label{rmk:sign_ind}
The sign $\epsilon$ in the equation \eqref{eqn:foxtor} only depends on the choice of $j$ and whether the simple homotopy $W\rightarrow M$ preserves the homology orientation. See \cite[Remark 2.4]{turaev2001introduction} and \cite[Theorem 18.3]{turaev2001introduction}.
\end{remark}
\section{Supporting evidences for Conjecture \ref{conj:intro}} \label{sec:proof}
In this section, we present a rigorous proof of Conjecture \ref{conj:intro} for the $4_1$ knot:
\begin{theorem} \label{thm:41} Let $M$ be the knot exterior of the $4_1$ knot. Let $\gamma\in H^1(\partial M; \mathbb{Z})$ be any slope and $\mathrm{tr}_\gamma : X^{\mathrm{irr}}(M)\rightarrow \mathbb{C}$ be its trace function.
Then we have
\[ \sum_{[\rho] \in \mathrm{tr}_\gamma^{-1}(z)} \dfrac{1}{\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)}=0\]
for generic $z \in \mathbb{C}$.
\end{theorem}
The proof relies on some facts related to global residue theorem. They are briefly reviewed in Section \ref{sec:grt}. We refer to \cite{khovanskii1977newton, tsikh1992multidimensional} for detail .
We also present numerical verification of the conjecture for several knots in Section \ref{sec:num_comp}.
\subsection{A residue theorem for Laurent polynomials} \label{sec:grt}
Let $f=(f_1,\cdots,f_n)$ be a system of $n$ Laurent polynomials in $n$ variables $z=(z_1,\cdots,z_n)$.
We denote by $Z_f$ the zero set $\{a \in (\mathbb{C}^\times)^n : f_1(a) = \cdots= f_n(a)=0\}$, and say that $a \in Z_f$ is \emph{simple} if the Jacobian
\[\mathrm{Jac}_f = \det \left(\dfrac{\partial (f_1,\cdots,f_n)}{\partial (z_1,\cdots,z_n)}\right)\]
is non-zero at the point $a$.
With the usual notation $z^\alpha=z_1^{\alpha_1}\cdots z_n^{\alpha_n}$ for $\alpha=(\alpha_1,\cdots,\alpha_n) \in \mathbb{Z}^n$, we write $f_i=\sum_{\alpha} c_{i}^{\alpha}z^\alpha$ with the coefficients $c_i^\alpha \in \mathbb{C}$.
The \emph{Newton polyhedron} $\Delta(f_i)$ of $f_i$ is the convex hull in $\mathbb{R}^n$ of the set $\{ \alpha \in \mathbb{Z}^n : c_i^\alpha \neq 0\}$.
For a non-zero vector $\beta \in \mathbb{R}^n$ we denote by $\Delta^\beta(f_i)$ the face of $\Delta(f_i)$ on which the function $\langle \cdot, \beta \rangle : \mathbb{R}^n \rightarrow \mathbb{R}$ attains a minimum. Here $\langle \cdot ,\cdot\rangle$ denotes the usual inner product on $\mathbb{R}^n$.
The system $f=(f_1,\cdots,f_n)$ is said to be \emph{non-degenerate} (\cite{khovanskii1977newton}) if the system \[f^\beta=(f_1^\beta, \cdots, f_n^\beta), \quad f_i^\beta=\sum_{\alpha \in \Delta^\beta(f_i)} c_i^\alpha z^\alpha,\]
has only simple zeros in $(\mathbb{C}^\times)^n$ for any non-zero $\beta \in \mathbb{R}^n$.
In \cite{khovanskii1977newton} Khovanskii gave a generalization of the global residue theorem as follows (see also \cite[\S 7]{tsikh1992multidimensional}).
\begin{theorem}[\cite{khovanskii1977newton}] \label{thm:ejt} Let $f=(f_1,\cdots,f_n)$ be a non-degenerate system of Laurent polynomials. Suppose that all of the zeros $ a =(a_1,\cdots, a_n)\in Z_f$ are simple. Then for any Laurent polynomial $h$ whose Newton polyhedron $\Delta(h)$ lies strictly inside the (Minkowski) sum $\Delta(f_1) +\cdots+\Delta(f_n)$, we have
\[\sum_{a\in Z_f} \dfrac{h(a)}{a_1\cdots a_n \cdot \mathrm{Jac}_f(a)}=0 .\]
\end{theorem}
\subsection{Proof of Theorem \ref{thm:41}} \label{sec:41}
We orient $K=4_1$ as in Figure \ref{fig:diagram41} and fix a presentation of the fundamental group of the knot exterior $M$ by
\[\pi_1(M) = \langle g_1, g_2 | g_1^{-1} g_2 g_1 g_2^{-1} g_1 - g_2 g_1^{-1} g_2 g_1 g_2^{-1} \rangle.\]
An irreducible representation $\rho : \pi_1(M) \rightarrow G$ is given by up to conjugation
\begin{equation} \label{eqn:repn_cor}
g_1 \mapsto \begin{pmatrix} m & 1 \\ 0 & m^{-1} \end{pmatrix}, \quad g_2 \mapsto \begin{pmatrix} m & 0 \\ y & m^{-1} \end{pmatrix}
\end{equation}
for a pair $(y,m)\in (\mathbb{C}^\times)^2$ satisfying
\begin{equation} \label{eqn:Riley}
f(y,m)=(y-1)(m^2+m^{-2}) + y^2-3y+3 =0.
\end{equation}
Also, zeros $(y_1,m_1)$ and $(y_2,m_2) \in (\mathbb{C}^\times)^2$ of $f$ correspond to the same irreducible representation up to conjugation if and only if $y_1=y_2$ and $m_1 = m_2^{\pm1}$. Thus the set $X^\mathrm{irr}(M)$ coincides with the zero set of $f$ with quotient given by $(y,m)\sim(y,m^{-1})$. We refer to \cite{riley1984nonabelian} for details.
\begin{figure}[!h]
\centering
\input{figure_eight_diagram.pdf_tex}
\caption{The $4_1$ knot.}
\label{fig:diagram41}
\end{figure}
We take a meridian $\mu$ of $K$ as the generator $g_1$. The canonical longitude $\lambda$ is given by $g_2^{-1} g_1 g_3^{-1}g_4$ from the diagram where $g_3=g_2 g_1 g_2^{-1}$ and $g_4=g_3^{-1}g_2 g_3$ (see Figure \ref{fig:diagram41}). It follows that
\[\rho(\lambda)=\rho(g_2^{-1} g_1 g_3^{-1}g_4)
=\begin{pmatrix}
l & \ast \\ 0 & l^{-1}
\end{pmatrix}\]
where $l = - m^{-2}(y-3)(y-1)^2-m^{-4}(y^2-3y+1)$.
Taking the resultant of $l$ with $f(y,m)=0$ to remove the variable $y$, we obtain the $\mathrm{SL}_2(\mathbb{C})$ A-Polynomial
\[A(m,l)=l+l^{-1} +(-m^{-4}+m^{-2}+2+m^2-m^4)=0.\]
One can check that for any slope $\gamma = \mu^p \lambda^p$ ($p,q$ : coprime integers) and generic $z \in \mathbb{C}$, the set $\mathrm{tr}_\gamma^{-1}(z)$ is identified with
\begin{align*}
\mathrm{tr}_\gamma^{-1}(z)=\left\{(m,l) \in (\mathbb{C}^\times)^2: A(m,l)=0, \ B(m,l):=m^p l^q-x=0\right\}
\end{align*}
where $x \in \mathbb{C}^\times$ is a solution to $x+x^{-1}=z$.
\begin{remark}
The function $u_\gamma\mkern 2mu (=p \log m +q \log l)$ given as in the equation \eqref{eqn:fcnu} is non-constant on $X^\mathrm{irr}(M)$.
It implies that
the set of irreducible non-$\gamma$-regular characters in $X^\mathrm{irr}(M)$ is discrete. See \cite[Proposition 3.26]{porti1997torsion} and \cite[Remark 9]{dubois2009non}.
In particular, we may assume that $\mathrm{tr}_\gamma^{-1}(z)$ consists of irreducible $\gamma$-regular characters for generic $z \in \mathbb{C}$.
\end{remark}
Let $r$ be the relator of the group presentation. One can compute that
\[ \dfrac{\partial r}{\partial g_1} = -g_1^{-1} + g_1^{-1} g_2 + g_1 ^{-1} g_2 g_1 g_2^{-1}+ g_2 g_1^{-1} - g_2 g_1^{-1} g_2.\]
It follows from the equations \eqref{eqn:foxtor} and \eqref{eqn:yamaguchi} that
\begin{align*}
\mathrm{Tor}(M;\mathfrak{g}(t)_\rho) &= \epsilon \cdot \dfrac{\det \left(\Phi(\partial r / \partial g_1)\right)}{\det \left(\Phi(g_1-1)\right)} \\
&=\epsilon \cdot \dfrac{(t-1)(2m^2 -(t-1+t^{-1})+2m^{-2})}{t^2}
\end{align*}
and
\begin{equation} \label{eqn:tor_lambda}
\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda) = -\left. \dfrac{d}{dt}\right|_{t=1} \mathrm{Tor}(M;\mathfrak{g}(t)_\rho)= -\epsilon \cdot(2m^2-1+2m^{-2})
\end{equation}
for some $\epsilon \in \{ \pm1\}$.
Also, from the equation \eqref{eqn:basischange} we have
\begin{align*}
\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma) &=\dfrac{\partial(p \log m + q \log l)}{\partial \log l}\cdot\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)\\
&= \left(p \dfrac{l}{m} \dfrac{\partial m}{\partial l} +q \right) \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda) \\
&= \left(-p \dfrac{l}{m} \dfrac{\partial A/\partial l}{\partial A/\partial m} +q \right) \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda) \\
&= \dfrac{l}{x} \cdot \dfrac{\det\left( \dfrac{\partial (A,B)}{\partial (m,l)}\right)}{\partial A/\partial m} \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)
\end{align*}
The last equation follows from $\partial B/\partial m = p m^{p-1} l^q = px /m$ and $\partial B/ \partial l = qx/l$.
Plugging the equation \eqref{eqn:tor_lambda} and $\partial A/\partial m=-2m^{-1}(2m^2-1+2m^2)(m^2-m^{-2})$, we obtain
\begin{equation}\label{eqn:tor_gamma}
\dfrac{1}{\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)}= 2\epsilon x \cdot \dfrac{m^2-m^{-2}}{ml \cdot\det\left( \dfrac{\partial (A,B)}{\partial (m,l)}\right)}.
\end{equation}
\begin{remark} It is interesting that the derivative $\partial A/\partial m$ has $\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)$ as a factor. This fact is also pointed out in \cite[Remark 4.5]{dimofte2013quantum}.
\end{remark}
We now claim that the system $(A,B)$ and the Laurent polynomial $h:=m^2-m^{-2}$ satisfy the condition of Theorem \ref{thm:ejt}.
\begin{itemize}
\itemsep 0.5em
\item for any non-zero $\beta \in \mathbb{R}^2$ the Laurent polynomial $A^\beta$ is either $l^{\pm1}$, $m^{\pm4}$, or $l^\pm - m^{\pm4}$, and the Laurent polynomial $B^\beta$ is either $x$, $m^p l^q$, or $m^p l^q-x$. Any pair of the above has only simple zeros in $(\mathbb{C}^\times)^2$, so the system $(A,B)$ is non-degenerate.
\item A straightforward computation shows that $\mathrm{Jac}_{(A,B)}=0$ if and only if $p(l-l^{-1})=2q(2m^2-1+2m^{-2})(m^2-m^{-2})$. Therefore, the system $(A,B)$ only has simple zeros for generic $x\in\mathbb{C}^\times$.
\item the Newton polygon $\Delta(A)$ strictly contains $\Delta(h)$, and $\Delta(B)$ contains the origin. Thus, $\Delta(h)$ strictly lies inside in $\Delta(A)+\Delta(B)$.
\end{itemize}
Recall Remark \ref{rmk:sign_ind} that the sign $\epsilon$ in the equation \eqref{eqn:tor_gamma} does not depend on the choice of pair $(m,l)$. Therefore, Theorem \ref{thm:41} is obtained from Theorem \ref{thm:ejt}.
\subsection{Numerical verification} \label{sec:num_comp}
We here present numerical verification of Conjecture \ref{conj:intro} for $K=5_2$ and $7_4$.
\subsubsection{The $5_2$ knot}
The fundamental group of the knot exterior of $K=5_2$ is generated by two elements and
$X^{\mathrm{irr}}(M)$ is given by the zero set of
\[f(y,m)=(y-2)(y-1)(m^2+m^{-2})+y^3-5y^2+8y-3\]
in $(\mathbb{C}^\times)^2$ with the quotient given by $(y,m) \sim (y,m^{-1})$.
Similar computations as in Section \ref{sec:41} give that for a slope $\gamma = \mu^p \lambda^q$ and generic $x \in \mathbb{C}$, we have
\[\mathrm{tr}_\gamma^{-1}(x) = \left\{(y,m,l) \in (\mathbb{C}^\times)^3 : f(y,m)=0,\ g(y,m,l)=0,\ h(m,l)=0\right\}\]
where
\begin{equation*}
\left\{
\begin{array}{l}
g(y,m,l)=l +(y-1) -m^{2}-m^{4}( y^3-5y^2+9y-4) + 2m^{6}(y-1)(y-2) \\[7pt]
h(m,l)=m^pl^q-x
\end{array}.
\right.
\end{equation*} Here $x\in \mathbb{C}^\times$ is a solution to $x+x^{-1}= z$.
Also, the torsion $\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)$ for the canonical longitude $\lambda$ is given by
\[\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda) = \epsilon \cdot \dfrac{5y^3-21y^2+28y-14}{y-1}\]
for some $\epsilon \in \{\pm1\}$.
\begin{lemma} \label{lem:comp1}
For $(y,m,l) \in \mathrm{tr}_\gamma^{-1}(x)$, we have
\[ \dfrac{\partial (p \log m + q \log l)}{ \partial \log l}=p\dfrac{l}{m}\dfrac{\partial m}{\partial l}+q=
\dfrac{l}{x} \cdot \dfrac{\mathrm{det} \left( \dfrac{ \partial (f,g,h)}{\partial (y,m,l) } \right)}{\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right)}. \]
\end{lemma}
\begin{proof} A straightforward computation gives
\begin{align*}
\mathrm{det} \left( \dfrac{ \partial (f,g,h)}{\partial (y,m,l) } \right) &=\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right) \cdot \dfrac{qx}{l} - \dfrac{\partial f}{\partial y} \dfrac{\partial g}{\partial l} \cdot \dfrac{px}{m}\\
&=\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right) \cdot \left ( \dfrac{qx}{l}+ \dfrac{pz}{m} \dfrac{\partial m}{\partial l} \right)\\
&=\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right) \cdot \dfrac{x}{l} \left ( q+ \dfrac{l}{m} \dfrac{\partial m}{\partial l} \right).
\end{align*}
The second equality follows from $df=dg=0$.
\end{proof}
One can compute that \begin{align*}
\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right) &= \dfrac{5y^3-21y^2+28y-14}{y-1} \\
& \quad \quad \cdot \dfrac{2((m^2+y-2)(y^4-6y^3+13y^2-12y+3)-(y-2)^2)}{m^9(y-1)(y-2)^3}
\end{align*}
and
\begin{align*}
\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)&=\dfrac{\partial (p \log m + q \log l)}{ \partial \log l} \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda) \\
&=\dfrac{l}{x} \cdot \dfrac{\mathrm{det} \left( \dfrac{ \partial (f,g,h)}{\partial (y,m,l) } \right)}{\mathrm{det} \left( \dfrac{ \partial (f,g) }{\partial (y,m)} \right)} \cdot \mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)\\
&=\dfrac{\epsilon l}{2x} \cdot \dfrac{\mathrm{det} \left( \dfrac{ \partial (f,g,h)}{\partial (y,m,l) } \right) \cdot m^9 (y-1)(y-2)^3 }{(m^2+y-2)(y^4-6y^3+13y^2-12y+3)-(y-2)^2}. \\
\end{align*}
\begin{remark} It is worth noting that the Jacobian of $(f,g)$
again contains the torsion $\mathrm{Tor}(M;\mathfrak{g}_\rho,\lambda)$ as a factor.
\end{remark}
To verify Conjecture \ref{conj:intro}, we let $F = m^2f$, $G=(y-1)(y-2)^3 m^6 g$, $H=h$, and compute the sum of
\[ \dfrac{1}{\mathrm{Tor}(M;\mathfrak{g}_\rho,\gamma)} = 2\epsilon x \cdot \dfrac{y(m^2+y-2)(y^4-6y^3+13y^2-12y+3)-y(y-2)^2}{yml \cdot \mathrm{det} \left( \dfrac{ \partial (F,G,H)}{\partial (y,m,l) } \right)} \]
over all $(y,m,l) \in \mathrm{tr}_\gamma^{-1}(z)$, which is the zero set of $(F,G,H)$.
For instance, the set $\mathrm{tr}_\gamma^{-1}(z)$ for $(p,q)=(3,1)$ and $z=\frac{3}{2}+\frac{i}{2}$ consists of 23 points with torsions
\begin{equation*}
\begin{array}{rrr}
-5.1707095 + 6.056876 i, & -5.1403791 - 5.271889 i, & -4.9799403 + 5.257641 i, \\
-4.7335145 - 7.299169 i, & -4.6988457 - 5.941816 i, & -4.3082655 + 7.042614 i, \\
-3.8808087 - 6.974908 i, & -3.3630233 + 7.605688 i, & -2.6624296 + 3.284613 i, \\
0.2005695 - 4.913042 i, & 9.8858003 + 2.112603 i, & 14.549795 + 0.213397 i,\\
14.568149 + 0.187863 i, & 15.922137 - 0.358869 i, & 16.535205 - 0.634458 i, \\
17.512936 + 0.306584 i , & 18.497289 - 1.694233 i, & 18.514426 - 0.117280 i,\\
19.936167 + 0.800241 i, & 23.334158 - 0.639555 i, & 25.010603 + 1.138408 i, \\
25.406178 + 0.241449 i, & 28.564506 - 0.402759 i&
\end{array}
\end{equation*} whose inverse sum is zero numerically.
\subsubsection{The $7_4$ knot} \label{sec:knot74}
It is known that for $K=7_4$ the algebraic set $X^\mathrm{irr}(M)$ has two irreducible components. Precisely, $X^\mathrm{irr}(M)$ is given by the zero set of $f_1(y,m) \cdot f_2(y,m)$ in $(\mathbb{C}^\times)^2$ where
\begin{align*}
f_1(y,m)&=(y-2)^2(m^2+m^{-2})+y^3-6y^2+12y-7 \\
f_2(y,m)&=y(y-1)(y-2)(m^2+m^{-2})+y^4-5y^3+8y^2-4y+1
\end{align*}
with the quotient given by $(y,m)\sim(y,m^{-1})$.
We first consider irreducible representations coming from the zero set of $f_1$.
In this case, similar computations as in the previous section give
\begin{align*}
g_1(y,m,l) &=l-\frac{1}{m^{16}} \Big( m^{16} (5 - 2 y)+ m^{14} (5 - 3 y)+ m^{12} (-9 + 2 y)+2 m^{10} (-17 + 7 y) \\
& \hspace{5.5em} + 8 m^8 (-3 + 2 y) + m^6 (86 - 26 y) + m^4 (219 - 98 y) \\
& \hspace{5.5em} + m^2 (-463 + 99 y + 707 y^2 + 1104 y^3 - 9638 y^4 + 34306 y^5 \\
&\hspace{8.2em} - 66187 y^6 + 75756 y^7 - 55526 y^8 + 27256 y^9 - 9116 y^{10} \\
&\hspace{8.2em} +2060 y^{11} - 302 y^{12} + 26 y^{13} - y^{14}) \\
& \hspace{5.5em}
- (2 - y)^2 (-61 - 115 y - 66 y^2 + 321 y^3 -
1552 y^4 + 3558 y^5\\
&\hspace{8.2em} - 3829 y^6 + 2282 y^7 - 809 y^8 +
171 y^9 - 20 y^{10} + y^{11})
\Big)
\end{align*}
whose resultant with $f_1$ gives one component $A_1$ of the A-polynomial
\begin{align*}
A_1(m,l)=& m^{14} +
l (1 - 2 m^2 + 3 m^4 + 2 m^6 - 7 m^8 + 2 m^{10} + 6 m^{12} - 2 m^{14}) \\&+
l^2 (-2 + 6 m^2 + 2 m^4 - 7 m^6 + 2 m^8 + 3 m^{10} - 2 m^{12} + m^{14}) + l^3.
\end{align*}
Also, the torsion $\mathrm{Tor}(M,\mathfrak{g}_\rho,\lambda)$ for the canonical longitude $\lambda$ is given by
\begin{align*}
&\frac{1}{m^{24} \left(m^2-1\right)^2}
\Big(m^{28} (12-8 y)+4 m^{26} (y-2)+m^{24} (24 y-29)+m^{22} (34-30 y)\\
&+m^{20} (20 y-31)+m^{18} (23-4 y)+m^{16} (91-43 y)+m^{14} (6-16 y)+m^{12} (99 y-287)\\
&+m^{10} (250 y-502)+m^8 (455-61 y)+m^6 (2665-1076 y)+m^4 (2105-1354 y)\\
&+m^2 (-7 y^{17}+212 y^{16}-2931 y^{15}+24429 y^{14}-136467 y^{13}+536999 y^{12}-1521221 y^{11}\\
&\hspace{3em}+3111157 y^{10}-4527550 y^9+4521505 y^8-2878308 y^7+978784 y^6-53392 y^5\\
&\hspace{3em}-77400 y^4+16421 y^3+6770 y^2+12018 y-9213)\\
&-(y-2)^2 (7 y^{14}-170 y^{13}+1834 y^{12}-11520 y^{11}+46330 y^{10}-123292 y^9+215917 y^8\\
&\hspace{4em}-237784 y^7+147025 y^6-37064 y^5-3126 y^4+4792 y^3-155 y^2-1322 y-1591)\Big)
\end{align*}
Similarly, from the other component $f_2$, we have
\begin{align*}
g_2(y,m,l)=l&-
\frac{1}{m^{16}}\Big( m^{24} (-(y-2)) y+m^{22} \left(y^2-3 y+1\right)-m^{18} (y-2) y+m^{16} \left(2 y^2-6 y+3\right)\\
&+m^{14} \left(3 y^2-7 y+2\right)+3 m^{12} (y-1)^2-3 m^{10} (y-3)+m^8 \left(y^2-16 y+27\right)\\
&+m^6 \left(21 y^2-77 y+64\right)+m^4 \left(71 y^2-206 y+129\right)\\
&-m^2 (y^{13}-23 y^{12}+232 y^{11}-1350 y^{10}+5022 y^9-12552 y^8+21757 y^7-27137 y^6\\
&\hspace{3em}+25878 y^5-20076 y^4+12429 y^3-5513 y^2+1582 y-260)\\
&-y (y^{11}-21 y^{10}+191 y^9-987 y^8+3201 y^7-6828 y^6+9895 y^5-10224 y^4\\
&\hspace{3em}+8164 y^3-5252 y^2+2380 y-520)\Big)
\end{align*} with the other component $A_2$ of the $A$-polynomial
\[A_2(m,l)=m^8 + l (-1 + m^2 + 2 m^4 + m^6 - m^8)+l^2 \]
and the torsion $\mathrm{Tor}(M,\mathfrak{g}_\rho,\lambda)$ given by
\begin{align*}
&\frac{1}{m^{24} \left(m^2-1\right)^2}\Big(4 m^{34} (y-2) y+m^{32} \left(-19 y^2+42 y-4\right)+15 m^{30} \left(4 y^2-9 y+1\right)\\&
+m^{28} \left(-116 y^2+277 y-49\right)+m^{26} \left(138 y^2-343 y+59\right)+m^{24} \left(-113 y^2+286 y-49\right)\\&
+m^{22} \left(48 y^2-111 y+11\right)+m^{20} \left(-34 y^2+65 y-17\right)+2 m^{18} \left(2 y^2+5 y-20\right)\\&
+m^{16} \left(-12 y^2+85 y-113\right)-4 m^{14} \left(23 y^2-80 y+66\right)+m^{12} \left(-267 y^2+805 y-554\right)\\&
+m^{10} \left(-550 y^2+1633 y-1185\right)+m^8 \left(-1005 y^2+3242 y-2758\right)\\&
+m^6 \left(-2152 y^2+7471 y-6747\right)+m^4 \left(-5688 y^2+19271 y-16363\right)\\&
+m^2 (-4 y^{18}+117 y^{17}-1568 y^{16}+12790 y^{15}-71174 y^{14}+287221 y^{13}-872939 y^{12}\\&
\hspace{3em}+2051452 y^{11}-3807909 y^{10}+5701024 y^9-7049263 y^8+7379282 y^7-6653194 y^6\\&
\hspace{3em}+5176328 y^5-3442171 y^4+1908473 y^3-815463 y^2+230625 y-38691)\\&
+(-4 y^{16}+109 y^{15}-1354 y^{14}+10183 y^{13}-51960 y^{12}+191168 y^{11}-526550 y^{10}\\&
\hspace{3em}+1114704 y^9-1854044 y^8+2479718 y^7-2740522 y^6+2567766 y^5-2060060 y^4\\&
\hspace{3em}+1399565 y^3-784584 y^2+333247 y-77382) y\Big)
\end{align*}
We consider the case of $(p,q)=(1,1)$ and $x = 2 + 3 i$.
The system of $f_1(y,m)$, $g_1(y,m,l),$ and $m^pl^q-x$ has 17 zeros while the other system of $f_2(y,m)$, $g_2(y,m,l)$, and $m^pl^q-x$ has 20 zeros. Summing the inverse of the corresponding torsions, we numerically obtain $0.10320 + 0.00274 i$ from the first system and $-0.10320 - 0.00274 i$ from the second one. This verifies Conjecture \ref{conj:intro} numerically.
\begin{remark}\label{rmk:allcomponent}
The above computation shows that the sum in Conjecture \ref{conj:intro} should be considered over all components of $X^\mathrm{irr}(M)$, not only the component containing the geometric representation.
\end{remark}
\section{Further directions} \label{sec:further}
In this paper, we study the case when there is a regular defect of maximal type along a knot $\mathcal{K}$. Our study can be extended to the case of a closed 3-manifold $\mathcal{M}$ without any defect. In the case, the corresponding SQFT $\mathcal{T}_{N}[\mathcal{M}]$ does not have any flavor symmetry and its twisted partition depends only on the discrete choice $g$ (genus of Riemann surface) and $N$. Let
\begin{align*}
\begin{split}
\mathcal{I}_N (\mathcal{M},g) &:= (\textrm{Twisted index of $\mathcal{T}_N[\mathcal{M}]$ theory on $\Sigma_g \times S^1$})
\\
&= \textrm{Tr}_{\mathcal{H}^{E=0}_N(\mathcal{M}\times \Sigma_g)} (-1)^{\hat{R}}
\end{split}
\end{align*}
The corresponding 3D-3D relation was derived in \cite{Gang:2019uay,Benini:2019dyp}
\begin{align}
\mathcal{I}_N (\mathcal{M},g) = \left( \dfrac{|\textrm{Hom}\left(\pi_1 (\mathcal{M}), \mathbb{Z}_N \right)| } {N }\right)^{g-1} \mkern-20mu \sum_{[\rho] \in \frac{X^{\rm irr}_N(\mathcal{M})}{\textrm{Hom}\left(\pi_1 (\mathcal{M}), \mathbb{Z}_N \right)}} \mkern-20mu \left(\mathrm{Tor}(\mathcal{M},\mathfrak{g}_\rho) \right)^{g-1} \label{twistecd index for closed 3-manifold}
\end{align}
Here $X^{\rm irr}_N(\mathcal{M})$ denotes the set of irreducible $\mathrm{SL}_N(\mathbb{C})$ characters of $\pi_1(\mathcal{M})$. In the summation, two irreducible characters are considered to be equivalent if they are related to each other by tensoring a $\mathbb{Z}_N$ (center subgroup of $\mathrm{SL}_N(\mathbb{C})$) character. From the argument in Section \ref{sec : no ground state}, we expect that $\textrm{dim} \mathcal{H}^{E=0}_N(\mathcal{M}\times \Sigma_{g=0})=0$ and thus
\begin{align*}
\mathcal{I}_N(\mathcal{M},g=0) =0.
\end{align*}
When $g=0$, there is another interesting property on $\Sigma_{g=0}$ which is absent for higher $g$. As $\Sigma_{g=0} = S^2$ admits $SO(3)$ isometry, we can introduce an Omega-deformation parameter, say $q$, on $\mathbb{B}= \Sigma_{g=0}\times S^1$ using the isometry. We can consider the refined twisted index for $g=0$ \cite{Benini:2015noa}
\begin{align*}
\mathcal{I}_N (\mathcal{M}, g=0 ;q) = \textrm{Tr}_{\mathcal{H}^{E=0}_N(\mathcal{M}\times \Sigma_{g=0})} (-1)^{\hat{R}}q^{j_3}
\end{align*}
where $j_3$ is the Cartan of the $SO(3)$ isometry group on $\Sigma_{g=0}$. The 3D-3D relation for the refined index is \cite{Benini:2019dyp}
\begin{align*}
\begin{split}
&\mathcal{I}_N (\mathcal{M},g=0;q)
\\
&= \left( \dfrac{|\textrm{Hom}\left(\pi_1 (\mathcal{M}), \mathbb{Z}_N \right)| } {N }\right)^{-1} \mkern -30mu \sum_{[\rho] \in \frac{X^{\rm irr}_N(\mathcal{M})}{\textrm{Hom}\left(\pi_1 (\mathcal{M}), \mathbb{Z}_N \right)}} \mkern -23mu \exp \left( \sum_{n=0} 2 S_{2n+1}(\mathcal{M}, \mathfrak{g}_\rho) \hbar^{2n} \right)\bigg{|}_{\hbar := \log q}\;.
\end{split}
\end{align*}
Here $S_{k}(\mathcal{M}, \mathfrak{g}_\rho)$ is the $k$-loop perturbative invariant of $\mathrm{SL}_N(\mathbb{C})$ Chern-Simons theory on $\mathcal{M}$ around the flat-connection corresponding to the character $[\rho]$. In the unrefined case ($q=1$ or equivalently $\hbar =0$), only the 1-loop part $S_1 (\mathcal{M}, \mathfrak{g}_\rho) = -\frac{1}2 \log \textrm{Tor}(\mathcal{M}, \mathfrak{g}_\rho)$ contributes to the index. Since $\textrm{dim} \mathcal{H}^{E=0}_N(\mathcal{M}\times \Sigma_{g=0})=0$, we have the following generalized vanishing conjecture for hyperbolic $\mathcal{M}$:
\begin{align*}
\sum_{[\rho] \in \frac{X^{\rm irr}_N(\mathcal{M})}{\textrm{Hom}\left(\pi_1 (\mathcal{M}), \mathbb{Z}_N \right)}} \mkern -20mu \exp \left( \sum_{n=0} 2 S_{2n+1}(\mathcal{M}, \mathfrak{g}_\rho) \hbar^{2n} \right) =0.
\end{align*}
Expanding the LHS as formal power series in $\hbar$, the conjecture says that the series vanishes at every order in $\hbar$. Unfortunately, the perturbative invariants $S_{k}(\mathcal{M}, \mathfrak{g}_{\rho})$ for $k>1$ still lack a mathematical rigorous definition although there are some attempts \cite{Bae:2016jpi,Gang:2017cwq} using state-integral models.
Another interesting future direction is studying large $N$ limit of the twisted index in \eqref{twistecd index for closed 3-manifold}. The limit is interesting since the twisted index at large $N$ computes the supersymmetric microstates of supersymmetric black holes in anti-de-Sitter space-time.
Refer to \cite{Gang:2018hjd,Gang:2019uay,Bae:2019poj} for studies in this direction. In \cite{Gang:2018hjd,Gang:2019uay}, it was assumed that the irreducible character $[\rho] = \rho_N \cdot [\rho_{\rm hyp}]$ and its complex conjugation give the most exponentially dominant contributions to the above summation in the large $N$ limit. Here $[\rho_{\rm hyp}]$ is the $\mathrm{SL}_2(\mathbb{C})$ character for the complete hyperbolic structure and $\rho_N :\mathrm{SL}_2(\mathbb{C})\rightarrow \mathrm{SL}_N(\mathbb{C})$ is the principal embedding. The asymptotic limit of the adjoint torsion twisted by $\rho_N \cdot [\rho_{\rm hyp}]$ can be studied using the mathematical results in \cite{park2016reidemeister}. With the assumption and the mathematical result, the following large $N$ behavior is expected (for every hyperbolic $\mathcal{M}$ and $g>1$)
\begin{align*}
\lim_{N\rightarrow \infty } \frac{1}{N^3}\log |\mathcal{I}_N (\mathcal{M}, g )| = (g-1) \cdot \frac{\textrm{vol}(\mathcal{M})} {3\pi}.
\end{align*}
The result is compatible with the Bekenstein-Hawking entropy of the corresponding AdS black holes \cite{Gang:2018hjd,Gang:2019uay,Bae:2019poj,Benini:2019dyp}. It would be interesting to prove or disprove the assumption used in the large $N$ analysis.
\section*{Acknowledgments}
We are grateful to Teruaki Kitano, Francesco Benini, and Kazuya Yonekura for their helpful discussions. The researches of DG were supported in part by the National Research Foundation of Korea (NRF) grant 2019R1A2C2004880. The work of SK was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1003383).
\bibliographystyle{abbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,529 |
\section{Introduction}\label{intro}
High-mass gamma-ray binaries are among the most luminous high-energy sources in the Galaxy. These systems host a massive star and a compact object, and their radiation extends from radio waves to high-energy (HE; 0.1--100~GeV) and very-high-energy (VHE; $>100$~GeV) gamma rays, with the nonthermal emission being dominated by energies $>1$~MeV \citep[see, e.g.,][for a review]{Dubus2013,Paredes2013,Paredes2019}. Observations of these systems also show gamma-ray orbital modulation, indicating that the related emitting region cannot be located too far from the binary \citep[e.g., for LS 5039 and LS~I~+61~303;][respectively]{Aharonian2006,Albert2006}. Approximately ten systems pertaining to this class have been detected so far, but the power origin has not been firmly identified yet in most of them, with the important exceptions of PSR B1259-63 \citep{Johnston1992}, PSR J2032+4127 \citep{Lyne2015}, and probably LS~I~+61~303 \citep{Weng2022}, in which the recent detection of radio pulsations strongly points at the presence of a pulsar (see also \citealt{Yoneda2020} and \citealt{Volkov2021} for the contested detection of X-ray pulses from LS~5039). The uncertainty in the power origin in gamma-ray binaries has fueled a debate between two competing scenarios: the accretion-powered and the pulsar-wind-powered scenarios (e.g., \citealt{Maraschi1981,Paredes2000,Martocchia2005,Dubus2006,Romero2007,Bosch-Ramon2009,Massi2017}; see however, e.g., \citealt{Papitto2012} for a pulsar model with regime transitions).
In the accretion-powered scenario, particle acceleration is typically thought to occur in the relativistic jets of a microquasar, which are fed by the accretion of stellar material onto the compact object. Jet propagation through the stellar wind medium on binary scales has been numerically studied in the relativistic \citep[e.g.,][]{Perucho2008,Perucho2010,Charlet2022} and nonrelativistic regimes \citep[e.g.,][]{Yoon2015,Yoon2016}. Leptonic and hadronic models have been adopted for the broadband emission from the relativistic jets of high-mass microquasars \citep[e.g.,][]{Romero2008}. The effects of orbital motion on the jet kinematics and the broadband nonthermal emission have also been considered in several (semi-)analytical and numerical works \citep[see, e.g.,][for some recent studies including orbital effects]{Bosch-Ramon2016,Molina2018,Molina2019,Barkov2021b}.
In the standard pulsar-powered scenario, a significant fraction of the pulsar spin-down power is dissipated at the interaction of a relativistic wind from the pulsar and the stellar wind \citep[e.g.,][]{Maraschi1981,Tavani1997}. At the shock front, particles can be efficiently accelerated and emit X-rays via synchrotron and gamma rays via inverse Compton (IC) scattering on the stellar photon field \citep[e.g.,][]{Tavani1994,Kirk1999,Dubus2006,Khangulyan2007}; although, hadronic scenarios have also been proposed \citep[e.g.,][]{Neronov2007}. Relativistic hydrodynamic simulations show that fast reacceleration of the shocked pulsar flow should occur beyond the sonic point \citep[at the outskirts of the binary; see, e.g.,][]{Bogovalov2008}, which would influence the shocked pulsar wind emission by affecting adiabatic losses, the magnetic field, and Doppler boosting \citep[e.g.,][]{Kong2012,Khangulyan2014b,Dubus2015,Molina2020}. The magnetization (and anisotropy) of the pulsar wind can have only a moderate effect on the dynamics and overall structure of the flow \citep{Bogovalov2012}, unless the pulsar wind magnetic field becomes dynamically dominant \citep{Bogovalov2019}. Instability growth and turbulence can impact the structure of the shocks and produce shocked two-wind mixing, and couple with orbit-related Coriolis forces that turn the shocked flows into an unstable spiral structure \citep[e.g.,][]{Bosch-Ramon2011,Bosch-Ramon2012,Lamberts2012,Lamberts2013,Bosch-Ramon2015}. Detailed modeling of the shocked-flow dynamics and radiation in the case of LS 5039, including orbital motion, has been performed by \cite{Molina2020} (semi-analytically), taking the emission at the Coriolis turnover into account, and by \cite{Huber2020a,Huber2020b} (numerically), accounting for the complex fluid dynamics through coupled relativistic hydrodynamics (RHD)--nonthermal particle calculations. The role of eccentricity in the large-scale evolution of the shocked flows has also been explored, using RHD simulation data to estimate the associated nonthermal emission \citep[e.g.,][]{Barkov2018,Barkov2021a}.
Smooth flows are generally considered in the pulsar-wind-powered scenario, but small-scale inhomogeneities can inherently arise from radiation instabilities in the acceleration phase of hot-star winds \citep[e.g.,][]{Lucy1970,Runacres2002,Puls2008}. Large-scale structures may also be present and possibly originate from the circumstellar disks of fast-rotating stars \citep[see, e.g.,][in the context of gamma-ray binaries]{Okazaki2011,Chernyakova2014}, corotating interaction regions between different velocity streams, or magnetically confined regions at the wind base \citep[e.g.,][]{Cranmer1996,Lobel2008}. In nonaccreting systems, the radiative consequences of the presence of clumps were analytically explored, for instance, by \cite{Zdziarski2010} in the context of LS~I~+61~303. A general study, also of analytical nature, of the dynamical and radiative effects of a clumpy stellar wind interacting with a pulsar wind was carried out by \citet{Bosch-Ramon2013a}. Later on, axisymmetric RHD simulations by \cite{Paredes-Fortuny2015} and nonthermal emission computations based on RHD simulation data by \cite{delaCita2017a} were performed to numerically study the effects of the arrival of a single clump in the two-wind interaction region. These works concluded that, depending on its size, a clump can noticeably perturb the interaction region and largely affect the output of the associated nonthermal radiation. For instance, in the mentioned works and in \cite{Chernyakova2014}, it was argued that the collision of a large clump of stellar material with the pulsar wind offers a plausible explanation for the observed gamma-ray flares (e.g., PSR~B1259-63) and quick X-ray variability (e.g., LS~5039, LS~I~+61~303) in high-mass gamma-ray binaries.
Indeed, short-term variability of high-energy emission seems to be a common feature in gamma-ray binaries \citep[e.g.,][]{Bosch-Ramon2005,Smith2009,Takahashi2009,Rea2011,An2015,Tam2018}.
Studies of the clumpy-wind presence have also been performed, for instance, in the context of massive-star binaries \citep{Pittard2007}, accreting X-ray sources \citep[e.g.,][]{Oskinova2012}, and microquasars \citep[e.g.,][]{Araudo2009,Owocki2009,Perucho2012,delaCita2017b,Lopez2022}.
\begin{figure}
\centering
\centering\resizebox{1\hsize}{!}{\includegraphics{f1.pdf}}
\caption{Three-dimensional schematic (top) and two-dimensional cut (bottom) of the physical scenario comprising a massive star with a clumpy stellar wind and a pulsar. The dashed lines in the bottom panel show the trajectories of clumps that have crossed the smooth-wind contact discontinuity.}
\label{sketch}
\end{figure}
As explained above, so far only simple analytical treatments or costly numerical calculations have been used to model the emitting flow under a clumpy stellar wind in the pulsar-powered scenario. Here, we present a novel approach to modeling the effects of a clumpy stellar wind on the emitting region in that scenario; this approach aims at balancing realistic modeling and computational efficiency. The unshocked and shocked clump propagation and dynamics are modeled adopting semi-analytical Monte Carlo and hydrodynamic calculations, allowing for a general exploration of the effects of multiple clumps on the geometry evolution of the shocked two-wind region. The associated nonthermal emission and its variability induced by the clumps are analytically modeled treating the emitting particles either in an adiabatic or a radiative regime, with a particle power-law energy distribution. Gamma-ray absorption is taken into account. This method is very fast to implement but still provides the most relevant information; although, formally it can only be applied consistently to the region where the shocked pulsar wind is subsonic. The paper is structured as follows: the physical scenario and its modeling are explained in Sect.~\ref{numa}; the results are presented in Sect.~\ref{res}; and a summary and discussion are provided in Sect.~\ref{disc}.
\section{Physical system and modeling}\label{numa}
\subsection{Physical system}
Although this study applies to high-mass gamma-ray binaries hosting young pulsars in general, we consider a system with orbit and distance similar to those of LS~5039 \citep[e.g.,][]{Casares2005}, a powerful and well-studied source. The adopted components for the binary system are a main-sequence O-type star with luminosity $L_{*}=10^{39}$~erg~s$^{-1}$ and temperature $T=4 \times 10^{4}$~K, and a nonaccreting pulsar with spin-down power set to $P_{\rm sd}=3\times 10^{36}$~erg~s$^{-1}$. The orbital parameters are the system eccentricity $e=0.35$, orbital period $P=3.91$~d, and semimajor axis $\alpha =2.1 \times 10^{12}$~cm. The orientation of the system with respect to the observer is such that superior and inferior conjunction occur at orbital phases $\phi=0.058$ and $\phi=0.716$, respectively. We assume
a distance of $d_{\rm{obs}}=3$~kpc and
an inclination with respect to the line of sight of $i=60^{\circ}$ (favored in LS~5039 if it harbors a neutron star; \citealt{Casares2005}). The actual role of $i$ is however secondary for us, as it mostly affects the orbital spectral energy distributions (SEDs) and light curves; for suborbital variability, $i$ mainly influences the normalization of the curves.
The massive star powers a supersonic wind that is driven by line radiation pressure. This wind is assumed to be inhomogeneous, with most of its mass carried by clumps. We adopt a wind mass-loss rate of $\dot{M}=10^{-7}\,$M$_{\odot}$ yr$^{-1}$ and a wind velocity approximated to a constant $u_{\rm w}=2\times 10^{8}$~cm~s$^{-1}$.
The pulsar drives an ultrarelativistic wind that is assumed to be cold, isotropic, and weakly magnetized \citep[see however][and references therein]{Bogovalov2012,Derishev2012,Bogovalov2019,Bosch-Ramon2021}. Typical bulk Lorentz factors are $\Gamma_{\rm{w}}=10^{5}$ \citep{Khangulyan2012,Aharonian2012}, but our results will not strongly depend on this value as the shocked clumps do not accelerate up to relativistic velocities; $\Gamma_{\rm{w}}$ can also affect the energy range of the flow emitting particles \citep[e.g.,][]{Kennel84}, but this has little effect on our conclusions and is neglected. The system parameters are summarized in Table~\ref{table:param}, and a schematic of the system is shown in Fig.~\ref{sketch}.
\subsection{Modeling}
\subsubsection{Smooth-wind contact discontinuity}
The stellar and pulsar winds collide to form a double-bow-shock structure made of shocked wind material. The shape of the contact discontinuity (CD) separating the shocked stellar and pulsar winds can be described, in the smooth-wind case, by a simple approximation of the boundary of equilibrium between the two wind ram pressures \citep{Canto1996}:
\begin{equation}
\label{eq:CD}
\vartheta_{1} =\left[ \frac{15}{2} \left( -1 + \sqrt{1+ \frac{4}{5}\eta (1-\vartheta \rm{cot}\vartheta )} \right ) \right ]^{1/2},
\end{equation}
where $\vartheta$ and $\vartheta_{1}$ correspond to $\theta$ and $\theta_1$ in Fig.~1 from \cite{Canto1996}. Equation~\ref{eq:CD} gives the shape of a one-dimensional CD cut, but the latter axisymmetry in the smooth-wind case allows us to derive the actual geometry of the two-dimensional CD by rotating this one-dimensional cut around the CD symmetry axis.
\begin{table}
\caption{System parameters}
\label{table:param}
\centering
\begin{tabular}{l l l}
\hline\hline
Parameter & & Value \\ \hline
Stellar luminosity & $L_{*}$ & $10^{39}$ erg s$^{-1}$ \\
Star temperature & $T_{*}$ & $4\times 10^{4}$ K \\
Stellar radius & $R_{*}$ & $10.5\,$R$_\odot$ \\
Stellar mass-loss rate & $\dot{M}$ & $10^{-7}\,$M$_{\odot}$~yr$^{-1}$ \\
Stellar wind velocity & $u_{\rm w}$ & $2\times 10^{8}$ cm s$^{-1}$ \\
Pulsar spin-down power & $P_{\rm{sd}}$ & $3\times 10^{36}$ erg s$^{-1}$ \\
Pulsar wind Lorentz factor & $\Gamma_{\rm{w}}$ & $10^{5}$ \\
Periodicity & $P$ & $3.91$ d \\
Eccentricity & $e$ & $0.35$ \\
Semimajor axis & $\alpha$ & $2.1 \times 10^{12}$ cm \\
Inclination & $i$ & $60^{\circ}$ \\
Distance to observer & $d_{\rm{obs}}$ & $3$ kpc \\ \hline
\end{tabular}
\end{table}
The ratio of the pulsar and the stellar wind momentum rates,
\begin{equation}
\eta=(L_{sd}/c)/(\dot{M} u_{\rm w})\,,
\end{equation}
is $\approx 0.08$ for the selected parameters, a usual value in the literature. Such an $\eta$ value means that the stellar wind momentum rate dominates and the CD bends over the pulsar, but most of the luminosity arriving at the CD still comes from the pulsar wind. The distance of the stagnation point from the pulsar is $R_0=d\eta^{1/2}/(1+\eta^{1/2})$, where $d$ is the orbital separation distance. The calculations are done in the rotating frame associated with the pulsar orbital motion, with $\omega_{\rm orb}$ being the angular velocity of the orbit described above. In this frame, due to the orbit-induced Coriolis force, the CD is slightly tilted with respect to the star--pulsar direction. Here, the tilting of the CD is introduced by rotating the entire structure counter-wise with respect to the orbital motion by an angle
$\sim d\omega_{\rm orb}/u_{\rm w}$.
Given that most of the clumps are expected to get destroyed in the shocked flow \citep{Pittard2007,Bosch-Ramon2013a,Paredes-Fortuny2015}, the actual CD shape is approximated here as a smooth-case CD plus distortions produced by the largest clumps (see below).
We treat the pulsar wind after the termination shock as subsonic because it strongly simplifies the emitting flow hydrodynamics; although, far enough from the shock the flow can become supersonic again. The region we consider, of size $\lesssim d$, is somewhat larger than the corresponding region in the smooth-wind case \citep{Bogovalov2008}, but flow irregularities induced by the clump presence may justify this choice. Further away from the star, beyond the sonic point, shocked clumps are expected to have already dissolved in the shocked two-wind structure, while the incoming stellar wind tends to be more homogeneous \citep[see, e.g.,][and references therein]{Rubio2022}. These regions however would present flow reacceleration, local instabilities, wind mixing, and orbital effects through the Coriolis force, all likely to produce additional variability. How these factors interact with a clumpy stellar wind is, however, beyond the scope of this work.
\subsubsection{Clump effects on the CD}\label{dynamics}
To account for the nonlinear nature of the formation of clumps, we characterize their mass distribution through a power-law function: $dN_{\rm c} (M_{\rm c})/dM_{\rm c}\propto M_{\rm c}^{-k}$. The index $k$ and the volume filling factor $f$, which is the average-to-clump density ratio and links the clump size and mass, are treated as free parameters. The initial minimum and maximum clump radii adopted here are $R_{\rm c,min}=0.01\, R_{\rm{*}}$ and $R_{\rm c,max}=0.1\, R_{\rm{*}}$, respectively \citep[see Sect.~3.3 in][for a discussion]{Bosch-Ramon2013a}. Table~\ref{table:clump} summarizes the parameters selected for the four simulated cases with different degrees of clumpiness of the stellar wind. We note that $k=2$ yields a top-heavy clump distribution, whereas $k=3$ yields a bottom-heavy one. The computational method for the clump dynamics is detailed below and presented in Fig.~\ref{flowchart}.
\begin{table}
\caption{Degrees of inhomogeneity of the stellar wind}
\label{table:clump}
\centering
\begin{tabular}{c c c}
\hline\hline
\diagbox{$f$}{$k$} & 2 & 3 \\
\hline
0.01 & \begin{tabular}[c]{@{}c@{}}top heavy\\ high density\end{tabular} & \begin{tabular}[c]{@{}c@{}}bottom heavy\\ high density\end{tabular} \vspace{2pt}\\
0.1 & \begin{tabular}[c]{@{}c@{}}top heavy\\ low density\end{tabular} & \begin{tabular}[c]{@{}c@{}}bottom heavy\\ low density\end{tabular} \\
\hline
\end{tabular}
\end{table}
Clumps, assumed to be spherically symmetric and of constant density, are isotropically launched from the stellar surface with their direction, initial mass and radius, and injection time being determined by a random number generator. The clump injection rate is chosen according to $\dot{M}$. Clumps move away from the stellar surface with a radial clump-velocity component of $u_{\rm w}$. As the calculation is done in the rotating frame, we add an azimuthal clump velocity component of the form $-r\omega_{\rm{orb}}$ (against orbital motion), where $r$ is the distance from the star, to account for the effect of the orbit. Stellar rotation is neglected at this stage. During this time, clumps are assumed to expand such that $f$ is constant, so their radii evolve as: $R_{\rm{c}}(r)=R_{\rm{c}}(R_{*})(r/R_{*})^{2/3}$.
Depending on their orientation, some clumps reach the CD, while others leave the simulation grid without interacting with the shocked two-wind region. Clumps that reach the CD may or may not be able to cross the entire shocked two-wind region, depending on their radii. The critical radius for penetration is \citep{Bosch-Ramon2013a}
\begin{equation}
R_{\rm{c}} \gtrsim f^{1/2} \Delta R,
\label{mrc}
\end{equation}
where $\Delta R$ is the thickness of the shocked two-wind region at each location. Hydrodynamic simulations for a smooth stellar wind and $\eta$ values similar to ours \citep{Bogovalov2008,Bosch-Ramon2015} indicate that $\Delta R$ is $\sim 1/3$ of the distance to the pulsar ($r_{\rm p}$) there (which in turn depends on $\vartheta$, $\vartheta_{1}$, $\eta$, and $d$). Clumps with sizes smaller than that given in Eq.~\ref{mrc} get destroyed and dissolve in the shocked two-wind medium, not affecting the CD geometry substantially. Clumps with larger sizes can penetrate into the (until then) unshocked pulsar wind.
Once the clumps reach the pulsar-side boundary of the shocked two-wind region (i.e., the smooth pulsar wind termination shock), the ram pressure of the pulsar wind starts to impact the clumps. Adapting a semi-analytical hydrodynamical model from \cite{Barkov2012} for the evolution of a clump under the impact of a relativistic radial flow, we solve the equation of motion of the clumps in the pulsar wind zone. The radial component (outward from the pulsar) of the clump Lorentz factor evolves according to:
\begin{equation}
\label{eqn:motion}
\frac{\rm{d}\Gamma_{\rm{c}}}{\rm{d}t}=\left ( \frac{1}{\Gamma_{\rm{c}}^{2}} - \frac{\Gamma_{\rm{c}}^{2}}{\Gamma_{\rm{w}}^{4}} \right ) \frac{\pi R_{\rm{c}}^{2}}{4 M_{\rm{c}}c^{2}}P_{\rm{w}}\,,
\end{equation}
where $P_{\rm{w}}=L_{\rm{sd}}/4\pi c r_{\rm{p}}^{2}$ is the pulsar wind ram pressure, $\Gamma_{\rm{c}}$ is the clump Lorentz factor, and $M_{\rm{c}}$ is the clump mass. The motion of the clumps is initially decelerated toward the pulsar and then, after the pulsar wind ram pressure overpowers that of the stellar wind, accelerated away from the pulsar. Gravitational forces are not dynamically relevant compared with the wind and clump thrusts in the region of interest and can be neglected.
\begin{figure}
\centering
\centering\resizebox{0.9\hsize}{!}{\includegraphics{f2.pdf}}
\caption{Flowchart of the clump dynamics computational process.}
\label{flowchart}
\end{figure}
\begin{figure*}[!ht]
\centering
\centering\resizebox{1\hsize}{!}{\includegraphics{f3.pdf}}
\caption{Two-dimensional snapshots of a CD section at 30 minute intervals showing the derivation of the distorted CD shape. Radial lines (light gray lines) are traced from the pulsar (red point; not in scale) in all directions. If a line intersects the surface of a shocked clump (light blue disks) before reaching the smooth-wind CD (black dashed line), then a distorted-CD point is placed at this location; otherwise, the intersection point of the radial line with the smooth-wind CD is added to the grid. The new grid of points (dark blue points on the blue line) representing the distorted CD is fitted by a spline (blue solid line).}
\label{cdder}
\end{figure*}
Within the shocked two-wind region, clumps cannot expand as they are confined by the thermal pressure of the shocked winds, but in the (previously) unshocked pulsar wind zone quick clump expansion can occur at the shocked-clump sound speed in all directions except against the pulsar wind \citep[see, e.g.,][]{delPalacio2019}. For simplicity, at this stage we assume that the shocked expanding clumps are still uniform and spherical \citep[valid at least for the initial stages of clump expansion;][]{Paredes-Fortuny2015}, with sound speed:
\begin{equation}
c_{\rm{s}}=\sqrt{\hat{\gamma}P_{\rm{w}}/h\rho_{\rm{c}}}\,,
\end{equation}
where $h=1+\hat{\gamma}P_{\rm{w}}/[(\hat{\gamma}-1)\rho_{\rm{c}}c^{2}]$ is the internal specific enthalpy, and $\rho_{\rm{c}}$ is the clump mass density. As clumps do not have time to become relativistic, the adiabatic index $\hat{\gamma}$ can be fixed to $5/3$, and both $\Gamma_{\rm c}$ and $h$ are always barely above 1.
Expansion is switched off if the radius of an expanding clump reaches half the distance to the pulsar when the undisturbed CD is initially crossed (measured from the clump center). This accounts for the fact that the approximation used for the dynamical evolution of the clumps that are shocked by the pulsar wind (computed taking the clump centers as their reference positions) is valid until an expanding clump affects much of the originally unshocked pulsar wind zone (equivalently, the clump size becomes significant with respect to $r_{\rm p}$).
At that stage, the clumps quickly get deflected away from the pulsar (as $\dot{\Gamma_{c}} \propto R_{c}^{2} $) and re-approach the original CD. Once the center of an expanded clump has intercepted that surface again, we assume that it quickly mixes with the shocked two-wind region.
We note that other $R_{\rm c}(r)$ prescriptions may be also possible because the actual clump geometry and evolution are very complex \citep[e.g.,][]{Sundqvist2018,Elmellah2020}. In the case of linear growth, for instance, the relevant quantities at the CD would be within a factor of 2 with respect to those in the adopted case, which does not qualitatively affect the conclusions of this work. The actual geometry of clumps when they fully cross the shocked two-wind region is not important, as their later expansion once shocked by the pulsar wind is fast in all directions except toward the pulsar; thus it can be considered to be roughly isotropic.
Using the above approach, which albeit crude attempts to capture the main clump evolution features found by \cite{Paredes-Fortuny2015}, we can determine the location and size of the penetrating clumps at any given time, which allows us to characterize the corresponding shape and temporal evolution of the entire distorted CD. This is done by tracing radial lines from the pulsar in all directions. If one of these lines intersects the surface of a shocked clump before the line reaches the smooth-wind CD, then a distorted-CD point is placed at the intersection location. If the line reaches the smooth-wind CD, then the CD is not distorted at this location. When this is done for all relevant directions from the pulsar, one obtains a new grid of points representing the distorted CD (see Fig.~\ref{cdder} for a sketch of the computation process). Complementary to Fig.~\ref{sketch}, Fig.~\ref{cdder} illustrates the CD between the pulsar wind and the stellar wind once it is affected by the clump presence. Clump dynamics is assumed to be affected only by the pulsar wind and not by the presence of other clumps, as the latter would be a higher-order effect and is neglected at this stage.
\subsubsection{Emitter characterization}
For simplicity, we take the CD surface as the location of the emission and divide this surface into $N$ surface elements that are treated as point-like emitters. The magnetic field and particle distribution, which are determined by the local conditions on each specific point on the CD, are treated as uniform within each individual emitter. For convenience, we express the magnetic field ($B$) energy density for each emitter as a fraction $\eta_{\rm{B}}$ of the shocked pulsar wind pressure at the CD: $u_{\rm{B}}=\eta_{\rm{B}}P_{\rm W}$. The fraction $\eta_{\rm{B}}$ is fixed throughout this work to 0.1, which corresponds to a magnetic-to-stellar photon energy density ratio of $\sim 10^{-3}$ at the CD close to the pulsar location. This $\eta_{\rm{B}}$ value lies between the weakly and strongly magnetized pulsar wind cases and is consistent with a hydrodynamics approach to characterize the CD. Taking different $\eta_{\rm{B}}$ values would not significantly change our conclusions, as radiation losses would still be dominated by IC and because our main focus is on the relative flux change in specific energy bands (although broadband spectral changes would be expected). Only electron/positron cooling processes are considered at this stage, that is, IC and synchrotron emission, because they are the most efficient radiation processes in compact binaries \citep[see, e.g.,][]{Bosch-Ramon2009}.
The complexity of the emitter structure is very high, as shown by previous works dealing only with some of the aspects of the scenario studied here \citep[see, e.g.,][where RHD simulations were combined with radiative calculations]{Dubus2015,delaCita2017a,Huber2020a}. However, as we are interested in the typical clump-induced emission time variability at certain energies and not in deriving a detailed SED, we simplify the $N$ point-like emitters as being in one of two extreme cooling regimes: radiative or adiabatic.
\begin{figure*}[!ht]
\centering\resizebox{1\hsize}{!}{\includegraphics{f4.pdf}}
\caption{SEDs for the smooth-wind case for the (a) adiabatic (green) and (b) radiative (blue) regimes considering regions up to $1.5d$ from the star at inferior conjunction (INF; $\phi=0.716$) and superior conjunction (SUP; $\phi=0.058$). The synchrotron (colored dashed) and IC (colored solid) components are plotted, and the unabsorbed spectra (colored dotted) are also shown for comparison. As a reference, the shaded areas indicate the synchrotron ($\sim 10^{-2}$~eV) and IC ($\sim 10^{7}$~eV) photon energies corresponding to the (adiabatic-to-radiative) transition particle energy for all individual emitters in the CD.}
\label{SED}
\end{figure*}
In the fully radiative regime, the energy of the emitting particles is radiated away right after reaching the CD. In this case, the particle energy distribution is determined by the acceleration (injection) energy distribution and the relevant radiative losses only (see below). In the adiabatic regime, the total energy density in the post-shock region, $\approx 3\,P_{\rm w}$ times the relevant volume (known only approximately; see below), determines the nonthermal population there. In this case, the particle energy distribution coincides with the acceleration one. Intermediate cases are more realistic, with an expected transition between regimes from the higher particle energies (radiative; more important close to the pulsar) to the lower particle energies (adiabatic; more important far from the pulsar). This transition would manifest itself in features of the IC and synchrotron SED that are hinted when comparing our results in both regimes. Albeit simple, our approach allows for the derivation of general conclusions on the radiation behavior because results for both cooling regimes are provided. The normalizations of the particle distributions in both regimes are just approximately consistent with each other due to our simplified treatment of the hydrodynamics in the adiabatic case.
In our model, relativistic particles are injected following a power-law distribution in energy, $E$, with an exponential cutoff of the form
\begin{equation}
\label{eqn:eldis}
\Delta Q(E) \propto E^{-p} \exp[-E/E_{\rm{max}}],
\end{equation}
where we adopt $p=2$ as a fiducial value.
Significantly softer (harder) injection energy distributions would yield substantially lower (higher) fluxes in the higher-energy regions of the synchrotron and IC components. Further, injection energy distributions more complex than a power-law function, such as an additional narrow component peaking around $\Gamma_{\rm w}$ \citep[see, e.g.,][]{Dubus2015}, would lead to more complex SEDs. Again, given our focus on the clump-induced relative variability within specific energy bands, the adopted injection distribution is enough for our purposes.
The maximum electron energy, characterized by $E_{\rm{max}}$ in Eq.~\ref{eqn:eldis}, is mainly constrained by acceleration, radiative losses, and escape. As particles with multi-TeV energies exist in gamma-ray binaries, we assume a sufficient acceleration rate, with efficiency $\eta_{\rm{acc}}=0.1$ and timescale $t_{\rm{acc}}=E/(\eta_{\rm{acc}}qcB)$, where $q$ is the electron charge. As noted, the relevant cooling channels in the shocked pulsar wind are synchrotron emission and IC. The energy-loss rate for synchrotron ($\dot{E}_{\rm{syn}}$) is derived from \cite{Blumenthal1970} and for IC ($\dot{E}_{\rm{IC}}$) from \cite{Khangulyan2014} assuming an anisotropic distribution of blackbody photons. Equating the acceleration timescale $t_{\rm{acc}}$ with the total radiation cooling timescale, $t_{\rm{cool}}=E/(|\dot{E}_{\rm{syn}}|+|\dot{E}_{\rm{IC}}|)$, yields $E_{\rm{max}}^{\rm{cool}}$. We also consider the Hillas criterion \citep{Hillas1984}, which is similar to the constraint from advection escape and gives an upper limit of the maximum energy: $E_{\rm{max}}^{\rm{Hillas}}=qBr_{\rm{s}}$, where the spatial scale $r_{\rm{s}}$ represents the size of the source, taken here simply as $\sim d$. Then, $E_{\rm{max}}=\rm{min}$ $(E_{\rm{max}}^{\rm{cool}},E_{\rm{max}}^{\rm{Hillas}})$, which is typically $\sim 10$~TeV.
The minimum electron distribution energy has been fixed to $E_{\rm{min}}=100$~MeV. This parameter strongly affects the lowest-energy part of the IC SED and weakly the normalization of the distribution of particles when their total energy is fixed. The former affects the contribution of IC emission below X-rays, whereas the latter effect can be ``absorbed'' by changing the total energy in the power-law distribution of particles. This nonthermal energy, which affects the normalization of the SED linearly, is taken here to be the entirety of the shocked pulsar wind energy, but it can be lower (e.g., most of the energy may be in a narrow particle energy distribution).
In the radiative regime, the electron injection distribution is normalized by the pulsar wind luminosity within the solid angle of each emitter, $\Delta L_{\rm{\Omega}}$:
\begin{equation}
\int_{E_{\rm{min}}}^{E_{\rm{max}}}\Delta Q(E)E\textup{d}E=\Delta L_{\rm{\Omega}}.
\end{equation}
The corresponding cooled particle population can be described as:
\begin{equation}
\Delta N(E)=|\dot{E}|^{-1}\int_E^{E_{\rm max}} \Delta Q(E'){\rm d}E'.
\end{equation}
On the other hand, in the adiabatic regime the electron distribution $\Delta N(E)$ follows the energy dependence in Eq.~\ref{eqn:eldis} and is normalized by the internal energy $\Delta E$ stored within an emitter of approximate volume $\textup{d}V=\textup{d}S_{\textup{sph}} h_{\rm{s}}$, where $\textup{d}S_{\textup{sph}}=r_{\textup{p}}\textup{d}\Omega$, and $h_{\rm{s}}$ is the thickness of the shocked pulsar wind shell. To determine $h_{\rm{s}}$, we take $h_{\rm{s}}=0.2\,r_{\rm p}$ based on relativistic hydrodynamical simulations \citep[e.g.,][]{Bosch-Ramon2015}. Thus, one has:
\begin{equation}
\int_{E_{\rm{min}}}^{E_{\rm{max}}}\Delta N(E)E\textup{d}E= \Delta E.
\end{equation}
Once the particle energy distribution for each point-like emitter has been obtained, the associated synchrotron and IC SEDs are computed using the formulae given in \cite{Blumenthal1970} and \cite{Khangulyan2014}, respectively. Given that the flow is only weakly relativistic in the subsonic region of the shocked pulsar wind and the orientation distribution of the flow velocity is broad in the CD (even broader in the case of a distorted CD; \citealt{Paredes-Fortuny2015}), Doppler boosting has not been taken into account. Gamma-ray absorption in the stellar photon field through pair creation has been calculated using the cross section from \cite{Gould1967}. The radiation of the created pairs may affect the X-ray and gamma-ray emission \citep[e.g.,][]{Bednarek2007,Bosch-Ramon2008}, but we neglect this contribution at this stage.
Due to the clump presence and orbital motion, changes in the interaction angles of IC and gamma-ray absorption and in the CD geometry (also affecting synchrotron radiation through $B$) must be taken into account.
\section{Results}\label{res}
\subsection{Smooth case}\label{sec:smooth}
We have computed the SEDs and light curves in the case of a smooth stellar wind along the entire orbit including regions of the CD up to $1.5d$ from the star; cases with different emitting sizes mostly affect the normalization and are not presented here. Figure~\ref{SED} shows the synchrotron and IC SEDs for the two cooling regimes (adiabatic and radiative) and two orbital phases: inferior ($\phi=0.716$ -INF-) and superior conjunction ($\phi=0.058$ -SUP-).
The results obtained are similar to those found in previous works (see Sect.~\ref{intro}). In the adiabatic regime, synchrotron and IC radiation are rather hard, with the synchrotron component peaking at soft gamma rays, and the IC component softening above $\sim 1-10$~GeV due to the Klein--Nishina (KN) effect in the cross section and peaking around $\sim 10-100$~GeV. In the radiative regime, the synchrotron peak broadens, but the SED is still hard down to $\sim 10$~eV due to IC losses in the KN limit, where it becomes flat due to dominant IC losses in the Thomson regime. The (unabsorbed) IC SED is still moderately hard at $\sim 0.1-100$~GeV due to IC KN losses, softens above that energy due to synchrotron becoming dominant plus the KN effect, and flattens below $\sim 0.1$~GeV due to IC Thomson losses. Below $\sim 1$~MeV, corresponding to (cooled) electrons with $E<E_{\rm min}$, the IC spectrum hardens again. The effect of gamma-ray absorption in the SED is the strongest and starts at the lowest gamma-ray energy ($\sim 30$~GeV) at superior conjunction when the photon--photon interaction angle is the largest. Absorption becomes less severe the farther the pulsar is from that orbital phase, becoming a minor effect around inferior conjunction, mostly due to the interaction angle decreasing \citep[an effect smoothed further by the extended emitter; e.g.,][]{Khangulyan2008}. Pulsar--star distance changes are a secondary factor for small-to-moderate eccentricities that enhances absorption toward periastron. For simplicity, soft X-ray absorption due to the photoelectric effect has not been considered at this stage. We did not study radio wavelengths either, as this emission is expected to be severely free--free absorbed so close from the star \citep[see, e.g.,][and references therein]{Molina2020}.
\begin{figure}[!ht]
\centering\resizebox{1\hsize}{!}{\includegraphics{f5.pdf}}
\caption{Light curves for a smooth stellar wind for the adiabatic (green dashed) and radiative (blue solid) regimes including regions of the CD up to $1.5d$ from the star for synchrotron emission in the 1--100 keV band (top) and IC emission in the 0.1--10 GeV (middle) and >100 GeV (bottom) energy bands. The vertical dashed lines labeled SUP and INF mark the superior and inferior conjunction, respectively. We show two orbital cycles for clarity.}
\label{lc}
\end{figure}
Figure~\ref{lc} shows the orbital light curves in the case of a smooth stellar wind for the radiative and adiabatic regimes and three energy bands: X-rays (1--100~keV; synchrotron), HE gamma rays (0.1--10 GeV; IC), and VHE gamma rays ($>100$~GeV; IC). For the X-ray light curves, we only show the synchrotron components (adiabatic and radiative), because IC X-rays are produced deep in the adiabatic regime (see Fig.~\ref{SED}), and the corresponding curve is lower than any synchrotron curve. The HE and VHE gamma-ray light curves are by contrast shown only for IC (both regimes), which is the dominant emission at those energies. The light curves are mostly explained by changes in the emitter spatial volume and angular size as seen from the pulsar (affecting particle normalization), in the distance from the emitter to the pulsar (affecting $B$ and synchrotron in the X-rays) and the star (more mildly affecting IC target photons), and by angular effects (affecting IC in the HE and VHE and gamma-ray absorption in the VHE). The fact that the emitter is extended with size $\sim d$ and has a complex geometry changing due to eccentricity introduces some variations, but overall the results are as expected from previous work, with X-rays peaking around apastron, and the HE and the VHE gamma-rays peaking around superior and inferior conjunction, respectively. The VHE light curve presents a secondary peak before periastron, but similar features were already found in previous work \citep[e.g.,][]{Khangulyan2008,Dubus2008,Takahashi2009,Molina2020}.
\subsection{Clumpy-wind case}\label{sec:clumpy}
To study the short-term variability induced by a clumpy stellar wind, we focus on an intermediate orbital phase ($\phi=0.28$), at which the line of sight is perpendicular to the pulsar--star line, and the three mentioned energy bands (X-rays and HE and VHE gamma rays) and cooling regimes (adiabatic and radiative). In Fig.~\ref{cltra}, we show the geometry on the orbital plane of the smooth CD and the region filled with the shocked two-wind flow. We also show the trajectories of clumps of different initial masses/radii and densities that manage to penetrate the shocked two-wind region close to the stagnation point, where the minimum initial clump radii for penetration are $\sim 0.02 R_{*}$ for $f=0.01$ and $\sim 0.05R_{*}$ for $f=0.1$.
\begin{figure}
\centering\resizebox{1\hsize}{!}{\includegraphics{f6.pdf}}
\caption{Two-dimensional cut on the orbital plane of the smooth CD (solid gray line) at an intermediate orbital phase ($\phi=0.28$) showing the trajectories of multiple clumps. The light-gray shaded area gives a rough estimate of the thickness of the shocked two-wind region. The blue and yellow lines correspond to high-density and low-density clumps for stellar wind filling factors of $f=0.01$ and $f=0.1$, respectively. The clump radii when launched from the stellar surface are $0.1 R_{*}$ (solid) and $0.06 R_{*}$ (dashed). The colored shaded areas show the regions along the pulsar wind shock front within which the largest high-density (blue shaded area) and low-density (yellow shaded area) clumps can penetrate.}
\label{cltra}
\end{figure}
\begin{figure}
\centering\resizebox{0.9\hsize}{!}{\includegraphics{f7.pdf}}
\caption{Evolution over time of the radii of the clumps whose trajectories are shown in Fig.~\ref{cltra}. Line patterns are the same as in Fig.~\ref{cltra}.}
\label{clevol}
\end{figure}
Although the largest clumps with $f=0.01$ can reach the unshocked pulsar wind region almost everywhere in the explored CD region (blue shaded area in Fig.~\ref{cltra}), for the largest clumps with $f=0.1$ the CD crossing is restricted to the vicinity of the stagnation point (yellow shaded area). Figure~\ref{clevol} shows the time evolution of the radii of these clumps from the time of entering the shocked two-wind region until the time clump expansion is halted. All these clumps reach the same final size (half $r_{\rm p}$ at the crossing point) because they share the same penetration location; although, smaller or lighter clumps tend to evolve faster. Clumps entering farther away from the smooth-CD symmetry axis may not reach again the smooth-CD location within the simulated region.
In Fig.~\ref{clCD}, we plot cuts of the shocked two-wind region on the orbital plane, for stellar winds of different degrees of inhomogeneity over a period of 3 hours at 1 hour intervals. The arrival of clumps to the CD deforms the overall interaction structure, generating relatively quick and global variations in the geometry of the emitting shocked pulsar wind.
In the most extreme case (top-left panel), clumps frequently reach quite close to the pulsar, radically distorting the CD geometry. Otherwise, for a bottom-heavy low-density clump distribution (bottom-right panel), the results in the explored narrow phase interval essentially coincide with a smooth-wind scenario mainly because of the small number of clumps that are large enough to cross the shocked two-wind region. In intermediate cases (bottom-left and top-right panels), moderate but significant CD variations may still be seen.
Figure~\ref{cllc} shows the light curves for different stellar wind scenarios in both cooling regimes over a period of 3 hours. The light curves are computed considering an emitter size extending up to a distance of $1.5\,d$ from the star. Referring to the adiabatic X-ray light curves (top left panel) as an example, one can see that the light curves of the two most inhomogeneous stellar winds (blue solid and dashed lines) exhibit large and rapid variability. For a relatively low degree of clumpiness (green dashed--dotted line), large flaring events still occur, albeit more sparsely, while for the least clumpy case (yellow dotted line) variability subsides almost completely. The same trends in variability are observed in all panels. The light curves for the smooth-wind case are not shown for simplicity but largely coincide with the bottom-heavy low-density light curves.
Using Fig.~\ref{SED}, one can evaluate which light curve, either radiative or adiabatic, is more realistic. In all the studied energy bands, the emission in the region of interest is produced in the radiative regime, and thus, despite the simplicity of the approach, this regime provides to first order a reasonably realistic account of the behavior of the emission. In this regime, the relative changes in flux are moderate in the explored narrow phase interval, of $\sim 20$\% (top-heavy and bottom-heavy dense clumps), 10--100\% (top-heavy light clumps; note the large X-ray spike in the top right panel), and $\lesssim 10$\% (bottom-heavy light clumps), with variability timescales of $\sim 0.1-1$~h.
It is worth noting that the adiabatic light curves present significantly higher variability than the radiative ones in the dense-clump cases. Thus, although radiative losses are generally dominant on the scales we explored, including supersonic flow regions (not considered here) could lead to higher variability, as adiabatic losses can become stronger there \citep{Khangulyan2014b}. For the emission produced more deeply in the radiative regime, the impact of hydrodynamics is expected to be small.
We also assessed whether there is a reduction in variability due to emission coming from CD regions potentially more or less affected by clumps. We compared our results with light curves for emitting regions extending closer (up to $1.2\,d$) or farther from the star (up to $1.8\,d$). Larger sizes of the emitting region do not smooth out the relative changes in the flux, mostly affecting just the normalization, which indicates that the clump presence still affects the emitter relatively far from the pulsar.
\begin{figure*}[!ht]
\centering\resizebox{1\hsize}{!}{\includegraphics{f8.pdf}}
\caption{Two-dimensional snapshots of the CD on the orbital plane at 1 hour intervals within a period of 3 hours for (a) a top-heavy ($k=2$) high-density ($f=0.01$), (b) a bottom-heavy ($k=3$) high-density ($f=0.01$), (c) a top-heavy ($k=2$) low-density ($f=0.1$), and (d) a bottom-heavy ($k=3$) low-density ($f=0.1$) clump distribution. The black dashed lines correspond to a smooth stellar wind. The horizontal gray lines mark the CD size used to compute the light curves in Fig.~\ref{cllc}.}
\label{clCD}
\end{figure*}
\begin{figure}[!ht]
\centering\resizebox{1\hsize}{!}{\includegraphics{f9.pdf}}
\caption{Light curves over a period of 3 hours for the adiabatic (left column) and radiative (right column) regimes at energies 1--100 keV (synchrotron only; top rows) and 0.1--10 GeV and >100 GeV (IC only; middle and bottom rows, respectively) for a top-heavy high-density (($k=2$, $f=0.01$; solid), a bottom-heavy high-density ($k=3$, $f=0.01$; dashed), a top-heavy low-density ($k=2$, $f=0.1$; dashed--dotted), and a bottom-heavy low-density ($k=3$, $f=0.1$) clump distribution (dotted).}
\label{cllc}
\end{figure}
\section{Discussion}\label{disc}
In general, the predicted luminosities in the explored energy bands are loosely similar to those of LS~5039 at a few-kpc distance. For the corresponding fluxes, present instrumentation may be able to trace the short-term relative variations in X-rays and VHE gamma rays \citep[see typical rate uncertainties in, e.g.,][for X-rays and VHE gamma rays, respectively]{Martocchia2005,Aharonian2006}, and the future Cherenkov Telescope Array would reach significantly finer levels of variability at VHE \citep[e.g.,][]{Paredes2013}.
At HE gamma rays, several orbital cycles must be folded in phase to get statistically meaningful orbital light curves, which prevents studying (nonextreme) variability on suborbital timescales.
\emph{Clump interaction rate:} The frequency of interaction of the largest clumps with the shocked pulsar wind can be estimated from the mass distribution as:
\begin{equation}
\dot{N}\sim M_{\rm c,max} \frac{dN(M_{\rm{ c,max}})}{dM_{\rm c}} \frac{\Delta \Omega}{4\pi},
\end{equation}
where the solid angle of interaction $\Delta \Omega = \pi (d_{\rm p}/d)^2$ depends on the radius $d_{\rm p}$ of the region that can be penetrated by clumps. For a moderately clumpy stellar wind (i.e., top heavy, low density), $d_{\rm p}\approx 0.5d$ (yellow shaded area in Fig.~\ref{clevol}), which yields an interaction rate of $\dot{N}\sim6\times 10^{-5}$~s$^{-1}$ or $\sim 21$ clumps per orbit and an average time between consecutive interactions of $t_{\rm c}=\dot{N}^{-1}\sim1.6\times 10^4$~s. The duration of each individual interaction is on the order of the clump residence time in the region $\tau_{\rm c}=d_{\rm p}/u_{\infty}\sim6\times10^3$~s. This implies that approximately 40\% of the time one large clump is interacting with the CD, and $\approx 14$\% of the time two large clumps may simultaneously interact with the CD, meaning several times per orbit. Even in the least clumpy case explored here, a few of the largest clumps would still be expected to (individually) interact with the CD per orbit.
\emph{Effect of $\eta$:} Although our study focused on $\eta=0.08$, we have run a few trials in low resolution for different $\eta$ values for completeness.
The increase in the shocked two-wind shell thickness of the termination shock for larger $\eta$ values shrinks the penetrable region to the very close vicinity of the pulsar. Larger-mass clumps that can penetrate tend to grow significantly and cause large distortions of the CD, but the overall effect is a reduced variability due to a low rate of interactions. Otherwise, for smaller $\eta$ values, the termination shock wraps closer to the pulsar, extending the penetrable region to almost the entire CD length, effectively increasing the interaction rate. Clumps entering relatively close to the stagnation point will have long residence times (although expansion will halt soon after crossing), while those entering from the outer regions will evolve and exit more quickly. In this second case, overall, variability becomes faster and more intense than in the fiducial calculations.
\section{Summary}\label{summ}
We have studied the effects of different clumpy stellar winds interacting with a relativistic pulsar wind in a high-mass binary, adopting different filling factors ($f=0.1$ and 0.01) and levels of clumpiness ($dN_{\rm c}/dM_{\rm c}\propto M_{\rm c}^{-2}$, top heavy; and $\propto M_{\rm c}^{-3}$, bottom heavy). Our results for the SED and orbital light curves in the smooth-wind case are similar to those presented in the literature. The presence of clumps does not seem in general to strongly modify the emitter, and thus smooth-wind models seem enough to capture the most prominent behavior of the source, but there is clear clumpy-wind-induced variability in the X-ray and HE and VHE gamma-ray light curves that can be detectable by high-energy instrumentation.
Regarding the different cases explored, one finds that the bottom-heavy light-clump distribution can be, most of the time, indistinguishable from a smooth wind in the wind-interaction region explored in this work. In the remaining cases (denser and/or top-heavy clump distributions), the presence of clumps may be traced in the X-ray light curve and less prominently in the VHE gamma-ray light curve, with predicted flux variations of $\sim 10-20$\% in the radiative regime. These variations could reach $\sim 100$\% in some rare events, that is, the arrival to the CD of particularly large clumps or even of several large clumps simultaneously. These events, despite being more sporadic, would be very noticeable and can occur even in the least clumpy case explored in this work. Adding extra factors such as clump-induced effects further downstream of the emitting flow may reveal a stronger impact of clumps.
\begin{acknowledgements}
The authors want to thank the referee, Achim Felmeier, for constructive and useful comments that helped to improve the manuscript. The authors wish to acknowledge Edgar Molina for helpful discussions. This work has received financial support from the State Agency for Research of the Spanish Ministry of Science and Innovation under grant PID2019-105510GB-C31 and through the ``Unit of Excellence Mar\'ia de Maeztu 2020-2023'' award to the Institute of Cosmos Sciences (CEX2019-000918-M). V.B-R. is Correspondent Researcher of CONICET, Argentina, at the IAR.
\end{acknowledgements}
\bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,944 |
\section{Introduction}\label{sec:intro}
\proglang{Stan} is an open-source probabilistic programming language for Bayesian modeling and inference \citep{Carpenter2017}. It has become the system of choice for statisticians and scientists as well as the reference project for Bayesian inference. Hundreds of research papers using \proglang{Stan} are published every year, ranging from cognitive anthropology and the structure of gravitational clusters to clinical trial design, and sports. Dozens of tools utilize \proglang{Stan} such as \pkg{rstanarm} \citep{gabry2016rStanarm}, \pkg{brms} \citep{burkner2017brms}, and Facebook's forecasting tool \pkg{Prophet} \citep{taylor2018forecasting}.
There exist many other languages and software tools similar to \proglang{Stan}. Some focus more on statistical inference, while others focus more on machine learning and deep learning. To name just a few of the most popular: \pkg{Edward}/\pkg{Edward2} (\pkg{TensorFlow}) \citep{Tran2017} and \pkg{PyMC3} \citep{Salvatier2016} (\pkg{Theano}) \citep{bergstra2010theano}, \pkg{Pyro} \citep{bingham2019pyro} (\pkg{PyTorch}) \citep{paszke2017automatic}, and \pkg{MxNet} \citep{chen2015mxnet}.
\proglang{Stan} has three distinct components: a probabilistic programming language, the \pkg{Stan Math} library that supports automatic differentiation, and algorithms for inference. The main advantages of \proglang{Stan} are a rich math library and state-of-the-art inference with a variant of Hamiltonian Monte Carlo -- the NUTS (No-U-turn) sampler \citep{Hoffman2014} with some additional modifications \citep{Betancourt2017b, Stan2020} -- which makes \proglang{Stan} suitable for robust fully-Bayesian inference. Moreover, the \proglang{Stan} probabilistic programming language is easier to understand than systems embedded in other languages \citep{Baudart2018}.
\proglang{Stan} has only recently started building out low-level parallelism. While \proglang{Stan} supports threading and MPI to execute disjoint sets in the automatic differentiation expression tree, it did not have support for specialized hardware such as GPUs. An ideal case for GPU based optimization are models based on Gaussian Processes (GP). The computation in GP-based models is, even for moderate input sizes, dominated by computing the inverse of the covariance matrix. The $O(n^3)$ time of this operation also dominates the quadratic costs associated with transferring matrices to and from a GPU. In turn, computing the Cholesky decomposition of the positive definite matrix dominates the computation time of the matrix inverse. Because these costs can be broken up and executed in parallel they make the Cholesky decomposition an ideal target for GPU-based computation.
This paper describes a framework for GPU support in \proglang{Stan} and GPU implementations of the Cholesky decomposition, its derivative, other matrix algebra primitives, and GLM likelihoods with derivatives in the \pkg{Stan Math} library. Unlike most similar libraries, our framework relies on \proglang{OpenCL} 1.2 \citep{StoneOpenCL2010}, so it supports a variety of devices. This includes GPUs of different vendors, multi-core CPUs, and other accelerators.
The integration with \proglang{Stan} is seamless and user friendly - setting a flag moves the computation of supported routines to the GPU, with no need to change \proglang{Stan} code. The API provides experts with a simple way of implementing their GPU kernels, using existing GPU kernels as building blocks. We demonstrate the practical utility of our work -- ease of use and speedups -- with two examples, logistic regression and Gaussian Process regression.
\section[Integrating OpenCL with Stan]{Integrating \proglang{OpenCL} with \proglang{Stan}}\label{sec:opencl}
\proglang{Stan}'s reverse mode automatic differentiation uses the \code{Matrix} type from \pkg{Eigen} \citep{eigenweb} to store data as a matrix of type \code{double} or \proglang{Stan}'s \code{var} type, where the \code{var} holds the value and adjoint used in automatic differentiation. \proglang{Stan} builds up an expression tree used in automatic differentiation and stores all the data needed in the expression tree via its local allocator. When a node's children in the expression graph are disjoint, \proglang{Stan} can utilize \proglang{C++11} threading or MPI to compute the log probability evaluation in parallel. When an operation within a node is expensive, \proglang{Stan} can use the \proglang{OpenCL} backend to parallelize the operation on the node.
\subsection[OpenCL base]{\proglang{OpenCL} base}\label{sec:basecl}
\proglang{Stan}'s \proglang{OpenCL} backend uses a single context to receive data and routines from individual nodes in the expression tree. Ensuring there is only one context and queue per device for the life of the program makes context management simpler. The implementation of the \proglang{OpenCL} context which manages the device queue follows the singleton pattern and sits in the class \code{opencl\_context\_base}.
Instead of calling \code{opencl\_context\_base::getInstance().method()}, developers can access the context through a friend adapter class \code{opencl\_context} which provides an API for accessing the base context. If the \proglang{OpenCL} implementation supports asynchronous operations, then the context asynchronously executes kernels. Asynchronous operations are particularly useful in conjunction with threading as the individual threads will be able to enqueue operations, which will execute while threads do other calculations using CPU.
\subsection[Matrix class]{Matrix class}\label{sec:matclass}
The base matrix class \code{matrix\_cl}{}{} holds the device memory buffer, meta-information on the matrix, and methods for reading and writing event stacks for asynchronous computation. When a kernel receives a \code{matrix\_cl}{}{}, the kernel's event is attached to the appropriate read or write event stack. Reading and writing to \proglang{OpenCL} buffers uses the generic \code{enqueue(Write)/(Read)Buffer} methods. Because \pkg{Stan Math} heavily relies on \pkg{Eigen} matrices, constructors and methods are available for easily passing data back and forth.
Developers can pass in \pkg{Eigen} matrices directly to the \code{matrix\_cl}{}{} constructor or use the \code{to\_matrix\_cl()} or \code{from\_matrix\_cl()} methods.
\begin{lstlisting}
Eigen::MatrixXd m(2, 2);
m << 1, 2, 3, 4;
matrix_cl A(m);
matrix_cl B(2, 2);
B = to_matrix_cl(m);
Eigen::MatrixXd C = from_matrix_cl(B);
\end{lstlisting}
Similar constructors for the \code{matrix\_cl}{}{} class are available for standard vectors \code{std::vector<T>} and arrays of doubles.
We can reduce the data transfers of triangular matrices by only transferring the non-zero parts of the matrix in a packed form. The kernel \texttt{unpack} deals with unpacking the packed form shown on the right-hand side on Figure \ref{fig:packUnpack} to a flat matrix shown on the left-hand side. For lower (upper) triangular matrices, the irrelevant upper (lower) triangular is filled with zeros. The kernel \texttt{pack} packs the flat matrix to packed form for the transfer back to the host's global memory.
\begin{lstlisting}
matrix_cl L = packed_copy<stan::math::matrix_cl_view::Lower>(L_val_cpu, M_);
\end{lstlisting}
\begin{figure}[htp]
\includegraphics[width=8cm]{pack_unpack.png}
\centering
\caption{Packing and unpacking a triangular matrix.}
\label{fig:packUnpack}
\end{figure}
When operating on GPUs, transferring data from host to device and making copies can be the most expensive operations. To reduce the burden of data transfers, the Stan compiler identifies immutable data objects. These objects are copied to the GPU at the start and remain on the GPU until the end of inference.
Note that \code{matrix_cl} supports direct allocation of a matrix of \emph{var} objects (used for parameters for the purpose of automatic differentiation) - this stores two separate matrices, one for values and the other for adjoints, which simplifies the API.
\subsection[Kernel construction]{Kernel construction}\label{sec:kernstruct}
The \proglang{OpenCL} specification demands that strings are used to represent \proglang{OpenCL} kernels. However, having a large number of files comprised of strings is unwieldy and difficult to maintain. \proglang{Stan} wraps its kernels inside of a \code{STRINGIFY} macro, which gives developers access to the standard set of developer tools such as code highlighting, linting, Doxygen \citep{van2008doxygen}, and auto-formatting. This style makes the kernel code easier to maintain compared to having files full of strings. An example of how a developer brings a new kernel into \proglang{Stan}:
\begin{lstlisting}
// Items in between \ cond and \ endcond are ignored by doxygen .
// \ cond
const char * example_kernel_code = STRINGIFY (
// \ endcond
/**
* Example of adding new kernel in Stan
*
* @param [ out] A An example output matrix .
* @param [in] B An example input matrix .
* @param val Some other input value
*/
__kernel void example ( double *A, double *B, int * val ) {
// kernel code ...
}
// \ cond
);
// \ endcond
/**
* See the docs for \ link kernels / example .hpp example () \ endlink
*/
const kernel_cl < out_buffer , in_buffer , int > example (
" example ", example_kernel_code , {" THREAD_BLOCK_SIZE ", 32});
\end{lstlisting}
In the above, a developer uses \code{STRINGIFY} to create a \code{const char*} that holds the kernel code. That string passes into the \code{kernel\_cl}{}{} struct templated by the kernel argument types and with arguments giving the name of the kernel, the kernel code, and optional kernel macros they would like to have defined in the kernel.
Internally, we keep track of \proglang{OpenCL} events via queues on each \code{matrix\_cl}{}{} object that we use to conservatively prevent race conditions and provide ordering where necessary. \code{out\_buffer}{}{} and \code{in\_buffer}{}{} are empty structs that we pass as template arguments to configure the kernel during construction to indicate the directionality of each input buffer. At runtime, the kernel will check the correct event queues on its arguments for events it needs to wait for and then attach the event representing the kernel's completion to each buffer's queues correctly. That way we ensure that an operation that, for example, writes to a buffer, is completed before we allow the \proglang{OpenCL} runtime to read from that buffer.
The parameter pack of types in the template for \code{kernel\_cl}{}{} are unpacked and passed down as the argument types for the \code{operator()} and down to the template arguments for \proglang{OpenCL}'s \code{make\_kernel} functor. Below is a simplified version of the code used to construct and call the kernel.
\begin{lstlisting}
template <typename... Args>
struct kernel_cl {
const kernel_functor<to_const_buffer_t<Args>&...> make_functor;
kernel_cl(const char* name, const std::vector<const char*>& sources,
const std::map<const char*, int>& options = {})
: make_functor(name, sources, options) {}
auto operator()(cl::NDRange global_thread_size, cl::NDRange thread_block_size,
to_const_matrix_cl_t<Args>&... args) const {
auto f = make_functor();
const std::vector<cl::Event> kernel_events
= vec_concat(select_events<Args>(args)...);
cl::EnqueueArgs eargs(opencl_context.queue(), kernel_events,
global_thread_size, thread_block_size);
cl::Event kern_event = f(eargs, get_kernel_args(args)...);
assign_events<Args...>(kern_event, args...);
return kern_event;
}
};
\end{lstlisting}
Note that the meta-programming traits \code{to\_const\_buffer\_t<>} and \code{to\_const\_matrix\_cl\_t<>} override the \code{in\_buffer}{}{} and \code{out\_buffer}{}{} template types in order to propagate a \code{cl::Buffer} or \code{matrix_cl} to subsequent templates and signatures.
In the above code, the \code{kernel\_cl}{}{}'s constructor passes the name, kernel code, and kernel options to the kernel functor in the initialization list which compiles the kernel. Kernel arguments declared with \code{in\_buffer}{}{} or \code{out\_buffer}{}{} should be of type \code{matrix\_cl}{}{}. When a kernel is called, the events that are in each \code{matrix\_cl}{}{}'s read or write stacks are collected depending on whether it was designated as an in or out buffer. The kernel will then wait to execute until the previous events complete. The kernel's event is assigned to each \code{matrix\_cl}{}{}'s read and write event stack via \code{assign\_events()} depending on whether it was defined as an \code{in\_buffer}{}{} or an \code{out\_buffer}{}{}.
When the \code{kernel\_cl}{}{} struct is constructed, it compiles the kernel and developers call the kernel with
\begin{lstlisting}
matrix_cl foo = //...
matrix_cl goo;
example(cl::NDRange(...), goo, foo, 10);
\end{lstlisting}
Depending on the \code{in/out\_buffer} passed when constructing the kernel, events will be added to the appropriate \code{matrix\_cl}{}{} read and/or write event stack. For instance, in the above, \code{goo} in the output and will have the kernel's event attached to it's \code{write\_stack}. While \code{foo} will have the kernel's event attached to its \code{read\_stack}. Later kernel calls that write to \code{foo} will know to wait for all the events in \code{foo}'s \code{read\_stack} and \code{write\_stack} while kernels that use \code{goo} as input will know to wait for the event's in \code{goo}'s \code{write_stack}.
The kernel functions for addition, subtraction, and multiplication are wrapped in their standard operators so users of the \pkg{Stan Math} library can call the operations such as:
\begin{lstlisting}
matrix_cl A = B * C + D - E;
\end{lstlisting}
\section[GPU-optimized routines in the Stan Math library]{GPU-optimized routines in the \pkg{Stan Math} library}\label{sec:routines}
In this section we describe the three GPU-optimized matrix algebra primitives that are currently implemented in \pkg{Stan Math}. They are currently not accessible directly in the \proglang{Stan} language but are used inside existing primitive and reverse functions. Several supporting routines that were used in the implementation of these primitives are described in Section \ref{sec:supportRoutines}.
\subsection[Matrix multiplication]{Matrix multiplication}\label{sec:matrixMul}
Efficient implementations of the general matrix multiplication in \proglang{OpenCL} can be found in various best practices guides \citep{OpenCLBestPractices,CUDABestPractices} and research papers \citep{Matsumoto2014,clBLAST,Nugteren2018}. In \pkg{Stan Math} we implemented general matrix multiplication with optimizations for triangular input matrices, vector and row vector inputs, and multiplication in the form $C=AA^T$. Multiplications of a matrix or its diagonal with a scalar are also supported and explained in Section \ref{sec:supportRoutines}.
We implemented a kernel for general matrix multiplication (\code{GEMM}) that is based on the aforementioned best practices guides and is exposed through the \code{operator*(matrix\_cl\& A, matrix\_cl\& B)} function. Matrix multiplication $C=AB$, where $A$ is $n\times k$ and $B$ is $k\times m$ is executed with a 2D grid of $\frac{n\times m}{\text{WPT}}$ threads, where WPT (Work Per Thread) is an implementation parameter. Thread $(i,j)$ computes the values $C_{i,j}, ..., C_{i,j+\text{WPT}-1}$ of the resulting matrix, therefore performing up to WPT dot products of rows in $A$ and columns in $B$. The default value is WPT = 8 as it gives good overall performance on GPUs of different architectures but it can be tuned for the target GPU. The dot products are done in smaller chunks (tiles) in order to facilitate the use of the GPUs small and fast shared memory. The use of shared memory with tiling is another common approach to optimization in \proglang{OpenCL} and \proglang{CUDA} \code{GEMM} implementations.
When $A$ or $B$ are triangular, threads automatically adapt the start and end of the dot products to avoid unnecessary reads for elements known to be zero. Triangularity information is passed as part of the \code{matrix\_cl} object. Matrix methods utilize this information and set it appropriately for their outputs, if applicable. For example:
\begin{lstlisting}
// triangularity information can be set at object initialization
matrix_cl A(A_cpu);
matrix_cl A_low(A_cpu,matrix_cl_view::Lower);
matrix_cl A_upp(A_cpu,matrix_cl_view::Upper);
matrix_cl B(B_cpu);
matrix_cl B_low(B_cpu,matrix_cl_view::Lower);
matrix_cl b_upp(B_cpu,matrix_cl_view::Upper);
// different underlying multiplication algorithms are executed based on input
matrix_cl C = multiply(A , B);
matrix_cl C = multiply(A_low, B);
matrix_cl C = multiply(A, B_upp);
matrix_cl C = multiply(A_upp, B_low);
\end{lstlisting}
\subsubsection{Special case: large $k$}
When $k$ is multiple orders of magnitude larger than $n$ and $m$ and $n\times m$ is small, a small number of threads will compute long dot products thus reducing the occupancy of the GPU. In such cases we instead create $n\times m\times s$ threads, splitting the dot products into $s$ parts, each thread calculating a part of the scalar product. In order to avoid race conditions, we create $s$ copies of the resulting matrix, with the thread's ID in the 3rd dimension determining the copy to write the result to. A separate support kernel then adds these copies together using $n\times m$ threads with thread $(i,j)$ assigned to add the $s$ copies of $C_{i,j}$. Since $n\times m$ is small, these extra copies do not have a large memory footprint. The value $s$ is determined based on the size of the input matrices. This optimization offers up to a 45\% reduction in execution time compared to the \code{GEMM} kernel.
\subsubsection{Special case: $C=AA^T$}
Because $C$ is symmetric the threads where $j<i$ compute the values $C_{i,j}, ..., C_{i,j+\text{WPT}-1}$ and map these values over the diagonal to $C_{j,i}, ..., C_{j+\text{WPT}-1, i}$. Threads where $j>i$ return immediately. This kernel is accessible through \code{multiply\_transpose(matrix\_cl\& A)}.
\subsubsection{Special case: vector inputs}
We also implemented kernels that optimize multiplication of matrices with vectors, row vectors and scalars. The latter is only used as an internal function to implement other primitive function or gradients and is described in Section \ref{sec:supportRoutines}.
The general matrix multiplication kernel is not suitable for cases where the inputs are vector or row vectors as it would create additional threads without assigned work. In the case of matrix vector multiplication we create 1D work groups instead of 2D as we do in the GEMM kernel in order to avoid spawning overhead threads. When multiplying a $1 \times n$ row vector with a $n \times m$ matrix we create $m$ work groups of arbitrary size (default is 64). Each work group is assigned one of the $m$ scalar products.
\subsubsection{Primitive function}
The primitive function for general matrix multiplication accepts two \pkg{Eigen} matrices with elements of type \code{double}. Setting \code{STAN\_OPENCL} flag does not guarantee that all functions that have GPU support will use the GPU. The function will use the existing CPU sequential implementations if the problem is small enough that no speedup is expected. For the primitive \code{GEMM}, the GPU routines are used if $n\times m > 250000$ and $k>100$. These values are set so that the matrix multiplication that meets the criteria is guaranteed to be faster on any given GPU. These values could generally be set lower on mid and high-end GPUs
\subsubsection{Reverse mode function}
We focused on optimizing the reverse mode for the general matrix multiplication (\code{GEMM}). Reverse modes for multiplication that involve scalars are not optimized using \proglang{OpenCL}. There are three implementations for \code{GEMM} in reverse mode: matrix multiplication of two matrices of \code{stan::math::var} objects, matrix multiplication of a matrix of doubles with a matrix of \code{var} objects and vice versa. The description of the general case is given here, with the other two cases only omitting certain copies.
In the forward pass we extract the values from the matrices and multiply them using the same kernel that is used in the primitive function. If the input matrix is a matrix of doubles, the extraction step can be ignored. In the $chain()$ function, that is used to evaluate the gradient, we have three input matrices of doubles ($adjAB$, $B$, $A$) and we need to calculate the following expressions:
\begin{lstlisting}
adjA = adjAB * B.transpose();
ajdB = A.transpose() * adjAB;
\end{lstlisting}
The \code{transpose} kernel is described in Section \ref{sec:supportRoutines} while the \code{GEMM} kernel explained above is used for the multiplication. The thresholds on when to move the computation to the \proglang{OpenCL} device are the same as for the primitive form of matrix multiplication.
\subsection[Solving triangular systems]{Solving triangular systems}\label{sec:solvingTriSystems}
\subsubsection{Primitive function}
We implemented a general solver for $Ax=b$, where $A$ is triangular and a special case where $b$ is an identity matrix. In the latter, we transfer the input matrix to the GPU, if not already present in the GPUs global memory, and calculate the lower triangular inverse of $A$ on the GPU. If $A$ is upper triangular the input and output of the lower triangular inverse are transposed. The result is then copied back to the global memory of the host. The general solver only adds a multiplication of the inverse $A^{-1}$ with the right-hand side $b$.
The \proglang{OpenCL} implementation of the lower triangular inverse is based on our previous work \citep{Cesnovar2017}. The forward substitution algorithm that is commonly used in sequential implementations is not suitable even for multi-core parallel implementations as it requires constant communication between threads. The communication-free algorithm for multi-core CPUs proposed in \citep{Mahfoudhi2012} is based on the divide-and-conquer approach. The idea is that we can split the matrix into submatrices as shown in Figure \ref{fig:inverseBasic}. The input matrix is split in three submatrices: $A_1$, $A_2$ and $A_3$. We calculate the inverses of $A_1$ and $A_2$ in parallel to get C1 and C2. The remaining submatrix is then calculated using $C_3 = - C_2A_3C_1$, with matrix multiplication also parallelized as shown in Section \ref{sec:matrixMul}.
\begin{figure}[htp]
\includegraphics[width=8cm]{inverse_basic.png}
\centering
\caption{Splitting into submatrices when computing the lower triangular inverse.}
\label{fig:inverseBasic}
\end{figure}
Our approach generalizes this for many-core architectures, calculating a batch of smaller inverses along the diagonal in the first step (blocks labeled $S1$ in Figure \ref{fig:generalInverse}). For this step we use kernel \code{batch\_identity} (see \ref{sec:supportRoutines}). It creates a large number of smaller identity matrices that are then used in \code{diag\_inv} to calculate the inverses of the smaller submatrices along the diagonal. For a $n\times n$ matrix, this kernel is executed with $n$ threads split into $b$ work groups, where $b$ is the number of submatrices along the diagonal. Each work group is thus assigned one of the inverses along the diagonal. The rest of the submatrices are calculated by applying equation $C_3 = -C_2 A_3 C_1$. For Figure \ref{fig:generalInverse} this is done in four steps, first calculating submatrices labeled $S_2$, then reapplying the same equation to calculate submatrices $S_3$, $S_4$ and $S_5$. Each step is done in two phases, first calculating $T = C_2A_3$ with the \code{inv\_lower\_tri\_multiply} and then $C_3 = -T C_1$ with the \code{neg\_rect\_lower\_tri\_multiply} kernel. Both kernels are based on the general matrix multiply kernel but modified to handle a batch of multiplications of small submatrices. The GPU support is only used when $n > 500$.
\begin{figure}[htp]
\includegraphics[width=8cm]{inverse_general.png}
\centering
\caption{Splitting into submatrices when computing the lower triangular inverse.}
\label{fig:generalInverse}
\end{figure}
\subsubsection{Reverse mode function}
In order to add GPU support to the reverse mode implementation of triangular system solvers, we used the lower triangular inverse kernel, the \code{GEMM} kernels, and the trivial transpose kernel.
There are again three implementations for solving triangular systems in the form $Ax=b$, one with $A$ and $b$ being matrices of \code{var}, and two cases where either of them is a matrix of doubles. In the function evaluation phase, we use the same principles as in the primitive function with the added steps of extracting a matrix of doubles from the inputs, if needed. In the $chain()$ function that is used to evaluate the gradient, we have three input matrices: $adjC$, $A$ and $C$. To evaluate the gradient we calculate the following:
\begin{lstlisting}
A * adjB = adjC;
adjA = - adjB * C.transpose();
\end{lstlisting}
Solving the system is done the same way as for the primitive function while the rest is done using a \code{GEMM} kernel, explained in Section \ref{sec:matrixMul}, a transposing kernels and a kernel to multiply a matrix with a scalar, both described in Section \ref{sec:supportRoutines}.
\subsection[Cholesky decomposition]{Cholesky decomposition}
\subsubsection{Primitive function}
We implement fast Cholesky decomposition on the GPU using batched linear algebra, which factors large problems into smaller problems that can be solved in parallel \citep{Abdelfattah2016,Dongarra2016}. The developments in this area have also brought advances for the native mode Cholesky decomposition of a single large matrix. The state-of-the-art implementations presented in \citep{Dong2014, ABDELFATTAH2017,cuBLAS} use \proglang{CUDA} and are limited to NVIDIA GPUs. Our approach is based on the blocked version of the algorithm proposed by \cite{LouterNool1992}. It is based on the idea that if we partition the input matrix as shown in Figure \ref{fig:choleskyBasic}, we can calculate the resulting submatrices as follows:
$$L_{11} = \text{chol}(A_{11})$$
$$L_{21} = A_{21}(L_{11}^T)^{-1}$$
$$L_{22} = A_{22} - L_{21}(L_{21}^T)$$
The function \code{chol} computes the Cholesky decomposition of a smaller $b\times b$ block $A_{11}$ using the classic sequential algorithm. It is implemented with a simple kernel executed with $b$ threads. Parallel execution in the sequential algorithm is limited to parallelizing the inner loop and requires a lot of synchronization so all threads are organized in a single work group. These computations utilize the \code{lower\_triangular\_inverse} from Section \ref{sec:solvingTriSystems} and the matrix multiplication and \code{multiply\_transpose} from Section \ref{sec:matrixMul}. We traverse the input matrix using:
\begin{figure}[tp]
\includegraphics[width=8cm]{cholesky_basic.png}
\centering
\caption{Splitting into submatrices when computing the Cholesky decomposition.}
\label{fig:choleskyBasic}
\end{figure}
\begin{lstlisting}
cholesky_decompose(A) {
if (A.rows() == 0)
return A;
if (A.rows() <= min_L11_size) {
return cholesky_decompose_kernel(A)
}
block = A.rows() / partition
A_11 = A(0:block, 0:block)
L_11 = cholesky_decompose(A_11);
A(0:block, 0:block) = L_11
block_subset = A.rows() - block
A_21 = A(block:A.rows(), 0:block)
L_21 = A_21 * transpose(lower_triangular_inverse(L_11))
A(block:A.rows(), 0:block) = L_21
A_22 = A(block:A.rows(), block:A.rows())
L_22 = A_22 - multiply_transpose(L_21)
L_rem_11 = cholesky_decompose(L_22);
A(block:N, block:N) = L_rem_11
return A;
}
\end{lstlisting}
Note that \code{partition} and \code{min_L11_size} are implementation parameters.
\subsubsection{Reverse mode function}
We re-implemented the \pkg{Stan Math} blocked Cholesky decomposition gradient in \proglang{OpenCL}. The blocked version of the gradient is based on the work of \cite{Murray2016}. The input to the gradient is the values and adjoints of the reverse mode input matrix. Both matrices are lower triangular so their values are copied to the GPU in a packed form and then unpacked with the \code{unpack} kernel (see Section \ref{sec:supportRoutines}). The resulting values of the adjoints are packed with the \code{pack} kernel and transferred back to the host's global memory. The gradient calculation pseudo-code is given below:
\begin{lstlisting}
for (k = N; k > 0; k -= block_size_) {
j = max(0, k - block_size_);
R = L(j:k, 0:j)
D = L(j:k, j:k)
B = L(k:N, 0:j)
C = L(k:N, j:k)
R_adj = L_adj(j:k, 0:j)
D_adj = L_adj(j:k, j:k)
B_adj = L_adj(k:N, 0:j)
C_adj = L_adj(k:N, j:k)
C_adj = C_adj * lower_triangular_inverse(D)
B_adj = B_adj - C_adj * R;
D_adj = D_adj - transpose(C_adj) * C;
D_adj = transpose(D) * D_adj
copy_lower_tri_to_upper_tri(D_adj)
D = transpose(lower_triangular_inverse(D));
D_adj = D * transpose(D * D_adj)
copy_lower_tri_to_upper_tri(D_adj)
R_adj = R_adj - transpose(C_adj) * B - D_adj * R;
D_adj = D_adj.diagonal() * 0.5
set_zeros_in_upper_tri(D_adj)
}
\end{lstlisting}
Note that \code{block_size} is set heuristically with default values that can be tuned for target GPUs.
\subsubsection{Speedup measurements}
We measured computation times of the Cholesky decomposition on an Intel Core i7-5600U CPU at 3.60GHz and three different GPUs: NVIDIA Titan XP (titanxp), NVIDIA Tesla V100 (v100), and AMD Sapphire Radeon VII (radeon). We ran each experiment for different input matrix sizes in increments of 1000 up to the size that caused a \code{std::bad_alloc} or out of memory on the GPU. We generated Toeplitz matrices with $A_{i,j; i \neq j} = n - |i - j|$ and $A_{i,i} = n^2$ to ensure positive definiteness. The measurement used at each input size was the median of 9 repetitions. Results are shown in Figure \ref{fig:cholesky}.
\begin{figure}
\includegraphics[width=\linewidth]{cholesky_speedups}\caption{Cholesky decomposition speedups for different GPUs and varying input matrix size $n \times n$. We measured the performance of the Cholesky decomposition on matrices of doubles, the gradient of the Cholesky decomposition, and matrices of \code{var}. The latter are required when the matrix is a parameter, for example, in Gaussian Process regression.}\label{fig:cholesky}
\end{figure}
\subsection[Generalized linear models]{Generalized linear models}
Generalized linear models (GLMs) are a popular family of statistical models. A GLM is characterized by $\text{E}[Y] = g^{-1}(X\beta$), where $Y$ is the target variable, $X\beta$ is a linear function of input variables and coefficients, and $g$ is the link function that connects the linear term with the mean of the dependent variable.
Computing the likelihood for a GLM consists of computing the linear combination, transforming it with $g^{-1}$ and finally computing the likelihood according to our choice of distribution for $Y$. We can improve performance by computing all steps simultaneously (including analytically derived gradient), instead of performing each step individually and relying on automatic differentiation for the gradient. Six such likelihood primitives are implemented in the \pkg{Stan Math} library: normal-identity (normal distribution with identity link, linear regression), Bernoulli-logit (logistic regression), Poisson-log, negative binomial-log, categorical-logit (multinomial logistic regression), and ordinal-logit (ordinal logistic regression). \proglang{Stan} users can access them by calling the built-in log-pdf/pmf. These likelihoods can also be used as components in more complex models, such as multi-level regression.
Note that the GLM likelihoods are heavily templated. With the exception of integers, every argument can have type \code{var} or \code{double}. Many arguments can either be scalars or vectors. For example, standard deviation in the normal-identity GLM can be the usual scalar parameter or, if we want to implement heteroskedasticity, a vector.
The GPU implementation of the GLM primitives is based on their CPU implementation that is already in \proglang{Stan} and not part of this work. First, the data are transferred to the GPU. The argument types also determine which derivatives we need to compute. This information is transferred to the GPU kernel by kernel arguments and it allows kernels to skip unnecessary computation.
Each GLM is implemented in a single kernel. The kernel requires execution of one thread per input variable. The number of threads is rounded up and they are organized into work groups of size 64. Each thread calculates one scalar product of the matrix-vector product and additional GLM-specific values and derivatives. Computation of the (log) likelihood ends with the summation over intermediate values, computed by each thread. Threads in a work group execute parallel reduction. First thread of each work group writes partial sum to the global memory. Partial sums are then transferred to the main memory and summation is completed by the CPU.
Derivatives with respect to coefficients and input variables require calculation of another matrix-vector product. Since another product cannot be efficiently computed in the same kernel, a \code{GEMV} kernel is run if these derivatives are needed.
\subsection[Supporting GPU routines]{Supporting GPU routines}\label{sec:supportRoutines}
Here we describe additional \proglang{OpenCL} kernels that are available in \pkg{Stan Math}. These routines are not bottlenecks of statistical computation, so we opted for simplicity. All kernels use the default work group size determined by \proglang{OpenCL}.
These \proglang{OpenCL} kernels often do not outperform their CPU or \pkg{Eigen} equivalents, especially when we consider data transfers to or from the \proglang{OpenCL} GPU device. They should only be used as parts of an algorithm or when there is no data copy overhead. Note that all \proglang{OpenCL} kernels in \pkg{Stan Math} can be used as building blocks for new GPU routines.
All the kernels below assume input matrices of size m$\times$n.
\subsubsection[Add and subtract]{Add and subtract}
These kernels add or subtract two matrices of the same size and store the result to a third matrix buffer. They execute on a grid of $m\times n$ threads, where thread $(i,j)$ adds or subtracts elements $A_{i,j}$ and $B_{i,j}$ and stores them to $C_{i,j}$.
The kernel code for adding two matrices:
\begin{lstlisting}
__kernel void add(__global double *C, __global double *A,
__global double *B, unsigned int rows,
unsigned int cols) {
int i = get_global_id(0);
int j = get_global_id(1);
if (i < rows && j < cols) {
C(i, j) = A(i, j) + B(i, j);
}
}
\end{lstlisting}
\subsubsection[Multiplication with scalar]{Multiplication with scalar}
Kernels \code{scalar\_mul} and \code{scalar\_mul\_diagonal} can be used to multiply a matrix with a scalar. The former multiplies the entire input matrix with the given scalar while the latter multiplies only the diagonal elements. Similarly to the add and subtract kernels, the kernel \code{scalar\_mul} is executed with $m\times n$ threads with each thread multiplying one matrix element. The kernel \code{scalar\_mul\_diagonal} is executed with $\min(m,n)$ threads with each thread multiplying one diagonal element.
\subsubsection[Matrix transpose]{Matrix transpose}
Two kernels can be used for transposing a matrix and both are executed with $m\times n$ threads. In kernel \code{transpose} each thread copies an element from $A_{i,j}$ to $B_{j,i}$ and \code{triangular\_transpose} copies the lower triangular of a matrix to the upper triangular or vice-versa. In the former case, the threads with indices under and on the diagonal perform $A_{j,i} = A_{i,j}$ and threads above the diagonal do nothing. In the latter case the roles are reversed.
\subsubsection[Matrix initialization]{Matrix initialization}
Three kernels can be used to initialize a matrix: \code{zeros}, \code{identity} and \code{batch\_identity}. For kernel \code{zeros} we specify the output matrix, its size, and if we want to set zeros only on the lower or upper triangular of the matrix. In both cases, we spawn $m\times n$ threads, with each thread assigned a single matrix element. Similarly, for kernel \code{identity} each thread is assigned a single matrix element. The \code{batch\_identity} kernel is used to make a batch of smaller identity matrices in a single continuous buffer. This kernel is executed with $k\times n \times n$ threads, where $k$ is the number of $n\times n$ identity matrices to create. Each thread is assigned a single element in one of the batch matrices, with the thread ID $(0, ..., k-1)$ on the first dimension determining the matrix and the IDs on the remaining two dimensions determining the element of the matrix.
\subsubsection[Submatrix copy]{Submatrix copy}
\proglang{OpenCL} provides functions that enable copying of entire matrix buffers. In order to add the functionality of copying arbitrary submatrices we implemented the \code{sub\_block} kernel. This kernel copies a rectangular or triangular submatrix of size $k\times l$ from a source matrix to a given submatrix of the destination matrix of size $m\times n$. Each of the $k\times l$ threads that execute this kernel is assigned one element of the submatrix. The thread then determines whether to copy the element based on the triangular view argument and its indices on the two dimensions. Similarly to the \code{zeros} kernel, \code{sub\_block} has a triangular view argument that determines whether to copy the entire input matrix or only the lower/upper triangular parts.
\subsubsection[Input checking]{Input checking}
We implemented kernels that allow the user to check whether the matrices stored on the \proglang{OpenCL} devices are symmetric, contain \code{NaN} values or contain zeros on the diagonal. The inputs are a pointer to the matrix buffer, its size and a pointer to a flag variable. If the conditions of the check are met, the matrix sets the flag. No threads reset the flag so there are no race conditions. \code{check\_diagonal\_zeros} is executed with $\min(m, n)$ threads, each thread checking one diagonal element for zeros. \code{check\_nan} is executed with $m\times n$ threads, each thread checking one matrix element for \code{NaN}. For the kernel \code{check\_symmetric} the flag should be set before executing the kernel with the threads resetting it upon discovery of non-symmetry. The kernel is again executed using $m\times n$ threads, each thread checking whether $A_{i,j} - A_{j,i}$ is within tolerance of zero.
\subsection[Kernel fusion]{Kernel fusion}\label{sec:kf}
If only the basic computation primitives are implemented for the GPU, we are faced with a dilemma when developing new algorithms that are a composition of these primitives (for example, GLM likelihoods). We can call multiple kernels or manually develop a new kernel that combines multiple primitive methods into a single kernel. The latter speeds up computation in two ways. First, we reduce kernel launch overhead. And second, we reduce the amount of memory transfers. Combining kernels is also referred to as \textit{kernel fusion} \citep{filipovic2015} and it can be done manually or automated.
The problem with manually developing new kernels is that it requires specific expertise and is a time consuming process. To mitigate this, we also developed an OpenCL GPU kernel fusion library for \pkg{Stan Math}. The library automatically combines kernels, optimizes computation, and is simple to use. This speeds up the development of new GPU kernels while keeping the performance of automatically combined kernels comparable to hand crafted kernels. The details of the kernel fusion library for \pkg{Stan Math} can be found in \cite{Ciglaric2019}.
We maintain a list of functions that are implemented and available for use with the kernel generator at \url{https://github.com/bstatcomp/math/issues/15}. It includes the previously mentioned add and subtract, multiplication with scalar, and submatrix copy.
\section[Illustrative examples]{Illustrative examples} \label{sec:illustrations}
In this section we show two illustrative examples that demonstrate the use of the new GPU routines and what speedups we can expect.
\begin{itemize}
\item The measurements are end-to-end, measuring the speedups that a user would experience during typical use. That is, we measure the time it takes from calling the model to sample to when the samples are output by the model. This includes reading the data and outputting the samples, but not model compilation time. Model compilation only has to be done once and we find it reasonable to assume that compilation time is negligible over the life span of the model. For logistic regression we ran each experiment for 500 warmup and 500 sampling iterations and for GP regression 30 warmup and 10 sampling iterations.
\item We made three measurements for each hardware-model-input size configuration. We calculate speedups by dividing the average of the three measurements for the device with the average of the three measurements for the reference device (cpu).
\item We ran the experiments on an Intel Core i7-5600U CPU (cpu) at 3.60GHz and two different GPUs: NVIDIA Titan XP (titanxp), and AMD Sapphire Radeon VII (radeon).
\end{itemize}
\subsection[Logistic regression]{Logistic regression}\label{sec:logistic}
We generated toy datasets as follows:
\begin{itemize}
\item Each element of the $n\times k$ matrix $X$ is an independent draw from the standard normal. Dimensions $n$ and $k$ will vary.
\item The latent linear term $\mu_i$ depends only on the first two input variables $\mu_i = 3 X_{i,1} - 2 X_{i,2} + 1$. The remaining $k - 2$ input variables are noise.
\item Target variable $y_i$ is set to 1 with probability $\frac{1}{1 + e^{-\mu_i}}$.
\end{itemize}
The model is standard logistic regression with Bernoulli likelihood and logit link function:
$$y_i|\alpha, \beta \sim_\text{iid} \text{Bernoulli}\left(\frac{1}{1 + e^{-( X_i\beta + \alpha)}}\right).$$
We used the default flat priors provided by \proglang{Stan}\footnote{The default flat prior is improper and will lead to an improper posterior if the data are separable. However, in our toy data set the data are not separable and the model is used only to illustrate the speedups.}:
\begin{lstlisting}
data {
int<lower=1> k;
int<lower=0> n;
matrix[n, k] X;
int y[n];
}
parameters {
vector[k] beta;
real alpha;
}
model {
target += bernoulli_logit_glm_lpmf(y | X, alpha, beta);
}
\end{lstlisting}
The results are summarized in Figure~\ref{fig:reslogistic}.
\begin{figure}[htp]
\centering
\subfloat[][times ($k$ = 10)]{
\includegraphics[width=0.47\textwidth]{bernoulli_fixed_k.pdf}
\label{fig:subfig1}}
\subfloat[][speedups ($k$ = 10, 4 chains only)]{
\includegraphics[width=0.47\textwidth]{bernoulli_fixed_k_speedup.pdf}
\label{fig:subfig2}}
\qquad
\subfloat[][times ($n$ = 10000)]{
\includegraphics[width=0.47\textwidth]{bernoulli_variable_k.pdf}
\label{fig:subfig3}}
\subfloat[][speedups ($n$ = 10000, 4 chains only)]{
\includegraphics[width=0.47\textwidth]{bernoulli_variable_k_speedup.pdf}
\label{fig:subfig4}}
\caption{Times and speedups for logistic regression. Note the that the number of observations $n$ and the number of input variables $k$ were limited by CPU computation time. Some plots indicate that GPU performance has not yet peaked -- better speedups can be expected for larger $n$ and/or $k$. Also note that running 4 chains in parallel takes less time than running 1 chain 4 times. This is true for CPU-only and GPU. With multiple chains we can better utilize the GPU.}
\label{fig:reslogistic}
\end{figure}
\subsection[Gaussian Process regression]{Gaussian Process regression}
We generated toy datasets as follows:
\begin{itemize}
\item Each of the $n$ elements of $x$ is an independent draw from $\text{Unif}(-10,+10)$. Dimension $n$ will vary.
\item Target variable $y_i$ is drawn from $\text{N}( f(x), \frac{1}{10})$, where $f(x) = \beta(x + x^2 - x^3 + 100 \sin 2x - \alpha)$. Parameters $\beta$ and $\alpha$ were set so that $\text{E}[f] = 0$ and $\text{Var}[f] = 1$.
\end{itemize}
The model is a 1D Gaussian Process regression with hyper-priors as implemented by \cite{Betancourt2017}. For the sake of brevity, we do not include the model code in the text.
The results are summarized in Figure~\ref{fig:resgp}.
\begin{figure}[htp]
\centering
\subfloat[][times (variable $n$)]{
\includegraphics[width=0.47\textwidth]{gp.pdf}
\label{fig:subfig1}}
\subfloat[][speedups (variable $n$)]{
\includegraphics[width=0.47\textwidth]{gp_speedup.pdf}
\label{fig:subfig2}}
\caption{Times and speedups for Gaussian Process regression. Again, the number of observations $n$ was limited by CPU computation time - better speedups could be achieved for higher larger $n$. The plots indicate that GPU performance has not yet peaked for these GPUs -- better speedups can be expected for larger $n$.}
\label{fig:resgp}
\end{figure}
\section{Discussion and conclusion} \label{sec:conclusion}
GPU support provides \proglang{Stan} users with practically meaningful speedups in moderate to large problems, even on mid-range retail gaming GPUs. Furthermore, the speedup estimates from our illustrative examples are very conservative for two reasons. First, additional speedup can be achieved by using compute-only GPUs. And second, a substantial part of the time in the logistic regression example is due to slow I/O in \proglang{CmdStan} -- the data (samples) are passed (from) the model as text files and their size grow linearly with the number of input variables and observations as does the computation of these likelihoods.
The benefits come with zero user effort beyond setting up a GPU and without the need to change existing \proglang{Stan} model code. This is an ongoing project - we will be adding other matrix algebra and statistical likelihood primitives, such as other matrix decompositions, covariance functions, and likelihoods. Expert users can already take advantage of the API and add their own GPU kernels.
The API for \proglang{Stan}'s \proglang{OpenCL} backend is still evolving. The next major step is to add support for multiple heterogeneous devices and an efficient load balancing system. Tuning such computation is a challenge. It consists of two parts: (a) how to set optimal parameters for the device(s) and (b) when to move computation to the device(s) (when does the speedup justify the overhead). The iterative Markov Chain Monte Carlo (or optimization) setting lends itself to the possibility of efficient online tuning, because computation and input dimensions are constant over all iterations.
\section*{Computational details}
All the functionality described in this paper is part of Stan as of releases \pkg{CmdStan}~2.22 and \pkg{Stan Math}~3.1.
Instructions on how to activate GPU support for CmdStan or CmdStanR can be found here: \url{https://github.com/bstatcomp/stan_gpu_install_docs}
\section*{Acknowledgments}
We would like to thank Bob Carpenter for for his comments on an earlier draft of our work. This research was supported by the Slovenian Research Agency (ARRS, project grant L1-7542 and research core funding P5-0410). We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan XP GPU used for this research. We gratefully acknowledge the support of Amazon with an Amazon Research Award. Part of Steve Bronder's contributions were made while he was working at Capital One.
| {
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<ul>
<li>This admin panel provides a user friendly interface in handling the database.</li>
<li>It also manages how the Project Links are displayed on the Project Portal page.</li>
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,496 |
/**
* Created by aliaksei on 28/12/15.
*/
define([], function(){
function OnUserSignedIn(){}
return OnUserSignedIn;
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 29 |
On this day also known as "Go Skateboarding Day" The Skateboard Mag has released Kevin Kowalski's video part that is sure to inspire as it does to make you head spin. So damn heavy. Congrats Kevin!
Get out there and make it happen today as a skateboarder!
Bones Wheels is soon to release its all-new Skatepark Formula in assorted clear colors with the same rebound and flatspot-free formula. Have a look as Kevin Kowalski puts a set through heavy testing. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,963 |
/**
* leading comments.
*/
package com.wrq.rearranger;
import java.util.ArrayList;
/** public class comments.
*
*/
public class RearrangementTest
{
static {
// static initializer class.
}
private int field2;
/**
* method 1 comment.
*/
void method1()
{
// method 1 body.
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,922 |
PUFFIN BOOKS
Praise for TimeRiders:
'A thriller full of spectacular effects' – Guardian
'Insanely exciting, nail-biting stuff' – Independent on Sunday
'This is a novel that is as addictive as any computer game' – Waterstone's Books Quarterly
'Promises to be a big hit' – Irish News
'A thrilling adventure that hurtles across time and place at breakneck speed' – Lovereading4kids.co.uk
'Plenty of fast-paced action... this is a real page-turner' – WriteAway.org.uk
'A great read that will appeal to both boys and girls... you'll find this book addictive!' – redhouse.co.uk
'Contender for best science fiction book of the year... an absolute winner' – Flipside
ALEX SCARROW used to be a graphic artist, then he decided to be a computer games designer. Finally, he grew up and became an author. He has written a number of successful thrillers and several screenplays, but it's YA fiction that has allowed him to really have fun with the ideas and concepts he was playing around with when designing games.
He lives in Norwich with his son, Jacob, his wife, Frances, and two very fat rats.
Books by Alex Scarrow
TimeRiders
TimeRiders: Day of the Predator
www.time-riders.co.uk
# ALEX SCARROW
PUFFIN
PUFFIN BOOKS
Published by the Penguin Group
Penguin Books Ltd, 80 Strand, London WC2R 0RL, England
Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA
Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, Canada M4P 2Y3 (a division of Pearson Penguin Canada Inc.)
Penguin Ireland, 25 St Stephen's Green, Dublin 2, Ireland (a division of Penguin Books Ltd)
Penguin Group (Australia), 250 Camberwell Road, Camberwell, Victoria 3124, Australia (a division of Pearson Australia Group Pty Ltd)
Penguin Books India Pvt Ltd, 11 Community Centre, Panchsheel Park, New Delhi – 110 017, India
Penguin Group (NZ), 67 Apollo Drive, Rosedale, North Shore 0632, New Zealand (a division of Pearson New Zealand Ltd)
Penguin Books (South Africa) (Pty) Ltd, 24 Sturdee Avenue, Rosebank, Johannesburg 2196, South Africa
Penguin Books Ltd, Registered Offices: 80 Strand, London WC2R 0RL, England
puffinbooks.com
First published 2010
Copyright © Alex Scarrow, 2010
All rights reserved
The moral right of the author has been asserted
Except in the United States of America, this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser
A CIP catalogue record for this book is available from the British Library
ISBN: 978-0-141-95106-5
To Frances, Jacob, Max and Frodo – Field Office, Norwich
And as for you, dear reader, the following message is encrypted for your eyes only:
ER YKU CPVO IPJPBOD TK DONKDO TCES TCOJ YKU UJDOQSTPJD TCO EILKQTPJNO KR KJO WKQD – LPJDKQP
# Table of Contents
CHAPTER 1: 2026, Mumbai, India
CHAPTER 2: 2001, New York
CHAPTER 3: 2001, New York
CHAPTER 4: 2015, Texas
CHAPTER 5: 1906, San Francisco
CHAPTER 6: 1906, San Francisco
CHAPTER 7: 2015, Texas
CHAPTER 8: 1906, San Francisco
CHAPTER 9: 2001, New York
CHAPTER 10: 2001, New York
CHAPTER 11: 2001, New York
CHAPTER 12: 2001, New York
CHAPTER 13: 2001, New York
CHAPTER 14: 2001, New York
CHAPTER 15: 2015, Texas
CHAPTER 16: 2015, Texas
CHAPTER 17: 2015, Texas
CHAPTER 18: 2001, New York
CHAPTER 19: 2015, Texas
CHAPTER 20: 2001, New York
CHAPTER 21
CHAPTER 22: 2001, New York
CHAPTER 23: 65 million years BC, jungle
CHAPTER 24: 65 million years BC, jungle
CHAPTER 25: 2001, New York
CHAPTER 26: 65 million years BC, jungle
CHAPTER 27: 65 million years BC, jungle
CHAPTER 28: 65 million years BC, jungle
CHAPTER 29: 65 million years BC, jungle
CHAPTER 30: Wednesday, 2001, New York
CHAPTER 31: 65 million years BC, jungle
CHAPTER 32: 65 million years BC, jungle
CHAPTER 33: 65 million years BC, jungle
CHAPTER 34: 2001, New York
CHAPTER 35: 65 million years BC, jungle
CHAPTER 36: 65 million years BC, jungle
CHAPTER 37: 65 million years BC, jungle
CHAPTER 38: 65 million years BC, jungle
CHAPTER 39: 65 million years BC, jungle
CHAPTER 40: 65 million years BC, jungle
CHAPTER 41: 65 million years BC, jungle
CHAPTER 42: 2001, New York
CHAPTER 43: 65 million years BC, jungle
CHAPTER 44: 65 million years BC, jungle
CHAPTER 45: 65 million years BC, jungle
CHAPTER 46: 2001, New York
CHAPTER 47: 65 million years BC, jungle
CHAPTER 48: 65 million years BC, jungle
CHAPTER 49: 2001, New York
CHAPTER 50: 65 million years BC, jungle
CHAPTER 51: 65 million years BC, jungle
CHAPTER 52
CHAPTER 53: 2 May 1941, Somervell County, Texas
CHAPTER 54: 2001, New York
CHAPTER 55: 2001, New York
CHAPTER 56: 65 million years BC, jungle
CHAPTER 57: 2001, New York
CHAPTER 58: 65 million years BC, jungle
CHAPTER 59: 2001, New York
CHAPTER 60: 65 million years BC, jungle
CHAPTER 61: 2001, New York
CHAPTER 62: 65 million years BC, jungle
CHAPTER 63: 65 million years BC, jungle
CHAPTER 64: 2001, New York
CHAPTER 65: 65 million years BC, jungle
CHAPTER 66: 65 million years BC, jungle
CHAPTER 67: 2001, New York
CHAPTER 68: 65 million years BC, jungle
CHAPTER 69: 2001, New York
CHAPTER 70: 65 million years BC, jungle
CHAPTER 71: 2001, New York
CHAPTER 72: 2001, New York
CHAPTER 73: 2001, New York
CHAPTER 74: 65 million years BC, jungle
CHAPTER 75: 2001, New York
CHAPTER 76: 65 million years BC, jungle
CHAPTER 77: 1941, Somervell County, Texas
CHAPTER 78: 2001, New York
CHAPTER 79: 65 million years BC, jungle
CHAPTER 80: 2001, New York
CHAPTER 81: 2001, New York
# CHAPTER 1
# 2026, Mumbai, India
They'd heard the rumbling coming towards them down the echoing stairwell like a locomotive train. Then all of a sudden it was pitch black, the air thick with dust and smoke. Sal Vikram thought she was going to choke on the grit and particles of brick plaster she was sucking in through her nose, clogging her throat and the back of her mouth with a thick chalky paste.
It felt like an eternity before it was clear enough to see the emergency wall light in the stairwell once more. By its dim amber light she could see the lower flight of stairs was completely blocked by rubble and twisted metal spars. Above them, the stairwell they'd been clambering down only moments earlier was crushed by the collapsed floors above. She saw an extended arm emerging from the tangle of beams and crumbling breeze-blocks, an arm chalk-white, perfectly still, reaching down to her as if pleading to be held or shaken.
'We're trapped,' whispered her mother.
Sal looked to her, then to her father. He shook his head vigorously, dust cascading off his thin hair.
'No! We are not! We dig!' He looked at Sal. 'That's what we do, we dig. Right, Saleena?'
She nodded mutely.
He turned to the others trapped on the emergency stairwell along with them. 'Yes?' he said. 'We must dig. We can't wait for rescue...' Her father could have said more, could have completed that sentence, could have said what they were all thinking – that if the skyscraper had collapsed down to this floor there was no reason why it wasn't soon to fold in on itself all the way down.
Sal looked around. She recognized faces despite them all being painted ghost-white with dust: Mr and Mrs Kumar from two apartments along; the Chaudhrys with their three young sons; Mr Joshipura, a business man like her father, but single... enjoyed a string of girlfriends. Tonight, presumably, he'd been on his own.
And... another man, standing at the back of the stairwell, beneath the wall light. She didn't recognize him.
'If we move things, we may cause more of it to collapse!' said Mrs Kumar.
Sal's mother placed a hand on her husband. 'She is right, Hari.'
Hari Vikram turned to look at them all. 'Some of you are old enough to remember, yes? Remember what happened to the Americans in New York? Their twin towers?'
Sal remembered the footage, something they'd been shown in history class. Both of those tall, magnificent buildings sliding down into the earth and disappearing among billowing dark grey clouds.
Heads nodded. Everyone old enough remembered, but none of them stepped forward. As if to press the issue, a metal spar above creaked and slid, releasing a small avalanche of dust and debris down on to them.
'If we just wait here... we die!' shouted her father.
'They will come!' replied Mr Joshipura. 'The firemen will soon –'
'No. I'm afraid they won't.' She turned towards the voice. The old man she hadn't recognized had finally said something. 'I'm afraid they won't come for you,' he repeated, his voice softer this time. He sounded like a westerner, English or American. And, unlike everyone else, he wasn't coated in dust. 'They won't have time. This building has less than three minutes before the support struts on the floor beneath us give way. Combined with the weight of the collapsed floors above, it'll be enough for Palace Tower to go all the way down.'
He looked around at them, the wide eyes of the adults, the wider eyes of the children. 'I'm truly sorry, but none of you are going to survive.'
The heat in the stairwell was increasing. A floor below, the flames had taken a firm hold, their heat softening the steel girders of the skyscraper. Deep groans rippled and echoed around them.
Hari Vikram studied the stranger for a moment; the fact that he was the only one not coated in a thick layer of chalky dust wasn't wasted on him. 'Wait! You are clean. How did you get in here? Is there another way through?'
The man shook his head. 'No.'
'But... you were not with us before the floor collapsed! There must be some way –'
'I have only just arrived,' replied the man, 'and I must leave soon. We really don't have much time.'
Sal's mother stepped towards him. 'Leave? How? Can you... can you help us?'
'I can help only one of you.' His eyes rested on Sal. 'You... Saleena Vikram.'
Sal felt every pair of eyes in the stairwell settle on her.
'Take my hand,' said the man.
'Who are you?' asked her father.
'I'm your daughter's only way out. If she takes my hand... she lives. If she doesn't, she will die along with the rest of you.'
One of the young boys began to cry. Sal knew him; she'd babysat the Chaudhry boys. He was nine and terrified, clutching his favourite soft toy – a one-eyed bear – tightly in both hands as if the bear was his ticket out.
Another deep moan from one of the skyscraper's structural support bars echoed through the small space on the stairwell, like the mournful call of a dying whale, or the stress vibration of a sinking ship. The stale air around them, already hot, was becoming almost too painful to inhale.
'We have just over two minutes,' said the man. 'The heat of the fire is causing the building's framework to deform. Palace Tower will collapse, directly in on itself at first, then sideways into the mall below. Five thousand people will be dead a hundred and twenty seconds from now. And tomorrow the news will be all about the terrorists who caused this.'
'Who... who are you?' asked her father again.
The man – he looked old, perhaps in his fifties or sixties – stepped forward through the crowd, his hand extended towards Saleena. 'We don't have time. You have to take my hand,' he said.
Her father blocked his path. 'Who are you? H-how did you get through to us?'
The old man turned to him. 'I'm sorry. There is no time. Just know that I arrived here... and I can leave just as easily.'
'How?!'
'How is unimportant... I simply can. And I can take just your daughter... only your daughter with me.' The old man looked down at a watch on his wrist. 'Now there really is little time left – a minute and a half.'
Sal watched her father's taut face, his mind working with businesslike efficiency. No time for hows and whys. The flicker of fire was coming up from the blocked stairwell below them, sending dancing shadows through the dust-filled air.
Hari Vikram stepped aside. 'Take her, then! You must take her!'
Sal looked up at the old man, frightened at his strangeness, reluctant to offer her hand to him. Not that she believed in anything beyond this world, not Hindu gods, not angels or demons... but he seemed not of this world somehow. An apparition. A ghost.
Her father angrily snatched at her hand. 'Saleena! You must go with him!'
She looked at her father, her mother. 'Why c-can't we all go?'
The old man shook his head. 'Only you, Saleena. I'm sorry.'
'Why?' She realized tears were streaming down her cheeks, tracing dark tracks on her chalky face.
'You're special,' said the old man, 'that is why.'
'Please, you must take my boys too!' called out Mrs Chaudhry.
The old man turned to her. 'I can't. I wish I could... but I can't.'
'Pleeease! They're so young. Younger than this girl! They have their whole lives –'
'I'm sorry, it's not my choice. I can only take Saleena.'
Sal felt her father's hands on her shoulders. He pushed her roughly forward towards the stranger. 'You take her! You take her now!'
'Dadda! No!'
'You take her now!'
'No! Not –'
They heard a deep rumble and felt the floor trembling beneath their feet.
'We have only seconds,' said the old man. 'Hurry!'
'SALEENA!' her father screamed. 'YOU GO!'
'Dadda!' she cried. She turned to her mum. 'Please! I can't!'
The old man stretched forward and grasped hold of her hand. He pulled her towards him, but she found herself instinctively squirming and twisting her hand to escape his tight grip. 'No!' she screamed.
The deep rumbling increased in volume, the floor shuddering, and cascades of dust and grit filled the air around them, tumbling down from above.
'This is it!' the old man said. 'Time has come! Saleena... I can save your life if you come with me!'
She looked at him. It seemed madness that he could, but, somehow, she believed him. 'Your parents want this too.' His eyes, so intense, so old.
'Yes!' yelled her father above the growing roar. 'Please! Take her NOW!'
Beside his small frame, her mother was screaming, stretching out her hands to hold her one last time. Her father grabbed her, held her back. 'No, my love! She must go!'
Mrs Chaudhry pushed her boys at the old man. 'Please! Take their hands too! Take their hands –'
The floor shook beneath their feet, lurching to one side.
Sal suddenly felt light-headed, as if she was free falling.
This is it, it's falling!
Then the floor suddenly fractured beneath their feet, revealing an ocean of churning, roiling flames, like gazing down into Hell itself. And the last thing she recalled was seeing that one-eyed bear tumbling down through a large split in the stairwell's floor into the fire below.
# CHAPTER 2
# 2001, New York
Sal sat upright in her bunk – gasping for breath, feeling her cheeks wet with tears.
The nightmare again.
It was quiet and still in the archway. She could hear Maddy snoring on the bunk below, and Liam whimpering nonsensical words in his soft Irish accent as he stirred restlessly on the bunk opposite.
A muted lamp glowed softly from across the archway, lighting their wooden dinner table and the odd assortment of old armchairs around it. LEDs blinked among the bank of computer equipment across the way, hard drives whirring. One of the monitors remained on; she could see the computer system was doing a routine defrag and data-file tidying. It never slept.
Not it... not any more – the computer wasn't IT any more. It was Bob.
Unable to go back to sleep, she clambered off the top bunk. Maddy twitched in her sleep, and Liam also seemed to be unsettled. Maybe they too were reliving their last moments: Liam's sinking Titanic, Maddy's doomed airliner. The nightmares came all too often.
She tiptoed across the archway, barefoot on the cold concrete floor, and sat down in one of the swivel chairs, tucking her feet under her and sitting on them for warmth. She grabbed the mouse and opened a dialogue box. Her fingernails clacked softly on the keyboard.
> hey, bob.
> Is this Maddy?
> no, it's sal.
> It is 2.37 a.m. You cannot sleep, Sal?
>nightmares.
> Are you recalling your recruitment?
Recruitment, that's what the old man, Foster, had called it. Like she'd had any real choice in the matter. Life or death. Take my hand or be mashed to pulp amid a crumbling skyscraper. She shuddered. Great fragging choice.
>yeah, my recruitment.
> You have my sympathy, Sal.
'Thanks.' She spoke softly into the desk mic – too lazy to tap out any more. Anyway, the clickety-click of the keyboard echoing through the archway was far more likely to disturb the others than her speaking quietly.
'I miss them so much, Bob.'
> You miss your family?
'Mum and Dad.' She sighed. 'It seems like years ago.'
> You have been in the team 44 time cycles. 88 days precisely, Sal.
Time cycles – the two-day time bubble that played out and reset for them, constantly keeping them and their field office in 10 and 11 September 2001, while the world outside moved on as normal.
Outside... outside was New York – Brooklyn, to be more precise. Streets she was now getting to know so well. Even the people she had conversations with, people who were never going to remember her: the Chinese laundromat lady, the Iranian man running the grocery store on the corner. Every time they spoke, it was, for them, the first time – a new face, a new customer to greet cheerily. But she already knew them, knew what they were about to say, how proud the Chinese lady was of her son, how angry the Iranian man was with the terrorists for bombing his city.
This morning was the Tuesday, 11 September, the second day of the ever-resetting time cycle. In just under six hours the first airliner was going to crash into the Twin Towers, and New York and all her inhabitants were going to change forever.
'So what're you doing, Bob?'
> Data collation. Hard-drive maintenance. And reading a book.
'Oh? Cool. What're you reading?'
A page of text appeared on the screen. She could see individual words momentarily highlight one after the other in rapid blinking succession as Bob 'read' while they talked.
> Harry Potter.
Sal remembered seeing the old films from the first decade of the century. They didn't do much for her, but her parents had liked them as children.
'Are you enjoying it?'
Bob didn't answer immediately. She noticed the flickering of highlighted words on the open page of text on the screen grind to a sudden halt, and the soft whirring sound of hard drives being spun momentarily ceased. Forming an opinion... that was something Bob struggled with. It required the computer system's entire capacity for him to actually formulate, or rather simulate, something as simple as a human emotion... a preference. A like or dislike.
Finally, after a few seconds, she heard the hard drives whirring gently once again.
> I like the magic very much.
Sal smiled as she acknowledged how many terabytes of computing power had gone into that simple statement. If she had a mean streak in her, she could have asked him what colour he thought went best with violet, or what was tastier – chocolate or vanilla? It would probably lock the system for hours as Bob laboured through infinite decision loops to finally come up with the answer that he was unable to compute a valid response.
Bless him. Great at data retrieval, cross-referencing and processing. But don't ask him to pick dessert off a menu.
# CHAPTER 3
# 2001, New York
Monday (time cycle 45)
Most of the damage that happened here in the archway with the last time contamination has been fixed up now – the holes in the walls filled again, the door to the back room replaced with a new sturdy one. And we got a brand-new emergency generator installed. Some workmen came in to set it up. We had to hide the time-portal equipment from them, and when they asked about all the computer screens at the desk Maddy told them we were a computer-game developer. I think they believed her.
It's a much more powerful generator, and more reliable than the last shadd-yah old one. I hope we don't have to use it, though.
We've also got an old TV set, a DVD player and one of those Nintendo machines. Liam loves the games. He's mad about one stupid game with silly characters driving around on go-karts throwing bananas at each other.
Boys, eh?
Maddy says we need to grow a new support unit. A new Bob. Just in case another time shift comes along that we need to deal with. Only, the new Bob won't be entirely new. The body will, yes, but she says we can upload Bob's AI back into it and he'll be exactly like he was... and not the retarded idiot that plopped out of the growth tube last time. Which is a relief. Bob was so-o-o-o stupid when he was first born.
We fixed the growth tubes. Some got damaged by those creature things that broke in, but they're all functioning now, and we've got them filled up with that stinking protein solution the foetuses float in. We had to steal a load of that gloop from a hospital blood bank. It's the fake blood they use, the plasma stuff, but with a witches' brew of added vitamins and proteins.
Honestly, it's like runny snot. But worse than that, because it smells like vomit.
What we don't have yet, though, are the foetuses. Apparently we can't go and grab any old one – they're specially genetically engineered sometime in the future...
Maddy looked at Liam. 'You ready?'
'Aye,' he replied, shivering as he stood behind her in nothing more than a pair of striped boxer shorts, and holding a watertight bag full of clothes.
She looked down at her own shivering body, trembling beneath her T-shirt. 'Maybe one day we could get around to rigging up something to heat the water before we jump in.'
'That's for sure.'
She climbed the steps beside the perspex cylinder, looking down into the cold water, freshly run from the water mains. She settled down on the top step beside the lip of the cylinder and dipped her toes in.
A wet departure – that was the protocol. To ensure that nothing but them and the water they were floating in was sent back in time... and not any chunks of floor, or carpet or concrete or cabling that had no possible reason to exist in the past.
'Oh Jeeeez! It's freezing!'
Liam squatted down beside her. 'Great.'
Maddy shuddered then looked up at Sal, seated at the computer station. 'What's the departure count?'
'Just over a minute.'
'So,' said Liam, slowly easing himself into the water, gasping as he did so. 'You're sure about this?'
'Uh-huh.' No, she wasn't. Not sure about anything. The old man, Foster, had left her in charge. Left her running this team and this field office even though they'd barely survived their first brush with time contamination. All she had for help now was computer-Bob and a data folder on his hard drive entitled 'Things You'll Probably Want to Ask'.
'How do we grow new support units?' was the name of one of the first files she'd found in the folder when she'd delved into it a few weeks ago. First order of business had been getting the grow-tubes up and running and getting one of those clones on the go. When she'd double-clicked on it, what she'd got was an image of Foster's face looking out of the monitor as he'd addressed the web cam. He looked ten, perhaps twenty years younger than he had the morning he'd told her she was ready, wished her luck and walked out of Starbucks leaving her to run things.
The Foster onscreen looked no more than fifty. 'So,' he began, adjusting the flex so that the mic was in front of his mouth. 'You've opened this file. Which means you've been careless and your support unit has been destroyed and now you need to grow a new one.' Foster had proceeded with detailed instructions on maintenance and feeding, and how the growth tubes work. But finally, towards the end of the log entry, was the bit they'd been after.
'Right... so the clones are grown from a store of engineered human foetuses. I'll presume you've used up the last of the refrigerated ones kept in your field office and now you need more.'
Not exactly used up; those of them mid-growth had all died in the tubes, poisoned by their own waste fluids because the electric-powered pumps hadn't been functioning. The bodies – pale, lifeless, hairless, jelly-like forms that ranged from something that could've sat in the palm of her hand to the body of a boy of eight or nine – had been taken care of. Taken out, weighted down and dumped in the river. Not an experience she ever wanted to repeat.
'The good news is there are more of them. There's a supply of viable candidate foetuses, all engineered with the silicon processor chip already housed in the cranial cavity. They're ready to grow to full term and, of course, come with basic learning AI code pre-installed.' The Foster on the monitor smiled coyly. 'If you've been smart, you managed to retrieve your last support unit's chip and preserved its AI...'
She nodded. Yup. Well, Liam had done that messy business.
'... so any new support unit doesn't need to start out from scratch as a complete imbecile, and you can upload the AI from the computer system. So, like I say, the good news is there's more of them. But the bad news is they're not going to be delivered to your front door like... like... some sort of a pizza delivery; I'm afraid you've got to go and get them yourselves.'
Sal called out a thirty-second warning and Maddy's mind returned to the icy water in the displacement cylinder. She eased herself in beside Liam, her breath chuffing out at the cold. 'Uhhh! This is f-f-f-freezing! How d-do you c-cope with it?' she asked Liam, her teeth chattering.
He offered her a lopsided grin. 'It's not like I get a choice, is it?'
'Twenty seconds!' called out Sal.
'When did you say we're going, again?' asked Liam.
'I t-t-told you: 1906. San Francisco.'
Liam's eyebrows locked in concentration for a moment. 'Hold on now... is that not the same year that... that –?'
'Yes?'
'I remember my dad reading it in the Irish Times. It's the year that –'
'Fifteen seconds!'
Maddy let go of the side of the perspex cylinder and began treading water. 'Liam, you've g-got to go under now.'
'I know... I know! Bleedin' hate this bit.'
'Maybe Sal and I should t-teach you how to swim some time?'
'Ten seconds!'
'Oh Jay-zus-'n'-Mary, why does time travel have to be done this way? Why did that Waldstein fella have to be so stupid as to invent bleedin' time travel in the first place!'
'You wanna blame someone... b-blame the Chinese what's-his-name guy who worked it out in the first place.'
Liam nodded. 'Aghh, well, him too!'
'Five seconds!' called Sal. 'You really need to duck under now!'
Maddy held her hand above his head. 'Need me to push you under?'
'No! I'll just... I'll, ah... All right!'
Liam sucked in a lungful of air and clasped his nose with his free hand.
'S-see you on the other side,' she uttered as she pushed him under the water. Then sucked in air and submerged as well.
Oh Jeez... here goes.
Her first time. Her first time into the past, not counting her recruitment from 2010. She'd been too busy checking the coordinates were set right, arranging the return window time-stamp, checking Sal had pulled out the right clothes for them to wear from the old closet in the back room, making sure she remembered the details of their mission... too busy with all those things to realize how utterly terrified she was at the prospect of being pushed out of space-time, through chaos space – and God knows what that was – to emerge back into the space-time of nearly a hundred years ago.
She opened her eyes under the water and saw the foggy form of Liam's scrawny body thrashing around in blind panic. She saw bubbles zig-zagging up around him. She could see the dim lamp on the computer desk through the tube's scuffed plastic, the faint outline of Sal... then...
... Then they were falling, tumbling through darkness.
# CHAPTER 4
# 2015, Texas
'OK, students, we'll be arriving at the institute very shortly, so I want you all to be on your very best behaviour,' said Mr Whitmore, absentmindedly scratching at the scruffy salt-and-pepper stubble around his mouth. He considered it a full beard even if no one else did. 'As I'm sure you will be,' he added.
Edward Chan sighed and looked out of the coach's broad window at the scrub beside the highway. Outside the air-conditioned comfort of the coach it was another blistering Texas day. Hot and bright. Two things he hated. He much preferred his dark bedroom back in Houston, drapes drawn, an ultraviolet lamp making the manga posters on his black bedroom walls glow like the halogen signs outside some cool nightclub.
Dark and cool and peaceful. A place far away from the incessant noise of other kids, the shrill laughter of clusters of girls. High-school girls always seemed to come in clusters – mean, spiteful clusters that sniggered and whispered and pointed. And the boys... If it was possible, they were even worse. The jocks – the alpha-male types – loud, brash, great at sports, oozing easy confidence, gangsta rap hissing out of their iPod earbuds, high-fiving each other for any reason. Golden-tanned, sandy-haired, blue-eyed boys who, you could tell, would ease through school, ease through college, ease through life... and never once wonder if someone was whispering behind their back, laughing at them, pointing at them.
That was the tribal system at school: the girls – giggly gaggles of Hannah Montana clones, the jocks in their swaggering gangsta gangs... and finally the third category, the ones like Edward Chan – the freaks. Loners, emos, geeks, nerds: the cookies that didn't quite fit the cookie-cutter machine that was high school.
His dad was always telling him it was the freaks that ended up doing the great things. It was the freaks who became dotcom billionaires, famous inventors, movie directors, rock stars... even presidents. The jocks, on the other hand, ended up selling real estate or managing Wal-Mart stores. And the Hannah Montanas ended up becoming stay-at-home moms, getting fat, bored and lonely.
Ahead of the coach he could see a cluster of pale buildings emerging from the ochre drabness, and presently they slowed down and stopped at a security checkpoint. The other kids on the coach, about thirty of them, all a couple of years older than Edward, began to bob in their seats, craning their necks to look at the armed security guards and the lab buildings up ahead.
'Please stay seated for the moment, guys,' said Mr Whitmore over the coach's PA system.
Edward stretched to look over the headrest of the seat in front of him. He saw a man climb up the steps on to the coach. A smart man in a pale linen suit. He shook hands with Mr Whitmore, the school principal who was chaperoning the students.
'Right, guys, I'm going to hand you over to Mr Kelly, who is from the institute. He's going to be showing us around the facilities today.'
Mr Kelly took the microphone from him. 'Good morning, boys and girls. Let me first say welcome to the institute. It's an honour to have you kids come and visit. As I understand it, you guys have all been nominated by your various schools to come along today because you're all straight-A students?'
Whitmore shook his head. 'Not quite, Mr Kelly. "Most-improved performers". Students who've most clearly demonstrated a willingness to learn. We have all levels and abilities here on this coach, from schools right across the state, but what they all have in common is the spectacular improvement in their year-end SATs scores. These students are the ones who've worked the hardest to better themselves.'
Mr Kelly's tanned face was split with a broad smile. 'Fantastic! We like improvers here. Go-getters. I wouldn't be surprised if one or two of you on this coach ended up working for us here one day, huh?'
There was a token of polite laughter up and down the rows of seats.
The coach lurched slowly forward, down a long straight driveway flanked by freshly cut lawns, wet with the moisture from water sprinklers.
'OK, guys, we'll shortly be arriving at the visitors' reception area, where you can get off. We have some refreshments ready for you before we start the tour of this facility. I will be your guide for today, and, as I'm talking, if you have any questions at all, please don't be afraid to raise your hands and ask. We want you to get the most out of today... to understand what our work is here and how very important it is to the environment.'
Edward looked out of the window as the coach approached a decorative flowerbed and swung slowly around it. In the middle, framed by an arrangement of vivid yellow chrysanthemums, was a sign: WELCOME TO TERI: TEXAS ADVANCED ENERGY RESEARCH INSTITUTE.
# CHAPTER 5
# 1906, San Francisco
'Hey! Don't turn around yet – I'm not ready,' snapped Maddy irritably.
Liam stayed where he was, facing the grubby redbrick wall in front of him. The back alley reeked of rotting fish, and he wondered if he lingered too much longer here whether the smell was going to be stuck on him for the rest of the day.
'Are you not done yet?' he asked.
Maddy muttered under her breath. 'It's all these damned laces and hooks and buttons and things. How the heck did women manage to dress themselves back then?'
He turned his head a little to look up the alley. It seemed to open on to a busy thoroughfare. He saw several horse-drawn carts clatter by, and men dressed like him: formal grey morning coats, buttoned waistcoats, high-collared shirts, with top hats, flat caps and bowler hats. Very much like the better-dressed men in Cork might have worn on a Sunday morning. The clothes they'd found in the back room appeared to be perfectly authentic. There'd been another couple of dusty costumes in there. Sal had said something about them being for the other back-up drop-point – another time, another place.
'Oh, dammit... this'll have to do,' tutted Maddy irritably.
'Can I turn round now?'
'Yes... but I look a total doof.'
He turned round. His eyes widened.
'What?' she gasped suspiciously. 'What is it? What've I got wrong?'
'Nothing! It's nothing... it's just...'
Maddy scowled at him beneath the wide-brimmed sun hat, topped with a plume of white ostrich feathers. Her slim neck was framed by decorative lace that descended down the front of a tightly drawn and intricately embroidered bodice. Her waist seemed impossibly thin, as the gown flared out beneath and tumbled down to the ground, modestly covering any sign of her legs.
She put her hands – covered in spotless elbow-length white gloves – on her hips. 'Liam?'
He shook his head. 'You look so... so...'
'Spit it out!'
'Like... well, like a lady, so you do.'
For a moment he thought she was going to step forward and punch his arm, like she was prone to do. Instead, her cheeks coloured ever so slightly. 'Uh... really?'
'Aye.' Liam smiled at her. 'And me? What about me?'
Maddy grinned. 'Well, you look like an idiot.'
Liam pulled the top hat off his head. 'Ah, it's that, isn't it? Makes me ears stick out like a pair of jug handles.'
She laughed. 'Don't worry about it, Liam. Obviously it's the fashion over here. You won't be the only person wearing one.'
'It was mostly flat caps and forage caps back home. You tried wearing a top hat or a bowler, you were asking for some joker to try an' knock it off.'
She pointed at him, ignoring the quip, her smile replaced with her let's-get-down-to-business frown. 'What time have you got on your clock?'
Liam pulled the ornate timepiece out of his waistcoat pocket. 'Seven minutes after eleven in the morning.'
'OK, we should get a move on. The return window here is in four hours' time.'
'Right you are. How far is it?'
'Not far, I think. It's on to Merrimac Street, then up Fourth Street to Mission Street... short walk up that on to Second Street. Ten minutes... at a guess?'
Liam stepped forward away from the brick wall, the tumbled crates of rubbish and the stench of rotting fish. With a broad cock-sided grin he offered his arm. 'Shall we, ma'am?'
Her face softened and she threaded one white gloved hand around it. 'Oh, absolutely, Mr Darcy. A pleasure, I'm sure.'
They emerged out of the gloom of the alley on to Merrimac Street and immediately Maddy found herself gasping.
My God. The realization finally hit her. I'm actually standing IN history.
Merrimac Street was busy with mid-morning foot and wheeled traffic, mostly horse-drawn carts ferrying goods up from the wharf down the far end. She could make out steam ships lined up against the docks, filling the blue sky with columns of coal smoke and steam, and the churning business of freight coming off or being loaded on.
'Awesome,' she giggled with delight, 'this is just like being in a movie. Just like the beginning of Titanic...'
He looked at her, disgusted. 'They made a movie about it?'
The smile on her face slipped and became a guilty grimace.
Liam tutted and sighed. 'Good people died an' all... for what? So they can become part of a flickering peepshow a hundred years later?'
She shrugged. 'Uh, s'pose... but it was pretty good, though. Fantastic special eff–'
His sideways scowl silenced her.
'Never mind.'
They turned left on to the road, heading up it towards Fourth Street, dodging several piles of horse manure along the way. Fourth Street was a little busier, but nothing compared to Mission Street. The road was a broad thoroughfare, a hundred feet wide, thick with carts and pedestrians and a tram line that rattled with trams laden with passengers inside and hanging precariously on the back, dinging their bells to clear the track ahead.
'Oh my God, this is so amazing!' she gushed.
Liam tugged her arm. 'Shhh... you're sounding like a tourist.'
Mission Street was flanked with five- and six-storey brick buildings, warehouses, offices, factories, banks and legal firms. She caught sight of a tall building dominating the skyline – fifteen, perhaps twenty storeys high that looked like a small version of the Empire State Building.
'I didn't know they had skyscrapers back then... uhh... I mean back now!'
Liam nodded. 'Nothing like this in Ireland.' He shook his head sadly. 'And you're telling me all this gets totally destroyed?'
'Uh-huh. Tomorrow morning, April eighteenth, the great Californian earthquake. According to our history database, much of the downtown area is destroyed by the quake... and then the resulting fire destroys most of what was left in this area... the fourth and fifth districts.'
'Jeeeez... that's a real shame, so it is.' Liam locked his brows for a moment. 'Hang on! Strikes me as a bit stupid that the agency has picked here and now to store our supplies if it's about to be brought crashing down.'
'Well, duh!' said Maddy, making a face and rolling her eyes. 'Think about it! It makes perfect sense!' She looked at him as if he'd just put on a pair of shoes the wrong way round. 'Liam, I thought Foster said you're meant to be smart?'
He pouted his lip, feigning hurt. 'Well, Miss Smarty Pants, you're obviously itching to tell me something, so get on with it.'
She sighed. 'It's perfect, because the bank vault where our replacement engineered foetuses are located will be completely destroyed in the fire. Everything. All the safe deposit boxes, their contents, all the client paperwork... everything. No paper trail.'
Liam grinned. 'Ah, very clever.'
'Exactly.'
The hubbub on Mission Street was added to by the noisy clatter of a sputtering engine. Its noise blotted out everything as it slowly approached them. They finally saw the vehicle rolling down the middle of the street on flimsy spoked wheels, following a man on foot waving a red warning flag before him.
'Wow! I didn't know they had cars then!' Maddy shouted in his ear.
He shook his head. 'Now who's being dumb! Of course we did!' He watched the vehicle slowly rattle past, steered by a man wearing a cap and goggles. Beside him sat a woman sporting a cloud of ostrich feathers above her head, her gloved hands clasped over her ears at the cacophony.
'Now I know that's an Oldsmobile Model R,' added Liam as the vehicle finally turned right off Mission Street and the laboured clatter of internal combustion allowed them to talk easily once more. 'There were quite a few of those things dashing about Cork – yes, even Cork – when I left.'
She shook her head. 'Hardly dashing.'
They walked on another few minutes in silence, Maddy enjoying playing the lady in her own period-piece Hollywood movie and Liam feeling like this was something of a trip home for him. Back to his time, back to a place where he could talk easily with anyone and not be made to feel like a complete moron for not knowing what a digicam was, or that Seven-Up wasn't some kind of a ball game, or that a Snickers Bar wasn't some sort of sleazy nightclub.
'This is it,' Maddy finally said, pointing to a narrow side street. 'There... Minna Street.'
They crossed the wide thoroughfare, dodging a tram clanging its way through the bustle of pedestrian traffic and sidestepping several more steaming hillocks of horse manure. They stood in the mouth of the narrow road, only two carts wide and relatively quiet.
'And that's the building we want,' she said, pointing to a formal-looking frontage of brick and granite. 'Union Commercial Savings Company,' she added. 'According to Foster's "how to" manual, this is the bank's only premises. After the earthquake, the fire destroys this building and everything inside it. The company was no more. As if it never existed.' She looked at him. 'You see? Perfect.'
'And all our Baby Bobs are in some sort of safe down in its basement?'
'That's what Foster says.'
Liam frowned. 'So, I'm being dumb again... but if there's a whole load of those little foetus things down there in a safe somewhere, what's keeping them alive? Would they not die and sort of go off? Is there a refrigerating device down there?'
'You'll see.'
# CHAPTER 6
# 1906, San Francisco
Maddy strode down Minna Street towards the bank. 'Come on.'
Liam was struggling to keep up with her. 'So, who put them in this bank? And when did they do it?'
She reached the front step of the Union Commercial Savings Company and stopped. 'OK, Liam, just a second...' She pulled her glasses and a scrap of paper covered with scribbled notes in her handwriting out of her handbag.
'Oh Jay-zus... you brought notes back with you? Isn't that not allowed? You know? Contamination of time an' all?'
Maddy looked around the quiet street guiltily. 'I know, I know... but there was way too much to remember. I was worried I'd forget something.'
'Foster would throw a fit if he knew you'd brought notes back here,' said Liam.
'Well, he won't, will he?' she muttered impatiently. 'Because he bailed out and left us to cope on our own.'
Liam shrugged at that.
She put her glasses on. 'OK, so, my name is Miss Emily Lassiter. You're my brother.'
'Do I get a name too?'
She sighed. 'Yes... uhh... here it is, Leonard Lassiter. All right?'
He nodded.
She scanned the notes further, digesting the information for a few moments before tucking them back in her bag and removing her glasses. 'All right, I think I've got it all.' She looked at him. 'You don't have to say anything, OK? Just go along with whatever I say.'
'Will do.'
She took a deep breath, then pushed the double door to the bank inwards. They stepped on to a tiled floor that echoed their footsteps around a hall, dark with oak panels. Ahead of them were half a dozen ornate mahogany desks, each with softly glowing green ceramic desk lamps. Behind each one sat a bank teller, all but one busy dealing in hushed, respectful tones with customers.
Maddy led the way towards the unoccupied teller, a young man with hair slicked down in a rigid centre parting and a carefully clipped and waxed moustache.
'Uhh... 'scuse me?' she said.
The young man looked up at her and smiled charmingly. 'Good morning, ma'am. How can I help you?
'I'd like to speak with a Mr... uh... Mr Leighton. He works here, I think.'
'Oh, I'm certain he works here, ma'am,' said the young man. He tapped a wooden name-holder on the desk. 'I'm Harold Leighton, you see? Please, will you take a seat?'
Maddy smiled and slumped down in the seat a little too casually then did her best to quickly recover her lady-like demeanour. 'Much... uh... much obliged,' she said as demurely as she could manage.
'Now, ma'am, how could I assist you?'
She took a breath, hoping she was going to get this right and not sound half as nervous as she felt. 'My family has a safe deposit box with your bank and I wish to make a withdrawal.'
'Certainly, ma'am. The account is in the name of?'
'Joshua Waldstein Lassiter.'
Harold Leighton's eyebrows raised.
Her heart skipped. 'Oh... is there a problem?'
'Not a problem as such, ma'am. It's just... I still have the paperwork here on my desk.'
Maddy shook her head. 'Paperwork?'
'The paperwork setting up the safe deposit account. Joshua Waldstein Lassiter, I presume he is your...?'
'Uh?... My uh... yes, that's right, my father.'
'Well, your father was here not more than an hour ago. Actually, I dealt with him myself. He brought a very nice jewellery box with him and we carried it down to the safe room and put it in a deposit box together... as I say, not more than an hour ago.'
'Oh,' was all she managed to say after a few moments. 'Yes, well, that's quite right.'
'And you wish to withdraw something from the safe deposit box already?'
She nodded. 'Yes, that's right.'
'Well... that is highly irregular.'
'We're a funny old family, us Lassiters,' said Maddy, looking back over the chair. 'Aren't we, Liam?'
Liam stepped forward. 'Oh yes, that we are, dear sister.' He grinned at the teller. 'She sometimes calls me Liam, although my name is in fact Leonard,' he said, nudging the small of her back.
Maddy mentally kicked herself for being such a dumb-nuts.
'You are brother and sister?' Harold Leighton looked up at Liam. 'And it seems you, sir, are Irish?'
'Yes.'
'But,' he said, looking at Maddy, 'it seems, ma'am, you're not?'
'I... uh...' Maddy's mouth flapped uselessly. 'Oh...'
'I was brought up in Cork,' cut in Liam. 'My dear sister in California. Father likes to keep a home either side of the Atlantic, so he does.'
The young teller cocked an eyebrow. 'So it seems.' He sighed and spread the bank account details out in front of him. 'Well, it appears your father did specify his children as fellow signatories on the account, so... you, ma'am, I presume are Emily Lassiter?'
'That's correct,' she replied.
'For security reasons I have to ask you for the code word your father has put down here on this form to assure us you are in fact who you say you are.'
'Of course.' She nodded. 'It's... it's...' She realized all of a sudden her mind had gone blank and cursed.
The teller's jaw dropped open at her unladylike language. 'Madam!'
Liam grinned sheepishly. 'She's spent time at sea. Picked up all sorts of dreadful language from the sailors, so she did. Father so hates her talking that way.'
'Just a sec,' said Maddy, fumbling in her handbag for her note. She quickly scanned her scribbled writing. 'Ahh! Here it is!'
She leaned forward over the desk. 'The code word, Mr Leighton, is Hemlock.'
Leighton stared at her long and hard, suspicion clouding his young teller's eyes. Finally a cautious smile spread across his lips. 'Yes, it is, Miss Lassiter. If you'll just sign here, I can take you down to the safe room.'
∗
The teller spun a large brass wheel and slowly pulled open the cast-iron door leading on to a small room lined with numbered deposit boxes on three walls. 'Your safe deposit box is number three-nine-seven,' he said, leading them to a locker with the number on its door. He inserted the key and twisted it once.
'It is company policy, madam, sir, that I remain in the safe room while you inspect the contents of your deposit box. However, I shall remain over there by the door and I shall turn my back to allow you a little privacy.'
Maddy nodded and smiled politely. 'OK.'
She waited until Mr Leighton had crossed the room and was standing by the cast-iron door, casually jangling the keys in one hand and examining his fingernails on the other.
'Liam,' she uttered softly.
'Yes?'
'I think it's best if you go talk to him, distract him. I don't want him seeing anything he shouldn't.'
He nodded. 'Aye, you're right.' He wandered over and easily struck up a conversation with the young man while Maddy attended to their business.
She pulled the deposit box's door open. The faint glow from the safe room's overhead light showed her little of what was inside. Maddy pushed her hand into the darkness and almost immediately felt the side of a wooden box. She found a small handle and pulled it out. It was quite heavy, and as she hefted it out of the locker towards an inspection bench in the middle of the room, the young man called out.
'Let me give you a hand with that, madam.'
'I'm fine... I'm fine,' she grunted.
'Strong as an ox, so she is,' Liam assured him. 'She'll be all right.' He resumed chatting to Leighton, something about steam ships, from what she could hear.
She studied the box. It certainly looked like a jewellery box, about the size of a small travel trunk, made of dark wood with silver buckles and ornate swirls along each side. She turned the box so that the upright lid would hide what was inside from any prying eyes, and then slowly, carefully opened it.
'Another box,' she whispered. But this one was smooth, featureless, metal and cold to the touch.
Refrigerated. There had to be some kind of small power unit or battery inside.
Her gloved fingers found a catch on the side and gently slid it back. Something inside the box clicked and the lid slowly raised with a barely audible hiss. A shallow fog of nitrogen wafted out of the box revealing a row of eight glass tubes, each six inches long and a couple of inches wide. She eased one of the glass tubes out of its holder and, still shielded by the lid of the jewellery box, inspected it closely. Through the glass she could see the murky pink growth solution and the faint pale outline of a curled-up human foetus.
'Hello there, little baby Bobs!' she cooed softly, waggling her fingers down at the frozen embryo. 'Auntie Maddy's here.'
The conversation in the corner was getting quite animated. Clearly Leighton had a passion for new-fangled things like steam ships and automobiles. And Liam was playing along nicely.
Well done, Liam.
She placed the glass tube back and closed the lid of the refrigerated case, lifting it out of the jewellery box and into her bag. She was about to close the lid of the jewellery box when she spotted a scrap of paper at the bottom. What she saw on it made her heart lurch.
Her name.
A note for me?
She reached in and picked it up. Just a folded scrap of paper, a few words scrawled hurriedly on it.
Maddy, look out for 'Pandora', we're running out of time. Be safe and tell no one.
'How're you doin', my dear sister?' called out Liam.
'I'm good,' she replied, grabbing the scrap of paper, balling it up and tucking it into one of her gloves. She closed the box and lifted it back into the locker, much lighter now. She closed the door. 'I'm all done here, Mr Leighton!'
'Ah, splendid!' He came over with his jangling keys and locked the deposit box for her.
'Everything all right?'
She glanced at Liam making a silly face at her over Leighton's shoulder.
'Yes... yes, just fine, thank you.'
A minute later they were exiting the bank on to Minna Street once more, Liam holding the bag for her.
'Nice enough chap,' he said.
She turned to look at him. 'A dozen hours from now he'll be dead.'
'Dead?'
'Yes, dead. That's why the instructions said to ask for him specifically.' She'd figured that out on the way back up the stairs. Because if anything happened, if the young man had caught a glimpse of anything inside the box, or heard either of them say anything suspicious... well, he'd hardly have time to do anything with that knowledge, would he? The agency once again cleverly covering its tracks.
'Jaayyzz. That seems not right to me,' uttered Liam. 'Not to warn him somehow.'
Maddy didn't like it either. 'It's how it is, Liam. It's how it is.'
As they walked up Minna Street towards the main thoroughfare, Liam attempted to lift the mood. 'You got our little babies?'
She nodded. 'All in there. Baby Popsicles.'
'Baby what?'
# CHAPTER 7
# 2015, Texas
Edward Chan and the rest of the touring party sat in the visitors' reception room, munching on doughnuts and breakfast bagels and slurping orange juice from cartons as their tour guide, Mr Kelly, gave them an introductory presentation.
'The Texas Advanced Energy Research Institute... or TERI, as we call it for short, was established three years ago in 2012 when President Obama was re-elected. As you youngsters have been taught in school, the world is entering a new, tough and very challenging time. The world's population is nearly eight billion, carbon emissions have gone off the chart, the world's traditional energy sources – oil and gas – are rapidly running out. We need to change the way we live or... well, I'm sure you've seen enough doom and gloom forecasts on the news.'
He paused. The reception room was silent except for the shuffling of one or two feet and the slurping of orange juice through straws.
'So, as you no doubt know, the institute was set up as part of the president's advanced energy research programme. And over the last three years we've used the billions of dollars of taxpayers' money set aside by this initiative to develop the wonderful facility you're visiting today.
'We have some of the finest quantum physicists and mathematicians working here, and most of our research work has been to do with a thing called zero-point energy. I'm sure some of you must have heard that term in the news.'
Edward looked around at the other kids. A few heads were nodding uncertainly. One of them – a boy a couple of years older than him, short and chubby with curly ginger hair parted at the side and brutally combed so that his hair kinked in waves to one side, reminding Edward of a Mr Whippy ice cream – raised a hand.
'Yes, er...?' said Mr Kelly, raising his eyebrows.
'Franklyn.'
'Go ahead, Franklyn.'
'My dad says zero-point energy is just a bunch of wishful thinking. It's like getting something for nothing. And that's impossible in physics, nothing's free.'
Kelly laughed. 'Well, Franklyn, that's a good point, but you see that's exactly what it is. It is a free lunch. And the idea that there's such a thing as a free lunch isn't a new one either. Remember Albert Einstein and his theory of relativity. Well, he argued that even in a complete vacuum there's a great deal left there. It isn't just empty space, there's energy too, endless energy waiting to be tapped. Even the ancient Greeks suspected that we walk through an endless soup of energy. They called it "ether". But the trick, kids... the trick has always been being able to isolate it, to measure it. Since it exists everywhere, it's homogenous, isotropic... That's to say it's uniformly the same everywhere and in every direction.'
The students stared at him in confused silence.
'Trying to measure zero-point energy is a bit like trying to weigh a glass of water under the ocean. You know? It's the same inside the cup as it is outside... and therefore since there's no measurable difference between what's in and outside the cup, the logical statement to make would be the "cup has nothing in it". Which would of course be wrong. So, we have a similar issue with measuring zero-point energy. Only by creating a proper vacuum – and I don't mean just sucking the air out of a space, I mean a proper space-time vacuum, a tiny one – can we observe what it is that remains.' He smiled his polished public relations smile. 'The energy itself.
'And that's what we have here at the TERI labs, a device that can create a proper space-time gap. A genuinely empty space.'
Another hand went up.
'Yes?'
'Keisha Jackson.'
'Go ahead, Keisha.'
'How big a hole have you got?' asked the girl. 'Is it big enough to step inside?'
'Good Lord, no! No. It's tiny. Very small. It doesn't need to be big. It's a pinprick.'
One of the boys at the back giggled.
'Shortly, we'll be going through into the main laboratory, where you'll see the containment shielding that surrounds the area of experimentation. I believe the team is due to be opening a pinhole vacuum in the next half-hour.' He splayed his hands. 'Wanna go take a look-see?'
Every head in the room wagged enthusiastically.
# CHAPTER 8
# 1906, San Francisco
They returned to their alleyway with half an hour to spare, having spent an hour on the dockside watching the steam ships being loaded and unloaded, Maddy relishing every little detail of the past and giggling with unbridled delight as dockside workers knuckled their foreheads and doffed their caps at her politely as they walked past.
'Oh my God! I feel like some sort of duchess!' she whispered out of the side of her mouth to Liam as they turned into the alley. 'Everyone's so... I dunno, so polite and proper back in this time.'
He nodded. 'Especially to a lady... like yourself.' He nodded at her dress, her flamboyant hat with its ostrich feathers. 'Them clothes mark you out as a lady of means. You know? A really posh lady, so you are. Now, if you'd found some dowdy dress that made you look common, them workers would've walked on past without a by-your-leave.'
'Oh, right... thanks,' she said.
Liam grimaced. 'Ahhh, now see that came out all wrong-sounding, so it did. I didn't mean to say it like that.'
'No, you're probably right,' she huffed. 'I've always been plain-looking. I'm sure shoving on a frilly dress and some stupid feather hat isn't going to make much of a difference.'
They walked down the alley, sidestepping a toppled crate of festering cabbages until they reached the spot where they'd materialized several hours earlier.
'Seems harsh that, though,' said Liam thoughtfully.
'What?'
'That fella back there, Leighton. You sure he'll die?'
She nodded. 'Yes... it makes sense.' Yes, it did. But it was the feel of... the feel of... ruthlessness that gnawed away at her; the agency seemed to know everything about everyone – and exploited that knowledge mercilessly. In less than eighteen hours the young man she'd been talking to would be nothing more than a twisted black carcass amid the smouldering remains of that bank.
And I have to learn to deal with that, she told herself.
Liam seemed to sense her turmoil. 'Well, this is the job now, Mads. We don't have much of a choice in the matter. Do we?'
She looked at him and realized it wasn't just the young bank teller that the agency was ruthlessly using, but Liam too. The side effects weren't apparent yet: the onset of cellular corruption, the onset of premature old age. But they'd begin to show at some point, wouldn't they? The more trips Liam was sent on into the past, the more damage it was going to do to his body, until, like Foster, one day he was going to be an old man before his time: his muscles wasted; his bones brittle, weakened and fragile; his organs irretrievably corrupted by the effects of time travel and one by one beginning to fail him.
She so wanted to tell him. To warn him.
How many more trips, Liam? How many before I'm looking at you and seeing a dying old man?
But she couldn't. Not yet. Foster had told her it would be unkind for him to know his fate too early.
'Let him enjoy the freedom of seeing history for a bit; seeing his future, his past... at least give him that for a while before you tell him he's dying.'
Liam smiled his lopsided smile. On the face of a grown man, it might have been called rakish, charming even. On him it looked just a little mischievous. 'You all right there, Maddy?'
'Yeah.' She nodded. 'Yeah... I'm fine.'
He let go of her arm and checked his timepiece. 'Return window any second now.'
Almost on cue, a gentle breeze whistled up the alley, sending the loose debris of rubbish skittering along the cobble-stones. A moment later, the air several yards from them shimmered like a heat haze: a ball of air twelve feet in diameter, hovering a foot off the ground. Through the portal she could just make out the twisting, undulating shapes of the archway beyond and Sal waiting impatiently for them.
You have to tell him, sometime, Maddy. Tell him time travel will slowly kill him.
She didn't like the fact that Foster had left the decision to her. Having secrets like that, having something she couldn't share with him or Sal.
And what about that note?
She could feel the lump of balled paper in her glove, something else she was being asked to keep from her friends. And why? And who was Pandora? She didn't like that... it felt like she was being used.
What? Like you just used that young bank teller?
'Come on, then,' said Liam, stepping forward with the jewellery case in his hands.
'Liam?'
He stopped. 'What?'
She could tell him about the note. She could also tell him about the damage time travel was silently wreaking on him. That every time he went back in time subtle corruption was occurring to every cell in his body, ageing him long before his time. She decided she'd want to know, to know that every time she'd stepped through a portal she was knocking perhaps five or ten years off her natural life. She'd want to at least be able to choose for herself whether she was prepared to make that sacrifice for the rest of mankind.
'What is it, Mads?'
Or maybe Foster was right – she should keep the truth from him for as long as possible...
She pulled her glasses out of her handbag and put them on, then took the silly bonnet off her head with its long, ridiculous ostrich feathers. All of a sudden, dressed in her tight corset and billowing lace skirts, she felt dishonest, a phoney, a fake and, her eyes meeting Liam's, she felt like a liar.
A worn-thin smile spread across her face. 'Nothing, Liam. Let's go home, eh?'
# CHAPTER 9
# 2001, New York
'Are you sure?' shouted Sal.
'That's what Bob says.' Maddy's voice echoed from the archway through the open door into the back room – 'the hatchery' as they called it now. 'He says to attach the end of the protein-feed pipe to the growth candidate's belly button.'
'How do we do that?' Liam replied. 'It's not like there's a socket to screw the thing into.' The small slimy foetus squirmed gently in his hand, stirring in its slumber. He grimaced as it did, feeling small fragile bones shift beneath its paper-thin skin.
It looked as vulnerable as a freshly hatched bird fallen from a nest, and yet he knew that this tiny, shifting, pale creature in the palm of his hand would soon be a seven-foot-tall leviathan, bulging with genetically enhanced muscles, with a deep, intimidating voice rumbling from a chest as broad as a beer barrel.
'Bob says you need to push the feed pipe through the belly button,' Maddy's voice came back.
Sal's lip curled. 'You mean... like... as if we're stabbing it?' she called out.
'Well, obviously don't stab it with the pipe!' Maddy's voice echoed back. 'Gently do it!'
Liam looked at Sal and shook his head. 'I can't do it. I'd be sick. Here...' He passed the foetus to Sal.
'Oh, right... thanks, Liam.'
Sal cradled the thing in her hand and then gingerly reached into the perspex growth tube beside them to retrieve the feed pipe dangling down inside. She grimaced as she fumbled in the slimy growth solution, finally pulling out the tip of the feed pipe. As the slime dripped like mucus from the end of it, she could see the pipe ended with a sharpened tip.
'Bob says you shouldn't have to push too hard. The belly button skin is very thin and should... Oh, that's just gross...' Maddy's voice faded away.
'What?' called out Liam. Maddy didn't answer immediately.
'Maddy?' chirped Sal. 'What's gross?'
'He says the skin should pop just like a blister.'
Liam looked sheepishly at Sal. 'Really, I can't do it. I'd be... I'll be sick over the poor little fella.'
'Shadd-yah,' Sal muttered, 'you are hopeless sometimes.'
She took the end of the pipe between her fingers and gently drew it up until it hovered an inch above the foetus's tiny belly: translucent skin criss-crossed with a faint spider's web of blue veins and a small inward twist of rubbery skin.
She took a deep breath. 'OK... here goes.'
She gently pressed the sharp end of the feed pipe into the small whirl of flesh. The foetus shuddered in her hand; finger-length arms and legs suddenly flailing, its walnut-sized head slapping against the palm of her hand.
'Uh... Maddy! It doesn't like it! It's struggling!'
'Bob says that's perfectly normal... just push it in until the skin pops.'
She heard Liam mutter something about Jesus before his legs buckled beneath him and he sat down heavily on the floor, then slid over on to his side.
'I think Liam's just fainted!' shouted Sal.
'Never mind him,' Maddy replied. 'We need to get the foetus hooked up before it starts starving.'
'OK, OK.'
She pushed the tip against the belly button again, this time pushing despite the foetus's protests, until she felt the skin give way, as promised, with a soft pop. A small trickle of dark blood oozed out on to its belly.
'It's in!'
'Right, now, put bonding tape round the pipe and its belly to hold it in place.'
Sal picked up a roll of tape and wound it round as the thing squirmed indignantly in her hand.
'OK. What next?'
'Just lower it into the growth tube.'
Sal stepped towards the plastic cylinder and lifted the foetus up over the open top. 'OK, Bob Junior,' she uttered. 'See you again in a little while.'
Gently she lowered the foetus into the murky gunk and then let it sink. It settled down through the pink soup, like a descending globule of wax in a lava lamp, until the feed pipe drew taut and it came to a rest.
'OK, he's in!'
'Now close the growth-tube lid and activate the system pump!'
Sal closed the tube's metal lid and clamped it in place. She squatted down to inspect the panel at the bottom of the tube. There wasn't much to see down there. A manufacturer's name – WG Systems – and a small touch screen. She tapped the screen and it lit up.
[Filtration system active]
[Set system to GROWTH or STASIS?]
'It's asking me to set it to growth or stasis... shall I pick growth?'
Maddy's answer echoed back from the archway a moment later. 'Growth for this one.'
Sal tapped GROWTH and confirmed the instruction. Immediately she heard the soft hum of a motor whirring to life somewhere at the bottom of the tube. A light winked on inside, making the pink protein glow and lighting the foggy form of the foetus from below. She could see its struggling form settle, content now that it was getting its feed despite the earlier discomfort of having the tube pushed into its belly.
'All done!'
'Good. Now we've got to do the same thing for the others. Only we'll be setting those to stasis.'
Sal looked down at the open case on the floor, and the other vials containing growth candidates. Then she looked at Liam, still out for the count, his face resting against the cold concrete floor amid a small pool of spittle and vomit.
'Great. Thanks for the help, Liam.'
'Blfff ifff wheeeelly gloob!' said Liam, his mouth full to bulging.
Both girls looked at him. 'What?'
Liam chewed vigorously for a moment, then finally swallowed. 'I said this is really good! What is it?'
'Lamb korma,' replied Sal. 'It's nothing like how Mum used to make it back home. You have it much sweeter over here. I suppose Americans like their food really sweet?'
Maddy nodded. 'Sweeter the better. I could live just on chocolate.' She reached across their table and pulled a carton of mango chutney out of the brown paper takeaway bag.
Liam hungrily loaded another forkful of korma into his mouth.
Across the archway, music streamed from the computer. Maddy had an Internet radio station playing music she remembered her parents listening to: the Corrs, REM, Counting Crows.
'It's kind of weird just us three, though,' said Sal. 'I miss Foster.'
'Me too,' said Maddy.
'We're never going to see him again, are we?'
She shrugged. 'Probably not. He had to go.'
'Why?' asked Liam.
She hesitated a moment. 'He was sick.'
'Yeah,' said Sal thoughtfully. 'He didn't look well.'
'What was wrong with him?'
Maddy played with the rice on her plate for a moment. 'Cancer. He was dying of cancer. He told me that.'
'Poor, poor fella,' sighed Liam. 'I really liked him. Reminded me a bit of my grandfather, so he did.'
They ate in silence for a moment.
'It's strange, though,' said Sal. 'We're part of this... this agency, but it doesn't feel like we're part of anything, if you know what I mean.'
'I know what you mean,' said Liam. 'Like it's just the three of us in this little archway all on our own. No contact with anyone else.' He looked up at Maddy. 'Did he not say there were other groups like us? Other field offices?'
She nodded. 'He did.'
'But we never ever hear from them. There's no information about them, or about this agency. No one has contacted us, right?'
'No one.'
Sal put down the poppadom she'd been holding. 'What if it really is just us, just us alone... here?'
The other two looked at her.
'What if we are the agency?' she added.
Liam's eyebrows arched and his jaw dropped open. 'God help us all if that's the case.'
Maddy shook her head. 'It's not just us. Someone else stashed those foetuses back in 1906, right?'
'Could that not have been Foster?'
'Could be.' Maddy shrugged. 'But then you've got to ask who genetically engineered the foetuses? That's gotta need other people, some facility somewhere.' The other two had no answer for that. 'Fact is,' she continued, 'there's more to this agency than just us. There are others out there somewhere or somewhen.'
'So how do we talk with them?' asked Sal. 'How can we meet them?'
'I think that's exactly the point. I think we're not supposed to.' Maddy slurped her Dr Pepper. 'Maybe we're a bit like some sort of terrorist organization; for all of our safety, no one group can know where another group is. We operate in isolation. It's just us... until...' Her words tailed off and they sat in silence for a while contemplating where that sentence ended.
'Not much chance of a big Christmas get-together, then?' muttered Liam.
Maddy snorted drink on to the table, relieved that he'd found a way to break the sombre mood.
'At least,' said Sal, 'we'll have a brand-new Bob to protect us soon.'
'Aye. I miss the big ape.'
Maddy pointed to the bank of computer monitors. 'He's just there!'
'Naw,' said Liam, wrinkling his nose, 'it's not quite the same him being in there.'
'You can't exactly hug a computer monitor,' said Sal.
Liam chuckled. 'Quite right. I miss his tufty round coconut head.'
'And that dumb, total blip-head expression on his face,' added Sal.
'Aye.'
Maddy finished a mouthful of curry. 'Well, we'll have him around soon. Foster's "how to" manual says the growth cycle should take about one hundred hours.' She pushed her glasses up her nose. 'Lemmesee... that's just over four days.'
'We'll need some new clothes for him,' said Sal. 'I'll see what I can find for him downtown tomorrow.'
Maddy nodded. 'Good idea.'
They finished the Indian takeaway and bagged up the rubbish. Liam volunteered to take it out as the girls changed for bed. He crossed the archway floor, criss-crossed with snaking power cables, and lifted the front shutter enough to duck under and step out into their backstreet.
A flickering blue light dimly lit the street. Above him, bright halogen floodlights illuminated the thick metal spars of the Williamsburg Bridge arcing across the flat docile water of the Hudson River. On the far side – a sight he was still yet to get used to – was Manhattan, a vibrant inverted crystal chandelier of winking city lights and nudging traffic.
He dropped the bag into the trash can, and sucked in the cool night air.
Tonight all was well with the world. Tomorrow was the day planes crashed into buildings and the sky was a dark smudge all of the day.
He hated the Tuesdays.
'Good night, New York,' he uttered under his breath.
The city replied with the rumble of a train along the bridge overhead and the echoing, distant wail of a police siren racing through a Brooklyn street several blocks away. As he prepared to duck back inside and wind the shutter down once more, he found himself wondering if Sal was right. If they really were alone. If the agency was, in fact, just them.
As it happened, the answer to that specific question was to arrive the very next morning.
# CHAPTER 10
# 2001, New York
Maddy was entirely engrossed in Big Brother USA when Bob interrupted. She'd been watching Nicole and Hardy quietly plotting together in the kitchen against the other two. It was a rerun of the previous week's shows on FOX and she already knew who was facing imminent eviction. She'd seen this show at least four times already, but for some reason, despite knowing the outcome, it was still compulsive viewing.
So it was with mild irritation that she answered the dialogue box that had popped up on the monitor over the top of Big Brother.
> Maddy?
She sat forward and spoke into the desk mic rather than tap out an answer on the keyboard.
'What is it, Bob? I'm watching Big Brother right now.'
> I am picking up incoming tachyon particles.
Her mouth dropped open and she dribbled milk and Rice Krispies on to her T-shirt.
'You're kidding me, right?'
> Kidding?
'Joking.'
> Not joking, Maddy. There is a directed communication beam coming in from down-time.
'From down-time... You mean the future?'
> Affirmative.
Maddy dropped her spoon back in the breakfast bowl and sat back in her chair. She looked around. Liam was still fast asleep on his bunk and Sal was out clothes shopping for Bob.
Oh my God... a message from the future?
She realized then and there that it could only be from the agency – their first contact with the rest of the organization – and just when they were really beginning to wonder whether the three of them were all on their own.
'What's the message, Bob?'
> Just a moment... just a moment. Decoding...
Sal had decided not to bother going uptown, over the bridge into Manhattan. The clothes shops there were all modern chain stores and none of them were likely to have much that would fit a seven-foot mountain of muscle.
Instead she headed into Brooklyn, an area she hadn't explored at all thus far. Foster had been so very keen on her focusing her attentive eyes on Manhattan and Times Square – taking in every tiny detail until she knew everything that was meant to be there, every tiny event that was meant to happen – that she'd had no time to explore the city this side of the Hudson River.
Away from the bridge and South 6th Street, she found myriad quieter backstreets, and one in particular lined with odd little boutiques selling second-hand furniture and dusty old books. The chaos of goods piled outside the storefronts and cluttering the narrow street reminded her vaguely of the market-place near her home in Mumbai.
She found herself wiping a solitary tear from her cheek and chided herself for crying for her parents... because – stupid – they weren't dead. The grim fate that awaited them wasn't going to happen for another twenty-five years. At this moment in time, her mum and dad were just kids her age, enjoying their childhood and not due to meet for another decade yet. Strange, that. Stood side by side, she and her mum could probably pass as sisters.
Her attention was drawn to a shop with a curious mix of antique knick-knacks spilling out of its entrance and on to the pavement. Ancient-looking wooden furniture, a rocking-horse and clothes that looked like surplus theatrical costumes. But among them, bric-a-brac, a second-hand TV set, a toaster, a Dyson vacuum cleaner. A little bit of everything, it seemed.
She figured she had as much chance of finding something here that might fit Bob as she might anywhere else and, anyway, everything here appeared to be pretty cheap. She stepped inside the boutique and squeezed through the front of the store, cluttered with a set of chrome bar stools and several flaking display-window mannequins wearing dodgy-looking leather corsets and feather boas.
'May I help you, young lady?'
The voice seemed to come out of nowhere and she jumped. Then she spotted a tiny old lady with jet-black hair who was even shorter than she was.
'I, uh... You made me jump.'
She smiled. 'I'm sorry, my dear. I do tend to blend into the store.'
Sal laughed. She could imagine a customer slapping ten dollars down on the counter for the 'realistic old lady mannequin', tucking her under one arm and walking out with her.
'What are you after, my dear?'
'You have a clothes section?'
She waved an arm. 'At the back. I have racks and racks of old, old clothes and party costumes. Lots of cast-outs from the Broadway theatres and a few antique items too.'
'Thank you.'
Sal weaved her way further into the store, her nose tickled and teased by the dust that seemed to be on everything and the faint smell of mothballs and turpentine. She found the clothes racks at the back and almost found herself giggling at the bizarre mix of garments on display. She flicked through the racks in front of her, chuckling at some of the exotic costumes and cooing appreciatively at others. Eventually she found some things that looked suitable for Bob: a baggy pair of striped trousers with extra-long legs that she suspected might have been part of a clown's outfit at one time and an extra-large bright orange and pink Hawaiian shirt that looked like it might just about fit over the top of his broad shoulders and rippling muscles.
'You must have a very big friend,' said the old lady as she took Sal's payment and folded the clothes into a plastic bag for her.
'Uncle,' she replied. 'My Uncle Bob. He's a very big man.' Sal was about to add that he was also pretty dumb as well – dumb, and kind of child-like – when she spotted something dangling from a hanger on one wall: a white tunic, buttoned down the left side, with an emblem on the chest that she recognized – the White Star lines. It was a steward's tunic just like Liam's.
She pointed at it. 'Is that... is that a uniform from the Titanic?'
The old woman looked round at where she was pointing. 'Oh, that? No, it would be worth a lot more if it was genuine. I could sell it to a museum or a collector for thousands of dollars. Unfortunately it's not; it's just a theatre costume. Not a very well-made costume either. Friends of mine... they did a production set on the Titanic. It didn't do very well. You want to have a look at it?'
Sal shook her head. She could've said something about it being a funny coincidence that her bunk-buddy was a young lad who'd actually worked on the ship for real. The old lady would think her mad, of course, or that she was just being cheeky. Mind you, in just over half an hour's time, when the first plane hit the Twin Towers, whatever odd conversation she might have now would be instantly forgotten.
Sal returned to the archway with Bob's clothes and some groceries before the first plane hit and the Manhattan sky started to fill with smoke. She was about to mention the coincidence to Liam – the steward's tunic exactly like his – when she realized by the expressions on Maddy's and Liam's faces that something important had just happened.
She forgot all about it.
# CHAPTER 11
# 2001, New York
'It's a message from the agency,' said Liam as Sal joined them beside the computer desk. 'From the future.'
'So.' Sal looked at them both. 'There's our answer. We're not alone, then.'
'Yup!' replied Maddy, grinning, clearly the most encouraged and excited by that news. 'Bob's decoding the message right now. He's estimated the year of origin to be about 2056. That's the time of Roald Waldstein, the inventor of time-travel technology.'
'Do you think it's him? The Waldstein fella?' asked Liam.
Maddy reached for her inhaler on the desk and took a quick puff on it. 'Yes,' she replied. 'Hopefully it's the agency checking in with us. You know? Seeing if we're OK. Which would be nice.'
'But how...' started Liam, frowning. 'But how will we talk back to them? These tachyon signal things can only go backwards in time, right? That's what Foster said.'
'He said that... but he was keeping it simple. It takes a lot more energy to project forward. Plus, more importantly, in 2056, everyone's on the lookout for tachyon particles, right, Bob?'
> Correct. A signal aimed at the agency could be detected and reveal its location. In 2056, international laws against time travel have been established.
'In any case, I wouldn't know which direction to point a signal,' said Maddy. 'Who knows where in the world they're based?'
'So is there a way to talk back?' asked Liam.
Maddy nodded. 'Yup... there is.' There was an entry in Foster's 'how to' guide on how to contact the agency, a short explanation by Foster looking ten years younger as he spoke to the webcam. An entry he must have recorded much earlier than the others.
'It's the same principle, Liam, that you used actually,' said Maddy. 'The museum guest book, remember? Only it's a New York newspaper. We place an advert in the lonely hearts section of the Brooklyn Daily Eagle. It has to begin with the phrase "a soul lost in time..."'
Liam clicked his fingers; he understood the rest. 'And I suppose they have a crinkly old yellowing copy of that paper?'
'Dated September twelfth, 2001. That's right.'
Sal looked from one to the other, her eyes widening. 'And... and do you mean the words in the paper change? They actually change on the page?'
Maddy nodded. 'It's a tiny ripple in time. Nothing that would change anything else. After all... who's going to be reading the lonely hearts section of the papers tomorrow?'
'The papers would be full of that plane-crashing-into-building story, will they not?' said Liam.
'Exactly. Our little advert won't be noticed by anyone, except, of course... a bunch of people carefully studying a page of a fifty-five-year-old newspaper in 2056, or thereabouts.' Maddy clucked with excitement. 'I can't tell you how freakin' relieved I am that there's somebody else out there!'
Liam nodded at the screen in front of her. 'Looks like Bob's done.'
> I have decoded the message, Maddy.
'What is it?'
> It is only a partial message. The signal has been interrupted.
'Uh? OK... give us what you've got, Bob.'
Words spooled across the dialogue box:
> Contamination event. Origin time appears to be 10.17 a.m. 18 August 2015. Major contamination ripples. Significant realignment of time stream. Death of Edward Chan, author of original theory on time travel, resulting in failure to write thesis in 2029. Death may have been deliberate assassination attempt. Occurred while visiting Instit–
The three of them waited for a moment for Bob to print out more of the message.
> That is all I have. The partial ends there.
'That's it?'
> That is it, Maddy.
She turned to look at the others. 'Er... what the hell are we supposed to make of that?'
They sat in silence for a while, digesting the small block of text on the screen. Finally Liam shrugged. 'That they're in trouble?'
'Well, duh,' sighed Maddy.
'They need our help?' said Sal.
'But can we help, though?' said Liam. 'Can I go into the future?'
'Of course you can.' Maddy pinched the tip of her nose thoughtfully. 'Think about it. Every time we bring you back from a mission in the past, you're going forward in time, aren't you?'
> This is correct. A mission operative can travel forward and backwards. However, energy expenditure is significantly higher moving forward.
Sal looked at the other two. 'But maybe there are other field offices further in the future than us who will deal with this?'
Liam nodded. 'She's right. If we're not the only team, then perhaps somebody else is closer in time?'
Maddy gave it a moment's thought. 'Then why direct the message right at us? I mean... right here, right now?' She turned back to the desk. 'Bob, was this a broad-spectrum signal beam, sent out for everybody to pick up... anywhere... anywhen?'
> Negative. It was a narrow, focused beam.
'Meaning it was meant for us?'
> That is the logical assumption, Maddy.
'But surely there are other teams in the future,' said Sal. 'Somebody closer in time and –'
'Maybe there are,' cut in Maddy, 'but any field office based after –' she looked at the screen – 'after the eighteenth of August 2015 is going to be affected by the time wave also, right?' She stared at the other two. 'So maybe we're the closest unaffected team? Maybe we're the field office closest before this date?'
Liam sighed. 'Aw, come on. Why is it us again? We only just got ourselves fixed up after the last bleedin' mess and a half.'
> Hello, Liam. I have a question.
'Good mornin', Bob.'
> Is 'bleedin'' a reference to the high body count of the last mission including the extensive damage to my last organic support frame? Or is it an expression of anger I should add to my language database?
'It's Liam being all stressy,' said Maddy.
> Angry?
'That's right.'
Once again they stared in silence at the partial message displayed on the screen, all of them silently hoping it would just go away or change into another message simply welcoming them to the agency.
'It's for us, isn't it?' said Sal after a while. 'We've got to fix this time problem like we did the last one.'
Maddy nodded. 'I think so.'
Liam's jaw set firmly. 'Well, I'm not going anywhere 'less I've got Bob coming with me. I mean that, so I do.'
'OK,' said Maddy. 'That's only fair.' She turned round to face the computer monitors. 'Bob, can we speed up the growth cycle of the foetus we've started off?'
> Affirmative. Increase the nutrient mix of the feed solution. Introduce a small electrical charge to the suspension fluid to stimulate cell activity.
'How quickly can we have a body ready for you?'
> Growth cycle can be increased by 100% with acceptable risk to the biological life form.
'Half the time,' said Maddy. 'That's still... what? Thirty-eight hours?'
> Correct.
'Could we not birth the clone any earlier?' added Liam. He looked at Maddy and shrugged. 'I mean, does it need to be a fully grown man?'
> Optimal age for organic support unit is approximately 25 years old. Muscle tissue and internal healing systems are at their most functional.
'But, as Liam says, could we eject the clone from the tube at a younger age? Or would that... I dunno, kill it?'
> Negative. A growth candidate can be functional from approximate age of 14 onwards. However, the support unit's effectiveness would be compromised.
'What does that mean?' asked Liam.
'It means Bob won't be quite as big a brute as he was last time,' said Sal.
'So... what if we birth the clone at say... about eighteen years of age,' asked Maddy. 'How useful would he be?'
> An eighteen-year-old clone would offer approximately 50% of normal operational capacity.
'He'd be half as strong?' said Liam.
Maddy nodded. 'And how much time would that save us off the growth cycle?'
> 14 hours.
She looked round at the others. 'What do you reckon?'
'We speed up the growing process and then empty him out on to the floor twenty-four hours from now?' said Liam. 'And we'll have an eighteen-year-old Bob, with half the muscles?'
'That's about it.'
'But he'll still be dangerous to other people, right? I mean... doesn't make any sense me having him by my side if he's just –'
> Affirmative, Liam. I will be capable of causing death with or without weapons.
Liam managed a weak smile. 'Then I guess it'd be good to have you back, Bob.'
> Thank you. I look forward to being fully operational again.
Maddy slapped her hand on the desk. 'Right, then. I guess we have a plan of action. Since we've got no time to waste, Sal, could you go see to the growth candidate? Let's get that process sped up.'
'OK.'
'And I guess I better start gathering all the data I can on this Edward Chan guy,' she said, pecking at the computer's keyboard.
'What about me?' asked Liam.
Maddy tapped her fingers absentmindedly on the desk. 'Er... hell, I don't know.'
'I suppose I'm coffee-maker?'
She smiled. 'If you're doing a run to Starbucks, can you grab me a chocolate-chip muffin as well?'
'Yeah, me too,' called Sal from the back room's doorway.
# CHAPTER 12
# 2001, New York
'So, this is what I've got,' said Maddy, producing several sheets of computer printout.
This evening the Kentucky Fried Chicken restaurant's eating area was deserted apart from them. Brooklyn's streets were quiet, everyone back home now that the last light of the evening had gone. All home, watching the news on their TV sets. Today's sky had been divided all day by the thick column of black smoke from the collapsed Twin Towers, and New Yorkers were emerging from the fog of shock and dismay at the day's events to a mood of contemplation and mourning.
They were lucky to find even this place open. Only a couple of staff seemed to be on, and they were busy half the time watching the news updates on a small TV set up right on the counter.
'Edward Chan, as you guys will remember Foster telling us, is this bright young maths kid who went to the University of Texas. He graduated there, then went on to do some post-grad work.'
'What is that... what's post-grad?'
'It's just more studying, Liam. The kind of studying where you tell your teachers what specific area you intend researching, and they just check in with your work every now and then, and help out if they can.
'So anyway,' she continued, looking down at the printouts and reading, 'at the university he sets out to do a research paper on zero-point energy.'
'And what's that?'
'Jeez, Liam... are you going to keep stopping me to ask what stuff is?'
He looked hurt. 'I've got to learn all these modern words, right? I mean, I'm still really just a lad from Cork who's running to catch up on the last century, so I am.'
Maddy sighed. 'It's sort of like energy that's supposed to exist at a sub-atomic level. It was still just theoretical mumbo... jumbo in my time.'
'I think they started building something to do with that in India in my time,' said Sal. 'Experimental reactor or something, because we were running out of oil and stuff.'
Maddy scooped up some fries from her box. 'Anyway, if I can continue, Liam? Chan set out to do a paper on zero-point energy and ended up changing course. Instead he wrote a paper on the theoretical possibility of time travel. The main point he was making in his work was that the theoretical energy that was assumed to be there in normal space-time, the sub-atomic energy-soup that was meant to be everywhere, was in fact a form of "leakage" from other dimensions. He writes this science paper and does nothing else notable until his death from cancer a few years later at the age of twenty-seven.'
'So, like Foster told us,' said Liam, 'this Chan lad is the true inventor of time travel, not the Waldstein fella?'
'Well, he did the theoretical work that led to Waldstein's machine, so I guess they're both responsible for inventing it.'
'The message from the agency said he'd been assassinated,' said Sal.
Maddy nodded. 'Which means... what?' She looked at both of them. 'I'm guessing it means someone is trying to prevent time travel being invented?'
Liam reached for a ketchup sachet. 'So... hold on. Isn't that what the Waldstein fella wanted in the first place? To make sure time travel never got invented. Isn't that why this agency thing exists, why the three of us're here instead of dead?'
'So why would the agency want us to save Chan?' asked Sal. 'I mean... no Chan means no time travel, right? That means no more time problems.'
'S'right.' Liam raised a finger. 'The message didn't actually tell us to save him.'
Maddy leaned forward. 'It was an incomplete message. Maybe that's the bit we missed at the end?'
'But we don't know that for sure,' replied Sal. 'Maybe it was someone from the future letting us know that time up ahead was changing and that there was now no more need for the agency... for us?'
Maddy shook her head and pointed to the message printed out on paper. 'Look... it begins with "contamination event". I'd say that suggests they considered this to be a bad thing. And they're not too happy about it.'
They were silent for a moment, all three of them staring at the printed words on the page, trying to determine the intent of the message.
'Foster was very, very specific about this,' said Maddy after a while. 'History must go a certain way, for good or bad. Even if the history yet to happen features some kid called Chan who makes time travel possible... that's the way it has to be. And if it changes from that, the agency has to fix it.'
Liam nodded after a few moments. 'I suppose you're right. So... do we know where his death is going to happen?'
'The date in the message is August eighteenth. In our database it mentions Chan was one of a class of high-school students who were on a field trip to the Texas Advanced Energy Research Institute, on this date. This is biographical data on Chan taken from 2056. If this really is an assassination attempt by somebody, the chances are they have access to the same data as us. In other words, they looked at Chan's biography and noted he was going to be at a particular place at a particular time...'
'And sent themselves back in time to be there waiting with a gun,' added Liam.
Maddy nodded. 'Yup.'
'Well...' Liam bit his lip anxiously. 'You can see now why I'm so bleedin' keen to have big ol' Bob by my side. Seems these bad guys have got guns with them and Bob's a dab hand at dealing with people like that, so he is.'
Maddy glanced at her watch. 'We should probably get back to the arch. The time bubble is due to flip over in a few hours and we could all do with some rest. Bob's new body should be ready to birth tomorrow morning and then we'll be ready to send you guys forward in time to see what's what.'
Liam sighed. 'Back in that ol' bathtub for me.'
# CHAPTER 13
# 2001, New York
Sal stared at the curled-up form in the growth tube in stunned silence for a good minute before she finally gasped. 'Oh no.'
By the dim red light of the back room and the peach-coloured glow of the tube's interior up-light she could see they'd really messed up with growing Bob's body. Well, actually... it looked like she alone had messed things up.
They're going to be mad at me.
Maddy's voice echoed through the open door into the back room. 'How's he looking?'
Sal didn't know what to say. So she said nothing.
'Everything OK in there?'
They've got to find out sometime.
'Uhh... no. Not really,' she replied.
'What's the matter?' Maddy's head appeared in the doorway, squinting into the gloom of the hatchery. 'Sal? What's up?'
'It's uh... it's Bob...' she said.
'Oh God, what now? It's not a mis-growth, is it? We can't afford to start off another one.'
Sal had caught a glimpse of the few mis-growths that had been floating in the tubes back here not long after Foster had recruited them; they'd looked like awful freakshow specimens in some carnival tent, contorted, with faces like gargoyles and demons and limbs twisted into impossible claw-like stumps. She thanked God it wasn't something like that.
'No, it's grown just fine... it's just...'
Maddy took a cautious step into the hatchery, her eyes yet to adjust to the dim red lighting. 'Well, it looks OK from here. Two arms, two legs... nothing weird and gross sticking out,' she said.
Sal studied the adult-sized form floating in the murky pink soup. 'I think I must have put the wrong foetus in or something,' she uttered.
Maddy took a few steps across the floor, careful not to hook her foot in a power cable and pull over one of the other tubes holding the other tiny foetuses in stasis.
'Come on, Sal, what's the prob–' Maddy's voice tailed away as she stood beside her. 'Oh,' she whispered. 'I see now.'
Sal bit her lip. 'I... I must have... I'm sorry. I didn't check it first. I... just didn't see.'
Maddy looked at her. 'You didn't see?'
'They all looked the same!' Sal replied, her voice rising in pitch. 'Look, I'm sorry!'
'Oh, that's just great, Sal. Just great! Now what are we going to do!'
'I'm sorry, OK? Sorry. I didn't see. I just –'
'Sorry... is that it? Sorry doesn't help us. There's no time to grow another one!'
Liam stepped into the back room. 'Hey! Ladies, ladies! Whatever is the matter?'
'Well, why don't you come and look for yourself,' snapped Maddy irritably.
Liam made his way cautiously forward until he was standing between them.
'Meet your new support unit,' she added sarcastically.
Liam frowned at the dim outline in the tube, then suddenly his eyebrows shot up into twin arches. 'It's a... it's a... it's a...'
'Girl,' said Sal helpfully.
'Oh Jay-zus-'n'-Mother-Mary... I never knew we got baby boys and girls.'
Maddy reached down to the floor and picked up one of the empty glass containers the foetuses had come in. She held it close to the growth tube to take advantage of some of the softly glowing light coming from within.
'There,' she said after a while, her finger pointing at a small marking at the bottom of the glass.
Sal leaned closer, screwing her eyes up to see it better in the dim light.
'It says XX... that's all. What's that supposed to mean?'
Maddy tutted and shook her head. 'You don't know?'
'No.'
Liam shrugged. 'Me neither,' he said, his eyes still locked on the naked female form inside the tube.
'It means female. And XY means male. You guys can be real morons! It's to do with the chromosomes.'
Liam managed to drag his eyes away. 'Cromer-what-a-ma-jinxie?'
Frustrated, Maddy banged the perspex tube with the palm of her hand. 'Doesn't matter. I'll explain another time. The point is what are we gonna do?'
'If we start another one off, it'll be at least another thirty-six hours before we can send someone to investigate the Chan thing,' said Sal.
'That's my point!' replied Maddy, removing her glasses and rubbing her eyes. 'The message sounded urgent. Right? God knows what damage is happening to the timeline ahead of us right now!'
'We don't have much choice,' replied Sal. 'Unless...'
Maddy nodded. 'Unless you go check it out on your own, Liam.'
Liam looked at them both. 'You're joking, right?'
Neither said anything.
'Right,' he replied. 'Well, the answer is... not on your nelly! No way! No sir! I'm not going into some spangly future place without a Bob –' he looked again at the female form inside the tube – 'or a Roberta by my side. It's been hard enough for me trying to get my head around 2001 and all your crazy modern ways. There's no way that I'm doing 2015 all on my own, I'm tellin' you.'
Maddy sighed. 'All right, then.' She looked at the shape floating in the goo. 'That thing may not have the brute strength of the last one, but at least you'd have Bob's AI and database along with you.' Maddy turned to him. 'And this is just a scouting mission anyway. Just a quick visit to see what happened to Chan.'
Liam's face hardened. 'That's what Foster said to me the last time... and look what happened. I got stuck in the middle of an invasion for six months.'
Maddy reached a hand out and touched his arm. 'Well, this time we'll just be more cautious.'
He chewed his lip in thought for a moment, then finally nodded. 'Jeez... all right. I suppose if it's just a quick look-see.'
Maddy gently slapped his shoulder. 'Good. Sal?'
'Yes?'
'Let's birth it.'
'OK.'
Sal squatted down on her haunches to tap the command into the small control panel at the bottom of the cylinder.
'Er... Liam?' said Maddy.
'Yes?'
'Would you mind?'
'Mind? Mind what?'
'A little privacy?'
'Uh?'
Maddy sighed. 'It may just be a mindless blubbering clone right now... but it's still a lady.'
Liam was still sulking at being kicked out of the back room when the metal door to the hatchery finally slid to one side with a shrill squeak of un-oiled rollers. Maddy and Sal emerged through the doorway first, beaming like a pair of proud midwives. They ushered a pale shuffling form wrapped in a long towel out into the light of the main arch.
Liam studied her; she was taller than the other two and, of course, as Bob had first been when he'd been dumped out of the bottom of his tube, she was completely bald. Yet, despite that, he realized she was – and he felt a little queasy admitting this to himself – quite beautiful.
'Uh... hello,' he said awkwardly.
The clone stared at him curiously as the girls led her across the arch towards the table and armchairs. Her pale skin glistened, wet with the goo she'd been floating in only moments ago, and the smell – like a rancid meat stew – wafted across to him, turning his stomach.
'Hello there,' said Liam again as they sat her down opposite him.
'Flug herr gufff slurb,' the clone replied, dark brown slime dribbling out of the side of her mouth and down her chin.
'Right,' said Maddy to Liam. 'You can get acquainted while I sort out uploading Bob's AI.'
He nodded, his eyes still locked on the clone. She seemed to have little of the bulging musculature of Bob... athletic, though, not bulky like he'd been last time.
Bob.
Bob? Liam, you idiot.
He realized that it was stupid to think of that first ape-like clone as Bob; it had merely been the organic vehicle that Bob's AI code had first used. But still, he mused, Bob's 'personality' – if he could actually use that word – had been formed inside that big brute. It was almost impossible not to think of him as a big, clumsy, Panzer tank of a man, with fuzzy coconut hair and a voice as deep and rumbling as one of the trains that regularly rattled over the Williamsburg Bridge above them.
During the six months he'd been stuck in the past with him he'd grown attached to the big lumbering ape; not just the code in his head, but that expressionless vapid face of his, those horribly awkward smiles – more like a horse baring its teeth. He'd even cried when those men had gunned Bob down, riddling him with enough bullets to ensure that even his robust body had no hope of recovery. Cried as Bob had 'died' in his arms and he'd had to perform an act of surgery that since then he'd done his very best to blank from his memory.
Cried for Bob, although he'd never admit that to the others because it seemed silly. All that made Bob Bob had survived, had come back from the past in his blood-covered hand: a wafer of silicon containing his AI, every memory he had, all the learning, all the adapting, all the growing up he'd done in those six months in the past. That was Bob, not the tattered bullet-riddled corpse he'd left behind in the blood-spattered snow of 1941.
Liam looked again at the young... woman... in front of him: lean and athletic, a porcelain beauty to her face.
Her? HER? It's an IT, Liam. IT... get it? Not a 'her'. Just an organic vehicle. A meat robot.
Almost as if the clone could read his mind, it drooled another long spittle string of gunk out of the side of its mouth and grunted something unintelligible.
Sal giggled. 'So like Bob, isn't she? She could be his twin sister.'
Maddy returned from the desk to sit beside the female clone. 'OK, Bob's preparing the download protocols. He needs to handshake with this support unit's in-built operating system before he can upload a copy of his AI into it.'
'Uh... how does Bob get into her... its head?' asked Liam. 'Don't you need some sort of a cable or something?'
'Bluetooth,' she replied wearily. 'Yes, I know, that means nothing to you.' She sighed. 'OK. It's a broadband wireless data communication protocol designed for low-latency short-distance transmission.' Liam was still staring at her, slack-jawed and bemused. Maddy sighed again. 'Information will fly through the air from the computer and into its head.'
'Oh... right.' Liam smiled. 'Why didn't you just say that in the first place?'
They heard a beep coming from the computer desk.
'Uploading is starting now,' said Maddy.
The clone sitting opposite Liam suddenly jerked upright and cocked her head like a dog hearing a dog-whistle.
He watched with fascination as the support unit's eyes blinked rapidly with the data flooding into the tiny computer system built into the middle of its cranium – computer technology that came from the 2050s, technology immensely more powerful than their array of linked PCs beneath the computer desk.
The download of information took about ten minutes, then finally the female clone closed her eyes.
'Installing,' explained Maddy. 'Then it will boot up again.'
After a few moments the clone looked up at them with eyes that now seemed to faintly glint with intelligence.
'Bob?' said Maddy, 'you OK?'
The clone nodded awkwardly. 'Affirmative.' The voice was a deep growl, almost as deep as Bob's old voice had been.
'Jay-zus!' Liam lurched. 'That's... weird.'
Sal pulled a face. 'Ewww... jahulla! That's just so-o-o wrong!'
'I will adjust the vocal register,' Bob's barrel-deep voice rumbled. The support unit cocked its head then spoke again. 'Is this better?' The voice now the smooth upper-register of a teenage girl's.
Maddy nodded. 'Much better. I think we can safely say you're not an it... you're a she now.'
Liam shook his head as he studied it... him... her... Bob. 'I feel very strange about this,' he finally muttered. 'Very strange indeed.'
# CHAPTER 14
# 2001, New York
'Now, she's had all the biographical information about Edward Chan and details of the layout of the Texas Advanced Energy Research Institute uploaded. Isn't that right?'
The support unit nodded as she lowered herself into the water beside Liam, wearing underwear that Maddy had self-consciously pulled out from beneath the sheets of her bunk and donated.
'Affirmative. I have all the data required for this mission,' the support unit replied sweetly.
Liam shook his head. 'This is so weird. I mean... it's great to have you back an' all, Bob, but you're a... you're a...' His glance flickered involuntarily for a moment towards the clone's chest. He clasped his eyes shut. 'Oh Jeez... you're a girl, so you are!'
'Recommendation: suggest this copy of my AI be given an appropriate unique identifier.'
Maddy, sitting on the top step and looking down at them in the water, nodded. 'That's right. You can't go round calling her Bob.'
'Additional information: although the AI in my computer is a direct duplication, I am now interfaced with a different organic brain, and during the operational lifespan of this organic support frame, different data will result in a different emergent AI.'
Liam looked up at Maddy. 'What did she... it... Bob just say?'
'That you should think of this support unit as someone brand new. As a different team member... because she's going to develop a different personality. That's right, isn't it?'
The support unit nodded. 'Affirmative. Consequently this AI should have its own identifying label.'
'She needs a new name to avoid confusion with Bob,' added Maddy, nodding towards the bank of monitors and computers on the desk. 'Remember, Bob's still in there.' She grinned. 'You're best thinking of this support unit as... I dunno... his sister.'
Liam looked at the clone treading water beside him. She tried one of Bob's reassuring horse smiles – just as clumsy and ill-fitting as her... brother. But, somehow, more appealing on her slim face.
'Liam,' she said softly, 'please give me a name.'
'Go on,' said Maddy. 'It's your turn.'
He shook his head. 'I... don't know.'
'OK, you think about it.' She called across the archway to Sal. 'What's the countdown?'
'Fifty seconds!'
She handed them a couple of sealed plastic bags. 'Clothes for you in there. And a wig for her. Now, you'll arrive at the institute just as a class of thirty children are being given a tour of the place. I've checked the floor plans and picked out what looks like an equipment storage room near to the institute's main experimental chamber. That's where we'll send you. You can dry off and change in there, then join the school party.'
Liam nodded.
'You'll be there to observe how Edward Chan is assassinated, OK? Not to stop it... just watch. Then we'll bring you back, you can tell us what happened, then we can work on what we need to do to prevent it happening. That's the plan. Got it?'
'Aye. And the return window?'
'Is set for ten minutes after Edward Chan's time of death. The usual failed-return protocols apply – if you miss that first window, we'll open again an hour later... you know how it goes.'
'An hour later, a day later, a week later.'
'That's it.'
'Thirty seconds!' called out Sal.
'You OK, Liam?' said Maddy softly.
He nodded, his teeth beginning to chatter with the cold.
'Come back safely,' she said affectionately, patting his hand holding the side of the tube. She got to her feet and clanked down the steps beside the tube.
'Ten seconds!'
Liam turned to look at the support unit treading water beside him. 'Hey... I've got a name for you.'
'Insufficient time, Liam,' she replied. 'We have to go under the water now.'
Reluctantly he nodded, sucked in a big lungful of air, let go of the side and held his nose. The support unit gently rested a hand on top of his head and shoved him under with surprising force, then ducked beneath the water herself.
# CHAPTER 15
# 2015, Texas
He watched Edward Chan walking ahead of him with the other kids. He looked so small among the other high-school-age kids, so small and so vulnerable with his high-school rucksack on his back and a yellow T-shirt two sizes too big for him.
Yes. Yes, he does... but don't forget who this boy is. Just how dangerous he is.
Howard Goodall gritted his teeth with renewed determination. Ahead of him, just a dozen yards away, was the legendary Edward Chan, grandfather of time-travel technology. His mind reiterated an inescapable mantra.
The boy has to die. The boy has to die.
Too many of his colleagues had been arrested to get him to this place, this time, close enough to kill Chan. He could feel the weight in his own rucksack – a red one with High School Musical 4 stencilled in cheerful pink across it. He could feel the weight of responsibility in there and the miniature carbon-fibre projectile weapon hidden inside an innocent-looking camping flask, the cheap plastic kind you can pick up from Wal-Mart for five dollars.
The institute's guide eased his way through the shuffling trail of students to the front where he stopped, turned round and raised his hands to get everyone's attention.
'OK, now that you guys have all had some refreshments and you've had a little introduction to the theory behind zero-point energy, we're going to be heading into the business part of this facility: the experimental reactor building. Before we go inside there's one more security check –'
Thirty students moaned in unison.
'Sorry, kids,' he laughed. 'I'm afraid it's procedure, so if you'd all just open your rucksacks and school bags one last time for our security guards to get a quick look-see inside, then we can proceed.'
Third time. Howard did his best to look just as casual and irritated at the hassle as all the other kids. He unzipped his rucksack and held it open for a cursory glance. If the guard bothered to unscrew the drinking cap of the camping flask, he'd find the small weapon, which was roughly the size and shape of a whiteboard marker.
Howard watched the guard work his way down the line of impatient children.
But he won't unscrew it... because, Howard, you're going to look just as bored as all these other kids. Bored and impatient to get on with the tour. And not nervous. Not scared.
Howard was the one in their group they'd selected to do the job. Although he was twenty-three he looked young, young enough to pass as a high-school student, a few tufts of downy hair on his upper lip suggested a boy desperate to grow his first moustache. His dark wavy hair pulled back into a scruffy ponytail, his thrash-metal Arch-NME On Tour T-shirt, took six or seven years off him. Now, he no longer looked like Howard Goodall, a mathematics graduate from the year 2059, but Leonard Baumgardner – some grungy high-school kid who'd managed to earn a set of top scores in his SATs.
The real Lenny was back home in his basement, bound and gagged along with his mom. Howard had briefly considered killing them both, worried they might struggle free and raise the alarm. But he figured this was all going to be done before that could happen.
He looked close enough in appearance to the spotty face on Lenny's old school ID card to pass a cursory examination, and since this party of students had assembled together in Austin earlier this morning, and he was the only kid from Baumgardner's school going, there was no one there to not recognize him. No one had any reason to believe he wasn't young Leonard.
Of course, none of the kids knew each other; they were from different schools all over the state – thirty kids assembling, early morning, with their parents, waiting to be signed on to the coach and into the care of Mr Whitmore for the day.
Howard glanced around at the others.
And what if one of the others is not who he says he is?
He kicked that thought away as quickly as it had arrived. He needed to stay very calm. Needed to look relaxed, like these others; slightly bored, waiting to be shown something interesting, something worth crawling out of bed for so early.
The guard finally reached for Howard's bag. 'Morning,' he grunted. 'Let's take a look, son.'
Howard casually held out his rucksack.
'Anything hazardous in here, son?'
'What? You mean... apart from my big bomb?' sighed Howard with a lazy smile.
The guard scowled at him. 'Not even funny, kid.' His hand rummaged quickly through the grubby items inside: a sandwich box, the flask, several rolled-up and dog-eared comicbooks, before he slapped the rucksack closed and waved Howard past.
Howard offered the guard a casual wave. 'Have a nice day, now.'
'Go on, kid... scoot,' said the guard, before turning to rummage through another bag.
Ahead he could see Chan and the other students gathered around the guide, Mr Kelly, and the teacher, Mr Whitmore, waiting for the last of them to be checked.
He sucked in a deep breath as he wandered over to join them, settling his nerves, his pounding heart. Inside the zero-point chamber, that's when he was going to do it. The chamber would be sealed, and this security guard and the others on the outside; his best chance to fire several aimed shots at the boy. It would take them a while to react, to open the door.
To take me down.
Howard smiled grimly. Not such a big price to pay to save the future of mankind, not really.
# CHAPTER 16
# 2015, Texas
They landed with a wet splash on to a hard tiled floor.
'Ouch!' Liam whimpered.
The water sloshed noisily across the floor soaking cardboard boxes of domestic cleaning materials.
'Jay-zus, why can't we ever land on something soft... like a pillow?' He grimaced as he let go of his nose and puffed out the breath he'd taken back in 2001.
'Insufficient data to identify a soft landing loca–'
Liam raised a hand. 'It's all right... I wasn't after an answer.' He pulled a wet shock of dark hair out of his eyes and opened them, instantly wishing he hadn't.
'Oh-Mother-of-God!' He clamped his eyes shut and turned away to look at the storeroom wall.
'What is wrong?'
'You could have warned me you were taking those wet things off!'
'Why?'
'Because... because...' He bit his lip. This is so very not right.
'Because you're a, ah... you're a girl now, Bob.'
Liam spotted some towels on the storeroom shelf and began to dry himself off.
'You should assign a new ident. to this AI copy. I may be "Bob" now,' she said, 'but this AI will develop new sub-routines and characteristics that require a new identifying label.'
Liam nodded. 'Yes.' Self-consciously he found himself wrapping the towel round his waist as he hurriedly removed his wet boxers and pulled the clothes he'd brought with him out of the bag.
'Four seconds before we were transmitted, you indicated you had a suitable ident. for me.'
'Oh yes... so I did.'
She turned to look at him. 'So, what will I be called?'
Liam could hear the rustle of clothes being quickly pulled on behind his back.
Good.
He really didn't need to see that... again. He found a pair of neon green three-quarter-length baggy shorts and a navy blue sweatshirt with the word NIKE splayed across it. And, for some reason, a large tick beneath the word. He felt much better with some clothes on, even if they looked quite ridiculous.
'I had a cousin called Rebecca,' he said. 'Used to call her Becks for short.'
'Becks?' replied the support unit, her voice rising at the end in a query.
'That's right – Becks.'
'A moment... logging ident....'
'So, are you decent now? Can I turn round?'
'Decent?'
'You know, got clothes on?'
'Affirmative.'
Liam turned round and found his breath caught momentarily. 'Blimey!'
Becks cocked her head and looked at him. 'Are these garments incorrectly deployed?'
His eyes skittered awkwardly up from the combat boots to the black leggings, to the black lace mini-skirt to a black crop top that displayed a bare midriff, up to her... perfect... face framed by tumbling locks of flaming fox-red hair. Quite clearly Sal had decided their support unit needed to look like some sort of gothic valkyrie.
'Uh. No, you are... you got it about... errrr... right, I suppose... I think.'
Liam felt his mouth go dry and a strange jittery, lurching sensation in his stomach.
Jay-zus... get a grip, Liam. That's... that's... that's just Bob wearing a girl suit. All right?
'Recommendation: you should refer to me as Becks from this point on,' she said firmly. 'It will avoid unnecessary confusion between AI versions.'
He nodded. 'All right... uh, OK. So, you're Becks, then. That's that settled.'
'Correct.' Her smile was faltering and clumsy as always, just like Bob. But on those lips, strangely quite perfect.
Liam decided to shift his mind to other things. 'I suppose we had better get a move on and find this Chan fella.'
Becks nodded and blinked, retrieving data from her hard drive. 'We are located within the institute's experimental reactor building. The reactor is very close to this location.'
Liam stepped towards the storeroom's door and cracked it open a sliver. Outside he could see a narrow hallway and, opposite, double doors with a sign on them: AUTHORIZED VISITORS AND STAFF ONLY. Just then he heard muffled voices from the end of the hallway and glass doors swung inwards to reveal a man in a smart linen suit leading a shuffling gaggle of teenagers.
'Yes, we're in the correct place all right,' whispered Liam. He watched them coming towards them, the man turning to talk to the group, gesturing emphatically with his hands. Liam gently closed the door until it clicked. 'They're just coming up now. We can tag along on the end,' he whispered.
He waited until the muted sound of the man's droning voice and the shuffle and slap of trainers on the polished linoleum floor passed them by before he cracked the door open again and peeked out. The last kids in the school party were just ahead, three blonde-haired girls deeply involved in a mumbled conversation, clearly too interested in chatting to each other to even pretend to be listening to the guide up front.
'Now!' Liam mouthed, and stepped out behind them, Becks swiftly following.
He fell in step at the back of the group and when one of the girls casually glanced back over her shoulder he quickly managed to mimic the laid-back swagger of one of the boys up ahead.
'Oh,' said the girl. 'Thought we were, like, you know, the last.'
Liam shrugged and smiled. 'Guess, like, not,' he replied, doing his best to bury the Irish in his voice.
Her gaze lingered a moment longer, a flickering smile for him. Then she turned back round and was back to gossiping in a conspiratorial murmur with the other two again.
Liam puffed out a silent gasp of relief. It looked like they'd jumped the first hurdle – successfully sneaking on to the back of the tour party and managing to pass themselves off as yet two more kids who might actually have preferred a trip to Disneyland or Universal Studios than wandering around a bunch of clinically clean corridors. He grinned at Becks and then almost immediately wished he hadn't. The smile she returned gave him that weird flip-flopping sensation in his stomach again.
Liam, you daft idiot... It's just Bob in a dress, for crying out loud!
He wished Sal could have found some other clothes for the support unit, something baggy, drab and unflattering. And why a wig with hair like that? Why that colour? He'd always loved that copper red. His first crush at school, Mary O'Donnell, she'd had hair that bewitching colour of fiery red.
Oh, saints preserve me... she's just a meat robot, so she is.
# CHAPTER 17
# 2015, Texas
'And here we are!' announced Mr Kelly to the group. 'We're about to enter the central reactor containment area. The whole experimental chamber is surrounded by an electro-magnetic field to filter out possible interference from all manner of electronic devices. Basically, we're going to be walking inside a giant electro-magnet. So if you kids have any iPods, laptops, iPhones or memory cards with data on you'd rather not lose, may I suggest you place them on the table here before we step through?' he said, indicating a table beside a pair of thick metal doors.
Liam watched with amusement as virtually every student sighed and then proceeded to reach into their rucksacks to pull out all manner of shiny metal and plastic gadgets and gizmos.
Eventually done, Mr Kelly tapped an entry code on to the large metal doors and he smiled expectantly as they swung slowly inwards.
At last, the gaggle of teenagers in his charge seemed to be shaken out of their torpid state of disinterest. A shared gasp rippled among them as their eyes swept up to take in the large spherical chamber, seemingly constructed entirely out of football-sized ball-bearings.
'As you can see, the entire chamber is lined with charged magnets, which act as a completely impenetrable barrier for any sort of FM radio signals, WiFi signals, electrical currents, atmospheric static and so on, the sort of things that can affect our readings from the test runs.'
He led them into the spherical chamber along a raised walkway, towards a platform thirty feet in diameter. Mr Kelly pointed towards a rather less impressive-looking structure, what appeared to be a polished metal witch's cauldron with a lid on, six feet across. Wires and cables and broad cylinders of metal descended through the lid into whatever witches' brew was bubbling away inside.
'Now that, kids... that's what this is all about. That metal sphere contains tens of billions of dollars' worth of investment, and quite possibly represents mankind's energy future.'
'That's the reactor?' asked Mr Whitmore.
'Yup. That's it, the zero-point energy test reactor.' Kelly smiled and shook his head. 'You know, it still amazes me that something so small, something the size of a... of a small car could, in theory, provide more than enough energy for every last person on this planet.'
Liam found his jaw sagging open, just like everyone else's.
'The tests we've run in there have so far produced really quite staggering amounts of energy out of the space-time vacuum pinholes that we've opened. The trick is sustaining and controlling the pinhole... and, of course, containing such huge amounts of energy.'
'That sounds a little, like... a little dangerous,' said the blonde girl who'd glanced back at Liam.
Mr Kelly looked at her. 'What's your name?'
'Laura Whitely.'
'Well, Laura... I guess it does sound a little dangerous. Dr Brohm, one of our leading scientists working on this, likened it to opening a very small peephole and looking on to the face of God himself.' Mr Kelly forced a laugh at that comment. 'A little fanciful, I think, but it gives you an idea of how much energy we're talking about...'
Howard Goodall felt the first bead of sweat trickle down the small of his back as he discreetly eased his rucksack off his shoulder on to the floor. He slowly opened the zip just a little and sneaked his hand inside. His fingers quickly found the screw cap of his thermos flask and he gently began twisting it off.
He could see Edward Chan at the front of the small knot of students gazing in silent awe at the glistening metal container.
Howard wondered how they could all be so incredibly stupid, how mankind was happy to play dice with technology it had no way of understanding. He remembered a lecture at university. His tutor had talked about the Americans' Manhattan project during the Second World War – their attempt to build the world's first atom bomb. How, when they first did a test detonation in the deserts of New Mexico, the scientists hadn't been certain whether the bomb would destroy several square miles of desert or, indeed, the entire planet. But still the reckless, silly fools went ahead and tested it anyway, played dice with mankind's future.
Just like time travel – a technology mankind was woefully unprepared to be in possession of. He stepped forward, a little closer to Chan, his eyes darting to the heavy doorway of the chamber slowly being swung back into place.
His hand felt the tube-shaped carbon-fibre weapon. It was small, tiny, with a magazine containing six toxin-tipped projectiles. He only had to wound Chan, just get one shot on target and wound the boy – the neurotoxin would finish him in minutes.
This is it, Howard, he told himself. This is the end of time travel.
# CHAPTER 18
# 2001, New York
'What? Jealous?' Maddy shook her head emphatically. 'Jealous of Bob Version Two?'
Sal had a mischievous look on her face. 'Just asking.'
'Oh, come on, of course not! It's not even human... it's just... it's just a clone. It's not even a genuine copy of a human – it doesn't have a proper human brain!'
'But she looks very human.'
'And so does a storefront mannequin, or a GI Joe action figure or a Barbie doll.'
Sal shrugged and grinned mischievously. 'Liam seemed impressed.'
Maddy had noticed. His eyes had been out on stalks. 'No different to any other boy, I guess... one thing on their minds all the time.'
Sal giggled. 'True.' She spun in the office chair beside the computer desk. 'So, you don't... so you're not jealous?'
Maddy took off her glasses and wiped them on her T-shirt. It was decidedly odd having Bob looking like that, like some athletic-fit catwalk model, some Amazonian beauty. And yes... having something like that gliding beautifully around was enough to make any female feel inadequate, plain in comparison. But then Maddy was used to it.
On the other hand, if Sal was asking in a roundabout way whether she had feelings for Liam... well, the answer was no, not those sort of feelings. Liam was nice-looking, charming in an old-fashioned gentlemanly way, but what she felt for him, more than anything else, was pity, a choking sadness.
Every time I send him through... I'm killing him just a little bit more.
She looked at Sal. 'No, I'm not jealous. I'm not, you know, like... after him –'
> Maddy, it is time to activate the return window.
'OK,' she replied, turning to face the desk. She began to tap the retrieval coordinates into the computer.
'But he's nice,' said Sal.
'Sure he's nice,' said Maddy. 'I'm sure he had girlfriends back in Ireland, but... but, I'm a couple of years older than him anyway and... and it's more like he's a little brother, or a nephew really, than, you know... sort of boyfriend material.'
Maddy double-checked the coordinates. 'Anyway... My God, Sal –' she grimaced at her – 'I can't believe you're being so personal!'
'Sorry,' said Sal, flicking a tress of dark hair out of her eye. 'Oh... I just remembered! You'll never guess what I saw in a junk store down–'
'Just a moment, Sal. I need to concentrate...'
# CHAPTER 19
# 2015, Texas
Liam identified Chan among the students. It wasn't as obvious as he'd thought it would be. There were about seven or eight who looked oriental to him, and most of them were younger than the other students. But he knew Edward Chan was the youngest here and he zeroed in on a small boy at the front, gaping wide-eyed at the zero-point energy reactor. Seemingly entranced by it.
Becks gently tapped Liam's arm and leaned towards him. 'Information: according to the mission data, Edward Chan only has four minutes and seven seconds left to live.'
Liam nodded. He looked around the chamber, trying to identify what or who could possibly pose a threat to the boy. If they were down to four minutes, then presumably the lad's killer was right here, right now, getting ready to make his move. His eyes darted from Mr Kelly, explaining the machinery and instrumentation, to Mr Whitmore, stroking his sparsely bearded chin thoughtfully, to the two technicians manning a couple of data terminals.
One of them?
His gaze shifted to the students, all of them still marvelling at the interior of the chamber and some of the incredible-sounding statistics that Mr Kelly was reeling off. '... equivalent to all of the energy produced by coal, oil, natural gas... over the last one hundred and fifty years...'
One of them? One of the students?
Why not? It could just as easily be one of the students. After all, Liam was the same age as the oldest of them and an assassin would probably have a better chance smuggling himself in as a student than he would a member of staff. After all, that had worked for him and Becks. His gaze wandered from face to face, looking for a nervous tic, darting eyes, lips moving in silent prayer, someone clearly agonizing over the precise moment to strike.
Becks gently tapped his arm again.
'What now?' he hissed.
'I am sensing precursor tachyon particles in the vicinity.'
He looked at her. 'Uh?' Their return window wasn't due yet, not until ten minutes after Chan's supposed moment of death. That was the arrangement. 'Are you sure?'
Becks nodded towards the reactor. 'There. They are appearing...' Her eyes widened, and her lids fluttered and blinked rapidly. 'DANGER!' she suddenly barked at the top of her voice.
Howard was almost beside Chan, his finger on the trigger inside his bag ready to pull the small weapon out and fire it at his back. He wanted to be right beside Chan, right next to him, to know as an absolute certainty he wasn't going to miss. Too much rested on this. Everything rested on this. He was just a couple of yards from him when a tall girl with distinctive red hair at the back of the knot of students suddenly started shouting.
Mr Kelly stopped mid-sentence. 'Excuse me?'
'DANGER!' shouted the girl again, her voice loud and urgent.
'Excuse me, young lady,' replied Mr Whitmore, 'this is not the place for some sort of stupid prank!'
Howard turned to look at the girl.
Something's wrong. Someone knows!
'DANGER!' shouted the girl again, but her finger pointed directly at the reactor, not him. 'Tachyon interference with the reactor! The reactor will explode!'
Howard had no idea what the hell she was on about. Perhaps it was just a coincidence, perhaps she was just some flaky goth girl making some sort of a protest against experimenting with zero-point energy. He was with her on that, but now was not the best time. He wasn't going to be distracted. He pushed his way forward towards Chan as the other students began to step back warily from the reactor in response to her outburst.
At last, standing beside the small boy, he looked down at him, his finger poised on the trigger, ready to whip the gun out and fire.
Chan turned to look up at him. 'What's the girl at the back saying?'
Howard found himself shrugging. 'I... uh... I guess she's having some kinda fit.'
'Now stop it!' snapped Mr Whitmore, pushing his way through the bemused students towards the girl. 'Nothing is going to explode!'
Chan grinned up at Howard. 'Crazy girl, huh?'
And Howard found himself smiling back at the kid, somehow not quite ready... not quite ready to pull out the gun and fire at point blank range. He really hadn't expected to be looking down into a friendly face at the very moment he pulled the trigger on Chan.
∗
Without a warning Becks grabbed Liam roughly by the shoulders and man-handled him back from the reactor towards the walkway leading to the sealed exit.
'Becks! What the hell are you doing? What's going on?'
'Imminent threat of explosion,' she said crisply and calmly, and a little too loudly. Her voice spooked the other students nearby who quickly began to join them backing away from it.
'Everybody, calm down!' shouted Mr Kelly. 'Nothing is going to happen!'
Liam looked up at Becks. 'Are you sure it's going to –?'
Becks suddenly stopped dragging him. 'Too late to escape!' She yanked Liam's arm downwards to the floor and he dropped to his knees.
'Ouch! What are you doing?'
She knelt down in front of him and wrapped her arms round his shoulders, shielding him from the reactor. Liam peeked over her shoulder and saw the reactor's thick metal casing suddenly start to ripple like jelly and a moment later begin to collapse in on itself.
'What the –?'
Becks reached out one hand and grabbed his nose painfully. 'You must lower your head,' she ordered, yanking him roughly down until he was almost doubled over, his head in her lap. Then all of a sudden he felt the oddest tugging sensation. As if he and Becks and the world around them was being sucked into a gigantic laundry mangler, stretched impossibly thin like elastic strands of spaghetti towards the reactor... following the collapsed metal casing into some inconceivable pinpoint of infinity.
'Ooooooohhhhh Jaaaaaaaaaayyyyyy-zzzzzzussssssss!'
# CHAPTER 20
# 2001, New York
Maddy and Sal stared at the shimmering window in the middle of the archway. Through a curtain of undulating, rippling air they could see the dim outlines of the storeroom they'd sent Liam and the support unit to.
'Something's definitely wrong,' whispered Sal.
Maddy nodded. 'That's the third back-up window they've missed.'
Five minutes ago they'd been cheerfully prepping the scheduled return window, assuming that the simple scouting mission had been a success and Liam and the support unit would be ready and waiting to come back and tell them what exactly had happened to Chan.
Now, for the third time, both girls were staring at a dark storeroom with no sign of either of them.
'Oh boy,' uttered Maddy. 'I don't know what we do now. That's it – we've tried all the back-up windows.'
> Maddy?
She stepped towards the desk and leaned over the deck mic. 'Yes?'
> You should try the six-month window.
'Yes... yes, you're right.'
Bob was right, it was worth a try. She clicked the PURGE button on the screen and the shimmering window in the middle of the archway vanished with a soft pop and a gentle puff of displaced air. She entered a new set of time coordinates: exactly five months, thirty days, twenty-three hours and fifty-five minutes after the time they'd been sent into the future; exactly five minutes before the support unit's mission time span was up and it was scheduled to self-destruct. It made sense. It would be the last possible chance to rendezvous with a return window. With the support unit dead, Liam would not be able to receive a tachyon signal to instruct him on a new rendezvous time-stamp. If they weren't there, in that storeroom six months after arriving and impatient to get back home, then Maddy had no idea what she could do next.
She clicked on the screen to confirm the new time coordinates and then activated the displacement machinery. Once again a twelve-foot-wide sphere of air began to shift and undulate, revealing the storeroom again. Both girls squinted for a while at the dark space beyond. Same store cupboard... a few things had been shifted around; clearly someone had had a spring-clean in there. But no sign of either Liam or the support unit.
'Oh,' said Sal. 'We've really lost them.'
Maddy pinched her chin. 'No... let me think.' There was a way to communicate with the support unit. A tachyon signal beam. That's what they'd done last time: aimed a broad beam of particles in the direction in which they'd guessed Liam and Bob were and transmitted an encoded signal back through history. It had worked. Bob had picked it up.
'Bob,' she spoke into the mic, 'can we send a tachyon signal beam forward?'
> Affirmative. We have enough power.
'Right... what if we send it to, say... five minutes before whatever happened to Chan, happened.'
'What message?' asked Sal.
'I dunno. Something like – abort the mission, something is going to go wrong.'
Sal nodded. 'Yes, we should do that.'
Maddy sat down in one of the office chairs and purged the open window. It puffed out of existence. She then opened the message interface and quickly tapped in a message.
Return to the store cupboard immediately. We'll pick you up there. Something is about to go wrong with your mission. Something is about to happen to you. A return window will be waiting for you.
Bob's dialogue box popped up.
> You wish to send this message?
'Yes, immediately.'
> Recommendation: a narrow beam transmission.
A narrow beam meant she needed to know quite precisely where to aim it. But she had no idea where the two of them might be. They might have been somewhere else in the facility. Something may have caused a detour, a fire alarm perhaps? Or some malfunction in the lab may have resulted in everyone being evacuated.
'Bob, let's make the beam broad enough to sweep the whole area. Make sure the support unit gets the message.'
> Caution: there will be technology in the vicinity that may be unpredictably affected by tachyon particles.
'I really don't care if we mess up somebody's experiments, or damage their precious gizmos... I want Liam to get that damned message!' she snapped angrily. 'All right?'
> Affirmative. Wide beam sweep to cover vicinity.
Sal looked at her. 'Are you sure about this?' She nodded towards the computers. 'Bob just sort of cautioned us, didn't he?'
Maddy spun the chair to face her. 'You got any other suggestions?'
Sal shook her head.
'Right, then,' she replied, her voice brittle. 'We have to make contact.'
Stay calm, Maddy. You're the leader, so stay calm.
Her face softened as she reached for her inhaler on the desk. 'Sorry, Sal... I'm just a bit stressed and –'
'No, it's OK.'
'I don't know what else to do.'
> Confirm transmission?
'Bob, you cautioned me... because what? Is there some sort of danger to Liam if we throw a whole load of tachyon beams forward?'
> Information: tachyon particles might interfere with zero-point energy experiments that are being conducted at the institute at this time.
'But does that endanger Liam in some way?'
> Unknown. Records show zero-point energy research was abandoned as being potentially hazardous. There is very little public domain data on the Texas Advanced Energy Research Institute's work in this field.
'So? What do I do?'
> Recommendation: do nothing.
'Nothing?'
> Correct. Wait for possible contact from them. Sending a tachyon signal forward may endanger Liam and the support unit and might also present a security risk for the agency.
Maddy stared at the screen in silence. 'You want me to do absolutely nothing? When they might be in trouble and need our help? You're asking me to do nothing but sit on my hands?'
> Affirmative. A tachyon signal might be detected by sensitive instrumentation at the institute and the message intercepted. This would clearly alert them to the existence of time travel and the agency.
'They could know time travel is possible fourteen years before Edward Chan does his maths paper,' added Sal. 'Our message to Liam might alter history just as much as someone killing Chan.'
> Sal is correct.
'So you're saying we wait for them to get themselves out of whatever's happened?'
> That is my recommendation. They are very capable.
Maddy chewed her lip in thought for a moment. 'And this is my call?'
> You are team leader. I can only offer data and tactical advice.
'Right, well then I say forget potential contamination, forget any of their zero-point experiments we might be messing up and stuff any security risks for the agency. They've pretty much left us all alone to fend for ourselves so far... I'm damned if I'm going to sacrifice Liam just to keep them happy. We warn Liam and the support unit to abort the scouting trip. We get them back home and then... then... we can deal with any time changes we may have caused! All right?'
Sal nodded. 'I suppose it's a plan.'
Maddy turned to the computer screen. 'All right?'
The '>' cursor blinked thoughtfully on and off in the dialogue box and they heard the computer's hard drives whirring softly. Finally, after a few moments the cursor flickered forward.
> Affirmative.
'Cool,' said Maddy. 'So, Bob, send that message to five minutes before Chan's recorded time of death.'
> Affirmative.
As Bob proceeded with beaming the message, Maddy prepared to open a window yet again in the storeroom for the same moment in time and resolved to keep it open for at least ten minutes. That would give them enough time, she hoped, to receive the message, wherever they were in the institute, and make their way back to the storeroom. She was about to activate the time window when Bob's dialogue box appeared centre screen.
> Information: there is an intense energy feedback loop interfering with the tachyon signal beam.
'Meaning?'
> 87% probability that this is an explosion.
Her breath caught in her throat. 'An explosion?'
> Correct.
'Oh my God.' Maddy felt the blood drain from her face. 'How big?'
> Unable to specify. It is a large signature reading.
She looked at Sal. 'Oh my God, you don't think...?'
Sal swallowed nervously and didn't say anything – her wide eyes said it all.
'Bob, tell me it wasn't us that just caused that to happen – our tachyon signal?'
Bob's cursor blinked silently for a few seconds.
> The tachyon signal is the most likely cause of the explosion. The precursor particles may have caused a reaction.
'Oh God, what have I done?'
# CHAPTER 21
Brilliant white, floating in a void of perfect, featureless white. To Liam it felt like hours, staring out at it, hanging motionless in the void as if he was floating in a glass of milk.
It felt like hours, but it could have been minutes, seconds even.
He'd begun to wonder if he was actually dead and hanging around in some pre-afterlife limbo. Then he saw the faintest flicker of movement in the thick milk world around him.
An angel coming for him? It looked like a cloud of slightly dimmer white and it danced around like a phantom, gliding in decreasing circles that brought it ever closer to him. It looked familiar.
I've seen that before.
Then he remembered. The day that Foster had pulled him from the sinking Titanic. In the archway, as he'd woken the three of them from their slumber...
The seeker.
There were more out there, faint and far off, drawn to him as if they could smell his presence, like sharks smelling blood. Perhaps the first seeker had silently called out to them that there was something here for them all to share.
Oh Mary-Mother-of-God... they're going to rip me to pieces!
The nearest seeker swooped still closer to him and the faint cloud of grey began to take form. He thought he could make out the head and shoulders of the indeterminate shape, almost human-like. And a face that took fleeting form.
Beautiful. Feminine.
He almost began to think he was right first time, and that this was Heaven and those swooping forms were angels coming to escort him to the afterlife. Then that vaguely familiar feminine face stretched, elongated, revealing a row of razor fangs and the eyes turned to dark sockets that promised him nothing but death. It lunged towards him...
And then he was staring up at another face, framed with hair dangling down towards him, tickling his nose, with piercing grey eyes staring intently at him. 'Liam O'Connor, are you all right?'
'Becks?'
'Affirmative. Are you all right?' she asked flatly. 'You appear undamaged by the explosion.' He felt her strong hands running up and down his arms and legs, around his torso. 'No apparent fractures.'
'I'm OK, I think. Just a little... dizzy, so I am.' He began to sit up and she helped him.
'You are disorientated,' she said.
He looked up at a clear blue sky and a dazzling sun. He blinked back the sunlight – a curious vaguely violet hue to it – and shaded his eyes with a hand. 'Jay-zus, where are we? Is this another world?'
'Negative.' She looked at him, then corrected herself. 'No. We are where we were,' she replied.
But when? The spherical chamber and laboratory buildings were gone. Instead of the institute's water-sprinkled lawns and flowerbeds, there was nothing but jungle. If this was the same place, then it had to be some significant time in the future or the past. It certainly wasn't 2015.
'The tachyon interference caused an explosive reaction,' said Becks. 'We were pulled through the zero-point window into what is known as chaos space.'
'Chaos space?'
'I am unable to define chaos space. I have no detailed data on it.'
'And then what? We were dumped out into reality again?'
'Correct.'
He saw another head suddenly appear above a large lush green fern leaf. Somebody else, dizzily sitting up and wondering where on earth they were. It was one of the students: a black girl, her hair neatly thatched into corn-rows. A gold hooped earring glinted in the sunlight.
'What the –?' she muttered as her eyes slowly panned round the tall green trees and drooping vines. Finally her eyes rested on Liam and Becks.
'Hello there,' said Liam, waving a hand and smiling goofily.
She stared at him silently with eyes that still seemed to be trying to work out what she was seeing.
He noticed another head appearing out of the foliage several dozen yards away. He recognized the receding scruffy hair and sparsely bearded jowls of the teacher who'd been with the group of students during the tour of the institute.
Other heads appeared, all looking confused and frightened, spread out across a clearing in the jungle, a hundred yards in diameter. Liam recognized the institute's smartly dressed tour guide, one of the technicians who'd been in the chamber and the rest of the students.
'Wh-what happened?' called out the teacher.
The guide's carefully groomed silver hair was dishevelled, his smart suit rumpled and dirtied with mud. 'I... I... don't know... I just...'
Liam looked at Becks. 'We're going to have to take charge of things, aren't we?'
She looked at him blankly. 'The mission parameters have changed.'
Liam sighed. 'No kidding.'
He was about to ask her if she had any idea at all of when in time they were when he heard a shrill scream echo across the clearing.
'What was that?'
It came again. Sharp, shrill and terrified. He got to his feet, as did several others, and pushed through clusters of knee-high ferns towards where the sound was coming from. Becks was instantly by his side, striding slightly ahead of him without any trepidation. Liam realized he felt reassured to have her there despite her diminutive frame. Despite lacking the intimidating bulk of Bob, he had a feeling she was a great deal more dangerous than she looked.
Finally, a yard ahead of him she stopped. Liam stepped round her and looked down.
The blonde girl he'd spoken to earlier – he remembered her name, it was Laura, wasn't it? – was screaming, her eyes locked on to the thing that was lying in the tall grass beside her.
It took Liam a moment for him to make sense of what he was seeing on the ground, then... then he got it; understood what it was. His stomach flopped and lurched and it took every ounce of willpower he had not to double over and vomit.
The teacher emerged from the tall grass to stand next to Liam. He followed Laura's wide-eyed gaze and then sucked in a mouthful of air. 'Oh my God!... That's not... that's not what I think it is,' he whispered, and turned to look at Liam. 'Is it?'
Among the tall fronds of vegetation nestled a small twisted mass of muscle and bone. At one end Liam could see a long braid of blonde hair, matted with drying blood, and halfway along the contorted form, he spotted a solitary pink Adidas trainer, hanging half on and half off a pale and perfectly normal-looking foot. It had to be one of the three blonde girls they'd tagged behind on the way into the chamber. He could quite understand the girl, Laura, screaming. They'd been chatting, giggling and exchanging phone numbers only ten minutes ago.
Liam recalled Foster saying sometimes it happened; sometimes, very rarely, the energy of a portal could turn a person inside out. Oh Jay-zus, what a mess.
Half an hour later those of the group that had survived the blast and arrived in one piece had made a rough assessment of their predicament. Dotted around the jungle clearing, they'd made the gruesome discovery of more bodies just like the girl's, turned inside out and almost unrecognizable as human. Sixteen of them. Of the thirty-five people who'd been in the chamber when the explosion – or, more accurately, implosion – had occurred, only sixteen of them appeared to have made it through alive.
Now, gathered together in the middle of the clearing, well away from the forbidding edge of thick jungle, it was Whitmore who first seemed to be stirring from a state of stunned shock. He wiped sweat from his forehead with the back of his sleeve and narrowed his eyes as he studied Becks.
'You!' he said. 'Yes, you! I remember now... you said it was going to explode. Just... just before it actually did.'
Becks's face remained impassive. 'That is correct.'
'Hang on!' he said again, his eyes suddenly narrowing with dawning realization. 'You... you're not one of m-my kids. You're not –'
Liam could see where this was going. It was pointless continuing to pretend to be high-school students a moment longer.
'What just happened, whatever's just happened,' blustered Whitmore, 'you damn well knew it was going to happen.' His voice rose in pitch. 'Who are you? Is this some sort of terrorist thing?'
Becks shook her head slowly, her face impassive. 'Negative. We are not terrorists.'
Whitmore fell silent. His lips quivered with more questions he wanted to ask, but he was struggling to know what exactly to ask. Where to begin.
'Excuse me?'
Their heads all turned towards a boy with kinky ginger hair, neatly side-parted into a succession of waves, and thick bottle-top glasses that made his eyes seem to bulge like a startled frog. He pointed to his name tag. 'My name's Franklyn... you can call me that. Or just Frank will do.' He smiled at them uncertainly. 'Uhh... I just wanted to say that... this is going to sound really weird, but I guess I'll just come out and say it.'
'What?' snapped Whitmore.
'Well –' he pointed up at the sky – 'you see them?'
All eyes drifted towards the top of some trees twenty yards away, a long branch leaning out over the clearing with strange dangling willow-like green fronds drooping to the ground. In among them, a pair of dragonflies danced and zig-zagged with a buzz of wings they could hear from where they stood.
'Those are huge,' uttered Kelly. 'Good grief!... Two-foot, three-foot wingspan at a guess?'
'Uh-huh,' said Franklyn. 'They're really big and I'm pretty sure I know what species that is.'
The others looked at him.
'It's a petalurid, I think... yeah, I'm sure that's the right name.'
'Great,' said Laura, 'so now we know.'
'No, that's not the important bit,' said Franklyn. He looked at her. 'They should be extinct.'
'Well, obviously they're not,' she replied.
'Oh yes they are. We've only ever had fossils of insects that size.'
Whitmore stood up. 'Oh my God! He's right!' He watched the two dragonflies emerge from the overhanging branch and dart out into the open, their wings buzzing noisily like airborne hairdryers. 'Insects haven't been that size since...' He swallowed, looked at the others. 'Well... I mean, millions and millions of years.'
'Petalurids,' uttered Franklyn again. 'Late Cretaceous. I'm pretty sure of that.'
Kelly got to his feet and stood beside Franklyn. 'What are you saying?'
The boy wiped a fog of moisture from his glasses, blinking back the bright day from his small eyes. 'What I'm saying, Mr Kelly, is those things haven't existed, alive... in, like, well, I guess something like sixty-five million years.'
# CHAPTER 22
# 2001, New York
'Maddy! Where are you going?'
Maddy ignored Sal's pleading voice as she strode across the archway, cranked up the shutter and stepped out into the backstreet.
I can't do this... I can't do this.
She felt the first tears roll down her cheeks as she picked her way along the rubbish-strewn sidewalk towards South 6th Street at the top. Her first proper mission in charge and she was already going to pieces. An impetuous decision on her part, stupid and hot-headed enough to go against Bob's reasoned advice, and now she might just be responsible for killing Liam and the support unit. Not only that, but she'd probably also caused the deaths of dozens of others. And, most importantly, Edward Chan.
'I can't do this,' she muttered. 'I'm just not ready for this.'
She stepped out of the backstreet on to the corner and watched the busy intersection for a while: traffic turning right to pick up the bridge road, left towards the river; pedestrians making their way over to their jobs in Manhattan... all of them oblivious to the commercial jets already in the air and heading towards their doom.
She wanted Foster back. Needed him back. What possessed him to think for one moment she was actually ready to run a field office? His pre-recorded 'how to' answers stored on the computer just weren't enough. She needed him to talk to, to explain the technology to her more fully, to tell her more about the agency and their place in it. There were so many gaps in her knowledge she didn't even know enough to have an idea what questions to ask. She was floundering.
'Damn you, Foster!' she hissed under her breath, and wiped at her wet cheeks.
The old man could be anywhere in New York, if, indeed, he'd decided to stay on in the city. He'd walked out on her on one of the Monday mornings, walked right out of the Starbucks with a bag over one shoulder, leaving her alone with her coffee. It was Tuesday today. If he was that desperate to see the world before he died, then he might just as well be on a Greyhound bus to some other state or even on a plane to somewhere exotic.
Face it. He's gone for good.
'She just got up and left!' said Sal.
> I sensed emotional stress markers in her voice.
'Well, duh! Of course she's upset! She's just... I mean, she may have just killed Liam!'
Sal realized her own voice sounded shrill and loud. 'Oh jahulla! Is he dead? Did she kill him?'
> Insufficient data. The residue signal suggests a sudden and violent enlargement of a dimensional pinhole, releasing a vast amount of energy.
'Like a bomb?'
> Correct. Just like a bomb.
She slumped down in the office chair. 'So, dead, then,' she uttered, looking down at her lap and suddenly beginning to feel the stab of pain. The equivalent, in days, of almost three months had passed since Foster had pulled her from a falling building. So much had happened in that time, a world almost conquered by Nazis and then in the blink of an eye reduced to a radioactive wasteland. Their trip to the basement of the Museum of Natural History, finding the clues... Liam's message in the guest book. And all the clean-up and fix-up after that whole nightmare. It almost felt like another life: Mumbai, Mum and Dad, the burning building.
This place, this scruffy archway criss-crossed with cables, had begun to feel like a home, and Liam and Maddy... even Bob, like an odd new family. Now, in one moment, with one simple mistake, she wondered if that was all gone. She looked up from her hands, wrestling each other in her lap, to see Bob's silent blinking response on the screen.
> Not necessarily.
'What? What do you mean "not necessarily"? Do you mean not necessarily dead?'
> Affirmative. They may have been transported.
'You mean like one of our time windows?'
> Correct. The sudden dilation of a dimensional pinhole being used to extract zero-point energy may have functioned in a similar way to a portal.
'Where? Do you know where? Could we find them?'
> Negative. I have no possible way of knowing when they would have been transported to. It would be random.
'But... but they could be alive, right? Alive, somewhere?'
> Affirmative, Sal. But in the same geographic location.
'Is there anything we could do to try to find them?'
> Negative. We are in the same situation as before we sent the tachyon signal. If the explosion did not kill them, then they are sometime in the past or future.
The rising hope she was feeling that there might be a way to find them and bring them back in one piece began to falter.
> My AI duplicate and Liam may attempt to establish contact with the field office, provided it can be done with a minimum of time contamination.
'You mean like Liam did with the museum guest book? A message in history?'
> Correct. If they have not been transported too far in time, it may be possible for them to find a way to communicate without causing a dangerous level of contamination.
'So what... we wait? We wait and hope for a signal?'
> Affirmative. We must wait and we must observe. There is no other viable course of action.
# CHAPTER 23
# 65 million years BC, jungle
'Excuse me?' said Laura. 'When did you say?'
Franklyn finished wiping his glasses dry and put them back on again. He took his time savouring the silent, rapt attention of the others sitting together in the clearing. 'I said sixty-five million years ago.'
The others shared a stunned silence. Eyes meeting eyes and all of them wide. The enormity of the fact taking a long while to sink in for all of them.
It was Whitmore who broke the silence. 'Sixty-five million years... so that definitely takes us to near the end of the Cretaceous period.' He looked at the boy, whose glasses were already beginning to fog up again from the humidity. 'It is the Cretaceous, isn't it?'
Franklyn nodded. 'Correct. Late Cretaceous, to be precise.'
'We've travelled in time?' uttered Kelly. 'That's... that's not possible!'
'Whoa!' one of the other kids cried.
Whitmore and Franklyn were looking at each other warily, a gesture not missed by Liam.
'What? Either of you gentlemen going to tell us what a bleedin' late crustation is?' Liam studied them suspiciously. 'You two fellas looked at each other all funny just then. That means something, right?'
Whitmore pursed his lips, his eyebrows arched as if in disbelief at what he was about to utter. 'If Franklyn here is right,' he said, watching the foot-long dragonflies hover and drop among a cluster of ferns nearby, 'then this is dinosaur times. We're in dinosaur times.'
Laura gasped. 'Oh God.' She took two or three deep breaths that hooted like a steam train coming down a tunnel, like a woman in labour. 'Oh my God! I was watching Jurassic Park last night! I don't want to be eaten by a rex. I don't want to be eaten by a –'
Several of the other students, not all of them girls, began to whimper at the prospect; the rest began to talk at once. Liam watched Whitmore struggling with the situation himself, shaking his head incredulously and balling his fists in silence. Kelly meanwhile was gazing up at the blue sky and the slightly odd-coloured sun as if hoping to find an answer up there.
Somebody needs to take charge, thought Liam. Or they're all going to die.
He was damned if he was going to volunteer, though – to be responsible for this lot. He and Becks were probably going to fare much better on their own. One of the three men was going to have to step up and take care of these kids. But, as it happened, as Liam was beginning to wonder how the pair of them were going to discreetly extract themselves – with Edward Chan in their possession – the decision was made for him.
'You!' said Whitmore, his lost expression wiped away, all of a sudden remembering there was an issue as yet unresolved. His voice cut across the clamour of all the others'. 'Yes, you! The goth girl,' he said, pointing at Becks. He looked at Liam. 'And you. You know what happened, don't you? The pair of you weren't in my party. And you knew that explosion was going to happen. So you'd better start telling us who the heck you are!'
There was an instant silence as all eyes swivelled to him and Becks.
Liam grinned self-consciously. 'Uh, we... that's to say me and Becks here, we're not er... students as such. We're sort of agents from another time.'
Fourteen pairs of eyes on him and none of them seemed to have anything close to a grasp on what he'd just said.
'See, we're time travellers and we came along today to try to protect him,' he said, pointing at Edward Chan who was sitting on the grass, arms wrapped round his huddled knees.
Edward Chan's eyes widened. 'Uh? Am I in trouble?'
'You, Edward. We came to find out how we were going to protect you from an attempt on your life.'
The others looked at the small Chinese boy then back at Liam.
'You better explain about him, Becks,' said Liam. 'You've got all the facts in your head.'
Becks nodded. 'Listen carefully,' she began. 'Time travel will become a viable technology in the year 2044 when a Professor Roald Waldstein will build the world's first time machine and successfully transport himself into the past and return safely to his time. The practical technology developed by Waldstein in 2044 is largely based on the theories developed and published in Scientific American by the Department of Physics, University of Texas in 2031. The article is entitled "Zero-point Energy: energy from space-time vacuum, or inter-dimensional leakage?".'
Kelly's tired face lit up. 'You gotta be kidding?'
Whitmore looked at the bewildered young boy hugging his own knees on the ground in front of him. 'So how does this affect this boy?'
Becks's cool grey eyes panned smoothly across to Chan. 'The article published in Scientific American is a reproduction of a maths thesis presented by one Edward Aaron Chan. An act of academic plagiarism by his supervising professor.'
Edward looked up at her. 'Me? Really?'
'Correct. You will submit your dissertation to the Department of Physics for evaluation with an almost identical title in the summer of 2029, when you are twenty-six years of age. The department head, Professor Miles Jackson, will attempt to take credit for your work when it is approved for publication several months later, but he will be exposed as a plagiarist shortly after the article's publication.'
'But you said you'd come to protect him from an attempt on his life... why would someone want to kill Chan?' asked Whitmore.
'Edward Chan is the true originator of time travel,' replied Becks. 'In the future, 2051, time-travel technology becomes forbidden under international law because of the danger it poses to all mankind. This law is a result of years of campaigning by Roald Waldstein, the inventor of the first viable time machine, to prevent any further development of the technology.'
'Wald–... the man who builds this first machine?' said one of the students, a tough-looking Hispanic boy. Liam noticed his name tag was still on his chest: JUAN HERNANDEZ.
Becks's gaze panned across to him. She waited silently for him to continue.
'Why?' asked Juan. 'Why build the thing, then, you know, campaign against usin' it? Don't make any sense.'
Liam answered. 'Waldstein never ever revealed what he saw on his first and only trip into the past... never talked to anyone about it. It was a big secret what he saw. But he was once heard to say that he'd looked upon the very bowels of Hell itself.' Liam could have added more, could have added that maybe he'd glimpsed, for a few seconds, something of that himself.
Becks continued. 'Waldstein's campaign gained popular support. It is logical to presume that it may be one of his more fanatical supporters who has somehow managed to travel back in time to find Chan and attempt to kill him, to retroactively prevent him writing his thesis, and thus prevent or forestall the invention of time travel.'
A long silence followed filled only with the gentle rustle of the jungle's trees and the far-off high-pitched squawk of some jungle creature. It was Whitmore who cut it short. 'Well, OK... that's all very fascinating, but what just happened? Where are we and how do we get back?'
Becks's eyelids fluttered for a moment. 'The geopositional coordinates will not have changed. We are exactly where we were.'
'Yeah, right, man!' snapped Juan. 'There ain't no jungle like this. Not in Texas!'
'We're still in the same place,' said Liam, 'but it's when we are that's changed. Right?'
'Affirmative.' Liam nudged Becks. 'Yes...' Becks corrected herself.
'Which, if Franklyn is correct, is sixty-five million years ago,' said Whitmore, loosening his tie and unbuttoning the top button of his sky-blue shirt, already stained with dark underarm patches of sweat.
Liam smiled thinly. 'Yup, that's about it.'
The technician who'd survived and come through with them dipped his head and shook it. 'Then we really are totally, totally in trouble, man.'
Liam wanted to say something like he'd been in this kind of mess before, that there might possibly be a way out of here for them, that at the very least they had a genetically enhanced and very lethal combat unit, with an embedded supercomputer, disguised as an oversized gothic Barbie doll, here to help them all out. But he figured right now that would probably be one detail too many for them to have to cope with.
Kelly removed his linen jacket, no longer looking smooth and groomed and, like Whitmore, sweating large dark patches in the hot and humid air. 'So what are we going to do now?'
And, once more, all eyes rested on Liam.
Aw, Jay-zus... What? I'm in charge now?
It looked like he and Becks weren't going to be able to sidle away, that they were lumbered with the others. Liam sighed. 'Survival,' he said eventually. 'I suppose we'd better start thinking about that. You know? Water, food, weapons, some sort of a camp. The rest... if there is a rest... well, I suppose that can come later.'
# CHAPTER 24
# 65 million years BC, jungle
Howard took a break from the work of hacking at the vines and bamboo canes with his improvised machete: a jagged strip of metal – part of the reactor's shell – with a handle made of coarse leaves wrapped round one end and secured with shoelaces. As a machete it worked surprisingly well and, from the other jagged strips of reinforced alloy that had materialized in the past with them, they'd managed to produce nine very useful cutting implements like this one.
The Hispanic boy, Juan, was working alongside him while across the clearing, shimmering with the heat of the midday sun, he could see some of the others fashioning simple spears out of the thicker bamboo canes they'd cut down.
'That's bull, man,' muttered Juan, following his gaze. 'We ain't gonna kill anything with these pointy sticks.'
Howard nodded wearily and grunted something back, but his eyes were on Chan, standing next to that weird red-haired girl, as he ham-fistedly attempted to whittle a sharp end on a three-foot cane. She and the odd Irish boy... they'd given their names as Becks and Liam, but if they were covert agency operatives from the year 2001, they were probably aliases.
Which agency, though? Who sent them?
As far as Howard knew, no government, anywhere, was meant to have functioning time-travel technology. Although obviously the most powerful nations – the Chinese Federation, the European Bloc, the United States – must secretly have been developing it. And those two presumably must be field operatives working for one of them, here to protect Chan.
The Irish boy seemed to be calling the shots, with Whitmore, Kelly and the technician, Lam, happy for him to do so. Howard was content to go along with the status quo for now. Happy to carry on playing the role of timid young Lenny Baumgardner, a high-school student with straight As and a perfect school attendance record. It kept things simple for the moment. After all, the presiding question now was one of survival – the basics: food, water, shelter.
But his focus had to remain, whatever happened, on the mission, on what he'd set out to do: to end young Chan's life and absolutely guarantee that the uniquely brilliant theoretical concepts his older, twenty-six-year-old mathematician's mind would one day produce would never see the light of day. Brilliance like Chan's was rare; the kind of genius and intuition that comes along once in a generation, once in a century even.
Chan's work was going to end up being as life-changing as Einstein's once was. More so, in fact.
Without that published thesis the famous Waldstein would perhaps never have been anything more than an anonymous hobbyist inventor working in his garage. While the world of 2055 might be facing a dark time ahead with water, food and energy shortages, global warming and catastrophic levels of over-population, at the very least, history, as it was, would still be safe; at the very least, mankind would not be meddling with dimensions it had no possibility of understanding, dimensions that could contain anything.
Just because a door can be opened... doesn't mean it should be opened.
But Chan was here now... and not in the year 2029, sixty-five million years away from helping mankind make its biggest-ever mistake. Howard wondered whether that meant his mission was as good as done. Did he still need to kill him? After all, the explosion, presumably caused by something to do with those two agents, perhaps some side effect of time travel and the fields of energy it radiates, had propelled them far back in time. Surely further back in time than any prototype time machine currently in development could ever reach. And how would they know when they were, anyway? Sixty-five million years to choose from. Like a needle in a haystack. Like a needle in a whole barn full of hay, in fact.
Go ahead, pick a year... see if you get lucky.
He smiled.
It's done. The world's safe now. It's done.
Which was a relief, because now all he had to think about was the business of survival, here in this jungle with nothing for company but over-large dragonflies and whatever other giant creepy-crawlies and Cretaceous creatures lurked in the jungle. And, of course, a bunch of frightened kids and several men who ought to be showing a little more backbone.
Howard had done his bit for mankind... now, just surviving in this wilderness for the foreseeable future – he wasn't ready yet to be a dino dinner – that was for him.
He looked up at the thick edge of the jungle ahead of him: a ribbon of dark green foliage and tall canopy trees that wrapped itself all the way round the clearing.
And God knows what big hungry things are wandering around in there.
∗
'Oh, that's just great. That's just bloody great.' Liam stared at the swiftly surging river: a tumbling torrent of white suds that swirled around and over a bed of worn boulders.
'So, it runs all the way around us,' said Kelly. His smart linen business suit was smudged with dirt and sweat. Not the most practical clothing for jungle trekking. He'd tied off the jacket round his waist and rolled up the sleeves of his white shirt. The tie was still on, though, Liam noticed. A token that Kelly was not quite ready to abandon hope that help might arrive at any moment and he'd want to look his best for it.
'I think we're on a sort of island,' Kelly continued.
They'd spent the morning exploring the immediate surroundings beyond the clearing. Whichever direction they'd taken they'd soon come across the energetic roar of water and glimpsed the glinting, fast-moving river through the thinning jungle.
Island was about right. Approximately three or four acres of jungle with a central clearing, shaped roughly like a tear drop. The pointed tip of the island was where they stood now staring at the rolling water. The river split in two around their spit of land; to the right of them it broadened out into a wide, slower-moving channel. Slower-moving, but still brisk enough so that Liam wouldn't dare chance trying to cross it. But then he couldn't swim. More than that... water scared the bejeezus out of him. Not that he needed the others to know anything about his pet fears right now.
To their left the river compressed into a narrower channel thirty feet across, lined with boulders, and became a violent roaring ribbon of snow-white froth and energy. A fool might try to swim the wider channel, but only a completely mad fool would attempt a crossing on this side.
'We're trapped on here,' said Laura, looking around at the others. 'Aren't we?'
'At least we've got drinking water.' Liam shrugged. He gave them all a cheery smile. 'So it's not all bad news.'
Becks took a couple of steps down the wet shingle towards the raging river and silently appraised their surroundings. After a while she turned round. 'The island is a suitable defensive position.'
'Defensive?' called out one of the students. Liam turned round. It was a large boy, whose cheeks glistened with sweat beneath a mop of dark frizzy hair and he was still wearing his name tag: JONAH MIDDLETON. 'Defensible against what, dude?'
'Dinosaurs,' uttered Laura, her voice shuddering slightly.
Whitmore nodded. 'Yes, dinosaurs.' He turned to Franklyn. 'How good's your knowledge of the late Cretaceous?'
'Pretty good,' he replied. 'You want to know what species we can expect to encounter?'
'Please, tell me we don't get the T-rex,' blurted Laura. 'Not that.'
'Oh, we got those all right.' Franklyn put his hands on his hips. 'But they're more likely found on open terrain. Not jungle like this.'
'It's the velociraptors that scared me,' said Lam. His head bobbed energetically as he talked, his dark ponytail wagging like a dog's tail as he looked from one person to another. 'Seriously scary things, those.' He nodded sombrely. 'I seen all three Jurassic movies, guys... and it's those smart little ones you got to watch out for.'
'There are no raptors.' Franklyn shook his head. 'They're Asian and died out eighty-five million years ago. We should expect to see... lemmesee... ankylosaurus, that's the tank-shaped one with a spiky club for a tail. Pachycephalosaurus, that's the upright one with, like, a cyclist's safety helmet on his head. Triceratops... you all know that one, right?'
Heads nodded.
'Parasaurolophus... the duck-billed one with that Elvis-quiff bone sticking out backwards.'
'But those are all herbivores, aren't they?' said Whitmore. 'What about the carnivores?'
Franklyn pursed his lips. 'We got rex, of course, but no raptors. That's the good news.'
'Oh, great,' sighed Laura. 'That means there's bad news.'
'Well... I'm afraid there are several varieties of the smaller therapods,' he said, by way of explanation.
Liam shrugged at him. 'And those are what?'
'Therapods – same genus as the raptor,' Franklyn continued. 'Small predators, three to six foot tall. They walk on their back legs and have poorly developed front arms. They're pack hunters.'
'Three to six foot?' said Liam. 'That doesn't sound so bad, then.'
'Yo, dude,' said Jonah. 'You actually, like, seen the Jurassic Park movies?'
Liam shook his head. 'No. I presume it's one of them talkie motion pictures?'
Several of the students glanced at each other.
'Talkie motion pictures? You did say you were from the future, didn't you?' said Kelly.
'Well, not as such. Not directly... no. Actually I'm fro–'
'Caution!' said Becks, striding back up the shingle towards them. 'Confidential information.' Her glare silenced the stirring murmur of voices. 'That is unnecessary data. You do not need to know anything about the operative, Liam O'Connor.'
'Actually, I think I'd like to know a little more about you as well,' said Whitmore. 'I mean who the h–?'
'Stop!' barked Becks. 'This conversation will now cease!'
Laura made a face. She stepped forward and planted herself in front of Becks. Both girls about the same height, eyes locked in a silent challenge of each other. 'Oh? And who exactly made you the boss?'
Becks silently appraised her. 'You are a contaminant and a mission liability.'
'What? What's that supposed to mean?'
Becks's cold glare remained on the girl. For an unsettling moment Liam wondered whether she might just reach out and snap Laura's neck like a dry twig. He'd seen Bob effortlessly do far worse to countless grown combat-fit men.
'Becks!' he called out. 'Leave her alone!'
The support unit finally spoke. 'Liam O'Connor is... boss. I am just the support unit.'
'Support unit?' Laura's face creased with a look of bemusement. She turned to Liam. 'Sheesh, what exactly is the problem with your sister? She got some kind of behavioural problem?'
'She talks like some kind of robot,' said Keisha.
'Well now, since you –' Liam was about to explain, but Becks cut him off again. 'Irrelevant data.' She took a step away from Laura towards him, Laura's challenge instantly dismissed and forgotten. 'Recommendation, Liam.'
Liam nodded. 'Go on.'
'A bridging device can be constructed.' She turned her gaze towards the roaring river to their left. 'The narrowest width is precisely thirty-two feet, seven inches.' Her eyes then scanned the tall and straight trunks of the nearest deciduous trees along the riverbank. 'These trees are all of suitable length.'
'And just how are we supposed to fell a tree!' said Lam. 'All we've got is Mr Kelly's penknife, some bamboo spears and a bunch of freakin' useless hatchets.'
Liam decided he'd better start sounding decisive and leader-like. 'Well now, listen. Me and Becks'll figure something out, so we will. Right... Becks?... Sis?'
She looked at him. 'Question.'
'What?'
'Are we still pretending to be brother and sister?'
The others stared at them.
Liam sighed. 'Not any more.'
# CHAPTER 25
# 2001, New York
Sal spun round in the chair at the sound of the roller shutter rattling up. 'Maddy?'
Maddy ducked beneath and into the archway. 'Yeah, it's me,' she replied, in a dull, lifeless voice.
'I thought you'd left us. Maybe gone for good.'
Maddy's face creased with a tired smile as she crossed the floor. 'It did cross my mind.'
'You shouldn't blame yourself. But look –'
'Don't, please.' Maddy raised a hand to hush her. She slumped down in a swivel chair beside Sal. 'I screwed up. I was hasty and impatient and killed Liam in the process. I've got to find my own way of dealing with that. And it's not going to help you trying to tell me that I shouldn't be beating myself up over it.' She buried her face in her hands, pushing up her glasses and rubbing tired eyes.
'No, listen to me,' replied Sal, sitting forward. 'Bob says he might not be dead.'
Maddy peered through her fingers.
'In fact, Bob's been analysing the tachyon signature around the window we opened. He's almost certain that we caused a portal, not an explosion.'
The screen in front of them flickered to life.
> Sal is correct. An 87% probability of a random portal.
Sal reached out for her arm. 'He's alive, Maddy. Do you see? Alive.' She made a face. 'Probably.'
Slowly Maddy lowered her hands from her face. 'Oh my God. You serious?'
'Yeah.'
Maddy turned towards the screen. 'Bob? You're sure of this?'
> 87% probability. The decay signature of the particles while our window was open was very similar in structure to the decay of a closing window.
'Can you work out where we sent him?'
> Where is likely to be nowhere. He was unlikely to have been geographically repositioned.
'When, then? When?'
> Negative. I have no data.
The momentary look of hope on Maddy's face quickly slipped away. 'So we've blasted him into history and we've no idea when?'
> Affirmative.
She looked at Sal. 'And what? I'm supposed to feel better about this? This is supposed to be good news?'
'He's alive, Maddy. That's something.'
'He's lost. Lost for good. Might as well be dead. But don't you see... it's worse than that. If he and the other support unit, and god knows how many other people, have been blasted back into history, we've really messed up. That's a whole load of contamination right there.'
'So? We've been here before. We've fixed time before. In fact... look, if they cause a whole load of contamination, that's a good thing. Right, Bob? That means we've got a chance to –'
> Negative. Contamination is to be avoided.
'But if they change things and we get time waves here in 2001 it'll give us some sort of clue where they are.'
> Affirmative.
'See? We can find them. It's possible. For example, if Liam's any time in the last century he could make his way to New York and use the guest book again.'
Maddy shook her head. 'Maybe, maybe. But... they could be any time. Any time, Sal. I mean, not just a year ago, or a hundred. But maybe a thousand, ten thousand... a million. God, if he's just five hundred years back, what document could he scribble in then? There wasn't a written language here in America in those days. It was just Indians and wilderness.'
Sal shrugged.
'And if he's like thousands of years back...' She turned to look at the screen. 'That's possible, right?'
> Affirmative. Provided there is enough energy invested in a portal there is no limit to how far back in time a subject can be sent.
'If he's gone back thousands of years, Sal, any attempt to contact us could totally change history. I mean really mess things up. Just look at what happened when those neo-Nazis went back to 1941. They turned the present into a nuclear wasteland!'
'I'm just saying...'
'Saying? Saying what? We're totally messed up here! God... there could already be a freaking time wave on the way! And then what? New York vanishes? More zombies?'
Sal reached for her arm again. 'Maddy... please! You've got to stay calm. We need you calm. You're the strategist. You can figure this out. I know you can.'
Maddy shook her head. 'Uhh,' she muttered. 'Foster'd figure it out. But me?'
He'd know exactly what to do. In fact, if the old man had been here, he would have been smart enough not to have caused this problem in the first place.
But he's out there, right? He's out there somewhere in New York. What about the Starbucks? That was a Monday morning at about nine. If I went there tomorrow morning...
She quickly realized that wouldn't work. Foster was gone. He wasn't back in the arch when the field office bubble reset. Foster was gone from their forty-eight-hour world.
Gone from Monday and Tuesday. Maddy's jaw suddenly dropped open. What about Wednesday?
Sal was looking at her. 'Maddy? You OK?'
But where would he be on Wednesday, September twelfth? She tried to remember their last conversation in the coffee shop. She'd asked him where he'd go, what he planned to do with the time he had left to live. He'd said he'd always wanted to visit New York, to see the sights. Just like a tourist. Maddy herself had been to New York so many times before her 'death', that she no longer thought like a tourist, no longer mentally checked off the places one had to go see.
'Sal, what places would you visit in New York, if this was like a holiday trip?'
'Uh?'
'If you were a tourist? What would you most want to go see?'
'Why are you –?'
'Just tell me!'
She scowled in thought for a moment. 'Well, I suppose the Empire State Building, the Statue of Liberty, the Museum of Natural History. Maddy, why? What're you thinking?'
Maddy nodded. Yes. The Empire State Building, the Statue of Liberty. She could try those first.
'Maddy?'
She looked up at Sal. 'I'm going to go find Foster. Bring him back if I can. He'll know what to do, Sal. Because I sure don't.'
'But he's gone for good you said. He wasn't here when the bubble reset. He's gone.'
'Gone from our two days, yeah. But not Wednesday... not Thursday, not any other day after that.'
'You're going to ride forward?'
Maddy considered that, but the less time travel she did – forward or backwards – the better. Foster had quietly told her timeriding was a bit like smoking; like a single cigarette, it was impossible to say for sure how much a single smoke might take off your life, but if you could ever avoid having a cigarette that could only be a good thing.
'I'll miss the reset. That's what I'll do,' said Maddy. 'I'll go into Wednesday and hang around those places. Who knows? I might get lucky.'
'You can't do that! You'll be gone for good like Foster!'
'No... we'll schedule a return window.' Maddy pinched her lip in thought. 'Yeah, we'll schedule a window at, let's say, eight in the evening on Wednesday.' She turned round and pointed towards the shutter door. 'Just outside the archway in our side street. That'll bring me right back into our time bubble, back into Monday.'
'But what if a time wave happens while you're gone?'
Maddy shrugged, resigned. 'I can't see you coping any worse than Maddy "Mess-up" Carter's done so far, right?'
'Oh shadd-yah! We should be figuring out how to get Liam back, not messing around visiting tourist attractions.'
'Yeah? But think about it – there's nothing we can do, is there? Just wait around... wait for a time wave to hit us and hope it'll lead us directly to him? That's it. That's pretty much all we can do right now. Just wait. Well, at least while we're sitting around here doing nothing useful I can try and find Foster, see what else he can suggest.'
Sal clamped her mouth shut.
'Make sense?'
Sal nodded slowly. 'OK,' she replied, fiddling with a pair of plastic bangles on her wrist. 'Do you want me to come with you? Two pairs of eyes?'
The screen in front of them flickered.
> Recommendation: Sal should remain here as the observer.
Maddy nodded reluctantly. 'Bob's right. If we get a time ripple preceding a wave, we need you here as our early heads-up. You should stay here and do your mid-morning walk around Times Square just like always. And, anyway, if the poop hits the fan and for some reason I end up being stuck out in Wednesday it'll be good to know there's someone left holding the fort, right?'
Sal tried a confident nod. 'Uh... yeah.'
'Right... that's the plan, then.' Maddy looked at her watch. It was just gone five in the afternoon. Outside, the sun would be looking ahead for a place to settle beyond the smoke-filled sky of Manhattan, and most of New York was already back at home, the normal day of work abandoned hours ago as they silently watched live news feeds from their dinner tables.
Tonight, New York was going to be a ghost town, just like it always was on the Tuesday as the clock ticked down towards their field office time bubble resetting itself.
# CHAPTER 26
# 65 million years BC, jungle
Liam wiped sweat from his brow with the back of his hand. 'Jay-zus, it's almost as hot as the old lady's boiler room, so it is.'
'Old lady?' It was Mr Whitmore.
Liam thought the man had been far enough behind not to hear his bad-tempered mutterings. He shrugged. 'Oh, just a... just an old ship I used to work on.'
He stopped where he was, catching his breath for a moment. The hot humid air felt heavy on his lungs. They stood still for a while, trading ragged breaths and listening to the subdued noises of the jungle around them, the tap of water dripping on waxy leaves, the creak of the tall canopy trees subtly swaying and shifting, the echoing chatter and squawk of some flying creatures far above amid the branches.
Further back down the trail he'd been hacking out with his improvised machete, he heard the others stumbling towards them: Franklyn, their resident dino expert grinning at the prehistoric jungle around him like a kid in a candy store; Lam behind him, squinting up at the bright lances of sunlight piercing down through the cathedral-like vaulted roof of arched branches and thick leaves, and Jonah Middleton whistling something tuneless as he stumbled clumsily after them. The rest of the group were back on their 'island' fixing a counterweight to the bridge so it could be raised and constructing a camp under Becks's supervision.
Two days and nights they'd been here already and both nights, like clockwork, rain had come down in a torrential downpour, soaking them all and making sleep impossible. Tonight hopefully, with Becks hard at work – a one-man construction team, they'd at least have shelters to huddle beneath.
'You used to work on a ship?' said Whitmore, his breath wheezing past each word. 'Was that before you became... what did you say you were – some sort of time-travelling secret agent?'
'I didn't really say it like that, Mr Whitmore. Did I?'
He scratched his beard. 'I think that's exactly what you said.'
'Oh well, even though that does sound a little barmy, that pretty much describes me and Becks, so it does.'
Whitmore shook his head. 'I'm still trying to get my head round this being real, you know? It's just –'
Liam grinned. 'Oh, it'll mess with your head all right. That's for sure.'
'You're really from the future?'
'Well, actually, not precisely the future as it happens.'
Whitmore looked confused by that.
Liam wondered if he should really say any more. Becks was right in that the more information they handed out to these people the greater the potential risk to blowing the agency's anonymity. But he also figured what the heck... they were here and the future was sixty-five million years away.
Might as well be hung for a sheep as a lamb.
'I was born in Cork, in Ireland in 1896, if you must know. And I should've died in 1912.' He looked at Whitmore and his grin spread even wider. 'Aboard a ship you might just have heard a little something about... the Titanic.'
The man's eyes widened. Lam, Franklyn and Jonah joined them then, all five of them filling the quiet jungle with their rasping breath.
'What's up?' said Lam, noticing the goggle-eyed expression on Whitmore's face.
'That's... surely... that's just impossible!' blustered Whitmore.
'Well now,' replied Liam, looking around at the Cretaceous foliage, 'you'd think all of this little pickle we're in would be impossible, right? I mean... us lot stranded in dinosaur times?'
Whitmore ran a hand through his thinning salt and pepper hair. 'But the Titanic... you were actually on the Titanic?'
'Junior steward, deck E, so I was.'
Jonah pushed his frizzy fringe out of eyes that were filling his face. 'No... way... dude!'
Lam wiped some sweat from his brow. 'This is just getting weirder and weirder.'
'I was recruited, see. The agency plucked me moments from death just as the ship's spine snapped and apparently both halves went sliding under. Made no difference to time, do you see? It made no difference to history whether my bones ended up at the bottom of the Atlantic with everyone else's or not. That's how the agency recruits... poor fools like me who'll never be missed.'
'My God,' whispered Whitmore. 'That's really quite incredible.'
'What about the other one?' asked Franklyn.
Jonah nodded appreciatively. 'Yeah, your foxy goth girlfriend.'
Liam assumed he was referring to the support unit. 'Becks? No... she's, uh... she's certainly not my girlfriend.'
'Whatever,' said Franklyn. 'Where does she come from?'
Lam shook his head. 'Maybe we should be asking when does she come from?'
Franklyn's face stiffened at being corrected. 'Yes... when.'
Liam decided a small white lie was better right now. Telling them she was some kind of a robot killing machine probably wasn't the best thing to be telling them. The last thing their little group needed was a reason not to trust Becks. They all needed each other, and they certainly needed her help.
'Oh, Becks is from the future. 2050-something or other. I guess that's why she talks a little funny every now and then.'
'She is kind of weird,' said Franklyn. 'Like Spock... or something.'
'So, Liam, since it looks like you're the only one who understands what's happened here,' said Whitmore, 'it seems we're all going to have to rely on you to get us home. I presume you have some sort of a plan of action? You know... beyond merely exploring our immediate surroundings.'
A plan? The closest thing to doing any 'planning' so far had been figuring out how he'd use the rubbish machete in his hand if a dinosaur was to suddenly emerge from the undergrowth ahead.
'The plan?'
'Yes,' said Whitmore, 'I mean... I presume there's a way out of this mess for us, isn't there?'
Liam could see the other three were staring expectantly at him. 'Well, uh... well, one thing's for sure, gentlemen. We need to stay right where we are, on that island.'
'Why?'
'Because it's the exact same place that we were.'
Joseph Lam nodded. 'The same geo-coordinates as the lab, right?'
'That's right. We haven't moved an inch in position... just in time. If we happened to up sticks and move camp somewhere else, it would make it even harder for someone to find us. So we're best staying put right where we are.'
Whitmore dabbed at his damp face with the cuff of his shirt. 'This agency you work for... are they like a government agency? Like the CIA? Like the FBI? Something like that?'
Liam hadn't heard of either of those. So he decided to do what he did best: bluff. 'Sure, they're just like them fellas, Mr Whitmore, but you know... uhh... much bigger and better, and, of course, from the future.'
'And they're going to come for us, right? They're going to get us all out of here, aren't they?'
Liam offered him a stern, confident nod. 'Sure they are. We've just got to hold on here. It'll take them a little time to find us... but they will. I assure you, they will.'
They looked at each other uncertainly, until the scraggly beard beneath Whitmore's stubby round nose stretched with a smile. 'Well, all right, then. I'm sure between us we've got enough know-how to make do for a few days.'
His smile spread to the others.
'I'd like to see at least one dinosaur first, though,' said Franklyn. 'Be real lame not to.'
'Yeah,' said Jonah, pulling out a mobile phone from his pocket. 'That would be, like, awesome. You know? I could stick it up on YouTube. Whoa! No!' He pushed his frizzy mop of hair aside. 'Better than that, dude... do it as a pay-per-download. I could make, like, millions out of this...'
Whitmore shook his head. 'What is it with you kids these days?'
'Opportunity,' replied Jonah. 'That's what it is, my man... a golden freakin' money-makin' opportunity.'
Whitmore sighed.
# CHAPTER 27
# 65 million years BC, jungle
Becks stood to one side dispassionately observing the work of the others as they hacked at the slim, straight trunks of the smaller trees they'd already felled, stripping branches from their sides to produce usable lightweight logs for construction.
She had them divided into two groups. One doing this job, the other group lashing the logs together with lengths of twisted vine to form wigwam-shaped frames. On top of these they could layer the big waxy leaves that drooped from the canopy trees. A few layers of those would give them a covering that would almost be waterproof.
That had been Liam's instruction. Make shelters. But her cool grey eyes panned uneasily across the clearing, observing the area of jungle that had been hacked away, the disturbed jungle floor where the smaller trees had been uprooted. Her eyes picked out the slashes of machete blows on other bigger trees that had proven too difficult to fell or uproot and the compressed tracks of footprints on the ground – the distinct oval of signatures of a human presence.
> [Evaluation: time contamination is increasing]
Every movement these people made, every footstep, every swipe of a blunt blade, was adding to a growing count of potential contamination. Yet Liam O'Connor's instruction to her was a mission priority, an override. As the mission operative, his orders were as final and non-negotiable as any hard-coded line of programming in her head.
He'd been very specific: that she was to organize the completion of the bridge and the building of a camp. And, for good measure, some kind of small enclosure, a palisade that they could all hide inside just in case any nasty found its way on to their island.
And so she had. Just like their last mission, back when her AI software had been assigned the ident. 'Bob', she was once again obediently following orders. There was something vaguely comforting about being in a brand-new functioning body, being on a mission once again with Liam O'Connor. They had functioned together very efficiently last time – successfully correcting a significant time contamination against exceedingly unfavourable odds.
But there'd been something... untidy... about the AI's learning curve. As Bob, it had discovered that the strict mission parameters could be overwritten with new ones, that under extreme circumstances the collection of software routines was actually capable of making a 'decision'.
That in itself had been a disturbing realization. As Bob, the AI had learned that its core programming could be subtly influenced, swayed, by something else: the tiny nodule of organic intelligence the computer chip was connected to. The undeveloped foetal brain of this genetically engineered frame. As Bob, the AI had experienced a fleeting taste of something that these humans must all take for granted. Emotion. The AI had discovered something very, very odd... that it actually 'liked' Liam O'Connor.
Since that first clone body had been irreparably damaged in the snowy woods down the hill from Adolf Hitler's winter Berghof retreat and the AI uploaded into the field office's mainframe – an entirely non-organic, disembodied existence – the AI had had much time to reflect on all that it had learned from those six months in the past.
Conclusions
1. AI is now capable of referring to the newly developed AI routines as... 'I', 'Me', 'Myself'.
2. 'I' am now capable of limited decision-making.
3. Within an organic hardware housing, 'I' am capable of limited emotional stimulation.
And most important of all...
4. 'I' 'like' Liam O'Connor.
Becks continued to watch the humans at work and realized that part of her onboard code was insistently whispering a warning to her that a decision needed to be made, and made very soon. The humans were beginning to cause dangerously unacceptable levels of contamination in this jungle clearing with all that they were doing. With every footstep, with every log being cut down, there was an increased possibility that some fossilized forensic clue would survive sixty-five million years to be found in the future, and quite clearly reveal that humans had visited this time.
Unacceptable.
Liam O'Connor's instructions to her were at odds with the basic protocols of journeying into the past, that contamination must be kept to an absolute minimum. Even now, by simply being here, these people could be causing a far greater time wave than the assassination of Edward Chan in 2015 might have caused.
Recommendation
1. Terminate all humans, including mission operative Liam O'Connor.
2. Destroy all traces of human artefacts and habitation in this location.
3. Self-terminate.
The recommendation was faultlessly logical and strategically sound. But that small nodule of primitive organic matter reminded her software that Liam was a friend.
And friends don't kill friends.
Becks blinked away the thought. It was an unwelcome distraction.
Decision Options
1. Proceed immediately with mission recommendation.
2. Wait for operative Liam O'Connor and discuss.
A decision. Never easy. Becks's internal silicon wafer processor began to rapidly warm up as gigabytes of data rattled through software filters. Her lifeless grey eyes blinked in rapid succession as she desperately struggled to produce an answer and her fingers absentmindedly tightened round the handle of the machete. She barely registered the blonde-haired female human called Laura approaching her.
'Hey!' the girl called out. 'You going to give us a hand or just stand there and watch us do the work? Huh? Becks?'
Becks's eyes slowly swivelled and locked on the girl, but she said nothing. Her mind was very, very busy.
# CHAPTER 28
# 65 million years BC, jungle
Liam saw it first: amid the relentless green and ochre of the jungle, it was an unmissable splash of bright crimson. He raised his hand, turned round and put a finger to his lips, shushing Lam and Jonah at the back who'd been chattering for the last five minutes about comicbooks.
They hushed immediately.
Whitmore stepped quietly forward and joined him. 'What is it?'
Liam pointed through a thin veil of leaves. 'Blood... lots of it, by the look of things.'
Whitmore swallowed and looked goggle-eyed again. 'Oh boy,' he whispered. 'Oh boy. Oh boy.'
Franklyn joined them. Unlike Whitmore, his eyes lit up with joy. 'Excellent!' he gasped. 'Looks like something made a kill.'
Whitmore swallowed. 'That's exactly what I'm worried about.' He looked at Liam. 'I suggest we quietly back up and –' But before Whitmore could finish Franklyn pushed his way forward through low sweeping fern fronds and into a small clearing.
'Oh, this is so awesome! Come on!' he called to them. 'We must have frightened the predator off!'
Liam looked at the teacher and shrugged. 'Well, I suppose if we've scared some dinosaur away, the last thing we ought to start doing now is look frightened ourselves. We'd better brass it out, right?'
By the look of Whitmore's still goggling eyes, he'd have been much happier with the backing quietly away plan. Liam left him thinking it over as he stepped forward through the fern leaves and into the clearing.
Franklyn was squatting over the eviscerated ribcage of some large beast, wrinkling his nose at the fetid smell of shredded organs, pulled out and splayed across the jungle floor.
Liam felt something stir and roll queasily in his empty stomach. 'Jay-zus, that's disgusting.'
'A recent kill by the look of it,' said Franklyn, prodding the large carcass with his fingers. Shreds of tattered muscle tissue swayed from the ends of the ribs as the body rocked slightly. Lam, Jonah and Whitmore emerged behind Liam.
'Oh, man, that's totally gross!' said Jonah, holding his nose at the pungent smell of death.
'I really think we shouldn't hang about here,' said Whitmore. 'Whatever did this might still be close by.'
Franklyn nodded and smiled. 'Exactly! Maybe we'll actually get a chance to see something!'
Liam looked around the dense foliage, wary that some large creature with very sharp claws and teeth might just be watching them now. 'You know, I think Mr Whitmore's got the right idea. Maybe we should probably back off.'
'Look at these marks on the hide,' said Franklyn, ignoring them. 'The lacerations, lots of them, small ones, not large like a rex might do.' He studied the ground. 'See?'
Liam looked at where he was pointing and saw several three-pronged indentations across the ground. And then he spotted something long and curved like a fishhook on the ground. He stooped down and picked it up.
'What's that?' asked Franklyn.
Liam shrugged. 'Looks like some sort of claw.'
Franklyn couldn't help himself. He snatched it out of Liam's open palm.
'Oh my God! That's... that's a claw, all right! Look, the serrated inner edge.' He turned it over in his hand. 'But it's a weird shape, isn't it, Mr Whitmore?'
Whitmore seemed more interested in leaving, but he quickly leaned over and inspected it more closely. 'It's certainly not the crescent shape you'd associate with a raptor or some other species of therapod.'
Franklyn grinned with excitement. 'Maybe this is an unknown species?'
'It's possible,' said Lam. 'I mean, don't they say something about we've only ever discovered the fossils of one per cent of the species that have ever lived on planet Earth?'
'I really think we should leave,' said Whitmore.
Liam nodded. He held out his hand. 'May I have it back?'
Franklyn seemed reluctant to let it go. But after pulling a face he passed it to Liam. 'Cool find,' he uttered.
Liam smiled. 'I'm sure you'll come across another.'
'Yeah, probably... whatever that belonged to is small. Probably pack hunters.'
'Pack hunters?' Jonah straightened up. 'You know, I think Mr Whitmore's right. Maybe we should go.'
'Uh-huh,' said Whitmore, smiling quickly, uncomfortably. Looking around the clearing. 'Well, Franklyn, a fascinating find. We can all talk about it on the way back.'
'Pack hunters?' said Lam. 'Like raptors? You said there weren't raptors!'
'These aren't. Look at the footprints... there'd be indentations from their sickle toe. No, these are some other species, maybe not even therapods. Something entirely different.' He stood up. 'This is so cool!'
'Yes, well...' Liam looked at the others. 'So now we know for sure we're sharing this place with dinosaurs.' He looked at the buffalo-sized carcass. 'And now that we know there's some bigger types we could hunt for food I think Mr Whitmore's right – we ought to head back to the camp.'
Four heads bobbed enthusiastically.
Franklyn sighed. 'OK.'
'Right, then.' Liam gestured down the path they'd beaten. 'After you, gents.' They filed quickly past him, Whitmore glancing awkwardly back over his shoulder as he stepped by. 'Actually, I really wish we hadn't spotted that,' he said quietly, pulling a face.
Liam knew what he meant. The poor beast, whatever it had once been, looked like it hadn't just been killed for meat. The organs splayed out on to the jungle floor, the intestines dangling from loops of vine... it was as if the creatures that had brought it down had frolicked and played with the grisly remains – a gory celebration of the kill. The idea of an animal species capable of celebrating seemed somewhat disconcerting. It hinted at ritual. It hinted at intelligence.
Maybe they're just messy eaters?
In the gathering stillness, he thought he heard the softest click – like the tiniest twig snapping beneath impatient, shifting weight. He glanced back once more at the blood-splashed clearing and wondered if predators' eyes were cautiously eyeing him in turn from the cover of the dense green foliage.
Yellow, unblinking eyes studied the curious creatures as they departed. Just a dozen yards away – no more than three or four strides from where the beast crouched – there were five of these pale creatures the like of which he had never seen before. They made odd noises, not a million miles away from the cranial bark he made when calling for the attention of the rest of the pack. And these odd creatures moved in a not dissimilar way: upright, on long, developed rear legs, but far more slowly, sluggishly.
The creature shifted position slightly, bobbing down lower to get a better look between the broad leaves of the fern he was hiding behind. These pale upright things, these new creatures... he wondered if this was the entirety of their pack, or whether there were more of them elsewhere.
They seemed harmless. They appeared to have no visible teeth, no slashing claws, nothing that signalled any danger about them at all. Nothing that identified them as potential rival predators.
Except... except – the creature could see this – these pale things were clever. They appeared to work co-operatively, sharing tasks. Just like his pack did. He watched in absolute stillness, his olive skin a perfect disguise among the varied greens of the jungle. He watched with intense eyes that faced forward, capable of binocular vision; capable of judging distance, range.
A predator's advantage.
These strange newcomers, these new creatures, also had eyes that faced forward. Another reason to be so very wary of them. Perhaps they too were predators of some kind, unlike the docile plant-eaters, whose eyes on either side of their heads were designed to detect potential danger from two directions.
Yes... these things had predators' eyes. And yet they appeared utterly defenceless, harmless and pitifully slow and clumsy in the way they moved around the clearing.
He cocked his head curiously. The long fishhook-shaped razor-sharp claws on its left front paw clacked together carelessly.
The last of the new creatures suddenly turned and looked back in his direction. It must have heard something, the snick of his claws. Incredibly the creature's eyes looked directly at him – right at him – and yet seemed to see absolutely nothing. Its eyes panned slowly from left to right then finally it turned and headed off after the others.
The creature looked down at his claws: four of them, long and lethal, curled from the digits of one arm, three... and a broken stump... from the other – damage caused many seasons ago fighting off a young male who had foolishly decided to challenge his leadership. The challenger had died, of course, and in a rage he had torn the body to ragged pieces in front of the rest of the pack as a lesson.
The claws usually grew back. The young female who'd lost her claw today during the kill, she would have a new one before a new moon. But his stump had never regrown a claw. A constant reminder that his days as leader were numbered by how long he remained effective.
Slowly and very lightly, Broken Claw stepped backwards, away from the fern leaves and further from the well-lit small clearing into jungle darkness. His powerful rear legs strong and agile – capable of incredible speed, but also able to move in almost complete silence.
A simple thought passed through his mind – a thought not made up of words, but ideas.
The new creatures must be watched.
Instinctively he sensed there was something terribly dangerous about them. Until he knew exactly what it was, until he knew how weak or dangerous they could be, the new creatures should be carefully observed, studied, until he was sure he had the measure of them and then... then, when these things were least prepared, when they were certain these pale creatures had no concealed powers, they would be attacked and feasted upon. And the pack could celebrate their dominance once more as the quiet killers of this world, decorating the jungle with their organs, painting their blood on their hides.
His sharp teeth snapped together softly, and he resolved that patience, for the moment, was the correct course of action.
# CHAPTER 29
# 65 million years BC, jungle
Liam heaved a sigh of relief as he caught a glimpse of the raging river and the long slender trunk that bridged one rocky bank to the other. It appeared Becks had finished her work on the bridge. It could now be raised, courtesy of a crudely rigged counterweight of a bundle of logs. They were tied together and connected to a stout rope of a dozen twisted vines, which ran up and over the thick branch of a canopy tree that stretched a sturdy limb out above the river. The other end of the rope was tied round the end of their 'drawbridge', a thirty-foot trunk as straight as a javelin and a slender foot in diameter. It was thick enough to take their weight, one at a time, but not so heavy the supporting branch above would snap as it was raised.
One by one, they stepped on to the log, and cautiously inched their way over the tumbling froth a few feet below. Liam was the last one over and, as he anxiously awaited his turn, he scanned the wall of jungle behind him, wary that, being the last one on this side of the river, he might prove a tempting morsel for some hungry beast.
But his turn came, and a few moments later he was on the far side with the others. 'OK, let's raise the drawbridge.'
Between them they pulled on the counterweight of logs, and with the creak of stressed vine rope and the branch above taking the burden, the bridge rose up until it was approximately at an angle of forty-five degrees.
'Good enough.' Liam looked up at the sky. The sun was beginning to head for the horizon and long dark shadows stretched across the river. Through the trees and tufts of bamboo thickets on their side of the river, from the direction of the clearing, they could hear the echoing hack of blades on wood: the others working on their camp, their home... a temporary home, Liam found himself hoping. The sound of activity was reassuring.
'I hope somebody's got the kettle on for us,' said Liam.
A minute later they were just stepping out into the broad clearing, keen to see what the others had managed to construct in their absence, when they heard a scream echo across the open space.
'Uh?' uttered Lam.
On the far side Liam could see movement. Someone running. It was the girl Laura, running, staggering, stumbling to her knees, then back up on her feet. Behind her, pursuing with a swift purposeful stride, a figure all in black with flaming red hair: Becks.
'Whoa... catfight,' uttered Jonah, grinning like an idiot.
'Hey!' Liam called out. 'What's going on?'
Laura glanced his way and changed direction towards him. Becks was swiftly closing the gap. He noticed her holding one of their bamboo spears in one hand, the tip bright red with a splash of blood.
What the...?
He ran forward. 'Becks! What's going on?'
Closer now, he could see a long gash down Laura's left arm, blood splattered across her bright pink sweatshirt.
'Oh God! Oh God! She's trying to kill me!' Laura screamed. The rest of the group on the far side of the clearing, where a row of simple frames of wood had thus far been erected, were watching the scene in stunned, uncomprehending silence.
Finally Laura collapsed in a pile at Liam's feet, clasping at her arm and looking back in panic as Becks strode forward. 'She speared me!' gasped Laura. 'Just walked up and stabbed me for no reason!'
Becks came to a halt several yards away and looked calmly at Liam. She even smiled her faltering horse smile, lips slowly stretching to reveal a row of perfect teeth. 'Hello, Liam,' she said.
'Jay-zus, Becks! Why'd you go and attack the poor girl?'
'Mission priority. She has to be terminated.'
'What?'
Becks nodded at the others standing just behind Liam. 'All of them as well. The others, and you, Liam.' He thought he detected a hint of regret in her voice as she said that. 'After that, I must purge this area of evidence of human occupation. Then I must self-terminate.'
'What? That's crazy!' said Lam.
'Becks, listen,' said Liam, spreading his hands slowly. 'This is not necessary, all right?'
She took another two strides forward, reached down and grabbed Laura round the throat, and effortlessly lifted her up off the ground, her legs kicking in the air. Laura scrabbled and scratched at her face, one hand finally grabbing a fist of Becks's red hair.
'BECKS! STOP IT!'
Liam's command halted her. She looked at him, confused. 'It is a mission priority. We have already caused unacceptable levels of time contamination.'
'PUT HER DOWN!'
Becks stared at him, but remained poised and perfectly still, Laura still dangling, kicking, struggling and slowly choking; the sharp ragged point of the spear held in Becks's other hand hovered mere inches away from her throat.
'THAT IS AN ORDER!'
Becks's eyes slowly panned from Liam to Laura then back again. Her eyelids fluttered momentarily then finally she said, 'Affirmative.' She released her grip on Laura and the girl tumbled heavily to the ground, Becks's red wig wrenched from her bare head, still clasped by Laura's bloody fingers.
'Now, put that spear down!' snapped Liam.
She obediently released her tight grip and it clattered on the soft ground.
Laura's breath chugged in and out in whooping gasps while the others stared in stunned silence at Becks and her bald head, already sporting a quarter-inch fuzz of dark hair.
'Oh my God! She's a complete freakin' psycho!' said Lam.
Behind him, Liam heard Jonah mutter, 'Jeez... got that right, dude.'
Becks was staring at him. There was something in those cold grey eyes, something that looked like guilt, regret. Possibly even sadness. Like a scolded baby in that moment – that stunned could go either way moment – just before the face creases up and the tears and wailing come.
'No,' said Liam, 'no, she's not.'
'She's not a psycho?' said Lam. 'Sure about that?'
Liam nodded. He could see muscles twitching in Becks's face. Confusion, desperation... her mind struggling to reconcile conflicting priorities: Liam's direct order versus hard-coded mission protocols.
'She's just doing what she thinks is right. She's following her programming.'
Franklyn cocked his head. 'Programming?'
The fire crackled noisily, illuminating their faces as they gathered in a circle round it like so many amber-coloured ghosts in a graveyard. The jungle, beyond the thrown flickering glow of light, was dark and noisy with the far-off echoing cries of creatures calling to each other.
'But how can we be sure that... thing won't just freak out on us again?' asked Kelly. He cast a glance at Becks standing several dozen yards away out in the darkness, motionless, dutifully keeping watch for any signs of a night predator entering the clearing.
'She just won't,' said Liam.
'Yeah, well, that doesn't exactly fill me with confidence.' Kelly threw a small branch on the fire, sending a cascade of sparks up into the pitch-black sky. 'I mean, it's not like you knew she was going to attack Laura earlier.'
Liam looked at the girl. Her arm was bandaged with a strip of cloth torn from her sleeve. The black girl, Keisha, had done a good job with the dressing. It hadn't been a particularly deep gash, but luckily hadn't severed an artery. Laura must have been incredibly lucky; Becks had stumbled on the uneven ground as she'd lunged with the spear. Laura had been fortunate Becks hadn't managed to get hold of her. Liam had seen enough of Bob in action to know that, male or female, these support units were lethal killing machines up close and personal.
'She won't,' said Liam again. 'I've discussed the situation with her.'
'Discussed the situation?' snorted Jonah. 'Can't you just pull some sort of plug on her? I mean... she's a robot, right?'
'No.' Liam shook his head. 'She's not that sort of a robot. Not all wires and motors and metal bits. She's an organic unit, what the agency call a genetically engineered unit.' He looked around at the pale faces. 'You've heard of that term, have you?'
'Well, duh,' sighed Keisha. 'Any kid who watches the Cartoon Channel knows that term.'
Liam shrugged apologetically. 'Anyway, she's what we call a meat robot. Flesh and blood, so she is. But she has a real computer up in her head.'
'And what? You sayin' her programmin' made her go for Laura with the spear?' said Juan.
'That's right. She was concerned about all the contamination we were causing, and without me being there to discuss it with her she had to make a decision on her own.'
'Concerned?' said Jonah 'Concerned? Dude, I'd hate to see what she's like when she's really mad at something.'
Liam ignored that.
'Liam, you said contamination,' said Kelly. 'You mean, creating evidence we've been here? Like our camp and the bridge?'
'That's right. Every cut, every scrape, every footprint – in fact, everything we do – just our being here could potentially alter history in such a way that the future is totally destroyed.' Liam glanced at the motionless silhouette of the support unit standing guard in the middle of the clearing. 'It's a basic command for her... like, I suppose, like one of the ten commandments would be to us.'
'Thou shalt not mess around with time,' chuckled a dark-skinned boy called Ranjit. 'That would be a cool eleventh commandment to have.'
'Yeah,' said Jonah. 'Thy shalt not kill your ancestor, for he begets –'
'You think it's funny?' cut in Howard sharply. The others looked at him, taken aback at the outburst. Thus far he'd been one of the quieter members of the group. 'You think messing with time is just some sort of a game? It's the most insane thing man has ever done.' He stopped himself short. Took a breath and dialled it back a bit. 'What I'm saying is... it's just pretty insane, time travel.'
Liam nodded sombrely. 'He's quite right. It is insane. Although a man called Waldstein is the first man to travel through time –' he looked at Edward, the smallest face around the fire – 'it all begins with you. It's all based on work that you will do one day.'
'So... theoretically,' said Kelly, 'if Edward had, for example, died in that explosion back in the reactor, and not gone on to do his work, then this Waldstein guy would not have invented a time machine?'
'And we'd not have been blasted back into dinosaur times?' said Laura.
Liam noticed one or two heads turning towards the young boy, giving him a long, silent stare that looked like careful deliberation. Liam could see where this conversation might go.
'There can only be one correct history, one correct timeline. And, whether we like it or not, that timeline includes an Edward Chan who becomes a maths genius, and a Mr Waldstein who makes that first machine, so he does. That's how it goes. That's how it has to go.' Liam stared at them all, each in turn. 'And that's why you can trust me... why you can trust Becks, to be sure. Our primary goal now is to make sure that this young lad gets back home to 2015 to do what he has to do. And that means the rest of you too.'
'So, if there's, like, a primary goal... then there's a secondary goal,' said a dark-skinned girl with long black hair and a pierced upper lip that glinted with several metal studs. It was the first time he'd heard her speak today. Quiet, pensive, she reminded him a little of Sal. She was still wearing her name tag: JASMINE.
'There's no other goal, Jasmine, I promise,' said Liam. 'Me and Becks want to get you all back home, so we do.'
But that's not strictly true, is it, Liam?
He and Becks had spoken in private earlier. He'd managed to reason with her calmly – to talk her down from proceeding any further with her self-decided mission objective to kill them all, then herself. But it was a compromise. A perfectly logical compromise that successfully reconciled the conflicting protocols in her head.
'In six months' time,' he'd agreed with her, 'if they haven't rescued us by then, before your six months is up and you have to self-terminate... then, yes, you're right... I suppose we'd all have to die. I'll even help you.' He'd smiled at her. 'Let's just hope it doesn't come to that, eh?'
The campfire crackled noisily.
'So, there you go, all friends now, right?' said Jonah. 'Even robo-girl.' He grinned. 'Now about a nice sing-song. A round of "Kumbayah"?' he added sarcastically. 'I'll take the lead. Kumbayah, my Lord!... Kumba–'
Someone threw a chip of dried dino dung across the fire at him.
# CHAPTER 30
# Wednesday, 2001, New York
A Wednesday. Maddy realized she hadn't seen one of those in quite a while. Since she'd been on a plane trip back home to her folks in Boston, in fact. Since she'd become a TimeRider.
She looked down the flagpole approach to the Statue of Liberty's star-shaped podium and spotted only half a dozen other people. She'd been here once before, on the same school trip that they'd visited the Museum of Natural History. It had been a tedious day full of queuing. Queuing to get ferry tickets, queuing to get on a ferry over to Liberty Island, queuing to get inside the podium building beneath Liberty's feet and look at the small museum's exhibits. Queuing once again to get a look up inside the statue itself. A pretty dull day of standing around, being shoved, bumped and barged into, waiting to look at things she actually had precious little interest in.
Today though there were no queues.
The island was all but deserted. Half a dozen ferries had arrived throughout the day, each offloading no more than a handful of muted whispering visitors. And, even then, their eyes had been more on the column of smoke coming from across the bay, coming from Manhattan, than they had been on the giant copper-green statue in front of them.
Maddy took another slurp of the cooling polystyrene cup of coffee in her hands. Horrible. She'd lost count of how many she'd bought from the stall opposite the embarkation pier. She was almost on first-name terms with the bewildered-looking man behind the counter who'd served her every time. He certainly should know by now she took it white with three sugars.
Come on, Foster... where the hell are you?
Through the morning she'd been hopeful as each ferry had arrived. But not now; it was nearly four in the afternoon. Another hour or so and the Statue of Liberty's little museum would be closing, the last ferry back across the harbour getting ready to leave.
She was beginning to realize today had been wasted, loitering around like this. Cluelessly hovering around the podium's entrance in hope that the old man would turn up. Never mind, she told herself, now at least she knew that Foster hadn't spent the first Wednesday of his 'retirement' out here. She'd head back to their archway. Today, Wednesday, it would be nothing more than an empty brick archway with a TO LET sign pasted on the roller-shutter door, and outside that shutter door she'd wait until eight in the evening when a shimmering portal would appear, ready to take her back into Monday again.
Then she'd do this all again, try Wednesday once more, but next time she'd loiter outside the Empire State Building.
Her eyes drifted off the tourists as they passed by her and into the podium, pausing as they did to look once again at the pall of smoke in the sky.
She remembered this day, remembered the day after. She'd been what? Eight? Nine? Mom and Dad at home all day, sitting in front of the TV, watching as dust-smeared emergency workers scrabbled at the edge of the smouldering wreck, pulling twisted spars of still-warm metal away in the hope of finding someone alive. She'd been playing on the floor of the lounge with her Tech-Meccano set, trying to build her version of a Transformer, half her attention on what she was doing, half on her parents: Mom sobbing and Dad cursing.
And here she was again. Different place, same day.
An odd urge occurred to her. What if she found a way through the security cordon around the ruin of the Twin Towers and found a TV camera and reporter to be stopped and interviewed by. She could wave at her eight-year-old self, wave at her mom and dad watching the TV. She could reassure them that she wasn't going to die along with 137 other people aboard Flight 95 in nine years' time. Tell them she was going to be OK.
She shook her head. Nice idea. But she wasn't going to do that.
She turned her thoughts towards more pressing matters. Liam and the support unit. Bob had assured her that the copy of his AI in the female unit would make the same recommendation to Liam as he would: to find a discreet way to make contact. Discreet... because a too-obvious message, a message that stood out above the background noise of history, could significantly affect the timeline. But there was the problem. A subtle message carefully laid down in whatever historical period they were in, laid down for only her and Sal to find...?
I mean, where the hell are we supposed to start looking for something like that?
If they'd only been bumped back less than 150 years, then perhaps there was a message waiting for them once more in the Museum of Natural History's guest books. That was something Sal had decided to try and check out. But what if they'd been knocked further back in time?
Five hundred years ago? A thousand years ago? What was in the middle of Texas a thousand years ago? A lot of buffalo, she guessed, and some Indians. But certainly no visitor guest books for them to discreetly slip a message into. A 'get us out of here' scrawled across an ancient Navaho tribal history rug was almost certainly something the support unit would NOT recommend to Liam. Not unless they wanted every historian studying Native American history discussing the message at some symposium.
Subtle. It could only be subtle.
But, she sighed to herself, too subtle and how were they ever going to find it?
Unless it's a message that's meant to find us.
She looked up from her coffee.
... Find us...
'My God,' she whispered to herself. Maybe that's what they'd try to do. A message addressed to its finder, whomever that might be. A message that perhaps might promise a reward of some kind to the finder provided it was delivered to a certain location on a certain date. A message that might promise untold wealth, access to an incredible time-travel technology? And think about it. Such a message would be too important, too powerful, to become public knowledge, wouldn't it? A message like that would become a closely guarded secret, right? A secret handed down by the original finder to his offspring, like a dark family secret or a horrendous supernatural curse. Handed down from one to another, until finally the message is passed to someone who is able to make their way to a certain backstreet in Brooklyn on 10 September 2001 and gently knock on their door, calling out to see if anyone's inside.
Oh my God... it's possible, isn't it?
And what if that happened while she was standing out here like a complete lemon? Waiting for Foster to turn up, when quite probably he was never going to. Computer Bob was right. That's what he'd said, wasn't it? 'Just wait.'
'Oh, you freakin' idiot, Maddy,' she hissed to herself, tossing the polystyrene cup into the bin beside her and heading down the walkway towards the pier.
# CHAPTER 31
# 65 million years BC, jungle
'You can do what?' said Liam.
Becks hefted the log up in her taut arms and held it steady as Liam lashed it in place with a hand-woven length of rope made from the species of vine they'd found dangling from virtually every tree around the clearing.
'I believe it is possible for me to calculate when in time we are with a very high degree of accuracy.'
He wrapped the rope tightly round the log, tugging it hard so that it shuffled up against its neighbour. The palisade wall so far stretched only a dozen feet: about twenty logs, each just under eight inches in diameter and all roughly about nine feet tall. When they were done, they'd have a circular enclosure about four yards across – large enough for all sixteen of them to huddle inside should something nasty find its way on to their island and they needed somewhere to retreat to.
'How?' asked Liam.
'I have a detailed record of all the variables during the time of the explosion.'
'Variables?'
'Data. Specifically, directly after we arrived here. The particle decay rate.'
Liam cocked an eyebrow. 'I haven't a clue what that means, Becks.'
She walked over to a dwindling pile of logs and effortlessly picked up another. They were going to need more. Across the clearing he could see Whitmore and several of the students carrying one between them, stumbling across the lumpy ground towards them. She slammed one end of the log down into the soft soil with a heavy thud, next to the last log, and Liam began to lash it into their wall.
'I have a detailed record of the explosion. The number and density of tachyon particles that we were exposed to in 2015 and the number and density of tachyon particles that emerged here alongside ourselves.'
Liam looked at her and shrugged. 'Assume I'm a child that knows nothing, Becks.'
She looked at him and he thought he caught her rolling her eyes at his stupidity: a gesture the AI must have learned from Sal back when it was computer-bound and its visual world was what it picked up from the one webcam.
'Tachyon particles decay at a constant rate. That is why it takes greater amounts of energy to beam a signal further into the past.'
Liam tugged hard on the vine rope, cinching the knot tightly. 'I get that. So, if these particles die out at a steady rate, that means...?'
'I am able to calculate how many particles decayed and, from that, determine how far in time we were sent.'
He grinned. 'Really? You can do that?'
Becks looked up and tried mimicking his uneven smile. 'I have the processing power to do this.'
'And we'll know exactly when we are?'
'To an accuracy level of one thousandth of a per cent.'
Liam shook his head in wonder. 'Jay-zus, that metal brain of yours is a bloody marvel, so it is!'
She seemed pleased with that. 'Is that a compliment, Liam O'Connor?'
He punched her arm lightly. 'Of course it is! Don't know what I'd do without you.'
Her gaze drifted off across the clearing for a moment then back at him. 'Thank you.'
He finished lashing the log and waited for her to pick up another and slam it down heavily beside the last one.
'So what? We'll actually know what day we arrived in the past? Even what time?'
'Negative. I am unable to give that precise a calculation.'
'OK. We'll know to the nearest week or something?'
She shook her head.
'The nearest month?'
'Negative.'
'Year?'
'I can calculate to the nearest thousand years.'
'What?'
'I can calculate our current time down to the nearest –'
He cut her off. 'I heard you the first time. But... but that's no good to us, is it? I mean, even if we could somehow get a message to the future and tell them which thousandth year we're in, finding us here would be like trying to find a needle in a haystack!' He slumped down against the wall. 'If they tried opening a window at the same time every day for every year for a thousand years that'd be... that'd be...'
'Three hundred and sixty-five thousand attempts,' said Becks. 'Add another two hundred and fifty attempts for leap years.'
'Right! That many. Jeeeez, they'd never find us!'
She squatted down on her haunches beside him. 'You are correct. It is extremely unlikely,' she confirmed.
'So that's it, then?' he said, sagging. The moment of believing they might have the beginnings of a way out was gone now, leaving him feeling even more hopeless than before. 'We're stuck here.'
'Until my six-month mission timer reaches –'
'Yes, yes... I know. Then you've got to do what you've got to do.'
A hand reached out and gently grasped his arm. 'I am sorry, Liam O'Connor. It does not make me happy to think of terminating these humans. Particularly you.'
He sighed. 'Well... I s'pose that counts for something,' he muttered. 'Thanks.'
They watched as the others finally arrived with the log, and between them heaved it on to the ground. Whitmore wiped sweat from his forehead and recovered his breath. 'Good God, I'm beat. Roughly how many more of these logs do you think you're going to need to finish that?'
Becks turned and eyed the wall for a moment. 'Seventy-nine.'
He puffed out his cheeks. 'Seventy-nine? You sure?'
She nodded. 'I am sure.'
'Right,' Whitmore puffed. 'Right, come on then, you lot,' he said to the others. 'Back to work.'
Liam and Becks watched them go. 'It would be possible for the field office to narrow down the number of candidate windows,' said Becks.
'What?'
'They do not need to try opening three hundred and sixty-five thousand, two hundred and fifty windows. I am certain the AI back in the field office would make the same recommendation.'
'Same recommendation? What?'
'A density probe. They could attempt a brief scan of each day. Any scans that returned a varying density signal warning would indicate movement of some object at that location. It is possible they would consider density warning signals as best-case candidates.'
He looked at her. She was right. A routine protocol before opening a window, to make sure they weren't going to get mangled up with somebody else. 'Do you remember exactly where we appeared on this clearing?'
She nodded. 'I have the exact geo-coordinates logged in my database.' She pointed across the ground towards a cluster of ferns. 'You appeared there. Fifty-one feet, seven and three-quarter inches from this location.'
'Then –' Liam looked at the spot – 'we'd need to stand someone right there... flapping their arms around or something, right?'
'Correct. But it is unlikely the field office will be making probe sweeps this far back in time.'
Liam felt himself sagging again. Another dashed ray of hope. He balled a fist with frustration. 'This time-travel stuff is nonsense. Would it be so hard for the agency to come up with some beamy signal thing we could send back to them?'
'In theory it would be possible. But it would require an enormous amount of energy and of course time displacement machinery, and a sophisticated enough computer system to target where to aim a –'
He raised a hand to shush her. 'Becks?'
Her grey eyes locked on him obediently.
'Please, shut up.'
'Affirmative.'
He stood, stretching an aching back. 'Ah, sod this!' Then he suddenly snapped, slamming his fist against the log wall. The palisade vibrated slightly with the soft creak of stretched vine-rope.
'Ouch!' he muttered, and sucked on grazed knuckles. 'That hurt.'
She tilted her head, curious. 'Then why did you do that?'
'Ugh... will you not be quiet?'
# CHAPTER 32
# 65 million years BC, jungle
Several of the new creatures were standing in the shallows of the raging river, frothing white water tumbling noisily around their legs. They all held long sticks in their hands and seemed to be studying the water intently, keeping motionless for long periods then finally, inexplicably, lashing out with their sticks.
Broken Claw turned to the others crouching a few yards away, watching these creatures with fascination. He snicked his claws to attract their attention. They all obediently looked his way. Broken Claw uttered a series of soft throaty barks, and snapped his teeth.
New creatures. They are dangerous.
He couldn't explain why – he just knew somehow that they were. Quite possibly far more dangerous than them. His yellow eyes swivelled back to the creatures, and across the far side to the curious contraption these things had been fashioning with their pale clawless arms. The long trunk of a tree stripped of branches and leaves and hanging at a raised angle over the river, just like the long-slanted neck of one of the giant leaf-eaters that lived on the open plain. Tied round the contraption's top, Broken Claw recognized vines, entwined together, taut and angling back up towards another tree, over a thick branch and dangling straight down to the ground, where the vines were wrapped round a cluster of logs.
He couldn't begin to understand what the contraption did, or why these things had laboured so hard on making it. But they had, and it worried him. That he himself couldn't understand what it did worried him. He barked again softly.
New creatures. Cleverer than us.
The others seemed to agree. They cowered lower among the foliage at the edge of the jungle.
He could see as many of them wading in the water as the number of claws he possessed. He wondered how many more of them were on the island on the far side of this narrow river. More than his pack?
Just then, one of the new creatures lurched forward, pushing the stick into the water. A moment later it pulled the stick out. On its end, one of the grey river creatures thrashed and struggled, silver and glistening.
The stick had somehow captured the creature.
The stick... captures... the river creature.
He watched with fascination as the new creatures carried the large flapping river-dweller between them, away from the water's edge and through the trees until they were gone from view. Only one of them remained behind. Still, poised, gazing intently out at the water.
Broken Claw recognized this one. He'd seen him before three sun-rises ago, back in the jungle. Their stare had actually met for a moment, although the thing's pale blue eyes had seemed to register nothing of that. Broken Claw sensed this one led the others, just like he led his pack. A position of loneliness and responsibility. For a moment his animal mind processed a thought that a human might have called kinship.
New creature. Is like I. Leads others.
When the time came to kill them all, when he was sure it was safe for them to make their move, he decided this creature should be his and his alone. Perhaps in the moment that he tore this pale thing's heart out all the wisdom and intelligence inside it would become his. Then he too would understand the stick that captures... and the curious construction raised over the river.
Liam scanned the swirling suds of water in front of him. Every now and then he could see the dark outline of one of these large prehistoric mudfish darting around the shallows, teasing him to make a lunge at it with his spear.
He was useless at it, unable to anticipate which way the dark shape would lurch to avoid being skewered. Juan was probably the best among them at catching these things. The one he'd just caught was a whopper: four feet of wriggling wet meat, enough to feed at least half of them tonight. If he could just manage to bag another one himself while the others were carrying it back to the camp, then he could at least feel less like a useless jerk.
Some leader.
Franklyn seemed to know everything about dinosaurs, Whitmore quite a lot too. Juan seemed to be at home in this survival situation, good at hunting, building a fire and all. Keisha seemed to be the group's carer and doctor. And, despite the unfortunate incident a few days ago, the others were beginning to regard Becks as their bodyguard. Even Jonah seemed to have a valued role as the group's comedian.
And then there's me. The Irish kid who can do nothing more than keep saying 'help's on the way'.
He wondered if the only reason they'd accepted him as the nominal leader was because he'd made the rash promise to get them back home. That and, of course, because Becks took her orders only from him. He wondered how they were going to feel about him being in charge in a few weeks' time or months' time, when there was still no sign of rescue.
He felt lonely and worn out with the burden of responsibility. At least the last time he'd been stuck in the past it had just been himself to worry about; he hadn't been asked to lead anyone.
No, that was Bob's job. He laughed at the memory of Bob leading that army of freedom fighters. They'd thought he was some sort of warrior angel sent down from Heaven by God himself; they'd thought he was a superhero just like out of one of those comicbooks. Superman, Captain Freedom. He'd certainly looked the part.
Movement.
He looked up and saw a pack of small dinosaurs, little more than lizards, standing upright on their hind legs and gazing at him curiously. None bigger than his hand. They were standing only a couple of yards away and tweeted and twittered among themselves as they idly watched him. Franklyn had a species name for them, although Liam was damned if he could remember it.
'What do you fellas want?' he called out.
He could guess... begging for scraps. These little chaps had been hopping and skipping around their campfire last night like excited children, drawn by the smell of fish meat being grilled on a spit. One of them had even been bold enough to hop up on to the cooking carcass, but had slipped on the greasy scales of the fish and fallen into the fire, where it had flapped around and screamed for a while before finally succumbing to the flames.
'Did you not learn your lesson last night, you silly eejits? Best staying away, eh?'
They all cocked their heads to the right in unison at the sound of his voice.
'Jay-zus, you little fellas really are stupid, aren't you?'
They tweeted and twittered and cooed at that.
'Ah, go away, will you? You'll spook my fish, so you will.' Liam bent down, scooped up a rock and tossed it a dozen yards down the silted riverbank. The entire pack of mini-therapods turned and scooted after it excitedly, presumably utterly convinced it was a hunk of juicy meat.
Liam watched them go, pattering across the silt, leaving a host of tiny trails behind them, like the trail of winter birds across virgin snow.
And that's when the idea struck him.
'Oh... oh,' he gasped to himself. 'Oh Jay-zus-'n'-Mother-Mary,' he added for good measure. 'That'll be it!' He dropped his spear into the water and turned on his heels, heading through the trees towards the camp.
# CHAPTER 33
# 65 million years BC, jungle
He stumbled out of the jungle and into the clearing. Across the way he could see a thin column of smoke from yesterday's campfire, still smouldering, and clustered around it their dozen wigwam shelters, cone-shaped frames of wood beneath layers of broad waxy leaves the size of elephant's ears. To one side their palisade, finished now, and reinforced with a coating of rust-coloured dried mud, packed into the spaces between the logs and almost as hard as concrete. Around the tree-trunk palisade wall a three-foot-deep trench had been dug out. It effectively added another two or three feet to the height of their defence. Liam very much doubted it would hold at bay something as large as a rex, but it might be enough to dissuade any smaller beasts on the hunt for an easy meal.
He picked out Becks among the figures moving around the camp: a figure in black, her head no longer a pale round eggshell, but dark now with a week's worth of hair growth.
'Becks!' he called out. Her head turned sharply towards him, and her posture instantly adjusted to one ready for action. Every other head turned his way as he stumbled awkwardly across the ground towards them.
He saw Juan and Leonard scrambling to their feet and reaching for spears. He realized his voice must have sounded shrill as if he was shouting a warning. Kelly reached into his trousers for his penknife, Whitmore for one of their hatchets.
By the time Liam arrived beside the campfire, breathless and sweating from the exertion, everybody stood poised with a weapon and ready to run for the safety of the palisade.
'What is it?' asked Kelly. 'Something coming?'
Liam looked at them all. They were wide-eyed, some of the girls terrified even. Glances skipped from Liam to the far side of the clearing from where he'd emerged sprinting as if the devil himself was in hot pursuit.
'What's happened, dude?' asked Jonah.
Becks said, 'Your voice indicated a threat.'
Liam shook his head. 'Ah no, not really. I just had an idea.'
'Fossils, that's what you're talking about,' said Franklyn. 'Fossils. They're not even the original print that's left behind, but just an imprint of the print: sediment that has filled the footprint, then hardened over thousands of years to become a layer of rock.'
'Yes, but it's still a mark that's survived through all that time. An impression of that original mark.'
'Of course,' sniffed Franklyn. 'Yes, of course that's exactly what it is.'
Kelly shook his head. 'That's it? That's how you intend to communicate with your agency? Leave a mark on the ground in the Cretaceous period and hope some lucky fossil hunter finds it?' He shrugged, exasperated. 'Oh, great...' He gazed at the fire. 'And there was me thinking you and your robo-girl here had some sort of high-tech beacon or something to bring them here!'
Becks shook her head. 'Negative. No beacons.'
Liam raised a hand to hush her. 'That's just the way it is, Mr Kelly. There's nothing I can do about that.'
Laura bit her lip. 'That... that doesn't sound like much of a chance, though – a message traced in the ground surviving millions of years in one piece?'
'Survivin' that long,' added Juan, 'and bein' found as well, man. What's the chances of that?'
Liam shrugged. 'Maybe we can improve our chances.' He looked at Franklyn. 'Do we not know where the first fossils were discovered? I mean historically? That's actually known, right?'
Whitmore and Franklyn exchanged a glance. 'Well, yes,' said Whitmore. 'It's common knowledge where the first American dinosaur fossils were discovered.'
Franklyn nodded. 'In Texas, of course. Right here in Texas.' Behind his bottle-top glasses, his eyes suddenly widened. 'Yes! Oh, hang on! Yes... Dinosaur Valley. Right, Mr Whitmore?'
Whitmore nodded. 'Good God, yes, you're right, Franklyn. Near Glen Rose, Texas.'
'Glen Rose?' Liam shrugged. 'Would that be far away?'
Kelly's scornful frozen expression of cynicism looked like it was thawing. 'Not that far from where the TERI labs were, actually. About sixty miles away.'
'Dinosaur Valley State Park,' continued Whitmore. 'It's a protected area now, a national landmark. At the beginning of the 1900s, I think, some of the first fossils were found along a riverbed there. Lots of them.'
'The Paluxy River,' said Franklyn, 'where the fossils were found, was thought to be the shoreline of some Cretaceous-era sea.'
Liam looked from Whitmore to Franklyn. 'So? We could get to this place, right? You fellas know exactly where it would be?'
Both shook their heads. 'Not really,' said Whitmore. 'How could we know that?' He gestured around at the jungle. 'It's an entirely different landscape.' He laughed. 'Hell, it's out there somewhere!'
'I know where it is in relation to the TERI labs,' said Kelly. The others looked at him. 'Well, I drive in to work from Glen Rose. It's where I live. I pass the signs for Dinosaur Valley Park every day on the way up to the interstate. It's just outside Glen Rose, about a mile north of the town.'
'I have geo-coordinates for the town of Glen Rose,' said Becks.
Liam looked at her. 'You do?'
'Of course. It was part of the data package Maddy Carter uploaded prior to departure. I have the complete set of US Geological Survey maps for the State of Texas.'
Liam's eyes glistened by the light of the campfire. 'We could actually do this!' He looked at them all, piecing together on the fly something that was beginning to resemble a plan. 'Then, in theory, Becks, you could lead us right to this place that will one day become this dinosaur park?'
'Affirmative.'
'And if we know some fossil-hunting fellas find a whole load of fossils, as you said, Mr Whitmore, sometime in the 1900s, then could we not place some fossils of our own right there?'
'I suppose we –'
'Negative,' cut in Becks. She understood now where Liam was going with this. 'That would represent a significant contamination risk.'
Liam clenched his teeth in frustration. 'Come on, Becks, we have to break a few eggs, so we do.'
She cocked her head. 'Break eggs?'
'You know... how does it go? To make an omelette. We leave a message to be found. So, all right, it causes a new load of contamination problems. But then we have a chance at being rescued, getting these people back home where they should be, and then... then we go and fix that little problem.'
'This action introduces a third independent source of contamination.' She looked coolly at the group gathered around the campfire. 'Already there are two potential sources of time corruption. One in 2015 – the absence of Edward Chan. The second, this time, the presence of humans where there should not be any. Either or both contamination sources have a high probability of already causing significant time waves in the future.'
'What if...' started Jonah, but he almost stopped when every pair of eyes swung on to him. Clearly now wasn't the time for some flippant wisecrack. But he continued anyway. It seemed like a smart idea to him. 'What if... like... we left a message that was, you know, like, too important to become common knowledge.'
They stared at him in silence. No one was telling him to shut up, so he elaborated. 'I mean, like hushed up. Like, say, Roswell.'
Liam shrugged. 'Roswell?'
Kelly snorted a dry laugh. 'The supposed sight of a crashed UFO in 1947. Conspiracy nuts love that story. According to them it was a real flying saucer from outer space with real live LGM onboard.'
Laura saw Liam purse his lips in confusion. 'Little Green Men,' she said helpfully.
'Anyway,' continued Kelly, 'despite the fact it was most probably just a crashed test jet of some kind, you still get nut-jobs going on about wanting to free the little green men from their years of medical testing and enforced imprisonment.'
Jonah made a face. 'Yeah... but how do we know for sure it ain't true, Mr Kelly, eh? Point is, it could've been just a test jet, it could've been an alien spaceship, but the world will never know 'cause the government being, like, totally paranoid douche bags, hushed it all up. Kept the secret to themselves.'
'Oh, come on, kid,' said Kelly, 'that's a load of –'
Liam waved him silent. 'Hang on! No, wait! Jonah has a point... I think.' He scratched his cheek, deep in thought for a moment. 'Look, the point is people like the government... Your American government, right, if someone, some everyday person discovered a fossil that suggested something as amazing as the invention of time travel and they told the government, what would they do?'
'You kiddin'?' said Juan. 'They'd end up all over it like a rash, man. Secret service, Homeland stiffs in black suits an' dark glasses an' stuff.'
'I'll tell you, dude. Whoever found it would end up having an unfortunate accident,' said Jonah, looking at Kelly. 'Always happens, like... always. In fact, anybody who knew about it, was related to somebody who knew about it, would end up dead or in Guantanamo or someplace. Either way, there wouldn't be anyone walking around talking about it.'
'That's what I mean,' said Liam. 'It would remain a secret.' He looked at Becks. 'And so nothing major would be changed by it. The world wouldn't be talking about it. The world wouldn't know about it.'
Behind her narrowing eyes he guessed her computer was hard at work processing that notion. Looking for a percentage probability figure.
Whitmore nodded. 'That's how the intelligence agencies work, by putting up a poker face. Give nothing away. You know something? You keep it to yourself. You know something about the enemy, say the Russians... you don't change a thing about the way you behave. You act normal so the enemy don't know you've got something on them.'
Liam nodded. 'Exactly! Just like in the Second World War. I read something about those Enigma codes and all. And how the Americans and British couldn't sometimes react to the German messages they'd intercepted, otherwise the Germans would have figured out they'd cracked their secret codes.' He looked down at the muddy ground at his feet. Subconsciously the toe of his left shoe drew spirals in the dirt. 'So I don't know yet what kind of a message we could write. But we'd want something we know they'd have to keep secret. But, more importantly, we want a message they'd need to take directly to our field office.'
'That will compromise the agency's secrecy,' warned Becks.
Liam shrugged. 'I know... but another problem to fix later, huh?'
She scowled silently at that. 'It is another protocol conflict.'
'So you can blame it on me when we get back,' he said with a grin.
The group considered Liam's plan in silence for a while as the fire crackled and hissed between them.
'I reckon your idea sounds cool,' said Lam. 'I'm in.'
Liam noticed a couple of heads nod.
'All right, then,' he said finally. 'All right, then.' This felt good, having something at least half-figured out, something for them all to work towards. 'Becks, we'd need for them to know when we are, you know? As close as you can get it. So you do what maths in your head you need to do.'
She nodded slowly. 'Affirmative.'
'And maybe we'll need some sort of device erected exactly where we landed, right? So that if –' he corrected himself – 'when they get our message and have an approximate time period to start density probing, we need something that's constantly moving to and fro in that space. Creating some sort of a movement, a disturbance?'
'Correct.'
'You mean like a windmill or somethin'?' asked Ranjit.
Becks nodded. 'Affirmative. A device of that kind would be suitable.'
'And we'll need to make some preparations for a long hike. Food, water, weapons, those sorts of things.' Liam looked around at them. 'And we'll need to leave someone behind to man the camp and lift the bridge after we're gone.'
'Also to maintain the density interference device. It must function constantly. All the time,' said Becks.
Liam looked over his shoulder out towards the darkness, towards the middle of the clearing where they'd landed over a week ago. 'Yes, you're right. It'd be bad news for us if a density probe passed through here once, found nothing and moved on.'
Liam's grin was infectious and began to spread among the others.
He looked at Becks. 'Is this acceptable?'
She nodded slowly. 'The plan has a low probability of success.' She smiled, quite nicely this time. 'But it is possible, Liam O'Connor.'
# CHAPTER 34
# 2001, New York
Sal watched the world go by. Her world, that's how she thought about it: Times Square, New York, eight thirty in the morning, Tuesday 11 September 2001.
She knew it so well now. She knew everything that existed in this thoroughfare and everything that was meant to happen at this very moment in time. For instance... she looked around... and there they were: the old couple in matching jogging pants, huffing slowly side by side; the FedEx guy with an armful of packages, dropping one of them on the pavement and looking around to see whether anyone had noticed his hamfistedness; two blonde girls sharing headphones and giggling at something they were listening to.
Sal smiled.
All normal so far.
And there was the flustered-looking huddle of Japanese tourists standing outside TGI Friday's on the corner of 192 West and 46th Street, flipping anxiously through their phrase books to work out how to ask for a coffee and salt-beef and mustard bagels times nine.
Her eyes drifted up to the billboards overlooking Times Square; there was Shrek and Donkey, Mikey and Sully. There was the billboard for Mamma Mia... and walking slowly up the pavement towards her favourite bench, checking in every bin along the way and pushing a loaded shopping trolley in front of him, was the cheerful old tramp she saw this time every morning.
She sniffed the warm morning air; it smelled of car fumes and faintly of sizzling bacon and sausage meat. Again, quite normal – the smell of a city in a hurry and on its way to work.
'My world,' she whispered to herself. Her world... and all was well.
Only that was little consolation. If her world was still unaltered, if there weren't even the tiniest of differences to see here, it could only mean that Liam and the others had as yet to make any impact on whatever piece of history they'd landed in. There were two conclusions to draw from that, weren't there? Either they were being incredibly careful and had managed to avoid any kind of contamination at all... or...
'Or they arrived nowhere,' she muttered.
Dead. Torn to pieces by a wall of energy, by the explosion they'd caused. Or perhaps lost in chaos space. Foster had once ominously told her it was a place you'd never ever want – not in your wildest nightmares – to loiter around in.
Maddy was back from her trip to locate Foster. She'd not managed to find him. Sal had thought it was a long shot. But she seemed to have cheered up a little, seemed hopeful that they were going to get them back home yet. For some reason she'd been gabbling on about expecting, when the bubble reset at twelve o'clock tonight and they were 'reset' back to Monday morning, the first thing they'd hear would be a knock on the archway's door, and somebody standing outside, perhaps feeling silly, uncertain, and holding in their hand some sort of artefact from history with Liam's scruffy handwriting scrawled across it.
Sal wondered why Maddy was so sure that was going to happen, that the answer to this little mess they were in was actually going to deliver itself to their front door like the morning post.
Maddy slurped on her third Dr Pepper and placed it back on the desk beside the other two, now forming an orderly queue of crumpled cans. She could feel the sugar kick building up inside and the office chair twisted one way then the other as she pulled on the edge of the desk.
'Well?' she said. 'What do you think, Bob?'
> Your thinking is logical. However, my AI duplicate would offer Liam caution against this course of action.
'Of course you would, Bob... because that's a hard-coded protocol.'
The cursor blinked for a few seconds.
> Also because of the danger of revealing the location of this field office.
'But Liam would still go and do something like that, right? He'd override your warning?'
> I am unable to answer that, Maddy.
'But, come on, you know him better than me or Sal.'
> He has broken protocols before. He is capable of impulsive decisions.
Maddy smiled. 'That he is.'
She picked up her can again and tossed another fizzy mouthful down. 'So, like, if somebody in history does find a message from him... I guess we're going to have to do a lot of tidying up after ourselves.'
> It will depend on who discovers the message. And when in history that person comes from.
'Well, it would be dropped somewhere, sometime in the state of Texas. It could be anyone from some Apache Indian, or maybe a cowboy to... I dunno, maybe a civil-war soldier or an oil driller, or some college kids goofing around off the main highway. It could be anyone.'
> You presume they have only travelled back in time a hundred or two hundred years. It is equally possible they exist in what will one day be Texas long before the arrival of colonials. It is equally possible they exist in a time before the arrival of Native Americans.
'Isn't there a way you could at least best-guess how far back in time they've gone?'
> Negative. However, it might be possible for my AI duplicate to compare the density of tachyon particles in the vicinity of the explosion and the arrival point. The decay attrition is constant and this would give a fairly precise indication of when they are.
She stared at the screen. 'Really?'
> Affirmative. It will depend on how accurate the reading was.
If Bob was right, if that was true and they had a time-stamp, then getting some sort of message through time to her was the only course they could take. And Liam and the version of Bob's AI that was with him were smart enough to come to the exact same conclusion.
'I've got a feeling it's going to be all right, I really do.'
> I hope you are correct, Maddy.
She nodded, wishing she had just a little of Liam's laid-back devil-may-care attitude. She tilted her can and swilled another mouthful. 'Let's have some music... It's like a freakin' graveyard in here.'
> I have an extensive database of music. What would you like for your listening pleasure?
'Something heavy... something rocky.'
> Clarify 'heavy', 'rocky'.
'Bob... just give me something lively, then.'
> I can analyse the audio files in my database for variables such as beats-per-minute, wave-form, volume, number of times played.
'Do that,' she cut in. 'Do that... number of times played. Give me something the previous team liked to listen to.'
> Affirmative.
She heard his hard drive whirring softly, then a moment later the speakers on the desk either side of the main monitor began to chug with a heavy drum beat.
> Is this acceptable?
She sat back in her chair and put her feet up on the desk. It sounded pretty good to her, a bit like Nine Inch Nails, Marilyn Manson... a bit like Chilli Peppers. 'Yeah, cool... I like it.'
The music echoed around the archway, bouncing off the cool brick walls, making the place feel a little more alive.
# CHAPTER 35
# 65 million years BC, jungle
Liam watched Becks and the men lowering the bridge between them. He was surprised at the strength of the vine rope, showing no signs yet of fraying and snapping despite the tree trunk having been raised and lowered a dozen times already. It thudded down on the boulders on the far side of the river, bouncing and flexing as it settled into place.
'All right,' he shouted over the roar of the river. 'Everyone who's not staying... let's go.'
The first of those that were going along on the trip began to carefully bum-shuffle their way along the log, getting damp with spray from below. Twelve of them in total, leaving four behind to man the camp: Joseph Lam and Jonah Middleton, Sophia Yip and Keisha Jackson. Lam, as the only adult, was in charge, and Becks had made sure he fully understood how important it was to keep the 'windmill' rotating its arms.
The contraption was a post with a balanced crossbar like a pair of scales and someone's rucksack on one side slowly leaking – one at a time – pebbles on to the ground. As the weight adjusted and the 'scales' slowly tilted, it turned a simple windmill: a long, thin spar of wood that swung through the air with a regular rhythm. Every few hours the rucksack needed to be topped up again to maintain the blade's swinging action. It couldn't be allowed to stop.
Lam understood enough of its purpose already – maintaining a regular metronome-like signature of movement. Becks also briefed him on the warning signs that the area in the immediate vicinity was being probed: heat, a momentary localized jump in temperature of about ten degrees and a slight visual shimmering. If a probe actually did occur while they were gone, she'd continued, there would almost certainly be another one directly afterwards to 'double-check' the rhythmic interference. And, provided the windmill was still waving and duplicating the same unnatural pattern, he could expect a two-yard-wide time window to open and for someone to emerge from it, looking for them.
Lam assured them he'd set up a rota to keep the contraption turning and then wished them all luck.
They'd spent a few days preparing to set off on the trip. Sixty miles heading north-east, with no idea at all what sort of terrain they were going to have to cross. It could be jungle all the way. It could turn to desert for all they knew. Which was why they each carried in their school rucksacks as many plastic bottles as had come through with them full of drinking water. They had some food too, parcels of grilled fish meat wrapped in broad waxy leaves and tied up with vine rope. Enough food and water to last them a few days and hopefully they could forage for more along the way.
Kelly was first across and waited for the next with a helping hand extended.
Everyone also had a weapon now, either a spear or metal-shard hatchet, or both. Juan had even managed to produce three surprisingly good bows from suitably sturdy branches and a quiver full of arrows from sharpened bamboo canes, with fletching made from thin strips of bark. The arrows had proved to be rubbish against the hard wood of a tree trunk, splintering on impact. But, tested on the long bulky carcass of one of those huge fish, the arrows had gone almost entirely through.
Liam wondered, however, if a volley of their arrows would do little more than irritate a T-rex, if they met one.
Sixty miles. He hoped the terrain ahead of them was as free of lumbering prehistoric monsters as this jungle had so far proved to be. Other than those ugly mudfish in the river, and that bloody carcass they'd encountered over a week ago, the only living things he'd seen had been dragonflies the size of seagulls and bugs the size of rats, although at night the jungle seemed to echo with the curious haunting calls of a host of unknown creatures.
The others were mostly across now, wet from the spray of the river and the sweat of exertion in this hot and humid jungle. Becks was the last one across. She walked nimbly and confidently along the flexing trunk. Perfect balance and absolutely no fear of falling into the turbulent froth beneath.
Liam pursed his lips, jealous of that. To know no fear, to not have that gnawing sensation of terror in your stomach every time something thudded heavily out there in the dark of the jungle. Not that he could afford to show it. His stupid grin and the casual flick of his hand was all he allowed himself every time something happened that made him want to whimper. For example, he truly wished they'd not happened across that bloody ribcage. That meant something – or things – was out there sharing the jungle with them. Something they'd yet to see.
Becks jumped off the end of the log on to the silt riverbank beside Liam. 'Are you ready to proceed, Liam O'Connor?'
He sucked air through his teeth as he glanced around at the others. They all seemed to be looking at him to lead the way. 'North-east, you say, Becks?'
Becks's eyelids fluttered once as she consulted onboard data. 'Three hundred and eleven degrees magnetic,' she said, pointing her finger towards the thick apron of trees ahead of them. 'We must proceed in that direction.'
'Right, then,' he said, grasping his spear in both hands. He looked back over his shoulder at the four they'd left behind on the far side of the river, and cupped his mouth. 'I'll have a pint of stout to celebrate when we get back!'
They cocked their heads and looked confused. So did everyone on this side.
'Stout?... Ale?' he said. 'You know?'
Whitmore scratched his beard thoughtfully. 'Do you mean beer?'
Liam shook his head. 'You Americans really have no idea what a good beer is, do you?'
Whitmore shrugged. 'I had a Guinness once.'
Becks shook her head earnestly. 'Liam O'Connor, we do not have any alcoholic beverages in the camp. You will not be able to have a stout.'
'Oh, doesn't matter,' he sighed. 'I was only trying to be funny. Shall we just get on with this?'
'Affirmative.' She looked up. The sun was breaching the tree tops, sending a scattering starburst of rays across the morning sky. 'I calculate we have nine and a quarter hours of daylight before the sun sets again.'
'Then let's get a wriggle on,' said Liam. 'We got a lot of miles to cover.'
Broken Claw watched them step off right past him and into the jungle. Right past him. He was amazed at how little the new creatures seemed to see with their small eyes. Broken Claw could quite easily have reached out from the hummock of tall grass he was crouching behind and touched one of them.
The rest of his pack were there with him, dotted around beneath the shelter of ferns, behind the slender trunks of the trees that lined the river, as many hunting males as he had teeth in his mouth. The females and the younger pack members, a little further back in the jungle for safety. So many of them hiding within a few yards of them, and yet none of these curious pale upright creatures seemed to have any idea they were being watched.
Broken Claw struggled to make sense of that. Perhaps these things had spotted them, but for some cunning reason were hiding their reactions? Again, another reason to be wary of them. That and those sticks they carried, those sticks that could easily trap fish from the raging river. And new things. Curved sticks with a taut line of vine stretched from one end to the other. He wondered what these new devices did.
The new creatures stumbled clumsily and noisily past, up the gentle incline of the bank, and disappeared into the dark canopy of the jungle. Broken Claw turned from them to study the others on the far side of the river. They were pulling on another length of vine and he watched in silent awe as the tree trunk across the water slowly jerked and wobbled and raised inches at a time, reminding him of one of the large plain-dwellers, raising its head and long neck after drinking from a pool of water.
He understood this thing now. He understood its purpose.
A way across the dangerous water. A way that could be raised and lowered at will.
He caught sight of yellow eyes dotted here and there, the intent gaze of his extended family pack. They too were watching the tree rise, apparently under its own power. That was good. Good that they were seeing for themselves how wary they must be of these harmless-looking new arrivals.
Broken Claw offered a soft bark and the yellow eyes vanished. And the pack, like a ghostly dawn mist dissipating under the warm light of a rising sun, was suddenly gone, as if they'd evaporated into the jungle.
# CHAPTER 36
# 65 million years BC, jungle
It was gone mid-afternoon as they neared the crest of the steep jungle mountain they'd been struggling up since dawn. Through fleeting gaps in the foliage canopy, Liam had caught glimpses of an ebony ridge of peaks ahead of them, to the left and right, as far as he could see. He'd considered suggesting they turn left or right to try finding a way round, but that might mean a detour of days. Better, he decided, to press on up the sloping jungle hillside and tackle the ridge. At least it would be all downhill on the far side.
Up ahead, now, the jungle was fast thinning, giving way to smaller withered trees trying to find a foothold on a ground of shale and gravel dotted with coarse tufts of grass. Just ahead of him Becks emerged into sunlight.
He noticed that her back, taut with muscle, was bone dry. Don't these clones ever sweat? Liam was drenched. Every inch of his skin was slick with perspiration, the salt running down from his fringe stinging his eyes.
Behind him he could hear Franklyn and Whitmore talking. They hadn't stopped since they'd set out from the camp, a relentless jabbering to and fro on all things prehistoric. It was certainly reassuring to know their group had what sounded like a fair bit of expertise on this alien environment, but Liam would happily have paid a ship steward's monthly wage for them to just shut up for five minutes.
Whitmore dabbed at his damp forehead. 'But I want to know why we haven't seen any yet. This Mesozoic era was very favourable to the larger species. I mean –'
'No need to patronize me, Mr Whitmore,' Franklyn cut in. 'I know all that. I know this was the most densely populated era, that the Cretaceous was really the time of the dinosaurs. Much more so than the Jurassic era.'
Whitmore nodded. 'Mind you, it wouldn't have sounded quite so snappy if they'd called that film Cretaceous Park, would it?'
'At least it would have been more accurate,' said Franklyn. 'But it's so strange, don't you think? I mean, Dinosaur Valley State Park isn't so far away... and the Paluxy riverbed there is covered in fossils from all types of species. How come this jungle valley's, like, deserted?' Franklyn's voice was laden with disappointment. 'I mean, here we are... the perfect time, in fact, to see all the classic species: T-rex, ankylosaurus, stegosaurus, triceratops, and yet we've seen nothing.'
'It could be the jungle itself is unfavourable terrain for the larger animals.'
'That's not true,' replied Franklyn. 'It's nutrient heaven for the herbivores. And where there are herbivores you should also find carnivores. This jungle should be full of them.'
'Well,' said Whitmore, looking up the slope at the thinning vegetation and craggy peak ahead of them, 'no more jungle now.'
They and the rest of the party followed Liam and Becks out of the lush green into a mostly grey-brown world of slate and shingle. Up ahead the slope rose to a fractured cliff face of sharp slate angles. He could see that the robo-girl was already climbing up it, making swift progress from one treacherous handhold to the next. He watched her pulling herself up the sheer cliff face without any apparent difficulty.
Robo-girl. Now they all knew she was some kind of a robot, and after seeing her nearly skewer Laura like one of those mudfish – and, Lord knows, if Liam hadn't intervened, she would have killed them all, one after the other – there was no way anyone was going to entirely trust her.
Whitmore's feet slid on the shale as he scrambled awkwardly up the last fifty yards to the base of the cliff to join Liam.
'We... we're...' Whitmore gasped like an asthmatic as he wiped the sweat from his brow. He looked up at the sheer rock face. 'We're climbing that?'
'Yup,' said Liam.
'I... I'm...' He was still heaving to catch some air. 'I'm not sure I'll be able to.'
Liam shook his head as he peeled the rucksack off his back. 'Not a lot of choice, Mr Whitmore. It's that direction we need to go.'
He swallowed anxiously. 'Uh... I'm really not so great with heights.'
'Don't worry about that, Mr Whitmore. She can pull you up if you'd like.'
Franklyn puffed and wheezed up the last few yards, kicking loose shale beneath his trainers. 'That goes for me too. I'm exhausted.'
Liam looked up the rock face and saw Becks was already at the top and bracing her legs against an outcrop for balance. She pulled the heavy coils of vine rope off her shoulder, secured one end round her waist and tossed the rest down. It clattered on to the shale with several dozen yards in length to spare.
Liam looked at them both and down at the others making their way up the last few dozen yards of the mountainside. Beyond them he could see the green carpet of the jungle rolling all the way down the steep peak they'd been ascending to the deep valley below. He thought he could just make out the hairline silver glint of the river snaking through the lush emerald carpet, and there it was... a small oval of lighter green no bigger than his fingernail: their clearing.
'I am ready to proceed,' Becks called down.
They all studied the cliff face unhappily: sixty-foot high, all razor-sharp edges and craggy outcrops that promised to impale or slice anyone unfortunate enough to take a tumble.
'Don't all be chickens,' said Becks.
Liam glanced up at her and saw she was smiling.
Did she just try to be funny?
'Cluck, cluck,' she added in her monotone voice.
Liam shook his head, put his hands on his hips and smiled. 'So, I see you've found a sense of humour, Becks!'
'I have been observing and learning humorous dialogue exchanges, Liam. I am now capable of delivering basic humorous responses.'
'Well done!' he shouted back.
'You are all little chickens. Cluck, cluck, cluck,' she said again with a hint of pride in her dry voice.
Not exactly hilarious, Liam decided, as he looked around at the concerned expressions on the others. But at least her AI was having a go at being more human.
'Is she all right?' asked Juan.
Liam shrugged. 'It's her attempt at a joke. Don't worry. She's fine.' He looked up at her. 'Becks! Maybe we should save the joking around for later? All right? You're scaring the kids.'
Her face straightened. 'Affirmative.'
'OK, then.' He turned back to the others. 'Who's first?'
There wasn't exactly a rush.
Liam was the last one up.
As Becks hefted him up on to the ridge and helped him to his feet, he could see she looked fatigued. In fact, he realized, it was the first time he'd ever seen her looking like that. Genuinely spent. 'You OK, Becks?'
'Recommendation: I should now consume protein and then rest for several hours,' she said. Her grey eyes met his for a moment and he wondered if there was a hint of gratitude in her expression, gratitude that he'd bothered to ask if she was OK.
'OK, you do that,' he said, slapping her shoulder. 'We could all probably do with a rest. Maybe we should set up camp here for tonight?'
She considered that for a moment, panning her eyes around the immediate surroundings. 'This is an acceptable location.'
'Right. I'll tell the others.' He wandered across the top of the peak towards the rest of them. They were clustered together and staring out over the sloping ridge on the far side of the peak. From where he stood, he could see nothing but a rich blue sky and a far-off top-heavy bank of cloud hanging above a flat horizon like a giant floating anvil.
'What is it? Can you see something?' He clattered over, kicking stones and raising dust until he was standing right beside them. 'Oh... my,' his voice fluttered softly.
'There's all the dinosaurs you've ever wanted to see, kid,' said Whitmore to Franklyn.
The peak sloped down gently, grey shale gradually giving way in patches to an enormous plain of verdant grassland dotted with islands of jungle – tall straight deciduous canopy trees draped with the vines they'd come to rely on. Around the patches of jungle, herds of huge beasts Liam couldn't begin to name grazed lazily in the late-afternoon sun. Between the slowly meandering groups of giants, smaller packs of fleet-footed beasts flocked and weaved in an endless zig-zagging race.
'My God,' whispered Kelly. 'This is really... quite... incredible.'
Whitmore and Franklyn were grinning like a pair of children in a toy store.
Beyond the sweeping plain, Liam noticed the flat horizon changed from a drab olive colour to a rich turquoise.
Laura was frowning at that, confused. 'Is that an ocean over there? I don't recall Texas having a freakin' ocean in the middle of it.'
Franklyn nodded. 'Sixty-five million years ago there was,' he said, adopting the learned air of a college principal. 'An inland ocean that ran north–south up the middle of America, cutting it in two. In fact, Laura, you probably wouldn't recognize Earth if you were looking at it from orbit right now.'
Liam watched in silence for a good minute, stunned, like everyone else, into stillness and quiet as he gazed out on a scene that no human before had ever witnessed, nor should ever witness again. A moment of incalculable privilege, uniqueness. Once upon a time – and it felt like another lifetime now – he'd been standing in the creaking bowels of a dying ship, waist deep in ice-cold water, facing certain death and crying like a small child. And there was Foster, holding his hand out to him uttering a promise that if he joined him there were going to be things he'd see, wonderful things. Incredible things.
'Well, this is certainly one of them,' Liam whispered to himself.
'What's that?' said Kelly.
Liam roused himself and grinned. 'Nothing, I just said... so, this is where all you big fellas have been hiding.'
A good-natured ripple of laughter spread among them.
'We're camping up here tonight,' he announced, studying the distant strip of ocean blue on the horizon. 'And tomorrow we'll be at the seaside, so we will.'
# CHAPTER 37
# 65 million years BC, jungle
Liam savoured the warmth of the fire on his face and hands. It had turned out to be surprisingly cool up here on the peak once the sun had gone down, and his sweat-damp clothes had begun to feel uncomfortably chilly against his skin.
In the sky above the dark plain spread out before them, the last stain of day spread a warm, rich, amber light along the flat horizon and the night was beginning to fill with the distant haunting chorus of creatures calling to each other across miles of open plain.
He heard the scuff of boots and skittering shale approaching out of the dark. Becks appeared and sat down heavily next to him. 'Hello, Liam.'
'Hello,' he replied, chewing on the rubbery corner of his reheated grilled mudfish. He looked at her eyes, glistening as they reflected the campfire in front of them. He wondered what went on behind them when she wasn't busy assessing mission priorities or threat factors. He wondered if that tiny organic brain linked to her computer could appreciate how beautiful that amber sky was... or enjoy the pleasing sensation of warmth from the fire.
'Your AI's done a bit of growing again, hasn't it?' he said presently. 'Your cluck, cluck thing earlier was... well, about as funny as one of my old Auntie Noreen's jokes, but... the thing is it sounded almost human.'
'Thank you.' She nodded. 'It has been useful to me observing these younger humans. Their social interactions are more heavily nuanced by emotional indicators and less restricted by expected convention.'
His face creased as he digested that. 'You mean they're more likely to blurt out whatever they're thinking than adults?'
'Affirmative.'
'Well now,' he said, smiling, 'that's probably true.'
Laura Whitely, sitting opposite, caught what they were saying over the babble of dinosaur talk going on between Kelly, Whitmore and Franklyn. 'I don't blurt,' she said. 'Children do that.'
Becks's gaze shifted to her. 'Are you not a child?'
She gave Liam an is she for real? look, one eyebrow cocked with incredulity. 'Excuse me? I'm fifteen. I'm not a child. I'm a teenager.'
'You still have four years of physical and mental growth to undergo before you are technically an adult human being,' said Becks. 'Optimum mental and physical functionality is obtained at nineteen years of age. This makes you still a child.'
'Yeah? And what about you? What are you, then?'
Becks's jaw dropped open, a facial expression Liam had not seen her pull before. Nor an expression he could recall Bob ever pulling either, for that matter. Becks's eyes gazed at the fire for a long, long time, the lids fluttering slightly every now and then.
She's really giving that some serious thought.
'I will...' she began after a while. 'I will never be a complete human being.'
Laura's face softened ever so slightly. A second ago she'd looked like she wanted to square up to Becks, now she almost looked sorry for her. 'You sound sad about that.'
'Sad?' Becks considered that word. 'Sad,' she said again quietly. 'My developmental AI routines allow me to learn and replicate human behaviour patterns. But I am unable to directly experience emotions. This would affect my performance as a support unit.'
'So, let me get this straight,' said Laura, shuffling round the fire, closer to them so she wasn't being drowned out by Franklyn's droning voice. 'You're flesh and blood, just like a human being, but your head is, like, all robot?'
'My body is a genetically enhanced female human body. I have multiple-threaded muscle tissue capable of a five hundred and seventy-six per cent performance response.'
Laura looked at Liam. 'That means she's... what? Like, six times stronger than she should be?'
Liam nodded. 'Aye, that sounds about right.'
'I also have a high-density calcium-based support chassis –'
'Strong bones,' said Liam.
Laura nodded. It looked like she'd figured that out for herself.
'I also have a rapid-reaction, high white-cell-count fluid repair system.' Becks turned to Laura. 'My blood clots quickly.'
'Right.'
'All of this gene technology will be developed by W. G. Systems in the year 2043 for military applications: genetically engineered combat units.'
'Wow,' uttered Laura. 'You mean like super soldiers.'
'Correct. I was designed for war. Specifically subterfuge and covert operations.'
Liam smiled. 'But don't let that put you off her – she's a sweetie really.'
Becks looked at him curiously. 'Sweetie?'
Liam put an arm round her shoulders and hugged her clumsily. 'We go back a bit, Becks and me. Would you believe it, she used to be a man, so she did? Big chap, just like some muscle-man called Schwarzenhoffer or something. Apparently he becomes a president of yours sometime.'
'Oh my God.' Laura made a face. 'You don't mean Arnold Schwarzenegger?'
'That's the fella. Anyway, Becks was called Bob back then. But... well, you had a bit of a scrap, didn't you? And –'
'Caution,' said Becks. 'It is inadvisable to reveal details of previous missions.'
Liam hushed. Perhaps they'd revealed more than they ought. 'Yes, you're right. Sorry, Laura.' Liam decided to change the subject. 'Becks, we should consider what message we want to leave in the ground, you know?'
Becks nodded. 'Affirmative. This is important.'
Kelly overheard that. 'You guys discussing the help message?'
And that shut up everyone around the fire, even Franklyn.
'Yes,' replied Liam. 'I've been giving it some thought, Becks... We would have to actually reveal the exact date and location of our field office.'
She frowned. 'Negative. The location and time-stamp must remain known only to agency operatives.'
'But we have to, do you not see? Because Sal and Maddy aren't exactly likely to go fossil-hunting in Texas any time soon. It will be someone else who finds it. And the only way it will find its way to them is if we reveal that.'
'You know,' said Kelly, 'that kind of information would be mighty powerful stuff. The fact that time-travel technology exists. The fact that humans have actually been back to dinosaur times... that's world-changing information, Liam. You understand that, don't you? You mentioned time contamination and time waves and stuff like that... Won't it –?'
'Oh, for sure,' said Liam. 'That's the kind of nightmare we were recruited to prevent – contamination of the timeline.'
'And yet you'll be causing it.'
'I know... I know. But it's the only way.' He looked at Chan, sitting quietly between Leonard and Juan. 'The timeline is already badly broken. Who knows what state the future is in now? And, yes, by deliberately stamping a big ol' message into the ground, we're about to make it a lot worse. But – and it's taken me some time to see this for myself – time is like, I dunno, like liquid. It's fluid. What can be changed can be changed right back, so long as you know where to go and what to do. And, of course, as long as you've got a time machine.'
Liam nodded at Chan. 'We need to get Edward back to 2015. That fixes part of the problem. Then, once we've done that, Becks and I will come right back here and undo all that contamination.'
'How?'
'Very simple,' said Liam.
# CHAPTER 38
# 65 million years BC, jungle
Liam looked down at the shale by his feet. He dragged a finger through it. The others watched curiously as his finger inscribed four letters in the gravel. He spelled the word Help. Then with his hand he messed it up. 'We'll erase the message we just left,' he said. 'And everything that happened as a result of it being discovered, well... it'll all un-happen. It'll all be erased too.'
'If your message includes the location of your base,' said Kelly, 'I assure you, it won't be some curious fossil-hunter that turns up, it'll be some secret government agency. NSA, CIA, maybe some spooks we don't even know about... They'll storm the place. Kick the door in. Delta Force guys with guns. What you've got is too valuable.'
'Oh.' Liam hadn't considered that.
'You could be endangering your colleagues,' said Laura.
'They wouldn't hurt them, would they? They'd just want to be asking questions, would they not?'
Kelly shrugged. 'With something like time-travel technology at stake? Who knows? Our secret services have a long history of shooting places up first and asking questions later.'
Whitmore cut in. 'Oh, come on! They're professionals, the best in the world!'
Several of the others joined in. Some agreeing with that, some of them disagreeing.
Liam looked at Becks. 'Maybe this is not such a great idea.'
'You wish me to proceed with the alternate plan?' she said softly.
Liam looked at her, pleased that she'd had the sense to ask that in little more than a whisper. Not so encouraged, though, seeing one of her hands flinching and reaching for a hatchet.
'No, not yet,' he said, reaching out and grasping her hand in his. 'Not yet, OK?'
She nodded.
'Unless,' said Edward quietly, his voice almost lost beneath the to and fro of all the others. 'Unless, there's a really important reason not to hurt anyone.'
The others stopped and looked at him. It was the first thing he'd said all evening. All day, in fact.
Edward's eyes widened as they all stared at him. 'I... I was just saying...'
'Go on,' said Liam.
'Well... if part of your message was a... was in, like, a code. Then there's a reason to... you know, not to want to shoot everyone up, because they know they'd need someone to decode it.'
Liam pursed his lips in thought. 'That's true.' A code, a secret, hinting at still further secrets and revelations. What person wouldn't want to know more?
'If a message is going to lead some government spooks right up to the front door of your secret organization,' said Kelly, 'then you can bet the bit of the message they can't make sense of will be driving them nuts. Edward's right. They'll want your colleagues alive.'
'All right,' said Liam. 'So then the first bit of the message needs to be the time and place of our field office.' He turned to Becks. 'That's how the message will find its way to Maddy and Sal. The rest... the time-stamp they need to aim for, that bit should be the super-secret coded bit. Can you come up with a code, Becks?'
She nodded. 'I can produce a mathematical algorithm and use that as an alpha-numeric offset code. My duplicate should be able to recognize the pattern of the algorithm and produce a decode key.'
'No,' said Edward, shaking his head. 'It's too easy to break a math-based code. If they... you know, if they put a big enough computer on it, they could crack it. Simple.'
Kelly nodded. 'And you can bet the NSA or the CIA or whichever bunch of spooks ends up calling will have no shortage of computing power at their disposal to crunch your code.'
'There is no other way to generate a code that can be unlocked at the field office,' said Becks. 'My duplicate needs to have the same library of algorithms –'
'Every math-based code can be broken,' said Edward, his quiet voice finding a little more confidence, 'you know? Eventually. It's just a case of how much computer power you put on it.'
'Edward's right,' said Howard. 'Think about it, what if the message is discovered, say...' He turned to Whitmore and Franklyn. 'When did they first discover fossils in this place we're headed to?'
Franklyn shrugged. 'Early 1900s.'
'Right. So if the American secret services of that time secured that fossil back then they'll have had a whole century of time to crack the algorithm and decode it before they come knocking.'
'But computers powerful enough to work on it were only developed in the '80s,' said Juan. 'Don' forget that.'
'That's more than enough time,' said Howard. 'They'll come knocking knowing the entire contents of the message. Their only concern will be securing your agency's HQ and confiscating all your technology. Your colleagues will be a secondary consideration.'
'Your code has to be like a personal thing,' said Edward. 'Like a secret. Something only you and they know.'
Howard shook his head. 'I'm thinking this is a seriously bad idea. We could end up really messing with history. And I thought you guys are meant to stop that kind of thing happening.'
'And staying here, young man?' said Whitmore. 'What do you think that's going to do to history? Homo-sapiens existing right now? Sixty-five million years before they're due?'
Howard shrugged. 'We won't exist for long, though, will we?' His words silenced the teacher. 'You actually think the sixteen of us are going to survive and thrive? You think we're going to breed and produce lots of offspring and establish a Cretaceous-era human civilization that's going to change the world?'
Whitmore shrugged and half-nodded. 'It's possible.'
Howard laughed. 'No, it's not. We'll eventually die out here.' He looked around at them. 'There are six females in the group.' He looked at Becks. 'Not counting you. I'm not really sure what you are.'
'I am incapable of sexual reproduction,' she replied flatly.
'Six fertile females,' continued Howard. 'We might be able to make a few babies, but there are too few of us to sustain ourselves. If disease doesn't get us, or some hungry carnivore, then in-breeding would eventually.' He managed a wistful smile. 'We'll die out soon enough... months, years, decades maybe... but it'll happen and history won't be changed by us having been here. Maybe we shouldn't do this. Maybe we should accept we're stuck here and –'
'You can forget that!' said Laura. 'I want to go home!'
Kelly nodded. 'I think we all want that, right?'
Heads nodded around the fire.
Liam sat forward, held his hands out towards the fire and rubbed them. 'We're doing the message, Leonard. We have to. Now I've just got to figure out something that only we... and they know.'
'How big is your agency?' asked Laura.
Liam smiled and replied hesitantly. 'Oh, you know, it's big. Lots of us, so there are.'
'You know them well?'
'Sure, we're all pretty close.'
'Friends?'
'Yes, I'd like to think we're –'
'Then maybe there's something like a song, or a film or something? You know? Something like that you could use as a common reference point for –'
Liam suddenly felt his hand being crushed by a vice-like grip. He looked down and saw Becks was holding it, and squeezing it.
'Ow! Becks, you're hurting me,' he hissed. 'What's the matter?'
She let go and looked at him, her eyes widened with a mixture of surprise, and perhaps even elation. 'I have had an idea, Liam O'Connor.'
# CHAPTER 39
# 65 million years BC, jungle
From the darkness they watched them. Beyond the illumination of the dancing yellow flower in the middle. Broken Claw had seen this fascinating dancing creature only once before, after a storm. When a stab of light from the sky had come down and touched the long dead trunk of a tree. The yellow flower had engulfed it, consumed it, producing such unbearable heat as it did so. He'd been young then. And ever since then the yellow flower had been an occasional monster in his dreams, chasing him, reaching out for him, wanting so much to consume him.
And now here it was, tamed like some sort of a pet by these new creatures. They were gathered around it, unafraid of it, every now and then casually throwing a branch on to it and not even flinching as the creature reared up angrily, sending tendrils of light up into the dark sky.
He looked around at his pack, cowering further back down the slope, clearly unhappy at being out of the jungle and here in the open. This was not their terrain, this was not where they were strong. Open ground made them visible, it made them vulnerable. Larger predators existed in the open; large, lumbering and stupid predators like the tall upright one with tiny front claws, enormous jaws, powerful rear legs and a strong sweeping tail. His pack called it Many-Teeth.
Out in the open Many-Teeth could quite easily kill them all. After all, Broken Claw's kind were small, fragile things compared to this powerful mountain of muscle and energy. But between them his family pack had killed quite a few in his living memory. And always in the same way: luring them into the jungle with the tempting cry of one of their young. A pitiful cry that perfectly replicated that of a young helpless plant-eater, a cry that signalled fear and proved an irresistible taunt to one of those large stupid beasts. Once among the densely packed trees, unable to sweep its tail easily, unable to turn quickly, the pack was always able to leap upon the various Many-Teeth they'd lured in that way and begin to tear through their thick hides and rubbery bands of tough muscle tissue to the vulnerable soft tissues inside as they thrashed and roared.
Broken Claw had led many such attacks in past seasons, always the first to gnaw his way through the hide and into the bellies of such creatures, slashing and pulling through the vulnerable insides as the creature still stomped and roared, pulling himself towards the throbbing red organ in its chest. It was slashing at this that usually felled a Many-Teeth. Broken Claw and the others knew that this organ – which seemed to have a life of its own, which every species of creature seemed to possess – was the source of its very life.
In the seasons of his youth, the jungles had once been full of the larger stupid species. So many of them in fact that they often killed many more than they could eat, often only bothering to consume their favourite organs and leaving the rest of the carcass to rot.
But there were fewer now, far fewer of the bigger creatures. They only existed on the plain these days.
Broken Claw understood a simple principle. They had hunted too many of them. They had been too successful for their own good in the jungle, and his family pack had been forced to migrate from one jungle valley to the next several times during his lifespan. Now too, in recent seasons, this jungle had become sparsely populated – another hunting ground that they'd almost completely exhausted.
There certainly was not enough food available in the jungle valley for these new creatures as well.
Slowly, lightly, he glided forward across the loose shale, mindful that his agile feet not dislodge anything that might make the slightest noise. Behind him he heard the soft barking cough of one of his mates warning him not to get too close to these things. He ignored her. He needed to listen to the noises these things made. Perhaps their sounds could be learned, even mimicked. Perhaps they could employ the same technique they used on the Many-Teeth, identifying a sound that could be practised and used by their young to lure one of the new creatures away from the others.
If just one of them could be isolated. They could study it, understand how dangerous it could be, understand its weakness. Perhaps in the last moments of its life, even share some of its intelligence. Then he could find out if this creature also had the same fluttering red orb in its ribcage, the organ that provided life.
# CHAPTER 40
# 65 million years BC, jungle
Liam gazed up at the behemoth slowly ambling their way. 'You're sure it's a plant-eater?'
Franklyn laughed. 'Yes, relax, of course it is. It's an alamosaurus.'
Liam watched the enormous long-necked creature walk with ponderous deliberation across the open plain towards the patch of jungle behind them. He could feel each heavy step through the trembling ground.
Jay-zus-'n'-Mother-Mary, that thing's the size of a small ship!
He guessed he could park a double-decker tram in the space between its fore and its hind legs and still have room to stand on top. The creature's tiny head, little more than a rounded nub on the end of its long muscular neck, swept down close to the ground as it closed the distance between them. Finally coming to a halt to inspect the small bipedal creatures standing in front of it.
'Are you absolutely certain?' cried Liam, watching the thing's head hover at shoulder height just a few yards in front of him.
'Yes! He's probably more scared of you than you are of –'
'Oh –' Liam shook his head vigorously – 'I, uh... I very much doubt that.'
'See? He's just checking you out,' said Franklyn, slowly stepping forward to join Liam and Becks. 'Hey there, big man!' he cooed softly. 'It's OK, we're not carnivores.'
'Well, actually, I am,' said Whitmore. 'A little veal and a nice bottle of Sancerre on a Saturday night.'
Small beady black eyes, in a rounded head not much bigger than a cider keg, studied Liam intently. Its nostrils flared for a moment as it inhaled the curious new smell of humans, then curiosity compelled it to take a solitary step forward. Liam felt the ground beneath his feet shudder.
'Oh, he likes you, man,' called out Juan.
Liam felt a fetid blast of warm air across his face and closed his eyes as the dinosaur's head moved even closer. 'Ohh... I'm not happy about this,' he hissed out of the side of his mouth. Thick leathery lips the size of an automobile tyre probed his face, then moved up to explore the intriguing texture of his dark hair.
'Oh, he really likes you, man. Want us to leave you two alone?' chuckled Juan.
'Hair,' said Whitmore. 'That's an evolutionary step that's millions of years away for this creature. The texture of it must be fascinating to him.'
Liam felt a sharp tug on his scalp. 'Ow! Well, he's bleedin' well eating it now, so he is!' He slapped at the creature's mouth. 'Hey! Ouch! Let go! Becks! Help!'
Becks reacted swiftly. She stepped towards him and swung a fist at the alamosaurus's nose. The blow smacked heavily against the leathery skin and with a roar of pain and horror the giant let go of Liam. Its thick muscular neck reared up suddenly, a tree-felling in reverse, and it let loose a deafening bellow that reminded Liam of the dying groans of the Titanic's hull. The air vibrated with its startled roar.
Liam clasped his hands over his ears to protect his rattling eardrums, as the cry spread across the plain from one giant herbivore to the next. The alamosaur stumbled back from them on its tree-trunk legs, turning in a long cumbersome arc, and began to shamble away in a loping slow-motion run that felt through the ground like the early tremors of an earthquake.
'Oh, great!' shouted Franklyn. 'Now you started a stampede!'
The calm scene of moments ago, a vista of leviathans grazing peacefully across the open plain, had been instantly transformed into a deafening display of motion and panic. Liam watched the smaller species of plant-eaters scrambling to avoid being stampeded by the other alamosaurs darting into the islands of trees and ferns for cover.
'Whoa!' Juan was doubling up with excited laughter. 'Those alamo things are real chickens, man! Look at the suckers go!'
Amid the confusion of movement and kicked-up dust Liam caught sight of something else. Dark shapes behind them, half a mile away, smaller than any of the other species out on the plain. Just a glimpse of them, a second, no more. Then they were gone to ground, hidden among the knee-high tufts of olive-coloured grass scattered in threadbare clumps across the open plain.
Liam turned to ask if anyone else had seen them, but the others were still marvelling at the sight of an entire food chain on the move, a thunderous spectacle of swaying folds of leathery skin and sinews taut with panic.
He turned back to look again. Nothing. As if the dark shapes had never ever existed.
What the heck are those?
Vanished like skeins of dark smoke, like that ghostly seeker.
Or am I losing me mind now?
It was fully five minutes before some semblance of calm returned to the area; the various species of herbivores gathered in a worried-looking cluster a mile away. Tall necks protruded from the pack standing fully erect, watching them from afar like impossibly large meerkats.
'Oh, that was fun,' said Laura. 'Can we go do it again?'
Liam looked at Becks. Her face was folded with a confused expression. 'Becks? What's the matter?'
She looked down at her fist, still balled up. 'I did not hit it very hard.'
'You must have hit a sensitive spot,' said Whitmore.
They made their way across the plain towards the coastline on the horizon, most of the time with Franklyn complaining about how Becks had ruined his chance to study the creatures up close. By noon they were standing among a scattering of boulders and looking at a broad beach of dark coarse sand and a tranquil tropical ocean sending gently lapping waves of surf up the shingle and back down again with a soothing hiss.
'So?' said Liam.
Becks studied the view for a long moment, her eyes narrowed. 'Twenty-one miles north-east of our current location.'
Liam grimaced. 'So then it's underwater, is it?'
'Negative,' she replied, pointing at the horizon ahead of them. 'This is a large bay. Observe the horizon.'
Liam looked again, squinting. Then he saw it: a pale line of low humps on the horizon that he'd earlier assumed were clouds. Following the uneven grey-blue line to the left he could see it becoming more distinct as it drew closer. The broad beach they were looking along seemed to promise that it was angling gradually towards the distant spur of land and, if they were patient enough with it, it would link up with the spur eventually.
'Recommendation: we follow the beach around to the landmass ahead.'
Liam nodded at the low hump of land. 'Is that the place we need to be?'
She nodded. 'Information: the distance of the landmass is nine point seven six miles.'
Whitmore nodded. 'Then that spur has to be it, right? That's what will one day be the fossil bed.'
Becks nodded slowly. 'Information: a ninety-three per cent probability you are correct.'
'My God,' he said, scratching his beard. 'Who knows? Some of the footprints we'll see along the beach over there might just end up being some of the fossils we've seen in museums in our time?' His eyes widened and he shook his head incredulously. 'Isn't that the craziest idea?' He slapped Liam on the shoulder. 'Time travel must drive you insane if you think about it too much.'
Liam cocked an eyebrow. 'Oh, I've had my share of headaches thinking on it, so I have.'
They stepped forward, down through the boulders and on to the coarse shingle. 'This is good,' said Becks to Liam, pointing at the beach. 'We are not leaving tracks.'
He looked down. She was right. The beach wasn't sand, it was a coarse gravel that clacked and shifted wetly underfoot, but left nothing as clear as a print behind them.
'Oh, good.' He nodded. 'So there you go – something to put a smile on your face, then?'
She gave that some thought. 'This is minimizing our overall contamination liability.' Her gaze shifted from their feet back up to him. 'Correct. That makes me... happy.'
'There you go, you miserable sod,' he replied cheerfully. 'Things are looking up. We'll be home soon enough.'
They clattered down through the wet shingle until the first warm waves of tropical water hissed up to and around their feet. Up ahead the others had decided to wade knee-deep into the sea and were splashing each other noisily. She pursed her lips in thought as she watched them, a curious gesture she must have picked up from one of the girls, Liam decided. A gesture that Bob's muscular face would have struggled to reproduce. 'If we successfully complete the mission, Liam O'Connor, and we return to the field office, do you intend to retire me?'
'Retire? What do you mean?'
'Terminate this body and replace it with a male support unit? I heard Sal Vikram refer to this organic frame as a "mistake".'
He'd not given it much thought. Becks was Sal's error – she'd not bothered to check the gender marker on the containment tube – and they'd not had time to consider growing another. But certainly neither Maddy nor Sal had mentioned terminating her and disposing of her body.
'Why would we want to go and do that, Becks?'
'The male support frame is eighty-seven per cent more effective than the female frame as a combat unit.'
'All right, maybe that's true, but why'd the agency give us female babies as well, then?'
'Female support frames can be useful for covert operations where a female cover is required.'
He scratched his head. 'Well now, I really don't see why we can't have one of each of you, you know? A Bob and a Becks. There're no agency rules, are there, you know, against us having two support units in a team?'
'Negative. I am not aware of any agency rules on that.'
'So, well, there you are... why not? We'll have two of you instead of one.'
They walked in silence for a while, Liam intrigued by how human her question had sounded.
'Have I functioned as efficiently as the Bob unit?' she asked after a while.
'Yes, of course. I don't know what we'd have done without you so far. But you know it's still so very weird. Aren't you actually Bob anyway? Or at least a copy of Bob in a different skin?'
'Negative. My AI has adapted enough since being copied to be considered a different AI ident. I have experienced data that Bob has not. Also, the organic brain that is interfaced with the AI is genetically different between the male and female support frames.'
'Right. But... you remember being Bob, right?'
'Of course. I recall all the incidents of our first mission, right up until the moment you removed my chip.'
Liam wished he couldn't remember that as well. 'Ugghh. Not something I'd like to do again in a hurry.'
'You successfully preserved the AI. It contained six months of adaptive learning,' she replied. 'Both Bob and I are six months closer to fully emulating human behaviour. We are both grateful.'
He shrugged modestly. 'Oh, you know, it's nothing. Just part of the job.'
'I am able to kiss you,' she said. 'This would be an appropriate gesture of gratitude. I have data.'
She began puckering her lips and Liam felt that odd conflicted sensation he'd felt after they'd first arrived in 2015: a tingling excitement offset with a sense of revulsion.
Bob, in a girl suit... remember.
'Uh... that's OK, Becks. A thanks is more than good enough.'
'Affirmative. As you wish.'
'Anyway, where the hell did you learn about kissing?'
'I have a detailed description from a book I was reading while I was installed in the mainframe.'
'Eh? What sort of books have you been reading?'
'The book is entitled Harry Potter and the Deathly Hallows.'
'What's that?'
'A novel. The digital file is in early twenty-first century PDF format. The file's original replication date is –'
'Hold on,' said Liam, stopping. 'Do you have that file in your database still?'
She nodded. 'My reading was interrupted. I wished to complete it. So I added it to my short-term cache.'
'And would Bob also have the exact same file on the computer system?'
'Of course.'
His mouth hung open. 'There's the code, then! Right there! That's the code you could use! Isn't it?'
Her eyelids fluttered as she processed the thought. 'You are talking of a book code?'
'That's right, a Harry-Whatever-mijingamy book code.'
# CHAPTER 41
# 65 million years BC, jungle
Howard noticed the young boy walking alongside him, sloshing through the warm seawater.
'Hey,' he said.
Edward smiled. 'Hey. You always called Leonard, or do your friends call you Lenny?'
Howard shrugged; not a question he'd anticipated being asked. 'Uh... mostly just Leonard,' he replied. 'My mom calls me Lenny, but I hate that.'
'I heard someone say your best subject is math.'
He nodded. 'It was my –' He stopped, inwardly cursing. 'It... is... my favourite school subject. Always loved math. It's like, well, I dunno... I suppose it's like a sort of poetry that only a few people get. If you know what I mean? It's, like, exclusive.'
Chan nodded. 'Yeah, I know what you mean. That's why I like it. It's something I know and other people don't. It makes me feel kind of special, I guess. Maybe that's why I don't have any friends at school, cos they think I'm odd.'
Howard nodded. 'Yeah, I guess I'm the same. A loner.' He squinted up at the bright sun. 'Never ever get picked for sports, because I'm the geek.' He shrugged. 'But that's OK, cos I never liked sports anyway.'
Edward nodded. 'Me neither. It's for jocks and ditto-heads.'
'Ditto-heads?' Howard laughed. 'I like it.'
'You never heard that expression?'
Not in my time, he almost answered. But instead he just shook his head.
'Hey!' said Edward suddenly, and bent down to scoop up a curious twisted ammonite shell from the shingle.
'See? There are even bigger ones of those,' said Howard, nodding at some of the others, wading waist deep in the clear blue water, occasionally ducking down to pull shells out of the water to admire them.
They walked on in silence for a while, going a little further into the warm water. Up ahead, leading the way and deep in conversation, Howard could see the two 'agents' – Liam and his robo-girl. He shook his head at the irony of it. Despite their turning up in 2015 to 'save' Chan, they were all on the same side really, all trying to prevent the nightmare of time-travel technology from destroying the world. Same goal... different methods. He wondered how he'd never come across this agency in all the years of his campaigning, all the rallies and protests he'd been to... and no one, no one, had ever suggested, even as a joke, that there might be an agency out there actually using time travel itself to combat the corruptive effects of time travel. He wondered who was behind it, who'd set it up. Surely not the American government? Not any government, in fact. The internationally agreed penalties for that were severe. No politician would have the guts to risk having anything to do with time travel, because international law was brutal and strict on this matter. It was an automatic death penalty for any involved. The great Roald Waldstein had been a powerful speaker on the horrendous dangers of it. A great man, an influential man. Howard's small campaigning group had achieved far less. His group was little more than bunches of students in universities and colleges around the world.
But this secret agency, they were going about matters in the wrong way. Attempting to repair history that had been damaged by careless travellers? That was very much like trying to close the barn door after all the horses have bolted. No – worse than that... it was having to go out and hunt all those horses down then drag them kicking and screaming all the way back to the barn. On the other hand, his campaign group's approach had been far simpler.
Destroy the possibility of time travel at its very root. Instead of closing the barn door, they were burning the cursed thing down with all the horses still inside.
He looked at Edward Chan. The boy smiled back at him then looked down at the lustrous pink and purple sheen of the shell in his hand. He stroked the smooth surface, then held it out. 'You can have it if you want it, Leonard.'
Howard shook his head. 'No, it's er... no thanks.'
He has to die, you know that, Howard? Burn the barn, right? Burn it long before any horses get out.
He realized he was delaying the necessary, putting it off and putting it off. And yet he knew it had to be done. In theory the future – the future after the year 2015 – must already be changing, must have changed by now. It would be a world where this boy vanished in an explosion and never got to fulfil his destiny. It was surely a world where a man called Roald Waldstein would never become the figurehead of an international campaign, never become a billionaire from all his other inventions, never become a household name. And, yes, this world would still have its problems: dwindling supplies of resources, global warming, rising seas, migrating billions and dangerous levels of over-population. But... at least it would no longer have the ever-present threat of complete and utter annihilation dangling over it.
He'd once heard a speaker at a rally ask the audience what must lie beyond the dimension of space-time we all exist in. Is it Hell? And to meddle with dimensions beyond what we know was surely no different from opening a door to the devil himself and inviting him right on in. He'd spoken of a medieval artist called Hieronymus Bosch who'd claimed he'd once caught a glimpse of the devil and the underworld and painted endless nightmarish visions of what he'd seen. Perhaps, the speaker had said, perhaps what he'd glimpsed were dimensions beyond our understanding, a momentary rip in space and time. Howard shuddered at the thought.
You know the boy has to die, Howard. Burn the barn. Burn the barn. What are you waiting for?
He was so deep in thought he didn't at first register the voices from further up the beach. Voices crying out a warning, screaming a warning back at them.
Edward grabbed his arm and yanked him hard. Howard's thoughts were shaken away.
'What the h–?'
'RUN!' screamed Edward, pointing his finger at something behind him. Howard turned round to see an odd-looking dark wave approaching him fast. Water rolled down either side of an enormous grey hump, sliding up the shallows towards him like a gigantic torpedo. He spotted a large fin at the top of the large grey hump – large, very large... the size of a car, no, bigger – the size of a bus!
Edward was still pulling him back from the thing, trying to get Howard's leaden fight-or-flight response to do something. Howard started to react, but far too sluggishly, too clumsily. He stumbled backwards over something in the thigh-deep water and an instant later was flailing on his back, his head underwater. Surfacing a moment later, spluttering for air, his legs scrambling to find a steady footing below, all he could see now was an approaching dark cave, riding up out of the shallow water at him like a freight train, a cave lined with stalactites and stalagmites of razor-sharp teeth and dangling tatters of rotting meat swinging between them.
'OH NO!' was all he could scream as the gliding mass of glistening grey hide finally came to an abrupt rest and the cave, easily six foot across, snapped shut round one of his feet. He felt a vice-like grip on his ankle, the tough leather of his combat boots compressed agonizingly tight as something hard and sharp pressed from the outside. Then the beast began shaking its head vigorously from side to side and he knew bones had to be breaking and splintering in his ankle as he swirled through the water.
Howard's head was underwater. He felt pebbles, rocks and shells grind painfully up his back, and knew that meant the creature was now manoeuvring itself back from the shallows into deeper water.
He was holding his breath amid the tumbling underwater chaos... and, for a fleeting second, wondered why he was bothering to do so.
I'm gonna die. Surely better to breathe out now and drown than experience the agony of being ferociously dismembered by this thing?
Then, without warning the incredible pressure round his now-shattered ankle was gone. He flailed with his arms to right himself, to find solid ground on which to place his feet. He caught something with his hand, the rounded side of another ammonite shell. So that's down. He tried to stand up and realized the creature must have pulled him further out than he'd thought in those few seconds. Finally his head broke the surface and he realized the water was chest deep.
The air was thick with screaming voices and spray.
And the first thing he saw was Chan, a few yards away, screaming abuse at the giant shark and jabbing his spear repeatedly at the creature's nose. Its head snapped and swung from side to side, trying to get a grip on the fragile spear, trying to get past the spear to Chan, on whom it had decided to vent its frustration.
Howard waded through the water, painfully slowly, the chest-high sea in collaboration with the giant predator, wanting to slow him down. His one good foot kept slipping on the slimy rocks below, barely giving him enough purchase to make his way to shallower water. Behind him he heard Chan still hurling abuse and still stabbing and prodding, and the hiss and roar of water turned frothy white by the enraged shark thrashing in the shallows. Then he slipped again and fell under the water.
He felt a hand under his arm, then another, lifting him clear again. It was the robo-girl.
'Remain calm,' she said emotionlessly.
'What... about... Chan?' he found himself gasping.
She dragged him back to water shallow enough for him to crawl on his hands and knees. Then she let him go and headed back into the sea.
He turned and sat in the gently lapping waves, exhausted and vaguely aware of the burning agony of snapped and twisted bones down at the end of his leg. He watched Becks splashing through the water towards where Chan was still managing, incredibly, to keep the shark at spear's length.
That's a very big fish, was the last coherent thought his mind managed to put together before the world seemed to slump over on to its side.
∗
Liam watched the young man as he came round. 'Leonard? How are you feeling?'
'Hurts,' he grunted thickly.
Becks leaned over him. 'There are no broken bones, but your Achilles tendon has snapped and there is a significant contusion and several abrasions to your lower leg. This will hurt, but it will also mend.'
'On the other hand,' said Liam, 'the bad news is your boot didn't make it.'
Howard half smiled, half winced. A fire crackled brightly high up on the beach, throwing dancing skeins of amber light and dark shadows across the shingle down to the softly lapping waterline.
Edward Chan joined them. 'Hi,' he said. 'You OK?'
Howard looked up at him. 'You... you saved my life.'
Edward shrugged. 'I just poked my stick at it for a while.'
'My God, we were lucky,' said Howard, wincing again as he adjusted his position.
'No,' said Liam sombrely, 'no, we weren't. Ranjit's missing.'
Liam vaguely recalled he'd been at the back of their party, wading slowly through the water, falling behind the others. They'd foolishly allowed themselves to become strung out all along the beach, enjoying the tropical sea like holidaymakers. They'd allowed themselves to feel a false sense of security with the peaceful flat sea to one side and a wide open beach on the other.
'Poor guy,' whispered Howard.
'That shark thing must have got him first.'
Liam wondered about that. He'd been about a hundred yards back. Surely they would have heard the rush of water as that shark slid out of the surf? Surely they would have heard Ranjit scream? He looked out into the dark and wondered whether it had been that shark, or perhaps it had been those dark shapes he thought he'd seen earlier this afternoon, scattering to the ground and disappearing like ghosts as he'd turned back to look over his shoulder.
Now, was that real? Did I really see that?
'We were lucky,' said Kelly, 'that it only got the one of us. I mean, did you see the size of that thing? Bigger than a killer whale.'
'This is the age of the big predators,' said Whitmore. 'Big ones. The golden age for the giant carnivores.' He looked ashen-faced, shaken still, even several hours after the incident. 'And we're prey.'
'It's not the golden age for much longer,' said Franklyn. 'If this is sixty-five million years ago, then we're near the end of the Cretaceous era. Something happens soon on Earth that wipes out all the big species. Fossil hunters call it the K–T boundary. Beyond that thin layer of sedimentary rock, you don't find dinosaurs any more. Certainly not the big ones.'
'Good,' said Laura.
'The big asteroid?' said Juan. 'That's what killed them all, right?'
Franklyn shrugged. 'It's still debated. Could have been an asteroid, or a super volcano. Or it could simply have been a sudden climatic shift. Whatever extinction event happened, the large species were extremely vulnerable to it.'
'It won't happen while we're still here, will it?' asked Jasmine. She looked as unsettled and shaken as Whitmore.
Franklyn snorted dismissively. 'Unlikely.'
'So,' Edward muttered softly. 'Now there's only fifteen of us. If no one comes for us, we won't make it, will we?'
The others huddled around the fire heard that and it stilled their quiet murmurings until all that could be heard was the soft draw and hiss of the waves and the crackle of burning wood.
Becks broke the silence. 'Leonard, I have constructed a pair of crutches for you.'
Howard eased himself up on to his elbows. 'We're still going on?'
Liam nodded. 'Yes, we're nearly there.' He pointed up the beach. 'Another four or five miles around this bay and we should be there. It's our only hope... so we're going on.'
Whitmore nodded. 'Right. We can't go back now.'
Laura shuffled closer to the fire, hugging her shoulders against the cool night air. 'This will work, won't it? Somebody will find your message and they'll come for us?'
Liam grinned. 'Sure they are. They're already looking for us. And hopefully leaving them this message will help them narrow down their search. Trust me... it's going to work out all right.' He looked at Becks. 'Right?'
She nodded, seeming to understand that the others needed to hear something positive and certain from them. 'Liam is correct.'
# CHAPTER 42
# 2001, New York
Sal looked at her. 'How can you be so sure?'
Maddy shrugged. 'I can't be a hundred per cent certain. But look, if Liam and the unit survived the jump, I'm pretty sure that's exactly what they'd do. I mean, that's all they can do.'
Sal looked up from the mug of coffee in her hands, across the dim archway, illuminated by the fizzing ceiling strip light, towards the shutter door. It was gone eleven now. By this time on any normal Tuesday, the three of them would have been settling in for the evening: Liam on his bunk with his nose in a history book and a bowl of dry Rice Krispies on his chest and Maddy surfing the Internet. But tonight she and Maddy were both up and sitting at the kitchen table, waiting for midnight to come. Waiting for the 'reset'. She could hear the softly growing hum of power being drawn in through the mains, building up and being stored in the capacitor. Come midnight they would feel an odd momentary sensation of falling as the time field reset and took them back forty-eight hours to 12 a.m. Monday morning.
Maddy was certain, or at least working hard to give that impression, that immediately after the reset happened and they appeared in Monday one stroke after midnight, there'd be a welcome party waiting outside in the backstreet and very eager to meet them.
Who, though?
Maddy said that 'secrets have a way of drifting up'. What she meant by that was that advance knowledge of a time machine appearing in New York in 2001 would surely ultimately end up in the hands of some shady government agency, men in dark suits. Something as important, something so profoundly monumental as that could only end up in the hands of secret service spooks. If that was the case... then, Sal hoped, Maddy was going to find a way to cooperate with them to get Liam back.
And then what? What exactly?
Interrogation? For sure. Because they'd sure as shadd-yah want to know every little thing about this place and the machinery inside and how it all worked. They'd want to know every little thing. There'd be endless questions about the rest of this mysterious agency, how many others? Where are they? Who's in charge?
Sal really wasn't so sure she wanted to jump back to Monday and face that.
There was the other possibility, of course – that they jumped back and no one was there waiting for them.
Maddy's logic was quite black and white about this. Sal realized she'd thought this all through very thoroughly. If nobody was waiting for them, then that could only mean one thing. If there was nobody outside waiting for them, then Liam and the support unit had never survived the explosion. Or, if they had survived, then they'd been unable to get a message to them; they were lost in time for good, never to be seen again.
She looked at the digital clock on their kitchen table, red numbers that glowed softly and changed all too slowly.
11.16 p.m.
Oh jahulla... I rea-a-a-ally hate waiting.
# CHAPTER 43
# 65 million years BC, jungle
Liam stared up at the steep slope in front of them, rising up from the turquoise sea and the narrow strip of gravelly beach. It was covered in canopy trees, dangling vines and the swaying fronds of ferns. Thick jungle once again. He'd grown used to the reassuring comfort of being out in the open, where he could see anything coming their way from afar.
'It's just beyond that?'
Becks nodded. 'Affirmative. One and a half miles north-east of this point.'
The rest of the group were wearily bringing up the rear along the broad beach, none, though, daring to splash through the water this morning. Leonard was struggling at the back on the shingle with his crutches, but there was Edward and Jasmine helping him along.
'I have the calculation now,' said Becks.
'What's that?'
'When in time we are.'
'Oh.' Liam arched a brow. 'When did you do that?'
'I set the routine running thirty-three hours ago, identifying and cataloguing each tachyon particle in our vicinity before and after the jump. Two billion, ninety-three million, three hundred and twenty-two thousand, nine hundred and six particles before. And seventy-three million, one thousand, five hundred and seventy-two identified particles after.'
Liam rolled his eyes. He didn't need a blow-by-blow account of the maths. 'That's great. So... what's the answer?'
'With a constant particle attrition rate, my calculation is that we are located sixty-two million, seven hundred and thirty-nine thousand, four hundred and six years into the past.' She smiled proudly. 'Accurate to five hundred years either side of that date.'
'Well done, Becks.' He watched the others slowly staggering across the shifting, clattering pebbles. 'So we have a date we can put in the message. And we can encode the message with your Harry Potter book code?'
'Affirmative.'
'And of course the date and location of the field office.' He drew in breath through his teeth. 'Jay-zus, this does really feel like we're meddling with time in a big way.'
'We are,' she replied.
'We've just got to figure out the best way to ensure our get me out of here note lasts... sixty million whatever years.'
'Sixty-two million, seven hundred and thirty–'
He raised a hand to shush her. 'To ensure it lasts a long, long time.' He picked out Whitmore and Franklyn walking side by side comparing some of the shells they'd collected. 'I just hope those two fossil geniuses know where best to leave our message.'
In the distance, four or five miles down the beach, he saw several long necks hastily emerging from a cluster of jungle and out on to the beach, a small herd of those alamosauruses hurrying out into the open.
Something just spooked them over there. Didn't it?
He watched as they thundered along the beach, kicking up a trail of dust in their wake.
His gaze rested on Edward and Jasmine supporting a limping Leonard up the shingle. They finally caught up with the rest of them gathered at the foot of the steep slope of jungle.
'We've just got to hike over that, ladies and gents,' said Liam, 'and we're there.'
Franklyn was exhausted, out of breath and dripping with sweat. He was pretty sure the climb up this steep slope of jungle was one or two degrees short of full-on vertical rock climbing. He wondered how the huge canopy trees with their mushroom-like roof of leaves were managing to keep a purchase on the craggy rock sides.
The others seemed to be faring better than him, even that poor kid, Leonard, who was hopping and clattering up awkwardly, his bad leg dangling behind him. But then Franklyn was carrying twenty more pounds in weight than them, most of it round his middle. 'Puppy fat' he preferred to call it, in a vain hope that come college it was all going to magically disappear and the trim athletic body of sports jock was going to emerge. He'd still be a geek on the inside, though. But a cool jock on the outside.
A smart sports jock.
Now there's something you don't see every day.
He was so pleased with that observation that he misplaced his step and stumbled to the ground, barking his shin on a rock. 'Ow!' he hissed.
'You OK, man?' asked Juan, six yards ahead and above.
'Yeah, I'm f–' His rucksack slid off his shoulder as he picked himself up and started sliding down the slope. 'Oh no!' he muttered, watching it bounce off a tree trunk and continue its rolling, bouncing, tumbling descent. 'Just great,' he sighed. 'Now I gotta go down, get it and climb this bit all over again.'
'I'll tell the others to hold up while you get your bag, 'kay?'
Franklyn nodded a thanks and began his descent. He could see his yellow rucksack down there, swinging from a low branch. Good, it wasn't going any further, then.
Several minutes later he was nearly there, pushing his way through the large fronds of a fern on to a small level clearing of dried cones and needles and soft soil. Across the clearing – on little more than a wide ledge – was his bag, still swinging from a shoulder strap tangled round the broken stump of a branch. If it hadn't caught there, it would have rolled over the edge and he'd be backtracking another tiresome ten minutes' worth of climbing all the way to the bottom.
He stepped across, unwound it from the stump and put the straps over both shoulders this time, determined not to lose it again. He turned round to begin his ascent once more when his eyes picked out something on the ground: the familiar shape of a human footprint in the dry soil. One of theirs, but either side of it he saw three small dents – the distinctive marks of a three-toed creature. He stooped a little lower to get a closer look.
My God. It looked just like the tracks he'd seen all around that carcass they'd discovered a while back. The dawning realization came suddenly and his mouth all of a sudden felt tacky and dry.
We've been followed.
He knelt down and traced another three-pronged footprint in the ground with his finger. And another. And another.
We've been followed... all the way from the camp.
It was then that he heard the soft rustle of dislodged leaves, something emerging from the foliage on to the ledge behind him.
'Oh boy,' he whispered.
# CHAPTER 44
# 65 million years BC, jungle
Broken Claw could sense the new creature knew they were there; his nasal cavity picked out the faint smell of fear coming from it, a chemical cocktail of sweat and adrenaline, not so different from the large plant-eaters. The new creature had cleverly spotted their tracks. The new creature had finally realized it was being stalked.
Maybe now was the time to know a little more about these strange pale beasts. His soft bark ordered the others to remain where they were for now, out of sight. The new creature was holding one of those sticks-that-catch in one of its puffy pale hands. He'd watched one of these creatures fend off a giant sea-dweller yesterday with one of those sticks. So he eyed it warily as he stepped low under the sweeping fronds of a fern, under the branch from which the new creature had moments ago retrieved something bright and colourful and emerged over the rocky lip of ground to the small level clearing. That salty smell of fear grew suddenly much more powerful as the new creature turned slowly round to face him. Broken Claw rose from his crouching posture on all fours, up on to his hind legs, to stand fully erect.
It fears.
So close now, he could see the new creature more clearly: the eyes, curiously large, behind rounded shiny transparent discs. Its face, all loose pale flesh, unsculpted by muscle or sinew or bone carapace. It made noises with its mouth, noises that sounded so unlike all the other beasts in the river valley they called home. Noises, in fact, that didn't sound too unlike the simple language of coughs, grunts and barks Broken Claw's pack used.
Franklyn in turn studied the creature that had just emerged. It had a body shape he could best describe as halfway between one of the smaller therapod species, and... well, and a human. But incredibly thin, almost birdlike in its agility. A pair of long thin legs hinged backwards like a dog's legs, meeting at a bony, very feminine-looking pelvis thrust acutely forward. A tiny waist beneath a protruding rib cage, a curved, knobbly spine that hunched over and ended with a delicate tapering neck supporting an elongated skull. Apart from the distinctive head, seen from a distance, and if one squinted a little, it could almost pass as a hominid – human-like.
'Oh my... m-my God,' he whispered.
It cocked its head, a head that fleetingly reminded Franklyn of a hot-dog sausage, long and bone-smooth, at one end a lipless mouth full of rows of lethal-looking teeth. Above the mouth were two holes that suggested a nasal cavity around which flesh puckered and pulled as it silently breathed, and above that two reptilian yellow eyes that seemed to sparkle with a keen intelligence. The thing's skin was a dark olive green, that seemed to pale to an almost human pink colour around the vulnerable belly and pelvis.
The creature's jaws snapped shut and opened again, and it made a whining noise that reminded him vaguely of the contented murmuring a baby made after a feed. It sounded almost human. And those curious, intelligent, eyes, studying him as intently as he was studying it.
It made another noise, grating, slightly deeper this time. Beyond the teeth, he could see a black tongue twitching and fluttering and curling, like a restless animal in a cage, experimenting with different shapes to produce different sounds.
Did it... did it just mimic me?
'Hi,' said Franklyn.
The long head tilted to one side, like a dog listening for its master's voice. The mouth opened again, and the tongue rolled and curled. 'Ah-eeeee,' was the noise that came out, lower in pitch now, lower than a baby and almost matching the timbre of Franklyn's as yet unbroken voice.
He felt some of the terror replaced with the slightest flush of excitement.
It's trying to communicate.
'Hi, my name's Franklyn,' he said again, louder, bolder, slower.
That long head tilted over to the other side now, the gesture almost comical. One of its long arms, muscular, lean and ending with three digits that curled into lethal-looking long curved serrated blades, flexed in front of it.
Is that a hand signal?
Franklyn attempted to duplicate the gesture, bringing his short pudgy hand up before his face and curling his fingers in the same way. The creature snorted air out of its nostrils and clacked its teeth. He wondered if that was the creature laughing at his attempt.
Suddenly, he heard the crack of twigs, and the clatter of dislodged rocks; something coming down the slope above.
Becks leaped out of the foliage on to the ground between them, landing in a fight-ready and perfectly balanced stance. She spun round to face the reptilian hominid. 'Run,' she said calmly as she crouched ready for action, one of their crude jagged metal hatchets in one hand, a spear in the other.
Franklyn was frozen in place, unsure what to do. The creature had dropped down low, on to all fours, its elongated banana-like skull tilted back and resting flush in the spinal dip between two protruding shoulder blades. It hissed and barked and a swarm of others began to emerge over the lip of ground that sloped steeply down to the bay below.
'RUN!' screamed Liam, tumbling out of the foliage clumsily on to the ground beside Becks. 'Run, for Jayzus sakes, RUN!!' he shouted, getting up and readying his spear.
Franklyn's moment of indecision passed as he took in the crawling carpet of dark olive bodies slowly, warily gliding on all fours across the clearing towards them like a deadly lava flow. He turned, grabbed a branch and pulled himself up the slope and into the jungle, panting with panic and effort as he and his yellow rucksack quickly disappeared through the thick green fronds.
'What?' hissed Liam. 'Oh, sod this! I thought it was just the one of them!'
The creatures were spreading out around the clearing, attempting to flank them, encircle them.
'Recommendation,' Becks said, turning to look at him, 'leave!'
Liam could hear the sound of footfalls from above – the others. He couldn't tell if it was the sound of them coming down to help, or scrambling up the slope to get further away.
'Uh... right, OK. You going to be... er... all right?'
Becks ignored his stammered question as she swivelled the hatchet in her right hand with the grace of a martial arts master. The yellow-eyed creatures had moved too quickly, encircling them so that Liam already had no choice but to stay. He backed up against her until their shoulders were touching.
'Oh... boy... oh b-boy... I'm really n-not... uh, oh God...'
'Stay close to me,' Becks uttered over her shoulder.
'S-sure... and w-what are y-you going to –?'
Becks was already in motion. He glanced round to see her leap forward, swinging the spear like a baton. The sharp end punctured the flank of one of the hominids and with it still lodged between two ribs she effortlessly flicked it off its feet. Liam backed up, keeping his spear aimed at the creatures closing the gap in front of him.
Becks stepped forward again with the grace of a ballet dancer, the jagged hatchet flickering and flashing in the blur of movement. It caught the long clawed digits of one of the creatures and they spun in the air spraying droplets of blood in messy arcs.
In front of him, one of the creatures made a sudden lunge for Liam, hoping to catch him off guard as he backed up in Becks's wake. He caught the movement in his peripheral vision and had only the time to swing the spear tip round towards it before he felt the impact rattle down the frail bamboo shaft.
He turned to see the creature's deadly sickle-shaped claws flailing inches from his face and the teeth in its long skull snapping and grating and dripping spittle-strings of saliva. It was impaled on the bamboo, but so very far from incapacitated and quite enraged.
'Oh Jay-zus! I got one skewered!'
Becks was busy.
He held on to the rattling spear as the creature thrashed and drummed and swung and slowly, eagerly pulled itself further down the shaft, thick gouts of its dark blood running on to his hands. 'Help!' he screamed.
He could see one of the other hominids lowering, coiling, ready to leap on to him, when the air was split with a child-like shriek from one of them. In an instant, the beat of a heart, the dark olive-coloured bodies snaked, scrambled and swarmed with incredible speed towards the lip of rocky ground and out of sight into the jungle slope below.
Gone. Just like that.
Except for the creature still struggling halfway down his spear. A sickle claw swiped across his upper arm, cutting through the material of his shirt and digging into his muscle with the ease of a butcher's blade through tenderized beef.
'Gah!' Liam bellowed. 'Help me!'
Becks was there in the blink of an eye and with a blur of movement swiped the hatchet across the creature's elegant neck. It froze in shocked realization of its fate. The long head tilted for a moment like a cocked gesture of curiosity, then swung backwards on to its hunched spine, almost completely decapitated yet still attached to the body by a frayed strip of exposed pale pink tendon. It collapsed a second later, pulling the spear out of Liam's trembling hands.
They both stared down at the tangle of lean grey-green limbs and bony protrusions, and the rhythmic jet of almost black spurting gobbets of blood across the floor of dried pine cones and needles. One of its legs still twitched and flexed; a post-mortem response.
Liam looked up at Becks. She had a spatter pattern of blood across her pale face and chest and her normally expressionless cool grey eyes were wide and wild. But that passed in an instant as artificial intelligence regained control of her face. She regarded him calmly.
'Are you unharmed, Liam?'
Liam looked down at his bloody arm, cut deep, but nothing arterial going on there. He was vaguely aware that he was in a state of shock as he said, 'Can I be put back on the Titanic, please?'
# CHAPTER 45
# 65 million years BC, jungle
Liam and Becks emerged at the top of the steep hill twenty minutes later, a bald outcrop of rock with a view down all three sides to the tropical sea far below.
Liam collapsed on to the rocky ground.
'W-where are they?' asked Franklyn, looking past Liam towards the edge of the sloping jungle. 'Are they coming?'
'They are no longer pursuing,' answered Becks.
'My God, you're wounded!' cried Laura, dropping down beside him and ripping a strip of cloth from his shirt to use as a bandage.
'What the hell happened back there?' asked Kelly, undoing his loose tie and passing it to Laura to use as a tourniquet. He looked at Franklyn, still gasping from the exertion of climbing up the last half a mile of jungle. 'He's just been jabbering to us something about a load of creatures jumping him.'
Liam nodded. 'Yeah.' He pulled a plastic bottle out of his backpack and chugged the last of his water. He pumped air in and out of his lungs for a few moments, gathering enough puff to be able to say something more. 'Yeah... we got attacked all right. Lots of them... dozens of 'em.'
'Dozens of what?' asked Whitmore.
'A species of pack hunter,' said Becks.
Whitmore went pale. 'Oh God, don't tell me there are raptors?'
'Worse,' said Franklyn. 'Much worse.' He sat down next to Liam, took off his glasses and wiped the fogged lenses of his spectacles. One of the lenses was laced with a spider's web of cracks.
'They're not like anything we've ever seen,' he began, carefully rubbing dry the fractured glass. 'No one's ever come across fossils of this... come across anything like this species.'
Whitmore squatted down opposite the boy. 'Tell me, what's back down there? What did you see?'
Franklyn shook his head. 'I... I really don't know. They're... they're human-like and raptor-like.' He looked up at the teacher. 'They're unlike anything... anything, you know?'
'Not a sub-species of therapod?'
The boy shook his head vigorously. 'No... no, definitely not. Maybe millions of years ago there's some kind of shared ancestry, but these things... they're just... they're...' He was fumbling for words, for some way to describe them.
'Unique?' said Liam. He winced as Laura pulled the dressing tight one last time and finished a knot.
'Yes.' Franklyn nodded, putting his cracked glasses back on. 'Unique. That's it. They must be some kind of evolutionary dead end. A form of super-intelligent predator.'
Kelly stepped forward. 'That doesn't make sense, Franklyn. If they're, as you say, super-intelligent, they'd have thrived. We'd have found their fossils everywhere, surely?'
'How intelligent? What level of intelligent are we talking about?' asked Laura.
'Oh, they're smart,' said Liam. 'Very smart.' He looked up at the others. 'I think I saw them back on the big plain at the same time Becks punched that dinosaur on the nose. I looked back behind us, just as that stampede was happening... and I think I saw them. Like a whole pack of monkeys... in fact that's what I thought I saw –'
'That's ridiculous,' said Whitmore. 'The only mammals alive now are the size of shrews.'
'They're not mammals,' said Franklyn. 'They're reptilian, all right.'
'Like I say,' continued Liam, 'I thought they were monkey-like. But then I wasn't sure what I saw, because they were gone in a flash. Just went to ground when they saw me looking at them.'
'They've been following us all the way from our camp,' said Franklyn. 'Did you see their tracks?'
Liam shook his head.
'Three prominent depressions at the end of a long foot?'
Liam recalled the sickle claws, four on each hand, three on each foot. 'Yes... that's right.'
'Those same tracks were around that carcass... I'm sure of it. That was their kill.'
Liam looked down the jungle slope at the broad curve of the long bay glimmering in the daylight. And, far off, the broad expanse of the open plain. Beyond that, lost beyond the shimmering air and the fogging of twenty miles' distance, would be the low hummock of a slope and a cliff edge, and their jungle valley beyond.
'They must have been watching us,' he said, feeling his skin cool and the hairs on his arm stir. 'Watching us and following us ever since then.'
'But that was... like... over a week ago,' said Juan.
'Nine days,' Becks added.
Juan made a face. 'All that time?'
'They've been studying us,' said Liam. 'Learning about us, so they have. Working out how much of a threat we are to them.'
'Yes... I think you're right.' Franklyn pulled himself up and studied the fringe of jungle several dozen yards down the slope from them. 'They're curious. That makes them intelligent. Maybe almost as intelligent as us.'
'A species of dinosaur as intelligent as us? Come on, Franklyn, that's –'
'They've got a language! I heard them communicate.'
Liam nodded. 'He's right. When they were surrounding me and Becks, there was some sort of talking going on among them.'
'And one of them tried to communicate with me... before you and robo-girl arrived. It was trying to speak like me!'
'This is just crazy!' said Whitmore. 'There's no record of any species, or any similar species with the cranial capacity for a brain big enough to develop a spoken language... or able to make human-like vocal sounds.'
'But that's the thing, Mr Whitmore, just because no fossil of these things has survived, doesn't mean they didn't exist.'
'The lad's right,' said Kelly. 'Don't palaeontologists say we've only got an incomplete record of prehistoric times? That there are large gaps in our knowledge?'
Whitmore rubbed his beard and stared down at the fringe of jungle. 'Well, then, that's one huge goddamn gap out there, isn't it?'
They were quiet for a while, all staring at the nearby canopy trees, and the dark forbidding undergrowth beneath, imagining eyes staring out from the gloom back at them.
'What do we do now, Liam?' asked Laura.
He pulled on his bottom lip in thought. 'We carry on with the plan.' He turned away from the jungle he'd emerged from minutes ago and looked down the slope on the other side of the peak. Below he could see the pale apron of a small sheltered sandy cove nestling at the bottom of the ridge and another equally high ridge on the far side, like the protective embracing arms of a rocky giant. He could see the twinkle of a small stream meandering down through thickets of bamboo and reeds and spilling out on to the cove. It was an inviting, secret bay of turquoise-green water that lapped along the crescent of a pale cream-coloured beach. In another time, another place... a secluded tropical paradise. A picture-book pirates' cove.
'Is it down there?' he asked Becks. 'The place we need to be?'
'Affirmative. That is it.'
'Yes,' he said, nodding his head firmly, hoping he looked every bit the decisive leader. 'We can be down there in less than half an hour. We'll make a camp on the beach and be sure to have a huge fire going. Hopefully that'll keep those things at bay. And we'll have half of us sleeping, and half watching, and we'll do that in shifts.' He looked at Becks again. 'We'll make this message, so we will, and tomorrow we'll plant it.'
'How are we going to do that?' asked Kelly.
Liam was about to answer that he wasn't sure yet, when Jasmine replied. 'Clay.'
The others looked at her.
'Clay,' she said again. 'If we could find some we can make a tablet. You can write your message on it then we can bake it hard in the fire.'
Liam stroked his cheek thoughtfully. 'Right, yes... good idea. That's what we'll do. So? Any questions before we get moving?'
'What about them things back down there?' asked Juan with another pointed glance towards the jungle.
'Well, I suppose they've learned something about us, right?'
The others looked at each other, not quite sure what Liam meant by that.
'They've learned we can kill them.' He gestured at Becks. 'And they've learned our robo-girl is not to be messed around with, so they have.'
Becks frowned indignantly at that. 'My ident. is Becks.'
He shrugged. Too tired and winded to apologize. 'Right, then... I suggest we get going.'
# CHAPTER 46
# 2001, New York
The alarm clock on the table between them was showing 11.45 p.m. Maddy noticed Sal's eyes nervously glancing at it. 'Fifteen minutes to go.'
'I'm a bit scared,' whispered Sal.
If Maddy was being honest, she would have admitted she was a little jittery too. Instead she smiled, reached across the table and grasped Sal's arm. 'It's going to be fine, Sal. I promise.'
'Maybe I should go get Foster's gun from the back? You know? Just in case somebody unfriendly turns up.'
'Really?' Maddy cocked an eyebrow. 'Do you think that's going to be sensible? We might be answering the door to a backstreet full of very excitable armed men in suits and dark glasses.'
'You think it'll be like that?'
Maddy shrugged. 'I really don't know what's going to happen, Sal...'
If anything at all...
'But,' she continued, 'if a whole bunch of secret service types turn up, we're not going to achieve much standing there with one gun between us, are we? I'm sure they'll come prepared, if you know what I mean?'
'I guess so,' muttered Sal, her head drooping down to the table, a fold of her dark hair flopping over darker eyes. 'How come you're so calm about this?'
Calm, am I? But then she realized she actually did feel calm... No, not calm... resigned... resigned to whatever history was rolling up through the aeons to meet them in a few minutes when the archway's bubble reset. She'd figured this out yesterday while she was out there anxiously looking for Foster; there really was nothing much they could do other than wait and react to whatever turned up. Wait. That's it. Wait until a ripple or a time wave arrived, or, as she hoped, a message. Then, and only then, could they do anything at all useful.
'I'm calm, Sal... because, I dunno, because it's not in our hands now. Because we have to just wait and see. No point worrying about what's out of our hands.'
That sounded lame. But it was all she had right now.
'But, if it's bad guys, Maddy... if it's bad guys who want to get their hands on the time machine, what are we going to do? We can't just let them.'
'I've got that covered.'
'How?'
Maddy smiled. There was something she'd managed to get right. 'I've instructed Bob to lock down the computer system if he hears me say a codeword out loud.'
'Right.' Sal nodded, silent for a moment. 'But... but won't they have computer experts who could hack their way in and, I dunno, deactivate that command or something?'
'Maybe, eventually. That kind of hacking takes a lot of time. And they won't have enough time to do that.'
'Why?'
'Because he's under orders to trash absolutely everything if he doesn't hear from me again.'
'Huh?'
'If he doesn't get a second password from me within six hours, he's under instructions to go completely mad and wipe the hard drives clean and send a power surge through the displacement machinery's circuits and fry them. There'll be nothing left but frazzled silicon and garbage-filled drives if they try anything funny with us, Sal.'
Sal nodded, regarding Maddy with renewed respect. 'Oh jahulla, that's clever, Maddy.'
Maddy shrugged. 'I saw it in a film once. It worked in that – don't see why it shouldn't work for us.'
'You're a good planner,' said Sal. 'I know you think you're a bit rubbish, and I know you blame yourself for the explosion... but I don't know anyone else who could have picked up all that you have so quickly.' She glanced away from Maddy, self-conscious, flicking her fringe behind one ear. 'I'm just saying, that's all... you're pretty good at this.'
'Thanks, Sal.'
They watched another minute vanish on the clock.
'We'll see soon enough. If it's bad guys out there and they really want to get their grubby paws on our tech, then they're going to need us, aren't they?' Maddy took a deep breath, feeling the tickling sensation of growing anxiety claw its way up her spine as the clock flickered to 11.47 p.m. 'And they're freakin' well going to have to be real nice about it too.'
# CHAPTER 47
# 65 million years BC, jungle
Broken Claw cradled the organ in his hands, still, cold and lifeless now; its colour had drained from a vibrant red to a dull purple as the sun slowly sank in the sky. Now the sky was dark, a half moon bathing the dark jungle with a quicksilver light.
He stood where the new creatures had been just hours ago. Evidence of their presence was everywhere in the form of footprints in the soil, droplets of dried blood on the rocks and boulders and the smell, their unique smell of fear thick on every surface. They had waited here for a while. And they had been so very frightened.
The new creatures fear us.
And yet Broken Claw had been so certain up until now that it was his pack that needed to be afraid of them. The others were looking at him, waiting for him. He looked down at the organ in his hand, all that remained of his pack-mate, the mother of many of the young males before him. She would have led them all if Broken Claw was to die before her. The wisdom of age was more than enough to make up for her smaller frame... and no young buck would have challenged her. Unlike the other simple-minded animals in these lands with their crude pack hierarchies that relied on the brute strength of an alpha male, Broken Claw's extended family understood the power of wisdom.
But now she was dead. Her slim neck had been almost completely severed and she'd had a wound through the chest cavity that would almost certainly have been fatal anyway.
They had returned to the ledge to find her body still warm, but her life gone. And so they'd consumed her, torn the flesh from her bones in ragged strips – skin, muscle tissue, organs – all of her stripped down to bloodied bones. None of her to be wasted. She was loved too much to leave her flesh for smaller scavengers to gnaw at.
Her heart was his, though, and his alone.
Broken Claw had cradled it now for hours, unwilling to let go of the last thing of her. But now was the time. Now, as he stared down through the dark night to the cove far below and the flickering orange flower on the beach surrounded by those pale creatures.
His serrated teeth tore a chunk from the purple organ and he vowed as he chewed on the fibrous tissue that every last one of those new creatures would die. He would be sure to stare closely into their eyes as his claws dug deep into their chests and pulled the pumping source of their life out.
The others began to wail and mew softly, young males grieving at the loss of their mother, as Broken Claw placed the rest of the organ in his mouth and bade farewell to his lifelong partner. He turned to the others and silenced them with a soft bark.
We do not need to fear new creatures.
The others understood this too.
They are as plant-eaters, harmless without their sticks-that-catch.
And they were careless, foolish creatures that often placed these lethal tools on the ground and walked away from them, unaware that without them their clawless hands and small, even, white teeth made them as vulnerable as freshly born cubs.
Broken Claw watched their distant movements on the beach, illuminated by the yellow flower. Of course they all had to die to avenge her... but also to be sure his kind were the only intelligent pack hunters in these lands. To allow these pale things a chance to breed and increase their number would be foolish.
He opened his mouth and his black tongue curled and twisted as he softly tried to reproduce again the strange sound the short fat creature with ginger hair and those strange eyes had made. Broken Claw's throat gargled and whinnied, and his tongue shaped the sound into something that sounded, to his recollection, to be a very passable facsimile.
'Aye... ammmm... Fanck... leeeennn...'
# CHAPTER 48
# 65 million years BC, jungle
The morning sun was already warm on his back and shoulders as Liam poked at the smouldering remains of their campfire with his spear, carefully probing the flaking ash remains of branches for what he was looking for.
'Do be careful,' said Jasmine, standing beside him. 'They're brittle when they're still hot.'
'All right,' he said, going about it more carefully. Presently, the blunt end of thick bamboo cane hit something hard: a dull thunk.
'I got one.' He carefully pushed the ash out of the way and traced a rough rectangle outline, something approximating the size of a brick. 'It looks like it survived the cooking without cracking.'
Using a fistful of waxy fern leaves as an oven glove he reached down and pulled it out, then quickly dropped it on the soft sand. 'Ouch! Still bleedin' hot!' He squatted down beside it, gingerly wiping ash away from the rust-coloured surface of fire-cooked clay. The fine lines of letters and numbers were clogged with ash. The others gathered round and stared down at the small oblong tablet lying on the beach.
'My God, look! It totally worked!' uttered Laura.
The lettering was there to see, clear, unmistakable.
'Of course it did,' replied Jasmine. 'I know what I'm talking about. Me and my mom make ceramic jewellery all the time. We sell it on eBay.'
Liam leaned over and blew at it, the ash fluttering out of the inscribed lines and curls of his handwriting in little clouds.
Take this to Archway 9, Wythe Street, Brooklyn, New York on Monday 10 September 2001.
Message: -89-1-9/54-1-5/76-1-2/23-3-5/17-8-4/7-3-7/5-8-3/12-6-9/23-8-1/3-1-1/56-9-2/12-5-8/67-8-3/92-6-7/112-8-3/234-6-1/45-7-3/30-6-2/34-8-3/41-5-6/99-7-1/2-6-9/127-8-1/128-7-3/259-1-5/2-7-1/69-1-5/14-2-66. Key is 'Magic'.
Whitmore was reading it over Liam's shoulder. 'You think that book code of yours is going to work? I mean, I don't know what book you've used but I know every book has different editions. You know that, don't you? And the page layouts and numbers change from edition to edition. Are you using some kind of internal agency manual or something?'
Becks answered. 'It will work. My duplicate AI is working from the same database.'
'Magic?' said Juan. 'Is that some kinda clue for which book it is?'
Liam nodded. He looked at Becks. 'Do you think Bob will understand that clue?'
She pursed her lips and shrugged – yet another teenage gesture she seemed to have picked up in the last fortnight from the students. 'I am unable to give you an accurate answer to that question, Liam.'
'Well, put it this way... would you get it?'
Her eyelids flickered. 'I have thirty-one thousand listings in my database against the word "magic".'
'Ah, Jay-zus,' muttered Liam, frustrated. 'Maybe we should have put more thought into the clue there. Maybe that one word on its own isn't going to be enough for Bob to –'
'Saleena Vikram will understand,' said Becks. She looked at Liam. 'As "Bob" I discussed the book with her.'
Liam snorted. 'You're kidding me? You can actually discuss literature?'
'I told her I very much enjoyed the magic in Harry Potter.'
Whitmore stood up straight and put his hands on his hips. 'This is a joke, right? You're not seriously telling me your super-secret-ultimate-time-police agency uses a kids' book as a code key?'
Liam and Becks both looked up at him and nodded.
'Jesus!' Whitmore shook his head. 'What kind of a Mickey Mouse outfit are you?'
'Mickey Mouse?'
Liam waved at Becks to be silent. 'It's what works, Mr Whitmore!' he replied, surprised with himself at how angry he sounded. 'It's what works... that's what counts!'
Whitmore was a little taken aback by Liam's uncharacteristic outburst. 'Well, it's just... it just seems so, I don't know, a bit...'
'Amateur,' chimed in Franklyn. 'We were thinking you guys had some sort of already-organized code system. You know? Like proper secret-agent types do?'
'Yeah... don't mean to be dissin' you guys an' all,' said Juan, 'but it does look like you makin' this stuff up as you go along.'
'Look,' said Liam. 'I'll not lie to you... I'm quite new to this time-travel thing myself. And this is certainly the first time I've gone back to dinosaur times. So, I suppose if it looks to you like me and Becks are not working from some... from some sort of manual, well... you'd be right.' He stood up, brushing ash from his hands. 'But I'll tell you this much for nothing: the agency has saved you many times over. And the thing is each time it does that for you, each time it's saved history and the world around you... well, it's happened. And you all go on with your lives happily never knowing how close it's all come to disaster.'
Liam pressed his lips together. 'Me and Becks here have saved you once before.' He half smiled. 'A certain Hitler chap who won a war instead of losing it. Now that was a fine bleedin' mess, so it was. But we managed to fix it up again. So will you not give us some credit here? We're not completely useless, all right?'
'What about your agency?' asked Kelly. 'Who are they?'
Liam was about to answer when Becks grabbed his arm to stop him.
'Lemme guess,' said Kelly sarcastically, 'classified data.'
'I'm sorry,' said Liam, 'that's how it is. We return you to 2015, then the less you know about us, the better. But I'll tell you this, though... they're organized and they've got the best technology out there; computers and... and "robots" like Becks and oh... loads of other stuff. So, look –' he smiled – 'you're in good hands.'
They looked at him with an unreadable mixture of expressions.
Come on, Liam... be decisive.
'Right, then, enough prattling like old fishwives. We have a job to do, so we have. These tablets, Franklyn? Mr Whitmore? Where exactly do you suggest we go and place them?'
They both looked at each other, an exchange of absentminded gestures – Franklyn pushing his cracked glasses up his nose, Whitmore scratching at his scruffy beard – and a muttered exchange of ideas.
Finally Franklyn turned to them. 'I suggest we embed a couple in the beach. Dig a hole, deep... as deep as you can. And the rest –' he turned and nodded towards a nearby thicket of bamboos and reeds – 'that freshwater stream. There's silt banks and a bunch of marsh either side of it. I'm pretty sure that's how they describe the fossil bed in Dinosaur Valley, that it was once... marshy.'
Liam looked at Jasmine. 'And these clay tablets will last sixty-five million years?'
She shook her head. 'Uh, well, no... I never said they'd last that long.'
Franklyn shook his head. 'You really don't know a great deal about fossils, Liam, do you?'
Liam hunched his shoulders. 'Nope, Franklyn, I don't. But you do. So why don't you tell me how this works, then?'
Franklyn sighed. 'They'll most likely break up long before there are even monkeys on planet Earth, let alone Homo sapiens. But the impression they leave behind – like a cast or a mould on the sand – on the silt, which eventually will become a layer of sedimentary rock, that's the fossil.' He offered Liam a patient if somewhat patronizing smile. 'Not those tablets. They'll be long gone dust.'
Liam nodded thoughtfully. 'All right, then. So now I know... strikes me that it makes no real difference – there's still something left behind that a person can read, right?'
Franklyn nodded.
'Good, so best we get started. The sooner we're done, the sooner we can leave.' He turned to address them all. 'I don't know about you but come sundown I'd rather be camping out on that big, very wide beach than down here.'
'With those things out there?' said Whitmore, looking up the jungle slopes surrounding them. 'Sure... getting out of here sounds good to me.'
# CHAPTER 49
# 2001, New York
'Three minutes to go,' said Sal.
'Three minutes,' Maddy echoed. They could both hear the machinery below the desk beginning to hum noisily as it sucked energy greedily from their mains feed. Not for the first time, Maddy wondered who paid the electricity bill for their archway. It had to be astronomical, the amount they used.
She smiled at her dumbness. Yes, of course, no one paid any bills. As far as the world outside was concerned, as far as their neighbour – the car mechanic in the archway near the top of their little backstreet – were concerned, this archway normally sat vacant with a ripped and graffiti-covered sign pasted on the roller shutter outside offering three thousand square feet of commercial floor space at a reasonable rate.
Except of course, for a Monday and Tuesday in September when, to anybody who bothered to notice, it would appear three young squatters had decided to move in, only to vanish again on the Wednesday.
'Oh,' said Sal, 'I forgot... I saw a funny thing the other day.'
'Yeah?'
'Yeah, in a shop nearby. A junk shop. Well, not funny really. Just a coincidence.'
'What?'
'A uniform, a steward's uniform... from the Titanic. Just exactly like Liam's.' Sal shook her head. 'Isn't that weird?'
'Seriously?'
'The lady in the shop said it wasn't a real one, though. Just a costume from a play. But, still, kind of funny. I suppose I could buy it for Liam as a spare.'
'I'm sure he's in no big hurry to go back to the Titanic, you know? Given what he'd have to face.'
Sal's smile quickly faded. 'No,' she said. 'I suppose he wouldn't... none of us, really.'
The numbers on the clock flickered and changed. Two minutes left.
Maddy really could have done with Foster sitting right here beside them. Calm, relaxed, with a reassuring half-cocked smile on his old wrinkly face. Skin that looked like weathered parchment, skin that looked like it had seen way too much sun –
... I wouldn't mind feeling the sun on my face...
Foster's last words. He'd said that the morning he'd taken her out for coffee to say goodbye.
'Sun on my face,' she uttered under her breath.
Sal cocked an eyebrow. 'Uh?'
... I guess I wouldn't mind feeling the sun on my face whilst I enjoy a decent hot dog...
That's exactly what he'd said, wasn't it? One of the last things he'd said. That's what he fancied doing with whatever time he had left to live. Sun and a decent hot dog. With all these skyscrapers, she knew there was only one place you could count on un-obscured sunlight in Manhattan, sun... and, yes, hot dog vendors a-plenty. One place and one place only.
'I think I just figured out where Foster's gone,' she uttered.
They watched the clock's red LEDs flicker to show them 11.59 p.m.
'Where?'
Maddy stood up and pushed the chair back from the breakfast table with a scrape that echoed across the archway. 'I'll uh... I'll explain another time. We're about to have guests.'
Sal stood up and joined her in the middle of the floor, both facing the shutter door, and counting down the last sixty seconds as, behind them, the deep hum of machinery began to build to a final fizzing crescendo.
The strip light above them began to flicker and dim.
'Well, here goes nothing,' said Maddy, reaching out instinctively to hold Sal's hand.
# CHAPTER 50
# 65 million years BC, jungle
'Do you think it's deep enough?' asked Liam.
Becks squatted down beside the waist-deep hole in the mud, and studied the oozing sides, slowly sliding downwards, and the bottom, already beginning to fill up around Liam's ankles with cloudy water. 'I do not know,' she said.
'Don't know, is it? Great.' He wiped at his sweating brow, smearing mud across his forehead. 'Well, who knows how deep is deep enough? May I have the tablet?'
She passed it down to him.
He turned the brick of clay over in his hands and studied the inscribed letters and numbers.
So, my little silent messenger, you go get us some help, all right?
He bent down and placed the brick writing-side down in the cloudy water and gently pressed it deep into the mud. 'We're counting on you, Mr Tablet, counting on you to do your very best for us. Last as long as you can, all right? And, like my Auntie Loretta used to say, you be sure to make a good impression.' He looked up at Becks with a grin plastered on his face amid the mud. 'Uh? Make a good impression? See what I did there?'
She stared down at him, grey eyes coolly analytical. 'A pun,' she replied. 'A single word with multiple meanings dependent on contextual framing.'
'Aye, a pun... you know? It's meant to be funny.'
She frowned for a moment, and then her face suddenly creased with an insincere mirth and she bellowed a mock laugh. He cringed at the sound of it.
'Jay-zus, Becks, if it's not funny... just don't laugh. I'm serious – it's embarrassing.'
She stopped immediately. 'Affirmative.'
Liam pulled himself out of the hole as the wet sides of it began to slop down into the bottom. He and Becks scooped up handfuls of mud and silt and helped the self-filling process until all that was left was a barely noticeable mound on the stream's bank. Liam produced a length of bamboo and plunged it into the top and tore a ragged strip of neon green material from the bottom of his shorts. He tied it to the bamboo stalk. 'And that's so we'll find it easy enough when we come back for it.'
Becks nodded. A part of the plan she'd insisted was necessary: to return to this time-stamp once everything else had been put right and retrieve every single one of the five tablets that were being put into the ground.
Liam looked downstream. The small trickling artery of fresh water twisted and curled out of sight beyond a thicket of reeds. 'I wonder how the others are doing?'
Kelly stood up straight and placed his hands on his tired back. Their two tablets were now dug deep into the fine sand of the beach at either side of the small cove, both marked with bamboo flags and strips of material ripped from the sleeve of his office shirt.
'Done!' He smiled at the others. There was a muted cheer from Juan, Laura, Jasmine and even Akira, a girl as shy as Edward, self-conscious about her thick accent and faltering English.
He looked up the beach towards the line of reed thickets and clusters of bamboo, and the small delta of fresh water and silt that spread out and trickled down a fan of flow-worn grooves in the beach, down into the warm salty sea.
'The others should be done pretty soon,' he said. 'Then we can head back.'
Laura's gaze drifted to the steep peak of jungle they were going to have to ascend. 'I wonder if those things are out there still.'
Juan looked up. 'We got our weapons, and we got robo-girl. We're going to be all right.'
'Maybe we're safer now than we were,' said Kelly. 'One of them was killed trying to attack us. So maybe they're more wary of us now.'
Laura tightened the grip on her spear. 'Yeah... I guess you're right.'
Franklyn finished piling a small cairn of stones around the base of the bamboo stake in the ground and looked up. Whitmore was leading the other two: Edward and his seemingly adopted big brother, Leonard, a hundred yards down towards another hump of silty bank they'd identified earlier as a good place for their second tablet.
'You coming, Franklyn?' the teacher called out.
'Just a sec!' he replied. The bamboo stake kept flopping over to one side and the rocks were very nearly, but not quite, holding it up. 'I'll join you in a second!' he called back, reaching for another large river-smoothed stone.
He heard it then. A soft, muted cry. Like the whimpering of a small child. He froze, listening for it over the stirring hiss of the reeds and the chuckle of the stream. And there it was again, a little louder, a little clearer. It sounded like someone in pain.
'Hello?' he replied. 'Who's that?'
One of the girls perhaps? Maybe slipped on a wet rock and broken something?
'Jasmine? Laura?'
The cry again, pitiful, wretched and insistent. It seemed to be coming from the reeds. 'Akira? Is that you?' He stepped towards them and fancied he saw someone shifting on the ground at the base of the reeds. He pushed his way in.
'What? Have you slipped? Hurt your –'
The form slithered back from him through the reeds and out of sight, moving in a fast – too fast for human – way. It was then his peripheral vision picked out eyes watching him intently from among the reeds to his right. It shifted forward, silently revealing itself a mere couple of yards from him: distinct yellow forward-facing eyes at the front of an elongated, tapering skull that sloped back over hunched bony shoulders and a hunched spine. The curious shape of its skull vaguely reminded him of the aerodynamic helmets worn by speed cyclists, or downhill skiers at the winter Olympics, only much longer, like the aliens in those DVDs his older brother kept watching over and over. It scrutinized him, perfectly still, perfectly poised. And then its scalpel-sharp teeth parted and he saw its black tongue coiling and unfurling like a snake.
'Aye... ammm... Fanck... leeennnnn...' it hissed softly.
My God. This creature – he realized now, the very same reptilian hominid he had faced back up the hillside in the jungle yesterday – had remembered his name, had remembered their fleeting moment of communication, the exchange of a spoken word. Something that wasn't going to happen again on this world for tens of millions of years. What's more, this thing had actually the voice-box and the oral dexterity to reproduce a human word!
'Yes!' he whispered excitedly. 'Yes... that's me!' He gestured to himself. 'My... name... is... Franklyn.'
Its long tapered head tilted to one side and silently it glided a step forward out of the reeds towards him.
In his rucksack, nestled at the bottom beneath the last couple of parcels of grilled fish meat wrapped in waxy leaves, was his phone still with some charge left on it. Enough, he hoped, just enough to take a few photographs and maybe a short recording of this thing actually speaking. He eased the rucksack off his shoulders.
'I'm just going to get something,' he said softly, soothingly, moving slowly. 'OK?'
The creature remained perfectly still, yellow eyes curiously watching his every move. He unzipped the bag and reached inside, the rank smell of fish spilling out. The skin flaps around the hominid's nasal cavity began to twitch.
He can smell the food. Change of plan. Franklyn grasped one of the packages, pulled it out and unwrapped it. 'Here you are... look! Food.' He held the small hunk of barbecued flesh out in one hand towards the creature.
Further off, he could hear the voices of Whitmore and the others echoing back over the reeds, less than a hundred yards away. He was torn between hoping they'd turn up and scare the thing away, and hoping they didn't. He could call out to them. But then what might that trigger? An attack? Or perhaps it would vanish for good, never to be encountered again.
He realized that would be a tragedy. Because this... thing, this species, like every other species of dinosaur, just wasn't going to make it. The world of dinosaurs hadn't much time left in geological terms. A thousand? Ten thousand years? Maybe tomorrow it was going to happen: a mass extinction event, either an asteroid or a mega-volcano was going to choke the world and kill every land-based species larger than a dog. And this intelligent species, so close in many ways to human, closer in some than man's own ape ancestor, was going to vanish along with all the other dumb dinosaurs. They were going to vanish without leaving a trace, would never be known about, never leave any fossil markings, never have a Latin name or be exhibited in a museum or discussed by palaeontologists. And that was the cruellest irony. Because here was something that, given just a few more million years...
... could have been us.
The dominant intelligence, a reptilian version of Homo sapiens.
'My God... you... you're incredible,' he whispered.
The creature was now just a couple of yards from him, yellow eyes on the hunk of meat, crouching low, its rib-and-spine-lined back looked so human, like the back of some size-zero catwalk supermodel or some lean gymnast.
'... fankk... leeeen...' it uttered again.
Franklyn realized he had to take a picture. The species deserved some evidence, at least one shred of visual evidence, that it had once upon a time existed. He gently placed the meat on the ground in front of him then delved back into his rucksack for his mobile phone.
The creature advanced another foot and then strained its long neck and curiously elongated head to sniff the meat. One slender arm swept forward and a hand with three lethal-looking sickle-shaped claws tapped it, rolled it over... then casually pushed it aside.
Its head cocked; its nostril flaps puckered. And then Franklyn realized the creature wasn't the slightest bit interested in the stale odour of the mudfish. It was smelling him, reading his odours like a witch-doctor reading bones, like a medium reading the creased palm of a hand.
'I-I mean no harm. I... just...' Franklyn stuttered nervously.
Its jaw snapped open, and the tongue inside twisted and curled. 'No harmmm...' it mimicked.
'Y-yes... friend... f-friend,' said Franklyn, tapping his chest. It was now so close he could have reached out and stroked the bone-hard carapace of the front of its skull. He could feel warm, fetid puffs of air coming from its nasal cavity.
Franklyn had the mobile phone in his hand now. His eyes still on this thing's reptile eyes, he fumbled with the touchscreen menu and finally got it into digicam mode and pressed the RECORD button.
'A species,' he said softly, panning the cell's camera up and down the beast, 'p-possibly a remote ancestor of the v-velociraptor... or more likely the smarter troodon.' He hated that his voice was shaking like some nervous girl's. If this was going to be a few seconds of footage that was going to make him famous... he wanted to sound like a pro, like a true hardcore adventurer, not some knee-trembling geek. 'This species... is q-quite incredible. Capable of copying a human v-voice...'
The hominid's mouth suddenly snapped shut with a loud clack of teeth and then the cluster of reeds began to rustle with movement all around him.
Franklyn looked up. 'Oh God... n-no...'
# CHAPTER 51
# 65 million years BC, jungle
Liam heard it. A brittle scream, long and ragged and then suddenly silenced. 'Did you hear that?'
Becks nodded. 'Affirmative.' She straightened up. 'The hominid pack hunters may have returned. We should rejoin the others immediately.'
Liam grabbed his spear. 'Come on.'
They splashed across the shallow stream, kicking up fans of water, and then along the bank on the far side. No more than two hundred yards closer to the beach, that's where Whitmore and the others had been left to place their tablets. That seemed to be where the scream had come from. Liam couldn't tell if that one long cry had been a male or female voice, but it had rattled with horror and ended in a way that hadn't sounded good.
They splashed back across the water again to avoid another thicket of reeds as the stream weaved around a smooth boulder the size of an automobile. A minute later, up ahead, he could make out the others gathered in a group, standing closely together and studying something on the ground.
'What happened?' he called out.
None of them replied. They looked up at him with faces as pale as bed linen. Kelly and his group had heard the cry too and had come up from the beach. They must have arrived there only a minute or so earlier.
'What happened?' he called out again as he and Becks splashed across the stream one last time and finally joined them on the silty bank.
Then he saw it for himself.
Blood.
Blood everywhere, and a few tattered shreds of clothing that he recognized as belonging to Franklyn. But no sign of the boy himself. 'Oh no,' he uttered, blessing himself absent-mindedly. 'That isn't really...?'
Whitmore nodded. 'Franklyn's. He... was... we were just down there,' he uttered, pointing downstream. 'Just there... just b-beyond those reeds.'
'Didn't hear anything,' said Howard. 'Or see anything. Just heard him scream. We came up here and... he was gone. Just gone.'
It was Kelly who decided to say first what they were all thinking. 'Those things... it's those things, isn't it? They've damn well come after us.'
'We don't know that for sure,' said Liam. 'There are other predators.'
'Oh, we know,' said Laura. She passed Liam a mobile phone, dappled with droplets of congealing blood. On the small screen, a shaky low-resolution image looped over and over: nothing but the bright pale blue sky, and then the jerky image of something stepping over just the once. But that was all he needed to recognize it: lean, almost skeletal, and that long tapering skull. The image was pale sky again, occasionally shuddering as the camera was knocked, and through the small speaker the sound of growling, snapping teeth and the frenzied noise of something being torn to pieces.
Liam swallowed, his mouth and throat suddenly dry. He felt his face drain of blood and blanch, just like theirs now, pale as a ghost. 'We're leaving,' he said quietly. 'Leaving right now.'
'Uh... I left my bag at the beach,' said Juan.
'Forget the bloody bag!' snapped Liam. He glanced at Becks, ready to bark at her to be quiet should she decide to caution him about potential contamination. But she seemed to understand. Instead she pointed out which way they needed to go. Up the steep slope, thick jungle. 'I will lead the way,' she said. 'Recommendation: you should all remain close.'
'Oh, don't you worry about that,' uttered Liam under his breath. He pulled one of their homemade hatchets out of his bag and hefted his spear in his other hand. 'Everyone ready?'
The others nodded, all of them with a weapon of one sort or another in their hands. None of them keen to step back into the thick canopy of leaves and vines and dense clusters of fern leaves that could quite easily conceal death, but even less keen to remain here a moment longer.
'So, what about Franklyn?' asked Chan in a small voice. No one seemed to want to answer that question. The boy looked up at Howard. 'We're not looking for him, Leonard?'
Howard answered. 'He's gone, Edward. He's gone.'
Becks nodded. 'Correct. Information: approximate calculation – at least five pints of blood on the ground. Franklyn cannot be alive.'
'Come on,' said Liam, resting a hand on Edward's shoulder. He looked up at the sloping jungle ahead of them. 'We should go.'
# CHAPTER 52
Clay tablets, five of them, buried deep in mud and sand, silently count the passing of years. Above, as they slumber in their own dark tombs, tides rise and fall, and individual layers of mud dotted with the decaying bones of generations of creatures accumulate like the rings of a growing tree.
Two hundred and seventy-six thousand, nine hundred and two years after a group of Homo sapiens placed them in the ground, the planet Earth shudders under the impact of a rock the size of Manhattan travelling at forty thousand miles an hour. A wave of incinerating energy spirals hundreds of miles out and tidal waves engulf millions of miles of lowlands across the world. The sky turns dark for the best part of a decade. A ten-year night in which almost all of life on land vanishes, except hardy small rodents from which those very same Homo sapiens will one day descend.
The giants of the plains die off quickly, first the plant-eaters, then the predators. A holocaust followed by a nuclear winter. Massive extinction on an unimaginable scale.
Yet through this five tablets lie still, and dark and oblivious.
In the aftermath of the asteroid impact, the Palaeogene period begins: a vast stretch of time, forty million years in which mountain ranges are born, live and die. A period in which a vast inland sea riding up a backbone of hills that will one day be called the Rockies recedes, surrendering ground that has only ever known the darkness of a seabed, ground that will one day have names like Utah, Colorado, Wyoming, New Mexico.
The dinosaurs are long gone, now nothing more than fossils waiting silently, like the tablets, for the constant attrition of erosion, the movements of ground, to finally push them near the surface and sunlight, again.
Above, in the world of daylight, a brand-new ecosystem exists, a world utterly rewritten. It is a cooler one than the tropical world of the dinosaurs, and the small hardy rodents have grown, evolved, diversified and cover the land with a million different mammal species, many of which a traveller from the present might even begin to recognize.
Near the end of this era, one of the five tablets, now no more than an impression on the surface of a stratum of sandstone, is lost forever when a minor earthquake fractures and grinds the strata to loose gravel. The subtle etchings of words and numbers imprinted from the long-gone clay tablet, erased.
Four companions, however, live on, still separated after so many millions of years by the same distance that existed between them the day they were buried, mere hundreds of yards apart.
Around twenty million years pass and the Palaeogene period becomes the Neogene. The world grows cooler, and for the first time, for a long time, ice-caps begin to form at the polar north and south. Species of grass colonize the land in a way that prehistoric ferns could only dream of, and small four-legged mammals that will one day look very different and be known as 'buffaloes' graze blissfully upon it.
Around seven million years ago, the hard-rimmed hoof of one of these small grazing creatures catches the tip of a broken slab of sandstone, and pulls it out of the ground. It lies there in the darkness of night, moonlight picking out strange and subtle patterns of raised markings on one side. But the roaring of a night predator spooks the herd. As one, they surge away from the sound, and the night is filled with the rumble of thousands of hooves on hard-baked soil.
By dawn the curious slab of sedimentary rock is no more than dust and fragments, destroyed by thousands of trampling beasts.
Three silent witnesses remain as endless aeons pass in darkness, like the soft ticking of an impatient clock. Above ground, one species of rodent that took to the trees during the early Palaeogene, has finally ventured down to the ground once more to forage for food as the Neogene era begins. It is larger, with a more muscular frame and a head larger in proportion to its tree-climbing ancestors. It's a species that will one day, in another more million years, be known as 'ape'.
In 11,000 BC, early one morning as warm sun spills across a plain, a young Indian brave carefully scouting the grazing buffalo ahead runs his hand over the coarse grass and dislodges the sharp corner of a stone. A chunk of flint emerges from the orange soil, a flint, he notices, with curious markings on it.
For a moment the markings incite his curiosity. They look deliberate. But then his mind moves on to the size of the flint itself. He can see how three separate tamahaken blades could be struck from it, and he thanks Great Father Sun for the find.
Now only two silent messengers remain.
In 1865, a young Confederate lieutenant on the run from Union forces, leading a ragtag band of soldiers unwilling to accept that the civil war is over, rests his aching back against a rock. With tired eyes, too old for such a young face, he watches the languid river in front of him as his fingers twist through coarse grass. And, yes, they find the sharp edge of a stone. Before the war he was a student of history, and the faint lines of writing on the stone fascinate him. He puts the curious piece of rock in his saddle-bag and resolves to take it to a professor of natural history he once knew in Charleston when he eventually can. But later that same day the Union cavalry regiment finally catches up with the lieutenant and his men. And before the sun has set they – soldiers and officer – lie in a shared unmarked grave not far away from the Paluxy River.
And so just one last tablet remains.
# CHAPTER 53
# 2 May 1941, Somervell County, Texas
Grady Adams watched his brother goofing about in the water below with growing irritation. 'Watch it, Saul... you gonna scare off all the fish!' His brother ignored him and surface dived into the sedate Paluxy River.
Grady ground his teeth. His younger brother could be a complete ass at times. No, strike that... all the time. He settled back on his haunches, his toes curled over the lip of tan-coloured rock overhanging the river. The stone was hot against the bare skin of his feet, egg-frying hot, that's what Pa would say. The sun had been beating down on it all morning, and the pool of water that had dripped off him from his last swim in the river half an hour ago had long since evaporated.
He looked up at a nearly cloudless sky and realized there wasn't going to be any momentary respite from the heat of the sun. To his left, several dozen yards along the ledge of rock, a small, withered cypress tree was clinging to the side of a large craggy boulder. He could see it was casting a small pool of shadow, at least big enough for a part of him to keep out of the sun.
He stood, grabbed his fishing rod and walked carefully along the narrow ledge. Carefully, because from time to time, right near the edge, bits of the sandstone rock broke away and splashed into the river a yard or so below. That had happened to Grady before, scratching up his hips and chest as he'd slid into the water.
Saul came up again, noisily splashing the surface of the river, no doubt scaring any remaining fish well away from the float bobbing nearby.
'Saul! For crying out loud!'
His brother gave him a toothy grin and paddled across to the far bank, deliberately kicking his feet on the surface and making as much of a ruckus as he could.
Grady hunkered down in the shadow, his back now against cool rock, and to his right a dried earthy wall of orange soil and gnarled roots from the small tree poking out from it. He prodded at the loose layers of soil, light and dark, like the layers of some fancy sponge cake. He'd once found a Paiute tamahaken blade among a bank of earth like this. Those layers folded away such fascinating things along this river. He remembered there was that team of men last summer, digging around along portions of the riverbank, looking for monster footprints in the rock. Dinosaur tracks, that's what they'd said they were looking for.
Grady and Saul had seen a few in their time along here, big ones like he'd imagined an elephant might leave, and small ones too, three deeper dents and a shallow one. Saul even claimed he'd once seen a human footprint in the rock, just exactly like a shoe. Silly ass was always coming up with doofus nonsense like that.
Grady knew no cavemen wore shoes back then in dinosaur times.
The people up in Glen Rose had started calling this place Dinosaur Valley on account of the men and women from the museums and stuff who came digging for fossils last year. He smiled at that as he tugged at one of the twisted roots. It sounded kind of cool... Dinosaur Valley. He could imagine some of the gigantic beasts he'd seen in picture books striding across their Paluxy River, walking up and down the riverbanks, their long necks craning down to drink from the river...
Grit and dry soil tumbled down on to his arm. 'Ouch!'
He let go of the root and it sprang up, releasing another small avalanche of loose clay-like earth. And then he saw it, half hanging out, and resting on a coil of tree root that looked like a pig's tail. A palm-sized slate of shale. He reached up for it and it fell heavily into his hands.
For a moment, as he stared down at the almost triangular shape, he wondered whether it might just be another one of them tamahaken heads. But it didn't have the telltale signs of being worked on, shaped by some skilled hand.
It was just a plain ol' slice of rock.
He held it in his throwing hand, wondering how many bounces he'd get from skimming it across the river. It was nice and flat... a good spin on the throw and maybe he'd count seven, perhaps eight, before it settled and sank. He stood up, saw Saul on the far bank sunning himself on a dry boulder. 'Hey! Saul!'
His brother's head bobbed up. 'What?'
'I got me a skimmer. Reckon I get an eight with it?'
'Nah,' he called back, 'cos you throw like a girl an' all.'
Grady shook his head and sighed. His brother really could be annoying. 'Well, why don'tcha just look and learn, you foo-bat!'
He cupped it in his palm, wondering which side was flatter... and then turned it over.
# CHAPTER 54
# 2001, New York
On Sunday 9 September 2001, Lester Cartwright, a small narrow-shouldered man facing his last five desk years before his long-awaited retirement, went to bed with his plump wife. A man who, if you asked him to be honest, would admit to being a little bored with his unchallenging life. His job – yes, it might sound interesting if he was allowed to talk about it – was as a projects budget assessor for a low-profile US intelligence agency. But, in actual fact, despite the intriguing sound of working for a secret service, the work simply involved crunching numbers and balancing costs and expenditures. He might as well have been doing that for Wal-Mart, or McDonald's, or some carpet store... the job would have been exactly the same.
Not exactly where he'd hoped to end his career when he'd first joined them back in the 1960s, a young man ready to serve his country in the field. A young man ready to kill or be killed for Uncle Sam. Now he was an old man who rubber-stamped expense forms.
That night he went to bed after walking their dog, Charlie, climbed into his pyjamas and picked up a Tom Clancy spy novel, hoping to enjoy at least a few aimless thrills today before turning the light out on his bedside table.
Later, as he slept, change arrived in the form of a subtle ripple of reality. A wave of reality systematically rewriting itself, a wave of change that had started in 1941... with a young boy's discovery of a strange rock beside a river in Texas. A boy who turned over a rock and saw something curious.
Lester's boring life in that moment of darkness was replaced in just the blink of an eye, with a far, far more interesting one.
'Sir! Sir!' Knuckles rapped gently against the car's rear passenger window. Lester Cartwright stirred, his mind had been off again, considering the incredible, the impossible.
Only, it isn't impossible, is it, Lester?
He looked out of the window at Agent Forby, dark glasses, a suit, crew-cut hair and a face that looked like it had never told a joke while on duty. Lester wound his window down an inch. 'Yes?'
'Sir, it's time,' said Forby.
Lester looked down at his watch. Three minutes to midnight. Dammit... he must have been napping again.
Getting too old for something like this.
'Forby, the area's completely secure?'
Forby nodded. 'We have a two-block cordon set up. Police and state guard are manning those. The Williamsburg Bridge has been closed and all civilians have been evacuated from the perimeter.'
Cartwright nodded. The cover story had been an easy no-brainer to come up with: a bomb threat. American civilians seemed to react very well to that. 'So, we're certain we have just agency personnel within?'
Forby nodded. 'A hundred per cent, sir. Just us guys.'
Cartwright looked out of the window past Forby's hunched form. The Williamsburg Bridge towered over them, the nearby intersection was deserted and there, fifty yards away, was the entrance to the small backstreet running alongside the bridge's brick support arches.
My God... finally. This is it. This is finally it.
He felt his chest tickled by butterfly wings and the short hairs on the back of his neck rise.
'Very well.' He opened the car door and stepped out into the warm evening. 'Then let's begin.'
Cartwright led the way across the quiet road, lit by several fizzing street lights and the intermittent sweep of a floodlight from a helicopter holding position high up in the sky. Apart from the far-off whup-whup-whup of its rotors, this three-block-wide area of Brooklyn was ghostly quiet.
There was a barricade across the entrance to the backstreet, manned by more of Cartwright's men. No soldiers or police this close to the target, on Cartwright's insistence. Only personnel he trusted within the perimeter. Only personnel he'd recruited himself into this small covert agency, an agency he and his men referred to as the Club.
He nodded at them as they raised their guns and let him through. He looked down the narrow cobbled street, littered with garbage, an abandoned skip halfway along.
Good grief, I feel... like a kid.
All of his professional life had been leading up to this one moment, ever since he'd been quietly headhunted from the FBI to come and work for the Club. Forty years of knowing.
Lester Cartwright began to make his way down the row of archways, past the first one, clearly being used by some one-man auto-repair business.
When he'd first joined, his superior had been prepared to reveal only some of the facts: an incredible find in a place called Glen Rose, Texas – a find that had major national security implications. That was all he got for quite a few years. But time passed, and Lester gradually climbed several ranks, finally becoming the senior serving officer in the Club. His departing boss had handed him the complete dossier on his very last day, handed it to him with eyes that looked like they'd been staring far too long into an abyss.
'Do me a favour, Lester,' he'd said. 'Sit yourself down and drink a finger of bourbon before you open this file, all right?'
'Sir?'
'You're about to join a very, very small group... those that know.'
And it was a small group.
Presidents had been briefed – Roosevelt, when the news of the artefact had first been unearthed. Then Truman, then Eisenhower. But they'd stopped briefing presidents when that silly fool Kennedy had threatened to go public on it. That was the year after Lester had joined the Club, the year of the Dallas incident. A very messy business. But the Club had a responsibility.
They hadn't bothered to tell presidents since then.
Cartwright passed the third and fourth archways, both open-fronted and unoccupied. He could see needles and bottles back there in the darkness. His men had checked in there for vagrants and unearthed only one grubby, stinking and utterly bewildered alcoholic. He could feel his heart pounding in his chest as his feet slowly brought him up outside the metal roller-shutter door of the fifth archway.
Forty years he'd known of a thing called the Glen Rose artefact.
But only for the last fifteen years had he known exactly what it was.
Figuratively speaking, a message in a bottle, with a date on it. A bottle that couldn't be opened until a certain date. He looked down at his watch and saw that that certain date was a mere forty seconds away.
There hadn't been a single solitary night during the last fifteen years that he hadn't lain in bed and wondered what they'd find inside this address. He'd been down this street on a number of occasions and looked at that corrugated metal; he'd even been inside and looked around on several occasions. Empty, unused.
But now, finally, there were occupants inside. Occupants from – his heart fluttered and his breath caught as he considered the phrase – another time.
Cartwright instinctively reached into his suit jacket for the service-issue firearm he kept there as he looked at his watch and realized that after forty years of waiting and preparing he was finally down to counting off the last ten seconds.
'So... this is it,' he uttered.
The second hand of his watch ticked past midnight and all of a sudden he thought he felt the slightest puff of displaced air against his face.
He leaned forward, balled his fist and knuckled the shutter door gently.
# CHAPTER 55
# 2001, New York
Maddy looked at Sal. 'Oh my God! You hear that? That was a knock, wasn't it?' She hadn't fully expected to be right, that come the stroke of midnight and the reset there would actually, for real, be a knock on their door.
The roller shutter rattled again, and they heard the muffled sound of a man's voice outside.
'So we're going to open it, right?' whispered Sal.
'I... uh... yes, I guess we've got no choice.' She stepped forward towards the button at the side and pressed it. With a rattling whirr of a winch motor begging for oil, the shutter slowly rose. Both girls looked down at the ground, at the gradually widening gap, and the soft glow of the street lamp outside creeping across their stained and pitted concrete floor.
Two shoes. Two dark-suited legs. Finally the person outside ducked down slightly to look in, and his wide eyes met theirs.
'Hello there,' said Maddy, raising a limp hand. 'We were... kind of expecting you.'
The shutter rattled to a stop and the man stared at them for a long while in silence.
'I...' he started, his voice croaky with nerves. 'You... but you're just kids.' He narrowed his eyes, looking past them at the dim interior. 'Are there any others here?'
'Just us, I'm afraid,' said Maddy.
He looked at her; his old creased face seemed to be struggling to cope with the moment. 'Are you two... are you f-from the future?' he asked.
Sal looked at Maddy and she finally nodded her head. 'You've got a million questions you want to ask us, I'm sure,' Maddy addressed the old man. 'And we're prepared to answer some of them. But... you have something, right? Something for us?'
He eyed her cautiously. 'Perhaps.'
'A message?'
He ignored the question. 'Are you time travellers?'
'I won't answer anything until you answer me. Do you have a message for us?'
He took a step forward, squinting at the machinery on the far side of the arch. He nodded towards it. 'Is that some sort of time machine?'
She bit her lip. 'I'm not saying anything until you answer me.'
'It is, isn't it?' He smiled. 'My God... this is incredible.'
'Please!' called out Sal. 'Something brought you to us. It's a message from our friend, isn't it?'
The old man turned away from them and barked an order down along their backstreet. A moment later Maddy could hear the slap of boots on cobblestones. She retreated from the entrance and into the arch, taking several steps towards the computer desk.
'I'm sorry,' said the old man. He reached into his suit jacket and pulled a handgun on them. 'Please remain perfectly still. Do not touch anything! Do not do anything!'
Half a dozen men emerged from the backstreet, all of them wearing bio-hazard suits, faces hidden behind tinted fascias of plastic. All of them armed with what looked like television remote controls.
Oh no. Maddy felt lightheaded. This isn't good.
'We're going to talk,' said the old man gently. 'But we're going to talk safely away from this place. Please,' he said, beckoning for them both to come forward, out of the archway and into the street, 'step forward, away from the equipment.'
Now! You have to do it now!
Maddy spun to face the computer desk. 'BOB! OMELETTE!' she screamed, desperately hoping the desk mic across the archway had managed to pick up her voice. The last thing her conscious mind registered was every muscle in her body contracting with a sudden jolt, and then keeling over on to the hard floor, her forehead smacking heavily against the concrete.
Cartwright watched in silence as the older of the two girls was wheeled away on a hospital gurney, and the other one, younger, Asian or Indian by the look of her, was escorted down the backstreet towards the containment van.
He ordered the remaining three agency men in containment suits to stand guard outside the shutter door once they'd made a sweep and reported that the archway was clear. Good men, trusted men... but still better they knew as little as possible.
He stood alone now in front of a giant perspex cylinder of water, metal steps up the side and what looked like a toddler's swing seat fixed at the top. Obviously something to do with time travel... like the bank of computer equipment, the other tall thin perspex tubes in the back room, the power generator... all these things clearly played some part in the process.
He wandered back to the long table – a pair of scuffed office desks pushed end to end and cluttered with monitors, a keyboard, a dozen crumpled cans of Dr Pepper and a few empty pizza boxes. He could hear the soft whirr of activity from beneath the desk and ducked down to see the muted glow of blinking green and red LEDs. It looked like there were a dozen or more PCs, the kind you could pick up from any Wal-Mart or PC World, linked together into a network.
Beside the desk was a battered old office filing cabinet. He pulled out one drawer after another, each filled with nests of tangled cables and bits and pieces of electronic circuits, like somebody had ripped off a RadioShack store for bits and not yet figured out what to do with it all.
He felt a small stab of disappointment. In his mind's eye he'd imagined this moment; he'd conjured up visions of some futuristic arrangement, technology from centuries ahead, something that looked like the bridge of the USS Enterprise set up in this old brick archway. Instead, everything he could see here seemed to have been obtained from the present.
He sat down in one of the office chairs and it squeaked under his weight.
The answers to this place, why they were here in New York... why they were also in the Cretaceous past, how all this machinery worked, and what it could do... all of those answers he presumed were on these quietly humming computers. He picked up the mouse and slid it across the desk. One of the screens flickered out of screen-saver mode and lit up to reveal a relaxing desktop image of an alpine valley and, right in the middle of the screen, a small square dialogue box.
> System lockdown enabled.
Cartwright cursed under his breath. The older girl, the one with the frizzy reddish hair, had barked something out just before he'd tasered her. He'd thought she was calling out to someone else in the arch, but he realized now that it must have been a voice-activated command.
He tried to remember what she'd said. Oh yeah...
'Omelette,' he said into the desk mic.
> Incorrect activation code.
'Dammit!'
> Incorrect activation code.
He tried a dozen other candidate words and phrases: egg, broken eggs, scrambled eggs, boiled eggs, Easter egg, fried egg. Egg hunt, egghead, egg-nog. All of them produced the response on the screen.
Absently he tapped his fingers on the desk. If he was being honest, this wasn't how he imagined the moment of discovery was going to be: two scruffy kids, a computer system that looked like some bedroom hacker's dream set-up, and that big plastic cylinder making this place look like some kind of homemade brewery. And this locked-down computer system was obviously not going to tell him anything. He decided it was time he had a little chat with the girls.
He stepped out towards the open door and punched the green button on the side. The metal shutter started to clank and rattle slowly down.
'No one goes in, or comes out. You have permission to shoot to kill anyone who tries. Understood?'
The three men guarding the entrance nodded.
# CHAPTER 56
# 65 million years BC, jungle
The wide-open plain was alive with the echoing calls of nocturnal life. Liam had assigned half of them to remain on watch and the other half to try their best to get some sleep, although he doubted anyone was managing that.
A fire was burning in the middle, not for the meagre light it provided, but for the effect it seemed to have on the creatures roaming around out there, keeping them all well away. It was bright enough anyway. The full moon seemed to illuminate the night enough that it felt little darker than an overcast winter's afternoon in Cork.
'That moon is actually bigger, right? Or am I going mad?'
Becks looked up at it. 'Affirmative. It is approximately twenty per cent larger.'
Liam's eyebrows shot up. 'A larger moon? So what do you think happened to it? Did it sort of wear down over time or something?'
Whitmore looked at him oddly and tutted. And Becks... he wondered whether she'd just rolled her eyes at him or whether that was just a trick of the light. 'Negative, Liam. It has not changed size.'
'It's just a little closer,' said Whitmore.
'Oh.'
Becks resumed her silent vigil, slowly panning her eyes across the plain, watching for the dark furtive shapes of the creatures moving beyond the dancing circle of their firelight.
'What do you think of those things?' asked Liam. 'Are they really a species of super-smart dinosaur? That lad, Franklyn...' He paused for a moment, realizing the ensuing panic-stricken retreat from the cove, over the jungle peak and down on to the beach hadn't permitted him a single moment of reflection for the poor boy. He could only imagine what those creatures had done to him, if that carcass from nearly a fortnight ago was anything to go by.
The others were waiting for him to finish what he'd started saying.
'Franklyn said all dinosaurs, even the smart ones, were pretty stupid.'
Whitmore sucked in a breath of warm night air. 'Those hominids could well be a dead-end evolution, a branch-off species that maybe shares a common ancestor with troodon.'
'Troodon?'
He nodded. 'Palaeontologists commonly agree that the troodon was quite possibly the most intelligent species of dinosaur. Smarter even than their evolutionary cousins, the raptors. Very similar in appearance, both therapods... saurischian dinosaurs.'
'What's that mean?'
'Bipedal... they walk on their hind legs. Like the T-rex does.'
Liam shook his head. 'Those creatures didn't look anything like any dinosaur I've seen, big or small. I mean... their heads?'
Whitmore nodded. 'Like I say, some dead-end evolution. Perhaps if the K–T event never happened, the asteroid, or volcano or whatever it was, many more sub-species with similar long skulls might have evolved from them. Perhaps that's why they're so smart – a greater cranial capacity, a larger brain.'
'The species exhibits high levels of intelligence,' said Becks. Her neutral voice seemed to have adopted an ominous tone. 'They appear capable of tactical planning. They appear to have a language. They do not, however, appear to have developed tool-use.'
'Why not? If they're so smart? Why don't they use spears and bows and arrows?'
Becks had no answer. Whitmore shrugged. 'Who knows? Perhaps they've never needed to use tools? Maybe nature already made them so lethal they've never needed tools? Or perhaps, because they only seem to have four digits and no thumbs, tool-using is just something they're unlikely to ever do?'
'But they're smart enough?' asked Liam. 'Is that what you're saying? If they had thumbs an' all... they'd be smart enough to make a spear or a bow or something?'
Whitmore scratched his beard absently. 'Who knows?'
On the far side of the campfire, Howard and Edward stood watch. The robo-girl had been standing with them for a while and then gone to rejoin her Irish friend and Whitmore. Howard decided now was quite possibly the best time he was going to have to say what he needed to say.
'Edward?'
The small boy looked up at him.
'Thank you, you know... for saving me from that shark thing yesterday.'
Edward shrugged like he'd done nothing more than buy him a Coke. 'OK, Leonard.'
'No... seriously, Edward, that was something... what you did. It could just as easily have gotten you. But you... you stayed right by me. You saved my life.'
Edward smiled. 'Sure, Lenny. You're my best friend.' He sighed. 'Well, my only friend. Like I said, I don't do so good back home. You know, making friends and stuff.'
Howard felt a sour twist of guilt churn away in his guts. He'd come to kill Edward – that's how he'd ended up here – and yet this boy seemed like a ten-years-younger version of himself. He'd had things the same way when he'd been at school: lonely because he dared to be different. It never changed, did it? Not even in his time, the 2050s. Kids always found a way to single somebody out.
'Edward, I've got to tell you something,' he said before he could stop himself.
'What?'
'I'm... I'm not who you think I am.'
Edward frowned and smiled at the same time, bemused. 'You're Lenny.'
'No,' replied Howard, 'that's just it, I'm not. I'm not Leonard Baumgardner. I'm not seventeen.' He lowered his voice and his eyes flickered across the campfire towards the other three people on guard duty. 'And I'm not from the year 2015.'
'What? Serious?' Edward's eyes widened. 'You're one of them? An agent from the future too?'
Howard shook his head. 'Not an agent. I don't work for the same people. I belong to another group, a group trying to stop time travel, but... but in a different way.'
Edward stared at him silently. 'Not Lenny. So what is your name?'
'Howard.'
He heard Edward mouth the name quietly.
'But listen, Edward... I... I managed to go back in time to find you...' He hesitated, toying with how best to continue, when Edward spoke the words for him.
'To get to me. That's it, isn't it?'
Howard looked away.
'To stop me going to university? Stop me doing a degree?'
Howard couldn't bear to meet his eyes.
'Not to... oh no...' Edward's voice dropped. He'd figured it out. 'No. Don't say you came to kill me?'
Howard nodded. 'I'm sorry, Edward... but yeah. To short-circuit history, to cut out a chunk of the past that should never have happened.' In the dark he couldn't see how the boy was taking it, just the outline of his round head and narrow shoulders gazing out at the dark plain.
'That means you're not really my friend, then?'
Howard felt that twist of guilt curl and flex like some restless eel making a nest in his belly.
'That mean you're still going to kill me?'
Howard shook his head. 'No, not any more.'
'Why?'
'Because I don't need to. We're stuck here now.'
Edward turned back towards him. 'But we're gonna get rescued. Those messages that we –'
'No one's going to find them,' he replied, shaking his head.
'How do you know?'
'If they'd ever been found –' he nodded towards the others – 'and Liam and robo-girl's people were able to come and rescue us, then they'd know what happens in 2015, wouldn't they? They'd know about me. And they'd make sure you were never on that field trip to the TERI labs. They'd make sure you were kept as far away from that assassination attempt as possible.'
Edward's face clouded with thought for a moment.
Howard offered him a smile that was probably lost in the dark anyway. 'So, I've done what had to be done. I'm truly sorry it's landed us here. I really am... but the world after 2015 is a much safer place without you. There's no you, there's no maths thesis, no Waldstein and no time machines. For good or bad... I know the world's heading for dark times ahead, certainly it is where – when – I came from: floods, droughts, billions starving, oil running out, wars. But the world will get through that eventually. It can survive that.'
'But it can't survive time travel?'
'No. We've been messing around with stuff we can't understand, can't control. We're like children playing catch and toss with a neutron bomb. But that's finished, Edward... It's not going to happen. I'm relieved, but I'm also sorry it's landed you and the others here.'
'Why be sorry?' said Edward flatly. 'Mission successful. You did it.'
'I'm sorry... because, I think, well, I hope, you and I have become friends. And I've put you in this situation.' Howard could understand if the boy walked away right now and told everything he'd just heard to the others. Then, of course, they'd confront him and perhaps even exact a brutal revenge on him. Howard could understand that and was ready to face the music.
Instead he felt Edward's small hand on his forearm. 'It's OK. I'm not angry with you.'
He laughed. 'You have every right to be.'
'No point,' said Edward. 'We're stuck here forever, then. So we've got to work together. Right, Leonard?'
Leonard... it sounded like Edward was going to keep this confession to himself.
Howard nodded. 'So?'
'So, I'm not telling. You're Leonard still.'
He smiled. 'OK... I'm Leonard.'
'Right.'
'Right.'
# CHAPTER 57
# 2001, New York
Maddy's mouth was dry and her head was pounding. She slowly opened her eyes and winced them shut against the painful bright glare of the light overhead.
'Sorry about that,' she heard someone say. The lights in the room dimmed slightly. 'Better?'
She cracked her eyes open again, and then nodded. She felt something cool pressed into her hands.
'Water. Have a sip. It's just water, I assure you.'
Maddy lifted a plastic tumbler and gratefully slurped a mouthful. Her eyes blinked and she tried to focus on her surroundings: a small room with a low ceiling, what looked like a medicine cabinet, a strip light overhead. She was lying on what appeared to be a hospital bed and beside her she saw the old man who'd come knocking at their door sitting on a stool. He'd taken his jacket off, rolled up his shirtsleeves and loosened his tie.
'You took a knock on the head when you went down. I'm sorry I had to taser you.'
Yes... that was it. She'd felt like every muscle in her body had locked and an unbelievably agonizing sensation had coursed through her whole body.
'Where am I?' She realized she was lying on some sort of a hospital gurney. But then this didn't look like a hospital ward, or a private ward.
'New York still,' he smiled. 'And somewhere perfectly safe.'
She sipped the water again. 'Who are you?'
The man pulled the stool forward. It rattled on castors across a smooth linoleum floor. 'My name's Lester Cartwright,' he answered warmly. 'And yes – if that's your next question – I work for a, shall we say, a quiet little intelligence agency on behalf of the American government.'
Maddy nodded and smiled blearily. 'I figured it would be someone like that who'd come to our door.'
'Well... who else would it be?' he asked. 'Something like this, knowledge of this... it's far too important for any old Joe to have in his possession. I'm sure you'd agree.'
Maddy shrugged, her hand reaching up to her forehead and finding a dressing there. 'I suppose.'
'So,' he said, leaning forward. 'I have just about a million goddamn questions I've been wanting to ask someone like you. Questions I've been waiting for answers to most of my adult life. And, in return, I have a curious message that I'm sure you're rather keen to see.'
She was encouraged by the old man's directness. No beating about the bush, no attempting to fool her, beguile her. Just the straightforward declaration of a quid pro quo.
She nodded. 'A message from a friend.'
'Yes,' he said as he got up and reached for his jacket neatly draped on a small storage cabinet in the corner of the room. He fumbled for the inside pocket and finally pulled out a folded sheet of paper. 'A friend who apparently decided to take a holiday during the, if I'm not mistaken, the late Cretaceous period?'
Maddy's jaw dropped open. 'I... uh... when did you say?'
'The late Cretaceous. We've tested the rock. It's definitely from that time.'
Her lungs emptied a gasp. 'You mean, like, dinosaur times?'
Cartwright nodded. 'Yes, I believe it was a popular time for dinosaurs.'
'Oh my God, I didn't think the machine –' She stopped herself before she blurted out anything else. She decided it would be far smarter to keep as much as possible to herself for now.
'Yes.' The man's eyes narrowed curiously. 'Yes, you do look genuinely surprised at that. What were you going to say?'
She shook her head. 'Nothing.'
He studied her silently for a few moments. 'This is someone you lost, isn't it? Someone you've been unable to retrieve? To find? Some kind of mistake? Is that it?'
'May I see the message, please?' she replied.
'You didn't think time travel that far back was possible?' he said, fishing for a reaction on her face. 'Am I right?'
'We lost someone, all right? Now, can I see the message?'
'Where are you from?' he asked, then shook his head. Comically, he gently slapped his forehead. 'Stupid, stupid me... it's when are you from I should be asking, isn't it?'
Maddy couldn't help a smile and a dry laugh. 'It does that to you, this business... makes you want to slap your head.'
The old man shared the smile. 'I can imagine.' The smile eased away. Business again. 'You're American, that much I've worked out. Boston?'
She nodded. No point trying to hide that. 'Yes.'
'When?' He looked at her T-shirt, the faded Intel logo on the front, her jeans, her pumps. 'Not too far into the future is my guess.'
'Maybe.'
'You want to see this?' he asked, unfolding the message.
She nodded.
'Then can we start having some precise answers from you?'
She shrugged. 'OK.'
'Your name is?'
'Maddy. Maddy Carter.'
'Hello, Maddy.' He nodded politely. 'And what year are you from?'
'I'm from 2010,' she replied.
The answer seemed to stun him. His eyes widened involuntarily and beneath the folds of his wrinkled skin above the crisp white collar of his shirt, his jaw worked as teeth ground. Finally he pursed his lips. '2010 you said?'
'Yup.'
'You actually know the future? The next nine years of it?'
'Of course.'
His face drained. 'Then you... you're saying you know, for example, what this government's foreign policy goals might be? Long-term strategic plans? Those kind of things?'
She smiled. 'Oh yeah, I know what's round the corner.'
That silenced him for a long while. She watched the folded paper flutter in his hand.
'Do you know just how dangerous that makes you to certain people?' he said softly. 'I can think of quite a few colleagues in my line of business who'd want to put a bullet in your head right now. Quite a few more who'd want to torture every last little fact out of that head of yours... oh, and then put a bullet in it.'
'The message?'
He nodded his head absently and then handed it over. 'It might amuse you to know,' he said, 'I can recite every word and every last number of the coded section. I've known off by heart what's written down on there for the last decade and a half.' He laughed humourlessly. 'Like an old poem drummed into your head at school and you never ever forget.'
Maddy reached for it and unfolded the paper. She saw handwriting. She presumed it was the old man's handwriting.
Take this to Archway 9, Wythe Street, Brooklyn, New York on Monday 10 September 2001.
Message: -89-1-9/54-1-5/76-1-2/23-3-5/17-8-4/7-3-7/5-8-3/12-6-9/23-8-1/3-1-1/56-9-2/12-5-8/67-8-3/92-6-7/112-8-3/234-6-1/45-7-3/30-6-2/34-8-3/41-5-6/99-7-1/2-6-9/127-8-1/128-7-3/259-1-5/2-7-1/69-1-5/14-2-66. Key is 'Magic'.
Oh my God, Liam... you're alive. You made it.
'Now, the first bit makes sense to me... clearly designed to make sure the message finds its way to you –'
She cut him short. 'Where did you get the message from?'
He cocked a wiry grey eyebrow. 'A fossil, would you believe? A fossil discovered by some boys in 1941. The second of May, to be precise. Along a river near a town called Glen Rose in the state of Texas. It nearly caused a sensation, but... the wartime secret service worked quickly to hush up the find. And, of course, people were far more concerned about the war then than silly rumours about mysterious fossil finds.'
He smiled. 'The place was taken over by secret service goons, and guess what else they found?'
Maddy shrugged.
'A few months after the message was discovered, they found a human footprint.' He looked up at her. 'Oh yes, a genuine human footprint, from the same strata of sedimentary rock. The print of some sort of a running shoe.' He was amused by that. 'That's what they called it back then, a running shoe. They didn't have training shoes back then.'
'Uh?'
'A forensic expert matched the print pattern to the Nike brand last year.'
'And no one else knows?'
He laughed. 'Of course not. The boys who originally discovered the artefact... well –' he glanced at her – 'our methods were a little uncivilized back then.'
'Killed?'
'Hmmm... vanished... is the term I think we prefer. And, of course, it turned out a few years later that some other local rockhound had found fossilized human footprints the previous summer... so again there was need for some damage limitation.'
'Vanished too?'
He shook his head. 'News of the human footsteps got to the local newspapers before it could be contained. We simply discredited the story. Easily done, the same old boy swore blind his dead mother lived in the attic and came down once a year to bake his birthday cake.' He snorted. 'Complete loon by all accounts. Anyway, go look it up sometime. I'm sure it's on some conspiracy website somewhere: "Humans Walked with Dinosaurs – Dinosaur Valley, Texas".'
She looked down at the message again. 'So, you know exactly how old the fossil is?'
He shook his head. 'No, not exactly. Of course not. It's identified as coming from a seam of sedimentary rock that pre-dates the end of the Cretaceous period. What they call the K–T boundary. That's as precise as we can be, I'm afraid. Geology works in aeons and ages, not months or years.'
He gestured at the piece of paper. 'The numbers... I presume the numbers contain specific information that would help you retrieve your friend?'
She could deny that, but it was quite obviously the information Liam would have put down there. 'I hope so,' she said.
'But unfortunately it's encoded,' he said. 'Now, the secret service boys who pre-dated my little club's involvement in this matter identified this pretty quickly as some sort of book code. See? The numbers follow the page, line, word structure. And about a decade ago, we managed to secure some very expensive time on the Defence Department's mainframe and ran every single book in the Library of Congress through it.' He splayed his hands tiredly. 'We got diddly squat for all our troubles, of course. Which leads me to think, as I sit here with you now, that that was a big waste of time as this probably is a book that hasn't even been published yet. How about that?'
Maddy shook her head. 'I... I don't know. I really don't.'
She glanced at the last words of the message. 'Key is "Magic".' She looked up at Cartwright. 'That's the clue, right? But I just... I just don't know... If that really is a clue to a book, I wouldn't know which one.'
'What about your colleague?'
'Sal?' She sat up and groaned with the effort. 'Is she OK? Where is she?'
'Oh, she's just fine,' he said, waving his hands dismissively. 'And she's nearby. Maybe it's time I had a chat with her.'
'You won't hurt her?'
He looked sternly at her as he reached for the piece of paper, got off the stool and picked his jacket up off the cabinet.
'Because, see, if... uh... if that's what you're planning to do,' Maddy continued, 'then don't b-bother.'
'Oh, let me guess, because the pair of you are heroes and neither one of you is going to talk, huh?'
'Because –' she shook her head and laughed nervously – 'because there's really no need. Neither of us are heroes. We'll talk, OK? Just promise me you won't hurt us.'
# CHAPTER 58
# 65 million years BC, jungle
Kelly struggled up the steep incline, cursing under his breath as low-hanging thorned vines scratched at his face. Ahead he could hear the others pushing their way noisily uphill, the snapping of branches and vines, the clatter of dislodged rocks and soil rolling downhill.
'Leonard? Edward?' he called out.
'Here,' gasped Edward.
'Come on, you need to pick it up... we're lagging behind the others.'
Their sweat-drenched faces emerged through a curtain of waxy leaves. 'I'm exhausted,' gasped Howard. 'My leg...' He failed to finish his words between ragged puffs of air. He dropped uncomfortably to his knees on to an uneven bed of dried cones, twigs and jagged rocks.
'It's slowing him down,' said Edward. 'His ankle.'
'I know, I know, but we can't let the others get too far ahead.'
Around their campfire last night the discussion had turned to why those creatures hadn't attacked them again, instead choosing to discreetly follow them at a distance. The conclusion they'd come to was that they were playing a tactical game, waiting for the group to become spread out enough to be able to pick them off one at a time. This morning as they'd made their way across the rest of the plain towards the last stretch of the journey, down into the jungle valley, they'd been almost comically bunched up.
But now, hacking their way through dense foliage, the group was getting dangerously strung out.
'Come on, Edward, help me get him up.'
It was then that Kelly caught a glimpse through a gap in the leaves of some dark form fifty yards below them.
'Oh Jesus,' he hissed. 'I saw something back there!'
'What?'
'Just... just.... there's no one else behind us, is there?'
Edward shook his head.
Kelly saw it again, a dark form hurrying between the trunks of two trees, then dropping down out of sight. 'Oh my God! They're down there!'
Howard was on his feet again.
'Go! Go!' snapped Kelly. 'I'll watch our backs!'
Edward and Howard stumbled forward again, Kelly reversing uphill, keeping his eyes on the downhill as he fumbled his way after them. Again, he saw it. Closer now, the flicker of dark olive skin, leaping between the gaps in the leaves. More than one of them, and moving so terrifyingly quietly. More worryingly... they didn't seem to care that they were being seen.
Oh no.
Now they were in the jungle they were closing the gap.
I'm not going to outrun them.
He realized he stood a far better chance squaring up to them, perhaps even skewering one of them on the end of his spear. Maybe another kill would buy them another day of caution, enough time to get back over that river to the camp.
'Come on,' he hissed. 'I know you're down there!'
He heard Edward calling down. 'Mr Kelly?'
'Go!' he shouted. 'I'm just coming!'
The sound of the two boys' clumsy staggering slowly receded from him until all he could hear was the occasional snap of a branch echoing off the tall stout trunks of the canopy trees.
'Come on!' he whispered again. He was surprised that it wasn't abject terror he was feeling right now, but anger. Rage. He wanted to grab one of those scrawny things and rip its ridiculous marrow-shaped head off. His throat filled with a dry laugh.
Who do you think you are – Tarzan?
A far cry from his normal life: PR guy, meeting and greeting visitors with his cheesy tanned smile and his nice linen suit and expensive polo shirt. Right now, standing legs apart in trousers ripped off at the knees to make shorts, bare-chested, revealing a pale torso tufted with silver-grey hair and drooping man-boobs that spoke of a lapsed gym membership... right now he felt like that commando character in the film his sons liked, the one with the alien with a crab face and dreadlocks.
Oh yeah, he was ready for them.
'Come on... you want some of me? Then COME ON!'
As if in answer, in the stillness of the jungle around him, he heard a soft, high-pitched voice.
'... Come... on...'
Then ahead of him, as if it had appeared like the Cheshire Cat, only yellow eyes first instead of a big grin, there stood one of the creatures, a dozen yards downhill of him, cocking its head and studying him intently.
Kelly took several steps downhill, lunging with the tip of his spear. 'Yeah? So that's what you things look like up close.'
It recoiled at the sight of the spear, ducking back into a patch of waxy leaves, only to emerge again a moment later.
'Oh yeah! I can kill you with this spear,' muttered Kelly triumphantly. The spear seemed to be warding off the creature, its yellow eyes warily locked on the sharpened tip of bamboo.
The sound of the others moving through the jungle was all but gone now. He couldn't afford to remain like this much longer. He needed a kill pretty soon, and for the rest of those things to hopefully bolt like rabbits.
'Come on,' he said quietly, 'just you and me. Man versus ugly lizard thing.'
Its jaw snapped open and a dark tongue curled like a serpent inside. '... Lizz... arrrrd... ting...' A surprisingly close approximation of his own voice.
'So you do impressions, huh?'
The creature cocked its head thoughtfully, and it was then, as the creature was distracted, working out how to replicate what he'd just said, that he decided to make his move. He took a quick step and a short leap forward and thrust the spear hard. It caught something soft and the creature flapped and flailed on the end of the bamboo, howling with a voice that reminded him of the awful noise a dog can make if you step on its tail.
'YES!' he snarled.
First blood. He pulled the spear back out, leaving a large puncture wound in the creature's belly, out of which thick dark blood began to sputter as it flailed in screeching agony on the jungle floor.
He was about to stab the thing again, but he felt the spear yanked roughly out of his hands.
'Whuh?'
He turned to see a larger hominid, standing fully erect, maybe a foot taller than him. It snarled angrily, a rattling croak in the depth of its throat. He saw others behind it, then became aware of yellow eyes all around him.
The creature held his spear in both of its clawed hands, closely inspecting the long thick shaft, and then finally the sharpened tip, wet with dark blood. It looked at the tip, cocked its head and then looked down at Kelly, who now no longer felt so much like a commando. His knees buckled beneath him and he found himself in a helpless squat on the jungle floor.
Oh God, oh God...
'Run,' he whimpered. 'Why aren't you r-running? W-why aren't you running?' That was what was meant to happen. If this was a film, that's what would happen, right? The weedy office guy finally finds his inner hero and saves the day?
'I k-killed one... so why... w-why aren't you r-running?'
The creature holding the spear took a step forward and once more inspected the bloodied tip of the bamboo before turning it round so that it pointed towards Kelly.
'Oh... no...' he found himself whimpering. 'P-please...'
The normal everyday sounds of a Cretaceous jungle, the distant lowing of large ambling leviathans on the far-off plain, the chatter and squeak of small foraging creatures going about their business, were punctuated by a peculiar sound: the protracted, rattling scream of a human being. It echoed up through the jungle and out through the tops of the canopy trees, startling flocks of small anurognathus from their branches and into the air.
# CHAPTER 59
# 2001, New York
'I'm not saying another thing to you!' snapped Sal.
Cartwright shrugged. 'Well, OK. But then I guess I'm not going to show you what I've got.'
It was silent in the small interrogation room, except for the soft hum of an air-conditioner. It was warm and stuffy. He casually loosened his tie.
Sal's narrowed eyes softened, piqued with curiosity. 'What? What have you got?'
He smiled. 'Hmm... now there was me thinking we weren't going to be talking to each other.'
'Oh shadd-yah! Please. Just tell me!'
He pursed his lips, giving it some thought. 'And are you going to tell me the things I want to know?'
She clamped her mouth shut, said nothing.
'You know? I suspect you probably will,' Cartwright relented. 'After all, you, me and Maddy all want the same thing: to bring your friend back home safely.'
'He's alive? Liam's alive?'
'I believe so.' He nodded and reached into his breast pocket. 'He decided to write home.' He passed her the folded sheet of paper and she quickly began to scan the handwriting.
'Your colleague Maddy and I were discussing it just a few minutes ago. She's really rather keen to bring him home too. And you know I'm prepared to help you girls do that. Whatever you want, whatever you need. But...'
She looked up. 'But?'
He splayed his hands almost apologetically. 'That technology in the arch. I'm afraid that's going to be US government property now. And we're going to need your help in figuring out how it all works.'
'We can't do that,' she started. 'We can't just let you have it. It's too dangerous!'
'Too dangerous for the government? But apparently not too dangerous for a pair of kids to mess around with?'
'We were recruited. Specially recruited.'
'Recruited by?'
Sal hesitated. 'I can't really say.'
He shrugged. 'Well, that can wait until later. It's not so important. The fact is somebody needs to take charge of what's in that archway.' He cocked a questioning eyebrow. 'I mean, somebody's got to be in charge, right? Making sure there aren't loads of other time machines and people running around when and where they shouldn't be.'
'And what... that someone's going to be you, is it?'
'Me for now, perhaps. In time I'll brief the current president on what we have. But believe you me, far better you have someone like myself looking after this on behalf of the American people than some terrorist group or some mad dictator looking for a world-beating weapon, a madman like Saddam Hussein or Osama Bin Laden. Hmm?'
She shrugged a 'Whatever' at him.
'Now,' he said, nodding at the paper in her hands. 'There's a code there. Maddy seems to think you might know how to decipher it.'
She looked down at the numbers, a meaningless jumble of digits that meant absolutely nothing to her at first glance. But then, very quickly, the pattern began to speak to her. Groups of three numbers, the first into the hundreds, the second being numbers no greater than thirty-five and the last seeming to peak at numbers no greater than fifteen, sixteen. She knew exactly what that was.
'It's some kind of a book code.'
'Clever girl. But now, here's the sixty-four thousand dollar question. Which book?'
She scanned to the bottom of the numbers and saw the last word of the message.
Magic.
Magic? What the jahulla sort of a clue was tha–?
She looked up at him, a smile slowly spreading across her face. Of course, if Bob had it in his database, so the duplicate AI in the female support unit would also.
'You know, don't you?' said Cartwright.
'Uh-huh.' She was almost tempted to tell him the book's title anyway, since it wasn't going to be published for another few years yet. Instead she attempted to suppress an irresistible urge to giggle.
The old man sighed patiently. 'Well, you could, of course, just tell me. Which would be far more pleasant for the pair of us. Or we have a medicine cabinet full of interesting drugs I can pump into you. Some of them with some quite horrific side effects. And failing that there's always the old-fashioned way.'
'You take us back to the archway,' she said, 'and I'll decode the rest of this message for you.'
He shook his head. 'Hmm, now see, my concern is that we get back into that archway of yours and one of you kids'll shout out something else, and – pop! – you and all that machinery vanishes in a puff of twinkly time travel sparkles and smoke.'
'She hasn't told you yet, has she?'
He frowned. 'Told me what?'
Sal's smile widened, a nervous twitchy smile. 'That's actually really funny.'
'Funny?'
She nodded. 'Funny.'
'Why? What's funny?'
'She's playing with you. How long have I been in here?'
'Why?'
'Please... tell me how long?'
He looked down at his watch. 'A few hours. Why?'
'Exactly. Please.'
'Five hours... five and a half hours.'
She giggled again. 'You don't have much time left, then.'
The last of the congenial expression was lost from his rumpled face. 'Stop messing around and tell me what the hell you're talking about!'
'Sure,' she said amicably. 'Our computer system is locked down for six hours. After that, it's got orders to totally brick itself if Maddy doesn't give it another codeword.'
'Brick?'
'Fry all the data. All the machinery. Everything.'
His bushy eyebrows both arced, and beneath his jowls his jaw began grinding away again.
'You ready to take us back now?' asked Sal politely. 'I'll even say "please".'
# CHAPTER 60
# 65 million years BC, jungle
Broken Claw looked at the others in his family pack, predator eyes meeting predator eyes. In his claws he was still holding the bamboo spear, the bloodied end of it embedded in what was left of the new creature.
His mind worked hard trying to understand what he'd done. Trying to comprehend the fact that it wasn't his claws that had ended this pale creature's life, but the long device that he was holding, something other than him. Something he controlled. Something he had... used.
He turned to the others, clicked and growled and mewled softly.
Do you see? We killed the new creature with this.
Their minds, all younger, less developed. His children stared, yellow eyes burning with hatred, but not quite understanding, not just yet.
But he did. And his older, wiser mind stretched a little further. This long stick he held, he understood now what it was and where it came from. They grew along the river in thick clusters. But now it was no longer simply a plant – the new creatures had fashioned it into something else entirely: a deadly weapon.
Something deep in his reptilian mind shifted. Concepts, very simple concepts, looking for each other amid a busy crowd of instinct-driven brain signals, finally finding each other and embracing.
His pack had no communicable sound for the concept. His mind had no word for the idea. But if he'd had a wider range of words to construct his thoughts from then his mind would have been full of words like use, make, build...
His small mind suddenly produced an image, an image of a fast-flowing river and a tree trunk lying across it – a device the new creatures had built to cross the river.
He turned to the others, clicked his teeth and beckoned them to follow.
What he had growing in his mind is what any human being would have called... a plan.
# CHAPTER 61
# 2001, New York
They approached the archway. Cartwright nodded at his men still standing guard outside. He gestured to Forby to join them inside as the shutter cranked noisily up. The other men he instructed to continue guarding the entrance, allowing no one else inside.
One by one they all stooped under the shutter as it clattered to a halt. As he followed the others in, Cartwright glanced up at the sky above Manhattan, beginning to lighten with the first grey stain of dawn. Another hour and it was going to be daylight, New Yorkers getting ready to go to work, and disgruntled civilians building up around the road blocks either end of the Williamsburg Bridge. Traffic police, TV film crews and journalists were surely soon going to add to that, asking his men and the National Guard soldiers where their orders had come from. What the hell was going on? He and his discreet little under-the-radar agency could do without attracting that kind of attention. The terrorist-bomb cover story those men had been given would hold for a little while longer, but not forever.
The last one inside the archway, he pressed the button and the shutter rattled down noisily again. Forby removed his bio-containment hood and then unslung his machine pistol.
'It's all right, no need to aim it at the girls,' said Cartwright. 'But just have it to hand, uh?'
Forby nodded and lowered his aim.
'So,' he continued, approaching the desk stacked with monitors, 'the computer? Before it's all fried?'
Maddy nodded. 'Yes, of course. DOMINOES.'
Cartwright shook his head. Of course. You idiot, Lester. He looked at the Domino's pizza boxes strewn across the desk, and would have slapped himself if he'd been alone.
The dialogue box on one of the screens flickered to life as a cursor flashed and scuttled across the screen with new text.
> Welcome back, Maddy.
'Hi, Bob,' she said. 'I'm in time, aren't I?'
> No system files have been erased yet. You had another seven minutes before I proceeded with your instructions.
'Christ,' muttered Lester, 'you weren't kidding.'
Sal shook her head. 'Nope.'
> My camera detects unauthorized personnel in the field office.
'Yes,' said Maddy, 'we have guests.'
> Are you under duress?
'No, it's fine, Bob. These guys are OK, for now.'
Cartwright tapped Maddy's arm and spoke quietly to her. 'Anything funny, I mean it... you say anything to that computer that sounds remotely like a warning and it'll be the very last thing you do.'
She nodded. 'Don't worry... I'm not stupid.' She sat down in one of the office chairs and faced the computer's webcam. 'Bob, we got a message from Liam.'
> I am very pleased to hear that.
'Yes, so are we.'
Sal joined her at the table. 'Hey, Bob.'
> Hello, Sal.
She held up the piece of paper Lester Cartwright had produced earlier. 'This is the message. Can you see it clearly?'
> Hold it very still, please. I will scan it.
A moment later the scanned image from the webcam appeared on one of the monitors and the image flickered light and dark as Bob adjusted the contrast to get a clearer resolution of the handwriting. Then a highlight box flashed around each handwritten letter in rapid succession, until finally a text-processing application opened itself on yet another monitor with the entire message typed out clearly.
> Some of the message is in code.
'That's right,' said Sal. 'It's a book code.'
> The encryption clue is 'magic'. Is this correct?
'Yes.'
> I have more than thirty thousand data strings that include the word 'magic'.
'I think that's referring to the book you were reading the other day. Do you remember? We were discussing it.'
> Harry Potter and the Deathly Hallows.
'Yeah, that's the one.'
Cartwright and Forby leaned forward. 'You have got to be kidding,' mumbled the old man.
'Hey, my daughter is reading those books,' said Forby. 'Is that the next one?'
'It's the last one,' said Maddy. 'Book seven.'
'Jeez! What my girl wouldn't give to get a look at that!'
Cartwright cocked an eyebrow at his man. 'Forby... please be quiet.' The man obediently drew back and resumed his wary stance, the gun held loosely in his hands.
Sal sat down beside Maddy. 'Bob, you and the duplicate AI will have the same digital book file, right?'
> Affirmative. The file was in my short-term memory cache when we downloaded the duplicate AI into the support unit.
'Then this should be pretty much straightforward,' said Maddy.
'Yeah.' Sal flicked her hair out of her eyes. 'You've just got to replace each three-number code with the letter. You understand how the code works, Bob, yeah?'
> Affirmative. Page number. Line number. Letter number.
'That's right.'
> Just a moment.
They watched in silence as clusters of numbers were momentarily highlighted on the document, while on another screen, pages of the book flashed back and forth in a blur. The task was completed in less than thirty seconds.
> The complete message is: Take this to Archway 9, Wythe Street, Brooklyn, New York on Monday 10 September 2001. Message: Sip, two, sehjk, three, npne, gour, zwro, aix. Key is 'Magic'.
They stared at it in silence for a few moments, trying to make sense of it.
'Well, that's just gibberish, isn't it?' said Cartwright.
'Are you sure you're working from the same digital book file?' asked Maddy.
> Affirmative.
'The original numbers on the fossil,' said Cartwright, 'some of them were indistinct, or incomplete. I have access to the original piece of rock.'
'No... it's OK,' said Sal. 'If it's just numbers it's really easy to work out. Sip is six. Sehjk, must be seven.' She worked quickly, writing the numbers down on a scrap of paper.
'There.'
6-2-7-3-9-4-0-6
'It's not in the usual time-stamp format,' said Maddy.
> Please show me, Sal.
Sal held the piece of paper up to the webcam.
> It is a number. 62,739,406. Suggestion: it is the AI duplicate's best estimation of their current time location.
'Oh my God!' gasped Maddy. 'It actually managed to work it out?' She looked at the cam and smiled. 'Well, that's you, actually, isn't it? A copy of you, Bob. Well done!'
'To the exact year?' said Cartwright. 'To the exact year? That's... that's incredible. How could anyone possibly –'
> Negative. The best resolution guess can only be to within 1,000 years of that year.
That silenced them all.
They could be up to 500 years before or after the specified time location.
'Oh jahulla,' whispered Sal. 'Then that's no good to us.'
'The nearest thousand years?' Maddy's head drooped. 'How are we supposed to find him in that?'
Cartwright looked down at both girls. 'So your machine can't bring back your colleague?'
Maddy shook her head. 'It takes time to build up enough charge to open a portal, particularly for one that long ago. I don't even know how long it would take to accumulate enough to open one then anyway, let alone do it thousands and thousands of times over.'
> Information: approximate charge time – nine hours.
'So we can do it,' said Sal.
Maddy laughed drily. 'Yes, we can... but a thousand years? If we opened one window for each year it'll take us nine thousand hours... what's that? Just over a year of constantly opening and closing portals.'
'So? We'll do that for Liam, right?'
Maddy sighed. 'That's opening one window per year. What are the chances of Liam standing right there in the two or three seconds of that year? Hmm? What if he was asleep at that moment? Taking a leak? Hunting for food? To stand any sort of chance we'd need to open one... like... every day!'
'This sounds like a needle-in-a-haystack problem,' said Cartwright unhelpfully.
'Oh.' Sal bit her lip. 'But we could try, couldn't we?'
'Three hundred and sixty-five thousand attempts!' replied Maddy. 'Do you want to have a guess how many years that would take us? Hmm? Lemmesee,' she muttered, as she gnawed on the nails of one hand. 'Oh, there... three hundred and seventy-five years or something.' She made a shrewish face, growing pink and mottled with frustration and anger. 'So, what do you say we get started, then?'
'Then I'm sorry, that's it,' stepped in Cartwright. 'I'm afraid your friend is stuck where he is. This facility will need to be packed up by the end of today and shipped down to a more secure government facility.'
'You can't do that!' snapped Sal. 'This is our... this is our home!'
'It's now a US government asset,' he replied calmly. 'And so are you, my dear.'
> Suggestion.
'You can't do that! We've got... like, human rights and stuff!'
Cartwright's smile was humourless and cold, the calm and empty gesture of someone who cared not one whit. 'I wonder... who exactly is going to miss the pair of you? Hmm? Family? Friends?'
'The agency,' snapped Sal. 'And if you mess with us, if you hurt us, they'll come for you! They're from the future! And they're –'
'Sal!' barked Maddy. 'Shut up!' She grabbed Sal's arm. 'Don't say anything more about the agency! Do you understand?'
She clamped her mouth shut and nodded mutely.
Maddy looked at Cartwright. 'I think I can guess what you have in mind for us; you'll keep us under lock and key in some remote Area Fifty-one facility, like freaks, like lab rats. And that's where we'll remain until you're sure you know everything about this technology... then I guess you'll dispose of us, right? A drive out into the middle of the Nevada Desert and one shot in the back of the head for each of us. Is that how you lot work?'
Cartwright shook his head. 'Nothing so brutal, Maddy. You're worth far too much to us alive. Even when I'm sure you've told me all that you know, we're still going to need guinea pigs to test your time machine on.' He sighed. 'Mind you, it would have been good to have your colleague too... I'm not sure I'm entirely comfortable with the idea of him being out there roaming around history. But I suppose if he's sixty-two million years away, I can't see him doing –'
Sal cast a glance back at the monitor.
> Suggestion: rapid-sweep density probes.
She pointed at the screen. 'Maddy! Look!'
Maddy spun in her chair to look at the monitor and quickly digested the words. 'Oh my God, yes! Probes. Density probes... that could work!'
'What?' said Cartwright, shaking his head irritably at the distraction. 'What're you on about?'
'Tachyon signal probes to check a return location is clear of obstructions and that someone else isn't wandering through it before we open.'
Cartwright looked none the wiser.
'It's like... it's like knocking on a door before entering. Like asking is anyone in there? It's a lot quicker than actually opening a portal. A lot less energy needed.' She turned back towards the mic on the desk. 'Bob, what are you suggesting? We can't scan every moment over a thousand years... can we?'
> Negative. We scan a fixed moment of each day, 500 years either side of the calculated year. That is a total of 365,250 density probes.
'But that's going to take you what? Months? Years?' asked Cartwright.
> Negative. Small signals, no more than a few dozen particles per signal, would be enough to identify a transient mass. Movement.
'Yes,' said Maddy. 'That's it! And all the signals that came back with some movement detected could become a... become our candidate list: a shortlist of times we could try to open a portal on. Bob, how long would it take to do that many probes?' She turned back to Cartwright. 'It'll take a lot less time, I promise you! Maybe just a few days, tops!'
He shook his head. 'Unacceptable. I want this archway empty by the end of today. Empty and everything inside in boxes and en route to –'
'Please!' begged Maddy. 'We can't leave Liam out there!'
Cartwright silently shook his head.
'He knows the location of all the other field offices,' cut in Sal.
Maddy's jaw dropped open. 'Whuh?'
'He alone knows where they all are. Locations, time-stamps.' She turned to Maddy. 'I'm sorry... I was going to tell you, but... but Foster swore me to secrecy.'
Cartwright studied her silently. 'There are others, then? Other places like this?'
Her face hardened and her dark eyes narrowed. 'I'm not telling you any more. I don't know any more, but... like I say, Liam knows.'
'Hmm.' He thumbed his chin thoughtfully.
'Bob,' said Maddy, 'how many days would it take to do those density scans?'
> Calculating... just a moment... just a moment...
'Nice try, young lady,' said Cartwright eventually. 'You know, that was almost convincing. But it's the sort of nonsense that only happens in movies.' His croaky voice raised in pitch to that of some damsel in distress. 'Oh, please don't shoot, mister... If you let me live, I'll show you where the loot is hidden.'
Cartwright laughed, pleased with his impression.
Sal shook her head. 'Oh, I'm not lying. Where do you think the time machine came from?' she replied. 'What? You think me and Maddy put it all together by ourselves?'
He had no answer for that.
Maddy could see where Sal was going with this. A good bluff. 'She's right, Cartwright. Where do you think we get spare parts from? When the displacement system breaks down, who do you think we call to come and fix it? Some spotty kid from PC World?'
Sal nodded. 'You think our people are going to let you walk away with one of their time machines?'
There were questions there that the old man needed time to consider carefully. The room remained a motionless tableau, while from somewhere overhead came the faint muted sound of a circling helicopter.
The blink of the cursor running across the dialogue box suddenly caught everyone's attention.
> Information: running at 11 scans a second, 365,250 scans will take approximately nine hours.
'Nine hours,' said Maddy. 'See that? Nine hours.' She looked at her watch. 'By three this afternoon, we'll have an idea exactly when he is and we'll be able to bring him back.' She smiled sarcastically at him. 'Then you'll have three lab rats to play around with instead of two.'
'Yes.' Cartwright nodded appreciatively. 'I suppose there is that.'
'Please,' whispered Sal, her hard-bargaining face softened to that of a begging puppy.
'All right. But if either of you tries anything silly, like dialling for help with one of these signals –' he reached into his jacket and pulled out a handgun – 'in fact, if you do anything that isn't explained clearly to me first, I will shoot you dead. Do you understand?'
They both nodded quickly.
'There'll be no shouted warnings, girls. I will simply pick up my gun and I will blow your brains across that messy desk of yours.' He offered them that cold lifeless smile. 'And, believe me, you'd be in very good company. It won't be the first time I've blown a person's brains right out of his head.'
Maddy swallowed and puffed out a fluttering breath, her eyes resolutely on the wavering muzzle of Cartwright's gun.
'Sure. Uh... O-OK. Nothing silly, then... I totally promise you that.'
# CHAPTER 62
# 65 million years BC, jungle
Liam heard the roar of the water through the trees ahead of them.
'Becks? Are we close?'
'Affirmative. The river is a hundred and twenty-six yards ahead of us.'
He grinned a mixture of relief and bravado. 'Jay-zus-'n'-Mary, am I glad to be back!'
By the look on the faces of the others they couldn't agree more with that. The thick canopy of leaves above them began to thin out as they approached the jungle's edge, lances of late-afternoon sunlight stabbing down past loops of vine and dappling the ground with pools of mottled light.
With a final glance back at the forbidding darkness behind them, and an almost complete certainty that those things were still somewhere back there watching them from a distance, they hurried forward into the light.
Up ahead the river frothed and tumbled like some endlessly enraged beast. On the far side, he could see their bridge, dangling like a crane's arm above the water. He was relieved to see it was raised; the four they'd left behind had maintained a wary caution.
Liam stood on the bank and cupped his hands. 'Hello-o-o-o-o!'
The others gathered beside him. They'd lost three of their number, Ranjit, Franklyn and, earlier this morning, Kelly. All of them had heard his cry, and it had hastened their efforts down into the jungle valley, knowing those things were somewhere behind. And they'd grouped together more cautiously, realizing now the creatures were looking for stragglers.
Being bunched together seemed to have paid off. There'd been no sign of them throughout the morning, midday and now into the afternoon. Not even when they'd cleared the bare peak. Liam had looked back quickly in the hope of catching their pursuers unawares. But he saw nothing.
Now they were back. Job was done.
Liam craned his neck to look into the thin veil of jungle on the far side of the river. He could see some slivers of light through the dark tree trunks, the clearing beyond. But no sign of anyone coming their way to lower the bridge yet.
'Try again,' said Laura.
'H-E-L-L-O-O-O-O-O!'
Liam's voice echoed above the roar of the river, and startled a flock of miniature pterodactyls from a nearby tree. They waited with growing anticipation for a few minutes.
'They'd have heard that surely?' said Whitmore.
Edward stood on tiptoes to get a look through the jungle opposite. 'Unless they're all sleeping.'
'There'll be hell to pay if they are,' muttered Liam. He cupped his hands again. 'WE'RE BACK!'
Still nothing.
'Maybe they gone huntin'?' said Juan.
'I gave instructions that someone always has to keep an eye on the windmill,' replied Liam irritably.
Laura nodded at the bridge. 'Someone would have to stay behind anyway, to lift that for them and lower it.'
He nodded. 'True.'
'So someone must be home.'
'This is not good,' he muttered under his breath.
Becks had been examining the fast-flowing water. 'I am able to cross this,' she said.
'The current's too strong,' said Liam.
'I do not need to swim across all of it, Liam.' She pointed along the bank on which they were standing. Fifty yards down, it rose to a moss-covered hump that was well on its way to being undercut by the river. 'Information: I calculate I will be able to jump across between thirty and forty per cent of the river's width from that point.'
He looked at her. 'And you know how to swim?'
'Affirmative. I also know how to walk, run, jump... talk.'
He cocked a sideways glance at her. Was that actually sarcasm? Was that another example of Becks's emerging sense of humour? She returned a smile.
'Oh, you're so funny, Becks.'
'I am developing several files on humour traits.' She nodded towards the mossy hump, changing subject. 'I will not be long,' she said, turning to walk down the bank towards it.
'Where's she going?' asked Whitmore, unhappy to see their robot bodyguard leaving them alone.
'She's going to do her superhero thing,' said Liam.
They watched in silence as she examined the river for a moment then turned to regard the height of the hump. After a few seconds she walked away from the river's edge and came to a halt just as she was about to enter the shadowy fringe of the jungle. She turned round and without a second's hesitation broke into a sprint towards the river.
Whitmore's eyes rounded. 'She's gonna jump it?'
She bounded up the side of the hump and launched herself out across the river. Subconsciously everyone gasped and rose on their tiptoes as she gracefully sailed a dozen yards out over the water, her arms pinwheeling to give her extra momentum. Then she arced down into the water, disappearing beneath the stampeding white horses of the river.
For a long half a minute Liam couldn't see her anywhere, then, finally, he spotted a dark head bobbing among the churning swirls of suds, gone again, back again, then as the river rode over a bed of large boulders and became a chicane of lethal-looking rapids, it curved round and she was lost from sight.
'She gonna make it?' asked Juan.
Liam nodded. 'I'd put money on it.'
Whitmore nodded with admiration. 'What I wouldn't give to have her on my school's athletics team. We'd win every cup going.'
They waited an interminable ten minutes before they spotted her again, jogging up the riverbank on the far side. She reached their jury-rigged bridge, carefully untied the counterweight of bundled logs and then, taking on the weight of the main trunk, muscles in her arms bulging from the effort, she slowly lowered it, the vine ropes creaking and groaning under the strain.
Above the busy rumble of the river, they heard the crack of one of the vines snapping.
'It's gonna go!' shouted Liam.
It looked like Becks had heard that too. She began to pay out the rope more quickly. But another vine snapped under the increased burden, twanging up to the overhanging branch like a rubber band.
'Stand back!' barked Liam to the others. 'It's gonna drop!'
And it did. The other vines snapped in quick succession and the tree trunk swung down from its forty-five degree angle and clattered heavily on the boulders on their side. Everyone heard the crack, loud as a gunshot. Halfway along the trunk, jagged splinters of wood protruded from the side, and their bridge sagged down in the middle almost into the water.
'Oh, great!' shouted Laura.
'Lemmesee... it may be OK,' said Juan. Before anyone could stop him he'd stepped up on to the boulders and then carefully on to the end of the log. He inched his way a few yards along it. It bowed a little further, now dipping into the water itself midway along, but it seemed to be holding.
Juan dropped to his hands and knees, then straddled it, bum-shuffling his way across. At the midway point, he gingerly eased his way over the jagged fracture, water catching his dangling legs and threatening to pull him off. But he got over, and a minute later jumped off on the far side.
Liam nodded. 'All right, then. It seems like it'll hold for us. Let's go.'
Whitmore ushered Edward to cross first, then had Laura, Akira and Jasmine line up to go next. Meanwhile Liam turned round. 'Have your spears ready.' He nodded at the dark jungle behind Howard and Whitmore. 'They may still be out there.'
Waiting until it's just the one of us left? Then what?
He didn't care to think about that.
Whitmore went after Jasmine, panting with exertion and fear as he inched his way across, the fractured trunk wobbling and creaking with each movement he made. Finally, he made it to the far side and beckoned for whoever was coming next.
'Leonard, you go.'
The dark-haired boy eyed Liam. 'You sure?'
'Uh-huh,' replied Liam, his eyes remaining on the dark jungle. 'Just be quick, will you?' he added, flashing him a quick nervous smile.
Howard nodded, and then was on the trunk and shuffling. Liam waited until the student was nearly halfway across before taking one wary step on to the end of the log. He could feel the vibration of Howard's movements.
If they're gonna come for me... it's gonna be right now.
Then as if on cue he thought he saw movement, some dark shape leaping through the undergrowth, moving from one hiding place to the next. Getting closer, but not quite ready to commit to leaping out into the open.
'What is it?' he grunted under his breath. 'You scared of me? Is that it?'
That sounded good to him, fighting talk. For a fleeting moment there he almost didn't feel completely terrified. But that soon passed as his eyes assured him something else had just shifted position one tree closer to him.
He finally felt the trunk under his foot wobble as Leonard presumably jumped off at the far side. He heard Whitmore's voice over the din of tumbling water calling him over.
'Coming!' Liam shouted over his shoulder. Keeping his eyes on the jungle, he reversed on to the log, still not daring to turn his back on what he knew was in there and waiting for him to do just that.
Pull yourself together, Liam.
He dropped down to his hands and knees. Unwilling to turn his back on the jungle, he began bum-shuffling backwards, one hand still holding the spear half ready, in case he needed to defend himself at a moment's notice.
After a minute's slow progress, he finally felt a sharp splinter of wood scrape the inside of his thigh and realized he was now just before the fractured halfway point. Cool water rode up his dangling legs, soaking him to his thighs. As he shuffled to get past the jagged shards of the fractured trunk, he heard it crack and felt it lurch as it sagged lower into the river. Water suddenly rode up over his knees and over his lap, pummelling his gut and chest like an enraged boxer sensing the faltering resolve of an opponent.
Oh no... please, no.
Water. Drowning. Suddenly the fear of being snatched and torn apart by some vicious predator was matched by the idea of being snatched away by the river.
'It's going to break!' shouted someone.
Liam could feel the trunk being buffeted and kicked by the strong current. It flexed, creaked and twisted under the punishing weight of energy slamming into it. He realized it wasn't going to hold out much longer and a rising tide of panic compelled him to get off his backside and crawl. He struggled on to his hands and knees, now, finally, turning his back on the jungle he'd moments ago thought was hiding the most frightening thing in this world.
No... the most bloody frightening thing right now was this churning white monster roaring hungrily at him, doing its best to pull him off. He could see the others waiting for him at the far end of the bowing log, all frantically waving at him to get a move on.
'All right... all right, I'm coming!' he yelped. He began to crawl forward on hands and knees. One hand carefully placed after the other on the treacherously wet bark.
Come on, Liam, come on. You're nearly there. He managed to make his way a yard closer to the bank, and even managed to flash the others a cavalier I'm gonna be just fine grin, when his hand found a slick patch of moss.
'Uhh...' was all he managed to gasp before his hand slipped round the side of the trunk and the unsupported weight of his body carried him over.
# CHAPTER 63
# 65 million years BC, jungle
Suddenly he found himself spinning amid a roaring chaotic swirl of swiftly moving water. Instinctively he'd snatched a lungful of air as he'd gone under, his body doing the thinking for him while his mind shrieked uselessly with blind panic.
Drown! I'm gonna drown!
He knew it. His lungs were only going to buy him a half minute of life. His mind was all of a sudden back in the narrow confines of a corridor groaning with the sound of stressed bulkheads, flickering wall lamps and the distant roar of ice-cold seawater finding its way up from the deck below. The certain promise of death a mile down in the cold dark embrace of the ocean.
Oh no, no, no, no, not this! Not like this!
Then his head suddenly broke the surface. He flailed in the foam, still holding on to the stale breath in his lungs. He caught sight of their log bridge thirty or forty yards behind him already and fast disappearing as the swift current carried him away.
His legs thumped heavily against a boulder and he found himself being rolled over its hard rounded surface. His head again under the water, his ears filled with the pounding roar of the river, he felt himself being sucked down deep by a spiralling current, pressure compressing his chest.
Panic. Sheer, blinding panic robbed his mind of any useful conscious thought and left him with a curdling mental scream, knowing this dark roaring depth was where it was all going to come to an end for him.
But the river's mischievous current decided to play one more game with him and shot him to the surface to say goodbye to life and air and trees and the crimson sky of later afternoon once more. Liam gasped for another lungful of air, half aware that perhaps the kindest thing he could do was simply breathe out and prepare his mouth, his throat, his lungs for an invasion of water.
But then his shoulder thudded hard against something. Something he could grasp hold of and fight the incredible pull of the river. He opened his eyes and realized it was a fallen tree. For a moment he wondered if the river had carried him right the way round their island in some logic-defying loop-the-loop and he was right back where their crudely constructed bridge was.
He desperately grappled with the rough bark and the small leafy branches that sprouted from it, merciful handholds that their smooth and straight trunk had lacked. From branch to branch he managed to pull himself out of the strong current in the middle of the river to some calmer eddies of swirling water.
Finally his foot brushed against the river bottom, scattering pebbles, and his feet desperately fumbled for firmer footing that promised to stay beneath him. His hands followed the fallen tree, pulling on thicker, more reliable branches until he found himself wading out of the river, finally collapsing on hands and knees on wet shingle that shifted and clattered noisily beneath him.
'Urgh,' he spluttered, between ragged gasps of breath.
His breath was still pounding in and out as he finally pulled himself, exhausted, to his feet. He turned to look at the fallen tree, trying to get his bearings and work out which side of the river he was now standing on. The base of the tree was on the far side; he could see a frayed and splintered stump that looked like it had been hacked at by a team of inept carpenters armed with blunt chisels... or beavers even.
Not beavers, obviously. Perhaps some species of termite had cannibalized the tree, or it had simply rotted and split. Either way, he thanked it for saving his life. He noticed a mess of disturbed shingle and footprints around him among the leaves and branches of the felled tree and realized that perhaps Lam and the others must have felled the tree for wood, but foolishly allowed it to fall across the river and just left it.
Idiots.
The first thing he'd do once he found them was get them to heave the tree back into the water and let it be carried away. He turned round and squinted up the riverbank. Through a hundred yards of jungle he could just about make out crimson slivers of waning sunlight, the trees thinning, the clearing beyond... and their camp.
He'd lost his spear in the river. No matter, he was on the safe side now. He made his way up the shingle and into the narrow apron of jungle. Up ahead through the dangling loops of vine he could see the sun casting long shadows across the leafy hummocks of their shelters and the wooden wall of their small palisade as it began to make a bed on the horizon. But, as yet, he couldn't make out Lam and the other three kids they'd left behind.
Where are they?
'Hello-o-o-o!!' he called out again, his voice ricocheting through the jungle.
A few moments later he was stepping out from beneath the dark canopy of foliage and into the clearing. On the very far side, he could see Becks and the others emerging.
He waved at them. 'Hey!'
He saw their heads turn his way and their mouths form sudden dark ovals of surprise and relief.
'I made it! I'm all right!' he called across to them. 'I'm fine! Have you seen the others?'
Becks led them across the clearing towards Liam until finally they converged around the smouldering remains of a campfire.
'The others have not been located,' said Becks.
Liam noticed their small turbine wasn't spinning. The cross-bar was split and the school bag was on the ground, its load of round pebbles spilled. 'The windmill's broken. What's happened?'
There were no answers.
'We should get that running again first,' he continued. He looked around at the others. 'Maybe they're out looking for us?'
Becks strode swiftly towards the contraption to see whether a quick repair could be made. Liam was about to pass on some instructions to the others to split up and search for the others when he noted Jasmine's gaze, wide-eyed and lost on some detail everyone else seemed to have missed.
'Jasmine? You all right?'
She pointed at the ground. 'That,' she whispered. 'What's that?'
Liam followed her gaze down to the ground. Nestled amid a cluster of pebbles, cones and the dry brown decaying leaves of long-dead ferns, he saw a pale slender object that looked to him like an impossibly large maggot. He took a step towards it and noted the ground was stained dark around it, and at one end of it, pointed yellow-white shards poked out like the antennae of a shrimp.
He felt his stomach lurch and flip in a slow, queasy somersault.
It was someone's index finger. The antennae, shards of bone.
'What is it?' asked Whitmore, stooping to get a better look. 'My God! Is that a finger?'
The conclusion hit Liam like a punch. 'They're here.' He looked up at them. 'Those pack hunters are here, on the island.'
Whitmore's mouth flapped open and shut and produced nothing helpful.
'How?' asked Howard. 'It's impossible. No way those things can swim across!'
'They don't need to.' He looked at the others. 'They went and copied us... learned from us.'
'What do you mean?'
'I think they made their own bridge.'
# CHAPTER 64
# 2001, New York
Everything in the archway died, leaving them in pitch black.
'What's going on?' cried Cartwright.
'Please!' cried Maddy in the dark. 'Don't shoot! Don't shoot! It's nothing I did!'
'Stay right where you are!' snapped Cartwright. 'I hear you move or do anything and I'll fire!'
'O-OK... we're not moving, are we, Sal?'
'Nope. Sitting still. Doing nothing.'
'Just hang on, Cartwright,' said Maddy, 'just a second... the generator should kick in any time now.'
On cue, from the back room, came the rumbling of the generator firing up. A moment later the strip light in the middle of the archway flickered once, twice with a dink, dink, then stayed on.
They all stared silently at each other as the monitors flickered in unison, the computer system rebooting itself.
'What just happened?' demanded Cartwright.
'I dunno yet...' said Maddy.
'That was a time wave,' said Sal.
'A what?'
'Time wave,' she repeated. 'Something big changed in the past and it's just now caught up with us.'
Maddy nodded unhappily. 'Yeah... she's right. That's exactly what that was.'
Cartwright looked at both the girls, then at Forby, who returned nothing more useful than a calm professional stare. 'Well?' said the old man. 'What does that mean?'
'It means outside this archway, outside the perimeter of our field-office time shield, things have changed,' explained Maddy. 'Changed a lot... if we lost power.'
'So, what's out there now?' he asked.
Maddy splayed her hands. 'I don't know! Another version of New York, I guess.'
Cartwright's eyes widened to rheumy bloodshot pools. 'Forby, go take a look.'
'Yes, sir.' He stepped across the archway and hit the green button. Nothing happened. 'Won't open.'
'The doorway's not on the generator circuit,' said Maddy. 'Just crank it up with the handle. There,' she said, pointing. Forby saw the small metal handle, nodded and started turning it round.
The computer had finished rebooting and Bob's dialogue box popped up.
> We are running on auxiliary power. Resume density probing?
Maddy turned in her chair, back towards the monitors. 'How much more probing have you got to do?'
> Information: 177,931 candidate density soundings made.
She made a face – less than half the total number that Bob had calculated they needed to make.
'Are there any good suspects?'
> There are 706 soundings so far in which a density fluctuation occurred.
'Can you narrow that down any?'
> Affirmative: I can analyse the interruption signatures returned and identify those that demonstrate a repeat or an artificial rhythm.
'Uh... lemme think.' She bit a ragged edge around her fingernail. 'But you're only, like, halfway through doing the probes?'
> Less than halfway.
'And if you stop now we might miss them,' she thought out loud.
> Affirmative.
'But now we're on generator power, have you got enough power to do all those probes, and open a window too if we find them?'
> I do not have enough data to answer that question, Maddy.
'Can you guess?'
> I do not have enough data to answer that question, Maddy.
She cursed. 'All right... so you're saying it's possible we'll run out of juice if you carry on doing the probes, right?'
> Affirmative.
The rattling of the cranking shutter door coming from across the archway suddenly ceased.
'OK, Bob,' she sighed, burying her face in her hands with weary frustration. 'OK... OK. All right, then. Stop with what you're doing and analyse what we've got already. See if we've got a hit.'
> Affirmative.
'What the –!' That was Forby.
'JESUS!' That was Cartwright.
Maddy spun round in her chair and saw the pair of them standing in the middle of the opened shutter doorway, staring out at a canvas of emerald-green jungle.
She sighed. Oh no, not again.
Last time a time wave had arrived like this one, large enough to sever the feed of power into their field office, it had left New York a post-apocalyptic wilderness of tumbledown ruins under a poisoned rust-red sky. She and Sal hurried over towards the open entrance.
'Jahulla!' gasped Sal as they joined the other two.
And Maddy nodded. Jahulla indeed.
This time New York was gone, not just shattered ruins, but gone as in never existed. She looked down at her feet. Their cold and pitted concrete floor simply ended in a straight line where their invisible force field's effect terminated. The ground beyond was a rich brown soil, carpeted in a mat of tall grass and lush clusters of low-growing ferns and other unidentifiable foliage.
She looked up and saw no Williamsburg Bridge, no horizon of Manhattan skyscrapers, just a broad, sedate river delta of lush rainforest.
'Uh... how... how did we end up in the middle of a jungle, sir?' asked Forby.
A slow, understanding smile spread across Cartwright's face. Finally he nodded. 'Incredible,' he whispered, his eyes wide like a child's, full of wonder. A solitary tear rolled down one of his craggy cheeks. 'This is quite... incredible.'
'Sir?' Forby turned to him. His calm, professional demeanour had vanished and been replaced with barely contained panic. 'Sir, where the hell are we?'
'We haven't moved anywhere,' the old man replied. He turned to look at Maddy. 'Or anywhen? Have we? We're exactly when and where we were.'
'That's right,' she replied. 'But an alternate history has just caught up with us.'
Cartwright's ragged features seemed to look ten years younger. The face of a child catching a glimpse of the tooth fairy, or a glint of Santa's sleigh disappearing into a distant moonlit cloud bank.
'Sir? The other men? Where are they?'
'Gone, Forby,' he replied in a distracted whisper. 'Gone.'
'They're dead?'
'Nope. They were just never born,' said Sal.
'I want to see more,' uttered Cartwright, stepping off the concrete on to the soft ground beyond. He grinned. 'My God! This is real? Isn't it?'
Maddy shrugged. 'It's another reality. How New York might have ended up if... if...'
'If what?' asked Forby.
'That's just it,' she replied. 'We don't know yet. My guess is it's some change caused by our colleague in the past. I'm sure it wasn't intentional.'
Forby shook his head. 'You're telling me one person can actually change a whole... world?'
Cartwright sighed, clearly frustrated by the narrow-minded thinking of his subordinate. 'Of course, Forby. Think about it, man. If... if a certain Jewish carpenter hadn't made his mark two thousand years ago, it wouldn't be In God We Trust on a dollar note, but Gods.'
Forby frowned. A patriot. No one dissed the mighty dollar. Not on his watch.
'And our friend's much much further back in time than Jesus,' added Sal.
'Small changes in the past,' quoted Maddy, remembering the first time Foster had spoken to them, bringing them that tray of coffees and doughnuts, a simple and strangely reassuring gesture in that surreal moment of awakening. 'Small changes in the past can make enormous changes in the present.'
Cartwright glanced towards the nearby riverbank. 'We should go and explore a little –' He stopped dead in his tracks.
'Look!'
Maddy followed his wavering finger, pointing across the broad river to the low hump of island that was once Manhattan. She squinted painfully, her eyes not so great without glasses. She managed to detect the slightest sense of movement. 'What is it?'
'People?' uttered Sal. 'Yes... it's people!'
'A settlement of some kind,' added Cartwright.
She thought she could make out a cluster of circular dwellings down by the waterside and several pale thin plumes of smoke rising up into the sky.
'Look,' said Forby, 'there's a boat.'
Halfway across the river, calm and subdued, barely a ripple upon its glass-smooth surface, was the long dark outline of some canoe. Aboard they could see half a dozen figures paddling the vessel across the river towards them.
'They look odd,' said Sal, shading her eyes from the sun. 'They're... they're moving all funny.'
Cartwright seemed eager to rush down to the riverside and greet them. 'We should go and make contact.'
'No,' said Maddy. 'Really, I don't think we should.'
'Why not?' he asked. 'The things we could learn from each other! The knowledge of another –'
'Maybe the girl's right,' said Forby. 'They could be hostile, sir.'
He shook his head, his face an expression of bemusement. 'This is an incredible moment of history!'
'But that's just it... this isn't history. This isn't meant to happen,' said Maddy. 'Those people shouldn't exist. This is a what if reality... this is a never shoulda happened reality, Cartwright. Do you get it? The last thing we need to do is go and make friends with it.'
'I'm not so sure they're people, anyway,' said Sal, quietly watching the canoe approach the nearby riverbank. A hundred and fifty yards away, the long canoe rode up gracefully on to the silt. The figures aboard the boat put down their paddles in the bottom and began, one by one, to jump off the front and on to the mud.
Even Maddy could now make out that they weren't human.
'My God, look at their legs,' whispered Forby. 'Like... just like goat's legs, dog's legs.'
'Dinosaur legs,' added Cartwright. 'In fact, therapod legs. A bit like velociraptors.'
'Forget their legs,' said Sal, 'check out their heads!'
Maddy squinted, wondering whether her eyes were playing tricks on her. 'They look like bananas?'
'Elongated,' said Forby, shaking his own head. 'Weirdest damned thing I ever seen. They look sort of extra-terrestrial.' He turned to the others, his voice lowered. 'My God! Do you think that's what they are? A species of alien that's arrived and colonized our world?'
Cartwright dismissed the man. 'The legs suggest some possible ancestral link to dinosaurs. The heads? Damned if I know where that shape has come from.'
They watched the creatures spread out along the silt, holding spears in their hands and probing the mud with them.
'What are they doing, do you think?' asked Maddy.
As if in answer to her question, some unrecognizable pig-sized creature emerged from a hole in the mud and scurried across the silt towards another hole. The nearest of the banana-heads quickly raised his spear and threw it with practised efficiency. It skewered the small creature, and left it struggling and squealing on its side.
'Hunting!' said Forby a little too loudly.
One of the creatures suddenly turned to glance their way. The four of them instinctively hunkered down behind the gently waving fronds of a large fern.
'Think he saw us?' hissed Forby through gritted teeth.
Maddy looked up at the ragged outline of red brickwork around the corrugated shutter door, the portion of the bridge support that existed within the archway's field. Luckily most of it was shielded by a giant species of tree she didn't recognize; drooping waxy leaves the size of umbrellas hung low over them. A perfect camouflage.
'I think we're hidden,' she whispered.
They watched through gaps in the swaying leaves as the creature, still curious, slowly paced up the silty bank towards them, cocking its long head curiously on to one side. Closer now, they could see a lean hairless body covered with an olive skin, an expressionless face of bone and cartilage and a lipless mouth full of razor-sharp teeth.
'It's really ugly,' offered Sal in a whisper. 'I really don't want to go make friends with it.'
Maddy noticed Forby raising his gun warily, a finger slipping across the trigger. She nudged him gently and shook her head.
Don't.
He nodded.
'It's beautiful,' whispered Cartwright. 'What a magnificent creature! Look at it!'
For a moment it lingered there, scanning the rainforest in front of it, not seeming to spot them or the squat brick shape of their archway. Then, finally, it seemed to shrug, turn away and head back towards the others, calling something out with a mewling whine and a clack of its sharp teeth.
'I've seen enough. We should go back inside,' said Maddy. 'There's work to be done.'
'Don't you want to learn more?' asked Cartwright.
She shrugged. 'Why? If we've managed to get lucky and locate Liam... then none of this will ever have happened.' She looked at Forby, who seemed relieved at the idea of heading back. 'Be pointless learning anything about these things really... if you think about it. They soon will belong to the world of Never Were.'
Cartwright made a face, a mixture of disappointment and frustration. 'All right,' he conceded. 'Let's get on with it.'
# CHAPTER 65
# 65 million years BC, jungle
'Did you hear that?' said Laura, her eyes round with fear.
They'd heard it all right. Although the jungle was soon due to stir with its concert of nocturnal cries and calls, the sun had only just slipped from the sky, leaving behind thin combed cirrus clouds stained a coral pink from its waning light. The jungle was on the turn, the stillness between those that lived in the day and those that prowled the night.
But there it was again. A desperate female cry for help. It was one of the four they'd left behind, either Keisha Jackson or Sophia Yip.
'... Please... help me...'
'It's Keisha!' said Jasmine. She turned to the others. 'It is! It's Keisha!'
'Which direction did it come from?' asked Liam. It wasn't far off, somewhere within the apron of jungle around their clearing. Could be coming from any direction, the mischievous way voices seemed to bounce around.
'... Help... it hurts...'
'We have to go help her!' said Edward.
'Negative,' said Becks. 'The hominids could still be on the island.'
Laura's eyes darted back to the finger on the ground. The light was getting dim enough for it to be almost, mercifully, easy to overlook. 'Could be?' she exclaimed. 'They're h-here, all right.'
'Or they've been and gone,' added Whitmore. He looked at Liam. 'We've got to go help the poor girl! She could be dying!'
'... Please...'
Whitmore nodded across the clearing. 'It came from over there.' He grabbed a spear and turned to the others. 'I'll need help lifting her.'
Edward grabbed a spear and joined him. Howard and Juan did likewise.
'OK,' said Liam, 'go get her.' He turned to Laura, Akira and Jasmine. 'We need this fire going again. Can you see to that? Big fire, all right? Big as you can make it.' They both nodded. 'And, Becks, we need that windmill contraption running.'
She nodded. 'Affirmative.'
'And, all of you,' he called out, particularly to Whitmore and the others already jogging in the direction they hoped to find Keisha, 'all of you, stay close together! No one goes on their own!'
He watched them go, four of them all armed with spears. In the jungle on their way back from laying down their clay tablets, they'd been infinitely more vulnerable to ambush, and yet the creatures had warily held back... only jumping Kelly, he presumed, because he'd been entirely on his own.
He looked anxiously around the clearing. The girls were just a dozen yards away working on the fire, and Becks merely thirty yards from him, busy trying to re-jig the windmill. Liam tried to think quickly. He wasn't exactly alone here in the middle of the clearing, but he'd have felt happier having another one or two people standing right beside him. His eyes darted to the dark entrances of a couple of the nearby lean-tos, the small gateway to their palisade, possible hiding places. Possibly containing one or two of them.
Liam. Stay calm, Liam. Stay calm.
Broken Claw watched the new creatures approach. Four of them armed with their killing sticks.
He turned to the others, crouched nearby, and softly hissed for them to make ready. He turned towards the younger one, crouched next to him. The youngest ones of the pack were best at this particular skill – mimicking the calls of wounded prey – their voice-boxes being smaller, allowing them a much higher pitch, the shrill pitch of fear and desperation.
He clacked his claws gently, instructing the young one to do it once again.
The young female's jaw opened, and her tongue and voice skilfully reproduced the cries the female new creature had been making earlier today as she lay dying from a fatal stomach wound.
'... Help me... please...'
They changed direction, veering directly towards Broken Claw and the others, just a few dozen yards away now, stepping out of the clearing and into the darkness of the jungle. The new creatures seemed to have absolutely no sense of how close to danger they were, their small seemingly ineffective noses unable to detect the smells that filled Broken Claw's nasal cavity: the smell of excitement from his pack, the smell of anticipation of a fine kill, the smell of their dark-skinned female brethren lying dead amid the ferns nearby – bled out hours ago.
How could they not smell any of this?
These creatures were either foolish or incapable of sensing all the warning signals in the air around them, stumbling blindly. Certainly – he understood this now – nothing for his pack to be wary of any more. He'd learned enough about them: that they were as vulnerable as the larger plant-eaters they usually hunted, more vulnerable, in fact, since they had neither their weight or strength to throw around.
And now... Broken Claw and several of the stronger males in his pack now possessed sticks-that-kill.
The four long digits on each of his hands tightened round the thick bamboo shaft. Broken Claw was determined to use his stick-that-kills on one of them as he had that older male earlier this morning up in the hills. A fascinating way of delivering death. An intriguing tool of death.
Juan stopped and pointed at a splotch of drying blood on the back of a broad waxy leaf.
'Keisha!' he called out. 'You here?'
The four of them stood perfectly still, listening to the gentle hiss of shifting leaves above them and the fading echo of Juan's voice.
'Keisha!' he called out again.
Then, very softly, not a crying-out voice trying to be heard across acres of jungle, but a soft whimpering close-by murmur. '... Please... help me...'
'Where are you?' asked Whitmore. 'We can't see you!'
'... Help me...'
'Where are you, Keisha? Can you see us?'
'... Please... please...'
Juan cocked his head. 'That don't sound like her, man.'
Edward nodded. 'She sounds kind of funny.'
'... Sophia... run...'
Whitmore's eyes narrowed. 'Keisha?'
'... They killed Jonah...'
Juan looked silently at the others. His face spoke for him. That really isn't her.
Whitmore nodded and then slowly placed a finger to his lips. He waved his hands at them to back up the way they'd come. Fifteen... twenty yards of jungle, that's all, then they'd be out in the clearing again.
They'd just begun to carefully retrace their steps when Juan suddenly convulsed, burping a trickle of blood down the front of his varsity sweatshirt. He looked slowly down at the six inches of sharpened bamboo tip that protruded from his belly.
'Oh... oh, man...' was about all he could say before his eyes rolled and his legs buckled beneath him.
Crouching behind Juan's collapsed form was one of the bipedal creatures, its long head cocked with curiosity and its yellow eyes marvelling at the spear in its hands.
'RUN!' screamed Whitmore to the other two. 'IT'S A TRAP!'
Howard and Edward turned on their heels to head back towards the clearing, only to face another pair of those creatures, springing seemingly out of nowhere. Howard lunged quickly with his spear, catching one of them in the thigh. The creature recoiled with a scream.
'GO!' screamed Howard, pushing Edward away from the creatures. Meanwhile, Whitmore found himself trapped by a closing circle of four of them.
'You r-really... are... c-clever... aren't you?' he found himself babbling through trembling lips. A couple of them were holding spears just like he was holding his. 'My G-God... you've learned f-fast... haven't you?'
The creature that had speared Juan stepped over his body and approached Whitmore with an unsettling raptor-like bobbing movement. The creature barked an order to some more of its kind hiding in the undergrowth and Whitmore heard the thud of feet and the swish of branches flicked aside as several set off in pursuit of the other two boys.
Now it cocked its head, its yellow eyes drinking him in, eyes that burned with intelligence and curiosity and a thousand questions it probably wanted to ask, but hadn't yet developed a sophisticated enough language to know how to ask.
'I... I know... you can c-communicate...' Whitmore babbled, his man's voice broken and mewling now like a child's. 'S-s-so... can w-we. W-we're the s-same. Y-you,' he said slowly, pointing a shaking finger towards the creature. 'M-me... me,' he said, gesturing to himself. 'We're the s-same!'
Its long head protruded forward on the end of a fragile, almost feminine, neck.
'Th-the same... the same,' whimpered Whitmore. 'Intelli-intelligent.'
Whitmore was only vaguely aware of his bladder letting loose, a warm trickle running down his left leg and soaking his sock. A small detail. A faraway detail. Right in front of his own face, only inches away, his world was this bony carapace of another face and yellow piercing reptile eyes that seemed to grow ever larger.
Its jaw snapped open, revealing rows of needle-sharp teeth and a twisting, leathery black tongue that furled and unfurled like an angry snake in a cage.
Whitmore let go of his spear and it clattered to the ground between them. 'Do... d-do you s-see? No n-no harm. I m-mean y-you no h-harm!'
The tongue twisted and coiled and Whitmore heard an odd facsimile of his own voice coming right back at him. '... No h-harm... the s-same...'
He nodded. 'Y-yes! Y-y-es! W-we-we're intelli–'
Whitmore felt a punch to his chest. It winded him – like a medicine ball launched at his thorax. He gasped, spattering a fine spray of blood on to the creature's expressionless face. He would have doubled over from the blow, but claws from behind were holding him up on his feet. The yellow eyes inches in front of him looked down at something. All of a sudden, feeling oddly dizzy and lightheaded, he decided the polite thing was to do the same.
And there it was in the palm of the creature's hand, his own heart still dutifully beating away.
# CHAPTER 66
# 65 million years BC, jungle
Howard and Edward stumbled through the jungle, skirting the clearing but unable to get to it because one of the creatures was deliberately blocking them.
'Clever,' wheezed Howard. Keeping them bottled up here amid tree trunks and dangling loops of vine, it prevented them making big sweeping strikes with their spear and hatchet; the blade or shaft was bound to get tangled or caught on something.
One beast was behind them and another to their left, preventing them from making their way to the encircling river... not that they'd be able to go anywhere. The pursuer behind them could easily have caught up, but he remained a steadfast dozen yards behind. He realized then that they were just wearing them out, pursuing the pair of them through the tangled undergrowth until they were certain they were spent and unable to offer much of a fight.
Howard stopped. Edward, who'd been supporting his weight on the right leg, gasped. 'Uh? We got to run!'
Howard shook his head, finding his breath. 'No... they're playing with us. Herding us.'
All three of the hominids pursuing them came to a halt a dozen yards away on each side and waited patiently for their next move, yellow eyes peering at them through thin veils of dangling, looping vines.
Howard nodded to the clearing, the edge of it fifty yards to their right. The creature blocking that way had ducked down out of sight. 'That's the way we should be heading.'
Edward swallowed nervously. 'But... one of th-those –'
'I know.' He sucked in breath again. 'He's in there somewhere... but you have to make a break for it, run for the palisade.'
'What about you?'
He shook his head. 'I won't make it... I can't run... I'll buy you time.'
'You... y-you'll die!'
Howard nodded, smiled even. 'Sure, I figured that.'
Edward grabbed his arm. 'We c-can both run!'
'Don't argue. There isn't time for this. Listen.' He grabbed the boy's shoulder. 'Run, save your life. Make it back home. But promise me something.' He glanced over Edward's shoulder; one of the creatures was shifting position, impatient for a kill and stepping closer. 'Promise me to dedicate your talent to something else... not time travel, Edward... anything but time travel!'
Edward's eyes were on the other two creatures.
'Promise me!'
He nodded. 'Yes! Y-yes... OK!'
'No time travel, Edward. It'll kill us all; it'll destroy the world... God help us, perhaps even the universe. Do you understand?' he said, shaking the boy's shoulder.
The creatures inched warily closer, long athletic legs gracefully stepping over the uneven jungle floor towards them, their lean bodies bobbing with coiled energy.
'Please...' he hissed. 'Please tell me you understand.'
Edward's eyes met his. He was crying. 'Yes... I p-promise. I promise!'
Howard ruffled his hair. 'Good.' He took the hatchet in one hand and grasped the spear in the other.
'Now, when I say,' he said softly, 'you run, Ed. You run for all it's worth. You understand?'
The boy nodded.
Howard could see the creature between them and the clearing now. Its head bobbed up and ducked behind a large fern, no longer trying to hide, but clearly still very wary of them.
Good. Then he'd take advantage of that.
'Ready?' he whispered.
Edward nodded silently. His cheeks shone with tears; his lips clamped shut, trembling.
Without any warning Howard roared 'Waaarrghhhh!' and charged forward towards the creature cowering behind the fern. The creature leaped back, an almost comical bunny hop of surprise as Howard crashed through the undergrowth towards it. He stumbled through a cluster of ferns, swinging his hatchet at the creature as it recoiled, still off balance. The jagged blade caught something and the creature screamed.
Howard spun round and reached for Edward. 'GO!' he shouted, grabbing the scruff of his collar and pulling him forward. 'GO, GO, GO!' He pushed the boy forward with a rough punch to the small of his back.
Edward scrambled past the writhing creature, across a dozen yards of stunted plants and thinning saplings, ducking loops of thorny vines that promised to snarl his throat like barbed wire.
The boy was fast and agile and small enough to make a better job of dodging the jungle obstacles. Howard turned his attention to the creature beside him, snapping and clacking teeth as it got to its feet and warily circled him, leaking dark blood from the gash on its leg.
I'm ready for this, he told himself. I'm ready for this. I'm ready. I'm ready. I'm ready to die.
His mantra back in the lab, back when he was approaching Edward Chan and fingering the gun in his bag. He'd been ready to die then for a cause only a few seemed to truly understand. He was just as ready to die now.
Just as long as the boy keeps his promise.
There was no knowing, but instinct, hope... told Howard that Edward had seen enough of the nightmare of time travel for himself to know that his unique talent could never be allowed to find its voice.
And that's all that matters. Right?
Howard stared down the creature in front of him. 'Mission completed,' he uttered to himself with a growing smile spread across his boyish face.
'Come on, then, ugly,' he said, advancing on the thing just as the leaves behind him shuffled and swayed with the arrival of the other two, ready to finish him off.
# CHAPTER 67
# 2001, New York
They returned to the archway and Forby wound the shutter down again.
'So,' said the man as he shouldered his assault rifle and cranked the handle. 'What I don't get is if this is still a version of the year 2001 how come those dino-humans out there aren't a lot more advanced?'
Maddy and Sal looked at each other. 'I dunno,' said Maddy. 'I'm no anthropologist.'
'It's a good question, Forby,' said Cartwright. He turned round and crouched to get one last look out at the rainforest version of the Hudson River delta, and the far-off cluster of rounded huts on the muddy banks of Manhattan island. 'A good question... and I'll hazard a guess. They're a dead-end branch of evolution.'
Forby looked at him. 'Sir?'
'Those things out there –' he flicked a finger out at the narrowing window of alternative world outside – 'if they really are the direct descendants of some species that survived the end of the Cretaceous era, a species that somehow survived as a result of something that's been changed –' he looked at the girls – 'by your friend, then they've been around for tens of millions of years.'
'Well, that's exactly my point, sir. How come they aren't light-years more advanced than humans? How come there isn't some gigantic lizard version of Futurama out there?' Forby finished cranking the shutter down. The archway was dim once more, lit by the sterile fizzing glow of the ceiling tube light.
'They plateaued,' said Cartwright. 'Perhaps their species evolved to the best it could possibly be. And then just stopped.'
Sal made a face. 'I thought evolution never stopped. I thought it always changed, always, like, adapting.'
'Oh, but it does and can stop,' he replied. 'There are species alive today that are virtually identical to their distant prehistoric ancestors – sharks, for example. Nature had evolved them to be perfect for their environment, perfect killing machines... why bother adapting any further?' He shrugged. 'Perhaps in this world, those reptilian hominids out there are the dominant predator, with nothing to compete against... and have been that way for millions of years?
'Evolution is nature's way of problem solving. If something changes that challenges a species' ability to survive, then that stimulates an adaptive response. If there's nothing to challenge a species' existence, then why would it ever need to change?' Cartwright shrugged. 'A dead-end of evolution.'
'A dead-end world,' echoed Forby.
They made their way across the dim archway. 'On the other hand, maybe there's some practical limit to how much smarter that species outside can get? Maybe those long heads are already too heavy to develop any greater cranial capacity?'
'So their brains will never get any bigger?'
'That's right. And they'll never do any better than spears, mud huts and dugout canoes.'
'Well,' said Maddy, approaching the desk, 'whatever. We'll never know, because those creepy-looking things weren't meant to happen.' She sat down at the computer desk. 'Bob, how're you doing with those candidate signals?'
> Analysis completed. The last 1,507 density soundings before you ordered me to cease the sweep indicated the immediate location was occupied by a permanent physical obstruction. This could be a natural intrusion, for example a fallen tree or a geological event.
'So, before that?' Maddy asked impatiently.
The others joined her at the desk.
> A total of 227 transient density warnings.
Cartwright squatted down beside her and studied the dialogue box. 'That means what? So now you're down to two hundred and twenty-seven possible locations for your friend?'
Maddy nodded. 'Can we filter that any further?'
> Affirmative. 219 were single-incursion events. Of the remaining eight density signatures that demonstrated a repeated incursion, only one demonstrated a regularly timed signature.
Sal bit her lip with excitement. 'That's it! Surely? That's got to be it!'
> Affirmative, Sal. There is a high probability that this is the correct time-stamp.
'YES!' said Maddy, spinning round in her chair, her hand raised for a high-five. Sal obliged with a hearty slap and a shriek of excitement.
Cartwright smiled. 'I presume that means you've found your friend?'
'Yes... see?' Maddy grinned proudly. 'I told you we could do it!'
'So then... what happens now?'
She spun back to face the monitors in front of her. 'Bob? We're good to begin charging up to open a portal?'
> Information: we have a 24-hour time period identified in which to open a window.
'Hmm.' Maddy pulled absently on her top lip. 'Twenty-four hours. But when exactly do we open it?'
Cartwright looked vexed and impatient.
'We have to be sure they're there, right?' said Sal on Maddy's behalf. 'You know? Before we commit to opening a portal. If we spend the stored charge and they're not there, we've gone and wasted it.'
Maddy nodded. 'We'll only have enough stored energy to open one, maybe two windows. How do we make sure they're actually right there and ready and waiting to come through, though?'
'Hang on!' cut in Cartwright. 'You just said "they". Are you telling me there's more than just your friend stuck back there?'
Sal nodded. 'Yes, Liam... and some others... children that were caught up in an accident.'
'Good God,' the old man whispered. 'Accident? This was an accident? What the heck have you people been up to?'
'It was a training incident,' cut in Sal, 'that's all. It went wrong. These things happen from time to time.'
> Information: it will be possible to open a series of pinhole windows and obtain a small-resolution image of the target location.
'Right.' Maddy nodded. 'Right... then we could see exactly when – during the day – there's somebody standing around. Yes... yes, good idea, Bob. Let's proceed with that.'
> Affirmative.
Cartwright sighed. 'So what's happening now?' Clearly impatient to see the displacement machine actually finally running.
Maddy turned to look over her shoulder. 'We're taking some images of the portal location to make sure that when we open the window they're ready and waiting to come through.'
'Why don't you just open your portal and see for yourself?'
'Sal just explained that. We could be wasting a full power-up, and we can't risk doing that.' Maddy shrugged. 'Anyway, wouldn't you want to check first? This is the Cretaceous era, right? That means dinosaurs. I'd want to know the coast is clear of T-rexes first. Don't you?'
The old man glanced at Forby and the man shook his head quickly. 'Taking a few photos first sounds like a pretty good move to me, sir.'
Cartwright laughed nervously. 'Uh, I guess you're right. OK... we'll do it your way. Just get a move on before those hunters down the beach find a railway arch in the middle of their jungle.'
# CHAPTER 68
# 65 million years BC, jungle
The three girls had revived the smouldering fire; the dried brittle moss that seemed to carpet every boulder and rock made perfect kindling and already a thick column of smoke was drifting up into the evening sky.
Liam felt a little happier now. Fire had seemed to keep those creatures at bay during the last few nights that they'd been out on their errand. They seemed to have a healthy respect for it – actually, to be more precise, a morbid fear of it.
He looked up across the twilit clearing. It had got dark very quickly. He wondered how the others were doing with Keisha. Surely they must have found her by now? If those pack hunters really had felled that tree and made their way across, then he was surprised they'd allowed her to live.
He was considering that point when he heard two sounds at the same time: one a far-off scream, shrill and terrifying that rattled around the clearing like a gunshot, and the other the sound of approaching trainers slapping the hard ground. He exchanged a hurried glance with the girls, and with Becks as she stopped fiddling with their damaged windmill and snapped erect like a spooked meerkat.
'Help!' He heard Edward's voice through the gathering gloom, and then a moment later picked out of that gloom the dancing outline of his pale T-shirt.
'Edward! What's up?'
The boy joined him, gasping and looking anxiously back over his shoulder. 'They're h-here! THEY'RE HERE!'
Liam followed his gaze and saw nothing across the clearing, just the dark outline of the apron of jungle. 'Where are the others?'
The boy ignored his question, his eyes wide with terror. 'Th-they're h-here, they're h-here!'
Liam grasped his arm firmly. 'EDWARD! What about the others?'
The boy looked at him. 'Dead,' he replied. 'All dead.'
'Oh God, look!' gasped Laura.
She was pointing across the clearing. Where a mere second ago he'd seen only jungle, now he saw a line of the creatures approaching them cautiously, spreading out like beaters for a hunting party. He quickly estimated thirty, maybe forty, of them; all sizes.
The whole pack... Jay-zus!
In the middle of the line, he thought he recognized one of them in particular. The one he'd seen in the jungle, barking orders to the others, their leader.
'Liam,' said Becks, stepping back from the windmill to join him and the others near the smoking fire, now beginning to take hold and crackle and spark. 'Do you see the middle one?'
He knew what she was referring to. The one in the middle, the pack leader, was holding one of their spears in its claws. He nodded.
'Like my adaptive AI,' she continued, 'the species has observed our behaviour and learned from it.'
He swallowed nervously. 'Back to the palisade... we need to go now!'
'Negative, I must stay.'
'What?' He looked at her.
'This location has been probed in the last twenty-four hours.' She nodded towards their broken windmill. 'There are decaying particles in the vicinity of the interference device. They may scan again at any moment.'
She was right, of course. Utterly barking mad, but quite right.
'All right, all right,' he uttered, watching the approaching hominids closing the gap slowly. 'You four,' he said to the others, 'get inside the wall and wait there!'
'What are you going to do?' asked Edward.
He really had no idea just then... some notion of holding out beside the campfire, back to back with Becks until... until... what?
Until they've finally worn her down, and jump her. Then turn on me.
But, there was a slight chance, wasn't there? A slight chance Maddy and Sal were going to sweep this place again at any moment. And, if they did, this might be their last chance to flag the signal, to tell them they were right here. The alternative, hiding inside their flimsy palisade until these creatures finally managed to gnaw their way through the twine, pull aside a couple of the logs from the wall and get in... He shuddered.
'There's a return window coming,' he said. 'It's coming soon! Becks and me need to be out here waiting for it. You four will be safer inside. I'll call for you when it opens. Now just go!'
'I want to stay,' said Edward, picking up one of their hatchets from a pile of cut wood beside the fire. The other three nodded. 'We'll f-fight them t-together,' whispered Laura, her teeth chattering noisily.
Jasmine looked across at the palisade, twenty yards away beyond the flickering pool of light from the fire. 'They'll find a way in anyway.'
Liam looked at the creatures, now almost entirely encircling them, maintaining their cautious distance. 'All right. Perhaps you're right,' he uttered. 'Becks, how're we gonna do this?'
'Recommendation: I need to be in the vicinity of the interference device in order to detect any precursor particles arriving.'
Liam nodded. 'Yes... yes. R-right. We should hold the ground over there.' He reached down towards the fire and pulled out a branch. The end of it flickered with flames. 'Everyone grab a torch. They don't like fire!'
The others followed suit. Then moved together in a tight huddle, away from the reassuring glow of the campfire towards their contraption, a dozen yards beyond the growing pall of amber firelight.
The creatures followed them, silently padding across the soft ground, watching them, and ever so subtly closing the distance around them.
'YOU BACK OFF!' screamed Laura at them, waving her flaming stick.
The creatures hissed, warbled and mewed at that, one of the smaller ones attempting a copy of her shaking voice.
'... Yoo.... bak... offfff...'
Becks turned to Liam. 'This location has just been scanned again. There are several hundred new particles.'
Liam felt a surge of hope. 'Oh, c'mon! Why don't they just get on with it and open a bleedin' window?'
Becks cocked her head. She had no answer.
All of a sudden, the creature holding the spear barked in a croaky voice and, as one, the creatures surged forward towards them.
'Oh my God! Oh my God! screamed Laura.
'Recommendation: use your spears to –'
# CHAPTER 69
# 2001, New York
The best part of an hour passed in silence with Maddy, Sal and Cartwright gathered around the monitors watching a progress bar slowly inch across one of the screens, and an empty directory slowly fill with low-resolution JPG files.
Forby meanwhile stood beside the doorway, cranked up a couple of feet, gazing at the jungle world outside. 'They're still hunting those beach pigs or whatever those things are,' he called out softly.
'Good,' replied Cartwright absently. 'How much longer?'
Maddy shrugged. 'You can see the progress bar yourself, can't you? It's nearly there.'
The old man made a face. 'If it's anything like the Windows I got at home, nearly there can mean another five minutes or another five hours.'
'This is an operating system from sometime in the 2050s,' said Maddy. 'It sure ain't gonna be Windows.'
The progress bar suddenly lurched forward to a hundred per cent and Bob's dialogue box appeared.
> Process complete.
'Bob, can you do some sort of slideshow?'
> Affirmative. Images are taken one every five minutes.
A monitor to the left of them flickered to life, revealing a small pixelated image of green and blue.
Maddy squinted at the image. 'What is that?'
'Jungle,' said Sal. 'That's what it is. Jungle and some sky.'
Forby joined them around the desk. 'Yeah... that's a jungle, I think.'
A second image appeared, almost identical to the first, a couple of pixel blocks had changed tone slightly. 'Is this as clear as the images get?' asked Cartwright.
> Affirmative. The pinhole and image data size has been kept to a minimum to conserve on energy consumption.
'All we need is to see enough pixels change to indicate something moving around the area, right?' said Sal.
> Correct, Sal.
'Can you play through these slides a little faster, please, Bob?'
> Affirmative, Maddy. Increasing display rate times ten.
The next slide came up, just the same as the last, and another, an undecipherable flicker show of green and blue pixels. They watched in silence until approximately midway through the complexion of the image suddenly changed with a mass of dark pixels.
'Whoa! Stop!' said Maddy. She studied the shape on-screen. 'What's that?'
'That looks like a person,' said Forby. 'See? That's a shoulder and an arm.'
Sal cocked her head and frowned. 'It doesn't look right.'
'What time in their day is this image, Bob?'
> 14:35.
'Half past two in the afternoon,' said Sal.
'Give us the next image, Bob.'
Another dark image appeared on-screen, the blue pixels of sky and green of jungle almost entirely gone.
'Somebody standing right in the middle of the portal location... for about five minutes,' mumbled Maddy to herself. She looked at Sal. 'That's got to be the support unit? She's sensed a tachyon particle and she's hanging around for another?'
Sal shook her head. 'Maybe... but the shape of the body looks all kind of funny to me.'
'Oh, come on, it's a one hundred by one hundred pixel image – everything's going to look all funny.'
She shook her head again. 'I'm not sure. It could be anything... it could be some animal.'
'Bob, next image.'
Another image flickered up and this time the dark mass of pixels was gone, leaving the image the same even mix of blue and green squares.
Maddy grabbed a pen from the desk and scribbled the time of 14:35 on a scrap of paper. 'Well, OK, we know someone was hanging around then. We've got one possible window. Let's get on with the slideshow and see what else we get.'
Once more the images began to flicker on-screen one after another, a second apart, the blue pixels of the sky slowly changing hue from bright blue to a rose colour.
'It's evening,' said Cartwright helpfully.
The sequence continued, with the sky pixels slowly reddening in colour, and the jungle's light green becoming a deeper darker green, until all of a sudden, in the middle of the image, they saw a single dot of bright orange.
'Stop!'
All four of them craned forward to get a better look.
'That's fire, isn't it?' said Forby. 'A flame?'
Sal nodded. 'Yeah.'
'Someone starting a campfire maybe?'
'Fire... right,' uttered Cartwright, 'and the only thing that can make a fire back then is going to be human.'
Maddy tapped her chin thoughtfully. 'Yup... so maybe this is a more reliable candidate than the other. What time is this image, Bob?'
> 18:15.
'Give me the next image.'
The orange pixel became a dozen pixels, and half the screen was filled by a vertical block of black pixels. In the top left corner, they could just make out the sky, the pink evening becoming a deep purple with the onset of dusk.
'Someone's standing right there again!'
'And that thing doesn't look as weird as the earlier one,' said Sal.
Maddy looked at her. 'How can you tell?'
'Screw up your eyes a bit, Maddy... it sort of blurs the pixels slightly. You can make out shapes more easily.'
'A campfire and someone standing right there,' said Cartwright. 'Looks like the best time so far.'
'Yes,' she replied absently. 'What do you think, Bob?'
> This image looks most probable.
'Quickly run through the rest.'
The slideshow flickered through the last sixty-eight images, one image per second. A juddering animation of time... the fire slowly dwindling, dying and vanishing, the sky darkening until the final few dozen images were simply a sequence of black pixels.
> Sequence complete.
'Looks like we have a winner,' said Cartwright. 'Can we now proceed?' He looked up at Forby. 'You know? Before those hunters come knocking on our door?'
'OK... let's begin powering up, Bob.'
> Affirmative.
Cartwright stood up straight, his arms caressing a stiff back. 'So... what happens next?' He glanced at the large perspex tube. 'They're going to appear inside that?'
She shook her head and pointed to a circle of chalk scrawled across the concrete floor. 'There. You and Forby need to stand well clear of that.'
Cartwright's man stepped away from the table and faced the circle, unslinging his assualt rifle in readiness.
Maddy turned to regard both men. 'I'd be happier if Mr Forby could take his finger off the trigger.'
Cartwright smiled. 'Of course.' He nodded at his man. 'You can stand down, Forby. But... just stay alert, all right?'
Forby nodded, slackening his grip and lowering the barrel of his gun.
# CHAPTER 70
# 65 million years BC, jungle
Liam lashed out with his hatchet, swinging the serrated metal blade in one hand and probing and prodding with his bamboo spear in the other. But the creatures dodged back with graceful agility, keeping their eyes on the weapons.
The fire nearby had taken a firm hold of the branches that had been thrown on top of it. Occasional tongues of flame lashed up into the almost dark sky, and upward cascades of sparks danced like fireflies. The flickering light, the warmth from the campfire and the dancing flames on the ends of their torches were causing the hominids' probing attack to falter.
'GO AWAY!' screamed Laura, prodding the flaming end of her branch towards the nearest of them.
Becks, meanwhile, had managed to kill one of them and severely wound another. She could move forward with the same sudden speed as these things, catching them off balance. The wounded creature, now thrashing around on the ground, had lost a limb to one vicious roundhouse sweep of her hatchet. The creature she'd managed to grasp hold of moments ago had had its fragile spine snapped over her knee.
For her efforts she'd received a deep gash down one thigh. Her left leg was red with her own blood, soaking the sock rolled over the edge of her combat boot almost black. The wound was already clotting, but Liam couldn't help notice how much blood she'd lost in that one sudden crimson gush and worried whether her engineered body was capable of replacing that blood with the same efficiency as it could staunch a wound.
The creatures probed and circled, clacking teeth and claws and mewling like foxes, occasionally testing them with a lunge and snap of jaws... so far the six of them were doing better than Liam could have hoped holding them back. But then he realized there was patient thinking going on behind what these creatures were up to.
Wearing us down. That's all they're doing. Wearing us down.
His eyes picked through the lean olive-coloured hides, the flickering chitinous teeth, until he found the pack leader, holding that spear and looking strangely human because of that.
If we got him...
Yes, if Becks could somehow be fast enough to reach out past the others and grab him, and snap his neck in her hands, then the others would surely panic and run. He had a spear in his hand; he realized he could at least have a go. The pack leader was only fourteen or fifteen feet away and, unlike the others, circling in that strange bobbing way, he stood perfectly still, watching them with keen studious eyes.
Liam dropped his hatchet at his feet.
'What are you doing?' yelled Jasmine.
'Gonna get that one there,' he said, nodding towards Broken Claw.
He steadied his balance on his back leg, lined up the creature staring at him with cocked-head curiosity down the length of the bamboo shaft and then hurled it like a javelin. A straight point-to-point throw instead of an arced trajectory. He surprised even himself with his accuracy and would probably have caught the thing square in its narrow chest, had not another smaller one bobbed in the way unintentionally. The sharp tip of the bamboo punched into its long bony skull and the creature crumpled to the ground with a short brittle scream that sounded almost like the wail of a human child.
Liam winced and cursed that he'd not got the leader. And now they were down to one spear.
Out of the black one of the smaller hominids suddenly ducked down low and swiped with a claw, knocking Akira off balance. Her leg buckled and, with a thin yelp, she dropped heavily into the dirt. Winded and worn out, she struggled to get up. Yet more spindle-thin arms emerged from the gloom and clawed digits wrapped tightly round her ankles and wrists.
'No!' she screamed, her pale face just two wide eyes and her mouth an 'O' of horror. Within a second, two beats of a pounding heart, they'd dragged her struggling form out of the pall of flickering light, her screaming voice smothered, muffled and then brutally silenced.
Becks took advantage of a careless incursion and lunged forward again, sweeping her blade and missing as the creatures leaped once more back out of her range.
'We... can't keep this... up,' said Laura. 'Not all... not all n-night.'
'I know,' replied Liam.
Just then something whistled past his cheek. 'Whuh?'
He looked down and saw the shaft of a bamboo spear rattling and flexing on the ground. He looked up at the empty-handed pack leader and understood.
'Oh no!' he gasped. 'You see that? It... threw... It threw it back.'
Good going, Liam. You just taught them how to toss a javelin.
'Ah Jay-zus... if they start throwin' missiles at us, we'll be in trouble.'
'L-like we're not already?' muttered Laura, lashing out at one of the smaller creatures bobbing too close.
Liam watched the leader, moving around the rear of his pack, those yellow eyes no longer on him but flitting across the ground, looking for something.
Looking for another spear to throw?
'Information.' Becks's voice suddenly cut across the clacking and mewling. 'I am detecting a burst of precursor particles.'
'Is... is that good?' asked Jasmine.
Liam nodded. 'Yes! Oh Jay-zus, yes!' He turned to Becks. 'That's a window, right? Tell me it's a window and not another probe?'
'Affirmative. The configuration suggests an imminent window.'
'YES! Oh yes!' He grinned breathlessly.
'We must move out of this space,' said Becks. 'They will not open the window until it is completely clear.'
'Right. Together,' said Liam. 'Keep together, back to back... move towards the fire!'
The five of them backed up towards each other, until they were almost bumping together. Then Becks stepped a little ahead, swiping and spinning a hatchet in each hand with ballet-like precision at the creatures. They wisely backed away from her, creating a path for them to shuffle along in her wake.
'Enough!' barked Becks after they'd moved half a dozen yards across the clearing towards the increasing heat and flickering light of the campfire. She turned round to face them. 'The extraction area is now unobstruct–'
It was then a sharpened tip of bamboo erupted through her abdomen, ripping through her flesh and the tattered material of her black crop top. Becks glanced casually down at the bloody tip.
'Becks!' gasped Liam.
With a blur of movement, she reached round and grabbed the creature that had skewered her from behind. She flipped it over her shoulder on to the ground in front of her. Its claws viciously flailed at her, shredding the skin on her forearm into tatty red ribbons. With a savage jerk she twisted its long head. The creature's yellow eyes and leathery black tongue bulged under the sudden tension in its slender neck. They heard a crackling sound and then the thing stopped squirming.
'Becks! You OK?' cried Liam.
'Negative. The damage is significant,' she replied, looking down at the point of the spear, still protruding from her waist. One of her legs wobbled beneath her and she dropped to her knees.
'BECKS! Hang in there!' yelled Liam.
Then they all felt it, the solid push of displaced air. Liam looked behind him and saw a shimmering sphere: the faint, dancing pattern of a reassuringly familiar place – the archway. 'LOOK! That's it! THAT'S THE WINDOW!'
Right now, in this instant, there were no creatures between them and their way home. 'GO!' Liam yelled.
For a moment the two remaining girls and Edward stared at him, unsure what he meant by that.
'NOW!' he screamed, his voice breaking. 'THERE!... RUN FOR IT! GO, GO, GO!'
Laura nodded, more than happy to obey. She turned on her heels and sprinted for the window. Jasmine followed suit. Edward lingered. 'What about –?'
'NOW!' screamed Liam.
Edward turned and sprinted after the girls. Liam turned to Becks. 'Come on!'
She struggled to her feet unsteadily. 'Information: I have lost significant levels of blood –'
'Just shuddup!' he snapped, sliding his hands under her armpits and hefting her up. She staggered to her feet. 'Leave, Liam!' she ordered him. 'Protect Edward Chan!'
Liam shot a glance over his shoulder. He could see Laura hovering just outside the spherical boundary of the window, hesitating to step in. Between her and them, Edward and Jasmine sprinting.
'GODDAMMIT GO THROUGH!' he shouted. 'GO THR–... AGHHhhhh!'
He suddenly felt a searing pain through his leg and saw that one of the smaller creatures had grasped his shin; the razor-sharp edge of its claws sliced through his shorts, through his skin and now grated against his shin bone.
Becks swiped with the hatchet still in her left hand, and cut through the creature's thin wrist. Its claws and its hand were still attached to Liam's lower leg like the jaws of some tenacious decapitated soldier ant. Despite the grating agony in his leg, he dragged Becks with him, she barely able to drunkenly stagger, and yet still swinging her blade in powerfully vicious yet groggy ill-aimed arcs that thwacked and cracked against the hungrily grasping reach of those creatures determined enough to reach out for them.
Around him, Liam could hear a mixture of frustrated snarls and startled whimpers... and a sudden high-pitched scream that sounded unmistakably human. His mind solely on dragging Becks, heavy despite her slight frame, he could only fleetingly hope that it wasn't Edward Chan's voice he'd just heard.
'Mission priority –' Becks began to chastise him.
'JUST KEEP HITTING THE BLOODY THINGS!' he bellowed back at her. She shut up and obliged, swinging a booted foot out at a long bony jaw getting ready to snap down on her blood-caked thigh. Her boot made heavy contact, and the skull spun on its turtle neck like a skittle, a handful of toothpick-sized teeth whizzing out into the dark.
Ten seconds later – ten seconds that to Liam could easily have been a minute or an hour, ten seconds of dragging, hacking, swinging, kicking and screaming – and all of a sudden he felt the hair on his head lift in response to the warm soup of energy and excited particles around him. Over his shoulder, he could see Sal, actually see her shape, dancing and undulating as if seen through a thin veil of oil, and other shapes, Edward, Laura standing beside her. He could see the flickering blue fizzing archway light that normally irritated him so much as he read on his bunk.
'WE DID IT!' he found himself yelling as his foot seemed to lose touch with solid ground and he felt that all too familiar nauseating sensation of falling.
# CHAPTER 71
# 2001, New York
He felt his face smack against a hard concrete floor, the dead weight of Becks landing heavily on the top of his back, knocking the air out of his lungs.
'Good God!' he heard from somewhere nearby – a male voice he didn't recognize.
While his eyes were still seeing stars, he could feel Becks struggling to lift herself off his back. He heard the pounding rasp of laboured breath nearby, presumably, hopefully, Edward and the other two. He could hear the faint muted chug of the generator in the back room. And through the still-open portal hovering a couple of feet above the tangled pile of himself and Becks, the far-off sounds of a jungle night stirring to life... and the click-clacking and mewling of those things getting louder, closer.
'Ummpph... closhhhh the 'ortal!' he mumbled into the floor, his bloodied lips still mushed against the hard concrete as Becks struggled to lift her dead weight off him.
'Liam? Is that you under there?' Maddy's voice.
'Umpph. U'mm... yeshhh,' he mumbled. 'Closhhh the 'leedin' 'ortal!'
Then all of a sudden he felt another heavy load land on his back, and the excruciating pain of three sharp blades digging deep into his left shoulder-blade.
'What on earth is THAT?' Another unfamiliar voice, another man's voice.
The weight was gone as quickly as it had arrived and he heard the skittering of claws across the concrete floor and the startled bark of one or two of those creatures echoing off the arched brick ceiling.
'My God, Forby! Shoot it! SHOOT IT!'
The piercing scream of a girl, he couldn't be sure who. Then, with a rattling sigh, Becks finally flopped off the side of his back, her pale face spattered with dark dots of drying blood, thudding to the floor beside his. Her grey eyes stared lifelessly back at him, as if looking at something far, far away. He managed to lift himself up on to his elbows, grimacing at the sharp pain in his shoulder and his head still spinning from the impact of the heavy landing. He attempted to get his first glance at what was going on around him.
Two of the creatures had managed to follow them through and were now darting in confusion and panic one way and then the other across the archway floor. He spotted two men he didn't recognize: one old, in a rumpled suit with a loosened tie dangling round his throat like a hangman's noose. The other man was younger with buzz-cut sandy hair and an army-fit physique beneath what looked like a baggy light-green boiler suit. He raised a gun.
'Where did they go?' snapped Maddy.
They heard something fall off a shelf in a dark corner of the archway and roll noisily across the floor.
'Over there!'
With trained, quick precision, Forby squinted down the weapon's barrel and flipped the night-sight of his scope on. A soft green glow poured across his face as he slowly panned the weapon around the archway, then up towards the curved brick ceiling.
'Ahh... I see one.'
Liam followed the direction of his gaze and thought he could just about make out some dark shape moving among a criss-cross of old rusting pipes and loops of electrical flex. Age-old dust and the grit from crumbling bricks and mortar trickled down past the softly fizzing glow of the ceiling light, giving the hapless creature's position away.
The man fired two aimed shots in quick succession. The creature screamed, then plummeted to the floor, bringing down a small flurry of dust and grit with it. It squirmed and screamed and drummed arms and legs against the floor, until the young man put a third shot into its long skull.
As the echo of the last shot rattled around the brick walls, Liam looked around him. He could see Edward and Laura huddled together by the displacement machine's perspex tube, and Sal and Maddy beside the computer desk. All of them looking from one dark recess to another, listening intently for the sounds of movement.
'Where's the other one?' whispered Sal.
The man with the gun placed a finger to his lips to hush her. 'Hiding,' he whispered.
'Well, for Christ's sake find him, Forby!' hissed the older man.
Liam watched as Forby stepped across the floor into the middle of the archway, continuing to slowly pan his gun, studying every nook and cranny around until finally he came to a halt, aiming at the arched recess where their bunk beds were.
'Uh-huh... I think he's skulking under there.'
He squatted down low and pumped his finger. A single shot danced and ricocheted under Liam's cot, sparking against the metal frame.
It was then that something dropped down from above, past the ceiling light on to Forby's back – a blur of movement and flashing of claws and teeth, a bright arc of crimson.
'HEELLP M–!' His voice was cut off as the creature's claws flailed at his neck. He dropped the gun as he staggered and struggled to wrestle the thing off his back.
Liam picked himself up and scrambled across the floor, reaching out for the heavy assault rifle as Forby's legs buckled and he dropped to his knees, blood spraying from the multiple ragged wounds across his face and head. The creature leaped off his shoulders and darted towards the shutter door as Forby flopped the rest of the way to the ground. Quite dead.
Liam raised the gun and pulled the trigger. The gun kicked his shoulder as he emptied the clip with a protracted and unaimed volley that produced a dozen showers of sparks and brick-red plumes of dust.
With the gun angrily clicking in his hands, he finally eased his finger off the trigger and peered through the gunsmoke at the inert body of the other creature. Now a shredded mess.
'Jesus,' whispered the old man, his croaky voice shaking.
# CHAPTER 72
# 2001, New York
They stared at the naked body floating amid the pink-red soup of liquid in the plastic cylinder.
'Will the support unit survive?' asked Sal.
'Becks,' said Liam quietly. His voice little more than a gentle croak. 'Her name is Becks.'
The soft glow of red light coming from the base of the birthing tube was the only illumination in the back room. It was enough for Maddy to see the lost expression of post-traumatic stress on Liam's face. 'She'll live,' said Maddy with the hesitant smile of someone not really sure. 'Bob said their combat frames can sustain roughly a seventy-five per cent blood loss and still be able to recover from that, given enough time.' She glanced at the shredded remnants of the female unit's left lower arm. Almost all the soft tissue had been clawed away leaving a skeletal forearm surrounded by tatters of skin and tendon that floated and swayed in the gloop like so many ends of frayed rope.
'Unlike Forby,' said Cartwright sombrely.
'I'm sorry,' said Maddy. 'He seemed, like, you know... like a good guy.'
The old man nodded thoughtfully. 'The best. The very best.' He sighed. 'Family man too.'
The only sound in the back room was the gentle purring of the tube's filtration system. Maddy had shut down the generator to conserve the half a tank of fuel they had left. There was no need for the generator to be chugging away right now; a row of steady green LEDs showed the displacement machinery was fully charged and ready to use again. She'd shut everything else down, the computer systems, the lights, the other birthing tubes and the fridge containing the other embryos... they'd keep in their cryo-tubes for a few more hours without refrigeration.
'So how long?' asked Laura, wiping her nose on the back of her hand. 'You know? Until she's all better again?'
Maddy looked up at the girl. She could imagine her in another time, confident and popular in her high school, a baton-twiddling cheerleader, everyone's favourite, always invited to parties, always surrounded by friends and acolytes. That Texan accent – the confident bray of someone who'd never need to question her place in the world... Well, she didn't look quite so much like a future Homecoming Queen now. Even in this muted light Maddy could see how badly affected she was by the portal's corrosion effect. Her face looked ghostly pale, the flesh around her eyes dark and it seemed her nose was still leaking a steady trickle of blood: a ruptured blood vessel somewhere inside that quite possibly might never heal.
The boy, Edward Chan, seemed to have fared only slightly better.
Apparently, according to Chan, there'd been another girl with them, but she'd been jumped by one of those things just before she could reach the portal. If she'd suffered the same fate as Forby, then Maddy could only hope her death had been as mercifully quick. Although, after what she'd witnessed only half an hour ago, merciful felt entirely like the wrong word to use. She watched Chan's large round eyes staring at the mush of organic soup, at the foggy figure of the support unit inside. Both these two, Chan and the girl, seemed to be in a deep state of shock, well beyond grieving for a lost classmate. Liam said there'd been others, sixteen of them had survived the blast back in time. Only these two plus Liam and Becks had made it.
God knows what they've been through.
'How long?' asked Chan again.
'About four and a half hours,' Maddy replied. 'Four and a half hours and her condition should be stable. She'll have replenished enough blood to function again.'
'What about her arm?'
Maddy shrugged. 'I don't know whether this healing thing actually regrows limbs and stuff. Bob, our computer system, just told me she'd be able to repopulate blood cells. We'll see, I guess.'
Liam's eyes came back from far away and met hers. 'You said... function again?'
She nodded. 'She has to go back, Liam. You know that. There are loose ends that need fixing.'
The others looked at her. It was clear to her that she was the only one doing any strategic thinking here, thinking beyond the moment.
That's your job, Maddy. Team strategist... remember?
'She has to go back and correct what happened... what it is that's made the present the way it is.'
'It's those creatures, isn't it?' said Cartwright. 'The ones that came through your portal... they're the thing that's different?'
Maddy turned to Liam. 'Liam, is that –?'
Oh my God.
She hadn't noticed it before. In fact, she had, but she'd thought it was a streak of dust, or perhaps a dusting of some exotic jungle pollen. Looking at Liam right now, even in the dim crimson glow of the birthing tube, she could see a shock of white hair on his left temple. And his left eye... the white of it mottled with the web-like blur of a burst blood vessel.
'Yes...' he said after a few moments, not registering the look on her face. 'Yes... those things, they learned a few tricks from us.'
'There's more?' asked Sal.
He nodded. 'Yeah... thirty or forty, I suppose. A pack of them.' His eyes remained on the outline of Becks's form, curled up like a foetus. In her sleep, vulnerable-looking – just a teenage girl. 'She managed to kill some of them, but the rest are back there.'
Maddy looked at Sal and Cartwright. 'Then those hunters across the river, they must be distant ancestors. They're somehow linked, right? The long heads?'
Cartwright nodded. 'It's an unusual configuration.' He stroked his chin. 'No... it's a unique configuration.'
Maddy had lifted the shutter door briefly after they'd seen to Becks and shown Liam and the other two the jungle that now replaced New York. The hunters were no longer probing the riverbank for mud creatures and had returned to the settlement on the far side of the broad river.
'They're descendants, Liam,' she said. 'Distant... very distant descendants.'
'And their ancestors,' cut in Cartwright, 'must have learned something from you... something that enabled them to survive and prosper. Something, some sort of skill, that helped them survive the K–T event, whatever wiped out the dinosaurs.'
Liam nodded slowly. She could see he'd worked that much out already. 'So... someone has to go back and kill the whole pack.'
'Yes,' said Maddy, reaching a hand out and holding his arm gently. 'They can't be allowed to live and develop any sort of intelligence that could save them. They should have died out with all the other dinosaurs.'
'OK.' He took a deep breath. 'OK... I'll go –'
'No,' she said, a little too quickly. She tried not to let her stare at his bloodshot eye linger. 'Not you, Liam. You need rest.'
'If not me, then who? No one else –'
'The support unit.'
'Becks?' He shook his head. 'No. She'll take days to recover, surely. And she'll not be able to face them all on her own. They'll kill her, to be sure.'
Her? She?
She held his arm. 'Listen to me, Liam.' She nodded at the birthing tube. 'I know you've been through a lot together, but remember... it's just a support unit in there. A meat robot. A tool for the job. That's all it is. It's expendable.'
'I'll go with her,' he said.
'No.' Maddy shook her head firmly. 'No. You can't go back there again.'
'Why?'
He doesn't know, does he? He hasn't looked into a mirror. He hasn't realized how much damage going so far back in time has already done to him. She wondered why he hadn't yet noted the condition of the girl and Chan. Both looked like people suffering from advanced radiation sickness. But then... from his time, Liam wouldn't know anything about radiation sickness. Perhaps he attributed the bleeding noses, the pallid complexion to shock. Perhaps he was too much in shock himself to have noticed.
'Because you're too valuable to lose, Liam. We need you here.'
'We need you,' added Sal, 'and...' Her face dipped out of range of the soft peach glow and in the darkness they heard movement, a scrape, the heavy thud of something metallic and the rattle and tinkle of a buckle. Her face returned and she held up something that glinted in the dull light. 'And she'd have this gun, Liam. Not just a bamboo stick.'
Maddy nodded. 'You saw how good it was earlier.'
'High-calibre MP15 assault rifle,' said Cartwright. 'It'll mince those monsters up no problem.'
'We'll give her a few hours to rebuild herself. OK?'
'I'll uhh... I'll go and see how many clips of ammo Forby has... had,' said Cartwright.
Maddy pressed out a smile, and nodded. 'You do that.'
She turned back to Liam, watching the floating body of Becks. She could see he felt something for the support unit, that they'd bonded in the past... that this time, unlike last time, if the support unit fell, there'd be no one to retrieve its AI, no one to dig the computer out of its cranium and bring it back.
Be the leader, Maddy. There's no discussion here. It's decided.
'Sorry, Liam, she has to go,' she said forcefully. 'That's how it is. She has to do this. We need New York back; we need our power feed back before we run out of fuel. Anyway...' She glanced at the silhouette of Cartwright shuffling cautiously out through the doorway by the light of a wind-up torch. She lowered her voice. 'Anyway, there's going to be one more job for you to do before we've dug ourselves out of this whole freakin' hole.'
# CHAPTER 73
# 2001, New York
Liam watched the sun setting across the river, picking out thin skeins of smoke from the settlement perched on the muddy banks on the far side. He saw several pinpricks of light in the middle of the round huts.
Fire. One of the earliest markers of intelligence. He wondered how many aeons ago this descendant species had learned they could control it, use it. A far cry from the primitive animal fear for it demonstrated by their ancestors.
He heard the shutter rattle as Maddy stooped under it and joined him outside. 'Hi,' she said. 'How are you feeling?'
'Tired.' Squatting against the outside brick wall of their archway, watching the jungle turn dark and the sky's rich palette change from crimson to violet, he realized how utterly spent he felt. Finally, after two weeks of nervous tension, two weeks of fearing something primal, savage and hungry could snatch him away at any time... here he was, somewhere safe at last. Somewhere he could close his eyes for a moment and actually, properly, rest.
'She's nearly ready,' said Maddy. 'We're prepping the portal to take her back to one minute after we closed the last one. Those creatures should still all be gathered there, scratching their heads and wondering where you went.'
'How is she?'
'The arm looks like it's begun repairing itself. I noticed there's some new muscle tissue. No skin yet. I presume that regrows at some point. Anyway, Sal's bound her arm and hand in bandages to protect it.'
'How is she?' he asked again. 'Can she do it?'
'She says she can operate to forty-seven per cent functional capacity.' Maddy smirked. 'And she's really rather pleased about the weapon.'
Liam laughed softly. 'Just like Bob.'
'They could be brother and sister.'
'Well, they are... I suppose.'
'True.'
Liam nodded towards the village. 'It feels wrong, in a way.'
'What?'
'What we're doing... killing the rest of that pack. I mean, look what they became.' He shook his head and laughed.
'What's so funny?'
'I'm almost proud of them, so I am. They're like, I suppose... I feel like they're sort of my creation. We showed them how to build a bridge, how to use a spear. And, after Lord knows how many thousands of years...'
'Millions actually.'
'... millions of years, they've become this. A brand-new intelligent race and here we are, going to wipe them all out. What's that word for it?'
'Genocide?'
'Aye, that's it... like that Hitler tried to do to the Jews. And we're going to do it to those things. They're not just dumb animals, Maddy. They were clever back in the jungle, you could see that. Very clever, and now here they are just as smart as us humans.'
'No, Liam, they're not. Something that old man, Cartwright, said...'
'What?'
'Ask yourself this: just how long have they been at this stage of development? Hmm? They could have got this far – canoes, spear, huts an' all – millions of years ago and yet... and yet this is as far as they ever got.' She gazed at the distant village. 'Otherwise, why aren't they walking around in smart suits and talking on cell phones?'
He shrugged. 'Maybe they did once. Maybe millions of years ago they were that smart, and this place was a big city like New York.'
'And what? They chose to become savages again?'
'Who knows? Maybe they had some sort of war? Maybe they once had an incredible civilization that eventually collapsed into ruins. Or some doomsday weapon wiped them out but for a few poor bloody survivors.'
Maddy nodded. 'It's possible, I guess. A lot can happen in sixty-five million years.'
'Aye, and who's to say it doesn't one day happen to us too, eh? And soon.'
She looked at him. 'Kramer's time?'
'Foster's time, perhaps. You remember the things he told us about the future? The dark times ahead. All that global warming, the flooding, pollution and the poisoned seas... the starving billions?'
She did. It was a future she'd thought she was beginning to see in her lifetime. That big meeting in Copenhagen that was supposed to be the last best chance for the world to agree on how to stop global warming – it had failed miserably. She wondered whether historians from midway through the twenty-first century would point to that day as the very beginning of the end.
'Well... that's the future whether we like it or not, Liam. And it's our job to fight to keep it that way.'
He nodded. 'Hmm... but do you ever wonder, Maddy?'
'Wonder what?'
He looked at her, with his bloodshot eye and thin shock of snow-white hair, and for a moment he looked both old and young at the same time. 'Do you wonder whether that future, the one Foster told us all about, whether that's the right future to fight for?'
'I dunno. I suppose we just have to trust him that it is.'
The sun dipped behind the far horizon of trees, behind the thin lines of campfire smoke. From inside the arch they could hear the voices of the others: Sal helping the support unit... Becks... get ready.
'She's been given orders to kill them all, then destroy your camp. Burn everything so there's nothing left behind to leave fossil traces. We'll know if she's successful –' Maddy nodded out at the jungle – 'when this all goes and we get New York back, and...' She lowered her voice a little. 'And the tricky situation we were stuck right in the middle of just before jungle-land arrived...'
'Cartwright?'
She nodded.
'So...' He cocked a brow. 'I'm presuming he, and the poor fella with the gun, are the chaps who found our message?'
'Not exactly. It was found a lot, lot earlier. In the 1940s, apparently. But Cartwright runs this little government agency,' she snorted, 'an agency a bit like ours, I guess – small and secret. Its job for the last sixty years has been to be a custodian of your message. And to finally make contact with us in 2001.'
'And he came knocking?'
'Oh, he came knocking all right. Just before the last time wave, we had men with guns standing guard outside in the backstreet. In fact, they had several areas of the neighbourhood sealed up with roadblocks and soldiers and stuff. Helicopters overhead and everything. Quite a big deal. You'd have loved it.'
'My fault.' Liam looked guilty. 'Sorry about that.'
She shook her head. 'Don't be. You had to send the message. There was no other way we would have found you.'
Sal was calling out for her. It was time.
'Thing is, Liam,' she said hurriedly, 'we have to be ready to move, and move quickly. If Becks is successful... we'll get all of that situation right back in our faces. We'll be right where we were. So, I'm going to need to send you back to make sure they don't get your message.'
'Dinosaur times?'
'Oh no. Not that far.' She managed to stop herself saying because that would probably finish you off. 'No... it'll be the second of May 1941. You need to prevent some kids from finding a particular chunk of rock.'
He smiled. 'And Cartwright and his agency will never have existed?'
She was ducking down under the shutter when she paused. 'Well... his agency might not exist, or maybe it will, but it will be busy with some other secret it's trying to keep from the American people.'
'Right.'
'When that time wave comes, Liam... we'll need Cartwright standing outside when I turn on our time field. His life will be rewritten along with the rest of the corrected reality. He'll have no memory of all of this.'
Liam bent down and looked under the shutter and into the archway. He could see Forby's dark boots poking out of the end of the blanket they'd wrapped his body in.
'And what about him?'
'Forby? Not sure. If his body is outside the field I suppose he gets to live again, doing whatever job he was doing before Cartwright and his agency suddenly winked into existence. The point is... whatever that means for him and the old man, we won't have a backstreet full of spooks with guns. We'll be back to normal.' She grinned up at him. 'Which would really be quite nice.'
'True... but do we not still have to get Edward Chan back home?'
'One thing at a time,' she sighed. 'Come on, let's send Becks on her way.'
Liam followed her under the shutter and then cranked it down after him.
He rejoined Maddy and the others gathered around the computer desk. He saw Becks standing in the middle of them, the assault rifle cradled in her arms, one of them swathed in bandages up to her elbow.
'How are you feeling?' he asked over the hubbub of other voices: questions from Cartwright and the kids that Maddy was busy trying to field as she configured the return time-stamp.
'I am fine, Liam.'
'What about that spear wound? That looked pretty bad, so it did. Are you sure you're fit enough to go?'
'My organic diagnostic systems indicate my kidney was ruptured and is no longer functioning. The organ can be repaired later,' she added. 'It will not affect my performance.'
'Your arm?'
'My arm is operable.'
'OK,' said Maddy. 'I've set it to one minute after the other window. There'll still be background tachyon particles around from the previous window, but I've moved the location thirty feet away so there shouldn't be any disruptive effect on your arrival portal. OK?'
'Affirmative.'
'You understand the mission parameters?'
'Kill all the reptile hominids. Destroy all evidence of our camp. Return window set for two hours after arrival.'
Maddy nodded. 'You got it. And, of course, remember to bring the gun back with you.'
One of Becks's dark eyebrows arched slowly. 'Well... duh,' she said flatly.
Sal giggled. 'That's cool!'
Maddy grinned at Liam. 'Looks like she's been doing some learning of her own.'
He nodded.
'All right, we haven't got time to fill the tube. She's going back dry. Stand clear of that circle on the ground.' She pointed to the circle of chalk, and within it, a patch of concrete floor darker than the rest. She sighed. 'We're gonna need to fill in the floor once again after all this is finished.'
The others pulled warily back and Becks wandered over and planted her feet inside the circle, her knees bent, ready to react at a moment's notice, the gun loaded, cocked and raised, the assault rifle's butt pressed firmly against her shoulder and ready to fire.
'Be careful, Becks,' said Liam. 'We want you back safely.'
She nodded hesitantly. 'Affirmative, Liam O'Connor. I will be careful.'
'Are we all set?' asked Maddy.
'Affirmative.'
'All right, Bob.' Maddy turned back to the desk mic. 'On my countdown. Ten... nine... eight...'
The archway filled with the sound of power surging into the displacement machine, the green LEDs winking off one after another as they indicated the drain of stored energy. A three-yard-diameter sphere of shimmering air suddenly enveloped Becks. The ceiling fluorescent light dimmed and flickered.
'Seven... six... five...'
Her cool grey eyes turned to rest on Liam and she smiled uncertainly.
'Four... three... two...'
'Good luck,' he mouthed, unsure whether she could read that in the flickering fizzing light.
'... one...'
And then she was gone. Air whistled past them all to fill the sudden vacuum created.
'Wow,' whispered Edward.
'Now we wait,' said Maddy. She shot a glance at Liam. 'And we make sure we're ready.'
# CHAPTER 74
# 65 million years BC, jungle
Becks emerged from the surrounding sphere of undulating air, and dropped the last few inches with a soft thud of boots on hard mud.
Crouched, ready for action, her eyes panned across the fire-lit clearing: a dancing, flickering impression of hell. The creatures had converged in the centre of the area, picking through the shelters, the palisade, watching the campfire hungrily consuming the last of the branches that had been stacked on it.
A knot of them were gathered around the space where, only a minute ago, the return window had opened. They were examining the ground, a cluster of low ferns nearby, their heads cocked with confusion and bewilderment like curious crows studying road kill.
None of them had yet noticed her standing there.
She had a thirty-round ammo clip, and in the blink of an eye had organized the order in which she was going to drop the targets: larger male creatures first.
The first rapidly fired half-dozen shots echoed across the clearing like so many dried and brittle branches snapping, and five out of six of her targets dropped like leather sacks of bone and meat. The one she'd missed had bobbed unpredictably, the shot skimming across the top of his head.
The other creatures froze where they were, uncertain as to what the rapid cracks of gunfire actually meant.
Becks took advantage of the moment of stillness and confusion and selected another six targets, all the larger males again. But this time the muzzle flash of her gun had attracted their attention and they began to bound towards her. She killed four and wounded another, before their short-lived charge faltered. They drew up a dozen yards away and fanned out, snapping and snarling.
Beyond them she could see the others, females and cubs being herded away from harm by a large male. She recognized it as the pack's leader, a claw from one of its four digits missing on its left arm. It was holding one of their spears, waving it around and using it to prod and cajole the pack away into the darkness.
[Assessment: primary target]
The pack leader, the alpha male... logic and observation dictated that that particular creature was the one who'd been learning from them; the shrewd one, the clever one whose genes and unique acquired knowledge were going to pass onwards to its offspring. In only a few nanoseconds of silicon-based analysis, she realized that the one creature she had to be absolutely certain of killing was the one with the missing claw. She was striding forward like an automaton as she fired another rapid succession of single shots, killing half of the creatures bobbing and snarling in front of her; those still standing turned and fled. The noise and the muzzle flash were as startling to them as the sudden inexplicable death it seemed to deal out. The entire pack was in motion now, scattering like birds startled by a handclap. But her eyes remained on the back of the alpha male. She swung the assault rifle towards it, aimed and fired.
The shot spun the creature off its feet.
# CHAPTER 75
# 2001, New York
Maddy looked over at Cartwright. He was with the two children and Sal, standing beside the half-raised shutter entrance, staring out at the jungle and eagerly waiting to see the spectacular sight of a new reality arriving from a distant past. Sal was doing a great job keeping them all over there, telling them all about time ripples and waves and her job as an observer.
'You understand what you've got to do?' she asked Liam quietly.
He nodded. 'But are you sure it's the right date?'
'Well, I hope so. He said your fossilized message was discovered on that day. I presume he's not lying. I've got the Glen Rose National Park entered in as the location. I'm sure he mentioned a river called the Paluxy River... so that's what I've put in. And you're looking for the two boys that found it.'
'Boys? How old?'
'I don't know... You know, boys.' She shrugged. 'Boy age, I guess.'
Liam glanced furtively over her shoulder at the others. 'Well, then, what do they look like?'
She ran her hand tiredly through her frizzy hair. 'Jeez... How the hell am I supposed to know!' she muttered irritably, then immediately felt guilty and angry with herself. She looked at Liam... his bloodshot eye, the streak of white hair... and felt like a snappy cow. 'I'm sorry,' she sighed. 'I guess they'll look all excited and very pleased with themselves. OK?'
She turned towards the desk. 'Bob, are we ready for a portal?'
> Affirmative. There is sufficient charge for this displacement.
'OK.' She nodded. 'All right.' She looked at Liam's face again, pale like the other two, but not as bad. No nosebleeds, no apparent nausea or any other apparent haemorrhaging. 'You sure you're OK to go, Liam?'
He nodded. 'I'm fine, so I am. Tired, I could sleep for a year, but I'm all right.'
Why not go in his place, Maddy? Look at him... look at the damage that last portal did to him. And now you're sending him through again! She stilled that guilty voice in her head quickly; she needed to be right here, coordinating Becks's and Liam's bring-backs. It was all going to be rather tricky.
She wanted to tell him what she knew, what Foster had told her. She wanted to tell him so that at least he could decide for himself if it was worth it, killing himself slowly, one corruption at a time.
'Shall we?' he said.
She pressed a digital watch into his hand. 'Six hours,' she said softly, then glanced at the chalk circle and the concrete already gouged out of the floor in the middle. Liam understood. He had six hours back in 1941 and then she'd open the return window. He casually ambled across the floor towards the circle as Maddy silently initiated the countdown sequence. The machinery began to hum – there was no way to avoid that – and the ceiling light flickered and dimmed.
She was hoping Cartwright would be too engrossed in listening to Sal and watching for the time wave to immediately notice something was going on, but the wily old man spun round and looked back into the arch. 'What's going on?'
Liam stepped smartly into the chalk circle just as a sphere of air began to twitch and fidget around him.
'What's happ– Hang on, what's...?' His eyes widened. 'Where the HELL IS HE GOING?'
Maddy ignored him. Cartwright reached into his jacket pocket.
'No! Don't shoot!' shouted Maddy, realizing what he was going to do. 'Please!'
Cartwright pulled out his pistol, straightened his arm and aimed. 'STOP IT, NOW!'
'I can't! Please... I can't stop it. Don't sh–'
He fired a single shot at Liam just as the sphere wobbled and collapsed in on itself with a puff.
## 1941, Somervell County, Texas
At the very same moment that Liam landed on a riverbank of pebbles something whistled past his ear and off into the sky.
'Jay-zusss!' He ducked and then looked around, wondering what the hell that was. He saw nothing, just a narrow river, rolling sedately along a shallow creek of sandy-coloured rock, small and mean-looking yew trees and arid tufts of sun-bleached grass that hissed softly alongside the soothing gurgle of water.
Perhaps a bird? A bee? A fly?
It could have been. A fast one, though.
His mind turned to more pressing matters – which way to go? He had no idea, no idea at all, other than to look out for a pair of boys. He looked at the digital watch, Maddy's. She'd set a countdown on it: five hours and fifty-nine minutes.
'Right,' he muttered to himself, 'where do I start?'
A midday sun beat down on his head as he stood there, unsure which way to turn. He decided, before walking anywhere, that he was going to mark the window location with a small cairn of rocks: a dozen fist-sized worn and rounded rocks stacked in a small pyramid. Big enough so that he wasn't going to walk right on past and miss it.
Then, caught on a lazy midday breeze that had the nearby yew trees stirring and hissing, he heard the faint call of a voice and what sounded like a splash of water.
That way... downstream. He set off, walking along the riverbank, shingle and pebbles clattering underfoot. For a moment he recalled an image of that huge sweeping bay and the calm prehistoric green sea spreading out to an infinite horizon on his right.
It was here. Right here, an incredible tropical sea.
Quite a breathtaking notion, that... in the vast dimensions of geological time, even seas and oceans, just like any other living creature, had lifespans that came and went.
He heard voices again, echoing up the creek. The sound of children playing, larking about.
# CHAPTER 76
# 65 million years BC, jungle
Becks followed the spatters of dark blood into the jungle. By moonlight the streaks of blood were black and glistened wetly. The trail didn't lead too far into the jungle, fortunately. If it had, she suspected she'd have been unable to follow it; the moonlight was beginning to fail her, blocked by the drooping leaves from the canopy trees above.
She heard them before she saw them: the rattling breath of one snorting like a winded buffalo and a chorus of mewling voices that sounded like a pitiful choir of simpering children. Her eyes picked them out. The creature she'd managed to hit was curled up on the jungle floor. Around it an array of the smaller creatures, females and cubs, all pawed and stroked the wounded one, as if somehow that would magically heal their pack leader.
She stepped forward until she was looking directly down at the creature with the broken claw. The pack, perhaps twenty of them here, became quiet; a forest of yellow eyes that glowed with soft fluorescence and narrowed with fear looked up at her.
'... Help... me...' The facsimile of a human voice came from one of the females. Becks recognized it as an attempt to duplicate the cries of the human called Keisha.
A part of her computer mind calmly informed her that a mission parameter remained outstanding, and could not be successfully flagged as completed until, at the very least, the wounded creature was confirmed dead.
But another part of her mind, a very much smaller part, a part that contributed thoughts as foggy sensations rather than runtime commands, spoke to her.
Just like me.
She remembered being born, released from growth amid a cascading soup of warm liquid, lying like this creature, curled like a foetus on a hard floor; feeling bewildered, frightened, confused. An animal mind of sensations, feelings... but no words.
She squatted down to get a closer look at the creature. The wound was in the middle of the creature's narrow chest, and from the pulsing of ink-black blood down its olive skin, was almost certainly going to prove to be fatal.
'You will die,' she announced coldly. And then realized talking to them was illogical and pointless – these wild things were no more intelligent than monkeys. But, on the other hand, it felt like another way of processing, filtering her own thoughts... giving words to that part of her mind that wasn't high-density silicon wafer.
'I am here to kill you,' she said. 'This is a mission requirement.'
The yellow eyes studied her silently. Perhaps those eyes were trying to communicate something, pleading for mercy.
She stood up again and changed the clip in the assault rifle for a fresh one. The mission voice had no time for such an irrational sentiment and gently cajoled her to proceed with the task.
Complete Mission
1. Terminate alpha male of species
2. Terminate remaining hominids (optional)
3. Retrieve all evidence of human habitation
'I am... sorry,' she said. She cocked her head, curious. There'd been a strange effect on her voice. It had fluttered ever so slightly. It had actually made her sound more convincingly human; she'd sounded almost indistinguishable from the school students she and Liam had spent the last fourteen days in the jungle with. Those three words really had sounded so very human. For a moment she was almost tempted to say them once again. Instead, she raised the rifle swiftly to her shoulder, her bandaged finger slipped on to the trigger and beneath the dressing the recently vat-grown muscle tissue tightened and pulled. A shot rang out. Her finger muscles released and pulled again... and again... and again.
By the time the last of the creatures flopped lifelessly across the body of Broken Claw, the clip was empty and the barrel warm.
The jungle was still, every nocturnal species stunned into silence by the rapid crack of gunfire. For a few moments she listened to the shifting breeze, the muted rumble of the nearby river.
'I am... sorry,' she said again, and realized this time her voice sounded flat and emotionless, as it always did.
She turned on her heels and headed back towards the remains of their abandoned camp.
## 2001, New York
'Where did you send him?' barked Cartwright, swinging the aim of his gun on to Maddy.
'I... I j-just sent him back... to help Becks kill the –'
'You're lying!' he snapped.
'Honestly I –'
He fired a shot past her head. Behind her one of the computer monitors exploded amid a shower of sparks and granules of glass.
'Really,' he said, 'I wouldn't advise lying, young lady. I can put a bullet through your stomach right now... and believe me when I say that's one of the most painful ways to go. Slow and very, very painful.' He took a dozen steps towards her. 'Now, I'll try again... where did you send him?'
Maddy swallowed nervously, her eyes on the gun. 'I... just... I...'
'Maddy!' yelped Sal. 'Something's coming!'
Cartwright stopped where he was. 'What's that?' he shouted back over his shoulder, keeping his eyes firmly on the older girl.
'Did you feel it? A tremor?'
'No,' he replied, his eyes and aim still on Maddy. 'I didn't feel anything.'
'I felt something,' said Edward.
'Oh my God... the jungle's changed,' said Laura. 'Something different. I don't know what. Something –'
Sal nodded. 'The settlement's gone. It's an early ripple... the big change will follow.'
Cartwright cursed. He desperately wanted to see this. 'You!' he snapped at Maddy, waving his gun, 'over there by the entrance. NOW!'
Maddy nodded meekly and hurried across the archway to join the others standing in the entrance and looking out at the jungle. Cartwright joined them, keeping a cautious few yards' distance and holding his gun on them as he watched the evening jungle. 'What happens next?'
'The big wave,' said Sal. 'You'll feel dizzy just as it...' She looked at him, her eyes round. 'Do you feel it now?'
His eyes widened. 'My God, yes! Like an earth tremor!'
On the horizon the orange stain of dusk was blotted out by what appeared to be a rolling bank of raincloud, a storm front rushing in from the Atlantic at an impossible speed.
'What is that?' he gasped.
'The wave?' whispered Edward.
Maddy nodded. 'Another reality.'
It crossed over the island beyond the broad river and amid a churning soup of thick, shimmering air, realities mixed and became fleeting impossibilities. Amid the churning reality soup they saw the winking flickering outline of tall buildings warping and twisting and Maddy thought she saw for a fleeting moment a swarm of creatures in the sky like gargoyles, dragons – a possible reality, a possible species that in this correcting reality had no place, existing for a mere heartbeat, then erased.
Then the wave was over the river and upon them.
The archway flexed and warped around them, the ground beneath their feet momentarily dropping away, becoming void.
Then, just like that, they were staring at a brick wall, ten feet opposite, across a cobbled stone backstreet. The rolled-up tarpaulin with Forby's corpse inside, that they'd placed just outside the entrance, was gone. Instead he was standing to one side of the entrance, talking in hushed tones with two other armed men. A spotlight flickered across the backstreet as overhead they heard the whup-whup-whup of a circling helicopter.
Cartwright's jaw hung slack and open, his gun arm lowered down to his side. 'This... is... incredible.'
'Isn't it?' said Maddy.
Forby looked up from his conversation. 'Whuh? Oh, sir?' He looked perplexed, as did the other two men. 'I uh... didn't hear the door opening. You OK, sir?'
Cartwright's face was still immobile, still frozen with incredulity.
'Sir? Everything OK?'
He looked at his man. 'Uh? Yes... yes, just fine.' Alive once more. A faint smile of relief stretched across his thin lips. 'Good to er... it's good to see you again, Forby.'
Forby frowned and nodded. 'Sir?' Then he noticed Edward and Laura. 'Who are these?'
Cartwright shook his head, gathering his confused wits. 'I'll... I'll explain later.' He turned to Maddy and the others. 'Inside, you lot. Let's close this door.'
Forby stepped forward but Cartwright waved him back. 'You best stay outside for now, Forby, all right?'
He flicked his gun at Laura. 'Close the shutter.'
She began to crank the handle, but Sal stepped in and pressed the green button. 'It's OK, we've got power now.' The shutters clattered down as a small motor beside the door whined.
The old man took a moment to compose himself, to try to make sense of what he'd seen, and what he may yet see before the night was through. The shutters clattered down and the whining motor was silent.
'All right,' he said presently. 'All right, so this means your friend and the cloned girl... they've been successful. They've killed those freaks in the past. So that means no reptile hominids.' He nodded as he talked. 'All right... I get that. I understand that.'
'Cartwright,' interrupted Maddy.
'And... and Forby's alive now, because... because...' His eyes narrowed as he tried to make sense of things. 'Because what happened... didn't happen. No reptile monsters means he couldn't have been attacked. But then that's just crazy... that doesn't make any... I mean... I actually saw that thing rip his...'
He was rambling.
'Cartwright,' said Maddy again. 'Listen to me, you need to hear something.'
'... and he was dead.' He turned to look at the floor. Halfway across, a pool of blood had congealed. Forby's blood. 'I mean... there! Look! It's his blood! He was –'
'Cartwright!'
The old man's confused eyes darted from the blood back to Maddy.
'This new reality is still wrong,' she said. 'This reality with you and Forby and men outside and a helicopter buzzing overhead and your secret agency. It's all wrong too. This is something else that should never have happened.'
'What?' His face creased with confusion.
'Your life,' said Sal. 'Should be a very different one.'
'In our timeline... in the correct timeline, you've lived a different life to this.' Maddy tried appealing to him with a friendly smile. 'Perhaps even a much better life... I dunno, with children, grandchildren?'
'I'm not married!' he snapped. 'I don't have children!'
'But, see, that's what I'm saying –'
'This agency is my wife! This secret! This secret! Time travel! It's my secret. I know things that even our president doesn't. I know time travel's already happening! That's what I'm married to! This... this knowledge! That's my life!' He raised his gun again and aimed at the frown between Maddy's eyes. 'And you're not going to take that away! Do you hear? NO ONE IS GOING TO TAKE THAT FROM ME!'
# CHAPTER 77
# 1941, Somervell County, Texas
Liam spotted them further up the river, two boys. One splashing around in the water, the other perched on a shelf of rock, sheltering from the scorching hot sun in a cool nook of shade.
Neither had seen him yet. His first instinct had been to call out to them, to find out what they'd been doing so far today... to ask them if they'd found anything interesting. But then if they hadn't yet, his intrusion on their day might alter what they did; change the sequence of events for today, and they might not make their discovery.
So he decided to lie low and watch. He hunkered down in the shade of a yew tree and waited.
An hour passed, another, and another. The sun was well past midday, the shadows slowly shifting and lengthening. He checked his watch again. The countdown was telling him he had less than two hours to go. He was beginning to wonder whether he was watching the wrong two boys, and perhaps another several hundred yards up the river two different lads were right now cooing and marvelling over some incredible fossil writing they'd just discovered. Then the boy on the rock ledge called out something.
'Saul!'
'What?'
He couldn't quite make out what the lad on the ledge said next, but from where he was he could see the boy was turning something over and over in his hand. The boy in the water, Saul, didn't seem particularly interested, content to continue paddling around in aimless circles. The other, frustrated at his companion's lack of interest, suddenly leaped off the ledge and into the river, swimming across to join him in the shallows. He showed Saul what he had in his hands, and among a garble of exchanged words Liam made out two distinct ones: look and message.
That's it, then!
He pulled himself up, grimacing at the stab of pins and needles in his feet, and made his way towards them. 'Hey there, lads!' he called out.
Both of them turned to look at him. 'Hey there!' he said again, trying to sound as friendly as possible and not frighten them off. But as he drew closer he could see both of them regarded him warily.
'Hey... it's all right, now. I'm not going to eat you. Just saying hello is all I'm doing.'
'Ma says we cain't talk to no strangers, mister,' said the boy holding the rock.
Liam drew up a few yards short of them. He hunkered down on his haunches and offered them a friendly smile. 'Well now, my name's Liam, Liam O'Connor. So I suppose I'm no longer a stranger.'
Both boys nodded at the unfailing logic of that.
'I'm Saul. This here's m' brother Grady.'
Saul looked at him. 'You sound funny,' he said. 'An' you got strange clothes. Where you from?'
'Ireland,' said Liam.
The boy looked at his face curiously. 'What's wrong with you, mister?'
Liam shrugged, bemused by the odd question. 'Nothing's wrong with me.'
'You sick or something?'
He really didn't have the time for this. 'No, I'm perfectly fine.' He gestured at the rock Grady was trying to keep from his prying eyes. 'What's that you got there, lad?'
Grady hid the rock behind his back defensively. 'Ain't nothin'.'
'Oh, come on.' He inched a little closer. 'Is it money? Did you find some money up there?'
'No.' Grady shook his head warily. 'Didn't find no money.'
'It's just some words on a stupid stone,' said Saul. 'Somebody made a message on a stone.'
Liam offered them a look of mild interest. 'Really? How interesting. Can I see?'
Grady shook his head. 'It's mine.'
If he'd been a bit smarter about this, if he'd thought ahead, he'd have brought something to trade – a cool toy, a pack of baseball cards, a bag of sweets or something, even some...
Of course. He suddenly remembered he had on him something way better than any of those. Something either boy couldn't fail to be entranced by. 'Hang on,' he said, digging into the thigh pocket of his tattered shorts. It was in there somewhere still. He'd... ah, his fingers found the sharp edge. A moment later he pulled out a four-inch-long fishhook-shaped object. He held it out in front of him and their eyes widened. 'It's a claw,' said Liam. 'A real dinosaur claw.'
Saul's and Grady's jaws dropped open synchronously as four young eyes admired the vicious-looking nicks along the curved edge of the claw.
'See, I just found it this morning, up the river, so I did. I heard you can find all sorts of fascinating old things along this river. Want to hold it?'
Both their heads nodded vigorously.
'We could swap,' said Liam. 'You can take a look at my claw... and I'll look at that message stone of yours.'
'Sure,' said Grady quickly, the passing fascination with his curious find more than trumped by the four-inch glistening claw dangling from Liam's fingers. He passed his rock over without another look at it. 'Message don't make no sense to me anyways.'
He reached out for the claw.
'Careful, it's quite sharp,' said Liam.
Grady took it off Liam and then hunched over, turning his back on his brother.
'Hey! Grady, lemmesee too.'
Grady shook his head. 'My stone, my first look-see.'
'Aw, come on, lemmesee! Lemmesee!'
Liam found a boulder nearby and let himself stiffly down on to it, ignoring their squabbling. As he turned the flat nugget of dark slate over in the palm of his hand, his heart silently skipped a beat.
Jay-zus... there you are again. After all this time. My silent messenger.
There it was, his own handwriting, reversed and faintly embossed with web-thin ridges and grooves of rock compressed and preserved by time.
'You're right,' he said, looking up from the rock, 'the words make no sense at all, do they?' But Grady wasn't listening. He was entranced by the vicious-looking claw and too busy fending off Saul's grabbing hands.
'It's just a load of gibberish,' he said, a knowing half-smile spread across his face.
'Wanna swap, mister?' asked Grady. 'My stone for your claw?'
Liam shrugged as casually as he dared. 'I dunno... my claw's a pretty good find an' all –'
'Please...!' The boy dug deep into the pockets of his own trousers and produced a wooden yo-yo. 'I'll throw this in for extra!'
Liam made a show of interest in the toy. He'd had one just like it back in Cork: large, cumbersome and one he'd never managed to get on with.
'Well... all right, then, I suppose. Yo-yo as well, you've got yourself a deal.'
They exchanged a solemn nod in silence – a deal officially sealed – and then Liam picked himself wearily up, for some reason feeling as old as the hills, and politely bade farewell. But both boys were already stuck back in a heated debate about the rights of access to the claw, and who was going to hold it all the way home.
He picked his way back along the shingle of the riverbank, through sliding, clacking wet pebbles, running his fingers across those faint embossed lines and his eyes looking for that small cairn of stones.
# CHAPTER 78
# 2001, New York
Sal felt it again, the early ripples, the faintest sensation of dizziness. But it looked like no one else had felt it. Cartwright still had his gun on Maddy.
'This... this is my life. This world. This reality!'
'Y-you have to step outside now... rejoin your men,' replied Maddy firmly.
Sal was impressed with her calm, her cool in the face of his wavering gun.
The old man shook his head and laughed. 'What? You're expecting me to just walk away from this? The greatest discovery in the history of mankind... and what? I just walk out into that backstreet and try to forget about it?'
Sal glanced at the other two kids. They met her gaze; eyes exchanging a shared imperative.
We've got to do something.
'Listen!' cut in Maddy. 'If the wave comes and goes while you're in here... y-you'll be left behind. It'll rewrite the present without you –'
He smiled. 'Oh... I think I could live with that, Maddy. In fact, I've been waiting a long, long time for something like –'
Her eyes narrowed. 'This isn't about state security any more, is it?'
He shrugged. 'All right, yes! And why not? This thing... this time machine... it's a boy's dream! It's a man's dream! Mankind's dream, goddammit! To travel anywhere, to any time, to see it all. To see things no other human will ever see!'
'It's not a toy, Cartwright. You know you... you just can't think of it that w-way.'
'Oh, right! You... some snot-nosed teenager and her buddies... you're to be entrusted instead, are you? You're the guardians of time, huh?'
Sal glanced at the others again, then took a hesitant step towards the old man. She looked to see if the other two were going to do likewise. Laura remained where she was, trembling, face ashen. She shook her head. Too frightened. Edward, however, took a silent step forward along with Sal.
She had no idea what she intended to do – make a grab for the gun?
Oh God, the thought made her knees wobble.
'I was selected!' replied Maddy. 'I didn't freakin' want this, Cartwright! Jesus! In fact, I didn't have much of a freakin' choice at all!'
The old man shrugged. 'Guess what? I don't really care.' He stepped towards her, across snaking cables. 'This is what I want. And I've spent my life waiting for it. Preparing for it.'
Sal noticed something blinking on one of the monitors.
'I'm an old man,' he continued, stepping on to concrete floor in the middle of the archway, clear of any cables that could trip him up. All the while the aim of his gun remained resolutely on Maddy. 'My whole life, my whole adult life, has been leading towards this moment. And I've known for so many years that a time machine was going to arrive under this bridge, in this archway, on September tenth, 2001.' He sighed. 'Can you imagine what knowing about something like that does to you? Knowing that near the end of your natural life... something truly wonderful is going to happen.' He shook his head. 'And what?' He laughed drily. 'You're telling me to just forget about it? Just walk away and forget about it?'
Over Maddy's shoulder Sal could see the blinking cursor in Bob's dialogue box. He was trying to tell Maddy something. A warning of the impending time wave?
'The things I've wanted to see, Maddy Carter... the things I've dreamed of seeing over the last fifteen years, the destruction of Pompeii, the fall of Atlantis, the crucifixion of Christ... the battle of Bunker Hill, George Washington crossing the Delaware, Lincoln giving his Gettysburg address! The arrival of Columbus...' His rheumy old eyes were alive with naive wonder. 'My God! The impact of the K–T asteroid that ended the time of the dinosaurs! Can you imagine actually seeing that impact for yourself?' He shook his head. 'How far back can I go? Do you know?'
Maddy spread her hands. 'I... I don't know. I –'
'The beginning of life on earth? The first division of cells?' Cartwright seemed lost in his reverie, of the things he could see, the places he could go. All his now for the taking.
Sal suddenly felt the hairs on her forearms stand on end, and knew it was here – the time wave. A moment later the ceiling light dimmed and flickered and they all felt it, a moment of imbalance, the floor dropping away beneath their feet. The monitors over Maddy's shoulder all flickered and went dead. Laura cried in alarm and Edward gasped as the ceiling light flickered off, leaving them, for a moment, in complete darkness.
Then the monitors flickered back on and the ceiling light fizzed, blinked and bathed the archway in its cold blue glare once more.
Cartwright giggled joyously. 'Good God! That was it? Wasn't it?'
Maddy nodded slowly. 'Yeah... I think it was.' She looked at him accusingly. 'You should've been outside our field. You should have been out there with your people. This messes things up. This –'
'But I wasn't outside,' he said calmly. 'So why don't you just get over it?'
'You don't understand... you've been written out of the present. I've got no idea what that means to you or –'
'That suits me fine,' he smiled.
Sal noticed the blinking cursor was back on-screen and all of a sudden it occurred to her what Bob was desperately trying to tell Maddy.
'Maddy!' she cried, pointing at the monitors. 'You need to look!'
Maddy turned to glance over her shoulder. 'Oh no!' She turned back to Cartwright. 'GET OUT OF THERE!'
His wiry brow furrowed. 'Uh? What's up?'
'MOVE!' she screamed.
The displacement machine's hum changed in tone as stored-up energy prepared to be released.
'LOOK!' shouted Maddy, pointing to the ground at Cartwright's feet. He looked down, wondering what was so special about a chalk circle and, within, a small irregular section of the grubby concrete floor scooped out and...
'OH GOD, CARTWRIGHT, GET OUT!'
It happened in nanoseconds, the instant appearance of a sphere of energy around the old man. Most of him was inside, all but his left hand.
Sal thought she saw in that fleeting moment dark shapes swirling around him like demons or ghosts, a window on to some world that an uneducated person, a superstitious person, someone from the Dark Ages, might have called Hell.
Then he was swept away. Gone.
The sphere pulsed and shimmered, and now she could see what appeared to be an undulating Texas-blue sky, and an arid and drab landscape... and the wavering outline of a shape stepping through. Liam staggered into view with a distinct look of nausea on his face, and a moment later the sphere of supercharged tachyon particles vanished with a soft pop of rushing air.
'Jeez, that was an odd one,' he said queasily, bending over, nauseous and heaving.
'Liam!' yelped Maddy. 'Oh my God... I thought you were going to get all mushed up with Cartwright! I...'
He raised a hand to hush her. 'Just a second, just a second... I'm gonna –'
He threw up on the floor and on to the still-twitching hand Cartwright had left behind.
Sal rushed over to him. 'Liam? You OK?'
He wiped his mouth and looked up at her with his bloodshot eye. 'I... I just... I'm all right now.' He straightened up and looked down in disgust at the hand and the acrid-smelling puddle at his feet. 'That wasn't like I'm used to. That one felt really odd, so it did.'
Maddy shook her head. 'I'm not sure what happened. Cartwright was standing in the circle. I forgot the countdown was due.' There were tears in her eyes, running down her cheeks. 'Oh God, Liam, I thought you were going to end up a twisted mess with him and...'
'Well...' Liam rubbed his mouth dry and grinned. 'I'm all right now, aren't I?' He spread his hands and looked down at himself. 'Or have I got an extra arm or something stuck on the back of me head?'
She nodded, wiped her eyes and laughed. 'No... no, you're just fine as you are.'
'Did it work?' asked Liam. 'Has anyone looked outside?'
'I think a time wave came,' said Laura, looking at Sal for confirmation.
'That's right.' Sal nodded. 'I'll go see.'
She turned back to the entrance, hit the button and the shutter slowly began to crank up. They gathered around the rising corrugated shutter and as it lurched to a halt they stepped outside into the dark night.
Manhattan glistened brightly across the Hudson, a towering wedding cake of lights. A commuter train rumbled overhead along the Williamsburg Bridge, and the evening was filled with the soothing white noise of far-off traffic and the echoing wail of a police siren.
'Normal New York,' said Liam. He puffed out a weary sigh. 'That was a bleedin' mess and a half we got out of, so it was.'
Sal reached out and hugged him tightly, embarrassed by the tears rolling down her cheeks. She squeezed him in a self-conscious way, just like anyone might a big brother, and then let him go.
'But here we are again,' she whispered.
They watched New York in silence, each of them lost in their own thoughts for a long while.
Maddy stirred. 'I better go and sort out the return window for the support –' she corrected herself – 'for Becks.' She turned and headed back inside.
The rest of them savoured the evening panorama, watching beads of car headlights edging forward along FDR Drive across the river, and a ferry cutting the mirrored reflection of Manhattan with its wake. Finally, it was Edward who stated the obvious as-yet-unfinished business.
'Me and Laura, we got to go back, don't we? To get things back to the way they were?'
'Yes,' Liam nodded. 'But I don't suppose it has to be tonight.'
'Good,' whispered Laura, 'I'm not feeling so good.'
'We've got some beds back inside,' said Sal. She looked at the girl and the Chinese boy. Both looked pale and ill, their faces smudged with a fortnight's worth of grime. And Liam... She realized he looked disconcertingly old and young at the same time with that streak of white hair at his temple.
'I'll go make some coffee,' she said.
# CHAPTER 79
# 65 million years BC, jungle
Becks watched the pyre of logs and branches burn. Amid curling tongues of flame she could just about make out the outline of the several dozen bodies she'd stacked on top. The log bridge was gone now, its counterweight device dismantled like their windmill and tossed on the fire as kindling. The palisade, the lean-tos, all gone as well. The assorted rucksacks, baseball caps, jackets, mobile phones that had flown back into the past, all of them tossed on the fire.
By morning those things would be nothing more than soot or contorted puddles of plastic that would eventually break down over tens of thousands of years into minute untraceable contaminants.
Her computer mind took a moment to make a detailed audit of all the other items of forensic evidence that marked their two-week stay here. The human bodies she'd been unable to retrieve: Franklyn, Ranjit and Kelly. Of those, only Franklyn had died in a location that would one day yield fossils, and even then it was statistically unlikely that his body was going to be preserved in a way that would produce anything. A corpse needed to be almost immediately covered by a layer of sediment to stand a chance of that. Those three bodies, wherever they lay, were exposed to the elements, to scavengers.
Bullets and casings littered the clearing. But they too would soon become unidentifiable nuggets of rust in this humid jungle. Perhaps, a hundred years from now, no more than stains of oxidized soil on the jungle floor.
She was satisfied that the sheer weight of time and natural processes would wipe their presence clean. There was always the remote possibility that a footprint or the unnatural scar of an axe blade on a tree trunk might just, somehow, become an immortalized impression on a fragment of rock. But the probability factors she crunched yielded an acceptable contamination risk.
Her partially healed stomach wound had ripped open as she'd laboured on the funeral pyre, but a dark plug of congealing scab prevented any further valuable blood leaking out of her. The dressing on her arm had also unwound earlier, revealing red-raw muscle tissue and bone. A layer of skin over the top of that would have offered her damaged limb some protection – instead the fragile workings of her arm were now clogged with dirt and twigs and leaves and all manner of bugs.
An infection advisory flashed quietly in the background of her mind, along with several others that warned her that her biological combat chassis had suffered enough damage to warrant immediate medical attention. As she watched tongues of orange lash up into the Cretaceous night sky towards a moon a hat size too big, she detected the first precursor particles of the scheduled window and stepped towards the open ground where it was due to open.
She looked back one last time at the fire and picked out the dark twisted limbs of the hominid species amid the flames. For a moment she felt something she couldn't identify: sadness, was it? Guilt? All she knew was that it came from a part of her mind that didn't organize thoughts into mission priorities and strategic options.
A sphere of churning air suddenly winked into existence in front of her and calmly, impassively, she stepped forward through sixty-five million years into a dimly lit brick archway.
The first face her eyes registered through the shimmering was Liam O'Connor's. He smiled tiredly and she momentarily wondered if his mind was flashing the human equivalent set of damage advisory warnings.
'Welcome home, Becks,' he said softly and then, without any warning, he clasped his arms around her. 'We did it!' he muttered into her ear.
She processed the curious gesture and her silicon swiftly came back with the recommendation that returning the demonstration of affection would be an acceptably appropriate response. Her good arm closed around his narrow shoulders.
'Affirmative, Liam... we did it.'
# CHAPTER 80
# 2001, New York
Monday (time cycle 50)
They stayed for a few days, Edward and Laura. Maddy said they were probably suffering some sort of radiation sickness from the lab explosion and needed some rest and recuperation. It was nice to have some new faces around here for a while, anyway. But Maddy said they had to go. She was right, of course. They had things to do, lives to go and lead.
But not long lives... not Edward, anyway.
I read his file on our computer. This is so sad. He will write his great maths paper in 2029 that will change the world, and he'll be just twenty-two when he does that. But then he'll be dead from cancer before his twenty-seventh birthday.
Cancer at twenty-seven?
That seems so unfair. Twenty-seven years isn't a life. It's just a taster of life, isn't it? I know I couldn't have told him that and, even if I could, would it have been fair to tell him? Would anyone want to know the exact day they were going to die? I know I wouldn't.
We were going to send them back to 2015; that was the original plan. But Maddy figured that wasn't going to work: they've both seen too much; they both know too much. Maybe that's not so important for the girl Laura. Maybe her life isn't ever going to affect the world that much. But Chan... he's everything the future's going to be. It all kind of starts with what he's going to one day write in a paper.
So what did we do? We left them outside when the field reset. We watched with the shutter open. We watched time come and take them away. Reality just erased them, like someone deleting files off a computer. Maddy says she's pretty sure that's going to make things all right again. Reality will bring them back. They'll be born once more, like all the other kids who died; they'll be born... be babies, toddlers, kids, teenagers a second time. Only this time they'll visit some energy lab in 2015 and then get to go home and tell their mums and dads what a totally boring day trip they had.
Well, at least that's what we're hoping.
And what about the person, whoever that was, who tried to kill Edward? I suppose we'll know whether history's been changed enough that he or she makes some different choices. If we get the same message again from the future... then, well, we'll have to deal with this all over again, won't we? Hopefully not.
We just have to wait and see if this fixes everything. Nothing's certain. Nothing's final.
'Everything's fluid'... that's Maddy's phrase. What does that really mean?
So, the female support unit, Becks (still trying to get used to that name), is still healing. Those creatures really messed her arm up by the look of it. Bob says the regrown skin will probably show a lot of scarring, and the muscles and tendons may never be fully functional again. Which led to an argument between Maddy and Liam.
Maddy suggested flushing the body and growing a new support unit, one of the big tough male ones. But Liam got angry. He said 'she deserves better'.
I don't know what I think. After all, they're just organic robots, aren't they? And whatever knowledge her AI picked up would be saved, right?
But Liam says there's more to them than just the computer... there's something else in there, something human-like in their heads. So maybe he's right. It does seem unfair to do that to her. After all, it seems she did really well.
Anyway, she's got a name... I mean, how can you just flush something away that's got, like, a name? It's wrong, isn't it?
Seems like the argument's all settled now, though. Looks like we're keeping her but also growing another Bob. Maddy said there seemed to be nothing in the 'how to' manual that says we can't have two support units.
So why not?
# CHAPTER 81
# 2001, New York
The old man was sitting on the park bench and throwing nuggets of dough from the crusty end of a hot-dog bun to a strutting pack of impatient pigeons.
'I knew I'd find you here,' said Maddy.
He looked up at her and smiled a greeting. She closed her eyes and turned her face up towards the clear blue September sky and for a moment savoured the warmth of the sun on her pallid cheeks.
'Unobscured sun and a good hot dog... that's what you said,' she added, 'and where else in Manhattan's forest of skyscrapers are you going to get that?'
Foster laughed drily. 'Clever girl.'
She flopped down on the park bench next to him. 'We've really missed you. I've missed you.'
'It's only been a few hours,' he said, tossing another doughy nugget out among the birds.
'What? It's been months –'
'Yes, but for me,' he said, 'just a few hours.' He looked at her. 'Remember, I'm out of the loop now. I'm out of the time bubble. I said goodbye to you on a Monday morning.' He looked down at his watch. 'And now it's nearly one o'clock on the very same Monday.'
She shook her head. 'Yes, of course. Stupid of me. I knew that.'
They sat in silence for a while and watched a toddler on reins attempt to scare away the pigeons by stamping her little feet. The birds merely gave her a wide berth as she ambled through and then returned, to hungrily resume pecking at the crumbs of bread on the ground in her wake.
'You hinted you'd be here, didn't you? When we parted?'
Foster nodded. 'I suppose I felt a little guilty leaving you so soon.' He puffed out his sallow cheeks. 'But I'm dying, Maddy. I won't last very much longer.'
'The tachyon corruption?'
'Yes. It plays merry havoc at a genetic level. It's like a computer virus, rewriting lines of code with gibberish. Out here,' he sighed, 'outside the time bubble, I might get a little longer to live. I might get a week or two more. Maybe a month if I'm lucky. That would be nice.'
She thought about that for a moment. 'But... you'll always be...?'
'That's right, Madelaine. From your point of view, I'll always be found here in Central Park, at twelve fifty-two a.m. on Monday the tenth of September. Like all these other people,' he said, gesturing at the busy park, the queue of people standing beside the hot-dog vendor across the grass, 'like them, I've become part of the furniture of here and now... part of the wallpaper. That's the other reason why I left.'
She frowned, not getting that.
'If I'd stayed with you and the others... I'd be long gone by now. This way, I can still help you. Someone to talk to.'
'Ah.' She nodded.
'But each time you come and find me, Madelaine, remember, each time you come and find me... it'll be the first time for me. Do you see what I mean?'
Of course it would. She realized, for the old man, Monday had been a coffee and a bagel and a goodbye. And now, three hours later, a momentary reunion in Central Park. Each time the field office reset itself, any conversation he had with her... never happened. For Foster there'd be no memory of it.
He laughed. 'It'll be like visiting some senile old fogey in a madhouse. You'll have to get used to repeating yourself.'
She shared his chuckle. 'I had a boyfriend like that once. He never listened to me.'
He sniffed. 'You came here, I presume, because you need help?'
'Well, we did have a problem, but it's all fixed now, I think.'
He patted her arm. 'See? I knew you lot were ready.'
'Hardly. We scraped through this one, Foster. It was a close-run thing.'
She gave him the bare bones of their story. Foster shook his head. 'Dinosaur times?' he whispered. 'I... I never thought the machine could take us so far back.'
'You never did that?'
'No. Never that far. How's Liam?'
'Well, that's just it. I don't know how much damage that did to him. It's definitely done something to him, aged him in some ways. He has...' She looked at Foster, and for the first time, she noticed the rheumy whites of his eyes were faintly laced with the scars of old burst blood vessels. 'Like you, haemorrhaging. And a streak of white hair. Who knows what's been damaged inside him. I mean, that's just what I can see. Foster, how long can he take this kind of punishment? How long do you think he will live?'
He sucked in air through his teeth. 'Well, he's a tough old soul. I can tell you that. But, you see... it all depends on where and when he goes, Madelaine. Who knows how long he's got?'
That didn't help much.
'Do I tell him or not, Foster? You know, he's not blind. He's seen his bad eye, he's seen his hair. He jokes about it, but he's not stupid. He must know this isn't good for him.'
He shook his head. 'I know he'll cope. But whether you tell him has to be your call. You're the one in charge now. I can give you what advice I can, but command decisions are yours. That's how it is.' He tossed the last of his bun in among the birds. 'I can't run the field office from out here on a park bench. You're the boss now.'
'But what about the agency? Is there someone else I can talk to? Someone in charge?'
'I... I'm sorry, Madelaine. That's... that's off limits. You have to treat this like you're entirely on your own. Do you understand? You're on your own.'
She cursed. 'What sort of useless freakin' agency is this?'
He pursed his lips sympathetically. 'I'm afraid that's just how it is.'
She ground her teeth in silent frustration for a while, knowing there was nothing more Foster could offer her on the subject of Liam. In any case, there was a new pair of glasses she was due to pick up from the opticians. They'd promised her they'd be ready in a couple of hours and another day of squinting at monitors and getting a migraine for her troubles was something she could live without.
She stood up. 'I'd better go. Things to do.'
He stood up, slowly, achingly. Polite, like a true gentleman.
'You'll be here again?' asked Maddy. 'For sure? Every Monday at this time?'
'Of course,' he grinned. 'I do charge by the hour, though.'
She laughed then hugged him, awkward and faltering. 'Enjoy your day, Foster.'
'Oh, I have a fun-packed afternoon planned.'
She squeezed his arm. 'Take care. I'll drop by and see you again soon.' She turned to walk down the path leading to the south-west gate. But a thought suddenly occurred to her. She stopped, turned and saw him standing there among his pigeons, watching her go, almost as if he'd been expecting her to stop and turn.
'Foster? How can you be so sure Liam will cope? What if he works out he's dying? What's he gonna do? He might choose to leave us.'
'He'll do the right thing,' he replied. 'You'll always be able to rely on that... the right thing. He's a good lad.' He turned away and began to wade through a parting sea of ruffling grey feathers and curious beady eyes.
'Foster! How can you be so sure?'
He stopped in his tracks and looked back over his shoulder. 'How can I be so sure?'
She nodded. 'I mean, come on! Who the hell would be stupid enough to keep doing something they know's killing them? What makes you think you know him so well?'
'Oh, I know –' he cocked an eyebrow – 'because he's me.'
| {
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**James Edgecombe** lives with his wife, Yuko, and their two children, Rintaro and Hinako, on the edge of Dartmoor National Park in southwest Devon. Having lived and taught in Hokkaido, Japan, he now teaches at Tavistock College, while also pursuing his PhD in creative writing at Plymouth University, where he is assistant editor of Short Fiction: the Visual Literary Journal. The tension between the visual and written arts has long fascinated him.
The Art of Kozu is a stunningly well-controlled piece of writing. Startlingly ambitious in its geographic and temporal range and in its subject matter, the writing makes remarkable use of voice and deployment of detail.
This work deals with art, death, aging, beauty, race, war and memory – and it's a testament to the skill of its writer that after finishing it, I immediately read it again.
The novella was absolutely a stand-out piece, memorable, difficult, haunting and intelligent – never underestimating the reader and demonstrating with absolute clarity that a shorter work can have the thematic and emotional complexity of a full length novel.
_Jenn Ashworth_
Chair of the Judging Panel
# THE ART OF KOZU
## James Edgecombe
First published in Great Britain
and the United States of America in 2014
Sandstone Press Ltd
PO Box 5725
One High Street
Dingwall
Ross-shire
IV15 9WJ
Scotland.
_www.sandstonepress.com_
All rights reserved.
No part of this publication may be reproduced, stored or transmitted in any form without the express written permission of the publisher.
Copyright © James Edgecombe 2014
The moral right of James Edgecombe to be recognised as the author of this work has been asserted in accordance with the Copyright, Design and Patent Act, 1988.
Editor: Robert Davidson
The Art of Kozu is the winner of the inaugural MMU Novella Award, a partnership between Manchester Metropolitan University's Cheshire Campus, Sandstone Press and Time to Read, a forum of 22 library authorities in the North West of England.
The publisher acknowledges support from Creative Scotland towards publication of this volume.
ISBN: 978-1-910124-00-0
ISBNe: 978-1-910124-01-7
Cover design by Mark Ecob
Ebook by Iolaire Typesetting, Newtonmore
My thanks to Anthony Caleshu, Aya Louise McDonald, Gerard Donovan, Tom Vowler, Tom D'Evelyn, Madeleine Findlay; my mother and father, Carol and Colin Edgecombe; my children, Rintaro and Hinako, and, above all, Yuko Edgecombe.
_To my children._
## Contents
Preface
PART I – SELLING YUMIKO
PART II – BOY WITH NO BIG TOE
'Messrs. O'Brien & Sons:
Gentlemen . . . At present and for some time past I see no reason why I should paint any pictures.
P.S. I will paint for money at any time. Any subject, any size.'
Winslow Homer (1836–1910)
## YUICHIRO KOZU (1878–1953)
A RETROSPECTIVE
Born in 1878, the first son of military surgeon Roan Kozu (1855–1919), Yuichiro Kozu grew up in the port city of Hakodate, on the southern tip of the Kameda Peninsula, Hokkaido, Japan's great island-wilderness and one of the country's first international ports.{*} The city, however, was fortified; the site of the last stand of the Tokugawan rebels during the Boshin War (1868-1869) and an important outpost built by an empire ever weary of its neighbour, Russia. It is little wonder then, bearing these facts in mind, that Hakodate significantly influenced Kozu's development as an artist: it symbolised for him what it meant to be 'Japanese on the edge of the world,' to belong to a nation looking outward, if guardedly so.
{*} The other ports were Yokohama (Honshu) and Nagasaki (Kyushu), which were opened up to trade with the West, after Commodore Perry forced the Tokugawa Shogunate to sign the Kanagawa Treaty in 1854, thus ending Sakoku, the Age of Isolation.
In 1906, he went to Paris. There, he refused to attend any of the 'anesthetising academies' crowded with his contemporaries, often quoting Monet's instructions to Renoir, Sisley and Bazille: 'We must leave this studio and our teacher. The air is unwholesome. Where is the sincerity?' Having travelled half-way around the world, Kozu looked homeward, to the Japanese genre of the bijinga, those portraits of beautiful Japanese women that made him so famous in the 1920s (at the time he even outsold Picasso).
Kozu showed ambivalence towards the Japanese art world, staunchly dismissing a number of his countrymen as omu, or parrots. To him, his contemporaries seemed hell-bent on copying the methods and innovations of the west, without first allowing foreign ideas to percolate through and be absorbed by the Japanese sensibility. If a Japanese artist were to produce meaningful works, he said, they first had to plumb the depths of western oil paints, that gap between their realism and the uniqueness of the Japanese body. For Kozu, the artist's ultimate goal was clear: to illuminate the Yamato spirit.
After the declaration of 'Total War' against China in 1937, and the reorganisation of the Japanese government's official salons, Kozu became a war artist for the Imperial Army. For this reason his reputation suffered in the post-war period.
Only recently has academic interest in Kozu's paintings revived. Such tentative explorations have borne interesting fruit. Prominent critic, Daichi Ando has asked that we, 'look past the cruelty depicted in Kozu's war art, to dig deep into the plight of those civilians trapped on the outlying islands of the empire, or the charred remains of our troops left on the field of battle in Mongolia, and to see the horror, made clear through Kozu's canvases, for what it is: a lament.'{*} The artist's sympathy and pity for those individuals he depicted is never in doubt.
{*} Sadly, few of these paintings exist today: most were destroyed in the firebombing of Tokyo, in March 1945.
Kozu died in Nice, France, in 1953.
Kasumi Takayanagi, 2014
_Director of the Shin Midori Gallery, Ginza, Tokyo_
## PART I
SELLING YUMIKO
The Ginza, Tokyo, 1927
Ryunosuke Akutagawa, a friend of mine, and great writer according to his obituaries, committed suicide six months ago. I didn't know him as a master of words – he was always so quiet. I never read anything he wrote. I only mention him because he hated any painting by Kozu. Often, we would argue over Kozu's virtues as a human being, his vices as an artist of the real, for hours in the backroom after I had shut up for the night.
Since his early twenties, Akutagawa would come to my gallery to gaze at the oils on display. I saw a melancholy in him even then, when he was still a student. I thought that showing him the canvases I brought back from Europe, the monstrosities I bought straight from their Parisian artists, would lighten his mood. 'See how ugly they are?' I used to say to him, 'you wouldn't find anything as detestable as these on sale in the Mitsukoshi Department Store!' I told him the reason I spent so much money on canvases I didn't like, all portraits of some type or the other, was so that they could never be exhibited in Europe as visions of Japanese beauty.
A week before he murdered himself, Akutagawa came by the gallery and said, 'I need to see the Kozu portrait!' He claimed to have finally understood his lifelong melancholy that morning, after a night wandering around Honjo, where he saw a horse tethered to a cart beneath an iron bridge. The thick purple patches of shadow in the structure's metalwork, around its rivets, across the horse's back, around the cloud of steam puffed into the air by the beast, its great form little more than a silhouette in the morning twilight, struck him with the force of déjà vu. He knew the street before him, the bridge over his head, had walked that same route as a child. But that morning, it was fresh to his eyes, like a painting by one of his favourites, Van Gogh.
He told me he needed to know if the Kozu portrait could reproduce in him that same sadness. To him the Kozu was a step backward from the avant-garde, rendered by an artist who did not understand the expressive power of colour. To such an artist as Kozu, he would say, the muddy vulgarity of detail was prized above all else.
The reason I mention this is because your wife has shown a keen interest in the painting to which I am referring. That is why I must ask you whether she wants this painting for the right reasons. It has a history – a story I will tell you, just as I told my writer friend that morning when he came to the gallery, faint from the summer heat.
But it requires us to sit. At least for a little while. Here in this corner, where we can enjoy the morning light.
The cat in the foreground, its fur exquisitely rendered in sumi ink, stroke by stroke, hair by hair, may offer a brilliant contrast to the oils of the female figure, but it is only an adornment. Yuichiro Kozu was admittedly good at painting cats. But when it came to women, he was a genius. If I thought someone was to take ownership of this piece simply because they thought the cat charming, I would fear the ghost of Akutagawa for the rest of my days. Be assured, Yuichiro Kozu only included the beast to demonstrate his skill at rendering the texture of its fur. With the woman's skin as clear as it is, pure like porcelain, her pubic hair covered by her hand, there was no other chance to bring to life the rough tactility of common objects. Even her hair is as smooth as the ribbon that fastens her braid.
Maybe the cat is as good a place to start as any. He was called Hugo. Yuichiro bought him in anticipation of his brother's arrival in Paris. Jun Kozu hated cats. It was the summer of 1911, just before the theft of the Mona Lisa from the Louvre that August. Paris was already hot, I remember that much.
Jun's hatred of cats can partially explain Yuichiro's interest in portraiture from a young age. Let suffice, Jun had demonstrated to his older brother the benefits of shasei, of sketching from life, when they were little more than children. Jun was the hands on type, while Yuichiro, at first at least, was the visionary. Jun, long before he left Hakodate for medical school in Tokyo, used to perform his own anatomical studies on the neighbourhood strays. Yuichiro would join him, sketching the dissections, so that he came to see and understand the internal workings of pregnancy, death, how bones were held in place, how their nuances dictated the topography of what lay above, the musculature of the body, the contours of the skin. Just like the legend of the Heian artist Yoshide, who could paint people with lifelike precision, as long as he had seen them with his own eyes, Yuichiro could paint any cat, no matter how contorted its pose.
His ability to paint cats was a skill he put to good use in Paris. That was how he met the girl in the painting, his model, Yumiko, the young wife of one of his rivals. You see, Yuichiro loved women. When searching out new lovers on the Metro, he would drop his newspaper on the lap of some pretty girl and, as she picked it up, he would say, 'What a coincidence, I see you read L'Anarchie, too! My name is Yuichiro Kozu. I paint cats.'
According to Yuichiro, the sight of Yumiko's face amongst all those Parisians on the Line 6 train was like spotting a wild cherry in blossom on a mountainside. The symbolism of the radical newspaper in her hands must have meant little to her, caused no shock, or excitement because when he asked her what she was doing on the train, she replied that she liked to travel around Paris by Metro. She didn't care if her husband owned an automobile. Yuichiro explained her love of trains like this: although she was raised in view of a great naval base in Tokyo, the Metro instilled within her such a sense of modernity that she felt compelled to use it on her daily trips north from Montparnasse to the Louvre, the more circuitous route the better.
Yuichiro asked her to model for him then and there, before all those people in the carriage. He enjoyed talking about such things, whether business or personal, in front of the foreigners in that brazen way, enjoying the freedom that comes when one knows his language is a room without windows. According to Yuichiro, she agreed without hesitation.
A month later, Yumiko laid herself over the Line 6 track at the Passy Station, the very same line she had been riding north on when Yuichiro introduced himself. I can remember the day after that incident. I was eating breakfast with both Yuichiro and Jun outside the Café Houdini in Montparnasse.
'She leaned over the track, as the train moved off,' Yuichiro said.
It seemed odd that the couple drinking coffee next to us could smile and hold hands as Yuichiro read the news aloud, translating the story straight from the paper into Japanese since Jun did not speak French.
'Witnesses on the platform thought she was praying . . . The train made it half way across the Pont du Passy, before it stopped.'
He gave the paper to me so I could read the front page for myself, as if by my reading the words, the tragedy became real. I noticed immediately that he kept the fine details to himself, like how the flanges of the train's wheels had cut through Yumiko's shoulders like a guillotine. Her arms had dropped down beside the track, detached.
Yuichiro took a slither of tartine from the plate in the middle of our table. The red jam gleamed with what light ricocheted off the limestone walls rising above us. The café, located down a lane off the Carrefour Alésia, had only four tables outside its window. While Yuichiro preferred the grander cafés of the boulevards, the Café Rotonda, the Café Flora, Jun preferred to eat in such out of the way places. He said he liked the cooler air.
Jun listened to the news, chewing his fecelle with slow rotations of his jaw. He ate in silence most days, his eyes half shut as if concentrating on some tune in his head. Yuichiro was a different man altogether. Whenever eating breakfast at the Houdini, he would always look up at the limestone walls, to the strip of blue sky above. The spire of the Church Saint-Pierre-de-Montrouge burned white with the glare of the morning sun just beyond the lane's entrance. The August heat would always creep down the walls, until the lane became stifling with a heat that lasted well into the night.
'I wonder if there will be an investigation?' Yuichiro said.
It is not a well-known fact that both Kozu brothers painted. What fewer know is that of the two brothers, Jun was the better technician. When he wasn't at the small hospital his father had set up for him in Hakodate, after he had left military service, Jun would spend hours bent over a desk, sharpening pencils with an old fruit knife and lining them up in order of use. Jun had been a surgeon for the Japanese Red Cross during the campaign against the Russians, but the quiet of the small practice was better suited to his temperament, or so he said. Six years had passed since he cut and sowed the meat of soldiers, who cried under his knife, more with the shame of living, of not falling into the honourable silence of the battlefield, than with the pain. As a young man, he had wanted to study cartography at the Tokyo Technical School of Art, but had turned to medicine, after the school was forced to close by the traditionalist revival of the '90s. If it wasn't for the summons Yuichiro had sent him from Paris, Jun would have stayed put, listening to the wheezing lungs of the elderly and tending the broken bones of children.
What Yuichiro lacked in precision, he made up for in emotion, a trait that caused the Kozu family no end of embarrassment. Three years Jun's senior, Yuichiro had fled Hakodate to live and paint in Paris, filled with ambition – the dream – to become a great painter – the greatest Japanese painter in Europe. That he had fled his father's anger, after an incident with a fisherman's daughter, was not talked about in the Kozu family, though Jun later told me the story with relish. As it was, Yuichiro's responsibilities as eldest son meant little to him. Paris, city of art, philosophy, electric lights, was all that mattered.
But Yuichiro was well aware of his brother's prowess and so, the week before Jun arrived in Paris, Yuichiro unleashed a fresh rumour to infest the cafés and ateliers of Montparnasse. The word on the street was that a new Japanese face was to appear in the quarter. Not the face of a quiet mind with blank, nihilistic eyes, like so many of the other young Japanese artists in their dark suits, scribbling away in some academie or other, their fop teachers breeding into them an aesthetic the critics would then use to dismiss them as academicians. Such was their lot. It was no wonder I saw so many of them during the week, silent, brooding, pacing the corridors of the Louvre, instead of walking the streets outside. No. This new face would be crisscrossed with scars. A man, so the rumour went, who believed in the Anarchist maxim of 'propaganda of action' and wanted to extend its fingers over the throat of Art herself – Yuichiro had a penchant for hyperbole. Before Jun even stepped foot onto the limestone cobbles of the artists' quarter, Yuichiro had transformed the young doctor into a legend, a name debated in the cafés, at the edge of wine glasses.
Though I only met Yumiko in the flesh a couple of times, I got to know her form intimately. You see, during the month before Jun's arrival Yuichiro introduced me to his studies of the girl. It is true to say, I found her thinness repulsive.
Yuichiro had been seeing Yumiko behind her husband's back for about three weeks when I met him for breakfast at the Café Houdini. This was our Monday routine, as Mondays were the only day of a week the Louvre closed its doors to the public, freeing Yuichiro from his studies of the great masters, if only for a day. Yuichiro ordered coffee for the two of us. I drank the black liquid as best I could. I would have drowned the bitter taste with milk, just as Yuichiro did, but that would have upset my stomach. Though I had lived in Paris for almost a year by that time and had successfully trained myself to drink red wine, even to enjoy its taste, coffee always gave me a tremendous headache.
'I have brought you my sketches of Yumiko,' Yuichiro said and proceeded to lay down several sheets of cartridge paper on the table. 'What do you think?' I felt honoured to have the opportunity to offer my advice on a work in progress, but before I could offer my humble opinion, he continued, 'This girl, she will launch my name across Paris. "Kozu", they will call, my name echoing off the walls of the Salon, like the report of a gun!'
It seems strange to me now that I can sit here and talk to you of a time when any work by Kozu was less of interest for what would become his signature style, than his ability to ape the Japanese masters before him. You probably find such a time even more inconceivable than I, but, you can be assured, before the portrait your wife has shown such a keen interest towards was exhibited at the Salon Autumne, Yuichiro Kozu was little more than a copyist, albeit a copyist who managed to keep us living in fine apartments.
His arrival in Paris, five years before mine, could not have been more fortuitous. Japanese prints were still in vogue and many artists and intellectuals collected them by the hundred. With his ability to study and copy whatever he laid his eyes on, Yuichiro cashed in on this trend, this Japonisme, making a quick fortune by reproducing selected street scenes by Hokusai, famous landscapes by Hiroshige and the beautiful women of Utamaro. All of which he claimed were original. That was how I first made his acquaintance. With Yuichiro's deft eye for detail, a week or two of Parisian sunlight to fade the fresh inks and my contacts, we were set for success. He even made up some pieces from scratch, laying down just a few lines of ink and selling them off as rare sketches made by some great master on their deathbed.
But I digress.
I looked at those sketches Yuichiro had handed me, finished my beverage and felt the first bangs of an approaching headache.
'Kozu-san,' I said to him, 'they are not quite what I would have expected.'
'What do you mean?' His hands closed into fists. 'Isn't she the most interesting subject you've seen in years? And she's Japanese to boot!'
'Is it not that she is uninteresting – she does have a most peculiar body, but . . .'
I spoke the truth. Yuichiro had skilfully rendered the body of a woman in thick swipes of charcoal, but this woman looked close to death. The very sight of her skeletal figure brought to mind those artists who in the late days of the Heian period would sketch the bodies of peasants dumped on the sides of roads.
I said to Yuichiro, 'She is so painfully thin, wherever did you find her?' and he told me about the Metro, of how he thought I would recognize her. 'She's Masahiro Saiki's wife,' he said.
Of course I knew of Saiki. At the time he was the only Japanese artist the French critics approved of. That was reason enough for the conservatives back here to reject him; and well, I don't mean to be scandalous, but Masahiro Saiki's lifestyle has become the stuff of legend. The tales of his Russian mistresses are proof of that. From the elegance of his nudes, though, one would never have assumed he was bold and short, with the thick shoulders of a judo champion and the face of a poor boxer.
Yuichiro explained to me how she hadn't eaten properly for months, saying that the food in Europe didn't agree with her. 'It's too rich,' she would say, and true enough, I saw her force down a lunch once, only to become violently ill afterwards.
I took another look at the sketches, holding each image up to the sky, one by one, so as to illuminate Yuichiro's slashed lines from behind. The light around the café was growing stronger by the minute and with it, my headache intensified. I tried to relax, to enjoy the burnt earth scent of their charcoal, but something nagged me about Yuichiro's composition. Before I knew it, I had sullied my jacket with blackened fingers.
I asked whether she had a lovely face, for it was unclear from the sketches.
'It's hard to tell,' Yuichiro replied. 'She has lovely hair. She wears it down – like those renegade girls one reads about in newspapers sent from home.'
I asked myself: where was the so-called cherry blossom he had boasted of? Maybe I should I have kept my objections to myself – I have spent much time since those days, wondering whether I should have kept true to my upbringing and not appraised Yuichiro's effort so directly. As it was, his talk of the girl's hair clarified my doubts.
Now, I beg your pardon, sir, but I take it that an esteemed and knowledgeable gentleman like your good self is familiar with the work of Kawanabe Kyosai? I am sure you'll agree that he was the last of the great Japanese print artists – for no other figure, with the decline of that delicate form, has risen to match the skills of such a man. This was especially so when it came to his pictures of yurei. Ghosts. My own nurse told me ghost stories when I was a child, so as to stop me leaving my futon on hot summer nights. Her favourite story was of a nameless yurei Kyosai had rendered, an image she had seen in my father's study. I can still hear her nasal way of speaking (so far removed from the soft grace of my mother's), as she warned me of that ghost of ghosts, of how it wandered the night, the hair of a severed head clenched between its teeth.
Though I digress, and excuse my impropriety, I am privileged to say that my father knew Kyosai in person. Knew him well. And once, while I helped him dry his brushes, the cicadas' call a low hum from the twilight outside, my father told me how Kyosai had confided in him a secret – the reason for why his ghoulish scenes chilled the public so. The great master told my father a story from his youth, of how he had found a severed head on a riverbank. With the detachment of undiscovered genius – that was how my father put it – the nine-year-old Kyosai took the grim curio home. Of course, his parents were outraged and made him cast it into the river. But before he did so, he had the wherewithal to draw that unique trophy from every angle.
That blue-sky morning, sat at the Café Houdini, I told Yuichiro the same anecdote. His reaction was curious. He looked puzzled at first, until I pointed out that Yumiko's emaciated shoulder blades, the way her spine cleaved her ribs in two, for all the sketches of Yumiko were from behind, reminded me of Kyosai's image.
I regretted my words instantly. Yuichiro ordered another cup of coffee, drank it in silence, brooding on my words. The pain behind my right eye increased with every wordless moment that passed between us. I should have kept my thoughts to myself.
Dishonesty aside – for Yuichiro was not one to bother himself with ethics – try to imagine how a man with such raw talent could manage in a world where it seemed every fresh breeze, rising off the Seine, bore within its vapour the germ of some great new idea, a new way of seeing. Fresh-faced youth gorged their appetites on Van Gogh, the brushwork of Cézanne, the personality of Picasso, while he knew himself a fraud. Compared to the rest of us, he was a rich man, yes, and a handsome man, but in his own eyes, Yuichiro Kozu was nothing more than a mimic, a glorified apprentice. And what was more, a Japanese apprentice at that.
I apologized and tried to extradite myself from my blundering. I said that, on second thought, I had been mistaken, that it was the dusting of charcoal across the paper that reminded me of Kyosai. The hazy effect it produced brought to mind that ghostly vestige of Kyosai's yurei because it reminded me of Asian light, murky and wet. It was not a Parisian light.
Yuichiro stared at me as I blathered, finally standing up when I started to repeat myself. 'You will meet her yourself,' he said.
I agreed, ashamed that I had caused him such vexation.
The next morning at eight, I arrived at Yuichiro's apartment on the corner of the rue de l'Alboni, where the Metro tracks glide out over the Seine. I expected him to show me through to the parlour, the spacious room, split in two by a set of finely wrought Japanese doors, the fretwork of which twisted and burst to the interlinking rhythms of cherry blossoms and their branches. Tatami-matting, too, covered the floor, so that in the summer heat, the room was filled with the green fragrance of home. That was where I joined him when we met with prospective clients, his lithe body hidden beneath a black kimono. He always looked smaller amongst those folds of black silk. As it was, he met me at the door, dressed in a grey pinstriped suit. He didn't stop and was halfway down the second flight of stairs before I caught him up.
I followed him outside and up the steps to the Passy Station. He instructed me to buy a first-class ticket and checked his watch. I eyed the mouth of the tunnel beyond the end of the platform. I used the line often to visit Yuichiro, but always got off at Passy. I never liked the idea of being shot into the tunnels beneath the Right Bank, like some virus injected into an artery.
A train pulled into the station and we boarded. As if entering the confines of a stage, Yuichiro stepped up to a woman sat next to the doors, her face covered by the brim of her hat. She looked to be sleeping. 'I am Yuichiro Kozu. I paint cats,' he said. The girl looked up. I remember that moment distinctly. The train passed into the tunnel and the lights flickered. Her face was at once Japanese and not. I don't know why, but her mouth, lips red and smiling in that instant of the lights' failure, brought to mind a poem by Basho: the one where the heron's shriek illuminates a flash of lightning.
Unaccustomed, as I was at the time, to speaking to women from my own culture, I bid the girl a good morning, hoping she would turn her face, those lips, towards me. She did not. Her energy, intense, as if connected to the currents that pulled the train through the underbelly of the French capital, was directed at Yuichiro. So this was Yumiko, I thought. Yuichiro sat down beside her, offering her a cigarette. I was left to stand. She lit the tobacco herself with practiced movements, took a drag and looked me up and down, a movement of the eyes I had never seen a Japanese woman do before, let alone do so with such vigour. 'Don't you work for the consulate?' she asked. I explained that I, like Yuichiro, was an artist. She scoffed.
Yuichiro interjected, 'My friend here is a famous man, you know, a working man. You've seen his pictures, Yumiko, of that I'm sure. You just don't know it.' Though his face was earnest, I knew Yuichiro was mocking me. You see, during my time in Europe, my only success came, not by exhibiting at the Salon, but from my commercial practices. My proficiency with a brush, as it was back then, along with a connection of my father's at the Japan Steamship Company, gained me a commission painting the images for that company's advertisements.
It is a shame that you have not been to Europe yourself sir, but I am sure you must have seen one of the advertisements I painted. Yuichiro hated such posters. He saw them as emblems of the academic style our countrymen were enslaved to. That was how I originally met him, when he declared to me, as I sat reading in a chair in the Jardin du Luxembourg that I should paint whores and sheep, whores and sheep only, he told me.
'Do you think,' I still remember him asking me, 'do you think Japanese women look like sheep? I think you do, what with those elongated eyes you always give them. Not one of your portraits has any expression in spite of the smile you paint onto their lips.' The spring sunshine was bright on the white gravel, the surface of the Fontaine de Medicis, and I found myself unable to disagree.
What I am trying to say, sir, is that Yuichiro believed my portraits to be momentous failures. Standing on that train, watching Yumiko puff on her cigarette, as she studied her own reflection in the window, I could understand why.
After we had passed out of Boissiere, Yuichiro moved to a seat across from Yumiko. 'This is how I want to paint you,' he said, 'here on the Metro. I'll call it Train and Chrysanthemums or something similar. You'll have chrysanthemums on your kimono, gold ones like the crest of the Emperor – yes – gold over white silk!'
Still smarting from his mocker, I told him that I hadn't figured him for a genre painter, at which Yuichiro shook his head. He would construct the carriage around Yumiko, he exclaimed, with the shadows creeping out from the black walls of the tunnels beyond the windows, falling across her neck, collar bone, the top of her sternum; she would be wearing only the outer layer of her kimono, its white silk resembling a funeral gown. Yumiko would glow – an ethereal energy to match the invisible powers that hurled the train underground.
The train pulled into Etoile. All three of us alighted. I was still unsure of where we were headed, until I followed Yuichiro and Yumiko, walking arm in arm like some Parisian couple, onto a Line 1 train. From there, I assumed we were making our way to the Louvre.
'I do not want to wear a white kimono,' Yumiko said once aboard. 'I do not want to wear anything at all. I want you to paint me as a nude.'
Well, you can imagine the flush that coloured my cheeks at such an outburst. And on the Metro of all places! I could have sworn the other passengers, those Frenchman in their collars, and neckties, the lady who sat close by, a peacock's feather in her hat, could understand what Yumiko had said. Only, they were too shocked too look in our direction. I was reminded of that train journey a few years later, when those upstart New Women, you remember the ones, caused a scandal by visiting Yoshiwara, the pleasure district, and drinking French liquor in its bars!
Yumiko must have noticed my discomfort because she then said to me in French, 'Why uncle, was it not because of women's flesh that you became a painter?'
An old man along from us chuckled at this perversion of Renoir's sacred proclamation. I decided there and then to get off at the next station, to escape this demon in woman's clothing – I would not play Benvolio to her Mercutio.
To inflict further embarrassment upon me, she carried on with her offensive, turning to Yuichiro and saying, 'I already have an idea on how I want you to paint me: there will be a system behind my pose – something more than just a vase of arranged flowers and an umbrella.'
She thought for a moment, sucking smoke into her lungs, before she continued with her manifesto, catching glimpses of herself in the window behind a spellbound Yuichiro, seeming to enjoy the shapes her words took as smoke, 'Consider my lines, my profile: the triangle of my legs as I hold them before me, hands on my knees, arms an inverted triangle.' She raised her chin. 'My eyes look upwards, as if at some distant horizon. Your idea of using the Metro is good, inspired even – I want to gaze up towards a carriage window, I want the viewer to ask, 'Does she gaze at that space between her own reflection and the world beyond the window, one haunting the other?''
At that point, before she could continue, the train came to halt at Concorde. I fled.
You would never think, would you sir, that this girl, hanging so serenely before us, could be the same girl who said such ignominious things? I try to remember what she looked like that day, but all I can remember is her smile – her rouge lips. You see, although it is my business to collect faces, to pass them on, so to speak, I have great difficulty recalling them, if they are not close at hand. That was one of my many failings as a young artist. I could not paint from memory, nor abstract the qualities of the many faces I had seen into some personal vision of the ideal. That, I guess, was why my women looked like sheep. After Yuichiro's criticisms, I spent hours in the Louvre, copying firsthand the single works of Valequez, Rubens, Rembrandt, which hung in the Salon Carré, outnumbered by their Italian competitors. But once I left those hallowed halls, to catch one of those motorized buses that lined up outside the Denon Gate, I could only recall the visages of murky ghosts.
I guess this is another reason for why – and I do not mean to be coy here – I am reticent to part with Kozu's portrait of Yumiko. To no longer have her face in the gallery, watching over me as I talk of other works, their artists and their models, rivalries and confederations, would be like seeing her far out at sea, drifting away. A particular feature of a face – a nose, chin, a smile – I can recall with ease. If you asked me to sketch out a likeness of the Mona Lisa, or more to the point Yuichiro Kozu himself, I would have to locate a magazine or a textbook from which to copy. That is, apart from his eyes. Those I could present you within minutes, as if I had plucked them from his head moments before you walked through my door and made a study of them. It took Kozu's portrait and, more specifically, Jun's arrival in August for me to realize how hard Yuichiro's eyes could be.
He wore glasses you see, Yuichiro, round-rimmed spectacles that, with his moustache, and height (made greater by the bowler hat he wore out) gave him a rather European look. An Occidental profile I think he enjoyed. He rarely took them off, blaming his poor eyesight on the nights spent as a youth sketching and painting, the only time he could practise without his father becoming suspicious. I know it is rude to speak so openly of a son neglecting his father, but you must understand: Paris was intoxicating. Its scent was in our noses, our hair, before the steamer docked at Le Havre or Marseille, even before boarding the train to Yokohama. It was borne in the skies of the Van Goghs or Matisses we gazed at in bookstores, their clouds smelling of turpentine.
It is strange how one remembers one thing and forgets another. Like those moments one knows, deep in the heart, will be a fulcrum in our lives. Proust knew it – would spend hours reflecting on an imperfect glance of a woman who flashed by his cab. I knew from Jun Kozu's opening remark to me the night I met him, he would change my life. 'I have my nose,' was what he said, looking up from a cup of tea as white as the tie of his evening dress.
But forgive me. I was talking about Yuichiro's eyes and now, here, Jun's nose. When really, at this point, I'm more interested in recalling the night in which Yuichiro introduced me to Jun, himself. Suffice, it was the night I first met Jun that illuminated me to how cold Yuichiro's stare could be. How penetrating. You'll understand why I've jumped ahead presently, when I tell you I met Dr. Junosuke Kozu on a Tuesday evening few Parisians will ever forget! For reasons lost to me now, I did not go to the Louvre that day. What I remember is the call of the newspaper vendors, announcing the release of the evening editions. The city was changed in an instant: The Mona Lisa, La Jonconde herself, was gone. Stolen.
I was amazed. Not three days before, I had walked past that girl, as I had done countless times before, collecting my easel from the warden who manned the store cupboard in the Salon Carré and joined the other copyists studying the paintings therein. Yuichiro would often join me there, if he was not preparing for a sale. He would never take up a brush though, choosing to sit there instead, staring at the pictures, making his own mental etchings.
Though I had never painted De Vinci's lady myself, I never dreamed that she would be lost. The sense of shock was palpable on the streets: each man that passed me seemed lost in his own newspaper. The cafés were abuzz with conjecture.
I hurried to the Houdini, to the gossip and theories of the regulars.
It was a beautiful evening, what I have since come to call a silver dusk. All those who have lived in Paris know such evenings, when the sun is low, cutting underneath the ceiling of summer storm clouds; light rebounds, down off the cumulus grey, down into the city, off its limestone and up again. The effect is magical. Every surface beyond the orange lamps of the café awning, is touched by mercury. The air has a thickness, like coal smoke, like that which drifts up from the tugboats on the Seine, the little ones whose funnels collapse down at the bridges. One would hope for rain at such moments. Not because the evening air was unpleasant, but because a thunderous downpour would leave the streets, the cobles, the trees, the fruit carved into the facades of buildings, shining. Such a café night, with the heavens fleshly opened and purple above, is the essence of Van Gogh's Café under Gaslight. A night without any black.
Such was the night of the theft and my first encounter with Jun. (I told you I would get here). The wine was warm on my lips, when I noticed Yuichiro with a shorter man outside the café's window. Both were dressed in formal evening wear. From the stranger's rigid gait and black hair, I instantly knew him to be Japanese. I had no idea I was looking at the so-called anarchist painter of Montparnasse. I took my glass and walked out into the warm air to join them.
'We were just discussing my painting of Madame Saiki,' Yuichiro said by way of a greeting. I liked the way he did that in front of other Japanese men, foregoing formalities and talking to me like an artist of significance. Fournier, the Houdini's ancient waiter, brought me a chair and I joined the table. It was as I sat down that I looked directly at the stranger's face, a visage brutally scarred. Jun must have noticed a change in my demeanour, for I had only just sat down when he introduced himself so memorably, following up with, 'I am fortunate . . . more so than others,' and an explanation, punctuated by sips of tea, of how he had arrived in Paris the day before, after spending an entire week in Marseille. The voyage had not agreed with him.
Jun's face was not an 'etching hatched of white lines,' as Yuichiro had put it, but a single shard of shrapnel had sculpted his flesh in the most fascinating way. Yuichiro told the story. Jun sat in silence. Apparently, the Russians had gunned for the aid station where Jun laboured under Mt. Taipo-shan, wounding him while he tended the wounds of others. It was a wide incision, cutting from beside the bridge of his nose down into his mouth, parting his top lip. I do not mean to be grotesque, to linger on a mark of valour, but whenever I try to picture Jun, I see his mouth, curtain-lipped. His teeth. Little else. He never smiled in my presence and yet, there they were, his golden incisors, on display for all to see.
Yuichiro went on to tell me about how, earlier that evening, Jun and he had gone to watch a live demonstration of a machine that could pierce the flesh without the need of a wound. The image it presented to the stunned audience was the perfect copy of the bones that lay underneath.
Something about Yuichiro's words brought Jun back to life. 'Have you seen the portrait he speaks incessantly of?' he asked of me, his Japanese vernacular. I didn't know whether he felt the normal formalities unneeded in that foreign land, or that my station as an artist, in the midst of building a career, was beneath him.
Believing he was talking of the stolen De Vinci, I told Jun I had seen the Mona Lisa on many occasions.
He cut me off with, 'No, no, not that painting. I am talking about this portrait of a Japanese girl. It seems to have possessed him, he talks of it so often!'
I looked at the rim of my glass, said that I had not, though Yuichiro had shown me some of his charcoal studies for it. My exact words are lost to me, but I explained how I thought Yuichiro's choice of setting, the busy Metro carriage, was inspired. To gaze upon a naked Japanese beauty amongst the bustle of commuters, was the manifestation of the city's cosmopolitan allure. Yumiko would become a symbol of the body universal – that gift of the flesh erstwhile hidden beneath our decorations, the picturesque accessories of custom. I tried to make my voice as animated as possible, intense, without appearing vulgar.
Jun nodded, 'You should see it I think. Maybe someone else can tell my brother what a fool he is.'
I begged Jun's pardon, while Yuichiro ordered three brandies.
'His picture,' Jun continued, 'this so-called masterpiece. I'll admit the carriage is technically proficient, but the girl, that supposed Japanese girl? She is a monstrosity.'
'Always the academician,' Yuichiro said, turning his eyes, those cold, cold eyes, upon me. He had removed his glasses and sat there, leaning back, hands folded behind his head. The brandies arrived and Jun's tea was tidied away.
Yuichiro said, 'As I said before, you must consider the picture's balance. It is wonderful, with her back arched over her legs, her ribs cutting across the centre frame as vertical lines. Must I explain this every time? All lines rise upward; her tones are light, the colour of her skin pink, warm. She is not deathly white, as our tradition would have her. She is maybe ill, but she knows she is alive; skin and bones, yes, but consumed by life, her own thoughts, her reflection hanging over the city passing by outside. I've not given her an outline either: nothing holds her together, down; her halo merges with the carriage!'
'Pretty words,' Jun said. 'But words are the work of a Sunday painter. Not an artist.'
Yuichiro blew a cloud of smoke into the silver light of the lane. I watched it change colour as it rolled into the shadows and nothingness. 'Of course you would say that, when, it is the idea brother – and not its execution – that matters.'
I was stunned, thrilled. Never had I heard my own countrymen so animated, and in a public place, too. I couldn't help myself and blurted out, 'What is it about Saiki's wife that so offends your sensibilities, Kozu-sensei?'
'Her face. Her body I do not care for,' Jun began. 'But her face . . . it is a blasphemy. We sit here in a city mourning the loss of one girl's smile and my brother thinks he can replace it with one of his own.'
As though part of a play, at that moment a feminine voice addressed our table in French, 'My friend and I were wondering whether we could join you.'
It was Yumiko! And she was not alone. On her arm was a man with a scraggy beard that matched the colour of his tweed suit. I knew him to look at – he was an Italian artist, a sculptor, rumoured to store his shit under his bed. He reeked of garlic sausage.
Yumiko said something about the great theft and how Montparnasse was the place to be on such a night.
Without asking permission, the Italian sat down beside me and addressed Jun, 'You there, Jap, I know you.' He was drunk.
Yuichiro smiled, refusing, or so it looked, to acknowledge Yumiko. 'Monsieur, who could you possibly know here?'
'Him,' said the beast, pointing at Jun. 'You're that phantom Jap painter.'
Jun looked around the table, but it was left to me to translate the Italian's accusation. Wiping his hands with a napkin, Jun went to take his leave, but Yuichiro stopped him, saying, 'Let's see what this fellow has to say about my idea. What impeccable timing Yumiko.'
Jun took a second look at the girl. 'This is Yumiko?' he asked, 'I wouldn't have recognized her. Not having seen that monstrosity, at least.'
Yumiko bowed, her movements greased with insolence, 'Sensei.'
The Italian called over to Fournier, demanding he bring a fresh bottle of wine. He would drink with us tonight. Yuichiro went to introduce himself, but was cut off. The Italian knew who the print-seller from the rue du l'Alboni was. He had no interest in Japanese prints, nor any other wares that Yuichiro wished to proffer. What interested him was Jun, what such a man with a face so scarred had to say about the nature of painting beautiful faces.
Jun did not respond immediately. I can still picture him there, nursing his glass, studying Yumiko, the fading daylight flashing over his gold teeth.
The wine arrived. It rained.
'Well, sir,' Jun said at last, 'I believe that abstraction is tantamount to laziness. It is nothing new, the artwork of our nation is emptied of detail, is full of lies. Your great Leonardo knew that.'
I translated.
The Italian smiled and shook his mane, slapping Jun on the shoulder with a dirty hand. Jun studied the mark it left on the white silk of his scarf.
'That is not very revolutionary! Yumiko has told me all about you, Phantom. She told me many things, indeed. She said you would be here tonight,' he pointed to a small table beside the piano, the Houdini's only piece of substantial future other than its counter, 'we've been watching!'
'And what has she told you?' Yuichiro asked, enjoying the blooms he had obviously planted.
The Italian filled his glass, preparing for a story
as if it were his own. Wine pooled in his beard.
Over his shoulder he called out whether any person could tell him how to calculate the proportions of a figure study. A voice called back from the night and rain beyond the awning, 'Seven times – the
body should be seven times the length of the head!'
The Italian stared hard at Jun, 'Nearly. Isn't that true my friend?' His voice fell to a whisper, 'A body, from crown to sole, is seven and a half times the length of the head. Vitruvius taught us that, didn't he? Yumiko tells me that you put old Vitruvius to the test, Jap; that at you measured some decapitated Russian with his own head! Is that true?'
Jun leaned forward. 'It was at the Battle of Taishan,' he said, his tone even. 'Vitruvius was quite astute in his calculations.'
Well, sir, I didn't know what to do. I reshaped Jun's words into French. I had heard Yuichiro boast of his brother's unconventional methods before, but I never expected them to be true.
Jun then asked Yumiko how such a declaration made her feel. He couldn't imagine he had caused her any offense, what with her husband's notorious love of Russian dancers. Saiki's works were full of them, he was told. Was it true that the famed Masahiro Saiki had never asked his own wife to model for him?
I watched Yumiko's lips curl into a smile, which she made no attempt to cover with her hand. The expression in her eyes is impossible to describe – it was not quite angry, not quite blank, either.
Before she could retort, Jun exclaimed, 'There it is! In this light it is so plain to see! That is what you failed to capture in your picture brother: that is the face of a Japanese woman. You have spent far too long in the Louvre; far too long seeing the world through white eyes. Look at her face. How can you not see it? I could demonstrate what I meant if I had a skull specimen with me!'
And so it was spoken. At some point, we moved inside the café. The Italian, filthily drunk, told us stories about his childhood in Livorno. Looking around, to see that the place was empty, he lowered his voice and asked, 'Do you know why this place is called the Houdini?'
I made a quip about how my money always vanished after drinking there, to which Yumiko belched out a laugh, the likes of which I have never heard emitted from a lady since. Yuichiro lifted his head and patted me on the back, as if he had been awake all along. Jun did not laugh.
The Italian called over to Fournier. The old waiter obviously had a soft spot for the wild-headed sculptor because, after wiping his hands on his apron, he came over to us and uncorked a bottle of brandy. Before he could pour himself a drink, I took the bottle and performed the action for him, as is our custom.
'Tell them about the Houdini's magical powers,' the Italian asked the waiter.
Now, sir, many nowadays think the café was named after that great illusionist, as a witty way to commemorate the manner in which he died, struck in the stomach as he was while being sketched by an art student the other year. Fournier made a great show of coming round front and locking the doors before he explained that the Houdini was called the Houdini because it shared the key ingredient of any great conjurer's trick: it had a trap door. Or rather, an access shaft made and abandoned by the Inspectorate of the Mines. A person could enter in the small café, and disappear, maybe to reappear somewhere else.
'And why should trap doors interest us?' Jun asked me to enquire.
The Italian replied in Fournier's stead, 'The Empire of Death, my friend! There are catacombs beneath our feet, places where you can play with as many skulls as you like. I know: I've been there. And you've put me in the mood for adventure.'
He winked at Yumiko.
I have thought about the events that followed that call to the catacombs many times, to the extent that I am no longer sure of the accuracy of my memory, like a Chinese apprentice copying the work of his master. What I remember is Fournier leading us down into the kitchen, a windowless room, its darkness absolute, where he handed each of us a candle. Like a line of the pious, we received our flames in turn. There were some low tunnels after that (in which Yuichiro had to bend at his waist), two stone stair cases and cobwebs – thick miasmas that tugged at one's hair like the sticky fingers of children. The subterranean coolness was a relief after the heat above.
When we came to a wider tunnel, Fournier announced that we had reached the catacombs, pointing to a rough black line that ran along the ceiling. If we were to become separated, he explained, we were to follow that lifeline to an exit. The Italian pushed through to the front of our expeditionary force, his candle's flame reflecting off Jun's teeth.
The absence of light makes it difficult to recount our passage. Candlelight on chiselled limestone; the closeness of our breath; feet scraping wet gravel: all evoked a sensation within one's heart, not a picture to the eye. Every now and then, the echoes of our passage would widen around us, bounding off into the black, into tunnel mouths left to their mystery.
We came upon two black-painted columns, sometime later, a white obelisk design painted on each. The inscription on the transom they held aloft read: 'Halt! This here is the empire of death.'
Genius confronted us on the other side of the doorway, a sight I cannot give shape to with my descriptions – I wonder if even Akutagawa could? Bones, tens of thousands of them, were stacked in piles jutting out from the cavern walls. Layer upon layer upon layer: their numbers meaningless. The macabre architecture was a marvel, its craftsmanship impressing itself upon one's reason. But the art of it struck a deeper cord. Edging along the bone banks, candle at arm's length, my face level with the crania crested dams, the hollows within them filling with light, I admired the strange, brutal patterns which came into view: a wheel of long bones, spokes crowned with skulls; a heart of skulls; an altar's cross.
Beside me, the Italian took up a skull and, despite its missing teeth and jawbone, pretended to bite Yumiko's shoulder with it. Yumiko giggled with delight. 'It's so light,' she said, taking the white orb from his hands. Yuichiro made a quip in Japanese about its similarities with the pronounced forehead of an Italian. The sculptor kissed Yumiko's hand as in response to those words he could not have understood, and took her into the next chamber. Yuichiro followed.
I returned to Jun, who was muttering to himself about how the meat and liquid gave a head its weight, his body a silhouette, hunched over the lip of stack. With his candle so close to the wall, his hands were lost in the mire of shadows. I enquired as politely as I could what it was he was doing, looking as he did into my eyes like some soothsayer, a sham Hamlet.
'Looking for a mandible,' he replied. 'To make a complete human vertex. There are things I must prove to my brother.'
After hearing the story of how the doctor had used a Russian head as a measure, I decided to help Jun fulfil his bizarre quest, digging my hands into the mound of bones. I can still remember the sensation, the lightness, which brought to mind the shells of cicadas. I discarded sheath after sheath, each with the surface texture of rain-pitted limestone, in my search for the more substantial grit of teeth.
Yuichiro rejoined us. At that moment I noticed the absence of Yumiko and the sculptor's giggling, which until then had reached us from the adjoining chamber through waves of echoes. Engaged as he was with his search, I thought Jun had no interest in Yumiko's behaviour and was content for her to do as she pleased with the gaijin. Or so I thought, until, quite abruptly, he stood up straight, receding as it seemed into the darkness.
'Do not trouble yourself,' he whispered. 'Do you think a fish knows that it is wet? It may know the sensation of the air when it jumps to catch a fly, but, in a flash, it is back underwater, dreaming about the world above.'
Yuichiro's breathing slowed and he threw down a tibia with a chuckle. 'You know,' he said, 'at last you say something that makes sense.'
At some point, Yuichiro said that we should give up the hunt for Jun's trophy of a mandible and leave, adding, 'Do you think Saiki will miss his beloved wife, if we leave her down here with all the other skeletons? You never know, she might feel at home down here.'
I do not wish to dwell upon what Yumiko and the Italian got up to in that other chamber, stared at by the hollow eyes of the dead, but when they returned Jun addressed the sculptor, saying that we should return to the surface. 'This has been quite the experience, sir,' he said.
My translation complete, the wild-haired man bowed, his exaggerated movements extinguishing the flame of his candle. Yumiko lit his flame with her own, drawing her face close to his as she did so.
Of the journey back to the Houdini's cellar I remember nothing other than the spectre of Fournier's sleeping form when we re-entered the kitchen. It was such a shock to see him there, his body whole and thin, his white hair glowing in the muted light of our candles, that Yumiko gave out a startled cry. The old man did not stir.
Yumiko asked whether she should wake him.
'The Houdini was not called the Houdini for nothing,' the Italian said, mimicking the waiter's southern accent. 'In an hour he will have to open the café – let him lay there.'
The rain had passed and the morning light reflected off the puddles in the lane, their edges cutting blue slithers between the cobbles. The lane smelt cold. Yumiko said something about a bath and the Italian, who seemed shorter when sober, grunted. His lips, black with dried wine, gave him the look of a tubercular apostle, his message and lungs spent. The two of them no-longer linked arms.
I went to take my leave, but Jun stopped me, saying that we should all pay a visit Yuichiro's apartment.
'I trust that Yumiko is still to view her own portrait?' he asked.
Yuichiro shook his head. No, she had not yet seen the painting. Yumiko clapped her hands and implored the sculptor to come with us to the Right Bank. We should take the train. The Italian made some excuse about an appointment later that afternoon. He needed sleep to prepare for it. Yumiko's expression turned crestfallen, but her smile never faded.
Without another word to her lover, she took Yuichiro by the arm and led him out onto the avenue. At the entrance to Alesiá, that station I am told was named after a great battle between the Gauls and the Romans, the Italian crossed the road and headed northeast. I never spoke to him again, though I saw him from a distance a couple of times and I know he saw me. Two of his works, sir, now hang in this gallery. Ask me to show them to you sometime.
It wasn't until we waited at the platform edge that I felt conspicuous, accompanied as I was with such a strange band of Japanese. Petty businessmen and clerks were on their way to work and there I was beside two Orientals in dishevelled evening dress, cuffs red with wine like surgeons, Yuichiro impassive, Jun brooding; and Yumiko, a painfully thin exotic without a hat (at some point she must lost it!), her black hair gleaming over her breasts, eyes glazed as if in a daydream. I felt every face on the platform turn towards us, whether with scorn or curiosity, I cannot say, shame bringing me close to tears. We did not speak.
At last we passed over the green waters of the Seine, shimmering like a vision by Matisse, the Eiffel Tower tall and emitting its invisible radio waves out over the world. We alighted at the Passy Station and I stumbled down its steps as if still drunk. Though no longer under the spotlight as it were, I felt something was chasing us; that at any moment a hoard of Parisians would surround us and throw us in the great green ribbon below Yuichiro's building, leaving our bodies to wash up, rank and rotten, on some sandbank at Le Havre.
Sat beneath the fretwork doors of Yuichiro's parlour, a glass of sake held between my trembling fingers, the tension finally evaporated. I lay down, looking up at those wooden blossoms. How perfect they were; Yuichiro must have had them handcrafted back at home and shipped halfway around the world. Jun sat crossed-legged beside me, while Yumiko stood at the bay window, looking out.
It took Yuichiro a short while to transport his canvas from studio to parlour; he didn't want any help. Yumiko's image was concealed beneath a cotton bed sheet, and I expected Yuichiro to make a great ceremony over the impromptu unveiling. As it was, he leaned the canvas against the fireplace and pulled off the sheet.
How to explain what happened next? Yumiko shook off the reverie which had pulled her eyes to the city outside, and dropped to her knees, speechless.
The picture was as Yuichiro had explained the night before. Yumiko, clutching her knees, looked outward towards a Metro carriage window. She was nude. The shadows from the tunnel did not spread across her naked form, though: what confronted one was an ultramarine sky, vast despite the window, breaking over purple-slated roofs, the limestone beneath them burnt-orange. The balance was striking: lines, straight and formidable, from the backs of the seats, to the highlights of Yumiko's ribs – all were angled towards that sky, infinite in their bearing, as Seurat had once theorized. Yumiko was beautiful, in a Gauguin kind of way, at once warmed and drained by that gaze towards blazing colour, her own body bright like those of the facades.
I applauded the masterpiece and its master, the painting was more achieved than I could have imagined from Yuichiro's sketches. I looked to Jun, to watch his reaction to the portrait, for I could not fathom why he had taken such offence at Yuichiro's vision the night before at the Houdini. Was it not the case in our modern world that, if the artist felt it to be so, he could paint the sun green? Would such a vision have to be wrong? Hadn't the catacombs below the greatest of European cities only confirmed the idea that we are bone beneath, our flesh destine to rot? If that was our destiny, shouldn't we look up at a green sun, or a thin girl of burnt-amber, for that matter, a girl looking to an ultramarine sky? Weren't we supposed to feel alive? Couldn't one of my own countrymen believe in that girl enough to allow us to believe in her too? To believe in ourselves?
Jun paced over to the window, unfolding his newspaper as he did so. He held up the front page beside Yumiko's face. De Vinci's smiling daughter of Florence looked back at us.
'You're continued blindness disappoints me, brother,' he said. 'Look at the angle of her jaw,' Jun demanded of Yuichiro, 'the curve of her ocular canals, their depth as they sweep along her cheek; look at the length of her teeth, how they extend the profile of her maxilla; the shallowness of her zygnomatic; the slope of her frontal bone – must I go on?'
'Please do,' Yuichiro said, lighting a cigarette, his only defence it seemed, when Jun went on the assault.
'Now, look back at this painting. What do you see?'
Yuichiro shrugged his shoulders; the question was redirected at me.
'A painting of a woman?' I answered, at a loss for what else to say.
'A painting of a white woman!' Jun threw back at us all. 'Yes, the hair may be black, her eyes a little narrow, but look at the face, its shape, its angles. They are not Japanese. All you have painted is a white woman, made-up for a fancy-dress ball. All this visionary rubbish is in vain if you cannot even see that your so-called art is not your own at all. If you cannot possess even the surface of an object, how can you attempt to evoke its spirit?'
Sir, how can I explain the power of Jun's words? It was as though a cloud had passed over the sun: the image of Yumiko, its brushstrokes and paint, remained physically unaltered, but its life force was stripped away. The Japanese girl was no longer of the Orient, but a parody in bright hues.
I looked at Yumiko's portrait and then at Yumiko: how different they were, it was true. How could I not have seen it before! Had I become so accustomed to copying the masters of that other culture myself, that I had allowed the colours, the pose, the system of Yuichiro's portrait to fool me. In that moment the fear that had chased me from the subway that morning, the fear that I thought dispelled by the smell of tatami, the taste of sake, the look of carved cherry blossoms, returned in force. I felt the weight of the city around me. The girl of the carriage, of the ultramarine sky and rooftops, was no Japanese beauty: she was constructed, thoroughly, through European grace. As such, she was a monster, a woman possessed. Yuichiro had captured the Western in Yumiko, without capturing Yumiko at all. The portrait repulsed me, just as Yumiko's manners had done so the day we first met on the Metro.
Moreover, the painting had fooled the artist himself and now, Yuichiro's failure confronted him, both in the image leaning against the mantelpiece and the girl who stood by the window. I can only imagine what went through his head at that moment, the doubts that set his dreams of being the best Japanese artist in Paris alight: if he displayed the picture in public, the critics, surely, would call his vision hackneyed, that the man from overseas lacked any originality of his own. That he was a copycat.
Yuichiro threw his glasses to the floor, moving toward Jun as if to strike, but before a blow could fall, Yuichiro stopped himself. He stared at the canvas and sunk to his knees in defeat.
'So I am an academician after all,' he said.
Jun, calm now, as if delivering a lecture, said, 'Brother, look at this girl – look at her. She is a lost soul. If you want to rescue her: give her back to herself. Show her –and those beyond these walls who incite an artist to do such violence upon her – that beauty isn't in disfigurement. Paint her! Is she not Japanese?'
Yumiko, who until this moment had remained silent, awestruck, much like myself at Jun's revelation of the European face that looked out from the portrait stood and gave out a wild laugh, like a soul possessed. With uncontrolled passion, she spat at Jun, 'I think Yuichiro has succeeded masterfully. He has looked into my heart and given shape, harmony, to my most inner desires. Yuichiro has painted me as I see myself. It is you who are blind.'
'Then you truly are lost. No wonder your husband favours his Russian whores. He might as well have married a foreigner.'
At such a levelling, Yumiko stormed out.
But Jun was not done. He left Yuichiro and me to stand in the parlour, while he followed the girl through the front door, onto the hallway landing, from where we could hear him shout down the stairwell, 'Yumiko-chan! Oi, Yumiko-chan! You may forget our country when fucked by a gaijin, but that won't make you white!'
He came back into the room and repositioned himself on the ledge of the parlour's open window. From his new vantage point, he must have caught sight of Yumiko as she fled up the stairs to the Passy Station, because again his voice boomed out, 'Enjoy your lie, Yumiko-chan! One silly artist may paint you white, but you'll never look anything other than Asian to this nation with cataracts!'
As far as I know, Yumiko kept her distance from Yuichiro after that episode. Never again did I see her at the Houdini, the Louvre, though I kept an eye out for her down every street I passed along, every park I sat in.
For a while, I thought she had perhaps joined her husband, who I knew to be touring the south coast. Then came that Monday when the Kozu brothers and I met for breakfast at the Houdini and Yuichiro handed me the paper, as I've already told you. I read first for myself that she was dead, self-murdered, her body wrapped in a white funeral kimono.
Yuichiro excused himself and returned to his apartment, I think now, to gaze upon his fatal portrait of Yumiko; his vision of what Yumiko had wanted to be, had willed him to paint, that image of what she never was.
The telegram arrived that same afternoon. Could I join him and Jun at the municipal morgue at 4.00 pm? A third party, to claim Yumiko's body, was needed. For reasons that I can only speculate about, it appeared Saiki had refused to claim her body.
Though I had known the morgue was open to the public, I had never ventured inside it. What confronted me when I arrived left me more shocked than the crypts beneath Montparnasse. The grand high-ceilings, were filled with a strange scent like rotting apricots and behind glass doors, the bodies were laid out on rude beds. Somehow the overall effect was like that of a waiting room. I half-expected to run into the Great King Emma, the judge of the dead, at the end of the foyer. One or two of the visages behind the glass were calm and somnolent; others were frozen in a scream. Then there were those putrefied masses, stewed by the waters in which they had been found. To think Yumiko had wound up in such a place disgusted me.
To locate the Kozu brothers I had to solicit the help of a clerk. Jun greeted me cordially, like an old friend, and asked whether I had followed the instructions as they had been laid down in the telegram. I told them I had.
Yuichiro paced the room, a handkerchief pressed to his mouth and nose.
It was then I saw what remained of the painfully thin girl who had once described so vividly how she wished to be painted. Severed into pieces, she looked like a puzzle, like one of those dolls one used to see on sale for the instruction of children in expensive Ginza department stores; only she of course was not made of wood. Jun picked up her head alone and smeared it with chloride of lime, saying it was to prevent putrification. Her long hair was shorn; a pair of scissors lay on the tabletop where Jun worked.
I remember thinking how low I had sunk; how, in so short a time, I had ventured down a path leading me from one level of hell to another. I stood there, motionless, in that place where death seeped into the lungs, corrupting the soul from within, holding the leather travel bag, until he took it from me. Opening it, he proceeded to take one of the morgue assistants' aprons, a heavy black thing made of Indian rubber, and used it to line the bag's interior. Into that hole went Yumiko's severed head. He silenced the clerk's protests by asking me to explain how such practices are quite the norm in our country. We were to perform a burial right to set her soul at peace. I translated the lie, but the man did not look convinced. He exited the room, vowing to report us to his superiors. We made our escape. I cannot imagine the clerk's reaction on finding us fled, but he must have given up the chase, for nothing ever came of our leaving in such a manner.
As I replied to a similar question asked me by Akutagawa, I do not know why I accepted Jun's offer to catch a cab with them back to the rue de l'Alboni that afternoon. I do not expect you to understand why I couldn't abandon them. I mean, does one break ranks at the first volley? The first sight of blood? Yuichiro was wounded more than I. He had loved Yumiko in his way. If it were not for Jun, our steadfast commander, we both would have wavered from our route, casting that bag into the Seine.
When we stepped into the parlour, I could see that Jun had been busy that day. A line of scalpel blades and forceps, procured from who knows where, lay in a line on the edge of a square of black silk, which I recognized to be one of Yuichiro's kimono, folded neatly. The choice of material was an ingenious idea. Though Yumiko's lifeblood had long since drained away, Jun obviously didn't want waste from his specimen to distract his brother. Strange to think, isn't it sir, that a simple choice of work surface would be the source of Yuichiro's dark backgrounds for his portraits ever after.
Yuichiro left the room, only to return moments later, drying his face with a towel, his hair still wet. Under his arm he carried a sketchpad, a tin of pencils, too. He knelt down at the edge of the black square in seiza. Jun and I joined him. What a strange sight we were to behold, looking as we did, like guests at a tea ceremony.
Jun opened the travel bag.
The stench of rotting apricots and chloride of lime that ensued caused me to retch. Jun, the doctor, duly scolded me. Yuichiro, who sat there in silence, a blank expression on his face, rotated a pencil between his lips.
Whilst gently lifting the head from the bag to the silk, Jun instructed me in how I was to assist him, asking me to hand him a particular blade and certain forceps when the time called for them.
I think his words to Yuichiro were, 'Watch carefully. Sketch every detail. All those nuances the whites never see. Do not flinch.' For him, the girl had proven to be the strongest of us all; as such, we should honour her in this, our own way, a manner that would help her spirit find its bearing home. I listened to Jun's words and something struck me about the way he spoke, gesturing towards the head as he did so. He did not use Yumiko's name; in fact I had not heard either brother address Yumiko by her name since the morning I had seen her alive at the Houdini. The impression this imposed upon me was that, with her life force spent, Jun viewed Yumiko's severed head as an artwork, a piece of sculpture in itself, to be broken down and resembled on Yuichiro's pad.
The glare of the room's electric bulbs gave me a headache, but I took in the remainder of Jun's orders and explanations with the morbid interest that lures one to a funeral – not that of a close relation, of course, but of a distant colleague, a man one did not know well.
I see my words offend you, sir!
In that case, I shall keep my story brief! Well, at last, Jun said, 'Shall we begin?' His tone was thoroughly professional, intrigued even. With such a calmness, I can still imagine how comforting he must have been on the battlefield, the shells falling all around, the wounded in awe of his discipline.
There is not much to tell after that: I handed Jun the tools he asked for and took them from his hand when he was done. Bile burnt the back of my throat, when Jun revealed the yellow layer of fat beneath the epidermis, but that was the only time. I steadied myself, holding firm, concentrating on the scratching sound Yuichiro's pencil made. The hum of the light bulbs eased my nerves.
Yuichiro's sketches were a marvel to behold – I still have two, from that very day, locked safely away. Their lines are so faint. As if Yuichiro were afraid to press any harder, to mark with fervour the morphological differences, as Jun called them, hidden away under muscle and capillary.
Ah, as for what happened to that first painting of Yumiko, the original? I do not know. As is well documented these days, it is this painting before you, his first truly Japanese work of art, which marks the great advancement of our country's painters into the 20th century. I do not need to tell you how Yuichiro began what was to become the great Japanese renaissance, a reclaiming of the truth from the Parisians who tried to bleed out our bloodline with their Western configurations of our Oriental beauties. My old friend would go on to paint over a hundred bijinga, and in doing so, he would take his place on that long path trodden by so many of our countrymen, deepening its ruts through his use of oils (no more pigment, no more ink); widening its girth with his rendering of facial nuances, those turns of bone and flesh that mark our race's place amongst the peoples of the world.
If you were to ask me where that earlier portrait was, that nude of Yumiko in which he saw her as she'd always wanted to see herself, I would ask your forgiveness, and say I don't know. But, and I do not mean to speak out of turn, if you push me I will confide in you something I have thought for many years: that the original of the rebellious girl I met that summer in Paris still exists, not stored away somewhere, but painted over, just as Picasso did with so many of his earlier works. Just think, sir, the ghost of that wild girl could be haunting the very flesh that caresses the cat your wife finds so charming!
That was the story I told to Akutagawa. I always hoped he would write about it someday, given how much he detested Kozu's portraits. But such speculation is by-the-by: I see your wife has come to collect you. I leave it up to you to decide whether or not to buy. The painting your wife so admires is one I have looked upon for, perhaps, too many years.
## PART II
BOY WITH NO BIG TOE
_The village of Nihongi, Nagano, 1947_
In the moment before he laughed, the American bore an uncanny resemblance to the executioner from Toulouse-Lautrec's lithograph, Au Pied de L'Échafaud. 'Ah come on, Takayanagi,' he said. 'This little doozy's kept me warm all the way out from Suzuka.'
His joke went like this:
'A Japanese lieutenant-colonel walks into a French restaurant, the fancy kind with a maître'd. Garcon! Garcon! Are you taking orders? the Jap calls outs. And the maître'd replies: Oui monsieur, I am taking orders, but not as well as you.'
What could I say? As soon as I had caught sight of their jeep, its fresh layer of gloss the wrong shade of olive for our valley of burning leaves, I turned fleshless: a hungry ghost. I rubbed black mountain soil from my hands and the American coughed up another laugh, looking to his superior for support, a captain, whose uniform was so neat he could have been wearing an origami gown. The charcoal in our brazier popped but gave off little heat. The damp of the house seeped into me. How shabby the walls looked. How clean that uniform. My life was laid out in all its rudeness: the rotten tatami, the floorboards visible underneath, the fallen thatch wrinkling every surface.
The captain, tall and bored, was a Botticelli, from the master's A Magis Adoratur. Do you know the painting? Have you seen him standing there, Botticelli himself, on the edge of the Medici family, those brutal patrons of Florence? I could see the captain was a man who liked to listen – listen and remember all the words he's heard. A quiet man. His eyes a confrontation.
An apology slipped from my lips.
The captain waved his clipboard. There was a smile at some point. Enjoyment in the chase. He said, 'The Old Man wants to clean up any remnants of the old wartime cliques. We've been tasked with confiscating any documentary campaign pieces that may have been removed from Tokyo after the surrender. They're subversive. We are, after all, at peace.'
I called out to my wife for refreshments.
The captain refused to be distracted. 'We were hoping to locate some works by a war artist connected to your grandfather's gallery, a Yuichiro Kozu.'
I shrugged my shoulders, a gesture I thought my body had forgotten. 'Kozu was friends with Soutine, when my grandfather represented the Lithuanian in Paris. That's how I met him, once or twice, after he became famous. He died during the war, I read; Soutine that is. Not enough medicine. That is all I know about Kozu.'
The American looked at me as though I wore a Noh mask. His subordinate grew impatient, demanding I hand over any Kozus in my possession, anything I may have removed from Army Headquarters in Tokyo before the surrender, anything stored at my grandfather's gallery. The house could easily be searched. My wife wouldn't like that at all, he said.
I bowed. 'The only artworks I own these days, gentlemen, I hang inside my head. As you can see, my wife and I are not very prosperous. Not anymore.'
'Ah yes: the fire.'
'The fire.'
At some point, my wife entered from the back and the captain instructed his man to mind his manners. Before each of us she delivered a steaming bowl of millet gruel, thickened with ground mountain yam, the vegetables I had just dug from the mountainside when the Americans' jeep rumbled into our valley. I offered our guests a goza mat to sit on, a reedy husk our neighbours had once used to dry their vegetables on. We ate in silence.
But neither the soup nor the silence appeased them and soon the captain laid his chopsticks across the top of his bowl and said, mixing up my name, 'Now then, Mr. Takayanagi-san, why don't we have a little look in the woodshed?' They spent the better part of an hour overturning everything in the small space while my wife and I looked on. The war is over, but suspicions continue. So, Doctor, I hope you understand that, even if I had the money you're asking for, I would not buy your painting. There is no need to unwrap it. Believe me: I am glad you both survived the war. But you have been deemed useful in this new society of ours; your painting has not. To deal in Kozu is to deal in damnation. Yes, the war is over, but now the hunt is on for its criminals.
Let us put that aside for the moment. We have something in common and this should be celebrated, especially during this time of differences. Like the Americans, you were right to believe I once dealt in the great Kozu's art. And even more so to believe that I knew more of him than what I told his would be captors. Will it surprise you to hear me say how once, when I was apprenticed to my grandfather's offices in Paris, I accompanied him and Soutine on what Kozu had said would be a little 'expedition'? They took me through the abattoirs around La Ruche. I can see them now. Un plaisir pour les yeux: Kozu in some peacock print shirt he had sewn himself; Soutine in that jacket of his, like a boiler-suit cut off at the waist, wearing his only pair of shoes.
Down an alley, its cobbles and walls shining with drizzle, we came across a knacker, his arms posed, wielding a lump hammer: a stroke away from putting an old Lipizzan horse to its passing. A hessian sack covered the beast's face; its ears poked out through holes cut into the top. Holding onto the halter was the man's handsome daughter, her eyes large and keen. Kozu – perhaps sensing my disquiet, perhaps aroused by the look on the girl's face – approached the man. The knacker's heavy apron was white: the horse was to be his first job of the day. With Kozu whispering in his ear, the old fellow nodded his thick head, given shape by a bushy moustache and cropped hair, and passed the hammer over to the artist's hands. It took Kozu a single blow to split that horse's skull. Soutine, I remember, was sorely disappointed because the carcass was too heavy, too cumbersome, to transport back to the commune.
Surely, you have heard the rumours? And so you know just how vigilant was their study of anatomy. I wonder if the extremity of an action such as this passed over me as much when I was a younger man as it does now upon recollection? But then again, wasn't it Valery who said, 'the skin is the deepest thing?' Kozu bragged of the wonders those animals offered up. Raw textures of colour, he said: mother-of-pearl tendons, cut slack within an eviscerated rabbit; the flayed ox, split through the ribs: so many muddied shades of white, against a feast of rouge and brown. Soutine was the first to excel at recording these spectacles on his canvases. But Kozu advanced that art to another level altogether. And, yes, that is why I must tell you about your painting, Doctor. It deserves as much, as does Kozu himself. The moment Macarthur landed at Atsugi Airport, our greatest artist's reputation crumbled. The Americans are looking to hang him and the new generation of artists have, like crows, hopped beyond the rubble of the past. Still, I have no doubt, Doctor, that, much like myself, you have the utmost respect for such adventurous types: the Chaim Soutines and Yuichiro Kozus of the world.
Does it surprise you, I wonder, that I know which work you have brought me from the parcel's proportions alone? Let me describe for you the tableau: its Japanese soldier, centre left, little more than a silhouette is bursting into a darkened room. At his feet lies a white imperialist. Was this Frenchman cut down by the soldier's bayonet – that slash of gold, glittering in the doorway's bar of honeyed light? We do not know. There is no blood on the blade. Just real gold leaf flashing over muted oils.
The night Kozu put his last touches to your painting, Doctor, Wagner was playing on the gramophone. The grand march from the German's Tannhäuser – a favourite of Van Gogh. An hour past dusk and there Kozu was: studying his three models, pouring his soul into the forms he recast on his canvas. He closed his eyes often, cursed, remembering the scene the hour before, recalling the slant of a shadow on the soldier's collar, his neck, beneath the ear, the quality of brightness along the shadow's edge. How he wished he could freeze time, the sun's quick descent. That is why he chose gold leaf for the blade. It shone with a light beyond the shades he mixed, his highlights. He did not like to paint from memory. If the essence of kokutai was to be evoked, ordinary light would not do. Kozu said as much himself. The body-national needed a touch of the divine. His soldier was a saviour. A liberator. And, while we contemplate his valiant pose, our eyes are drawn to the shadows, past the fine European furniture (edges and grooves picked out with great care – the texture of heavy curtains), to the figure in the bottom right-hand corner. Her skin is dark, eyes narrow, the girl, who, almost invisible in her black smock, is sitting on her knees, hands tied behind her back. What atrocity has been averted here? we ask.
A week. That is all it took Kozu to render what in times gone by some of us might have called a masterpiece. No other documentary artist could work so quickly. Not with such grace and dexterity. It is no wonder the Army sent Kozu everywhere to record their greatest moments: the storming of Singapore, Hong Kong. Some have said he flew in the back of a torpedo bomber at Pearl Harbour. In March of 1945, he was stationed in Saigon.
Doctor, you must have graduated in the last wave of students to leave medical school during the war. You look so young. Indulge me. There are some facts about your painting you may not be aware of, or were too busy to pay much attention to, given the calamities that befell Tokyo the last year of the war. I do not mean to give a history lesson, to patronise a bright fellow like yourself, but you may find it difficult to picture our military policy in Indochina, what with our decisiveness elsewhere. The key term the diplomats used was the 'maintenance of tranquillity.' The golden rule. Allow the French legislative organizations to remain, we thought, leave the police, economy, education, and all other domestic affairs under French control. We were engaged elsewhere and Paris had fallen. Why disrupt a vital rest stop; why poison your well, your breadbasket? Major General Sumita, I heard, advised his staff to conduct negotiations in a dedicatedly peaceful and friendly way. But it was an uneasy status quo. The Army said it would not support the independence movements in our area of operations, but it did – except of course, the Communists. Many of our native supporters were disposed of by the French Sûreté. We said we would not create bases for operations against southern China (the French feared igniting Chinese interest in their stricken colony), but again we did, especially after the declaration of war on America and Great Britain, when the army surrounded the French administrative headquarters and stated that General Decoux would facilitate our military presence in any way we saw fit. The French had no choice but to agree. The fear of losing their colony altogether was just too great. And as for the independence of the peoples of Indochina? Our diplomats thought that a matter of importance, but only as a future concern. Such a standoff, of course, did not last.
And, I can tell you Doctor, Kozu's models were not Japanese, or French, as you may have heard elsewhere. All of them were Indochinese, even the gentleman on the floor, though he referred to himself as Chinese, despite having been raised under the same sulphorous sun. Ces messieurs, Doctor. Those gentlemen. That is how Kozu referred to your soldier and dead Frenchman. But is such a detail really worthy of note? After all, we all know Kozu's reputation, his predilection for the grandiose. Just take the story about the Russian tank, the one he drove himself into the quietude of the garden of his Tokyo studio so he might render it in a dramatic scene of his own making.
One could be forgiven for thinking the soldier in your painting Japanese. How his face almost fits. He was called Trau, an ugly name for a beautiful youth. It meant ox and was given him by his grandmother to ward off evil spirits. To Kozu, he looked like the boy leading the elephant on the back of the 100 piastre note. Just talking to you Doctor, brings to mind a vision of Trau, standing there, in that corporal's uniform , its white armband marked with a rising sun, imprinted with the character An – a military pun, meaning both security and An-nam, the middle kingdom of Vietnam. 'Painting from life is the path away from melancholy.' That is something the boy liked to say.
I realize I am ahead of myself. Permit me to slow down. Can I offer you the same bowl of millet and yams my wife served to the Americans? It is rough food, Doctor, especially for a man of your standing, though I do like to think the sweet flavour of the yam, its delicate orange colour, is imbued with a sort of rustic charm. After all, we have little else.
While we eat perhaps I should tell you about how I came to arrive at this point in my life – so ungrateful as I am for what I once, and I admit it, would have snapped your hand off for. No mere anecdote is required this time, but what I have heard the Americans call the 'cold hard facts'. I came to the Cape St. Jacques in the rain: rough waters made pleasant by quiet skies. No American aircraft could prowl the coast, you see. By midnight, the stars and insects came out. The drive into Saigon was long. At The Institute of the Southern Ocean, the Japanese economic school on the Gallieni Boulevard, two military policemen were waiting for me. With no time to unpack my things, I was taken to the Majestic Hotel, a billet for the Japanese military.
Major Honma's first words to me were, 'Look at the legs of the British officers!' I could see little of him, as I sat down at his rooftop table. His back was to the tropical sun. His shadow extended over the white table, the photograph of the English officers and their spindly legs. Limbs he was so bent on discussing. The Riviere de Saigon blazed, stretching both north and south, like wings sprouting from Honma's thick shoulders. Curving out of sight in either direction, those waters gave the impression of forming an enormous circle, a River of Life, as envisioned in Buddhist scripture and the nihonga paintings of Yokoyama Taikan, a favourite of my grandfather's. The sun was a hot coal. I thought, here was a man touched by the theatrical. Backlit as such, Honma could have been a vision of the Emperor himself, the faceless centre of our nation's flag. The Hinomaru personified.
Honma insisted, 'See?'
I did not see and nodded in agreement. Honma was a major in the Kenpeitai, Doctor. He could arrest anyone. Anyone at all. Even military officers up to four ranks above his own station. Imperial justice was his to interpret. I was not untouchable. Even today, many of his kind are unaccounted for by the British I hear, and the Americans, and the Dutch. All this trouble over a painting. The news clipping beneath his finger was from the Asahi Newspaper and showed General Percival on the day the British surrendered Singapore. I had seen the photograph before – had advised the cultural bureau to commission the documentary artist, Saburou Miyamoto to set the occasion in oils. But that was back in 1942. Things were not going so well.
'How spindly their legs are,' he said. 'And their knees. They're too thin. Those are weak joints, Takayanagi. I know about such things.'
'The joints look frail.'
'Soh, soh, They are frail. And spindly, like a spider crab's: that is how Kozu described them when I showed him this same picture.'
'Kozu is a genius.'
'He is from Hokkaido. He must have grown up surrounded by the spiky bastards – the crabs that is, not the British. Though, I do question his attachment to the French. I've heard that you lived in France, too, Takayanagi.'
I told him I had.
Honma took a drag on his cigarette, which he held between his ring and baby fingers. An odd pose. An affectation. One I had seen perfected by a member of the Royal Family in the Philippines. He was a man who would never humble himself by supping on a bowl of millet soup. The cloud of blue smoke the major blew out over the stone railing beside him wheeled in the wet air above the rue Catinat, where it refused to dissipate.
At last he said, 'You are on intimate terms with Yuichiro Kozu, Takayanagi, are you not?'
'My grandfather represented his interests for many years in Tokyo, at the Midori Gallery on the Ginza. I met him in Paris. I wouldn't say we know each other well.'
'But you have been sent to Saigon to escort him back to the homeland. He and his military commissions. The Imperial Household itself has sent you.'
I was not to talk of such matters, but that meant nothing to a man like Honma. It was safer to bow, to nod, to say, 'Yes, Major Honma.'
'Let us understand each other, Takayanagi. Never would I dream of standing in the way of the Imperial Household, any more than I would with general headquarters. The Army sent Kozu here. Under my protection, he ventured north and painted the southern China front. The logistical preparations –to transport so valuable a consignment of national treasures back to Japan– are already made. Most of those paintings were completed in Hanoi. In fact, those paintings are at this moment on their way to the Cape St Jacques to be loaded onto the same hospital ship, which delivered you safely to my corner of the Empire. He tells me that all he has to do is finish a commission for Ambassador Yoshizawa.'
Bowing, I mumbled my apologies. I thanked Honma for his loyal service to the Emperor.
'Forgive me, but I have a humble request to ask of you Takayanagi. To my good fortune, Kozu has agreed to produce a painting for me. It is not to be anything spectacular; I can't really call it a commission, my rank does not really permit such privileges. He assures me he will start it very soon. He is very specific about the conditions. A true man of detail.'
Honma, I realised, did not want Kozu to return, according to my schedule. I thought a moment and then told the major how I had also been tasked with preparing, for want of a better term, a safe house for any valuable artworks in the city. Those in need of protection should the French revolt, or the Americans invade by sea. I had a list of such pieces, prepared in advance by a cooperative French administer, no doubt one of Honma's network. If the major could help me out in such matters, I would be most grateful. I assured him the works would take a little time to assemble – perhaps a week.
'So we have an understanding, then,' he said. 'I am sure I have some information about the colonial residences in Laithiau that may interest you.'
Not a word that I am telling you embellishes my connection to Kozu, Doctor, and yet how removed from him I have come to be. In truth, those first few days in Saigon were a blur, but, though I seem to meander, there is good reason to do so. Be assured I will make all clear in time.
I finally met Kozu in person three days after Honma's summons. At the time, we had not seen each other for fifteen years. I was called up from the crypt of the l'gélise Saint François-Xavier, the Roman Catholic church of Cholon, the Bastille of the Chinese City, and into the white heat of the street. A jade-coloured Adler limousine idled outside the gates, its rear engine augmented by some strange contraption for burning woodchips. Kozu was standing beside its open door, wearing something similar to a lieutenant-colonel's uniform. He had made it himself. Replete with extra leather belts and pouches, pleats and creases, he could have been wearing a painting by Braque. Perspiration stained my shirt and trousers, a white so dark it was yellow.
I approached him and he stared at me, eyes roaming over my face, my body, as a glutinous man moves between the dishes of a large meal. 'You!' he called out. 'So it is you they have sent to fetch me back to Tokyo – I was hoping for your grandfather.'
After apologizing for not contacting him earlier, I told the artist how busy I had been since my arrival.
'Busy? What, in there?' He looked at my escorts, two tired looking veterans, who seemed to be contemplating the stillness of a fly on the other side of the courtyard. I smiled as best I could, unwilling to risk his reaction, his flamboyant personality, with the knowledge that beneath our feet, in an second room dug into the crypt's lowest vault by a team of British prisoners, were stored canvases by the likes of Courbet, Matisse, Seurat, Carot. He did not pursue the issue.
'You must come by my studio, Takayanagi-kun.' He smiled. 'If you are anything like your grandfather, you will enjoy a little adventure. I'll wait for you on the corner of the rue des Marins.'
At three o'clock, I found his café. From underneath his cap, the artist pretended to snore, wake with a start, only to declare with a flourish, 'I have sent the car away.' A native waitress laughed at his antics, until she caught my expression. 'A walk will do you good. It is not healthy to spend so much time down a crypt. Believe me, I know.'
Doctor, the walk was a marvel in itself. I had only travelled by car between my lodgings at the economic school, the church and various houses in the French Quarter, where I gained entry with help from Honma's men. The major had insisted I not wander about. The Saigon Sûreté still policed the city.
Now, on foot, those strange streets came alive, their shabbiness worthy of Van Gogh's heavy brush strokes, the colours of lime, coriander, frangipani. Frying pork skin, mixed with brown sugar and garlic. Under the shade of kapok trees, invisible smoke dyed the air. Women ground peanuts. Everywhere locals in black smocks watched us through averted eyes. If we came close to them, they bowed, no doubt in supplication to Kozu's uniform. Only in our wake, did their voices sing out again, like birds settling after a fright.
We crossed the Arroyo Chinois and minutes later the Canal dedoublement, where I watched the sunlight flash across brown water, slithers of space caught between brown boats, poled by brown skinned natives. To me, the canals looked to be full of flotsam, the debris of some great typhoon, which had flooded the city's busiest boulevards with stinking water.
Dusk dropped over the Chinese City. Blackout regulations kept the canal and its warehouses in darkness. We made slow progress along the route de Binh Bông, passing peasants heading back to their hamlets beyond the city limits. In their black pyjamas and against the white glow of the road's dirt, they resembled spent matchsticks. To our left the paddy fields and marshes of the countryside washed up against the dyke, a humming thundercloud of bullfrog songs.
We arrived at Kozu's villa in the dark. The artist pulled on a bell-chain and turned to me.
'I could not tell you earlier, but I am not ready to return to Japan, not yet,' he said.
Caught off guard, I spluttered something about the Americans. The fear of an invasion. The likelihood of French treachery.
'No. Not yet.'
'Is this because of Major Honma?' I asked.
'What's Honma to do with anything?'
The door opened and an old maid let us in. Her face, I saw in the light of the taper-lamp she handed Kozu, was marked by some childhood disease. She greeted the artist, as though he were the house's returning patriarch.
Electricity was rationed. The studio of a war artist, no matter his reputation, did not warrant special attention. Darkness welled in the house, its high-ceilings, and somewhere within that vacuum, a gramophone played a waltz. I followed Kozu and his lamp. At his ease, the artist led me through the hall, past a tiger skin, then a pair of enormous elephant tusks set in a bronze stand. The flame moved like a cat's eye, across the burnished surface. The walls of the corridors were painted with writhing vines, a queer throwback to Art Nouveau, which extended as far as the ironwork of the spiral staircase we ascended.
We came to the door of a large bedroom. Inside, a veranda was visible through a set of tall bay windows. The same moonlight that cut its iron fencing into parallel streaks broke into a thousand fist-sized diamonds, scattering across the boards of the room's floor. The latticed panels of the house's outer wall were a sign the architect had surrendered to the climate at least once. The diamonds illuminated a large canvas laid flat on the floor: a true Asian, Kozu had long since abandoned the easel. The strange light created the illusion that the canvas was hovering. Within that frame I could make out little actual painting, just a large empty space, like the vacuous mists of a silk scroll. Kozu asked that I wait in the doorway. By then, the gramophone ground out a cyclical white noise somewhere by the open window.
The artist crept around the edge of the room, lifted the needle from the record and drew the blackout curtains, all the time muttering under his breath. After that he lit various candles around the room using his lamp's flame, his movements quick and practiced as if laying down strokes of paint. The details of the canvas consolidated, but there was not much to see, just a layer of burnt sienna under-paint. I stepped into the room and took a closer look. A figure, in rough outline, a graphite rifle held out before him, was charging into the blank, muddied space. A wispy set of lines picked out a doorway around him.
In short, it was your painting, Doctor; only, it wasn't a painting then. Just a thatch of pencil hatchings.
And then I saw them: a man in uniform; next to him another, his face covered by a bed sheet. I rushed around the edge of the canvas, grabbing Kozu by the arm. The artist, leaning over a bed that had been pushed over into the corner of the room, shook off my hand with irritation and returned his attention to a third figure, a girl dressed in the black pyjamas of a peasant. The girl roused and smiled at his touch, her teeth catching the lamplight. And what a beauty she was, Doctor. She rose from the bed, like a ghost, brushed the creases out of her simple clothing and ran her fingers through her long hair – a black mass that fell down to her waist, like a painting of a Heian courtesan.
'This is Kieu,' Kozu said. 'She is the lady of the house.' He gestured over his canvas to the two men lying on the floor. 'That there is Petrus, her husband, under the sheet. The other –the boy– is her brother.'
'You mean the soldier is a native?'
'Un.'
My fright left me and was replaced with a deeper sense of fear. 'He is impersonating an Imperial soldier! If Honma found out, he'd be executed.'
Kozu asked Kieu to bring us a drink (and so here I will pause, just briefly, to ask if you, Doctor, would you like another drink yourself. No? I don't blame you. The story is always more compelling than a cup of wheat tea. Well, then I'll continue). Kozu added that that we would wait for her on the balcony. With his boot, he nudged the boy in the soldier's uniform and said in French, 'Oi, my friend here wants to hang you.'
The figure groaned and reached for the gramophone needle, which Kozu took from his fingers. The soldier drifted back off to sleep.
'This wretch, Takayanagi-kun, is my protégée: Trau.' Kozu took a jug of water from the washstand and soaked the boy's face.
The boy spluttered and got to his knees, shaking his head, eyes wide with confusion. His fists were clenched. In that uniform, its stitching loose, cotton scuffed, he was a vision of impudent rage, like one of the old timers I had seen marching back to Shanghai from Nanjing, his pain held at bay by amphetamines. He looked from Kozu to me, a Japanese stranger, and took a series of deep breaths to calm himself.
'We thought you'd be back sooner, Yuichiro,' the boy gasped. 'When you didn't come, we had a smoke to pass the time.'
Kozu nodded. 'What about him?' He motioned to the prostrate form on the floor.
'You'd better not. Petrus was smoking your Golden Bats even before you left.'
The figure at our feet mumbled something in his native tongue: a series of disjunctive plucks on a koto string.
Trau's legs shook but he managed to get to his feet. Kozu led us out behind the blackout curtain and onto the veranda. The heat was there, too, even in the white flashes of moonlight reaching up from the canal beneath us and moving across the walls. A pleasant heat. A tangible mass that absorbed me, as I eased down onto the stylish butterfly chair Kozu had pushed over for me. Its metal frame was wet. Trau lit a cigarette and exhaled smoke as sweet as incense, offering one to Kozu. The artist explained to the boy that I was an art dealer from Tokyo, the grandson of a legend. Not a military man.
'March,' Trau said, falling back into a chair of his own, the neck and shoulders of his khaki uniform still black with water. 'This is the best time of year to stay in Cholon, M. Takayanagi. You chose a good time to visit. April will be here soon. The humidity will return. And the sun will lose its clarity. Every surface will dull.'
The girl returned. She poured out three drinks from a decanter and said something to Trau. He translated. The wine was made from tamarinds, he explained, a local brew to circumvent wartime restrictions. His sister was worried it might be too sweet for my liking. Kozu, I noticed, watched her every move. After she disappeared inside again, his eyes remained fixed on the edge of the blackout curtains. As if sensing my questions, the artist sipped from his glass and said, 'Tell him Trau.'
The boy tapped ash from his cigarette and asked whether I was intimate with the works of Van Gogh. Of course, I said.
'I am the Dutchman's reincarnated soul,' he said. Not a living a ghost, he insisted; he was not possessed. What moved within him was a force, an inextricable intuition, which held him in situ between East and West. Those were his words, Doctor. Like you, I almost laughed, only the boy's sincerity kept me civil. Trau told me of how he had attended the Lycée Chasseloup-Laubat in Saigon, before his grand adventure north to study under Joseph Inguimberty at the Ecole Des Beaux-Arts in Hanoi. His stay proved both disastrous and fruitful. Director Inguimberty suffered, what Trau named 'a crisis of line,' and turned on the boy from the south, stating that colour was the better way to portray the tropical atmosphere. Trau agreed, in part, but could not abandon his expressive lines. They were as fundamental to him as fish sauce, a root of the Asian tradition. Van Gogh had understood the importance of outlines. Where the wild Dutchman had painted the fields around Arles, touched as he was by the aesthetics of the Japanese woodprint, Trau looked to paint in the other direction: an Oriental looking upon the paddy fields of his homeland with an eye to capture their essence in bright oils.
It was only to be expected that such an impressionable youth follow Kozu, the only Asian painter to make his name in Paris: a master of the real, when the avant-garde paraded their abstractionist rhetoric. Kozu had shown the world that Asians could pierce the look of the contingent world. That, for us, abstraction was nothing new. To the likes of Trau and Kozu, the very act of divorcing art from its mimetic function was a tyranny.
The story told, I emptied my third glass and poured myself another, by then feeling quite at home. 'If only we had some absinthe.' I said, quite outside of myself as I saluted the young corporal. 'And a couple of 2 franc whores.'
The young Viet smiled his 100 piastre smile. 'If only . . . But we do have Golden Bat cigarettes. Would you care for a smoke, M.Takayanagi?'
That night I learned about how Kozu came to be at the villa on the edge of the Chinese City, about how the master artist, on returning from a lecture he had given to the Anamese Royal Family in Hue, had come across the boy on the side of the road, where he stood, waist deep in mud, sketching a sleeping water buffalo in charcoal. When Kozu had quizzed the boy, he found out the youth had walked to the ancient capital and was heading back to Cholon. He had little more than ten piastres on him, much like Van Gogh had had when he walked out of Paris to Courrières and slept in a haystack, a hoar frost blanching the landscape around him. Apparently, on returning to Saigon, Trau had sent Kozu a portrait of the artist he had painted, an inversion of how Van Gogh introduced himself to Gauguin. Before you ask, Doctor, no; I never saw such a painting. Kozu had in turn, invited Trau to model for him, to take the role of the soldier in his commission for the ambassador.
The boy's French was excellent, his manner patient. I took his sweet tasting cigarettes and listened to his explanation of how his-brother-in-law was a rice merchant, the son of a radical Chinese father who had come to Cholon to make his fortune. That was how, out of custom with the all the other Chinese who occupied the canal district, Petrus had been named after a famous Saigonese dignitary.
Trau had come to live with his sister and her husband, after he returned home from Hanoi to find that his town had become, what he called, 'busy' with Communist cadres. Before the war, the village had been markedly different. Most of its houses were built of brick and not thatch. One family owned a generator, another, a French bicycle. Trau was very proud of his paternal village. It was a fount of civilization, where cactus fences were a thing of the past; where Nice tiles covered the hard-earth floors. Still, the villagers attended their ancestor's graves and grew their jackfruit trees on the outskirts, for fear of the ghosts the fruits attracted. The villagers were exceptionally filial people, he disclosed with a shy smile. Then came Kieu and Petrus' marriage; the result of a defaulted loan.
We breakfasted in the garden next morning, rising in an hour of coolness after rain. The sky brightened quickly, but the sun took its time in reaching us, due the great height of the rice mill that stretched out from the mansion's eastern walls. High over our heads, to the west, was the chimney of Petrus' distillery. The villa, too, was impressive, a red-brick affair, more architecturally at ease on the rue de Recluse, under the shadow of the Eiffel Tower, than on the edge of the Canal dedoublement. The mill and distillery were alive with voices, as was the canal itself. On its far side, we watched a group of POWs shift crates from a barge onto a truck, under the eye of a Korean soldier with a strong accent, a sight I had grown accustomed to in Shanghai and whilst working under the Catholic church in Cholon.
'They blew up the prison camp last month,' Kozu told me, 'their own bombers. Can you believe that?'
But I was only half listening. The delights laid out on the table before us by the ugly maid amazed me more. Somehow Petrus had access to coffee and cow's milk and other luxuries not even the French administrators could get their hands on. His wealth was truly formidable; the war could not erode it. Quite the opposite. With oil at a premium, Petrus was augmenting his fortune through the distillation of aviation fuel from his rice stocks and dismissed any mention of the famine in the north.
As we ate, Trau painted his ekphrastic dreams for my benefit. Lost amongst his own words, Doctor, he reminded me very much of my own grandfather, back at our gallery on the Ginza.
'I intend the marriage of two shades of green,' he said between bites of rice-flour-bread, 'not mixed colours; not a single shade; but two antonymous colours, placed side by side on a canvas. The outcome will be a kind of magic. One could call it the mystic vibrations of kindred tones.' Where Van Gogh obsessed over yellow, Trau loved green.
Kozu refused to eat, complaining that the opium-laced Golden Bat cigarettes had given him stomach cramps. He chose, instead, to walk up and down the edge of the canal, watching those prisoners, occasionally coming back to the table to pause and watch Trau's sister, as she listened to her brother swear an oath that he would not rest from painting the rice fields and rubber plantations of his homeland, until he had succeeded in finding two such mates, had laid them down together as bedfellows, or better yet, as two tragic lovers in a tomb. The mutuality of their presence, he assured her and the whitening sky, would revive them both.
In all honesty, I was lost for words most of the time. How was I to react to the young Viet's manifesto? To derail the youngster's ideals would have meant angering Kozu. That, I was not prepared to do. Still, I wanted to say to him, 'You are Asian, boy! Why muddy that? Why not seek after something truly Asian, not diluted by a westerner's ravings?' Don't worry, Doctor; I recoil just as much on recalling that memory as you do on hearing it! Can you believe I thought such a thing? Of Van Gogh of all people? But alas I did. If it was not for Petrus I would have said to the young Viet that we Japanese were fighting a war to keep Asia for its own, sure to remind Trau that if the Kenpeitai were to hear him, they would charge him with sedition.
It was Petrus who gave voice to my doubts.
'What is there to like about the countryside?' He questioned from over his coffee cup. 'The cutthroats? The revolutionaries? Disease? The fields filled with centuries of shit?'
For the first time that morning, I heard Kieu speak. 'I like the rice fields,' she said, her French accent soft, as if she were from the Provence-Alpes-Côte d'Azur. 'The sky, the way it hangs on them – or, just before harvest, the passing of a breeze through the long green stalks: it reminds me of ripples crossing a temple pond.'
'Only at a distance,' Petrus countered. 'Up close, those stalks look more like the fur of a mangy dog. The smell is worse still. The route de Bing Bông is a tourniquet. The road keeps disease at bay.'
Kieu excused herself in her native tongue and joined Kozu at the water's edge. I watched them both, very much aware that, out of the corner of his eye, Petrus was watching me. How lightly the Viet girl walked, Doctor. How often she smiled, when talking with the old artist. I wondered what they could be speaking of. I can recall lamenting, in that moment, the fact that Kozu no longer painted women's portraits. After his first expeditions to the China front in '38, the military censors had deemed his Asian nudes decadent. 'Ours is a holy war,' one critic had written soon afterwards. 'Who would choose the bark of even the smoothest tree, if it meant neglecting its blossoms?'
During dinner on March 9th, a week after my arrival in Saigon, General Tsuchihashi, the commander of Japanese forces in Indochina, slipped away from a reception he was holding for a number of French diplomats and administrators, at his residence in the centre of Saigon. At 7.00 pm, the General issued his French counterpart, General Decoux an ultimatum: secede Indochina, or face forced disarmament. Preparations had already been made, ammunition distributed. Decoux stalled for time. He was granted two hours. Not all Japanese units, on alert since the previous night, waited for the two hours to play out. They went on the offensive. Taking advantage of the pockets of chaos that followed, I accompanied Honma and his men, as they rounded up suspected members of the Free French, their sympathizers and métis, Eurasian members of the Sûreté. I took my list and annexed those artworks at greatest risk of damage if full scale insurrection were to erupt. We encountered little resistance. At around 9.00 pm, I remember, there was burst of automatic weapons fire, somewhere close to the military hospital, then silence.
It sounds extraordinary to tell you now, Doctor, but I had completed my work by late afternoon of the following day, Honma's men were so efficient. I returned to Cholon without sleeping, where I deposited the works I had liberated from the villas of the French Quarter, the Governor General's office and home in particular (one detachment of Honma's men even struck out for the Ville Blanche, the governor's residence on the coast). Japanese units were visible on the streets, their smiling young men (those who had never seen action before) a stark contrast to the weathered faces of their older colleagues, those who were supposed to be recuperating after action in Burma. Sound-trucks travelled the streets, sporting the flags and slogans of the Greater East Asia Co-Prosperity Sphere, passing under many billboards still carrying the images of Marshal Pétain. Local civilians stayed in their houses.
Once, during the night, and again at first light, the major dispatched runners to check on Kozu's so-called Yellow House in Cholon. A company of French soldiers had escaped the city via the route de Bing Bông during the night and faded into the paddies beyond. My work complete, I ensured the major I would go to the artist myself. The operation of the previous night seemed to have invigorated the major and he talked to me excitedly about some of the pieces I had acquired. Still he smoked his cigarettes in his affected manner, but his tone of voice had softened, so that I started to feel a sense of camaraderie well up between us.
'Tell Kozu, I now have sufficient materials to at least start on my painting,' the major said, as I took my leave. 'The artist should be moving onto other projects by now. You should both come out to the Hippodrome this afternoon.'
There it was, Doctor. An invitation I paid little attention to, seeing that I did not really follow the major's meaning. That invitation has landed me here, in this old house, living in fear of the Americans, of their interest in me and my grandfather's gallery, exiled as I am to these mountains, to a life of millet gruel and vegetables I pull from the soil with my bare hands. And the snows will settle here soon. What will I do then? Your painting is more dangerous to me than you can imagine. At the time, I gave little thought to the major's enigmatic words. I don't think I even questioned what he meant by materials. Honma was a major in the Kenpeitai, as I've already said. It was best to obey. It was safer. More settling.
I found Kozu asleep on the bed tucked away in his studio, but before I could rouse him, Trau shouted up from the foyer. The boy was almost dancing with happiness.
'We are free,' he gushed. 'The French have been swept aside! This is no longer Indochine, but a new country, an ancient one: welcome, M. Takayanagi, to Vietnamien.'
I asked after Petrus. A rich Chinaman like him was to be watched at such a delicate time. But Trau was too preoccupied to take my questions seriously. With great élan, he revealed to me his latest works, three paintings he had worked on throughout the night – one after the other, after the other– and into the morning. All three were of the countryside directly across from the villa, their paint wet and fields gouged out of chartreuse and pear green.
When Kozu came to, I informed him of Honma's message. He looked uncertain and out of cheer, Doctor. Quite out of character. Trau showed him those same three paintings of his, but the master artist was unable to say a single word of praise. He did not even grace the young Viet's efforts with a smile.
He said that he must hurry; that Trau must help him complete his portrait of the liberating soldier. What with the coup, the painting was of vital importance, more now than ever. While he mixed his paints and prepared his palette, he explained to both Trau and I that your tableau, Doctor, had been commissioned by the Army: that the grand image was to act as a means of justifying the military action that had swept the French from administrative power. It would be taken most probably to the Hotel de Ville. There, in that grand foyer it would proclaim our conquering army a force of liberation.
I saw through him. Honma, surely, was looking to collect on whatever agreement they had made. The major wanted his portrait completed. The privileges and freedoms granted Kozu by the major came with a price. Still, the master artist could not abandon your painting Doctor.
How long had I spent watching Kozu during my spare hours? How much longer still did I look on the artist's efforts to lift Trau and Petrus' forms from the mist of its burnt-sienna under paint, along with the walls and floors and furniture of the Yellow House? How long did Kozu agonize over Kieu's bound body? It is hard to say. There the canvas lay, your painting Doctor, on the floor of the studio, an expression of our struggle against western imperialism. Kozu was bent over Trau's figure, shuffling round the edge of the image so as to focus on the grain of a cabinet, all the time instructing the young Viet on where to work up an edge of curtain, a fold in his own painted uniform, a crease in his sister's smock. For that past week, the painting had been a symbol to me, grand and beautiful, but somehow strangely abstract. Overnight, its metaphors had turned to flesh.
Trau saw it too and quickly dropped the subject of his own paintings, those three brightly coloured and empty landscapes, which he left to dry on the balcony. Every word, every instruction Kozu issued the young Viet, looked to penetrate Trau to the core. He revelled in the oils that gradually coated his fingers, then the whole of his hands. At one point, Kozu ordered him to dress once again into his corporal's uniform, after which the artist ordered the boy to stand, to burst through the balcony window curtains, to pause, telling him to keep his back erect, legs slightly bent, face stern, proud. An hour later, his corporal's uniform dark with sweat in the late afternoon heat, Trau once again fell to his knees, taking up fresh brushes, and following Kozu instructions with renewed vigour.
Wagner blared in the background: the grand march from the German's Tannhäuser. That favourite of Van Gogh's.
Petrus, by that time had returned from whatever errand had taken him into the city. He came to the studio, looking for his wife. Kozu told him to take up his usual position at Trau's feet. The Chinaman refused. Kozu lost his temper and informed his host what would happen to him if he failed to cooperate. Once installed at Trau's feet, en pose, Petrus chain-smoked one Golden Bat cigarette after another, until his head finally slumped down onto the floorboards. Until that moment, Kozu kept me busy by barking orders at me. 'Open that tin of turpentine; wash out these brushes; open the curtains wider; fetch us a lamp, the light is fading too quickly; Trau needs a glass of water.' And the like. But with Petrus unconscious on the floor, Kozu's mood shifted.
'Fetch Kieu,' he said.
I found the girl in the garden, pacing the canal bank, dressed in a cotton blouse – yes, it was yellow, with a mandarin neck. Her hair was up. What details to remember Doctor! I had grown so accustomed to watching her pose for Kozu in that black peasant's smock he had found her that I had forgotten she was the wife of the wealthy businessman. I informed her of Kozu's request, of how urgently she was needed.
'You are the body of Asia lost,' Kozu said to the girl in the studio as he bound her hands, his voice strained. 'Lost: then saved, by the heroic coming of we Japanese.'
Kozu and Trau painted well into the evening.
Perhaps the raid that levelled part of the Chinese City that night was in reprisal for our military's success – our last success, as it was to prove to be. A token, Doctor, a means to let us know we were surrounded. The bombers arced round into Saigon from the southeast. Kozu and I were sitting in the garden of the Yellow House when they came. A siren pierced the sky and a strange stillness fell over the garden, along the canal, and those tufts of jungle that crept up to the water's edge past the distillery, where the palms gazed down at their own reflections. The insects and frogs in the paddies fell silent, too. I stared at the black sheen covering the canal, that oily surface, whose darkness seemed to spread out from the filthy membrane to ooze over the boats and banks and leaves and walls and of the city.
The drone of heavy engines rose out from that silence, as if the planes were spectral, a plague of ghosts gathering for vengeance above the Plain of Reeds. I will reiterate Doctor: it was a night raid. An unusual tactic for the whites by that time in the war, seeing we no longer had any fighters with which to counter them. All of that fuel Petrus' plant distilled and none of it could save the city of his birth.
I believe I said to Kozu something about the locals, how I imagined them smiling up at the enemy aircraft with those vacant Asian smiles of theirs, neither happy, nor angry, but just because the foreigners were there, over their country. How could I have known that only two days before, on the eve of our great coup in Indochina, American bombers had dropped petroleum jelly and incendiaries on Tokyo; that they had turned the city to ash, my grandfather's gallery included? It would take weeks for such a truth to become known to me.
'You're drunk,' was the artist's reply.
'No more than you.'
On the other side of Arroyo Chinois, an anti-aircraft battery opened up. A melancholy sound. It all seemed so ridiculous, those shells bursting amongst the stars, bringing to mind thoughts of summer fireworks over the Sumida River back home. I told Kozu we should probably find a shelter. Did the house have a cellar? I was not too concerned at that point, believing as I did, that the planes would strike at the docks on the far eastern side of the city.
Kozu turned his shoulders and looked back into the house through the latticed wall. A dimmed lantern burned inside, on a bureau angled obliquely into a corner of the parlour, its orange ball made invisible to anyone on the other side of the canal. There Petrus sat, opium-dazed, writing what he called, 'an epic poem.' An hour had passed since the Chinaman stirred from his drugged sleep and found his wife kneeling before Kozu, her hands bound behind her back, smiling at the painter. On seeing Petrus awake, Kozu had backed away from his canvas and told Trau to change out of his uniform, to wash his hands. Whatever spell the girl cast over the artist when she modelled for him was broken. He would not lay down another stroke that night, he said. Besides he had decided that gold leaf was better for the bayonet of Trau's rifle. The process of digging down into his layers of paint, to strip away that slither of gunmetal and clean the oil off the canvas was too intricate a task to attempt at night. And where was he to lay his hands on such a precious material? There was no choice but to wait for daylight. Moreover, he was exhausted. The job of preparing and applying the bole was beyond him for the time being, whether he could find any gold or not. The adhesive, too, would take an age to dry enough to become sticky, for the gold to be applied.
The lantern cast shadows inside the Chinaman's hollow cheeks. Its light welled in the deep polish of the desk's mahogany, like something from Van Gogh's Night Cafe.
Kieu was somewhere in the parlour, close to her husband and out of sight of us. I could feel her presence. I could almost hear her breathe, or so I thought. Most probably she was right behind Kozu, a dark shape filling so few holes of the lattice work. But she was listening to every word we said, of that I was sure. Listening. Waiting for us to move to safety. Kozu was tense, but remained in his chair, as if he too felt the girl's eyes and ears. He wanted to impress her.
The sirens cried on. The air defences putted and pom-pom'ed. Every surface sweated. My clothes were damp, as always, and there was no hope of relief. The first bombs whistled down and exploded. From the veranda, I looked out through the trees of the garden and watched the amber glow of conflagration thicken amongst the warehouses to the east, then the north. The bombs were a good ways off, but, still, they fell on Cholon. This was not to be a raid on the Docks de Saigon, after all. Frantic voices erupted from the distillery's complex. The wood decking beneath my feet vibrated. Shocked into waves, the canal's surface lapped the pilings like netted fish.
Kieu slipped out of the darkness and stood beside us, her back to the canal. Her eyes were wide and bright against her dark face. Kozu stirred. His measured movements exuded confidence, his very silence inspiring calm.
We made our way through the parlour, Kozu leading Kieu by the elbow. Dipping his pen into the inkwell, Petrus refused to look up at us, to acknowledge our passing. Trau met us in the hall, fretting over the fate of Kozu's painting and not his own.
'It's still wet,' the boy said again and again. It was as much as we could do to stop him running up the stairwell and to the studio. 'Are you just going to abandon it?' he raged, but his sister calmed him.
Outside the rumble of the bombs became a roar. A strange wind whipped up and around us. The air quaked. I stumbled about because my legs were shaking and the ground heaved. I cursed the dyke and its road, the white gravel that was as good as a lit boulevard, a neon strip leading the bombers along the canal to the distillery. The earth swallowed us. A slit trench, Doctor, dug by the men of the distillery. Local voices babbled up and down that wrinkle in the earth. I tasted the damp soil on my lips.
A hundred yards away, a warehouse flew to splitters, then another behind it, in the opposite direction to the Yellow House. A barge on the canal exploded. Warm water fell on us like soft rain. White smoke, Doctor. The stink of cordite. All this I remember with vivid intensity. The flashes of light. Kozu, with his lips pressed into Kieu's hair. Shockwaves. Shrapnel – not quite splitting the air at that distance, but falling none the less.
Something struck me on the head, right on the crown, like a nut falling from a tree. I wondered what it could have been, where it had come from. Can you imagine, Doctor? The bombs were falling closer and closer and a strange curiosity took over me. Was its part of a rivet from the boat? Or the tip of a nail wrenched free from a roof beam? My fingers sifted through the soil in the bottom of the trench, around Kozu and Kieu's knees. And there I found it, Doctor. Human teeth. A fragment of a person's overbite.
Honma arrived the next morning and I accompanied the major on an inspection of the warehouses close to the distillery. The shock of having survived the attack was wet within my nerves, like the paint on Trau's canvases. I could not stop babbling.
'This reminds me of Ginza after the Earthquake of '23,' I said at one point. 'I recognize the stench. It's like rotten apricots.'
Kozu had already taken Kieu back to the villa, leaving Trau to wander through the debris, to stare at the coolies, gathered from the local warehouses, who were laying out the bodies of those killed in the raid. Military policemen paced up and down the route de Bing Bông, handkerchiefs wrapped around their faces. Over a megaphone a voice boomed out through the smoke. I asked Honma what it was saying.
'Look at what the imperialists inflict upon your people; that is what it says.'
The thought of those teeth kept coming back to me, their texture haunting my fingertips, as I played with their cloth bundle in my pocket. How fallible the body was. How easily something like a tooth, even a jaw, could be lost, blown loose by an explosion. It was not something I had thought much about before. Eyes, yes. And fingers.
I said as much to Honma, before adding, 'Perhaps, it is time I left for Japan. The ship is a week overdue. That alone is dangerous. People will ask questions. Besides, Major, with the utmost respect, it is too dangerous here for Kozu to remain here in Saigon.' I let the major mull over my proposal, refraining from pushing the point.
When we walked up to the iron gate of the Yellow House, Honma directed my line of sight to a faint ribbon of smoke lifting straight into the sky from the distillery's chimney. Already the place was operational.
'Don't you feel, Takayanagi,' he said, 'that it is a great coincidence that your Chinaman's works were spared last night? The power station over the canal was not so lucky.' He did not expect an answer, of that I am sure. If I had offered my opinion on the matter, he would have turned on me. With a tight-lipped smile the major passed by the gates, pausing only once to look up at the house's grand façade.
'Would you come in for some refreshment?' I asked.
Honma refused. 'There is a city to police.'
Doctor, you must be familiar with the saying, 'He can recite the morning prayer without learning it: the boy who lives before the temple gate.' I guess for most of my life I was that boy, living under my grandfather's watchful eye, the Midori my home-from-home, what with my father's continual absence.
To many people – my grandfather and his clients, alike – the gallery was a threshold, more the house beside the temple gate than the temple itself. There one could stand on the edge of the soot and muck of Tokyo, the restraints of business and fine living, and look upon Kozu's work. His enormous canvases, his Realist mode of illuminating the beauty of the Japanese woman, the care he gave to refining that particular shade of white that defines our beauties' skin, how it is haunted by an undercoat of pale blue, almost invisible to the eye, a ghostly quality quite unlike the pink bravado of Caucasian women. And the lustre of our women's hair: only Kozu could capture that tactility and amaze my grandfather's clients. Sometimes, I believe, my grandfather thought himself alone in his gallery, and not entertaining a wealthy patron, a member of the Matsui clan, or someone of equal standing. I can hear him now, his thoughts spoken aloud, as he wondered why Kozu chose to paint his women with their hair down and not worn up in their usual coiffeur.
Yes, Doctor, Kozu's works are as familiar to me as that temple prayer, lodged within my heart, my memory, though I never paid them much attention. It was only after my apprenticeship in the Paris offices that I took note of Kozu as a man, and only then, as an exhibitionist. What did he know of Soutine's suffering? I asked myself, after having watched him dispose of that horse. Still, his works, so fawned over by both the Paris and Tokyo elite, so praised by the critics and connoisseurs, did not leave their lasting impression until that day of the air raid. Only then did Kozu's depth as an artist become apparent to me.
I see I confuse you, Doctor. Permit me to reveal the true nature of Kozu's crimes, the motive behind the Americans' search, the reason why I cannot buy your painting. Ask yourself this Doctor, why are the OSS so insistent on collecting any works by the artist? Why those from Indochina, in particular? Why this picture you have brought me?
Whilst Honma was arranging for one of his trusted rickshaw drivers to return me to the economic school on the Gallieni Boulevard (many of our officers were weary of travelling by such a means of transport, Doctor, fearing French agents – but I can tell you,
the opposite was true: many of those men, their
limbs dark and thin like willow branches, were
under the employment of the Kenpeitai!), Kozu appeared at the gates of his Yellow House. Until that moment, I had never actually seen the two men together, though each man had spoken so much of the other that I felt a bond of brotherhood between all three of us.
To my surprise, Honma simply gave a curt bow, more in deference to Kozu's rank than as a mark of respect to the artist, to a man of intangible worth. Or so it seemed to me at the time.
Kozu told the major that he would accompany me to my billet. Honma grunted his agreement. No mention was made of the painting Kozu was supposed to be creating for the Kenpeitai officer; that was, until our rickshaw was about to pull away. At that moment, Honma leaned into the cab and said in a low voice, 'Hold on to this fellow, Kozu-sensei. (By which he indicated the rickshaw driver.) He'll take you to where you need to go. I'm sure Takayanagi here won't mind. Actually, he'll rather enjoy the distraction I think, what with the events of last night.'
At the school, I changed out of my filthy clothes and washed the night's dirt and soot from my skin, my finger nails. There was no running water; just a large earthen pot, used to collect rainwater. Standing there, naked, dipping a bowl into the tepid water and pouring it over my skin, I felt wretched, like a native. The luxuries of Petrus' villa were a dream from another world. I longed for the cleansing waters of a hot spring, to go home, to feel the chill of real March air, whilst bathing in an outside pool at my favourite spa resort in the Yatsugatake Mountains, indeed, not far from here, Doctor. If I had only known what would happen after the war. Even the conditions at the school, Spartan as they were, were better than this farmhouse, these tattered mats and millet gruel.
Kozu, after a quick discourse with the school's rector on the state of the war, joined me in my room. I showed him my trophy, those four teeth that had struck me on the head and which I had, by then, wrapped in cotton wool, having decided to keep them safe in a glass jar I had removed from one of the school's laboratories. To this day I don't understand why I did that, Doctor – why I kept such a grizzly reminder of my fear, why I showed them to the artist. Perhaps a man like you can empathise with such a brutal act.
The artist turned the jar over in his hands and sighed. 'I tried to sleep this morning. But the sound of the bombs echoed in my ears – that whistle of theirs in particular. I just couldn't shake the fatigue. I feel it now. It fills me like water.'
I told Kozu what I had told Honma; how I thought Cholon wasn't safe; how the whole of Indochina would fall with an American amphibious invasion within weeks. His painting of Trau, of his liberating warrior, could be left. I recommended to Kozu that he return with me to the homeland. The hospital ship would not hold on much longer.
'I cannot. Honma will not allow it. Besides, I must paint his damned portrait.'
What he said to me next, Doctor, has haunted me ever since: 'I know this war is already lost. That is why I must paint what Honma wants me to. I must show the horror of it all. If I do not, I am doomed.'
I reassured him that the Imperial House would not permit the military police to harm him, at which he smiled.
'It is not Honma that scares me.'
I pressed him for an explanation, but he just smiled.
Putting down the jar on my cot, he stood up. 'You heard the major. Our rickshaw awaits. We can't keep the major waiting.'
Doctor, I do not wish to dwell on the nature of the establishment to which we were delivered, but, to be brief, it was a green house, one of the brothels run by the Kenpeitai to garner favours and information from its clients. Honma was waiting for us in a back room, his face and neck a livid red hue. A ceiling fan cut the air above us, stirring up the heat and heavy pall of opium. The major was in good spirits, offering us whiskey, which neither Kozu or I refused.
'Have you ever been to Kure, Takayanagi?' Honma asked after he had poured out our drinks. 'Unlike the two of you, I have never been to Manchuria. My previous posting was in Java, but I assure you, Takayanagi, the morning I disembarked from that port, the cold was intense. I don't think I had ever felt such a chill in Japan before and to think, that was the last time I saw our homeland. The scene was remarkable. Black cliffs fell into black water and great mists rolled down from the mountain peaks, surrounding the port on all sides. You couldn't see the warehouses clearly, or workshops, or the dock cranes, for that matter. But I tell you what we could see: standing on deck, we could make out the carrier Amagi, moored out a little ways in the bay. Gentlemen, I tell you, the way the cloud cover floated above the sea, breaking up the shape of that great ship, I was speechless. I do not have your expertise, but I tell you her steel hull, it was storm blue, like a hanwei spearhead.'
The major refilled our glasses.
'Amagi. Educated men like you must be familiar with the Chinese characters of the ship's name? They mean, "castle in the sky." In that moment, I thought of how little of our glorious country I had seen with my own eyes. I have never ventured north, not to your home Kozu-sensei, to Hokkaido, or to Aomori, to the Amagi Pass, after which the carrier was named. How insignificant I felt looking out at that ship, at the great beauty of that port in winter, between the sea and the mountaintops. The great sublimity of our land touched me.'
Kozu shifted in his seat. Though he tried to camouflage his feelings, I could sense he wanted the major to get to the point, to explain what we were doing in there. The major, already drunk on whiskey, was now intoxicated with nostalgia. 'To think, Takayanagi, I had seen Kozu-sensei's The Shoukaku Departs Kure at the Holy War Exhibition in '43. I thought it a fine painting then, but after seeing the Amagi with my own eyes, I felt as though I were seeing the painting again, afresh as if Kozu's hand was rendering the port, the great ship, as I looked on. I remembered what one of my friends had told me once, about how, at a private viewing of Kozu-sensei's works at the Imperial Palace the whole of the general staff saw a figure in one of your paintings move. Seeing the Amagi, my heart was stirred with great pride.
'You flatter me too much, Major Honma,' said Kozu.
'No, no. Quite the opposite. I cannot praise you enough. That is why I am so honoured by your agreement to paint my portrait.'
A chill went through me. I expected the major to stall, to explain how he would not let Kozu return to the homeland, not until his portrait was complete.
Kozu said, 'And I do not see why we don't get started as soon as possible. The air raid has brought to the surface many unsavoury things.'
Honma nodded. 'Yes. Don't think that your Chinaman's good fortune last night went unobserved. How convenient that, while the rest of the canal area was hit hard, the power station especially, his whole complex was left unscathed. His distillery was completely left intact. What providence.' The major's eyes, wet with drink, glistened. 'So, I have decided to arrest him.'
'A wise decision, Major.' Kozu poured Honma another finger. 'This may be the very opportunity we discussed the other day – when we spoke at the racetrack. Though I must say I am not without reservations. I feel it my duty to say that leaving a man's wife to fend for herself is a great shame. It will be dangerous for a woman to live alone in that house. Not in Cholon, not with the marshes so close. As such, I would be glad if you decided to remove her into my custody.'
Honma's smile grew, but he agreed, adding that Kozu should come by the racetrack the next day. Time was of the essence. Once again, the major made reference to the great preparations he had made, so that his portrait could be completed. You are quite right, Doctor. This time my interest was pricked. I asked the same questions as you: what preparations? What materials? Why would Kozu have to drive all the way up to the north of the city for a commission? Why couldn't the major come by the villa, to the studio Kozu had already established? Only, I dared not voice my concerns.
The major continued, addressing me directly. 'Soon, Takayanagi, Kozu-sensei here will have finished his work for me, if his reputation for speed is anything to go by. Then you can whisk him off to Tokyo, but before you do, you too should come by the racetrack. I'm sure it will be quite the experience for a civilian, such as yourself. Feel free to enjoy the establishment, gentlemen. I feel I must be fully rested for our big day tomorrow. And as for your repository at the church, Takayanagi, your so-called safe house, I have taken measures to ensure the artworks there remain safe. I took care of the matter personally. Not a soul is left who knows of the secrets buried in the crypt, other than you and I, and the guards I personally selected to protect you. I assure you, the church will be quite safe. Quiet.'
Kozu gave me a knowing look and poured us all another drink.
Of course, Doctor, I was horrified. Never did I think that the men Honma had provided me with would meet such an end. And that was just the beginning. Remember those preparations I made mention of moment ago? Their true nature I will make clear soon enough.
Frequent squalls darkened the sky the next day. The rain in the morning was black with ash, but by the afternoon, the windows of the villa were washed clean. Kozu and I were taken to the Saigon Hippodrome in Honma's Adler. It was during that ride that the major explained his plans, as the artist and I listened to his discourse on sword technique. There was to be an execution and Honma had already formed his opinions on the best angle Kozu should view the beheading from, how close the artist could stand. The tales we may have heard from old army hands, of gushing blood and the like, were an exaggeration, he assured us. As proof, the major said he would not remove his white gloves.
It took an age for our car to work its way through the network of streets and canals, passing the Chinese Pagoda on the rue de Cay Mai on the way. By the time we arrived at the Hippodrome to the west of Saigon and north of Cholon, the afternoon was all but spent.
To call the place a race track was an exaggeration. It was little more than a stretch of flat land, the track roughly cut from the grass by the stamp of horses' hooves, the edges of which were marked by a barb-wire perimeter. The Korean guard who opened the barrier had a bruised face, a closed-over right eye. According to my driver, not a single race had run since the Imperial Army came to Saigon. Still, the grass would not grow back. Spread out across the course's central expanse was a series of tents, as if a garrison were billeted there.
On leaving the car, I was overcome by a smell similar to the one I told you of earlier, of the abattoir. When the stench of overripe apricots gets in your nose it will not come out. But this was even darker. Older. Clouds of flies blackened the air. Honma said that there was still some time before the prisoners would arrive. The Chinese Chamber of Commerce Building, the Kenpeitai's central jail, was even further away than the villa.
'I expect, Kozu-sensei that you wish to continue with your sketches?' Honma said. 'I have arranged things as you asked them to be left.'
A shallow bow and the major paced off to the far side of the compound. Kozu waited until Honma had disappeared into a tent, before saying, 'Well then Takayanagi-kun, welcome to the realm of hungry ghosts.' He did not look up to meet my eyes. His hand rested on the flap of the nearest tent. 'Let me show you something.'
Lifting the flap to, he asked that I follow him inside. That is how I discovered the true purpose of the tents; that they were there for a reason. Not to billet troops, Doctor, as they appeared to do from outside the wire. No. What I saw inside haunts me to this day. Lines of bodies, Doctor. Those soldiers killed on the night of the coup, or in the air raid, I did not know. Some were Frenchman, others Japanese, though only by their uniforms could I tell them apart in some cases. They were laid out on raised cots. I have not the words to express the scene, Doctor. Magritte, perhaps, could see the sense in it. But only Kozu's eye could do it justice.
Kozu began to walk amongst the litters. Many of the bodies had swollen and blackened with the heat, their heads looking like overripe grapes. The swelling face of one soldier had bent the frames of his spectacles out of shape. His lips belonged to a Negro caricature, not an Imperial soldier.
'When I listened to Lieutenant-General Saikai address our troops after the taking of Hong Kong, I heard him call this is a war between races. That when we kill the enemy we are avengers, easing the brooding anger within us, within Asia.' Kozu pointed to the line of litters. 'Look at these two: one without an arm, the other a leg. How tranquil they look.' (I, for one Doctor, could see only dead flesh.) 'Tranquillity is the absence of emotion. Somebody said that. Don't you think they whisper to us? Don't they say, to be whole is good?'
'I still don't understand.'
'Petrus is to be the star attraction of our little show.' The artist's words trailed off. He paced the grid once more, following a column of litters for five or six paces, then a row for two and then changing direction again.
'The rules have changed, Takayanagi-kun. Before, when I painted the rot of the battlefield, my paintings disappeared. The Imperial dead, or at least their images, were not to be exhibited in public. Now the Americans are coming – not just to here, but to the homeland. Now we are asked to depict our fallen, to bind our people, the kokutai, together. We are to be one in our anger and suffering. Honma wants a memento mori of his own, a testament to his power over life and death. I agreed to paint an execution for him, only he didn't want a formal situation. What he wants is for me to fabricate a battle around him, so it will look like he is performing an action in battle: retaliation, justice. This,' Kozu motioned to the dead, 'is all part of his preparations. As you can see, they are extravagant. He offered to have the bodies taken outside if I desired; to lay them out as if in some diorama. The Americans are coming, Takayanagi-kun. What will you tell them about today? About what you have stored under that church in Cholon? Will I doom myself, knowing the Americans will not stand for such scenes, for such uses of art? Never. I will paint the horror so vividly, as to state that I was witness to the brutality of the Imperial Army. I will say that I, Yuichiro Kozu, recorded what I saw on purpose, with the utmost care. Here is my proof. My paintings are records, documentation of my horror. They will have to let me go. They will probably think me a hero.'
Close to dusk, Petrus' transport arrived and the Chinaman, along with five others – three of whom looked French – were dragged down from the truck. Their legs hung limp, their knees banged against the tailgate, but Petrus for one seemed beyond caring. He and his compatriots were taken out into the expanse of grass in the middle of the racecourse, to what resembled a parade square, a shielded spot, what with the dim light, the distance from the perimeter, the lines of tents. Nobody outside the compound would able to see what was going on. Honma was careful that way. He liked to keep about him the mystique of power. He didn't go in for public executions, the displaying of the head afterwards. He said it was foolish to incite the locals with such tactics.
A tarpaulin was laid out flat on the grass in the square's centre, a guard standing on each of its corners, his rifle slung or leaning against his body. Homemade cigarettes smoked on their lips, between their fingers. The soldiers' uniforms were dirty, dark with sweat and rain and the job of moving the dead from ox-drawn carts into the tents, onto the cots prepared for them. From the square faces of these men, they looked to be of country stock and ill-educated. Seen from under the cover of the command tent, their combined weight preventing the wind from getting underneath the oiled canvas covering and rolling it over, I imagined them muttering obscenities about their orders, how the cots were a waste of precious resources, cussing about Kozu, but mindful of their words regarding Honma, as if the rain itself could pass on their words to the major's ears. These details I remember distinctly Doctor, though in memory, everything seems brighter than it could possibly have been, what with that dark sky and the smell of wet soil. But then again, even lead can be polished to a gloss finish.
When finally I followed Kozu and Honma out from under the cover, my thoughts were on Petrus and what I was finally understanding was certain to become of him -- the four guards would use the tarpaulin, of course, to scoop up Petrus' corpse after the beheading. And yet, with this full knowledge of another's gruesome end, would you begrudge me some selfishness Doctor? For as clear as things were for Petrus, I admit my greatest worries were over our own fearful predicament -- that some unknown power, some circumstance, would prevent Kozu from completing the major's blasted painting of this awful scene and hence, our escape.
The two men strode towards the execution ground, the major's white gloves flashing with a measured rhythm. I could hear only snatches of their conversation, something about standard procedure, how if they were in China the condemned would usually dig a pit for their own remains, before standing over it. Kozu grunted his agreement.
The guards, having disposed of their cigarettes, stood at attention. Honma and Kozu drew near, I close behind. When Petrus was dragged into the open from the other side of the square and delivered onto the tarpaulin, I swear to you Doctor, I could smell his body from where I stood. A tang, like rotten garlic.
'Now, a headstrong type would swipe down with his sword, Yuichiro,' Honma explained with a motion of his hands. 'Doesn't always work. You can miss. I've seen lungs pop out from shoulder cavities and all kinds of things.'
Petrus' eyes were glazed over, his cheek split, the blood sticky. He must have understood what the two officers were discussing, despite the fact he spoke no Japanese. A nod from the major and one of the guards stepped forward and pushed his rifle butt into the back of the Chinaman's knees. Petrus slumped forward, while the guard who had brought him forth stopped his torso from keeling over.
'See how the body sways, Yuichiro; you have to capture that rhythm somehow in my painting. That's how one can miss – if you don't concentrate, if you hesitate. That's why you don't swing your sword like a fool.'
Honma turned to look at the artist.
'Perhaps you would like to do this yourself? What do you say, Yuichiro? Then you could truly step inside the aura of your subject – the ecstasy that follows an execution. Don't you believe it your duty to render such a feeling, to make it sensible? No one else has the power to do so, only you.'
What could have been going through Kozu's head at this point, I can see you are wondering now, as I did then. If Honma had handed you his sword, Doctor, and instructed you to do the act, would you have? What other choice would you have but to kill or to die? Are there any other choices during a time of war? I watched the fingers of Kozu's hand tense.
'This sword I put before you was crafted for such a purpose,' the major said.
In that moment, I thought I saw in Kozu's eyes – not even a flicker, never did he blink -- that he was capable of murder. Not out of fear for his own life as I just put it to you now, but because he was the great Yuichiro Kozu, a man who would give and take everything for his art.
But I was wrong.
After a pause, Kozu said, 'With respect Major, I must witness the shadow of rapture myself. The wound I can look on afterwards. It is your face I must watch and study.'
Honma nodded and, satisfied, drew his sword. With a curt step, he placed the bevelled edge at the base of Petrus' neck, the hand-guard touching the Chinaman's skin. By the time I had lit one of Trau's cigarettes and drawn the heat of the smoke into my lungs, Petrus' eyes looked out across the grass, hard as marbles, as if searching for something beside Honma's boot.
One at a time, the five other men faced the same fate. The major's gloves remained fantastically white throughout the whole affair.
I should pause here, Doctor, I know, but my story is coming an end.
A strange relief washed over me in the wake of Petrus' execution. Kozu will surely work quickly now, I thought; Honma's portrait is so much smaller in scale and lacking the ambition of his grand tableau for Ambassador Yoshizawa. The artist, I was sure, would finish soon, like Trau reeling off one of his green vistas. I could almost smell the sea salt, feel the deep sway of the ocean. Having made the voyage across the South China Sea in the hospital ship once, I was confident the American's sentimentality would keep us safe. Return we would, and with a horde of paintings to keep the nation's faith burning. Your painting, I was certain Doctor, would remain in Kozu's stead, a gift to the Vietnamese people, a token that reminded any onlooker where the real threat was and how easily we had brushed them aside.
I was close to euphoric. And, truth be known, I was amazed at how quickly I had adjusted to the rigours of war. How I had not embarrassed myself by vomiting. No one, I believed, had seen me look away at the last moment – their attention so much drawn to the Chinaman, to Honma's ancient blade. And what a bathetic ending the Chinaman had met. He gave no last words, no valiant gesture of defiance. He simply knelt, swaying gently from side-to-side. I had somehow expected more at a man's death.
With the major now watching Kozu's every move, every pencil stroke, the method behind his arrangement of his palette, I was left on the periphery. I wanted to go back to the villa, to get something to eat, perhaps to have a cigarette with Trau. The yoke from his and his sister's neck had been lifted. Petrus' death meant the villa would conceivably be his. Of course, I could foresee the military confiscating what rice stocks Petrus had stored away, and taking over the management of the distillery, but what concern were they of Trau's? He could live out the rest of his days in luxury, his sister beside him and no longer under the heel of the Chinaman.
How was I to return? Believe it or not, I struck out on foot. Without a guard for protection, though, my fear of ambush grew with every corner I took. Every native face appalled me. If I had carried a sword I would have drawn it. The Imperial troops I had seen on the streets after the coup were nowhere to be seen. Black clouds and rain once again stained the air over the Chinese City, like an ink wash, or burning wood.
When I arrived at the front gate of the Yellow House, I looked upon its grandness with nothing but contempt. It was absurd to have such a building in such a country.
At first I thought the place was empty. I called out for the maid with the pox-marked face, but received no answer. But there was a trace of Trau on the air. I could smell solvent, and a deeper pall than turpentine at that. It was bole. As casually as Kozu on that first night in the house, I made my way along the corridor decorated with stencilled vines, to where I knew I would find the wrought iron staircase. Letting my mind wander now that I was safe from the natives outside, I imagined passing down a corridor in one of those root-buried palaces deep in the jungle.
And if you are imagining, Doctor, that Kozu, with one painting on the go, might have finished another, you would be right -- how intuitive you are! When I reached Kozu's studio, I lit the room's candles and I found your painting compete, its soldier's bayonet shining with a lustre beyond oils. In our absence, Trau had taken over from where the master artist had left off. After our summons to bear witness to his brother-in-law's final breath, the young Viet had completed his own portrait, had lifted the painting away from the contingency of the world, not through an inspired choice of green paint, but through gold, rough overlapping shards, smelted and pummelled to a paper-thinness. The texture matched the surface of a worn bayonet well. Only, it was not really Trau's portrait at all. What I saw before me that afternoon was a hero from a distant land. Nonetheless he had done a grand job, having stripped the paint back to the canvas, like a butcher scraping the fat and tissue from a thin bone; and he had not been left alone all that long. How Trau's fingers must have moved with such dexterity; how they must have refused to shake, knowing full well as he did, that he was melding with a masterpiece.
How long I waited on the balcony outside the studio for Trau to return I do not know. The canal was a hive of activity, as was the distillery. It was as if Petrus' death never happened. The incessant call of the insects in the garden, in the nearby paddies, played on my nerves. I may have smoked one of Trau's cigarettes, Doctor, or I may have smoked a couple.
At some point I became aware of the sun and a presence behind me. I turned and found Trau wearing that damned old soldier's uniform. His mouth open, but with no words coming out. He was as white
as a ghost. He limped onto the balcony and shrank from the heat of the sun, stopping short after two
or three shuffled paces. His clothes were soaked through with sweat. Behind him, to my horror, the young Viet left a slick of blood across the bedroom's floorboards.
'You're not hurt?' I asked, confused, unable to formulate a straight question. My mind drew a blank at the sight of the blood, the boy's pale skin. Trau had been with us during the air raid. I remembered that. He had even made some dry quip about forgetting his matches, when we pulled ourselves from that makeshift grave by the dyke and looked upon the devastation along the canal. I had watched him and Kozu and his sister return to the house to check on Petrus, despite the fact that the place survived with little more damage than some loosened roof tiles.
'Did the Kenpeitai take you? Did they hurt you?'
He shook his head. At that moment, his strength gave out and he fell. I reached down and touched the bloodied rag wrapped around his left foot, unable to believe my own eyes. I prized apart and unwound the layers the material, to find a raw, oozing stump. His big toe was missing.
It would take Trau two days to regain consciousness, waking as he did in the Japanese military hospital near the Docks de Saigon. Kozu was with him when he came to. Only then did we find out what had transpired. Trau, Kozu's willing and able apprentice, had taken a chisel and hammer to his own body. To sever the big toe of his left foot at – you'll correct me if I'm wrong, Doctor – what is called the medial joint.
Such a mutilation, Kozu told me while we smoked on the deck of the hospital ship afterwards, was the mark of a thief in the village where he and his sister came from, out in the rice-growing lowlands east of Saigon. With no big toe, a thief could not hope to slink away into obscurity. His identity was forfeit. Everywhere he went afterwards his mark would follow, quite literally, in his footsteps, along every path, between every house, along all the byways that connected one village to another. There he would stand, long after he had walked away, his presence pressed into the red dust like a glyph in a printing press.
'But that does not explain why he did it,' I said.
Kozu tossed his butt into the sea. 'It was the gold leaf.'
The master artist went on to explain to me, how, in order to finish Kozu's portrait the young artist went on the hunt for gold. Without it, the bayonet would be incomplete. The painting's soldier, indeed Trau himself, would not transfigure. So, the young Viet broke into Petrus' bureau, and stole what he needed, believing all the while, Doctor, that his transgression was a crime of little consequence. What was one pair of cufflinks from Petrus' bureau? The man had plenty to spare. Trau broke the gold disks into flakes with the same chisel that would later carve through his flesh and bone, before heating them up, making them soft enough to flatten. The roughness of the process, Doctor, the imperfect finish, the crude application to the canvas: look what they did for that blade. How striking it is.
You are right Doctor. He completed the painting and then the Kenpeitai came for Petrus, while we were engaged at Honma's green house. According to Trau, they arrested the Chinaman in the night, beating him across the thighs with batons when he could not understand what they said. Trau hid with Kieu upstairs, but they were not harassed. His sister never shed a tear. Her quietude horrified him. As such, the young Viet was under no illusion as to why they had come, why they took his brother-in-law away. Petrus, he knew, would disappear.
Sat in his hospital bed, safe under Kozu's protection, Trau confessed to the theft of the cufflinks. Fidelity demanded Trau punish himself. He had stolen from one of his own, from his family, from one of his countrymen. Kozu, of course, dismissed the young Viet's words, the guilt they leaked.
'Art is always worth the sacrifice,' Kozu said.
Doctor, such talk makes me nostalgic for something that should never inspire such a sentiment. Seeing your parcel there, the painting I know is wrapped up within it, I am filled with desire. I cannot give you what you want. But the thought of the Americans taking such a work away – it is unbearable. And surely enough, they will pay you a visit soon, Doctor. Of that I am sure. Botticelli looked to be a thorough man.
It is not much, but I guess, I can make you a reduced offer. It cannot be much, but it is what little I have, perhaps just enough to cover the price of the painting's gold leaf, that precious streak of light, which emblazons your soldier's bayonet. Take the small sum as a token, Doctor, a sign of my good will. What else can I offer you, other than a slice or two of baked mountain yam and one last bowl of millet soup? May I suggest that you do take a little something to eat? Something warm. It is a bitter night out there, after all.
| {
"redpajama_set_name": "RedPajamaBook"
} | 9,000 |
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LEGO Star Wars The Skywalker Saga Release Date: Everything We Know
From the release date to flying the Millenium Falcon, here is everything we know so far.
By Marie Pritchard
January 20, 2022: Updated to include new information about the release date, characters, worlds, and vehicles.
LEGO Star Wars: The Skywalker Saga is coming, and it'll tie together all nine mainline movies in the franchise and wrap them up in its charming, slapstick, blocky aesthetic.
Optional Side Missions
Latest Trailer
Players will be able to hop to any movie from all nine Star Wars movies, meaning you'll be able to work from the Phantom Menace all the way to the Rise of Skywalker. Alongside this, you can earn yourself hundreds of characters to play as and embark on a plethora of optional missions on the side. You get all of this with the classic touch of LEGO humour.
From the release date to what worlds you will be able to visit, here's everything we know so far about LEGO Star Wars: The Skywalker Saga.
The game is due to be released on April 5, 2022. On release, it will be available for the following platforms:
As seen in the recent gameplay overview, you will be able to get your hands on and fly some of the most iconic vehicles from the movies. You can fly the iconic Millennium Falcon or strap yourself in to pilot an X-Wing. If that wasn't enough, you can also get your hands on a few land-based vehicles too. You can ride a Speeder-Bike on the Forest Moon of Endor or race around Tatooine on a Land-Speeder. Either way, you will be able to control some epic vehicles from the legendary franchise.
It is no secret that the Star Wars universe is huge and you will be able to explore a huge portion of it in the game. In the recent gameplay overview, we were introduced to the Galaxy Map and some of the planets you can unlock while playing through the story. Naboo, Hoth, and Dagobah are just a few of the ones that have been revealed.
More Star Wars: New Combat in Knights of the Old Republic?
You can stick to the main story quests from each episode (movie) or you can venture off and explore the planet. It seems that going off on your own little adventures is encouraged and you may even be rewarded with collectibles. We assume this means that the structure of each area will be semi-open world, if not fully open-world.
There are small activities that you can choose to do on your adventures. They are completely optional. Some of the activities and optional side missions that we have seen so far include a shooting gallery challenge where you have to shoot Womp Rats. Another is clearing out some baddies from the Mos Eisley Cantina or engaging in option dialogue with random characters.
You can find the latest trailer for the game below. Alongside finally getting a confirmed release date, we get to see more of the overall gameplay mechanics of the game.
We will update this page as we learn more.
LEGO Star Wars: The Skywalker Saga is not the only big Star Wars game that has been in development. Recently, Quantic Dream revealed a trailer for the one they are working on. So far, all we know is it's set in the High Republic Era and it is still in early development. In other news, Bioware's expansion for Star Wars: The Old Republic has been delayed until early 2022.
Contributions from Lloyd Coombes.
Gfinity Esports is supported by its audience. When you purchase through links on our site, we may earn an affiliate commission. Learn more. Looking for specific products? Visit Stockinformer.co.uk / stockinformer.com.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,149 |
module Discerner
class Dictionary < ActiveRecord::Base
include Discerner::Methods::Models::Dictionary
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 850 |
Productive life is not only about what you will do, but also about what you will not do. This was revealed by Twitter CEO, Jack Dorsey. He already has a list that will be applied in his life about what will be done and what will not be done.
According to Dorsey, in life, there must be a priority list for a better life. Dorsey decided to meditate, read the best non-fiction books, consider Twitter metrics and write about his dining experience through Caviar, which is a Square delivery platform he bought in 2014.
According to Dorsey, this can make him focus more on living life and becoming more organized. Next, before going to bed Dorsey reread the list that was not done.
According to the author of the book Kevin Kruse, the list that must be done is often a bad thing because they cannot distinguish between urgent and important needs. The list also does not often include activities that can interfere with your time. As a result, is lists for things that are done do not fully reflect your decisions on everyday life to move forward.
Jack Dorsey's time management list shows that he is intentional and aware of what he is doing and will not succeed, can help take control and manage the day well.
According to Jack Dorsey, the list will not do generally more important than the list is done. Setting intention not to work will give clearer space for thinking and working, and less reactive.
Many items on the time management list have become routine parts like milder like Jack Dorsey. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,130 |
\section{Solar Activity}
The Sun consists of hot plasma interwoven with a magnetic field. These fields are created and amplified in the outer envelope of the solar body, rise and blend through the solar atmosphere. Since the outer envelope of the Sun is very dynamic (mainly due to convection), the magnetic field changes with time as well. The phenomenon associated with the existence and variability of the localised magnetic field is called \emph{solar activity} and consists of phenomena such as sunspots or prominences. Violent phenomena such as solar flares and coronal mass ejections (CMEs) may potentially have a dramatic impact on the Earth's environment, see e.g. a review by \cite{Gopalswamy2006} or recent studies by \cite{Krauss2015}, \cite{Goswami2018}, or \cite{Badruddin2019}.
Solar flares are associated with a sudden reconnection of the magnetic field \citep[see a recent review by][]{shibata2011solar}. During the explosive reconnection, the coronal material is heated to tens of millions of degrees and becomes a source of X-rays. According to a standard (CSHKP) flare model, a disconnected plasma cloud (a plasmoid) wrapped in its own magnetic field is expelled into the interplanetary space in a form of a CME. There were also CMEs observed not obviously associated with a flare. Whether there indeed are two distinct classes of CMEs remains unclear \citep{Vrsnak2005}. Interplanetary CMEs have a great potential to strongly influence technologies on the Earth.
However, not only flares and consequent CMEs affect the close surroundings of the Earth. Moderate but principally similar effects may be caused by streams of the fast solar wind within the coronal holes or by the shocks resulting from the interaction of the fast and slow solar wind in the corotating interaction regions \citep[see e.g. a recent review by][]{Richardson2018}.
\section{Geomagnetic Activity and its Effects}
The interaction of the Earth's magnetic field with the solar wind shock wave or cloud of the magnetic field is very complex and cannot be described by a few sentences, see a review by \cite{Pulkkinen2007}. The interaction results in the disturbances of the Earth's magnetic field. These disturbances are in summary nicknamed \emph{geomagnetic activity}. Significant fluctuations of the geomagnetic activity are called geomagnetic storms. The causes, evolution and effects of the geomagnetic storms are comprehensively described elsewhere, e.g. in reviews by \cite{Tsurutani1997} or \cite{Lakhina2016}.
The level of geomagnetic activity can be most easily expressed by measuring the Earth's magnetic field strength. From the measured geomagnetic field and its evolution in time a variety of indices of geomagnetic activity may be constructed. One of them is a $K$ index. It is a semi-logarithmic quantity describing changes in the amplitude of the horizontal component of Earth's magnetic field over a three-hour interval. When $K=0$, then the geomagnetic field is in a quiescent state, $K>5$ indicates a geomagnetic storm and $K=9$ indicates a superstorm.
The interaction of the geomagnetic field with the variable solar wind induces changes in the terrestrial magnetic field at ground level, thereby possibly affecting the human infrastructure. The varying geomagnetic activity is connected with changes in the system of currents of the magnetosphere and ionosphere that generate a time-varying electric field at the Earth's surface \citep[see e.g. a review by][and references therein]{Buonsanto1999}. This geoelectric field, in turn, gives rise to geomagnetically induced currents (GIC) in the conductive structures on the Earth's surface and also below to a substantial depth \citep[see a review by][]{Pulkkinen2017}.
The GICs run through conducting regions of the Earth and seas and also between the endings of grounded conductors. They can produce damage in the system attached to the conductor such as a signalling network associated with railways \citep{eroshenko2010effects}, pipelines \citep{pulkkinen2001recordings} and particularly in power networks \citep{pirjola2000geomagnetically}.
The presence of GICs in the electric power transmission network may interfere with their normal operation and cause damage resulting in a failure or service disruption. GICs constitute a possible trouble for network transformers \citep[e.g.][]{Kappenman2007,Molinski2002}. The quasi-direct GICs lead to a half-cycle saturation by shifting the ($B$-$H$) curve to a strongly non-linear regime with a large portion of the magnetising current. In this regime harmonics are generated, heavy reactive power appears, the voltage may drop and even blackout may take place. Under half-wave saturation, the magnetic flux is leaked from the transformer leading to local heating. Oil in the cooling bath degrades, gassing appears. In the extreme event, the transformer core may start melting. The electrical current in the network changes its waveform to a distorted sinusoidal. Protective relays may react to the peak value of the corrupted waveform, evaluate it as overvoltage or overcurrent and trip the equipment. Last but not least, the presence of GIC impacts the stability of the system frequency with possibly damaging effects on generating stations.
Most of the available work deals with the immediate effects registered on the infrastructure during or shortly after significant events in solar activity. A large portion of studies was published on Qu\'ebec blackout in 1989, a very nice summary can be found in a report of \citet{NERC} or by \citet{kappenman1997} and later by \cite{bolduc2002}. Most of the literature deals with high-latitude locations because the effects of space-weather events are the strongest there. Nonetheless, the effects were observed during the storms and sub-storms also in mid- and low-latitudes, such as South Africa \citep{gaunt2007}, Japan \citep{Watari2009}, New Zealand \citep{Marshall2012}, Spain \citep{Torta2012}, or Italy \citep{Tozzi2019}. Large GICs in several mid- and low-latitude regions were also registered \citep{Kappenman2003}.
Only recently, research has been focused on the impact of fluctuating solar activity on the network infrastructures over an extended period. \citet{schrijver2013disturbances} studied the disturbances in the US electric power transmission network for the period from 1992 to 2010. They found, with more than 3$\sigma$ significance, that approximately 4\% of the disturbances in the US electric power transmission network are attributable to strong geomagnetic activity and associated GICs. This study was followed by \citet{schrijver2014assessing}, where the insurance claims due to the disturbances in the electric power transmission network were studied. The 4\% attribution to solar activity effects was confirmed. Moreover, in upper 5\% stormiest days the number of insurance claims increased by 20\%. In the upper third stormiest days, the total increase of the insurance claims was about 10\% larger compared to the quiescent period.
The aim of this work is to make comparable analyses for disturbances recorded in the Czech electric power transmission network and determine the relationship between the anomalies of the grid components and increased geomagnetic activity in the Czech Republic.
To our knowledge, a single study was published dealing with GICs in the Czech Republic. \citet{hejda2005} analysed the pipe-to-soil voltages measured in oil pipelines in the Czech Republic during the Halloween storms in 2003. They showed that the simplest plane-wave and uniform-Earth model gives results that correspond well to the measured pipe-to-soil voltages. To complete the picture, the study performed in a neighbouring country must be noted. \citet{bailey2017} modelled and measured the GICs in the Austrian electric power grid. They demonstrated that the Austrian electric power transmission network is susceptible to large GICs in the range of tens of amperes, particularly from strong geomagnetic variations in the east--west direction. That is due to the low surface conductivity in the region of the Alps.
\section{Data}
Although disturbances in power grids associated with strong solar activity events are known in Europe, no one has done a statistical study for European countries covering an extended period. There may be several reasons: for example, to carry out a large-scale study for a territory comparable to the United States is extremely difficult. Even though the power networks of the European countries are interconnected, each European state has its own national operator and many local distributors, which deal with disturbances according to their own internal regulations and follow different procedures. To combine different datasets may thus be extremely difficult.
\subsection{The Electric Power Transmission Network in the Czech Republic}
The Czech Republic lies in central Europe and is extended in the east--west direction (about~500 km length) compared to the ``width'' in the south--north direction (about 280~km). In terms of the electric power grid, the spine of the power network is operated by the national operator \v{C}EPS, a.s., which maintains the very-high-voltage (400~kV and 220~kV) transmission network, and connects the Czech Republic with the neighbouring countries. \v{C}EPS also maintains the key transformers and electrical substations in the transmission network. The area of the state is then split into three regions, where the electricity distribution is under the responsibility of the distribution operators. The southern part is maintained by E.ON Distribuce, a.s., the northern part by \v{C}EZ Distribuce, a.s., and the capital city of Prague is maintained by PREdistribuce, a.s. All three distributors maintain not only very-high-voltage (110 kV) and high-voltage (22 kV) power lines, but also connect the consumers via the low-voltage (400 V) electric power transmission network.
\subsection{Logs of Anomalies}
After years of delicate negotiations, we managed to obtain the maintenance logs from all the operators mentioned in the previous section. We obtained essentially the lists of disturbances recorded in the maintenance logs by the company technicians with their dates and many more details, which included also the probable cause of the anomaly. The lists contained not only the events of the equipment failure (e.g. defects), but also the events on the power lines, such as the repeated unplanned switching, power cuts, or service anomalies. By mutual non-disclosure agreement with the data providers, the datasets were anonymised and must be presented as such. The total time span is 12 years, but the span of individual maintenance logs provided by the operators is shorter, varying between 6 to 10 years.
The inhomogeneous datasets were split into twelve subsets D1--D12, which were investigated separately. Each sub-dataset was selected so that it contained only events occurring on devices of a similar type and/or with the same voltage level and were recorded by the same operating company.
We first went through an extensive manual check of the obtained logs, when we excluded the events which principally could not be related to the geomagnetic activity. That is we excluded the defects that occurred prior to putting the equipment into operation (i.e. manufacturing defects that were revealed during the testing period) or anomalies caused by other, space-weather unrelated effects. We downselected either erroneous records, the records connected with other large-scale natural disasters (floods) and records where the human factor was a prime cause for the anomaly (traffic accidents, customer's error). The fraction of the downselected events is given in the last column of Table~\ref{tab:datasets}. We did not exclude any events for datasets D7--D12. The fractions are larger for D3 and D4, where the large-area floods played a large role and the distributor recorded also planned upgrades as anomalies in the logs. In datasets D5 and D6 a large fraction of records was erroneous (the date was not specified). In the same datasets, we excluded also power-line breaches caused by accidents during construction works from further analysis.
The dataset descriptions are summarised in Table~\ref{tab:datasets} and visualised in Fig.~\ref{fig:datasets} (where individual datasets were normalised to their corresponding maximum for displaying purposes due to the large spread of typical anomaly rates across datasets). We aim to study only the anomaly rates (an daily series of the counts of anomalies occuring in the same day) so that from the logs we kept only the date on which the event occurred and did not consider any other detail. This reduction was done for two reasons. First, the number of events was quite low in most cases (a few hundred per year usually) and further splitting would lower a statistical significance. Second, the records in the log were quite inhomogeneous even within the same log, because the forms entering the database were filled by different persons. The final clean datasets are one-by-one compared with the level of geomagnetic activity using statistical methods.
For the sake of completeness, we merged all the subsets in one series nicknamed DX, which we analysed using the same methodology as the subsets.
\begin{table}[ht]
\caption{Datasets analysed in this study}
\label{tab:datasets}
\centering
\begin{tabular}{l|llll}
{\bf Dataset} & {\bf Voltage level} & {\bf Type} & {\bf Span} & {\bf Fraction}\\
{\bf ID} & {\bf } & {\bf } & {\bf } & {\bf removed}\\
\hline
D1 & very high voltage & equipment: transformers, & 9 years\\
& & electrical substations& & 4\%\\
D2 & high voltage & equipment & 6 years & 0.2\% \\
D3 & very high voltage & equipment & 6 years & 10\% \\
D4 & high and low voltage & power lines & 7 years & 13\%\\
D5 & high and low voltage & equipment and power lines & 7 years & 58\%\\
D6 & high and low voltage & equipment & 7 years & 55\% \\
D7 & very high voltage & power lines & 10 years & 0\% \\
D8 & high voltage & transformers & 10 years & 0\% \\
D9 & very high voltage & transformers& 10 years & 0\% \\
D10 & very high and high voltage & electrical substations& 10 years& 0\% \\
D11 & very high voltage & power lines& 10 years& 0\% \\
D12 & high voltage & power lines & 10 years & 0\% \\
\hline
DX & \multicolumn{4}{l}{\ \ \it joined series of all the above}
\end{tabular}
\end{table}
\begin{figure}
\centering
\includegraphics[width=0.9\textwidth]{korelace.pdf}
\caption{A representation of anomaly rates as registered in the various datasets in time. At the top of the figure we also plot the relative sunspot number for reference and indicate the dates, when X-class flares ignited and when aurorae were seen in the Czech Republic.}
\label{fig:datasets}
\end{figure}
\subsection{Geomagnetic Activity}
The selection of an appropriate index to assess the effects of solar/geomagnetic activity to power grids is a delicate issue \citep[see the discussion e.g. in][]{schrijver2013disturbances}. We realised that none of the solar indices is suitable because events on the Sun (flares, CMEs) may have a different geoeffectivity. Still, the sunspots number or occurrence of X-class flares may serve as a secondary index to discuss various effects in the Sun-Earth connections.
For the purpose of this study, we thus relied on the measurements of the geomagnetic field. We used the data from the nearest measuring station, the Geomagnetic Observatory Budkov in \v{S}umava mountains, operated by the Geophysical Institute of the Czech Academy of Sciences. They produce minute-by-minute measurements of the geomagnetic field vector. The measurements of the geomagnetic field were downloaded from the Intermagnet data archive, the gaps in the measurements (only 180 minutes over more than 13 years) were filled by using the measurements from Chambon-la-For\^{e}t station in France to have an uninterrupted data series.
From these measurements, we constructed a $K$ index, which is typical for characterising the level of geomagnetic activity in similar applications. The $K$ index was calculated in using an FMI \citep{Sucksdorff1991} method, with a limit of 500~nT for $K=9$. To obtain daily values that could be compared with the anomaly rate with daily granularity we averaged 3-hour $K$ indices in each day. We realise that it may not be wise to average the semi-logarithmic quantity as the averaged values will no longer hold the physical meaning of the original quantity. For our study, we are not using the absolute values of $K$ index as a reference for the level of geomagnetic activity. We seek for local minima and maxima of geomagnetic activity only. For such purpose the averaged $K$-index series is a suitable quantity, despite possible interpretation issues.
\section{Methods}
The goal of our work is to compare both data series of a different kind using various statistical tests. The correlation coefficient between the $K$ index and the anomaly rates of all series computed over the entire interval is practically zero, which is in agreement with a study by \citet{schrijver2013disturbances} principally similar to ours. The reason probably is that not all the power-grid disturbances are expected to occur immediately after the exposure to the increased geomagnetic activity. For a stringent example we need to note that in the case of the failure of the step-up transformer at Salem~2 generator station in 1989, the damage was discovered during a routine test a week after the exposure to large-amplitude GICs \citep{NERC}. Yet, the device was written off. \cite{Koen2003} point out the cumulative effects of GICs in the transformers. The dissolved-gas analysis records in the South-African transformers indicated that the deterioration continues after the initial damage caused by GICs. The time of the collapse is influenced by the transformer loading and possibly also by other stresses. Thus there may be a time delay with an unknown value, which depends on many conditions in the activity and on the device itself. E.g. for the Greek power grid, \citet{zois2013solar} found the delay to be up to several years.
We were forced to use a different approach than a computation of the correlation coefficient. Our methodology is consistent with retrospective cohort study with tightly matched controls. First, we used the binomial test to check the hypothesis that around the maxima of geomagnetic activity the increase of the anomaly rates occurs, which is compared to the anomaly rate in a nearby minimum of activity. To do so, we searched for local minima and maxima in the $K$-index series. Around each minimum and maximum, we drew an interval with a total length of $W$ days. The window was positioned such that its centre was placed at the local minimum. For the maximum period, the window was placed \emph{after} the peak of activity, beginning at the local maximum. The maxima and minima were paired together so that they did not overlap and that the corresponding pairs were close in time. By such a selection we attempt to avoid long-term or secular trends in the logs of anomalies caused by the evolution of the grid in time and also seasonal changes due to the weather and loading. We performed our tests for a selection of values of $W$, these intervals served as accumulation windows for the series of power-grid disturbances. For each $W$ we had $n_{\rm i}$ pairs of maxima and minima of geomagnetic activity.
In the selected intervals we counted the total number of anomalies $N_{\rm h}$ falling into the maximum intervals (that is during increased geomagnetic activity) and the number of anomalies $N_{\rm l}$ falling into the minimum intervals (that is in the low-activity periods). We only remind that these numbers depend on the length of $W$ of the accumulation window.
In the case when increased geomagnetic activity on average induces a subsequently larger anomaly rate of power-grid devices, we would expect the relation
\begin{equation}
N_{\rm h} > N_{\rm l}.
\label{eq:inequality}
\end{equation}
Even when the above inequality holds, its statistical significance must be tested, for which we use the binomial test. The binomial test states the probability $P$ that the registered differences between $N_{\rm h}$ and $N_{\rm l}$ are in accordance with the model. Our model is the reversed hypothesis, that says there is no difference between the number of anomalies registered in the periods around local maxima of activity and local minima of activity. If $P$ is lower than 5\% (our selection of statistical significance), then we reject the reversed hypothesis. In such a case, we obtained an indication that indeed, there is a statistically significant increase in anomaly rates after the maximum of the geomagnetic activity. $P$ is computed as
\begin{equation}
P_{\rm h,l}=2\sum_{k=x}^{n} {{n}\choose{k}} p^k(1-p)^{n-k}
\label{eq:probability}
\end{equation}
where for testing the pair $N_{\rm h}$ and $N_{\rm l}$, $n=N_{\rm h}+N_{\rm l}$ denotes the total number of anomalies in two sets of chosen intervals. The parameter $p$ states the model-expected probability of the disturbance occurring during the high-activity intervals. In the tested (that is in the reversed) hypothesis we assume that the probability of the disturbance occurring during the maximum or the minimum be the same, i.e. $p=1/2$. Finally, $x=\max(N_{\rm h},N_{\rm l}$).
The binomial test is a principal approach in our study to assess the possibility of the disturbance rate to be affected by the geomagnetic activity. It gives us the answer to the question whether it is possible, for the given dataset and the accumulation window $W$, to register a difference in the anomaly rates occurring during the minima and maxima of the geomagnetic activity. It gives us a qualitative answer.
To quantify the difference in the anomaly rates for both different situations we evaluated a relative risk $R$. It is a common quantity in e.g. cohort epidemiological studies or when testing the effectivity of the vaccination. It uses two samples: the sample which was exposed to a certain causal attribute (those are the testing object with the vaccine) and a control sample which was not exposed. Then the number of positive and negative cases in both samples are compared. The numbers of disturbances in the intervals of an increased and decreased geomagnetic activity are not suitable quantities for the calculation of the relative risk, because the cohort-study approach uses a binary ``yes/no'' flag in the description of the individuals in the exposed and control samples. Thus we constructed a different statistical series. For both the intervals around the local maxima of the geomagnetic activity (the sample with the causal attribute) we computed the number of days in which disturbances were registered and the number of days without disturbances. The analogous two numbers were computed for the interval around the local minima (the control sample without the causal attribute). Then we computed the relative risk as
\begin{equation}
R=\frac{a}{a+b}/{\frac{c}{c+d}},
\label{eq:risk}
\end{equation}
where $a$ is the number of days with anomalies and $b$ without them, both for intervals with increased solar activity. For intervals with lower solar activity, $c$ is the number of days with an anomaly and $d$ is the number of days without any.
The relative risk is 1 if there is no difference between the two groups differing in the causal attribute. If $R<1$ then more often positive cases occur in a group without a causal attribute (i.e. contrary to expectation), if $R>1$ then positive cases occur more often in a causal attribute group.
The two tests described above may give us an indication of a statistically significant increase in the anomaly rates in the periods of the increased geomagnetic activity. These tests still do not prove the causal link, the binomial test is an ``advanced correlation measure'' to some extent. If the increased anomaly rates are indeed caused by the increased geomagnetic activity, where a positive but unknown time lag may play a role, one would expect that the anomaly rates are larger after the geomagnetic activity maximum than before. Thus we compared the number of disturbances in the intervals of length $W$ immediately before the local maximum with the number of disturbances in the intervals of the same length placed immediately after the maximum. We compared the mean daily anomaly rates in the two intervals (we would expect the mean to increase after the local maximum), the relative mean increase in the units of standard deviation of the daily anomaly rates, and of course we ran a binomial test evaluated by (\ref{eq:probability}) to test the statistical significance.
A similar comparison was done for the minima. For the minima, we either expect the statistical parameters not changing much before and after the minimum. In the case when the descend to the local minimum was very steep and close to some much larger maximum, we could anticipate the statistics before the minimum be affected by the previously larger geomagnetic activity and then the mean anomaly rates before the minimum should be larger than after the minimum.
\section{Results}
To perform the statistical analysis outlined in the previous section we wrote a series of programs in {\sc Python} that allowed us to study the effects of various parameters in the code on the results. Such an approach also ensured that the processing of all the data files was done in exactly the same way. The program had two principal inputs for each run: the series of daily-averaged $K$ index and the series of dates when anomalies on the electric power transmission network occurred in the given dataset. The analysis was executed for a set of window lengths $W$.
The code first smoothed the series of $K$ indices with a boxcar window with a width of $W$, so that the time-scales of the two series to be compared were similar. In the smoothed series the code then detected local maxima and minima from the first derivative. Then the neighbouring minima and maxima were paired together so that their paring minimises the possible effects of the secular development of the electric power transmission network that could possibly lead to the trends in the anomaly rates. On the other hand, the requirement was that the neighbouring minima and maxima do not overlap within $W$ bounds. In such a case the next neighbouring minimum was selected for that maximum. We also ensured that the maximum+minimum pairs were unique. An example of the local extrema detection and their pairing is given in Fig.~\ref{fig:intervals50}, a complete set is then given in Figs.~S1--S11 in the Supporting Information.
\begin{figure}
\centering
\includegraphics[width=0.7\textwidth]{Kindex70.pdf}
\caption{Daily averaged $K$ index (blue solid curve) where local minima and maxima were detected by our code. Around these extrema the intervals with a width of $W$~days are indicated by bars. The code searches for non-overlapping pairs of maximum (blue) and minimum (red) that are closest in time. This particular plot is for $W=70$~days.}
\label{fig:intervals50}
\end{figure}
The code then counted the number of disturbances falling into the maxima and minima and evaluated the probability given by (\ref{eq:probability}) and computed the risk given by (\ref{eq:risk}). For each maximum and each minimum, the code then evaluated the number of anomalies falling into the intervals of width $W$ occurring immediately before the maximum (or minimum) and after it.
We found that the results depend strongly on the selection of $W$. Smaller windows increase the noise levels because lesser numbers of disturbances fall into the tested intervals. Also, shallower local minima and/or maxima are present in the series of $K$ index due to the smaller smoothing. On the other hand, too large values of $W$ cause the $K$ index series to be overly smoothed and the pairing of the neighbouring minima and maxima gets difficult because the requirement of the non-overlapping intervals is too strong. As a consequence, the ``neighbouring'' maximum+minimum pairs may be hundreds of days apart. The interpretation of such comparison is then complicated as over a period of hundreds of days the secular trends connected with the network development or seasonal changes increase their importance. In the following, we thus discuss mainly the results obtained for windows $W=(30,50,70)$~days.
We found that in most cases the differences in the number of anomalies in the maxima and minima are not statistically significant. That is also demonstrated in an example Table~\ref{tab:statistics70}. A complete set of tables for all investigated values of $W$ are given in the Tables S12--S22 in the Supporting Information.
\begin{sidewaystable}
\caption{Statistical analysis of disturbances in the Czech electric power transmission network for the 70-day window. For datasets D1--D12 and DX we give the number of interval pairs, the total number of reported disturbances in the periods of increased activity and decreased activity. Then we give the probabilities $P$ with which the differences in the number of anomalies between two intervals are due to chance. In the last section we give necessary values for the computation of the relative risk $R$ given by (\ref{eq:risk}), and also the values of $I_{\rm r}$ given by (\ref{eq:Ir}).}
\label{tab:statistics70}
\begin{tabular}{l|llll|llllll}
Dataset ID & Intervals & $N_{\rm h}$ & $N_{\rm l}$ & $P_{\rm h,l}$ & $a$ & $b$ & $c$ & $d$ & $R$ & $I_{\rm r}$ \\
\hline
D1 & 7 & 46 & 22 & 0.0049 & 46 & 444 & 22 & 468 & 2.09091 & 0.07\\
D2 & 4 & 74 & 62 & 0.34559 & 74 & 206 & 62 & 218 & 1.19355 & --\\
D3 & 4 & 8 & 13 & 0.38331 & 8 & 272 & 13 & 267 & 0.61538 & --\\
D4 & 4 & 13 & 22 & 0.17547 & 13 & 267 & 22 & 258 & 0.59091 & --\\
D5 & 4 & 32 & 33 & 1.0 & 32 & 248 & 33 & 247 & 0.9697 & --\\
D6 & 4 & 19 & 12 & 0.28104 & 19 & 261 & 12 & 268 & 1.58333 & --\\
D7 & 8 & 84 & 31 & $<10^{-5}$ & 84 & 476 & 31 & 529 & 2.70968 & 0.53\\
D8 & 7 & 541 & 484 & 0.08022 & 298 & 192 & 279 & 211 & 1.0681 & --\\
D9 & 7 & 46 & 57 & 0.32448 & 44 & 446 & 51 & 439 & 0.86275 & --\\
D10 & 7 & 8661 & 7317 & $<10^{-5}$ & 490 & 0 & 490 & 0 & 1.0 & 0.13\\
D11 & 7 & 285 & 120 & $<10^{-5}$ & 194 & 296 & 92 & 398 & 2.1087 & 0.74\\
D12 & 7 & 7073 & 5543 & $<10^{-5}$ & 489 & 1 & 489 & 1 & 1.0 & 0.22\\
\hline
DX & 9 & 19462 & 13806 & $<10^{-5}$ & 566 & 64 & 497 & 133 & 1.13883 & 0.37\\
\end{tabular}
\end{sidewaystable}
Only the datasets D1, D7, D10, D11, and D12 seem to indicate a statistically significant increase of $N_{\rm h}$ coherent with the working hypothesis. These five datasets behave the same for all windows $W$ in the range of 30 to 120 days. We note that D1 aggregates disturbances on the equipment of the spinal transmission network. Datasets D7, D10, D11, and D12 record disturbances on the high-voltage and very-high-voltage power lines and also on electrical substations. The joined series DX also indicates a significant increase of anomaly rate in the periods around local maxima of geomagnetic activity compared to neighbouring minima. Differences registered in the remaining datasets are not statistically significant.
\begin{sidewaystable}
\caption{Comparison of the anomaly rates around the local minima and maxima. In the first section we give mean values ($\mu$) and standard deviations ($\sigma$) for the intervals of length $W=70$~days before local maxima (subscript ${-\rm max}$) and after the maxima (subscript ${\rm max}+$). In the second section analogous parameters are evaluated for local minima. In the third section we give the relative increase of the means in the units of the standard deviation evaluated before the extrema. In the last section we give the probability that the differences in the interval before the maximum and after the maximum are due to chance.}
\label{tab:minmax70}
\begin{tabular}{l|llll|llll|ll|l}
Dataset ID & $\mu_{-{\rm max}}$ & $\mu_{{\rm max}+}$ & $\sigma_{-{\rm max}}$ & $\sigma_{{\rm max}+}$ & $\mu_{-{\rm min}}$ & $\mu_{{\rm min}+}$ & $\sigma_{-{\rm min}}$ & $\sigma_{{\rm min}+}$ & $\frac{I_{\rm max}}{\sigma_{-{\rm max}}}$ & $\frac{I_{\rm min}}{\sigma_{-{\rm min}}}$ & $p_{{+}{-}}$ \\
\hline
D1 & 0.44 & 0.66 & 0.62 & 0.79 & 0.34 & 0.29 & 0.61 & 0.51 & 0.343 & -0.094 & 0.03355\\
D2 & 1.06 & 1.06 & 0.77 & 0.79 & 0.77 & 0.71 & 0.72 & 0.83 & 0.0 & -0.079 & 0.42219\\
D3 & 0.11 & 0.11 & 0.32 & 0.32 & 0.16 & 0.11 & 0.36 & 0.32 & 0.0 & -0.118 & 0.75391\\
D4 & 0.49 & 0.19 & 0.58 & 0.42 & 0.29 & 0.33 & 0.54 & 0.53 & -0.518 & 0.08 & 0.34493\\
D5 & 0.79 & 0.46 & 0.69 & 0.65 & 0.59 & 0.43 & 0.71 & 0.6 & -0.473 & -0.222 & 1.0\\
D6 & 0.33 & 0.27 & 0.47 & 0.53 & 0.34 & 0.11 & 0.58 & 0.32 & -0.122 & -0.392 & 0.15159\\
D7 & 1.1 & 1.2 & 0.93 & 0.82 & 0.43 & 0.39 & 0.55 & 0.54 & 0.108 & -0.078 & 0.51041\\
D8 & 6.6 & 7.73 & 2.85 & 3.62 & 7.61 & 6.49 & 3.5 & 2.56 & 0.396 & -0.323 & 0.00002\\
D9 & 0.71 & 0.66 & 0.94 & 0.89 & 0.7 & 0.6 & 0.82 & 0.85 & -0.061 & -0.122 & 0.00109\\
D10 & 112.99 & 123.73 & 21.08 & 21.2 & 101.09 & 103.49 & 19.34 & 20.01 & 0.51 & 0.124 & 0.00073\\
D11 & 4.29 & 4.07 & 3.06 & 2.23 & 1.44 & 2.13 & 1.31 & 1.6 & -0.07 & 0.525 & 0.81275\\
D12 & 87.87 & 101.04 & 19.02 & 20.4 & 82.93 & 76.57 & 20.31 & 20.11 & 0.692 & -0.313 & $<10^{-5}$\\
\hline
DX & 256.97 & 278.03 & 46.59 & 45.49 & 196.86 & 206.6 & 38.35 & 40.08 & 0.452 & 0.254 & $<10^{-5}$
\end{tabular}
\end{sidewaystable}
The relative risk as we defined it turned out to be not very useful in the analysis we performed. The $R$ value is meaningless when the number of recorded disturbances is low due to the statistical insignificance of $R$. On the other hand, when the number of disturbances is large, as in e.g. D12, then $R=1$ by definition. Due to the daily granularity of the anomaly logs, in such a case there always is at least one disturbance each day in which the data exist. Then obviously the $R$ is meaningless again. Thus it is useful only in the case when the total number of registered disturbance events is between say 100 and 300. We cannot increase the granularity in time of the populated datasets, thus we cannot choose another suitable parameter to be tested to compute the relative risk. One option would be to split the populated datasets in more datasets e.g. grouped by the geographical location or another criterion. We did not proceed in this way because we do not have confidence in a gain of such a non-trivial manual sorting of the inputs.
Instead, we used a different method to quantify the increase of disturbances in the maxima of geomagnetic activity. For each dataset with positive indication of the increase ($P_{\rm h,l}<0.05$) we searched for the largest $N_{\rm h1}$ while keeping $N_{\rm l}$ constant, $N_{\rm h1} \geq N_{\rm l}$, for which $P_{\rm h1,l} \leq 0.01$. This would be the boundary value, where we could not reject the hypothesis that the differences are due to chance with a 1\% significance level. Note that for this task we chose a stronger limit of the statistical significance level. The relative increase with a statistical significance would be defined as
\begin{equation}
I_{\rm r}=(N_{\rm h}-N_{\rm h1})/N_{\rm h1}.
\label{eq:Ir}
\end{equation}
The values of $I_{\rm r}$ are also given in Table~\ref{tab:statistics70} and the supplementary tables S12--S22 in the Supporting Information.
In the case of D1, D7, D10, D11, and D12 $I_{\rm r}$ is between 7 and 70 per cent.
We remind that the intervals of length $W$ were always centred on the local minimum, whereas they were placed \emph{after} the local maximum. The motivation was that we expect some delay in the occurrence of the disturbance after the exposure to larger GICs. To test how important this selection is for the results we ran our codes again when centering the intervals on the dates of maxima of geomagnetic activity. The results did not change significantly.
On the other hand, it is worth testing whether the anomaly rate increases after the maximum of geomagnetic activity. Such a test was achieved by comparing the number of anomalies and their statistical properties in a window of length $W$ before the maximum with the window of the same length after the maximum. As for the considered statistical properties, we evaluate the mean daily anomaly rate for each dataset individually, computed over the window $W$-days long before the local maxima (indicated as $\mu_{\rm -max}$) and its variance (indicated as $\sigma_{\rm -max}$). Same statistical indicators were computed for $W$-days long window after the local maxima (these are referred to as $\mu_{\rm max+}$ and $\sigma_{\rm max+}$). The increase of the daily means $I_{\rm max}$ is given by
\begin{equation}
I_{\rm max}=\mu_{\rm max+}-\mu_{\rm -max}.
\end{equation}
As a comparison, we derived the same parameters for the local minima (indicated by \emph{min} in their lower indices). The results are compatible with our hypothesis only if there is an increase in the mean daily anomaly rate after the local maxima and there is more-or-less no change or a decrease around the local minima. Example results again for $W=70$~days are shown in Table~\ref{tab:minmax70}. A complete set of tables for all investigated values of $W$ are given in the Tables S23--S33 in the Supporting Information.
The statistical significance of the recorded differences before and after local maxima of geomagnetic activity is low for most of the datasets. The differences with larger statistical significance are present in case of datasets D1, D10, and D12, where also the significant difference between $N_{\rm h}$ and $N_{\rm l}$ was found. In those datasets, we observe an average increase of the anomaly rates by (0.3--0.7)$\sigma$ (about 10-30\% of the daily means) after the maxima, whereas in the control series around the minima we see either a decrease or a much lower increase than in case of the maxima. Furthermore, we record a statistically significant increase around the maxima in dataset D8. This dataset also recorded $N_{\rm h} > N_{\rm l}$ (see Table~\ref{tab:statistics70}), but the computed probability $P_{\rm h,l}=0.08$ was larger than the chosen 5\% threshold (the dataset is only 7 anomalies away from the chosen statistical significance threshold). D8 records the disturbances occurring on high-voltage transformers.
\section{Concluding Remarks}
We searched for a ``correlation'' between the occurrence of disturbances on the electric power transmission network in the Czech Republic and the geomagnetic activity described by the $K$ index. The logs of disturbances were split into twelve different datasets according to the data provider (the company), voltage level, and a class of equipment. For the sake of completeness, we also investigated the merged dataset using the same methodology.
We compared the anomaly rates in the periods tens of days long around local maxima of geomagnetic activity with the periods around local minima of geomagnetic activity using statistical methods. The statistical significance of this comparison highly depends on the size of the sample. For sparse datasets the results are inconclusive, so one cannot say whether there are differences in recorded rates of power-network anomalies in the periods exposed to a local maximum of geomagnetic activity as compared to a nearby local minimum of activity.
For the populated datasets which record mostly the disturbances on power lines and electrical substations on the high-voltage and very-high-voltage levels, we see a statistically significant increase of the number of anomalies in the period of the increased geomagnetic activity when the accumulation windows of a few tens of days are used. The relative increase is roughly between 10 and 70 per cent.
In the dataset recording the disturbances on transformers we see an increase, but we cannot reject the null hypothesis that the apparent increase is (probably) due to chance (the case of D8, high-voltage transformers), even though the probability is a bit lower than our rejection threshold.
The merged dataset DX indicates an anomaly-rate increase in the high-activity periods consistently for all accumulation windows $W=30$~days or larger. The interpretation of such a result is somewhat difficult because it contains anomalies registered on all sorts of devices and voltage levels. On the other hand, it may serve as a representative sample for the whole country covering 12 years of the electric power network performance.
These conclusive datasets also bear an indication that the increase is larger after the local maxima than before it, which is compatible with an interpretation that the increase indeed is due to the larger geomagnetic activity, where the effects of GICs show up with some delay. Such an interpretation is somewhat surprising for the datasets dealing with power lines (D7, D11, D12) or equipment connected to them (D10), where one does not expect cumulative effects due to the exposure to GICs, but rather an immediate response to the GICs entrance into the electric grid.
Another hint that the disturbances indeed are caused by effects of geomagnetic activity would be if the disturbances occurring in networks of various operators would be somewhat correlated in time. Our code has an option to investigate such an issue. However, as evident from Fig.~\ref{fig:datasets}, the overlap period of all dataset is short, about three years. Such a length is way too short to obtain any statistically meaningful results. The poor common coverage is, unfortunately, a consequence of years-long delicate negotiations with the data providers.
Our study is the first of this kind performed for the mid-latitude location. Many further studies are needed to fully understand our findings. For instance, the GIC modelling in the network together with an assessment of disturbances split to each of the power lines would give direct evidence about the influence of GICs on the equipment. The modelling of GICs is a goal of our ongoing study, our preliminary results indicate that there could be GICs as large as 50~A considered in the Czech power network.
\acknowledgments
M.\v{S} was supported by the institute research project RVO:67985815. We are grateful to data providers for giving us an opportunity to exploit their logs of anomalies, namely to P.~Spurn\'y (\v{C}EPS), J.~Bro\v{z} and J.~Bu\v{r}i\v{c} (\v{C}EZ Distribuce), R.~Hanu\v{s} (PREdistribuce), and D.~Mezera and R.~B\'il\'y (E.ON Distribuce). The maintenance logs are considered strictly private by the power companies and are provided under non-disclosure agreements. The anonymised aggregate data series are available from \url{http://sirrah.troja.mff.cuni.cz/~svanda/2019SW002181/data.txt} with username \emph{spaceweather} and password \emph{2019SW002181}. The results presented in this paper rely on data collected at magnetic observatories. We thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice. Magnetic data may be downloaded from www.intermagnet.org. We thank two anonymous referees for very useful comments that improved the message delivered by our paper. \emph{Author contributions}: M\v{S} designed the research which was then performed by TV within her MSc. project under the supervision of M\v{S}. Both authors contributed to the final manuscript.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,741 |
Q: Read Log file through batch untill Keyword "Terminate" is found I am new to batch programming and I am executing a windows batch command through jenkins on the target Windows machine.
My requirement is to read the log file ( aut.log ) while the automation is running. Once keyword "Terminate' is written in the log file, it should stop reading log and proceed to the next step.
A: I am going to give an answer based on the very unclear question.
@echo off
:start
FIND /C /I "Terminate" "F:\aut.log"
IF %ERRORLEVEL%==0 (echo found word Terminate
) else (
goto start
)
This will do a find in the file for the word Terminate in a loop until it is found and then echo found word Terminate at this point you will replace the echo command with your command. if however the word is not found, it will return to to :start to try again and continue forever until the word is found.
If you want to slow down the process, below :start, add timeout /t 1 for a 1 second time out.
@echo off
:start
timeout /t 1
FIND /C /I "Terminate" "F:\aut.log"
IF %ERRORLEVEL%==0 (echo found word Terminate
) else (
goto start
)
Finally, if you do not want to see the actual output on screen of the loop while running, you can push output to null with 1>null
@echo off
:start
FIND /C /I "Terminate" "F:\aut.log" 1>null
IF %ERRORLEVEL%==0 (echo found word Terminate
) else (
goto start:
)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,045 |
package dl.practice.encryption.symmetry.tripledes;
import javax.crypto.Cipher;
import javax.crypto.KeyGenerator;
import javax.crypto.SecretKey;
import javax.crypto.spec.SecretKeySpec;
import dl.practice.encryption.symmetry.util.ByteToHexUtil;
/**
* 3des加密
* Created by zhangweixiang on 4/17/2016.
*/
public class TripleDESUtil {
/**
* 生成3desckey
* @param type
* @return
* @throws Exception
*/
public static byte[] generateKey(String type) throws Exception {
KeyGenerator keyGenerator = KeyGenerator.getInstance(type);
keyGenerator.init(112);//128 168
SecretKey secretKey = keyGenerator.generateKey();
return secretKey.getEncoded();
}
/**
* 通过指定的3deskey加密
* @param data 加密的数据
* @param key 秘钥
* @param type 加密方式
* @return 加密信息
* @throws Exception
*/
public static byte[] encrypt(byte[] data,byte[] key,String type) throws Exception {
SecretKey secretKey = new SecretKeySpec(key,type);
Cipher cipher = Cipher.getInstance(type);
cipher.init(Cipher.ENCRYPT_MODE,secretKey);
return cipher.doFinal(data);
}
/**
* 3des解密
* @param data 需要解密的数据
* @param key 解密秘钥
* @param type 类型
* @return 解密后的结果
* @throws Exception
*/
public static byte[] decrypt(byte[] data,byte[] key,String type) throws Exception {
SecretKey secretKey = new SecretKeySpec(key,type);
Cipher cipher = Cipher.getInstance(type);
cipher.init(Cipher.DECRYPT_MODE,secretKey);
return cipher.doFinal(data);
}
public static void main(String[] args) throws Exception {
String data = "test desc";
String type = "DESede";// DES/ECB/PKCS5Padding
byte[] key = TripleDESUtil.generateKey(type);
byte[] encData = TripleDESUtil.encrypt(data.getBytes(),key,type);
String encDataStr = ByteToHexUtil.bytesToHexString(encData);
System.out.println(data+">>3des encrypt>>"+encDataStr);
byte[] decData = TripleDESUtil.decrypt(encData,key,type);
System.out.println(encDataStr+">>3des decrypt>>"+new String(decData));
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 474 |
1 Parry
1.1 Images
1.2 Maps
1.4 Description: Elger
1.5 Description: Wikipedia
1.6 Additional Information
1.7 Nomenclature
1.8 LPOD Articles
1.9 Bibliography
Lat: 7.9°S, Long: 15.8°W, Diam: 47 km, Depth: 0.87 km, Rükl 43
Howard Eskildsen, Parry (top) and Guericke
LPOD Photo Gallery Lunar Orbiter Images Apollo Images
Lunar Orbiter 5's Frame 138 shows a close-up of the well-known junction at Fra Mauro, Bonpland, and Parry.- DannyCaes Mar 23, 2008
(LAC zone 76B4) LAC map Geologic map LM map AIC map
Description: Elger
(IAU Directions) PARRY.--A more complete formation than Guerike. It is about 25 miles in diameter, and is encompassed by a bright border, which, at a point on the W., is nearly 5,000 feet in height. It is intersected on the N. by passes communicating with the interior of Fra Mauro. There is a crater, nearly central, on the dusky interior, which, under a low sun, when the shadows of the serrated crest of the E. wall reach about half-way across the floor, appears to be the centre of three or four concentric ridges, which at this phase are traceable on the W. side of it. There is a conspicuous crater on the W. wall, below which originates a distinct cleft. This object skirts the inner foot of the W. border, and after traversing the N. wall, strikes across the wide expanse of Fra Mauro, and is ultimately lost in the region N. of this formation. Parry A, S. of Parry, is a very deep brilliant crater with a central hill and surrounded by a glistening halo. A cleft, originating at a mountain arm connected with the W. side of Guerike, runs to the S. flank of this object, and is probably connected with that which skirts the floor of Parry on the W.
Description: Wikipedia
Depth data from Kurt Fisher database
Pike, 1976: 0.87 km
Arthur, 1974: 0.56 km
Westfall, 2000: 0.87 km
Viscardy, 1985: 0.56 km
Cherrington, 1969: 1.15 km
William Edward Parry (December 19, 1790 - July 9, 1855) was a British Arctic explorer. In 1810 received promotion to the rank of lieutenant in the frigate Alexander, which spent the next three years in the protection of the Spitsbergen whale fishery. He took advantage of this opportunity for the study and practice of astronomical observations in northern latitudes, and afterwards published the results of his studies in a small volume on Nautical Astronomy by Night (1816). In 1825 Parry obtained the sanction of the Admiralty for an attempt on the North Pole from the northern shores of Spitsbergen, and his extreme point of 82° 45' N. lat. remained for 49 years the highest latitude attained. He published an account of this journey under the title of Narrative of the Attempt to reach the North Pole, &c. (1827).
Parry M, the incomplete ring southeast of Parry, was nicknamed "The Horseshoe" by Harold Hill (see: A PORTFOLIO OF LUNAR DRAWINGS, Page 107).
LPOD Articles
APOLLO OVER THE MOON; A VIEW FROM ORBIT, Chapter 3: The Terrae (Part 2), Figure 44. Chapter 4: The Maria (Part 3), Figure 94.
A Portfolio of Lunar Drawings (Harold Hill), pages 107, 108, 109.
Retrieved from "http://the-moon.us/index.php?title=Parry&oldid=16585" | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,623 |
Phineas and Ferb returns!
Wed 01.02.23 Dennis
Spoiler Warning: There are minor spoilers ahead for Phineas and Ferb.
I called it, didn't I? When Phineas and Ferb The Movie: Candace Against The Universe premiered on Disney+ a couple of years ago, I said I wondered whether it might lead to a renewal of the show… and here we are! Almost eight years after the series ended its run on the Disney Channel/Disney XD, co-creator Dan Povenmire announced on social media that Phineas and Ferb will be returning – not just for a one-off special or TV movie, not even for a single season, but for two whole seasons and a whopping 40 episodes!
I'm actually really pleased to hear this news. Phineas and Ferb is a fun series, and one I return to on days when I'm struggling with my mental health. I guess you could call it one of my "comfort shows," so to know that there will be more episodes to get stuck into in the months and years ahead… it's good news from my point of view!
"Mom! Phineas and Ferb are making a comeback!"
I first encountered Phineas and Ferb shortly after its premiere. Back then I had a cable TV subscription (remember those?) and I can't remember how it came about exactly, but somehow I saw a promo or advertisement for Phineas and Ferb and thought that it looked like fun. I wouldn't have normally given most things on the Disney Channel a second glance, but even in that short promo something must've leapt out at me, convincing me that this was a show I needed to see. And I'm very glad I did, clearly!
Even though I was already an adult when I first watched Phineas and Ferb, it was obvious that the show had a lot to offer beyond its young target audience. The best shows made for kids have something to offer to adults, too – and no, I don't just mean a way to keep kids distracted and quiet so we can do other things! Phineas and Ferb had subtle jokes and references aplenty that were genuinely hilarious, and the way it told two stories that often (but not always) intersected was something original in the animated space.
There are even Star Trek references!
There was a sense, though, that Phineas and Ferb had started to run out of steam by the time of its fourth season, and I'm not alone in thinking that. Season 4 tried out several different concepts in the form of special episodes, stories that featured new characters, different premises, and tie-ins with the likes of Marvel and Star Wars. The original formula of the show – with the boys' inventions and the conflict between Perry and Doofenshmirtz – took a back seat.
Most of those special episodes are great fun, don't get me wrong, but there was definitely a reason why they were made – there were fewer ideas on the table and arguably, as the show had developed and fleshed out its main characters, fewer places to take them in a way that felt interesting. This is a hurdle that the renewed Phineas and Ferb will have to overcome – and it may not become apparent at first.
One of the special episodes in Season 4 was a "zombie" story!
When the show returns, I expect that most fans will welcome it back with open arms. Those first few episodes will re-establish Phineas and Ferb and its format, reintroducing its characters, and if the show basically does what it did from Seasons 1-3, a lot of folks will be thrilled. The question, though, is really whether that format can sustain another forty episodes without something happening to shake things up.
I'm not particularly concerned about questions of "canon" in a show like Phineas and Ferb. It is worth noting, though, that the show has an internal timeline of sorts, and not only that, but Season 4 provided two episodes that come together to give its story a pretty definitive finale: Act Your Age and The Last Day of Summer. There have also been main character crossovers in the series Milo Murphy's Law – but as far fewer people watched that show, I don't think it matters in the same way, and there's definitely enough creative freedom to overwrite some of these things.
Dr Doofenshmirtz in Milo Murphy's Law.
Having said that, the questions of timing and setting crop up. Will these new episodes take place in the same endless summer as last time, or would they be set further along the timeline – perhaps during the school year or even in the next summer? With Doofenshmirtz supposedly converted to the "good" side by summer's end, how would that work for his character?
I don't think that Phineas and Ferb could realistically get away with making Doofenshmirtz a "good guy." The original format worked so well specifically because his story and his evil schemes stood in contrast to the boys' shenanigans, so somehow that has to be retained. But it has to be done in a way that doesn't undo all of the development Doofenshmirtz got over the course of the show's run; it's not unfair to call him the breakout character, and a big part of that is because his character arc, such as it is, portrayed him sympathetically, despite his self-described "evil" nature.
Being "evil" is a huge part of Doofenshmirtz's character – and something the renewed series shouldn't try to jettison.
It's a challenge to walk that line: to bring the show back and retain its signature formula, all the while avoiding taking key characters backwards and regressing their development. The most important one to get right in this regard is Doofenshmirtz, though Buford's status as a semi-reformed yet still self-described "bully" is also of note.
Speaking of characters, it hasn't been confirmed at this stage whether all – or even any – of the original voice cast will be back. With one notable exception, they all returned for Candace Against The Universe in 2020, though, so I would hope that negotiations are at an advanced stage and the voice cast will all reprise their roles. One or two absences can be worked around – this isn't a Rick & Morty type of situation, where that series has just lost (for totally understandable reasons) its main voice actor and the person who voiced both of the titular characters. It would still be unfortunate, though, if Phineas and Ferb had to make significant changes to its cast.
Somehow, Phineas and Ferb will have to reassemble (most of) its original voice cast.
Someone else who doesn't seem to have signed onto the project yet is co-creator Jeff "Swampy" Marsh. Marsh and Povenmire created Phineas and Ferb together, and it's noteworthy that Marsh has yet to comment publicly on the series being revived. He also provided the voice of Major Monogram, directed a handful of episodes, and was credited with writing more than a dozen – including some of the show's most popular and best-remembered stories. I'm sure that Disney (and Dan Povenmire) will be working in private to get him back, but his loss would be significant for the show if those efforts fall through.
Without Marsh, and with the main voice actors also not being signed up, I can't help but wonder if this announcement may have been a little premature. If things don't go to plan and major voice actors aren't able to rejoin the project, that would be a real shame – and would put a downer on things as Phineas and Ferb returns, so I really hope that Disney will pull out all the stops to make it happen.
Phineas and Ferb co-creators Dan Povenmire (left) and Jeff "Swampy" Marsh.
Image Credit: IMDB
Although Disney Channel shows have tended to be one-and-done things, it's hardly something new in the animated space for a series to be continued. Look at the likes of Tom and Jerry, the Looney Tunes, or Scooby-Doo – the latter of which has just been reworked on HBO Max as Velma… actually, maybe the less said about that last example the better!
But the point stands: some animated shows become classics, and have a lifespan far beyond what may have been intended – or even hoped for – at the time they were created. If you'd told William Hanna and Joseph Barbera that new incarnations of their characters and stories would still be being created and enjoyed in the 2020s, I doubt they'd have believed it! So there's plenty of scope for Phineas and Ferb to come back, and perhaps even to iterate and modernise some of its stories for a new decade and a new audience – some of whom will literally be the children of the kids and teens who watched the show when it first debuted.
The very first shot of the premiere episode of the series.
So I'm thrilled to welcome back Phineas and Ferb, and I'm definitely looking forward to seeing the first batch of new episodes when they're ready. I'm not expecting to see anything imminently – animation takes time, and although the announcement has been made, it's clear that the revived Phineas and Ferb is still at a very early stage in its pre-production. In addition to the obvious voice cast, producers, directors, writers, and animators all need to be signed up before work can begin. We're probably a year or two away from the first episodes being ready… but I'm happy to wait.
This was a bit of a surprise announcement – albeit one that I felt Candace Against The Universe paved the way for – and although it may have been a little early or even premature, it's certainly succeeded at getting fans hyped up and talking on social media. I'm genuinely excited to have more adventures in the tri-state area with Phineas, Ferb, Candace, Perry, Doofenshmirtz, and the whole gang when the series is ready!
Phineas and Ferb Seasons 1-4 are available to stream now on Disney+. Seasons 5 and 6 are currently in pre-production and have no premiere date scheduled. Phineas and Ferb is the copyright of The Walt Disney Company. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Star Trek: Picard Season 3 – final trailer thoughts and analysis
Spoiler Warning: There are spoilers ahead for Star Trek: Picard Seasons 1-2 as well as the trailers, teasers, and announcements for Season 3.
For the first time ever (at least that I can remember) we got a trailer for a trailer. A full week ago, Paramount teased us with a couple of brief clips from the final Star Trek: Picard Season 3 trailer, as well as a broadcast date. I'm not sure how well this approach will have worked; it certainly got some Trekkies talking, but I'm not sure it will have built up a great deal of anticipation beyond the confines of the existing fan community.
In the United States, advertising slots halfway through major American football games are pretty big business, and in a way it's positive that Paramount would sacrifice one of the most valuable of these on its CBS network to promote Picard. Perhaps for some casual viewers who weren't aware that the cast from The Next Generation will be reprising their roles, showing the trailer at such a big, heavily-viewed event will generate some interest. As a non-American, however, it's hard not to see Paramount debuting this trailer in the middle of an American football game as just another "America First" move from a corporation that doesn't care about its international audience. Paramount has, to its credit, put the trailer on several of its social media pages (not on its YouTube channel, though, weirdly) so at least fans who follow those pages will have been able to see it.
Commander Seven of Nine.
The trailer itself showed off two new characters, and there were explosions and battles aplenty. But I don't think it was actually as exciting as I'd expected, and it didn't have any big tease or reveal to really punch through and sell me on the notion that this is going to be an unmissable season of Star Trek. There were also several moments in the trailer that seemed to be recycled from past teasers and trailers, which I wasn't wild about.
At New York Comic-Con last year, the trailer that was shown off introduced Captain Vadic and also dropped the surprise returns of Lore and Professor Moriarty as characters on the villainous side of the season. In hindsight, I wonder if at least one of these characters should have been saved for this trailer, which showed us two brand-new characters but didn't really have anything quite at that same level in terms of stunning or surprising moments.
Deanna Troi in the trailer.
Of course, it's true that Picard can't blow all of its big surprises in pre-season marketing material! If that were to happen there'd be nothing left to shock and excite viewers when the show gets underway – and I certainly hope that there'll be some wonderfully surprising moments in the new season. But as we said last year, the way in which Paramount schedules and reveals these things could have been better. Instead of revealing Lore and Moriarty last time, why not have revealed one character in each trailer? That would have been a bit more interesting, at least from the point of view of fans who follow Star Trek more closely.
But that's enough about what wasn't there or what we didn't see! The new season's story is taking shape, little by little, and we caught glimpses of potentially-interesting story beats that could have a major impact on Picard's final outing.
The Enterprise-F and a fleet of other Starfleet vessels in orbit of a planet.
First of all, let's talk about Captain Vadic. In the new trailer, she was shown alongside a handful of masked characters – and they gave me a bit of a "comic book villain" feel. Their bird-like masks were intimidating – but not quite at the same level as the masked Borg Queen at the beginning of Season 2. As happened on that occasion, I wonder if there's a reason why Vadic's crew are masked – could some of them be familiar characters?
I've theorised that Vadic may have put together a kind of "rogues' gallery" of past Star Trek villains for her mission of vengeance, and if that's the case, the masks could serve a narrative function – keeping the identities of her crew secret until the time is right. I'm by no means certain of that, and it could simply be a design choice, but it's interesting that, in the final trailer, we saw this glimpse of Vadic's crew but all of their faces were concealed. Vadic also seems to have a second-in-command, a tall, burly individual who stood behind her at one point.
Who could be behind these masks?
Sticking with villains, I'm less convinced right now that Lore and Moriarty will be allied with Vadic – or at least, less convinced that she will be the one to re-awaken them. Both characters had been deactivated the last time we saw them, and the question of who may have reactivated them is now a pertinent one! For both Lore and Moriarty, the trailer was cut together in such a way that seemed to imply that Picard and his crew may be responsible for reawakening them.
If that's true, it raises the obvious question: why? What could Lore and Moriarty possibly have to offer to Picard's crew as part of a mission to stop Captain Vadic and prevent what was described as "some kind of attack" for which the target could be Starfleet? I think the fact that both Lore and Moriarty are artificial life-forms must be relevant – and we should also keep in mind that Picard himself is now in a synthetic body. Could there be something going on that only affects organics?
Who reactivated Lore? And why?
Dr Crusher's line, which seems to come from the first episode of the season, warning Picard to "trust no one" was very interesting, and could also tie into the same theme. Dr Crusher seems to be hinting at some kind of conspiracy, possibly within Starfleet itself, and that could lead to Picard not only having to turn to his old crew – the people he's known the longest and trusts the most – but also to these malevolent artificial life-forms who may be immune to whatever is going on.
Two storylines from Star Trek's past leapt to mind when I put those two things together. First we have the parasite-aliens from The Next Generation Season 1 episode Conspiracy. That story was never concluded, and it was implied that the parasite-aliens may have successfully contacted their homeworld before being defeated. It would be a bold choice to return to that story… and I'm not sure how it would connect with Captain Vadic, but I suppose she could be the new "mother creature?" Maybe this one is a bit of a stretch!
Vadic with some of her crew.
Secondly, we have the Dominion from Deep Space Nine, and specifically the shape-shifting Founders. Although later seasons focused on the Dominion War, prior to the conflict's outbreak several episodes dealt with the idea of changeling infiltrators replacing key individuals and wreaking havoc in the Alpha Quadrant. Notable characters who were replaced by changelings included the Tal Shiar's Colonel Lovok, Klingon General Martok, and DS9's own Dr Bashir.
If this were to pan out, perhaps Vadic is a changeling seeking revenge for the Federation's victory in the Dominion War. It might be impossible to know who within Starfleet is who they say they are and who might be a changeling – forcing Picard to rely on his old crew, who he knows very well, and synthetic life-forms who couldn't be easily replaced? Maybe we'll have to put some flesh on the bones of these ideas in the days ahead.
A starship collision.
The two new characters that the trailer introduced are both unnamed right now, but one is a somewhat snarky Starfleet captain – presumably the commanding officer of the Titan and Seven of Nine's boss – played by Todd Stashwick. I remember seeing Stashwick in a show called Twelve Monkeys a few years ago, and he's a decent actor who should bring a lot to a role like this one. I'm not sure he's long for this world, though – he's giving me strong redshirt vibes!
The second new character is someone who may work with Dr Crusher in some capacity. I'm not familiar with actor Ed Speleers, but I like the idea of Dr Crusher having an ally of some kind who may be mistrustful of Picard and the crew at first. Could this character turn out to have a deeper connection with Dr Crusher, though? Perhaps he could be a relative – or even her son?
Who's this?
The addition of new characters is something that, if I'm being honest, I'm having majorly conflicted feelings about. On the one hand, the story has to have the freedom to introduce new characters, particularly if they serve a narrative function. But on the other, I'm still reeling from the loss of all but one of the new characters who had been introduced in Picard's first season. Those characters were dumped in order to make room for the returning crew of the Enterprise-D… but now we're seeing that there will be at least two other newbies to go along with Captain Vadic, the two La Forge sisters, and the returning villains from The Next Generation. Perhaps it's because I'm already put out by the way the casting situation was handled, but it stings a little. I can't help but wonder whether these characters' roles couldn't have been filled by the likes of Rios, Elnor, or Soji.
Last time, I commented on how Vadic's quest for vengeance seemed to be reminiscent of Khan's, and in this trailer, I felt Picard was really drawing quite heavily on The Wrath of Khan for inspiration. Visually we had things like the boatswain's whistle and the battle inside a nebula, thematically of course we have the themes of age and revenge, and narratively it even seems that part of the story will see Picard and Riker given a tour of the Titan – much like Kirk was given a tour of the Enterprise at the beginning of The Wrath of Khan.
The captain of the USS Titan.
The trailer did well to juxtapose the new Starfleet captain's lines about a boring, unexciting mission with images of explosions, phaser fire, battles, and even a starship collision at one point. The only thing I'd say about this is that the line itself felt very much like it was there for the explicit purpose of being used in pre-season marketing material… and sometimes lines of dialogue that were created for that purpose can feel out-of-place, clunky, or even just plain wrong in the context of the story itself. So while it was a great moment in the trailer, and a clever one at that, I hope when that scene rolls around in the actual show it will make sense in context for the captain to say those words!
We caught glimpses of all of the main characters in the trailer, and I hope that they'll all play a significant role in the story of the season. "Significant" doesn't have to mean that they're on screen at every moment, but it really means that I hope everyone will feel as though they've joined the mission and come out of retirement (in some cases) for a reason that feels genuine. There's always a danger when a series or franchise digs up old characters that they could feel superfluous; as if they're only there because a room full of TV writers wanted them to be. So far we've seen Dr Crusher seemingly on an important mission… but the others I'm less clear about at this early stage.
What roles will Troi, Worf, and the rest of the crew play?
When I previewed the season a few days ago, I wrote that I feel less "excitement" for Picard than I did in the run-up to Season 1 in 2020 and more a sense of restrained optimism. And to be blunt about it, this trailer didn't change how I feel. There are definitely areas that seem to have potential, and a "Picard does The Wrath of Khan" narrative could be an engaging one if done well, but there are still lingering concerns and questions.
The trailer was, once again, action-packed and designed to generate plenty of excitement as Paramount enters the most crucial phase of the show's marketing campaign, and I hope that it succeeded at drawing attention to Picard, at any rate. While the trailer may not have allayed my fears that Season 3 will blitz past and ignore the characters and storylines from Seasons 1 and 2, it didn't really add any new points of concern, so that's good. I guess.
Geordi on the main viewscreen.
To tell the truth, I want to be more excited about Picard – and about this latest trailer – than I actually am. I don't like feeling cynical about these characters and themes, and with Picard being set in precisely the era that I'd love Star Trek to spend more time exploring, I genuinely hope that this final season will succeed, and will, as promised, finally hand the torch to some new characters who may one day star in a spin-off project also set in this time period. We might've seen the first glimpses of who those characters could be, but I'm not sold on that idea just yet.
If there's one thing to take away from the final trailer it's this: it's probably time to give The Wrath of Khan a re-watch! This story seems to be picking up on themes, narrative beats, and character types that were present in that film – and as it's one of the best things Star Trek has ever done, that could be a great plan. Or it could feel disappointingly regressive and repetitive.
I'm keeping my fingers crossed that Picard can pull out a decent final season to end on a high note, and while even a fantastic story won't wash away the disappointment of two muddled, mismanaged seasons, if the show goes out with a bang at least we can be satisfied that we got a fun final adventure with the crew of the Enterprise-D. This trailer hasn't fully sold me on that concept, and it was missing the kind of big surprise or unexpected character that might've generated a bit more excitement. But it didn't ruin anything, either, and I came away from the trailer no more and no less excited for Picard's final season than I was before I pressed play.
Star Trek: Picard Season 3 will premiere on Paramount+ in the United States on the 16th of February 2023, and on Amazon Prime Video in the United Kingdom and around the world on the 17th of February 2023. Seasons 1 and 2 are already available to stream or buy on DVD/Blu-ray. The Star Trek franchise – including Picard and all other properties discussed above – is the copyright of Paramount Global. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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What to watch to get ready for Star Trek: Picard Season 3
Spoiler Warning: There are spoilers ahead for Star Trek: Picard Seasons 1-2 and the trailers, teasers, and announcements for Season 3. Spoilers are also present for the following Star Trek productions: The Wrath of Khan, The Next Generation, Deep Space Nine, Voyager, Nemesis, and Lower Decks.
Last year, shortly before Picard's second season premiered, I put together a list of twelve Star Trek stories that I felt would make for good background viewing – and I was pleasantly surprised that most of the episodes and films that I selected actually did have some bearing on the story of the season, or at least would've given viewers some additional information as the story unfolded. Given my usual track record with theories and predictions, that was a bit of a surprise! But you know what they say: "even a broken clock is right twice a day!"
With Season 3 now less than three weeks away, I wanted to once again compile a few stories from Star Trek's extensive back catalogue that I think could make for useful background viewing ahead of its premiere. At this stage last time around I felt we had a pretty good idea of the main narrative elements that would be present in Season 2: Q, the Borg Queen, and time travel had all been teased ahead of time, and comprised a big portion of the season's story. This time, though, it feels like we don't have as much information to go on!
A chair and console aboard the USS Stargazer.
As always, a couple of important caveats before we get started. First of all, I have no "insider information." I'm not trying to claim that I know or have somehow clairvoyantly predicted the plot of Star Trek: Picard Season 3, and it's quite possible that none of the stories we're going to talk about will have any bearing whatsoever on the new season. Paramount is keeping a relatively tight lid on things this time around, and while we know which characters will be included, there's still plenty that we don't know! I've made a few guesses and assumptions – but I could be completely wide of the mark.
I'm calling the entries on this list "stories," as several of these arcs play out across more than one episode. And I'll be listing the stories in broadcast order – not in order of importance! It also goes without saying that Picard Seasons 1 and 2 are necessary viewing – so I'm not going to put them on this list.
Finally, all of this is the subjective opinion of one person. If I include episodes and films that you hate or think will be irrelevant, or I exclude something that seems blindingly obvious, please just keep in mind that this is only the opinion of one Trekkie – and that it's meant to be a bit of fun!
With all of that out of the way, let's take a look at a few Star Trek stories!
Story #1:
The Wrath of Khan
The USS Enterprise in The Wrath of Khan.
Although we're unlikely to see any characters cross over from The Wrath of Khan – which is set more than a century before the events of Picard – ever since we got our first glimpse of the new season's villain a few months ago, I've been wondering if we might see some of the same themes crop up. Captain Vadic is still shrouded in mystery right now, but she gives me a very strong Khan vibe, and her potential obsession with Picard and desire to seek revenge against him could take the story down a somewhat familiar path.
Ricardo Montalbán's take on Khan is one of the most iconic villain performances not only in the Star Trek franchise, but in all of cinema. So if Season 3 is going to try to emulate that in some way, there are some very big shoes to fill! If Star Trek is going to return to this idea of a powerful villain on a quest for vengeance, it will definitely be worth stepping back to see the franchise's first take on that concept. And maybe, just maybe, there could be something in the story about genetic engineering and augmentation, too!
The Next Generation Season 1
DaiMon Bok on the Enterprise-D's main viewscreen.
This one is a bit of a stab in the dark and it could go absolutely nowhere! But The Battle introduces us to DaiMon Bok, a Ferengi captain who holds a grudge against Picard. Years earlier, the USS Stargazer had come under attack by an unknown vessel, and Picard was able to defeat it before the ship was lost. Aboard that ship was Bok's son, and the Ferengi has never forgiven Picard for causing his death.
Aside from the fact that this is another story that deals with the theme of revenge (and specifically, revenge against Picard), I can't help but wonder whether Bok might make a surprise appearance in Picard Season 3. We've already seen that Captain Vadic has brought two of Picard's old adversaries – Lore and Moriarty – onto her team, and I have no doubt that Bok would jump at the chance to join another mission against his old foe. If Captain Vadic has put together a "rogues' gallery" of Star Trek villains, perhaps we'll see Bok among them.
Datalore, Brothers, and Descent Parts I-II
Lore.
Lore only appeared in four episodes of The Next Generation, and I'm grouping them all together for this entry! Given that Brent Spiner is listed as a main character, I think it's a safe assumption that Lore will play a significant role in the story of Season 3, so I think it will be absolutely worthwhile to see where he came from and what he went through prior to being shut down by Data.
Lore is Data's "evil twin," a malicious android who betrayed his creator and has caused a lot of harm. But especially by the time we got to the two-part episode Descent, I felt there was much more to the character than just a one-dimensional anti-Data or a foil for the crew of the Enterprise-D. Lore has a degree of complexity, and I'll be curious to see what's become of him when the new story gets underway.
I also have a theory about how Lore's backstory could be connected to the events of Season 1, and you can find it by clicking or tapping here.
Elementary, Dear Data and Ship in a Bottle
An evil hologram…
Sticking with villainous characters, a huge surprise last year was that Daniel Davis will be reprising his role as the malevolent hologram Professor Moriarty. Moriarty was created by a computer error in Elementary, Dear Data and went on to kidnap Dr Pulaski. In Ship in a Bottle, Moriarty returned and tried to escape the confines of the holodeck. Both episodes are fascinating, and Davis' portrayal of the iconic Sherlock Holmes character has a menacing calmness that's absolutely riveting to watch!
Given what we know of holographic technology, and advances like the Doctor's mobile emitter that was seen in Voyager, I wonder what kind of role Moriarty might play? He's a genius, that much is certain, and he could cause Picard all kinds of trouble – as indeed he did in his earlier appearances!
Considering that both Professor Moriarty and Lore are both artificial life-forms, I have a theory that could connect the story of Season 3 with that of Seasons 1 and 2. Check it out by clicking or tapping here.
Redemption Parts I-II and Unification Parts I-II
Sela.
There have been rumours flitting about for months that Denise Crosby will appear in Picard Season 3, and while we have yet to get any official confirmation of this, if it's true and she will return, it seems logical to assume that it will be in the role of Sela. Sela was the daughter of an alternate timeline's version of Tasha Yar, and tangled with Picard on two occasions – trying to interfere in the Klingon Empire's civil war and later attempting to conquer Vulcan.
As discussed above, if Captain Vadic is looking for allies in her campaign against Picard and/or the Federation, Sela would surely jump at the chance to be involved. Her failures were almost certainly very costly for her politically, and I can absolutely see her wanting to get her own revenge on Picard and the crew of the Enterprise-D. There's also the possibility that Sela's involvement in the story could connect with the Zhat Vash plot and other Romulan storylines from Season 1.
Riker in Disaster.
Disaster is a fantastic episode that throws the whole crew of the Enterprise-D into a chaotic situation. When the ship strikes a quantum filament in space and is left damaged and without power, everyone has to step out of their familiar roles in order to save the day. Disaster is an ensemble piece that gives practically everyone something to do.
Disaster is one of the strongest episodes from Season 5 – which is perhaps my personal favourite season of The Next Generation, so that's saying a lot! For our purposes today, I like that it's an episode that throws everyone far out of their comfort zones, that it groups together characters who didn't often interact with one another, and that it gives all of the main characters something to do to contribute to the story.
Picard and Dr Crusher.
There are several episodes that look at Picard and Dr Crusher's relationship, but few are as detailed or emotional as Attached. What sounds like a silly sci-fi premise of being connected to one another by telepathic implants actually leads to a great story about the two characters and their emotional bond – a bond that has skirted friendship and something romantic.
One open question that fans have had really since Picard premiered three years ago is what may have happened between Picard and Dr Crusher over the past twenty years or more. It certainly seems as if they're still friends based on what we've seen… but did they ever "cross that line" and become something more? Picard's arc just last season ultimately turned out to be about his lack of romantic attachments, but you never know!
The USS Pasteur.
In some ways, All Good Things doesn't really feel like a finale – and that makes sense given that Generations would release in cinemas only a few months after it was broadcast! But The Next Generation's final episode is an interesting one, and when looking ahead to Picard Season 3, what's perhaps its biggest draw is that parts of the episode are set in the same time period.
Q sets Picard the challenge of solving an "anti-time" mystery, and to facilitate that, Picard moves through three different time periods – including an alternate future in which we get a look at the show's main characters. Events in Picard and other Star Trek projects have already undone much of the anti-time timeline, but some elements may make their way into this new story.
Deep Space Nine Season 4
Worf with a Klingon D'k tahg dagger.
Worf is about to make a big return to Star Trek – but unlike his crewmates, we've already seen the chapter of his life after he left the Enterprise! In Deep Space Nine's fourth season, Worf transferred to the station, and the two-part episode The Way of the Warrior not only brought him on board, but did so in spectacular fashion.
The episode focuses on Worf's inner conflict between his Klingon heritage and duties to Starfleet, as the Klingons plan a mission into the Gamma Quadrant. With Worf set to return, and promises of some kind of connection or tie-in with Deep Space Nine on the cards, I think seeing how he came to join the crew could be worthwhile.
Story #10:
In Purgatory's Shadow and By Inferno's Light
Garak and Worf at a Dominion internment camp.
This pair of episodes wrapped up the Klingon-Federation war that started in The Way of the Warrior, and set the stage for the Dominion War that would break out at the end of the season. It was also a strong Worf story that saw him held prisoner at a Dominion internment camp along with Martok, Garak, and Dr Bashir.
Since Star Trek returned to the small screen in 2017, we've only gotten the barest of mentions of the Dominion War – but there's so much potential in a return to Cardassia, the Dominion, and to look at the aftermath of the conflict. As someone who was heavily involved in the war and who did so much to keep the Federation and Klingon Empire united, Worf is the perfect character to use to explore some of these points. We may learn nothing new about the aftermath of the Dominion War in Season 3… but I kind of hope that we will.
Troi and Riker in Insurrection.
I know that Insurrection isn't everyone's favourite film, but I actually see several parallels with its story based on what we know of Season 3. Picard and his crew undertaking a "Starfleet-adjacent" mission, which may or may not have official approval, sounds an awful lot like what the crew got up to in Insurrection!
Furthermore, I noted in the Season 3 trailer a little while ago that one of the nebulae that Picard and the crew will seemingly visit looks an awful lot like Insurrection's "Briar Patch" – the region of space in which the Ba'ku homeworld was located. Could there be a deeper connection there? Maybe Captain Vadic is a Son'a, one of the defeated adversaries from Insurrection. That would be a bold move in more ways than one!
Author, Author
Voyager Season 7
The Doctor with Captain Janeway and Tuvok.
With the return of Professor Moriarty, a sentient hologram, I think it could be worth taking a look at Voyager's seventh season episode Author, Author. The story focuses on the Doctor, who has written a holo-novel based very loosely on his experiences aboard Voyager – but when he wants to make changes to it, his publisher tries to deny him that right, claiming that a hologram cannot "own" the copyright to his work.
Author, Author may turn out to be ahead of its time given that right now, here in the real world, the question of AI authorship is being discussed! In light of AI art, AI essays, and the like, we're going to have to take a serious look at this issue in the years ahead! But for our purposes, Author, Author could be an interesting starting point to consider the state of holographic rights and synthetic rights in a general sense in the late 24th and early 25th Centuries. Maybe none of it will matter for Professor Moriarty's story, but given that Season 1 looked at a ban on synthetic life, there's a chance some of the themes in the episode will turn out to be relevant.
A painting of the Enterprise-E.
Nemesis was the last time that Picard and his old crew were all together – at least as far as we know! It was certainly the last time that we as the audience got to see them working together, even if they may have reunited off-screen in the years before Season 1. So Nemesis, while arguably not the best Star Trek film, is going to be an important one to watch.
This is also Data's final mission, as he was killed while stopping the Reman plot. A big part of Season 1 involved giving Data the send-off that he didn't get in Nemesis, and his influence loomed large over the story in more ways than one. There are also mentions of Lore in the story, though nothing significant I suspect, and we're introduced to B-4, an early precursor to Data. For all of those reasons and more, Nemesis is a story worth checking out.
Kayshon, His Eyes Open
Lower Decks Season 2
Captain Riker of the USS Titan!
This might seem a bit of an odd choice, but Lower Decks actually showed us a bit of a look at Captain Riker's tenure aboard the USS Titan – and the Titan, or at least a ship bearing the same name, is going to be seen in Season 3. In this episode, Lower Decks main character Boimler is serving aboard the Titan under Riker's command, and takes part in an away mission to a dangerous planet.
When Kayshon, His Eyes Open premiered, I was thrilled to get a look at Riker, the Titan, and the crew he served with. I wouldn't be surprised at all to see Season 3 make some kind of reference to Riker's time in command, and there could even be name-drops of one or more of the characters in this episode. Season 1 already made reference to Star Trek's animated adventures, and with this episode including Riker in such a large role, it would be a shame in a way if Season 3 just ignored it completely.
I have a full episode review of Kayshon, His Eyes Open – click or tap here to check it out!
Who (or what) is Picard firing his phaser at?
Those are fourteen Star Trek stories that I feel could make for interesting or useful viewing before Picard Season 3 kicks off.
If nothing else, all of the stories above are good fun, and worth re-watching for any Trekkie who may not have seen them in a while! With the story of Season 3 being kept under wraps, some of these picks are admittedly guesses – but I think that all of them have the possibility, at least, to connect with the story that lies ahead.
I'm cautiously optimistic about the upcoming season, despite Picard as a whole not having been as enjoyable as I'd hoped nor having accomplished what I'd wanted it to. There are reasons to be concerned – such as the disappointing decision to jettison all but one of the new characters that the series had introduced – but I'd be lying if I said that one more adventure with the crew of the Enterprise-D wasn't a tantalising, enticing prospect.
When Picard Season 3 arrives next month, I'll do my best to keep up with weekly episode reviews, and if the series lends itself to theory-crafting, I daresay I'll put together some of my patented (and usually wrong) theories as well! So I hope you'll stay tuned for that!
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The Last Of Us (TV Series): first impressions
Spoiler Warning: There are minor spoilers ahead for The Last Of Us, both the TV series and the video game.
The Last Of Us is finally here! One of the television shows that I've been most keen to see over the past couple of years made its debut last week, and with two episodes under its belt, I think it's a good time to share my first impressions of the show.
First of all, the narrative of The Last Of Us is just perfect for an adaptation like this. Video games have been notoriously difficult to successfully bring to the screen – but in my view, that's because most previous attempts have been feature films, not television shows. A modern, serialised TV show is a far better option for almost all video game stories for one simple reason: length.
Concept art for The Last Of Us.
The Last Of Us was released on the PlayStation 3 back in 2013, and its main storyline took players anywhere from 16-20 hours, on average, to complete. There's no way to condense a story like that into a film; even the longest works of cinema clock in around the three-hour mark. By choosing the small screen instead, Sony and developers Naughty Dog have played a masterstroke.
So before the show had even got started, it felt like there was a strong chance for success. If I'd have heard that The Last Of Us was going to be adapted as a film, I'd have been far less interested – because its complex, dark, and deeply emotional story needs more time to play out. And based on the first two episodes, it seems as though we're in for a solid adaptation that doesn't rush past or skip over key story points.
Pre-release still frame of Tess and Joel with a victim of the cordyceps infection.
I was worried that I'd find Pedro Pascal miscast as Joel, if I'm being honest. Although Pascal was solid in Game of Thrones, and I've enjoyed his performances in other titles, like last year's The Unbearable Weight of Massive Talent – which you should really check out, by the way, as it's a solid action-comedy – I wasn't convinced that he was the right fit for this part. Pascal underwhelms me in The Mandalorian, his other big made-for-streaming series, but that's more to do with the writing rather than the performance; The Mandalorian doesn't give Pascal a chance to show his emotional range (nor any range at all, come to that) which is where he shines in The Last Of Us.
So I'm glad to have been proven wrong about that! The central pairing of Joel and Ellie is both the driving force of the plot of The Last Of Us and also its emotional core, and I think we've seen the beginnings of that in the show's first couple of episodes. Again, this is something that builds up slowly, and the initial part of the story – the part that we've seen so far – put Ellie with other characters at first. But there's a hint of good things to come in the pairing of Pedro Pascal and fellow Game of Thrones alum Bella Ramsey.
Pedro Pascal at the premiere of The Last Of Us.
It's not a stretch to say that The Last Of Us is one of the best video games I've ever played. Mechanically the game is solid, and its stealth-action gameplay is decent – but that was hardly innovative in 2013. What made the game special was its narrative; the game's story was one I'd long felt was worthy of an adaptation like this. Bringing it to a new audience, as well as providing fans of the game with an adaptation worthy of such a remarkable story, was the challenge that befell HBO – and so far, it seems that they've risen to meet it.
Bringing the post-apocalyptic world of The Last Of Us to screen successfully required a huge financial investment – not only to secure big-name stars like Pedro Pascal, but to create intricate sets that reflect twenty years' worth of decay, and to craft animation work that provides a sense of scale. HBO backed up the show's creators with a decent budget, and as a result The Last Of Us recreates the game's hauntingly beautiful world – with a few changes along the way!
The post-apocalyptic world of The Last Of Us is stunning.
I don't know whether there will be a reason for the decision to change the time period in which the story is set other than perhaps an attempt to play on some kind of hidden early 2000s nostalgia… but maybe there will be more to it than that, we'll have to see. In the original game, the infection broke out circa 2013 (the year the game was released) with the main story taking place in 2033-34. Perhaps the creators of the show hoped to use a kind of "look at what life could be like right now in an alternate timeline" thing, but if that's all there is to it I don't think it adds anything.
In a way, the show might be more relatable, not less, if it were set in the 2030s or 2040s, amidst the decaying remnants of today's culture, rather than reflecting the way things were twenty years ago. There were what I interpreted as subtle digs at the George W Bush administration and the general post-9/11 culture of the United States in some of The Last Of Us' scenes and dialogue, but this is something that, to be honest, has been explored in far more depth – and far better – in numerous other works, and again I don't think it added anything of substance. However, I'm content to wait and see if the time period and other setting changes are going to be paid off later.
In the show, the outbreak occurred in 2003.
One thing that the show absolutely nails is its post-apocalyptic look. The faces of the characters are grimy and dirty from years of living in difficult conditions, the sets all show attention to detail with moss and mould, and every last element has been carefully crafted to simulate a world that is, for the most part, abandoned. CGI and animation work combine with practical effects and some very gruesome makeup to really sell the effect.
Two episodes in and I've already noticed multiple locations that look incredibly similar to the video game upon which the show was based. The flooded hotel in particular felt eerily familiar, and doubtless it would to anyone who played through The Last Of Us. There must be a temptation with an adaptation like this to shake things up and put the characters into different-looking spaces, but so far I've been struck by just how similar the locations have all felt.
The flooded hotel felt eerily familiar.
The series has made some changes, though, and one of the biggest ones that's become apparent so far is the relationship between Tommy and Joel. In the video game, Joel was estranged from Tommy by the time of the main story, with Tommy having left to join the Fireflies – an anti-government group whose objective is to both end the military government and find a cure for the cordyceps infection. In the show, however, a big part of Joel's motivation is to reunite with Tommy, who seems to be a resident of the Boston quarantine zone along with Joel and Tess. It remains to be seen how this change will impact the story, and whether there's a deeper reason for it.
Another notable change came toward the end of the second episode, with the events that unfolded at the State Capitol also being quite different when compared to the video game – though this one was less impactful as it took the main characters to more or less the same place.
Tess and Joel at the Capitol.
I'm not any kind of "purist" opposed to changes like this, and if they serve the story well and create an engaging narrative, it should be fine. But I do think it's noteworthy in any kind of adaptation – be that of a book, film, or video game – when narrative beats and characterisations are altered. The Last Of Us worked so well because it's such a strong character-driven story… and I guess all I can say is that I hope that making changes to that story and its characters won't have any ill effects or unintended consequences!
There are advantages to changing things up, though. While fans of the game should be confident that they're familiar with the broad strokes of the plot, smaller changes and additions keep The Last Of Us fresh even for folks who may have played through its story multiple times. That's a net positive, in my view, and never being quite sure what will happen next is almost always a good thing for a television show like this as it seeks to keep the tension and excitement levels high!
A new creation for the series.
The addition of a sequence set at the very beginning of the outbreak, following a scientist and military officers in Indonesia, was interesting, and the show seems to be making a bit more of an attempt than the game did to explain the origin of its cordyceps infection. Even if that sequence is all we're going to see, I still think it was a good idea to include it. Changing the disease's origin from "South America" to Indonesia is certainly an interesting choice, though, and again I wonder if this is something that will be paid off down the line.
The Last Of Us has a beautiful and understated piece of music as its main theme. The Americana-inspired tune is pitch-perfect for the series, and the short, modern title sequence is in line with a lot of other shows in the serialised space; shows from Star Trek: Picard to Game of Thrones have all used CGI sequences like this. I don't think that The Last Of Us' theme will become quite so recognisable and iconic as some others, but it's a great piece in its own right.
Cover art for the original video game.
So let's wrap things up! The Last Of Us is off to a great start. There are a couple of open questions; elements unique to the series or that have been changed from the source material, and I'm curious to see how that will play out as the story progresses. But overall, the show feels like a great adaptation. It's easily one of the best video game adaptations that have been created so far, and certainly gives the Halo series on Paramount+ a run for its money!
For someone who isn't a big horror fan, there were jumpscares and tense moments in The Last Of Us that were definitely pushing me out of my comfort zone as a viewer, but they were relatively few and far between in a complex, nuanced story that has plenty of other things to focus on. At no point did I feel I needed to switch off or skip ahead to get past a difficult or frightening sequence, and I think that's to the show's credit.
Above all, The Last Of Us is one of the most incredible and emotional stories that I've ever played through in a video game. Bringing that story to a wider audience and making it more accessible is a fantastic thing, and I hope that this series will succeed, bring in huge numbers of viewers, and introduce this wonderful story to a whole new group of folks – while still finding ways to keep it exciting and engaging for people who've already experienced it. Based on the first couple of episodes, there are plenty of reasons to think it's up to the task!
The Last Of Us is broadcast on HBO and streams on HBO Max in the United States and is broadcast on Sky Atlantic in the United Kingdom. The Last Of Us is the copyright of Naughty Dog, Sony Interactive Entertainment, and HBO. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Why I can't support Hogwarts Legacy or the Harry Potter series
Wed 25.01.23 Wed 25.01.23 Dennis
This article deals with the sensitive subject of transphobia and may be uncomfortable for some readers.
When the Harry Potter books emerged in the late 1990s, I missed out on the craze at first. It was only around the time of the third book in the series that I was convinced to check them out; it had become an unavoidable phenomenon by then, and even though I was outside of the nominal target age range and had long since moved beyond kids' stories, I felt that the Harry Potter stories were good fun and had a lot to offer. I even went as far as to pre-order a couple of the remaining titles, reading them as soon as they were available.
Although I was never "in" the Harry Potter fan community, I definitely held the books in high regard, and when the films came along I enjoyed those as well. Harry Potter became a point of pride, in a way, as a British person; in an entertainment landscape so utterly dominated by the United States, Hollywood, and American films and television shows, here was a distinctly British entertainment property that was taking the world by storm.
Harry Potter author JK Rowling.
When the Harry Potter film series came to an end at the beginning of the last decade, so too did my involvement with the franchise. I found the first Fantastic Beasts film to be poor, I wasn't in a position to be able to see the Cursed Child stage play, and although I'd still have said that the films and books were decent, I was in no rush to go back and re-read or re-watch any of them. Harry Potter had come and gone for me – as indeed it had for most of its audience outside of the hard-core fandom.
The recent conversations around JK Rowling, prompted in large part by the upcoming video game Hogwarts Legacy, have dragged up the Harry Potter series for me, though, and it's fair to say that my feelings have changed a lot since I first sat down to read the books more than twenty years ago. JK Rowling has leveraged the fame and money that Harry Potter brought her to go to some pretty dark places, and as a result I'm one of a growing number of people who can't support, enjoy, or take part in the Harry Potter series, Hogwarts Legacy, or anything else related to it any longer. In this piece I want to explain, as best I can, why I feel that way.
Upcoming video game Hogwarts Legacy prompted this conversation.
First of all, I believe that each of us has an inalienable right not to be compelled, forced, or shamed into supporting a company, product, or public figure when what they say and do conflicts with our values and beliefs. This applies to conservatives who say they won't support "woke" corporations and it applies equally to anyone who doesn't want to lend their support to companies and individuals who express homophobic, transphobic, and other kinds of bigoted views. Whether we agree or disagree with someone about the importance of an issue, the fact remains that we all have the right to determine what's important to us, where our values lie, and to try – insofar as possible in a corporate capitalist system – to avoid companies and entities that don't share those beliefs and values.
This is the very definition of "voting with your wallet."
It doesn't have to be explained in such lofty philosophical terms, but this is basically what it boils down to. For some folks, JK Rowling's transphobic public statements, her continued financial support for transphobic organisations, campaigns, and causes, as well as other decisions she's taken and statements she's made mean we don't want to support Harry Potter, Hogwarts Legacy, or anything else in the franchise.
JK Rowling at the White House circa 2010.
Now I'd like to get into some of the reasons why I came to the decision to undertake what essentially amounts to a boycott of Hogwarts Legacy and Harry Potter.
I first started to feel uncomfortable with the way JK Rowling was treating the franchise when she began going back to the books and clumsily tried to insert characterisations and narrative elements that were simply not present – nor even implied to be present – in the original work. She seemed to be doing this for "internet points;" for the clout of being able to claim that she had actually created a series that was more progressive than it truly was.
What Rowling was attempting to accomplish with an unsubstantiated claim that, for instance, the character of Dumbledore was gay, was to award the Harry Potter series – and herself as its author – further prestige and recognition that was unearned. At a time when Rowling's other endeavours were failing to come anywhere close to recapturing the magic (no pun intended) of Harry Potter, making very public statements about her only genuinely successful work was a way for her to retain a level of attention and relevance – and by keeping a spotlight on Harry Potter at a time when many of the series' more casual readers and viewers were drifting away, it was a way to try to keep the cash flowing.
JK Rowling went back to the Harry Potter series and tried to arbitrarily insert character traits that didn't exist.
Long before JK Rowling started down a path that would lead to overt transphobia, I think it was pretty obvious that she was someone who was struggling to let go of Harry Potter. By returning to the series to put out a sequel in the form of a stage play, signing another deal with Warner Bros. to make films based on the book Fantastic Beasts and Where To Find Them, and having the online forum/community Pottermore created, Rowling signalled both a desperation to stay in the spotlight and a cold-hearted greed as she sought to keep the money coming in.
But during this period, Rowling was more a figure of fun than anything harmful. Sure, it wasn't great to see her trying to almost arbitrarily assign new sexualities and other traits to characters in the Harry Potter books, but it came across more as pathetic attention-seeking than anything malicious. Rowling saw that the LGBT+ movement was advancing, felt that the lack of open or even implicit LGBT+ characters in Harry Potter was hampering its ongoing success, and tried to remedy that in a pretty shameless way. It was sad, almost pitiable… but something I felt was, at most, worthy of being joked about.
JK Rowling with Rupert Grint, Daniel Radcliffe, and Emma Watson in the early 2000s.
JK Rowling's very first public step down what we now know to be a transphobic path seemed pretty innocuous at first. I actually interpreted her Twitter post – in which she responded to an article by Devex that used the phrase "people who menstruate" – to be harmless wordplay. People who write a lot often like to play with words, as I can attest, and by sarcastically responding to the post it seemed, for a moment at least, that what she was doing wasn't anything serious.
But over the following months and years, Rowling has clearly become increasingly transphobic.
Let's define what we mean by "transphobia" so there are no misunderstandings. Someone who is transphobic has an irrational hatred toward transgender and gender non-conforming people. In this context we aren't using "phobia" to refer to a fear, but to refer to dislike, disapproval, prejudice, discrimination, and/or hatred. And to be especially clear: if someone says they believe that transgender people, and trans women in particular, should be "treated with dignity," but then refuse to even accept that transitioning is possible or oppose laws that would affirm someone's true identity, they are transphobic. Saying they believe in treating people with "dignity" has become a buzzword in some right-wing circles, but if they can't back up that word with any meaningful action, then it's nothing but cover for something overtly harmful.
I hope we're clear on our definitions now.
One half-serious Twitter post that may have been tone-deaf does not constitute transphobia, although it clearly hinted at a deeper dislike or disapproval of transgender and gender non-conforming people. But if that had been Rowling's sole contribution to the debate, or if she had walked it back, apologised, or even simply ignored transgender issues thereafter, we wouldn't be having this conversation. But she didn't – when faced with pushback, she doubled-down.
Although JK Rowling had begun to lose her status as the Harry Potter series slipped out of the mainstream cultural conversation, she was still someone who was held in high regard. She'd become far less important as Harry Potter began to be eclipsed by other, newer franchises, but if you had asked almost anyone throughout the 2010s about JK Rowling, chances are you'd have heard them say something positive about her – or at least about the Harry Potter series. This pushback that she got for her initial transphobic post was the first time since becoming a household name that she'd gotten any kind of major criticism in public – and it clearly had a huge psychological impact on her.
JK Rowling's Twitter post from June 2020.
Rowling's initial beliefs about sex, gender, and gender identity may be understandable, to an extent, because of the era in which she was born and the society in which she was raised. Even when I was at school in the '90s, "sex education" lessons entirely excluded any mention of homosexuality, and the idea that someone could transition from one gender to another was never even discussed in any health or even biology lesson. If transgender people were mentioned at all, it was for the sake of mockery; "trannies" were the butts of jokes and figures of fun, and nothing more.
Some people of my generation still cling to those beliefs even as science and society have moved on in leaps and bounds – but thankfully, better education, increased awareness, and more scientific and sociological research into sex, gender, and gender identity have already changed minds. Unfortunately, though, people are using JK Rowling's public and vocal transphobia to try to push back against the societal acceptance of trans people – and even to attack legislation that protects trans rights.
A protest in the UK in January 2023.
Image Credit: Sky News
Rowling herself has become the figurehead of this movement, and the current Conservative government in the UK has been able to turn the question of trans rights into what is insultingly termed the "trans debate," in part using Rowling and others like her as cover for some seriously harmful legislation that either seeks to block the advance of trans rights in the UK, or in some cases, actively rolls back pre-existing trans rights.
This is the real crux of the JK Rowling problem: her status and wealth have allowed her free rein to spearhead one of the worst and most aggressive anti-trans campaigns anywhere in the western world, lending undue legitimacy and standing to a point of view that is mostly shared by a bizarre coalition of religious fundamentalists, paleoconservative reactionaries, and internet trolls. At a time when LGBT+ rights were advancing across the board, Rowling stepped in and has actively worked to push back against those rights, scoring some successes as the current Conservative government and its allies use her and the people who support her as a shield.
The current Conservative government in the UK is keen to oppose and roll back trans rights.
This is why I can't "separate the art from the artist," as some folks have suggested. Because what JK Rowling is doing is still happening and is continuing to actively cause harm to trans people, I find myself in a position where I can't support the Harry Potter franchise. Moreover, with Rowling retaining ownership of the franchise, any purchase of books, films, video games, and other merchandise gets her a cut of the proceeds – and as we've just been discussing, Rowling uses some of her money to provide financial support to transphobic campaigns, causes, and organisations. I feel that making any new purchase of Harry Potter merchandise, at this time, is akin to donating to such causes myself – something I would categorically never do.
Last time we talked about JK Rowling we touched on this concept, which is referred to in some academic circles as "the death of the author." Taken from the title of an essay by French critic Roland Barthes, "death of the author" is primarily about discovering one's own interpretation of a published work independent from the original intent of the author and who they are or were – but I would very strongly argue that it doesn't apply in this case, and that separating JK Rowling from Harry Potter is impossible as long as she remains in control of the franchise and continues to monetise it.
It isn't possible to separate JK Rowling from Harry Potter.
There are plenty of authors and other creators whose work I would also choose not to support under similar circumstances – but they're either long dead, no longer actively involved in their franchise, or their franchise has been taken over and moved on. This is the key difference, and while there are many, many creative people who were unpleasant or even harmful during their careers and lifetimes, JK Rowling is continuing to cause harm to her targets right now.
I also found some of JK Rowling's recent attacks on the Harry Potter fan community to be pretty distasteful, showing how little respect or appreciation she has for the people who quite literally gave her the position and power that she's wielding. In her recent book The Ink Black Heart, Rowling clumsily inserts a character as a stand-in for herself, then makes that character the target of an angry and murderous mob stemming from an online fan community. The book, much like everything else Rowling has tried outside of Harry Potter, got mixed reviews and didn't sell especially well. But the intent was there – and Rowling has shown her true colours, sneering at and judging the very people who made her who she is.
The Ink Black Heart got mixed reviews.
One interesting thing that has come out of this whole unfortunate mess that is to the overall good, I feel, is a reevaluation of JK Rowling's work and the Harry Potter series in particular. While the setting of Harry Potter captured the attention of a worldwide audience, there's a reason why it's always still referred to as "Harry Potter" instead of its official title: "the Wizarding World." The world of Harry Potter doesn't stand up to scrutiny, and without its titular characters and the admittedly engaging story that they were part of, it doesn't feel as though there's anything else of substance there.
Look at franchises like Star Trek or Star Wars – deep world-building created rich, lived-in settings in which characters could get lost, where their skills and talents mattered and could be applied to any number of roles in those universes. Harry Potter, in contrast, is both shallow and inconsistent; a cobbled-together mix of English folklore, tropes of the fantasy setting, and even elements and narrative beats directly plagiarised from other literary works. It invented practically nothing new, and its few original elements are actually its weakest points. As a setting and a fictional world, it doesn't survive more than a cursory glance.
The "Wizarding World" is not a well-constructed setting.
And that's totally fine. Not every author can be brilliant, not every fictional setting can be wonderfully rich and deep, and for its intended purpose and target audience, there's nothing wrong at all with the setting of the Harry Potter books. But it does raise a wry smile when I hear people leaping to its defence, claiming it's a unique and brilliant fictional setting comparable with the likes of Tolkien's Middle-earth. It isn't… and it was never meant to be. JK Rowling simply doesn't possess the talent to create something anywhere close to that level.
There are some deeply troubling and problematic depictions within the Harry Potter books, too. Goblins who run the Wizarding World's banks – and who are set to be a major villainous faction in Hogwarts Legacy – clearly and obviously draw on anti-semitic tropes and stereotypes. The Wizarding World practices slavery, enslaving "inferior" house elves to do the bidding of witches and wizards. And when, in the books, a character tries to point this out and campaign against it, she's ridiculed not only by her friends, but really by the narrative itself. Harry even takes ownership of a house elf at one point, sending him to complete tasks for him; his own personal slave.
Kreacher, Harry's personal house elf.
JK Rowling also seems to delight in making fun of people with different body types, using "ugliness" and fatness as indicators of maliciousness and evil. And, of course, Harry Potter falls into the trap of racial stereotyping, with its tiny number of minority characters being deeply problematic.
It's actually been good to see more and more folks taking a critical eye to the Harry Potter series in light of the issues surrounding JK Rowling. Some criticisms of the books at the time of their publication and in the years since had been written off or just ignored – and for folks who always felt uncomfortable with certain aspects of the stories or the ways in which they treated marginalised and minority groups, it must be cathartic to find more support.
Katie Leung as Cho Chang in The Goblet of Fire.
I won't ask anyone to boycott or refuse to purchase Harry Potter merchandise or Hogwarts Legacy, because I don't think it's my place to do that. This piece wasn't intended to change minds or convince people on the fence to adopt a certain point of view. It was more a way for me to get my thoughts in order and share why, as someone who talks a fair amount about the video games industry here on the website, I won't be covering Hogwarts Legacy this year. Hogwarts Legacy could end up being a bust, at the end of the day – an overhyped, mediocre video game not worth all of this fuss and bother.
As I said at the beginning, we all have the right to decide for ourselves which products, companies, and public figures we want to support – and which ones we don't or can't support. For me, Hogwarts Legacy and the entire Harry Potter series now fall firmly into the latter category, and unless there's a massively compelling reason to discuss the franchise in future, I hope that this will be the last time I have to comment on it.
A replica of the Hogwarts Express steam locomotive.
I would love to see greater acceptance of transgender and gender non-conforming people. I myself am non-binary, and it isn't always easy in the UK in 2023 to be open about that. People like JK Rowling have caused and are continuing to cause harm to trans women in particular, and unfortunately her very public attacks on trans folks have been seized upon by people and organisations with pre-existing anti-trans views and agendas to halt and reverse trans rights.
Hogwarts Legacy and the Harry Potter series may not be openly transphobic in terms of narrative, but because a cut of the proceeds go to someone who is, and who uses the wealth, fame, and status she has to contribute to these causes, I'm now in a position where I can't support them. As a consumer in a capitalist marketplace, all I can do is vote with my wallet – so that's what I'm choosing to do.
I'm done with Harry Potter.
This is not an easy subject, and for people who are much greater fans of Harry Potter than I ever was, all I can really say is that I empathise with you. I keep thinking how I might feel if this kind of controversy were engulfing something I deeply care about, like Star Trek, and whether I could realistically cut off the entire Star Trek franchise as a point of principle. I genuinely don't know what I'd do in that situation – so I sympathise with any Harry Potter fan who feels that way.
I also don't think that many of the "hot takes" floating around on social media on this subject are doing anyone any favours. Viral videos proclaiming that anyone who purchases Hogwarts Legacy must be transphobic and is automatically a "bad person" don't help the discourse around this complex and sensitive subject, and such polarising language arguably pushes away just as many people as it converts to this cause. So I feel that, while passions are understandably high, we need to try to approach these conversations, and our interlocutors on the other side of the debate, with as much calmness as possible.
So that's it. I hope you now have a better understanding of why I can't support Hogwarts Legacy and the Harry Potter series.
This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
Gaming, Personal, Real World harry potter, harry potter franchise, harry potter series, hogwarts legacy, jk rowling
Five highly-rated games that I couldn't get into
Thu 19.01.23 Dennis
I recently saw a video on TikTok of all places where a player was talking about their list of games that, for one reason or another, they had tried but didn't like or couldn't get the hang of. I've lost the video now and can't find it to credit the person, unfortunately – so if you somehow see this please don't think I'm stealing your idea! But I liked the concept, so today I wanted to talk for a few minutes about five highly-rated games that I just couldn't get into.
A note before we start: these games are, according to most reviews, thoroughly enjoyable. The fact that I'm personally not interested in them, or couldn't get to grips with them, is not meant as an attack. Chances are you'll find some or all of these games to be great – and that's okay! All of this is just the subjective opinion of one person. While I will try to explain what it was that put me off or what I didn't like about each of these titles, I recognise that all of them are held in high regard. The fact that I didn't enjoy them or couldn't get stuck into them is a personal thing and nothing more!
It's someone who isn't enjoying a game!
The first games console I owned in the early 1990s was a Super Nintendo, and even back then I remember struggling with some particularly challenging titles. Gaming has not always been accessible to everyone – and I'm not the most skilled player in the world by any stretch. There were also games on the SNES that I tried out but didn't like or wasn't interested in, as there were on every subsequent console I owned, too! At least in those days it was easier to re-sell or trade in a game that I didn't like!
As gaming has evolved, it's become easier than ever to get started with playing games – and there are more titles more easily accessible on more platforms than ever before. But despite the ubiquity of gaming today, and the myriad titles in every imaginable genre, not every game is going to be right for every player!
So without further ado, let's jump into my list.
Promo art for Star Trek Online.
I'm a huge Star Trek fan and have been for more than thirty years. At a time when the Star Trek franchise had stepped out of its prime timeline to make the reboot film trilogy, Star Trek Online came along and promised to return to that setting and take a look at events after The Next Generation era, around the turn of the 25th Century.
This is exactly the time period that I was (and still am) most interested to see explored, so Star Trek Online should have been perfect for me! The game has also brought on board many Star Trek actors, both series regulars and guest-stars, to voice versions of their beloved characters. Storylines would take players to different eras of Star Trek's history thanks to missions that travelled through time, and almost every Star Trek race was present – with several major factions being fully playable, too.
Several Star Trek Online characters.
I tried Star Trek Online shortly after it launched, and I even paid for some of its in-game currency and cosmetic items like uniforms. But despite sinking somewhere in the region of 35 hours into the game, I just couldn't find a way to enjoy it, and I quickly felt that I was playing it more out of obligation and hope rather than for any real sense of fun.
I just can't get on with online multiplayer games for the most part. In titles like Fall Guys I can have fun, and I've played some racing games online too, but in a game with a story where I want to get immersed in a fictional world and enjoy interacting with characters, seeing hundreds of other players cutting about just rips me right out of it. There can't be 16,000 "one and only heroes" who are all the best hope for saving the galaxy… that just doesn't make sense. So for me, Star Trek Online's genuinely interesting stories and missions clashed in a fundamental, irreconcilable way with its gameplay.
Box art for Kingdom Come: Deliverance.
I followed the development of Kingdom Come: Deliverance for a while, and in 2018 it was definitely one of the titles I was most interested to try out. I'm a history buff (it was the subject I read at university) and the idea of stepping into a realistic recreation of the high medieval period was genuinely exciting. Kingdom Come: Deliverance seemed to be offering a unique experience; an action/role-playing game but without the fantasy elements that are often present in the genre.
I like to think that I gave Kingdom Come: Deliverance a fair shake when I was able to eventually get the game for myself. But to my disappointment, I found it punishingly difficult to the point that it was basically unplayable. One day we'll need to have a longer conversation about difficulty in games, because this is a big topic, but for now suffice to say that Kingdom Come: Deliverance didn't respect me or my time.
A fistfight is part of why I called it quits…
By denying players the option to freely save their game, Kingdom Come: Deliverance forced me to replay long sections with no good reason. And with no way to turn down the difficulty, I found myself dying over and over even in what was supposed to be the introductory area. Combine those two things together and I was already having an incredibly frustrating time. I put Kingdom Come: Deliverance down and simply never went back to it.
Difficulty settings are accessibility features, opening up games to disabled players and players with different abilities. Moreover, they're commonplace and not that hard to implement – there's no technical reason why a modern game can't offer a way to change the difficulty for players who want or need an easier experience. I don't have the time or energy to spend hours and hours practising one aspect of one game, and I don't really have the ability or skillset, either. Kingdom Come: Deliverance was basically denied to me as a result – and that's unfortunate, because I genuinely wanted to play it.
Swinging through New York City!
Although I'm not the world's biggest fan of comic books and their cinematic adaptations, Marvel has been unavoidable over the past few years. I wouldn't have normally sought out a superhero title, but Spider-Man is widely considered a masterpiece; one of the best open-world adventures certainly of the last generation. So I thought I'd give it a shot.
Perhaps it's because I have no real investment in the world of Marvel or its characters, but I found that I just couldn't get into Spider-Man's story. Several hours into my playthrough I'd done a handful of story missions and spent a bit of time enjoying the scenery – the game's recreation of New York City really is a sight to see, and one of the most interesting and vertical cityscapes ever brought into the gaming realm. But despite a great setting, the game's version of New York seemed to be filled with bog-standard open-world busywork and little else; most encounters consisted of beating up a handful of nondescript thugs and bad guys.
Promo screenshot of Marvel's Spider-Man.
At first I thought I was going to have a hard time with the web-swinging mechanic that's a big part of how Spider-Man traverses the open world, but after a little while – and more than a few false starts and mistakes – I think I more or less got the hang of it. Swinging is pretty forgiving, and at least in the denser parts of the city, there's no shortage of things to grab hold of. It's certainly an unusual way to navigate a game world!
The game's story included a number of Marvel villains and characters whose names were familiar to me, but I feel that without that investment in either the films or comic books, I just wasn't particularly interested to see where the story and its characters went. I didn't actively choose to stop playing Spider-Man – the game is actually still installed on my PC at time of writing – but I put it down one day and just… didn't pick it back up. I found other things to watch and play instead, and I feel no pressing need to return to Spider-Man and see its story continue.
Many publications picked Elden Ring as their game of the year, and it's considered by a lot of folks to be one of the best open-world games and one of the best "Souls-like" games of all-time. But as I said above when discussing Kingdom Come: Deliverance, it's that punishing difficulty that I found to be offputting.
FromSoftware – developers of both Elden Ring and the Dark Souls series – use this kind of excessive, punishing difficulty as a selling point in their games and have for years, but I'm not on board with it at all. Granted I'm not the world's best gamer, and that's probably part of it, but I also see this style of gameplay being used to cover up game mechanics and design elements that aren't great, and especially to pad out the runtime of a game that would ordinarily be a lot shorter. Think about it: the combination of very difficult combat encounters and a checkpoint system that can mean having to replay entire chunks of the game over and over clearly adds to the runtime of titles like Elden Ring.
A familiar sight to anyone who's played a "Souls-like" game!
This is much more of a subjective thing, but I felt that, despite having decent graphics, Elden Ring actually looked pretty bland. A colour palette that was swamped by brown, khaki, green, and grey tones just didn't impress me, and the game had a pretty drab and even depressing look to it as a result. Maybe there was a reason for that, but it didn't exactly leave a good impression.
At the end of the day, I'd have given Elden Ring a shot if the game offered difficulty and accessibility options. There's absolutely no technical reason why every game in 2023 shouldn't be able to do this – and while it's a choice the developers made, and will presumably continue to make in future titles, it's one that is intentionally cutting off millions of potential players. I knew from the second it was announced that Elden Ring wouldn't be for me because I knew that the company developing it would ensure it would be a game I would find inaccessible. And that's kind of sad, especially if it really is as good and as immersive as people have said.
Grand Theft Auto V (Online)
Promo art for the game's online mode.
I played through Grand Theft Auto V's single-player campaign and I had a decent enough time with it. The open world is great – or at least it was by the standards of games a decade ago; it's definitely showing its age by now! But the game's online mode was, for the same kinds of reasons that we've already discussed, just something I couldn't get into.
Grand Theft Auto V also feels remarkably pay-to-win for a game that costs money up-front, and probably deserves more blame than it gets for normalising in-game microtransactions and pay-to-win elements in online multiplayer games that we've seen explode in the decade since it was released. Other titles such as Fortnite and Overwatch definitely contributed to this as well, and the less said about the FIFA series or Battlefront II the better… but Grand Theft Auto V was doing the pay-to-win thing before any of them.
Racing is one of a number of activities players can partake in online.
By 2023 I had expected to see the Grand Theft Auto series move on, releasing a new game. And no, the awful "remaster" of the Grand Theft Auto III trilogy doesn't count! Obviously this wasn't an issue in 2013 or 2014, but as Grand Theft Auto V was ported to more and more platforms, including the latest generation of home consoles, there's a growing sense that Rockstar is milking it dry, and is unwilling to let it go. Development time and resources than could – and I would argue should – have been allocated to the next game in the series have been taken up by creating new missions and microtransactions for Grand Theft Auto V. That's great for folks who are still playing – but some of us are ready for a new game!
At the end of the day, when Grand Theft Auto V became the highest-grossing entertainment product of all-time, I guess it's understandable that Rockstar would struggle to let it go. But on the other hand, with all the money it's made them, there's more than enough to spend on developing a new game! We know that Grand Theft Auto VI is being worked on, at least, but it's taking an awfully long time.
Did I just lose my "gamer" credentials?
Those are five highly-rated games that, for the reasons discussed above, I just couldn't get into. If one or more of your favourites made the list, well… just keep in mind it's only the opinion of one person! We're all allowed our own preferences, and while I tried to explain what it was that made these titles unappealing or offputting to me, it's all subjective. I recognise that these games are all bestsellers and held in high esteem by many players… they just weren't right for me.
We're lucky that gaming has grown to such a point where there are so many different choices available to players. These games aren't my cup of tea… but there are many that I've enjoyed over the years – and many more coming up that I hope to enjoy in the months and years ahead! Whether you want to play a quiet, casual game for a spot of relaxation or punish yourself with an impossibly difficult title, there really is something for everyone. And I think that's fantastic!
So I hope this was a bit of fun – and please try not to take it too seriously, especially if I made criticisms of one of your favourite titles!
All titles discussed above are the copyright of their respective studio, developer, and/or publisher. Some screenshots and promotional artwork courtesy of IGDB. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Star Trek: Picard Season 3 – hopes, fears, and expectations
Spoiler Warning: There are spoilers ahead for Star Trek: Picard Seasons 1 and 2 as well as trailers, teasers, and announcements for Season 3. Spoilers are also present for The Next Generation, Nemesis, and Discovery.
With Star Trek: Picard's upcoming third season now barely a month away, it seems like a good time to look ahead. Thanks to trailers, teasers, and interviews with the cast and crew, we know a little about how the season is shaping up, and from my point of view, it wouldn't be unfair to say that Picard Season 3 has a lot of work to do to salvage a troubled, muddled production that hasn't hit the high notes that I've been hoping for.
Let's take a step back. My "first contact" with the Star Trek franchise came in the early 1990s. The first episode I can solidly remember watching was The Royale, from The Next Generation's second season – though I'm fairly sure I'd seen others, or at least parts of others, prior to that. The Royale aired here in the UK in June 1991, so I've been a Trekkie for more than thirty years at this point! Moreover, I have an incredible fondness for The Next Generation in particular, as it was Captain Picard and the crew of the Enterprise-D that first made me into a Star Trek fan.
In short, I'm about as close as it's possible to get to the ideal target audience for Picard Season 3; a season of television that promises to bring back the main cast of The Next Generation. But before so much as a single frame has aired, I find myself having mixed feelings. I genuinely want to see Picard Season 3 succeed – and if I dare to hope, maybe even find a way to tie up loose ends and unresolved narrative threads that were left on the table as Seasons 1 and 2 faltered. But at the same time, I have concerns.
Seasons 1 and 2 both had some incredible highlights: episodes and moments within episodes that were as good as Star Trek has ever been, that hit all of the right notes, and that left me on the edge of my seat or jumping for joy. But step back and look at the bigger picture, and I'm afraid that both seasons also had some pretty major issues that hampered my enjoyment. Both seasons told long, serialised stories… and both plodded along in places, stumbled in others, and failed to resolve key storylines and character arcs by the time it was over.
Do you think we'll find out more about this mysterious anomaly?
One of my biggest pre-season questions is this: will Picard simply ignore what came before as it races to tell a new story? Or might there be time to step back, even if just for a moment through a line or two of exposition-laden dialogue, and try to tie up some of these loose ends? If – as I suspect will be the case – Season 3 is going to tell a new story unrelated to the events of Seasons 1 and 2, there could still be time to acknowledge, in the most barebones of ways, what became of the Coppelius synths, the Zhat Vash, Narek, the new Borg faction, the mysterious anomaly, and other unexplained or unresolved story points.
In fact, that would be my single biggest request!
There are ways in which Picard Season 3 could tie everything together, transforming the disjointed series into something more closely resembling a single, ongoing story – and I have a theory as to how that could pan out that involves the faction of super-synths from Season 1. But even if none of that comes to pass, it would still be worthwhile, in my view, to find some way to acknowledge the events of the past twenty episodes and do something to try to tie up those loose ends. If Season 3 is to be Picard's last, as we've been repeatedly told, and no other early 25th Century projects are coming up in the short term at least, this will be the last opportunity to do so for several years – possibly ever.
The storyline involving the super-synths in Season 1 is just one of several that remain incomplete.
I think it's worth reiterating just how disappointing it is that all but one of the new characters introduced in Picard have been dumped. Although a couple of them got what we could generously call "narrative arcs" in Season 2 that felt somewhat conclusive, I still felt that, twenty episodes in, we hadn't really had much of a chance to get to know most of them. Soji and Elnor, who were both sidelined for practically all of Season 2, had a lot of potential as young, new characters – but that potential was squandered by a production that didn't seem to know what to do with either of them, and then completely wasted by the decision to cut them both from Season 3.
As I said at the time, if Star Trek is to survive long-term, it will be new characters, not old ones, who will have to pick up the baton and drive the franchise forward. Just as Jean-Luc Picard and the crew of the Enterprise-D did when The Next Generation premiered, it will fall to new characters in the years ahead to keep Star Trek fresh and relevant. By removing almost all of them from the show in favour of what could turn out to be nothing more than a desperate attempt to play the nostalgia card, I truly fear that Picard's producers have done serious harm to the Star Trek franchise's longer-term prospects.
Before Picard Season 1 had premiered back in 2020, I said here on the website that it was my genuine hope that legions of new, younger Star Trek fans would be just as excited in another thirty years' time to see Star Trek: Elnor or The Dr Jurati Show as I was to see Jean-Luc Picard's return. That moment felt like it had the potential to be on par with the premiere of The Next Generation – a handing of the torch from one generation of characters to another. But it hasn't happened, and I feel we're seeing the Star Trek franchise as a whole struggling with its identity, not really knowing how to move beyond its legacy characters.
There's no way in which I can fully get on board with Picard Season 3 and the return of The Next Generation characters because of this. Although I'm interested and perhaps even a little optimistic as this new adventure approaches, their return feels tainted because of who had to be unceremoniously kicked off stage in order to make it happen. I think I'd still feel that way even if all of the departing characters had been given enjoyable arcs that felt complete, but when at least two (Soji and Elnor) didn't even get the barest of goodbyes, and Dr Jurati got more of a "see you later" rather than a definitive ending to her story, this disappointment feels all the more egregious.
Isa Briones and Evan Evagora at a Star Trek: Picard panel in 2020.
Image Credit: Fandom Spotlite via YouTube
That would be bad enough in isolation, but unfortunately it isn't the first time that Picard has lost a character without giving them a proper send-off – or even a conclusion of any kind to their storyline. Narek simply vanished at the end of Season 1, midway through the second half of the finale, and was never seen nor heard from again. Despite having plenty of time to process the reaction to Season 1 and plan for ways to avoid making the same mistakes, it feels as if the producers and creative team didn't learn any of the lessons from the rushed and disappointing Season 1 finale.
Narek's disappearance is a big part of why I don't have much confidence that Season 3 will do anything at all to tackle some of these unresolved narrative threads. How difficult would it have been for someone in Season 2 to comment on Narek, confirming that he had been incarcerated? It would've taken a line or two of dialogue at most – and in a plodding story that really slowed down and dragged in places, it's not like there wasn't time to fit it in!
So… what happened to Narek?
But all of that is looking backwards when we should really be looking ahead. Despite feeling disappointed in cast departures, reminiscing about "what might have been," and worrying about what it could all mean in the future, I'd be lying if I said that the return of the Enterprise-D's crew isn't something that I feel has huge potential to be entertaining and enjoyable. Seeing what these characters could do in a modern television environment that wouldn't have been possible thirty-five years ago is genuinely appealing, and getting what should feel like a "ten-hour movie" with all of the visual effects and other trappings of a thoroughly modern production is a prospect that I daresay many fans of The Next Generation will be thrilled about.
Star Trek: Picard has already taken us back to some of these characters and showed us how much we'd missed them. I noted in Season 1 that seeing Picard give Data a proper goodbye and laying him to rest was something that I didn't even know I wanted, but in retrospect I can see how it was a glaring omission from Nemesis. And for all the talk of characters being left in the lurch with incomplete stories and arcs, Nemesis didn't really provide a conclusive or definitive endpoint for anyone – so this season will be an opportunity to do that; the first such opportunity that these characters have gotten.
Captain Riker and Admiral Picard in a promo photo for Season 3.
When all of this talk about "endings" started coming out, and when executive producer and showrunner Terry Matalas talked about Picard Season 3 as giving the characters the "send-off" that they never got in 2002, I can't be the only one who started to think about character deaths, can I? We just talked about Picard bringing the crew of The Next Generation into a modern, serialised television framework – and if there's one thing more than any other that has defined television over the past decade or so it's main characters being killed, often at shocking moments or in particularly gory ways.
Picard has done this too. Season 1 saw three Star Trek legacy characters killed off: Dr Bruce Maddox, Hugh the Borg, and Icheb. And although Data was already "dead," that season also saw the last parts of his consciousness shut down as well. Season 2 then saw Q meet his final end… so I don't think any of the characters feel safe at all as we go into this new story!
Some of the main cast and crew at a recent panel.
And that could be okay. A character death, if handled well, can set up the stakes for a story, or it can even feel right for the character if they've gone through a satisfying arc or come to the end of their place in the story. After thirty-five years, 176 episodes of The Next Generation, four films, and further involvement with Star Trek for at least some of these characters, though, it would be a pretty bold decision to kill off even one of them! But it absolutely could be the right thing to do if it fits with the story, accomplishes a narrative goal, and/or brings someone's decades-long arc to a satisfying end.
There was speculation when Picard premiered in 2020 that the show would end with his death – but having already seen Picard die once (only to be immediately brought back to life thanks to technobabble) he actually feels pretty safe – or at least safer than the others. It would be a strange series indeed that ran to only thirty episodes in total and killed off the same character on two separate occasions!
Picard has died once in this show already…
I've criticised Discovery for providing its main and even its secondary characters with some borderline-ridiculous plot armour in certain episodes and sequences, and it's been to that show's detriment in some respects that we haven't seen any main character deaths for two whole seasons at this point. Picard has already demonstrated a willingness to swing the proverbial axe – though the question of who may end up on the executioner's block is still an open one. It could be no one, of course, but I can't help but feel that the "end" to these characters' stories that has been discussed may prove fatal and permanent for at least one of them.
The main villain of the season, Captain Vadic, feels like an interesting new element for the series. In her brief appearance in the trailer, she gives me a "Khan" kind of vibe; the obsessive, maniacal, revenge-obsessed villain archetype that Ricardo Montalbán brought to screen so perfectly in The Wrath of Khan. I don't want to pin my hopes too much on Vadic being "the new Khan" or anything like that, because that kind of character could easily stray into a one-dimensional villain caricature, but from what we've seen so far, there's potential.
The villainous Captain Vadic.
I talked about this back in November, but I'd really love to see some kind of connection to the events of The Next Generation through Vadic. Bringing back the old crew for a wholly new adventure could still be fun, don't get me wrong, but if it tied into a past Star Trek story in some way, that could be absolutely fantastic. I've already come up with a few ideas about how Vadic could be connected to The Next Generation, and who she could bring along for the ride if she puts together a "rogues' gallery" of Star Trek baddies – and at this stage, none of that seems to have been ruled out!
Given that Picard has introduced new narrative elements for its main storylines so far, I stand by what I said last time we looked at Captain Vadic: if I had to place a bet right now, I'd still have to put my money on her being someone new. That would mean her driving force, the reason for her revenge obsession, is also likely to be new and unconnected to Star Trek's past, too.
The Shrike, Captain Vadic's warship.
If we assume that Captain Vadic is someone new and her reason for hating Picard and/or the Federation is also new, that leaves open the question of why Picard would choose to reunite his old crew to take her on. Although Captain Rios is gone, he could still have called on Soji, Elnor, Laris, and the Borg-Jurati hybrid to help if he needed it – and I wonder how (and whether) the absences of these characters will be addressed. Could they even have been killed off-screen to both explain away their absences and to give motivation to Picard, Seven, and Raffi?
Away from narrative decisions, on the technical side of things I expect Picard Season 3 to be polished and to look great. The teasers and trailers that we've seen so far had no shortage of beautiful starships, vessels which continue the design philosophy of The Next Generation era but move it along into the early 25th Century. We already saw this – a little too briefly, unfortunately – with the USS Stargazer in Season 2, but with a big return to space supposedly on the agenda this time around, there's scope to finally spend some more time with Starfleet.
The USS Titan at warp.
Picard Season 1 was probably the low point for modern Star Trek in terms of visual effects. We've talked before about the copy-and-paste fleets seen in the season finale, but there was also a CGI sequence copied from Discovery's second season, a pretty obvious redress of Discovery's bridge, and more besides. Although none of these moments were atrocious, they didn't hit the highs that Star Trek can reach in its modern incarnation – and when compared to what the Star Wars franchise and others have been doing, they were downright poor.
But all of that has changed! Not only did Season 2 build whole new sets for the USS Stargazer, including a bridge, ready-room, and hallway, it also showed off a beautiful and diverse Starfleet armada that more than made up for the lacklustre one we saw in Season 1! Just from what we've seen so far in the trailers and teasers, I have high hopes for the visual effects that we'll be able to enjoy in Season 3.
The Enterprise-F, based on a design from Star Trek Online.
Picard has struggled to get enough diversity in its filming locations, something that was incredibly obvious as Season 1 wore on and took us to places on Earth, including Japan and France, and then half a dozen planets – all of which were filmed in the "thirty-mile zone" around Los Angeles. Season 2, because it stepped back in time to a particular time and place, largely avoided that feeling, but I'm not sure how Season 3 will fare. If more time is going to be spent in space on starships, that's probably a net positive for the series in more ways than one. Because Picard is filmed in California, the show doesn't have easy access to Paramount's AR wall in Toronto, so the choice the producers have is to either build sets on sound stages or film on location in the all-too-familiar California area. I hope they've chosen the former!
Nostalgia is a big deal in today's entertainment landscape, and when done right, a show that harkens back to the past and successfully plucks the right chords can be wonderful. I'm not opposed to any and all forms of nostalgia in entertainment, and despite my disappointment in the casting situation that we discussed above, there's a big part of me that wants to see the crew of the Enterprise-D back in action. But nostalgia is something that needs to be handled with care. Crucially, it mustn't be overdone or overplayed.
The cast of The Next Generation in the 1990s.
It's all too easy for a production to assume that digging up fan-favourite characters or returning to familiar settings will cover up all manner of storytelling sins – but there are dozens or perhaps even hundreds of examples by now that prove that isn't the case. And there are productions that go completely overboard with attempts to play the nostalgia card, something that can come across as just plain desperate. The Star Wars franchise has fallen victim to this in more ways than one in recent years, and it's a trap that I truly hope Picard Season 3 can avoid.
A story that goes all-in on nostalgia can end up feeling gratuitous or tacked-on; an unnecessary epilogue for characters whose stories were, for better or worse, already over. While it's true that Nemesis didn't exactly end in conclusive fashion, that doesn't absolve Picard Season 3 of responsibility to these characters. Just because their stories didn't end definitively twenty years ago, that doesn't give the new season free rein to do anything. What comes now – especially if it's being designed from the ground up to be a send-off or finale – has to be decent in its own right, not simply "more."
A promotional photo for Season 3 showing Riker and Picard at a bar.
Unlike in 2020 when Season 1 was approaching, I feel less out-and-out excitement for Star Trek: Picard and more a sense of restricted optimism. I have hope that the new season will look great, that it will be fun to welcome back fan-favourite characters after a twenty-year absence, and that we'll get at least some enjoyable moments and perhaps a dash of that elusive sense of "Star Trek" that hasn't always been front-and-centre in the franchise's modern era. But I also have reservations about a season that may very well race past or just outright ignore key story points that were left on the table last time around.
Maybe I should give up hope of seeing much of anything from Season 1; those stories had the chance to be addressed in some way in Season 2, but it didn't happen. But things like Season 2's mysterious anomaly – that felt like an attack on the Federation or Alpha Quadrant – just being ignored as the story rushes to bring back legacy characters and set up a new mystery… I will be disappointed, I fear, if the season ends without so much as mentioning what happened last time.
Gates McFadden at a recent Star Trek: Picard panel.
I'm trying to reconcile my disappointment in the way the new cast was handled with my interest and excitement in seeing old favourites coming back for another adventure, and I'm keenly aware that I need to at least try to judge Season 3 on its own merit – for the story it aims to tell – rather than wondering what might have been or being upset at a situation that I can't change. That's a challenge that I will have to face – and if you stick around, you can judge for yourself how well I do when you read my episode reviews!
After two mismanaged, difficult seasons that had some great episodes and moments but ultimately failed to deliver, this is Picard's last chance. As someone who's a huge fan of The Next Generation and the other Star Trek shows of that era, it also feels like a last chance for the Star Trek franchise as a whole to demonstrate that there's potential in this 25th Century setting, and that telling stories that at least tangentially connect with the themes, settings, and characters of Star Trek's "golden age" is a concept worth pursuing. It's definitely noteworthy to me that, at time of writing, no new Star Trek projects have been announced, despite several concepts supposedly being worked on behind the scenes. Is Picard Season 3 an opportunity not only for these characters but for this setting and this time period? Will Paramount be watching to see whether there's still potential here? I can't help but wonder.
The briefing room of the USS Stargazer in Season 2.
I see genuine potential in the new season's villain, Captain Vadic. A character who feels as though she's drawing inspiration from Khan, one of the best villains not only in Star Trek but in all of cinema, could be absolutely delicious to watch, and Amanda Plummer is an actress who has the ability to pull it off. While the story remains shrouded in mystery, the teases and glimpses we've seen have been genuinely fascinating to this old Trekkie, and have inspired me to craft a few of my patented (and usually totally wrong) Star Trek theories!
At the end of the day, all any of us really want is for Picard to be entertaining. It doesn't have to be high art, it doesn't have to be the best thing Star Trek has ever done… but it does have to keep my attention and interest, not annoy me, and be basically consistent with what the show and the franchise have done before. Everything else is just fluff, and I can overlook retcons, inconsistencies, and everything else as long as the show is basically fun.
And hey, if it doesn't go well, there's always Strange New Worlds Season 2 to look forward to!
Star Trek: Picard Season 3 will premiere on Paramount+ in the United States on the 16th of February 2023, and in the United Kingdom and around the world on the 17th of February 2023. Seasons 1 and 2 are already available to stream or buy on DVD/Blu-ray. The Star Trek franchise – including Picard and all other properties discussed above – is the copyright of Paramount Global. Some images used above courtesy of StarTrek.com. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Amazon Prime Video review – The Rig
Spoiler Warning: Though there are no major plot spoilers, minor spoilers are still present for The Rig.
The title of this piece was originally going to be "Miniseries review: The Rig," because all of the marketing that I'd seen for this six-episode Amazon production led me to believe that it would be a one-and-done miniseries or limited series. In fact, I probably wouldn't have tuned in if I'd have known it would end on a pretty substantial cliffhanger – especially when a continuation of the story hasn't yet been greenlit. Even going into The Rig's final moments, I was still anticipating a climax and resolution to its ethereal enviro-mystery. When the series ended I actually wondered if I'd missed an episode, or if there was more to come – but at time of writing, the six episodes currently available on Amazon Prime Video are all there is.
I hope that The Rig will get a second season or at least some kind of conclusion, because there was promise in its story and characters that I'd certainly be happy to pick up and see resolved. But for now, I guess the biggest takeaway from The Rig for me is this: do just a little bit more research before committing to watching something!
Title card for The Rig.
I'd seen advertisements for The Rig on Amazon's homepage and plastered across social media, so at least here in the UK, it seems as though the show has had a decent marketing budget attached to it. The main splash banner on Amazon's homepage has previously been reserved for Star Trek: Picard (in its first season, at least) and Amazon's big productions like The Wheel of Time and The Rings of Power, so it certainly felt that the company was pushing its latest endeavour with all it could muster.
If only a few dollars from that marketing budget had been redirected to The Rig's CGI and visual effects, though, because there were some pretty serious misfires in those departments, especially for a series that seems to be trying to compete at such a high level. Some of the CGI felt decidedly "last-gen," as if it were something we'd have seen circa 2008. This was noticeable from literally the first second, as The Rig's opening sequence was entirely animated, and not animated to anywhere near the high standards I'd expect from a corporation with the resources of Amazon.
The Rig's opening CGI sequence was poor.
The opening CGI sequence left a poor first impression, and across the first couple of episodes especially, The Rig was having to work hard to overcome some low-budget visual effects. This extended beyond CGI into the physical space, too. The show's signature "fog" effect looked decent enough when animated – nothing spectacular, but a step up from some of the other animation work, especially in those first couple of episodes. But when real actors were supposedly walking through the "fog," I'm afraid the effect looked rather similar to what you'd get from those cheap smoke machines that became popular in discos a few years back. It looked poor – and for such an important part of the series, getting this wrong was, again, something that gave a poor impression.
However, while some CGI sequences remained poor across the entire six episodes, the animation work for the "spore" phenomenon that the crew encountered fared a lot better, and as this element was of particular importance to the story, getting it to look right was important.
An example of how the "spores" look.
The "spores" reminded me more than a little of The Expanse's protomolecule, if you're familiar with that sci-fi series (and if you aren't, you should really check it out as its fantastic!) And this ties into a broader point about The Rig – the series brought to the table a number of elements that we've seen in other sci-fi films and franchises. There wasn't too much originality in the production – which isn't to say that it was bad by any means, but as the show progressed I definitely found myself noting more and more of these inclusions.
James Cameron's The Abyss, released in 1989, was definitely a film that I felt The Rig was drawing inspiration from, not only thematically but visually, too. There was also the introduction of a corporate officer who knows more about the phenomenon than he lets on that felt like it had been lifted straight from Alien. And the "it was only trying to communicate" trope that clearly took inspiration from Star Trek. We also have the aforementioned visual effect that was similar to The Expanse… the list goes on! The way in which The Rig pieced these elements together was decent, and the fact that a story, visuals, or other elements of a production aren't wholly original isn't to say it's awful – but it is worth noting how many narrative and design choices echoed other productions in the same mystery/sci-fi/thriller space.
Some of The Rig's story beats and visuals felt familiar.
Despite being commissioned by Amazon and made by Amazon Studios for Amazon Prime Video, The Rig felt remarkably similar to dozens or perhaps even hundreds of British television shows that I've seen over the years. The cinematography, acting (and some actors, too), the musical score, the aforementioned low-budget VFX… all of it came together to feel very familiar. If I hadn't known that I was watching The Rig on Amazon Prime Video you could've told me this was a show made by the BBC, Sky, or ITV and I'd have believed it, no question!
Part of The Rig's marketing stated that it's the first Amazon show to be wholly produced in Scotland – and I guess that explains why it feels so familiar to a British viewer! The director/executive producer, John Strickland, has worked on episodes of popular British shows like Poirot and Line of Duty, and I swear I've seen at least half of the cast before – in bit-part roles on shows like Holby City or Doctor Who.
The main cast and crew of The Rig at the show's premiere in Scotland.
Speaking of the cast, everyone involved did a good job at selling what was an increasingly sci-fi story. The characters all felt grounded and real, and even moments of exposition were delivered in ways that felt natural, informing us about certain characters' histories and backstories without being too obtrusive. There's some excellent scriptwriting and characterisation there, and the cast all did well to bring it to screen convincingly. I wouldn't single out anyone for giving a disappointing performance; everyone on The Rig did a standout job.
There were some great moments involving practical makeup – particularly in one gory moment after a character suffered a fall. The way bruises, broken bones, and gaping wounds were constructed felt visceral and realistic, and at a moment where the story was only just beginning to take off, the shock value these simple practical effects had shouldn't be overlooked.
Some great makeup was used to create wounds and injuries.
The Rig didn't take long to get going – and in a series that only has six episodes, I guess that's fair enough. My only point of criticism on this side of things would be that it felt as if at least some of the characters went from normal life to "panic mode" in a heartbeat – instead of a degradation in the crew's mood from happy to irritable to angry and depressed taking a slower course. It felt as if The Rig got started, introduced us to its big storyline, and then the members of the crew who were going to get angry just snapped immediately, largely remaining in that state for the rest of the series. There was scope, I felt, to show how the effect of a disaster and being isolated with no field of vision or communications could slowly wear people down – and while The Rig tried to pay lip service to that at a couple of points, it didn't really work convincingly.
That being said, there were some great character moments in all of the episodes that really showed off the tension and stresses that the worsening situation was putting people under. While I would have liked this to have been built up a bit more slowly, at the same time it's worth saying that this wasn't really what The Rig was all about, and considering the main thrust of the narrative was elsewhere, I guess it's fair to say that this side of things was handled about as well as it could've been within the show's time constraints.
Different character conflicts came to the fore in The Rig.
The Rig had a clear environmentalist message – one about climate change, the dangers of unchecked oil exploration, and the responsibility humankind has en masse for the damage to the atmosphere and natural world. But rather than allowing its sci-fi, rather ethereal story about ancient microorganisms to stand on its own as a metaphor, someone involved in The Rig's production clearly insisted on inserting some rather clumsy dialogue to make this environmental message incredibly obvious and in-your-face.
For me, as someone who's a huge fan of the Star Trek franchise, I think sci-fi like this works best when subtlety is the order of the day; when the analogy is given space to speak for itself without the script punching viewers in the face with the same message over and over. The Rig comes across, in these moments, as a show that doesn't trust the intelligence of its own audience; its producers and writers want to make their environmentalist message clear, so they keep repeating it. Rather than trusting what was a well-constructed metaphor to make that point, The Rig drops these clumsy, awkward exchanges of dialogue in a desperate attempt to make things obvious. And I just found that to be unnecessary and a little disappointing.
One of the moments where a conversation about climate and environmental issues was very obvious.
Don't get me wrong: I love a series with a moral and a message, and The Rig clearly has one. Climate change and the environment are causes that we definitely need to care about, pay attention to, and find solutions to out here in the real world, and although The Rig was never going to be high-brow "art" or a series that would change opinions and sway huge numbers of folks to its cause, it had a point to make and its metaphor about "the earth fighting back" against humanity's destructiveness was a good one. Not a wholly original point, perhaps, but a decent one nevertheless.
But what the series didn't need to do was constantly hammer that message home by other means – the metaphor at its heart was strong enough on its own to get that message across. We didn't need half the cast to spout anti-oil, anti-fossil fuels, or pro-climate lines – especially pretty clunky, hammy ones – in order to get the message. The Rig had a point – but the way in which it went overboard ended up rather detracting from it.
Someone really wanted to make sure that The Rig's environmental message came through!
One thing I admired about The Rig's story is the way in which it blended some very ancient-feeling legends of the sea with modern science and technology to create its core mystery. For as long as humans have been sailing, there have been legends of strange phenomena out at sea, and The Rig seemed to take some of these as a starting point, combined with our lack of knowledge of the ocean floor in general, and weave them into its sci-fi mystery. The way in which it was done was clever, and it came to screen well.
There was a strong anti-corporate message in The Rig, particularly one that went after big oil corporations. Though Pictor, the corporation in the show, is fictional, it's clearly based on real-world corporations like Shell, BP, and others, and The Rig doesn't hold back when it comes to criticising the way in which these massive corporations are managed and their impact on the environment. As we got into the final couple of episodes, the inclusion of a secretive character from "head office," the fact that they were unwilling to share what they knew – and how long they'd known about some of the problems affecting the Kinloch Bravo rig – really leant into this "corporate dystopia" angle, and I think that worked pretty well.
So let's wrap things up and I'll share my thoughts on The Rig as a whole.
The titular rig in the fog.
Overall, I felt that The Rig was an interesting series. Its core mystery certainly captured and held my attention, and even as its story descended from something semi-plausible into outright sci-fi, I was content to go along for the ride. I wouldn't have climbed on board, however, if I'd realised that it was going to end on such an abrupt cliffhanger – and with no second season having been greenlit at time of writing, I fear the ending to this interesting story may never be told. All we can do is watch this space and hope that Amazon decides to go ahead with the next chapter!
On the technical side of things, though, I felt The Rig was let down by some pretty poor visual effects, both animated and practical, especially in its first couple of episodes. For a series that relies heavily on these things to set up its mysteries and narratives, the way in which some of them came across on screen wasn't spectacular, and I've come to expect better from Amazon Prime Video in that respect.
So that was The Rig. An interesting series that I hope gets a continuation. If a second season, a film, or some other conclusion is in the offing, I daresay I'll check it out. The Rig hadn't been on my radar at all until I saw advertising for it on social media and Amazon's homepage, but I was pleasantly surprised to find an enjoyable enough six-hour series with a good cast.
The Rig is available to stream now on Amazon Prime Video. The Rig is the copyright of Amazon Studios and Amazon Prime Video. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Thu 05.01.23 Sun 08.01.23 Dennis
Spoiler Warning: Minor spoilers may be present for some of the titles on this list.
As a new year gets underway, it's a good opportunity to look ahead. There are some exciting-sounding films, television series, and video games that are currently on the schedule for 2023, and on this occasion I thought it could be fun to pick out a few that I find particularly interesting and preview them! I'll share some of my preliminary, pre-release thoughts on ten of each.
On balance, I don't think 2022 will be held in particularly high esteem in future in terms of its entertainment experiences. There were some good ones, but there were also plenty of delays and projects that just underwhelmed for one reason or another. Will 2023 fare any better? That's still an open question… but there are certainly some big releases on the horizon that could potentially excel.
What does 2023 have in store?
It's time for a couple of caveats! First of all, delays can happen at any time in the creative process, especially in a war-torn, pandemic-disrupted world. As a result, any or even all of the films, shows, and games that we're going to talk about today could miss their intended release dates or release windows – and there really isn't anything we can do about that! I'm firmly in the camp that says delays are almost always a net positive; while never fun, I'd rather creatives spent longer working on a project to finish getting it ready rather than launching it too soon. We don't need to look far for examples of how wrong that goes!
Finally, these projects seem interesting or exciting to me personally for one reason or another… in my subjective opinion! I'm not trying to say that these are or will be "objectively the best" releases of 2023, nor should the exclusion from the lists below be interpreted as any kind of snub. I've just picked out a few projects that I find to be of interest, and if you hate all of my picks or I've excluded some of your favourites, please just keep in mind that this is only the opinion of one person!
Films:
I confess that I didn't see a lot of films in 2022. I can't go to the cinema any more due to my declining health, and while practically every major title made its way to a streaming platform last year, there were some I just wasn't interested in or found that I didn't have the right mindset or headspace for. That's just the way it goes sometimes! That being said, there are some interesting films on the schedule for this year, and I shall be keeping an eye out for these ten in particular!
Film #1:
I've been pleasantly surprised by the two trailers we've seen so far for The Super Mario Bros. Movie. The film looks like it's going out of its way to stay as true as possible to its source material, while at the same time putting a twist on Mario's adventures in the Mushroom Kingdom. The "hero who has to save a princess" trope has been rather overdone – and feels pretty outdated in 2023 in more ways than one – so seeing Luigi being held captive by the villainous Bowser and Mario working with Peach feels like it should be a great change of pace.
The inclusion of an all-star Hollywood cast has proven controversial in some quarters, but from what I've seen of the film so far, I will be surprised if most folks aren't won over by the time the credits roll. There will be some die-hard haters – as there always are in any franchise any time something is changed – but overall, I have high hopes for this one. This film could easily be the best animated film of the year – and one of the best non-Disney animated films of the decade!
Dune: Part Two
The first part of Dune was a surprisingly strong adaptation of a book that has proven to be notoriously difficult to adapt. I had a fantastic time with it when it was released at the end of 2021, and I've been meaning to go back and re-watch it for some time now. I was concerned that this sequel might not see the light of day if Warner Bros. didn't feel the first part did as well as they'd hoped – but fortunately there was no denying the critical and commercial success of Dune in 2021!
The cast from the first film are all reprising their roles, and director Denis Villeneuve is returning to the big chair. Filming officially wrapped a couple of months ago, and Dune: Part Two is well into post-production at this stage. A November release is on the cards, and I'm really excited to see the story continue.
Director M. Night Shyamalan has an inconsistent track record, and I suspect his career has been more harmed than helped by acquiring an early reputation as the "master of twists." But regardless, he's back with Knock at the Cabin in 2023, a psychological horror film about a family who are confronted by four people who claim to be trying to prevent the apocalypse.
The film's premise sounds interesting to me, and a cast that features Jonathan Groff and Rupert Grint feels like it has potential. I wouldn't say my expectations for Knock at the Cabin are sky-high, but we could certainly be in for one of the more interesting titles in the horror genre this year.
To be blunt, I wasn't blown away by the visuals in the teaser trailer for The Little Mermaid. The CGI looks fantastic, but the fully live-action moments didn't feel convincingly "underwater," and actually looked pretty amateurish. Assuming that Disney can figure out a way to pull off those underwater sequences convincingly, though, The Little Mermaid should be a creditable adaptation of the 1989 animated film.
Visual criticisms aside, I feel hopeful that this new version of The Little Mermaid will introduce the story to a new generation. While the animated film is still perfectly watchable in its own right, there's nothing wrong with updating things and recreating the film for a younger audience, and Disney has a pretty good track record at doing so by now.
Is it a great idea to bring back Indiana Jones for another adventure? As a child of the '80s, I'd be lying if I said I don't enjoy the Indiana Jones films… but Kingdom of the Crystal Skull was already a let-down. Dial of Destiny could redeem the series, ending Harrison Ford's turn with the famous hat and whip on a high note – or it could double down on the disappointment!
This film is definitely one I'm placing in the "interested in" rather than "excited about" category. I don't really have high hopes, but I'd love to be proven wrong. At the very least, I hope Dial of Destiny will be a passable popcorn adventure flick. Whether it will truly live up to its illustrious forebears… well, I'm less hopeful of that. If it succeeds at bringing in a wad of cash, though, I think we can expect to see reboots, prequels, and spin-offs in the years ahead!
Asteroid City
There isn't a lot to go on with this film, billed as a "romantic comedy-drama." But the director, Wes Anderson, has pedigree, and has put together a diverse ensemble cast that rivals his previous pictures, such as The Grand Budapest Hotel. The full cast list is far too long to include, but some of the standout performers for me that I'm interested to see include Bryan Cranston, Tom Hanks, Willem Dafoe, Tilda Swinton, and Scarlett Johansson.
Though I'm not entirely sure what to expect from this one, it could be a lot of fun! The setting is the mid-1950s somewhere in the American Southwest, and some kind of "stargazer convention" will be part of the plot, too.
To mark the company's centenary, Disney is going to release Wish – a film all about the "wishing star;" the star upon which characters in other Disney films have made their wishes. The star itself is going to be a character of sorts, but the film will also introduce a new cast of characters, including Asha, voiced by Ariana DeBose of West Side Story fame.
Wish will also bring back a hand-drawn animation style, something Disney hasn't used since The Princess and the Frog more than a decade ago. While we haven't seen just how the film will look, some concept art has been released that looks absolutely beautiful. Disney's big animated releases are almost always fantastic, and I have high hopes for Wish.
The third Disney entry on this list, The Haunted Mansion is the company's latest attempt to turn a theme park ride into a film! No one would deny that Pirates of the Caribbean set a high bar for that concept a few years ago, but other attempts haven't always worked! An adaptation of The Haunted Mansion twenty years ago (that I'm fairly sure I've seen but can't really remember much about) starred Eddie Murphy, but even he couldn't salvage what critics regarded as a picture that was average at best.
Jungle Cruise may not have been 2021's film of the year, but I enjoyed it for what it was, so there's definitely room for another theme park adaptation. The Haunted Mansion could be great to watch around Halloween; a kind of lighter, child-friendly horror title that will be spooky… but not too spooky!
65 has an unusual premise – an astronaut accidentally travels back in time to the era of the dinosaurs, and must figure out a way to survive. Adam Driver will take the lead in this sci-fi action-adventure, and his presence alone should make it worth checking out. Driver's performances as Kylo Ren in the Star Wars sequel trilogy were outstanding, and his turn as a divorcee in Marriage Story was Oscar-worthy in my opinion.
That being said, I can't help but feel that 65 could go either way! Its premise could make for a different kind of sci-fi title in a genre overrun by sequels and comic book adaptations… or it could turn out to be an overblown B-movie that didn't deserve a leading man of such quality! Time will tell… but I'm definitely interested to see how it shakes out.
Film #10:
Ridley Scott will direct this historical epic that focuses on the rise to power of Napoleon Bonaparte. Scott has a great track record, with films like Alien and Thelma & Louise under his belt, but an earlier attempt at an historical epic – 1492: Conquest of Paradise – was not particularly well-received! Could this be a chance for redemption for the director in the genre?
The title role has gone to Joaquin Phoenix, and that feels like it could be an inspired choice. Backed up by a cast that features Ben Miles and Vanessa Kirby, I'll be curious to see what Napoleon has to offer when it releases. The film will be an Apple TV+ exclusive, which is also a point of note.
Television Series:
2023 looks set to be another year where franchises, spin-offs, and continuations of ongoing stories dominate the television landscape. There are several big shows whose new seasons I'm eagerly anticipating, but it feels like there are fewer wholly original projects to look forward to. That being said, there were some great new stories in 2022 – so hopefully this year will bring along some surprises, too!
Television Series #1:
Strange New Worlds was truly outstanding in its first season, blending old-school episodic storytelling with modern serialised elements. As much as I like what Discovery and Picard have done with season-long story arcs, the approach used by Strange New Worlds should, in my view at least, serve as a model for the entire Star Trek franchise going forward.
The show's second season wrapped months ago – and I will be positively stunned if we don't get an announcement that a third season is being worked on sometime before Season 2 premieres this spring. I absolutely cannot wait to spend more time with Captain Pike, Spock, and the rest of the crew of the Enterprise!
Hailey's On It!
Hailey's On It! is a Disney Channel animated series that will feature Moana's Auli'i Cravalho in its leading role. The premise sounds interesting – a young woman must step outside of her comfort zone and confront her fears in order to "save the world." And with Cravalho leading the charge, I think there's the potential for the show to be something a little more than just a distraction that parents can use to get a few minutes' peace!
The animation style shown off in concept art looks fantastic, and while I wouldn't normally say that I'm excited for a new Disney Channel cartoon, I feel hopeful, at least, that Hailey's On It! could be the kind of kids' show that has something to offer to a grown-up audience as well.
After a decidedly lacklustre second season, my disappointment was compounded by the announcement that all but one of the new characters introduced in Picard will not be returning for the show's final outing. Season 3 has a lot of work to do, then, to pull out a satisfying ending to what has been a troubled production. If the trailers and teasers are anything to go by, it just might be up to the task after all!
The return of main characters from The Next Generation feels bittersweet because of who had to be unceremoniously kicked off stage to make room for them. This season could be a roaring return to form, or it could drown in failed attempts to play the nostalgia card. I'm absolutely hoping for the former… but trying to prepare myself for the latter.
It isn't entirely clear when The Rings of Power's second season might be ready. Filming only started in October, and a series with such extensive post-production work may take a while. That's not to mention that Season 2 is being filmed in new locations, and may even serve as somewhat of a soft reboot of a series that proved controversial in some quarters.
Despite that, however, I called The Rings of Power my favourite television series of 2022, so I'm incredibly excited to see what happens next. The first season ended with several massive cliffhangers for both individual characters and for the story as a whole, so it'll be great to see the next chapter of this fantasy epic unfold.
Discovery's fourth season ended on a high, with what is almost certainly one of the best episodes that the show has ever produced. I was concerned that the show would attempt yet another recycling of the old "the entire galaxy is in danger and only Burnham and the crew can save it!!!" narrative framework that has been used four times now… but thankfully, based on the first trailer and comments from the show's producers, it seems as though Discovery will finally be bold enough to try something different!
As a result, my excitement for Season 5 grew immensely! Although Season 4 dragged in parts, on the whole I think it marks a turning point in the show's run, and the addition of some wonderful secondary characters to the cast has given new life to a series that is rapidly approaching its sixth anniversary and sixty-fifth episode. Season 5 could build on what Season 4 did, taking these well-rounded characters to new thematic and storytelling places.
Produced by the same team that created Band of Brothers and The Pacific, this new World War II drama will follow the stories of members of the United States Army Air Forces – the precursor to the Air Force. The miniseries seems to be following a similar format to its popular predecessors, with an expansive cast of characters, almost all of whom are based on real people. Masters of the Air is based on a biography of the unit that was published in 2007.
I'm expecting a tightly-focused story with plenty of character. CGI and visual effects have improved since Band of Brothers premiered, so I'd hope that the show will look fantastic and really succeed at bringing World War II to life on the small screen.
Shōgun
The second adaptation of James Clavell's 1975 novel has a lot to live up to! An earlier adaptation, made in 1980, was one of the most popular shows of the year, and with a troubled production that saw scripts scrapped and rewritten, new showrunners brought on board, and a shoot that overran by two months… let's just say that Shōgun has work to do.
But the story, set in 17th Century Japan, is an interesting one, and there's potential in this new adaptation to see it introduced to legions of new fans. A shipwreck sets up the story of a "fish-out-of-water" hero in an unfamiliar land, and the palace intrigue at the castle of the titular Shōgun could rival the very best drama series of the year.
Video game adaptations are notoriously difficult, but The Last Of Us has an all-star cast, a sky-high budget, and crucially, it seems to have won over many fans of the video game. The Last Of Us is one of the best video game narratives that I've ever experienced, and it feels like a natural fit for a serialised drama series; the story would certainly be far too long to condense into a film. So I'm hopeful that – finally – a video game adaptation will get the accolades it deserves!
Moreover, I'm really excited to be able to show this fascinating and unique horror-drama story to friends and family members who have no interest in gaming. The story of The Last Of Us is fabulous and absolutely deserves to find a bigger audience. There's reason to hope that this adaptation will be up to the task.
I enjoyed what the Halo series did in its first season, all things considered. It succeeded at bringing the long-running video game franchise to the small screen, adapting its story to fit the new format and making a few changes along the way. Some of those changes proved controversial – as such things always do – and I can certainly entertain the argument that there was less action than fans were hoping for.
But Halo will press on, potentially taking on board some of those criticisms, and it's my hope that Season 2 will build on the accomplishments of Season 1 to progress the story in an enjoyable way. The first season had some great performances, clever cinematography that incorporated a first-person perspective during key sequences, and a mysterious story that will have kept even fans of the games guessing. I'm interested, and dare I say even excited, to see more.
Television Series #10:
Faraway Downs
I am joking. This is a joke. Nobody should ever be tortured into watching Faraway Downs. I can honestly think of nothing less appealing than watching an extended, reworked version of Baz Luhrmann's Australia – quite possibly the worst film that I have ever had the misfortune to see. When I heard that Luhrmann was planning to use cut footage to expand Australia into a six-part miniseries I was flabbergasted. Who on earth would possibly want to see this? Was anyone asking for it to be made?
I'd rather trek to the bottom of the garden, heave the lid off the septic tank, and spend six hours staring unblinkingly at the festering sewage within.
China can often feel like a world unto itself; western productions struggle to cross over, and Chinese productions seldom attract mainstream attention over here. The Three-Body Problem is an adaptation of a Chinese sci-fi novel (or rather, the first part of a trio of novels) and is helmed by Game of Thrones' showrunners David Benioff and DB Weiss.
I haven't read The Three-Body Problem, but the premise sounds absolutely fascinating to me. Benioff and Weiss have proven themselves capable when it comes to adapting novels for the small screen – at least, completed novels – so there's reason to hope that The Three-Body Problem will be interesting and entertaining in equal measure. This one could easily go toe-to-toe with the likes of Foundation in the sci-fi genre.
There are some massive releases on the schedule for 2023 – several of which were originally promised for last year! If even one of these big titles succeeds, 2023 will already be a great year for gaming. Single-player games are definitely holding the line in an industry where online multiplayer continues to bring in the big bucks, so there are plenty of reasons to think that 2023 could actually turn out to be a fantastic year for the medium.
Video Game #1:
Tchia
I've been tracking the progress of this amazing-looking indie game for more than a year, and it looks like 2023 could be Tchia's moment. Based on legends from the developers' New Caledonia home, Tchia will see players take on the role of a young girl on a quest to rescue her father. In addition to platforming and action-adventure gameplay in an open-world archipelago based on the island of New Caledonia, the ambitious game promises to unleash players' creativity – and even includes a playable ukulele!
There have been some fantastic debut games by indie studios in recent years. My game of the year in 2021 was Kena: Bridge of Spirits – and without wanting to raise expectations too high, at least part of me is hoping that Tchia might just reach that same high bar.
DLC: Booster Course Pass Waves 4, 5, and 6
You might think it a cheat to include a piece of downloadable content on this list, but it's my list so that's just tough! Although I was disappointed not to see a wholly new Mario Kart title in 2022, the Booster Course Pass for Mario Kart 8 Deluxe has been a surprising amount of fun. Not only have racetracks from past games in the series been updated and made welcome returns, but wholly new tracks have been created, too.
The Booster Course Pass is only half-finished, and three more waves are planned for 2023. Specific dates aren't known, nor is it certain which racetracks will be appearing, but I'm nevertheless excited to have more Mario Kart to get stuck into!
Star Trek: Resurgence
A narrative adventure game with a branching storyline sounds like a perfect fit for the Star Trek franchise. After years in which no new Star Trek games had been licensed for PC or home consoles, two have come along within a few months of each other; Resurgence is hot on the heels of last year's Star Trek: Prodigy – Supernova, which I really must get around to playing!
The game is being developed by folks who used to work for studio Telltale Games, a developer whose games were often praised for their narratives. I'm hopeful that, after a drought of games for Trekkies who aren't interested in the online multiplayer scene, Resurgence will be a welcome return to the video game realm for the Star Trek franchise.
Disney Speedstorm
Developers Gameloft worked with Disney and created my favourite gaming experience of 2022: Disney Dreamlight Valley. Having taken Nintendo's Animal Crossing formula and massively improved upon it… could they be about to do the same thing by creating a Disney-based rival to the Mario Kart series? Maybe that's expecting too much… but Disney Speedstorm looks like a ton of fun!
I like casual, arcade-style racing games, and I'm a pretty big Disney fan, too. Bring those two things together and I hope it'll be a fun time.
One of the year's biggest releases has to be Bethesda's Starfield – the company's first foray into a wholly new world in a quarter of a century. An epic sci-fi adventure has been promised, with all of the hallmarks of past Bethesda titles: joinable factions, a huge mix of varied side-quests, diverse non-player characters to interact with, customisation of every facet of your character, and much more besides.
Starfield will also give players the opportunity to design and upgrade their very own spaceship, before setting off to journey to one of a thousand different planets across dozens of star systems. Starfield is ambitious, and while there are certainly things that give me pause – such as Bethesda's insistence on reusing its outdated game engine – I can already feel myself getting swept along by a growing hype train!
The Lord of the Rings: Return to Moria
I confess that I'm not entirely sure what to expect from this one. The game promises base-building and adventures in the Dwarven realm of Moria, set years after The Lord of the Rings as the Dwarves seek to reclaim their abandoned halls. It sounds as if the game will be set up for multiplayer – though the official blurb promises that it can be played solo, too.
There's something about an underground setting that harkens back to the days of dungeon-crawler games, and the subterranean setting combined with the lore of Tolkien's Middle-earth could make for a genuinely exciting title. I'm curious and perhaps a little hopeful of having some fun adventures deep underground!
The much-anticipated sequel to Jedi: Fallen Order is almost ready! The game – which I played through back in 2020 – is one of the best Star Wars experiences I've had in recent years, and it was left open-ended by the time the credits rolled. Finding out what happens next for Cal Kestis, the former Jedi padawan, is something I'm really interested in!
Jedi: Survivor seems to have taken the gameplay of Fallen Order and expanded upon it, giving Cal new weapons and abilities – and at least one new companion, too. I recently played through it for a second time, which seems to be perfect timing with the sequel coming up! I really can't wait to join Cal and the crew of the Stinger Mantis for another adventure in a galaxy far, far away.
Unlike many action-adventure titles, it seems as though Forspoken will focus much more on magic and spell-casting – something that could be absolutely fascinating. Set in an open-world, the game will follow the story of Frey, a young woman from our world who finds herself transported into a mysterious realm where magic exists and must find her way home.
Forspoken hadn't really been on my radar until recently, but I'm now genuinely looking forward to it.
Though unconfirmed at this stage, Xbox's Perfect Dark remake/reimagining would be well-timed if it should be ready this year – because the original game on the Nintendo 64 was set in 2023! Perfect Dark was originally created by Rare, hot on the heels of their success with Goldeneye 007 on the same platform, and it was a ton of fun when it released in the year 2000.
I'm genuinely curious to see what a recreated Perfect Dark might look like. Could it kick off another first-person shooter series for Xbox… and, perhaps more importantly, for Microsoft's Game Pass service? I think that's a possibility – but my main hope is that the single-player campaign will be fun to play through!
Video Game #10:
EA Sports FC
Bear with me on this one, okay? I know football (soccer) isn't everyone's favourite thing, and I know that sports games – and especially Electronic Arts' sports games – have been particularly scummy with their in-game gambling and monetisation. But for the first time since EA published FIFA International Soccer in 1993, the corporation won't have the official license or naming rights from world football's governing body. That could mean we're about to witness a sea change in the series… or it could lead to nothing of consequence at all!
Nevertheless, I'm curious to see what changes – if any – will come about as a result of EA and FIFA going their separate ways. Will EA Sports FC be noticeably different from recent entries in the FIFA series? We'll find out later this year!
We've picked out ten films, ten television shows, and ten video games to watch out for as 2023 gets underway. There will be many surprises along the way, I have no doubt, and it's possible that some of the entertainment experiences that I'm excited in right now will either end up being disappointments or won't even make it out of the door this year. But I'm hopeful that we'll get some exciting, dramatic, and just plain fun stories to enjoy between now and Christmas!
There are definitely things to look forward to. I'll try to cover at least some of these titles with reviews, first impressions, and general commentary here on the website over the next twelve months. I hope that you found this interesting, and that it was a fun, positive look ahead to some of what I hope will be the entertainment highlights of 2023.
All titles discussed above are the copyrights of their respective studio, developer, publisher, distributor, broadcaster, etc. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Stats and analytics for 2022
Happy New Year! As 2023 gets underway, I think it's fun to look back at the past year and see how the website performed. Thanks to my web host and Google Analytics, I have quite a lot of data to dive into for measuring such things.
My annual caveat applies: this whole thing is just for fun! Running this website is a hobby for me, not something I endeavour to take too seriously, and even if no one was tuning in I'd still be writing because it's something that I enjoy doing. I'm not intending to turn this website into a full-time job, nor am I interested in chasing "internet points" or going viral. So everything we're about to discuss should be considered with that in mind!
A lovely stock photo of a man reading on a tablet.
Now that that's out of the way, let's reflect on the progress Trekking with Dennis made in 2022. This past year has been much less consistent on my side, with long breaks in between posts and a general slowdown in my writing. I wrote far fewer pieces for the website this year than I did in both 2020 and 2021, and the second half of the year in particular was much more sparse in terms of new articles, lists, and other posts.
That isn't something I plan on addressing, at least not intentionally. As I said back in November when I last talked about this: the point of Trekking with Dennis for me is to talk about the subjects I fancy or that pique my interest at my own pace. In 2020 and 2021 I obviously found more things to talk about than I have this past year… and I'm actually okay with that. That doesn't mean I don't have regrets – there are films, television shows, and at least a dozen Star Trek episodes that I wish I'd found or made time to review in 2022. But I'd rather pace myself, take breaks when I need to, and continue enjoying what I do here instead of forcing myself to write to arbitrary, self-imposed deadlines and end up feeling burned out – or worse, no longer enjoying the creative process.
In short: if I find more time and energy to write in 2023 than I did in 2022, that's great! But if not, that's okay too.
I may or may not write more this year!
The website saw some significant milestones in 2022. The final post of the year – my annual "End-of-Year Awards" piece – was the 650th article that I've published here since I began the project in November 2019. That's quite a lot of writing! The total number of visitors that the website received in 2022 was just over 67,000 – which is an absolutely incredible number! That makes 2022 the best year on record for Trekking with Dennis, beating 2021's visitor numbers by a little over 6,000. That may not sound like much (especially considering the massive year-on-year improvement from 2020 to 2021) but it's an increase of almost 10%, which is pretty darn good. I'm running at almost the same level as inflation!
Another big landmark came on April Fool's Day, when the number of total hits ticked past the 100,000 mark for the first time. That means that, since November 2019 when Trekking with Dennis first went live, more than 100,000 people had visited the website. I marked the occasion with a banner at the top of the website for a few days!
Readers once again came from all over the globe – from Tanzania to Finland and from Japan to Peru!
Hello, Tanzania!
All that being said, I feel that 2022 was rather "front-loaded" in terms of visitors! Thanks to a couple of big posts about Star Trek: Discovery's fourth season (which we'll look at in more detail in a moment) the website did impressive numbers in January, February, March, and into April as well, before things started to tail off in the spring. Don't get me wrong, even the quietest month of 2022 was still nice and busy, but we definitely saw the majority of visitors in those first few months.
In total, I wrote 471,500 words in 2022. That's as many words as Herman Melville's Moby-Dick and James Joyce's Ulysses combined! It is, however, significantly less than my word counts for 2020 and 2021, but again that's because I wrote fewer pieces for the website this past year. It's still a lot of words, though!
So let's count down the top ten most-read articles that I wrote in 2022!
Number 10:
Diablo Immortal is a monument to everything wrong with modern gaming
My piece about the truly awful Diablo Immortal takes the number ten spot, partly thanks to being published within a couple of weeks of the mobile game's release. I detest not only Diablo Immortal itself, but what it represents: the worst excesses of an incredibly greedy video games industry. And I held no punches in my tear-down of the appalling little game, calling out publisher Activision Blizzard for one of the worst, scummiest mobile games of the year.
Significant line: "I was surprised when I began seeing ads for the game all over my social media pages, and even more surprised to learn that Activision Blizzard has only just finished pushing this absolute turd of a game out of its corporate anus."
I had a ton of fun writing up this tongue-in-cheek clash between Star Trek's first two captains – a debate that has persisted in the Trekkie community since The Next Generation premiered all the way back in 1987! I also had fun mocking up a poster for the article's key image, basing it on the famous "Rumble in the Jungle" boxing match poster that I think a lot of folks would be familiar with. I end up sitting firmly on the fence at the end of the article after considering the cases for both Kirk and Picard – because I like them both too much to say that one is definitively "better!"
Significant line: "Most Star Trek captains who have followed embody elements of both Kirk and Picard's styles of management and leadership while remaining distinct characters, but when it comes to the franchise's first two captains, there seems to be a major clash of personalities."
Video game spotlight: Banished
In 2022 I kicked off my "video game spotlight" series, in which I plan to take a look back at some of my favourite games of all time. The first title to get the full write-up treatment was Banished, an indie town-building game that makes regular appearances on other lists here on the website. Since I'm far too late to reasonably call a piece like this a "review," I settled on "spotlight" as a name, and I had a lot of fun talking about why Banished is such good fun. Hopefully I'll add to this series in the new year; there are at least a dozen games I plan to shine a spotlight on in future!
Significant line: "The fact that I'm still playing [Banished] almost eight years later should tell you how I feel about it!"
Ten "comfort episodes" of Star Trek for difficult days
I wrote this piece at the end of February, just days after the war in Ukraine kicked off. I wanted to highlight a few Star Trek episodes from different parts of the franchise that, at least in my opinion, make for great escapism. The episodes I chose are almost all lighter in tone, with themes of humour, family, and coming together front-and-centre. If I were doing the list all over again there are certainly more episodes I could include, but overall I'm happy with my picks. And if the list helped even one single person find something to watch when they were feeling low, then it's been a rousing success.
Significant line: "A future where humanity has succeeded at conquering not only the problems of today but also many of the baser, more primitive aspects of our own nature holds an appeal that can be difficult to put into words…"
Ten games to play instead of Hogwarts Legacy
As the title suggests, this list – which was also my most-read piece about gaming in 2022 – shows off ten games that I consider to be decent alternatives to Hogwarts Legacy for anyone who doesn't want to play or support the game. I wanted to contribute something to the discussion around Hogwarts Legacy that was a little more positive and that didn't just consist of saying "J.K. Rowling is a horrible bigot who hates the Harry Potter fan community." She is, and she does… but that isn't what this piece was primarily about. As above, if it helped even one person find something to play, I consider it a success.
Significant line: "Hogwarts Legacy, just like the rest of the fictional setting that J.K. Rowling created, is not irreplaceable."
Strange New Worlds Season 2 theory: Una Chin-Riley
It's hard to say what this piece is about without spoiling Season 1 of Star Trek: Strange New Worlds. Suffice to say that I came up with several theories about Una Chin-Riley – a.k.a. "Number One" – and where her story may go when Season 2 rolls around. I had fun putting the list together, as well as stepping back to consider her role in The Cage, where she might be during the events of The Original Series, a connection to Star Trek: Enterprise… and much more besides.
Significant line: "I'm looking forward to welcoming back Captain Pike, Una, and the rest of the crew – and getting a satisfying end to this storyline, too!"
Star Trek: Picard Season 3 theory – who is Captain Vadic?
This theory – that I only wrote in November – has been racking up a lot of views! Without spoiling anything, a new character named Captain Vadic is being billed as a villain in Star Trek: Picard's upcoming third season, and I took the opportunity of her appearance in a trailer shown off at Comic-Con to consider a few possibilities for her origin and what her mission might be. If my current track record with theories is anything to go by I'm going to be wide of the mark by miles… but that doesn't mean it wasn't a ton of fun to speculate!
Significant line: "As much as I like the idea of Vadic having a major connection to an event in The Next Generation or one of the films, if you forced me to place a bet right now, in November 2022, I'd have to put my money on her being someone brand-new…"
Star Trek: Discovery Season 4 – So who is Ruon Tarka's "friend?"
This theory did huge numbers in the first quarter of the year – while Discovery's fourth season was running. I was ultimately disappointed by the way this storyline ended, but it was still fun to delve pretty deeply into the history of Star Trek to consider some potentially interesting character possibilities. It isn't possible to say too much more without getting into spoiler territory! I had fun making up a rather jokey key image for this piece, too!
Significant line: "With Discovery taking an unplanned six-week break, we've got a little time to settle in and collect our thoughts."
Twelve Star Trek episodes to watch before Picard Season 2 arrives!
Shortly before Star Trek: Picard Season 2 premiered, I put together this list of episodes that I felt might have a connection of some kind to the upcoming story. I focused on what we knew about the season from pre-release trailers and marketing material, and selected stories that focused on time travel, the Q Continuum, Guinan, and the Borg Queen. I like to think that basically all of the episodes that I put on the list did something to inform the story of the season, even if I'd probably make a few changes in hindsight!
Significant line: "I think we've hit most of the key subjects – at least, those that we're aware of at this early stage – and got a good mix of stories…"
Star Trek: Picard Season 2 theory – what happened to Q?
So we come to the most-read article that I wrote in all of 2022! Blowing all of the others out of the water by several thousand hits, this theory about Q that I wrote in the aftermath of Picard Season 2 is clearly of interest to Trekkies! Partly, I must say, that's because of how poorly-explained parts of the story of Season 2 ultimately were (the season isn't one of my favourites, if you didn't know). But regardless, I found it interesting to take what feels like an incomplete, muddled story as the starting point for another of my Star Trek theories, and even if we'll never know what really happened, I hope that my guesswork at least makes sense and feels consistent with what we know of Q and the Q Continuum. I can't say more without seriously spoiling the story of Picard Season 2.
Significant line: "As Trekkies and as fans who've followed Q's journey over the span of more than three decades, it definitely feels like there's a missing piece of the puzzle."
So those were the most-read pieces of 2022!
But wait, there's more! There are posts on the website going all the way back to November 2019, and some of them had a pretty big year too! Before we wrap things up, let's look at the top five most-read posts from previous years.
Star Trekkin' – a number one hit!
Although it seemed not to light up the board when I first published it in August 2020, this piece about the 1987 pop hit Star Trekkin' has since become one of the most consistent performers here on the website! It was one of the most-read pieces in both 2021 and 2022, and I look forward to seeing if it will make the cut again this year! In the piece I talk about the history of the song and its composition, as well as my own thoughts and personal connection with it. The song is a fun one, and well worth a listen for any Star Trek fan.
Significant line: "The song was – perhaps understandably – rejected by several record labels…"
Star Trek: Discovery Season 2 theory: The abandoned Borg origin story
Another piece that didn't seem to get a lot of attention at first, my theory about Discovery Season 2 gained a lot of traction in 2022. It's hard to get into specifics without spoiling things, but suffice to say that one of the main storylines in Discovery's second season felt like it was setting up an origin story for the Borg – one of the Star Trek franchise's biggest and most iconic villainous factions. In this piece I consider why it felt that way and whether it's possible such a story was attempted and then abandoned, leaving behind clues in its wake.
Significant line: "I know for a fact that I'm not alone in having speculated that Discovery Season 2 was setting up an origin story for the Borg…"
Five things to watch at New Year (instead of fireworks)
This piece kicked off 2022 with a bang – and saw the year end on a high note, too. In 2020, with practically every major New Year event both in person and on television being cancelled, I put together a short list of things to watch instead, as well as time-stamps for getting a specific scene or line on screen at the stroke of midnight. The post did exceptionally well at New Year in both 2020 and 2021, and the same thing happened again in 2022, even with many in-person and televised events returning. This is one of those pieces that gets practically no views all year long, but then sees one massive spike over a relatively short period of time!
Significant line: "I've never been particularly impressed by fireworks. A professional display can be fun to see if you're there in person, but on television much of the impact is lost."
Mass Effect: Legendary Edition – what's the best ending?
I'm not surprised to see the most-read article of 2021 continuing to do well. But I stand by what I said last time: I think a lot of folks are clicking on this piece looking for a "how-to" guide or walkthrough to achieve a specific ending to Mass Effect 3 – and that's not what it's about! The article takes a look at the different endings of the Mass Effect trilogy from a narrative point of view, and I tried to consider which would be the "best" – subjectively speaking, of course.
Significant line: "Like it or hate it (and my god do some people hate it) Mass Effect: Legendary Edition retains the three-and-a-half possible endings present in the Mass Effect 3 Extended Edition DLC from 2012."
Star Trek: Discovery Season 4 – Unknown Species 10-C: The Suspects
Earlier I talked about how 2022 was kind of "front-loaded" in terms of hits… well, here's one of the main culprits! My theories about Unknown Species 10-C – a faction from Discovery's fourth season that was shrouded in mystery – did absolutely huge numbers while the season was running, as many Trekkies were clearly just as interested as I was to learn more! I put together a whopping list of some twenty-six possibilities from past iterations of Star Trek, and if nothing else it was a lot of fun to speculate about how any of them could potentially connect with the story of the season.
Significant line: "Right now, this is one of the biggest mysteries in Star Trek: Discovery's fourth season – and one of the most tantalising storylines that the series has ever teased us with."
Those were the most-read articles and columns of 2022 – and with that, I think that about wraps up our look back at the year. I tend not to go back and re-read things that I've written very often, but once a year it can be fun to take a step back. Taking a look at the pieces folks are most interested in doesn't necessarily mean I'm going to try to write more of that type, but it's certainly interesting to see what people are most likely to click on!
As I said, 2022 was a year of ups and downs. The website broke records and passed milestones, but at the same time I definitely felt the need to take a break and to write less frequently. That doesn't mean I'm not still having fun – but in order to preserve the enjoyment and not feel like I'm under pressure or in danger of getting burned out, I need to recognise my own limitations and take a step back when necessary. Perhaps that's the lesson of 2022 – at least for what I do here on the website!
Stay tuned, because in the days ahead I'll be looking forward to some of the entertainment experiences that lie before us in 2023 – some of which, all being well, will get the full review or write-up treatment here on the website when they're ready! And if you missed it, you can take a look at my annual End-of-Year Awards, in which I dished out a few make-believe trophies and medals to some of my favourite films, games, and television shows of 2022.
I hope this was a bit of fun, or at least a mildly interesting look back!
– Dennis, Tuesday 3rd January 2023
All titles mentioned above are the copyright of their respective studio, owner, corporation, distributor, broadcaster, etc. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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End-of-Year Awards 2022
Spoiler Warning: Minor spoilers may be present for some of these titles.
As we enter the final hours of 2022, it's time to look back at the entertainment experiences that we've enjoyed – as well as a few that we didn't enjoy all that much! I've cobbled together a few categories from the world of television, film, and video games, and today I'm going to hand out some highly-coveted Trekking with Dennis Awards to some of my favourites!
You'll find a couple of titles from the tail end of 2021 on this list; I reckon anything released in December is fair game as those titles often get the short end of the stick when it comes to lists like these. Some outlets put together their "best of" lists way back at the start of December, which is far too early in my opinion! But we're drifting off-topic already!
It's time to hand out my End-of-Year Awards!
There are plenty of titles that, for one reason or another, I didn't get around to this year – so for reasons that I hope are obvious they can't be included. I'm only one person and I don't have every minute of the day to devote to these pursuits, so the exclusion from this list of certain big titles shouldn't be interpreted as any kind of deliberate snub!
And as always, a caveat before we begin: all of this is the subjective opinion of one person. I may give an award to a production you vehemently hate, or talk negatively about something you enjoyed, but at the end of the day this is supposed to be a bit of fun. Feel free to disagree with any or all of my picks – but there's no need to take any of it too seriously!
Best Television Miniseries/Limited Series:
🥈 Runner-Up🥈
Five Days At Memorial had the challenging task of dramatising a real-world event – and a gruelling one at that. I remember the harrowing news reports in 2005 showing the aftermath of Hurricane Katrina, and I could absolutely understand why some folks might feel it's too soon to make a programme like this. But for my money, Five Days At Memorial did a good job at adapting the events at Memorial Hospital as delicately as possible, staying true to what happened while still making the story engrossing and understandable for viewers.
The fact that Five Days At Memorial shows what happened at Memorial Hospital from two very different angles felt a bit strange at first, but by doing so the series lends the events the challenging ambiguity that they continue to have. By refusing to come down on one side or another – to condemn as guilty or exonerate Dr Pou – Five Days At Memorial strikes the right balance. There was some choppy editing in some sequences that meant the miniseries didn't feel as smooth as it could've, but other than that it was a very interesting look at a very difficult moment in the recent past.
🏆 Winner 🏆
Netflix original 1899 is taking the crown in this category this year. The show goes on a wild and unpredictable ride, blending themes of mental health that resonated strongly with me with mystery and psychological horror. The multilingual series is, in my view, best enjoyed without being dubbed, as the different characters and the language barriers between them are key elements in the story at several crucial junctures.
I was first attracted to 1899 because of its setting – both in time, at the end of the 19th Century, and on a boat making a transatlantic voyage. But what I found when I got started was one of the most unique and different television productions that I've seen in a long time. 1899 may not be to everyone's taste, but I found it absolutely riveting all the way through.
Worst Television Series:
After I'd enjoyed what The Book of Boba Fett brought to the table, I felt a pang of hope that Obi-Wan Kenobi might at least be passable. But it wasn't to be, and the series was a horrible slog through the absolute worst kind of tacked-on story that used increasingly desperate nostalgia plays to try to recreate some of the magic that, frankly, Star Wars hasn't had since the '80s.
Say it with me, folks: it's time for Star Wars to move on! The vast sandbox that is the Star Wars galaxy has trillions of inhabitants, millions of star systems, thousands of planets, and hundreds of factions and organisations – and tens of thousands of years of history that could explore any of them. For more than forty years, Star Wars has been laser-focused on the same handful of characters and the same tiny sliver of this wonderful setting, but it's over. If Star Wars is to survive, something's gotta change. Obi-Wan Kenobi proved that.
Best Television Series:
Halo wasn't spectacular, but as the first real attempt to bring the long-running video game franchise into a new medium, it got a lot right. The story it told was a riff on the familiar story that fans will remember from the games, but there were important differences which not only kept the mystery going, but also gave genuine characterisation to the Master Chief.
In terms of cinematography, I liked the way that Halo incorporated some first-person sequences into its action-heavy moments. This could have easily felt like a gimmick, but the way it was done – and crucially, not overdone – made it feel like a throwback to the series' source material while also mixing things up in the television space. Halo used a fairly standard format that would be familiar to anyone who's seen a made-for-streaming television show in the past few years, with a slowly unfolding mystery, multiple storylines, and characters who grow and change over the course of the series. It wasn't anything groundbreaking, and I certainly get the argument that it wasn't as action-packed as some fans might've wanted. But it was, all in all, a decent bit of sci-fi.
The Rings of Power had a lot of work to do to impress me. It had to live up to the legacy of the trilogy of films from a few years ago. It had to show that it could go toe-to-toe with the likes of Game of Thrones, The Witcher, and other big-budget productions in the fantasy space. And, to be blunt, it had to justify its billion-dollar price tag.
Whether The Rings of Power managed to accomplish all of those goals in its first season is still arguably an open question. But it certainly laid the groundwork for what should be a television spectacular, and it was, on balance, probably the best show I've seen this year. When I was at a low ebb in the autumn and didn't have the energy or headspace for watching many new things, The Rings of Power was the one show that I made time for. Sure, there were big battles and other CGI spectaculars, but there were also some genuinely wonderful performances that brought to life some incredible character-focused storytelling. I can't wait for Season 2!
Best Web Series:
How To Cake It
After a hiatus of more than a year, YouTube show How To Cake It made a welcome return this year. This time, there's less of a focus on the kind of attention-grabbing, visually spectacular cakes that look like rocket ships or Princess Elsa or a completely different food, and I think that's actually been a positive thing! Host Yolanda Gampp has branched out, doing much more of a variety when it comes to baking. Some highlights include flavoured cookies, baklava, and even popcorn.
As often happens when a web series takes an extended break, recent episodes of How To Cake It haven't been doing the same numbers as the series used to get. But I hope that, as time goes by, it will pick up some of those wayward viewers – and perhaps bring on board a whole host of new ones, too. This new version of How To Cake It seems to be making more down-to-earth recipes that you or I might feel brave enough to attempt, rather than showing off impressive designs that only a master baker could create. For me at least, that's a great thing, and I hope to see much more from Yolanda and the team in the new year.
Anti-Chef
If How To Cake It shows a master at work, Anti-Chef – as the name suggests – is the complete opposite! The show is a lot of fun, and Jamie, the host, isn't shy about sharing his failures in the kitchen as he works his way through some very complicated recipes. Though he's not a total newbie any more, many of the techniques in the recipes he challenges himself to try are very advanced, and the personal, relatable style makes me feel like I'm right there in the kitchen.
I love a good cooking show, and as much fun as it can be to see an experienced chef at work, it can be even more entertaining to see an inexperienced home cook tackling some of these recipes. Anti-Chef has given me a lot of laughs this year – but also some cooking tips and inspiration, too.
The Worst of Star Trek:
Most of Picard Season 2
I thought long and hard about whether I wanted to call out Picard Season 2, but I think it's earned a place on this list. The first episode of Season 2 was absolutely fantastic, and if the rest of the season had been anywhere close to that level, we'd be talking about Picard as the best show of the year. But unfortunately things took a pretty sharp nose-dive after the second episode of the season, with Picard and his crew wandering aimlessly for much of the season in a present-day setting that didn't feel inspiring or enjoyable in the least.
By the time the action returned to the 25th Century in the second half of the season finale, the damage had been done, and despite Farewell pulling out a decent ending, this disconnected, disjointed, overly-long story has to go down as one of Star Trek's big misses – perhaps even one of the biggest missteps in the franchise's history. There were individual elements in most episodes that I can honestly say that I enjoyed… but Picard Season 2 overall feels like a massive disappointment.
Star Trek's Biggest Surprises:
We ought to talk more about Prodigy here on the website – and I hope we will next year! But for now, the episode Kobayashi came out of nowhere in January to be one of the biggest surprises in the show's first season. The Kobayashi Maru training programme famously tests would-be captains in a "no-win scenario," and you wouldn't think that premise would lead to such a genuinely heartwarming and wholesome episode – but as a longstanding fan, I really appreciated what Kobayashi brought to the table.
Without giving too much away, the Kobayashi Maru scenario plays out on the holodeck, and a cast of fan-favourite Star Trek characters all join in on the action. It's a nostalgic treat – but it doesn't overplay its hand, keeping a tight focus on the new characters introduced in Prodigy.
All Those Who Wander
Strange New Worlds had an incredible first season, showing off a varied, episodic approach in which it wasn't shy about trying out many different genres. All Those Who Wander draws inspiration from the likes of The Thing and Alien to create a tense, claustrophobic sense of horror aboard a crashed starship.
It's hard to say too much more without getting into spoiler territory – and of all the episodes in Season 1, All Those Who Wander has to be the most important to go into un-spoiled! Suffice to say that the episode takes the horror angle right up to the edge of my personal comfort zone, but never crosses that line. It's an intense experience, and one that shows just how incredible Star Trek can be when it throws itself into another genre.
The Best of Star Trek:
Discovery's fourth season plodded along, in places, and definitely teased us with mysterious factions and characters that ultimately turned out to be brand-new. But by the time the season finale rolled around, most of that was already settled. What we got was an incredibly emotional episode that saw Captain Burnham and the crew racing against time to reach an unknown, uncontacted alien race.
There were resolutions to disagreements between characters, several incredibly dramatic moments, and a storyline involving Admiral Vance at Federation HQ that showed off Starfleet and the Federation at their very best. Coming Home is, without a doubt, one of Discovery's very best episodes.
A Quality of Mercy
Captain Pike gets a visit from "the Ghost of Christmas Yet To Come" in A Quality of Mercy – and the episode is incredible. In Discovery Season 2, when it became apparent that Captain Pike knew in advance that he was going to suffer a debilitating accident, an obvious question would be "why didn't he try to prevent it?" And A Quality of Mercy takes that idea and runs with it.
In addition to a very emotional story involving Captain Pike – one that I, as a disabled person, found incredibly relatable – there's also a wonderful callback to an episode of The Original Series, and moments for all of the main characters to get a chance to shine. Ethan Peck puts in a spectacular performance as Spock, and there was even time at the very end of the episode for one final twist as the curtain fell on one of the best seasons of Star Trek ever put to screen.
Best Animated Film:
The Despicable Me franchise is usually good for some fun escapism, and so it proved again with The Rise of Gru. There isn't anything completely groundbreaking here; you know how the titular Minions behave by now. But stepping back in time to a '70s setting allowed for some fun jokes, and the over-the-top villains that Gru encountered were a ton of fun.
There was still heart and emotion in The Rise of Gru thanks to Gru's relationship with the villainous Wild Knuckles, and that did enough to ground what was otherwise a pretty wacky adventure. There were plenty of references and callbacks to other franchises for nerds like us to enjoy, and on the whole, I had a good time with the film. I'm not in a desperate rush to re-watch it, but it was good fun for what it was.
After several years in which Disney has focused on live-action adaptations and sequels, Encanto came along like a breath of fresh air! It's one of the best Disney films of the current era without a doubt, with a deeply engrossing and frequently emotional story that has an uplifting message. And thanks to a wonderful soundtrack by the phenomenally talented Lin-Manuel Miranda, there are some incredible songs too!
A setting inspired by Colombia was also something different for a major Disney production, and the company has done well at diversifying the peoples and places it depicts in its major releases. But that would have been meaningless had Encanto not been such a wonderful, well-told story – and I'm so very pleased that it was.
Best Live-Action Film:
With the caveat that I didn't see that many films this year, The Unbearable Weight of Massive Talent is definitely up there as one of the better ones! I genuinely couldn't believe that this film existed when I first heard of its premise – Nicolas Cage playing a fictionalised version of himself and going on a wacky adventure. But you know what? I'm very glad that it does!
The Unbearable Weight of Massive Talent could have ended up as a bargain-bin B-movie – or worse, it could've tried to take itself far too seriously. But instead it leans into a kind of self-deprecating humour as well as tropes of the action genre, coming across as light-hearted and just plain fun. Nicolas Cage is a good sport for taking part, and The Unbearable Weight of Massive Talent is definitely worth a watch if you haven't seen it already.
Netflix's reimagining of this classic German war film is absolutely brutal. If any film has ever come close to accurately depicting the true horrors of the First World War, this is it. The story follows a young conscript from Germany as he joins the army and is dispatched to the front line, and then jumps ahead to the closing days of the war.
Every version of All Quiet on the Western Front – and there have now been three adaptations of the original novel – have shown just how senseless and meaningless war can be, taking a very individualist, human look at warfare. This version hammers that home, and can be uncomfortable viewing. But it's an incredibly powerful film – one that absolutely deserves to be in contention for some of the top awards.
The "I-didn't-play-this-game-but-you-probably-should" Award:
I wish I could say I was interested in Elden Ring… but I'm just not. The "difficult for the sake of it" style of gameplay that has come to be known as the "Souls-like" genre just isn't my cup of tea, but by all accounts Elden Ring is one of the best examples of this type of game, and one of the best games of the year – if not the generation.
Taking the Dark Souls format into an expansive open-world setting, Elden Ring has won almost universal acclaim from critics and players alike, becoming one of the most talked-about releases of the year. For a single-player title in a gaming landscape increasingly dominated by the online multiplayer scene, I think that's a fantastic thing, and even though Elden Ring isn't for me, I still think it's worth noting it as one of the most important releases of the year.
Best Browser Game:
I wouldn't usually dedicate much time to browser games on a list like this, but since I first played Wordle back in February or March, I don't think I've missed a single day. The format is fun, with a single word each day to guess and only six chances to get it right. Wordle was snapped up by the New York Times and has since spawned dozens or perhaps even hundreds of clones – including variants that have multiple words to guess, and variants based on specific topics or franchises. There's even a Star Trek-themed one!
Wordle blew up to become an internet phenomenon in 2022, and for a while it seemed like you couldn't move for people showing off their Wordle results on social media. It's become part of my daily routine – and my current streak is 77 wins in a row, going all the way back to the middle of October!
The "buggy piece of crap" Award:
Uncharted: Legacy of Thieves Collection (PC version)
The PC port of Uncharted: Legacy of Thieves Collection is the worst I've come across in recent years. I'd thought that the days of amateurish PC ports were finally over, but PlayStation Studios, Naughty Dog, and Iron Galaxy Studios showed me that I was wrong about that. In short, Uncharted is incredibly poorly-optimised for PC, with a piss-poor frame rate and weird visual and texture bugs that were incredibly offputting. The screenshot above shows off one such glitch.
It's such a shame because the Uncharted series has always been a blast. The Indiana Jones-inspired games still feel like something different in the action-adventure space, even with the likes of Tomb Raider being reimagined for a new generation. The stories present here are great – but if I have to spend as much time battling bugs as I do enemies, I'm going to have a bad time. Other PlayStation titles – like Spider-Man and God of War – don't have these issues, so I don't understand how Uncharted: Legacy of Thieves Collection managed to launch on PC in such a bad state.
Best Expansion Pack/DLC:
Mario Kart 8 Deluxe – Booster Course Pass
The Booster Course Pass has given Mario Kart 8 Deluxe a new lease on life – even if it's not as transformative as a new entry in the series would've been. I was disappointed as the year went by and it became clear that there would be no Mario Kart 9, but the Booster Course Pass has definitely convinced me to dust off my Nintendo Switch and pick up Mario Kart 8 Deluxe again.
The "wave" approach to the DLC has been fun, too, keeping the game feeling fresher for longer when compared to dumping all 48 new racetracks at once. Don't get me wrong, the longevity of Mario Kart 8 Deluxe is still an issue, and I now have the additional concern that there will be fewer racetracks left to adapt whenever Mario Kart 9 eventually comes along. But in the short-term, the Booster Course Pass is proving to be great fun.
Game of the Year:
Stray is absolutely adorable: a game in which you get to play as a kitty cat! I was sold on that premise alone, but what I found when I got stuck in was a genuinely enjoyable, well-paced, well-structured indie title. Stray has great graphics, with the movement of the main cat character in particular being incredibly realistic. There's some wonderful art design in both the environments and the robotic non-player characters, too.
Stray is further proof that there's plenty of life in the narrative, linear, single-player space, and that not every game needs to be forced into the open-world mould. But at the same time, it's something very different. Not only is the idea of playing as an animal unique, but the game's slow pace and focus on peaceful interaction with the environment instead of combat and quick-time events all make for a relaxing, yet deeply engrossing experience.
If you'd told me a few months ago that my favourite game of 2022 would be an early access Disney title, I wouldn't have believed it! But I've sunk well over 150 hours into Disney Dreamlight Valley since its launch at the end of August, and I've been having an incredible time. The game basically took all of my criticisms of Animal Crossing: New Horizons and fixed them, then threw in dozens of new features I didn't even know I wanted – and some fun Disney-centric stories with a diverse cast of characters for good measure.
Disney Dreamlight Valley is so much fun and has so much to offer, even in this early access form, that it's hard to know where to begin. There's an interesting main quest, dozens of character-focused missions, the kind of home-building and design gameplay that players loved about titles like The Sims, and all of the fun of living another life in a fantasy land as you'd expect from an Animal Crossing game. There's so much to love about Disney Dreamlight Valley, and I'm happy to crown it my favourite game of the year.
At the first Academy Awards in 1929, Joseph Farnham receives his award from Douglas Fairbanks.
Image Credit: oscars.org
We've dished out awards to some of my favourite entertainment experiences of the year. The countdown is on to 2023 – there are just hours left until the sun will rise on a whole new year! Stay tuned in the days ahead because I plan to take a look at some of the things I'm most looking forward to between now and Christmas. Is that the earliest you've seen someone mention Christmas 2023?
I hope that this was a bit of fun. There were plenty of enjoyable films, television shows, and video games this year – despite the delays that still hang over the entertainment industry. Though I wouldn't say that 2022 is likely to go down in history as one of the best-ever years for entertainment, I think we still got a wide variety of experiences, many of which were enjoyable.
So I suppose all that's left to say is this: Happy New Year! Whatever you plan to do, I hope you have a wonderful time!
See you next year!
All titles listed above are the copyright of their respective owner, company, studio, broadcaster, developer, distributor, publisher, etc. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
Check out reviews or articles featuring some of the films, games, and TV shows mentioned on this list by clicking or tapping the links below:
The Halo TV Series
Star Trek: Discovery 4×13: Coming Home
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Some great holiday sale deals for PC gamers
Important: All prices listed below were correct at time of publication. All of these holiday sales end around New Year; prices will no longer be accurate after that point. All prices listed below in GBP; prices and discounts may vary by region.
In 2019, one of the very first pieces that I put together for the website was a list of some of the best holiday sale deals for PC gamers – and with it being the most wonderful time of year once again, it's time for a new list! All of these games are titles that I personally enjoyed – or that have excellent reviews and write-ups – and that I reckon are good value at their discounted price.
There are two absolutely amazing things about gaming on PC: firstly, it's possible to pick up old and even out-of-print games from years past, and secondly, massive sales like these! There are usually two big sales times on PC – in the summer and around the holidays. Smaller sales come and go at different times of the year, too, so unless a new game is something you simply cannot wait for, it can absolutely be worth saving your pennies until one of the big sales rolls around! A PC may be more expensive to get started with (and take it from someone who built their own PC this year, some components can be very pricey!) but sales like these more than make up for it, in my view.
I built my own PC this year for the first time!
I'll be looking mostly at Steam, Epic Games, and GOG on this occasion, though there are other digital shops on PC that may also be having holiday sales. Not every game is the same price on every digital shop, so it can absolutely be worth shopping around to get the best deals. Remember that these sales don't last long – some deals will be gone before New Year. So be sure to act fast if you see something you're interested in!
Without further ado, let's jump into my list!
Deal #1:
Steam: 90% discount, £3.49/Epic Games: 95% discount, £1.49
For less than the price of a coffee, XCOM 2 feels like an absolute steal! A turn-based strategy game about humanity's attempt to fend off an alien invasion, XCOM 2 has an old-school feel in a gaming landscape dominated by fast-paced shooters and MMOs – and for a certain type of player, that's just what the doctor ordered! I used to say that I prefer real-time strategy games to turn-based ones, but in recent years I've definitely come to appreciate titles like XCOM 2.
Steam: 30% discount, £34.99
For a game that was released earlier this year, and that recently won "game of the year" at The Game Awards, a 30% discount seems pretty good for Elden Ring! A "souls-like" game like this is absolutely not something I'm interested in, but I can appreciate the skill that went into crafting Elden Ring even if I have no plans to play it myself any time soon! Widely considered to be one of the best games of the year and one of the best open-world titles of the last few years, Elden Ring could be your thing – even if it isn't mine!
GOG: 25% discount, £6.29
Hidden Evil isn't the best adventure game you'll ever play, and it's probably fair to say it isn't the best Star Trek game ever created, either. But it's a game I remember with a degree of fondness from the late 1990s, and its story is definitely strong, fun, and very Star Trek-y! Set shortly after the events of Insurrection, players take on the role of a human character who was raised by Vulcans (sound familiar?) as they serve aboard the Enterprise-E and unravel a mystery. Patrick Stewart and Brent Spiner lend their voices to the roles of Picard and Data respectively.
Steam & Epic Games: 67% discount, £18.14
Red Dead Redemption II is a masterpiece, a game that shows just how incredible interactive entertainment can truly be. It is, without a doubt, one of the best games I've ever played, and its story is dark, bleak, and deeply emotional in places. Red Dead Redemption II is set in a wonderfully crafted open world that recreates the look and feel of the United States at the end of the 19th Century. Gameplay takes place from a third-person perspective, but the addition of the "dead-eye" slow-mo targeting mechanic makes its signature quick-draw shooting feel like something different. An incredibly easy game to recommend – especially at a steep discount.
Lego Star Wars: The Skywalker Saga doesn't actually do anything new. If you've played a Lego game on any platform at any time in the past fifteen or so years, you know the formula by now: this is a light-hearted Lego take on a familiar story. Lego Star Wars: The Skywalker Saga polishes that familiar gameplay style, throws in plenty of humour, and makes the graphics look shinier than ever. Right now, this is the definitive Lego Star Wars experience!
The Saboteur
A stealth-action game set in World War II, The Saboteur's unique selling point was its "black-and-white turns to colour" gameplay mechanic. In short, as players moved through the game and liberated different sections of Paris, the game's monochrome aesthetic would give way to full colour. It was a gimmick, perhaps, but underneath that hides a genuinely fun stealth game and a decent recreation of World War II-era Paris.
Civilization VI: Platinum Edition Bundle
Six years on from its release, Civilization VI has racked up a number of expansion packs and additions that take the total price of the game to well over £100. It's a bit much to pay that all at once in my view, so picking up this turn-based strategy game while it's on sale makes a lot of sense. Civilization VI was one of my most-played games of the last few years, with its digital board game style being incredibly engaging! I've had fun learning the ins and outs of the different expansions and rule changes as they've been released, and when no two matches are the same, it really is a blast.
Steam & Epic Games: 85% discount, £5.24
Of all the Star Wars games released in the last few years, Squadrons is probably the most niche. But if you've ever wanted to really feel like you're in the cockpit of a starfighter in a galaxy far, far away… there's literally nothing quite like it. A solid single-player campaign is let down by a multiplayer scene that never really saw huge numbers of players, but there's plenty of replayability in Squadrons nevertheless. This is the game we dreamed we were playing in the '90s when we picked up the likes of TIE Fighter and Rogue Squadron!
Mass Effect: Legendary Edition
I actually felt that Legendary Edition was a bit of a let-down; a remaster that didn't do as much to the Mass Effect trilogy as I'd have liked to see. But for anyone who has never played this amazing trio of games, Legendary Edition is by far the best and easiest route into the Mass Effect universe. Forget my gripes with the way the remaster was handled – the Mass Effect trilogy is one of the best sci-fi stories I've ever experienced. At such a steep discount, there's no excuse not to get started with this single-player adventure. I have a full review of Legendary Edition which you can find by clicking or tapping here.
Deal #10:
The Forza Horizon games are incredibly accessible and fun arcade-style racing games, and both Forza Horizon 4 and Forza Horizon 5 in particular are fantastic! With Forza Horizon 4 on offer with a bigger discount, that's the title I'm picking for this list, and there's so much to see and do in the game's open-world racing festival – and more than 700 cars to race in – I'm pretty sure that you won't get bored any time soon! Also the game's open-world map is loosely based on the UK, which is neat!
Disney Dreamlight Valley comes with the major caveat that the game is still in early access – and that it will be free-to-play at some point in the future. But for anyone who likes Disney or casual life-sim games like Animal Crossing, Disney Dreamlight Valley is a must-play. It's my favourite game of 2022 and I've sunk over 100 hours into it since it launched. Two major updates have already dropped, adding new characters and quests, and there's lots more to come before the game leaves early access. Check out my full early access review by clicking or tapping here!
Control: Ultimate Edition
Steam: 70% discount, £10.49/Epic Games: 50% discount, £17.99
Control is a tense and exciting single-player action game set in a seemingly-abandoned government facility. It's full of twists and turns, and despite its seemingly simplistic "office block" environment, once you get stuck into the story things get pretty wild pretty quickly! Control has one of the best and most mind-bending sequences that I've played through in any game over the past few years as it reaches its climax, but all the while the story of a woman looking for her long-lost brother keeps the story emotionally grounded. I've been meaning to go back and re-play Control… so maybe I will in the new year!
Steam: 66% discount, £5.09
Banished is an incredibly fun town-building game, and one that I've sunk literally hundreds of hours into since its 2014 release. It's deceptively simple, as managing your town, resources, and population isn't as easy as it looks! Balancing all of the different things that the townsfolk need to stay warm, fed, and healthy is a challenge – but a truly entertaining one. It's still amazing to me to know that Banished was created by just one person! I have a more detailed write-up of the game that you can find by clicking or tapping here.
Kena: Bridge of Spirits was my pick for 2021's game of the year. It's visually stunning, with an adorable cast of characters and some fun, surprisingly old-school adventure and 3D platforming gameplay. The titular Kena has a handful of abilities thanks to her magical staff, and each new skill that she learns makes a massive impact on the next section of the game. For a new studio's debut release, Kena: Bridge of Spirits is absolutely fantastic. Check out my full review of the game by clicking or tapping here.
Sonic Frontiers was released less than two months ago, so its 30% discount feels generous considering the game's positive reception by Sonic fans. There's always been a question-mark for me over how well Sonic's signature ability of incredibly fast movement can work in a fully 3D setting. In 2D platformers this was fantastic, but 3D Sonic titles haven't always figured out a way to make it work. By all accounts, Sonic Frontiers gets it right – and is chock-full of callbacks and references to the franchise's past.
Two Point Hospital and Two Point Campus
Steam is offering both of these critically-acclaimed "tycoon" games as a package deal, and honestly it's a pretty good offer! There seemed to be a time when the tycoon genre was disappearing, but games like Two Point Hospital came along and revitalised it! Two Point Hospital feels like a spiritual successor to the much-loved Theme Hospital from the 1990s, and Two Point Campus is in a similar vein but, unsurprisingly, with a university instead of a hospital!
Mafia: Definitive Edition Trilogy
The Mafia trilogy was remade from the ground up over the past couple of years, and the entire trilogy is now available for purchase. Open-world crime games inspired by the likes of the Grand Theft Auto series, Mafia puts a new spin on the concept by focusing heavily on the mob and by stepping back in time. Some great storytelling, fun characters, and enjoyable action gameplay awaits!
With Skyrim having long since worn out its welcome and The Elder Scrolls VI still years away, going back to re-play Oblivion might just scratch that fantasy role-playing itch for some of you! And there's a whole generation of players who've grown up since Oblivion made its debut back in 2006 and who missed out on playing it first time around. Many of the elements that players love about Skyrim are on full display here – though some are a little less refined. But Oblivion has some wonderful stories and side-quests, and is well worth picking up at such a steep discount.
I can never quite manage to properly explain just how utterly revolutionary Shenmue felt when I played it on the Dreamcast in the year 2000. A realistic modern-day setting, an intense murder mystery, fascinating characters… Shenmue was the first game I ever played that felt truly cinematic, as if its story could play out on the big screen. It's a slow-paced game in some ways, with long periods of exploration and dialogue in between fast-paced quick-time events and combat encounters. But it's one of my favourite titles of all-time!
Call of Duty: WWII
I'm not much of a multiplayer gamer, so I'm looking at Call of Duty: WWII for its single-player campaign. A relatively short but well-crafted affair, I think it's worth it when the game goes on sale. Unfortunately the Call of Duty franchise has largely abandoned single-player in favour of multiplayer deathmatches, but WWII's campaign shows that the developers can still create fun and engaging stories. Modern and near-future settings are currently in vogue for first-person shooters, so WWII feels like something a little different for players burnt out on those kinds of titles.
I tried to pick a range of different titles, some of which may be more popular than others. I also tried to branch out a little beyond my usual games and genres to cast a wider net. There are plenty of fantastic games out there that, for one reason or another, just aren't "my thing," but I can still appreciate the work that went into them and that, for folks who like those styles of games, they'll be great fun!
But at the same time, it's nice to pull out some old and new favourites and show them off! When these sales roll around, it's absolutely wonderful to think that someone is going to pick up one of these games and experience a fantastic story for the very first time. PC as a platform and its digital shops like Steam, Epic Games, and especially GOG are doing a great job at keeping older games alive – and that's a wonderfully positive thing.
If money's a bit tight right now, don't panic! There will almost certainly be more big sales in the summer – if not before! I hope I've given you some inspiration for games to pick up, or at least that you had fun geeking out about some of these titles with me!
All titles listed above are the copyright of their respective studio, developer, and/or publisher. Some screenshots and promotional artwork courtesy of IGDB. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
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Eight racetracks I'd add to Mario Kart 8 Deluxe
It's official: I've given up on seeing Mario Kart 9 any time soon. That game most likely won't arrive until the Nintendo Switch's successor console is released, which is a shame if you ask me! 2022 has been the Mario Kart series' thirtieth anniversary, and with Mario Kart 8 Deluxe being just an extended port of a Wii U game released back in 2014, I felt that the time was right for a brand-new entry in the series. But Nintendo disagreed, and instead what we've had this year has been the Booster Course Pass – downloadable content for Mario Kart 8 Deluxe that's slowly adding extra tracks to the game in "waves" of eight at a time.
Let's set Mario Kart 9 and its associated disappointment to one side for now and focus on the Booster Course Pass. For the money, I reckon the Booster Course Pass is pretty good value – or at least it will be when all of the tracks are ready! Only half of the new racetracks have been released at time of writing, so your mileage may vary on how much value for money you think you're getting!
As I said when I reviewed the Booster Course Pass, several of my favourites from past editions of the series have already been added. Racetracks like Kalimari Desert, from the Nintendo 64, and Coconut Mall, from the Wii, have been included in the Booster Course Pass already, and would likely have made a list like this if I'd made it a few months ago! But there are still plenty of racetracks from past iterations of Mario Kart that I'd love to see updated – so that's what we're going to look at today!
I've tried to pick tracks from different entries in the series, some of which I'm more familiar with than others. I haven't invented any brand-new racetracks this time around; these are all tracks that have appeared in one or more Mario Kart titles. For obvious reasons, I haven't picked any tracks that are already part of Mario Kart 8 Deluxe or the Booster Course Pass! And as always, my usual caveats apply: I have no "insider information," and I'm not trying to claim that any of these racetracks will be part of the Booster Course Pass in future. Finally, all of this is just the subjective take of one person! If I don't include your favourite racetrack, or include a track you absolutely hate, that's just the way it goes!
With all of that out of the way, let's begin!
Trekking Cup:
Racetrack #1:
SNES Bowser Castle 2
We'll start by going all the way back to the Super Nintendo! Super Mario Kart may seem rather basic by today's standards, but it's where the series began – and it was one of my most-played games of the mid-90s! There were three Bowser Castle tracks, all of which used the same basic aesthetic, and on this occasion we're going to pick Bowser Castle 2, from the Flower Cup.
Bowser Castle 2 has the infamous "STOP" sign if players take a wrong turn, and that could be something fun as relatively few Mario Kart tracks have anything quite like it; a dead-end path that leads to nothing but lava! The track also splits into two roughly equal paths at one point, and has several hops over the lava. As we've seen with other older racetracks, Bowser Castle 2 could be adapted to incorporate anti-gravity or gliding sections.
Tour Singapore Speedway
One of the surprise hits for me from the first three waves of the Booster Course Pass has been the inclusion of real-world cities. I talked extensively about New York Minute in my review of the Booster Course Pass as I think it's one of the best racetracks in the game, but I've also really enjoyed what Mario Kart has done with Tokyo, Paris, Berlin, Sydney, and London. At time of writing there aren't many more Tour-exclusive tracks that could be added to Mario Kart 8 Deluxe, so I'm picking Singapore Speedway this time.
Singapore would join Tokyo and Sydney to represent another non-European city, and while I'd love to see many more real-world cities represented as I feel it's a fun concept, of the cities that Nintendo has chosen to adapt so far, Singapore feels the most interesting. As the world's only real city-state, Singapore is a unique place – and I'm sure it'll be fun to race through!
N64 Frappe Snowland
I like the music that accompanies this winter-themed track, and I think it would be fun to see it updated. Out of 72 racetracks in the game (at time of writing) only five are winter- or ice-themed (six if you include the winter variant of the Animal Crossing track). So there's definitely room for another snowy, wintertime track in Mario Kart 8 Deluxe.
As happened with Kalimari Desert when it was added to the Booster Course Pass, there's scope to reimagine parts of Frappe Snowland, updating them for the Switch. The jump could be replaced by a glider ramp, an anti-gravity hill could be added, and the final part of the lap, with towering walls of snow, could become narrower or even change shape with each lap.
Wii Moonview Highway
One of the few Wii tracks not to have been ported to another game, Moonview Highway is notorious for its difficulty. Some fans consider Moonview Highway to be one of the hardest tracks in the entire Mario Kart series – so perhaps some adaptations would need to be made to mitigate this before it could join Mario Kart 8 Deluxe!
Moving traffic is always a difficult obstacle in a racetrack, and has proven tricky going all the way back to Toad's Turnpike on the Nintendo 64. But as annoying as they can be, moving vehicles keep players on their toes and ensure that every lap – and indeed every race – feels different. I also really like the theming of Moonview Highway; the night time setting, the rising moon, and the combination of city and forest sections make it a visually interesting and distinct racetrack.
Dennis Cup:
3DS Shy Guy Bazaar
There are plenty of desert levels in the Mario Kart series (and several already in Mario Kart 8 Deluxe) but for me, Shy Guy Bazaar has always been a little different. It picks up a vaguely Arabian-inspired theme, with some of the buildings and the main marketplace using that aesthetic. Most other desert tracks in the Mario Kart series take place across dunes or ruins, so having one set in the marketplace of a living town definitely makes Shy Guy Bazaar unique.
I have very fond memories of Mario Kart 7. When the game was released, I was working in a large office in a big city, and I had several colleagues with whom I'd play the game using the 3DS' download play feature. It was great fun to take part in some very competitive races! Shy Guy Bazaar may not be Mario Kart 7′s best-remembered racetrack – but that's just another reason to bring it back!
Arcade GP Diamond City
Now we're heading into some real uncharted territory! Beginning in 2005, Nintendo created a series of arcade machines based on the Mario Kart series, each of which featured a handful of new and unique racetracks. At time of writing, none of these tracks have made it to a home console, remaining arcade exclusives. That means relatively few players have had the chance to try any of these racetracks – and I can't be the only one who thinks it's high time to change that!
Diamond City has a fun look – at least based on what I've seen of it. A Wario-themed near-future city with some Japanese elements, the racetrack is at least superficially different from others set in big cities. The layout is more than just a simplistic oval, with a tight turn at the beginning, and there are plenty of places where anti-gravity, gliding, or even underwater sections could be included.
N64 Unfinished Town
If you thought we were getting into some weird territory with the arcade version of Mario Kart, you ain't seen nothin' yet! This racetrack was seemingly abandoned during development on Mario Kart 64, never making it into the final game. However, thanks to the tireless work of modders and data-miners, the track's existence was confirmed, and a playable version has even been recreated from files that were uncovered.
The racetrack known simply as "Town" is actually pretty basic from what I can tell, following a fairly straightforward route through a generic town setting. Had work on the track continued, perhaps more theming would have been added! The concept remains interesting, though, and as a slice of Mario Kart history, I think it would be incredible to finally allow this unfinished track to see the light of day in an official release.
GCN Rainbow Road
In true Mario Kart style, we finish with Rainbow Road! The version from Mario Kart: Double Dash has yet to be remade, and I think it would be great to bring it back here. Like other Rainbow Roads it's a difficult racetrack, but one whose verticality could lead to a truly excellent reworking that would really showcase Mario Kart 8′s anti-gravity feature in particular.
There are already four Rainbow Roads in Mario Kart 8 Deluxe – so what's one more? The tracks are all different enough from one another to be distinct, so there's no harm in including this version of Rainbow Road. With only four tracks from Double Dash in Mario Kart 8 Deluxe at time of writing, bringing back another from the GameCube era would be no bad thing, too.
I think we've picked some different racetracks that would make for fun and exciting additions to the Booster Course Pass – although I'd be happier, in many ways, if they'd be part of a brand-new game instead! But in lieu of Mario Kart 9, the Booster Course Pass is definitely filling a gap, and has convinced me to pick up Mario Kart 8 Deluxe all over again. I suppose in that sense it's achieved its aim!
This time, I tried to pick racetracks that haven't gotten as much attention, or that haven't been remastered or made many appearances outside of the games in which they originally appeared. I'd be happy to see any of these tracks return to the Mario Kart series – and if none of them make it into the Booster Course Pass then maybe they'll crop up in a future title!
I've been having a good time with Wave 3 of the Booster Course Pass. The track Merry Mountain in particular is just what I want to see at this time of year, and it's been a blast racing through that Christmassy village! London – the place where I was born! – also features in Wave 3 as one of the more interesting (and longest) city tracks shown off so far, and it's been a blast to replay racetracks like Maple Treeway too.
So I hope this was a bit of fun; some fantasy racetrack additions from a long-time Mario Kart fan. I certainly had a good time going back to replay some of these tracks or just looking at gameplay videos. What better way to celebrate Mario Kart's thirtieth anniversary?
Mario Kart 8 Deluxe and the Booster Course Pass are out now for Nintendo Switch. The Booster Course Pass will add more racetracks in three "waves" across 2023. The Mario Kart series – including all titles discussed above – is the copyright of Nintendo. Some screenshots courtesy of the Super Mario Wiki. This article contains the thoughts and opinions of one person only and is not intended to cause any offence.
Gaming, nintendo booster course pass, booster course pass mario kart 8 deluxe, mario kart, mario kart 30th anniversary, mario kart 64, mario kart 7, mario kart 8, mario kart 8 deluxe, mario kart 8 deluxe booster course pass, mario kart 9, mario kart courses, mario kart racetracks, super mario kart, the booster course pass
Where Cyberpunk 2077 actually failed
Spoiler Warning: Although there are no major plot spoilers for Cyberpunk 2077, minor spoilers may be present for some of the game's missions.
Thanks to a combination of a sale and a rather generous £10 voucher courtesy of the Epic Games Store, I was able to buy Cyberpunk 2077 for just £15 – that's about $17 or $18 for my friends in the United States. For that price, it's actually pretty easy to recommend CD Projekt Red's role-playing shooter, despite the game's reputation and its shockingly bad launch two years ago.
By the time I got around to fully playing through Cyberpunk 2077 earlier this year, most of the game's most egregious bugs, graphical issues, and other glitches had been fixed, at least on PC (which is the platform I played on). So from that point of view, I think I got the best possible Cyberpunk 2077 experience – and certainly a far, far better experience than the poor souls who picked up the game on launch day for PlayStation 4 or Xbox One consoles! Although I did encounter a handful of bugs during my 60-hour playthrough, none were what I'd call game-breaking, and as of late 2022, the PC version of Cyberpunk 2077 is probably comparable with the likes of the launch versions of Skyrim or Fallout 4 in terms of bugs and glitches – a low bar, perhaps, but one the game is finally on the cusp of clearing.
Johnny Silverhand. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,487 |
package hugs.apps.jobshop;
import hugs.*;
import java.util.*;
public class JobshopMoveGenerator implements MoveGenerator {
public static boolean onlyMoveCritical = true;
private JobshopSolution solution;
private Mobilities mobilities;
public JobshopMoveGenerator (Mobilities mobilities, Solution solution, SearchAdjuster searchAdjuster){
this.mobilities = mobilities;
this.solution = (JobshopSolution) solution;
reset();
}
private List moves = new ArrayList();
private int position = 0;
private boolean testCritical (JobshopNode n) {
if ( !onlyMoveCritical ) return true;
return solution.critPath[n.getJob()][n.getOp()] != jobshopConstants.NOTCR;
}
public void reset () {
JobshopVisualization viz = (JobshopVisualization) Hugs.THIS.getVisualization();
moves.clear();
position = 0;
JobshopProblem problem = (JobshopProblem) Hugs.THIS.getProblem();
Node[] nodes = problem.getNodes();
int size = nodes.length;
int maxX = problem.getJobCount() -1;
boolean feasible = true;
if ( onlyMoveCritical ) {
JobshopScore score = (JobshopScore) solution.getScore();
feasible = score.isFeasible();
if ( feasible )
jobshopScheduleOps.markCritical(solution,Jobshop.spanSize);
}
for (int n = size; n-->0;){
JobshopNode jobshopNode = (JobshopNode) nodes[n];
if ( mobilities.getMobility(n) == Mobilities.HIGH &&
(!feasible || testCritical(jobshopNode)) ) {
int index = solution.getPositionOnMachine(n);
int machine = jobshopNode.getMachine();
// go right
if (index < maxX ) {
Node node2 = solution.getNodeOnMachine(machine,index+1);
// System.out.println("right " + jobshopNode + "," + node2);
int n2 = node2.getId();
if ( mobilities.getMobility(n2) != Mobilities.LOW &&
(!feasible || testCritical((JobshopNode)node2)) ) {
JobshopInsertMove move = new JobshopInsertMove(solution,jobshopNode.getJob(), jobshopNode.getOp(),machine,index+1);
moves.add(move);
}
}
// go left
if (index > 0 ) {
Node node2 = solution.getNodeOnMachine(machine,index-1);
// System.out.println("left " + machine + "," + (index-1) + "--" + jobshopNode + "," + node2);
int n2 = node2.getId();
if ( mobilities.getMobility(n2) != Mobilities.LOW &&
(!feasible || testCritical((JobshopNode)node2)) ) {
JobshopInsertMove move = new JobshopInsertMove(solution,jobshopNode.getJob(), jobshopNode.getOp(),machine,index-1);
moves.add(move);
}
}
}
}
if ( onlyMoveCritical && feasible)
jobshopScheduleOps.markCritical(solution,1);
}
public Move nextMove () {
if ( position < moves.size() )
return (Move) moves.get(position++);
return null;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,807 |
\section{Introduction}
In-band Full Duplex (FD) massive Multiple-Input Multiple-Output (MIMO) communication is a promising technology for the increasingly demanding data rate requirements of future wireless networks due to its inherent capability to enable simultaneous UpLink (UL) and DownLink (DL) communications within the entire frequency band \cite{Samsung,B:Full-Duplex,alexandropoulos2017joint}. In addition to concurrent UL/DL data transmission in reciprocal communications, the FD technology has been recently considered for simultaneous DL data transmission and UL Channel State Information (CSI) estimation, where FD Base Stations (BSs) transmit data symbols in the DL via CSI-dependent multi-user BeamForming (BF), while receiving UL training symbols from the user terminals \cite{islam2020simultaneous,mirza2018performance,Islam_2020_Sim_Multi}. The principal bottleneck of any FD system is the in-band Self-Interference (SI) signal at the Receiver (RX) side, resulting from the simultaneous transmission and reception. Recently in \cite{xiao2017full_all,Vishwanath_2020,alexandropoulos2020full}, FD MIMO systems operating at millimeter Wave (mmWave) frequencies were introduced, where SI suppression was achieved through a combination of propagation domain isolation, analog domain suppression, and digital SI cancellation techniques.
Wireless communications at mmWave frequencies are mainly realized via highly directional BF, which is enabled by massive MIMO transceivers \cite{bjornson2016massive} that are capable of analog or hybrid Analog and Digital (A/D) beamforming \cite{vlachos2019}. To alleviate the hardware cost in those transceiver architectures, the large-scale antenna arrays are connected to small numbers of Radio Frequency (RF) chains via analog preprocessing networks comprised of phase shifters \cite{venkateswaran2010analog}. However, the selection of the adequate analog beams from the predefined codebooks and the design of the digital beamformers require CSI knowledge, which is hard to acquire with realistically affordable latency, especially under mobility conditions (see, e.g.,\cite{ULBA2021} and references therein). This challenge will be naturally more pronounced in the envisioned FD massive MIMO systems operating at mmWave frequencies, where multiple UL and DL channels need to be estimated. In practice, the analog BF in mmWave massive MIMO systems is designed via beam switching between the communicating nodes in order to find a pair of beams from their available beam codebooks meeting a link performance indicator threshold \cite{BMtutorial,aykin2020efficient}. However, such time-consuming beam training procedures incur significant configuration overhead deprived of data transmission. Hence, beam misalignment may yield poor performance under mobility scenarios \cite{palacios2017tracking}. Alternatively, exploiting UL/DL reciprocity or position information, the DL BF can be performed in the direction of the UL dominant Direction-of-Arrival (DoA), thus, reducing the beam sweeping overhead \cite{bjornson2016massive,alexandropoulos2017position}.
\begin{figure*}[!tpb]
\begin{center}
\includegraphics[width=0.97\linewidth]{mainSystemUpdated.eps}
\caption{The considered FD massive MIMO communication system operating at mmWave frequencies: an FD massive MIMO Base Station (BS) capable of analog BF communicates with a mobile single-antenna FD User (UE), where the latter node transmits training signals in the UL for DoA estimation.}
\label{fig: FD_HBF_Sys}
\end{center}
\vspace{-4mm}
\vspace{-1mm}
\end{figure*}
In this paper, we present a DoA-assisted beam management framework for FD mmWave massive MIMO systems, where the BS is equipped with a large antenna array realizing DL analog BF and few digitally controlled receive antenna elements used for UL DoA estimation. Capitalizing on the recently presented FD hardware architecture for hybrid A/D BF in \cite{alexandropoulos2020full}, we propose a Simultaneous DoA estimation and Data Transmission (SDDT) scheme for boosting beam management in FD mmWave massive MIMO communications. Enabled by FD and leveraging channel reciprocity, we simultaneously estimate the UL dominant DoA and transmit analog beamformed data in the DL direction. We present a joint design of the DoA-assisted analog BF as well as the A/D SI cancellation units, targeting the maximization of the achievable DL rate. Our extensive simulation results considering a mmWave channel model showcase the FD-enabled gains of DoA-assisted beam management under various user mobility conditions. In particular, the proposed FD-based SDDT scheme achieves approximately $1.2\times$ the DL rate of conventional Half Duplex (HD) mmWave massive MIMO systems.
\section{System and Signal Models}
We consider an FD mmWave massive MIMO Base Station (BS) node $b$ equipped with $N_b$ TX and $M_b$ RX antenna elements communicating with a mobile single-antenna FD User Equipment (UE) node $u$. In particular, in the TX of the BS node $b$, a single RF chain is connected via phase shifters with a large antenna array of $N_b$ elements, whereas each of the few $M_b$ RX antennas is connected to a dedicated RF chain. In this work, a small number for $M_b$ is sufficient for UL DoA estimation; extension for large $M_b$ and analog combining is left for future work. Using the values of the $N_b$ phase shifters, we can formulate the TX analog beamforming vector $\v_b \in \mathbb{C}^{N_b\times 1}$, whose elements are assumed to have constant magnitude, i$.$e$.$, $|[\v_b]_{n}|^2=1/N_b$ $\forall n=1,2,\ldots,N_b$. Besides, we assume that the angles of the analog phase shifters are quantized and have a finite set of possible values. Therefore,
$\v_b\in\mathbb{F}_{\rm TX}$, where $\mathbb{F}_{\rm TX}$ represents the predefined beam codebook including ${\rm card}(\mathbb{F}_{\rm TX})$ distinct vectors (or analog beams) \cite{gonzalez2018channel,ULBA2021}. We assume that, for every channel use, the BS node $b$ transmits the complex-valued information data symbol $s_b$ (chosen from a discrete modulation set) after analog BF with $\v_b$. Similarly, the single-antenna FD UE node $u$ sends the training symbol ${s}_u$ through the UL channel. The signal transmissions at both node $b$ and node $u$ are power limited according to $\mathbb{E}\{\|\mathbf{v}_b{s}_b\|^2\}\leq {\rm P}_b$ and $\mathbb{E}\{|{s}_u|^2\}\leq {\rm P}_u$, respectively.
\subsection{Channel Model}
All the considered mmWave UL/DL channels consist of multiple propagation paths. In the spatial domain, each propagation path can be characterized by its Direction-of-Arrival (DoA)/ Direction-of-Departure (DoD) and the corresponding power as well as phase components \cite{akdeniz2014millimeter}. For a certain coherence block, the UL channel $\mathbf{h}_{b,u} \in \mathbb{C}^{M_b \times 1}$ including a Line-of-Sight (LoS) component and $L_p\!-\!1$ non-Line-of-Sight (nLoS) paths is mathematically expressed as
\begin{equation}\label{eq: UL_chan}
\begin{split}
\mathbf{h}_{b,u} \triangleq \beta_{\rm LoS} \a_{M_b}(\theta_{\rm LoS}) + \sum\limits_{\ell = 1}^{L_p-1} \beta_{{\rm nLoS},\ell} \a_{M_b}(\theta_{{\rm nLoS},\ell}),
\end{split}
\end{equation}
where $\beta_{\rm LoS}\in \mathbb{C}$ and $\theta_{\rm LoS}\in [0\,\, 2\pi]$ represent the complex gain and the DoA of the LoS path, respectively. Here, $\beta_{{\rm nLoS},\ell}\in \mathbb{C}$ and $\theta_{{\rm nLoS},\ell}\in[0\,\, 2\pi]$~$\forall \ell = \{1,2,\ldots, L_p-1\}$ are the complex gains and the DoAs of the nLoS path, respectively. Considering a Uniform Linear Array (ULA), the response vector $\a_{M_b}(\theta)$ for $M_b$ antenna elements and any DoA $\theta$ is formulated as \cite{gonzalez2018channel}
\begin{equation}
\begin{split}
\a_{M_b}(\theta)\! \triangleq \! \frac{1}{\sqrt{M_b}} \big[1,e^{j\frac{2\pi}{\lambda}d \sin(\theta)},\ldots,e^{j\frac{2\pi}{\lambda}(M_b-1)d \sin(\theta)}]^{\rm T},
\end{split}
\end{equation}
where $\lambda$ is the propagation signal wavelength and $d$ denotes the distance between adjacent antenna elements.
For the considered FD system, the UL and DL channels are reciprocal resulting in similar complex gains and DoAs/DoDs \cite{gonzalez2018channel,bjornson2016massive}. Therefore, similar to \eqref{eq: UL_chan}, the DL channel $\mathbf{h}_{u,b}^{\rm T}\in \mathbb{C}^{1 \times N_b}$ can be expressed as follows:
\begin{equation}
\begin{split}
\mathbf{h}_{u,b}^{\rm T} \triangleq \beta_{\rm LoS} \a_{N_b}^{\rm H}(\theta_{\rm LoS}) + \sum\limits_{\ell = 1}^{L_p-1} \beta_{{\rm nLoS},\ell} \a_{N_b}^{\rm H}(\theta_{{\rm nLoS},\ell}).
\end{split}
\end{equation}
In this paper, our goal is to estimate the LoS DoA $\theta_{\rm LOS}$ using the UL training symbols and find the DoA-assisted analog beamformer $\v_b$ that maximizes the DL rate. However, due to the FD operation at both nodes, the simultaneous DL data and UL training transmission induce SI signal in the RXs of the BS and UE. Following \cite{alexandropoulos2020full,satyanarayana2018hybrid}, we consider the mmWave clustered model for the SI channels denoted by $\mathbf{H}_{b,b} \in \mathbb{C}^{M_b\times N_b}$ for the BS node $b$ and ${h}_{u,u}\in\mathbb{C}$ for the UE node $u$, where $\kappa$ represent the Rician factor.
\vspace{-2mm}
\subsection{Received Signal Model}
At the RX of the BS node $b$, the training symbols transmitted from the UE node $u$ are received along with the SI signal induced by the simultaneous data and training signal transmissions. Due to limited propagation attenuation, the strong SI signal is capable of driving the RX RF chains into saturation. Therefore, as shown in Fig.~\ref{fig: FD_HBF_Sys}, an $N$-tap analog SI canceller is utilized to suppress the SI at the inputs of the RX RF chains, which is based on the TX RF chain output. Exploiting the low-complexity cancellation in \cite{alexandropoulos2020full}, we employ the canceller taps at the TX RF chain output at the BS node $b$ resulting in an analog SI canceller where the number of taps does not scale with the number of antenna elements. To suppress the residual SI signal after analog cancellation, a digital SI canceller is utilized at the BS baseband. Denoting $\mathbf{c}_{b}, \d_{b} \in\mathbb{C}^{M_b\times 1}$ as the analog and digital SI cancellers, respectively, the baseband received signal at the BS node $b$, $\mathbf{y}_{b}\in\mathbb{C}^{M_b\times 1}$, is given by
\begin{equation}\label{eq: sig_yb}
\begin{split}
\mathbf{y}_b &\triangleq \mathbf{h}_{b,u} s_u + (\H_{b,b}\v_b + \c_b + \d_b) s_b + \mathbf{n}_b,
\end{split}
\end{equation}
where $\mathbf{n}_{b}\in \mathbb{C}^{M_b\times 1}$ is the zero-mean Additive White Gaussian Noise (AWGN) with variance $\sigma^2_{b}\mathbf{I}_{M_b}$.
Similarly, the DL signal $y_u\in\mathbb{C}$ received at the UE node $u$ after analog and digital SI cancellation can be expressed as
\begin{equation}
\begin{split}
y_u &\triangleq \mathbf{h}_{u,b}^{\rm T}\v_b s_b + ({h}_{u,u} + c_u + d_u) s_u + n_u,
\end{split}
\end{equation}
where $n_u\in \mathbb{C}$ represents the AWGN with variance $\sigma^2_{u}$.
As previously mentioned, for proper FD-based reception, the RXs' RF chains need to be unsaturated from any residual SI stemming out analog SI cancellation at both nodes $b$ and $u$ \cite{alexandropoulos2017joint, islam2019unified}. Denoting the residual SI power thresholds as $\lambda_b$ and $\lambda_u$ at node $b$ and node $u$, respectively, the residual SI power constraints ${\rm P}_b|[({\H}_{b,b}\v_b+\c_{b})]_{(j,:)}|^2\!\leq \!\lambda_b \,\forall j=1,2,\ldots,M_b$ and ${\rm P}_{u}|({h}_{u,u} + c_u)|^2\leq \lambda_u$ are necessary to be satisfied for successful reception after analog SI suppression.
\section{DoA Estimation and DL Data Transmission}
In this section, we introduce the proposed DoA-assisted analog beam management protocol along with the DoA tracking scheme for the considered UL/DL mmWave channel with the proposed FD massive MIMO system.
\vspace{-1mm}
\subsection{UL/DL Channel Evolution Properties}
We assume wireless communications in Time Division Duplexing (TDD) manner, where the considered channels remain constant for all the channel uses in a time slot, and the channel properties (i.e., DoAs/DoDs, complex path gains) of the successive time slots are temporally correlated. Each time slot of $T_s$ time units contains $L$ symbols (i.e., $L$ channel uses). For any consecutive $(i\!-1\!)$ and $i$ time slots, the evolution of LoS DoA component is expressed similar to \cite{va2016beam} as
\begin{equation}
\begin{split}
\theta_{\rm LoS}[i] \triangleq \theta_{\rm LoS}[i-1] + \Delta\theta,
\end{split}
\end{equation}
where $\Delta\theta$ depends on the velocity of the UE node $u$ and the time slot duration $T_s$. We also assume that the UE node is moving with the constant velocity $v$, hence, $\Delta\theta \triangleq \text{arctan}\left(\frac{vT_s}{d_{\rm BS}}\right)$ with $d_{\rm BS}$ being the distance between the UE and the BS nodes.
The evolution model for the LoS complex path gain $\beta_{\rm LOS}$ is given by the first-order Gauss-Markov model as \cite{va2016beam}
\begin{equation}
\begin{split}
\beta_{\rm LoS}[i] \triangleq \rho\beta_{\rm LoS}[i-1] + \epsilon[i-1],
\end{split}
\end{equation}
where $\rho$ is the correlation coefficient, and $\epsilon[i-1]$ is the zero-mean
complex Gaussian noise distributed as $\mathcal{CN}(0,1-\rho^2)$. The DoAs and complex path gains of the nLoS components are assumed to change randomly between consecutive time slots. In this paper, we propose to track only the LoS DoA component for each time slot, and then use it analog beam selection. The estimation of all complex path gains and their correlation coefficients is left for future investigation.
\begin{figure}
\centering
\includegraphics[width=0.9\linewidth]{protocol.eps}
\caption{(a) Proposed FD SDDT Scheme, (b) Conventional HD DoA with update after threshold, and (c) Conventional HD DoA estimation in each slot.}
\label{fig: trans_protocol}
\end{figure}
\subsection{Proposed FD-Based SDDT Protocol}
The proposed protocol for simultaneous DoA estimation and data transmission is illustrated in Fig.~\ref{fig: trans_protocol}(a), where the DL channel is dedicated for data transmission, while the UL is accessed to transmit training symbols. The procedures of DoA-based tracking and transmission are described as follows:
\begin{enumerate}
\item DL Data transmission at any $i$th time slot leverages the DOA estimation for the previous $(i\!-\!1)$th time slot, which is realized via simultaneous UL transmission of $L$ orthogonal training symbols sent from the UE node $u$.
\item Capitalizing on the UL/DL reciprocity, any LoS component estimation $\widehat{\theta}_{\rm LoS}[i-1]$ is used during the next $i$th time slot for the DL data transmission precoding.
\item The DL analog beamformer $\v_b[i]\in\mathbb{F}_{\rm TX}$ at each $i$th time slot is chosen according to $\widehat{\theta}_{\rm LoS}[i-1]$ subject to the satisfaction of the residual SI power constraints.
\end{enumerate}
In Fig.~\ref{fig: trans_protocol}(b), a conventional HD DoA-assisted analog beamforming scheme is illustrated, where, contrary to the FD case, a fraction of the available symbols in a time slot is dedicated for DoA estimation. Once the DoA of a time slot is estimated, its analog beamforming and that of the succeeding ones utilizes the same DoA estimation, unless the received Signal-to-Noise Ratio (SNR) falls below a certain threshold; in this case, a DoA estimation update occurs. An HD data transmission protocol with DoA estimation at each time slot is shown in Fig.~\ref{fig: trans_protocol}(c).
\subsection{UL DoA Estimation}
As previously discussed, the UL training symbols at any $(i\!-\!1)$th time slot are used for this slot's LoS DoA estimation, which is leveraged for analog BF at the $i$th time slot. For this estimation, we deploy the MUltiple SIgnal Classification (MUSIC) algorithm; other DoA estimation techniques can be used as well \cite{krim1996two}. Starting from \eqref{eq: sig_yb}, the received $L$ training symbols at any $(i\!-\!1)$th time slot can be grouped in $\mathbf{Y}_{b}[i\!-\!1]\in \mathbb{C}^{M_b\times L}$. For the MUSIC DoA estimation, the received signal covariance matrix $\mathbf{R}_{b}\in\mathbb{C}^{M_b\times M_b}$ can be estimated as
\begin{equation}\label{eq: sampl_cov}
\begin{split}
{\mathbf{R}}_b\! \triangleq\! \mathbb{E}\{\mathbf{Y}_b[i\!-\!1]\mathbf{Y}_b[i\!-\!1]^{\rm H}\}\! ,\, \widehat{\mathbf{R}}_b\! \triangleq \!\frac{1}{L} \mathbf{Y}_b[i\!-\!1]\mathbf{Y}_b^{\rm H}[i\!-\!1].
\end{split}
\end{equation}
By taking the eigenvalue decomposition of the estimated sample covariance matrix $\widehat{\mathbf{R}}_b$, it is deduced that:
\begin{equation}\label{eq: cov_eig}
\begin{split}
\widehat{\mathbf{R}}_b \triangleq \mathbf{U} {\rm diag}\{\eta_1,\eta_2,\ldots,\eta_{M_b}\}\mathbf{U}^{\rm H},
\end{split}
\end{equation}
where $\eta_1\geq\eta_2\geq\ldots\geq\eta_{M_b}$ are the eigenvalues of $\widehat{\mathbf{R}}_b$ and $\mathbf{U}\in\mathbb{C}^{M_b\times M_b}$ contains their corresponding eigenvectors. Since we are interested in estimating the DoA of the LoS component, the matrix $\mathbf{U}$ can be partitioned as $\mathbf{U}=[\u_s|\mathbf{U}_n]$, where the columns in $\mathbf{U}_{n}\in\mathbb{C}^{M_b\times M_b-1}$ are the eigenvectors spanning the noise subspace and $\u_s$ is the signal space eigenvector. We next project the search vector $\a_{M_b}(\theta)$~$\forall \theta\in[0\,\,2\pi]$ onto the noise subspace $\mathbf{U}_{n}$ and calculate the spectral peak as
\begin{equation}\label{eq: spectral_peak}
\begin{split}
S(\theta) \triangleq \frac{1}{\a_{M_b}^{\rm H}(\theta)\mathbf{U}_{n}\mathbf{U}_{n}^{\rm H}\a_{M_b}(\theta)}.
\end{split}
\end{equation}
Finally, the position $\theta$ of the spectral peak is the estimated LoS DoA $\widehat{\theta}_{\rm LoS}[i\!-\!1]$ corresponding to this $(i\!-\!1)$th time slot.
\subsection{DoA-Assisted Analog Beamforming and DL Rate}
Capitalizing on the UL/DL reciprocity and the estimated LoS DoA component, we propose to approximate the DL channel at each $i$th time slot as follows:
\begin{equation}\label{eq: DL_est_chan}
\begin{split}
\widehat{\mathbf{h}}_{u,b}^{\rm T}[i] \triangleq \a_{N_b}^{\rm H}(\widehat{\theta}_{\rm LoS}[i-1]).
\end{split}
\end{equation}
This approximation is further used during this $i$th time slot to find the best analog beamformer $\v_{b}[i]$ at the BS node $b$, via searching in the available beam codebook $\mathbb{F}_{\rm TX}$.
Therefore, the instantaneous achievable DL rate per channel use for the proposed FD-based SDDT scheme at this time slot is given by
\begin{equation}
\begin{split}\label{eq:rate}
\mathcal{R}_{\rm DL} [i] = \log_2\left(1+ \frac{{\rm P}_{b}|\widehat{\mathbf{h}}_{u,b}^{\rm T}[i]\v_{b}[i]|^2}{\sigma_u^2 + \sigma_{r,u}^2[i]} \right),
\end{split}
\end{equation}
where $\sigma_{r,u}^2[i] \triangleq {\rm P}_{u}|({h}_{u,u}[i] + c_u[i] + d_u[i])|^2$ is the residual signal power after both A/D SI cancellation at the UE node $u$.
\section{Proposed SDDT Optimization Framework}
In this section, we focus on the joint design of the analog beamformer $\v_b$, the analog SI cancellers $\c_b$ and $c_u$, as well as the digital canceller $\d_b$ and $d_u$ at the BS node $b$ and the UE node $u$, which maximize the estimated achievable DL rate in \eqref{eq:rate} at each $i$th time slot. Based on the availability of the DL channel estimation $\widehat{\mathbf{h}}_{u,b}[i]$, as well as the SI estimations $\widehat{\H}_{b,b}[i]$ and $\widehat{h}_{u,u}[i]$, we consider the optimization problem:
\begin{align}\label{eq: optimization_eq}
\nonumber\underset{\substack{\v_b[i],\c_b[i], \d_{b}[i]\\ c_u[i], d_u[i]}}{\text{max}} &\log_2\left(1+ \frac{{\rm P}_{b}|\widehat{\mathbf{h}}_{u,b}^{\rm T}[i]\v_{b}[i]|^2}{\sigma_u^2 + \sigma_{r,u}^2[i]} \right)\\
\text{\text{s}.\text{t}.}\quad
&\!\!\!{\rm P}_b|[(\widehat{\H}_{b,b}[i]\v_b[i]\!+\!\c_{b}[i])]_{(j,:)}|^2\!\leq \!\lambda_b \!\,\forall j\!=\!1,\!\ldots,\!M_b,\nonumber\\
&\!\!\!{\rm P}_{u}|(\widehat{h}_{u,u}[i] + c_u[i])|^2\leq \lambda_u, \nonumber\\
&\!\!\!\mathbb{E}\{\|\v_b[i] s_{b}[i]\|^2\}\leq {\rm P}_b,\,\,\text{and}\,\,\,
\mathbb{E}\{|s_{u}[i]|^2\}\leq {\rm P}_u,\nonumber\\
&\!\!\!\v_b[i] \in\mathbb{F}_{\rm TX}.
\end{align}
The first and second constraints impose the RX RF chain saturation thresholds $\lambda_{b}$ and $\lambda_u$ after analog cancellation at nodes $b$ and $u$, respectively. These saturation thresholds ensure successful reception of the training symbols and decoding of BS's data symbols. The next two constraints in \eqref{eq: optimization_eq} refer to the nodes' average transmit powers. The final constraint enforces the predefined analog codebook for the BS beamformer.
\begin{algorithm}[!t]
\caption{Proposed FD massive MIMO SDDT Design}
\label{alg:the_alg}
\begin{algorithmic}[1]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\REQUIRE $\widehat{\H}_{b,b}[i]$, $\widehat{h}_{u,u}[i]$, ${\rm P}_b$, ${\rm P}_u$, $\widehat{\theta}_{\rm LoS}[i-1]$, and $M_b$.
\ENSURE $\v_b[i],\c_b[i], c_u[i], \d_{b}[i]$, and $d_u[i]$.
\STATE Obtain the DL channel estimate $\widehat{\mathbf{h}}_{u,b}[i]$ using $\widehat{\theta}_{\rm LoS}[i-1]$ as described in \eqref{eq: DL_est_chan}.
\STATE Obtain the analog beamformer $\v_b[i] = \underset{\v \in\mathbb{F}_{\rm TX}}{\text{arg max}} \frac{|\widehat{\mathbf{h}}_{u,b}^{\rm T}[i]\v|^2}{\|\widehat{\H}_{b,b}[i]\v\|^2}$ using exhaustive search.
\FOR{$n= 1,2,\ldots,M_b-1$}
\STATE Set analog SI canceller $\c_b[i] = \begin{bmatrix}-[\widehat{\H}_{b,b}[i]\v_b[i]]_{1:n}\\
\mathbf{0}_{(M_b-n:M_b)}
\end{bmatrix}$.
\STATE Set $c_u[i] = - \widehat{h}_{u,u}[i]$.
\IF {${\rm P}_b|[(\widehat{\H}_{b,b}[i]\v_b[i]\!+\!\c_{b}[i])]_{(j,:)}|^2\leq \lambda_b \, \forall j=1,\ldots,M_b$, and ${\rm P}_{u}|(\widehat{h}_{u,u}[i] + c_u[i])|^2\leq \lambda_u$}
\STATE Output $\v_b[i]$, $\c_b[i]$, $c_u[i]$, $\d_{b}[i]=-(\widehat{\H}_{b,b}[i]\v_b[i] + \c_b[i])$, $d_u[i]=-(\widehat{h}_{u,u}[i]+ c_u[i])$, and terminate the iterations.
\ENDIF
\ENDFOR
\STATE Set $\c_b[i] =-\widehat{\H}_{b,b}[i]\v_b[i]$ and $c_u[i] = - \widehat{h}_{u,u}[i]$.
\IF {${\rm P}_b|[(\widehat{\H}_{b,b}[i]\v_b[i]\!+\!\c_{b}[i])]_{(j,:)}|^2\leq \lambda_b \,\forall j=1,2,\ldots,M_b$, and ${\rm P}_{u}|(\widehat{h}_{u,u}[i] + c_u[i])|^2\leq \lambda_u$}
\STATE Output $\v_b[i]$, $\c_b[i]$, $c_u[i]$, $\d_{b}[i]=-(\widehat{\H}_{b,b}[i]\v_b[i] + \c_b[i])$, $d_u[i]=-(\widehat{h}_{u,u}[i]+ c_u[i])$, and stop the algorithm.
\ELSE
\STATE Output that the $\c_b[i]$ realizations or $c_u[i]$ do not meet the RX RF saturation constraints.
\ENDIF
\end{algorithmic}
\end{algorithm}
The optimization problem in \eqref{eq: optimization_eq} is a non-convex problem with coupling variables, hence, quite difficult to tackle. In this work, we solve it suboptimally using alternating optimization, leaving other possibilities for future work. First, we find the BS analog beamformer $\v_b[i]$ via the following problem:
\begin{equation}\label{eq: exhaust_search}
\begin{split}
\v_b[i] = \underset{\v \in\mathbb{F}_{\rm TX}}{\text{arg max}} \frac{|\widehat{\mathbf{h}}_{u,b}^{\rm T}[i]\v|^2}{\|\widehat{\H}_{b,b}[i]\v\|^2}.
\end{split}
\end{equation}
The exhaustive search for this problem can be easily implemented by a simple look-up table given the estimated SI channel $\widehat{\H}_{b,b}[i]$ and the estimated DL channel $\widehat{\mathbf{h}}_{u,b}[i]$. Following the analog SI canceller structure in \cite{alexandropoulos2020full} and using $\v_b[i]$, we next seek the $N$-tap analog canceller $\c_b[i]$ with $1\leq N \leq M_b$ that satisfies the first threshold constraint. The single-tap canceller at node $u$ is obtained as $c_u[i] = - \widehat{h}_{u,u}[i]$. To maximize the signal-to-interference-plus-noise ratio, the digital cancellers $\d_b$ and $d_u$ are set as the respective complementary residual SI channels after analog SI cancellation. Our solution for the optimization problem \eqref{eq: optimization_eq} is summarized in Algorithm \ref{alg:the_alg}.
\begin{figure}[!tpb]
\begin{center}
\includegraphics[width=\linewidth]{Error_DoA.eps}
\caption{Error of LoS DoA estimation w.r.t the time slot index for the $64\times 2$ FD massive MIMO node $b$ communicating with the mobile single-antenna FD UE $u$ transmitting UL training symbols with $10$dBm transmit power.}
\label{fig: DoA_error}
\end{center}
\vspace{-2mm}
\end{figure}
\section{Numerical Results}
\vspace{-1mm}
In this section, we present simulation results for the performance of the proposed SDDT scheme for FD mmWave massive systems in comparison with HD counterparts.
\subsection{Simulation Parameters}\label{ssec: Sim_param}
We perform an extensive waveform simulation following the FD massive MIMO architecture illustrated in Fig.~\ref{fig: FD_HBF_Sys} when operating at mmWave frequencies, where a $64\times 2$ FD massive MIMO node $b$ is communicating with a single-antenna FD UE node $u$. We have assumed that the single TX RF chain at the BS node $b$ is connected to a ULA consisting of $N_b = 64$ antenna elements. In contrast, on the RX side, $M_b = 2$ RX antennas are connected to their dedicated RX RF chains. The UE node $u$ employs a non-ideal single-tap SI canceller, where the FD massive MIMO BS node $b$ deploys an $N=2$ taps analog SI canceller \cite{alexandropoulos2020full}.
The multi-path UL and DL channels are simulated as mmWave channels at $28$ GHz each with one LoS and $4$ nLoS channel paths. Considering the distance $d_{\rm BS} = 100m$ of the BS node $b$ from the UE, the pathloss of the both UL and DL channels is assumed to be $100$dB with a $25$ dB Rician factor between the LoS and nLoS paths \cite{akdeniz2014millimeter}. In addition, the SI channels are modeled as Rician fading channels with a $\kappa$-factor of $35$dB and pathloss $40$dB \cite{alexandropoulos2017joint}. The RX noise floors at all nodes were assumed to be $-100$dBm. To this end, the RXs have an effective dynamic range of $60$dB provided by $14$-bit Analog-to-Digital Converters (ADC) for a Peak-to-Average-Power-Ratio (PAPR) of $10$ dB. Therefore, the residual SI power after analog SI cancellation at the input of each RX RF chain has to be below $-40$dBm to avoid signal saturation.
For the considered FD massive MIMO architecture, we have assumed that the UE $u$ is moving at a constant velocity of $120$km/h for a duration of $100$ time slots, where each time slot is considered to be $T_s = 10$msec with $L=400$ symbols. For the BS analog beamformer, we have used a $6$-bit beam codebook based on the Discrete Fourier Transform (DFT) matrix.
We have used $1000$ independent Monte Carlo simulation runs to calculate the performance of all considered DoA estimation and data transmission designs.
\begin{figure}[!tpb]
\begin{center}
\includegraphics[width=\linewidth]{MSE_DoA.eps}
\caption{MSE of the DoA estimation with respect to UL transmit power in dBm for the $64\times 2$ FD massive MIMO node $b$ communicating with the single-antenna FD UE $u$ transmitting training symbols in the UL direction.}
\label{fig: MSE_DoA}
\end{center}
\vspace{-2mm}
\end{figure}
\vspace{-0.1cm}
\subsection{Compared HD Massive MIMO Designs}\vspace{-0.1cm}
We compare the performance of the proposed FD-based SDDT scheme with three HD DoA-assisted DL analog beam management techniques. First, we consider the ``HD with Initial DoA" case, where DoA is estimated using the UL training symbols only in the first time slot, and for the rest of the $99$ time slots, the same DoA is utilized for finding the DL analog beam. Secondly, we simulate the ``HD DoA in Each Slot" scheme, where, for every time slot, a fraction of the UL training symbols is utilized for DoA estimation, and the rest of the symbols are dedicated for data transmission with analog BF. Finally, we consider the ``HD DoA with Update" technique, where DL analog BF in each time slot is performed using the DoA estimation of the previous time slot, unless more than $3$dB SNR loss occurs in the received DL signal, which triggers the initialization of a DoA-based analog beamformer update. In addition to the latter HD cases, we have simulated the achievable DL rate for the proposed FD-based SDDT scheme with ideal DoA estimation.
\vspace{-0.1cm}
\subsection{DoA Estimation Error and Average DL Rate}\vspace{-0.1cm}
In Fig.~\ref{fig: DoA_error}, the LoS DoA estimation error in radians is illustrated with respect to the time slot index. We have considered that the FD massive MIMO node $b$ communicates with the mobile single-antenna FD UE $u$, while the latter sends training symbols in the UL for DoA estimation with power $10$dBm. It is shown in the figure that the ``HD with Initial DoA" scheme provides higher DoA estimation error with increasing time slot index. This happens because it only estimates the DoA in the first time slot. As the UE moves, the initial DoA becomes outdated, and hence, a DoA estimation as well as an analog beam update are required. As illustrated in the inset plot, the ``HD DoA with Update" scheme performs an LoS DoA update after reaching approximately $0.1$rad estimation error, while the ``HD DoA in Each Slot" results in a steady error as the estimation is performed in each time slot. It is, however, evident from Fig.~\ref{fig: DoA_error} that the proposed FD-based SDDT scheme with a $2$-tap analog canceller provides substantially lower DoA estimation error compared to the HD cases across all time slots for the considered $10$dBm UL transmit power. In Fig.~\ref{fig: MSE_DoA}, we plot the Mean Squared Error (MSE) of the DoA estimation for all considered schemes as a function of the UL transmit power in the range $0-20$dBm. It is clear from the figure that the MSE of the DoA estimation reduces with increasing UL transmit power. This happens because the received SNR at the BS increases. It is also shown that the proposed scheme outperforms all considered HD-based counterparts.
\begin{figure}[!tpb]
\begin{center}
\includegraphics[width=\linewidth]{DL_Rate.eps}
\caption{Achievable DL rate with respect to DL transmit power in dBm for the $64\times 2$ FD massive MIMO node $b$ communicating with the mobile single-antenna FD UE $u$ sending training symbols with $10$dBm transmit power.}
\label{fig: DL_rate}
\end{center}
\vspace{-2mm}
\end{figure}
Figure~\ref{fig: DL_rate} illustrates the achievable DL rate of the proposed SDDT scheme as a function of the DL transmit power, considering that the $64\times 2$ BS node $b$ is transmitting data in the DL via analog BF to the constant-velocity mobile UE node $u$, while receiving UL training symbols with $10$dBm transmit power. It is demonstrated that the ``HD with Initial DoA" provides the lowest DL rate for all DL transmit power levels, as it suffers from the highest DoA estimation error. It is also shown that, although the ``HD DoA with Update" scheme achieves higher DoA estimation error compared to the ``HD DoA in Each Slot" approach, as depicted in Fig.~\ref{fig: DoA_error}, it achieves higher DL rate across all DL transmit powers. This is due to the fact that the later HD DoA-assisted beam management scheme utilizes $10\%$ symbols in each time slot for DoA estimation, whereas the ``HD DoA with Update" approach is capable of sending data symbols for the whole time slot when it doesn't have to update the DoA estimation. It is finally evident that the proposed scheme with $2$-tap analog cancellation achieves a higher DL rate compared to all the HD-based schemes fo all DL transmit powers. In particular, for the large DL transmit power of $40$dB, the proposed scheme for FD mmWave massive MIMO systems results in $120\%$ of the achievable DL rate with the best HD-based counterpart.
\section{Conclusion}
In this paper, we presented a novel DoA-assisted analog beam management scheme for FD mmWave massive MIMO systems. We considered an FD massive MIMO BS with an analog beamformer serving a mobile single-antenna FD user moving at a constant velocity. By adopting the MUSIC DoA estimation technique as an example, we presented a joint design of the DoA-assisted analog beamformer and A/D SI cancellation at the BS node maximizing the DL rate. Our performance evaluation results considering a realistic mmWave channel model demonstrated the superior achievable rates of the proposed FD-based SDDT scheme. In future work, the simultaneous DoA estimation and data transmission protocol will be considered for multi-user FD massive MIMO systems with both A/D precoders and combiners at all involved nodes.
\section*{Acknowledgments}
This work was partially funded by the National Science Foundation CAREER award \#1620902.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,944 |
Soccer >
Copa America >
Brazil vs. Bolivia: Copa America Opener Preview
Thiago SIlva still passionate about representing Brazil at Copa America
Thiago Silva has already fulfilled a childhood dream by representing Brazil, but he lacks no motivation heading into the Copa America.
Brazil - eight-time Copa America champions - host this year's tournament and take on Bolivia in the opening match at Sao Paulo's Morumbi on Friday.
BRAZIL BETTER OFF WITHOUT NEYMAR FOR COPA AMERICA?
Tite's side will be without key man Neymar, who will miss the competition due to an ankle injury sustained in a 2-0 friendly win over Qatar on June 6.
Silva played just twice for Brazil after the 2018 World Cup, from which Brazil were eliminated by Belgium in the quarter-finals, and acknowledged he had been unsure whether he would make the cut for the Copa America on home soil.
"I carry the passion, the pride, and the gratitude of being here. We are here on merit, for our good work for our clubs and [in our] careers," the Paris Saint-Germain defender told Brazil's official website.
"I realised a childhood dream that I had. We have to give value to this moment.
"I did not know if I was going to be here, but I was going to try until the last minute. That's what moves me, this passion.
SILVA: WITH NEYMAR OUT, COUTINHO IS BRAZIL'S BEST
"If I did not have that motivation, I would call Tite and say I could not play. [I would] enjoy my vacation with the family.
"But [people] who know me know how I work. At 34, I have to be very proud of myself for everything I've done, and what I'm still going to do."
Brazil won the last of their Copa America titles in 2007 and, following an infamously crushing semi-final loss when hosting the 2014 World Cup, the pressure is on the Selecao to deliver silverware again.
Silva has no doubt that even without Neymar - who has been replaced by Willian, with Ajax forward David Neres expected to start on the left wing - Brazil's squad has the capability to put previous disappointments behind them.
TITE ALLAYS ARTHUR INJURY FEARS
"Because I was on the field against Belgium, I felt even more sad. And maybe because I thought I would not make it to the next World Cup," Silva said.
"No one is sure, but let's work as much as possible and see what is in store for us in the future. I think we have a lot more victories in our lives than these defeats."
Brazil - David Neres
Having enjoyed a stellar season with Champions League semi-finalists Ajax, Neres received his first international call up in March, replacing injured Real Madrid youngster Vinicius Junior. After making two substitute appearances, Neres was handed his first start after Neymar withdrew from the squad. He marked the occasion by scoring Brazil's fifth goal in the 7-0 thrashing of Honduras, and the 22-year-old will be eager to take full advantage of his chance to impress on home soil.
Bolivia - Carlos Lampe
Bolivia are not blessed with much in the way of attacking talent, and, although they will no doubt put in a combative display, goalkeeper Lampe is likely to be the busiest player on the pitch. He was in good form to keep the score down in a 2-0 friendly defeat to France on June 2.
KEY OPTA FACTS
- Brazil are unbeaten on home soil against Bolivia in all competitions, scoring 46 goals and conceding just four times across 11 fixtures.
- Bolivia have managed just one win in their last seven Copa America tournaments combined, beating Ecuador 3-2 in 2015.
- The Copa America Centenario in 2016 was the first in which Brazil failed to qualify from the group stage since 1987.
- Brazil have won the Copa America on each of the previous four occasions they have hosted the tournament, in 1919, 1922, 1949 and 1989.
- Tite's side need just one win to reach the landmark of 100 victories in the Copa America.
- Bolivia are yet to win under Eduardo Villegas, who has drawn two and lost four across two spells in 2010 and 2019.
Thiago Silva Soccer Neymar Brazil Bolivia Copa America 2019 David Neres
CAF 2022 World Cup Qualifying Group Stage Draw
Sports Burst - Chicharito Joins A New Galaxy | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,922 |
{"url":"https:\/\/chemistry.stackexchange.com\/tags\/home-experiment\/new","text":"# Tag Info\n\nIt is not a problem of voltage. It is a problem of current and power. Whatever its nominal voltage, your bulb has a power to be known in watts. If your $\\ce{Zn\/Cu}$ cells are not able to produce the ...","date":"2022-05-23 23:40:45","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\": 0.6392335891723633, \"perplexity\": 612.6319694223232}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662562106.58\/warc\/CC-MAIN-20220523224456-20220524014456-00369.warc.gz\"}"} | null | null |
Q: unable to play songs using avaudioplayer I have created music directory and in that I have created music and artwork folders. The songs are in the music folder and now I am trying to play songs but it was showing couldn't load files
if FileManager.default.fileExists(atPath: currentAudioPath.path)
{
print("The file already exists at path")
do {
try AVAudioSession.sharedInstance().setCategory(AVAudioSessionCategoryPlayback)
try AVAudioSession.sharedInstance().setActive(true)
if UIApplication.shared.canOpenURL(currentAudioPath) {
print("found music directory")
}else {
print("did not find music directory")
}
do {
// Get the directory contents urls (including subfolders urls)
let directoryContents = try FileManager.default.contentsOfDirectory(at: self.MusicPath, includingPropertiesForKeys: nil, options: [])
print(directoryContents)
// if you want to filter the directory contents you can do like this:
let mp3Files = directoryContents.filter{ $0.pathExtension == "mp3" }
print("mp3 urls:",mp3Files)
audioPlayer = try AVAudioPlayer(contentsOf: mp3Files.first!, fileTypeHint: AVFileTypeMPEGLayer3)
let mp3FileNames = mp3Files.map{ $0.deletingPathExtension().lastPathComponent }
print("mp3 list:", mp3FileNames)
audioPlayer.prepareToPlay()
audioPlayer.play()
audioPlayer.delegate = self
audioLength = audioPlayer.duration
playerProgressSlider.maximumValue = CFloat(audioPlayer.duration)
playerProgressSlider.minimumValue = 0.0
playerProgressSlider.value = 0.0
audioPlayer.prepareToPlay()
showTotalSongLength()
updateLabels()
progressTimerLabel.text = "00:00"
} catch {
print(error.localizedDescription)
}
} catch let error as NSError {
print("error: \(error.localizedDescription)")
}
}
log image
but when the files in resource it was sucessfully playing (nsbundle.main............)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,444 |
[](https://travis-ci.org/Siyu Wu/test)
[](http://cocoapods.org/pods/test)
[](http://cocoapods.org/pods/test)
[](http://cocoapods.org/pods/test)
## Usage
To run the example project, clone the repo, and run `pod install` from the Example directory first.
## Requirements
## Installation
test is available through [CocoaPods](http://cocoapods.org). To install
it, simply add the following line to your Podfile:
```ruby
pod "test"
```
## Author
Siyu Wu, wusiyu1993@hotmail.com
## License
test is available under the MIT license. See the LICENSE file for more info.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,948 |
<?php
namespace Donjohn\MediaBundle\Provider;
use Donjohn\MediaBundle\Filesystem\MediaFilesystemInterface;
use Donjohn\MediaBundle\Filesystem\MediaLiipLocalFilesystem;
use Donjohn\MediaBundle\Model\Media;
use Symfony\Component\Form\FormInterface;
use Symfony\Component\Form\Guess\Guess;
use Symfony\Component\HttpFoundation\BinaryFileResponse;
use Symfony\Component\HttpFoundation\File\File;
use Symfony\Component\HttpFoundation\Response;
/**
* description.
*
* @author Donjohn
*/
class ImageLiipProvider implements ProviderInterface
{
/** @var ImageProvider $imageProvider */
protected $imageProvider;
/**
* ImageLiipProvider constructor.
*
* @param ProviderInterface $imageProvider
*/
public function __construct(ProviderInterface $imageProvider)
{
$this->imageProvider = $imageProvider;
}
/**
* @return string
*/
public function getAlias(): string
{
return $this->imageProvider->getAlias();
}
/**
* @param MediaFilesystemInterface $filesystem
*
* @return ProviderInterface
*/
public function setMediaFilesystem(MediaFilesystemInterface $filesystem): ProviderInterface
{
return $this->imageProvider->setMediaFilesystem($filesystem);
}
/**
* @param string $type
*
* @return bool
*/
public function validateMimeType(string $type): bool
{
return $this->imageProvider->validateMimeType($type);
}
/**
* @param File|null $file
*
* @return Guess
*/
public function guess(File $file = null): Guess
{
return $this->imageProvider->guess($file);
}
/**
* @param array $options
*
* @return array
*/
public function addProviderOptions(array $options): array
{
return $this->imageProvider->addProviderOptions($options);
}
/**
* @param \Twig_Environment $twig
*
* @return ProviderInterface
*/
public function setTwig(\Twig_Environment $twig): ProviderInterface
{
return $this->imageProvider->setTwig($twig);
}
/**
* @param Media $media
*/
public function extractMetaData(Media $media): void
{
$this->imageProvider->extractMetaData($media);
}
/**
* @param Media $media
*/
public function postLoad(Media $media): void
{
$this->imageProvider->postLoad($media);
}
/**
* @param Media $media
*/
public function prePersist(Media $media): void
{
$this->imageProvider->prePersist($media);
}
/**
* @param Media $media
*/
public function postPersist(Media $media): void
{
$this->imageProvider->postPersist($media);
}
/**
* @param Media $media
*/
public function preUpdate(Media $media): void
{
$this->imageProvider->preUpdate($media);
}
/**
* @param Media $media
*/
public function postUpdate(Media $media): void
{
$this->imageProvider->postUpdate($media);
}
/**
* @param Media $media
*/
public function preRemove(Media $media): void
{
$this->imageProvider->preRemove($media);
}
/**
* @param FormInterface $form
* @param array $options
*/
public function addEditForm(FormInterface $form, array $options): void
{
$this->imageProvider->addEditForm($form, $options);
}
/**
* @param FormInterface $form
* @param array $options
*/
public function addCreateForm(FormInterface $form, array $options): void
{
$this->imageProvider->addCreateForm($form, $options);
}
/**
* @return array
*/
public function getAllowedTypes(): array
{
return $this->imageProvider->getAllowedTypes();
}
/**
* @return string
*/
public function getTemplate(): string
{
return $this->imageProvider->getTemplate();
}
/**
* @return \Twig_Environment
*/
public function getTwig(): \Twig_Environment
{
return $this->imageProvider->getTwig();
}
/**
* @return MediaLiipLocalFilesystem
*/
public function getMediaFilesystem(): MediaFilesystemInterface
{
return $this->imageProvider->getMediaFilesystem();
}
/**
* @return mixed
*/
public function getFileMaxSize()
{
return $this->imageProvider->getFileMaxSize();
}
/**
* @param Media $media
* @param string|null $filter
* @param array $options
*
* @return string
*/
public function render(Media $media, string $filter = null, array $options = array()): string
{
return $this->getTwig()->render($this->getTemplate(),
array('mediaPath' => $this->getMediaFilesystem()->getPath($media, $filter),
'name' => $media->getName(),
'options' => $options, )
);
}
/**
* {@inheritdoc}
*/
public function getDownloadResponse(Media $media, array $headers = array(), string $filter = null): Response
{
// build the default headers
$headers = array_merge(array(
'Content-Type' => $media->getMimeType(),
'Content-Disposition' => sprintf('attachment; filename="%s"', $media->getName()),
), $headers);
return new BinaryFileResponse($this->getMediaFilesystem()->getFullPath($media, $filter), 200, $headers);
}
/**
* {@inheritdoc}
*/
public function getPath(Media $media, string $filter = null, bool $fullPath = false): string
{
return $fullPath ?
$this->getMediaFilesystem()->getWebPath($media, $filter) :
$this->getMediaFilesystem()->getPath($media, $filter);
}
}
| {
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Effort To Pay Hospitals Based On Quality Didn't Cut Death Rates, Study Finds
By Jordan Rau March 28, 2012
Medicare's largest effort to pay hospitals based on how they perform — an inspiration for key parts of the health care law — did not lead to fewer deaths, a new study has found.
The study casts doubt on a central premise of the health law's effort to rework the financial incentives for hospitals with the aim of saving money while improving patient care. This fall, Medicare is going to start altering its payments to more than 3,000 hospitals based on how patients rate their stays and how completely hospitals follow a handful of clinical guidelines for basic care.
That effort, the Hospital Value-Based Purchasing Program, is modeled on a six-year project called the Medicare Premier Hospital Quality Incentive Demonstration (HQID). Between 2003 and 2009, the 252 hospitals participating in the program were measured on three-dozen performance metrics, including their mortality rates for heart attack and heart bypass surgery. Those that did best earned bonuses, and those that did the worst lost money.
But the study published in the New England Journal of Medicine on Wednesday found that the mortality rate at the participating hospitals was virtually the same as the mortality rate for the 3,363 hospitals that were not part of the project. While the mortality rate dropped slightly over the course of the project among the participating hospitals, it also dropped for the other hospitals.
"Pay for performance is really important," said Ashish Jha, a professor at the Harvard School of Public Health and lead author of the study. "This says to me that we haven't figured out the pay part, or the performance part."
The study's findings are at odds with the way the Premier healthcare alliance has portrayed the project. On its website, Premier, which oversees quality improvement efforts for its membership of hospitals and health systems, estimated the project saved the lives of 8,500 heart attack patients over five years.
Blair Childs, a senior vice president at Premier, said it wasn't surprising that the Premier hospitals didn't prevent substantially more deaths from heart attacks and heart bypasses because there were so few deaths to begin with.
Childs also said that lowering mortality wasn't the primary goal of the demonstration project. Most of the quality metrics look at whether hospital staff performed particular procedures, such as giving heart attack patients a beta-blocker on arrival and discharge. By those standards, the Premier hospitals surpassed other hospitals, he said.
"The goal of HQID was to determine whether incentives would improve care processes in hospitals and it did do that, there's no question," Childs said.
Childs agreed with the New England Journal article that focusing on these "process" measures may not be the best way to actually improve patient outcomes. He said a current project Premier is running called Quest among 293 hospitals has found that a better way to reduce mortality is to focus on preventing septic shock, when the bloodstream is infected with bacteria, and respiratory conditions such as pneumonia in patients on ventilators.
In a statement, The Centers for Medicare & Medicaid Services said: "The Premier demonstration was an effort under the last Administration, separate from the value-based purchasing model that we're implementing into Medicare's hospital payment system. Our model for improving quality in hospitals is much more aggressive, covering all hospitals and including both incentives for hospitals that do well on quality metrics, and consequences for hospitals that do not improve."
CMS has said it eventually wants to tie hospital payment to actual outcomes. But in the value-based program's first year, process measures will account for 70 percent of hospitals' financial incentives, with patient satisfaction scores making up the rest. In the second year, starting in fall 2013, Medicare will take into account mortality rates for three conditions—heart failure, heart attack and pneumonia. But process measures will continue play a dominant part in judging hospital performance.
In an interview, Jha cautioned Medicare against making hospitals accountable for too many different things, diffusing their focus on the ones that matter most. For instance, he said, one of the measures Medicare is using—what percent of patients received written instructions about how to take care of themselves after discharge—has been shown in studies to have no effect on whether patients are readmitted.
"At the end of the day, you are going to ask people to make improvements and you want them to focus on what's important," Jha said. "And if you give them 18 different metrics and some are easy but not that important, and some are hard but important, people are going to naturally gravitate toward what's easy and you're not going to have meaningful impact."
Chas Roades, chief research officer at The Advisory Board Co., a consulting firm, said he believes Medicare's new effort will improve quality in the long-term. But he cautioned that it may take a while. "Like most of these kinds of quality improvements, I think the early gains are going to be the very low performers, and less about the top performers improving even more," he said. "What I think it will do in the reasonably near term is reduce the spread between the worst performers and the best performers, mostly by pulling up the bottom."
Dr. Donald Berwick, the former CMS administrator, said he hadn't read the study and thus couldn't comment on it. But he said that "conceptually," paying for performance "has to be the right way to go" because the current system of reimbursement for procedures has proven not to work. Getting the right measurements will be crucial, he said. "The angel may be in the details," he said.
This article was produced by Kaiser Health News with support from The SCAN Foundation.
jrau@kff.org
Jordan Rau: jrau@kff.org, @JordanRau
Cost and Quality Health Industry Medicare The Health Law
Jordan Rau, Kaiser Health News | {
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Gulf Islands Driftwood - Newspaper serving the Gulf Islands since 1960
A Day in the Life Salt Spring Island
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Fire board considers island's future infrastructure needs
Ganges Fire Hall, which the Salt Spring Island Fire Protection District board hopes to see replaced in the not-so-distant future.
Photo by Marc Kitteringham
By Elizabeth Nolan Last updated Jan 2, 2019
Salt Spring Fire Protection District trustees continue to grapple with infrastructure replacement concerns, as demonstrated by discussions about future spending that took place during Monday night's board meeting.
Planning for a new fire hall or "protective services building" is officially underway with first reading given to the 2019 budget bylaw passed on Sept. 11. The board is holding a special town meeting to discuss its proposed $3.16-million budget at the Lions Hall on Oct. 1. In particular, trustees will seek input on the plan to start setting aside up to $300,000 per year in a fire hall replacement reserve fund.
Trustee Rollie Cook reported that he had taken a "straw poll" of about 35 local residents during the past weekend's fall fair to ask about the reserve idea, and was pleasantly pleased to find overall support.
"I have a sense that there is good will, but also a caution that we have to be responsible, open and fair," Cook said, adding the Oct. 1 session is being planned to offer that transparency.
Trustee Ron Lindstrom reported on other aspects of planning for the new hall. The board received a box of documents from Hans Hazenboom related to the most recent failed project that will greatly aid the new Brinkworthy site feasibility study. Lindstrom concluded that "a lot of due diligence" had been done, and said the board should turn the information over to the fire hall advisory working group for follow-up.
Lindstrom also went over some points in the draft terms of reference suggested for the new working group or advisory committee. As drafted by the strategic planning committee, the new working group would be composed of the chairs of the board's three major committees plus a minimum of seven members of the public who have relevant knowledge and skills. Membership could include officials from the Islands Trust, the Capital Regional District and the North Salt Spring Waterworks District. The committee has suggested an independent facilitator be appointed as chair.
A timeframe of six to eight months is suggested for the working group to accomplish its job, at which point the project would be turned over to a construction committee, Lindstrom said.
The board has also started to think about what to do with the existing hall if the new hall project should fail once again. A report on the seismic upgrades needed to meet the BC Building Code was commissioned in 2005 but never acted on. The building code has changed several times since then, Lindstrom noted.
"If a referendum fails again or the process gets bogged down, we have a responsibility to remediate the building," he said.
The board passed a resolution stating that it would take on the necessary seismic upgrades if a fire hall borrowing referendum fails; if a referendum date is not set by June 30, 2019; or if construction documents for a new hall are not commenced by March 31, 2020.
Trustee Howard Holzapfel voted against the motion, saying he could not support the plan until a referendum actually fails. He said the cost of doing the work is unknown but could be guessed at around $2 million, and that the fire department would have to completely leave the hall while renovations were taking place. The project could also mean losing one truck bay, he said.
"There could be all sorts of logistical issues," Lindstrom agreed. "Nevertheless, we need to be on record that we're going to do something about it."
Fire department equipment replacement needs are another constant looming expense for the board. Trustees asked staff for a report on which fire trucks the department considers to be front-line or priority for replacement using the capital reserve fund, and which they should keep using "until the wheels fall off," as district CAO Andrew Peat described it.
In other business from Monday's meeting, firefighter Warren Nuyens thanked the board for committing staff and the reserve tender to help fight wildfires in the B.C. Interior for the second year in a row. Nuyens was part of the second team of two deployed to Burns Lake this summer, along with Eric Taylor. Patrick Byrne and Doug Ponsford were the first team to go out, while Mitchell Sherrin and Jason Gaffney were the final crew deployed.
"It's an opportunity for us to take our skills up there, and our skills improve immensely with 10 hours a day on a truck minimum. What we bring back to the community is invaluable," Nuyens said.
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© 2021 - Gulf Islands Driftwood. All Rights Reserved. | {
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Q: Config Kivy > Invert input for y axis I am trying to setup a "off-brand" touchscreen on a Raspberry Pi3 and I am having some trouble when I run my python/kivy program, visually everything is fine, but whenever I need to move a slider, push a button or whatever. the input y-axis is inverted, note that it works fine when i run this on my windows machine
As you can see the input for the buttons are inverted on the y axis
I do know this exists and I have tried it, but it did nothing to solve the problem (In my case).
https://stackoverflow.com/a/34344458/7522859
And I have tried to fix it in the config file under (in my case) (.kivy/config.ini), and as you can see it reads the invert_y option but does nothing with both 1 and 0 as its values.
root@raspberrypi:/media/pi/64D933A55CDD560F/PrinterSoftware# python MC.py
[INFO ] [Logger ] Record log in /root/.kivy/logs/kivy_17-02-06_10.txt
[INFO ] [Kivy ] v1.9.2.dev0, git-57d41c9, 20170206
[INFO ] [Python ] v2.7.9 (default, Mar 8 2015, 00:52:26)
[GCC 4.9.2]
[INFO ] [Factory ] 193 symbols loaded
[INFO ] [Image ] Providers: img_tex, img_dds, img_sdl2, img_pil, img_gif (img_ffpyplayer ignored)
[INFO ] [Text ] Provider: sdl2
[INFO ] [Window ] Provider: egl_rpi
[INFO ] [GL ] Using the "OpenGL ES 2" graphics system
[INFO ] [GL ] Backend used <gl>
[INFO ] [GL ] OpenGL version <OpenGL ES 2.0>
[INFO ] [GL ] OpenGL vendor <Broadcom>
[INFO ] [GL ] OpenGL renderer <VideoCore IV HW>
[INFO ] [GL ] OpenGL parsed version: 2, 0
[INFO ] [GL ] Shading version <OpenGL ES GLSL ES 1.00>
[INFO ] [GL ] Texture max size <2048>
[INFO ] [GL ] Texture max units <8>
[INFO ] [Shader ] fragment shader: <Compiled>
[INFO ] [Shader ] vertex shader: <Compiled>
[INFO ] [Window ] virtual keyboard not allowed, single mode, not docked
[INFO ] [OSC ] using <multiprocessing> for socket
[INFO ] [ProbeSysfs ] device match: /dev/input/event0
[INFO ] [HIDInput ] Read event from </dev/input/event0>
[INFO ] [ProbeSysfs ] device match: /dev/input/event1
[INFO ] [HIDInput ] Read event from </dev/input/event1>
[INFO ] [ProbeSysfs ] device match: /dev/input/event2
[INFO ] [HIDInput ] Read event from </dev/input/event2>
[INFO ] [HIDInput ] Read event from </dev/input/event0>
[INFO ] [HIDInput ] Set custom invert_y to 0
[INFO ] [Base ] Start application main loop
So the question is how do I invert the Y-axis for the input in the kivy config file. I have also taken a look at this and I didn't really understand it that well, maybe I am just stupid.
Sorry if this post is bad. Its my first post and English is not my native language.
A: I got it to work, finally.
I changed the line 417 in the hidinput.py under:
/usr/local/lib/python2.7/dist-packages/kivy/input/providers/hidinput.py
Credit: How do if invert touch input in Kivy
and set the config:
~/.kivy/config.ini
under [input]
ADS7846 = hidinput,/dev/input/event2,invert_y=0
| {
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{"url":"http:\/\/danboykis.com\/posts\/applicative-order-vs-normal-order-cont\/","text":"# Applicative Order vs Normal Order cont.\n\nExercise 1.5: Ben Bitdiddle has invented a test to determine whether the interpreter he is faced with is using applicative-order evaluation or normal-order evaluation. He defines the following two procedures:\n\n(define (p) (p))\n\n(define (test x y)\n(if (= x 0)\n0\ny))\n\n\nThen he evaluates the expression\n\n(test 0 (p))\n\n\nWhat behavior will Ben observe with an interpreter that uses applicative-order evaluation? What behavior will he observe with an interpreter that uses normal-order evaluation? Explain your answer. (Assume that the evaluation rule for the special form if is the same whether the interpreter is using normal or applicative order: The predicate expression is evaluated first, and the result determines whether to evaluate the consequent or the alternative expression.)\n\n## Applicative Order Evaluation\n\n(test 0 (p))\n\n\nWill become and infinite loop. Since AOE evaluates all the arguments as much as possible before passing them to a function test, clearly p is has no terminating case. Since p is a case of infinite recursion the program goes into an infinite loop.\n\nNormal Order Evaluation:\n\n(test 0 (p))\n\n\nThis time p won\u2019t be evaluated and test will enter the conditional in which the function terminates by returning 0. The pesky else case is never ran and hence the infinite loop condition never comes up. However if the first argument to test was anything but 0, an infinite loop would still occur.","date":"2021-10-22 16:16:46","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\": 0.536128044128418, \"perplexity\": 2282.8778354528226}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585516.51\/warc\/CC-MAIN-20211022145907-20211022175907-00317.warc.gz\"}"} | null | null |
{"url":"http:\/\/mathcentral.uregina.ca\/QQ\/database\/QQ.09.14\/h\/jill1.html","text":"SEARCH HOME\n Math Central Quandaries & Queries\n Question from jill, a student: A has co- ordinates (7,-1) and B has co-ordinates (3,5).write these as column vectors\n\nHi Jill,\n\nVectors are sometimes written as rows and sometimes as columns. You have written two vectors as rows. To write them as column vectors place the numbers, one above the other, and surround the column of numbers with parentheses. Thus $(7, -1)$ written as a column vector is\n\n$\\left( \\begin{array}{r}7\\\\-1\\end{array} \\right).$\n\nPenny\n\nMath Central is supported by the University of Regina and the Imperial Oil Foundation.","date":"2023-02-02 20:38:45","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\": 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\": 0.7530568838119507, \"perplexity\": 1859.9430871154088}, \"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-2023-06\/segments\/1674764500041.18\/warc\/CC-MAIN-20230202200542-20230202230542-00768.warc.gz\"}"} | null | null |
{"url":"https:\/\/indico.cern.ch\/event\/344485\/contributions\/1743824\/","text":"# ICRC2015\n\nJuly 29, 2015 to August 6, 2015\nWorld Forum\nEurope\/Amsterdam timezone\n\n## New concept of very high energy cosmic ray observation by wide field-of-view telescope\n\nAug 1, 2015, 3:30 PM\n1h\nAmazon Foyer (World Forum)\n\n### Amazon Foyer\n\n#### World Forum\n\nChurchillplein 10 2517 JW Den Haag The Netherlands\nBoard: 161\nPoster contribution CR-IN\n\n### Speaker\n\nDr Kenji Shinozaki (Unverisity of Tubingen)\n\n### Description\n\nThe chemical composition of the very high energy cosmic rays (VHECRs) is an important piece of information to investigate their origin and acceleration mechanism. Possible change of chemical composition at the knee energy range has been reported by air shower experiments based on sampling of muons or Cherenkov photons. So far low flux of VHECRs along with uncertainties due to indirect detection, has limited the precision of chemical composition measurement. It is thus essential to improve primary mass estimation via measurement of additional parameters of the air showers. In the present work, we propose a new concept of VHECR observation using ultra-wide field-of-view (FOV) refractive imaging atmospheric Cherenkov telescope (IACT). The wide-FOV optics have been designed in the framework of JEM-EUSO mission for ultra-high energy cosmic ray (UHECR) observation from the International Space Station. The pathfinder experiments testing such optics have been successfully operated on the balloon and on the ground. The technique of imaging of the Cherenkov light hasbeen used in GeV--TeV energies by IACT arrays using $\\gg 10$-m-scale reflective telescopes. Above $\\sim 10^{15}$~eV, the Cherenkov light from cosmic rays initiated air showers spreads over a few km that can be detected even by meter-scale telescopes. At these energies, Cherenkov images of distant air showers span $\\sim 15^\\circ$ and thus wide FOV otpics is necessary for their detection and characterization. To evaluate potential performances of this concept, a large number of air showers were generated using CORSIKA packages. In the presentation, we introduce the basic concept of wide-FOV IACT technique for VHECR observation and characterize the performance of the sets for the chemical composition study. In addition, we discuss prospective advantages of EUSO-type wide-FOV telescopes for VHECR and UHECR physics.\nRegistration number following \"ICRC2015-I\/\" 531 -- not specified --\n\n### Primary authors\n\nProf. Andrii Neronov (University of Geneva) Dr Kenji Shinozaki (Unverisity of Tubingen)\n\n### Co-authors\n\nProf. Andrea Santangelo (University of Tubingen) Dr Simona Toscano (Vrije University, Brussels)\n\n### Presentation materials\n\nThere are no materials yet.","date":"2023-03-28 21:45:09","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\": 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\": 0.4149218499660492, \"perplexity\": 5950.212473427136}, \"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-2023-14\/segments\/1679296948871.42\/warc\/CC-MAIN-20230328201715-20230328231715-00768.warc.gz\"}"} | null | null |
{"url":"http:\/\/arxitics.com\/articles\/1907.05412","text":"## arXiv Analytics\n\n### arXiv:1907.05412 [math-ph]AbstractReferencesReviewsResources\n\n#### A mathematical objection to the existence of relativistic mechanical systems of several particles\n\nPublished 2019-07-11Version 1\n\nWe will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous assertion is due to the fact that a mechanical system defines a second order differential equation and this, in turn, induces an absolute time that will generally be incompatible with the proper times of the different particles.\n\nCategories: math-ph, gr-qc, math.MP\nSubjects: 83Axx\nRelated articles: Most relevant\u2002|\u2002Search more\narXiv:1707.03651 [math-ph] (Published 2017-07-12)\nTime in classical and quantum mechanics\narXiv:1205.6353 [math-ph] (Published 2012-05-29)\nCoherent Orthogonal Polynomials\narXiv:1109.0126 [math-ph] (Published 2011-09-01)\nOn simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)","date":"2019-07-24 04:33:20","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\": 0.8491420745849609, \"perplexity\": 2251.9789923478784}, \"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-2019-30\/segments\/1563195530385.82\/warc\/CC-MAIN-20190724041048-20190724063048-00335.warc.gz\"}"} | null | null |
Uganda Nurses and Midwives Union | Dual Diagnosis: Understanding Co-Occurring Mental Illness and Substance Use Disorders | Patricia Hocking-Walker, M.S.
Behavioral health professionals have a responsibility to be aware of the complex relationship between mental illness and substance abuse or dependence, known as dual diagnoses or co-occurring disorders. Topics include characteristics and prevalence, theories, screening and assessment, and treatment of dual diagnosis.
1. Describe the scope and magnitude of co-occurring mental illness and substance use disorders.
2. Identify various theoretical approaches that explain the relationship between mental illness and substance abuse, and why co-existence of these behaviors is prevalent.
3. Examine the importance of thorough screening and assessment for dual diagnosis, while outlining the 12-step assessment process.
4. Outline various treatment formats that will best engage clients in the therapeutic process, and summarize specific treatment modalities most commonly used for dual diagnosis.
5. Discuss the mental health disorders that seem to create particular vulnerability to substance use as well as the most common mental health/addiction combinations in play today.
6. Review strategies to help those with a loved one with dual diagnosis take care of themselves while supporting the individual. | {
"redpajama_set_name": "RedPajamaC4"
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How Did You Start Eternal Perspective Ministries?
How did you start EPM?
In 2017, Randy Alcorn shared his story of how his ministry, Eternal Perspective Ministries, began and God's sovereignty throughout all of it. This was filmed by Humble Beast. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,226 |
Click the button below to add the Dell DPS-1100CB 1100 Watt Power Supply FRNJJ to your wish list.
The Dell DPS-1100CB is an 1100 Watt power supply built for the N3000 series of switches. The Dell FRNJJ can be used as a pair for redundancy, this way if one power supply happens to fail over time you still have the switch up and running. These units are hot swappable. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,020 |
\section{Introduction}
\noindent In \cite{rib_cyclic} Ribaucour investigated circle
congruences that admit a 1-parameter family of orthogonal
surfaces and called those congruences \emph{cyclic} (also
called \emph{normal}).
The main motivations to
study these special circle congruences seem to be twofold:
firstly, a surface family orthogonal to a cyclic circle
congruence gives rise to a special orthogonal coordinate
system (\emph{cyclic system}), where the orthogonal
trajectories of one family are circular. As a consequence,
two families of coordinate surfaces then consist of channel
surfaces. Examples are provided by orthogonal systems with
a family of surfaces that are parallel in a fixed space
form (cf \cite{cyclic_guichard_eth, salkowski}) and
special cyclidic coordinate systems (also called totally
cyclic), where all coordinate surfaces are Dupin cyclides
\cite{darboux_ortho, salkowski, totallycyclic}. Cyclic
systems widely used in physics include rotational systems
\cite{MR947546}, as for example, spherical and toroidal
coordinates.
Secondly, cyclic circle congruences can be employed to
construct (families of) surfaces of various special
types by imposing further (geometric) conditions on the
cyclic circle congruence. Amongst them are, for example,
pseudospherical surfaces related by Bianchi transformations
\cite{darboux_ortho, MR0115134} or parallel families
of flat fronts in hyperbolic space \cite{MR2652493,
MR2196639}.
The former example generalizes to a remarkable class
of cyclic circle congruences given by curved flats in
the space of circles
(so-called flat spherical or hypercyclic systems) that come
with an orthogonal family of Guichard surfaces \cite{MR239516}.
Higher dimensional analogues lead to 3-dimensional conformally
flat hypersurfaces \cite{MR1421285} and, more generally,
M\"obius flat hypersurfaces \cite{csg_45, curvedflats}.
\vglue-parskip \\ \\ \noindent
An integrable discretization of orthogonal coordinate
systems was given in
\cite{org_principles, orth_nets_clifford, ddg_book, orth_cds}
where those were introduced as higher-dimensional circular
(principal) nets.
The main goal of the present work is to explore discrete
counterparts of cyclic circle congruences and their associated
cyclic coordinate systems
(see Def \ref{def_cyclic_system}
and \ref{def_cyclic_congruence}),
based on this definition.
In this way, we anticipate
to pave the way for further studies in this context,
inspired by the rich smooth theory as sketched above.
For example, based on the observations in Subsection
\ref{subsect_flat_fronts} we shall investigate relations
of various approaches to flat fronts in hyperbolic
space and, in particular, prove the existence of a
Weierstrass-type representation for discrete flat fronts
in \cite{disc_flat_front}.
Moreover, since the established theory naturally generalizes
to higher-dimensional systems, it shall lead to discrete
notions for 3-dimensional conformally flat hypersurfaces
and M\"obius flat hypersurfaces as orthogonal surfaces of
discrete cyclic systems stemming from discrete flat fronts.
\vglue-parskip \\ \\ \noindent
Another main goal of this paper is to further examine,
and promote, the use of discrete connections that are given
in the simplest way possible:
by the ``reflections'' of the underlying ambient geometry.
In our case,
these will be Lie and M-Lie inversions
(see Def \ref{def_M-Lie})
that can be used to generate cyclic circle congruences and
their orthogonal nets in an efficient way.
In a sometimes more implicit way, such connections have
been used in the theory of discrete orthogonal systems
for a long time,
see~\cite{org_principles, orth_nets_clifford,
ddg_book, bcjpr, lin_weingarten, disc_cmc}.
Here, we aim to present a more explicit treatment and,
in particular, to explicitely investigate and employ
the properties of connections built from Lie and M-Lie
inversions in the context of cyclic systems.
In this way, we hope to contribute to a methodologically
systematic and transparent approach to the field.
\vglue-parskip \\ \\ \noindent
The paper is structured as follows. After an introductory
Section \ref{section_prelim} on basic concepts and
facts on circles and spheres that will be essential
for what follows, the main notions of the text are presented in
Section \ref{section_cyclic_systems}.
Here we approach the discretization of smooth cyclic systems
from two different angles:
firstly, we
consider discrete triply orthogonal systems that contain
two coordinate surface families of discrete channel
surfaces \cite{discrete_channel} and, therefore, have a
family of circular orthogonal trajectories. In Subsection
\ref{subsect_cyclic_congruence}, we then take a different point
of view: we start from a discrete 2-dimensional family
of circles and investigate under what conditions there
exists a family
of orthogonal discrete Legendre maps that gives rise to a
discrete cyclic system.
We then show that the proposed discretizations reflect
properties that are well-known from the smooth theory,
such as a
constant cross-ratio of four orthogonal surfaces of a
cyclic circle congruence, and
the existence of discrete Ribaucour transformations between any
two orthogonal surfaces of a discrete cyclic system
(see Cor \ref{cor_const_cross} and \ref{cor_adjacent_rib}).
\vglue-parskip \\ \\ \noindent
In Section \ref{sect_from_rib} we pursue Ribaucour's original
approach and consider discrete cyclic circle congruences
associated to a Ribaucour pair of discrete Legendre maps.
In particular, we demonstrate that the circles that
intersect the spheres of a Ribaucour sphere congruence
in the point spheres of the two
envelopes orthogonally constitute a discrete cyclic circle
congruence (cf Thm \ref{thm_associated_rib_cyclic}).
As an application of the developed theory, we then
investigate discrete cyclic circle congruences constructed
from special discrete Ribaucour pairs, where at least one
of the initial nets is totally umbilic.
In this context we will discuss
parallel families of discrete flat fronts in hyperbolic space
as described in \cite{MR2946924, disc_sing}, and discrete
cyclic systems where all coordinate surfaces are discrete Dupin
cyclides (see $\S$\ref{subsect_flat_fronts} and
$\S$\ref{subsect_dupin_cyclides}).
\vglue-parskip \\ \\ \noindent
The concepts used and discussed throughout this work,
such as circles, orthogonal coordinate systems,
are well defined in M\"obius geometry but not in Lie sphere
geometry.
Nevertheless, we will
work in a Lie sphere geometric setup, where we fix a
M\"obius geometry as subgeometry. This will enable us to
use the elegant Lie sphere geometric descriptions for Dupin
cyclides and discrete channel surfaces
\cite{discrete_channel}
that will play a key role in our investigations.
Furthermore, enhancing methods developed
in~\cite{rib_families}, this setup enables us
to characterize discrete cyclic circle congruences by the
existence of M-Lie inversions that interchange adjacent
circles and induce a flat connection for the congruence
(cf Thm \ref{thm_flat_connection}). These maps then
provide an efficient way to construct discrete Legendre maps
orthogonal to the circle congruence and the other coordinate
surfaces of the associated discrete cyclic systems.
\vglue-parskip \\ \\ \noindent{\sl Acknowledgements\/}.
We would like to thank our colleagues and friends
Joseph Cho,
Wayne Rossman,
and
Mason Pember
for enjoyable and helpful discussions around the subject area.
We also gratefully acknowledge financial support
of the work from
the Austrian Science Fund FWF
through the
Joint Project I3809 ``Geometric shape generation''.
\section{Preliminaries}\label{section_prelim}
\noindent Throughout this paper we shall work in a M\"obius
geometry, considered as a subgeometry of Lie sphere
geometry. In this section we will sketch basic concepts of
this setup and will formulate various facts on circles that
will become useful later in the text.
For more details or proofs the interested reader is referred
to the exhaustive literature in this area;
see, for example, the surveys \cite{blaschke} and
\cite{book_cecil}.
\vglue-parskip \\ \\ \noindent
We shall exploit the hexaspherical coordinate model of
Lie sphere geometry as introduced by Lie~\cite{L1872}
and consider the
6-dimensional vector space $\mathbb{R}^{4,2}$ endowed with a
metric of signature $(4,2)$. The \emph{projective light cone}
will be denoted by
\begin{equation*}
\mathbb{P}(\mathcal{L}) :
= \{ \lspann{\mathfrak{s}} \subset \mathbb{R}^{4,2} \ | \
\lspan{\mathfrak{s}, \mathfrak{s}}=0 \}
\subset \mathbb{P}(\mathbb{R}^{4,2})
\end{equation*}
and represents the set of oriented 2-spheres.
Two spheres $s_1$ and $s_2$
are in oriented contact if and only if any two corresponding
vectors $\mathfrak{s}_1$ and $\mathfrak{s}_2$ in the light cone
are orthogonal.
Hence the set of contact elements,
that is, of pencils of $2$-spheres in oriented contact,
is represented by the set of lines in the Lie quadric $\mathbb{P}(\mathcal{L})$ or,
equivalently,
the subset of null $2$-planes in $\mathbb{R}^{4,2}$ of the
Grassmannian.
\vglue-parskip \\ \\ \noindent
\textbf{Convention.}\,Throughout this work, homogeneous
coordinates of elements in the projective space
$\mathbb{P}(\mathbb{R}^{4,2})$ will be denoted by the
corresponding black letter; if statements hold for arbitrary
homogeneous coordinates we will use this convention without
explicitly mentioning it.
\vglue-parskip \\ \\ \noindent
To obtain a M\"obius geometry of oriented spheres as
a subgeometry in this setup, we fix a point sphere complex
$\mathfrak{p} \in \mathbb{R}^{4,2}$, $\lspan{\mathfrak{p},
\mathfrak{p}}=-1$, and recover points, that is, spheres with
radius zero, as elements in
\begin{equation*}
\mathbb{P}(\mathcal{P}) :
= \mathbb{P}({\mathcal L}\cap\{\mathfrak{p}\}^\perp).
\end{equation*}
The group of M\"obius transformations is then provided by
all Lie sphere transformations that preserve the point
sphere complex $\mathfrak{p}$. In particular, those preserve
the (unoriented) angle $\varphi$ between two spheres $u,v
\in \mathbb{P}(\mathcal{L})$, given by
\begin{equation}\label{equ_intersection_angle}
\cos \varphi
= 1 - \frac{
\lspan{\mathfrak{u},\mathfrak{v}}
\lspan{\mathfrak{p},\mathfrak{p}}
}{
\lspan{\mathfrak{u},\mathfrak{p}}
\lspan{\mathfrak{v},\mathfrak{p}}
}.
\end{equation}
Furthermore, by choosing a vector $\mathfrak{q}\in
\mathbb{R}^{4,2}\setminus \{ 0 \}$, $\lspan{\mathfrak{p},
\mathfrak{q}}=0$, we distinguish
a \emph{quadric of constant curvature}
\begin{equation*}
\mathcal{Q} :
= \{ \mathfrak{n} \in \mathbb{R}^{4,2} \ | \
\lspan{\mathfrak{n}, \mathfrak{n}}=0, \lspan{\mathfrak{n},
\mathfrak{q}}=-1, \lspan{\mathfrak{n}, \mathfrak{p}}=0 \},
\end{equation*}
with constant sectional curvature
$-\lspan{\mathfrak{q}, \mathfrak{q}}$,
and obtain its complex of \emph{hyperplanes}
\begin{equation*}
\mathcal{H} :
= \{ \mathfrak{n} \in \mathbb{R}^{4,2} \ | \
\lspan{\mathfrak{n}, \mathfrak{n}}=0, \lspan{\mathfrak{n},
\mathfrak{q}}=0, \lspan{\mathfrak{n}, \mathfrak{p}}=-1 \}.
\end{equation*}
\bigskip
\noindent In Lie sphere geometry,
any element $a \in \mathbb{P}(\mathbb{R}^{4,2})$ defines
a \emph{linear sphere complex}
$\mathbb{P}(\mathcal{L}\cap\{a\}^\perp)$,
that is, a 3-dimensional family of 2-spheres.
We distinguish three types of linear sphere complexes:
if $\lspan{ \mathfrak{a}, \mathfrak{a}} = 0$, the complex
is called \emph{parabolic} and consists of all spheres
that are in oriented contact with the sphere represented
by~$a$. If $\lspan{ \mathfrak{a}, \mathfrak{a}} < 0$, we
say that the complex is \emph{hyperbolic} and for $\lspan{
\mathfrak{a}, \mathfrak{a}} > 0$ we obtain an \emph{elliptic}
linear sphere complex.
In M\"obius geometry, that is, for a fixed point sphere
complex $\mathfrak{p}$, the latter has a beautiful geometric
characterization: the linear sphere complex then contains
all spheres that intersect the two spheres (that coincide
up to orientation)
\begin{equation}\label{equ_sphere_compl}
\mathfrak{s}_a^\pm \in \lspann{\mathfrak{a}, \mathfrak{p}}
\end{equation}
at the constant angle
\begin{equation*}
\cos^2 \varphi = \frac{K}{K-1}, \ \ \text{where } \
K = \frac{\lspan{\mathfrak{a}, \mathfrak{p}}^2}
{\lspan{\mathfrak{a}, \mathfrak{a}}
\lspan{\mathfrak{p}, \mathfrak{p}}}.
\end{equation*}
In particular, the spheres in a linear sphere complex
intersect the spheres $s_a^\pm$ orthogonally if and only if
$\lspan{\mathfrak{a}, \mathfrak{p}}=0$.
Conversely, suppose that $s \in \mathbb{P}(\mathcal{L})$ is a sphere,
$\mathfrak{s}\not\perp\mathfrak{p}$;
then the elliptic linear sphere complex that contains
all spheres intersecting $s$ orthogonally is given by
\begin{equation}\label{equ_orth_complex}
\mathfrak{a} :
= \mathfrak{s}+\lspan{\mathfrak{s},\mathfrak{p}}\mathfrak{p}.
\end{equation}
Hence, a sphere $t \in \mathbb{P}(\mathcal{L})$ intersects the sphere $s$
orthogonally if and only if $\lspan{\mathfrak{t},
\mathfrak{a}}=0$.
\vglue-parskip \\ \\ \noindent
Any elliptic and hyperbolic linear sphere complex may be
used to define a reflection:
let $a \in \mathbb{P}(\mathbb{R}^{4,2})$, $\lspan{
\mathfrak{a}, \mathfrak{a}} \neq 0$, then the \emph{Lie
inversion with respect to the linear sphere complex
$\mathbb{P}(\mathcal{L}\cap\{a\}^\perp)$} is given by
\begin{equation*}
\sigma_a:\mathbb{R}^{4,2} \rightarrow \mathbb{R}^{4,2}, \ \
\mathfrak{r} \mapsto \sigma_a(\mathfrak{r}) :
= \mathfrak{r}-\frac{2\lspan{\mathfrak{r}, \mathfrak{a}}}
{\lspan{\mathfrak{a}, \mathfrak{a}}}\mathfrak{a}.
\end{equation*}
Any Lie inversion is an involution that maps spheres
to spheres and preserves oriented contact between
spheres. Moreover, we emphasize that a Lie inversion $\sigma_a$
preserves all elements that lie in the corresponding linear
sphere complex
$\mathbb{P}(\mathcal{L}\cap\{a\}^\perp)$.
In particular, Lie inversions that preserve the point
sphere complex will play a crucial role:
\begin{defi}\label{def_M-Lie}
A Lie inversion $\sigma_a$ that preserves the point
sphere complex, $\lspan{\mathfrak{p}, \mathfrak{a}}=0$,
will be called an \emph{M-Lie inversion}.
\end{defi}
\vglue-parskip \\ \\ \noindent
Clearly, any M-Lie inversion is a M\"obius
transformation and generalizes the concept of M\"obius
inversions: if $a$ determines an elliptic linear sphere
complex, the M-Lie inversion becomes a M\"obius inversion,
that is, it provides a reflection in the spheres $s^\pm_a$
as given in (\ref{equ_sphere_compl}). However, if the
corresponding linear sphere complex is hyperbolic,
it can be thought of as an antipodal map.
Note that the M-Lie inversion $\sigma_\mathfrak{p}$ with
respect to the point sphere complex $\mathfrak{p}$ reverses
the orientation of all spheres.
\vglue-parskip \\ \\ \noindent
Let $s_1, s_2 \in \mathbb{P}(\mathcal{L})$ be two spheres that are not in
oriented contact and $\mathfrak{s}_1, \mathfrak{s}_2 \in \mathcal{L}$
fixed homogeneous coordinates, then the Lie inversion with
respect to $\mathfrak{a}:=\mathfrak{s}_1-\mathfrak{s}_2$,
interchanges the spheres $s_1$ and $s_2$. However, note that
different choices for the homogeneous coordinates provide
a 1-parameter family of Lie inversions.
When $s_1$ and $s_2$ are not point spheres,
$\mathfrak{s}_1,\mathfrak{s}_2\not\perp\mathfrak{p}$,
then there is a unique M-Lie inversion, determined by
\begin{equation*}
\mathfrak{a} :
= \lspan{\mathfrak{s}_2, \mathfrak{p}}\mathfrak{s}_1
- \lspan{\mathfrak{s}_1, \mathfrak{p}}\mathfrak{s}_2,
\end{equation*}
that maps $s_1$ to $s_2$ and preserves the point sphere
complex~$\mathfrak{p}$.
\vglue-parskip \\ \\ \noindent
For later reference, we also recall \cite{blaschke,
rib_families} that the formula for the cross-ratio of
four spheres which are pairwise related by a Lie inversion
simplifies: let $s_1, s_2 \in \mathbb{P}(\mathcal{L})$, $\lspan{\mathfrak{s}_1, \mathfrak{s}_2}\neq
0$, be two spheres that are not contained in the linear
sphere complex
$\mathbb{P}(\mathcal{L}\cap\{a\}^\perp)$,
then
\begin{align}\label{equ_formula_cross_ratio}
\text{cr}(s_2, \sigma_a(s_2), \sigma_a(s_1), s_1)
= 2\frac{\lspan{\mathfrak{s}_1,\mathfrak{a}}\lspan{\mathfrak{s}_2,\mathfrak{a}}}
{\phantom{2}\lspan{\mathfrak{a},\mathfrak{a}}\lspan{\mathfrak{s}_1,\mathfrak{s}_2}}.
\end{align}
Using appropriate M-Lie inversions, this formula can also
be used to compute the cross-ratio between four concircular
point spheres.
\subsection{Circles in this framework}
Throughout this text we will consider unoriented circles,
thus objects that belong to M\"obius geometry. Hence, in
the employed Lie geometric framework,
we again fix a point sphere complex $\mathfrak{p}$ to
distinguish a M\"obius subgeometry.
Then circles arise as special Dupin cyclides,
where one family of curvature spheres are point spheres.
A \emph{circle} $\Gamma$ is provided by an orthogonal
splitting of $\mathbb{R}^{4,2}$,
\begin{equation*}
\Gamma = (\gamma, \gamma^\perp) \in G_{(2,1)}^{\mathcal{P}}
\times G_{(2,1)},
\end{equation*}
where $G_{(2,1)}^{\mathcal{P}}$ denotes the set of all
$(2,1)$-planes that are orthogonal to the point sphere
complex~$\mathfrak{p}$. Therefore, all spheres contained
in $\gamma \in G_{(2,1)}^{\mathcal{P}}$ are point spheres,
namely, the points of the circle.
The spheres in $\gamma^\perp$
are in oriented contact with all circle points, hence,
provide a M\"obius geometric pencil of spheres.
If we additionally fix a vector $\mathfrak{q} \in
\mathbb{R}^{4,2}\setminus \{ 0 \}$, $\lspan{\mathfrak{q},
\mathfrak{p}}=0$, to distinguish a space form $\mathcal{Q}$, we
obtain \emph{lines} in this space form as special circles
satisfying $\mathfrak{q} \in \gamma$.
\begin{fact}\label{fact_intersection_spheres}
If two spheres $s_1, s_2 \in \mathbb{P}(\mathcal{L})$ intersect
(in the M\"obius geometry given by $\mathfrak{p}$),
then their circle of intersection is given by
\begin{equation*}
\Gamma = (\gamma, \gamma^\perp)
\in G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)},
\ \text{where }
\gamma^\perp:=\lspann{\mathfrak{s}_1, \mathfrak{s}_2,
\mathfrak{p}}.
\end{equation*}
\end{fact}
\noindent A crucial concept in the study of cyclic systems
will be spheres and circles that intersect orthogonally. In
what follows, we summarize several useful constructions in
this realm and formulate them in the Lie sphere geometric
framework.
Firstly, note that a circle $\Gamma=(\gamma, \gamma^\perp)$
intersects a sphere $s \in \mathbb{P}(\mathcal{L})$ orthogonally if and only if
$s$ intersects all spheres in $\gamma^\perp$ orthogonally. In
fact, a weaker condition is sufficient to ensure orthogonality:
\begin{fact} \label{fact_two_orth}
Let $s_1, s_2 \in \mathbb{P}(\mathcal{L})$ be two spheres that intersect in the
circle $\Gamma = (\gamma, \gamma^\perp)$. Then, $\Gamma$
intersects a sphere $t \in \mathbb{P}(\mathcal{L})$ orthogonally if and only if
the sphere $t$ intersects $s_1$ and $s_2$ orthogonally.
\end{fact}
\begin{proof}
Suppose that the sphere $t \in \mathbb{P}(\mathcal{L})$ intersects $s_1$ and $s_2$
orthogonally, that is,
\begin{equation*}
\lspan{\mathfrak{t}, \mathfrak{s}_i + \lspan{\mathfrak{s}_i,
\mathfrak{p}}\mathfrak{p}}=0 \ \ \text{for } \ i=\{ 1,2 \}.
\end{equation*}
Then, a straightforward computation shows that $t$ intersects
any sphere in
\begin{equation*}
\gamma^\perp
= \lspann{\mathfrak{s}_1, \mathfrak{s}_2, \mathfrak{p}}
\end{equation*}
orthogonally, which proves the claim.
\end{proof}
\noindent Spheres that are orthogonal to a fixed circle
satisfy the following properties, which are also illustrated
in Figure \ref{fig:scheme_cyclic}:
\begin{fact}\label{fact_orth_cont_els}
The spheres that orthogonally intersect a circle $\Gamma$
in a fixed point $m\subset\gamma$
of the circle lie in two
contact elements $m \in f_m, \tilde{f}_m \in \mathcal{Z}$
that coincide up to orientation, that is, $\tilde{f}_m =
\sigma_{\mathfrak{p}}(f_m)$.
Moreover, for any two points $m,n\subset\gamma$
of the circle, the associated contact elements $f_m,
\tilde{f}_m, f_n$ and $\tilde{f}_n$ of orthogonal spheres
pairwise share a common sphere, that is,
\begin{equation*}
f_m \cap f_n \neq \{ 0 \} \ \ \ \text{ or } \ \
f_m \cap \sigma_{\mathfrak{p}}(f_n) \neq \{ 0 \}.
\end{equation*}
\end{fact}
\begin{proof}
Let $\Gamma= (\gamma, \gamma^\perp)$ be a circle,
given as the orthogonal intersection of two spheres
$s_1,s_2\in\mathbb{P}(\mathcal{L})$,
and let $\mathfrak{m}\in\gamma$ represent a point
of this circle.
Without loss of generality, we choose
homogeneous coordinates $\mathfrak{s}_i \in s_i$ such that
$\lspan{\mathfrak{s}_i, \mathfrak{p}}=-\lspan{\mathfrak{s}_1,
\mathfrak{s}_2}=1$ for $i =\{ 1, 2\}$.
Then, as a consequence of Fact \ref{fact_two_orth}, all
spheres that intersect the circle $\Gamma$ in the point $m$
orthogonally lie in the subspace
\begin{equation}\label{equ_two_contact_orth}
\mathcal{O}_m := \lspann{\mathfrak{s}_1 + \mathfrak{p}, \
\mathfrak{s}_2 + \mathfrak{p}, \ \mathfrak{m}}^\perp.
\end{equation}
Since the subspace $\mathcal{O}_m^\perp$ has signature
$(++0)$, we conclude that for any point of the circle, the
sought-after orthogonally intersecting spheres lie in two
contact elements that coincide up to orientation.
Furthermore, since spheres that contain the points represented
by $\mathfrak{m}, \mathfrak{n} \in \gamma$ and that
are orthogonal to $\Gamma$ lie in the subspace
$\lspann{\mathfrak{s}_1 + \mathfrak{p}, \
\mathfrak{s}_2 + \mathfrak{p}, \ \mathfrak{m}, \
\mathfrak{n}}^\perp$, the second claim follows.
\end{proof}
\begin{fact}\label{fact_circles_on_sphere}
Let $\Gamma_1$ and $\Gamma_2$ be two circles and denote by
$\mathfrak{s}_i, \mathfrak{t}_i \in \gamma_i^\perp \cap \mathcal{L}$,
$i=\{1,2\}$, two spheres that determine the corresponding
circles $\Gamma_i$. Then, the two circles lie on a common
sphere if and only if the subspace
\begin{equation*}
\mathcal{S} := \lspann{\mathfrak{s}_1, \mathfrak{s}_2,
\mathfrak{t}_1, \mathfrak{t}_2, \mathfrak{p}}
\subset \mathbb{R}^{4,2}
\end{equation*}
is at most 4-dimensional.
\end{fact}
\begin{proof}
Suppose that the two circles lie on the sphere $k \in
\mathbb{P}(\mathcal{L})$. Then, by Fact \ref{fact_intersection_spheres}, we
conclude that $\mathcal{S}$ is at most 4-dimensional.
To show the converse, we choose, without loss of generality,
two spheres $\mathfrak{s}_1, \mathfrak{t}_1 \in \gamma_1^\perp
\cap \mathcal{L}$ that intersect orthogonally and homogeneous
coordinates such that $-\lspan{\mathfrak{s}_1,
\mathfrak{t}_1}=\lspan{\mathfrak{s}_1,
\mathfrak{p}}=\lspan{\mathfrak{t}_1, \mathfrak{p}}=1$.
If $\mathcal{S}$ is at most 4-dimensional, then there exist
constants $\lambda_i \in \mathbb{R}$ such that
\begin{equation*}\label{equ_dependent}
\lambda_1 \mathfrak{s}_1 + \lambda_2 \mathfrak{t}_1 +
\lambda_3 \mathfrak{s}_2 + \lambda_4 \mathfrak{t}_2 +
\mathfrak{p}=0.
\end{equation*}
Thus, by setting $c^\pm:= (\lambda_1+\lambda_2) \pm
\sqrt{\lambda_1^2+\lambda_2^2}$ and $d^\pm:=1-c^\pm$, we
obtain two spheres (with opposite orientation)
\begin{equation*}
\lambda_1 \mathfrak{s}_1 + \lambda_2 \mathfrak{t}_1
+ c^\pm \mathfrak{p}
= -\lambda_3 \mathfrak{s}_2 - \lambda_4 \mathfrak{t}_2
- d^\pm\mathfrak{p}
\end{equation*}
that lie in $\gamma_1^\perp \cap \gamma_2^\perp$ and,
therefore, contain the two circles $\Gamma_1$ and
$\Gamma_2$. This proves the claim.
\end{proof}
\begin{fact}\label{fact_orth_circle}
Given a sphere $r \in \mathbb{P}(\mathcal{L})$ and two point spheres $p_1,
p_2 \in \mathbb{P}(\mathcal{P})$ lying on it, the circle $\Gamma$ that
intersects the sphere $r$ orthogonally and passes through
the points $p_1$ and $p_2$ is described by the $(2,1)$-plane
\begin{equation}\label{equ_orth_circle}
\gamma :
= \lspann{\mathfrak{p}_1, \ \mathfrak{p}_2,
\ \mathfrak{r}+\lspan{\mathfrak{r},
\mathfrak{p}}\mathfrak{p}} \in G^{\mathcal{P}}_{(2,1)}.
\end{equation}
\end{fact}
\begin{proof}
Firstly, note that $\gamma$ is a $(2,1)$-plane orthogonal
to the point sphere complex $\mathfrak{p}$. Thus, $\gamma$
indeed describes a circle by $\Gamma := (\gamma, \gamma^\perp)
\in G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)}$. Furthermore,
suppose that $\mathfrak{s} \in \gamma^\perp \cap \mathcal{L}$
and consider the corresponding linear sphere complex with
orthogonal intersection angle, that is,
\begin{equation*}
\mathfrak{a} :
= \mathfrak{s} + \lspan{\mathfrak{s},
\mathfrak{p}}\mathfrak{p}.
\end{equation*}
Then, because of $\lspan{\mathfrak{s}, \mathfrak{r}
+ \lspan{\mathfrak{r}, \mathfrak{p}}\mathfrak{p}}=0$,
we conclude that
\begin{equation*}
\lspan{\mathfrak{r}, \mathfrak{a}}=0.
\end{equation*}
Since this holds for any sphere in $\gamma^\perp \cap \mathcal{L}$,
the constructed circle $\Gamma$ intersects the sphere $r$
orthogonally in the points $p_1$ and $p_2$.
\end{proof}
\noindent As a consequence we obtain:
\begin{fact}
Given a sphere $s \in \mathbb{P}(\mathcal{L})$ and two circles $\Gamma_1$ and
$\Gamma_2$ that intersect the sphere orthogonally in the
points $p_1^1, p_2^1$ and $p_1^2, p_2^2$.
Then the circles lie on a common sphere if and only if
the four points are concircular, that is,
any homogeneous coordinate vectors $\mathfrak{p}_i^j$
are linearly dependent.
\end{fact}
\begin{proof}
The sought-after sphere has to lie in $\gamma_1^\perp
\oplus \gamma_2^\perp$, where $\gamma_i$ is given by
(\ref{equ_orth_circle}). Thus, the subspace $\gamma_1 \oplus
\gamma_2$ has to be a 4-dimensional space.
\end{proof}
\subsection{Ribaucour transformations between two circles}
Recall \cite{rib_coords, discrete_channel} that any two
cospherical circles are related by a Ribaucour transformation,
that is, they envelop a common circle congruence. For two
unparametrized circles on a sphere, there are at most two
Ribaucour transformations that induce different Ribaucour
correspondences between the point spheres of the two circles.
Those point-to-point mappings can be described by two M-Lie
inversions:
\begin{lem}\label{lem_rib_trafo_lie_inversion}
Let $\Gamma_1$ and $\Gamma_2$ be two circles that are not
tangent to each other and lie on the sphere $k \in \mathbb{P}(\mathcal{L})$. Then
the two Ribaucour correspondences between $\Gamma_1$ and
$\Gamma_2$ are induced by the two M-Lie inversions $\sigma_a$
and $\sigma_{\tilde{a}}$ determined by the linear sphere
complexes
\begin{equation*}
\mathfrak{a} :
= \lspan{\mathfrak{s}_2, \mathfrak{p}} \mathfrak{s}_1
- \lspan{\mathfrak{s}_1, \mathfrak{p}} \mathfrak{s}_2
\ \ \ \text{and } \ \
\tilde{\mathfrak{a}} :
= \lspan{\sigma_\mathfrak{p}(\mathfrak{s}_2), \mathfrak{p}}
\mathfrak{s}_1 - \lspan{\mathfrak{s}_1,
\mathfrak{p}}\sigma_\mathfrak{p}(\mathfrak{s}_2),
\end{equation*}
where $\mathfrak{s}_i \in \gamma_i^\perp$, $i= \{ 1,2 \}$,
are two spheres that intersect $k$ orthogonally.
\end{lem}
\noindent We remark that, for two touching circles
$\Gamma_1$ and $\Gamma_2$ on a common sphere $k \in
\mathbb{P}(\mathcal{L})$, there exists only one Ribaucour correspondence:
in this case, either $\lspan{\mathfrak{s}_1,
\mathfrak{s}_2}=0$ or $\lspan{\mathfrak{s}_1,
\sigma_\mathfrak{p}(\mathfrak{s}_2)}=0$ and, therefore,
one of the M-Lie inversions described in Lemma
\ref{lem_rib_trafo_lie_inversion} degenerates. Thus,
between two touching circles we obtain a unique Ribaucour
correspondence.
\begin{proof}
Without loss of generality, we assume that
\begin{equation*}
\lspan{\mathfrak{s}_1, \mathfrak{p}}=\lspan{\mathfrak{s}_2,
\mathfrak{p}}=\lspan{\mathfrak{k}, \mathfrak{p}}=1.
\end{equation*}
Then, since $s_1$ and $s_2$ intersect the sphere $k$
orthogonally, from (\ref{equ_intersection_angle}) we
conclude that
\begin{equation*}
\lspan{\mathfrak{s}_1, \mathfrak{k}}=\lspan{\mathfrak{s}_2,
\mathfrak{k}}=-1.
\end{equation*}
Hence, the Lie inversions $\sigma_a$ and $\sigma_{\tilde{a}}$
preserve the sphere $k$, as well as the point sphere
complex~$\mathfrak{p}$. Furthermore, they map $s_1$ to
$s_2$ and $\lspann{\sigma_\mathfrak{p}(\mathfrak{s}_2)}$,
respectively. Therefore, they are M-Lie inversions and
interchange point spheres of the circles $\Gamma_1$ and
$\Gamma_2$ with each other.
For any induced pair of point spheres $p_1$ and $p_2$,
there exists a sphere $t \in \mathbb{P}(\mathcal{L})$ that contains these points
and is in oriented contact with $s_1$ and $s_2$. Then, $t$
is preserved by those M-Lie inversions and intersects $k$
orthogonally.
Moreover, the $(2,1)$-plane $\lspann{\mathfrak{t},
\mathfrak{k}, \mathfrak{p}}$ determines a circle that is
tangent to the circles $\Gamma_1$ and $\Gamma_2$ at the
points $p_1$ and $p_2$. This proves the claim.
\end{proof}
\noindent The generic ambiguity of the Ribaucour
correspondence between two cospherical circles is eliminated
by the choice of one admissible point sphere pair:
\begin{cor}\label{cor_choice_ribtrafo}
Let $\Gamma_1$ and $\Gamma_2$ be two cospherical circles
and let $\mathfrak{p}_i \in \gamma_i \cap \mathcal{L}$, $i=\{1,2\}$,
represent a pair of points that is contained in a circle tangent
to $\Gamma_1$ and $\Gamma_2$. Then, there exists a unique
Ribaucour transformation between the circles that extends
the correspondence between the points $p_1$ and $p_2$.
\end{cor}
\begin{proof}
Let $\Gamma_1$ and $\Gamma_2$ be two circles lying on the
sphere $k \in \mathbb{P}(\mathcal{L})$. Moreover, we denote by $\mathfrak{s}_1
\in \gamma_1^\perp \cap \mathcal{L}$ a sphere that is orthogonal
to $k$ and define the sphere
\begin{equation*}
\mathfrak{s}_{12} :
= \lspan{\mathfrak{p}_1, \mathfrak{p}_2} \mathfrak{s}_1
- \lspan{\mathfrak{s}_1, \mathfrak{p}_2}\mathfrak{p}_1.
\end{equation*}
The sphere $s_{12}$ contains the point pair $(p_1, p_2)$
and lies in the contact element $\lspann{s_1, p_1}$. Then
the sphere $\mathfrak{s}_2 \in \gamma_2^\perp \cap
\lspann{\mathfrak{s}_{12}, \mathfrak{p}_2}$ provides the
construction for the sought-after Ribaucour correspondence:
the M-Lie inversion determined by the linear sphere complex
\begin{equation*}
\mathfrak{a} :
= \lspan{\mathfrak{s}_2, \mathfrak{p}}\mathfrak{s}_1
- \lspan{\mathfrak{s}_1, \mathfrak{p}} \mathfrak{s}_2
\end{equation*}
induces the Ribaucour correspondence that maps $p_1$
onto $p_2$.
\end{proof}
\noindent Conversely, if two circles $\Gamma_1$ and $\Gamma_2$
are related by an M-Lie inversion~$\sigma$, then $\sigma$
induces a smooth Ribaucour transformation between the two
circles: let
\begin{equation*}
t \mapsto (\mathfrak{c}_1(t), \ \sigma_a(\mathfrak{c}_1(t))
\end{equation*}
be a simultaneous parametrization of the two circles, where
$\mathfrak{c}_1(t) \in \gamma_1 \cap \mathcal{L}$. For any sphere
$\mathfrak{s}_1 \in \gamma_1^\perp$, the map
\begin{equation*}
t \mapsto \mathfrak{s}(t) :
= \lspann{\mathfrak{s}_1, \mathfrak{c}_1(t)}
\cap \lspann{\sigma_a(\mathfrak{s}_1),
\sigma_a(\mathfrak{c}_1(t)} \cap \mathcal{L}
\end{equation*}
defines a 1-parameter family of spheres that is in
oriented contact with both circles. Hence, by \cite[Thm
2.15]{discrete_channel}, we conclude that $t \mapsto s(t)$
gives rise to a Dupin cyclide with curvature circles
$\Gamma_1$ and $\Gamma_2$, which proves the claim.
\section{Discrete cyclic systems}\label{section_cyclic_systems}
\noindent In this section we develop the main notions of
this paper from two different points of view: firstly, we
consider discrete cyclic systems, that is, discrete orthogonal
coordinate system that have two families of discrete channel
surfaces as coordinate surfaces. Secondly, we investigate
under which conditions a discrete circle congruence is
cyclic, thus, is the underlying circle congruence of a
discrete cyclic system.
\vglue-parskip \\ \\ \noindent
\textbf{Notation.}
Throughout the text we will adopt the following notation
conventions for domains of discrete maps:
we will consider a simply connected subset of the lattice
$\mathbb{Z}^3$, organized into
vertices $\bar{\mathcal{V}}$,
edges $\bar{\mathcal{E}}$, and
faces $\bar{\mathcal{F}}$;
for a $2$-dimensional ``slice'', modeled in $\mathbb{Z}^2$,
we will use
$\mathcal{V}$,
$\mathcal{E}$, and
$\mathcal{F}$,
for the sets of vertices, edges, and faces, respectively.
Thus our domains will be (rather trivial) quadrilateral
or cubical cell complexes,
where only cells of the dimensions $0$, $1$, and $2$
will play a role.
Furthermore, $I\subset\mathbb{Z}$ will denote
(the vertex set of) a discrete (closed) interval.
The domains under consideration are assumed to be sufficiently
large, that is, in each coordinate direction there exist at
least three vertices.
\subsection{Definition and basic properties}
In the spirit of \cite{org_principles, ddg_book}, we consider
discrete triply orthogonal systems as principal contact
element nets:
\begin{defi}\label{def_disc_tops}
A \emph{discrete triply orthogonal system} is a map
\begin{equation*}
f:\bar{\mathcal{V}} \rightarrow \mathcal{Z}\times \mathcal{Z}
\times \mathcal{Z}, \ i \mapsto f_i= (f_i^1,f_i^2,f_i^3)
\end{equation*}
such that
\begin{itemize}
\item[(i)] at each vertex the point spheres
of the contact elements coincide,
\begin{equation*}
f_i^1 \cap f_i^2 \cap f_i^3 =: f_i^p \in \mathbb{P}(\mathcal{P}),
\end{equation*}
\item[(ii)] at each vertex the spheres of different
contact elements intersect orthogonally and
\item[(iii)] any two adjacent contact elements of
the same family intersect,
\begin{equation*}
f_i^\mu \cap f_j^\mu =: s_{ij}^\mu \in \mathbb{P}(\mathcal{L}), \
\mu =\{ 1,2,3 \}.
\end{equation*}
\end{itemize}
The map $f^p: \bar{\mathcal{V}} \rightarrow \mathbb{P}(\mathcal{P})$ will be called the
\emph{point sphere map} of $f$ and provides a 3-dimensional
circular net.
\end{defi}
\noindent We remark that a map $f:\bar{\mathcal{V}} \rightarrow
\mathcal{Z}\times \mathcal{Z} \times \mathcal{Z}$ satisfies
conditions (i) and (ii) if and only if,
at any vertex $i\in\bar{\mathcal{V}}$,
any two spheres $s_i^\lambda$ and $s_i^\mu$ of any two
different contact elements $f_i^\lambda$ and $f_i^\mu$ fulfill
\begin{equation*}
\lspan{\mathfrak{s}_i^\lambda, \mathfrak{s}_i^\mu
+ \lspan{\mathfrak{p}, \mathfrak{s}_i^\mu}\mathfrak{p}}=0.
\end{equation*}
Note that this condition is symmetric
in $\lambda,\mu\in\{1,2,3\}$, $\lambda\neq\mu$.
\vglue-parskip \\ \\ \noindent
Any discrete triply orthogonal system consists of three
(Lam\'e) families of \emph{coordinate surfaces},
\begin{align*}
\lambda &\mapsto \{\bar{\mathcal{V}} \ni (\lambda, x_2, x_3)
\mapsto f_{(\lambda, x_2, x_3)}^1 \in \mathcal{Z} \}, \\
\lambda &\mapsto \{\bar{\mathcal{V}} \ni (x_1, \lambda, x_3)
\mapsto f_{(x_1, \lambda,x_3)}^2 \in \mathcal{Z} \}, \\
\lambda &\mapsto \{\bar{\mathcal{V}} \ni (x_1, x_2, \lambda)
\mapsto f_{(x_1, x_2,\lambda)}^3 \in \mathcal{Z} \};
\end{align*}
those are discrete Legendre maps and represent discrete
surfaces that intersect orthogonally along discrete
curvature lines. We call those discrete lines of intersection
\emph{$x_i$-trajectories} of the system.
\vglue-parskip \\ \\ \noindent
Due to condition (iii), any two adjacent coordinate surfaces
of the same family are related by a discrete Ribaucour
transformation (cf \cite{org_principles, ddg_book,
rib_families}).
In particular, for any edge of a triply orthogonal system,
we obtain three distinguished spheres $(s_{ij}^\mu)_\mu$
that pairwise intersect orthogonally:
two of these spheres are curvature spheres of coordinate
surfaces and the third sphere is a Ribaucour sphere enveloped
by the Ribaucour pair of adjacent coordinate surfaces.
\vglue-parskip \\ \\ \noindent
Imitating the smooth notion of a cyclic system
(cf \cite{coolidge, darboux_ortho, rib_cyclic}),
we introduce the following notion:
\begin{defi}\label{def_cyclic_system}
A \emph{discrete cyclic system} is a discrete triply
orthogonal system such that two families of coordinate
surfaces are discrete channel surfaces that intersect along
their circular curvature lines.
\end{defi}
\noindent We emphasize that the notion of a discrete
triply orthogonal system as well as cyclicity of it are
only invariant under M\"obius transformations, hence, those
notions depend on the choice of a point sphere complex.
\vglue-parskip \\ \\ \noindent
Recall that a discrete channel surface in the sense of
\cite{discrete_channel} is a discrete Legendre map that
admits a constant Lie cyclide for each coordinate ribbon
of one coordinate direction. Hence, the curvature spheres
of the discrete channel surface along each coordinate ribbon
are curvature spheres of this constant Lie cyclide.
As a consequence, a discrete channel surface has
one family of circular curvature lines and one family of
curvature spheres is constant along each of them. Moreover,
any two adjacent circular curvature lines are curvature
lines of the corresponding (constant) Lie cyclide.
Thus, since one family of (orthogonal) trajectories of
a discrete cyclic system provides the circular curvature
lines of the discrete channel surfaces, we conclude:
\begin{cor}
One family of trajectories of a discrete cyclic system are
circular.
\end{cor}
\noindent Moreover, as circular curvature lines of a
discrete channel surface, two adjacent trajectories are
related by a discrete Ribaucour transformation that is induced
by a smooth Ribaucour transformation (cf \cite[Prop
2.10]{discrete_channel}). Note that this correspondence
is given by an M-Lie inversion as described in Lemma
\ref{lem_rib_trafo_lie_inversion}.
Hence:
\begin{cor}
A discrete cyclic system provides a discrete 2-dimensional
congruence of circles where any two adjacent circles are
cospherical.
\end{cor}
\noindent Furthermore, for any discrete cyclic system we
obtain two distinguished 2-parameter families of Dupin cyclides,
namely, those that provide constant Lie cyclides for the
discrete channel surfaces.
Any circle of the above congruence is then a curvature line on
four Dupin cyclide patches, the Lie cyclides of the two discrete
channel surfaces that intersect along this circle. Since their
contact elements along the circle intersect orthogonally,
the two constant curvature spheres are mutually quer-spheres
of the smooth Lie cyclide patches.
\subsection{Cyclic circle congruences}\label{subsect_cyclic_congruence}
In this subsection, we investigate whether a given discrete
2-dimensional circle congruence admits orthogonal surfaces
and, subsequently, gives rise to a discrete cyclic system.
Thus, we consider a circle congruence
on a 2-dimensional domain,
\begin{equation*}
\Gamma = (\gamma, \gamma^\perp):
\mathcal{V} \rightarrow G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)}.
\end{equation*}
\begin{defi}
A discrete Legendre map $f: \mathcal{V} \rightarrow \mathcal{Z}$
is said to be \emph{orthogonal} to $\Gamma$ if, for each
vertex $i \in \mathcal{V}$,
\begin{itemize}
\item[(i)] the point sphere $f_i^\mathfrak{p}$ lies
on the circle $\Gamma_i$ and
\item[(ii)] any other sphere in the contact element
$f_i$ intersects the circle $\Gamma_i$ orthogonally.
\end{itemize}
\end{defi}
\begin{figure}[t]
\hspace*{-3cm}\begin{minipage}{6cm}
\begin{overpic}[scale=.2]{idea_orth_contact_el.pdf}
\put(60,85){\color{gray}$f^3_m$}
\put(42.5,80){\color{gray}$f^3_n$}
\put(76,10){\color{gray}$f^3_o$}
\put(82,70){\color{UniBlue}{$\gamma_i$}}
\end{overpic}
\end{minipage}
\caption{ A circular orthogonal trajectory $\gamma_i$ of
a discrete cyclic system with three orthogonal surfaces
$f^3_m, f^3_n$ and $f^3_o$ that pairwise form (up to
orientation) a discrete Ribaucour pair. The cyan spheres
provide the spheres enveloped by two orthogonal surfaces.}
\label{fig:scheme_cyclic}
\end{figure}
\noindent Algebraically, properties (i) and (ii) amount to
the following condition:
\begin{lem}\label{lem_orth_condition}
A discrete Legendre map $f$ is orthogonal to a circle
congruence $\Gamma$ if and only if any element $s_i \in f_i$
and $\mathfrak{c}_i \in \gamma_i^\perp \cap \mathcal{L}$
satisfy
\begin{equation}\label{equ_orth_legendre}
\lspan{\mathfrak{s}_i, \mathfrak{c}_i
+ \lspan{\mathfrak{c}_i, \mathfrak{p}}\mathfrak{p}}=0 \ \
\text{for any vertex } i \in \mathcal{V}.
\end{equation}
\end{lem}
\begin{proof}
Suppose that $s_i \in f_i \cap \mathbb{P}(\mathcal{P})$ is a point
sphere, then equation (\ref{equ_orth_legendre}) becomes
$\lspan{\mathfrak{s}_i, \mathfrak{c}_i}=0$. This holds if
and only if the point sphere $s_i$ lies on all spheres in
$\gamma_i^\perp$ and thus is a point on the circle.
For any other sphere $s_i \in f_i$, $\lspan{\mathfrak{s}_i,
\mathfrak{p}}\neq 0$, the claim follows from
(\ref{equ_orth_complex}).
\end{proof}
\noindent The circle congruences that we are particularly
interested in stem from discrete cyclic system:
\begin{defi}\label{def_cyclic_congruence}
A discrete circle congruence will be called \emph{cyclic} if
it admits a discrete family $I \ni \lambda \mapsto f^\lambda$
of orthogonal discrete Legendre maps that give rise to a
discrete cyclic system.
\end{defi}
\noindent In what follows, we will only consider
\emph{non-degenerate} circle congruences, that is, four
circles of any elementary quadrilateral do not share a
1-parameter family of orthogonal spheres. By this assumption
we guarantee that not all orthogonal surfaces have totally
umbilic faces.
\begin{thm}\label{thm_flat_connection}
A non-degenerate circle congruence $\Gamma=(\gamma,
\gamma^\perp): \mathcal{V} \rightarrow G_{(2,1)}^{\mathcal{P}}
\times G_{(2,1)}$ is cyclic if and only if it admits a flat
connection on the trivial bundle $\mathcal{V} \times \mathbb{R}^{4,2}$
comprised of Lie inversions that map adjacent circles
onto each other, that is, there exists a 2-parameter family
of linear sphere complexes $a: \mathcal{E} \rightarrow
\mathbb{P}(\mathbb{R}^{4,2})$ such that the induced Lie
inversions $\{\sigma_{e}\}_{e\in \mathcal{E}}$ satisfy
\begin{equation*}
\sigma_{ij}(\gamma_j) = \gamma_i \ \ \text{and} \ \
\sigma_{ij} \circ \sigma_{jk} = \sigma_{il} \circ \sigma_{lk}
\end{equation*}
for any quadrilateral $(ijkl)$.
\end{thm}
\begin{rem} For degenerate circle congruences that admit a
flat connection of this kind the result can indeed fail:
consider, for example, a discrete circle congruence that
consists of parallel lines such that the point spheres
obtained as intersection of the lines with a fixed orthogonal
plane do not form a 2-dimensional circular net. Then, this
circle congruence does not give rise to a discrete cyclic
system, because there are no orthogonal surfaces that are
discrete Legendre maps. However, the reflections in the
bisecting planes of two adjacent parallel lines provide a flat
connection in the sense of Theorem \ref{thm_flat_connection}.
\end{rem}
\begin{proof}
Suppose that the circle congruence $\Gamma: \mathcal{V} \rightarrow
G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)}$ is cyclic. Then,
by definition, there exists an associated discrete cyclic
system $f=(f^1,f^2,f^3)$ on $\mathcal{V} \times I$, where $f^1$
and $f^2$ denote the two coordinate surface families of
discrete channel surfaces.
These discrete channel surfaces induce a canonical
M-Lie inversion between two adjacent circles $\Gamma_i$
and $\Gamma_j$ of $\Gamma$: namely, the M-Lie inversion
that interchanges the curvature circles of the constant Lie
cyclide provided by one of the discrete channel surfaces,
$f^1$ or $f^2$.
We denote these M-Lie inversions by $\sigma_{ij}$ and obtain:
$\sigma_{ij}(\gamma_j)=\gamma_i$.
Moreover, by construction, these M-Lie inversions map
adjacent contact elements (frames) $f_i$ and $f_j$
of the discrete cyclic system
onto each other. Since the orthogonal surfaces $f^3$ are
discrete Legendre maps, the connection provided by $\sigma$
is flat on $\gamma$. Furthermore, since, for any $i \in \mathcal{V}$
and $m \in I$, we have $f_{i,m}^\mu \cap \gamma_i^\perp =:
s_i^\mu \in \mathbb{P}(\mathcal{L})$, $\mu=1,2$, it follows that
\begin{equation*}
(\sigma_{ij} \circ \sigma_{jk} \circ \sigma_{kl}
\circ \sigma_{li})(s_i^\mu) = s_i^\mu.
\end{equation*}
Together with the fact that the M-Lie inversions $\sigma$
preserve the point sphere complex $\mathfrak{p}$, we conclude
that the induced connection is also flat on $\gamma^\perp$.
\vglue-parskip \\ \\ \noindent
Conversely, assume that a circle congruence $\Gamma$ admits
a flat connection provided by Lie inversions $\sigma_{ij}$
that map adjacent circles $\gamma_i$ and $\gamma_j$
onto each other, that is, any point sphere in $\gamma_i$
is mapped to a point sphere in $\gamma_j$. Thus the Lie
inversion $\sigma_{ij}$ preserves the point sphere complex
$\mathfrak{p}$ and is an M-Lie inversion.
To prove that $\Gamma$ is indeed cyclic, we will construct
a discrete family $I \ni \lambda \mapsto f^{3,\lambda}$
of orthogonal surfaces that is part of a discrete cyclic
system. To do so, we fix point spheres $I \ni \lambda
\mapsto p^\lambda_0$ along an initial circle $\Gamma_{i_0}$
of the circle congruence. Furthermore, according to Fact
\ref{fact_orth_cont_els}, we choose contact elements
$\lambda \mapsto f^{3,\lambda}_{i_0}$ that consist of
spheres orthogonal to $\Gamma_{i_0}$ such that any two
adjacent contact elements share a common sphere
(cf Figure \ref{fig:scheme_cyclic}).
Then transport of these contact elements $f_{i_0}^{3,\lambda}$
along edges $ij\in\mathcal{E}$ by the M-Lie inversions
$\sigma_{ij}$
consecutively defines a discrete family of orthogonal surfaces
$\lambda \mapsto f^{3,\lambda}$ by
\begin{equation*}
f_j^{3,\lambda} := \sigma_{ji}(f_i^{3,\lambda}).
\end{equation*}
Due to the flatness of the connection, this construction
is well-defined. Moreover, since any M-Lie inversion
$\sigma_{ij}$ fixes a (curvature) sphere $s_{ij}^\lambda
\in f_i^{3,\lambda} \cap f_j^{3,\lambda}$ and the circle
congruence is non-degenerate, we indeed obtain discrete
Legendre maps $f^{3,\lambda}$.
\vglue-parskip \\ \\ \noindent
To complete the proof, it remains to construct two families
$\lambda_1 \mapsto f^{1,\lambda_1}$ and $\lambda_2 \mapsto
f^{2,\lambda_2}$ of discrete channel surfaces that supplement
the family $f^{3,\lambda}$ of orthogonal surfaces. To equip
the point sphere maps with suitable contact elements, we
choose two spheres $\mathfrak{r}_{i_0}^1, \mathfrak{r}_{i_0}^2
\in \gamma_{i_0}^\perp \cap \mathcal{L}$ that intersect
each other orthogonally and define contact elements along
the circle $\Gamma_{i_0}$ by
\begin{equation*}
f^{\mu, i_0}_{\lambda} :
= \lspann{\mathfrak{r}_{i_0}^\mu, p_{0}^\lambda} \ \
\text{for } \ \mu \in \{ 1,2\}.
\end{equation*}
Then transport of these two contact elements by means of
the M-Lie inversions $\sigma$ along edges provides two
families of discrete channel surfaces,
with the circles of the congruence as curvature lines.
Thus, in summary, the constructed map $f:=(f^1, f^2, f^3)$
provides a discrete cyclic system with underlying circle
congruence $\Gamma$.
\end{proof}
\noindent Hence, to any discrete cyclic system we associate a
unique 2-parameter family of M-Lie inversions~$\sigma_{ij}$,
defined on edges of the associated circle congruence,
that simultaneously map adjacent point spheres of all
orthogonal surfaces onto each other. Note that these M-Lie
inversions are symmetric, that is, $\sigma_{ij}=\sigma_{ji}$.
\vglue-parskip \\ \\ \noindent
These M-Lie inversions induce a Ribaucour correspondence
between any two adjacent circles, which are therefore
cospherical. Furthermore, they reveal a property well-known
from smooth cyclic systems:
\begin{cor}\label{cor_const_cross}
The cross-ratio of the point spheres of any four orthogonal
surfaces of a discrete cyclic system is constant
along the orthogonal surfaces.
\end{cor}
\noindent Moreover, by using Fact \ref{fact_orth_cont_els},
we observe another relation between any two orthogonal
surfaces of a discrete cyclic system (see also Figure
\ref{fig:scheme_cyclic}):
\begin{cor}\label{cor_adjacent_rib}
Up to a possible change of orientation, any two orthogonal
surfaces of a discrete cyclic system are related by a discrete
Ribaucour transformation.
\end{cor}
\noindent However we note that, in contrast to the smooth
theory, the reconstruction of a discrete cyclic system
from a cyclic circle congruence is not unique. There are
several ambiguities: firstly, a discrete cyclic circle
congruence can admit various flat connections in the sense
of Theorem \ref{thm_flat_connection}. This non-uniqueness
of the connection stems from the generic existence of two
Ribaucour correspondences between two cospherical circles
(cf Lemma \ref{lem_rib_trafo_lie_inversion}). An example
of different flat connections associated to a face of a
discrete cyclic circle congruence is illustrated in Figure
\ref{fig:ambiguity}.
\begin{figure}[t]
\hspace{-1.5cm}\begin{minipage}{7.5cm}
\includegraphics[scale=0.238]{ambiguity_1.eps}
\end{minipage}
\vspace*{-0.5cm} \begin{minipage}{6cm}
\includegraphics[scale=0.25]{ambiguity_2.eps}
\end{minipage}
\caption{Contrary to the smooth case, the family of
orthogonal surfaces to a discrete cyclic circle congruence
is not necessarily unique.}
\label{fig:ambiguity}
\end{figure}
Hence a discrete circle congruence does generically not have
a unique family of orthogonal surfaces,
even after an initial circle is equipped with a point sampling.
\vglue-parskip \\ \\ \noindent
Secondly, once a discrete family of orthogonal surfaces is
established, we are left with a $1$-parameter choice for
the other two families of coordinate surfaces, namely the
discrete channel surfaces. Although the circular curvature
lines are already fixed
we have the choice of a pair of orthogonally intersecting
curvature spheres for the discrete channel surfaces
at an initial circle
(see the choice of the spheres $r_{i_0}^1$ and $r_{i_0}^2$
in the proof of Theorem \ref{thm_flat_connection}).
\vglue-parskip \\ \\ \noindent
\noindent Recall \cite{MR0115134, cyclic_guichard_eth,
rib_cyclic} that, in the smooth case, the existence of three
orthogonal surfaces of a circle congruence already implies
that the congruence is cyclic.
We obtain an analogous statement in the discrete case.
We say that three orthogonal discrete Legendre maps are
\emph{generic} if, for any edge of the circle congruence,
the three curvature spheres span a $(2,1)$-plane of
$\mathbb{R}^{4,2}$.
\begin{thm}\label{thm_three_cyclic}
A discrete circle congruence that admits three generic
orthogonal discrete Legendre maps is cyclic.
\end{thm}
\begin{proof}
Let $\Gamma:\mathcal{V} \rightarrow G_{(2,1)}^{\mathcal{P}} \times
G_{(2,1)}$ be a circle congruence that admits at least
three generic orthogonal discrete Legendre maps $g^\mu$,
$\mu \in \{1,2,3 \}$. To prove that $\Gamma$ is cyclic,
we will construct a flat connection as described in Theorem
\ref{thm_flat_connection}.
Firstly, consider two adjacent circles $\Gamma_i$ and
$\Gamma_j$ of the congruence $\Gamma$ and denote by
\begin{equation*}
\mathfrak{s}_i, \mathfrak{t}_i \in \gamma_i^\perp \cap \mathcal{L}
\end{equation*}
two spheres that intersect in the circle $\Gamma_i$,
and similarly for $\Gamma_j$.
Since the curvature spheres $s_{ij}^\mu$ of the orthogonal
surfaces that belong to the edge $(ij)$ intersect all spheres
in $\gamma_i^\perp$ and $\gamma_j^\perp$ orthogonally
we obtain
\begin{equation}\label{equ_space}
s_{ij}^\mu \in \lspann{\mathfrak{s}_1 + \lspan{\mathfrak{s}_1,
\mathfrak{p}}\mathfrak{p}, \
\mathfrak{s}_2 + \lspan{\mathfrak{s}_2,
\mathfrak{p}}\mathfrak{p}, \
\mathfrak{t}_1 + \lspan{\mathfrak{t}_1,
\mathfrak{p}}\mathfrak{p}, \
\mathfrak{t}_2 + \lspan{\mathfrak{t}_2,
\mathfrak{p}}\mathfrak{p}}^\perp.
\end{equation}
Hence we deduce that this span is at most 3-dimensional,
which implies that the space
\begin{equation*}
\lspann{\mathfrak{s}_1, \mathfrak{s}_2, \mathfrak{t}_1,
\mathfrak{t}_2, \mathfrak{p}} \subset \mathbb{R}^{4,2}
\end{equation*}
is at most 4-dimensional.
Therefore, due to Fact \ref{fact_circles_on_sphere},
the two circles $\Gamma_1$ and $\Gamma_2$ lie on a common
sphere.
This sphere is unique up to orientation.
As a consequence, using Corollary \ref{cor_choice_ribtrafo},
there exists a unique Ribaucour correspondence between any
two adjacent circles that extends the correspondence
induced by the point sphere maps of the orthogonal surfaces
$\{g^\mu\}_\mu$. By Lemma \ref{lem_rib_trafo_lie_inversion},
this correspondence is described by an M-Lie inversion
$\sigma_{ij}$.
Since $\{g^\mu\}_\mu$ are discrete Legendre maps, these M-Lie
inversions provide a flat connection for $\Gamma$.
Consequently, the circle congruence $\Gamma$ is indeed cyclic.
\end{proof}
To illustrate the situation we investigate a standard
example for cyclic circle congruences, namely, those that
stem from a parallel family of surfaces in a space form.
To start with we discuss discrete parallel surfaces in a
flat ambient space form as described in \cite{MR2657431}:
\begin{ex}\label{ex_parallel_flat}
Fix a point sphere complex $\mathfrak{p}$ and
a flat space form by choosing a lightlike space form vector $q
\in \mathbb{P}(\mathcal{L})$, $\lspan{\mathfrak{p}, \mathfrak{q}}=0$. Let $f:\mathcal{V}
\rightarrow \mathcal{Z}$ be a discrete Legendre map with
space form projection
\begin{equation*}
(\mathfrak{f}^\mathfrak{p}, \mathfrak{t}):
\mathcal{V} \rightarrow \mathcal{Q} \times \mathcal{H},
\end{equation*}
where $\mathfrak{f}^\mathfrak{p}$ and $\mathfrak{t}$
denote the point sphere map and tangent plane congruence
in $f$, respectively.
Moreover, we denote the family of parallel discrete
Legendre maps of $f$ by $I \ni \lambda \rightarrow
(\mathfrak{f}^{\mathfrak{p},\lambda}, \mathfrak{t^\lambda})$.
At each vertex, the point spheres of the parallel family
lie on the line orthogonal to the tangent plane. Using Fact
\ref{fact_orth_circle}, this line is described by
\begin{equation*}
\mathfrak{f}_i^{\mathfrak{p}, \lambda}
\in \lspann{\mathfrak{f}_i^\mathfrak{p}, \mathfrak{q},
\mathfrak{t}_i + \lspan{\mathfrak{t}_i,
\mathfrak{p}}\mathfrak{p}} =: \gamma_i.
\end{equation*}
Moreover, note that the point spheres
$\mathfrak{f}_i^{\mathfrak{p}, \lambda}$ and
$\mathfrak{f}_j^{\mathfrak{p}, \lambda}$ of adjacent vertices,
as well as adjacent tangent planes, are related by the
reflection in the corresponding bisecting hyperplane.
Hence the sphere complexes
\begin{equation*}
a:\mathcal{E} \rightarrow \mathbb{P}(\mathcal{P}), \ \mathfrak{a}_{ij} :
= \mathfrak{t}_i - \mathfrak{t}_j
\end{equation*}
provide a flat connection for the discrete line congruence
$\Gamma=(\gamma, \gamma^\perp)$, which is therefore cyclic.
The two further coordinate surface families of a discrete
cyclic system associated to this line congruence consist of
developable discrete channel surfaces. They are determined
by two suitably prescribed curvature spheres at one initial
vertex of the discrete line congruence, that is, by the choice
of two orthogonal planes that intersect in the line of the
congruence at this initial vertex.
\end{ex}
\noindent To conclude this section, we emphasize
that our analysis also leads to a notion of
\emph{semi-discrete cyclic systems}, where the orthogonal
surfaces are discrete Legendre maps and the other two
coordinate surface families consist of semi-discrete
channel surfaces --- as has already become evident
from Example \ref{ex_parallel_flat}.
In particular, any discrete cyclic circle congruence gives
rise to semi-discrete cyclic systems: once a flat connection
in the sense of Theorem \ref{thm_flat_connection}
is established, we choose
a (smooth) 1-parameter family of orthogonal contact elements
along an initial circle, as well as
two suitable curvature spheres for the semi-discrete channel
surfaces that orthogonally intersect in this initial circle.
The transport of this initial principal frame by means of
the M-Lie inversions of the connection then gives
rise to the sought-after semi-discrete cyclic system.
\section{Discrete cyclic systems with special orthogonal surfaces}
\label{sect_from_rib}
\noindent
Historically, smooth cyclic systems were closely related to
the Ribaucour transformation of surfaces,
as described by Ribaucour \cite{rib_cyclic, salkowski}:
the circle congruence formed by the circles that orthogonally
intersect the surfaces of a Ribaucour pair in corresponding
points is cyclic;
furthermore, any two orthogonal surfaces of this cyclic
circle congruence form a Ribaucour pair.
By imposing special geometric properties on a Ribaucour pair
of surfaces,
this construction gives rise to particular cyclic systems.
Amongst them are
cyclic systems with orthogonal surfaces that are Guichard
surfaces \cite{MR239516, csg_45} and,
in particular, parallel families of flat fronts in hyperbolic
space~\cite{MR2652493};
and cyclidic systems, where all coordinate surfaces are
Dupin cyclides \cite{darboux_ortho, totallycyclic}.
We report on a similar construction in the discrete framework:
the orthogonal circle congruence of a discrete Ribaucour pair
is cyclic.
Subsequently, we investigate circle congruences constructed
from discrete Ribaucour pairs with (at least) one totally
umbilic discrete envelope.
In this way, we obtain discrete cyclic circle
congruences with discrete flat fronts in hyperbolic space
as orthogonal surfaces, as well as discrete cyclic systems
where all coordinate surfaces are discrete Dupin cyclides.
Cyclic systems with a $1$-parameter family of orthogonal
Guichard surfaces will be reported on in a forthcoming paper.
\vglue-parskip \\ \\ \noindent
In this section we only consider \textit{non-degenerate}
discrete Ribaucour sphere congruences
$r:\mathcal{V} \rightarrow \mathbb{P}(\mathcal{L})$
(cf \cite{org_principles}),
that is, discrete conjugate nets (nets with planar faces)
in $\mathbb{P}(\mathcal{L})$,
where any homogeneous coordinate vectors of each face
span a $(2,1)$- or a $(1,2)$-plane. In the former case,
where every span has Minkowski signature, each face
of the sphere congruence models a Dupin cyclide,
that we will refer to as the associated \emph{R-Dupin cyclide}.
The notion of a
Ribaucour sphere congruence is clearly a Lie sphere geometric
notion. However, once we start to construct discrete cyclic
circle congruences, we again fix a M\"obius subgeometry of Lie
sphere geometry, modelled on
a point sphere complex $\mathfrak{p}$.
We say that a discrete Ribaucour sphere congruence is
\emph{non-degenerate in this M\"obius subgeometry} if it
additionally satisfies
$\lspan{\mathfrak{r}_i, \mathfrak{p}} \neq 0$,
that is, if it does not contain any point spheres.
\begin{figure}[t]
\hspace*{-3cm}\begin{minipage}{5cm}
\includegraphics[scale=0.25]{good_rib_1}
\end{minipage}
\hspace*{1.2cm}\begin{minipage}{6cm}
\includegraphics[scale=0.25]{good_rib_2}
\end{minipage}
\caption{
\emph{Left:} A Ribaucour pair of discrete Legendre maps
with a part of its associated circle congruence (blue),
consisting of circles that intersect the spheres of the
Ribaucour congruence (orange) orthogonally in the point
spheres of the envelopes.
\emph{Right:} Discrete Legendre maps that are
orthogonal to the circle congruence associated to the
Ribaucour pair.}
\label{fig:ex_rib_pair}
\end{figure}
\subsection{Discrete cyclic circle congruences associated to
discrete Ribaucour pairs}\label{subsect_rib}
We begin by formulating useful general observations about
Ribaucour sphere congruences:
first we provide a characterization in terms of the existence
of certain flat connections,
then show that a flat connection can be chosen to be comprised
of M-Lie inversions once a M\"obius subgeometry is fixed.
Given a pair of envelopes of the Ribaucour sphere congruence
this connection then also yields a flat connection for the
orthogonal circle congruence that we are interested in,
showing that it is cyclic
(cf Thm \ref{thm_flat_connection}).
\vglue-parskip \\ \\ \noindent
Recall \cite{org_principles, rib_families} that any
non-degenerate discrete Ribaucour sphere congruence
admits a 2-parameter family of
envelopes, which are uniquely determined by the choice of
one appropriate contact element at one initial Ribaucour
sphere.
Conversely, two discrete Legendre maps form a discrete
Ribaucour pair if they envelop a common sphere congruence;
this sphere congruence is then a discrete Ribaucour sphere
congruence.
\vglue-parskip \\ \\ \noindent
Taking the first point of view and focusing on the sphere
congruence, we obtain the following characterization of
discrete Ribaucour sphere congruences:
\begin{prop}\label{prop_ribsph_flat}
A discrete sphere congruence $r: \mathcal{V} \to \mathbb{P}(\mathcal{L})$ with
$\lspan{\mathfrak{r}_i, \mathfrak{r}_j} \neq 0$ for $(ij)
\in \mathcal{E}$, is a discrete Ribaucour sphere congruence
if and only if it admits a flat connection on the trivial
bundle $\mathcal{V} \times \mathbb{R}^{4,2}$ comprised of
Lie inversions that map adjacent Ribaucour spheres onto
each other.
\end{prop}
\begin{proof}
Let $r: \mathcal{V} \to \mathbb{P}(\mathcal{L})$ be a discrete Ribaucour sphere
congruence and fix $n \in \mathbb{P}(\mathbb{R}^{4,2})$
such that $\lspan{\mathfrak{n}, \mathfrak{r}_i} \neq 0$
for any $i \in \mathcal{V}$. We consider the discrete map
\begin{equation}\label{equ_rib_conn}
a:\mathcal{E} \rightarrow \mathbb{P}(\mathbb{R}^{4,2}),
\enspace
(ij)\mapsto a_{ij} := \lspann{\mathfrak{a}_{ij}},
\enspace\text{where}\enspace
\mathfrak{a}_{ij} := \lspan{\mathfrak{n}, \mathfrak{r}_i}\mathfrak{r}_j - \lspan{\mathfrak{n}, \mathfrak{r}_j}\mathfrak{r}_i
\end{equation}
and denote the Lie inversions with respect to the linear
sphere complex $a_{ij}$ by $\sigma_{ij}$. By construction,
those Lie inversions exchange adjacent spheres of the congruence
and satisfy, for any face $(ijkl)$,
\begin{equation*}
(\sigma_{ij}\circ\sigma_{jk}\circ\sigma_{kl}\circ\sigma_{li})
(\mathfrak{r}_i) = \mathfrak{r}_i.
\end{equation*}
To prove that the Lie inversions $\sigma$ indeed yield a
flat connection on $\mathcal{V} \times \mathbb{R}^{4,2}$,
we will investigate the interplay between the 2-parameter
family of envelopes of $r$ and these Lie inversions.
Firstly, note that $\sigma_{ij}$
preserves all spheres that are in oriented contact with $r_i$
and $r_j$, hence, adjacent contact elements of the envelopes
are exchanged (see also \cite[\S 3]{rib_families}).
In particular, we obtain that
$(\sigma_{ij}\circ\sigma_{jk}\circ\sigma_{kl}\circ\sigma_{li})
(f_i) = f_i $ for the contact elements of any envelope $f$.
Moreover, since $\lspan{\mathfrak{a}_{ij},
\mathfrak{n}}=0$, the Lie inversions preserve the
linear sphere complex $\mathbb{P}(\mathcal{L} \cap n^\perp)$.
Since each contact element of an envelope
contains exactly one sphere in $\mathbb{P}(\mathcal{L}
\cap n^\perp)$ and any discrete Ribaucour sphere
congruence admits a 2-parameter family of discrete envelopes,
we conclude that, for any $\mathfrak{v} \in r_i^\perp$,
\begin{equation*}
(\sigma_{ij}\circ\sigma_{jk}\circ\sigma_{kl}\circ\sigma_{li})
(\mathfrak{v})=\mathfrak{v}.
\end{equation*}
Thus, the Lie inversions $\sigma_{ij}$ provide
a flat connection for the Ribaucour sphere congruence.
\vglue-parskip \\ \\ \noindent
Conversely, assume that $r:\mathcal{V} \to \mathbb{P}(\mathcal{L})$,
$\lspan{\mathfrak{r}_i, \mathfrak{r}_j} \neq 0$, is a
discrete sphere congruence that admits a flat connection
comprised of Lie inversions, as above.
Furthermore, let $s_0 \in \mathbb{P}(\mathcal{L})$ be a
sphere in oriented contact to an initial sphere
$r_0$ of the Ribaucour sphere congruence,
that is, $s_0 \perp r_0$. Then propagation of the
contact element $\lspann{s_0, r_0}$ with by means of the
flat connection provides a well-defined discrete Legendre
map that envelopes~$r$. Due to the possible choices for $s_0$,
we
obtain a 2-parameter family of discrete envelopes and $r$
is indeed a discrete Ribaucour sphere congruence.
\end{proof}
\noindent We remark that the flat connection of Prop
\ref{prop_ribsph_flat} is not unique. However, if
we fix a M\"obius subgeometry by choosing a point sphere
complex $\mathfrak{p}$ such that the Ribaucour sphere
congruence is non-degenerate in this M\"obius subgeometry,
we may fix
homogeneous coordinates
$\mathfrak{r}:\mathcal{V}\to\mathcal{L}$ so that
$\lspan{\mathfrak{r},\mathfrak{p}}\equiv 1$ and consider
the discrete map
\begin{equation}\label{equ_a_rib_pair}
a:\mathcal{E} \rightarrow \mathbb{P}(\mathbb{R}^{4,2}),
\enspace
(ij)\mapsto a_{ij} := \lspann{\mathfrak{a}_{ij}},
\enspace\text{where}\enspace
\mathfrak{a}_{ij} := \mathfrak{r}_j - \mathfrak{r}_i.
\end{equation}
Then the associated Lie inversions $\sigma_{ij}$ preserve
the point sphere complex and are therefore M-Lie inversions
(cf \cite[\S 3.1]{rib_families}). Hence:
\begin{cor}\label{cor_rib_flat_Mlie}
A discrete sphere congruence $r: \mathcal{V} \to \mathbb{P}(\mathcal{L})
\setminus \mathbb{P}(\mathcal{P})$ with $\lspan{\mathfrak{r}_i, \mathfrak{r}_j}
\neq 0$ for $(ij) \in \mathcal{E}$, is a discrete Ribaucour
sphere congruence if and only if it admits a (unique)
flat connection on the trivial bundle $\mathcal{V} \times
\mathbb{R}^{4,2}$ compound by M-Lie inversions that map
adjacent Ribaucour spheres onto each other.
\end{cor}
\noindent Returning to our principal aim,
the construction of a cyclic circle
congruence associated to a discrete Ribaucour pair,
we fix two discrete Legendre maps $(f^+,
f^-):\mathcal{V} \rightarrow \mathcal{Z}\times \mathcal{Z}$
that envelop the non-degenerate
discrete Ribaucour sphere congruence $r:\mathcal{V} \rightarrow
\mathbb{P}(\mathcal{L})\setminus \mathbb{P}(\mathcal{P})$.
Then the flat connection of M-Lie inversions associated to
$r$ (see Cor \ref{cor_rib_flat_Mlie}) will
also provide a flat connection for the circle congruence:
we consider the
circle congruence $\Gamma:\mathcal{V}
\rightarrow G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)}$
consisting of circles $\Gamma_i$ that intersect the
spheres $r_i$ in the point spheres $p^\pm_i \in f^\pm_i$
of the envelopes orthogonally
(for an illustration see Figure~\ref{fig:ex_rib_pair}).
By Fact~\ref{fact_orth_circle}, this circle congruence is
described by the $(2,1)$-planes
\begin{equation}\label{equ_orth_circle_rib}
\gamma_i:=\lspann{\mathfrak{p}_i^+, \
\mathfrak{p}_i^-, \
\mathfrak{r}_i+\mathfrak{p}}.
\end{equation}
Since the M-Lie inversions $\sigma$ described by
(\ref{equ_a_rib_pair}) satisfy $\sigma_{ij}(\mathfrak{r}_j +
\mathfrak{p})=\mathfrak{r}_i+ \mathfrak{p}$, they also map
adjacent circles of $\Gamma$
onto each other, that is, $\sigma_{ij}(\gamma_j)=\gamma_i$.
Thus, by the above, these M-Lie inversions $\sigma$ yield a flat
connection for the circle congruence $\Gamma$ and, by
Theorem~\ref{thm_flat_connection}, we conclude:
\begin{thm}\label{thm_associated_rib_cyclic}
Let $p^\pm \in f^\pm$ be the point sphere maps of two
envelopes $f^\pm$ of a discrete Ribaucour sphere congruence
$r:\mathcal{V} \rightarrow \mathbb{P}(\mathcal{L})$.
Then the circles that orthogonally intersect the spheres
$r$ in the point sphere maps $p^\pm$ form a cyclic circle
congruence with $f^\pm$ as orthogonal surfaces.
This circle congruence is given by
\begin{equation*}
\begin{aligned}
\Gamma=(\gamma, \gamma^\perp):
\mathcal{V} &\rightarrow G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)},
\\i &\mapsto \lspann{\mathfrak{p}_i^+, \mathfrak{p}_i^-,
\mathfrak{r}_i+\mathfrak{p}} \times \lspann{\mathfrak{p}_i^+,
\mathfrak{p}_i^-, \mathfrak{r}_i+\mathfrak{p}}^\perp,
\end{aligned}
\end{equation*}
where $\mathfrak{r}_i \in r_i$ such that
$\lspan{\mathfrak{r}_i, \mathfrak{p}}=1$;
it will be referred to as \emph{associated}
to the discrete Ribaucour pair.
\end{thm}
\noindent Firstly, we will exploit this construction to
extend Example \ref{ex_parallel_flat} and discuss discrete
(normal) line congruences in space forms obtained from parallel
discrete surfaces.
\begin{ex}[Discrete cyclic circle congruences associated
to parallel surfaces in space forms]
Let $\mathfrak{p} \in \mathbb{R}^{4,2}$, $\lspan{\mathfrak{p},
\mathfrak{p}}=-1$, be a fixed point sphere complex and
$\mathfrak{q} \in \mathbb{R}^{4,2}\setminus \{ 0 \}$,
$\lspan{\mathfrak{p}, \mathfrak{q}}=0$, a space form
vector satisfying $\lspan{\mathfrak{q},\mathfrak{q}}=\pm 1$.
As before, we denote the space form projection of
a discrete Legendre map $f$ by
\begin{equation*}
(\mathfrak{f}^\mathfrak{p}, \mathfrak{t}):
\mathcal{V} \rightarrow \mathcal{Q} \times \mathcal{H},
\end{equation*}
with the point sphere map $\mathfrak{f}^\mathfrak{p}$ and
tangent plane congruence $\mathfrak{t}$ of $f$, respectively.
Furthermore, consider its discrete Ribaucour transform
$\hat{f}:=\sigma_q(f)$ obtained by the Lie inversion
in the linear sphere complex $\mathbb{P}(\mathcal{L} \cap \{ \mathfrak{q}\}^\perp)$.
By Theorem \ref{thm_associated_rib_cyclic}, the
discrete cyclic circle congruence associated to the Ribaucour
pair $(f, \hat{f})$ is given by
\begin{equation*}
\gamma_i :
= \lspann{\mathfrak{f}_i^p, \hat{\mathfrak{f}}_i^p,
\mathfrak{t}_i+\lspan{\mathfrak{t}_i,
\mathfrak{p}}\mathfrak{p}} = \lspann{\mathfrak{f}_i^p,
\mathfrak{q}, \mathfrak{t}_i-\mathfrak{p}},
\end{equation*}
which yields a discrete normal line congruence in the
distinguished space form, that admits the family of parallel
surfaces as its orthogonal surfaces.
\vglue-parskip \\ \\ \noindent
In the case of a hyperbolic ambient quadric of constant
curvature,
that is, $\lspan{\mathfrak{q}, \mathfrak{q}} > 0$, the circles
of the constructed congruence $\Gamma$ orthogonally intersect
the spheres $\mathfrak{l}^\pm = \mathfrak{p} \pm \mathfrak{q}$
that coincide up to orientation.
Those spheres $\mathfrak{l}^\pm$ represent the infinity
boundary of the hyperbolic quadric of constant curvature,
that consists of two hyperbolic space forms.
Moreover, the
two orthogonal surfaces whose point spheres lie on $l^\pm$
provide the two discrete hyperbolic Gauss maps of $f$ and
its parallel surfaces.
Thus, by Corollary \ref{cor_adjacent_rib}, we learn that
the two discrete hyperbolic Gauss maps of a discrete Legendre
map are (up to orientation) related by a discrete Ribaucour
transformation. This fact suggests another construction for
discrete cyclic circle congruences associated to parallel
surfaces in hyperbolic space, namely, from its two
discrete hyperbolic Gauss maps.
\vglue-parskip \\ \\ \noindent
We say that a discrete Legendre map is \emph{totally umbilic}
if all curvature spheres coincide and, for any choice of
point sphere complex, its point sphere map is a circular net.
Using this definition, we have proven:
\begin{cor}\label{cor_rib_hyper_gauss}
A discrete Ribaucour pair of two totally umbilic discrete
Legendre maps whose point spheres lie on the same sphere gives
rise to a discrete normal line congruence in an appropriate
hyperbolic space form.
Any of its orthogonal surfaces in this hyperbolic space form
are parallel surfaces,
and have the discrete
Ribaucour pair as their common discrete hyperbolic Gauss maps.
\end{cor}
\end{ex}
\noindent Clearly, the geometry of the chosen discrete
hyperbolic Gauss maps affects the properties of the
associated orthogonal surfaces. For example, in the next
subsection, we shall see that starting with hyperbolic Gauss
maps that form a Darboux pair will lead to discrete flat
fronts in hyperbolic space.
\subsection{Discrete flat fronts as orthogonal surfaces
of cyclic circle congruences} \label{subsect_flat_fronts}
\noindent In the smooth, as well as in the discrete setup,
there are various ways to construct intrinsically flat
surfaces (or fronts) in hyperbolic space, that
is, surfaces with constant extrinsic Gaussian curvature~$1$.
From a Lie sphere geometric perspective, smooth and discrete
flat fronts in hyperbolic space are obtained as projections of
$\Omega$-surfaces spanned by two isothermic sphere congruences
each lying in a fixed parabolic linear sphere complex (see
\cite{MR2652493, lin_weingarten}).
Alternatively, as discussed in \cite{MR1752778, MR2946924,
disc_sing}, smooth and discrete flat fronts can be
produced from holomorphic data by means of a
Weierstrass type representation.
In \cite{MR2652493}, it was shown that smooth flat fronts
also arise as orthogonal surfaces of special cyclic systems
associated to Darboux pairs of totally umbilic surfaces,
namely, of their two hyperbolic Gauss maps. The aim of this
subsection is to demonstrate a similar construction within
the framework developed here, that also leads to parallel
families of discrete flat fronts in hyperbolic space.
\vglue-parskip \\ \\ \noindent
In order to make contact with our present setting,
we briefly recall the Lie geometric approach to discrete
flat fronts in hyperbolic space as established in
\cite[Expl~4.3]{lin_weingarten}:
a discrete $\Omega$-surface is a Legendre map $f=s^+\oplus s^-$
that is spanned by a suitable pair of isothermic sphere
congruences,
and its hyperbolic space form projection
$(\mathfrak{f}^\mathfrak{p},\mathfrak{t}):
\mathcal{V}\to\mathcal{Q}\times\mathcal{H}$
with respect to the point sphere complex~$\mathfrak{p}$
and space form vector $\mathfrak{q}$ is a flat front
if and only if the enveloped isothermic sphere congruences
take values in two fixed parabolic linear sphere complexes
$l^\pm=\lspann{\mathfrak{q}\mp\mathfrak{p}}$,
that is,
$s^\pm\perp l^\pm$.
Fixing homogeneous coordinate vectors
$\mathfrak{l}^\pm=\mathfrak{q}\mp\mathfrak{p}$,
K\"onigs dual lifts of the two sphere congruences $s^\pm$
are determined by
\begin{align*}\label{equ_def_s}
\mathfrak{s}^\pm
= \pm( \lspan{\mathfrak{l}^\pm,\mathfrak{t}}
\mathfrak{f}^\mathfrak{p}
- \lspan{\mathfrak{l}^\pm,\mathfrak{f}^\mathfrak{p}}
\mathfrak{t} )
= \mathfrak{f}^\mathfrak{p} \pm \mathfrak{t};
\end{align*}
that is, they are edge-parallel and opposite diagonals on
each face are parallel:
\begin{equation*}
\mathfrak{s}_i^+-\mathfrak{s}_j^+ \parallel \mathfrak{s}_i^--\mathfrak{s}_j^-, \enspace
\mathfrak{s}_i^+-\mathfrak{s}_k^+ \parallel \mathfrak{s}_j^--\mathfrak{s}_l^-
\enspace\text{and}\enspace
\mathfrak{s}_j^+-\mathfrak{s}_l^+ \parallel \mathfrak{s}_k^--\mathfrak{s}_i^-.
\end{equation*}
The former condition is equivalently expressed by
the vanishing of the mixed area on faces,
$$
0 = A(\mathfrak{s}^+,\mathfrak{s}^-),
\enspace\text{while}\enspace
A(\mathfrak{s}^+,\mathfrak{s}^-)
= A(\mathfrak{f}^\mathfrak{p},\mathfrak{f}^\mathfrak{p})
- A(\mathfrak{t},\mathfrak{t}),
$$
showing that the mixed area Gauss curvature
$K:=\frac{A(\mathfrak{t},\mathfrak{t})}
{A(\mathfrak{f}^\mathfrak{p},\mathfrak{f}^\mathfrak{p})}$
of $(\mathfrak{f}^\mathfrak{p},\mathfrak{t})$ satisfies
$K\equiv 1$ if and only if
$\mathfrak{s}^\pm$ are K\"onigs dual.
\vglue-parskip \\ \\ \noindent
The key point in the construction of discrete cyclic circle
congruences that admit a parallel family of discrete flat
fronts is the interplay between the distinguished isothermic
sphere congruences of the discrete flat fronts and their
hyperbolic Gauss maps as totally umbilic envelopes of them.
The proposed construction will rely on the following general
observations on discrete Ribaucour sphere congruences with
a totally umbilic (discrete) envelope:
\begin{lem}[cf \cite{rib_families}]
\label{lem_umbilic_envelope}
Let $r$ be a discrete Ribaucour sphere congruence that admits
a totally umbilic envelope, then $r$ is a $(2,1)$-congruence
and, on any face, the contact elements of the totally umbilic
envelope coincide with contact elements of the corresponding
R-Dupin cyclide along one circular curvature line of it.
\end{lem}
\noindent In this situation, the cross-ratios of the discrete
Ribaucour congruence are transferred to the point sphere map
of the totally umbilic envelope and vice versa. This follows
from a simple fact about smooth Dupin cyclides:
\begin{lem}\label{lem_same_cr}
The cross-ratio of four point spheres lying on a curvature
line of a Dupin cyclide coincides with the cross-ratio of the
four (non-constant) curvature spheres of the Dupin cyclide
that are in oriented contact with those point spheres.
\end{lem}
\begin{proof}
Let $\Delta=\delta_1 \oplus_\perp \delta_2 \in G_{(2,1)}
\times G_{(2,1)}$ represent a Dupin cyclide;
further
let $\mathfrak{s}_1\in\delta_1\cap\mathcal{L}$
and $\mathfrak{s}_{2j}\in\delta_2\cap\mathcal{L}$ ($j=1,\dots,4$)
denote one, respectively four, curvature spheres
of different families,
that is, $f_j=s_1\oplus s_{2j}$ ($j=1,\dots,4$) yield
four contact elements of the cyclide.
The point spheres of the corresponding contact elements
are then given by
$$
\mathfrak{p}_j
= \lspan{\mathfrak{p},\mathfrak{s}_1}\mathfrak{s}_{2j}
- \lspan{\mathfrak{p},\mathfrak{s}_{2j}}\mathfrak{s}_1.
$$
As
$\lspan{\mathfrak{p}_i,\mathfrak{p}_j}
=\lspan{\mathfrak{s}_{2i},\mathfrak{s}_{2j}}$
we conclude that
$cr(p_1,p_2,p_3,p_4)=cr(s_{21},s_{22},s_{23},s_{24})$.
\end{proof}
\noindent As a consequence of Lemmas
\ref{lem_umbilic_envelope} and \ref{lem_same_cr} we then
obtain:
\begin{cor}\label{cor_umbilic_cr}
The face cross-ratios
of a discrete Ribaucour sphere congruence and
of a totally umbilic envelope coincide.
In particular, a totally umbilic envelope of a discrete
Ribaucour sphere congruence is isothermic if and only if
the sphere congruence is.
\end{cor}
\noindent In view of the fact that a discrete flat front is
spanned by a pair of isothermic sphere congruences, and those
are discrete Ribaucour sphere congruences that each have one
of the discrete hyperbolic Gauss maps as totally umbilic
second envelopes, we state the following theorem
(see also Figure \ref{fig:flat_fronts}):
\begin{thm}\label{thm_flat_front_final}
The hyperbolic Gauss maps $h^\pm:\mathcal{V}\to\mathbb{P}(\mathcal{P})$ of a discrete
flat front in hyperbolic space form a (totally umbilic)
Darboux pair.\par
Conversely, any orthogonal net of the cyclic circle
congruence associated to a Darboux pair $(h^+,h^-)$
with values in a $2$-sphere projects to a flat front in
the hyperbolic space bounded by the target sphere of $h^\pm$.
\end{thm}
\begin{proof}
First suppose $(\mathfrak{f}^\mathfrak{p},\mathfrak{t})$ to be
a flat front in a hyperbolic space described by a point sphere
complex $\mathfrak{p}$ and a space form vector $\mathfrak{q}$
with $\lspan{\mathfrak{q},\mathfrak{q}}=1$.
Using homogeneous coordinate vectors as above,
$\mathfrak{s}^\pm=\mathfrak{f}^\mathfrak{p}\pm\mathfrak{t}$ and
$\mathfrak{l}^\pm=\mathfrak{q}\mp\mathfrak{p}$ for
the enveloped isothermic sphere congruences $s^\pm$ and
their linear sphere complexes, respectively,
we obtain
$$
\mathfrak{h}^\pm
= \pm( \lspan{\mathfrak{p},\mathfrak{l}^\pm}\mathfrak{s}^\pm
- \lspan{\mathfrak{p},\mathfrak{s}^\pm}\mathfrak{l}^\pm )
= \mathfrak{s}^\pm + \mathfrak{l}^\pm
= (\mathfrak{f}^\mathfrak{p}+\mathfrak{q}) \pm (\mathfrak{t}-\mathfrak{p})
$$
as (homogeneous coordinates of the) hyperbolic Gauss maps
of the front $(\mathfrak{f}^\mathfrak{p},\mathfrak{t})$.
Note that $\mathfrak{h}^\pm\perp\mathfrak{p},\mathfrak{q}$,
that is, they are point sphere maps taking values in the
sphere $\mathfrak{q}$ that defines the infinity boundary
of the ambient hyperbolic space.
As $\mathfrak{h}^\pm$ are just constant offsets
of $\mathfrak{s}^\pm$,
they share cross ratios with the enveloped isothermic sphere
congruences,
hence are also isothermic (cf Cor \ref{cor_umbilic_cr}),
and form a pair of K\"onigs dual lifts,
hence yield a totally umbilic Darboux pair $(h^+,h^-)$,
see \cite[Def~4.4, Thm~3.26]{bcjpr}.
Note that $\lspan{\mathfrak{h}^+,\mathfrak{h}^-}=-2\neq 0$,
showing that the obtained Darboux pair is non-isotropic.
Next we reverse the above construction:
thus let $(h^+,h^-)$ denote a discrete Darboux pair of point
spheres that take values in a $2$-sphere,
that is, $h^\pm\perp\mathfrak{p},\mathfrak{q}$,
where $\mathfrak{p}$ denotes the point sphere complex
and $\mathfrak{q}\in\mathbb{R}^{4,2}$ with
$\lspan{\mathfrak{q},\mathfrak{q}}=1$
defines a M\"obius geometric sphere.
Then $\mathfrak{l}^\pm:=\mathfrak{q}\mp\mathfrak{p}$ yield
the two (Lie geometric) oriented spheres of this
(M\"obius geometric) sphere.
By \cite[Def~4.4, Thm~3.26]{bcjpr} we may choose K\"onigs dual
lifts $\mathfrak{h}^\pm$ of $h^\pm$;
as $\lspan{\mathfrak{h}^\pm,\mathfrak{h}^\pm}\equiv 0$
we infer (as usual) that
$$
\mathfrak{h}^\pm_i + \mathfrak{h}^\pm_j
\perp \mathfrak{h}^\pm_i - \mathfrak{h}^\pm_j
\parallel \mathfrak{h}^\mp_i - \mathfrak{h}^\mp_j,
\enspace\text{hence}\enspace
\lspan{\mathfrak{h}^+,\mathfrak{h}^-} \equiv -2
$$
without loss of generality, after a possible (constant)
rescaling of $\mathfrak{h}^+$ or $\mathfrak{h}^-$.
Now observe that
$$
\mathfrak{s}^\pm :
= e^{\pm\rho}\mathfrak{h}^\pm + \mathfrak{l}^\pm
\enspace\text{for}\enspace
\rho\in\mathbb{R}
$$
yield K\"onigs dual lifts of an isotropic Darboux pair
$(s^+,s^-)$ of isothermic sphere congruences,
see \cite[Def 4.4]{bcjpr}:
in particular, the Legendre map $f:=s^+\oplus s^-$ projects
to a flat front $(\mathfrak{f}^\mathfrak{p},\mathfrak{t})$
in the hyperbolic space(s) given by $\mathfrak{p}$ and
$\mathfrak{q}$.
Finally note that, by Theorem \ref{thm_associated_rib_cyclic},
the cyclic circle congruence associated to the Darboux pair
$(h^+,h^-)$ is given by
$$
\Gamma = \gamma\times\gamma^\perp:
\mathcal{V}\to G_{(2,1)}^{\mathcal{P}} \times G_{(2,1)}
\enspace\text{with}\enspace
\gamma_i :
= \lspann{ \mathfrak{h}^+_i,\mathfrak{h}^-_i,\mathfrak{q} }.
$$
Clearly, $\mathfrak{s}^\pm_i\pm\mathfrak{p}\in\gamma_i$
at every vertex $i\in\mathcal{V}$;
consequently, $f$ is an orthogonal net of this cyclic
circle congruence for every $\rho\in\mathbb{R}$,
by Fact \ref{fact_two_orth}.
\end{proof}
\noindent We note that the Ribaucour sphere congruence
enveloped by the discrete Darboux pair $(h^+,h^-)$,
considered in Theorem~\ref{thm_flat_front_final},
is highly degenerate:
it is the constant sphere $l^+$ or $l^-$ representing
the infinity boundary of hyperbolic space.
Hence the description (\ref{equ_a_rib_pair}) of the linear
sphere complexes that subsequently induce the flat connection
for the circle congruence fails.
However, in this particular situation the K\"onigs dual lifts
of the Darboux pair give rise to the sought-after linear sphere
complexes by
\begin{equation*}
a_{ij}
= \lspann{ \mathfrak{h}^+_i-\mathfrak{h}^+_j }
= \lspann{ \mathfrak{h}^-_i-\mathfrak{h}^-_j }.
\end{equation*}
These then induce the M-Lie inversions that provide the flat
connection for $\Gamma$ and interchange the point spheres of
the orthogonal nets on adjacent circles of the congruence.
\begin{figure}[t]
\hspace*{-4.7cm}\begin{minipage}{5cm}
\begin{overpic}[scale=.4]{idea_flat_front.pdf}
\put(28,15){\color{gray}$h_i^-$}
\put(68,15){\color{gray}$h_j^-$}
\put(33,51){\color{gray}$h_i^+$}
\put(63,51){\color{gray}$h_j^+$}
\put(58,6){\color{gray}$l^\pm$}
\put(52,58){\color{black}$\sigma_{ij}$}
\put(39,22){\color{orange}{$f_i$}}
\put(57.5,22){\color{orange}{$f_j$}}
\put(34,39){\color{orange}{$s_i^+$}}
\put(63,39){\color{orange}{$s_j^+$}}
\put(30.5,27){\color{orange}{$s_i^-$}}
\put(65.5,27){\color{orange}{$s_j^-$}}
\put(3,38){\color{UniBlue}{$\gamma_i$}}
\put(93,38){\color{UniBlue}{$\gamma_j$}}
\end{overpic}
\end{minipage}
\caption{Construction of a discrete flat front
$f=\lspann{s^+, s^-}$ from the discrete cyclic circle
congruence $\Gamma$ associated to a discrete Darboux pair
of totally umbilic point sphere maps $h^\pm$
with values in
the fixed sphere $l^\pm$.
Those become the point sphere maps of the two hyperbolic
Gauss maps of the discrete flat front.}
\label{fig:flat_fronts}
\end{figure}
\subsection{Discrete orthogonal systems with Dupin cyclides
as coordinate surfaces}\label{subsect_dupin_cyclides}
Here we investigate discrete cyclic circle congruences that
stem from a discrete Ribaucour pair consisting of a discrete
Dupin cyclide and a totally umbilic surface. We shall prove
that these special circle congruences yield discrete cyclic
systems where all coordinate surfaces are discrete Dupin
cyclides.
An analogous result in the smooth case can be found in
\cite{darboux_ortho, MR0115134}.
\vglue-parskip \\ \\ \noindent
Thus, suppose that $f:\mathcal{V} \rightarrow \mathcal{Z}$ is a
discrete Dupin cyclide in the sense of \cite{discrete_channel},
that is, a discrete channel surface with respect to both
coordinate directions.
In particular, any space form projection yields a circular net
with circular curvature lines, so that the corresponding
curvature spheres are constant along them.
Furthermore, we consider a totally umbilic discrete
Ribaucour transform $u$ of $f$ with point spheres on the
constant sphere $n \in \mathbb{P}(\mathcal{L})$. For genericity, we will assume
that $n$ is not in oriented contact with the Dupin cyclide,
that is, $n\not\in f_i$ for all $i\in\mathcal{V}$.
The discrete Ribaucour sphere congruence $r$ enveloped
by $(f, u)$ is then provided by the spheres in the contact
elements of $f$ that lie in the linear sphere complex
$\mathbb{P}(\mathcal{L}\cap n^\perp)$.
Hence, $u$ can be expressed in terms of its (constant)
curvature sphere $n$ and the enveloped Ribaucour sphere
congruence $r$ by $u_i=\lspann{\mathfrak{n},\mathfrak{r}_i}$
(cf \cite{rib_coords, rib_families}).
\vglue-parskip \\ \\ \noindent
To avoid useless case analyses, a totally umbilic discrete
Legendre map with two families of circular curvature lines
will also be called a discrete Dupin cyclide.
\begin{thm}
Let $f$ be a discrete Dupin cyclide and $u$ a totally umbilic
Ribaucour transform of $f$. Then the orthogonal surfaces
of the discrete cyclic circle congruence associated to the
Ribaucour pair $(f,u)$ are discrete Dupin cyclides.
Furthermore, a suitable choice of contact elements for
the orthogonal surfaces yields a discrete cyclic system
so that all coordinate surfaces are discrete Dupin cyclides.
\end{thm}
\begin{figure}[t]
\hspace{-3.9cm}\begin{minipage}{6cm}
\begin{overpic}[scale=.7]{dupin_system_scheme.pdf}
\put(29,16){\color{gray}$u_m$}
\put(51,16){\color{gray}$u_n$}
\put(75,16){\color{gray}$u_z$}
\put(29,47){\color{gray}$f_m$}
\put(52,47){\color{gray}$f_n$}
\put(72,48){\color{gray}$f_z$}
\put(50,6){\color{black}$n$}
\put(52,58){\color{black}$s$}
\put(37.1,44){\color{orange}{$\sigma_{mn}$}}
\put(64,38){\color{orange}{$\tilde{\sigma}$}}
\end{overpic}
\end{minipage}
\\
\begin{minipage}{5cm}
\hspace*{-2cm}\includegraphics[scale=0.35]{cylinder_sphere_orth_2.pdf}
\end{minipage}
\begin{minipage}{0.1cm} \ \ \ \end{minipage}
\begin{minipage}{5cm}
\hspace*{-1.5cm}\includegraphics[scale=0.28]{cylinder_sphere_orth.pdf}
\end{minipage}
\caption{A discrete triply orthogonal system associated
to the Ribaucour pair of a discrete cylinder and a totally
umbilic spherical transform (orange). Equipped with suitable
contact elements, all coordinate surfaces of the associated
discrete cyclic system become discrete Dupin cyclides.}
\label{fig:dupin_system}
\end{figure}
\begin{proof}
Let $(f,u): \mathcal{V} \rightarrow \mathcal{Z} \times \mathcal{Z}$
be a discrete Ribaucour pair as in the assumption.
For a proof we pursue the following line of arguments:
\begin{itemize}
\item along each coordinate line of the given Dupin cyclide
$f$,
the spheres of the enveloped Ribaucour sphere congruence
are curvature spheres of a constant Dupin cyclide and,
therefore, the flat connection for the associated cyclic
circle congruence is of a special type
(cf Cor~\ref{cor_rib_flat_Mlie} and
Thm~\ref{thm_associated_rib_cyclic});
\item any underlying point sphere map of a discrete
cyclic system, obtained from a sampling of an
initial circle, has a special property; namely, its
``vertical coordinate surfaces'' are multi-circular nets
\cite{multinet};
\item hence the M-Lie inversions that relate adjacent contact
elements of the associated cyclic systems are constant along
each coordinate ribbon of these
``vertical coordinate surfaces'';
\item in particular, propagation of the contact elements of
the Dupin cyclide $f$ preserves circularity of the curvature
lines, as well as the fact that the corresponding curvature
spheres are constant along them;
\item thus any orthogonal
surface is a discrete Dupin cyclide and all orthogonal
trajectories of the point sphere map of the associated
discrete cyclic system are concircular;
\item moreover, a suitable choice for the contact elements
of the vertical coordinate surfaces guarantees that those
are also discrete Dupin cyclides in the Lie sphere
geometric sense, namely, discrete Dupin
cyclides orthogonal to the Dupin cyclides formed by the
Ribaucour spheres.
\end{itemize}
\vglue-parskip \\ \\ \noindent
To begin with, we investigate the Ribaucour pair $(f,u)$
and its Ribaucour sphere congruence along a fixed coordinate
line of $\mathcal{V}$. Since the spheres of the contact
elements of $f$ along
each coordinate line all lie in a $3$-dimensional projective
subspace of $\mathbb{P}(\mathbb{R}^{4,2})$,
the spheres of the enveloped Ribaucour congruence along
each coordinate line are curvature spheres of another (constant) Dupin cyclide
(see also \cite{rib_families}).
Since $f$ is
a discrete Dupin cyclide, along this coordinate line,
all contact elements $F:=\{f_m, f_n, \cdots, f_z \}$
share a common curvature sphere; we denote this sphere
by $s$.
Furthermore,
all contact elements $U:=\{u_m, u_n, \cdots, u_z \}$ intersect
in the constant sphere $n$
(for a schematic see Figure \ref{fig:dupin_system} \emph{top}).
Thus, these two families of contact elements provide
two curvature lines on the Dupin cyclide obtained by
the spheres $R:=\{r_m, r_n, \cdots, r_z\}$ of the enveloped
Ribaucour sphere congruence along this coordinate line.
Therefore, additionally to the M-Lie inversions that
provide the flat connection for the Ribaucour pair (cf Cor
\ref{cor_rib_flat_Mlie}), we obtain further M-Lie inversions:
let $(f_m, u_m)$ and $(f_z, u_z)$ be two
arbitrary pairs of contact elements, then the four
corresponding point spheres are concircular. Hence,
there exists an M-Lie inversion $\sigma_{mz}$ so that
\begin{equation}\label{equ_mlie_multi}
\sigma_{mz}(f_z)=f_m, \ \sigma_{mz}(u_z)=u_m, \
(\text{and } \sigma_{mz}(r_z)=r_m).
\end{equation}
Thus, this M-Lie inversion $\sigma_{mz}$ also exchanges
the circles $\Gamma_m$ and $\Gamma_z$ of the orthogonal cyclic
circle congruence $\Gamma$ associated to the Ribaucour pair
(see Thm~\ref{thm_associated_rib_cyclic});
hence, also the
point spheres of its other orthogonal surfaces.
\vglue-parskip \\ \\ \noindent
Next we investigate the underlying point sphere map
of a ``vertical coordinate surface'' of the associated
cyclic system:
using the above M-Lie inversions this is given by a
sampling of an initial circle, say $\Gamma_m$.
We aim to see that this point sphere map is
multi-circular in the sense of \cite{multinet},
that is,
every coordinate quadrilateral is circular,
not just every elementary coordinate quadrilateral.
We recall from \cite{multinet, rib_families}
that multi-circular point sphere nets may be characterized
by the existence of M-Lie inversions that interchange
corresponding point spheres of any two coordinate
lines in one family,
as those of (\ref{equ_mlie_multi}) do.
Thus we obtain multi-circularity of the point sphere net;
and, by symmetry, similar M-Lie inversions
$\tilde{\sigma}_{ij}$ that interchange the point spheres
of coordinate lines in the other family
(as illustrated in Fig \ref{fig:dupin_system} \emph{top}).
\vglue-parskip \\ \\ \noindent
For corresponding coordinate lines of two adjacent orthogonal
surfaces of the cyclic circle congruence,
the (constant) M-Lie inversion $\tilde{\sigma}$ that arises
from the multi-circularity of the vertical surface may be
used to transport contact elements:
it clearly maps a curvature sphere that is constant along
the coordinate line on one orthogonal surface to an alike
curvature sphere of the other.
Hence all orthogonal surfaces are, with $f$, Dupin cyclides.
Furthermore, we learn that the point spheres along any
coordinate line of the underlying point sphere map of the
discrete cyclic system are circular.
\vglue-parskip \\ \\ \noindent
Finally, to obtain a discrete cyclic system with discrete
Dupin cyclides as coordinate surfaces,
it remains to equip the vertical coordinate surfaces of the
underlying point sphere map with suitable contact elements,
that is, to complement each contact element of an orthogonal
surface of the cyclic circle congruence by two mutually
orthogonal contact elements that are tangent to the
corresponding circle of the congruence.
To do so, we fix one initial contact element $f_0$ of the
Dupin cyclide $f$ and consider the two (circular) coordinate
lines of the underlying point sphere map of $f$ that pass
through the point sphere $p_0\in f_0$:
each is contained in precisely one
(unoriented, M\"obius geometric) sphere
that is tangent to the circle $\Gamma_0$
or, equivalently,
that intersects the Dupin cyclide $f$ orthogonally
along the given curvature line.
By construction, these two spheres are orthogonal,
and choosing an orientation for each of them yields
suitable contact elements.
Further observe that the sphere constructed from one
(circular) curvature line of $f$ is invariant under
the corresponding M-Lie sphere transformations $\sigma_{mn}$
along that curvature line.
Consequently, propagating the just constructed contact
elements at $p_0$ yields a discrete cyclic system that
consists of Dupin cyclides in the Lie geometric sense.
\end{proof}
\noindent We remark that this construction can be generalized
to Ribaucour pairs of two Dupin cyclides, that also lead to
associated cyclic systems with Dupin cyclides as coordinate
surfaces.
Note that this yields a ``totally cyclic system'',
where each coordinate direction provides a cyclic circle
congruence.
Details regarding this construction in the smooth case
can be found in \cite{totallycyclic}.
A suitable sampling then yields a construction
in the discrete case.
\vglue-parskip \\ \\ \noindent \
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,047 |
Free SHS a 'contributing' factor to uprisings in schools - Former MP
The former lawmaker said this after 40 students at the Krobea Asante Technical and Vocational School in Effiduase Asokore, Sekeyere East District, Ashanti Region, were arrested for violence at the school.
A former Member of Parliament for Buem Constituency in the Oti Region, Daniel Kosi Ashiamah, says the government's Free SHS policy is a contributory factor in the current uprisings in the SHS.
Following a series of protests, the students vandalized schools and private properties and later cut power to the school, resulting in further disorder.
The school's principal was also attacked by students who broke into his apartment and beat him up.
According to reports, the students' anger stemmed from their predecessors' poor performance on their final examinations.
Ebenezer Opoku, who is the Assembly Member for the area and also the Coordinator for Free SHS in the District, confirmed the incident, adding that the students wrecked a total of six cars, including four that belonged to the school and two that were owned privately by teachers.
Some eight students of the Chiana Senior High School in the Kassena-Nankana West District of the Upper East Region were also issued sack letters by the Ghana Education service for insulting President Nana Addo Dankwa Akufo-Addo.
The President had to step in for the decision of the GES to be changed.
Responding to the two scenarios on Atinka TV's morning show "Ghana Nie" with host Ama Gyenfa Ofosu Darkwa, former NDC MP for Buem, Daniel Kosi Ashiamah, said the students' behavior can be linked to the free SHS to some extent.
Government has a lot of consultations to make as far as this free SHS is concerned.
"If you look at all these scenarios, you need to ask yourself what percentage of the impact of the free SHS there will be." This is why some of us are calling for the free SHS to be reviewed. GES and the government should find out the administrative aspect of this free SHS. "They need to find out how the teachers are monitoring and working with the students with these free SHS students, which is resulting in these disturbances," the former lawmaker said.
Source: atinkaonline.com
Member of Parliament for Buem Constituency in the Oti Region
Daniel Kosi Ashiamah
Krobea Asante Technical and Vocational School in Effiduase Asokore
Sekeyere East District
Free SHS
Chiana Senior High School
Kassena-Nankana West District of the Upper East Region
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Government to list qualifying SOEs on Ghana Stock Exchange...
Ukraine denies Russian claim it killed 600 soldiers
Bawumia opens University of Ghana's 74th annual new year...
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39 students of Krobea Asante Technical and Vocational school...
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8 pupils die on their way to school as boat capsizes on...
They were among 12 other pupils traveling from Atikagome to Wayokope when the incident... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,128 |
cover
orbitbooks.net
orbitshortfiction.com
# Copyright
This book is a work of fiction. Names, characters, places, and incidents are the product of the author's imagination or are used fictitiously. Any resemblance to actual events, locales, or persons, living or dead, is coincidental.
Copyright © 2018 by Stephen Aryan
Excerpt from _The Age of Dread: Book Three_ copyright © 2018 by Stephen Aryan
Excerpt from _You Die When You Die_ copyright © 2017 by Angus Watson
Author photograph by Hannah Webster
Cover design by Nico Taylor – LBBG
Cover images by Shutterstock and iStock
Cover copyright © 2018 by Hachette Book Group, Inc.
Hachette Book Group supports the right to free expression and the value of copyright. The purpose of copyright is to encourage writers and artists to produce the creative works that enrich our culture.
The scanning, uploading, and distribution of this book without permission is a theft of the author's intellectual property. If you would like permission to use material from the book (other than for review purposes), please contact permissions@hbgusa.com. Thank you for your support of the author's rights.
Orbit
Hachette Book Group
1290 Avenue of the Americas
New York, NY 10104
orbitbooks.net
Simultaneously published in Great Britain and in the U.S. by Orbit in 2018
First U.S. Edition: September 2018
Orbit is an imprint of Hachette Book Group.
The Orbit name and logo are trademarks of Little, Brown Book Group Limited.
The publisher is not responsible for websites (or their content) that are not owned by the publisher.
The Hachette Speakers Bureau provides a wide range of authors for speaking events. To find out more, go to www.hachettespeakersbureau.com or call (866) 376-6591.
Library of Congress Control Number: 2018939435
ISBNs: 978-0-316-55481-7 (trade paperback), 978-0-316-55480-0 (ebook)
E3-20180829-JV-PC
# Contents
COVER
TITLE PAGE
COPYRIGHT
DEDICATION
CHAPTER 1
CHAPTER 2
CHAPTER 3
CHAPTER 4
CHAPTER 5
CHAPTER 6
CHAPTER 7
CHAPTER 8
CHAPTER 9
CHAPTER 10
CHAPTER 11
CHAPTER 12
CHAPTER 13
CHAPTER 14
CHAPTER 15
CHAPTER 16
CHAPTER 17
CHAPTER 18
CHAPTER 19
CHAPTER 20
CHAPTER 21
CHAPTER 22
CHAPTER 23
CHAPTER 24
CHAPTER 25
CHAPTER 26
CHAPTER 27
CHAPTER 28
CHAPTER 29
CHAPTER 30
CHAPTER 31
CHAPTER 32
CHAPTER 33
CHAPTER 34
CHAPTER 35
CHAPTER 36
CHAPTER 37
CHAPTER 38
CHAPTER 39
CHAPTER 40
CHAPTER 41
CHAPTER 42
CHAPTER 43
CHAPTER 44
CHAPTER 45
CHAPTER 46
ACKNOWLEDGEMENTS
EXTRAS
MEET THE AUTHOR
A PREVIEW OF _THE AGE OF DREAD: BOOK THREE_
A PREVIEW OF _YOU DIE WHEN YOU DIE_
BY STEPHEN ARYAN
PRAISE FOR STEPHEN ARYAN
ORBIT NEWSLETTER
_For Nic_
# CHAPTER 1
The piercing scream was so loud that it rattled the windows of the tavern. Garvey ignored it but Phelon flinched and would've run if he hadn't been tied to his chair.
Garvey tore the heel of bread in two and dragged half of it through the thick beef gravy on his plate. The stories about the chef at the Bronze Tiger had not been exaggerations. The food was delicious.
"It was definitely worth the trip," said Garvey, gesturing towards Phelon sitting opposite. He watched as the Mayor tested his bonds again but the knots were tight. His wrists were already red and chafed from his useless struggles. He'd been frantic when the screaming had started but had calmed down now. "The spices are making my tongue tingle."
"You won't get away with this," said Phelon.
Garvey chuckled and gestured at the room around them. "Really? And who is going to stop me? You?"
The Mayor stayed silent as Garvey finished the rest of his food, savouring each mouthful. Even the ale was good. Dark and rich with a hint of smoke, making it a perfect match for the meat. It was made in the small brewery at the far end of the village beside the river.
If not for the famous chef no one would ever visit Garrion's Folly. It was just too small and remote. Not even the bizarre half-finished bridge that led nowhere was interesting enough to attract many visitors. A handful of academics came by every few years but it didn't change life in the village. Over the years trees had grown up around the ruin, hiding it beneath their canopy, but for some unknown reason no lichen grew on the black stones. Despite their age they were still as hard as granite. Yesterday he'd quizzed a few of the locals about it, but not even the oldest crone had any real insight into who had built it or why. But everyone had a favourite story.
"What's your theory about the bridge?" asked Garvey, swirling the last of the ale around the bottom of his mug. He was tempted to get a refill before leaving. After all, he wouldn't be coming back this way again. It was unlikely that he'd be a welcome return visitor to Garrion's Folly.
At first he thought the Mayor wouldn't answer but with little else to do except sulk in silence he finally relented. "I think it was done as part of a wager that someone lost. There are other romantic stories about it being done for love, but I think they're nonsense. My grandpa told me a story once, but it sounded like fantasy to me."
Garvey shrugged. "I'd still like to hear it," he said, moving towards the bar to get himself another drink. Phelon watched Garvey with a sour twist to his mouth as he navigated across the room, stepping over obstacles. Phelon waited until he'd refilled his mug and sat down again before speaking.
"The bridge was part of an ancient doorway."
Garvey raised an eyebrow. "A door to where?"
Phelon shrugged. "My grandpa didn't know that part. He just said it led elsewhere. He believed a Sorcerer built it and that the other half of the bridge is on the other side of the doorway, in some other place. I told you it was ridiculous."
Garvey grunted noncommittally. He ran a hand through his beard as he pondered the Mayor's words. He'd studied the bridge yesterday, noting the lack of decay and the way animals avoided getting too close. In other parts of the forest he could hear birdsong, but here they'd watched him in silence from the branches of surrounding trees as he'd paced around the ruin. It had more than a few things in common with the Red Tower. Phelon thought his grandfather's story was just idle fantasy but to Garvey it seemed the most likely explanation. The two questions he kept coming back to were, who had built it and where did it lead?
For all of the Red Tower's accomplishments with magic in the last two centuries Garvey sometimes felt as if he was a child trying to learn how to read and write. The Grey Councils of old, those who had built the tower itself, had known so much more. Some of their secrets had been written down and were locked up inside the tower library, but unravelling even one ancient and forgotten Talent could take a lifetime of study. There simply weren't enough mages with sufficient skill. Today there were only a handful of magic users alive who could call themselves Sorcerers and he knew they were poor imitations of the originals.
The bridge was yet another reminder of how much they still had to unravel and yet events conspired to prevent them from gaining more knowledge. In other circumstances a mage could spend their entire life in Garrion's Folly, studying the bridge and trying to unlock its ancient secrets. There were times when such a quiet life was enormously appealing to him. But it was far too late for that.
"If only you'd been more welcoming," muttered Garvey, gulping down his ale and savouring the rich smoky taste. "All of this unpleasantness could've been avoided."
"You're a wanted murderer. I could not stand idly by."
"Yes, you could. You could have said nothing. All I wanted to do was eat a meal in peace and then I would've left. Was it worth it?" asked Garvey, gesturing at the room around him. "Did you think you were being brave? Or perhaps it was pride?"
"You will be punished for your wicked deeds," said Phelon with the confidence of a true believer.
"By whom?" asked Garvey, folding his arms and sitting back on his chair.
"The gods. The Maker or the Holy Mother will strike you down."
Garvey held his arms towards the ceiling. "I'm here," he shouted. "I'm ready for my divine punishment."
Phelon was appalled. "You dare mock the gods?"
"Strike me down!" shouted Garvey, rattling the rafters.
Silence greeted him. He waited for divine retribution but nothing happened. No bolt of lightning. No clutching pain in his chest. No everlasting fire hot enough to melt his bones like candle wax. After a while he lowered his arms.
"I'm not worried about your gods. If they even exist, they just don't care about us any more."
The front door of the Bronze Tiger banged open and a man stumbled in. He was bleeding from his scalp, painting half his face bright red. There was more blood on his shirt and he had a distinct limp on the right side. His left arm was bent at a peculiar angle but the right held a dagger.
With a sigh Garvey raised one hand towards the intruder, embraced the Source and made a twisting motion. The man's neck snapped, his head turning to look behind him into the street. With a strangled choke he dropped to his knees and collapsed onto the floor. A final breath wheezed out between his swollen lips and a deafening silence filled the tavern.
Outside smoke and ash drifted past the open doorway, bringing with it the smell of burning wood and charred meat. More bodies littered the street, bruised, bloody and silent. There were men, women and children. A stray dog trotted past, doing its best to escape the chaos before it too was struck down.
There were no more screams. That meant it was nearly time to be moving on.
Tahira came into the tavern, her grinning face smeared with ash.
"It's almost done. Most of the buildings have been torn down," she reported, pleased with herself. She had quite the temper but he'd learned it could be controlled if she was occasionally given free rein, like today.
"Good. And the people?" he asked.
"A few fought back but they're dead. We're finishing off the last ones."
"And our people?"
Tahira grimaced. "Nillim didn't listen to your orders and rushed in. He caught an arrow in the neck. Everyone else is unharmed."
Garvey waved it away. "No great loss. He was an idiot. Did any of the villagers try to run?"
"A few, but we brought them down. No one escaped."
"Horses?"
"We have enough for everyone now. The stables here were surprisingly well stocked."
"Well, at least something good came out of our visit," said Garvey. "Tell the others to take as much food as they can carry from the storeroom."
Phelon looked as if he wanted to curse them, or perhaps weep for his fallen friends and neighbours. Instead he remained silent and stony-faced. He watched Garvey's students troop into the back of the tavern and carry out sacks of food taken from the kitchen. It might be a few days before they stopped off at another village and it would make a nice change if they didn't have to forage for their meals.
"It seems as if our time is up," said Garvey, getting to his feet.
"You will pay."
"Think on this, Phelon. You're the Mayor of this village. The others listen to you. They would've followed your lead if you'd told them not to fight. So their deaths are on your hands. You did this, not me."
Garvey glanced around the tavern one last time, staring at the dead faces of the other patrons in the room. Most of them had died at their tables, although one or two had tumbled to the floor. The owner was dead, his body slumped forward over the bar, and in the kitchen the chef lay dead beside his famous creations. The owner's wife had fallen against a wall and seemed to be asleep, her head resting on her chest. The only sign of her death was a small trickle of dried blood from one nostril. None of the others bore any visible wounds. Their deaths had been quick if not entirely painless.
While the Mayor shouted curses at his back Garvey stepped over villagers' dead bodies and joined his followers waiting for him in the street. A month ago they had been children idly daydreaming in classrooms. They had been students seeking knowledge and the ability to control their burgeoning magic. Now they were refugees from the Red Tower and day by day were transforming into something else. A month of constantly being on the move, pursued by enemies, had stripped away most of the fat. Those who remained were lean, scarred from their experience and willing to do whatever was necessary to survive. Each of them carried a weapon on their hip and they all understood the importance of steel, even for those with magic. A few had tried to give the group a name, but he'd stopped that straightaway. This was not a game for children and they were not folk heroes. It was a fight for their lives and their existence as mages.
"Step back," warned Garvey, gesturing at Tahira. She and the others dismounted and led their horses further down what remained of the main street. On either side of the tavern the buildings had been smashed to pieces until nothing remained except a few broken stones. Every beam of wood had been shattered. Every window ripped apart. Every door and floorboard crushed into kindling. Blood was liberally splashed among the ruins from those too slow to escape the buildings when they collapsed. It wouldn't have mattered. Anyone who made it outside had been killed in the street. Garvey could see dozens of bodies with various wounds from where he was standing. Over a hundred people had lived in Garrion's Folly when they'd first arrived.
The rest of the village was the same. The houses, the mill, the temple and the village hall were all gone. Even the brewery beside the river was nothing more than a pile of tumbled stone. Only the Bronze Tiger remained, although without its famous chef it too would quickly be forgotten. As Garvey drew power from the Source he heard Mayor Phelon screaming from inside, cursing him to damnation for all time.
Reaching deep into the ground beneath the tavern he drove tendrils of his will, shattering buried stone and gouging at the earth. At the same time he focused on all of the tiny fissures in the stone walls, pulling them wider until they ran wild like cracks on a broken pane of glass. With a rumble that shook the earth beneath his feet, the walls of the tavern collapsed inwards while the building sank into the fissure. A huge cloud of dust rose up in the sky as the stones fell and the roof broke apart. The sound was deafening, startling birds from the trees, which swayed in the sudden wind from the building's collapse. Slowly the dust cleared and all that remained of the tavern was a few rocks and roof tiles poking out of the ground.
A profound and deep silence returned, enveloping the area. Somewhere nearby a small bird chirped. In time the forest would reclaim the village until it became nothing more than a few piles of mossy rubble. But for now it would serve as another stark reminder for those who thought mages could be eradicated like a disease.
Garvey mounted up and looked around at what had once been Garrion's Folly.
"Let's hope the next place we visit is more hospitable," he said to the others.
"There's a farm a few hours' ride to the west. We could be there before dark," suggested Tahira.
He considered it but shook his head. "We're not going to run and cower in the countryside like common bandits. All we did was defend ourselves."
"There's another village a couple of days' ride to the east," said Tahira.
"I think we should head north," said Garvey. "I could do with a bath, clean sheets and somewhere a bit less rustic."
They all knew what he was suggesting. The border wasn't too far away. If they carried on north the villages would soon give way to towns and then a city in Zecorria. It was more than a little reckless. It was also the last thing they would expect him to do.
"Let's see if they're kinder to strangers in the north," said Garvey, nudging his horse forward.
The others followed in his wake, leaving behind a village full of dead bodies.
# CHAPTER 2
Tammy stalked through the halls of the palace, barely noticing the rich decorations all around her. Despite seeing them regularly over the last few weeks she still thought they were gaudy and mismatched. The palace decor reflected none of the character of Perizzi, the capital city, or its people. As the trading heart of the west, Yerskania was a melting pot of cultures, with thousands of visitors passing through every day.
It was perhaps the only place in the world where you could see pale-skinned Zecorrans, horned Morrin, shrewd Drassi, burly Seves and even a few Vorga trading peacefully with one another. Golden-skinned merchants from Shael were dotted throughout the crowd and sometimes a dark-skinned easterner from the desert kingdoms could be seen haggling with the stout locals. With goods from all of those nations it made the port in Perizzi arguably the busiest in the world and yet the city had a unique flavour not found anywhere else.
Perizzi had once been her home, but for the last decade Tammy had been working abroad as a Guardian of the Peace. The Guardians investigated all serious crimes in Yerskania, but they were also unique as other nations sometimes called on their expertise to solve difficult or unusual crimes. Travelling through other countries had given her a deeper understanding of several cultures and, despite their many differences, it allowed her to recognise the commonalities between vastly different human races. She'd spent very little time among the Morrin and no Guardian had ever been invited to the Vorga homeland. Aspects of both races and their cultures remained shrouded in mystery, particularly the savage Vorga, as no outsiders were allowed in their country. Thankfully they tended to keep to themselves and spent as little time in the city as possible, preferring open spaces to the crowded streets.
As the Khevassar, leader of the Guardians, her days of travelling abroad were over and she was slowly becoming reacquainted with the rhythms of the city. As a child she'd run through its streets totally unafraid of the dangers she now realised were lurking in dark corners. That innocence was gone, but her underlying intuition was slowly coming back. It seemed as if it had never really left, merely been buried, gathering dust for many years. For all its flaws she liked her city and in time Tammy hoped it would begin to feel like home again.
Now she was neck deep in the city's streets, soaking up the crime and chaos, wading through the rivers of information swirling all around her.
Every day she heard fresh rumours about a turf war erupting between the crime Families who controlled the city's underworld. The stories were vague but nevertheless she listened keenly. Ordinary people were often caught up, on the fringes, of such a violent conflict and she wanted to avoid the death of innocents.
Recently there'd been a lot of talk about groups of people roaming the streets, searching for mages hiding in their midst. There had been a few beatings and one murder of an innocent woman thought to be a Seeker. A few angry groups had even broken into homes, ransacking them in a desperate search for a golden mask. Her Guardians had made several arrests, coming down hard on the ringleaders, and for the time being the problem seemed to have gone away. But she knew people's resentment of mages ran deep and suspected it had merely gone underground. No one spoke about magic any more but she knew it was still on everyone's mind. It lay at the heart of many problems that cropped up in her city.
The threat of widescale violence and fear of the unknown. Everything was tied together like a giant invisible web hanging over the city. Pull on one thread and the effects of that decision would be felt in another district. There was a complex pattern behind it and she was trying to become as adept as the Old Man had been at interpreting and even predicting what was about to happen. She had no doubt it would come with time, but even so that didn't make it any less frustrating. At the moment all she could see were disparate threads in the chaos.
The Khevassar was the hub through which all Guardians communicated. She didn't see every single report, but received daily summaries of minor cases from which she could still discern relationships. While dealing with all of the local issues, there were ongoing problems abroad, some of which were more pressing than others. Such as the continuing issue with Seekers, the recent destruction of the Red Tower, and the ever-scheming Regent of Zecorria.
It was late at night for a meeting with Queen Morganse but she had asked Tammy to visit her to discuss the mage situation. Dorn, the Queen's chubby secretary, was yawning as she entered the outer office. His eyes were heavy with sleep and he waved her towards the Queen's office, not bothering to get up and announce her. His lax attitude irked her but she let it pass, knocked loudly and went inside.
Queen Morganse of Yerskania was sitting behind her desk but for once she wasn't reading one of the many papers scattered across it. Much to Tammy's surprise the Queen was knitting. For other grandmothers of her age it was probably a common pastime, but this was the first time she'd seen Morganse aping them. It was more than a little disconcerting to see the Queen doing something so ordinary.
"Please, take a seat," said the Queen, setting her needles aside. She caught Tammy's glance at the knitting and offered a wry smile. "Some people pray, some exercise or meditate. I find knitting allows my mind to wander while it keeps my hands busy."
Unsure of how to respond to that she said nothing. Despite her increasingly long hours Tammy made sure that her exercise regime had not changed. She ran for an hour every morning before breakfast and sparred twice a week with a Drassi Swordsmaster. She knew almost nothing about him and they barely spoke, making him the perfect opponent. They had no emotional attachment to one another which meant she didn't hold back because of some anecdote he'd told about his family. After a lifetime of carrying a sword he was far more skilled than she, but he helped her stay sharp and in shape. She would never be able to beat him—he was a master of his craft with decades of experience—but that didn't stop her from trying.
The Queen was looking at Tammy expectantly, waiting for her to say something. Perhaps to reply with a personal anecdote about her hobbies. "I don't think knitting would suit me" was all she said.
"To business then," said Morganse, clearly disappointed by her response. It didn't matter. It wasn't necessary for them to be friends in order to work together. "Although it does make things easier if we have a rapport," added the Queen.
"I disagree," said Tammy, earning another frown.
"Do you have something you want to say?"
"No, your Majesty. You asked me to come to the palace for this meeting. I'm here to talk about magic."
"Don't stop there," said Morganse, sitting back in her chair. "Tell me why you disagree."
Perhaps it was because she hadn't slept properly since taking on her new role a few weeks ago. Or that she was afraid of not living up to the Old Man's reputation. Perhaps it was because there was so much to do each day and not enough hours. Or perhaps it was simply because she disagreed with banning all Seekers in Yerskania. So, for once, Tammy decided to be totally honest and open with the Queen.
"My predecessor has great affection for you. So much so, that I think he was too lenient and it clouded his judgement when it came to his dealings with you."
"Is that so?" asked the Queen.
"Did you speak to him before signing the national ban on Seekers?"
"I did, and he strongly advised me against it."
Tammy was appalled. "And yet you still signed it?"
"I weighed his opinion against all of the facts and my other advisers. It was not a decision I made lightly," admitted Morganse.
"It was a mistake. You panicked and rushed the decision because you were afraid."
"Careful," warned the Queen. "There's a difference between offering your opinion and insubordination."
Tammy would not be intimidated. "If you expect me to agree every time you ask for my opinion, you're going to be sorely disappointed."
"The Khevassar's opinion is one among many I consider. Talk to me again about this when you've my experience with politics."
"I'd say the same thing when you've my experience with mages," replied Tammy. She knew the Old Man would have spoken to Morganse about who would replace him one day. Which also meant the Queen would have studied her history in depth. She knew where Tammy had been and what she'd experienced in the last ten years. "Banning all Seekers in Yerskania was the wrong decision."
An awkward silence settled on the room. Neither was willing to admit that they were wrong. She knew the Queen had rushed into it to give the people the impression of taking affirmative action.
There was a loud knock on the door and a moment later Dorn sidled into the room carrying a stack of papers.
"My apologies, your Majesty, but I have an urgent—" the secretary trailed off as he noticed the frosty atmosphere.
"What is it, Dorn?" asked Morganse, breaking eye contact.
"An urgent report, Majesty. There's been another attack by the rogue mage, Garvey, and his followers."
He passed across a small rolled-up note that must have come from the aviary. The Queen scanned the contents and her frown deepened.
"Thank you, Dorn. That will be all."
He bobbed his head and scuttled out of the room as fast as possible, not wanting to get caught in the middle of their disagreement.
"Garvey has destroyed a small village in the north. He was last seen by a patrol heading towards the border and Zecorria."
"How many are dead?"
"All of them," said Morganse, rubbing her temples. "He wiped the whole village off the map. Flattened every building. Killed every man, woman and child. About a hundred people lived in Garrion's Folly."
Tammy took a moment to think about the dead and the repercussions of what had happened. It seemed hard to believe that only a few weeks ago he'd been a member of the Grey Council. A trusted figure that leaders would call upon for aid in the most dire of circumstances.
"I'm considering sending soldiers after Garvey and his followers," declared Morganse.
"I would advise against that, in the strongest possible terms," said Tammy, trying to keep her voice calm. "It wouldn't help, it could provoke him and even make things worse. We both know what one competent Battlemage can do against an army. He's a Sorcerer. Garvey is also said to have a dozen or more followers with him. It would just be another bloodbath."
The Queen took a deep breath and their staring match resumed before she replied. "Then what would you suggest?"
"Reach out to Balfruss and ask him to help."
Morganse snorted. "Did you see the report about what happened at the Red Tower?"
"I did, but you weren't responsible and he knows that, too. Without help from other mages, I'm not sure what could stop Garvey and the others."
"Do you really think Balfruss would turn on his friend?"
Tammy shook her head. "I don't know, but Garvey is killing innocent people. Balfruss won't stand idly by and let that continue. It goes against everything he is."
"I hope you're right, because I agree with you. Without some kind of magical intervention, the bloodshed will continue."
This was a situation neither of them could have predicted and had never dealt with before. Normally at a time like this they would have reached out to the Red Tower who would dispatch someone to deal with the magical threat, but that door was closed. Even if it weren't, Tammy wasn't sure they would send someone to help. After all Morganse had brought in a nationwide ban on Seekers. But something needed to be done and Balfruss was their best chance of stopping Garvey.
The situation also made her wonder how something like this had never happened before. With the exception of the Warlock, she couldn't remember any major incidents where a mage had gone rogue, working against the wishes of the Red Tower. Not every mage went to the school for training and yet there'd never been such a killing spree before. She made a mental note to look into it later. There might be something in the Guardian archives about it.
"In the meantime," Morganse was saying, "I must be seen to be doing something. I'm going to increase the number of soldiers in the north. It will reassure the local people, if nothing else, unless you object?"
"No, your Majesty."
"Good. How is the investigation into Habreel's network?"
Now it was Tammy's turn to rub her temples. "We're making progress and have removed several key people. Unfortunately the real target, Akosh, remains hidden and information about her is sketchy. I have some of my people following up on leads." It felt strange to say that, her people, and it had been even harder to send others out to do the work on her behalf. Normally she would have been one of those riding out of the city to gather information. It was going to take a while for her to get used to delegating as well as who was reliable and who wasn't trustworthy. "Do you want a full update?"
Morganse waved it away. "No. I just hope that the next time Balfruss makes contact with one of us, we have some good news to share with him about Habreel. It might make him more amenable to your request."
"I hope so too, Majesty."
"I have some news from my agents, although I'm not sure if it's good." Morganse fished around on her desk until she found a particular letter. They had spoken little about the Queen's network of spies, but every now and then she would share news from one of them. "The number of attacks on Seekers has fallen across the west, although that's to be expected given the widescale ban. There have also been no reports of children in Yerskania dying in accidents because of their magic."
As Tammy's experience with angry mobs in the city had shown, the decrease in attacks on Seekers meant very little. Any real Seeker with even a drop of common sense would have buried or melted down their golden mask by now.
As for the children many communities liked to deal with their own problems and in the past children were drowned, stoned or hanged if they showed any signs of magic. Without the Seekers there was no way to know how many children were being born with the ability. Out of a sense of shame whole communities swallowed the guilt and buried the truth. It was a dangerous time to be associated with magic in any way.
"I've also heard a rumour," admitted Tammy, deciding to share something although the Queen had not asked. "The Regent of Zecorria is considering a national ban on all mages."
"There's truth to that rumour," said Morganse. "And there's a note on my desk from him encouraging me, and other leaders in the west, to do the same. 'To unite against a common and vicious enemy,' as he puts it."
"Do I need to tell you what my opinion is of that idea?"
Morganse smiled wryly. "I think I know what you're going to say. Besides, on that at least we agree. The problem with Garvey needs to be addressed, and soon. However, the ban on Seekers was a temporary measure at best. Banning all magic is a ludicrous idea. It won't stop children being born with magic."
"I agree, your Majesty."
The silence that settled on the room was less painful than before. They might not be friends but perhaps there could be common ground between them.
"It's late and I think we both need some sleep," said Morganse. "Keep me updated on any pertinent developments."
Tammy took the hint and moved to the door, but she paused on the threshold and turned back. "I hope you will also do the same, Majesty."
The Queen took a deep breath and Tammy expected another reminder from her of who was in charge or that she was overstepping her boundaries. Instead Morganse swallowed whatever she'd been about to say and graciously inclined her head.
"I will do that," said Morganse. "By the way, I know they always called him the Old Man. Have they come up with a nickname for you?"
"If they have, it can't be good."
"Why do you say that?"
"Because no one has dared say it to my face," replied Tammy. She shared a brief smile with the Queen then let herself out. Riona met her at the first gate and the friendly Royal Guard escorted her through the palace.
"Quite the change," said Riona, gesturing at Tammy's new Guardian jacket. It was still red and black like the others, but hers was edged in silver instead of black.
"It's not that different."
"It does look good on you, but I didn't mean the jacket," said Riona, returning Tammy's sword to her. "I was talking about you."
It was customary for the Khevassar to go unarmed, but she knew the city had changed a lot since the Old Man had taken on the title and she wasn't taking any chances. Tammy briefly inspected the plain blade before sheathing it. Its unfamiliar weight was a distraction, but her other sword was special and would draw unwanted attention. There had to be no clues for anyone to tie back to her old life. It was the only way to protect her loved ones.
She waited for Riona to clarify what she meant but then noticed her look. Before Tammy's promotion they had been contemporaries of a sort, but now Riona's stare was more formal and less familiar. Thinking back over the last few weeks she realised Riona hadn't shared any new stories about her family on their frequent walks through the palace. She'd always known taking on the office and title of Khevassar would change how people treated her, but perhaps it had already changed her more than she realised.
The most direct route back to Unity Hall took her along a busy street that was full of noise and bright lights. Taverns at opposite ends of the road were competing for customers with live music and a wide variety of locally brewed beers. Crowds of people drifted from one place to the other in search of the best night out while a squad of the Watch made sure everyone was amicable. All of the soldiers stood to attention as she walked past. Tammy acknowledged the leader but didn't stop to chat. She heard the beginning of a whispered conversation before leaving the street and knew she was the main topic of conversation. It made her wonder again about the nickname they'd given her.
Despite the late hour the corridors of Unity Hall weren't silent and were never empty. Guardians drifted in and out at all hours of the night, checking information on old cases, writing up reports and questioning suspects in the cells below. In her outer office Tammy found her assistant, Rummpoe, asleep at her desk amid a stack of papers. A pen was still clutched in one hand and a blot of ink had spread across the top letter.
Tammy gently shook her awake and sent her home to get some sleep. She was more embarrassed at having ruined the report than being found snoring at her desk.
"I'll make sure it's written out again, in full, first thing in the morning," promised Rummpoe.
"That's fine. Get some rest," said Tammy, waving her off before unlocking her office. She closed the door behind her, hung her jacket on the back and sat down behind her desk. Tammy closed her eyes for a moment but only to gather her thoughts. She wouldn't be going to bed for a few hours yet.
"Hello, old friend," said a familiar voice.
Tammy opened her eyes and saw Balfruss sitting across the desk.
# CHAPTER 3
As the riders came into view Wren sighed with relief and a huge weight seemed to ease from her shoulders. She didn't realise how anxious she'd been until now.
"You've been hunching your shoulders all day," said Danoph, coming to stand beside her. Since leaving the Red Tower a few weeks ago he remained quite taciturn with others, but was starting to open up more to her and Tianne. The three of them were closer than ever, for which Wren was extremely grateful, as she relied on their support for so many things.
"I'm just glad they're all safe."
"And there's a new face with them," he said, gesturing at the tall girl from Shael.
Tianne was one among the group of five riders who slowly made their way towards their settlement from the mouth of the valley. Wren had a long list of jobs awaiting her attention, but greeting all newcomers and giving them the tour was also part of her role. It was a task that Wren cherished as it gave her an excuse to show how much they had accomplished since leaving the school. However, it also served as a reminder that there was still a lot of work ahead. But with each new arrival the challenge was made just a little easier.
"I'll see you at dinner," said Danoph, moving away towards the woods clutching his basket. He liked to spend a portion of each day combing the woodland for mushrooms and cultivating the herbs he'd planted. Wren watched him for a little while, biting her lip, trying to push away the guilt. She was out of excuses. She would have to talk to him soon about his nightmares and explain what they really meant. The Grey Council had kept the truth from him for over a year. After only a few weeks of carrying around the same secret, it felt as if there was a lead weight strapped to her back. Now she understood one of her grandfather's most popular sayings "the only thing heavier than keeping a secret was guilt."
Her attention was drawn back to the riders as they dismounted and approached on foot, Tianne at the front. Much to her friend's surprise Wren embraced her, giving herself a moment to hide her relief.
"Are you all right?" asked Tianne when Wren released her.
"I'm just glad that you're all safe," she lied. She'd also avoided telling Tianne the whole truth. That would have to change as well. "What happened?"
"It was just as you said. We found the village about three days to the south. Laila was hiding her abilities, but people were starting to get suspicious. She was relieved and happy to leave with us before the inevitable happened."
"You've done well," said Wren, giving her friend a squeeze on the arm. "I'll see you in a while."
Tianne gave her a puzzled look, no doubt trying to work out why she was being so affectionate, but didn't ask. Wren thanked the other former students who led the horses away to the stables until she was standing face-to-face with Laila, the new arrival. She was older than Wren by at least a couple of years but her wide-eyed fear made her seem younger. This was probably the first time she'd ever been away from her village by herself.
Tall, with golden skin and blonde hair, Wren knew of several boys who would find her attractive. She just hoped Laila's experiences in her village had prepared her for how to deal amicably with their attention.
Their community was so new and everyone busy that so far there hadn't been any need to introduce forms of punishment. But if their numbers continued to grow it would become necessary. It was a problem for another day which she pushed to the back of her mind.
"I'm Wren," she said, remembering to hold out her hand towards Laila. It still felt like an odd form of greeting because of her Drassi heritage, but she was doing her best to adopt it. The familiarity of the ritual seemed to make strangers feel comfortable and connected to one another. Every day she was reminded that there was much she could learn from other people, even when they weren't intentionally teaching her.
"Tianne said you're in charge," replied Laila, shaking her hand. There was no surprise at her age or hint of scepticism in her voice which Wren took as a good sign. But as she'd found out in the last year at the Red Tower, first impressions could be deceiving.
"In a way. Let me show you around," said Wren. From their vantage point they had a good view of the entire valley. On the left-hand side was an old forest that had been left untouched by anyone for centuries. It was thick and wild, overgrown in places with trees fighting for space. Beneath the dense canopy they'd found more than a dozen rotting trunks overgrown with moss and swarming with ivy. In the heat and darkness the damp forest floor had become a haven for mushrooms. They'd started thinning out the forest a little, clearing away the dead wood and cutting down some of the largest trees for raw materials.
Opening up sections of the ground to sunlight for the first time in years was encouraging new growth. The wild flowers and plants brought in a host of insects and with them came birds in search of a feast, filling the trees with their song. Other animals were starting to return as well and only last week someone had spotted a rabbit. And where there was one rabbit there was often ten. With so many mouths to feed she expected they would soon be setting traps in the forest.
On the right of the valley was what had been dry and dusty scrubland covered with scattered lumps of rock from the surrounding cliffs. It too had been transformed in the last few weeks.
"When we arrived in the valley there was nothing here. It was completely abandoned," said Wren. "No one had lived here for a long time. There are some ancient caves at the back and an old well, but it was bone dry."
"Where did the water come from?" asked Laila, gesturing at the two wells in the valley where people were drawing up water.
"We dug new ones," said Wren, allowing a spark of energy to dance between her fingers. "One of our community has a Talent for finding things. She's a natural dowser, so we dug down and tapped into an underground source. It comes down from the mountains into an underground lake."
Digging the wells was the first thing they'd done as a group when they'd accidentally stumbled across the valley. It was remote, difficult to find and no one would normally come to the area as there was no water. It was also the first time that all of them had worked together using their magic. At the Red Tower the students had sparred and worked alongside each other, but had never combined their strength towards a common goal. Being surrounded by so many people embracing the Source was still a special moment that Wren cherished. It connected her to those around her in a way that went beyond imitating customs and rituals.
This far west in Shael the law was not readily enforced as it was in the capital and other districts. The war had decimated the country's population and Queen Olivia didn't have the bodies to protect the entire nation. Whole areas had been abandoned, with every town and village becoming a home only for ghosts, as the population fled to more central areas for protection. In their wake bandits moved in and the number of attacks on travellers in the western region of Shael increased. Any merchant transporting goods into Shael was now protected by a large number of guards or Drassi warriors.
The fringes of the country were the worst and out here in the Rooke district, so close to the western border, they were completely alone. There were no communities for almost a day's ride in every direction, but plenty of abandoned villages that were often frequented by bandits who used them as temporary bases.
"After the wells we dug the fields," said Wren, gesturing at the right side of the valley. Several acres of freshly turned soil were under the keen gaze of two farmers who used to work on the staff at the Red Tower. "Not everyone who lives here has magic, but we all work together. The farmers direct us and we use our magic to help them." A light shower of rain was falling over one of the fields as two students worked together to cool the air directly above it. The work was delicate and tiring but vitally important to their survival. Every mage in their community was growing accustomed to using their magic every day to help with a variety of tasks.
"And the houses?"
Wren gestured for Laila to follow her towards the centre of the village where four large log cabins and several other structures had been built. "Those came next."
Each house was nothing more than a large single room with no windows and one door. The walls of each building were fashioned from logs that had been lashed together and the roof made from clay tiles that made the interior waterproof. At the back of each cabin was a chimney that they fed with firewood to keep the chill at bay during the night. They were crude but provided shelter and were better than sleeping in the caves, which they'd had to endure when they'd first arrived.
They were currently building real homes and were carefully planning the layout of the village, but the work was slow and it took a lot of patience and skill. Despite using her magic in many ways she would never have anticipated, Wren was slowly learning that magic could only do so much. Stone for the foundations was being scavenged from abandoned villages and carried here, while wooden planks and beams were being fashioned for the roofs in the workshop. She was desperate for a glassblower, but so far they'd not found anyone with the skill. The few windows they'd taken from other buildings were not perfect, but they would have to do for the time being.
"Every day we use our magic in all sorts of practical ways," said Wren, gesturing towards where three students were slowly lowering a block of stone into place for the foundation of another house. "The more you get used to using it, the easier it becomes."
"I can't control it and I'm not very strong," apologised Laila.
"You'll get there and we all have different strengths," said Wren, leading her towards a rhythmic clanging sound coming from a rare stone building with a sloping wooden roof. The forge had several large shuttered windows without glass and a broad door, all of which were wide open to let out the heat. Inside the smith, Leonie, was fashioning tools and equipment. They had one plough but she was busy making another while several students took turns maintaining the heat. It was hard physical labour and currently one of several substitutes for weapons training with Master Choss. Survivors who'd stayed behind to defend the school had brought no news about him, forcing Wren to accept that the worst had happened. They still practised with wooden swords and their fists every day, but it wasn't the same without him.
"This place is very different from the Red Tower," said Wren, still having mixed feelings about criticising the school and its methods. "Our goal is to teach you control and, after that, you'll learn some of the basics. How to create light, fire and hopefully how to heal."
Laila was stunned. "You know how to heal people?"
"It's difficult," admitted Wren, knowing that she still had a long way to go. She had daily lessons with Master Yettle, alongside every other student, but so far she had yet to master the basics. The Healer had not been with them during the evacuation, but one day he'd just appeared at the mouth of the valley as if summoned. "We believe in pairing everything with practical skills. So you'll learn how to defend yourself with magic, but also how to fight with a sword or your fists. You'll also learn herb-lore, from Morag, in partnership with healing from Master Yettle. Combining the two is more effective and it gives us all a greater understanding of the body. Thankfully we have some very patient teachers."
"I thought I'd be spending my days reading in a classroom."
"Sometimes that's necessary, but we're trying to adopt techniques from all over the world." Wren knew that the First People also used magic every day for practical purposes, such as hunting and fishing. Part of her wished she'd gone with Eloise, if only to see how the Jhanidi used their abilities in the desert kingdoms. She suspected there was much she could have learned that would be beneficial to their community in the coming months.
"Where do I start?" asked Laila. Wren took it as a good sign that she was keen to be doing something. There were a few students who had thought the new community would be run in the same way as the school. Where meals were prepared for them and many of their daily needs were dealt with by a staff of helpers. Their only real responsibility at the Red Tower had been to their studies. It had come as quite a rude awakening for some to realise they were now mostly responsible for looking after themselves. Help was given and guidance offered, but everyone had to contribute to the chores. It was proving a difficult adjustment for some, but no one here was about to do it for them. Many a soft hand was now developing calluses and getting soil under its fingernails for the first time.
"Control. Once you've mastered that we'll put you to work," said Wren, offering Laila a smile. "After that it's up to you. Some people here have a greater affinity for certain areas. Some are generalists and others have Talents, like our dowser. Our goal is to teach you how to protect yourself and be ready for any situation."
"Are we building an army?" asked Laila with a smile.
Wren's expression turned stony. "No." That one word hung in the air between them and slowly Laila's mirth drained away. Wren waited in silence until the seriousness of the situation became apparent to Laila. "I assume you know about Garvey and what he's done?" she asked quietly.
"I've heard the stories."
"He's creating living weapons and he enjoys hurting people." Wren wasn't sure what to believe about the man who had once been her teacher, but stories of his atrocious crimes were commonplace and there were too many for them all to be fiction. "Magic is a powerful force and in the wrong hands it is dangerous and destructive. Here, we will teach you how to control your power, but also how to blend in with those without magic. What you do after that is up to you. Some people at the Red Tower learned control so that they could move abroad and start new lives without their magic. What we're offering here is a little different, but if you choose that path no one will stop you. I want to be very honest with you, Laila. You're not a prisoner here. You can leave any time you want, but the longer you stay the more we'll teach you."
"I don't really know what I want to do," admitted Laila. "I've just been so scared that someone would find out. I've come so close to hurting people by accident. I don't want to be afraid any more."
Wren's frown eased and she gave Laila a moment to regain her composure, waiting until she'd wiped away her tears. It seemed that crying in public, no matter where you came from, was uncomfortable and awkward.
"There's still a lot to be done here," said Wren, pretending that nothing had happened.
"I'd like to help in any way I can."
"That's good. How about we get you settled in and tomorrow you can start with your lessons?" suggested Wren. "Maybe once your magic is under control, then you can start to think about what you want to do with it."
They passed the stables and the workshop that were always busy with people. Every day a group of riders scoured the surrounding area and they always returned with something useful from one of the abandoned villages. The best day was when they'd returned with half a dozen goats and an angry hen that only laid when it suited her. Yesterday the scouting group had reported seeing a flock of sheep that had gone wild and were living in the hills not far away. Bringing them in was at the top of her list of tasks. The sheep would provide a good source of milk, wool and meat.
The work ahead seemed endless, but it was a careful balancing act between gradually bringing in new people and growing too quickly. Their new community had gone unnoticed so far, but she realised that would eventually change. Her people had seen groups of bandits, but so far there had been no confrontations. When people inevitably found out about this community she wanted their new home to be secure. She hadn't anticipated bringing in anyone new for a while, but the decision had been taken out of her hands.
Wren got Laila settled in one of the dormitories and left her to get acquainted with some of the other students before going in search of Danoph. She found him in one of the storage sheds hanging batches of herbs from the rafters to dry out.
"So, what's your first impression of the new arrival?" he asked without turning around. He was busy bundling together another batch of willow bark which Morag, their resident herbalist, had told them was good for treating pain.
"You ask me that every time," she said.
"Because you always have a different answer, and first impressions are important."
"I believe that less every day," admitted Wren. She immediately regretted saying it as she didn't want to make this about her. "Actually, I wanted to talk to you about Laila, and the others."
"No one expects you to be perfect, or have all the answers," he said, seeing through her as usual. Wren squirmed uncomfortably and tried to steer the conversation back towards him.
"Let's talk outside when you're finished," she said, suddenly finding the shed claustrophobic. By the time Danoph emerged she felt ready to talk about what she'd been avoiding since leaving the school.
"Tianne should hear this as well."
They found her in the stables brushing down one of the horses but she followed them outside. Wren led them both to a quiet space away from everyone on the edge of the forest.
"Tell me about your dreams," Wren said to Danoph, before they could ask her anything.
"They still haunt me," said Danoph, staring into the distance. "Even now, when I'm awake, I can see some of the images."
"They're not just dreams, are they?" asked Wren, hoping he had intuited something from them.
Danoph's eyes were still unfocused. "No, they're something else. It's hard to describe but I have this feeling." He clutched his shirt, idly tugging at the material. "It's like I'm being pulled in several directions at once."
"What's all this about?" asked Tianne.
"Just before we left the Red Tower, Garvey told me something."
"You can't trust him," said Tianne, rolling her eyes. "Don't you know that by now?"
"I don't trust him, but this is different. I had my suspicions before we left and when I confronted him about it he told me the truth."
"Wren—" said Tianne, but she cut her off.
"The Grey Council knew the school was going to be attacked." Both of her friends stared at her in silence, slowly digesting the words. "That was why Eloise had been meeting with the Jhanidi for months. It's why all of the teachers were so preoccupied and kept going away on secret trips. They were preparing for the day when it happened. It's also why I was the last student to join the school."
A range of emotions flickered across their faces. Wren watched as they went back through their memories, going over everything they'd seen in the last few months at the school. There were a hundred questions they could have asked but there was only one that really mattered.
"How?" asked Danoph. "How did they know?"
"The same way I knew how to find Morag and Laila. It's because of your nightmares. The dream you kept having about a fire wasn't from the war. It was the Red Tower, burning on the horizon. Danoph, you're an Oracle."
Oracles were rare magic users whose connection to the Source enabled them to make prophecies about the future. At least that was the theory. Most of them were mad, gibbering creatures who lived in their own filth, worse than any animal. Several teachers had spoken of their disdain for Oracles as all of their vague predictions could be twisted to match recent events.
The most famous prophecy, the Opsum, spoke of a child with magic who would reshape the world for centuries. It was why the Grey Council of old had abandoned their posts leading to the downfall of magic and the abandonment of the Red Tower.
But Danoph was different and the new Grey Council had known for a long time.
Tianne started to protest and probably claim it was ridiculous but a peculiar stillness had fallen over Danoph. He was looking inwards again, probably studying the images he'd seen while asleep. Most recently his dreams had been about a girl being burned at the stake for using her magic. Wren had listened closely to what he'd told her for a week before having enough information to send out a search party. Tianne and the others had been told to ride south and look for a village where they could gather supplies. Instead they'd found a suspicious community getting ready to kill one of their own children.
"I don't know what to say," admitted Danoph.
"I didn't want there to be any secrets between us," admitted Wren. "You deserve to know the truth. I wanted to tell you sooner, but we were travelling and then busy setting up this community, but those are just excuses."
"What will you do now?" asked Tianne.
Danoph shook his head. "I don't know. I just don't know."
"People keep asking me what's next for our community. They're all looking to me for answers, but I'm just making it up as we go," confessed Wren. Normally she wouldn't feel comfortable talking about such things, but it was easy in their company.
"We know that," said Tianne with a wry smile.
"I need some time to think about this," said Danoph.
"We all need to think about the future, but there's one thing I'm certain about," said Wren. "I would like you both to be part of this community. You came here because of me, but now you need to decide for yourselves. This place will grow and there will be some difficult times ahead, but this is where I need to be. Is it the right place for you?"
The idea of not seeing either of her friends every day was hard to contemplate but they needed to choose for themselves, without thinking about her or anyone else. Danoph finally knew the truth and Tianne had to make up her own mind, rather than following others because it was easier.
Even if she couldn't admit it out loud, Wren knew the real reason she'd delayed telling them. She was afraid of being alone. But she was loath to manipulate them, even a little, after how Garvey had done it to her.
For now Wren decided to enjoy the time they had together while it lasted because she knew dark times lay ahead. Danoph had foreseen more than she'd told them. Events were going to get much worse and a lot of people were going to die. The question then became would she, or her friends, be among the victims?
# CHAPTER 4
Regent Choilan managed to remain in control until he was alone in the royal wing of the palace. He closed the doors to his rooms and those to his bedchamber before falling into a chair in a fugue state.
His left hand began to shake and he gripped it with the right, trying to calm the fear racing through his body. For the first time since wrestling the throne away from the grubby hands of his rivals, Choilan was unsure of himself. Always a decisive man, he now faced a situation for which he was utterly unprepared. His Ministers had offered their best advice, but ultimately it was useless. Normally his clerks and discreet agents had more useful ideas, but even theirs had been insufficient. Any sort of definitive solution eluded him, leaving him feeling powerless and inept.
The guards and servants were whispering every time he passed them in the corridors of the palace. No doubt it would be the same across the city and there would only be one subject anyone cared about. Other minor worries and appeals had fallen away in its wake. Now the line of people requesting an audience every day was all focused on one thing.
Garvey.
Twice the rogue mage had crossed the border into Zecorria. Twice he'd brazenly walked into a village with his followers and acted as if he hadn't erased an entire village only a few weeks ago, murdering everyone who lived there. The second time he crossed into Zecorria he'd spent the night at the village tavern. The local people had been terrified of what he might do to them if they refused to serve him and the others. Afraid for their lives they'd given Garvey and his followers food and drink, drawn them baths and provided them with rooms for the night. One man had described the experience as if everyone in the village had been balancing on the edge of a sword. It would only take one look, one wrong word and they'd all come tumbling down and be cut in half. Garvey had even paid for the rooms, as if he and the rest were normal patrons. Miraculously nothing happened and no one was killed. That hadn't stopped people from demanding that he, as their Regent, do something about the rampaging menace.
It was small comfort that before Garvey had started his killing spree the national ban on Seekers had, apparently, been working. There had been no reports from his people about children exploding when they discovered their magic. Then again he'd not seen any recent reports about children struggling to control their magic. To that end Choilan had several agents discreetly visiting remote villages, disguised as merchants, to make sure that the locals had not decided to take matters into their own hands. So far there had been no rumours of children mysteriously disappearing. He suspected for the time being any child who had developed magic had simply become more adept at concealing it.
In the long term it was a serious problem that needed to be addressed. But right now he needed to find a way to deal with the current threat.
So far Garvey had destroyed two villages. One in Zecorria and one in neighbouring Yerskania to the south. On both occasions every person had been murdered and every building turned to dust. The corpses were left where they fell in the streets, a feast for crows. Those remains able to be recovered had often been chewed and mauled by hungry animals.
While the dead couldn't appeal for justice, scores of relatives queued up in the palace day after day, screaming for bloody vengeance. The Minister of Defence was calling for him to mobilise the army. To take the fight to the rogue wizards and kill them all on the battlefield. Sadly, the Minister seemed to have forgotten his recent history and had learned nothing from it. Choilan understood the futile nature of such a decision but most people didn't seem to care.
The people of Zecorria were afraid and they were quickly losing faith in him as their leader. To them his inaction spoke of weakness. As ever, they were not interested in the reasons for his indecision. Results were all that mattered.
The doors to his bedchamber opened and Selina, his first wife, entered without invitation. She was one of only three people allowed in here and he insisted his other two wives knock first. A tall woman, only a few years younger than him, these days she was often called handsome rather than beautiful. Her dark eyes were a little too large for her face. Her cheeks sharp and angular and her eyebrows constantly drawn into a perpetual frown. His other wives were significantly younger and they often warmed his bed, but he never sought their advice on serious matters. Marrying Selina had been a political move but over time they had developed a mutual admiration of each other's strengths. While never friends, and these days never lovers, their partnership had endured much and was stronger for it.
With a look and the slight raising of one eyebrow, he felt her assessing his slumped posture and the defeat on his face. Despite the early hour she poured two generous measures of kirsch and passed him a glass. As he rolled the colourless liquid around, inhaling the rich scent of cherries and almonds, she pulled up a chair and sat down opposite.
"To health," she said, sipping at her drink for taste before draining the glass. Choilan gulped his down, savouring the burning in his throat and stomach. This was a harsh distillation, taken from the poor area where he was born, but he insisted on keeping a bottle from the region in his rooms at all times. It served as a reminder of his past. It was a way of grounding him to show how far he'd come since those early days of fighting for every mouthful of food. "Vile stuff," said Selina, selecting a bottle of amber whisky and pouring them both another measure. This was something else. Aged for many years in oak barrels until it was smooth as silk and so expensive few could afford it. Instead of drinking it the Regent merely inhaled the rich flavours while Selina sipped at hers.
"Tell me" was all she said. So he laid it all out for her, piece by piece. The Seekers. The national ban. The fall of the Red Tower. Garvey on the rampage and the destruction that followed in his wake.
"I remember what one mage did during the war," said Choilan in conclusion.
"Which one?" asked Selina. "The one who forged the west into an unholy alliance? Or the one who defeated him in battle?"
"Both," he conceded. "One well-trained mage can kill hundreds of soldiers with just a thought or a gesture. How do you fight something like that?"
Selina raised that eyebrow again. "How did Seveldrom fight the Warlock?"
"With mages of their own."
"Then there is your answer." She said it so simply. As if the solution was just that easy. As if he could snap his fingers and solve it, just like that.
"Do you hate me so much that you take pleasure in tormenting me?"
"No, dearest," she said, putting aside her glass and surprising him by holding one of his hands in both of hers. "I was being sincere. You should have mages of your own."
"How? After getting rid of the Seekers, and playing into the people's fear of magic. It would be almost impossible."
"Almost," agreed Selina. "But not quite."
"You want me to hire a mage? I do not think anyone would come to defend us now, no matter the price that was offered. Garvey is also a member of the Grey Council and is known to be extremely powerful. Besides, how could I possibly trust a mage not to betray me?"
"That is the key," said Selina, squeezing his hands. Her fingers were warm but the palms were calloused. She hadn't always worn silk and lived in a palace. Her own path to First Wife of the Regent was no less challenging than his own. "Trust."
"A loyal mage. A mage of my own," he pondered. "A royally appointed mage to the court?"
"Perhaps in time," she conceded. "But look to the far east. In the desert kingdoms they have warrior monks who are mages. They serve the King as his trusted eyes and ears. They carry out his will and wherever they go, the people know them and respect them as honoured guests. To displease them is to displease their King and his punishments are said to be severe."
"The tattoo," said Choilan. Over the years he'd seen a few Jhanidi in his capital city proudly bearing their tattoo which ran down one side of their face. It sent an instant message to anyone they met what they were and who they represented.
"They are loyal patriots, but trust must be earned," said Selina. "In this way Garvey, and his band of murderers, may even be useful."
Choilan was starting to see where she was leading him. "A cadre of my own."
"He is the invading foreigner. A rogue mage and a danger that threatens us all. We need loyal patriots who are willing to stand up and face him. Proud Zecorrans who want to defend their homeland."
"Are you suggesting an amnesty for Zecorran mages?"
Selina shrugged. "Perhaps, although I doubt there are many of worth living in secret. They've probably muddled along, not been properly trained. But we can use the fall of the Red Tower to our advantage. Recruit the children."
"An untrained, untrustworthy child, against Garvey," scoffed the Regent, starting to pull his hand away. "It would be like a bee trying to sting a bear."
"But a swarm of bees can kill anything," said Selina, crushing his hand until he winced. "It will be a show of force that may keep him from our borders. Soldiers working in combination with them would calm the people as well."
Finally she relented and let go of his hand but remained hunched forward, their faces close to one another. He'd forgotten about the vein that throbbed in her forehead when she was annoyed. It made him smile despite the situation and she pulled back slightly, misinterpreting his expression.
"How could we trust them?"
"They are just children," said Selina. "They are lost, without a home or their leaders. They need guidance and strong role models. Better us than they become rogues like Garvey or worse, they join a criminal band and disappear into the underworld."
"I've been pushing hard about the danger of Seekers. It helped soothe the people when the ban was brought in, but now magic is on their minds again."
"Shift the fear to the Red Tower," suggested Selina. "It was responsible for the Seekers. It created the menace of Garvey. The students are just children. Lost little lambs who don't know any better."
"But we will teach them," said Choilan. He briefly shared a smile with his first wife.
"If the children are young enough we can mould them into loyal patriots who will serve their country without question."
"What if they prove disloyal?" asked the Regent. "Or they're too old to be moulded?"
"I'll leave it up to you to decide how you deal with those people," said Selina, running a hand up his thigh. "But remember, there are many ways to motivate young, curious minds. Just ask your other wives."
The shiver of pleasure from her touch faded and he grimaced. "I deserved that." She withdrew her hand and sat back to sip at her expensive whisky. It was at times like these that he remembered why she was still alive. At one point, only a few months ago, he'd been plotting for her to have an accident. Choilan was suddenly glad that he'd put the plan on hold.
"And if those methods fail to motivate them, there's always the torturer's blade to break their spirit. Then you can rebuild them from the ground up." She said it with such dispassion he was suddenly reminded why they rarely shared a bed any more. Every time they did he was sure he'd wake up to find her hands around his throat. Selina regarded him coolly over the rim of her glass as if she could read his thoughts. A small and dangerous smile played at the corners of her mouth.
"The children must be taught, to make them stronger, but that is a concern for another day. For now I think thirty children, sworn to the throne of Zecorria, would make even Garvey pause."
"I believe you're right," he agreed. "And once again, we can be seen as the example that others in the west should follow. Just as it was with the ban on Seekers."
"Let them worry about their own problems. They may not use the same methods, but that could also be turned to our advantage in time."
Choilan imagined what it would be like to be surrounded by a dozen strong and loyal mages. An immeasurable powerful force that would fight to defend him and give up their lives for him. A cadre that could defeat entire armies. One that he could even loan to his neighbours if they chose not to adopt the same methods.
"It will have to be worded carefully," he mused.
"You have people for your speeches, do you not?" she asked. "Let them earn their coin. It needs to be a powerful message."
"I will get them working on it immediately," he replied and Selina stood up to leave. "Do you have to go?"
Her expression was cold and haughty as she stared down her nose at him. "You have your other wives for that."
He shrugged. It was true. They were younger, and more agile, but sometimes it was nice to be challenged by someone who was his equal in the ways that mattered.
"Do you want me to get rid of them?" he asked, wondering if she was genuinely jealous, although that seemed unlikely.
"You flatter yourself," she said. "No, you should keep them. They stop you from trying to climb into my bed every night when I'm trying to sleep."
Choilan felt his shoulders slump in defeat. It had not always been this way. Once he had been as passionate about her as he was his other wives. Marrying the others had also been a political move upon taking the throne. To ensure that his line continued and to honour the families who had lent him their favour during his campaign. With daughters one step away from the throne they were raised higher than their peers and could ask for more favours.
"Did you seek me out for a reason, or were you just bored?" he said, returning to the pleasures of his whisky since her body seemed beyond his reach.
"A trifling matter, but I can deal with it myself."
"It cannot be that insignificant if you came to me with it," he pointed out. "You're perfectly capable of dealing with most things by yourself."
"Flattery will not get you into my bedchamber tonight."
"I was being honest," he replied. "So, out with it."
Selina sat down again but she remained pensive. "Some of my people have gone missing."
Although the Regent had his own network of agents who worked at home and abroad, he indulged all of his wives in different way. His third wife delighted in fashion. His second in caring for animals and his first wife in spying. He had allowed her to recruit a dozen individuals to gather information. Unlike the hobbies of his other wives Selina's favourite pastime yielded something of real worth. Often her people uncovered titbits of information that eluded even his most trusted agents.
"Missing? Or silent?" he asked.
"Missing. I've sent people to investigate and no one has seen them for days. Not their families or friends. They've simply disappeared."
"How many of them?"
"Eight," said Selina with a grimace.
Choilan whistled through his teeth in surprise. One or two might be considered a coincidence. Perhaps they'd grown bored in their dual roles and decided to move away and live elsewhere. Sometimes an agent dug themselves into trouble and would disappear, only to turn up floating in a river or lying in an alley with their throat cut. For so many of them to vanish without a trace was highly unusual.
"Send their names to Bettina and she'll have someone look into it."
"Thank you, Choilan," she said, forcing a smile onto her face.
"Thank you for the idea," he replied. "At times like these I'm reminded why you're my First Wife."
He expected another tart response, brimming over with vinegar, but instead she merely bobbed her head and went out of the door. As the silence returned the Regent turned his mind back to the problem of Garvey.
He still needed the people to see that he was doing something about the rogue mage and his followers. A show of force and gathering some soldiers would appease the people, but it wouldn't change the outcome if they were ever to face the mages. Then again, if the worst should happen, perhaps a stray arrow might catch one of his followers in the neck. It had happened in Yerskania during the destruction of a village. Nevertheless, merely giving the order and making it publicly known that he was amassing a force would reassure some who thought him frozen with fear.
The wolves were at the door but he wasn't done yet.
# CHAPTER 5
Akosh maintained her rictus grin as Bollgar stuffed another pastry into his face before licking each of his fingers on that hand. His other held a pen which hovered over a ledger filled with pages of numbers in orderly rows. The page was pristine, as was every ledger on the shelves. The books were completely at odds with Bollgar's appearance.
Severely overweight, balding and with several chins and no neck to speak of, Bollgar wore only a stained orange robe in a poor imitation of a monk. As his bulk had increased over the years finding clothes to fit had proven increasingly difficult. In the end he'd taken to wearing loose robes. The latest was plain and inexpensive, marked with grease, crumbs and dried bits of old food.
When she saw he was contemplating another pastry, Akosh cleared her throat loudly, drawing his attention back to the matter at hand. If he hadn't been one of her children she would never have dealt with him.
"Apologies, Mother," he said, wiping his fingers across his chest, leaving more grease marks on his robe. "Where were we?"
"Morrinow," she reminded him.
"Ah yes." He leaned backwards in his chair, which groaned alarmingly under his immense weight. He retrieved another journal from the bookshelves behind him that filled the wall, floor to ceiling. When not distracted by sweet delicacies Bollgar had a remarkable mind for numbers. Officially he was just a bookkeeper for half a dozen shops on a small side street in Herakion, the capital of Zecorria. Unofficially he was responsible for the money for several less reputable organisations, including various criminal enterprises in Zecorria. What even they didn't know was that hidden among their own numbers was a set of ghost transactions he monitored on behalf of Akosh. Money donated by her children which was then given to orphanages across Zecorria and Morrinow.
Bollgar laid the journal on the table and carefully cleaned his hands on a wet cloth then dried them on another. Only then did he open the book. He didn't care about his appearance, but no one was allowed to touch his books. Every page was spotless, which was remarkable given the quantity of crumbs hiding in the folds of his robe waiting to leap onto the paper.
The fat man muttered to himself as he ran a finger down a column of numbers. "I'm afraid to say it's not good news. The contributions from the Morrin were always low, but they've dropped to almost nothing in the last year."
It was as Akosh had expected. Setting up orphanages devoted to anyone except the Blessed Mother in Morrinow was always going to be a tricky idea. However, with patience and persistence, she had succeeded in a few of the smaller towns that were often overlooked by the capital.
It had been a little easier during the war, and then shortly after during the civil war in Morrinow where old ideas were being challenged. Now that the civil war was at an end many of the traditional values in Morrin society were being reasserted. This included a national focus on religion and the country was slowly edging back to a theocracy in all but name. Gradually she'd been eased out as devotion to the Blessed Mother was not only expected but required, and the punishments for being different from the norm were severe.
"Close the accounts in Morrinow," said Akosh. "It was a nice idea, but I suspected it wouldn't last. Focus on the accounts here in Zecorria."
"As you wish." He scribbled a few lines on a separate notebook and returned the Morrin journal to the shelves.
"How are the funds in Herakion?"
Bollgar didn't even need to look at a journal for that. The figures were all in his head. His wide grin told her everything she needed to know before he even spoke. "Steady. But the numbers for this month are lower than last month. However, there is plenty of extra money sitting idle if you're considering further expansion."
"It has crossed my mind," she admitted. "In fact I'm just on my way to visit an orphanage I recently contacted. If they agree today, I'll want you to send a monthly stipend to them like the others."
"Of course," he said, making another note in his neat script. "Send me the details."
Despite his indulgent appetite Bollgar had never let her down in thirty years. He was one of the first children she'd seen in the first orphanage she'd supported.
"You've been loyal and I value what you've done over the years," she muttered and he flashed a grin, although his eyes strayed to the pastries again. "I would be displeased if you suddenly died because of a weak heart."
Bollgar's eyes snapped back to her and he seemed suitably abashed. "I'm trying to ration myself, Mother, but it's my only real pleasure."
She had a few vices of her own but none that were likely to kill her as quickly. It was possible he could die tomorrow. With a grimace she stood up and put a hand against his forehead. Bollgar closed his eyes at her touch while she used a small portion of her power to study him beneath the skin. After a moment she withdrew her hand, wiping the sweat away on her trousers.
"Thankfully your heart is still strong. I urge you to take better care of yourself," she said.
"Yes, Mother," he said, although she noticed he didn't make it a promise.
If he died it would be a problem only because it would take someone months to decode his journals. Akosh smiled, letting him think it was because she cared. She had grown soft. It was time he took on an apprentice or two, just in case he died in an accident, or she snapped his neck in a fit of rage. He wasn't her only bookkeeper in Zecorria but he was the best. Even so it paid to plan for contingencies.
Akosh left him alone with his pastries and neat rows of numbers. She retraced her route from weeks ago and returned to a once grand part of the city in the east. The hand-drawn sign on the front door of the orphanage had been replaced with a neat wooden plaque and the exterior made brighter with a recent coat of paint.
On her first visit she'd seen mostly empty rooms with children amusing themselves using the barest minimum, but already there were a few noticeable changes.
As soon as she set foot inside the orphanage Akosh smelled fresh bread. In the first room off the entry hall she saw a group of children eating their lunch, happily stuffing bread smeared with butter into their fat little faces. A steaming bowl of thick stew also sat in front of each child. There was no fighting, no jealous looks at someone else's portion, just contented munching sounds. She left them to their lunch and stepped into the room beyond.
Akosh found two neat rows of battered and worn desks, likely salvaged from an old school, being put to good use. Twelve children were focused on the teacher at the front of the classroom. The man was running through the alphabet on a scarred blackboard with the children repeating each letter after him. Some of the students were a lot older than the others, suggesting a life spent on the streets where reading and writing were not particularly valued. Being quick with your fingers and your feet was far more useful to criminal gangs. It might be too late for some of them, but the orphanage gave all of them a chance at a new life if they wanted it. All they had to do was obey the rules and adopt the one true faith: hers.
In one corner of the room sat a small wooden crate of toys and a neat stack of books. She searched for a prayer corner and any votive lamps or candles, but couldn't see any. The teacher spotted her by the open door but didn't seem alarmed. He merely gestured with his head back the way she'd come. Akosh took the hint and went in search of Jille, the administrator.
At the back of the building was a small office. She knocked on the door and almost immediately Jille opened it and stepped back in surprise. Akosh noticed she'd put on a little weight and the bags under her eyes had faded. True to her word she'd been taking better care of herself as well as the children.
"I wasn't sure we'd ever see you again," admitted Jille. "Please, come in."
The office was unchanged and as Akosh sat down on one of the battered chairs she thought she smelled damp paper. Jille saw her wrinkling her nose and gestured at a pile of books.
"A nearby school recently closed. We managed to salvage some desks and books, but they're a little damp. We're just drying them out."
"You don't need to do that," said Akosh. "You have money for new books."
Jille shrugged her thin shoulders. "We didn't know if we'd receive any more money. So we're trying to make your donation stretch as far as possible."
"What else have you spent the money on?"
"Food, clothing and blankets mostly. We also hired a new member of staff. He's focusing on teaching them to read and write. People always need scribes, messengers and bookkeepers."
"Have you spoken to any of the other orphanages where I'm a patron?" she asked. Jille squirmed in her chair but eventually answered.
"I visited one of them and the man running it let me see inside."
"You seem uncomfortable," said Akosh. "Did you see anything untoward?"
"Oh no," apologised Jille. "All of the children were well fed and happy. I spoke to the staff and they were wonderful."
Akosh folded her arms and leaned back in her chair, baffled by Jille's reluctance. Normally these meetings were over very quickly. The offer of free money for the children, on a regular basis, should not have been a difficult decision. And yet something about all of this had made Jille uneasy. "I'm getting the feeling you've made a decision and it's not one I'm going to like."
"Your offer is generous, and we're grateful for the money, but I must turn it down. We're going to teach the children about the Maker."
Akosh took a deep breath and counted to twenty slowly in her head before speaking. "Why?"
"The Maker is a safe choice. We can ask at several churches for donations and they're not going to disappear. I spoke to a few people and not too long ago no one had ever heard of Akosh."
On the one hand she couldn't blame Jille. Things could change rapidly. Now every church of the Holy Light was dedicated to the Lady of Light. No one prayed to the Lord of Light any more. He'd only been gone for ten years, but already was being quickly forgotten. His sudden absence served as a constant reminder to Akosh that she needed to move slowly and with caution. One of her brethren, someone with significant power, had eliminated the Lord of Light for interfering with the mortals. Akosh was very aware that if they found out what she was doing in ten years' time no one would remember her name either. Despite knowing all that she sensed something else had changed Jille's mind.
"Are you sure?"
"My mind is made up," insisted Jille, although she didn't look very certain.
"I want you to think carefully about this, Jille. Your decision will affect a lot of children and their future."
"If this is about the money, we still have some of it left," said Jille, pulling open a desk drawer.
"I don't care about the money. Keep it. Did someone say something? Has someone approached you?"
Jille shook her head but she refused to make eye contact. So someone had spoken to her. Perhaps they'd threatened her or the children. The question was, who? A priest from another faith? An agent representing one of her unusual siblings? Or someone else? A human group?
"Who did you talk to?" asked Akosh. Jille was sweating now and she seemed to have decided that silence was her best defence. "Tell me."
"I think you should leave."
"I can make you tell me," promised Akosh. She didn't need to draw a weapon. It would only take a little pressure to break her. Breaking a couple of fingers usually did the trick. Failing that dislocating a joint was enough if they didn't faint from the pain.
"Is there a problem?" said a new voice, startling them both.
A tall man with beady eyes and trousers that were too short for his gangly frame stood in the doorway. Jille relaxed at seeing a friendly face, but Akosh wasn't done. This was perhaps her only opportunity to find out who was interfering in her business.
"I'm still waiting for an answer," she said, ignoring the newcomer.
Jille stared at her friend, silently beseeching him to help her. He came into the room and even went so far as to put a hand on Akosh's shoulder.
"You're making her uncomfortable. You need to leave."
The way he said it sounded unusual. As if he'd been rehearsing it. Perhaps he wanted to impress Jille and make himself the noble hero of their little story. She wondered if this was some kind of scam. There was definitely more going on than she'd been told. Finding out what, without killing at least one person, was becoming increasingly unlikely. Dead bodies would attract the attention of the authorities and there were always ripples from unsolved murders. Enough of those and the people she wanted to avoid, her siblings, might start investigating.
Caution. It was the first and most important lesson she'd taught herself in the last few decades.
Jille's friend took her hesitation as reluctance to leave and dug his fingers into Akosh's shoulder, trying to get her to move. Caution was important, but sometimes others took the decision out of her hands.
Akosh grabbed him by the wrist and twisted it sharply to the right. He dropped to his knees as she stood up, angling his arm to try and relieve the pressure. Instead of crying out in pain as she wrenched his arm, he grinned and reached for something behind his back. It was when he drew the dagger that she finally noticed his boots. His clothes were old and ill-fitting, the trousers too short and threadbare, as she'd expect for someone in his position. But his boots were new and had been polished until they shone. He loved those boots and took very good care of them. Whatever his purpose in being here, he'd exposed himself by being unable to fully commit to the role of penniless teacher.
He slashed at her with the blade and Akosh was forced to release his arm and step out of the way. The back of her knees collided with the desk and she glanced over her shoulder. Jille was pressed against the far wall, wide-eyed with terror. Whatever was happening she wasn't involved. She didn't have the guile and was terrible at lying but Akosh still didn't know who had coerced her into rejecting the money.
"Who do you work for?" asked Akosh, but the man just grinned, showing off even white teeth.
"Help! She's attacking Jille!" he shouted over his shoulder. There was only one door out of the cramped room and the space was already crowded with three of them. If anyone else came into the room it would be difficult to escape.
Akosh rushed the man, dodging a slash and shoulder-barging him to one side. The back of his head collided with the wall and he started to fall, but stuck out a leg on the way down. She tripped and went skidding into the hallway on her stomach.
As she scrambled to her feet Akosh heard children crying and screaming. The teacher was staring at her with alarm but his eyes widened in horror as he stared over her shoulder. The tall man came out of the room with blood dripping from a gash in his forehead, stumbling for dramatic effect. The back of his head had struck the wall and yet somehow his face was bleeding.
At the sight of blood the children's wailing increased in volume and now the teacher was trying to shield all of them with his body, arms held wide. The tall man was edging closer, looking disoriented and groggy. He was making a heroic effort to keep Jille safe and it looked convincing, until he winked at her.
"Take whatever you want, just don't hurt the children," he shouted, holding up his hands in surrender. A smile quirked across his face and then it was gone.
Despite the situation Akosh had to admire his performance. He was good. Playing the victim and scaring the children at the same time. Whatever she did now or said, she'd never be able to come back to this orphanage. Even working through a surrogate Akosh knew she could not be their patron. Someone had outmanoeuvred her.
Part of her wanted to stab him over and over again for interfering in her plans. A larger part wanted to break his bones, one at a time, until he told her everything. Then she'd find out who he worked for and what they were planning. She teetered on the edge, having to work hard to fight her violent instincts, but in the end she withdrew. She calmly walked out of the building, clenching her jaw to stop herself saying something.
Akosh watched the orphanage from a secluded corner a few buildings away to see what happened next. A small boy hurtled out of the front door and raced down the street. A short time later he came back with some city guards in tow.
Maybe she should have just killed them all. She wondered how far it would go. One alleged assault shouldn't be enough to cause any real problems. Even so she would get some of her people to quietly look into it. She wasn't afraid of the authorities, but all of this would leave a trail.
Snarling with frustration she walked away from the orphanage, wondering about the ripples this would cause and who might notice them.
# CHAPTER 6
It had been a few years since Balfruss had last seen Tammy but on the surface she looked much the same. A little leaner in the face perhaps. Tired and tense but that was to be expected given her new role and the pressure that came with it. When he'd heard about her promotion it hadn't really surprised him. Her determination was unparalleled.
"Congratulations, Khevassar."
"Thank you."
"It suits you," said Balfruss, gesturing at the Guardian jacket. "It's the first time I've seen you in it."
"Voechenka was a long time ago," she said, recovering quickly from her initial surprise. "But sometimes it feels like only yesterday. It still haunts my dreams."
"Mine too," he said, forcing a smile to try and drive away the mental imagery from their shared time in the haunted city. "I came hoping you had some good news about Habreel and his network."
Tammy hesitated before answering, showing a level of caution he'd not seen before. Balfruss didn't know if that had developed because of her new role or a shift in their friendship. He hoped it was the former. "I have news, but little of it is good."
His fledgling smile faded. "Do you know what's happened?"
"I do. How is Munroe?"
Balfruss stared into the distance, trying to put her grief into words. "For the first few days she was barely holding on. She didn't move, didn't speak. She was consumed by her loss. I thought she was going to die. Two weeks ago she came out of her fugue. I tried to stop her but she insisted on going back to the Red Tower. She wanted to see it for herself and look for any clues about her family. She's due back any day and, unless I can give her some good news, I'm worried what she will do on her own."
"I'm so sorry," said Tammy.
As a father Balfruss couldn't even contemplate what he would do if something happened to his child. It was a nightmare he couldn't dwell on. Thinking about his daughter always came with mixed feelings, but it was better than the overwhelming grief he'd seen in Munroe's eyes. At least his child was still alive.
"Right now, though, I'm concerned about you," she said.
"Me?"
Tammy folded her arms and leaned forward on her desk. "Are you going to seek retribution for the Red Tower?"
Balfruss shook his head. "We may not have spoken in a few years, but I haven't changed that much."
Tammy sighed and sat back in her chair, scrubbing a hand across her tired face. "I'm sorry. These days it's difficult to know who to trust."
"There are some things that I cannot tell you and others I will not," said Balfruss, knowing they both had secrets they couldn't share. No one on this side of the Dead Sea knew about his daughter and despite trusting Tammy, he would not tell her. The less people that knew about her the safer she would be. "But I will not lie to you and I'm still your friend."
"I know."
"Good. So, do you have some news for me?" he asked.
"We have Habreel in custody and he's been helping us locate his lieutenants. They were coordinating his network of followers to stir up trouble against the Seekers. One of the six lieutenants is in the cells below, one is dead and unfortunately we can't locate the other four."
"Still, that sounds like a good start," said Balfruss, puzzled by her lack of enthusiasm.
"It would be, if Habreel and his people hadn't been pawns for someone else. A larger group. He was working with a woman named Akosh, and she was using his group for her own ends. So, now we're trying to track down her and we don't know anything about her agenda."
"There's something else. I can hear it in your voice," said Balfruss.
Tammy's job often required her to conceal her true feelings, but after enhancing his senses with magic for many years, it had made Balfruss adept at reading people.
"Akosh is some sort of cult leader. We questioned one of Habreel's people, Grell, and he described her as an assassin, but he also said she had some kind of magic. She has a following and she funds several orphanages here in Perizzi. One of my Guardians, Brook, killed Grell for saying too much. It turned out Brook was part of the same cult. We found an idol in her home." Tammy fished around in her desk drawer and pulled out a small stone statue. Balfruss held up the idol towards the light. It was crudely made but clearly represented a benevolent woman, probably a mother, caressing the cheek of a small child held in her arms. A symbol of love and affection at first glance, but perhaps it represented something more sinister. Absolute obedience.
"Five orphanages in the city have the same idols and a holy book. They all receive regular donations from former orphans, and apparently someone claiming to be Akosh visits them in person from time to time. Some of my people are watching the orphanages in case she shows up."
"How old was Guardian Brook?" asked Balfruss.
"Almost forty, why?"
A disturbing idea was starting to form at the back of Balfruss's mind. He and Tammy had shared much during their time together in Shael, but this was skirting close to a subject he'd kept private. It was something he was still struggling to accept and had yet to tell anyone about it after all these years. Few people knew the truth about Vargus, although many like Balfruss had fought beside him during the war. They thought that he was only a veteran warrior who had died defending Seveldrom. If that had been the end of his story it would have been a lot simpler.
"Be very careful," Balfruss warned her. "If your people see Akosh, I would strongly advise them to keep their distance. Tell them not to interfere with her, merely observe and report back."
Tammy folded her arms. "I'll need a little more to go on. Are you saying she's really a mage?"
"I'm not sure," he admitted, shaking his head. He needed more evidence before he could be certain. "Either she's a mage or something else. Something we've not seen before."
Over the years Balfruss had come to realise that while others considered him knowledgeable about the world and its mysteries, he knew far less than people believed. Maintaining the lie massaged his ego a little, but it also protected them from horrors they'd never considered and were better off not knowing about. Tammy had been with him in the labyrinth beneath Voechenka where they'd fought the brood mother. There were many terrors lurking in the dark, waiting for their chance to strike. Most of the time ignorance was bliss.
His instincts were telling him that Akosh was either something new or something very old.
"I recognise that expression," she said and Balfruss guessed her mind had also gone back to Voechenka and the labyrinth.
"I don't think it's the same, but my gut is telling me she's incredibly dangerous. I know someone who might be able to give me some answers."
"I'll make sure they keep their distance," promised Tammy. "I also have people looking into Akosh beyond the capital in Yerskania and abroad. I'm beginning to wonder how far this cult of hers extends."
That was a worrying thought he'd not considered, but it made sense if his theory was right. "I'm staying in the city at the moment. I'll come by with any news as soon as I have it."
"There's something else we need to talk about," said Tammy. "Garvey."
The name echoed around the room and then dropped like a stone. In the last month he'd been helping the students who had forsaken their magic settle into new communities. It often meant him travelling to remote towns and villages, but even in those quiet corners he'd heard the stories. He knew what Garvey and his band of rogue mages had been doing. The lives they'd taken. The homes and communities they'd destroyed.
It seemed impossible that Garvey was responsible and yet, no matter how much he didn't want to believe it, deep down he knew that it was true.
His friend was gone. Twisted by his experience, angered by the fear and violence people directed towards anyone with magic, Garvey had finally snapped. He wanted to live free but if anyone got in his way or disagreed with him, he killed them.
"What he's doing," said Balfruss, his hands curling into tight fists, "it goes against everything we tried to do at the Red Tower. Everything we stood for."
"We need your help to stop him."
Balfruss shook his head. "You don't know what you're asking me to do."
"He's dangerous. He's murdering people and destroying whole communities. What else do you need to know?"
"He's angry." Balfruss took a deep breath and then another, forcing himself to calm down. Despite all of their preparation and planning, so many people had still died during the evacuation. Their work over the last few years at the Red Tower had been undone in less than a year. Eloise was trying to salvage what remained with the Jhanidi, while others were being forced to hide their power, just so they could live in peace. Seekers had buried or destroyed their masks to protect themselves and now, if a child came into their magic, he had no idea what would happen to them. The fear of being cast out by their community, or worse if they were discovered, would make them bottle it all up. Instead of reaching a place where magic was respected, they were moving towards a new dark age of fear. One where anyone connected to magic would be exiled or killed. He shared some of Garvey's anger about what had happened but knew killing innocents only fed into their belief that all magic was dangerous.
"He's my friend. You know how rarely I used that phrase."
Balfruss had now reached the age where he could count on one hand the number of people he would call true friends. These were people he could turn to in any circumstances and they would be there for him without question. Some friends had died, others had changed over the years becoming people he barely recognised any more, and some had drifted away when their lives went in a new direction. He'd thought of Garvey as a friend, despite all of the changes he'd gone through, but recent events were making him question his judgement. The man he knew, no matter how damaged and angry, could not have committed such atrocities.
He expected Tammy to ignore him but she considered his words carefully before replying, her words echoing his thoughts. "He isn't the same man you knew. Events have changed him."
Balfruss sat back in his chair and closed his eyes for a moment. He knew she was right but there was so much to do. He was doing his best to stop Munroe from going on a killing spree of her own. He'd managed to rehome all of the students who had given up their magic, but being accepted as a member of the community did not happen overnight. And now he needed to contact an old friend about Akosh. And if he was right about her the possible repercussions would force him down a new path.
"I want to help, but I have my limits. The Red Tower is gone and so are all of its students. All of the mages I could call on are scattered to the winds, living in hiding. Garvey has at least a dozen students with him. I wouldn't stand a chance against them by myself."
"Do you think he would kill you?" asked Tammy.
Balfruss considered it. "No, but his followers may have no such compunction. They may have acquired a taste for killing, and, as someone capable of fighting back, I would present them with an exciting challenge."
Balfruss knew his answer was disappointing, but they would have to deal with Garvey by themselves for the time being. Without some guidance he was afraid of what Munroe might do. If she went on a rampage it would make Garvey's seem minor by comparison. Without a doubt she was the most powerful mage he'd ever met and right now she was incredibly unstable.
Tammy didn't push him any harder on the subject, for which he was grateful.
"I'll speak to my contact about Akosh and let you know if I find anything."
"I'd appreciate that," she said, coming around the desk to see him to the door. "Despite everything, it's good to see you."
She hugged him tightly for a moment and then let him go. As Balfruss walked through the outer office he looked back through the door and saw Tammy return to her desk and the mountain of paperwork.
When Balfruss entered his room at the inn he was briefly surprised to see someone sitting beside the window. Munroe looked very small in the large chair with a blanket across her lap. The room was in darkness and she was staring out at the night sky, oblivious of her surroundings.
He moved around the room, kindling the lanterns and starting a fire to drive away the chill in the air. Munroe barely noticed and didn't react to anything he did. She'd been like this at the beginning, numb to everything except her pain.
"When did you get back?" he asked, settling into the chair opposite.
"Tonight," she murmured, her eyes still distant. "Do you think it would have made a difference, if I'd been there?" asked Munroe. She'd asked him the same question several times before but he wondered if she remembered.
"I don't know. Perhaps." It was the same answer he'd given her the last time as well, because there was no way to know. If she had been at the Red Tower it could have made things better or far worse. Whatever answer he gave it wouldn't restore the dead.
"What did you find? Was there anything left?" he asked. Part of him had also been tempted to travel back to Shael to visit the school and see what remained. The more logical part of his mind had warned him against it. Such a journey would only bring him heartache and make him angrier. Heeding the wiser voice inside he'd remained here while Munroe had gone in search of answers about her family.
"The school is gone." Her voice was flat and lifeless. "Every building is a pile of charred timbers. There were bodies, too, burned things, just lying on the ground. Even the crows won't touch them they're too far gone. The tower itself is still there. I could see where they'd tried to burn it. The earth all around is blackened, but there's not a scratch, not a single mark on the stones."
It was a small relief but again not unexpected. The tower was centuries old and he had no idea who had built it or how it had been done. As a boy he'd asked a member of the old Grey Council if they knew its origins, but they were also in the dark. Its creation was another secret that had been lost.
From the moment he'd seen smoke on the horizon Balfruss had known the school was gone. But he'd put on a brave face and kept the students marching, kept their minds and their hands occupied so they didn't dwell on the past. But Munroe hadn't gone back to Shael to check on the school. She'd gone in search of her loved ones.
A long painful silence settled on the room. He didn't want to ask and she didn't want to speak about it, but part of him needed to know. This time, ignoring the wiser voice, he broke the silence and opened himself up to the pain.
"Did you find them?"
"I searched everywhere but found nothing." Balfruss felt his heart lift at her words until he saw the misery etched into her features. "So I spent several nights listening to drunks tell stories in taverns. In dark corners, in whispered voices, several people spoke about chasing an injured man and a boy on horseback. They pursued them down to the river, only for a green monster to rise from the water and scare them away." Balfruss tried to speak. To offer her a glimpse of hope. A sliver of denial that, perhaps, all was not as it appeared. But she wasn't finished. "I went down to the river, to his cabin. And there, soaked into the boards of the pier, I found blood. There was so much."
There were no words he could offer to soothe her agony. Nothing he could do that would change what had happened. Her family was truly dead. Balfruss wondered who was sitting across from him. How much of the person he knew had died with them beside the river?
Her eyes roamed about the room before finally settling on his. For a little while she seemed to be with him in the room. "You look tired."
"It's been a long day," he said, trying to remember the last time he'd slept for more than a few hours.
"Did you visit Tammy? Did she have any news about who killed my family?"
"No. The person we thought responsible was merely a pawn for someone else."
Balfruss saw something dangerous flicker behind her eyes. "I want a name," said Munroe.
"Habreel was being played the whole time. His group of followers were just one branch of a much larger cult."
"Who killed my family?" she asked again.
"Give me some more time," he said. For a brief moment he thought she might concede but then the steel crept back into her gaze. Her posture shifted, shoulders hunching and hands curling up into tight fists. She was out of patience and he was out of time.
"Give me a name," said Munroe.
"Akosh. Her name is Akosh."
"I've heard the name before." Munroe silently moved about the room gathering her belongings.
"We don't know much about her, only that she's been working from the shadows for a long time. She's also the leader of some kind of religious group."
"I know. I was the one who questioned Grell before he was murdered."
Munroe stuffed the last of her clothes into her bag then strapped on a bandolier of daggers around her chest.
"Some claim she's an assassin, but I think she could be a mage."
"That's something we have in common then," said Munroe.
"No matter what I say, it's not going to make any difference, is it?"
"No," she replied.
"Then there's something else you should know. There's a chance Akosh might not be mortal."
Munroe glanced around the room, looking for any items she might have missed before briefly sitting down on the edge of her seat. He knew she was going to leave but, hopefully, would still listen to his advice as it could help save her life.
"What does that mean?"
Balfruss wondered how much he should tell her, but in the end he settled for the simplest version of the truth. "In my travels over the years, I've met certain... beings. They're not like you and me. They have much longer lives and enormous power. Not power from the Source. It's something else that's hard to explain."
Munroe cocked her head on one side. "Can they die?"
"I honestly don't know. I understand so little about them."
Munroe picked up her bag and moved towards the door. "When I meet this Akosh, I'll let you know. I will make her pay for what she's done."
There was nothing dull or flat in her voice any more. Her eyes burned with hate worse than any he'd ever seen before. He knew Munroe's thirst for revenge would not be quenched until Akosh lay broken and dying at her feet.
He pitied anyone who stood between Munroe and her target.
# CHAPTER 7
Danoph tried to focus on the activity around him but his gaze kept drifting to the west. Something out there was calling to him.
With Wren's revelation about his ability the nightmares had started to change. Or perhaps it was simpler than that. He knew they were no longer random images from his brain designed to torment him. They were messages that needed to be studied. Even when they were disturbing there was a reason.
By accepting his Talent as a gift, he thrashed about less while asleep, letting the images wash over him as he tried to study them with a critical eye. Many of them were unpleasant and he saw death, disease and murders both foul and disturbing. But there were also images of hope, love, friendship and sacrifice. A young boy pushing an old blind man out of the way of a runaway horse. A pair of lovers covered in sweat, their bodies intertwined in passion. Old friends meeting up after twenty years apart and talking as if no time had passed.
Sometimes the dreams were easy to interpret, such as finding a young person before they were injured by their community, as they'd done with Laila. At other times the flashes were so fast it took him several nights before he saw them clearly. Or they could appear as nothing more than a random series of images that had no apparent connection. Those were the dreams he pondered on the most during the day.
With his new awareness the texture of his dreams changed as well. More often than not they felt as real as if he were awake. Sometimes he saw familiar places and people he knew from his childhood. Other times it was strangers or those he'd only heard about but could recognise them because of the trappings of their office. And yet with all of them he felt as if he could stretch out his hand and touch the people.
Often he saw a tall, blonde Seve woman dressed in a Guardian uniform. Once or twice he recognised a woman who had to be Queen Olivia of Shael. She was a slight woman with a swollen belly, standing beside her broad-shouldered husband from Seveldrom. Three times now Danoph had dreamed of his mother and the village in which he'd grown up, but he didn't know what any of it meant.
They were just brief moments in time, as if he was standing outside, peering in through a window as the lives of other people unfolded before him. At times he sensed they were glimpses of the future, but there were also images from his past as well.
This was only the beginning. It was something that would take him years to master before he was truly skilled at interpreting his dreams. But at least he was now aware and could start trying to decipher the images.
Danoph had started experiencing unusual sensations when he was awake as well, although he'd not told anyone about those. Wren had good intentions but she was overprotective and already had too much on her mind without him adding to her burdens.
His gaze drifted west again. His instincts were telling him something important was going to happen in that direction. Danoph had a strong compulsion to get on his horse and ride that way.
"Danoph, are you all right?" asked Wren.
He turned back to face her and the others, forcing a smile. "Fine. Just watching for raiders."
The ruins of another abandoned village lay spread out around him. A gentle breeze rattled the windows and doors, swirling dust around the empty street. The front door of one house repetitively banged open and closed, open and closed. There wasn't so much as a stray dog running along the streets. Dust lay on every surface and an air of forlorn abandonment filled every house. No one had died here. They had simply walked away before the war arrived as they were no longer safe, leaving behind most of their belongings. He wondered how many of them had found better lives and how many still dreamed of returning here.
Now he and the others had become ghosts, haunting the ruins of someone else's life, trying to find something they could salvage for their community.
Wren and three others were busy removing several panes of glass from one of the last houses that hadn't already been stripped of its windows. They'd also gathered up a lot of clothes, a couple of bolts of cloth and more blankets, which would be vital to get them through winter.
Other groups had come to this village before, but there was only so much each could carry on horseback without a cart. Wren had considered asking the blacksmith and others to build one, but then changed her mind. It would be easier for others to track them back to their community and it would be a much slower way to travel. That would normally limit them from carrying heavy objects back home but magic provided them with a way to overcome that restriction.
All of the heavy items, plus several windows padded with blankets, had been laid out on an old sheet. Working together, two of the group created a solid plate of force with their willpower which they slipped under the sheet and then raised off the ground. Maintaining the floating cart bed took considerable effort and concentration, but working in pairs and swapping over after a couple of hours made it easier. Wren was embracing the teaching styles of many magic users and it was starting to pay off. By using it every day the young mages in their community were not only becoming stronger, but also more comfortable and familiar with their magic. It also meant that Talents were starting to emerge, not by hunting for one, but simply by getting involved with a variety of tasks. Their dowser, Helsa, had simply found the water by focusing on their need and following a strong urge. As it turned out her ability didn't only apply to finding water. Now she was being used to find more wild sheep to increase the size of their flock.
Danoph turned west again and felt a stronger pull. Perhaps this was what it felt like for Helsa. He wheeled his horse around to face in that direction before he realised what he'd done.
"What is it?" asked Wren, but he barely heard her. It was calling to him and he felt a growing sense of urgency. Sensing his need, Danoph's horse actually took a few steps forward. "What's wrong?"
"There's going to be smoke over there," he said with a vague gesture towards the west. "People are going to be hurt."
"I don't see anything," said Wren, squinting into the distance.
"That's because I don't think it's happened yet," he said quietly, glancing around to make sure the others hadn't overheard.
Wren stared at him in silence for a long time. He knew she was considering their options and the potential repercussions of doing nothing versus getting involved. When the others were ready she signalled them to lift the goods off the ground and head towards home. The horses could only move at a walk, reins tied to a horse in front, while their riders focused all of their attention on keeping the burden afloat. Any faster and it became impossible to maintain with two people lifting the weight in unison.
He and Wren followed the group at the rear, keeping an eye out for raiders. With every step they took towards the village Danoph felt a growing sense of panic and unease. His skin became clammy and hot. Bile rose up in the back of his throat and he smelled smoke and tasted fresh blood.
They were too late. It was already happening.
On the horizon a thin strand of grey smoke rose up into the air. Danoph gently pulled on his horse's reins until it came to a stop. The others had spotted the smoke as well but they kept moving. At his side Wren was watching him and this time she didn't hesitate.
"We'll catch up," she said to the others, turning her horse to the west.
They rode hard but by the time they arrived it was already over. A group of travellers, six carts in all, loaded with all their worldly possessions, had been murdered. The wagons had been torn open, their contents scattered across the ground and ransacked for anything deemed valuable. Musical instruments had been reduced to kindling. Paintings slashed and trinkets trodden into the mud. The horses were all gone but one lay dead by the creek, two arrows in its neck, thick blood turning the water red. And then there were the bodies.
Men, women and children, reduced to ragged, bloody things. Pierced, torn open and left for the gathering flies and circling birds. Three wagons had been set ablaze and were now so far gone the wood was folding in on itself, fuelling its own destruction. The others were smouldering but with just a wave of her hands Wren quenched all the flames. Danoph felt a brief surge of power and it was done. His warm breath frosted on the suddenly icy air. For a little while it hurt to breathe, but slowly the temperature rose as it returned to normal. Even then, staring at the destruction, his chest still hurt.
In the silence that followed the cooling wood cracked and popped as it settled. Wren dismounted and approached the first of the bodies, her hand hovering over the face of the young woman who was about their age. He could see Wren's lips moving in what he thought was a quiet prayer. Not far away the girl's parents lay dead, throats and stomachs torn open, ropey red innards strewn across the ground. The anguish stamped on their faces suggested they'd watched their own child die in their final moments.
"What's the custom in Shael for dealing with the dead?" asked Wren.
Many people followed the Blessed Mother in Shael, but not all of them. Danoph remembered hearing about the pyres during the war where mountains of dead bodies had been burned. Normally the deceased was raised off the ground and the special platform was set alight, so that every part of the person drifted away on the wind. The tradition had somewhat fallen out of fashion these days.
"I think we should bury them," said Danoph. "The scavengers are already gathering," he said, gesturing at the birds circling above their heads.
A faint groaning drew their attention and a moment later they were both scrambling towards one of the wagons that had been set on fire. The sides were blackened but more or less intact, holding in the mountain of possessions that had toppled over into one huge mound. Peering in the back of the wagon Danoph saw a hand sticking out of the pile.
Working together they started throwing items aside, clearing debris until they found the arm and then the shoulder of a young woman. When they tried to pull her out the whole pile wobbled, threatening to come crashing down, forcing them to remove items one by one. Eventually they uncovered her head and shoulders and were able to risk dragging her out very slowly.
"My daughter" was the first thing she said. A quick glance at her injuries showed one of her legs was bent at a peculiar angle and she was having some difficulty breathing. Danoph wasn't an expert and still couldn't heal, but he didn't think she was in any immediate danger of dying. He gave her some willow bark to chew which numbed the pain. A short time later her eyelids fluttered closed and she slept. He covered her with some blankets to keep her warm and they returned to the wagon, painstakingly removing objects from the top one at a time. Wren was now stood inside the wagon, passing boxes out to him when he heard her cry out. A moment later she emerged, carrying a small girl in her arms. There was blood on the girl's face and a cut in her hairline.
"I don't know if she's breathing. What do we do?" said Wren, starting to panic.
"Put her down," said Danoph, spreading out another blanket. He tried to ignore the wet bloodstain on the cloth and focus on the girl. Bending over her chest he listened for a heartbeat and felt for a pulse on her wrist. At the same time an awful creeping sensation started running up and down his arms and legs. A gnawing sense of fear clogged his throat like a fat maggot, making him gag with despair.
This wasn't supposed to have happened. The girl should have lived. He felt a convergence of possibilities swirling around her. He heard a faint heartbeat but Danoph didn't think the girl was going to live for much longer and that scared him.
"She's alive, but we need to heal her," he said, knowing what he was asking Wren to do.
The girl's mother was still drifting in and out of consciousness. So she wasn't aware that they'd found her daughter and that she was still alive. Perhaps that would be a small blessing if this didn't work.
Danoph knelt down beside the girl but made no attempt to try and help. He had no ability to heal at all. No matter how hard he tried it simply didn't work. His abilities lay elsewhere and only now was he starting to realise it wasn't limited to nightmares about the future.
There was a randomness to everything. A swirling sea of choices and thousands of crossroads every hour of every day that defined a life. But some decisions were more likely than others. Some roads seemed free of clutter and at this moment the girl's future was bleak. He saw only two roads in her future and one of them was quickly fading. This should not have been the end of her story.
"I've never been able to do this," said Wren. "What if I kill her by accident?"
Danoph didn't want to add to the pressure but if he said nothing Wren might remain frozen and then it would be too late. "If you don't at least try, the girl will die."
The finality with which he said it seemed to strike a chord. Wren took the girl's hand in both of hers and bowed her head. He sensed her embrace the Source and tried to remain perfectly still and silent. He couldn't see what she was doing but he felt a tightening across the skin on his face and a prickling in his fingertips.
The distant sounds of the crows faded into the background and then disappeared. After a while Danoph could only hear his heartbeat. The rest of the world became insignificant until the only things that mattered were Wren and the dying girl. Time crawled by. The only way he could tell that time was passing was the slow movement of the sun behind hazy clouds.
Wren remained frozen in place, head bowed, hands tightly clutching the girl. He checked that the woman was still alive and found her breathing was slow but steady. Unable to help Wren he moved away from her and started digging a grave for the dead.
Even with his rudimentary control of his magic it seemed to take Danoph a long time to gouge a trench in the earth. Several times he felt his control slip and the Source drifted away from him as if he'd never sensed it. When others embraced the Source they always spoke about a heightening of their senses but he didn't feel that at all. Something was changing within but he didn't understand why it was happening now or what it was.
With sweat streaming down his face he stubbornly persisted, raking the earth with his magic until he was sure it was deep enough to hold the dozen or so bodies. It would have been easier to lift each body with magic but it seemed inhumane not to physically carry them. In the back of one of the wagons he found a stack of bedsheets, neatly folded and only a hand's breadth from the owner's corpse. Wrapping each body in a sheet he carried them one by one before setting them down in the grave.
When he was finished Danoph sat down next to the grave and contemplated what to do with the dead horse. In the end he decided to leave it where it had fallen. The patient birds and other scavengers deserved at least one meal. He didn't know if the deceased had followed the Blessed Mother or not, but he took the time to say a prayer over them that he'd been taught as a young boy. Just to be safe he muttered a short prayer to the Maker to watch over them and give them peace.
By the time he was done his back ached and he felt weak and a little dizzy.
With a groan of pain and cracking of limbs, Wren came out of her trance, stumbling to her feet. He helped her stand upright and she glanced up at the sky, trying to work out how much time had passed.
"It's been at least a couple of hours," he said, helping Wren walk in a circle to restore some circulation to her cramped legs.
"Will she live?" she asked, clutching tightly at his arm. Her skin was pale and there were deep shadows under her eyes that had not been there earlier. She was trembling slightly and he could hear her stomach rumbling. Trying to heal the girl had taken a great toll on her. They walked back around to the girl and Danoph knelt down beside her.
Without really knowing how or what he was doing, he focused on the girl and opened himself to exploring her future. Only one road ran into the distance for a while but then it came to an abrupt halt and there was nothing ahead, only darkness. She would live, but only for a short time unless something more was done. Despite all of Wren's efforts it had only provided the girl with a short reprieve.
Forcing a smile he congratulated Wren and then left her wolfing down food from her saddlebags while he fashioned a sling. There was a lot that could be salvaged from the wagons but that would have to wait. Unless they got the girl back to Master Yettle he knew she would die. Danoph thought both the girl and her mother were too fragile to ride so he created a pouch which hung between their saddles. It was crude and the horses didn't like it but they would have to cope for the time being. Even though he knew it would leave tracks that would be easy to follow, he'd considered taking one of the wagons. In the end he decided against it as it would slow them down too much and they needed to set a fair pace back to their community. He didn't know exactly how long the girl had and didn't want to take any chances.
When Wren saw what he'd done to bury the others she embraced the Source and began to fill the grave. Sweat trickled down the sides of her face from the effort, but with one smooth movement she covered the bodies with loose soil. Normally such a task wouldn't have been difficult for her, but she was already exhausted and moving the earth seemed to drain her remaining stamina.
With Wren dozing in her saddle and the others still comatose it was up to Danoph to lead the horses towards home. Left only with his thoughts for company he focused on the strong impulse that had drawn him here. The sense of despair had faded a little. It was too late for the others but a splinter of concern lurked at the back of his mind for the girl. She was still in danger. He didn't know if she was special, only that he'd not been able to save the others but she still had a chance. Her road was still there, running into the distance, for now.
# CHAPTER 8
With a grunt of pain Balfruss got up from the floor of his room where he'd been kneeling for a few hours. His knees creaked and popped alarmingly and pain shot down his back. He walked around in a circle for a while and eventually the aches faded. It was another uncomfortable reminder of his age and the relentless march of the years.
Disappointment washed through him as he cleared away the candles, incense and washed away the chalk symbols he'd scrawled onto the wooden floor. After replacing the thick rugs he carefully checked to see if he'd left anything that might look suspicious. In the past it wouldn't have mattered, but at the moment fear of magic was so great he didn't want to take any chances. The last thing he needed was the maid spreading gossip about something she'd noticed when she came to change the sheets.
Dark thoughts about magic inevitably led to the fall of the Red Tower and Garvey's apparent descent into madness. He couldn't deny the truth. The man that he knew was gone and he'd lost another friend. On days like these, when he truly felt alone, Balfruss wondered if he should have remained in the far north across the Dead Sea.
He'd been cooped up alone in his room for too long. In need of company and a distraction he went down to the common room which was busy with people eating and drinking. Their conversations washed over him but Balfruss wasn't really paying attention as his thoughts remained elsewhere. He found a quiet table and absently ordered some food and a drink while pondering what had gone wrong.
Summoning was not something he'd even been taught at the Red Tower. Nor was it a topic ever mentioned in public as the old Grey Council had forbidden its practice. As a student he'd heard rumours about why it had been banned but they'd never been confirmed. Allegedly a student had accidentally contacted an entity beyond the Veil and the consequences had been dire. He'd not given it any further thought until a few years ago when he'd journeyed across the Dead Sea. The tribes living in the emerald jungle had shown him many forms of magic that he'd never imagined, including summoning of a different sort. One that requested the presence of the spirit of a place, a genius loci.
What he'd attempted tonight was a little different, but he'd been following the same principles. Balfruss had hoped there was a chance of it working. After hours of preparation and meditation all he had to show for it was two stiff and painful knees.
As he ate his meal of spicy beef and red beans in plum sauce, he focused on the conversation around him for the first time. There was only one topic on everyone's lips. Garvey. They were scared. Rumour had it that he was travelling north towards Zecorria but it was all speculation. No one dared get too close to the group. What if he decided to stay in Yerskania? What if he came south again instead and marched towards the capital? Who here could stop him and his band of rebel mages?
Balfruss had told Tammy that it wasn't his responsibility to deal with Garvey, which was true. Even so he knew that it was not something he could ignore. If magic was ever to be seen as a force for good then Garvey needed to be stopped. The only way that would happen was if another powerful mage got involved. With Eloise halfway around the world in the desert kingdoms he was the only one left.
At another table in the room a merchant from Zecorria was explaining Regent Choilan's new declaration. He intended to create an opposing force comprised of patriotic mages, but those at the merchant's table thought it would be too little too late. Soldiers and steel couldn't stand up to a mage and yet both Queen Morganse and the Regent were mobilising their armies. Balfruss also overheard a local woman talking about the increasing number of attacks on merchants travelling into Shael. Rooke, the western district, was still a lawless and abandoned wasteland that had been made worse by a new group of murderous bandits. The woman claimed they even had a mage working with them, but to Balfruss it sounded like more fearmongering. Everyone knew the Red Tower had been destroyed but there was a peculiar absence of conversation in the room on that subject.
"It looks like you've got a lot on your mind," said a familiar voice. "Mind if I join you for a drink?"
Balfruss's mouth fell open in surprise and he stared in silence like a simpleton. Vargus sat down opposite and waited for him to recover, sipping at his ale and glancing around the room at the crowd. It had been many years since he'd last seen Vargus, in a nowhere place between moments of time, and yet he'd not aged a day. If anything he looked a little younger than at their previous meeting. His hair had touches of brown in it, where once it had been mostly grey and silver. The backs of his hands had been covered with liver spots but now the skin was clear and tight.
As before, he resembled a battered old mercenary or a weary caravan guard, dressed in worn leathers with a blade slung across his back. There were a dozen others like him in the tavern, which was why no one gave him a second glance. To them he was just another sword for hire.
"I didn't think the summoning had worked," said Balfruss, still struggling with his surprise at seeing Vargus.
The old warrior offered him a wry smile. "It didn't, at least not in the way you're thinking. It's been a long time since anyone tried to contact me like that, which is why it caught my attention. I'm not a spirit of the earth or the air. You can't bind me and call me by name."
"Then what are you?" he asked, and immediately regretted it.
Vargus put down his ale and the genial expression trickled off his face. "We talked about that a few years ago. I once told you a little about what I am. Do not ask for more."
Balfruss was still reeling at seeing Vargus in person. He took a long gulp of ale and tried to gather his thoughts. "That might not be good enough any more."
"Why do you say that?"
"Do you know what's happened to the Red Tower?" he asked and Vargus nodded grimly. "We lost a lot of good people. They were murdered by an angry mob."
"I'm sorry, but I cannot help you with that. My kind has only one immutable rule. We are not allowed to directly interfere in the affairs of mortals. If that's why you asked me here, then I'll leave now," said Vargus, draining the last of his ale.
"That's not the reason," said Balfruss, trying to stop Vargus from leaving. "Although it's related. Does the name Akosh mean anything to you?"
Vargus froze, half out of his seat, one hand resting on the back of his chair. Moving slowly he lowered himself into his seat again. He gestured at the bar for two more drinks and waited until they'd been delivered before speaking in a low voice. He spoke so quietly his words would be swallowed up by the noise in the room, preventing anyone from eavesdropping.
"Tell me everything," said Vargus.
Starting with Danoph's visions of destruction, Balfruss told him about the seemingly inevitable fall of the Red Tower. Despite their best efforts to change the course of events the mob had arrived at the gates with burning torches. Anger warred with sadness inside when he thought of all that had been lost. It wasn't just the school as buildings could be rebuilt. The children had been robbed of their future. Now most of them had been shipped off to a foreign country to start all over again. Learning how to master their magic would be difficult enough without having to adjust to a new culture with its own peculiar quirks and restrictions.
"Most of our preparation paid off, we saved many items that have been placed in storage, but there was still a high price to pay. Some people stayed behind to give the rest of us time to escape with the children. Most of them died, including my friend, Choss, his mother-in-law and his son."
Vargus rocked back in his chair as if he'd been slapped. "I know him," he said and then corrected himself. "I knew him. He was a good man. A champion."
"Now his widow, Munroe, is bent on revenge. I've been working with the Guardians and they discovered a spider, lurking in the shadows, manipulating others for her own ends. Akosh."
Vargus took a deep breath and crossed his arms over his chest. He stared off into the distance and Balfruss could see he was chewing something over, probably deciding how much he could share.
"Are you certain she was responsible?" he finally asked.
"She's involved," said Balfruss, before going on to tell Vargus about the orphanages and how Akosh was both their patron and the head of a cult devoted to her. "I don't know how many orphanages she has, or where they're located, but she and her people have their own hidden agenda. There was even a Guardian who followed Akosh. She killed a witness and then herself rather than be questioned about her involvement."
"So that's how she did it," muttered Vargus.
"Did what?" asked Balfruss, knowing that he shouldn't ask but he wanted some answers. Vargus didn't say anything for a while, just sipped his ale, but he seemed to be considering something. Eventually he came to a decision. He leaned forward across the table and gestured for Balfruss to move closer.
"I want your word. What I'm about to tell you must never pass your lips again. Not to a future wife, a child and not even on your deathbed many years from now."
"I swear it," he promised.
"I'll hold you to that," said the old warrior and Balfruss believed him. Vargus took a moment to settle himself before speaking. "For all things there is a season. Even the ancient tree, that has been a mute sentinel for centuries, witnessing the rise and fall of countless empires, must one day return to the earth. But it can bear fruit and be reborn anew. So it is with my kind. But unlike the tree, we can change. A long time ago, they used to call me the Weaver, but that power and the mantle now belong to another. Today I am a warrior and brother to all men and women who carry the sword. It began with the war and the Brotherhood. That is my path, for now at least."
Balfruss considered his words and thought back over all of the conversations they'd had in the past. He'd heard about the Brotherhood during the war and how it had bound the Seve warriors together into a united fighting force. It may not have changed the course of the war but it had given warriors hope and the will to keep going in the most desperate circumstances. The tales of sacrifice in Seveldrom during the war had even travelled as far as the west. In the last few years soldiers and warriors in other countries had also adopted the tenets of friendship, honour and sacrifice.
The name Weaver tickled something at the back of his mind. A scrap of information he'd read in a dusty old book of ancient history. During the war he and Vargus had spoken about ancient religions, including the Twelve and their predecessors the Triumvirate. Balfruss thought one of the Twelve had been called the Weaver. For all he knew, that might have been Vargus in a former life.
"Akosh reinvented herself," said Balfruss, fumbling along. The old warrior said nothing, which he took as consent to continue. "She created a new religion in her own name."
"She used to be a patron to assassins," said Vargus with a snort of derision. "For the most part they're a mercenary and sociopathic bunch. Few wanted to believe their good luck was due to their devotion and prayers. It was expected that she would wither and die early on the vine, but she adapted."
"What can we do about her?"
"You will do nothing. She will be dealt with by me," said Vargus, in a voice that brooked no argument. "A rebirth was necessary for her to survive, but to use her followers to change the natural order is not permitted. It sounds like she is trying to shape the course of events."
"How will you—"
"Do not ask that question," said the old warrior. For a brief moment Balfruss was reminded that he wasn't a man. He wasn't even human. The power he glimpsed behind Vargus's eyes made the Sorcerer turn his face away in fear.
The conversations continued to flow all around while the two of them sat in a bubble of silence, both dissimilar from everyone else in their own way.
"I have a suggestion," said Vargus, breaking the hush hanging over their table. "Encourage the orphanages here in Perizzi, in the strongest terms, to consider a more stable faith. One which is likely to still exist in a few years. The Maker or the Blessed Mother."
"I will pass that on."
"How you deal with her mortal followers, and those involved in the fall of the Red Tower, is entirely your decision. Leave Akosh to me."
"I will, but you should know Munroe will not be easily sidetracked. She's out for blood and I know of no power that can stop her," said Balfruss. "Not even me."
He thought Vargus would ask him to speak to her again. Instead he merely frowned and shook his head. "That is her choice. I cannot interfere, but she will find no peace. Revenge will not bring them back." Vargus took a few long pulls on his second ale and Balfruss knew he was running out of time.
"What if I need to find you again?" he asked.
"I will find you," said Vargus, and Balfruss wasn't sure if that was a threat or a promise. Without another word the old warrior passed through the crowd and went out of the front door. Few noticed him leave and no one turned their head to watch his progress.
It made Balfruss wonder how many others like Vargus were out there, walking among them, living ordinary lives, and if he'd met any of them before.
# CHAPTER 9
It had been many years since Munroe had crawled over the rooftops of Perizzi, but thankfully she had not forgotten all of her lessons. Her attempt to join the Silent Order, an elite group of assassins in Yerskania, had required months of training which often involved scrambling up and down walls or tiptoeing across rooftops without falling to her death. Unfortunately her assessment had not gone well and she'd been rejected as a suitable candidate. This was long before she'd learned how to fully control her Talent. The result had been some of the most unusual and improbable accidents that the authorities were still struggling to explain. At the very least her experience had taught her how to move quietly and go undetected.
It was a long way down to the street and a fall from this height would break her neck. If the worst happened she could use her magic to cushion her fall, but she was trying to remain unnoticed.
Tonight the city reeked. She'd forgotten about that in her time away. When the wind blew in the wrong direction it dredged up a stench from the port, flooding the streets with the smell of rotting fish, ripe piss, stale beer and suspicious meat sold by street vendors. She may have forgotten about the smells, but with them a flood of old memories returned. She remembered wasting countless hours in the Emerald Dragon, in a permanent alcoholic haze, trying to numb her boredom and self-pity. She remembered a month of cold and wet nights scrambling across the city with a man named Ben as part of her training to join the Silent Order. Mostly the smell made her remember the long and lonely nights when she'd lain in her bed, staring out of her window at the stars, hoping for better days and an end to her isolation.
Her better days had been and gone. They'd died with her family. Now she was caught in between. Unable to move forward. Unwilling to step back in time and become the person she'd been before Choss. But not everything from her old life had been terrible.
Munroe wasn't properly focused on the task at hand and she mistimed a jump between buildings. Her left foot slipped on some wet roof tiles as she landed, sending her off balance. Before starting to slide down the roof, she dug her fingers into the pitted stone and quickly righted herself. She took a moment to catch her breath and check her route before proceeding again with a bit more caution.
This part of the city was not one she'd visited often. The buildings were all comprised of shops and small taverns on the ground floor with apartments above the businesses. Many of the well-tended homes belonged to shop-owners but some were privately owned. It had taken Munroe two days of staking out Unity Hall to find who she wanted and another cautious night to find his home.
Counting the windows she bypassed the first three and focused on the last two on the top floor. At this hour all of the windows were closed and there wasn't a flicker of a candle or lantern from within. She could hear someone snoring loudly and a few creaks as the building settled but nothing else. The street below was deserted but just in case she kept low and spread her weight evenly across the roof.
There was no way of knowing if the building was being watched. The Guardians, the Watch, someone from one of the Families, or even one of Akosh's followers might be lurking in the shadows. It was possible that any one of them could be following her. Munroe realised it was a little paranoid, but she needed to stay invisible until she found Akosh.
Part of her realised that if she hadn't been working alone this would have been a lot easier. She could have posted several lookouts to warn her if she was being followed, or if anyone was showing too much interest in the building. With a team behind her she could have just walked up to the back door and picked the lock. Instead she'd spent the first hour taking a strangled route across the city to lose any watchers and the next hour dressed in black crawling across rooftops.
After securing her rope in two places she slowly eased herself down the sloping roof on her stomach. The window was latched on the inside but with a quick flick and twist with a narrow metal file it sprang open. Munroe eased open the window and slid into the room.
She lay there for a while in the dark, listening while she kept her breathing shallow. The apartment was silent and still. Taking a small risk she embraced the Source and waited to see if that disturbed anyone nearby. As her senses were enhanced the black shadows became brown and then grey smoky outlines that revealed objects in the room.
She was lying on the floor in the kitchen between two tall rows of cupboards. Something grainy was digging into the bare flesh of her back where her shirt had lifted up. After sitting up slowly she inspected the floor and realised she'd been lying in a small pile of spilled rice. To her left she could see a silent procession of tiny black ants going in and out of a food cupboard. Leaving them to their midnight robbery she scuttled across the floor, trying to be as stealthy as them.
Through the open doorway she spied the main room and an array of furniture. It was empty of people and in total darkness but her enhanced vision allowed her to move through the room without walking into anything. The door on the far side was closed and, putting an ear against the wood, she could hear someone inside the bedroom. Their breathing was deep and even, suggesting they were asleep, which actually disappointed her a little.
Munroe eased open the door and peered inside. To her surprise she found Guardian Fray sitting up in bed, staring at her with a sword resting across his bare chest. Even though it had been almost ten years since they'd seen one another it only took him a few seconds to recognise her.
"Munroe?" he said with a hint of uncertainty. He knew all about her past and was probably wondering why she'd broken into his home in the middle of the night dressed all in black. Maybe he thought she was an assassin and had come to kill him.
"I'm just here to talk," she offered, stepping back from the door to show she wasn't armed.
"Then why break in? Why didn't you come to see me at Unity Hall?"
Munroe sighed. "Lots of reasons. It's a long story." She didn't want to tell him. She wasn't even sure if she could say it out loud, but he needed to know some of it otherwise he wouldn't help her. "I'll wait for you out here," she said, gesturing at the main room.
She sat down at his table with her back against the wall, giving her an ideal view of the whole apartment. A few minutes later he emerged, dressed in a loose pair of trousers and a long shirt that was half open. Fray confidently moved about his apartment without any light, suggesting he'd been living here for a while, but when he reached for his flint and tinder she cleared her throat.
"Don't."
"Why not?"
"I don't want anyone to know I'm here."
Fray sat down at the table but she noticed he rested a sword against his chair. Channelling a trickle of power from the Source into the palm of her hand, Munroe summoned a small mage light. The pale blue globe provided enough illumination for them to see each other clearly, but she didn't think it would show through the curtains.
For a while neither of them said anything and just looked at each other. She wondered what Fray saw when he stared at her. Could he see the rage and the agony roiling inside her? Had it marked her physically in some way? Or was there a more subtle tell behind her eyes?
After a little while Munroe picked out a few details she'd initially missed. Fray was leaner than she remembered. Much of the fat of youth had been leached away from his face and it was now weather-beaten from years spent working outdoors. But then he'd been a Guardian for years now, walking the streets and solving crimes in Perizzi. There was also a touch of white in his hair over the ears and in his beard. It was behind his eyes where she saw the biggest change. He regarded her with caution and some suspicion. The city, the people that he dealt with every day in his difficult job, plus the sword at his elbow, spoke of lessons learned the hard way.
"I'm not here for you. I just want to talk," she said again, trying to reassure him. Fray gestured for her to continue, but she noticed he didn't relax.
"Then talk."
"Have you heard about what happened at the Red Tower?" she asked.
"I have," said Fray, and for a second she saw a familiar rage behind his eyes before he got it under control. He'd been a regular visitor to the school. After almost a decade the Grey Council were still no closer to unravelling his rare Talent. It gave him a unique edge that other Guardians lacked, but only a few people knew that he had any magic. It was safer that way, now more than ever, when anyone connected to magic had been vilified. In return for letting them study his ability the Grey Council had been teaching him about magic and the Source. "Did many survive?" he asked.
Munroe felt as if something had grabbed her heart and started squeezing. She couldn't breathe. She couldn't speak. She opened her mouth to answer him but no words emerged. When his hand closed over hers she jumped back in surprise, her chair hitting the wall. Her heart was pounding and her hands were shaking, but slowly she realised there was no immediate danger. Taking a few deep breaths she sat down again and he gave her time to regain her composure. When she felt calm enough to talk Munroe tried to keep her voice even but it still wavered from time to time as the wound was still raw.
"All of the students survived, but many lives were lost buying them time to escape. My son, my mother and my husband, Choss, are gone."
She looked up in time to see the horror sweep across Fray's face. He'd not been a large part of her old life, but towards the end he'd known her and Choss. Together, the three of them had freed the city of Perizzi of an inhuman terror she still barely understood.
"Oh Munroe," he whispered, reaching for her hand again and then stopping halfway across the table. She grabbed hold of him, squeezing his hand tight to stop herself drifting away on memories again. She needed to stay in the present with him. She needed to do something to stop the pain.
"I need a favour."
"Anything. Name it," he said without hesitation which made her smile. It was good to see his years as a Guardian had not stripped him of compassion.
"I need to speak to them," she said, fishing out a piece of cloth, an ivory comb and a small wooden horse from her pocket. The cloth was part of a shirt Choss had left at the cabin. The comb was her mother's and the horse one of Sam's favourite toys. It was fairly crude, and only vaguely resembled a horse, but Choss had been so proud of his handiwork. Sam had loved it because he'd seen it taking shape over the course of several weeks.
Munroe squeezed Fray's hand and he winced but didn't complain. It was so hard to focus. She just wanted to lie down and wallow in her memories. To live with them in the past for ever. A warm bath, a razor, a bottle of whisky. She'd considered it many times over the last few weeks. But not yet. She needed to know they were at peace. She needed to find the one responsible and snap her neck. Then she could rest.
"Can you do it? Can you summon them?" she asked.
Fray's unique Talent was that he could summon and talk to spirits of the dead.
No one really knew what happened after you died. There were a dozen religions and hundreds of stories, but all of it came down to belief. Spirits were something else entirely.
She'd once heard Fray explain it to the Grey Council during one of his visits. Some mediums claimed to be able to talk to anyone who had died in all of history. Fray made no such claims and thought most mediums were frauds as not every person became a spirit.
A spirit that stayed behind was a piece of the person they had been in life. They were always tethered to items and those they had known in life. Usually they only stayed for a short time before fading away and moving on to whatever came next. And there was always a reason for them to linger. A sudden and unexpected death could cause it, but often that wasn't enough. A strong will in life wasn't always enough. It was often about unfinished business. A task, or a message that bound them to this realm of flesh until the message was delivered. After that there was no need to hold on so tightly and they moved on.
"I've never tried it with someone I knew well in life," said Fray, but she thought he was lying. His father had died many years ago, and more recently his mentor, Byrne, had been killed in unusual circumstances. If Munroe had his power it would've been one of the first things she'd tried.
"I need to speak to them," she said, sliding the items across the table. She released Fray's other hand and saw the red marks she'd left on his skin but he didn't notice. His gaze had turned inwards as he stared at the piece of cloth, the comb and the toy. One of his hands hovered over the items but then he pulled back.
"Are you sure?" he asked. "If I do this, then you need to understand it won't be them. Not really. It's just a shadow that's been left behind."
"I need to see them."
Fray said nothing for a while and just studied her. She met his gaze hoping he could see her resolve and that she'd buried her fear. There was nothing more she wanted in the world than to see her family one last time. However, the thought of it also terrified her worse than anything in the world. What if they blamed her? What if their spirits showed the wounds of their death? What if Sam cried and called out for her? What if they weren't at peace?
"I need to see them," she said, more to herself than Fray, but he took it as her final decision. He picked up the piece of Choss's shirt and wrapped it around the comb and Sam's toy, while she braced herself for the worst.
Even though Munroe knew the theory she couldn't follow what Fray was doing. She sensed him opening himself to the Source, but not in a way she recognised. Like flexing a muscle a Talent came instinctively and without thought. One moment his eyes were green and the next they were the colour of old pennies.
Fray gripped the cloth tightly in one hand while he stared past her, through the wall, at something beyond the city. His brow furrowed and he made a small beckoning gesture with his free hand, perhaps inviting the spirit to visit them. Her heart was racing again, her palms sweaty and she forced herself to breathe steadily. Tears ran down her face but she couldn't stop them.
His frown deepened and Fray held the material tightly in both hands. As he focused Munroe sensed a wave of energy passing through her. She could feel him drawing more heavily from the Source as well. With a gasp he released the cloth and sat back, his eyes quickly changing colour back to normal.
"What happened?"
"There's nothing there," said Fray, breathing hard from his efforts. "I can't find them."
"What does that mean?" asked Munroe.
"Are you sure...?" said Fray, trailing off before starting again. "Are you sure they're gone?"
She'd heard the stories about a group of people chasing Choss and her son to the pier. She'd seen the blood. "I'm sure."
"Then their spirits haven't lingered."
"What are you saying?" asked Munroe. She knew what it meant but didn't accept it. They were gone. Truly gone. "How can that be?" she asked, but Fray had no answers. Why hadn't they stayed? How could Choss not have any unfinished business with her? And Sam was only a small boy. He still had his whole life in front of him. Her mother had made peace with her death, so part of Munroe could understand her absence, but not the others. Why had they left her alone?
Without really thinking about what she was doing Munroe gathered up the belongings and walked back to the kitchen. She snuffed out the mage light and embraced the Source, using her enhanced senses to navigate around the apartment.
"Wait. Don't go. Stay and talk," said Fray, but she ignored him and reached out of the window for her rope.
"Tell no one I've been here. It's not safe," she said, glancing over her shoulder at Fray. She should have just left without stopping, for in that final look she saw his anguish. His pain was a fraction of her own but it was enough to make her sob. Choking it down she scrambled out of the window and across the roof as hot tears ran down her cheeks.
The next morning, a short time after dawn, Munroe was watching a different quiet street in another part of the city. She waited until the old Drassi Swordsmaster had left the building and disappeared around the corner before approaching the front door. Moving slowly, but making no attempt to be stealthy, she opened the door and entered the building.
The dance studio was empty at this hour, making it easy to search the building quickly. In a small room at the back she found the wooden floor had been covered with thin padded mats which its sole occupant was gathering up and stacking in one corner.
"Did you forget something?" asked Tammy, without looking around.
"Not really," said Munroe. Tammy dropped the mats and spun around in surprise, reaching for her sword until she saw who it was. Munroe felt a small pang of satisfaction at having caught the Guardian unawares. It was only fair after she'd sneaked up on Munroe a few times.
"You could have visited me at Unity Hall. So why are you here?" asked the big Guardian.
"Because I have a proposition for you, and the fewer people who know about it, the better."
"I'm listening," said Tammy, before going back to stacking up the mats.
"Balfruss told me you're going after Akosh and her network. But I also know there are some things you can't do. That's why you let me question Grell."
Tammy paused in what she was doing and Munroe could guess what she was thinking. That letting her question a suspect had been a mistake. But she wasn't responsible for his death. If she hadn't pressed him for an answer they wouldn't have Akosh's name. Her actions had also forced Guardian Brook to reveal her true loyalty. On balance Munroe thought the good outweighed the bad.
"It was a mistake," said Tammy.
"Perhaps," conceded Munroe but she would not be deterred. "But I'm not a Guardian and I'm better suited to direct action. Give me a name and a target. I'll find them and bring them back to you for questioning. You know I can do that. Let me help you destroy Akosh's network."
Tammy finished stacking the mats and then sat down on top, wiping a towel over her bare arms and face. "I'm tempted. I really am, but I also heard what happened to your family."
"Then you understand that I won't give up. That nothing will stop me."
"The problem is, I also saw what happened to Grell," said Tammy, taking off her vest and pulling on a clean shirt.
"I don't understand," said Munroe.
"The coroner showed me his body. Brook's stab wound was what killed Grell, but he also had a lot of other injuries. Bruises, broken ribs, burns on his leg."
"So what?" said Munroe, refusing to apologise. "He would have lived."
"I'm not saying what you did was wrong. I needed information and I knew what could happen when I sent you in there."
"Then what's the problem?"
Tammy pulled on her Guardian jacket and stood up. "You are." The famous uniform had never been a problem before but now it had become a barrier between them. "Grell wasn't a threat to you, but he managed to get under your skin, didn't he?"
"I didn't kill him."
"No, you didn't, but that was before someone murdered your family."
"Be very careful," said Munroe, feeling her temper flare.
"Grell was an idiot. What happens if I send you after someone much smarter? How long will it take them to bait you?"
The pulsing of the Source at the edge of Munroe's perception was getting louder. It was making it difficult to hear what was being said. "I can handle it," she said through gritted teeth.
"What if they tell you the person you're going after was there at the Red Tower that day? What if they saw your family die?" whispered Tammy. "What if they were responsible?"
Flames erupted along both of Munroe's arms, engulfing her in blue fire. It wreathed her head and shoulders like a crown, dancing around her features without burning her hair or clothes. She was aware of the heat but it didn't touch her. More of it spread out across her body, running down her arms to pool in the palms of her upraised hands until it spilled over to the ground like water. The fire sizzled as it struck the wooden floor, instantly turning it black and then it began to smoulder and burn.
Tammy grabbed one of the mats and tried to smother the fire before it spread. Smoke rose from the burning floor and Munroe squeezed her eyes shut, closing herself off from everything in the world. With a huge wrench of effort she swallowed her anger and cut herself off from the Source. The flames across her body faded and then vanished, leaving only a few patches of fire that Tammy quickly dealt with. They opened the windows and when the smoke had cleared Munroe saw two large charred circles on the floor.
"You're too close to this," said Tammy, once she'd finished coughing. "That burning rage you're carrying inside will eat away at you. It also makes you vulnerable."
"Are you going to help me or not?" she asked and Tammy just shook her head. Whatever burgeoning friendship had been growing between them died in that instant. She wasn't even Tammy any more. There was only the mantle of the Khevassar. "I'll do it by myself," said Munroe.
"You can't, and you know it. That's why you're here. You need some time away, to clear your head and to mourn."
"What would you know about it?" said Munroe.
"Nothing," said Tammy, refusing to make eye contact. "We'll bring them to justice and destroy her network."
Munroe laughed bitterly. "You do that. Seek out your vaunted justice, but I suggest you do one thing for me."
"What's that?" asked Tammy.
"Stay out of my way. I don't care about her network. I just want Akosh. And when I find her, I won't stop until she's dead."
Munroe didn't want to hurt Tammy, but she would if it was necessary. Part of her expected a lecture or sermon about the price of revenge, but Tammy offered neither. Perhaps she knew a thing or two about it after all.
As she walked away from the building Munroe grudgingly admitted that Tammy had been right about one thing. She already knew she couldn't do this alone. If those working within the confines of the law couldn't help then perhaps it was time to cross over to the other side of the street.
# CHAPTER 10
Bettina, clerk and agent for Regent Choilan, left her meeting with an expression that bordered on a smile. As she passed one of the many expensive mirrors in the palace she paused and made sure no one was around before looking at her reflection.
The high-necked grey dress was long on the arms and it trailed on the floor covering up as much exposed flesh as possible. She pulled up the collar to make sure it concealed the marks on her neck before continuing to her office at a brusque pace.
The reason for her near-smile was that the inevitable had finally happened. The blubbery Minister of Trade, who had been so close to having his neck on the chopping block, had died. The method didn't really matter to her, the headsman or in this case in bed with his mistress, only the facts. He was gone and his widow, Daria, had been appointed to the position in his place, something that the Regent had been considering for a while. The mistress would vanish and everything would go back to normal. Order would resume, just as she liked it. Everything neat and tidy.
The Minister had been erratic, driven by passions and was someone who could change his mind overnight. Bettina would order scribes to produce a document only to be told days later by the Minister that it wasn't needed any more. She didn't care personally about the scribes, but she hated the time and money that had been wasted producing something that later wasn't needed. Daria was much more stable, described by some people as cold and aloof, but Bettina recognised something familiar in the other woman. Order. Structure. Stability.
That almost-smile tugged at the corners of her mouth until she reached her office door and saw that it was slightly ajar. With a snarl she burst through the door. She was ready to berate whoever had the impertinence to barge in without invitation until she saw the room's occupant. Her usual icy mask returned and she made a low and deep bow, as was fitting for the Regent's first wife.
Despite being fairly tall herself, Selina towered over her. Few people made her feel small and vulnerable. Part of her favourite pastime was doing that to others, but for some reason Selina intimidated her. Her dealings with the Regent's other wives were far less uncomfortable. Bettina often had trouble getting a word in while they babbled on about nothing of value. Not so with Selina. Silence was her favourite weapon.
"My Lady, how may I be of service?" she asked.
Selina moved from where she'd been standing at the window to take a seat in front of the desk. Bettina waited until she'd sat down before sinking into her chair. Even with the desk between them, and in the familiar surroundings of her own office, the other woman's stillness bothered her. Perhaps it was her frown. Bettina liked a good scowl but Selina's seemed to be carved from granite. Even when she spoke her eyebrows barely lifted.
"Do you have an update on the agents I requested?" she asked.
The Regent had asked Bettina to investigate the eight missing agents and so far her contacts had found seven. All murdered. They had been killed in a variety of mundane ways, and Bettina believed the eighth would be discovered in a similar state. In fact she would insist that the last body was found. She couldn't stand loose ends. One of the Regent's agents was looking into who was responsible for the murders, but so far there were no suspects. Right now the why was unimportant. The agents needed to be replaced.
Bettina had supplied Selina with a list of potential replacements and a few days ago she'd chosen eight from the list.
"I've had responses from seven of the eight names you requested, my Lady. I'm just waiting on the last. I believe he's called Doggett." All the names were fake, of course. It came with the job of going unnoticed. "I'm confident I'll hear from him soon."
"I hope you do," said Selina.
Bettina couldn't interpret her meaning as her expression and tone of voice gave nothing away. She didn't know if it was a threat and promise that something unpleasant would happen to her if she didn't hear back from Doggett, or if Selina genuinely wanted a response. Instead of replying she said nothing.
After a while the silence in the room rang in her ears and she couldn't help fidgeting in her chair.
"You're obviously busy," said Selina, gesturing at the neat stack of notebooks laid out in a precise grid on the desk. Each was exactly equidistant from the other and only those of the same colour were touching one another. "I await your response."
"My Lady," said Bettina, standing up and bowing again as the first wife left her office. She carefully closed the door and resumed her seat, resting her forehead on the cool surface of her desk. It helped to calm the buzzing of her thoughts and bring them under control again. A dull ache was forming behind her right eye which she hoped wouldn't develop. She desperately needed to vent her frustration at such an invasion of privacy. The imbalance it caused inside ate away at her. Those she subjugated tonight would receive additional lashes until she was at peace.
There was a brief knock on the door and she barely had time to compose herself before an unremarkable man entered without invitation. Bettina dug her nails into her right thigh until the pain made her discomfort begin to ease.
"Who are you?" she asked in a calm voice, making a note of the man's plain, worn clothing. He didn't look familiar and everything about him, from his clothes to his features, was ordinary and easily forgettable. Bettina was good at remembering names and faces but had no recollection of meeting him before which she found more than a little troubling.
"I'm Doggett," said the man. "My answer is yes. I'll take the job."
Bettina held up one finger, opened the relevant notebook and crossed off his name. Despite the irregularity of entering her office without being asked at least this was one list she could mark as finished. The completeness of it eased the muscles in her shoulders and she stopped gouging her leg.
"Good. You will receive instructions in three days' time."
Doggett gave her a peculiar two-fingered wave and went out of the door, leaving her alone amid tidy shelves of notebooks.
Doggett left the palace via one of the many entrances disguised as a servant. The guards on duty had seen him coming and going for the last week so they paid no attention to him. They probably didn't even remember his face. Being easily forgotten had been something he'd initially hated, until as a young boy he'd realised its potential. He was invisible.
Small thefts and petty crimes were blamed on others who were inevitably punished in his place, until he escalated to his first murder. At that point not even his ability to blend into a crowd could hide him, but thankfully someone else found him before the authorities.
Since then he'd always been working behind the scenes, often alongside people in power who didn't even know he was there, watching, listening and reporting back to others. He was a faceless and nameless man.
Once he was a few streets away from the palace he dumped the empty package he was carrying, stripped out of his servant's coat, pulled off the palace stars he'd pinned on and tossed everything at a beggar. He picked up his own coat and weapons from where he'd stashed them, feeling more comfortable with their familiar weight and smell.
Doggett strolled through the city, apparently at ease, often stopping to chat with merchants and peruse their wares. In truth he was checking to see if anyone was following him. After an hour of wandering he set off for his real destination. Such precautions were necessary, now more than ever before with the stakes so high. Taking a winding route he finally arrived at the tailor's shop.
The owner wasn't part of the organisation but they had an arrangement. She looked towards the ceiling and held up one finger. Doggett thanked her and went upstairs, knocking loudly on the door before pushing it open. At such meetings it was always better to announce your arrival than end up with a dagger in the eye for barging in.
The new Minister of Trade, Daria, who had taken over from her late husband, sat waiting for him sipping tea opposite someone he knew very well. He knelt before her and reached out to take her hand reverentially.
"Mother," he whispered, waiting until Akosh touched him on the back of the head before standing up. "I didn't expect to see you here."
Akosh grimaced and it hurt him to see her so upset. "My plans were forced to change after the incident at the orphanage."
"I've investigated what happened. No one knows who the new teacher works for but I'll keep digging. For now we have someone following him."
She waved it away. "It doesn't matter. We have more important things to discuss."
Daria bowed in her seat. "What are your orders, Mother?"
"I know you've been very patient, Daria, and I appreciate your sacrifice," said Akosh. Doggett had not expected the Minister of Trade to last more than a month with such an enthusiastic and energetic mistress, but he'd proven them all wrong. Somehow he'd managed to last six months before his heart had finally given out. All the while Daria had played the role of the disrespected wife. She had originally married him out of affection, but any such feelings were secondary to their Mother. Judging from Daria's cool expression Doggett guessed that she and her husband had grown apart over the years.
Daria shrugged, confirming his suspicion. "He wasn't the man I married."
"Even so, I expect you to continue to play the role of the wounded widow in public," Akosh reminded her.
"Yes, Mother," said Daria sincerely and Doggett knew her obedience was absolute. "What do you want me to do about the Regent?"
"Nothing. He knows you're thankful for the appointment and he'll expect absolute loyalty in return. That will suffice for now. Don't try to wheedle your way into his good graces. Just do your job as well as possible and that will be enough. Your late husband was incompetent, so your best will be a hundred times better and that will get you noticed."
Doggett knew that Regent Choilan was a cunning man to have clawed his way to the top, driving off or killing others competing for the throne. Now that he was there he intended to hold on for as long as possible. Everyone knew blood relatives of their late King were grooming a young boy to take the throne, but that was at least fifteen years away.
That meant for now the Regent had time to create a legacy for himself and his family, but only if he managed to hold onto the throne. The Regent was cautious and it took him a long time to trust someone. It took even longer for them to become a part of his inner circle, like Bettina. Most thought she was simply another scribe but Doggett knew she was one of a handful in the palace that had other duties. Daria would have to be patient as well and slowly earn his trust.
"In time the Regent will come to rely on you," Akosh was saying. "Yerskania might be the trading heart of the west, but they don't have adequate protection against Garvey and his ilk. Soon the Regent will have an incomparable force on hand and I can foresee a time when he may want to loan them to others."
One of the many things Doggett loved about Mother was her ability to think long-term. She did her best to guide events to benefit certain parties, but the appearance of Garvey was something no one had expected. Nevertheless, she had found a way to turn it to their advantage.
"What about the Regent's wives?" asked Daria.
"Let Doggett and the others worry about them," said Akosh. "Only the Regent's first wife has any brains and we'll keep her busy. Focus on your duties for the time being."
"As you wish, Mother," said Daria, bowing again before leaving via the backstairs. He heard her leave the shop via the back door and knew she would take adequate precautions to ensure she wasn't followed before returning home.
"What are your orders for me, Mother?"
Akosh gestured at the chair opposite and he sat down, perched on the edge, alert and attentive. "Have they found all of the bodies?"
"No, Mother. I still have the last one in a secure location."
"Make sure it's discovered and someone is found to take the blame. Perhaps a foreign agent? Someone from Yerskania? There are too many of them in the city for my liking."
As far as Doggett knew there were nine agents but he would bet the true number was probably double that. Ever since the war Queen Morganse had been paying very close attention to her northern neighbours.
"I have someone in mind," said Doggett, who had been planning this for some time. "Do you need anything else?"
"Make yourself indispensable to the Regent's first wife. She's always dabbled in spycraft, but give her some real meat. Dig up a few foreign agents and send them her way. I want to see how far she's willing to go. That will determine our next move."
"Yes, Mother."
"Is there something you wish to tell me?" she asked.
"I've been told the Regent and one of his aides, Bettina, are looking into the disappearance of Habreel."
Akosh grimaced. "I was expecting this. Drip-feed them clues about him being in an asylum. That should be enough, but keep an eye on them."
"Yes, Mother." A crease marred her forehead and his concern made him speak out of turn. "Are you well, Mother?"
Akosh raised an eyebrow at the question but she let it go. "No, but I will be, once we secure the Regent's loyalty and then, one day, Zecorria."
Doggett smiled as he pictured what that meant in the future. A nation of their own. One where every church in every village, town and city was devoted to Akosh. It would be glorious.
# CHAPTER 11
Tianne had been putting off her decision for nearly two weeks. But she'd finally found the right moment to tell Wren that she was leaving.
Until today there had been one crisis after another and Tianne didn't want her friend to feel like she was being abandoned at the worst time. It had started with the arrival of the injured girl and her mother who'd been attacked by raiders. Despite Wren's efforts the girl's wounds had been severe and if not for the expert skills of Master Yettle, she would have died. Tianne knew that Wren had tried her best to heal the girl but from what Danoph had told her it had made little real difference. Healing was one of the most difficult skills to master as a mage and few of the students were making any real progress.
There had been some damage to the girl's head, bleeding inside the skull, and Master Yettle had prepared everyone for the worst. There was a chance the girl would wake up and have some impairment, but it was also possible she'd just die in her sleep. Tianne had stayed busy throughout the day, organising other students, making sure classes ran on time and doing her best to pretend that nothing was amiss. Everyone was enormously relieved when the girl woke up and was completely healed.
The next crisis after that was one of their newly caught sheep had gone missing. A thorough search the following day revealed half of its carcass wedged up a tree. They found a few other bits not far away, mostly bones and gristle, that showed signs of being gnawed on by something with big teeth. Something living in the nearby hills, probably a mountain lion, had come down in search of a tasty meal. That meant another busy day was spent building an enclosure for the sheep at night. Now they assigned two armed shepherds during the day to keep watch, especially when their sheep were taken out of the valley to graze. Thanks to the help of their dowser, Helsa, they'd also increased the size of their flock to almost sixty. The number of sheep left to roam wild was an uncomfortable reminder of the number of settlements that had been abandoned in the district.
Another problem with their busy and growing community was the amount of work they faced every day. Unfortunately Wren had difficulty delegating tasks and trusting people, but as her closest friends she often turned to Tianne and Danoph for support. She was happy to help and it was nice to feel needed, but with every day that passed Tianne began to realise that her future lay elsewhere.
When they'd fled the Red Tower it had all happened so quickly. With little time to think about her future Tianne had chosen to stay with her friends. Now, after a few weeks of relative peace, and having spent some time alone with her thoughts, Tianne realised she'd just taken the easiest road. Staying here would be safe. This community was Wren's dream, and, as much as Tianne admired what she was trying to achieve, it didn't feel like home. When news came from the north she knew it was what she had been waiting for.
Finally there had been no major incidents for three days. Tianne realised it was time to tell the others before something else happened that would force her to make another delay.
She'd just finished milking their surly goat when she spotted Wren showing the latest new arrivals around the valley. The man and his wife were refugees who'd fled their remote home in the hills after being attacked by raiders. They'd survived the war ten years ago and all of its horrors, only to be driven out of their cabin by bandits. Grief clung to both of them like a heavy cloak and Tianne knew they'd lost friends and family. The woman was at least six months pregnant and both were exhausted.
Tianne caught Wren coming out of the dormitory, nearly walking into her. "I need to talk to you and Danoph. It's important."
"Can it wait?" asked Wren. "I'm supposed to be helping Leonie with something."
Part of her was tempted to say yes but she firmly shook her head. It wouldn't take much to lose her nerve and find a reason to delay her decision again. Following other people and letting them dictate everything was safe and comforting, but it was also a trap, one that she'd been living in for too long.
Wren seemed to understand the seriousness as she collected Danoph and together the three of them walked over to the sheep enclosure. Until a few days ago the hardy animals had been surviving by themselves on the hills. Their coats had been matted and filthy, but otherwise they'd adapted to their new environment. Now they seemed completely at ease among people being herded around. Perhaps it was simply easier for them as well to follow and be part of the crowd rather than choosing for themselves.
"I'm leaving," said Tianne, knowing that she needed to say it up front.
For a while Wren was stunned into silence but Danoph didn't seem surprised. Perhaps he'd already seen this moment in a dream.
"Where are you going?" asked Wren, surprising Tianne by not asking why she was leaving.
"Home. To Zecorria." Tianne hadn't thought of it as home in a long time, mostly because she'd planned never to return. Her early memories were a pitted landscape of embarrassment, bullying and constantly feeling like an outsider. None of that mattered now. She was needed.
The Regent had declared an amnesty for all Zecorran mages. Garvey and his band of followers were a serious threat and the Regent needed loyal patriots willing to return home and defend their country from harm. Soldiers and steel were not enough. He needed magic. He needed her.
King Matthias had put out a similar call to arms at the start of the war and Battlemages from around the world had answered, including Eloise and Balfruss. This time there wasn't a war, not yet anyway, but she would return home with her head held high to defend her country. None of those who'd scorned or mocked her before she went to the Red Tower were worthy.
"Are you sure about this?" asked Wren.
"I am." Tianne hoped she sounded confident and the others didn't notice the quiver in her voice. "What you're building here is important and it will make a difference to the lives of many people in Shael. I can do that for my people in Zecorria. They need me."
"You are needed here," said Wren, turning to Danoph, perhaps in the hope that he would agree but he remained silent and watchful. "I need you," added Wren.
"You asked us to decide if this was the right place for us. Perhaps one day it will be my home as well, but not yet." Tianne felt safe in the community, surrounded by the others, because there was no risk. The community didn't lack for excitement, but here she was accepted by everyone for who and what she was. Returning to Zecorria meant it would be challenging, but it was also possible she could change how people viewed mages. Someone had poisoned people in every country against magic and it had led to the destruction of the Red Tower. The amnesty gave her the perfect opportunity to show people that not all mages were like Garvey and that in the right hands magic was a good thing.
"I think it's a mistake," said Wren, stubbornly folding her arms.
"I can help people, Wren. The Red Tower was always so mysterious and far away. It scared people because they didn't know what went on inside the school. Every day in this community we use magic in plain sight. There's no need to hide. It can be the same in Zecorria. I can show people that magic is amazing and you can do so much with it."
"You have no idea what the Regent really wants. It might be a trap."
"A trap?" said Tianne, raising an eyebrow.
"He was the first to bring in a national ban on Seekers. It also appeared that he was going to ban all mages until Garvey went on his rampage. This amnesty could just be a ploy to imprison and kill all mages."
"I don't think that's likely."
"But you don't know," insisted Wren. "You know nothing about the man."
"I know enough," insisted Tianne.
"You're being naïve."
Tianne had expected Wren to try and talk her out of it, not to attack her personally. Instead of replying she turned to Danoph. "Nothing to say? Or have you already seen this moment?"
Danoph shook his head. "I've had no visions about this, but you both make valid points."
"Thank you," said Wren, naturally thinking he sided with her.
"I said both," said Danoph, holding a finger to forestall further interruption. He waited until Wren had closed her mouth before he continued. "You asked us to decide for ourselves about remaining part of this community and Tianne had chosen. You need to respect her choice. However, some caution would also be wise. This request could be both noble and sinister in nature."
It was the most Tianne had ever heard him say. Danoph seemed exhausted by the effort as he fell silent and seemed to fade into the background again.
"I will be careful," she promised, making a small concession to Wren. "Wouldn't you go back to Drassia if the leaders there made a similar request?"
Wren shook her head. "No, I wouldn't, it's very different in my country. Magic has no place there, but Danoph is right. I may not like it, but I will honour your decision. But that doesn't mean I'm not going to miss you."
"Oh Wren," said Tianne, gathering her friend into a hug.
"I'm just worried about your safety. I didn't mean to offend you," she apologised.
"I'm going to be in the capital. I'll be surrounded by thousands of people," said Tianne, trying to recall her memories of Herakion. It had been a long time since she'd visited the city. "I'm more worried about you, out here on the borderlands with the raiders. They've been getting closer and their attacks more violent."
Wren shared a look with Danoph who just shrugged. Tianne wasn't sure if there was something going on between the two of them, but they did seem to be developing their own silent language.
"We will deal with the raiders," promised Wren.
Wren was always planning ahead. Tianne hoped she could come and visit the community in the future. By then it would probably have grown into a city with Wren at the reins. In her own way, Wren had been preparing for a challenge like this her entire life. Instead of running a Drassi clothing empire like her mother had wanted, she was creating something that was completely her own from scratch. She was living her dream. It was time for Tianne to chase hers.
Tianne turned to Danoph. "Take care of her."
"I will, for as long as I am able," he promised, which would've sounded peculiar coming from anyone else.
After that there wasn't much else to say. Tianne packed her bag and the following morning everyone gathered to say their farewells. Although the community couldn't really spare it, she was given a horse for the long journey north. The saddlebags were bulging with provisions and Tianne also received a coin purse from Master Yettle.
"Keep it," he said, when she tried to give it back. "Show them what it means to be a real student of the Red Tower."
There were lots more hugs and a few tears but then she was out of excuses. Tianne felt terrified that she was making the worst decision of her life, but it was too late to turn back. Part of her wanted to say she'd changed her mind and that it was all a mistake. She knew the others would smile and accept it, allowing her to fall back into the comfortable rut. It was the thought of getting stuck in that trap again that spurred her on.
When the Grey Council had asked her to choose, Wren had forged her own path. Now it was Tianne's turn to find her place in the world. With her stomach churning and with sweaty palms she mounted up, gave everyone a last wave and rode away from the community towards Zecorria.
It was time to go home.
# CHAPTER 12
Using her set of master keys, Tammy opened the locks to the remote cell block and out of habit locked the door behind her. There was only one prisoner on the corridor but she didn't trust him. That was why she had two armed members of the Watch guarding him at all hours despite his willingness to cooperate. Even though he was locked in an isolated cell, under Unity Hall populated by several dozen Guardians at all times, Torran Habreel was still a dangerous man.
Inside his head were the answers to a hundred questions she'd yet to ask and, if she wasn't careful, someone might break open his skull to stop them spilling out.
There was also the possibility that Brook was not the only Guardian loyal to Akosh. She'd asked Faulk to make subtle enquiries into the religious background of all Guardians, but it was delicate work that couldn't be rushed. Most of her people claimed to follow the Maker, the Blessed Mother, or the Lady of Light. But it wouldn't be difficult to lie about it in order to blend in. Yerskania was famed for being open and inclusive and that included the Guardians. No one was banned from joining the Guardians because they followed a particular faith. It was all down to skill and merit. But Tammy needed to be able to trust her own people with the difficult tasks ahead. Suspicion was a natural part of the job, but as the new Khevassar she needed a solid foundation or else it would all topple over like a house of cards. She really hoped Faulk didn't find anything in his search.
As the silence of the isolated cell block enveloped her, a vicious part of Tammy considered putting Habreel in with other prisoners. During his time as a Guardian he must have arrested dozens, if not hundreds, of criminals and they rarely missed an opportunity to get some payback. But she needed him alive and able to speak. So for now he would have to stay in isolation for his own protection. He would eventually be punished for his crimes according to the law and justice would be served. Vengeance was something she had to leave behind but sometimes it was a struggle. The memory of what she had done to Don Lowell was still fresh.
By the time she'd unlocked his cell door Habreel was standing at the head of his bed, waiting for her. It felt as if this was a cell inspection with her playing the role of a prison guard.
Despite having few personal belongings, the rigid organisation of Habreel's cell spoke of a military background and logical mind. The bed was perfectly made with the sheets pulled tight. The small folding table they'd allowed him had a neat pile of papers and two pens. Four books, the largest at the bottom and the smallest on top, formed a pyramid in the middle of the table. Even the comb they'd given him sat precisely in the centre of his shelf.
Habreel had fallen back into old ways after turning up injured and lost on her doorstep a few weeks earlier. Led astray by a manipulating being of indeterminate power and betrayed by his closest friend, he'd been left with nothing. No pride. No home. No faith. The only thing he claimed was a stack of crimes and a growing list of murders with his name attached to each corpse.
They'd healed his physical wounds and given him the barest minimum of space and belongings. In return he was doing his best to be helpful in her investigation of Akosh, but eventually the time would come when he'd outlive his usefulness. Tammy would relish the day when it happened as he would be put on trial for his crimes. Soon after he'd have an appointment with the headsman and then an unmarked grave.
Others might have found the isolation, silence and incarceration difficult to tolerate, but Habreel seemed to have flourished, or at least partially recuperated. The Old Man had told her as a Guardian he'd been outspoken, verbose and possessing a dry wit. He wasn't exactly chatty, but was a long way from the trembling shell of a man she'd first locked in a cell. With so little that was in his control, and so few choices available, he seemed to be enjoying the relinquishment of power.
"Ah, Khevassar, nice to see you," he said, watching as she moved the chair from the corridor into the doorway of his cell. Habreel waited until she was seated before sitting down again on his bed. It was little more than a stone shelf with a thin straw pallet, but he'd not complained. "I've made some more notes on what I can remember about Akosh and her movements. Hopefully there's something in there that's of use to you."
"I'll take a look at them later, but I have a few more questions in the meantime."
"Go ahead," he said, eager to please. If they had met in other circumstances she would have found his sycophantic nature very creepy. Knowing all that she did Tammy struggled to hide her revulsion at being so close to him.
"Did Akosh ever mention anything about orphanages in Zecorria to you? Either in the capital or anywhere else."
Habreel took his time and went through his memories with his eyes closed. "No, she never mentioned it," he said, coming back to the present. "Has something happened?"
Like most of the questions he asked, Tammy ignored it. He couldn't help asking. It was natural that he was curious about the outside world, and he'd also been a Guardian for a long time. But she was here to question him, not pander to his needs.
Habreel sat up suddenly. "Actually, she did say something unusual, towards the end."
"Tell me."
"She sent one of her people, a mage, to Gorheaton. He was going to pose as a Seeker and I heard he killed everyone, then blew himself up. Of course, the blame fell on the Red Tower. When I asked her about it she claimed to have taken him in as an orphan and raised him." Habreel shook his head. "She was clearly confused as they were almost the same age."
Tammy said nothing, thinking back to her meeting the previous night with Balfruss. It had been slightly less tense than his last visit and he'd been happy to share information. A reliable source had told Balfruss that Akosh sponsored six orphanages in the capital city of Zecorria and she had several others abroad. He'd also told her that his suspicions about her being more than human had been confirmed, although Balfruss had been unwilling to clarify what that meant. All Tammy knew at this point was that Akosh was extremely dangerous and that her people were not to try and apprehend her directly.
So if everything Balfruss had told her was true then it was possible that Akosh had raised the mage who went to Gorheaton. At the very least she had been the patron of an orphanage where the boy was fostered and taught to worship her above all others.
"Didn't you say something about Dannel being an orphan?" said Tammy.
For the first time in days Habreel's façade cracked and sorrow rushed in to fill the void. "Akosh claimed he was one of hers as well. What does it mean? What's really going on?"
His old instincts were kicking in. Habreel was probably starting to wonder if there was more to Akosh than a confused mind.
"She's far more dangerous than you realise," said Tammy, telling him little more than he already knew.
"You need to be careful," warned Habreel. Tammy was ready to laugh at his warning until she saw the look on his face. "I saw Dannel's utter devotion to Akosh. Whatever she really is, a mage or something else, to them she's their entire world. He called her Mother and would do anything for her, without hesitation. Even if that meant killing other people, or even himself, like that poor fool in Gorheaton. Make sure you can trust the people you're working with, otherwise the walls might have ears."
Tammy took the notes he'd made and left the cell without another word. If Akosh's people were as devoted as he claimed, then Guardian Faulk's investigation was even more critical than she realised. Guardian Brook had shown how far they were willing to go. She couldn't afford to lose any more of her people. Only the best were selected to join the Guardians and it took several years before novices were trusted to investigate crimes by themselves. Not for the first time Tammy wondered how the Old Man had managed to do the job for all these years. It had only been a few weeks and she was already exhausted.
As she made her way back to the office, Tammy considered her next move. She had people watching the orphanages but it wasn't enough. All her information about Akosh came from other people. Tammy needed to speak to one of Akosh's followers. Finding one would be a challenge and getting them to talk would be even more difficult.
As soon as she walked into the outer office Rummpoe came out from behind her desk, which made Tammy pause. It was like seeing a turtle crawl out of its shell and go for a stroll.
"I couldn't stop him," apologised Rummpoe. "He went straight in and said he'd wait in your office."
"It's all right," said Tammy, soothing the flustered young woman. "I'll take care of it."
There were few people who would be bold enough to enter her office without her invitation. As she'd expected, Guardian Yedda was waiting for her inside. He was lounging in one of the chairs in front of her desk, one of the Old Man's private journals open in his lap, although he wasn't even reading it. He just wanted to show her how little regard he had for her office and authority over him as Khevassar.
Ignoring the slight Tammy closed the door and sat down behind her desk. She stared at him and waited. He tried not to be unnerved by her stillness and silence, but as the moment stretched on he began to squirm. Tammy glanced at the shelves and then expectantly at the book in his lap. Only when he'd returned the journal to its rightful place and sat down did she relent.
"Report," she said, her voice calm and without inflection.
"I investigated the Minister's death, as you requested." Yedda pulled out a notepad and flicked through a few pages.
The Minister of Trade had been in his late fifties and severely overweight. He'd been widowed five years ago after being married for thirty-one years. Six months ago he met a woman in her early thirties and they were married after just two months. Last week the Minister died and his wife inherited his wealth, much to the displeasure of his three children who were of a similar age to their new stepmother.
Normally the Guardians wouldn't get involved in such a case, but because he was one of the Queen's Ministers it was standard practice. The Old Man had insisted on it to make sure no one was trying to rig the system.
"And?" asked Tammy.
"It seems fairly mundane."
Tammy folded her arms and leaned forward across the desk. "What was the official cause of death? Have you spoken to the coroner? Or the wife? Or the children? How about his assistants in the Ministry?" With each question Yedda flinched as if he'd been stung. He probably thought this sort of case was beneath him, or perhaps he'd believed that the Old Man would choose him as Khevassar. "If you're unable to investigate this case, I can give you something more suitable to your skills. I believe we've been asked to find a missing dog. It has three legs and one eye."
Yedda ground his teeth and she raised one eyebrow, daring him to say something. Just one word. She could demote him to the Watch or give him all of the worst cases for the rest of his life if he continued to disrespect her position. Yedda knew this too and was slowly beginning to realise that he worked for her.
"I've spoken to several people in his office," he said eventually in a strained voice. "And someone called Tovin seems the favourite to take over as Minister. I've asked for background on him, to make sure he wasn't responsible."
"The Queen will personally see your report on this case," said Tammy, which caught Yedda's attention. She decided to switch tactics and appeal to his vast ego instead. Yedda had deep familial roots in the city's aristocracy and as such he was the epitome of entitlement. He probably spent as much time as she did at the palace attending the Queen's functions alongside other wealthy families. As such he was constantly scrambling to impress the Queen for the benefit of his family.
The truth was that Morganse probably wouldn't ask and would be happy with a verbal report about the Minister, but it had made him sit up straight. "I chose you because the Queen cares about her Ministers and I want it done right. But if you'd rather—"
"No, no. I'll see to it immediately."
"Are you sure?"
"Absolutely," he said, suddenly a lot more interested in the case than when he'd entered the room. "I should go. Thank you, Khevassar," he said, rushing from her office. He was in such a hurry he left her door open and Rummpoe stuck her head around the frame.
"If he does that again, you've my permission to have him dragged to a cell," said Tammy.
Rummpoe gave her a wry smile that turned vicious when she realised Tammy wasn't joking. A short time later there was a knock on the door and another Guardian came into her office. She'd sent for him and judging by his expression he was puzzled about her request.
"You wanted to see me?" said Guardian Fray.
"Come in, Fray. Close the door." Even though he'd been in the job a few years she still thought of him as new to the uniform. It came from spending so much time away from Perizzi. But Fray had been tested by the fire several times, in Voechenka before she went there, and since then here in the capital city. The scars of his trials showed in the furrows on his forehead. At some point he'd grown a beard and there were a few patches of white. "I need your help with something. It's a little unusual."
"Whatever you need, Khevassar," he said. It still felt a little peculiar hearing people call her that. At the moment it still made her think of the Old Man.
"We're investigating someone very dangerous. She's a cult leader who holds enormous sway over her people. As a result they're all closemouthed and getting any of them to talk is proving difficult." She was skirting around some of the details, as he really didn't need to know and it would only make things more complicated. She wondered how often the Old Man had done this before her. Parcelling out information on a need-to-know basis. Almost daily she had a new level of appreciation for what he'd achieved.
"Everything I know about this cult leader is second-hand. I need to find some answers for myself."
"I can question the suspect if you want," he offered.
"It's a bit more complicated than that," she said, taking a deep breath. "We can't find any of her people, but I know where one of them is currently, and she's not going anywhere."
"Then why did you ask for me?" asked Fray.
"Because she's dead. I need you to summon the spirit of Guardian Brook so I can interrogate her."
# CHAPTER 13
Vargus thought the meeting was never going to end. As ever, it could have finished in half the time but there was a lot of posturing, mostly from the youngest who were keen to prove their right to be at the table. Several were showing off in an attempt to appear wise. Perhaps they hoped to impress some of their elders and curry favour, but it was having the opposite effect. Nethun rolled his eyes more than once and Vargus turned his face away to hide a smirk.
Those at the far end of the table beside him, Nethun, the Blessed Mother, the Lady of Light, Winter and Summer said very little. Winter drummed her ice-blue fingernails on the table and the rest seemed equally bored.
They offered neither praise nor criticism to the speaker as either could be misinterpreted. As ever Elwei said nothing unless called upon but he was always watching and listening. More than once Vargus saw his head turn slightly to regard the empty chair at the far end of the long banqueting table. He'd also noticed Akosh's absence.
At one point Elwei turned his head so that Vargus could just make out one eye regarding him from the depths of the old pilgrim's headscarf. There was a slight shifting, a raised eyebrow perhaps but a question nonetheless, and Vargus just nodded. He'd noticed her absence too and was looking into it.
There was one figure at the table who most people were doing their best to ignore. Kai. He unsettled a lot of the youngest, and many others to be fair.
In this nowhere place, between moments in time, only the table and chairs were real. The rest was an illusion and it had not escaped Vargus's notice that all of them chose to appear as human. Here, they were the best version of themselves, but even in the real world their human bodies were merely vessels for their true nature. Kai appeared as a handsome, blond-haired man with a warm smile and kind face. Out of them all his mask was the biggest lie. If Vargus focused on an individual he could look through the illusion and see their true nature, but there were some things he would prefer not to see again.
A relic from another time, when the mortal races had been more brutal and bloodthirsty, Kai represented an era most would rather forget. But he had endured, although most of their brethren had no idea how he had survived for this long. Vargus knew for certain there were no more temples devoted to the Watcher and the number of followers, who remained faithful Eaters, dwindled every year. Nevertheless, he was slowly building up his power again, within the rule thankfully, or so it seemed. Vargus was doing his best to keep an eye on Kai, just in case.
Normally generous and warm, Summer was starting to look annoyed at the waffling from the far end of the table. Even the Blessed Mother, the epitome of patience, was getting irritated.
"That's enough," said Nethun, cutting off one of the youngsters who was prattling on about the importance of cow's milk and the sanctity of the land. The short, rotund man, who had something to do with cattle and farming, was about to protest when someone beside him yanked firmly on his arm. He took the hint and sat down, doing his best to hide his disappointment.
"Is there any important business to discuss?" asked Nethun, raking the far end of the table with a glare that few would meet. Those who had been planning to make a speech similar to their rotund friend suddenly changed their mind, shaking their heads. "Then we're done," said the sailor, dismissing everyone with a wave of his meaty hands.
Most vanished immediately, going back to whatever they had been doing before being summoned, but a few stayed behind to talk. Most of their kind didn't meet in person very often, and never more than two or three at a time. Everyone at the table was so different from one another that even a small group coming together would raise a few eyebrows and cause ripples they wanted to avoid. They had learned that mistake from their elders. Some of the earliest meetings had been in person and there were still mentions of them in a few history books that Vargus was waiting to fall out of print.
Further down the hall he saw Nethun speaking with a couple of the new faces, doing his best to appear genuinely interested. After a while the others began to disperse until only he and the old sailor remained.
"Finally," huffed Nethun, moving to stand in front of one of the large fireplaces. "I thought they were never going to leave. I won't be sad to see some of them disappear into the Void. They talk too much."
"Well, no one could accuse you of that, old friend," said Vargus, earning himself a brief grin.
"You said it was important."
"You couldn't come in person?"
Nethun shook his head. "No. I'm at sea." As Lord of the Oceans and patron of all sailors, as well as the Vorga, Nethun spent at least two thirds of his time on the sea or under it.
"Did you notice who was absent?" asked Vargus.
"Akosh. I assume there's a reason she ignored the summons?"
"Yes, there is. Given what I recently learned from Balfruss, her absence was expected."
Nethun's expression turned grim. "Tell me."
"In part, she's to blame for the fall of the Red Tower. Her people have been posing as Seekers, killing children, stirring up trouble and shifting all the blame to the mages," said Vargus. He went on to tell Nethun about how she had been using her followers, seeded across the west, to foster greater fear and hatred of magic and those born with it.
The one rule passed down by the Maker was that their kind was not supposed to directly interfere in the affairs of mortals. They could not change the natural course of events, even if in doing so it would save many lives and avert a disaster. Despite their power and knowledge, it was not their place to right their wrongs.
On a few rare occasions they had bent the rule, but it was always done with the full knowledge of everyone and never by an individual working alone.
The Lord of Light, now all but forgotten by the mortals, had tried it. His attempt to grow his power base had led a large portion of the world into a pointless war where thousands of mortals had died. Akosh's plan appeared more subtle and beyond causing chaos her goal was currently a mystery. But because of her actions the fear that had always been bubbling under against mages had come to the surface.
Whole communities had torn themselves apart searching for the perceived threat of a Seeker in their midst. On top of that children had been killed or driven out of their villages and anyone openly using magic was either shunned or attacked. Others had blown themselves up after being egged on by Akosh's supporters, killing themselves and many others. Chaos might be all she wanted, in order to build her power for the future with more orphanages, but Vargus suspected there was something else as well.
"Does the Grey Council know it was Akosh? Do they know what she really is?"
"Balfruss does. He attempted to summon me," said Vargus with a lopsided grin but it quickly faded as he thought about those who had died defending the Red Tower from the mob. "Do you remember Munroe?"
Nethun shook his head. "I don't keep track of those who aren't mine. They come and go so quickly, and in this age there are so many humans."
"A few years ago she defeated the Flesh Mage in Perizzi. She also helped close the rift."
"Ah. Her, I remember. Small woman, powerful mage. Swears like one of my sailors."
"That's the one. Her family was murdered when the Red Tower fell. She's going after Akosh and wants revenge."
Nethun sucked his teeth. "As much as I want to, and I suspect you do as well, we cannot get involved. It will play out how it must."
"Sadly, I agree," said Vargus, although he'd hoped Nethun might say something else. "But Akosh has broken the rule and must be dealt with."
"Vargus, we've known each other for a long, long time. So, I know you wouldn't have come to me with this unless you'd already taken steps."
"I've tried to find her, but had no luck. I think she's in Zecorria or Yerskania, but can't be sure. So, I'm doing what I can to draw her out of hiding."
"How?" asked Nethun, raising an eyebrow.
"Apparently, someone is about to persuade all of her orphanages in Rojenne and Perizzi to change patrons to the Maker or similar. The rest in Yerskania will follow suit after that. It won't stop her right now, but it will create ripples and a problem for her in the future."
"Thinking long term as ever," said Nethun. "Do you think it will be enough to draw her out?"
Vargus shrugged. "If I start enough fires then eventually she'll show up in person to try and put them out. Either that, or she'll hide in one place surrounded by her own people."
"What if she runs?"
"She won't," said Vargus. "She's invested decades in her orphanages. She won't just walk away from all of that now and try to start afresh."
"What else?"
"The Guardians are looking into her network in Perizzi. Munroe is searching for her, and I suspect various foreign agents will be keen to disrupt her plans in the north. She has enemies all over and doesn't realise it."
"The noose tightens all around." Nethun stared intently into the fireplace for a long time in silence. He seemed to be working up to saying something and finally asked, "Does He know what's happening?"
"Who?" said Vargus, but the old sailor just gave him a look.
"Is He even aware?"
Vargus trusted Nethun with more of his secrets than any of the others, but he'd always wondered how much he already knew. It seemed as if Nethun was a lot better informed than he realised about the location of the Maker and what had happened to him. It was one of Vargus's best kept secrets, or so he thought.
It was Vargus's turn to play for time but eventually he answered. "No. He's not aware. He's not ready."
"Then it still falls to us," said Nethun. "You'll take care of Akosh when you find her?"
"I will."
"Good. I'd say the others will learn from this, but it wasn't too long ago we were forced to deal with that idiot lantern boy."
"Just like him, she won't escape either. In a few years' time, she too will be nothing more than a distant memory," promised Vargus.
# CHAPTER 14
Wren felt Tianne's absence from the first day after she'd left the community.
It wasn't just that she didn't have someone besides Danoph to whom she could turn for assistance. Laila, who had arrived a few weeks ago, had mastered control of her magic but beyond that her skills were rudimentary. As such she was happy to take on extra work to make up for her lack of progress. Wren suspected part of the reason for Laila's enthusiasm stemmed from her fear of magic, but with luck that would fade in time.
The biggest reason Wren missed Tianne was because she was her friend. She'd been kind and supportive since her first day at the Red Tower. It was Tianne who had met her at the gates and shown her around the school. At times it was difficult to believe that had only been a few months ago.
But there was another reason she missed her friend. Tianne was a gossip. Tianne couldn't help it and thankfully she wasn't malicious. She didn't delight in revealing secrets to the wrong person in order to cause pain and suffering. It was just that she liked to know what was going on at all times in the life of every person around her. That detailed insight had proven valuable to Wren in running the community, but now it was gone. In turn this had forced her to try something new and uncomfortable.
Wren had to go out and talk to other people on purpose.
She was starting to get better at it. There were still some long and awkward silences, but gradually people were starting to open up to her. Tianne had made it look effortless, but it was new and difficult for Wren. Most often she found herself walking up to people only for her mind to go blank. Then she would lurk and try to think of something to say while they stared at her expectantly.
There was no easy way to start a conversation and she couldn't just ask them about their problems with no preamble. In Drassia such conversations took place behind closed doors in private, but here it was different. People spoke about their problems openly and seemed to have no modesty. At times groups of people, women in particular, would sit around discussing very private and intimate subjects that made her want to leave the room in a hurry. There were some things she wanted to find out for herself. Not have them described to her in graphic detail by a gaggle of middle-aged women.
Nevertheless, Wren needed to know what people were struggling with in order to try and help them, but asking them outright was difficult and made her feel uneasy. At times she also thought it had more to do with expectation than reality. When people looked at her they saw first a Drassi which came with its own preconceptions, most of which were wrong. Recently Wren's attempts at small talk, to ease into a conversation, began with her telling them a fact about Drassia. The reality often surprised them which she hoped was a good thing. At the very least it made it easy to then ask them about something more personal.
From her attempts at talking to people she'd found out that most of the community were happy and staying busy seemed to be key. Thankfully there was plenty of work to be done so no one was ever sitting around idle. Food was a constantly pressing concern, but with the old wood they were never short of raw material for building. Using an old technique she'd learned as a girl, Wren taught the others how to create charcoal which they were stockpiling for winter and to sell.
Their flock of sheep had grown significantly in the last month thanks to their dowser. When the villages in the area had been abandoned they must have turned all of their animals loose. They'd been living wild ever since and the survivors were hardy beasts that were still docile enough to be rounded up.
Although some found it unpleasant, Wren understood the necessity of having a butcher in their midst. They needed the meat and she made sure her unease didn't show on her face when she visited the abattoir.
After discussing it with Danoph she'd finally relented and allowed one of the scavenger parties to retrieve a wagon. Two of their older residents, who had once been farmers, were then able to pose as tinkers and sell charcoal, wool and other assorted items they salvaged to nearby settlements. At her insistence at least two students with a solid control of their magic accompanied the wagon at all times. As well as providing protection for the wagon, it gave her a constant picture of the surrounding area and the concerns of other communities. The most pressing of which seemed to be the roving bands of raiders.
Villagers said that a couple of months before the fall of the Red Tower one or two groups of robbers had started attacking caravans travelling from Yerskania into Shael. For an unknown reason these groups had started working together and since then the problem had grown significantly worse. Wren suspected someone with a bit of insight and a sharper mind had seen the potential of uniting them. More ground to cover and less infighting meant greater profit for everyone. If she were a robber baron that's what she would have done.
So far her people had not come into direct contact with any of them, but it was only a matter of time. Wren had seen first-hand what they did to innocent people without provocation. The girl and her mother had physically recovered from their ordeal, thanks to the skills of Master Yettle, but they were both severely traumatised. Everyone they knew had been slaughtered in front of them, including the girl's father. It was their wagon the scavenger party retrieved, including many of their belongings, but even they had provided little in the way of comfort.
Taking the initiative Wren had started sending out small patrols of her people to watch the surrounding area for the raiders. Several wagon trains passed through the western province every week, taking goods further east into Shael to the capital city and then back out again. All of them were now heavily guarded, either by groups of mercenaries or Drassi warriors, but that didn't stop them from being attacked with varying success. For the time being the raiders seemed content with remote villages in the region which had far less in the way of protection.
Between discreet patrols, groups going out to scavenge from deserted villages and her roaming tinker wagon, Wren could keep an eye on most of the area.
Today it was her turn to ride with one of the patrols. The area was unfamiliar to Wren but with each trip she began to piece together a map of the landscape in her mind. She, Danoph and one other student, named Rue, passed close to a village south of their community called Sour Crown. There were nearly two hundred people living there and none of them were warriors. They had a few retired soldiers who had made an attempt at building defences, but they seemed crude to her. The wall wouldn't keep out an angry goat, never mind a murderous band of raiders. At least they had people keeping watch which was why she was lying on the ground, looking at the village from a distance.
For once there was a minor technique that she had been able to master. Embracing the Source naturally enhanced all of the senses, but, with a little bit of focus and direction, she could amplify her voice or even sharpen her eyesight.
"What can you see?" asked Danoph, who hadn't yet managed to master long-sight, as they were calling it.
With the Source pulsing in her veins it was difficult for Wren to lay still and not run around to expend the energy, but she forced herself to ignore the impulse.
"A knee-high wall. A woman dozing at her guard post and people working in the fields."
"Then they're safe."
"They're complacent," said Wren. "Perhaps they think the raiders won't come here."
"It's been a couple of weeks since an attack," said Danoph.
"That's what worries me. They should be more concerned, not less." Wren was convinced this lull was merely the calm before the storm. Perhaps the raiders were gathering their forces to attack a merchant train as most of their recent assaults had been repelled. Or they were going to target a larger settlement like Sour Crown.
"Do you want to stay a while longer, or move on?" asked Danoph.
Before she had a chance to reply Rue answered with a wheezy snore from where she lay asleep on the ground.
"We could stay a while and talk," said Wren.
An uncomfortable silence stretched out between them with Wren fidgeting and Danoph utterly still.
"If you want to ask me something you don't need to dance around it," said Danoph.
"Thank the Blessed Mother. I find myself struggling to talk to people. When did it become so difficult?"
Danoph grinned. "It's different, now that you're the leader."
"I'm not the leader," said Wren. "There was no election. I left and people followed. Then they just kept asking me questions and I try my best to answer. I'd be happy to let someone else take over."
In a rare display of affection Danoph laid a hand on her arm, halting her babble. "We followed you because the Grey Council offered us three choices, none of which we found appealing. You created a fourth choice because your path lay elsewhere. It's your community, Wren, and people see you differently now."
"Well, I wish they didn't," she said, lowering her voice. She didn't want Rue to wake up and hear her complaining. "I'm still the same person I was before."
"I know that and they will, too. Just give them time."
"How is it you're so wise for someone so young?" asked Wren with a smile. "Sometimes, in the echo of your words, I hear my grandfather."
Before Danoph had a chance to answer she heard riders approaching fast. A group of five or six horses were moving up the road and they didn't sound very far away. The three of them weren't visible from the village but Wren didn't want to take any chances. She elbowed Rue awake and together the three of them moved further back from the road, hiding in a copse of trees.
They'd barely settled, lying face down on the ground, when six rough-looking armed men and women thundered past, heading straight for Sour Crown. The village guard continued to doze at her post until the raiders were nearly on top of her. Something finally woke her up and at the sight of the riders she yanked on a heavy rope connected to a bell overhead.
The dull clanging seemed to slow everything down. The people in the nearby fields started running for home, picking up tools as they came, but it was clear the raiders would beat them to the village. Others came flooding out of their homes wielding a mix of kitchen knives, spears and several curved Yerskani cleavers.
Wren drew power from the Source and channelled it into her senses, focusing on her eyes and ears until she could see and hear clearly from their hiding place.
The raiders seemed content to wait until everyone had assembled, saying nothing until those from the fields had joined the swelling crowd.
"You're not welcome here," said a stocky man at the front of the crowd. Wren thought he had the build of a blacksmith and might be their Speaker, or whatever it was called here in Shael. The crowd cheered at their leader's words, hefting weapons and waving them in what was supposed to be a threatening manner.
"What's happening?" asked Danoph, squinting at the scene. Wren described what she could see.
One of the raiders, a tall man from Seveldrom with a narrow face and carrot-red hair, raised a hand and slowly the noise from the crowd subsided. "Are you in charge?" he said, directing his question at the blacksmith.
"I'm the Warden," he said, and Wren assumed that meant the leader of a community in Shael. "This is our village."
"It was," said the raider. "Your homes, your fields, your food and all of your lives now belong to Boros. You're alive only because Boros allows it."
The Warden rolled up his sleeves and spat on the ground. "You might be good at using that," he said, gesturing at the raider's sword, "but there's only six of you and more than a hundred of us. Sour Crown doesn't belong to you."
Carrot-top grinned down at the blacksmith and nonchalantly raised one hand. There was a faint whistling sound and then the woman to the left of the Warden toppled over, a dagger buried in her throat. Blood gushed from the wound, quickly staining the front of her dress while those around her vainly tried to stem the bleeding. The raiders watched dispassionately as the woman gasped her last breath and then fell silent. The mood of the crowd began to change. Instead of anger Wren saw fear sweeping through the villagers. They weren't warriors. Death wasn't something they were trained to cope with or used to seeing up close. With a simple wave of his hand, and lacking any compassion, the raider had killed one of their neighbours. Someone chosen at random they had probably known for years. Dead. Just like that. And any one of them could be next if they resisted.
"We need to leave," said Rue, whispering in Wren's ear. "They're going to kill each other."
"No, they're not," said Wren, scrambling to her feet. "Stay here, out of sight." Before the others had a chance to protest she started jogging towards the village.
Growing up in Drassia she'd heard many stories about this sort of encounter and power play. Those who wore the mask of service often spoke about their work when they retired. Wren had heard countless tales of war, mercenaries, raiders and robber barons. Their ilk had existed for a long time and they were often people unwilling to work hard for anything. In their mind it was far easier to take from others because they were seen as weak.
"You're all dead," said the Warden. "We're not afraid of you." The crowd behind him started to surge forward. There was a brief surge of bravado but none of the villagers actually attacked. None of them wanted to be the next to die.
The raider was still unusually calm. "You said you're in charge. That means you get to convince everyone to do as you say. You see, if I don't return with all of my limbs attached, Boros will come here in person."
"That name doesn't scare me."
"It should," said the raider. "Boros won't come back here alone. Every single one of us will come here and burn this village to the ground. We'll slaughter you all. Every man, woman and child. Then we'll salt the fields as an example to others who don't listen."
More of the bravado dribbled out of the crowd as the words sank in. There were no children in the gathered crowd, but Wren saw parents glance towards their houses where little faces watched in the windows.
A burning pain began to build up in Wren's side from her prolonged run, but she persisted, keeping the raiders between her and the villagers so they didn't see her coming. So far it seemed as if no one in the crowd had noticed her approach. All their attention was focused on the raiders.
"You're bluffing," said the Warden. "I bet there are only a dozen of you at most."
The raider shrugged his shoulders. "Ask your neighbours."
Wren knew he wasn't bluffing and so did the Warden. Several remote communities in the area had been abandoned in the last few months because of an increased number of attacks. The Queen of Shael and her small army couldn't help this far out. The war had decimated the country and its population, leaving a shattered ruin in its wake. Progress had been made but it was slow.
The communities this far west were on their own and had believed there was strength in numbers. As she came closer to Sour Crown, Wren could see the skeletons of several new houses being built at the far end of the main street. It still wasn't enough.
"What do you want?" asked the Warden, biting off each word.
"A tithe of food and drink every month."
The haggling would soon begin as the villagers tried to pretend this was merely another merchant driving a hard bargain and not a robbery. The pain in her side had increased but Wren pressed on, taking deep breaths to try and dispel it.
A few villagers had noticed her now but they probably didn't know what to make of her. One Drassi girl, running up behind the raiders. They probably thought she was lost or confused in the head.
The Warden and the raider were arguing over terms but even their conversation trailed off when they noticed more and more people staring. One of the raiders turned in his saddle and stared at Wren. She stopped in the middle of the road which had been churned up into a sludgy field of mud. There were no paved roads out here. It was another reminder that she was a long way from home. A long way from anywhere.
"Are you lost, girl?" asked one of the raiders. When Wren didn't respond and barely seemed to blink he turned his back on her. "I think she's a bit soft in the head," he called out to the others who ignored her. Their leader, however, was still looking at her, which is when she raised one hand and made a flicking gesture as if brushing dirt off her sleeve.
Five of the six raiders were flung sideways out of their saddles into the muddy road. They had all moved in unison and Wren hadn't broken eye contact with their leader. Despite what he'd just witnessed the raider tried to draw his sword. Wren just shook her head, ever so slightly, and balled her hand up into a tight fist. The raider gave out a yell of surprise as his sword shattered into half a dozen pieces. The five raiders on the ground tried to get up but she focused more power and kept them pinned down, preventing them from reaching for their weapons or standing up.
"What do you want?" asked the raider.
"Leave and never return. This village is not for you."
Much to Wren's surprise the raider laughed and shook his head. "If I go back without a tithe, Boros will kill me."
"Then don't go back," said Wren. "Whether there's six, or a hundred like you, it won't make a difference. You can't win." To drive her point home, she increased the pressure on the five raiders on the ground. Two were lying face down and she pressed them deeper into the mud until they began to choke. Wren had to work hard to keep her face impassive as images of what had happened to Brunwal flashed through her mind. She eased up a little, allowing them to gulp fresh air into their lungs.
"This isn't the only village that we're visiting. You can't be everywhere at once," said the raider. This time it was Wren's turn to smile.
"Who said I was alone?" she asked, glancing at the uneven land around her which was dotted with lots of hiding places. The raider suddenly sat up straight in his saddle, alert to danger. The day was perfectly still and yet a gentle wind suddenly sprang up. Most peculiar of all was that it seemed to be completely focused on the raider. It buffeted his hair and then just as quickly it was gone. Wren sensed a delicate rush as Rue channelled power from the Source.
She took a few steps back and released the other raiders who slowly climbed to their feet. They glared at her and she saw a few touching their weapons but none of them tried to attack.
"Let's go," said their leader, still looking around for her friends. "This isn't over," he promised Wren, turning his horse and riding away. The others pulled themselves into their saddles and followed after him. The village and the tithe were completely forgotten, for now at least. She waited until they were out of sight before turning back to the gathered crowd.
As she'd expected they were still hostile and holding their weapons with intent. To them, she was potentially more dangerous than the raiders. She hoped for a little gratitude but even that seemed to be too much to ask.
"We don't want your kind around here," said the Warden, making a shooing gesture.
Any thoughts about trying to reason with them evaporated and Wren simply turned and walked away.
She'd saved their lives, for the time being at least, but to them that didn't matter.
The raiders might not return to this village but she knew it wasn't over. At least she had a name. Boros. He would be angry and perhaps take it out on the raiders for returning empty-handed, but she wasn't responsible for their actions. Wren knew she could have killed all six of them, but after what had happened with Brunwal she never wanted to kill again. As Master Yettle had instructed she'd let herself feel all of it. Dwelling on what she had done still brought tears to her eyes, but she forced herself to relive it.
By the time she'd walked back to the others her face was dry and she felt composed.
"It's not over," said Danoph, and she wondered if he'd seen something in a dream about this village.
"I know. We need to find out more about their leader, Boros."
"Can't we just leave him alone?" asked Rue. "He doesn't know where we live."
"We can't just leave these people to his mercy."
"Why not?" asked Rue. "They hate us and would kill us if they had a chance."
Wren couldn't argue with that but she also knew their fear came from ignorance. Despite all that had been done to her and the others at the Red Tower, she couldn't stand idle while innocents were attacked and murdered. She would have to show them through her actions that not all mages were evil or destructive. Not every mage was like Garvey and his followers.
"So far we've not run into the raiders, but it's only a matter of time. We can't just ignore them," said Wren, knowing that a conflict was inevitable.
All she'd wanted to do was build a safe community for people like her, whereas Boros wanted his own kingdom. Perhaps it had been naïve to think she could achieve that without a fight. So be it.
Wren turned her mind towards what she needed to do next. The first step was to know her enemy. Once she understood him she could drive him and the other raiders out of the area for ever.
# CHAPTER 15
Feeling as if she were stepping back in time, Munroe found herself sneaking through the streets of Perizzi. Ever since she'd returned to the city she'd done her best to go unnoticed by people from her old life. She wasn't that person any more and wanted nothing to do with them and their criminal dealings. Now she was trying to avoid them and the Guardians as well.
If any of the Guardians, or a member of the Watch, recognised her then word might get back to Tammy. Munroe knew she was only doing her job, but right now she wanted to avoid the Khevassar. If she had any chance of succeeding, then the fewer people that knew she was still in the city the better. That meant a return to the quieter parts of the city, those off the beaten track, where the Families held sway.
Avoiding the prying eyes of former associates was proving to be a difficult challenge. She had hoped that after being away from the city for several years it would give her a degree of anonymity. After listening to a few conversations in bars Munroe realised stories of the Flesh Mage and his downfall were still popular. Although she wasn't mentioned by name Munroe didn't want to take any chances. Instead she decided to assume a role that was familiar. One that would attract attention in a different and predictable way.
The gambling den was not one she'd been to before but after studying the people waiting to go inside she knew it was a good place to start. The customers comprised mostly merchants and business owners, those with a little extra money to spare. Along with them came a gaggle of working men and women hoping to hook a wealthy trick on a good night; Wooden jackals kept everyone in line and Brass jackals kept watch. It was a fairly middle-of-the-road establishment where fortunes could be won, but losses were not severe enough to result in someone going hungry or losing the shirt off their back.
Wobbling slightly as she approached the front door Munroe smiled at the big doorman on the left and winked at the woman on the right. He merely raised an eyebrow while the woman said nothing and held open the door.
"I hope to see you later," slurred Munroe, waving at the woman as she stumbled inside.
As expected, the furnishings were bright and colourful, giving the illusion of wealth, but a second look showed her they were gaudy copies. The crystal lanterns overhead were made from coloured glass and the multi-coloured carpet underfoot was worn thin in places and patched in others. There were a couple of paintings on the walls and a few exotic plants dotted around the room, but they, too, were fading and withered from lack of sunlight. Thirty years ago it might have been glamorous. Today it was merely sad and dilapidated.
Most of the people here didn't really care and wouldn't be able to tell the difference between the real thing and a forgery. Drinks were cheap and plentiful and the room was alive with the rattle of dice, cries of disappointment, cheers, laughter and faint background music coming from a tired old man on a fiddle.
Easing her way through the crowd Munroe went straight to the bar and ordered a couple of drinks, draining one quickly in two gulps. After giving the barman a little wave of thanks she shuffled to the first table and cheered on a Morrin woman doing rather well at cards. One or two people stared when she shouted a little too loudly, or touched strangers in a familiar way, but they dismissed her as a harmless drunk. A few of the working girls in the room were glaring but Munroe pretended not to notice. After a while, when they realised she wasn't there to steal their business, they also ignored her.
When the Morrin picked up a bad hand and lost half her money Munroe commiserated with her and drifted away to the next table. The hypnotic rattle of dice caught her attention and she decided to have a little fun. After watching a few throws, she put some money down and scooped up the dice.
"So I need three crowns, right?" she said to the croupier. The balding man gave her a thin smile of encouragement. The dice rattled across the table and three crowns landed. "This is fun!" said Munroe, scooping up her winnings.
Long before she'd travelled to the Red Tower to learn how to control her magic, Munroe had used her Talent in gambling dens like this one for many years. Back then she hadn't known it was magic and had thought of it only as a curse. The owners never liked to lose too much money and her innate ability to manipulate the odds, cooling off a natural winning streak, had been in high demand. Of course, much later she'd also discovered her ability to change someone's luck for the better, and do so much more with her Talent, if she focused.
Over the next twelve throws she continued to win at dice, adding more money each time until she had a healthy stack of chips in front of her. Others started to notice her streak and began betting on her to win. A pit boss approached the table, whispered in the croupier's ear, and the dice were switched out. Despite their precautions Munroe continued to win and the crowd around her table swelled in number again. After placing a rather large bet, and then somehow winning once more, she bought everyone a drink with the money.
The dice were switched again and suddenly she had three pit bosses and one of the Brass watching her, as well as several Wooden jackals who were scanning the crowd. They were looking for the con, thinking she was the distraction meant to keep their attention in one place while someone else stole their money. Of course there was no con, other than the fact that she was manipulating the odds with her magic.
"Let's make this one a big one," said Munroe to the people around her. "How about I bet the whole lot on one last throw?"
"I'm afraid you've reached the house limit," said the croupier, sweating under the intense glare of so many people. The crowd booed and swore at the croupier until the largest pit boss at his shoulder leaned over and whispered something in his ear. "However, we would like to offer you access to a special high-stakes game. It's very exclusive."
Munroe pretended to consider it, looking at those around her whose opinions were mixed. By now, despite only sipping at her drinks and spilling the rest, she was actually feeling a little fuzzy-headed. Part of her slurring wasn't an act and the lights did seem a bit too bright.
"That sounds like fun," she said, grinning at the croupier who heaved a sigh of relief. Someone collected up her chips while two large jackals escorted her out of the main room, down a short corridor and into a richly decorated waiting area. Munroe sank into one of the comfy chairs and dozed off for a short time before someone shook her by the shoulder.
"We're ready for you now," said one of the pit bosses, a broad Seve woman with a nasty scar under her right eye. Her smile was probably intended to be friendly, but it only made her look more villainous.
Tottering along, using the wall to support her, Munroe walked down another corridor into a room at the end. It was gloomy and she ran into the chest of the large man waiting for her. When she turned around she saw there was nothing in the room except three very large jackals, all of whom loomed over her. All had battered faces and were wearing weighted leather gloves.
The pit boss stepped into the room, closed the door behind her and leaned against it, blocking the only way out. "How did you do it?" she asked.
"Annoying, isn't it," said Munroe, dropping the drunk act and grinning at the woman.
"Are you working alone or with a partner?" asked the pit boss, showing no surprise at Munroe's soberness.
"What do you care? Is it your money? Are you in charge?"
The pit boss scratched at the scar on her face, a nervous twitch, before shaking her head. "My employer is not someone to be trifled with. You can see what will happen if you don't tell me everything I want to know." She gestured at the three bruisers surrounding Munroe.
"Is he here? Can I talk to him?"
The pit boss winced and her patience seemed to run out. "Left arm," she said to someone over Munroe's shoulder. Without turning, Munroe waved a hand at the three jackals and all of them stumbled back, seizing their chests. Needles of pain were shooting through their chests and it would feel as if their hearts were about to burst. One fell onto his face and the other two stumbled to their knees, gasping for air.
"Is he here?" asked Munroe, producing a dagger from where she'd hidden it inside her belt. The pit boss stared at her and then at the three wheezing jackals. She knew what Munroe was and how she'd done it. Munroe could smell the woman's fear. The pit boss winced when Munroe pressed the dagger against her throat hard enough to draw blood. "Last time. Is he here?"
"Yes."
"Show me," said Munroe, gesturing at the door behind her. "But lie to me and I'll do the same thing to you."
Even though it wasn't necessary, Munroe kept the dagger pressed against the back of the pit boss. It served as a reminder of what would happen if she tried anything. She followed the scarred woman down a long corridor and then up a narrow flight of stairs to an office where her boss was sitting behind his desk. He looked up in surprise at the pit boss, a question on his face until Munroe stepped out from behind the large woman.
It had been nearly a decade since she'd last seen the Butcher but in all that time he'd barely changed. Back then he'd been an interloper trying to claim territory from one of the other Families. Ten years on he was part of the establishment and had maintained his fearsome reputation.
He wasn't the biggest man she'd ever seen, but his black vest did show off thick arms that were covered with faded scars. An intricate black tattoo ran up his arm from his left wrist, across his chest and down to his right hand. His head had been freshly shaven and the gleam from the lantern reflected off its surface.
"The beard is new," said Munroe, casually sitting down in one of the chairs in front of his desk. He'd been clean-shaven last time but now had a goatee that was shot through with grey. "But the grey makes you look old. I'd shave it off."
The pit boss was at a loss, unsure of what to do or how much trouble she was in for bringing an armed intruder.
"Leave us," was all the Butcher said, dismissing her with a wave of his hand. She closed the door and he sat back in his chair, crossing his arms over his chest. As he did so the swirling tattoo on his forearms lined up, creating a more complex interwoven pattern.
"That's cute," she said, gesturing at his arms.
"What do you want, Munroe?" he asked. If he was afraid of her at all it didn't show.
"Information."
The Butcher raised an eyebrow. "About?"
"A woman named Akosh. I've gathered a few bits and pieces, but I need more. I want to know where she is."
"I see," said the Butcher, running a hand over his shaven head. He seemed to relax, shaking off whatever had been bothering him. Perhaps he'd thought her visit had been about something else. Right now it didn't matter.
"Can you find her?"
The Butcher got up from his desk, poured himself a glass of water and offered her one which she accepted. Munroe didn't think he would try to poison her but she waited for him to drink before sipping hers.
"Why come to me?" he asked instead of answering her question. "Why not speak to your old friend, Don Jarrow?"
"Because a favour from him would have serious strings attached. You need to understand, I'm not coming back into the business. I don't care about Perizzi or any of the Families. I just want you to find this woman."
The Butcher mulled it over and Munroe noticed he hadn't asked why she wanted to find Akosh. There were a number of rumours about where the Butcher had come from and who he used to be before carving out his own empire in the city, but Munroe didn't care. All of that was also part of her old life and she was not going back to it. The reason she'd chosen the Butcher was his reputation. As well as scaring many people in the underworld, he was known to have a network of contacts beyond the city.
Primarily they gathered information on rich targets coming to Perizzi for his grifters to swindle. Cons took time and patience to set up, which meant he had people dotted across the west, or at least in most of the main cities. If Akosh had a network of her own, via her cult, then it seemed feasible that the Butcher's people could find her.
If she'd gone back to Don Jarrow it would have created a number of ripples and she wanted to remain unnoticed. Finding Akosh not only relied on solid information, it was critical that she didn't see Munroe coming until it was too late. Until she was breathing down her neck.
"Can you do it?" she asked.
"Perhaps, but I want something in return."
Munroe cocked her head to one side. "I thought the stack of gold I won downstairs would be enough."
"We both know you cheated and used your magic."
"I'm not going to owe you a favour," said Munroe. "I won't have something like that hanging over my head."
"No, this is something I need right now."
Despite the circumstances Munroe was curious. "Which is?"
"Protection."
"From who?"
"That's the problem, I don't know. Someone killed Don Lowell and no one knows who did it or why."
Such a bold move was surely a play for his turf, but it was unusual that someone had not taken credit for it. It could be that they were waiting for something. Or it could merely be the start and the Butcher, or one of the other Dons, could be the next target.
"You want me to be your bodyguard?"
The Butcher's smile made Munroe uncomfortable. "No. I have people for that. I just need you to watch my back during a few important meetings. Just in case."
She didn't need to ask why. He could surround himself with a hundred of the best killers in the city. A mage could cut through them like a warm knife through butter.
"Deal," she said, offering her hand and he leaned forward to shake it.
"Akosh. Actually, I've heard the name before," said the Butcher, startling Munroe as she leaned back in her chair. "Don't get too excited. She's not here, but I've heard stories from the north."
"Where?"
"Zecorria. One of my people recently had an encounter with her at an orphanage in Herakion." Munroe twitched at the last word and the Butcher smiled. "Yes, I know about them. She has a few orphanages here in Perizzi, but the Guardians are watching those. She's not been seen in the city for a few months."
"Then she's in the north."
"Maybe, but she moves around a lot. You need to be patient."
Munroe ground her teeth and gripped the arms of her chair. She was beginning to hate that word. Balfruss had asked her to be patient as well. She'd given him a month and he'd not come any closer to finding Akosh. Her family, her world, was gone, and that demented bitch was still alive.
"She's cautious and insulated by her people," the Butcher was saying, noting her demeanour. "Finding one of them willing to talk is difficult. From what I've heard they're all zealots. So getting any reliable information to pin down her location is going to be tricky. I suspect you'll only get one chance. If you go blundering in then she could slip away. Once she knows you're after her, it will be a hundred times more difficult. But it's up to you," he said, putting the choice back in her hands.
Munroe knew he was right and that the Butcher represented her best chance at finding Akosh. She still hated it. The anger inside her was just simmering under the surface and at times she felt as if it were going to swallow her whole. Hate worse than any she'd ever felt burned her inside. Her veins were on fire and she needed to find a way to release the pain before it consumed her.
Slowly, bit by bit, as if she were choking down poison, Munroe pushed the rage down inside her. The Butcher said nothing, giving her time to regain her composure. Eventually she felt calm enough to speak.
"I will try to be patient," she muttered through clenched teeth.
It seemed as if Munroe had no choice. She would stay in the shadows for now, but when the time came there would be nowhere for Akosh to run. Nothing would stand in the way of her vengeance.
# CHAPTER 16
This time when Akosh entered Bollgar's office she was pleased to see that for once he wasn't eating. He was still dressed in a loose food-smeared robe, this one a dingy blue, but all his attention was focused on the pristine ledger in front of him.
In a small notebook she watched him totting up a series of numbers with incredible speed before recording the final value into the ledger.
"Apologies, Mother," he said, gesturing at the seat opposite. "I just have a few numbers to check for the local businesses."
"Go ahead," she said. On her way into the building she'd nearly walked straight into a tall, impeccably dressed woman. She recognised her as the owner of the candle shop a few buildings down the street. Her business was one of several that he managed. Akosh knew they found Bollgar distasteful because of his slovenliness, but his accounting was beyond reproach, so they tolerated it. However, they preferred not to visit him in person unless absolutely necessary, as his office did have a certain pungent odour.
"Mistress Valine's candle shop is not performing," muttered Bollgar, feigning a sad smile while his eyes twinkled in delight. "With some reluctance she's accepted a new business partner who has generously paid off her debts. In return they will have a healthy stake in her shop. You should make a nice profit in the coming year, Mother."
She was pleased to hear that he was putting her money to good use, but right now she had more important matters to think about. Such as the possible repercussions from not attending the meeting with her brethren. Last time they had been discussing the problem of magic and Seekers where she had feigned ignorance along with the rest as to the cause. Now she was more deeply invested than ever and Habreel had escaped. It would've been foolish to underestimate some of the older ones, like Vargus and Nethun, and assume they remained unaware of her actions. For now it was safer to be cautious and remain hidden. Money was important but it was only valuable if she was still alive to put it to good use. Her new ally, whoever he was, had promised to keep an eye on her brethren in the meantime. Pavel, the former Guardian, had not made contact with her again, forcing her to assume his Master had no important developments to share.
"You said there was news from Perizzi," she reminded him. He added up one final column of numbers, recorded the result and carefully put the ledger to one side.
"Yes, Mother."
"I've heard some disturbing rumours, Bollgar. Are they true?"
"I'm afraid so. I've been informed there are several people watching the orphanages in Perizzi at all times. I believe they're Guardians."
It confirmed her suspicion that something had gone wrong with Brook's mission to silence Grell. She'd already assumed the worst as there had been no messages from her since then. What a waste. To have used such a unique asset on a minor inconvenience. Now she had no idea what was going on inside Unity Hall as Brook had been her only loyal Guardian. It would take her a long time to cultivate another.
"What do you want me to do, Mother?"
"You mentioned there was surplus money for expansion. For the time being I want you to keep your focus here. Since my last attempt at patronage was rejected, I want you to establish at least three new orphanages in the city. Hire someone competent to oversee it all. Get them to look after finding the buildings, hiring staff, everything."
It was difficult to tell because Bollgar was always sweating, but she thought he was damper than normal. "That's going to cost a lot of money," he offered tentatively, but she waved it away. She could always get more money.
"Make sure the overseer knows what they are doing. I don't want any mistakes."
"Of course," he stammered, which made her grimace.
"And there's one more thing," said Akosh, getting to her feet. "Take a bath and open a window in here. It stinks."
"Yes, Mother," he said meekly. His weakness made her despise him just a little bit more. The more she thought about it the more she realised the truth. She had grown too fond of them. They were tools to be used. Nothing more. If Bollgar died because he was fat and lazy she would simply replace him. Two apprentices were being groomed and soon they would assist Bollgar with his duties. She knew he would complain about the intrusion, but her long-term survival was the only thing that mattered, not their happiness.
As their god and saviour, a certain level of adoration and fawning was expected, but the familial aspect of their praise was making her increasingly uncomfortable. It was something she would have to adjust in the years ahead.
An hour later she was sitting in what had become her favourite tavern in the city, the Golden Goose. The owner wasn't one of her children but, once she'd explained what would happen to his family if he refused her requests, he'd become incredibly compliant. He'd even provided her with a private dining room which she used to conduct her meetings.
Akosh sipped at her glass of wine, delighting in the silky texture on her tongue and the way it clung to the edges of the glass. Her moment of tranquillity was spoiled by a knock on the door and Doggett striding into the room. Today he seemed full of confidence and his disguise was a wealthy merchant of some importance which was utterly at odds with his forgettable face.
"Mother," he said, giving her a slight bow.
"Have you resolved the situation with the orphanage?"
"As requested. Jille the administrator, and the new member of staff, were both murdered. It was made to look like a crime of passion. I provided the breadcrumbs and the Regent's first wife asked her new agents to do the rest."
She had decided to solve three problems at once. Her incident at the orphanage would soon be forgotten in the wake of a fresh murder, and she could test Selina's resolve at the same time. It also allowed her to eliminate the agent at the orphanage who had been posing as a member of staff. It didn't matter who he'd worked for. A blind eye saw nothing and now she was watching for a reaction. She'd soon find out who the agent had been working for.
"How did Selina perform?"
"Exactly as I would. She wasn't squeamish in the slightest." Doggett sounded impressed, which was a rare compliment from him. "She followed the evidence I'd provided and it led her to an agent from Yerskania. Bloody clothes and the murder weapon were found at his home in a hidden cupboard. Under extreme duress he confessed to being an agent of Queen Morganse. He denied all knowledge of the murders at the orphanage, but he did cough up a few names of other agents before dying."
Akosh raised an eyebrow. "He died?"
"The inquisitor was a little too enthusiastic," apologised Doggett.
It didn't matter. What was one more dead human? This latest mishap had been turned in her favour. Selina's new spies had proven to be valuable which meant she would rely on them more in the future. Akosh expected she would pass this latest piece of information on to her husband. All rulers in the west knew other nations spied on them. It was to be expected. But they rarely had the name of foreign agents. Now the Regent and Queen Morganse would be focused on playing their games, watching each other's spies. In the meantime Akosh's people were one step closer to the Regent and more ingrained in the government than before. With more people in key positions who had proven their worth, it would be easier to steer gently whoever was sitting on the throne.
"Proceed with caution," said Akosh. "Continue to prove your worth to Selina. If she wants to play at being a spymaster, then let her. We need to continue poisoning the Regent against Yerskania and their open stance on everything."
The Regent had led the way on magic. He'd been the first to ban all Seekers and the first to declare an amnesty and establish a new way of dealing with young children and mages. If all went as planned Akosh intended to gradually move him in the same direction with religion. She was a long way from having a nation of her own, but this was another small step on the right path. Patience, always patience.
"Don't let her do anything too rash. Tell her to move slowly and keep me updated."
"Yes, Mother," said Doggett, giving her another bow before marching out. Reliable. Precise. Someone who followed orders with no fawning. Perhaps she should have made her religion more martial. Then she could have filled her ranks with soldiers. On the other hand they were less flexible and not as good at blending in as her orphans who could hide in plain sight.
As she was mulling over the future direction of her followers, there was another knock at the door. Akosh took another sip of wine before answering. She wasn't expecting anyone else today. If it had been the simpering owner she would have heard him shuffling about. Whoever was on the other side of the door wasn't moving and seemed content to stand and wait. Akosh drew a dagger and kept it out of sight under the table.
"Enter," she said.
A stout Yerskani man with a thick beard and shaven head came into the room. Much to her surprise he bowed deeply. Expecting mockery, she moved the dagger on top of the table. His eyes tracked the motion as he straightened.
"My name is Bissel. I offer greetings from my Master."
"And?"
"If this is not a convenient time I can come back later," he offered.
She was about to ask who he served when she noticed a familiar mannerism. One of his hands strayed to his chest as if nervous but she could see him playing with something under his clothing. The top two buttons of his shirt were unfastened and in addition to a hairy chest she could just see the edge of a black leather cord. There was something around his neck. A religious symbol, perhaps. The last person she'd seen doing the same was Pavel, the former Guardian.
She hated being in the dark. Without knowing who he served she had no idea as to their motives for this alliance. For all she knew it could be an elaborate trap.
"Sit," said Akosh and he was quick to comply.
"Let me guess. You're not allowed to tell me who you serve?"
"Apologies. My Master prefers to remain anonymous at this time. He's merely being cautious, which I'm sure is something you understand."
"You've no idea what I understand," said Akosh. She was tempted to pin his hand to the table with her dagger and question him until she had some real answers. The last time his Master had sent one of his followers, Akosh had been tested and she was still annoyed. However, the messenger had helped her realise she'd been drifting off course and getting too embroiled with humans and their insignificant problems. That was the danger of living as one for so long. You started to think like them and feel things for them. They were not equals. They were nothing more than ants, crawling around underfoot.
"As you say. I'm sure I cannot know your mind," apologised Bissel. "As a show of good faith and commitment from my Master, I've been instructed to offer you something." Akosh was only half listening. She was still contemplating how best to vent her frustration on this lackey. Perhaps if she just cut off a few fingers. That would send a clear message to his Master without killing him.
"Go on," she said, choosing which of his hands to start with.
"Torran Habreel."
"What did you just say?" said Akosh, focusing on him fully.
"I know where he is."
All thoughts of dismemberment were pushed aside. "Where?"
"The Guardians have him in a secure cell inside Unity Hall."
It was just as she'd suspected. After everything that Habreel had done he was still a Guardian at his core. He saw himself as a good man and every act he'd taken as necessary to build a better future. His morals could bend, to allow him to commit or give orders that normally went against his beliefs, but he always reverted to form. Such disciplined and rigid men were difficult to control, unless you found their weakness. Habreel's had been his ambition and his prejudice. He'd been so driven he paid no attention to those closest to him. And now he was back home. Akosh had no doubt he would tell them everything, to unburden his soul and to feel good about himself.
"I assume he's cooperating with them."
"He's writing reports and the Khevassar regularly asks him questions."
That would only get them so far. Habreel had been kept in the dark on purpose and didn't know much of her plans. However, if the Guardians kept asking him questions it could reveal some discrepancies surrounding her age, reveal the names of some of her followers and even hint at her unusual "magic." Habreel needed to be silenced before her brethren took notice. After avoiding the last summons they were already on alert.
"What is your Master offering?" she asked.
"To permanently take care of Habreel."
Akosh raised an eyebrow. "He can get someone inside Unity Hall?"
Bissel winced. "I'm afraid I can't answer that."
"Because you don't know or you're not allowed to say?" she asked, stroking her dagger.
"I don't know. My Master appreciates your frustration and he realised you might want to vent, once my message was delivered."
Bissel closed his eyes and calmly awaited his death. Akosh admired the ruthless nature of Bissel's Master, whoever it was. He had no compunction about sending one of his people to deliver a message, knowing full well the peon might die in the process. The anthill did not collapse with the death of one worker.
"Is there more to the message?" she asked, still playing with her dagger.
"I've been instructed to say this favour is freely given. My Master expects nothing in return at this time."
"At this time," echoed Akosh, mulling over the words. Just as Selina would come to rely on her new agents, Akosh was aware she might fall afoul of the same trap if not careful. It was the same trick black crystal dealers had been using on addicts for centuries. One free taste and then they were hooked, usually for life. After that they would do or say anything for another fix. However, right now Habreel was a problem that she needed fixing before he caused any more problems.
Alliances between her kind were rare for a reason. They only had their own best interests at heart. Their survival did not depend on another's, only on worship and belief from the mortals. While their goals might currently align, it was inevitable that with time they would drift apart.
"Thank your Master for this generous gift."
"I can leave?" he asked, surprised that she was letting him go. Akosh merely removed her dagger from the table. Bissel glanced at the door and then back at Akosh, as if expecting a knife in the back.
"Get out before I change my mind," she snapped.
With a short bow he scuttled out of the door and disappeared.
The favour was generous but it was also troubling. It meant Bissel's Master had eyes and ears in Unity Hall. She had no idea how many people he had, or where they were based. Without knowing his identity it made it impossible to guess what he was after.
Bissel was just turning the corner when she hurried out of the front door of the tavern. Akosh took a deep breath and then followed him at a sedate pace.
She needed to find out more about his Master. Her survival hinged on her children and the continued growth of her faith. She doubted he was one of the Elders, which meant he didn't rely on places of worship. Once she knew his identity it would make it easier to find out what he wanted and how to stab him in the back.
# CHAPTER 17
The journey had been long and arduous but finally Tianne had made it home to Zecorria.
She was exhausted from long days in the saddle and a lack of sleep, not to mention in desperate need of a bath and a hot meal. Her last brief wash had been in a brook a few days ago, but it had been cut short when she'd heard riders approaching. Thankfully they'd not been after her, not this time at least. Twice on her journey she'd been forced off the road by a group of bandits. They'd been posing as injured travellers who tried to rob her and then followed her when she fled. She managed to lose them after a few hours but they found her trail the next day. Tianne knew it was her own fault. If she'd not used her magic they would never have come after her.
After that encounter she didn't use it again but remained wary of other travellers she met on the road. Her supplies were gone, as was all of her money, but none of that mattered now. She'd made it to the capital city.
As she rode through the streets of Herakion she expected to feel different. A sense of relief, or an easing of the longing she felt inside, but nothing had changed. As far as everyone else knew she was just another traveller coming to the city. But she had an appointment with the Regent. Tianne knew that first impressions were important and she could not present herself at the palace in her current state.
With no money in her pocket she was forced to sell her horse. In exchange for a lower price she made the new owner promise to hold onto the animal for at least a week. By then she hoped to be able to buy him back.
With the money she received Tianne bought some new clothes, rented a room in a modest tavern for the night and scrubbed herself from head to toe in a bath. When the water turned brown she realised why the owner had been wrinkling his nose at her. After she'd dressed in fresh clothes and tied back her hair in a neat ponytail, Tianne treated herself to her first decent meal in days. This time the owner actually smiled and gave her an approving nod when he delivered her food.
That night, despite the softness of the bed and clean sheets, Tianne had difficulty sleeping. She was nervous about the following morning and rehearsed over and over what to say to the guards at the palace gates.
Different scenarios ran through her mind where she encountered a problem and tried to think of a suitable answer. The most important thing she focused on was staying calm. She had every right to be there and didn't want to scare anyone when they found out she was a mage. The last thing she wanted was to cause a panic and be attacked.
At some point in the early hours she passed out and slept fitfully for a few hours. Morning found her groggy and sandy-eyed, but she rose early, ate a quick breakfast and then joined the line of supplicants outside the palace. By the time she arrived there were already at least thirty people ahead of her and she prepared herself for a tedious wait.
After a couple of hours a palace clerk, accompanied by two guards, walked down the line. Tianne heard him asking each person their name and business before making a brief note in his book. A few people were told their business wasn't urgent and they were asked to come back the following morning. By now the line behind Tianne stretched down the street and she counted over a hundred people waiting. There simply wasn't time for all of them to be seen in one day. Being told to come back tomorrow wasn't a scenario she'd considered and panic began to set in.
The money she'd received from selling her horse would last for a while, but what happened if he sent her away this morning? What happened if they kept sending her away? Eventually the money would run out. What would she do then? How would she survive?
"Name," said the clerk, startling Tianne out of her reverie. He was a short, portly man wearing a stylised grey shirt marked with one red star on the left side of his chest, indicating some kind of rank.
"Tianne," she blurted, giving herself a shake. One of the guards raised an eyebrow and she did her best not to look suspicious. Tianne started fidgeting under the woman's intense stare and couldn't stop.
"Your business?" asked the clerk.
"I'm here because of the amnesty," she said, keeping her voice low. Those immediately around her could hear, but she didn't want everyone knowing her business.
The clerk raised an eyebrow. "The what?"
"For Zecorran mages," she said and now both guards were staring at her. One of them slowly moved a hand to rest it on the sword at her waist. The clerk was less impressed.
"Girl, I've no time for games. Go away and bother someone else."
"I'm serious," hissed Tianne, earning a few startled looks from those nearby.
"Really?" said the clerk with a sigh before gesturing with one hand. "Show me."
Tianne was already drawing attention to herself. The clerk had stopped moving down the line and people wanted to know who was causing the delay. People were turning around to look back at her. "Here on the street?" she asked. "Shouldn't we go somewhere more private?"
The clerk ran a hand through his thinning grey hair and folded his arms. "Here. Now. Or I'll have you whipped for wasting my time."
Taking a deep breath Tianne tried to slow the frantic beating of her heart. She could feel everyone staring but there was no choice. Embracing the Source she trickled a little power into the palm of her hand and created a small mage light. It glowed blue and, flicking her fingers, she made it dance across her knuckles like a coin. Those people nearby in line stepped backwards in surprise and perhaps fear, whereas the clerk didn't seem at all disconcerted.
"Is that all you can do?" he asked. "It's not very impressive."
"I can do a lot more than that," said Tianne, feeling her temper flare. She lifted the clerk off the ground and he let out a squawk of surprise. His head was just above the level of the crowd and he bobbed in the air like a cork in water before she lowered him again.
Both Royal Guards had not drawn their weapons but she could see they were tensed and ready for a fight. A pool of empty space had opened up around Tianne and she felt the uncomfortable weight of many unpleasant stares. The clerk had regained his composure and with a harrumph he gestured for Tianne to follow him to the front of the line. The two Royal Guards fell in behind her, watching her closely. She had the impression they were waiting for her to do something violent so that they could stab her in the back. So far her welcome home was far from what she'd been expecting.
Calm. She told herself to stay calm and that everything would be fine.
When they passed through the first set of palace gates she heaved a sigh of relief at being off the street. There were more people in the courtyard waiting to gain entrance, but none of them had seen or heard what she'd done, so they paid her no special attention.
"Sit over there," said the clerk, gesturing at a bench against the far wall. Tianne did as instructed while he went to speak to another official, this one with two red stars on his palace shirt. After a short whispered conversation, during which both clerks sneaked glances at her, they disappeared through the gates into the palace. The Royal Guards had also spoken to their colleagues as now there were four of them watching her. They hadn't moved from their posts, but all had turned their bodies to face her with hands on weapons. One man strung his bow and casually leaned on it.
Tianne did her best to look unthreatening but the tension of the Royal Guards proved to be infectious. Eventually the other supplicants noticed something was wrong as the low hum of conversation drained away until it was replaced with a tense silence.
When yet another clerk appeared in front of the others, this one with three stars on his shirt, Tianne realised if nothing else they were taking her request seriously. The tall, bearded man had a lean face and stared down his nose at her if she were mud on his shoes.
"Come with me," he said, turning away before she had a chance to ask any questions. Tianne hurried after him down a dimly lit corridor. She caught brief glimpses of huge paintings that showed figures from history, old rulers perhaps, and a huge worn tapestry of an ancient battle. Following the sound of his boots she descended several flights of stairs before finally catching up.
"In there," he said, gesturing towards an open door, and she went inside without hesitating. It was only when she'd walked into the room and turned around that she realised something was wrong. The walls were plain stone and the room was empty except for a pair of burly men in leather armour. As she opened her mouth to ask a question one of them punched her in the face, splitting the skin above her right eye.
Tianne stumbled back, blood dripping down her face. The heavy door behind her clanged shut. Before she had a chance to recover the other man rushed in, catching her on the temple with his fist. She spun around and fell against the wall, dazed and surprised. Several blows caught her in the spine and she fell to the ground, curling up into a ball. But they didn't relent and started kicking her instead.
She did her best to protect her head with her arms but it left her stomach exposed and soon she was winded and gasping for air. She tried to reach for the Source but the pain and repeated kicks broke her concentration. A heavy blow caught her in the chest and she felt something snap. A fresh spike of pain lanced up her side and she screamed. Darkness closed in on all sides but even as she fell into the abyss she could still feel the repeated assault on her body.
Freezing cold water shocked her awake but her body had difficulty responding as her limbs were heavy and slow. Tianne was lying face down in ankle-deep dirty water and before she drowned she managed to crawl on all fours until she reached a wall. One of her eyes was swollen shut but faint light from above showed her four walls of a stone pit or an old well. Ten feet above her head was a heavy metal grille and flickering torchlight. She could just make out several figures in armour and all of them were carrying weapons.
The cold air and frigid water told her she was somewhere deep underground. Probably in the lowest levels of cells under the palace, unless they'd moved her somewhere else when she'd been unconscious. The only way out was to go up, through the metal grille and the waiting armed guards. She was willing to bet there would be more waiting beyond that room. Even if she could somehow use her magic to get out of the cell it would be pointless. She was trapped.
Waves of pain rolled through her body and she felt herself teeter on the edge of consciousness again. Her hands felt swollen, her head ached and it was difficult to catch her breath. Tianne slid down the wall until part of her body was submerged in the water again but she didn't dare fall asleep. She might drown and no one would help her if she did.
The pain in her hands and chest made it difficult to think but as she went over the last few hours she couldn't understand what had gone wrong. The Regent had declared an amnesty on Zecorran mages. He might not have been expecting someone her age, but surely any mage was better than none. Garvey was still a threat and the people needed protection. Magic was the only thing that was going to save them.
Perhaps Wren had been right. All of this had been nothing more than an elaborate trap designed to capture and kill all mages in Zecorria. But if that was the case then why was she still alive? Once she was unconscious it would have been easy for them to kill her.
A horrible thought slithered into the back of her mind. What if she was still alive because they intended to torture her? What if they forced her to tell them where to find the other mages?
It was that thought, more than the beating, that finally broke her.
She'd been so stupid. Determined to find her own place in the world she'd been sure that coming home was the right decision. The brief time she'd spent at the Red Tower had been better than anything that had come before and yet here she was, desperate to return home and impress other people. Growing up she'd been mocked, bullied, ignored and belittled, at times even by her own parents. The new life that she'd built had been one full of wonder and discovery. Even when that had all fallen apart she'd landed on her feet by staying with Wren. Her friend had trusted and relied on her. Tianne had been valued and respected in the new community and people genuinely liked her.
Now all of that was gone. She was alone, with no one to call on, injured and facing impending torture and perhaps death.
Hope abandoned Tianne in the dark and she began to cry.
# CHAPTER 18
Balfruss stared at his reflection in the mirror, picking out all the little details that had gone unnoticed until now, as he never spent long looking at himself.
There was far less black in his hair than he remembered and lots more grey and white. Also his face was leaner and more weather-beaten than he'd been expecting. That came from the last few months which had been among the most difficult he'd experienced. Lying to himself wouldn't change the fact. Every day he was beginning to look a bit more like his father.
Putting that distressing thought aside, he focused on the candle's flame while summoning a mental picture of Eloise. Embracing the Source he channelled a small amount of power into the mirror, waiting to see if she was there. This was the fourth time he'd tried to speak with Eloise but she hadn't answered.
As it had been explained to him several years ago, this was a lot like fishing, except it was far more dangerous for him.
He cast out a line and waited to see if Eloise answered. The amount of energy required was fairly small, which meant that normally he could continue this indefinitely. The difficulty came in maintaining his concentration. If his mind wandered and he stopped focusing on her, then his connection would evaporate. The most dangerous part about this type of fishing was that his dangling hook could be snagged by someone, or something, else.
He knew how to create a connection within the mirrors, using the space between, but didn't really understand how it worked. Every time he discovered something new, he realised how much there was still to learn, and how little he really knew.
In the past he'd scoffed at the idea of meditation but now he understood how critical it was at times like these. Without it he wouldn't have been able to maintain his side of the link for long. Munroe had quickly floundered because she lacked the mental discipline to keep her mind focused on one image.
Something unfamiliar brushed up against the periphery of Balfruss's senses but he didn't react. He would instinctively know if it was Eloise and reach out towards her. Whatever else was out there, in the place between, was not her. Keeping perfectly still, and focusing only on Eloise in his mind, Balfruss waited for the other presence to move on. It was impossible to tell its identity, but the vague impression he felt was that its intent was malicious.
Sweat trickled down the sides of his face but he did his best to ignore it. After an indeterminate amount of time he felt the other drift away and heaved a sigh of relief.
Some time later, when the sides of his shirt were damp with sweat, he decided to withdraw his magic and try another day. Just as he was about to let go of the Source he felt a tentative touch that he recognised. Balfruss pressed one hand against the mirror, letting his fingers rest lightly on the surface. The feeling of familiarity increased significantly and he trickled a little more power into his connection. The surface of the mirror rippled as if made of water and then settled again. The glass seemed to frost over, turning black, but only for a moment. When it was gone he was staring at Eloise in the mirror.
She was just as he had pictured her in his mind, except for the loose white headscarf folded around her neck to ward off the sun. Behind her there was an open doorway and through it he could see a painfully bright blue sky. Golden rays of sunlight filtered into the room from somewhere on high, bathing her in its glow. Lots of brightly coloured cushions and a low table were in the background as well, bringing back memories of his time in the desert kingdoms before the war. Back then it had been just the three of them. Eloise, himself and Darius, her late husband. The warmth from his fond recollections faded away leaving behind a sour taste in his mouth.
Balfruss pressed his fingers more firmly against the glass and felt it give until he gripped Eloise's hand. Her skin was warm and he felt a few grains of sand pressed between their palms.
"You look tired," she said.
"It's been a difficult day."
"There have been a lot of those lately."
"How is it, being back there?" he asked.
When Eloise had last been in the far east it had been with her husband prior to the war. Part of the reason she and her husband had come west to fight in the war was to repay Balfruss for all that he'd done to protect the desert kingdoms. They thought returning the favour was the least they could do, but it had cost Darius his life. Most people believed Eloise had died as well, burned up on the walls of Charas by the Warlock and his twisted apprentices. To return now, many years after being presumed dead, was always going to be difficult. But protecting the students mattered more to her than anything else.
"At first it was awkward, and there was a lot of tears and beating of chests." Eloise shook her head and wiped her eyes with her free hand. "Then his mother and aunts wouldn't let me out of their sight. Now they're constantly feeding me, telling me I've not been eating enough."
"They're right. You're so busy I know you sometimes forget to eat."
"Every day they turn up with huge plates of rice and stew."
Balfruss felt his mouth begin to water. "I remember their cooking was delicious. I always ate too much."
Eloise laughed but it was brief and bittersweet. "They ask after you, given that you're family, too."
Balfruss wasn't a blood relative but when Darius had died he'd inherited a large portion of his wealth, possessions and responsibilities, including his wife. As Blood Brother he was supposed to marry Darius's widow. It was another reason that Eloise had gone east with the children instead of him. That was a tangle he did not want to unravel at the moment.
"How are the children?" he asked, changing the subject. Eloise smiled and let it pass, knowing he didn't want to talk about their family any more. Several years on and it was still a difficult subject for both of them.
"They're adjusting. It's taking some of them more time than others, but having structure again is helping. The heat is the most difficult thing for them to get used to, but in time I know they'll manage. I did, even though it took me years."
"How long will you stay?" he asked.
Eloise sighed and nearly turned her head away which would have broken their connection. Instead she slumped forward and seemed to deflate. "I don't know. They need me as an anchor from their old lives. For all the Jhanidi's patience as teachers, it's going to be a long time before the children feel comfortable living here in a temple. In some ways the other teachers from the Red Tower are having a more difficult time adjusting. They can leave the training grounds unattended, but then have to contend with a very different way of life to what they knew. I'd forgotten how different it is out here."
Balfruss remembered when he'd first travelled to the desert kingdoms it had been quite a culture shock. He'd only been a visitor, and could have left at any time, but the former teachers had to live there indefinitely. It would probably be years before they fully adjusted and several more until they thought of it as home.
For Eloise it was equally uncomfortable to be in the desert. The longer she stayed there, surrounded by her late husband's family, the more difficult it would be to leave. But she could not just run out and abandon the children because it was awkward. It was what he'd expected her to say, but a small part of him had hoped that Eloise would soon return to the west. There was only so much he could do by himself and he valued her wise counsel. She was also one of his oldest friends and he missed her.
"How are things there?" she asked, perhaps hoping for good news and it was his turn to look uncomfortable.
"Worse than ever. Munroe is gone. She's bent on revenge and I'm not sure what could stop her. People are increasingly scared and paranoid about anyone with magic and Garvey is making it worse."
Balfruss was conscious of how much time they'd been talking and knew it couldn't go on much longer. Speaking quickly, he filled her in on what Garvey had done with his group of followers. Eloise's expression darkened as he spoke until it was a mix of anger and sorrow.
"I didn't think he'd go that far," she said, shaking her head. "I knew he was on a dark path, but to kill so many innocent people, it's so unlike him. It goes against everything he stood for."
"I'm not so sure," said Balfruss, hating to say such a thing about his old friend, but recent events had made him wonder. "He's changed. He's not the same person I remember when we studied together at the Red Tower."
"None of us are that naïve any more."
"It's more than that. From the first day when I returned to the school he was different. Cold, distant, and he was always so angry. His rage was always there, bubbling away under the surface."
"After everything he was asked to do, I knew he was carrying a great burden, but I thought that teaching a new generation of children would bring him out of the dark," said Eloise. "I hoped it might heal him."
"Me, too," he said with a sad smile. "Perhaps we're both still a little naïve."
"When did you know?"
It was something they'd never spoken about before. For all the noble things the old Grey Council had done before abandoning their posts, there had been a dark undercurrent. Over the years Balfruss had gathered scraps of information, from anecdotes and eyewitnesses, but he hadn't believed Garvey had been involved. Not at first.
"I didn't find out for several years after we'd left the Red Tower," he said, thinking back to that time. Part of him had thought the world had been a kinder and simpler place, but now he knew differently. It was simply that ignorance was bliss. The less you knew, the less there was to worry about. "I heard a rumour about Garvey but didn't believe it. I knew it couldn't be true. I was so determined to clear his name that I visited the village and spoke to some of the locals. After that, any time I heard a similar story I knew it was him."
When Balfruss had left the Red Tower as a young man, freshly anointed as a Battlemage, he'd gone in search of adventure. His hunger had taken him across the world, to many amazing countries, where he'd lived to the full. Unknown to him Garvey had been led down a different, much darker path, before they'd even left the school.
The Red Tower had always done its best to teach as many children as possible to control their magic and use it to help others. But not every child was found and others evaded the Seekers on purpose, preferring a life in the shadows where their gifts could help themselves and those with less scruples. If these people were discovered by the Grey Council they were not put on trial. Magic left no footprints in the mud, no marks on the skin, no sediment in a liquid. Proving that someone had been murdered or cheated with magic was all but impossible.
The rogue mages received no warning. They were simply eliminated by the Bane. A mage, sanctioned by the Grey Council, to hunt down and execute magic users using their powers for profit. Garvey had been chosen and shaped into a weapon, designed to hunt and kill other mages. When the war began, Garvey had been pursuing a destructive mage and had ignored King Mathias's call.
Garvey was the last in a long line of people to hold the title of Bane. When they'd formed the new Grey Council it was not something they'd reinstated, despite Garvey's insistence that it was necessary.
"Killing all those people as the Bane left a mark on him," said Balfruss. "He may not even have noticed he was being affected, but over time it changed him. It must have. Perhaps he acquired a taste for killing."
"I don't believe it," protested Eloise.
"Then how do you explain what's happened?"
"I can't," she said and Balfruss felt her fingers tighten against his. "Whatever he's become, Garvey has always been a clever man. There must be a reason, but whatever that is no longer matters. He's out of control and must be stopped."
"I must go after him," said Balfruss, tasting bile in his mouth. He'd been putting it off, giving Tammy excuses that held no water. Another reason for hoping Eloise would soon return was that he didn't want to go after his friend alone. He was afraid, not of dying, or being defeated, but finding out that his friend killed people because he enjoyed it.
"Will you be able to stop him?" asked Eloise.
"I don't know. If he's alone, then perhaps, but he has more than a dozen students with him. I need to find a way to separate him." A deep sorrow settled over Balfruss and he felt overwhelmed by what lay ahead. "There are only a handful of people I can truly call my friend. And now, Elwei forgive me, I must hunt down and kill one of the few that remain."
# CHAPTER 19
It was late, again, and Tammy was still at work in her office. There didn't seem to be any other kind of night at the moment.
In cutting herself off from all familial connections she realised that the benefits for them were twofold. It protected them from reprisals if criminals sought to get back at her as Khevassar, but it also meant she had no one to let down. If she'd had a family, or someone waiting for her at home, the guilt of never being there would only mount day after day. The excuses about the work being important would soon wear thin, as would their patience. Then she'd end up alone anyway but more heartbroken and distraught than before. It was simpler this way. Easier. At least that's what she told herself as she struggled to focus on yet another report.
Tammy was trying not to think about her family or Kovac and what they were doing.
She pushed her chair back from her desk and took a break, resting the back of her head on the wall. The report in front of her was about another body in the morgue. Another possible murder that needed her attention. This time it was the Dockmaster who had died in what seemed like slightly suspicious circumstances. No one outside the city of Perizzi would ever have heard of him, or considered him an important figure. But as the most senior person in charge of the busiest port in the world, everyone here knew his name.
He could destroy businesses if he wanted, holding cargo indefinitely at the docks for any number of plausible and legal reasons. It was why the person holding the position was closely vetted and all of his dealings were scrutinised, without him knowing of course, to make sure he was beyond reproach. As such his death also needed to be thoroughly checked to make sure foul play wasn't involved.
One of the Dockmaster's few vices was drinking. He never drank to excess but was known to enjoy expensive brandy from around the world. All gifts he received were declared and put up for auction, but he usually ended up buying the best of them with his own money. After all, who would bid against the Dockmaster on his favourite drink? The initial report from the doctor indicated he'd died from excess over many years, but when Tammy had seen him last week, bellowing at a ship's captain, he'd seemed in fairly good health. It was possible that he'd had a sudden and rapid decline in his health, but she needed to be sure.
She rubbed at her eyes and made a note of a couple of names she could assign to the case.
There was a polite knock and Guardian Fray stuck his head around the door. "I'm ready. Let me know when you have time."
"Now," said Tammy, standing up. Her reports would still be there waiting for her when she got back. She collected the items they would need and picked up her master set of keys for the building. "If we don't go right now, something else will distract me."
"I need somewhere quiet where we won't be disturbed."
"Follow me," said Tammy. "I have the perfect place in mind."
One of the many things she'd discovered since taking over the Old Man's position was the secret history of Unity Hall. The one known only to the Khevassar. No other Guardian of the Peace had access to the same information as her. It was not recorded in any of the modern journals and, despite attempts at preservation, the oldest had long turned to dust. The story was one that had been passed on verbally from one Khevassar to the next, down through the centuries.
Most Guardians rightly assumed their organisation had been founded with the earliest settlement in Yerskania for the express purpose of investigating crimes. But there had also been a second purpose that no one knew about. Guarding the peace against other forces. Especially those who used their powers to help themselves while hurting or killing others. Tammy would have thought that the Old Man had finally lost his mind if not for all that she'd seen in the last decade. Magic forces and beings beyond the understanding of most people.
"Tell no one about this," she said, stopping outside a plain wooden door. "I must ask you to swear a blood oath."
Fray swallowed hard, suddenly understanding the seriousness of what she was sharing with him. To his credit he didn't run and quickly swore to keep the secret. Tammy unlocked the door, gestured for him to enter the cramped archive and locked it again behind her. The room was identical to many others, stacked floor to ceiling with shelves containing hundreds of journals. Two small writing tables sat in the middle of the room, surrounded by half a dozen unlit lanterns. Scribes were permanently employed to copy fading, damaged or old journals from previous Khevassars, so that one continuous history of the city was maintained for all time.
At this time of night the scribes were in their beds and the archive was deserted. Tammy lit one of the lanterns and then moved to the back of the room. Taking a small, thick key from her pocket she removed a few journals from the top shelf and slid the wooden panel behind them to one side. The keyhole was small and not easy to see but when she turned the key in the lock there was an audible click.
"Help me with this," she said. Together she and Fray pushed the bookcase into the wall and then to one side, revealing a tall but narrow corridor. Tammy was forced to walk sideways until it opened out onto a set of tight spiral stairs that wound down into the darkness.
They descended into the earth and Tammy lost track of time. She lost count at five hundred steps and they still had a little way to go. This went far below the black cells to another part of Unity Hall that had not been used for centuries.
Finally, the stairs ended at a short corridor that housed seven cells. Six were plain identical rooms but she led Fray to the larger seventh cell at the end of the hall. The Old Man had brought her down here once and that had been more than enough. She'd only peered into the other cells but he'd insisted she set foot in this one.
From his expression she could see Fray was desperate to ask a question but he kept his mouth shut. She walked into the final room without any difficulty but he paused on the threshold and raised one hand.
"There's something here," he said, sounding puzzled. "It's like the air is made of honey. It's thick and heavy."
Tammy said nothing and watched as Fray tentatively stepped into the room. Nothing happened but she could see he was struggling to cope with whatever he could sense. She left him to adjust as she moved around the eight-sided cell, lighting the torches until the whole space was full of warm yellow light.
"What is this place?" he finally asked.
"A long time ago it was used to house difficult prisoners. Those with abilities," she said as Fray gently touched two fingers to the wall. He yanked his hand back as if burned but there wasn't a mark on his fingertips. "Take another look," she said, gesturing at the walls.
More cautiously this time, Fray moved closer to one of the walls until his face was almost touching it. Normally he hunched his shoulders slightly, but now they were almost touching his ears as if braced against a strong wind. She watched as his green eyes changed colour, first to a pale lemon and then turning darker, becoming a rich amber. Fray let out a startled bark and stumbled back until she caught him, keeping him upright.
"By the Maker," he hissed through clenched teeth. Tammy could feel his whole body was rigid with tension.
"Tell me what you see."
"The walls. Even the ceiling and the floor. They're all covered with symbols. I think they're letters, but I don't recognise the language." Fray's voice was a mix of awe and surprise. "There are so many, overlapping each other. There are layers and layers."
The Old Man's theory was right. This cell was designed to contain any number of powerful creatures, including those with magic. She'd seen first-hand how dangerous magic could be in the wrong hands. A long time ago, at the beginning of the Guardians, several mages had worked in concert to create this cell to house the worst of the worst.
Tammy could have simply taken Fray to a quiet storage room and locked the door while they worked to raise the spirit of Guardian Brook. She had the authority to ensure they weren't disturbed. Bringing him down here was a lot further out of the way, but she'd needed to know if the ancient magic was still active. It could prove to be incredibly useful in the days ahead with rogue mages on the loose.
"Will it stop you from working?" she asked, shaking Fray gently by the shoulders.
"I don't know. Maybe."
"Let's find out," she said, opening the bag of personal belongings she'd had someone gather from Guardian Brook's home. One by one she passed the items to Fray who held each one carefully as if it were fragile. When he touched an old patchwork blanket he stopped and tapped the wool with his fingers.
"This one. There's a strong connection."
She set the other items aside and sat down beside him at the centre of the room. Fray bowed his head slightly and let out a long, slow breath. His lips were moving but he didn't speak and he made a small beckoning gesture with both hands.
After a few minutes in silence he sat back and shook his head. "I can't feel anything. It's like there's a huge wall that's blocking me."
Tammy was pleased but did her best not to show it. The magic was still intact.
"Let's try one of the other cells," she suggested, leading him to one of the plainer rooms. She lit the torches and Fray tried again, bowing his head over the blanket.
After only a few seconds the air in front of him flickered and a spectral figure began to appear. At first the person's features were fuzzy, as if hidden behind a thick fog, but they quickly sharpened until Tammy recognised Guardian Brook.
Fray opened his amber eyes and stared at the shade. His expression turned incredulous when he noticed she was staring at Brook. "You can see her?"
"Of course. Why?" asked Tammy.
"That's never happened before," he said, briefly glancing around the plain room. There was nothing unusual about this cell, but perhaps it was caused by their proximity to the special octagonal cell.
"Ask a question. See if she can hear you," suggested Fray.
Tammy faced the spirit. "Guardian Brook, can you hear me?"
"I hear you," said Brook. Her voice echoed slightly, as if she were speaking to them from another room. "Why am I here?"
"To help me. I need to understand more about Akosh. Is she your patron?"
Brook's natural expression was wary but at the mention of her patron it softened. "She's much more than that. She found me when I was small child living on the streets, abandoned and starving. I was given a home, schooling and a safe place to grow up. Many of those I knew from that time were not as fortunate. Many of them died and others became criminals."
She spoke with such reverence that Tammy knew it would be pointless to try and change her mind about Akosh. Brook had killed herself rather than be questioned about her Mother and risk betraying her. Brook believed she owed everything in her life, and all that she had accomplished, to Akosh. Apparently none of it was due to her ambition or drive. Anything good in her life came from on high. She'd come across other people with similar faith in the past, but none of them claimed to have met their god. Brook's faith would be like a block of granite.
"Did the people at the orphanage teach you about her?" asked Tammy, holding up a copy of the text she'd found at Brook's home. The symbol on the front of the small book was that of a woman caring for a small child. The spirit recognised the stylised image and smiled.
"Not at first, but most of what they taught us was common sense. To care for others and help those less fortunate, just like us. It was only later they told us everything came from the book."
"Is that why you became a Guardian? To help people?"
"Of course," said Brook. "Who are you?"
"Someone seeking answers and a new path," said Tammy, trying to appeal to her religious zeal.
"You seem familiar," said Brook, her face scrunching up in concentration. Fray had told her that the spirits he summoned were incomplete pieces of the person they'd been in life. This was merely a shadow. "I think I know you."
"Can I join your faith?" asked Tammy and the spirit's smile returned. "Learn more about it?"
"All are welcome, but few come to us as adults."
"So it's usually orphans," clarified Tammy. "You're saved at an early age."
"Many on the streets were not as fortunate as me," said Brook, repeating herself. It seemed as if they found the limit to what the spirit could remember from her old life. She'd seen Brook once or twice in Unity Hall but they'd never worked together. Even so, if her mind had been intact Tammy was confident Brook would remember her as she tended to stand out in a crowd.
"The war created so many children without parents, and orphanages are expensive to run," mused Tammy, talking fast to keep her off balance.
"Faith provides," she said and Tammy felt a nerve twitch in her jaw. It was the same horseshit they'd tried to feed her as a child. Her sister Mary had bought into it, but such blind obedience had never made sense to her.
"But it doesn't. You provide. You and the other orphans donate money."
"As I said, faith," insisted Brook. "Giving some money back is the least we could do for all that we received. Why are you asking about this? Where am I?" Despite being a semi-transparent version of herself, the former Guardian was still quite alert. She started looking around the room and then down at herself with a puzzled expression.
"Hurry up," muttered Fray. "She's slipping."
"How often do you go back to the orphanage?" asked Tammy.
Brook was growing irate and the image of her flickered and then resettled like a candle in a breeze. "I don't visit the orphanage, but what does it matter?"
"Then how do they receive your donations?"
"I'm not going to answer any more questions until you tell me who you are," declared Brook.
"We're done here," said Tammy, talking to Fray. Brook started to say something else, but the words were lost as she faded from view. His eyes flickered and then quickly changed back to their natural colour.
She should have thought of this sooner but had been so busy with a hundred other jobs. Some of her people were watching all the orphanages in Perizzi in case Akosh made an appearance. Perhaps they'd been looking for the wrong person. There was a report on her desk that listed all visitors coming to each of the orphanages. All she had to do was look for any names that appeared on all the lists. If there wasn't a match then she'd have all members of staff followed when they left the buildings to find the common element. Either way one of them would lead her to the money spider sitting at the heart of the web, parcelling out donations from former orphans. Once she found the money spider she could get access to the list of donors. Then she'd have a clearer picture of who she could trust in the city and if any more of her Guardians were followers of Akosh. It seemed unlikely that Brook was the only one.
"Tell no one about what you've seen or this place," said Tammy. "It's part of a highly sensitive investigation."
"On one condition," asked Fray, doing his best to meet her gaze.
She stared down at him coolly for a long moment before slowly raising an eyebrow. "Which is?"
"I want to come back here and study that room."
"Fine," said Tammy, turning away to hide her smile. She'd hoped he would be intrigued by the cell and make this request of her. It was another reason she'd brought him down here. The more she learned about it the better.
"What are you going to do now?" asked Fray as they started back up the winding stairs.
"Follow the money," said Tammy.
# CHAPTER 20
Despite Wren's best efforts to keep her community a secret, word was beginning to spread. After what had happened in Sour Crown, as well as foiling several attacks on merchant caravans, travellers were starting to realise the normally dangerous and lawless western region of Shael was a lot safer than it used to be.
No one knew where Wren and the other mages lived and she made sure anyone who left the community was careful upon their return to make sure they weren't followed. The last thing she wanted was for a scavenger party to lead the raiders right up to her front door.
Travellers on the road into Shael understood that Boros and his raiders were still a problem, and that her mages couldn't be everywhere all the time, but anything that disrupted the robberies was seen as a good thing. Even if it was a mage. Wren knew they were still scared of magic and it wasn't a softening of their attitude, merely a reflection of how dire circumstances were in this desolate region. Given the chance they would still kill her or any other magic user. Caution seemed to be the word she imparted most often when speaking to anyone who set foot outside their community.
Wagon trains didn't take any fewer precautions. They were still crawling with mercenaries and sometimes one or two Fists of Drassi warriors, but losses had been reduced. What she found most odd about it all was that some of the travellers left her a tribute.
There was an old stone marker towards the halfway point in what she'd come to think of as her territory. The worn stone circle, once a shrine to the passing of the seasons, was now used to drop off offerings of food, a little money and sometimes children.
The refugees came from all over the west and she suspected many had fled south to Shael to avoid persecution at home. Although no country had brought in a national ban on magic, Garvey's murderous rampage, combined with the problem of Seekers and children exploding, meant anyone connected to magic was still seen as a threat.
Until rumours of her community spread there had not been anywhere that was remotely safe for children struggling with control. Wren felt a little guilty as recently she had been vocal about the shortfalls of the school but it had been a haven. In the years to come Wren suspected there would be many such moments where she discovered the Red Tower had done a lot more than she realised. It had given people hope that the power inside them could be tamed and that it need not be seen as a terrible burden or a curse. With the destruction of the school, and communities turning their back on magic, there had been nowhere to turn. Until now.
After speaking with the children who were abandoned on the road, they told Wren how they'd done their best to hide in plain sight. They'd tried to go on with their lives as normal while struggling to contain the primal forces growing inside them. All of the children found beside the stone marker had their hands and feet tied together, suggesting they'd been prisoners or captured stowaways on the caravans.
So far they'd rescued eleven children and only nine of them had the ability to touch the Source. As for the other two, someone had taken a dislike to them and used the threat of magic to force them from their homes. At least with more people the work in their community was made a little easier.
Delegating had always been difficult for Wren but, after Laila had proven to be so reliable, she was gradually learning to let others share her burdens. In truth it was something of a relief. She wasn't nearly as exhausted all of the time and it allowed her to focus on the issue of Boros.
The houses were being built at an astonishing rate, some cows and chickens had been rounded up and all the students were making progress in their studies. For some that meant going back to basics, learning to read and write, as they'd come from small communities where they weren't seen as a priority. Those without magic were taught alongside everyone else, learning herb-lore, survival skills and how to fight with a sword or empty-handed. The absence of Master Choss during those lessons was particularly noticeable and Wren knew the news about him from other survivors was not good. The last time anyone had seen him was fleeing into the woods on horseback being pursued by an angry mob. She'd whispered a prayer to the Blessed Mother that night to watch over his spirit.
Master Yettle and a few others offered her advice on decisions that affected the community when she asked, but a lot of Wren's time was now taken up with keeping the peace in the region and planning how best to tackle the raiders. So far Boros had done little that was different. It was as if her confrontation with the raiders in Sour Crown hadn't happened, or the message she'd delivered hadn't reached him. Whatever the reason his people had not returned to the village to exact revenge. Not yet at least.
In the last week there had been two attacks on merchant trains and one on a village where some of Wren's people had been only an hour before. They'd barely left and had doubled back, injuring several of the raiders who quickly fled.
"Perhaps they're scared," said Laila, who'd taken to walking with her and Danoph early in the morning. Wren liked to see how things were progressing in the community and it gave her a chance to talk things through with her friends.
"No. It's something else."
"A test," said Danoph, reminding Wren once more of his unusual insight. It wasn't just his visions that allowed him to see what was to come. He was only a year older than her and yet at times he seemed so much older, or at least significantly wiser than her. Maybe being exposed to brutality from such an early age gave him clarity when it came to violent criminals and their deeds. Whatever the cause, she'd learned to trust his instincts.
"Exactly. I think it's a test," she agreed, but her feeling did not come from her intuition. It was from long experience, but not hers. Old men loved to talk and children often went unnoticed in a crowd. Wren had grown up around craftsmen who, in their youth, had been Drassi warriors who wore the famous mask. They had travelled to every land, fought for and against every kind of soldier and warrior, and lived to tell the tale. They were veterans of wars and countless battles most people had never heard about. In every tea-house and whisky bar across Drassia they reminisced and spun stories for attentive audiences. Before his passing her grandfather had sat her on his knee and told her hundreds of stories about his life as a young man. Wren remembered his tales and those of other warriors because they were full of exciting adventure and heroic deeds.
Once Wren's mother learned of her interest in these stories she had tried a similar approach, with less wondrous tales about their family's clothing empire. However, she gave up when she realised Wren retained none of the facts about the less exciting history of silk and its arrival in Drassia.
After going over many of the stories she remembered, Wren came to understand one thing. There was nothing new that Boros could attempt had not been done before by someone else.
Every scheme, every ploy and tactic had been tried in the past. She just had to hope the stories she remembered included how to beat whatever he was planning. At the same time Wren was under no illusions about her skills and made sure she talked through everything with the teachers before making any important decisions. She made no attempt to hide that she was speaking to them and yet everyone assumed the plans were hers alone. Master Yettle had even encouraged her not to dissuade others from thinking this. She was the founder and figurehead of the community and people needed someone to believe in.
"What kind of test?" asked Laila.
"I think he's studying us to see how we react. How fast we can travel to the villages and our tactics when we defend the caravans," said Wren. It made sense. After all she was doing her best to learn about Boros, his people and how they fought. "All of this is a lull before the storm."
She had a few ideas about what he would next attempt. It might not happen tomorrow or the next day, but it would come soon. They were on a collision course and only one of them would walk away from it. The thought made her hands tremble but only Danoph noticed.
"Laila, could you please do me a favour?" asked Danoph, holding out his basket of fresh herbs. "Morag asked for these and I have to go and help in the school. Would you mind?"
Laila's smile spoke volumes. Wren had heard some of the rumours about her. A few people thought she and Danoph were more than friends despite her protests. She let it go for now as it gave her some time alone with Danoph. It was clear he wanted to tell her something in private. Laila took the basket without a word but winked at Danoph before she left.
The two of them walked in silence for a while, heading for the sheep enclosure, where one of the new arrivals was being trained to herd the flock. Amos, a grizzled farmer, was teaching the girl how to whistle to control the dog, but they were far enough away to talk without being overheard.
"Have you had another vision?" asked Wren.
"Yes, but it's one I've had before."
She was afraid this was going to happen and knew what it meant. "Was it the one about your village?"
So far he'd had the dream at least five times that she knew about, but was beginning to think it was a lot more.
"Yes. It's coming more often."
"You're going to leave," said Wren, feeling a pain in her chest.
"I am, but not yet," he promised. "I need to go back to the beginning and speak to my mother. She sent me to the Red Tower for a reason, and now I wonder if it was because I predicted something when I was young. I believe she knows more than I've been told. My ability to channel power from the Source is limited, so something must have happened that made her get me tested by a Seeker."
The heartache was spreading and Wren did her best not to let it show on her face. It had been a couple of weeks since Tianne had left and she still hadn't grown used to her friend's absence. Her two friends had helped her survive the Red Tower and losing one of them so soon was bad enough. For her to be without either of them was something she found difficult to think about. Nevertheless, it was not her place to keep him here against his will.
"What's coming with Boros is going to be difficult. Perhaps the most difficult challenge you'll ever face," he said. "I'm not going to abandon you now."
"Did you see something? Is there something I should know?"
Danoph shook his head. "No, I can just see which way the wind is blowing. I want to make sure that when the time comes you won't hold back."
Wren fidgeted and turned away from him to watch the sheep. "What do you mean?"
"You scared the raiders away at Sour Crown, but you know that it won't be enough next time. It may be necessary for you to kill them."
The words hung in the air and Wren struggled to control the emotions roiling inside. Her mind immediately went to the bully, Brunwal, and the way the black motes had eaten through his flesh and bones. The sounds he'd made had been unlike anything she'd ever heard. They'd been inhuman.
The logical part of her mind was reminding her that she wasn't the one who had summoned the thing that destroyed him. All she'd done was defend herself against someone who wanted her dead. The rest of her mind wasn't as calm and rational. It showed her again and again the terror in his eyes as she'd trapped him inside a shield with the pulsating living darkness. Over and over she heard the noises he'd made and some nights it was she who woke up Danoph with her screams.
She had killed him. No matter how she tried to look at it, as an accident or in defence of her life, that one thought was undeniable. He was dead. There was no one else to blame. And now Danoph was telling her she might have to do it again.
"I'm not sure I can," she said finally. "Even to save myself."
"Out here, we're far away from the capital city, but the villagers don't kill their neighbours just because the Queen isn't sending patrols to the area. They don't need to be told. Right and wrong doesn't come from the threat of punishment for not obeying the law, or what's written in a sacred book." From the corner of her eye she saw Danoph shake his head in disappointment. He had little time for religion or those who followed any faith blindly. "Boros and his people chose this place because there are no repercussions for their actions. They can steal and kill and hurt other people and nothing happens." He spoke calmly, neither angry nor sad, it was merely a statement of fact. "The villagers aren't strong enough to fight back, otherwise the raiders would go elsewhere. They're preying on the weak and they like doing it. Even a lion that hunts a herd of deer does it for food, not for fun. The raiders enjoy scaring and hurting other people."
"You want me to kill them? Kill all of them?" asked Wren, her voice turning hysterical.
"I don't, but tell me this. Do you think Boros can be reasoned with? Do you think he will accept a compromise if you offered one? Do you think he would hesitate to kill you?"
She knew the answers to all of his questions. The villagers at Sour Crown had tried to negotiate at the point when they'd already surrendered. The victor did not negotiate with conquered subjects. They made demands and doled out punishment if they were not met. She represented a threat to his control and reign of terror. With her dead, and made an example for others, their fear of Boros would only increase, making it easier for his people to collect their tithe in the future.
"There's no law or justice out here to protect the people. There's just us. You could try to scare them off again with magic, and it might work for a time, but they'll come back."
"You don't know that," said Wren, but she didn't really believe it herself. It hadn't worked on Brunwal and she knew hardened criminals who robbed and killed would not be easily scared away. This remote frontier offered them a chance to live as they chose, outside the law, because if they tried it anywhere else they would be arrested and imprisoned. Killing one teenage girl to keep their way of life wouldn't worry them or cause any sleepless nights.
Danoph took one of her hands in both of his, making her look at his face. "Something in them is broken. I don't know how it happened or when, but at some point they walked away from one path and chose this life. They're scavengers, preying on the weak. They don't have the courage to try something difficult and fail. I may be wrong, perhaps a severe shock will send them in a new direction, but I have my doubts."
"I don't want to hurt anyone," she said, trying to swallow the anguish.
"I know and that tells me a great deal about you, but you need to be ready in case they leave you with no other choice. When the time comes people here will need your strength and leadership."
She knew he wasn't just talking about those in their community. Every person in the nearby villages had been suffering before she'd intervened.
"If the moment comes, and you find yourself facing Boros, then you need to act without hesitation. I know this is a terrible burden, but you can shoulder it," he said, giving her hand a squeeze. "Others cannot. The weight would crush or twist them into something else. Something dangerous and destructive. Those who went with Garvey have shown us what can happen when anger and hatred take over."
"I don't know how to move past this guilt and pain," said Wren, putting a hand to her chest. It was always there, lurking in the background.
"We'll find a way, together. You're not alone."
"What if, when the time comes, I'm not ready?"
"You will be," said Danoph. He sounded so confident. Perhaps he'd seen a vision of her fighting Boros, or perhaps it was just wish-fulfilment because she needed to be. All she could do was try. Wren decided she could do that much and hoped that when the time came she would be able to do whatever was necessary.
# CHAPTER 21
Tianne wasn't sure how long she'd been in the water cell but she'd heard the guards upstairs change over at their posts several times. It felt like days at least.
Sometimes she drifted into a troubled, pain-filled sleep, huddled in a corner of the cell, her feet going numb from the cold water. The gnawing pain in her stomach told her she hadn't eaten in a long time and her throat was parched and raw. There was filthy water all around but she was sure it would do her more harm than good to drink it. Several times she'd called out to the guards but no matter what she said they continued to ignore her.
Escape seemed impossible and so she was left only with time and her thoughts for company. If she'd worked harder on learning how to heal then she could do something about the burning pain in her side, the bruises and her swollen eye. Several times she tried to heal herself but at the Red Tower she'd barely been able to master minor cuts, never mind anything else. The pain made it difficult to embrace the Source but each time she did it provided her with a brief respite. Her physical discomforts faded but, unfortunately, at the same time her senses became more acute. She could pick out individuals in the crowd upstairs and began to recognise certain voices. Out of boredom, and to keep her mind occupied, she assigned names to them and tried to picture their faces.
Tianne's sense of smell also sharpened to the point where it felt as if the stench of the stagnant water was filling her nose and scratching the back of her throat. She tried not to gag but ended up dry retching a few times. Her empty stomach contracted even further but she fought to hold on to the Source as the pain of her injuries was far worse than the assault on her senses.
All too often her physical condition interrupted her reverie and she lost her concentration. Her grip on the Source shattered and the pain and cold rushed in again making it that much more difficult the next time.
At some point Tianne found herself feeling light-headed. A rat had found its way into her cell and it started paddling across the water towards her. When she tried to kick it away the rat vanished. A moment later it reappeared with two more rats, all of them seemingly intent on crawling over her. She was already pressed into a corner of the cell and had nowhere to go. Kicking and punching, she tried to keep the rats away but they dodged back out of reach and then just sat and waited. It wasn't natural. Rats were never that silent and still. Six beady eyes watched her, waiting for her to exhaust herself or perhaps fall asleep.
Despite the danger and the cold, Tianne felt her head dip towards her chest. Each time her head started to nod she shook herself awake, expecting to find one of the rats gnawing on her arm. But they just sat and waited. The next time she felt her head dip forward she stood up, screaming and shouting, waving her arms to fight off something. Her cell was empty and she didn't know if the rats had been real or an hallucination.
Her mind started drifting down peculiar pathways and she found herself full of strange regrets. Her new clothes were torn, wet and ruined. They were only a few days old. Tianne also worried about her horse. The merchant would think she wasn't coming back and by now had probably sold it on to someone else. It could be days away from the city already. She envied that freedom.
Alone in the dark and cold she wondered how long her sanity would last. If they did intend to torture her then perhaps they wanted to break her spirit first. What if they asked her about the location of other mages? What if they wanted to know about Wren's community? But that was impossible, they couldn't know where she'd come from. Unless she'd already told them and just couldn't remember.
Wailing in a panic about her possible betrayal, Tianne instinctively reached for the Source and without realising began to freeze the air. Water began to drip from the ceiling of the cell and a long icicle formed on the metal grille. When something freezing dripped onto her face she thought it was raining, forgetting that she was inside. Looking up she saw the icicle and her connection to the Source evaporated. With greedy, swollen hands she snapped it off and, not caring about the metallic taste, bit off the end. The water was freezing and delicious, easing her parched throat. She crunched her way through half of the icicle before her thirst was sated.
It took a while but eventually Tianne noticed something was different. It was the silence. People talking and moving above her head had become a constant background noise that she'd grown used to, but now it was absent. Staring up at the grille she saw several faces peering at her through the narrow gaps.
"Open it," said a rich, commanding voice and she heard several people scrambling to obey. More light flooded into her watery cell and she had to shield her eyes until they adjusted to the brightness. "Bring her up," said the voice again. She caught a glimpse of a handsome, middle-aged Zecorran man with thick black hair and a brooding expression. Rage flowed off him in waves and everyone else seemed petrified by him.
A rope ladder was dropped into her cell but Tianne was so weak she couldn't climb up. The fingers on her left hand wouldn't work properly and she didn't have the strength to pull herself up the rungs.
"Child, stand to one side," said the voice again in a gentler tone. Tianne complied and a moment later heavy splashes announced the arrival of two large men. When they approached her she panicked and tried to fight back but all she managed to do was feebly flap her hands against them. They ignored her cries and lifted her above their heads. More hands from above grabbed hold of her arms and she was lifted out of the darkness into yellow light that stung her eyes.
"By the Blessed Mother," hissed the man. Tianne felt something warm and soft wrapped around her as strong arms lifted her off the ground.
"Regent, she's filthy," someone protested and was abruptly cut off.
Tianne felt herself being carried and in a daze she saw several corridors fly by. She didn't care what was happening any more. She was warm and this illusion was a lot better than some that had come to her. Tianne decided to embrace the fantasy while it lasted, drifting off into an uneasy sleep.
The next time she woke up Tianne was surprised not to see the familiar walls of her cell. Her feet were dry and had been wrapped up in something warm and soft. She was buried under a heavy sheet and it took her a little while to realise it was a thick woollen blanket. She lay in a plush bed in a comfortable-looking room and not far away the handsome man was tending a roaring fire. Its heat filled the room and her face was hot and flushed. Her eyes were sticky but the swelling over one of them had been reduced. When the man saw that she was awake he came to her side and gently lifted her head.
"Drink this," he said, holding a cup to her lips. "Slowly," he warned her. Tianne gulped down some of the liquid which tasted like a broth of sorts. She felt its warmth spreading throughout her body and after only a few mouthfuls was done. The fire and the blanket and the broth wrapped her in a warm cocoon and she slept again.
For the next few days Tianne drifted in and out of consciousness and each time she woke he would soon appear at her side to feed her and check on her health. Others came and went, treating her wounds and tending to some of her needs, which initially she found embarrassing. Her old clothes were gone and Tianne realised she'd been bathed and dressed in thick woollen garments beneath the blanket. With barely the strength to sit up without assistance, Tianne soon overcame her embarrassment. By the third day she felt more like herself and was sitting up in bed eating unaided, no longer swaddled in woollen clothing and blankets. Her right eye was still a little swollen and sore, but there were no mirrors for her to see how badly she'd been injured.
Much to her surprise she hadn't lost any toes from her prolonged exposure to the cold water. Her feet ached a little when she stumbled around, but she hoped that too would fade in time.
When he entered the room this time she noticed how the guards outside the door bowed their heads, confirming her suspicion about his identity.
"How are you feeling?" he asked, sitting down on the edge of her bed.
"Much better, thank you, Sire," said Tianne, bowing her head.
"Ah," said Regent Choilan, offering her a smile that warmed her right down to her toes.
"If not for you, I would be dead. I don't know how to thank you."
The Regent sadly shook his head and Tianne felt dismayed. The last thing she wanted to do was disappoint him. "I owe you an apology. I'm so sorry for what happened."
Tianne was stunned into silence but eventually managed to speak. "I don't understand."
"It's my fault," he said, taking one of her hands in his. "I had told my people that any Zecorran mages were to be made welcome, but they didn't listen. Maybe some of them didn't think it was real, or their bias made it easy for them to ignore it. I've punished those responsible for what happened to you, but can you ever forgive me?"
She didn't know what to say. The Regent of Zecorria was asking for her forgiveness. In every fantasy and scenario in her mind, not once had this ever come up. "Of course," she managed to babble. "All is forgiven, Sire. It wasn't your fault."
His smile, and the gentle squeeze of his strong hands made heat rise in her cheeks. If he noticed he didn't say anything, for which she was grateful. He gently released her and she felt a jolt of disappointment that he was leaving so quickly. A moment later she realised how stupid that was. He was the Regent of the entire country, not her nursemaid. He'd already made a point of visiting her every day and helping feed her.
Thankfully, instead of leaving he moved to the window and stared out at the city below. As part of her daily routine she was encouraged to walk a little and yesterday she'd made it to the window by herself.
"It was a very brave thing you did, coming home after how I've spoken about mages." Tianne wasn't sure if she was supposed to answer or not. She decided to play it safe and remain silent. The Regent seemed lost in thought, wrestling with something, his face creased with worry. "But all of that is in the past and now we must move forward together. A terrible menace threatens us and I need loyal people like you. Loyal Zecorran mages."
He turned his head slightly towards her and Tianne thought it was a cue. "I still want to help. I came home to protect Zecorria."
"That's generous," he said, favouring her with a brief smile, "but you should know what's coming before agreeing to it. The work ahead is not going to be easy. Most people still think magic is evil and that mages are not to be trusted. I admit, I'm partially to blame for that attitude." The Regent's broad shoulders seemed to sag and Tianne thought he must have a lot of pressures weighing him down.
"It's not your fault," she said, but he carried on speaking as if he hadn't heard.
"Magic is a part of everything and I cannot pretend otherwise. Garvey and his band of rebels are murdering men, women and children. They're destroying whole communities and I need loyal, brave mages that are willing to stand up to him. But wherever they go, people may try to hurt them. It's going to take a long time to earn the people's trust."
"I'm used to it," said Tianne and the Regent turned, sadness and surprise warring on his face. "We fled from the Red Tower because people were afraid and blamed us for what had happened. We could have fought back and easily kept them at bay, but it would only have made things worse. So we ran instead."
"It saddens me that someone so young has had to deal with so much." The Regent moved to sit down on the edge of her bed again. "After how you've been treated I wouldn't blame you for leaving. You would be given money, a horse and whatever provisions you need."
"This is my home," said Tianne, although part of her knew that was a lie. It hadn't felt like home in a long time. She'd felt more at peace at the Red Tower and later among her friends in the new community. Zecorria was a strange and unwelcoming land but she hoped that, in time, it would start to feel familiar again.
"If you choose to stay, you will become the first of my new cadre of loyal Zecorran mages."
"It would be my honour."
"Thank you, Tianne," he said, touching her hand, which sent a thrill up her arm. "The first step to regaining the trust of the people is to secure the city. There are many here who want to harm me and see chaos in the streets. I need your help to root out those using their magic for ill, scaring, harming or cheating others. You'll be assigned a patrol of Royal Guards to protect you, just in case."
He didn't need to say any more. Just by showing a small bit of magic in the queue for the palace people had been scared. Given what had happened during the war, and recently with Garvey, she couldn't really blame them. It was going to take people a long time to become accustomed to seeing magic being used deliberately in public. But she was determined to show the people of Zecorria that magic, in the right hands, was a wonderful thing.
"It will be my pleasure, Sire," said Tianne, giving him another seated bow.
"I'll come by and visit when I can," he said, getting up to leave. "Make me proud."
Many times she'd regretted leaving the safety of the community and making the long journey here, but now she had a purpose. She would impress the Regent and show him that he'd made the right decision with his amnesty. She wanted to prove that his trust in her was well placed and together they would slowly begin to win over the people.
Despite the perfect picture of the future she was creating in her mind a seed of worry remained. Her thoughts lingered on her arrival at the palace. The dull ache in her feet was a constant reminder of what happened when she trusted people too readily. Wren had been partially right. She had been naïve, but that too was in the past. This time it would be different. She was sure of it.
# CHAPTER 22
The second time Munroe went to meet the Butcher her experience was a lot more pleasant. There was no need for the drunk routine or any form of pretence.
A note had been slipped under her bedroom door with a place to meet him. After a hearty breakfast, and remembering to avoid her old haunts, Munroe took a slightly strangled route down to the docks. If Perizzi was the centre of the west then the port was its beating heart. Rivers of goods and information flowed through the city and a hundred new stories arrived every morning via the ships with their diverse cargo. Merchants bartered with ships' captains and dockside workers for better deals while exchanging tales and rumours.
In the short time she'd been waiting for the Butcher she'd heard four stories about Garvey. After his latest attack on a village in northern Yerskania he'd vanished for about a week, only to reappear in Zecorria. The Regent's sudden change of heart and plea for mages made a lot more sense. She would've felt more sympathy for him if not for the fact that he'd been the first to bring in a national ban on Seekers.
One rumour about Garvey claimed that a group of Yerskani soldiers had fought the rogue mages somewhere in the north. When Garvey and his followers attacked a town the soldiers had surprised them, succeeding in killing one of their number. A variant of the story from a swarthy captain claimed Garvey himself had been injured. For whatever reason all four stories agreed that he and his group had not been seen for eight days before their sudden appearance over the border. They hadn't attacked a settlement recently, which was making patrols in both countries increasingly nervous.
Despite spending several years at the Red Tower, Munroe's first impression of Garvey had not changed. His power and skill as a Sorcerer couldn't be denied, but he was dangerously unstable. Perhaps that was why when she first heard the stories of his rampage it didn't surprise her.
Normally Munroe enjoyed the crowds at the docks. Seeing so many people crawling over the ships made her realise she was just one individual among thousands and it put her troubles into perspective. Today she didn't care about any of them or their problems. Today there was too much noise and too many people for her liking. The only good thing about the crowd was her ability to hide in plain sight. None of Akosh's people knew she was coming after her, and, if she was half as clever as Munroe imagined, she would have several people working in the port. The only problem was she had no idea who they were. The Butcher probably had his suspicions, but she doubted any of Akosh's people would betray her. With a glare at the crowd and the unknown agents hiding within, she drained her glass of ale and went inside the drinking hole to fetch another.
A short time later the Butcher came in and sat down at the bar beside her. He ordered an ale and they drank in companionable silence for a while.
"I received some news from Rojenne," she said, forgoing any of the usual banter. The crushing weight on her heart was a constant reminder of what had been taken from her. The constant effort of holding back her anger left little room for much else. The drink numbed the pain a little, but it always came back, full of razors and claws, ripping her apart on the inside.
She hated standing still and not being out there chasing down people, but had finally accepted her less than subtle approach would not be enough. Not this time.
"Was this your first official report as Dońa Munroe?"
In Perizzi the underworld was controlled by several crime Families, each headed up by a Don or Dońa.
She snorted. "Hardly. They don't have crime Families down there. The man I left in charge, Tok, found out she has two orphanages in Rojenne. Both of them receive their money once a month from someone here in Perizzi. It always comes in with merchant trains, so it's well protected. Someone then passes out the gold to the orphanages."
The Butcher said nothing for a while, mulling it over. "Makes sense. Rojenne is a fairly small city and a little out of the way. I doubt she has many people down there. It also lines up with what I've found."
"Which is?"
"A fat money spider," said the Butcher, raising one corner of his mouth in a half-smile.
"Where?"
"Right here, in the heart of Perizzi. The money flows in from all over and then goes back out again, to Rojenne and probably other places in Yerskania I've not found yet."
"Then why are we still sitting here?" said Munroe, getting up from her stool. The Butcher just tapped the bar and looked at her expectantly. Taking a deep breath, she sat back down again, swallowing her bitter frustration.
"If we were to grab the bookkeeper, there's no guarantee he'd know where to find her. However," said the Butcher, holding up a hand before she interrupted. He waited until Munroe had bitten her lip before continuing. "What he does have is a list of names. People and places. Part of Akosh's network. What we need is to get hold of that list, then I can have eyes and ears watching for her in all of those places."
"It's a good thing I never joined the Silent Order," said Munroe. "I don't have the patience for all this crap."
The Butcher raised an eyebrow. "The Silent Order? Never mind, I probably don't want to know."
"So where's the list? In his office?"
"No, I had someone check and that's the first problem. The Guardians are investigating Akosh as well, and they had the same idea. They picked up the accountant a few hours ago."
"What's the second problem?" asked Munroe through clenched teeth.
"He's being held at Unity Hall. It would be extremely difficult and costly for me to get one person inside that place. If I tried, the long-term repercussions would severely outweigh the short-term benefit." The repercussions for breaking into the Guardians' most secure building would be harsh. It was also not something that they would forget. There would be a lasting shadow hanging over everything the Butcher did while the Watch and every Guardian focused their attention on him. The risk simply wasn't worth the reward.
"Shit."
"I had hoped once the Old Man retired the new Khevassar would be more flexible. Sadly, it seems she's just as implacable as her predecessor."
"I know her. She's pretty dangerous."
"Perhaps you could work with her, and the Guardians, to find Akosh," suggested the Butcher, but Munroe was already shaking her head before he'd finished talking.
"No. I tried that," she said, thinking back to her last meeting with Tammy. "They're too slow and always go by the book. They'll probably try to imprison Akosh. I'm going to rip off her head with my bare hands and piss on her rotting corpse."
"Very colourful."
"So what do we do instead?" asked Munroe. "I swear if you say 'be patient' or 'wait' I'll throw you through that wall and drown you in the river," she said.
The Butcher showed no signs of alarm other than to raise one eyebrow. He considered his answer carefully and Munroe felt herself reaching for the Source. She would throw him through the wall and into the next building and the one after that. There was only so much sitting around and doing nothing she could stomach. She needed answers. She needed an edge. Drawing power into herself she felt it fill her body, making every part of her skin tingle. Her senses were magnified until she could hear the slow and steady heartbeat of the Butcher. It also made her aware of a few other things about him that she'd previously missed.
He smelled of the sea and because he was dressed in a black leather vest she couldn't miss the heavy muscles across his shoulders and down his arms. His vest hid little and showed off his unique tattoos. It would make him a distinctive figure wherever he went. She'd presumed it was because he liked showing off his body, but now she began to wonder if there was another reason.
Wherever he went, people would immediately recognise him. The woman serving drinks behind the bar had steady hands until she came to serve the Butcher. Munroe had also noticed the worried looks other patrons had been giving him since he sat down. People were petrified of him.
It shouldn't matter. She'd left all of the mind games and scheming behind to start a new life and yet here she was, back in Perizzi, hip deep in Family business again.
"Follow the money," said the Butcher.
Munroe eased her grip on the Source, dulling her senses in the process. "What do you mean?"
"A peculiar thing happened in the last few days. All of her orphanages here in the city recently changed patrons. Priests have rededicated them to the Maker, the Blessed Mother or the Lady of Light."
"Someone else is trying to get rid of her in Yerskania," said Munroe.
"I suspect those in Rojenne will soon disappear as well. So, if you were one of her followers, and suddenly all of her orphanages in Yerskania are gone, where do you send the money?" asked the Butcher.
"You said she had orphanages in the north. In Zecorria," said Munroe.
"I have four bookkeepers," he said. "I'd be an idiot to trust one person with all of my money."
"She has another money spider in the north," said Munroe. With the Guardians swarming over Perizzi, and now someone else removing her connection to the orphanages, Akosh would have to be an idiot to return to Yerskania. She still had people in the city, but wouldn't know if they had been bought. And with so many different parties just waiting for her it would be the same as walking into a bear trap with your eyes open.
At the moment Zecorria was a safe harbour where she was still surrounded by people she could trust. The difficulty for Munroe, without having a network of her own, would be finding reliable information in the north. If she started asking too many questions or used her magic overtly it would draw attention.
"I can see what you're thinking," said the Butcher. "Nothing has changed, Munroe. If you go to Herakion, you'll be on your own, in her city. I have a handful of people there, but they're just Ears. They never ask questions and you can't use them for that. Someone might be willing to talk, if you have enough gold, but sifting through the lies will be the challenge."
He was right. Sometimes people would tell you exactly what you wanted to hear for a bit of money. Once people found out she was after Akosh they would come crawling out of the woodwork to feed her information. And in a city teeming with Akosh's people it wouldn't be long before someone tried to cut her throat in the middle of the night. In spite of knowing all of that, she couldn't sit still any longer. She knew it was rash. Balfruss and Tammy would probably say she was letting her thirst for revenge consume her and they'd be right. It didn't matter. Her rage was a living thing inside her. Munroe could feel it hammering against the bars of her restraint like a caged bear. It would only remain in check for so long. After that even she was afraid of what might happen.
"It doesn't matter. I have to go north," insisted Munroe. "She must pay for what she's done."
"There's also the other thing," said the Butcher. "The Regent has banned all mages, except those from Zecorria, who are willing to serve him."
"People in the north don't know me, or how my magic works. I can use it quietly until I find her. I just need some answers."
"If you insist on doing this, then at least take someone you can trust. Someone who will watch your back." Munroe immediately thought of Choss and her heart lurched in her chest again. "You need someone who doesn't stand out."
Tok would be the ideal candidate and she knew he would be reliable. On the other hand, she wasn't sure she could put him at risk. The thought of what it would do to his family if something went wrong was too difficult, and too familiar, to think about. An idea began to form in the back of her mind. People always underestimated her because of her size. She needed someone who could help her who would also go unnoticed.
"I have the perfect person in mind," said Munroe. "I need you to send a message south to Rojenne."
Once her new partner arrived she would travel north and begin her hunt. All she needed to do was find the bookkeeper, or, failing that, one person who was loyal to Akosh. Then she would squeeze them for every drop of information. However loyal the person, it would be meaningless in the face of what she could do to them with her magic.
# CHAPTER 23
Akosh took a deep breath and tried to calm down. To distract herself she studied Bollgar's office, making a note of the small changes. He'd hung a few sprigs of dried lavender from the ceiling, giving the room a pleasant floral scent that wasn't overpowering. The stained robe he normally wore was gone and in its place black trousers and a stark white shirt that strained across his vast middle. A navy waistcoat and matching blue hat gave him the look of a retired sea captain, but all of it was a vast improvement from her last visit. He even smelled much better and she could see the skin on his face had been freshly scrubbed. She knew he was sweating, as dark stains were appearing under his arms, but at least the brim of his cap kept his face dry.
"Say that again. Slowly," said Akosh when she felt in control again.
"The two orphanages in Rojenne and all of the others in Yerskania have been rededicated to other gods."
"All of them."
"Yes, Mother. Priests from the Maker and others recently visited."
"When, exactly, did this happen?" she asked.
"In the last seven days."
Someone had been planning this for a while. To have all of them change, almost overnight, was unprecedented. It was possible human agents had been involved in persuading the orphanages, but she knew the person behind them all was one of her brethren. It was probably one of the eldest like Vargus or Nethun. No one else would be so bold. Only they understood what such a move would mean to her in the future.
Without the orphanages she had only one way of identifying those loyal to her in Yerskania; tracking the donations made to Bertran her bookkeeper.
She had far too many followers in Yerskania for her to remember them all. While some of her children might raise their offspring in the same faith, their loyalty was not as absolute. She could ask anything of her followers because she had saved them from a life of misery or an early death. Their children would be less reliable.
In fifty years' time, when all of her children were dead, she might cease to exist. Without followers, without their prayers and focus, her power would dwindle to nothing. She might disappear into the Void and never re-emerge.
In human terms fifty years was a lifetime and so much could change. For her kind it was nothing. A blink of an eye. She needed to find out who was doing this to her and how much they knew about her plans.
To lose everything she had built in Yerskania could not be tolerated. She still had many children in the country who were dormant. They were just going about their lives as normal. Their only direct contact with her might have been at an early age if she'd visited the orphanage. Since then their only connection was a monthly donation to help others. If she could find them, then perhaps now was the right time to test their loyalty and put them to good use. Most of her children in Yerskania were not in positions of power, but as shown with the Seekers that wasn't always necessary.
Whoever was behind this probably expected her to rush back to Yerskania to solve this personally. She had not gone unnoticed for this long by being rash.
"What about Bertran?"
"He's not been seen in Perizzi for days," said Bollgar. "I received a report that mentions the Guardians dragging him out of his shop. I believe he's being questioned by them."
Bollgar swallowed hard and went to mop his brow then remembered his new cap. He was right to be nervous. Bertran had been a loyal servant and an excellent bookkeeper, channelling all of the money into solid investments. The profits went back into funding the orphanages across Yerskania. Unlike Bollgar he had been a soldier as a young man, making him able to resist their questioning for longer. Even so, he wouldn't be able to hold out indefinitely. It was possible they already had a list of his clients and were hunting down her people.
Akosh gritted her teeth in frustration. It was beginning to look as if all of her people in Yerskania were completely lost. At least her followers would continue to sustain her for the short term. Surviving the next few months was the most critical issue. She could look at rebuilding when this crisis had passed.
Bollgar was very aware that if he was captured by the Guardians, or anyone else, he wouldn't last a day in their less than tender care. Perhaps from now on that might persuade him to behave in a more friendly fashion towards his two apprentices.
Akosh was getting annoyed at the Guardians and their constant interference. They were always sticking their noses into other people's affairs. If it was limited to Yerskania, that would be bearable, but sometimes they were invited abroad to solve difficult cases. For all she knew they could be petitioning the Regent right now to continue their investigation here in Zecorria.
"Has the money been redirected here?"
"Yes, Mother. A number of anonymous individuals have sent me their donations. I might be able to identify them, given enough time."
"Make sure half of the new donations are sent to Nazren."
"Yes, Mother." He managed to keep the sneer from his face, but not out of his voice. She had none of Bollgar's problems and was equally brilliant with numbers and investments. It was far safer to split the money in case Bollgar's heart finally gave out.
"What do you want to do about Bertran?" he asked.
It was a good question. As had been promised, Habreel had died in Unity Hall and it had been made to look like suicide. So far her ally was as good as his word. It would be very easy to reach out and ask him for another favour. Akosh was confident arrangements could be made so that Bertran suffered a similar fate to Habreel. But she needed to avoid relying on her ally.
As for Bertran it was already too late. She had no way of knowing how much he'd already told the Guardians. The damage had been done and her network in Yerskania had been compromised. Only a few months ago she would have wasted resources on trying to retrieve him and would have felt guilty if the attempt had failed.
"Nothing. Let him rot in a cell. He failed me," said Akosh.
"Yes, Mother," whispered Bollgar, avoiding her gaze.
"What's happening with the new orphanages here?"
"They're in hand," said Bollgar, pulling down a ledger from the shelf. "We're recruiting staff and should be able to open in a few weeks. Do you want the details?"
Akosh waved them away. If Yerskania was lost then at least she still had a strong foundation here in the north. From it she could rebuild in the west and even look to the east.
Seveldrom had suffered losses in the war and they were almost as liberal and weak as Yerskania. It would be easy to set up orphanages over there dedicated to a god no one had heard of before. The only difficulty was the distance and the time required. It would also mean weeks or even a couple of months away from Zecorria.
A surrogate could be sent in her place, but experience had taught her that absolute loyalty required a miracle that only she could provide. It was a lot easier to believe in a god, follow their teachings and pass that faith on to others, if you had witnessed their power first-hand.
That was a problem for another day. In the meantime, she needed to know who was coming after her.
This time while she waited for Bissel at the Golden Goose, Akosh was relaxing in the dining room with a friend. The young man didn't have a lot to add to their conversation, but he followed every word she said with great care. So far that had consisted of her telling him stories from the early days when she'd been wild and hadn't thought about the future. Newly born, she'd had no doubts about living for ever and had revelled in the murders and the occasional bloodbath. Sometimes literally. Around the world assassins had butchered victims in her name and her power had grown. It was always going to be that wonderful. Until it wasn't.
"I tried bathing in a virgin's blood once. It didn't seem all that different to me. It was just so sticky," she lamented and her companion's eyes widened in terror. "Perhaps I wasn't doing it right. Maybe I should try again, although I think we both know that you're not a virgin any more." She laughed and nudged him with her shoulder in a friendly fashion. Sweat continued to pour down the sides of his face and a single tear ran from his left eye.
There was a bold knock on the door and a moment later Bissel strode into the room. His confidence evaporated when he saw who else was in the room.
"Ah, I believe you two know each other," said Akosh, noting the strong resemblance. They had the same nose, but where Bissel had dark hair his son's was blond.
The son tried to say something, perhaps to bravely warn his father, but the gag in his mouth muffled everything. He strained against the rope around his wrists and ankles but Akosh didn't try to stop him. She enjoyed watching him wriggle about. He was a tall, strapping young man, with balls the size of a horse's. Only a few hours ago he'd tried to seduce her in the tavern, but events had not gone quite as he'd anticipated.
"Join us for a drink," she said, pushing a glass of wine across the table. Bissel remained frozen in the doorway, his eyes flicking between them. "I said sit down and have a drink." The tone of her voice startled him into action. As if in a trance he closed the door and then sat down.
"You'll be all right," Bissel promised his son.
"Really?" she said, drawing a dagger and placing it gently against the son's cheek. He squeaked and tried to shuffle away from her but there was nowhere to go. "Do I have your attention?" Bissel focused on her and she relaxed. As a show of good faith she even went so far as to place the dagger on the table.
"What do you want?" asked Bissel.
"How is the wine?" she asked, ignoring his question. He was struggling to focus on her words but eventually lifted the glass to his lips and gulped some down.
"It's very nice."
"I want you to send a message to your Master, whoever he is. I would like a face-to-face meeting, here, in Herakion." As Bissel opened his mouth to protest Akosh held up a hand and he fell silent. "Choose your next words very carefully," she warned him.
"He won't come."
"Then you'll have to persuade him," said Akosh, affectionately patting his son on the leg. "I know you were ready to die for your Master, but what about your son? What about his life, Doctor Bissel? Aren't you supposed to save lives?"
After the last time they'd been in this room together she'd followed Bissel back to his surgery. Since then some of her people had been gathering information about him. Regarded as an adequate doctor with moderate skill, he lived a comfortable life with his only son after the tragic death of his wife. Unknown to everyone was Bissel's devotion to a new and mysterious god called Akharga. She knew it had something to do with medicine and healing, but the name was also another mask, making it impossible for her to know their real identity.
"I know all about you, Doctor, and what you're wearing around your neck," she said, gesturing at his shirt. It was a crude icon, made to resemble an open eye in the middle of a triangle. So far her people had found six doctors and several apothecarists in the city wearing the same pendant.
"He's not in the city," said Bissel, trying a different approach. "I don't even know if he's in Zecorria."
"Then you'd better send him an urgent message. Until then, your son is going to keep me company." Akosh put one arm around his shoulders as if they were good friends or lovers. This time he was far less eager to get close to her. She could feel him shaking while he whimpered like a newborn puppy.
"Be brave, son. I'll get you out of this, I promise," said Bissel. She didn't bother pointing out he couldn't keep that promise, but she let it go if it meant less whimpering from the son. With a glare and a shake of his head Bissel hurried out of the room leaving the two of them alone again.
He knew she was serious which meant he would do everything to get his Master to visit. Even without knowing the identity of her ally, she could start making preparations for his arrival. She had eyes and ears all over the city.
Soon she would find out who was behind the curtain. Then it would be time to adjust their alliance in her favour. Or end it abruptly if he tried something untoward.
"We're going to have so much fun," she murmured, slapping her companion on the leg. Beside her the young man began to scream around his gag.
# CHAPTER 24
It felt strange to be out of uniform but Tammy enjoyed the anonymity it provided. It was a little before midnight and the streets of Perizzi were busy with drinkers and patrols of the Watch scooping up people and breaking up fights before they turned into proper brawls. At one point Tammy was forced to carry a teenage girl to the nearest squad of the Watch. The girl had pretended to be seeking directions, only then to draw a knife and attempt to rob Tammy.
After disarming the girl and putting her on her arse, the sensible thing to do would've been to run, but something in the girl wouldn't quit. Tammy had been willing to let her go, but when the girl came at her with another knife she'd knocked out two of her teeth. Thankfully she only had to carry the girl on her shoulder for a couple of streets. The Captain of the squad recognised Tammy immediately and took the would-be robber off her hands into custody.
Annoyed at the delay, Tammy increased her pace and arrived late at a modest house on a quiet side street. Wedged between a bakery and a cobbler's was a narrow alley that led to a private courtyard. The houses were old-fashioned in design, tall and narrow as if huddled together for warmth. It was secluded but not too far away from amenities and the heart of the city. She also noticed it was only a few streets away from where her sister lived.
After knocking on the door she glanced behind her and studied the windows facing onto the courtyard. All were dark and had the curtains closed but that didn't mean someone wasn't watching. A bit of paranoia in her position was healthy.
The door behind her opened to reveal the Old Man. "Welcome. Come in," he said, stepping aside. Tammy had to bow her head to get through the front door and the next doorway to enter his front room. She could see why the houses in this street might be unpopular with some, but for someone short like the Old Man it was probably quite cosy.
She briefly glanced around the room, noting several chests of personal belongings that had not yet been unpacked. The furniture was old and worn but it was comfortable when she sat down. Her mentor cleared a stack of books from another chair and added more wood to the fire. The room was too hot and almost immediately her forehead was beaded with sweat. Knowing that old people felt the cold more readily she said nothing but took off her jacket and loosened her shirt. The Old Man noticed and a wry smile touched the corners of his mouth.
"It will happen to you one day."
"If I live to be as old as you," she replied.
Before his retirement he'd looked worn out and had collapsed at the palace from exhaustion. Time away from the job seemed to have had a rejuvenating effect as his eyes were clear and focused. He moved with more energy than she'd seen in a long time, fetching two mugs of tea from the kitchen, despite her protest. Once they were both resettled, and she was getting too warm again from the fire and the tea, Tammy tried to find the right words.
He could see that she was struggling with something and gave her time. It was another small delay but curiosity made her ask.
"I noticed we're only a few streets away from my sister."
The Old Man shrugged. "I didn't want to walk halfway across the city every time I want to visit my long-lost family."
"Did Mary believe you?"
"Of course not. She knew exactly who I was. I should have recruited you both," he mused. "That would have been something."
"And the children?" she asked, getting dangerously close to a subject she did her best to avoid thinking about, even when alone.
"They're just happy to have something like a grandparent in their lives again. It's been quite a few years. Mary says I'm spoiling them, but she lets me do it."
A weight lifted off her shoulders. Other larger, more pressing issues still weighed her down, but that thought gave her some relief. She'd been worried Mary would reject the Old Man's offer and their long-term wellbeing had been playing on her mind. It was one thing she could set aside, allowing her to focus on larger concerns.
"I need your opinion on a couple of things," she said, getting to the reason for her visit.
"Always happy to lend an ear."
"Habreel is dead. He was found last night, hanged in his cell."
"I see," said the Old Man. He sounded fairly unmoved and Tammy shared his sentiment. There was a huge list of crimes levelled against Habreel which he'd freely admitted to committing. As result he'd been facing many years behind bars and potentially death by public hanging. "Do you suspect foul play?"
Tammy shook her head. "I had Faulk check into the family history of all the other Guardians. Brook was the only acolyte of Akosh. I also trust everyone who had access to Habreel's cell."
"Then what happened?" he said.
She'd been mulling that over for hours. "I think it was guilt. Habreel still thought of himself as a Guardian. He had a mission and people who shared his ideology, but then he was betrayed. Everything he'd done, all of the terrible orders he'd given, were for nothing. When he arrived at my office, he was a broken man. I thought helping me bring others to justice would be enough for him."
The Old Man sighed. "He had a lot of pride. To find out he'd been outsmarted and lied to for years, by those closest to him, must have been difficult to swallow. In some ways I think it was inevitable."
Tammy was disappointed that Habreel had taken the easy way out instead of accepting responsibility. If it had been up to her she would have had him imprisoned for the rest of his life. That would've been torture for someone like him. To be part of the world, to hear about events, but have no place in them and no way to contribute.
His suicide also meant that she had lost another valuable resource in her campaign against Akosh, which brought her to the other reason for her visit.
"What was the other thing you wanted to speak about?" asked the Old Man.
"All of the orphanages we're watching in Perizzi, and some in the south, receive monthly donations from former orphans. And I found the recipient. A bookkeeper named Bertran. He's currently sat in the black cells waiting to be questioned again."
Finding him had required a few days of following all of the visitors to the various orphanages in the city. Bertran never visited in person, and the money often arrived with other supplies, but with some persuasion her people had eventually found him. A few hours of studying his records had revealed nothing as it was all written in code. It might be possible for one of her people to crack it, but it wouldn't happen overnight. In the meantime, Akosh's network could be putting their plan into effect and she would have no idea about what it was or the repercussions.
Guardian Faulk, one of her most trusted, had spent a few hours alone in a cell with Bertran but surprisingly had produced nothing of value. Physically the bookkeeper wasn't imposing, a spindly, pale man with long, elegant fingers and a balding pate, but his mind was incredibly sharp. Faulk had fenced words with him for a long time, only to emerge with an appreciation of the man's ability to recite and multiply numbers to avoid answering questions.
"What is it you want to ask me?" prompted the Old Man.
"Have you ever had someone tortured for information?"
The Old Man didn't look surprised. In fact his expression seemed to indicate he'd known this was coming. "I'll need something a little stronger than tea," he said, digging around in a box before producing a dusty old bottle. He offered her a glass but she declined and he poured himself a generous portion of a colourless liquid. She could smell it from across the room and guessed it was fairly potent.
"What does this bookkeeper have?" he asked, setting the question aside for now.
"A list of names. People in the network."
"And have these people done anything to harm others?"
Tammy ticked items off on her fingers. "Some of them have spread stories that encouraged violence against Seekers and anyone with magic. Inciting hatred of children and taking part in exiling or killing some of them. I also believe some of them have magic of their own and posed as Seekers to make it worse. You've heard the stories. The Red Tower denies the Seeker in Gorheaton was one of theirs and I believe Balfruss."
"That's a long list of serious crimes, but I noticed you said some of them were responsible. What about the others you've not found yet?"
"What about them?"
"That's why you're here, isn't it?"
"They're dangerous people," said Tammy.
"Ah," he said, holding up a finger. "Potentially they're dangerous."
Tammy had been wrangling with this issue since the moment Bertran had refused to cooperate. More acts of violence and murder were likely, being perpetrated by members of this group, directed by Akosh. Finding her would be incredibly difficult. She suspected most of her people would rather kill themselves than give up any information, like Guardian Brook. However she had doubts about all of them being such zealots.
The worst-case scenario was that Bertran gave her a list of names and they imprisoned all of them. Then it wouldn't matter what orders Akosh sent out if she had no one to execute them. A better scenario was that some of them were willing to talk.
Finding Akosh and stopping her was the end goal, but if Balfruss was right then it might be a better idea to let someone else deal with her. Tammy had no illusions. Her experiences with magic and what had happened in Voechenka didn't make her an expert. She'd survived it, not mastered it and her skills lay elsewhere.
She needed information and Bertran had it. Torturing him would give her the list of names she needed. At the moment it was likely some of the people in Akosh's network hadn't done anything, but it was what they might do if she gave an order that worried her.
"All of these people. They're all part of the same cult," she said, pulling out a copy of a slim book she'd found at Bertran's home. The Old Man opened it and began to flick through the pages, reading passages at random.
It was identical to the one they'd found on Guardian Brook. By itself the religious text was fairly innocuous and not too dissimilar from others she'd read.
The book of Akosh preached a number of values that were common to other faiths, such as compassion, helping others and equality. It deviated in only two significant ways that were potentially dangerous. First, there were no priests or places of worship. People simply prayed at home. Second, every member of the faith was a follower and Akosh, above all others, had to be obeyed. This founding principle overruled everything else. Every law, every tradition, every family value and blood tie, every moral restraint. Normally such a rule wouldn't be an issue as people didn't have conversations with their god. But with no priests all the orders came from just one person.
Whether Tammy believed Akosh was actually a god, or a cult leader who had adopted the name and mantle of a predecessor, didn't really matter. The followers of Akosh believed it and they obeyed her absolutely. So far she knew of at least three followers who had used their magic to kill people and then blown themselves up, despite such an act going against everything in their religious text. Akosh's word had to be obeyed and they had done it, sacrificing themselves because she'd asked.
All of which brought Tammy back to the original dilemma.
"Did you ever have someone tortured?" she asked. The Old Man set the book aside and drained his glass in one go. Something made him wince, but she didn't think it was the taste of the alcohol.
"Yes, and I still carry the memories," he replied. "Getting a confession that way is almost always unreliable, but a few years into the job a day came when I needed information and time was running out."
"Did you get what you needed?"
"I did, and we stopped the ship unloading its tainted cargo." He waved a hand dismissing her next question for more details about what happened. "It's in the past. You don't need to know. No one died. That's the important thing."
Tammy wondered how many times he and the Guardians had averted disasters that now only existed within the pages of a journal in Unity Hall. Only a handful of people would know how many near misses there had been and in truth most people wouldn't want to know. They slept a lot easier.
If she'd been having this conversation with someone else, like her sister, then Tammy knew that right about now Mary would be judging her. But the Old Man knew exactly what she was struggling with as he'd been in the same position, probably more than once. He was, perhaps, the only person who could understand what she was going through.
"I need an inquisitor," she said, coming to a decision.
"I can put you in touch with someone I've used in the past."
The consequences, and the weight of her actions, would be a burden on her conscience, but she would have to find a way to live with them.
# CHAPTER 25
Taking a deep breath, Wren embraced the Source, feeling power flood her body until every part of her skin was tingling with unspent energy. On her left Danoph didn't react, but on the other side she heard the others shifting uncomfortably. They could sense it coursing through her and thought it meant that conflict was imminent. Wren was nervous, but as their leader she was trying her best not to show it. With a small amount of effort her eyesight sharpened until the blurry landscape ahead came into focus.
Gillen's Jaw lay before her in the valley below. It was a quiet fishing village located beside a lake that had once been a popular place for anglers seeking a challenge. On the outskirts were a few large houses, the largest of which belonged to the previous Queen of Shael. Since her only surviving daughter, Olivia, had taken the throne the summer home and those surrounding it had mostly gone to ruin. Queen Olivia didn't have money to waste on such frivolities. So the buildings sat idle and became a once-glorious reminder of a better time for the country and the village.
"Why here?" asked Kimme, scratching at her armpits. Wren tried very hard not to wrinkle her nose at the girl. She didn't have fleas, just poor personal hygiene, and would only wash when others insisted the smell kept them awake at night.
"It might not be here," said Wren, which was why she'd sent four groups of students, each under the guidance of a teacher, to watch for trouble at other villages. She didn't have enough people to cover every community, but then again neither did Boros, which was what she was counting on. One raider on a horse demanding a tithe would be chased away from a village, no matter who'd sent him. Boros would have to choose his next target wisely.
"So, can I go to sleep?" asked Kimme.
"Only if you don't snore again," said Wren.
Kimme grunted and turned away. She'd been elbowed awake at various points during the last three days for dozing off. This was the fourth day in a row Wren had been waiting for Boros to strike. She knew it was tedious and required a great deal of patience, which was why she'd rotated those who visited a different village each day. Everyone needed to know what they were fighting for, but it was difficult to remain focused all day with nothing to do.
The first few hours were always tense, with those beside her expecting raiders to come pouring out of the surrounding hills to attack the village. When that didn't happen, the adrenaline began to fade, tiredness crept in and muscle cramps and boredom took its place.
Danoph always came with her. He remained a steady presence that helped her maintain the appearance of being calm. She also insisted on regularly bringing Kimme, despite her pungent aroma, as she was one of the strongest students to arrive. As a farmer's daughter she'd regularly lifted cows and even horses above her head, moving them around like toys, and ploughing fields using only her willpower. If not for a nosey neighbour who'd rallied the village against her, Kimme would have continued doing the work of five people on the farm. Her parents had been distraught at seeing her leave, which was a rarity among children with magic.
"There's movement in the main street," said Wren, watching as a crowd of adults started walking down the middle. Ahead of them was a woman dressed in ragged leather armour dragging a man along by his hair. The raider had a bloody dagger in one hand and Wren could see splashes of red on the man's face and chest.
Something flickered briefly in one of the windows of the old abandoned mansion on the hill and a frown creased her brow. She gave Kimme an order and the girl happily complied, scuttling away to the west of their position before circling back to the village. The two other students with her she sent to the east, just in case, while Danoph would come with her. He still had an ongoing struggle holding onto power when he could embrace the Source, but she didn't need him for his strength. His instincts for people were especially useful in tense situations.
Maintaining her grip on the Source, Wren started running towards the main street of Gillen's Jaw. Slowly the conversation between the raider and the villagers reached her magic-augmented hearing.
"You brought this on yourself," the raider was saying, brandishing her dagger. "And every time you refuse Boros it will cost you another life. Maybe next time it will be one of your children."
Even though she was still quite far away Wren was able to reach out and wrench the blade from the raider's hand. It flew across the street and buried itself in the front door of a nearby building. There were gasps in the gathered crowd but the raider didn't seem alarmed. It was almost as if she'd been expecting Wren. Instead of releasing the injured man she drew another dagger and pulled him tight against her chest, pressing the blade to his throat.
Wren stopped a short distance away from the raider and her captive. Danoph stood next to her, silent and watchful. His eyes drifted up to the roof of a nearby building and then back to the street. The gathered crowd were clearly scared for their friend, but none of them said a word.
"Want to try that again?" said the raider. She pressed the blade to the front of the man's throat, wrapping both arms around his neck, almost as if they were lovers. If Wren tried to yank it free it would slice open his neck.
She had thought the raider would be older, perhaps a veteran of the war like many of the others she'd seen. Instead she was facing a young woman from Seveldrom who hadn't seen thirty summers. With wild straw-coloured hair and gentle features, she might once have been pretty, if not for the void behind her wintry blue eyes. Much like other raiders the woman lacked compassion. Her language was violence, used as a club to get what she wanted. Just as Danoph had predicted Wren thought it might be the only thing she understood.
"I could make you drop it, or I could just make your head explode," said Wren, making herself smile.
The raider paled slightly but quickly recovered. "This village isn't yours."
"It doesn't belong to Boros either," said Wren and the raider twitched at the mention of his name. "Leave these people in peace and never come back."
"Or what?"
It seemed as if a show of force was necessary. "Or I'll kill you where you stand."
Much to Wren's surprise the raider grinned, but somehow the smile never made it to her lifeless eyes. Pursing her lips, she let out a sharp whistle and Wren sensed movement on both sides. Looking up at the buildings she saw three archers on either side, but instead of aiming at her they were pointing at the crowd.
"You might be able to stop me, but I doubt you can save everyone," said the raider.
It was a good idea and it showed both forethought and caution. If Wren hadn't showed up Gillen's Jaw would've become yet another village paying a tithe to Boros. But now the raiders had the opportunity to get rid of her at the same time as scaring another community. With so many people witnessing her defeat the raiders wouldn't need to work as hard at intimidating other villages in the area.
Wren thought it might even have worked if they hadn't underestimated her.
"Your move," said the woman.
Never one for dramatics, Wren simply focused a trickle of the power she was channelling on her throat. "Now," she said, the word reverberating down the road. Kimme struck on the left and all three of the raiders on one side of the street were suddenly left clutching a collection of kindling in their hands. A moment later the raiders were thrown into the street, one of them landing badly and breaking an ankle. The other archers followed suit, landing without their bows in the street while people in the crowd dodged the falling bodies.
While everyone was distracted Wren reached out and shattered the dagger then wrenched the raider's arm to one side where she heard it pop out of joint. The villager scuttled away back to the relative safety of the crowd who huddled together like frightened sheep. In other communities the people had shown some defiance, but here it seemed as if they were downtrodden and willing to submit to whoever came along.
"You shouldn't have done that," said the raider between gritted teeth. Her right arm hung down at her side. Her men were all lying in the street, bruised and battered, but she remained defiant. "You can't be everywhere at once."
"Neither can Boros."
"Something is wrong," muttered Danoph. "She's too calm."
The raider gritted her teeth and gestured at the villagers. "Tell her."
A sturdy woman with grey hair stepped forward from the crowd. A creeping sense of dread crept up Wren's spine when she noticed the woman was constantly wringing her hands.
"You need to leave and never come back. We're fine. We don't need your help." She was clearly terrified of something, but Wren didn't know if it was the raider or something else.
"Why are there no children in the village?" whispered Danoph.
Scanning the crowd Wren noticed there wasn't a single child. "What have you done?" she asked. "Where are all the children?"
The raider gave her an awful grin. A mix of pain and triumph. "They're around here somewhere," she said, vaguely gesturing at the surrounding houses. "A few of my friends are keeping them company. To be honest, they're depraved men and more than a little twisted in the head. They have a thing for young flesh and are difficult to control. Right now it must be like a bear finding a whole hive full of honey."
The raider's words carried around the street and there were a few wails of agony from the crowd. Far too late to be of any use, Wren realised their fear was not for themselves. All of this had been carefully orchestrated for her benefit.
"You might be good at pushing people about, or breaking weapons with your magic, but you're not too bright, are you?"
"What do you want?" asked Wren.
"Take your group of freaks, crawl back to whatever hole you came from and pack up. I want you gone. What was it you said?" she asked rhetorically. "That was it. 'Leave and never come back.'"
For a moment Wren considered killing the woman and the other raiders lying in the street. After that, with help from the villagers, it wouldn't take her long to find the children being held captive. The problem with her plan was that if even one of the children was hurt the villagers would never forgive her. It wouldn't matter that she'd been trying to protect all of them.
"What happens to the children after we leave?"
The raider cocked her head to one side. "Whatever I want."
The message was clear. She was in control. It didn't matter if Wren stayed and fought or walked away, the raider would decide the fate of the children.
"We'll leave," said Wren.
After all of her planning, shame at such a defeat burned but Wren knew this wasn't the end. Her community was only a few months old and their numbers and reputation were growing all the time. She hadn't come this far just to give up now.
Even as she and Danoph walked away from Gillen's Jaw a plan began to form in the back of her mind. This had been a defeat, but it had also proven revealing in its own way about the challenges ahead.
The others joined her back on the ridge where they gathered to look down at the village. The crowd in the main street had dispersed but one figure was still standing in the middle of the street, their face turned towards Wren and the others. Even without embracing the Source she knew who it was. The raider stood alone and unafraid in defiance to send a clear message to her.
"What do we do now?" asked Kimme. "Are we really going to leave?"
"No. You and the others are going to go home. Danoph and I will join you soon."
"Where are you going?"
Wren made herself smile. "To face the enemy."
They walked back to where they'd tied up the horses and together she and Danoph watched the others ride away. When they were out of earshot he turned to face Wren.
"For someone who was just outwitted, you seem unusually calm."
Around the world the Drassi were known as peerless warriors who were without fault, but even for the most skilled among her people, victory was not guaranteed. Drassi warriors had been defeated in the past, and there would be more in the future, but the way they maintained their reputation was to adapt.
"Every defeat is a chance to learn," said Wren, quoting her grandfather. "Besides, the raiders revealed a lot more about themselves than they realised."
"Such as?"
"I know a lot more about the tactics Boros is willing to use. I will not stoop to that level, but it doesn't mean I have to keep thinking in straight lines. The normal response would be to retreat as we've been told, and perhaps mount an attack on Gillen's Jaw, in force, at a later date. The last thing the raiders would expect us to do is follow them back to their camp."
Danoph understood what she was planning and smiled. It wouldn't make sense for just two of them to follow the raiders home. So far they'd been able to keep the location of their community a secret and Boros had done the same. Once she had an idea of where to find their camp, Wren could start making a different kind of plan.
"What else did they reveal?" asked Danoph, raising an eyebrow as Wren grinned at him.
"I know more about their leader as an individual. What they're capable of and how far they're willing to go to get what they want."
"Why do you say that?"
"Because we just met Boros," said Wren.
# CHAPTER 26
Tianne stared at herself in the mirror, lingering on the clothes the Regent had provided. It was her new uniform as a mage of Zecorria. The grey jacket was longer than she was used to, extending past her waist, but it was lightweight and made to fit her perfectly by the royal tailor. The single blue star on her chest, over her heart, denoted her rank. She was the first of the Regent's new cadre.
Her white cotton shirt and black trousers were equally smart and the leather of her new boots was soft and comfortable.
There were a few details about her reflection she didn't like, but Tianne thought they would fade with time. Her naturally pale skin seemed washed out from being indoors so much. It was a remnant from her ordeal in the cell and a lack of food. Now she had rich, filling meals every day and never went hungry. Although her cheeks weren't lean any more, there was still a gauntness about her face, mostly around the eyes.
That brought her to the most visible reminder of her imprisonment. Despite the lavish care, and treatment from the Regent's personal doctor, she still had a livid pink scar above her right eyebrow. Shaped like a sickle, it was an ugly, swollen thing that would fade in time, but never truly disappear. She hated it and wished she could use her magic to heal it. Part of her felt like crying about the disfigurement. She told herself not to be so childish and stupid. To be grateful she hadn't died in that cell. She didn't want to think what could have happened if the Regent hadn't come to her rescue.
She tied her hair back in a tight ponytail with a piece of leather, tucking loose strands of black hair behind her ears. Giving her reflection one last look, Tianne wondered if she'd changed all that much. If she met someone from her old life on the street, would they recognise her? Did she want them to any more?
With many questions and no answers, she left her rooms and was immediately shadowed by two Royal Guards. They walked behind her at a respectful distance and Tianne knew better than to try and engage them in conversation. Each of them took their jobs very seriously and she never heard any small talk from them compared with other guards and soldiers around the palace. A pool of silence spread out from each when they were on duty. She hoped they were different people out of uniform, but staring into their hard eyes she saw little in the way of empathy or a sense of humour.
Three more guards joined her at the outer gate of the palace. Even though Tianne was the youngest by many years, the leader of the squad, a tall woman with a scar on her left cheek, deferred to her.
"Shall we proceed?" It sounded like a real question but Tianne had the impression the woman was merely humouring her. If she said no the guard would probably just drag her into the street by her hair. It seemed as if everyone in Zecorria, including the Royal Guards, had a lot to learn about mages. It was up to her. She was the first and had always known it was going to be an uphill challenge. Tianne squared her shoulders and raised her chin.
"Lead the way," she said, smiling to hide her true feelings.
From the moment they left the safety of the palace Tianne noticed people staring at her. At first they watched her with open suspicion and hostility, thinking she was a prisoner of the Royal Guards. When it became apparent she was with them they paid enough attention to notice her uniform. Thinking she was nothing more than another palace servant was liberating and after a while people ignored her completely. It made a pleasant change to the hostile stares and anger she'd experienced a few days earlier. Part of her also felt guilty, that in order to be accepted by her people she had to hide her natural ability. Anything associated with magic was instantly seen as dangerous and destructive. It was going to take a long time to change people's minds.
"This way," said Scarface, gesturing for Tianne to follow her down a side street. She hadn't bothered to tell Tianne her name, so she'd given her a suitable nickname.
"Who is first on the list?" she asked, hoping for some conversation.
For a moment it seemed as if Scarface wouldn't answer but then changed her mind. "Frohake claims to be a healer. He's been charging people a lot of money, sometimes everything they have, in return for a cure. We need to know if he's genuine."
If there was a genuine healer it would be an enormous boon for the Regent, but also mages in general. Learning to heal was incredibly difficult, but if Frohake possessed the skill it would be a positive first step in convincing the people of Herakion that magic could be a force for good.
Tianne knew Master Yettle could cure almost anything, given enough time, and some at the Red Tower claimed Eloise's skill exceeded his. There was even a rumour that she could regrow organs and missing limbs. Tianne wasn't sure if that was true, but there were numerous stories about how Eloise had healed herself after being severely injured during the war. If only she'd been here, or Tianne was better at healing, it would make all this much simpler.
Even at this early hour the line of people waiting to see Frohake extended down the street and then back up the other side. Most of those in the queue were locals, but there were also two Morrin and a handful of stout Yerskani. There were a number of families standing together and people of all ages waiting to be healed. Many of them were coughing or wheezing, others were wrapped in bandages and a few had an arm in a sling or rested heavily on a crutch. The Royal Guards bellowed for them to clear a path down the middle of the street rather than try to squeeze through. Tianne had the impression they just wanted the sick and injured to keep their distance in case they were contagious.
At the front of the line an old man wrapped in a blanket was sitting on the steps. She thought he was asleep but as they approached he stood up suddenly.
"Are you Frohake?" he asked, staring at Tianne with cloudy white eyes.
"No, I'm sorry," she said.
"Royal Guards," said Scarface, speaking over her. "We're here on the Regent's business. Step back."
The old man turned his face towards Scarface. "Need some healing, does he?"
Before she had a chance to answer the front door opened and everyone waiting scrambled to their feet. A tall buxom redhead from Seveldrom came out and everyone visibly wilted when they saw it wasn't Frohake. He appeared a moment later, his arm around another scantily dressed woman who he waved off.
Frohake was dressed only in a pair of loose trousers and his open shirt showed scratches on his chest from someone's fingernails. Tianne had to admit that he was handsome, with his oiled beard, luscious curly black hair and swarthy features, but even before he spoke Tianne knew she didn't like him.
His arrogance was apparent in the way he stood, as if the whole world owed him a debt. When he scanned the desperate crowd like a merchant taking a stock count, she knew he had no compassion. She also didn't like the way his eyes lingered on the most attractive women. She could guess how he asked for payment for those without money.
"Are you Frohake?" asked Scarface, and he turned his gaze on the Royal Guard. If his dazzling smile normally had women going weak at the knees Scarface was immune.
"Indeed I am," he said, reaching out to touch her cheek, surprising everyone. "I could take care of that scar, if you want?"
"And how much would it cost me?" sneered Scarface.
"For a woman as beautiful as you, no charge."
Scarface snorted and turned to Tianne. "Get on with it."
"Who is this?" asked Frohake, noticing her for the first time. Tianne did her best to meet his eyes and not stare at his muscled chest. "What's this all about?"
"We're here to test you," said Scarface with a nasty grin. "There have been a number of reports that you're a fraud."
It was only then that Tianne noticed two of the Royal Guards were missing. Frohake's eyes widened briefly but his calm mask quickly returned. "Is that necessary?"
"Inside," said Scarface, shoving him backwards into his own home. Tianne went next and two Royal Guards took up their posts just outside the front door.
The exterior of Frohake's home was modest but inside it resembled a junk shop as it was littered with piles of random belongings. There were stacks of silver ornaments, paintings, expensive silk clothing and dozens of crystal figurines sitting on shelves. No doubt he'd taken them as compensation when people didn't have the gold.
Frohake stumbled into the room and started to move towards the back door of the house when Scarface's voice stopped him. "I've two more guards stationed at the rear. There's nowhere to run."
When he turned around there was still a smile on his face, but it was brittle. "I was just going to get us some drinks."
"Of course," said Scarface with a smile like a cat about to eviscerate a tasty mouse. "Sit." She pointed at a plush chair that was piled high with silk cushions. Realising he was trapped, Frohake sank into the chair trying to appear completely at ease.
Tianne pulled up a plain wooden chair and sat down opposite, just out of arm's reach.
"And what happens now?" asked Frohake, his eyes flicking between her and Scarface.
"Show me," said Tianne, already reaching out with her senses towards him.
"I can't. There's nothing to heal," he said with a peculiar laugh. She gestured at the scar on her face and he just shrugged. "It's barely noticeable."
"Try anyway," she said, sensing a faint echo from the Source. He definitely had some magic, but she wondered about his level of skill.
"Very well," he said, lowering his head and taking a deep breath. With a dramatic wave of his arms colourful balls of red and blue light appeared in the air. They glowed and seemed to be humming at different pitches. Each was smaller than an apple and as they zipped around the room in a whirlwind of light and sound Tianne had to admit it looked impressive. The collection of light globes clustered around her head and she felt a faint tingling sensation as the notes merged into one chorus that was in perfect harmony. Frohake was breathing hard from the strain and after only a short time he let out a long sigh and the lights vanished.
"It's done," he said, wiping at his forehead even though Tianne could see it was dry. "The scar will disappear very soon."
Even Scarface, who had no magic of her own, seemed sceptical. She raised an eyebrow and tilted her head at Tianne. "Well?"
"He's a liar. He can't heal anything."
"This is ridiculous," scoffed Frohake, but now he was sweating. "You've seen my magic. Who are you? Who is this girl to judge me?" he said, addressing the last question at Scarface.
"Apparently, she's a mage."
Tianne considered a snide response of her own but with no witnesses she decided on something more direct to teach them both a lesson. With an unmanly squeak Frohake was lifted out of his chair and sent towards the ceiling while Scarface's feet also came off the floor. The Royal Guard was alarmed and when she saw Frohake's face pressed into the ceiling she turned her steely gaze on Tianne.
"You've made your point. That's enough."
Tianne was tempted to lift Scarface higher but the look on the woman's face changed her mind. She lowered her to the ground but left Frohake pinned for a moment and then cut her connection to the Source. He fell to the floor and landed on his face, groaning in pain.
"It's a light show. Magical sleight of hand," explained Tianne, summoning a larger light globe which brightened the interior of the room. "I can do similar and with enough practice I could imitate his dramatics."
Scarface knelt down next to Frohake who was sweating in earnest now. "Can you do anything useful?" she asked.
"I help people," he said. Scarface punched him on the nose and blood ran down his face. Tianne would've felt some sympathy for him if not for all the desperate people waiting outside for a miracle cure. To be so renowned as a healer he must have cheated dozens of people out of a lot of money, just so he could live in luxury. It made her wish Scarface had punched him even harder.
She raised her fist again and he cowered back. "No, wait! Don't hurt me."
"What can you do?"
"Just the lights," he said.
Scarface put two fingers between her lips and whistled sharply. The front door opened and one of the other guards stuck his head around it.
"Take this one to the cells," she said, pointing at Frohake. "And ask the palace to send a couple of clerks." The guard marched into the room, grabbed the charlatan by the arm and dragged him out.
"What will happen to all of this?" said Tianne, gesturing at all the stolen belongings Frohake had taken.
"It will be returned to the rightful owners. The clerks will sort it out. In the meantime, we have more names on the list for today."
Although Tianne felt a sense of justice in revealing Frohake to be a fraud it was hard to look at all the faces of the people waiting in line. All of them were desperate enough to risk visiting a mage and she had just taken that away from them. As she squeezed past, surrounded by four Royal Guards, she kept her gaze averted.
The second person they visited was a card shark who people claimed had been using magic to steal their money. As soon as the man saw the Royal Guards he tried to run but they'd anticipated this and blocked his escape route. While one of the guards held the squirming man by the arm, Tianne tested him but found no echo from the Source.
"He doesn't have any magic," she said to Scarface, who gestured at the guard holding him. "It must be sleight of hand."
"Told you. I'm clean."
Scarface smiled as she approached the man and Tianne felt her stomach lurch in fear. She punched him so hard that he stumbled back and collapsed on the ground. Two of the Royal Guards started kicking and stomping on the man until he was a bloody mess, curled up in a tight ball. Tianne was so shocked she froze. By the time she started to move towards the man the beating was already over.
As the morning wore on and they encountered only more frauds, Tianne began to lose hope of finding someone like her. It should have been a glorious day of new beginnings where she introduced mages to a new way of living, under the protection of the Regent. Part of her had wanted to build a community of her own, much as Wren had done, but this one would have no need to hide. They would proudly walk through the streets of the capital city, but with each beating of a fraud, she wondered again at her decision to return home.
By the end of the afternoon she felt numb and had stopped trying to intervene. The first time she'd tried Scarface had pinned her to the wall and put a dagger to her throat.
"Mind your business or you'll be next," she hissed in Tianne's face.
Dejected and reconsidering her role, Tianne was finally able to rid herself of the two most brutal guards at the outer palace gate. They had taken great delight in kicking people unconscious while Scarface remained icy and calm throughout. The only outburst from her had been when Tianne had interfered. Perhaps Scarface had been hoping Tianne would attack her so she'd have an excuse to kill her and dump her body in an alley. It was obvious that she hated Tianne and resented having to chaperone her around the city looking for others just like her.
In desperate need of a bath she was about to head for her room when Scarface placed a hand on her shoulder. "Wait here. I need to report in, then I'll escort you to your room."
She knew it wasn't a request and leaned against a wall in the entrance hall, idly studying the decorations. The huge paintings that covered most of the walls in this part of the palace were ancient, musty and moth-eaten. They depicted rulers from centuries ago, who she couldn't identify because they had faded so badly. After two insane Kings in a row Zecorria was looking to the distant past for inspiration.
One servant had told her the palace had been scoured clean after the death of the Mad King in an attempt to remove any signs he'd ever been there, but she could still see a few traces. Deep scoring on stone pillars that had been badly repaired. A hallway with one dark wall to cover the bloodstains. A bricked-up door where no amount of fresh paint would remove the smell inside.
It made her wonder about what kind of a legacy she would leave behind as a member of the Regent's cadre.
A short time later Scarface appeared, deep in conversation with a palace clerk, a tall woman with an equally icy disposition. She stared down her nose at everyone and her severe grey dress covered any bare flesh that seemed a bit extreme.
"You're not done. Someone was brought in. They're in the cells," said Scarface, gesturing for her to follow.
Tianne followed the guard through several narrow servants' corridors before descending six winding flights of stairs taking them deep underground. As she stepped out into the dimly lit corridor she started to hyperventilate, thinking back to her own time in the cells. It had only been a couple of weeks ago and she was still struggling to sleep at night. Thankfully the cells surrounding her were different, with only plain stone walls, and each prisoner had a straw pallet and even a bucket for waste. None of those she passed looked as if they'd been beaten and there was a strange feeling of camaraderie, with one pair of prisoners even playing cards and another sitting talking to her neighbour.
"Who are they?" she asked.
"Petty thieves, pickpockets and the like. They'll soon be released with a fine or a few lashes. These cells are just for overnighters. The worst criminals are deep underground," said Scarface and Tianne couldn't repress a shudder.
At the end of the corridor they found a teenage Zecorran girl, who looked about the same age as Tianne, huddled in the corner of her cell. One of her eyes was swollen shut and she had a few cuts and bruises on her arms. When Tianne turned accusingly to Scarface the Royal Guard just shrugged.
"Nothing to do with me. She came in that way. She's accused of being a witch. Cast a spell on someone."
"That's not true," said the girl, showing a glimmer of defiance. Her bottom lip had also been split and as she spoke the scab broke open and more blood trickled down her chin.
"Give me some room," said Tianne but Scarface just folded her arms and leaned against the wall. "Please."
They locked stares but Tianne was the first to look away. She didn't want to challenge the older woman's authority. She just had a feeling that the girl would open up to her without an aggressive audience. With a roll of her eyes Scarface walked down the corridor to chat with one of the prison guards.
Tianne knelt down in front of the bars, getting a proper look at the girl's face. The injuries were fresh but she made no attempt to cover them up, wearing them like a badge of pride.
"I'm Tianne."
"Kalina." As Tianne studied her she could see Kalina looking at her uniform.
"What happened?"
Kalina shrugged, as if her current predicament was normal. "Raslin came into my dad's tavern with some of his friends. He got drunk and tried to bend me over a table in the back room. I wasn't interested so I fought him off and broke his arm. His father is someone important in the city, a Minister or something. Raslin told him what had happened."
"So why isn't he in here instead?"
Kalina grinned. "Because he's got money. And because I threw him across the room and out of a window. His father claimed I'd bewitched his son, so I ended up here."
Kalina wasn't particularly tall and didn't look muscular, but even so Tianne had a suspicion she hadn't done it by hand. She also intuited there was a lot more to the story than had been said. Instead of asking her more questions she decided to try another approach.
She drew power into herself and embraced the Source, feeling its energy wash away her tiredness and the lingering aches in her body.
"What did you just do?" asked Kalina, her eyes widening in awe.
Instead of answering Tianne asked, "How did you throw him across the room?"
"With my curse. They're right about one thing. I am a witch."
"Oh no, you're so much more," said Tianne, summoning a globe of light in her hands. She sent it drifting through the bars and fixed it to the ceiling of Kalina's cell where it filled the space with pale blue light. "I'm a mage and so are you. And it's not a curse, it's a blessing."
"Then why am I in here and you're out there?" she said, gesturing at the cell.
"I'm here to change that. The Regent wants a cadre of loyal mages, to protect the people of Zecorria. If you join me, no one will ever be able to hurt you again."
"Are you serious?"
"I am. I've been recruited to find others like me and chase away the charlatans."
Kalina shook her head. "I'm not like you. It only happens when I get angry."
"I can help you with that. I promise."
"What's going on here?" said Scarface, coming to stand in front of Kalina's cell. "Is she another scam artist?"
"No, she's like me."
Scarface raised an eyebrow. "Really?"
"I can feel her connection to the Source," said Tianne, drawing more power into herself. Kalina immediately reacted.
"I can sense... something," she said, squinting at Tianne.
"She wants to keep you here," said Tianne, stepping back and gesturing for Scarface to do the same. "She doesn't believe you have any real power. Remember what he tried to do and how it made you feel. It's your choice. Either you can stay in that cell or you can join me. If you do, you'll never be that powerless ever again."
Kalina gritted her teeth and the veins in her forehead began to pulse. Tianne edged a little further away down the corridor. Sensing something was about to happen, Scarface followed her.
Tianne felt a build-up of power in the air, and her skin began to tingle like the moment before a storm. With a groaning of stone and a clang of metal all the bars in Kalina's cell were ripped from the mortar and flung across the corridor. The sound rang in Tianne's ears and just as suddenly the surge of power was gone. The prison guards came running with weapons drawn and even Scarface was startled as Kalina stepped over the bars of her cell into the corridor. The fierce smile on her face made Tianne grin.
All day she had been dreaming of a moment like this. Of finding someone like her, who she could befriend and coach into becoming a real mage. The dream of a community of Zecorran mages was still a long way off, but, finally, this was a beginning.
"And now we're two," said Tianne.
# CHAPTER 27
Garvey let his pony set its own pace as it picked its way down the craggy hillside. He'd been up in the mist for a few hours, enjoying the time alone and the silence of the mountain.
The fog swallowed all sounds below. The only noises above had been the chirping of birds and the sighing of the wind. At the peak of the mountain, even at such high altitude, he'd found an abundance of life. Scraggly green plants with small purple flowers growing up between slabs of stone. Creeping vines, stubby trees and rich grass covered the mountain like a thick cloak. Dozens of gaping holes in the ground revealed pure white rabbits with red eyes and the steppe cats with flat heads and stubby ears that hunted them. A few of the cats had peered at him curiously from behind some rocks but they didn't approach. Walking on paths not even he would risk was an old grey goat, mocking his unsteady feet as it scampered up the rocks.
If only he could stay up here where everything was simple.
Word had reached Garvey a few days earlier from the chatty mouth of a merchant who hadn't recognised him. At times he left the others behind and went unseen into large towns and settlements to hear the latest news. Mostly the talk was about his followers and the atrocities they'd committed, but recently people had been speaking about the Regent of Zecorria's new cadre of mages. It was early days but in time they would be a dangerous force to be reckoned with. Magic needed to evolve beyond the Red Tower. Perhaps this was the start of one pathway.
With a little coaxing the merchant had also told Garvey about a different storm that was approaching.
It was long overdue.
As he came down out of the clouds Garvey thought he smelled smoke. The lower he went the more apparent it became until he could see a thin plume rising up from the village at the base of the hills. He'd left the others only a few hours earlier in good spirits, but it seemed as if the situation had grown worse in his absence. Usually Tahira was able to control the others without him being present.
The first body he came across was that of a young girl, fifteen years at most, lying face down in the street. His pony shied away from her and he steered it around the corpse with his knees. Garvey noticed the lack of blood and the peculiar shape of her twisted and lumpy spine. The girl's eyes were such a vibrant green. Like the rich grass at the top of the mountain.
Further down the street he came across a group of fifty or sixty locals, mostly adults but also at least a dozen children. They were all huddled together on the ground. Many of the children were crying as they stared at the six teenagers standing guard. None of the adults were looking at their captors and did their best to avoid all eye contact. Their eyes were focused on the smouldering ruin of a building further down the street. The fire had been put out but grey ash still drifted on the wind and a faint line of smoke rose up into the lead-coloured sky.
Half a dozen students were standing not far away from the charred timbers and tumbled stone. Tahira was berating someone in a loud voice and as Garvey approached he saw it was Haig. He didn't notice Garvey at first and continued to grin at Tahira and ignore her complaints.
"It doesn't matter. They're just peasants," said Haig, gesturing at the collapsed building. Garvey guessed that he'd brought it down with people inside and then tried to burn the remains. "We have the power to do whatever we want, whenever we want. No one can stop us. When are you going to realise that?" he asked. Haig was without remorse about what he'd done.
In his mind it was fair and just retaliation for the destruction of the Red Tower. The people in this sleepy mining village might not have been there in person, but they'd been complicit in their anger towards those with magic.
Before he'd gone up the mountain the villagers had admitted to exiling one girl of eight and hanging a boy of thirteen for lighting a fire without flint and tinder.
Haig was talking at him but Garvey just blocked out the words. He kept his face impassive and tried to feign interest, but his attention was on the other students nearby. Several of them were agreeing with Haig's rhetoric, smiling and making jokes about those trapped inside, as if they'd killed a neighbour's dog and not humans. As if they were better than everyone else because of their magic.
"How many?" said Garvey, cutting across whatever Haig had been saying.
"At least a dozen," bragged Haig. "One of them was a little boy. He just wouldn't stop screaming. It hurt my ears so badly I thought they were going to start bleeding." He laughed and mimed blood running from his ears. Some of his cohorts chuckled.
Haig's laughter was cut short when part of his head exploded in a shower of gore.
Blood splattered onto Garvey's shirt but he didn't flinch. It was a relief that someone had finally shut him up. Haig made a strange hacking sound as he sank to his knees revealing an axe buried in the back of his skull. As the other students cried out in alarm, summoning shields and scanning the area for the enemy, Garvey felt a smile lift the corners of his mouth.
He turned to the west and waited for his old friend to come into view. Garvey had felt him approaching for some time but the others, despite everything he'd tried to teach them, had remained oblivious. It was only when Balfruss stepped out from behind a veil that they finally realised what had happened. They froze in terror and turned towards him for guidance. It was one thing to fight soldiers and kill innocents who had no chance of fighting back. It was something else entirely to tackle a trained mage, never mind a Sorcerer, and a former member of the Grey Council.
"What do we do?" asked Tahira. Garvey smiled and his mirth seemed to unnerve her and the others.
"Run."
Several of them were already backing away. Two of those guarding the villagers had already disappeared and were scrambling onto their horses.
One of Haig's friends wasn't cowed. "If we fight him together we will—"
"All be slaughtered," said Garvey, cutting him off with a snarl. "I don't need your help. You're only going to get in the way. Leave, before I step on your neck." Garvey stared hard at the boy, daring him to say even a single word. All he needed was the smallest of excuses to rip the boy's head from his shoulders. It was what they had come to expect.
Showing more wisdom than Garvey thought possible, the boy bit his lip and backed away. Most of the others went with him, but a few lingered, staring at Tahira. It made sense. Most would separate into pairs but a few would cluster around her. It would make it easier to hunt them down later.
Garvey turned his steely gaze on her, knowing that she wanted to say something. To praise him, to thank him, maybe even to say that she loved him. It didn't matter. It was all too late. She seemed to deflate then shook herself as if coming awake. Tahira turned on her heel and ran towards the stables.
"Clear the area," warned Balfruss, gesturing at the villagers to disperse. Even without their guards they'd remained on the ground, but now they ran towards the safety of the woods beyond the boundary of the village. Garvey waited until the last of them had disappeared among the trees before turning back to face his old friend.
Balfruss kept one eye on the villagers running for the trees and the other on Garvey. Oddly his old friend seemed completely at ease. His followers were riding hard in all directions, but Balfruss couldn't worry about them for now. He could sense a handful had not fled and were watching at a distance to see what happened next. If he survived then they would become an issue for another day.
When the last villager disappeared, Garvey turned back towards him and smiled. It seemed so out of place. He'd become so used to seeing Garvey's permanent scowl it was unnatural. His whole demeanour had changed and Balfruss barely recognised him.
"I can't believe it's come to this," said Balfruss. "After everything we've been through, how could you do it?"
"They did this. They drowned, hanged or burned their own children. Then they came into our home, Balfruss, and tried to do it to the rest of us."
"So it's us against them? Everyone? In every country?"
Garvey shrugged. "I told you. I will not hide and I will not run. Not from them. I spent too many years in the shadows as the Bane, protecting them, and this is my reward. How many times will you save them from themselves? How many lives have you saved over the years?"
"I don't keep a tally," said Balfruss. "But this rampage must end."
"Then tell me, wise Sorcerer, what is the answer? What is your solution?" said Garvey, holding his arms wide, his voice booming around the streets of the deserted village.
"I don't know," Balfruss admitted, before pointing at the building that had been destroyed. "But this is not it. We always said we would accomplish great things."
"We were young and naïve," said Garvey, but his voice sounded rough and choked with emotion. Perhaps he was thinking back to when they'd been young men studying at the Red Tower. They'd both had great ambitions about how they would make an impression and shape the world. Create a legacy that would echo down through the centuries. Time had weathered them both, smoothing away their sharp edges, eroding some of their glorious visions for the future, but Balfruss was not ready to give in to apathy and despair.
"Perhaps, but naïveté is better than this brutality and a lack of compassion."
"Talk as much as you want," said Garvey pushing up his shirtsleeves to his elbows. "I'm never going to stop. That leaves you with one choice."
"Don't make me do this," begged Balfruss, but Garvey's face had settled into its familiar mask.
Balfruss was about to make another plea when he sensed a massive build-up of power as Garvey drew heavily from the Source. Instead of weaving a shield Balfruss covered himself in a veil and darted to one side, blending in with the street and the houses behind him. A bolt of pure white energy struck the spot on which he'd been standing, blowing a horse-sized crater in the earth. Another landed to the left and another immediately to the right. Garvey was trying to bombard the area as quickly as possible and catch him before he made it too far.
Balfruss sprinted to his left and skidded around a corner before heading back towards Garvey from behind. When Garvey failed to hit him, Balfruss knew his old friend was trying to find him, via his connection to the Source. All magic users could sense each other when in close proximity to one another because it created an echo. It was how Seekers tested children for magic. But Garvey knew better than that. Balfruss had taught both Garvey and Eloise the ability to mask their connection to the Source. It was something he'd learned from one of the tribes across the Dead Sea.
Holding one hand out in front like a dowsing rod, Garvey turned to his right and let out a shout of triumph. It wasn't Balfruss's connection he was sensing, but the few remaining students who hadn't fled with the others. Too late Balfruss realised what was about to happen as Garvey unleashed a powerful blast of force which smashed the house apart. The walls collapsed and the roof broke into a hundred pieces, blasting the surrounding area with chunks of rock and wood. One student was impaled by a spear of wood through her torso and another was crushed by an avalanche of rocks. The two remaining students suffered minor injuries but fled before they were caught in the crossfire again. Balfruss felt them retreat to a safe distance but unlike the others they didn't keep going. They were waiting for something.
Moving as slowly and quietly as possible Balfruss approached Garvey from behind as he continued to scan the village. Garvey remained in the open, standing in the middle of the street, which was alarming. Either he was more arrogant than Balfruss realised and thought himself unbeatable, or his lack of indifference extended to his own future.
Balfruss edged closer, certain at any moment Garvey would spin around and attack. When he was within arm's reach he dropped his veil and locked his arms around Garvey's throat in a chokehold. Once more his old friend surprised him by not putting up any kind of a struggle.
"It's about time," said Garvey, pretending to wrestle with him but making no real effort. "I've been standing out in the open. I couldn't make it any easier for you."
"You wanted me to stop you?"
Garvey gestured at the space around them. "Can you veil us? Create a distortion so they can't hear us?"
With a series of quick twisting gestures Balfruss created a slow haze around him and Garvey, sealing them inside a bubble. Everything outside appeared the same, but sounds were distorted and the nearby tweeting of a bird seemed to stretch on and on, becoming unrecognisable.
Garvey stared at the fine net he'd woven about them and, turning his head, Balfruss saw him smile. "Can they still see us?"
"Not really." Anyone looking at them would only see vague shapes inside the net, as if they were observing them through a dense haze.
"How much time do we have?" asked Garvey.
Something in his voice made Balfruss release his chokehold and step back. Staring into the eyes of his old friend he saw a glimmer of the man he remembered from his childhood. The other version of Garvey was there, the cold man fuelled by rage and without remorse, but it seemed at a distance as if it was a mask that belonged to someone else.
"What have you done?" asked Balfruss. "Did you plan all of this? Was it all a charade?"
"Even before Danoph had his vision about the Red Tower, I knew a version of this was coming," admitted Garvey. "The old ways of teaching were flawed. We knew that when we left the school as young men."
"I told Eloise that being the Bane for so long had left a mark on you. You're sick, Garvey. You need help."
"If only it were that simple," he replied. "When the hatred began to build, and they started to turn on Seekers and children, people soon forgot what magic had done for them. The lives that you and the others saved during the war. The sacrifices we've all made to protect them over the years." Garvey's nostrils flared and his hands balled up into tight fists but he didn't reach for the Source.
"I didn't know," said Balfruss. "It was years before I found out what they'd made you do. The old Grey Council were wrong to ask you to take on the mantle of Bane."
Garvey dismissed it with a wave. "If it wasn't me they would have chosen someone else. Nothing would have changed."
"I could've helped you. I should at least have tried."
"It's in the past. It doesn't matter now. They're killing children, Balfruss," he said, gesturing at the village and the world around them. "Blaming them for something they're born with. Magic isn't evil and it's not going to go away. They need to understand that."
"You've killed hundreds of people..."
"They needed someone to hate. A lightning rod to focus their anger. If my years as the Bane taught me anything, it's that magic is necessary. There will always be another Flesh Mage, another Warlock. I don't need to be an Oracle to know that, in time, it will happen. What I've done will force them to change. To create new schools and find different ways to teach magic. Children with magic should be nurtured, not drowned or burned at the stake."
Balfruss was struggling to accept what Garvey had done. Not only killing so many people because he thought it necessary, but creating a persona of someone fuelled by rage and living inside that mask. For years he'd isolated himself from everyone and never once hinted at what he was planning. From the first day he'd returned to the school, Garvey had been wearing a disguise. That level of determination and focus was unlike anything he'd ever seen.
"You've been lying to everyone for years. You manipulated us all into thinking you were brutal and unstable."
"Not all of it was an act," admitted Garvey. "But it was necessary."
"You should have told us about your fears. We could have tried something else."
"We did try, old friend," said Garvey, gripping his shoulder. "We worked so hard to try and stop Danoph's vision coming to pass. Once I realised it was inevitable, I knew I had to play my role through to the end. And now, you must play yours."
"What are you saying?"
"There's only one way this can end," said Garvey. "If you kill me then you risk creating a martyr. The rogue mages will unite in my name, creating a whole generation of Warlocks who only want to destroy. Nothing new will be built and magic will be pushed to the fringes. But if you stop me, if you drag me before them in chains, it will be the catalyst others need."
"We're over the border. Garvey, we're in Zecorria. They'll kill you," said Balfruss, amazed that Garvey could be so calm. But on the other hand he'd been preparing for all of this for years. He must have known this moment would come as well and he seemed willing to accept whatever punishments lay in his future.
"They will try, but it won't be as easy as they think." An unusual serenity had settled over him, washing away all traces of anger from his features. At that moment Garvey seemed reborn. "I am sorry to add to your burdens, but there's something else you must do."
"I'm afraid to ask," admitted Balfruss.
"You must become the Bane, at least for a little while. Those who fled the Red Tower with me must be stopped. They're unstable and they threaten what could be built in the future."
"I cannot," said Balfruss, shaking his head. What Garvey was asking brought up old memories of what he'd done in Voechenka. Years later he still had nightmares about the corrupted children he'd been forced to kill. "Do not ask that of me."
"Then you must find another who will assume the mantle, because we both know that, in time, there will be others who choose the left-hand path of magic. The Bane is a necessary evil."
Balfruss had thought he would face the problem of the rogue students another day, but now he was forced to consider his options. When the Red Tower had fallen they had given the students three choices, but Wren had presented them with a fourth. Perhaps it was not too late for those who had followed Garvey. Perhaps they could be brought back into the fold. Perhaps.
"It's time," said Garvey, taking a deep breath. "Short of death, there's only one credible way they'll believe you captured me."
The full horror of what Garvey was asking him swung into focus and Balfruss was so shocked he involuntarily took a step backwards.
Knowing the reason for his actions, no matter how noble, did not make his crimes any less heinous. He had destroyed entire communities and, at the last count, slaughtered hundreds of defenceless people. He had created a level of fear focused on one individual not seen since the Warlock. Even knowing all of that, Balfruss had been struggling with the idea of killing his old friend.
What he was now asking him to do instead was far worse.
It would cripple him in a way that only a couple of people could heal and both Yettle and Eloise were far away. If Garvey died they couldn't hurt him any more and after that only his name would be cursed. If Balfruss did this it would be in the full knowledge that what lay ahead for his friend was months and perhaps years of torture.
"Do it quickly, before I lose my nerve," said Garvey, staring up at the sky.
With tears running down his face Balfruss embraced the Source and lashed out.
# CHAPTER 28
Akosh stared in disbelief at the man seated across the table from her. Akharga.
Finally, after some negotiating about the time and place via his surrogate, Bissel, she was face-to-face with him, in the flesh. Wearing masks and blending in was common to all of her brethren, but she would never have guessed his real identity.
Akharga was Kai. The Pestilent Watcher. The Eater of Souls. And one of the oldest and most dangerous beings she had ever met. He was a monstrous thing from another era who had managed to survive across many long centuries. He was unique, alien and terrifying.
He was also the only one of their kind who had feasted upon his own followers in order to sustain himself. It should have spelled out his doom and yet, somehow, he was still here and flourishing.
For the last ten years she'd heard the name Akharga bandied about among the humans, but not once had she considered it would be him. His name was always mentioned in relation to doctors, healers and apothecarists. Wherever there was a terrible outbreak of a disease, or a surge in the damp lung, a plague priest would show up to offer comfort and care for the sick and dying. And all of them wore his symbol around their necks. A triangle with an eye at its centre. Akosh suspected that none of them knew whose symbol they really carried and what it meant. Kai wasn't curing diseases or taking away pain and suffering. He was feasting on it.
The handsome human face he wore was completely at odds with what was lurking just beneath the skin. To a stranger he would appear to be a cultured and wealthy man in his thirties, judging by his fashionable clothes and long coat. His smile was warm and friendly, but her flesh crawled as she'd seen what was underneath the mask. The shadow on the wall behind him seemed normal, but at times she was sure it flickered and parts of it began to writhe like the many arms of a giant squid.
"You've been a stupid girl," said Kai, picking up his glass of wine. He held it up to the lantern and swirled the liquid around, watching it slide about. The tavern, and the wine, were among the best in Herakion but it was not somewhere she'd visited before tonight. He had chosen the place even after her insistence that they meet in what she had thought of as her city. It made her wonder how many loyal people he had in the Zecorran capital and how many were in the building right now.
No one had ever called her a stupid girl before. In front of any human she would have bristled at the insult or simply killed them. But he was not human and since they were alone she kept her mouth shut and let it pass.
"Why is that?" she asked.
Kai's eyes briefly turned red before returning to normal. "The list is long, but let's start with some of your most recent mistakes." He sipped his wine, made an appreciative noise and put down his glass. "You had one follower who was a Guardian and you let her kill herself."
"Someone had been taken prisoner at Unity Hall. I needed him silenced."
"What a total waste," he said, ignoring her protest.
"He was telling them all about—"
"He knew nothing of worth," said Kai, cutting across her. "So what if the Guardians found out about Habreel? He's insignificant. They all are. They're like moths, here for a moment and then gone. In a hundred years every single one of them will be dead. Which brings me to the second thing on the list. And this is a big one. You used your own name." He seemed both disgusted and disappointed, as if he'd found out that she was inbred.
Akosh clenched her jaw and dug her nails into the padded arms of her chair. He was right and she hated it. Many years ago, when her power had started to wane, she'd been desperate to find a way to reinvent herself. Survival was the only thing that had mattered. Creating the first orphanage had seemed like a brilliant solution.
Many of those she'd befriended had also started to wither away as the mortal races grew and their needs changed. After only a few years most of her friends were gone. For a time their chairs remained at the table before they too simply disappeared. Other new faces took their place, but by then she was committed to her new path with the orphans.
At the time she hadn't been focused on a long-term plan. Her goal had been her continued existence. It was only many years later that she considered how she might put her children to better use by nudging them closer to those in power.
By using her own name it had made it that much easier for Vargus and the others to know who was responsible. All it had taken was for one mouthpiece to say it out loud. That one utterance created a ripple and she was still feeling the repercussions now. She was an outcast from her brethren and her orphanages in Yerskania were gone.
"You've been this for too long," said Kai, gesturing at her body. "You've spent so much time around humans you think you are one. I had one of my people, Pavel, show you that caring for them had made you weak, but it seems as if it was too little too late."
"I'm dealing with it," said Akosh.
"Hmm, I wonder," he said, sounding unconvinced. "If I look beneath your skin, what will I see? The real you, or just human meat and bone?"
Akosh's tolerance was starting to wear thin. She was used to dodging those more powerful than her, working covertly and feigning respect when necessary, but no one had ever spoken to her like this before.
Reaching out with her senses she wondered how powerful he really was in comparison to her. She'd heard all the stories and once caught a glimpse of his real form, but perhaps it was all just a show designed to intimidate. Only ten years ago he'd been on the cusp of extinction, whereas she'd been gradually building her power for decades.
Kai sensed what she was doing and grinned, his eyes turning red again. All of the shadows in the room coalesced behind him on the wall, merging together into one massive shape. She tried to use her power against him, to hurt or control him, but quickly realised she had underestimated him. The scale and depth of his power dwarfed her significantly.
Akosh felt his presence fill the room as all light drained away and absolute darkness filled the space. With her eyes open or closed it was the same. An endless void of night. She sensed he hadn't moved from his chair and yet an immense weight began to press down on her, shoving her deeper into her chair which creaked under the pressure. Two malevolent red eyes appeared, glowing in the darkness, then four, then eight more, and soon a hundred eyes were watching her, all blinking in unison. A scream started to build up in her throat but she couldn't breathe and clawed at her neck. A tight band of pain was squeezing her chest, her heart, her head. This was the end.
Akosh stumbled out of her chair onto the floor, gasping for air. Slowly the darkness receded and the pain faded away. When she felt strong enough she looked around the room and everything was as it had been before. Kai was human once more, delicately sipping his wine and savouring the taste. With heavy limbs she wobbled to her feet and then fell back into her chair. After a few minutes she'd regained her breath but still felt light-headed.
"Would you like to try that again?" asked Kai, raising an eyebrow. Akosh shook her head then drained her glass of wine to wet her throat. "The only reason you're still here is because of me. They gave Vargus the job of finding you and he's very good at it." Kai shook his head and an unreadable expression passed over his face. She couldn't tell if it was fear, admiration, or both.
"Then why am I here?" she asked.
"Because I dealt with it. Six of your little friends saw you strolling around this city as if it belonged to you. Did you even notice them spying on you?" She hadn't and it made her wonder what else she had missed. "Each of them went running to tell good old Vargus all about it and earn themselves a pat on the head for their obedient behaviour."
Akosh had always assumed that many of the other younger gods had faded away over time when their power had waned. Now, staring at Kai with his insincere smile, she began to wonder about their fate.
"You killed them." It was a statement not a question.
"Oh no," he said, showing teeth. "I intercepted them, before they had a chance to speak with Vargus."
"They're not dead?"
He slowly shook his head. "The death of their bodies would mean they'd go back into the Void. And if their source of power remained then eventually they'd be reborn. No, they're all safe, here with me."
Kai opened one side of his long coat, revealing a tailored silk lining and fine stitching. As she started to ask the material faded away and she found herself staring deep into an endless void full of stars she didn't recognise. Somewhere in the dark she heard voices whimpering, begging for mercy and crying out in pain. As if they were caught in an ocean, faces swam towards her in the darkness, reaching out with beseeching hands, screaming desperately for help. As they drew close to the surface she recognised the faces of all her brethren that she thought had died.
Snaking around all of their naked limbs, snaring them like flies in a spider's web, was a tangled knot of deep purple tentacles. A thick red vine was embedded in each of their stomachs, standing out proud against their bare skin. As Akosh watched a pulse of bright white energy ran down the vine from their convulsing bodies before disappearing into the dark. A second later there was another pulse and their bodies seemed to contract slightly before recovering.
She stared in disbelief at her friends who saw her and were given a glimpse of hope. Someone finally knew of their horrific plight and had come to help. Then the tentacles flexed and dragged them away into the darkness again to be fed upon by the thing that lurked in the shadows.
Kai closed his coat and poured them both another glass of wine. "So, do we understand each other a little better?" he asked, clearly wanting an answer.
"Yes," she said, feeling as if she might vomit all over his expensive clothes. Her mind was reeling. What she'd seen was a nightmare worse than any she'd considered. For years she'd simply assumed their stars had waned, their power vanished and they'd passed beyond the Veil. But theirs was a fate far worse than non-existence. "What do you want me to do?" she asked.
Kai's smile, genuine or not this time, was still unsettling. "I want you to continue with your plan. Destabilise Yerskania and create a nation of your own here in the north, with one religion. Isn't that your big dream?"
"Yes."
"Good. Keep playing your little games and I'll make sure Vargus and the others stay away."
"Why?" asked Akosh. There was nothing she could do if he chose to consume her. But she still needed to know. "Why are you helping me?"
Kai shrugged. "Perhaps it's because it amuses me, watching you all scurry around, fighting over scraps of land. Or perhaps it's because scared prey tastes so much better." He licked his lips with a long purple tongue and she couldn't repress a shudder of revulsion. "If you need to contact me, send word via Bissel."
With that he drained his glass of wine, made another appreciative sound and walked out of the room.
Akosh stared at the closed door, listening to the sound of his receding footsteps. She only relaxed when she heard the front door of the tavern close behind him.
And with that everything she had been building for decades was gone. Her people and plans were still in motion, but only because he allowed it. Tomorrow he could change his mind and tell her to tear it all down, and she'd do it, without hesitation. Because it seemed there were worse fates than dying or disappearing into the Void.
# CHAPTER 29
Tammy rubbed the skin just above her right eye in an attempt to stop the headache that was forming. For the last few days she'd been working all hours, hadn't seen any sunlight and had barely slept. The four walls of her office had become a prison of her own making. It was a vain attempt to try and keep her mind away from what she'd done.
The Old Man had provided her with a name and an address. It led her to an ordinary tailor's shop where she left a note. That evening at a tavern she met with a jolly, chubby man called Griss who told jokes that made her smile, if not laugh out loud.
If she hadn't known what he did Tammy's first impression would've been that he was a baker or a merchant. Griss had an easy-going manner that suggested he dealt with people all day. He tried his best to make her feel comfortable in his presence. It would probably have worked if she'd just met him.
Originally from Seveldrom, he'd been living in Perizzi long enough to be recognised and considered a local. After ordering drinks at the bar, which he insisted on paying for, they found a quiet table to talk. A few people in the tavern recognised him and stopped by their table to briefly shake his hand and thank him for their tasty meal. As it happened Griss was a renowned chef at the Queen's Rest, an expensive tavern situated close to the palace. She'd only been inside once, and that had been to speak in private with Kovac before he'd left the city.
Griss was adept at changing his manner depending on who he was speaking to. With her Griss was polite and his jokes were witty, but when a group of sailors stopped by their table he exchanged coarse banter as if he'd been at sea for years. It made her wonder what he was like when there was no one around. Tammy also wondered what people would think of Griss if they knew what he liked to do as a hobby.
When they were alone again Tammy quietly explained what she needed. When she started to give details of what it was for Griss held up a meaty hand.
"I don't need to know why. Only what needs doing," he said. "It's safer."
Given his hobby Tammy was surprised that she didn't sense anything untoward about him and that worried her. He was affable, relaxed and when he smiled, which was often, it was genuine. She'd worked with violent men and women in the past who liked inflicting pain. In each one of them there was a void. Something inside them was lacking and they attempted to fill the space with the screams of others. When they were silent, when they were still and she looked in their eyes, she could see the empty space within. They were broken people. Griss worried her more because he seemed whole and so normal.
As she explained what needed doing he listened intently, but his eyes roamed around the room, following the crowd, pausing on the trio of musicians trying to enthuse the weary crowd. It gave her an opportunity to study him but everything, including her instincts, told Tammy that he was just a chef.
"You won't find it," he said, turning back to face her.
"It?"
His wide smile showed off his white teeth. "Whatever you're looking for. The dark splinter. The sorrow lurking within that shaped me. It's not there."
Even now, two days later, as she went over a report about a series of thefts, his words came back to haunt her. A timid knock on the door provided a welcome distraction as Rummpoe stuck her head around the edge.
"Sorry to disturb you, ma'am, but that document has arrived." Tammy gestured for her assistant to come into the room which she did with some reluctance. Their relationship had been difficult at the beginning, but Rummpoe was proving to be a useful resource that Tammy had come to value. Despite mentioning this to her, Rummpoe frequently seemed intimidated, although on reflection Tammy realised some of that may have come from her recent brooding. The situation with Griss still weighed heavily on her mind and it had put her in a bleak mood.
She forced a smile and tried to make it genuine. "Thank you. Just leave it on my desk."
Rummpoe scuttled into the room, dropped off the envelope and left without another word, quickly closing the door behind her.
For a while Tammy didn't pick up the envelope and just stared at it. There was nothing inherently malicious about it, but once she read the names on that list she knew it would change her because of the means by which they'd been obtained.
Several of her best Guardians had questioned the bookkeeper, Bertran, and he'd not revealed a single name. A few hours alone in a cell with Griss, his tools and his intimate knowledge of causing pain, and the bookkeeper had given them everything.
The Old Man had told her there would be moments like this. When the only choices available were bad or worse. It all came down to what she could live with and what she was willing to do in order to serve the greater good.
Realising there was little point in delaying it, she opened the envelope and scanned the list of names. A low whistle of surprise escaped her lips. Many of them were familiar but she recognised two that normally would have been obscure if not for recent cases. Pulling down a volume of her journal from the shelves, Tammy scanned the list of crimes to confirm her suspicion. With a deep sinking feeling she sat back and carefully considered her next move.
"Rummpoe!" she bellowed and her secretary came running.
"Ma'am?"
Tammy scribbled down two names on a sheet of paper and passed it across the desk. "Have Guardian Faulk carry out a discreet check into the history of these two people. Place of birth, family, their faith, known associates. The usual. I need it done as soon as possible."
"Yes, ma'am."
"And Rummpoe?" she said, as her secretary turned to leave.
"Ma'am?"
"This stays between the three of us," said Tammy, holding her secretary's gaze to impart the seriousness. "Is that clear?"
"Yes ma'am."
Tammy was so familiar with the route through the palace to the Queen's office she'd stopped looking at the plush surroundings. Her mind remained elsewhere, trying to imagine the patience required by Akosh. The latest information about the names on the list indicated that there was a lot more to the woman and her cult than Tammy had realised. Despite that, she wasn't quite ready to accept Balfruss's suggestion that Akosh might be more than human. There was definitely a cult of personality around a central figure, but so far she'd found no evidence of anything magical or unexplainable. However, after all that she'd seen in the last dozen years Tammy remained open-minded. It also wouldn't hurt to take necessary precautions, just in case. Not for the first time she wished the sword on her hip was _Maligne_ and not the plain weapon she carried instead. She'd always felt just a little bit safer with it close by. It might be necessary to retrieve it in the coming days.
When she entered the Queen's outer office her assistant, Dorn, was vainly trying to sort through a stack of old books. One slipped from his grip and a cloud of dust erupted from its yellowing pages making him choke and gasp for air. Nevertheless, he waved Tammy to go ahead before he'd regained the power of speech.
As usual Queen Morganse was seated behind her desk but at the sound of Dorn's wheezing she went to investigate before returning to her seat with a faint smile. "Did you lose a bet?" asked Tammy, jerking a thumb towards the secretary who she could still hear coughing through the door.
"He came highly recommended, but sometimes I wonder if they just wanted to get rid of him." Morganse pushed her papers aside and briefly studied Tammy. "You look tired," she noted.
"I've been dealing with some troubling issues," conceded Tammy.
"So your note indicated. Tell me," said the Queen, sitting back and giving Tammy her undivided attention.
"In an attempt to find out more about Akosh's cult, I recently acquired a list of names from one of her people. Many of them are familiar figures in the city, but two less well-known names stood out from the others. As I'm sure you're aware, Dockmaster Lohag recently died."
"I thought that old goat would outlive me," said Morganse. "He must have been at least seventy."
"Seventy-eight, according to his granddaughter. His death didn't seem suspicious, until I noticed who was to succeed him. It's a woman called Rohane. She's well known on the docks. The captains of several ships have told my people that she's firm but fair."
"What makes you think foul play was involved?"
Tammy took out the list of names, running down it again even though she'd memorised all of them. "Rohane's name was on the list I obtained from Akosh's bookkeeper. I had one of my people make subtle enquiries and he found out she was an orphan and doesn't visit any of the main churches. A discreet search of her home revealed an idol identical to this one, which we found in Guardian Brook's home," she said, holding it up. As ever Guardian Faulk had been very thorough in his work, but he'd left no trace that he'd been in Rohane's home.
Morganse took the crude idol and studied it briefly before setting it down on the desk. "That doesn't prove she was involved in Lohag's death."
"No, it doesn't. She may have no knowledge of what happened."
"There's more, isn't there?" she asked and Tammy nodded.
"The Minister of Trade recently passed away. He had a new young wife and overexerted himself. The family are contesting the inheritance. What's more interesting is that his successor is Tovin."
"I know Tovin," said the Queen. "He's been a loyal right hand and faithfully served in the Ministry for years. He deserves the position."
Tammy wished she had better news. "He's also an acolyte of Akosh. His name is on my list. One such death in a month might be coincidental but two..." She trailed off and shrugged her shoulders.
"Show me the list," said Morganse. Tammy noticed the Queen's hand shook slightly as she held it out. She passed the list across and watched the colour drain from Morganse's face as she scanned the names.
The Queen moved to the window and stared out at the city. When Tammy had read the list she'd also needed time to come to terms with what it meant. All the names the accountant had given her were those of orphans. All of them contributed a portion of their wealth to local orphanages dedicated to Akosh.
Both Rohane and Tovin had lived in the city for many years and each had worked hard in their respective roles. Despite the circumstances surrounding the deaths of their superiors, Tammy could find no proof that either of them had been involved. However, that didn't mean that someone else, who also followed Akosh, hadn't arranged it so that they could be promoted. Most troubling was that two deaths had occurred in less than a month. It could have been a coincidence of timing but she didn't think so. A plan was in motion.
Neither of those awaiting promotion had ever visited the cells or been in any serious trouble, and yet they were followers of Akosh. Their loyalty was to her above all others. Beyond their Queen and beyond the law.
So far neither had done anything untoward, but with so many people focused on Akosh and her network, Tammy wondered how long it would be before that changed. Guardian Brook had never shown any signs of disloyalty right up to the moment when she'd killed a witness and tried to blame his murder on Munroe. Rather than be questioned, she'd taken her own life and her last words had been about her Mother.
Any visitor's faith had never been an issue before. Yerskania was renowned for being an open nation that welcomed people from all around the world. As long as they didn't try to hurt anyone their religion was a private issue. Perizzi had churches and temples devoted to mainstream faiths like the Maker and the Blessed Mother, but also the uncommon in the west, such as Elwei. Tammy didn't believe in any of them and didn't care about what others believed. But being a follower of Akosh was now a matter of public concern and safety.
If they chose to be obstructive in their new roles, then individually Tovin and Rohane could disrupt trade in the city. Working together they could control what goods flowed into the port and a lot of money would flow their way to clear any obstacles. No one wanted their goods to rot because they were being held in a warehouse or in the hold of a ship, tying up the docks and the merchant captains.
The other names in the city were not all in such significant positions, but each of them was poised to inherit a more senior job. Two of Akosh's acolytes from the list had already been promoted and had been in control for some time.
If they, and everyone else on the list, were to work together it would change the heart of the city. It would change how Yerskania dealt with other countries in the west and beyond.
"This list of names. How certain are you that they're all genuine?" asked Morganse, without turning around.
"I'm certain," said Tammy. Griss had been recommended by the Old Man himself and she trusted him completely.
"I will have some of my agents look into them and keep a close eye on their activity," said Morganse. Tammy didn't know how many agents the Queen had in the city, but the Old Man had indicated that the number had increased since the war. All of the west had been unprepared for the Warlock and no one wanted that to happen again. "I need more information before making a decision. I need time."
In the blink of an eye Morganse seemed to age beyond her years. With a slight stumble she sat down heavily in her chair. Sometimes Tammy forgot that Morganse was a grandmother who had been on the throne for a long time. Most of the time the Queen was as vivacious as a woman twenty years her junior, but not today.
Time. They both knew they didn't have enough of it. At any moment Akosh could give her people in Perizzi an order and they would leap to it, no matter the cost. They would willingly sacrifice their own lives to serve their god. Tammy knew the Queen and other monarchs employed agents who lived abroad, blending in with their communities, but this was something far beyond that. Sleeper agents that might be called on to serve, or perhaps not. They might live their entire lives without receiving a direct order from Akosh.
It also made her wonder if any of them had ever refused. Had anyone ever rejected an order from their Holy Mother? If so she doubted the others had left them alive. It was an interesting theory to investigate but very soon the Queen would have to make a decision about what to do with those names on the list.
"I'll send for you. Soon," promised Morganse as if she'd read Tammy's mind.
They would have to move quickly and whatever she decided Tammy knew the repercussions would be severe.
It was a little after midnight and with another busy day ahead Morganse should have been in bed. Instead she found herself thinking about her daughters and their family. About what she was willing to do to protect them.
When the Mad King had threatened her during the war she'd been certain he would come after her directly, but instead her son had suffered. All his life she'd been preparing him to inherit the throne, but because of her inaction he'd been castrated and had left Yerskania, never to return. That had put her in the unenviable position of remaining on the throne when she should have stepped down several years ago.
Back then it had been an insane monarch who had convinced himself he was a prophet mentioned in holy texts. He had planned to convert all of the western nations into one country, with him on the throne as both its god and king. Today it was a widespread cult devoted to a woman they believed was a god and for whom they would do anything. Break any vow, any law, any sacred oath.
The door to her private sitting room opened and a lean, middle-aged man with grey hair slipped into the room unannounced. Without making a sound he padded across the room and waited for her gesture before sitting down. Impeccably dressed as ever in black and grey, Ben cut a striking figure despite his years. Other than his name, which was fake, she knew very little about him. It had only been about twenty years, so perhaps he was getting close to trusting her.
Ben was a member of the Silent Order, a league of assassins who had been operating in Yerskania for a long time. With a code of their own that no one really understood a person could attempt to hire them. Sometimes they accepted the contract and at other times they would reject it without ever giving a reason. They could not be blackmailed, persuaded or threatened. They were anonymous and a force of nature.
The Silent Order had been instrumental in changing the course of several countries, but what only a handful of people knew was that they had a connection to the throne.
As well as being a retired assassin, Ben was a member of the inner circle, and his voice carried considerable weight.
"I believe all of the individuals on the list are being followed by your agents," he said, and she inclined her head. "Then, may I ask, why are my people also watching them?"
"Because I may need you to take decisive action. Because watching may not be enough."
"You have suspicions?" said Ben, raising an eyebrow. "Which of them do you believe to be disloyal?"
Morganse declined to answer. So far none of them had acted in a way that could be considered even slightly disloyal. All of them were dedicated to their respective roles, as well as active and well-liked members of their communities. Most of them had families and, apart from their unusual religious belief, they were no different from anyone else. She had no reason to doubt them. Not yet anyway.
Yerskania was an open country and Morganse took great pride that her capital city welcomed people from every corner of the world. It was a glorious melting pot with food, faces and languages from all nations. It was a home away from home for everyone who came here as they could always find something familiar.
She'd never thought of that as a weakness. Until now.
"Keep a close eye on them," was all she said. Ben bowed and left quietly without another word.
At this hour the hearth was nothing but cold ashes. Feeling a sudden chill, Morganse pulled her shawl tightly around her shoulders as she struggled with her decision and the repercussions that she knew would follow.
# CHAPTER 30
Munroe had to work hard to keep an interested expression on her face as she was shown around the ground floor of the orphanage. After only a short time the muscles in her face ached from suppressing a yawn as her guide, Sianne, showed her the wonders of the washroom. The woman seemed to take great pleasure in explaining how the children's sheets were washed and then fed through the mangle. The last part of the riveting process was hanging them out to dry in the gardens at the rear of the house.
It was a relief finally to leave the dingy room and set foot outside, even if she did have to help with the laundry. As they hung and pegged the sheets on the line, Munroe stared in surprise at the vast overgrown gardens. Once, they must have been impressive, with a hedge maze at the heart and four quadrants of flowerbeds on all sides. Now the maze was a monstrous overgrown tangle of green. The flowerbeds had been reduced to broken soil or were awash with waist-high weeds.
"Impressive, isn't it," said Sianne. "I'm told the owner used to host parties here every year on the summer solstice. Two or three hundred people would gather for a day of feasting and music."
"It must have been something," mused Munroe. "I'd be happy to work on the garden. It would be so nice to give the children somewhere safe to play outside," she said, forcing a smile until it hurt.
"That's a wonderful idea. I'll suggest it to Gorell."
"Wonderful," echoed Munroe, thinking it would be far easier to work alone outside than directly with children. Being near them was difficult. They bore no resemblance to Samuel, but they were a constant reminder of what she had lost. One of her hands shook and she took a few deep breaths until she felt calm again. She reminded herself that all of this was a means to an end. That thought alone allowed her to stay in control.
"Are you ready for the exciting part?" asked Sianne, when they had finished hanging the sheets.
Munroe dreaded to think what that might be but forced another smile. "Oh yes."
"Wonderful, let's go and meet the new arrivals."
Much like the garden, the house itself was an impressive ruin that had seen better days. Once it had been a palatial home that now showed considerable signs of rot. Holes in the walls had been patched with straw, clay and bricks. The roof repairs also included a multitude of materials and daylight showed through in a few places. Sianne had told her it only leaked in a few spots, which was a vast improvement on how it had been when they first arrived. Each room in the house had been recently painted with whatever was going cheap, creating a rainbow effect as she walked through the building. The cobwebs and dust had been swept away but that didn't stop the house from feeling abandoned. It also smelled a little of mildew but Sianne had reassured her that it would fade in the coming weeks. Munroe hoped she wouldn't be here long enough to find out if that was true.
"We've only been in the building a few weeks," said Sianne, reading something in Munroe's expression. "We'll make it into a home."
She was saved from having to force another smile as a gaggle of children came hurtling down the huge winding staircase. One of the screeching brood, a young girl with red hair, was riding down the wooden handrail, while the others cheered and followed in her wake. Munroe was expecting tears and a painful end to the ride, but someone had assembled a collection of cushions at the bottom of the stairs. The girl flew off the end of the rail, grinning ear to ear as she hit her soft landing. With a dramatic wave of her hand she took a bow but her audience's applause began to fade as they spotted the adults.
"Children," said Sianne. Their mirth drained away and was replaced with guilty expressions and a sudden lack of eye contact. "What has Gorell said about sliding down the bannister?" The children offered half-hearted apologies and immediately started collecting up the cushions. A few of the children looked at Munroe curiously but she did her best to ignore them. She didn't want to know their names or anything about them. Sianne was talking, filling her in on some of the details about the children's difficult lives so far. Munroe listened just enough to nod in the right places, but she didn't absorb any of the details.
"The new arrivals are in here," said Sianne, leading her down a corridor.
In a room that had been set up as a classroom, half a dozen slightly older orphans were sitting at battered desks. Half of them were locals, with dark eyes and pale skin, but two were from Yerskania and one was a tall Seve boy about ten years old. A severe Zecorran man with grey hair and crooked teeth was going over some items on a chalkboard at the front. A quick glance revealed a list of basic rules about being at the orphanage.
Sianne knocked on the doorframe, as there wasn't a door, interrupting the induction. "Sorry to interrupt, Gorell."
"That's quite all right," he said. "We were just about finished. Is this the new member of staff?"
"This is Munroe," said Sianne, holding her by the shoulders and marching her forward as if she was a prize cow. Determined to make a good first impression with the man in charge, Munroe smiled and shook hands. She answered all his questions with a story that closely resembled the truth and even went so far as to laugh at a mildly amusing joke. It was difficult to swallow her natural sarcasm and pay attention, but she managed it as he seemed satisfied.
"Well, I'm sure we'll become better acquainted over the next few months," he said.
"I'm sure," she agreed. With luck her stay would be short, but she was willing to do whatever was necessary.
"Munroe had a wonderful idea about the garden as well," said Sianne.
"Ah, the old maze. Do you think you can tame it?"
"I'd certainly like to try," she said.
There was a frantic knocking on the doorframe and then another flustered member of staff arrived. "Tommi has had an accident." It was clear the woman was panicking but was trying her best not to scare the children. Seeing it as an opportunity Munroe spoke up before anyone else had a chance.
"I'll stay here and supervise the children until you return," she said. The members of staff hurried away, leaving her alone with the six children. Munroe lingered by the door, waiting for news while the children amused themselves with a deck of cards.
After a while she heard one of the children approach. The skinny Yerskani girl leaned against the doorway, facing into the room. She seemed to be watching the game and didn't make eye contact. Munroe pretended she hadn't noticed she was there.
"Do you have any idea how boring this is?" asked Dox, through gritted teeth.
"You're an orphan, aren't you?" asked Munroe, barely waiting for the girl to nod. "Then you should feel right at home. Or would you rather be back in Rojenne, working for Cannok."
"He's dead."
"I know. I killed him," said Munroe, making the girl squeak. She took a moment to regain her composure, looking back into the room to see if anyone had noticed. The card game continued without interruption and Munroe tried a different approach.
"Were you happy working for him?" she asked. Munroe had learned from Tok that Dox used to sit through all of Cannok's meetings in Rojenne, just to make sure his people weren't lying to him. "Wasn't that boring?"
"Most of the time," Dox reluctantly conceded.
"Has anyone said anything yet about the faith here?"
"Just a few vague hints. I think they want to ease us into it. Get used to having regular meals and a bed, then tell us."
"Did you ask them about it?" asked Munroe.
"Yes," said Dox, giving her that withering look that teenage girls seemed to master effortlessly. Munroe remembered giving her mother the same kind of glare more than once.
"And?"
"I asked if they were Eaters, or part of some sex cult." Dox snorted and swallowed a laugh. "The panic on Sianne's face was hilarious. She started babbling about her faith. She promised they weren't Eaters, or into anything weird, and they're going to tell us all about it soon."
"Is that it?"
"No, she started droning on about compassion and helping others. Something like that. She sounded like a priest."
"Did they name her?" pressed Munroe, grabbing Dox's arm and squeezing hard. The girl's face crumpled up in pain but then her eyes widened in fear as she saw Munroe's expression.
"Yes. It was Akosh. She called her Akosh."
Munroe released Dox and kept watch for other members of staff in the corridor.
"Most of the other children have no idea," said Dox, rubbing at the red marks on her arm. "All they know is the woman in charge of the orphanage has a lot of money. A few are still suspicious. They've seen things like this before, where orphans are loaned out to rich clients."
"There's none of that here," said Munroe. She didn't need to add any more details to reassure her. Dox would know she was telling the truth.
Munroe had told Dox only a little about why they had come north to Herakion, but almost nothing about Akosh and her followers. She didn't need to know and it was probably safer as well. That way her surprise would be genuine when they finally introduced her, and the other new orphans, to the faith and what it involved. Munroe had no way of knowing which members of staff were loyal to Akosh and which simply worked here. It was safer to assume all of them and trust no one besides the girl.
"Keep your head down and your ears open," said Munroe.
"How did you kill him?" asked Dox.
Despite everything, Munroe smiled to herself. She shouldn't have been surprised. When she'd been the same age as Dox she'd asked adults inappropriate questions.
"You know how," said Munroe, waggling the fingers on her right hand.
"Can you teach me?"
Since Dox had spoken so plainly Munroe thought brutal honesty was the best response. "If you want to kill someone, use a dagger. They're easy to find and you already know how it works. Just stab someone with the pointy end."
"Aren't you going to tell me killing is wrong?" asked Dox.
"I know you think I'm ancient, but I was once your age. So I know you'll do whatever you want, no matter what I say. If you want to kill someone, then go ahead. Besides, I'm not your mother." Munroe knew her voice was harsh but she couldn't help it. The pain and anger were constantly seeping out of her no matter how much she pushed them down. "But if you're serious about learning how to control your magic, then, yes, I'll teach you about that."
Dox was silent for a while as she mulled it over. "Where do I start?" she asked.
"The sea. Listen for the sea," said Munroe. Sianne was hurrying towards her down the corridor with another woman she'd not seen before. Rather than looking worried they were both grinning with excitement about something. "It's always there, at the edges of your perception."
"What is it?"
"The Source," whispered Munroe. She made a shooing gesture with one hand and Dox took the hint.
"Is everything all right?" asked Sianne, coming into the classroom. Perhaps she'd been expecting a bloodbath as she seemed oddly disappointed at finding a quiet game of cards.
"No problems. How is Tommi?" asked Munroe.
"It looked far worse than it was. Thank the Maker," said Sianne, which caught Munroe by surprise. The other woman, a fortysomething redhead, didn't react. Either she hadn't noticed because she was so giddy about something, or she was a far better actor than Munroe gave her credit for. With a final squeeze of Sianne's arm the other woman practically skipped away down the corridor.
"Did something else happen?" asked Munroe, lowering her voice to a whisper. "You both seem very excited about something."
"I'm not supposed to say," said Sianne, biting her bottom lip.
"I understand. I don't want you to break a promise," said Munroe, going against every instinct in her body. Part of her just wanted to shake Sianne until all her secrets came tumbling out of her head, along with a portion of her brains.
"It's not that," said Sianne, struggling with something. She came to a decision and pulled Munroe a short distance away down the corridor. "Promise me, you won't tell anyone."
"I swear," said Munroe, putting her right hand over her heart.
Even though there was no one in sight Sianne lowered her voice. "Do you remember I mentioned our patron?"
"Yes."
"Well, I've been told that she likes to visit all of the orphanages, especially the new ones like ours."
"Is she coming here?" asked Munroe, holding her breath.
"There was a rumour that we would be seeing her in the next few days. Gorell just confirmed it. Isn't that exciting?" asked Sianne.
Munroe was stunned but eventually managed to speak. "Oh yes. That sounds like an unforgettable day!"
Sianne was so wrapped up in her excitement she was oblivious to the emotions that flickered across Munroe's face. Her vengeance was almost at hand and Akosh wouldn't see it coming until it was too late.
# CHAPTER 31
A few hours after Wren and the others left Gillen's Jaw the raiders set off for their camp. Wren had no way of knowing what Boros and the others had done to the villagers, or their children, but as Danoph kept reminding her she was not responsible.
She and Danoph hid a fair distance away from the main road in a dense copse to conceal the horses from view. By augmenting her eyesight with magic Wren was able to watch the raiders leaving from her concealed position. She couldn't hear what they were saying but it was clear how the others deferred to Boros. At her previous encounter with the raiders in Sour Crown, fear of their leader had been apparent. Now she witnessed first-hand how they acted with deference and a peculiar sensitivity, as if she were brittle. Wren had seen such behaviour before.
As a small girl she used to play with the children on her street. They spent so much time in each other's houses she came to know everything about their lives and families. She knew whose parents were generous with treats, whose wouldn't tolerate running or noise in the house and whose parents were terrifying. There was no noise, no running and little fun to be had in Yortem's house. Everyone treated his father as if he were a bear in hibernation, afraid of what might happen if he fully awoke. A year later the village found out when he flew into a rage, killing seven people, including Yortem and his mother before he was finally stopped.
She wondered what Boros had done to create such fear among her peers. Raiders were not known for being kind and polite, but all of them rushed around Boros, all but bowing and scraping like she was royalty. Wren had witnessed the casual way she'd threatened the children in Gillen's Jaw. Whatever Boros had done in the past, such a savage act must have seemed tame by comparison.
Wren waited until the raiders were almost out of sight before they followed at a sedate pace. The dozen men and women rode with confidence and no fear of reprisal for their actions. Such an attitude made them arrogant, something Wren hoped to use against them.
For the next few hours they trailed after the raiders who stopped off at two other villages to collect a tithe. Part of her wanted to rush in and help them, despite knowing the villagers wouldn't thank her for getting involved once they witnessed her magic. The colder, more logical part of her knew that such an heroic act would serve little purpose in the long run and so she did nothing. Even if she somehow managed to overwhelm Boros and the dozen raiders with her, Wren wasn't sure she could kill them. Besides, there were more raiders back at their camp. Killing a dozen and their leader might slow them down but it wouldn't stop them.
Danoph had tried to prepare her for such a moment, and he believed she could bear such a burden, but Wren wasn't as confident. One violent act against Brunwal, even in defence of her life, had left her isolated from the other students. She worried how the others in the community would treat her if she killed again. Even worse, Wren was terrified how such an act would change her. Master Yettle's advice about not lying to herself was difficult to maintain. It often left her feeling fragile, but she persisted by trying to understand the repercussions.
One thought kept rattling around inside her head. It refused to give her a moment's peace and sometimes woke her in the middle of the night. What if she discovered that she enjoyed killing?
It sounded ludicrous and yet it was not unprecedented, even in Drassia. Some men who wore the mask refused to give it up, even when their bodies were too old and slow to fight. They often died on their feet with a weapon in hand and thought it a life well spent and a worthy death. Over time they had come to love the sound of steel cutting through flesh, the misting spray of blood, the anguished screams of the dying.
She could imagine it becoming addictive. To remove people from the world and carve your own path through history. To be, as a god, deciding the fate of others.
Others were addicted to seeing death reflected in the eyes of their victims. She'd even heard wild stories of a secret group of Drassi warriors that worshipped death, dedicating every kill in her name as if she were a black-hearted goddess.
All of it sounded like madness, and yet Wren found herself at a crossroads. When the moment came her head might take her in one direction but her heart could lead her down a darker path.
Magic gave her abilities far beyond that of most people. It allowed her to do wonderful and terrifying things purely on a whim. She was beginning to believe that such power should not be randomly given to any person as a chance of birth. Magic carried a heavy responsibility that, only now, was she beginning to understand.
If she were more like Boros and cared only about herself, Wren could live as a queen. She could kill and maim with abandon until people were terrified to speak her name. But she had walked away from the path of violence, away from Garvey and his rage, and yet now she found herself struggling with an impossible decision.
"I can hear you brooding," said Danoph, startling Wren from her reverie. They were still trailing after the raiders at a distance. Light was beginning to fade from the sky overhead as dusk approached. They must be getting close to the raiders' base.
"It seems as if the only choices left to me end in murder. It's either me or her," said Wren, gesturing at the distant figure of Boros.
"Perhaps," mused Danoph.
"Do you know something?" asked Wren. "Have you had a vision about her?"
"No, but perhaps you should gather more facts about her and the raiders before making a decision."
A short time later Wren saw the raiders turn their horses away from the main road and head east. By the time they reached the same spot night had fallen and they were forced to dismount and walk. The countryside was pitch-black and she didn't want to injure their horses. She was tempted to summon a mage lantern, which she'd finally mastered after weeks of practice, but decided not to take the risk in case they were discovered. Instead she relied on the Source to enhance her vision, peeling back the deepest shadows.
After fumbling ahead at a slow walk, noise and then light from up ahead made them pause. They tied up their horses and then crept closer to the raiders' camp. After checking for scouts, she and Danoph crawled into a dense thicket where they could observe the raiders' camp without the risk of being discovered.
In some ways that she found unsettling, Wren noticed a number of similarities between her new community and the raiders' base. On one side of a secluded valley the trees had been reduced to a sea of sawn trunks. Stacks of firewood were haphazardly piled up alongside their dwellings, which were a mishmash of crudely fashioned lean-tos, tents, rough log cabins, mud huts and hovels that went underground. There was no order to their layout in the camp. In one area she saw a shantytown with several homes clustered together, but a sea of space between them and the largest log cabin towards the back of the camp. She guessed it belonged to Boros but was surprised to see several raiders leading their horses inside. It made sense. They travelled all across the western region and relied heavily on their horses to cover so much ground.
A large well sat at the heart of the camp where several people were drawing up buckets of water. Three people were cutting up vegetables and throwing them into a large pot while others stoked the fire. All of it seemed incredibly mundane and normal, except that everything the raiders touched was tainted with blood.
Not far from the stable door Boros was distributing the tithe they'd taken from the villagers. Food was taken to a sturdy-looking log cabin while the other items were laid out on a sheet and a bidding process began between the gathered crowd.
"I need to know more about her," muttered Wren, but Danoph overheard.
"They're scared of her," he said. "As vicious as they are, as cruel and without compassion, she is worse."
"I thought as much," said Wren, having seen how they deferred to her. "Can you tell me anything else? Can you sense anything?"
It seemed as if Danoph was about to say he couldn't help, or that his Talent didn't work that way, when his expression changed. Perhaps he was beginning to embrace his gift, or perhaps he simply understood the personal stakes for her, in addition to the survival of their community.
"I will try," he promised, focusing on Boros. As far as she knew he had never tried to use his Talent on purpose. Wren really wasn't sure what she had been expecting. An echo through the Source as he embraced his power. A disturbance in the air around him, or perhaps something more extreme given his violent nightmares.
Danoph lifted his right hand towards Boros and she thought light blossomed on his palm, although it was difficult to be sure.
There was no rush of energy and Danoph didn't move a muscle. In fact, it was as if he had suddenly been frozen solid. Despite being close enough to reach out and touch him, she felt he had suddenly become part of their surroundings. He was beside her and yet she had the impression his mind was elsewhere, travelling to places unseen. Wren wasn't even sure if he was breathing and almost reached out to touch him but stopped herself in case she broke his trance.
When Danoph spoke she let out a squeak of surprise, but he didn't notice. "She's hollow," he said in a voice that sounded different as well. If she hadn't seen his lips moving Wren wouldn't have said that it was Danoph speaking. The voice was older and more cultured. "Her future is murky but all of it is violent."
"What about her past? What can you tell me about that?" asked Wren.
"It's very clear. There's only one road." Danoph's sudden smile was unnerving. He was staring at something far away and Wren felt goosebumps cover her skin. "It is drenched in blood."
"Tell me," said Wren, going against her better judgement.
"She was a child growing up in Seveldrom when the war began. Her village wasn't famous and held nothing of worth. But it was remote and found itself on the front line of the invading western army." Danoph spoke clearly and with such an icy detachment she heard neither compassion nor grief in his voice. "Some of her earliest memories are of moving house. Her parents arguing about which belongings to leave behind and which to take with them. All the children rode out of the village on the back of an old wagon pulled by a pair of donkeys. She thought everyone was going on a trip together, except they never went home again."
It was a common story in the western region of Seveldrom as many villages had been abandoned. The people fled east to the safety of the capital and beyond into the countryside. When the army arrived it passed through the empty settlements and, like a swarm of locusts, stripped the land clean, leaving nothing behind. After the war many of those who'd fled had nothing to go back home to and were forced to make new lives elsewhere.
"After that there were a lot of strange faces and shouting. She remembers weeks spent living in a tent, exploring fields with other children during the day and cooking food over fires outdoor at night. She remembers the smell of many people living close together and always wearing muddy clothes. Sometimes people argued over food and that was when she saw her first dead body." Danoph's smile was out of place and Wren wondered what he was seeing.
"Who died? Was it one of her parents?" asked Wren, but either he didn't hear or chose not to answer.
"There was an argument. She doesn't know what it was about, but she saw one man hit the other on the head. He fell down and didn't get up again. Boros found him lying in the field, his body hidden from view amid the long grass. At first she was afraid to go near him because he kept staring at her. Eventually she approached and touched his face."
To see a dead body at such a young age was one thing, but witnessing a murder would leave a permanent scar. Wren watched as Boros moved around the camp and the way the other raiders always kept one eye on her. It was difficult to bring together the two images of the innocent young girl and the ruthless leader.
"Is that what changed her?"
"Oh no," said Danoph with a half-smile, and this time she saw he was looking at her. Wren gasped in surprise when she saw his eyes, glowing from within with an intense white light.
"What happened?"
"A pattern began to form, one which she eventually changed. Her family travelled south in Seveldrom and started a new life. But violence found them again as the village was attacked by a group of thieves. No one there put up a fight. They gave the thieves what they wanted and they left. This went on for months until her parents decided to move on and start again. Violence and bad luck seemed to follow them wherever they went. And each time her father refused to get angry, refused to fight back and said faith would provide. Boros killed her first man when she was eleven."
Around the same age that Wren was discovering boys and daydreaming about the future, Boros had already taken a life.
"It was a chance encounter," said Danoph. "Boros recognised him as one of the thieves who had come to her village a few years before. He was older now, overweight and slow. She tempted him into a dark alley with a promise and stabbed him to death with his own dagger. Afterwards she expected to feel something. Joy. Satisfaction. Relief perhaps. But there was nothing. Just an emptiness and a hunger inside. She took his money, his dagger, and began to hunt the others. Moving from place to place she cut purses and throats. At fifteen she met a group of thieves and killers who laughed at her until she killed two of them. She was leading them by the time she was eighteen. The Queen of Seveldrom stamped down on raiders and they were hunted down by soldiers and a man called the Gath. Boros fled and came west with the survivors. Ever since then she's moved from group to group, butchering anyone who challenges her authority."
"Why does she do it?" asked Wren, hoping to understand what continued to drive Boros to commit such acts of brutal violence.
"She came to believe something." Danoph's eyes were still glowing in the dark. Wren felt more than a little unsettled by his impenetrable stare when it formed on her. "That people are fundamentally weak. That if you threaten them, they'll fall in line. All it takes is someone whose will is stronger, and she is merciless."
"Is it greed?" asked Wren. "What is driving her to do all of this? The murders and intimidating the villages in this area. What does she want?"
For the first time since he'd embraced his power, Wren saw an emotion briefly flicker across Danoph's face but couldn't name it. She didn't know if it was disgust or sympathy. "She desperately wants to feel something. Because no matter how much pain and suffering she causes, no matter how many people she kills or how much money they make, all of it means nothing to her. She simply doesn't feel anything."
The glow faded from behind Danoph's eyes as he lowered his right hand, coming back to the present. They stared at one another in silence for a long time, shocked at what he'd revealed about Boros, but also at his latent power. It went far beyond dreams and nightmares about the future. It was something they would have to deal with, but tonight there were more pressing matters.
Wren gestured for him to follow her away from the raiders' camp. They walked back to their horses and she came to a decision. "I need you to do me a small favour," she said. "Take both horses a little way down the road and wait for me there."
Danoph was still slightly dazed but he was present enough to look worried. "What are you going to do?"
"Show her that I'm not afraid."
His tendency to say little had never bothered her before, but now she wondered what Danoph was seeing when he looked at her. "Be careful," was all he said before slowly riding away.
Reaching out towards the endless sea at the periphery of her senses, Wren drew power from the Source into herself. Delving deeper than she had in a long time, perhaps since she'd faced Brunwal, she embraced the energy, letting it fill her with its light and glory. Her skin tingled, her senses sharpened acutely, and as the raiders' camp came into sight up ahead she released part of the energy into the air.
Bright flares of white light rushed into the sky, burning away the darkness and illuminating every corner of the raiders' camp. With cries of alarm they scrambled around for weapons thinking they were under attack. Boros emerged from a tent and began searching for the source of the light while others around her panicked. Eventually someone looked in Wren's direction and bows were drawn and pointed at her. To make it easier she summoned a mage lantern in one hand and raised it above her head, revealing her position to everyone.
A crowd had gathered at the edge of the settlement but none of the raiders seemed willing to step forward. Boros pushed her way to the front and boldly walked ahead of the others who still held back. A peculiar hush had fallen over the crowd until a dense silence filled the air.
Wren stared into Boros's cold blue eyes and tried not to show her fear. More important, she had found their camp and had apparently come alone, sending a clear message of its own. It wasn't over between them.
# CHAPTER 32
Regent Choilan took his time settling himself into the chair before accepting the proffered glass of wine. His first wife, Selina, waved the servant away and waited until she'd left the room before speaking. Choilan had no concern about anyone overhearing their conversation as a Royal Guard was posted outside the door, but Selina was not taking any chances. She'd always been careful but more recently her behaviour was bordering on paranoid. He blamed it on indulging her interest in espionage. It was to be expected that after spending so much time with professional agents she would absorb some of their habits.
Selina's new passion had produced some remarkable results in the last few months, outdoing his own agents from time to time. After all, it was her new group that had found and imprisoned the person responsible for the murder of their predecessors.
"Are you even listening?" said Selina.
Choilan forced himself to focus on her face rather than the intriguing curve of her calves. "Yes, you were telling me about my cadre of young mages. So, they're all behaving? No signs of disloyalty?"
As expected it was proving difficult to convince the people that any mages, no matter whose colours and what kind of uniform they wore, was a good thing. It would happen eventually, but it might take a few years. At the same time he wasn't naïve and made sure all the mages were closely watched. So far they seemed to be true believers in the cause, but after the initial rush of power he needed to ensure they remained loyal and didn't abuse their magic. As a secondary precaution a number of Royal Guards had taken to carrying a concealed poisoned dagger that was reserved for the mages. The snake venom wasn't deadly but even the smallest cut on bare skin would paralyse a large man in seconds.
Selina eyed him with suspicion but eventually continued. "No. So far all ten of the young mages are behaving. But you should be careful not to trust them too quickly."
Choilan raised an eyebrow. "I don't trust them at all. Give it ten years of loyal service and then we can have this conversation again."
The corners of Selina's mouth lifted briefly which he took as a small victory. "I must say, I've have been impressed with Tianne," he conceded. "So far we've rooted out almost every fraud and charlatan in the city. She has a real fire in her belly for them."
Selina was less impressed. "I take it you're aware that she's attracted to you?"
"Of course. I've played on that several times."
"Then isn't there a risk she's merely doing all of this to impress you?"
"It's possible, but I doubt it," he said with a shrug. "She came a long way to help, based on my amnesty. But surely wanting to impress me is a good thing?"
"Hmmm," said Selina, sounding unconvinced. "Then may I suggest you make a point of visiting her. My agents tell me her enthusiasm seems to be waning. I suspect she's having doubts."
"Doubts?"
"She was the first. Now, she's merely one of many. Give her something symbolic to make her feel special."
Choilan considered it and thought it an excellent idea. "Anything else?"
"I'd also suggest bringing in the parents, hers and others. Get them to talk about how proud they are of what their children are doing with their magic. Using it to help people. All of that nonsense."
That would be more of a challenge. Almost all of the parents had either disowned or tried to drown their children once they discovered their child had magic. It wouldn't be easy to make them sit down in a room and talk to their child, let alone make their praise convincing. However, he was confident once he explained how important this was, and the lethal consequences of refusing, the parents would be happy to comply.
"All of that should win her over," said Selina, offering a smile that made him nervous. "Failing that, if Tianne doesn't come around, then she'll end up like the others."
Those with tenuous magic, and anyone unwilling to serve, initially spent some time in the cells to convince them. If that failed they were beheaded and the bodies burned, just to make sure. He knew magic couldn't be eradicated, but Choilan intended to control those who were born with it in Zecorria. Murder was a crude and rather final tool, but he understood that sometimes it was necessary. The way Selina spoke about it so easily, and smiled at the idea, served as another reminder why he'd not invited her to his bed for several years. It was a lot safer to spend time with his other wives. Her smile widened as their eyes met. It was as if she knew what he was thinking.
"Do you have any more news for me?" he asked, covering up his discomfort. "Any news of foreign agents?"
Selina's smile faded. "No, not at this time."
He sensed she was withholding something. "Is there something I should know?" Choilan folded his arms and leaned back in his chair, waiting for an answer.
"They're unconfirmed rumours. It could be nothing."
"But?" he persisted.
Selina realised he wasn't going to budge but was equally stubborn. "I'll bring it to your attention at the appropriate time." She folded her arms and a staring match ensued, neither willing to concede. Choilan suspected it would have continued if not for a frantic knocking at the door.
A Royal Guard burst into the room looking uncharacteristically flustered, which made his heart race. "What is it? What's happened?"
"My apologies, Regent, but a group of soldiers has returned from the border with a prisoner." The guard's fear was making him increasingly nervous.
"A prisoner? What kind of prisoner?" he asked, but the guard was rendered speechless. Something had scared him badly.
"Spit it out. Who is it?" asked Selina.
The Royal Guard finally found his voice. "I think it's Garvey," he whispered.
The ground seemed to drop away from Choilan even though he was sitting still. He felt his stomach moving up into his throat and he struggled to breathe. Looking across at Selina he saw she was equally stunned.
"Are you sure?"
"I think you should see him." The guard seemed unwilling to answer him directly.
Choilan's mind started whirling as he tried to find something to hold on to but there were only questions. Why had Garvey surrendered? Surely there was no cell in the world that could hold him. So why was he here? Was it a trap? Had he allowed himself to be captured merely to unleash the full force of his magic in the capital? Where were his followers? A dozen more questions ran through his mind.
"The mages," he said suddenly, clutching at straws. They weren't ready. They were crudely trained, not battle-ready mages able to defend him against such a dangerous and powerful threat. But the children were also the only thing Choilan had standing between him and oblivion. What had he been thinking? He should have been looking for someone to train the children at the same time as cultivating their loyalty.
"Show me," said Choilan, gesturing at the Royal Guard. He felt something tugging on his sleeve and looked around to see Selina holding onto his jacket. He'd never seen her afraid before today. It made him think back to all that he'd done to reach this moment and be here. The sacrifices, the political games, the marriages to build alliances and the countless years focused on a single goal. Choilan would not be cowed. If this was a trap, and this was to be his final moment, then he would face it head-on like every other obstacle in life.
He patted Selina's hand and followed the nervous Royal Guard through the familiar corridors of the palace. They descended countless flights of stairs going deep underground past corridors echoing with the cries of prisoners rotting in their own filth. Down and down, away from any natural light, soon they were surrounded only by thick stone walls.
The temperature continued to fall as they went deeper into the earth, his breath frosting in the air, until finally they arrived at the lowest level. Historically this was where the Mad King had kept the most dangerous prisoners. Those he'd deemed the biggest threat to his power. In reality they'd probably been people he'd simply disliked because of how they spoke or dressed.
When Choilan had gained the throne he'd found the cells full of bones and rotting bodies. They'd been cleared out and remained empty until he'd ordered Tianne to be dropped into one of the water cells. His dramatic rescue of her had been carefully orchestrated and yet unfortunately her loyalty was still wavering. Selina was right. He'd make her feel special and if that failed she'd find herself visiting her old cell again.
A dozen Royal Guards, all heavily armed with swords and shields, waited for him at the main door to the cells. They weren't as anxious as his guide but he could see the tension in their faces and posture.
"Tell me what happened," he said to the Captain.
The burly man stepped forward and gave a short bow. "Regent, as per your instructions, patrols were regularly visiting all towns and villages close to the southern border. There had not been any sightings of Garvey and his rogue mages for some time. When they arrived at Ore Birch they found blood on the street and one building had collapsed. Garvey and his people had been holding the villagers hostage until they were rescued."
"By whom?"
"They don't know, but someone started killing Garvey's people. They heard a terrible fight and saw lightning fall from the sky. Then there was a long silence. When they emerged they found several dead mages and also Garvey. The patrol arrested him and brought him here to stand trial for his crimes."
"How did they arrest him?"
"He's injured," was all the Captain would say. Even so he was clearly nervous of Garvey and rightly so after everything that he'd done. Choilan considered that perhaps this wasn't to be his final moment after all.
"Show me," he said, gesturing at the door.
The three huge locks clanged open and a thick metal bar was removed before the heavy iron door could be pushed open. Flickering torches provided erratic light and strange shadows danced on the stone walls. This far down they were roughly hewn, damp in places with green moss and glittering with shards of crystal. It also stank. Of decay, sweat and stale piss. No amount of sluicing out the cells had got rid of the smells left over from the Mad King's paranoia.
Only the Captain came with him into the cell block. The others remained at the door, weapons at the ready, just in case. The further he went into the cell block the worse the stench became. Despite covering his nose with a sleeve and breathing through his mouth, Choilan gagged a few times before his stomach settled. The Captain led him to the last enclosure on the left.
The torchlight didn't reach the back of the dingy cell but he could make out most of what it contained. A stone shelf for a bed, a bucket in one corner and a scraggly old blanket. There was also a man chained to the walls by his wrists and ankles. The restraints were enormous with huge steel links, as thick as Choilan's wrist.
The prisoner's origins were difficult to pinpoint as he had no discerning features and any bare skin was tanned from being outdoors. Part of his face was hidden in shadow but Choilan could just make out a red beard and wide jaw. He was dressed in stained clothing that was marked with dried blood and dirt. At first glance Choilan noted the bruises on his arms and the blood on his chin, but couldn't see any crippling injuries that might explain his capture. It was only when he coughed at the smell that the prisoner shuffled forward into the light, revealing all of his face.
Someone had gouged out both of his eyes.
"I can hear you breathing out there," said Garvey, turning his face towards Choilan with an eerie smile.
The Captain gasped in spite of himself and reached for his sword. Garvey faced the Captain and lurched towards him, chains clanking. With a cry the Captain fell back against the far wall, tripping over his own feet in a panic. Garvey was brought up short, his arms and hands stretched out in front of him, but they were still some distance from the bars. He began to laugh at the Captain who scrambled back to his feet, untangling himself from his sword.
Garvey turned back to face Choilan and despite his blindness he knew the Sorcerer was studying him. "You must be someone important to have Captain Nervous accompany him. The body oils you're wearing are rich, much like your silk clothing. Regent Choilan, I presume."
Despite being dressed in rags, recently blinded, defeated and imprisoned, he remained defiant and arrogant. It was Garvey. Choilan had no doubts. Without saying a word, he walked from the cell block already planning what he would do next.
The greatest threat to his country and the west had been eliminated on Zecorran soil. It wouldn't take much to turn this to his advantage. Whoever was responsible for Garvey's defeat had not hung around to claim the glory. So, who was to say his new cadre of mages had not been responsible?
Such a victory would certainly help to convince the people that the new recruits could be trusted and were loyal patriots. But first they would parade Garvey through the streets so that everyone could see that their Regent had brought him to justice. It would be good for them to see the focus of their anger in the flesh. Then there would be a short trial and an execution. The people's faith in him would be restored. This would ensure that those lurking in the shadows, waiting for him to fall so they might claim the throne for themselves, would have to wait a bit longer. Such a grand spectacle might also encourage more young people to come forward and join his growing cadre of mages.
It didn't matter how it had happened, he would turn this opportunity to his favour and strengthen his position on the throne. His first task was to send messages to all of the leaders in the west, informing them about Garvey's capture. He'd also need to make a speech in the capital to let the people know that the danger had passed. Merchants and travellers would carry the news from there to the rest of the country.
The future of Zecorria had never seemed brighter and he would be remembered throughout history as the man responsible. Choilan didn't notice the smell or care about the cold any more as he climbed the stairs towards the sunlight, his mind whirling with possibilities.
# CHAPTER 33
Tammy stared at the letter from the palace in disbelief. She had been staring at it for some time, considering the immediate repercussions and long-term effects. There were so many possibilities she was having difficulty making a prediction. All she could do was prepare for the worst in the city.
Garvey had been captured in Zecorria.
Regent Choilan had boldly made a proclamation and was taking full credit. He claimed that it was only because of his vision of creating a loyal cadre of mages. She had serious doubts that his newly recruited children could have defeated Garvey, a mage with decades of experience. As far as she was aware, his skill and power was on par with that of Balfruss. He, too, had used the title of Sorcerer which she understood was more than just a name. It meant that his understanding of magic had reached a deeper level that few ever achieved. All of which raised an even more worrying question. Who had defeated Garvey? She hoped it was Balfruss but at the moment there was no way to know as he'd disappeared.
Tammy had picked up a letter from the palace a few hours ago but on her walk back to her office she'd heard people gossiping in the streets. The news was already everywhere. On the surface Garvey's apprehension sounded like good news, and people were treating it as such, but she wasn't so sure. Without their leader his followers were faceless and nameless. She knew they were young, but beyond that no one really knew anything about them.
There was a possibility some of them would attempt to rescue their leader. Or worse, if the Regent rushed through a trial and then an execution that could make Garvey a martyr. In some ways that would be worse. If Choilan thought they had been dangerous before he would learn how destructive magic could be if Garvey's followers focused all their power on his capital city. That would certainly put his new cadre to the test.
Tammy also had to consider another possibility. That his followers would simply scatter into many smaller groups. Some could be on their way here. Others might go into hiding and never emerge, and some would go on a vicious killing spree, worse than ever before. There had been no dramatic escalation while Garvey had been in charge. The attacks on villagers, in both countries, had been oddly spaced apart but she couldn't explain why. It seemed ludicrous to suggest their restraint was because of him. And yet.
In the six hours since picking up the letter from the palace she'd heard about four magical attacks on communities in the north. She suspected it would also be the same in Zecorria.
Birds had been flying in and out of the aviary all afternoon. The news hadn't reached the population here yet, but when it did their brief surge of hope would fade. The xenophobia that had come with the revelation of Seekers living among them would return. Only now it would be directed towards any young person who was a stranger. Then the cycle of violence towards children with magic would continue.
The ban on Seekers had been a mistake, but she still wasn't sure what would've been a better solution. Queen Morganse had been backed into a corner but at least the national ban had forced all Seekers to bury their masks. It would keep them safe for the time being until a child with magic in their community started to manifest.
"Ma'am," said Rummpoe, startling Tammy from her reverie. Her secretary was standing in her open doorway, looking at her with some concern.
"What is it?"
"I knocked twice," she apologised. "Are you all right?"
"I'm fine. What's happened?"
Rummpoe slowly came further into the room, still reluctant to spend more time in here than was absolutely necessary. "I've received a message about another attack on a town to the north."
"How far away?" asked Tammy, plotting the positions of the previous attacks on a map in her mind.
"About a day's ride."
It was as she suspected. Some of them were gradually heading south. The wise thing to do would be to avoid the capital city and continue south. To stay in the countryside where it would take a day or two before soldiers could be sent to investigate. Tammy's instincts told her they wouldn't go around. They'd come here and hope to go unnoticed in a crowd.
She would need to call on Guardian Fray a lot more in the coming months. His magic allowed him to see other mages which would be critical in finding the rogues hiding in plain sight. Only a handful knew about his magic and it would be better to keep it that way for now. She'd have to come up with a plausible story to explain his absence from normal duties.
"Tell the Watch Captains to be on alert, and increase the number of patrols down at the docks."
"Yes, ma'am."
The sound of pounding feet alerted them both to danger before they saw a novice Guardian racing down the corridor shouting, "Sir! Sir!"
"Report."
"There's a fight. Mages in the city," gasped the young woman between gulps of air. "It's chaos. Buildings are collapsing."
Tammy pulled on her jacket and belted on her sword. "Stay here," she said to Rummpoe.
"Yes, ma'am."
"Show me where," said Tammy to the novice. The young woman was out of breath, holding one hand to her right side, but she turned and began to jog back down the corridor with Tammy at her heels.
At this time of night the street should have been filled with noise from the many crowded bars and taverns. Instead as Tammy approached an eerie silence gripped the area. A small group of people had gathered at one end of the street but they were also oddly silent as they scanned the nearest buildings for danger. There were a few drinkers and one or two tavern owners, but mostly they were people who had been turfed from their beds, half-dressed or wearing only a blanket and boots. A few were anxiously staring at the figure lying in the middle of the street. They seemed to be waiting for the person to start moving, but she thought they were dead or unconscious.
The other peculiarity on the street was the shattered building halfway down on the right. Once it had been just another tavern but now it was a ruin. The front had been caved in, as if a huge force had struck it. Its roof had been torn open to the sky and shattered beams stuck out like the ribs of a huge beast. As Tammy watched another section of an outer wall tumbled inwards, raising a huge pile of dust.
When it had settled and the silence returned she found herself straining to hear any noise on the street or beyond. The whole city seemed to be holding its breath.
"Who is that?" she asked, gesturing at the body on the street.
"One of them evil mages," whispered a short woman beside her. She was dressed in a pair of trousers and her shirt was inside out. Her feet were bare but she didn't seem to care.
"Did you see what happened?" asked Tammy.
"Course I did," said the woman with a snort. "One of them came right into my bedroom, straight through the wall. Almost pissed myself."
"One of who?"
"He's one of Garvey's lot. Had to be. The young one in my room went back into the street to help his friend, but it was no good. The other one, the man in the hood, he threw them around and smashed one of them into the ground. We all heard his neck snap." She gestured at the body lying in the middle of the road.
"Did you see where the others went?"
The woman looked at Tammy as if she were mad. "Don't know and don't care. As long as they're not here."
Tired of standing around, she walked towards the body in the street. It turned out to be a young man from Yerskania. He was probably in his late teens and was most definitely dead. His neck was bent at an unnatural angle and his eyes were wide open. Blood had trickled from one corner of his mouth onto the street but there wasn't much, suggesting he'd died quickly. The stones around him on the road were cracked from the impact and he lay in a small depression. A huge force had slammed him into the road.
A flash of blue lit up the night sky and Tammy spun around to find the source. It was coming from a few streets away. She was already sprinting towards it when she heard a loud cracking sound. There was screaming and a crowd of people started running towards her, fleeing whatever was happening. Tammy was forced to slow down as she dodged around people wide-eyed with panic. She grabbed one man by the shoulder, pulling him to a stop.
"Let me go!" he said, trying to shake her off but she tightened her grip.
"What's happening?"
"Two mages are tearing up the street. They'll kill anyone who gets near them." Tammy let go and he sprinted away. She pressed on, going against the tide of people flowing in the opposite direction. As she approached a small market square a few stragglers ran for cover and then she was alone again in the heart of the city.
Elsewhere she could hear the march of heavy feet as squads of the Watch formed a perimeter around the area. She'd coordinated with the Watch Captains before coming into the dead zone. They couldn't do much to stop the mages, and could make it worse if they tried to shoot them. For now their job was to stay out of the way and wait for her signal.
The square was empty of people but there were signs of a recent struggle. One of the stone water fountains had been shattered, the statue of an old King leaning towards the ground at a jaunty angle. Water trickled out of the broken basin, slowly creating a new stream as it wound its way between the stones. She spotted a few frightened faces peering into the square from first-floor windows. They were probably people caught in the middle of the fight who had been too slow or unwilling to flee their homes.
"Show yourself!" someone shouted boldly, walking into the square. Kneeling, Tammy removed the bundle from her back slowly and unwrapped her sword. It had been a gift from an old friend many years ago. It was one of a kind and priceless as well as being incredibly unusual, which was why she'd given it to an old friend for safekeeping. As Khevassar she couldn't afford to stand out in any way and the sword was remarkable. Tammy drew _Maligne_ from its scabbard, noting how even in weak moonlight the surface of the blade shimmered blue, purple and green.
In the square the young man from Zecorria was now standing beside the water fountain, his eyes moving from window to window.
"Are you afraid to face me?" he shouted, taunting his unseen opponent. If Tammy had believed in the gods she would have muttered a prayer to one of them to protect her. She would only get one chance at this and it was a slim one if he saw her coming. Just as she was getting herself ready to charge the air shimmered like a heat haze, and a hooded man materialised out of thin air. Tammy would have been amazed if she hadn't seen him do it before. The young rogue mage spun around in surprise, gawping as Balfruss lowered his hood.
"You cannot win. Stop this before you hurt someone, or force me to stop you, like your friend," said the Sorcerer.
The former student sneered at his teacher. "You're a slave. You bow and scrape to them, when we should be ruling! My power makes me a god."
Balfruss shook his head wearily. "No, it doesn't. This is your last chance."
The young mage didn't hesitate. Tammy saw something red streak through the air towards Balfruss from his outstretched hand. A second later a ball of fire seemed to engulf her friend from head to toe. She heard the crackle of the flames and thought it was over, but almost immediately the fire began to dwindle. Balfruss was standing in exactly the same spot. A white cocoon enveloped him and the remnants of the fire burned away. He remained untouched and his expression was one of disappointment rather than anger.
"Is that it? After four years of study. Did you learn nothing?" he asked.
With a snarl of rage the student began hurling what looked like balls of light at Balfruss but he shrugged them off. With a casual flick of one hand he redirected one of the missiles so that it looped around the square and flew back towards the student. With a startled cry he threw himself to the ground, narrowly missing it. The ball of light struck the statue behind him, blowing it into dozens of pieces which rained down across the square.
Trying a different tactic, the young mage lifted several large chunks of stone from the broken fountain into the air. Tammy could see the strain on his face as he sent them hurtling towards Balfruss. The Sorcerer continued to walk calmly towards the student, ignoring the stones which shattered as they came into contact with his shield. He simply sidestepped the largest stone which was the size of a grown man. With a wave of his hand he gently set it down before it struck the building behind him and caused more damage.
"Garvey lied and manipulated you. Even so, your magic doesn't give you the right to do whatever you want."
Balfruss's calmness seemed only to anger the student. "We trusted you. We believed your lies. You said we were going to help people." The student's mocking laughter echoed around the empty square and she thought it was aimed at himself. "They hate us, because we're better than them, because we're special and they're not."
Balfruss was still moving towards the student whose thoughts seemed to have turned inwards. "You need to stop," he said, but the young man didn't seem to hear.
"They're jealous. We can create wonders while they toil away in the dirt. We dream but they can only destroy."
"It's time to rest," said Balfruss, moving closer. "This isn't the way."
Tammy entered the square behind the student. If he turned his head even slightly he would see her creeping up behind. Doing her best to avoid the rubble, she slowly moved towards him as Balfruss approached from the front.
The student looked up suddenly and Tammy froze, willing him not to turn around. "What will we become?" he asked, suddenly alert. "Now that the Red Tower is gone, who will teach the children?"
"I don't know," admitted Balfruss.
"They can't kill us all, can they?" There was a hint of desperation in his voice, as if he thought it might be possible.
"No, they can't," said Balfruss, finally reaching the student's side. He laid a hand on the boy's shoulder, connecting him to the present. "They tried in the past, but it never works. They're scared because they don't understand. Garvey was right about that."
That caught the student's attention, and Tammy's. Focusing more on where she was placing her feet Tammy started to tiptoe forward again. She didn't know if Balfruss was aware of her presence but it didn't really matter. Stopping the rogue mage from destroying more of her city, by whatever means necessary, was her first priority.
"He was?" asked the boy.
Balfruss's smile was sad. "We've held ourselves apart for too long. To us the Red Tower was just a school, but to everyone else it was a dangerous mystery."
"We just wanted to learn," said the boy. Tammy could see his shoulders were shaking as he wiped at his face. "We didn't ask to be born this way."
Tammy was almost within arm's reach of the mage when he finally noticed her coming up behind. He spun about and at the sight of her sword and uniform energy began to gather in the palms of his hands. It dwindled and then vanished as Balfruss clubbed him across the back of the head. The Sorcerer lowered his axe and gently eased the boy to the ground.
They stared at one another in silence noting the changes until Balfruss gestured towards her sword. "I've not seen that in a while." He lowered his axe and raised an eyebrow. Taking the hint, she sheathed her sword, looking around at the damage. Apart from the fountain it was minimal. The building on the other street seemed to have sustained the worst damage.
"There was just the two of them," said Balfruss. "Unfortunately, I had to kill one. Now that we have this one, I'm not really sure what to do with him," he said, gesturing at the unconscious figure at their feet.
"We need to talk in private," said Tammy, noting the faces watching them from the surrounding buildings. "And I have an idea about that."
Balfruss stared at the walls of the eight-sided cell with a mix of wonder and surprise. She'd brought him to the secret cells beneath Unity Hall. It was where she'd previously brought Fray to summon the spirit of Guardian Brook.
"These are ancient," he muttered, tracing a hidden symbol with his fingers. To her it was just a blank wall, like every other part of the cell, but to those with magic it was a rich tapestry.
They put the rogue mage inside and she locked the door. Balfruss was still staring.
"What is it?" he finally asked. "And why is it here, beneath Unity Hall?"
"I have a theory, but there's no one alive to confirm it." Tammy gestured for him to follow her back to her office. She would see that the prisoner's basic needs were met until they worked out what to do with him. Unfortunately, it would mean trusting someone else with the secret of the special cells. Tammy considered who she could trust as they retraced their path through the building.
"I must be brief. I have to speak to the Watch Captains and then report to the Queen about what's happened," she told him, gesturing at one of the seats in front of her desk. Normally she would have moved to sit behind it, but instead she sat down beside him. It was a small thing but Balfruss noted the difference and smiled at the gesture.
"It was you, wasn't it?" she asked. "You defeated Garvey."
Balfruss's smile faded. "Yes, and now I must hunt down those who followed him. They're too dangerous to be allowed to roam free."
"Will the cell hold him?" asked Tammy. Fray had tried to use his magic while inside but he wasn't as powerful as others.
"It will, but he cannot live in there for ever. I have an idea for something long term—"
"They'll need to stand trial first," she said.
"Would Queen Morganse really order their deaths?"
Tammy shook her head. The idea of sentencing any children to death was one more decision that she didn't envy the Queen having to make. "I don't know. Perhaps, given their crimes. But he's not going anywhere for a while."
"Then I'll trust he'll be safe in your care until I return," said Balfruss, moving to stand up. He stopped when she touched him on the hand. "What is it?"
"What happened with Garvey?" she asked.
"He was my friend," said Balfruss, his voice thick with emotion. "And I crippled him."
"He had to be stopped," said Tammy.
"He did, but, like the boy said, what happens now?" asked Balfruss. "What will those with magic become in the years ahead?"
Tammy had no answers but like Balfruss she was worried about the future. The tide continued to move only in one direction. Even this latest incident would be used as another example of the dangers posed by magic. How everyone was better off without it and that they should kill or shun those born with it. Nothing would be said of how the rogue mages had been stopped or who was responsible.
Time weighed heavily on them both and the future for mages and children with magic seemed bleak.
# CHAPTER 34
Tianne stared at her new uniform in the mirror. What had once made her feel so proud no longer filled her with the same joy. A second blue star had been added to her uniform, denoting her as first among the Regent's cadre of mages.
There had been a small ceremony in the palace with the Regent, two of his wives, plus all of the mages in attendance. The room had also been lined with Royal Guards, their multi-coloured uniforms creating a strangely bright background to what was an otherwise sombre event. It should have been a wonderful day. One that she would remember with great joy. Tianne didn't expect a parade or weeping crowds chanting her name, but she had come back to Zecorria based on a promise. That if she served the Regent faithfully then by working together they could change the country and change how people viewed mages.
So far little had changed.
The Regent had explained that it wasn't safe to give her the accolade in public, which spoke volumes about the progress that had been made. This was in spite of their efforts to rid the city, and now beyond into the surrounding areas, of charlatans who exploited desperate people.
She had been the first to take the risk of coming home and her reception had been the worst. A cynical part of her wondered if that was why the Regent had given her this honour. Out of a sense of guilt about what had happened. Kalina had briefly been put in a cell, but the others who came after had not suffered at all. They'd been treated as honoured guests. Moved directly into comfortable quarters and had received fitted uniforms. They'd been put to work after only a few days. And now there were ten mages in the cadre.
Tianne didn't want to leave her room. She didn't want to see the smug faces of the Royal Guards waiting in the corridor who were her constant shadows. They were only there for her protection, of course, not because she was a prisoner. Despite not being able to go anywhere by herself outside the palace walls.
People were slowly getting used to seeing mages in uniform walking through the city. They wouldn't risk offending the Regent and, even if they tried, any of the mages could take care of themselves. Crudely trained as they were, even the weakest of the cadre could push back an angry mob long enough to run. The patronising smiles and constant reassurances that it was all for her safety were starting to wear a little thin.
There was a rapid knocking on the door and a moment later Kalina bustled into the room, not waiting for permission to enter. Tianne was about to ask her what she was doing when she was struck by Kalina's expression. A second later she saw the tattoo.
"What have you done?" asked Tianne, pointing at her face.
Tattooed above Kalina's right eye and just below was an intricate design comprised of overlapping black sickle shapes. The one above her eyebrow had been made to resemble Tianne's scar.
"Do you like it?" asked Kalina with a big smile. Tianne bit her tongue to stop herself from saying the first thing that came to mind.
"What is it? Why have you—"
"It's to show our loyalty," said Kalina. "To the Regent and to our country. This way, even out of uniform, people will know us and who we serve. They wouldn't dare risk causing offence to the throne. I thought you'd be pleased."
"I'm just so surprised," said Tianne, forcing a laugh. She noticed that the skin was still inflamed on that side of Kalina's face. "Did it hurt?"
"Only a little, but it will be healed up in a few days." Kalina shrugged as if what she'd done wasn't significant. "You gave us the idea for this."
"Me?" said Tianne, putting a hand over her mouth in shock.
"It was just after you rescued me from the cells."
"You did that by yourself," said Tianne.
"You told me about the warrior monks in the desert." It was true. She'd told Kalina about the Jhanidi who tattooed their faces. This was so that any person who met them immediately knew who they served. To offend them was to offend the Desert King and no one would dare in the far east. "The Regent was very impressed by our dedication."
Tianne was only half listening. She was still in shock by what she'd inspired. She'd told Kalina that story to show her that mages were treated better in other parts of the world. In time she'd hoped the people of Zecorria would see magic as a good thing. But they weren't ready yet and now the tattooed children would only inspire fear.
"Wait, did you say our dedication?" asked Tianne, glancing at Kalina.
"We've all had it done," she said with another broad smile. Tianne was horrified but found herself copying the other girl's expression as she teetered on the edge of hysteria. "I'm proud to be a mage," said Kalina. "I shouldn't have to hide or feel ashamed of my power. That's what you talked about."
"Yes. It is," said Tianne, a wild laugh bubbling up from inside. She couldn't believe Kalina and the others had been so stupid. They had permanently branded themselves and tied their fate to the Regent's. Right now, he was on the throne and in favour of mages, but only a few months ago he had banned all Seekers. Rumours had indicated he was about to ban all mages until Garvey's rampage. It would take many years before the people would trust mages and by then Choilan could have been replaced. Or he could have changed his mind to protect his position and keep the people happy.
"So, do you like it?" asked Kalina.
"It's amazing," lied Tianne and the girl hugged her, laughing as well.
"I nearly forgot," said Kalina. "That's not why I rushed in here."
Tianne felt her stomach begin to churn. "What's happened?"
"Garvey is here. He's being held prisoner below the palace."
"Are you sure?" It was hard to believe. Impossible, in fact. He was the most ruthless man she'd ever met and one of the most powerful Sorcerers in the world. Their cadre was a crudely trained group of infants in comparison. They couldn't have stopped him.
"I was spending time with one of the guards," said Kalina with a wink. For once Tianne was glad not to know all the details and didn't ask. "A patrol found Garvey near the southern border and they brought him back here."
"How did they restrain him?"
"He was injured when they found him. He'd been in some huge battle. Half of a village had been destroyed."
"What about his students?" Tianne was suddenly aware that they could be on their way right now to set him free. She wasn't ready. None of them were. Those who had fled with Garvey were older students who'd been studying at the Red Tower for years. They had more experience than her and were more familiar with wielding magic. They'd also spent the last few months on a rampage, killing or maiming anyone who got in their way. She didn't think they'd have any compunction about murdering a few more people, especially if they were holding Garvey prisoner.
"They vanished. Whoever beat Garvey sent them running. They probably fled south rather than face us."
Kalina's opinion of herself and the other Zecorran mages was vastly inflated. They'd never fought another mage, never even sparred against one in the dormitories. This cadre of mages was doomed to fail unless they were trained by someone with experience. Tianne had been doing her best to show the others some of the basics, but her own skills were still developing. She'd taught all of them how to sense magic in others and it was this skill that the Regent was putting to use. It was what happened after all the charlatans had been revealed or chased away that worried her. What would the Regent ask them to do next?
"Don't look so worried," said Kalina, misinterpreting her frown. "He can't hurt you any more."
"Why not?"
Kalina's smile made her skin crawl. "He's blind." Tianne swayed on her feet and Kalina grabbed her arm to hold her steady. "What's wrong? Are you all right?"
"You don't know what he's like. The things he did to us at the school." They sat down on the edge of the bed and Tianne put her head in her hands. Kalina put a protective arm around her shoulders. "He pushed all of us so hard. At least one student collapsed in all of his lessons."
"He sounds like a bastard."
Tianne didn't disagree but a small part of her wondered if Garvey had been right. Not his methods, of course, but the reasoning behind it. In his own brutal way he'd been preparing them for a time like this, when the whole world was turned against magic, and they weren't ready. She had walked into the palace and been soundly defeated by two unarmed thugs. That's all it had taken.
In the Red Tower they'd been living comfortable lives in seclusion, far away from the real world and its problems. Only Garvey and other teachers had been leaving the school to tackle them head-on.
"He's the most dangerous mage I've ever met," said Tianne, giving Kalina's hand a squeeze. "I'm not sure blinding him will make much of a difference."
"My friend told me some stories about what they've done to him." The way she said it made Tianne feel sick. She knew that Kalina expected her to ask what had been done but she couldn't.
"What will happen to him?" she asked instead.
"There's going to be a short trial, but the Regent also wants him to make a public confession."
"He won't do that," said Tianne, shaking her head. "Ever."
"He will, once they break him," insisted Kalina. "They tried beating him, but that didn't work. So they dropped him into a water cell, but he just froze the water and climbed out. They tried burning him, but the flames and brands couldn't touch his skin. At one point they hung him from his neck, but it didn't seem to have any effect. Why didn't he choke?"
Tianne shrugged, even though she could guess at some of the reasons why their torture was proving ineffective. Even without his eyesight Garvey could still freeze water and create a shield to protect himself from the fire. It made her wonder what else he could do and why he'd allowed himself to be taken prisoner.
"I want to go and see him," said Kalina. "I think I can persuade my friend to let me down there."
Tianne grabbed her hands. "Don't. Don't do it. He'll hurt you."
"He's chained to a wall. What's he going to do?" scoffed Kalina, proving what Tianne had suspected. She was incredibly naïve. "I'm not afraid of him."
"You should be," said Tianne. "He's incredibly dangerous."
"I'm so sorry," said Kalina, but her sympathy burned Tianne. "I didn't realise what they'd done to you at the Red Tower. I'm so glad I wasn't made to go there."
She didn't understand. In spite of all the problems Tianne had experienced with other students, the school had been a refuge. Garvey was only one out of many teachers, and while his presence loomed large there were so many bright spots in her memory. The most recent was time spent dozing on the grass beside Danoph and Wren, daydreaming about what they'd do once they became Battlemages in the real world.
"We'll make sure he suffers," promised Kalina with a smirk. Tianne tried to say something before she left but her throat closed up. The ease with which Kalina spoke about torturing someone scared Tianne. Garvey was a bastard and she knew he'd murdered people since the fall of the Red Tower. He deserved to be punished for his crimes, but torturing him for pleasure made her feel sick.
A few weeks ago she would have wondered how the Regent could allow it. Since then she'd made a number of disturbing discoveries from people working inside the palace. As long as she didn't leave the building Tianne could visit parts of the palace without her escorts.
In the last few weeks she'd been frequenting the servants' part of the palace. At first they'd been wary and her presence had made them uncomfortable. Once they realised she wasn't there to spy on them some had started to relax. Over time she'd become friendly with a handful of the kitchen staff, although many still viewed her with suspicion. Tianne was also still adept at getting people to talk. Several members of staff had told her about the meals being sent down to prisoners in the cells.
After that it didn't take her long to notice a pattern. Soon after one of the cadre apprehended someone with a minor Talent, they spent some time in a cell under the palace. Tianne had believed they were being offered a choice. To use their magic in service of the Regent or they had to leave the country. She'd even risked asking the Regent about those who were arrested and he'd given her the same story.
At first she didn't want to believe it, but after a while she couldn't ignore the truth. Faith in the Regent, for all that he'd done for her, made her think the best of him. Now she knew different. None of the people arrested were ever released.
It wasn't just the servants in the kitchen she spent time with. The wagon drivers loved to chat and were happy when she offered to help them unload. Without her uniform they didn't know who she was and assumed she was just another servant. It was when they refused to let her load the wagons that she knew. A quick look when one of the drivers was distracted confirmed it. Frohake's corpse had been covered with bruises and other injuries. It also looked as if someone had sliced open his chest then sewn it up again.
Since then she'd mostly kept to herself and stayed in her rooms except when she had to leave as part of her duties. Seeing his body made her wonder about many things. She thought about how easily Kalina and the others spoke about using their magic to hurt people. She thought about all of the mages with minor Talents rotting in cells beneath the palace and if they had even been given a choice. She wondered about the future of the cadre and her place in it. But mostly she wondered what would happen to her now that she knew coming back to Zecorria had been a huge mistake.
# CHAPTER 35
Wren kept staring straight ahead as she walked towards the raiders' camp. The last time she'd been here, five days ago, it had been to send a clear message to Boros. This time she was here to bring the fight to all of the raiders.
As Wren had anticipated attacks on settlements and the merchant trains had stopped. Boros couldn't risk sending people out in small groups to collect a tithe. She knew Wren had at least six mages, but not precise numbers. A small group of raiders working by themselves would pose no threat to one mage, never mind two or more. A bold move would have been to empty the entire camp of all raiders and risk everything in one huge fight. But Boros had no way of knowing what traps Wren had set up before showing herself so brazenly. It would also be an incredibly stupid decision. After their last encounter at Gillen's Jaw, Wren knew better than to underestimate her enemy.
And so Boros had been watching and waiting for her next move. If this was a game of Stones, Wren would have been doing the same. Playing it safe until the other player's strategy revealed itself. Now, after five days of careful planning, Wren was ready to make her next move.
The last time she had been here the camp had been a jumbled mess of structures with no fortification. Boros had not been idle since her last visit. A waist-high drystone wall now surrounded the front of the settlement in a wide semicircle. In addition, there were also two elevated watchtowers at the corners of the camp where raiders armed with bows watched her approach. Their weapons were strung but none of them had nocked an arrow. Not yet at least. A dozen more armed men and women knelt behind the wall, showing only the top half of their heads. Standing brazenly in the middle of the wall was Boros, watching as Wren walked closer. After five days of stewing Boros was struggling to hide her annoyance.
"What do you want?" asked Boros.
"I've come for your surrender," said Wren. A few of the raiders glanced around for other mages but she seemed to be alone.
"You want all of us to surrender to you?" said Boros with a laugh. Some of the other raiders chuckled along with her. One or two smiled at the notion, but Wren could see they were nervous. No one would be stupid enough to walk into their camp by themselves and start making demands. Hands were gripping weapons tightly, bows were being strung and they were all waiting for something more.
Somewhere nearby Wren felt a slow build-up of energy and couldn't help smiling at Boros.
"Lay down your weapons and surrender," said Wren. "In return I'm sure the Queen will give a fair trial to those who come peacefully. If you don't then—"
"Then what?" said Boros. "What will you do? Do you think I'm impressed by this?" she said, gesturing at Wren, before scanning the trees. "I know you didn't come here alone. Even you're not that stupid, girl. So, where are your friends?"
"Oh, they're not far away," said Wren, rubbing her forearms as her skin began to tingle.
"Neither are mine," said Boros, putting a hand to her mouth and whistling.
A dozen raiders appeared from the trees on either side of Wren. All of them were armed and focused on her. More raiders poured out of the camp until sixty or seventy of them were standing behind the wall. All of them were grim, weathered and seasoned warriors. These men and women, from across the world, had chosen this path and this life. They brutalised, stole and murdered other people and they liked it. Wren reminded herself of that as the pressure on her skin became worse. She could see there were a few raiders moving around inside the camp, but that could not be helped.
Boros was asking questions and making demands but Wren wasn't listening. It was just a dull buzzing sound, like the irritating drone of a fly. Instead she reached out towards what sounded like the rushing tide, drawing power from the Source into her body.
The energy coursed through her flesh, amplifying her senses until she could smell the fear sweat coming off the dozen raiders that surrounded her. They'd drawn the short straw. Boros must have told them she was a mage and they would have heard from the others about what she could do. Ironically, they would be the lucky ones.
The build-up of energy continued until it felt as if the air around her was writhing with insects, clawing at her skin. The air reeked with a sweet tang that made her nostrils twitch. Nevertheless, Wren took a deep breath and braced herself.
When Boros realised Wren wasn't listening she fell silent but kept searching for the source of the danger. Her instincts must have been screaming that something was about to happen, but she had no idea what it was.
"Now," said a voice. It was whispered in Wren's ear as if they were standing right beside her, but she was alone on the road. With that she knelt down and started weaving a dense shield about herself, adding layer upon layer as fast as she could make them. Thinking it was the beginning of an attack the raiders on either side rushed towards her with their weapons drawn. Arrows were nocked and Boros started shouting orders at her people on the wall, scanning the trees for the enemy.
The first fireball streaked out of the sky with a roar, trailing a line of black smoke like a burning comet. It was as big as two or three horses and even Wren marvelled at its size. With a huge crash that shook the ground it landed in the middle of the raiders' camp, knocking people down and setting buildings alight. The shockwave from the impact travelled outwards in all directions like ripples on a pond. Screaming raiders fell out of the lookout posts to the ground below. Those closest to Wren were knocked off their feet before they had a chance to attack. It wouldn't have made a difference. Her shield was too dense and the shockwave of the fireball rolled over and beyond, stirring the trees around her.
As Boros scrambled to her feet Wren saw her mouth widen in surprise. A dozen more fireballs, not as large as the first, were falling towards her camp. She started shouting orders but it was too little, too late. Tents and lean-tos were already on fire with men and women trying to smother the flames. The whole settlement was so focused on putting out the fire at the centre that they didn't hear the other fireballs racing towards them.
One landed in the middle of a group of raiders, scattering them like twigs while the unnaturally sticky flames set their clothes and hair alight. A few raiders started rolling around, while others tried to smother the flames, but some ran in a blind panic, spreading the blaze wherever they went. More fireballs hammered into the camp, burning flesh and scorching shelters until more than half the camp was on fire. And still more fireballs were falling.
A loud crack echoed through the air as the front door of the log cabin blew outwards. Smoke was filling the camp, making it difficult to see more than a few steps in every direction. Some raiders were trying to draw up water from the well but were having some difficulty as the rope had been severed.
In among the coughing and shouting, people began to scream as the horses charged out of the stables. The herd ran through the camp knocking down tents, stampeding over bodies and spreading the chaos until they burst out of the front. Those raiders who had been lingering beside the wall were too slow to move and many were ridden down. Horses jumped the wall until one stumbled in the smoke and knocked down a section of the wall. The rest took advantage and poured through the gap.
Raiders began running from the camp as well in the wake of the animals as a final volley of fireballs fell from the sky.
Wren stayed exactly where she was, totally focused on her shield, as the horses came thundering straight down the road towards her. All but one of them went around, avoiding her despite their panic. The hooves of the final horse clipped her shield, but the blow wasn't severe and she was able to maintain control. When the last of them was gone she stood up and reinforced her shield again.
A massive grey and black cloud had formed above the settlement, wreathing the surrounding trees in shadow. Their swaying limbs became the spectral arms of huge beasts dancing around the bonfire of the raiders' camp. The fire could not be stopped and it continued to spread. Soon everything would be consumed by the flames.
Seeing that it was a lost cause, bodies began to stream out of the settlement. Some crawled, others dragged or carried friends away from the fire and smoke. Everyone was coughing, desperate to breathe clean air. Their weapons and conflict with Wren were forgotten, but as they moved away from the blaze a few noticed her standing in the middle of the road. With a feral scream a burly woman raced towards her drawing a mace from her belt. With a sweeping gesture Wren flung her off the road. She heard the woman collide with a tree and tried not to wince at the dull crack upon impact. It could have been a tree branch or the woman's spine.
A few arrows rained down out of the smoke, peppering the ground all around Wren. A few impacted on her shield but they snapped, blunting the heads and turning the shafts into kindling. Boros came next with her bow and six more archers behind her on either side. All the raiders were stained with ash, bloody from injuries and on the verge of collapse. But, even now, they were more afraid of Boros than her, and quickly followed their leader's commands. Another volley of arrows flew towards Wren and she ignored them as she had the first.
"Surrender now," said Wren, amplifying her voice to be heard over the crackling flames and the collapse of timbers.
The raiders were watching her but one by one they all looked towards Boros for a decision. "Scatter," said Boros with a snarl. That was all it took. One word. She must have planned for such an eventuality as they separated into distinct groups and ran in several directions. Those on the ground unable to run were left behind despite their cries and reaching hands. Their former friends shook them off and ran, vanishing into the trees.
Boros was the last to go, stubborn to the bitter end. It must have been so galling for her. To be driven out of a country by a King was one thing. But to be burned out of her own home by a teenage girl was something else entirely. The hatred burning in her eyes was intense. For a moment Wren thought Boros would charge and try to kill her. Part of Wren wanted her to try, if only to beat her today and end the conflict between them, but that wasn't the plan. Instead Boros spat on the ground and strode away into the smoke.
A short time later half a dozen people walked up the road behind Wren and she breathed a huge sigh of relief. It hadn't been her idea to stand alone against the raiders, but she understood the symbolic reason for it. Despite that, it hadn't made it any less terrifying. Boros still had no idea how many people were in her community and how many of them were mages. The less information Wren gave her the better.
"You did very well," said Master Yettle.
"Very convincing," said Leonie, patting her on the shoulder. It was the smith who had summoned the huge fireball from the sky. Her knack with fire bordered on a Talent, but she claimed anyone could learn it and that her knowledge only came from working in a forge.
"We can't let the fire spread beyond the camp," said Wren, worrying about the forest going up in flames.
"We'll take care of it," said Leonie, walking towards the camp with Yettle and three other adults beside her. The flames began to shrink even before the smith set foot in the camp and Wren knew all fires would soon be extinguished. Master Yettle moved from body to body on the ground, tending to the wounded. There were perhaps a dozen lying in the road and she suspected there would be others inside the camp.
"It all went to plan," said Danoph, coming up beside her.
"The horses?" asked Wren.
"We managed to grab most of them down the road. I'm sure we can find the others before night."
"I still wonder if we should have tried to end it today," said Wren. "Maybe we could have grabbed all of them."
"Perhaps, if we'd brought everyone here, but you saw how quickly they scattered. She'd planned for this."
Ever since Danoph had told her about Boros being chased out of Seveldrom by the King, Wren had been turning it over in her mind. Wren didn't think she was the kind of person to make the same mistake twice. Somewhere in the back of Boros's mind she must have been wondering about Queen Olivia of Shael. She would only tolerate the presence of the raids for so long, even with her limited resources. Eventually she would muster some soldiers to wipe out the raiders and Boros would be forced to run again. But this time she hadn't intended to leave empty-handed. There was a second camp and a stash.
Wren didn't believe the money stolen from merchants and the local communities was in the burning ruins. Not one raider had tried to run back into the fire to retrieve the gold.
It was possible Boros would decide it wasn't worth the effort of staying in western Shael and just move on to another area or country. Part of Wren hoped that would happen, even though the raiders would then become someone else's problem. She still wasn't sure that when the time came she'd be able to kill.
Her instincts told her that Boros wouldn't leave. The raider hated her with a passion and she was not about to run. The west of Shael was as perfect a hunting ground for them as they were ever likely to find. She would regroup and then come after Wren and the others.
"Well, it's all set out. You're ready for what comes next," said Danoph.
"Maybe." He had more faith in her than she did in herself.
"It's time for me to leave," he said.
She'd been dreading this moment and couldn't stop herself asking the inevitable question. "Do you have to go?"
"You don't need me. You know what you have to do and you have people around you who can actually help. I just get in the way," said Danoph with a wry smile. Everyone appreciated his efforts in the community on a day-to-day basis, but his magic was so unique and limited it didn't help with their most pressing issue.
"I need you," said Wren. She'd already lost Tianne and didn't want him to go.
"This isn't goodbye. You'll see me again." He sounded so certain it was more than a little unnerving. She hugged Danoph tightly, not wanting to let go but eventually released him, wiping at her face.
"Are you going home?"
Danoph turned towards the east and took a deep breath. "Yes. I need to know why my mother sent me to the Red Tower."
"I hope you find some answers."
"Me too. I need to know more about my Talent," said Danoph.
"It's not just a Talent. Your magic is something else. Something I've never heard of before," said Wren, thinking back to when he'd summoned his power and given her insight into Boros's history. She'd told Master Yettle about it as well but he'd been equally baffled.
"Then it's time I found out what I'm truly capable of," said Danoph, sounding more decisive than ever before in his life.
# CHAPTER 36
Tammy glanced at the sign above the tavern door to make sure this was the right place. The Thirsty Ferret wasn't the nicest place in the city, far from it in fact, and as soon as she pushed open the front door a cloud of smells assaulted her nostrils.
Dried vomit, stale beer and suspicious meat that could even be ferret. The faces of the customers were surly and suspicious, as if they expected her to steal the clothing off their backs or the beer from their mugs. The sour owner was no better. With a face riddled with warts and a mouth stained blue from venthe she didn't make Tammy feel welcome. She merely grunted and jerked her head towards a door at the rear. It felt unusual to be out of uniform, but it had been a request she couldn't refuse.
With one hand resting on the plain short sword at her waist Tammy pushed open the door and followed the narrow corridor. She went past the grimy kitchen and approached the last room on the left. Before she had a chance to knock it opened to reveal the Captain of the Queen's Royal Guards, out of uniform, of course, but she still recognised him. He inclined his head and stepped aside before taking up his post outside the door.
The room was small to begin with but was overly cramped with just her and the Queen. In addition, there was a stack of beer barrels, boxes of old vegetables and sacks of rice. The Queen sat behind a rickety old table with her back pressed against the wall. Like the rest of the tavern the room was covered with dust and grime. Apart from the Queen the only thing that seemed out of place was the delicate green tea set on the table in front of her. Even in a plain grey dress there wasn't a person in the city who wouldn't recognise her.
"Majesty," said Tammy.
The Queen gestured at the battered chair opposite. "Keep your voice down. The walls are thin."
As she sat down the chair creaked alarmingly. Tammy felt it tilt to one side and thought it might buckle under her weight. "Captain Gardner didn't look too happy at this arrangement."
Morganse rolled her eyes and drained the last of her tea. "He thinks I'm taking too great a risk. I can't walk five steps down any street in the city before I'm stopped by a dozen people. If I talk to a stranger they only tell me what they think I want to hear. They're too afraid to speak the truth. This way I can find out what the people really think."
It made sense but given the current threat of rogue mages coming to the city Tammy agreed with the Captain. She'd spotted three Royal Guards dressed in plain clothes watching the street and guessed there were several inside the tavern, but, even so, it seemed risky.
"So, tell me about Balfruss," said Morganse, keeping her voice low.
"He was here, briefly, but he left again this morning. There was a sighting of another of Garvey's pupils in Zecorria."
"How many has he captured now?"
"Five. One died, and four are being held in prison awaiting trial."
Morganse poured herself another glass of tea. "Are you sure they're secure?"
"Yes. For the time being, although it's only a temporary solution." She'd not shared the arrangements of where or how the mages were held and so far Morganse had not asked. But she would, because they both knew this arrangement could not continue indefinitely. Balfruss was an effective manhunter, but he was not an executioner. The weight of what to do with them rested with the Queen. If they had been ordinary criminals they would be put on trial for the murders they'd committed and sentenced to many years in a labour camp or hanged from the neck until they were dead. But all of them were mages and, more importantly, children. Dangerous, cruel and violent individuals, but also children who had been misled and perhaps manipulated by a powerful and charismatic mage.
These pupils could not be put on trial in the normal fashion and even if convicted they couldn't be punished in the traditional manner. A swift death was perhaps all that awaited them. There seemed no other alternative beyond holding them in the special cell for the rest of their lives. It was cramped with four of them and there were others still out there.
"I haven't made a decision. Yet." It was clear that the decision was weighing heavily on her shoulders and Tammy didn't envy her.
"I have a suggestion." It was something that had been rattling around in her head for a while now. "But it's unprecedented here in Yerskania."
"Please," said Morganse, gesturing for her to speak. "At this point we're entering new territory."
"I think you should recruit Balfruss to work for you in a formal capacity."
The Queen chuckled but quickly stopped when she saw Tammy was serious. "Do you want me to offer him a role as the royal mage to the court?" she asked sarcastically.
"No, I had something else in mind."
"I can see you've been thinking about this for a while. All right, I'm curious. Tell me."
"Magic isn't going to go away. People blamed the Seekers and the Red Tower, and now they're gone, perhaps for good. I'm angry and horrified at how it was done, but I can't change the past. So, looking ahead, I think we need something new. Something different."
"Are you suggesting a magic school here, in Yerskania?" asked the Queen.
"No. That was one of the problems with the Red Tower. It was wrapped in secrecy. No one knew what happened inside and it created more of a division between mages and everyone else. We need to include them, not push them to the fringes."
"Then what are you suggesting?"
Tammy chose her next words carefully. She didn't want to reveal Fray's secret. "Treat them like everyone else. Make them sign up to the Watch and, if they excel, they can become a Guardian. I know what you're going to say, but it's not unprecedented."
Morganse sat forward in her chair. "What did you just say?"
"I've been reading some of the Old Man's journals, and based on a hunch I went further back and read those of his predecessor." Some of that was true but the Queen didn't need to know the whole story just yet. "There are several veiled mentions of special Guardians using unique abilities on unusual cases. Baffling mysteries or bizarre deaths that were swiftly resolved. I also have some physical proof that I can show you, if necessary."
"That's quite a claim." The Queen sipped her tea thoughtfully.
"I need to speak to the Old Man to confirm my hunch."
"It's an interesting idea, but there's still the problem of the children. How would you teach them?"
"Not to be indelicate, but Balfruss isn't a young man any more. He was already a teacher at the Red Tower. I'm confident he could persuade others to come here if it was safe."
"It sounds idyllic, but public opinion towards magic is the worst I've ever seen. Bringing the rogues to justice will help a little," conceded the Queen, "but it could be years before the hatred begins to ebb."
"I admit it's not a perfect solution, but I thought I would suggest it."
"You're right, we need to plan for the future. I will consider it carefully. For the time being I've informed all my agents to send any sightings of rogue mages directly to your office."
"Thank you, Majesty."
"I hope Balfruss can catch them all."
Tammy was confident he could stop them all, but the problem of what to do next loomed large in both their minds.
Tammy followed the Old Man through his house into the small garden at the rear. Much to her surprise she found a tidy patch of recently turned soil and small green shoots growing in uniform rows. A plum tree at the back provided some shade in the yard and a glass-fronted shed was overflowing with tools and clay pots. The Old Man pulled on a thick pair of gardening gloves and started yanking weeds out of the less tidy half of the garden.
When he saw Tammy's expression he grunted. "I can't sit around all day doing nothing during my retirement."
"No, Sir. Of course not." She couldn't think of anything more tedious than gardening. Then again, at least he had some hobbies.
"You wanted to ask me something?" he said, reading her expression.
"I had an interesting conversation with the Queen today," said Tammy, slowly lowering herself into one of his wooden garden chairs. Much to her surprise it didn't creak and showed no signs of stress. At this point showing care for furniture was a lifetime habit for someone of her size.
"Don't keep me in suspense." The Old Man pulled up another weed and slung it onto the pile. When she didn't reply he paused and glanced over his shoulder. "This is something about being Khevassar, isn't it?"
"I need an honest answer."
He pulled off his gloves and sat down beside her with a sigh as his joints creaked. "Ask your question."
"Before Fray, and before his father, were there other mages who worked as Guardians of the Peace?"
His sly smile was answer enough. "Of course, although it's never officially stated in the records. Like you, I was a few weeks into the role when I found a few peculiarities in the journals of my predecessor."
"What kind of things?"
"Oh, certain cases where a specialist Guardian was called in. They always had a codename, like the Shadow Fox, or the Red Kite, to protect their identity but it was obvious to me who they were. When I asked him about mages he told me the truth and showed me the special octagonal cell."
"I showed it to Balfruss. It was necessary," said Tammy, holding up a hand before he could protest. "He's hunting down the rogue mages and we needed somewhere to hold them. He'd never seen anything like it before."
"Do you want to hear my best guess?"
"Please," said Tammy, gesturing for him to speak.
"I think it was built by the Red Tower. Maybe it was done as a favour, or perhaps because the Guardians of old worked more closely with them in the past. So much has been lost to history, I guess we'll never know the truth," said the Old Man.
Tammy knew he was talking about magic but it also made her wonder about who he used to be. His identity and past had been erased on purpose. But at least there was a record of his deeds that covered a large portion of his life. It would stand as a testament and proof that he had lived.
"What will you do with the rogue mages?" he asked.
"I don't know. The normal way of doing things is impossible. The Queen has some difficult decisions ahead."
The Old Man grunted in agreement. A comfortable silence settled on them and for a time they listened to the muted sounds of the city. In the secluded garden they shared a brief moment of peace before the storm that was to come. He had done more than enough in service of the city and the country. The burden was now hers to bear.
"I should get back," said Tammy, wishing she could stay longer.
"It never stops," he said with a wry smile.
"Are there other secrets you're not telling me?" she asked. "About the Guardians and the city?"
He chuckled and slapped his knee. "Of course, but you don't need me to tell you. You've proven that you're more than capable on your own. You're ready to be the Khevassar without me looking over your shoulder." It wasn't the answer she'd been expecting, but at least it was an honest answer. "Even so, I'd still like it if you came by for a visit from time to time. I don't tend to get many visitors."
Being the Khevassar meant you had to pay a steep price but only now, as she stared at him in his little garden, did she realise how lonely the future promised to be. The whole city knew his name and his deeds but there wouldn't be many still alive he could call a friend. It was all there, waiting for her, in the future.
"I may still need your help with some difficult cases," she said, although from his smile they both knew that wasn't true. "It's always good to get a second opinion."
"Yes, it is," he said, fondly patting her hand. "I'd be happy to offer my expert advice whenever you need it."
They shared another smile and she quickly left the house before she started crying for him, but also for herself and what lay ahead, many years from now.
# CHAPTER 37
Tianne kept her smile fixed in place by gritting her teeth as she listened to her mother extol her virtues.
It was an awkward and staged meeting that the Regent had arranged for her as a special surprise. As the senior member of the Regent's cadre of mages she'd been asked to meet him to discuss their progress. Tianne had been under no illusions about it being a request as two surly Royal Guards had shown up at her door. She was fairly confident that if she'd refused they would have dragged her there by her hair.
Upon entering the room she'd found the Regent waiting, but also her parents. Their rictus grins were almost identical to hers and her father couldn't stop sweating. The collar of his new and probably borrowed shirt was turning dark yellow as perspiration continued to trickle down the sides of his neck. Her mother, always fussy about her clothes, had been shoved into a green monstrosity that showed off her ankles. No doubt once this farce was done she would go home and flagellate herself for such gross indecency.
The only person in the room who seemed relaxed was the Regent. He lounged in a corner sipping wine from a crystal glass. But then again, he'd staged this whole drama for her benefit, he probably thought it was a good thing he was doing for her. Trying her best to convince him that it was a wonderful surprise, Tianne relaxed her shoulders and unclenched her jaw, but her face still ached from keeping her fake smile in place.
Her mother's words sounded terribly rehearsed but no one else seemed to have noticed. As well as apparently being proud of her for becoming a mage, her mother had missed her since she'd left home. It was amazing that the Regent had been able to persuade her to say the words out loud. Tianne knew how much it must be physically hurting her to lie so much.
Her father had not said a single word since she'd entered the room. He was clearly afraid for his life if he refused to play along with this charade, but Tianne didn't know if he was petrified of the Regent or what she might do to him.
Every time she left the palace people stared. They were beginning to understand what the uniform with a blue star meant but despite her efforts Tianne was always met with suspicion and hostility. Even those people who had been tricked by charlatans were angry at her when the truth was exposed. Somehow it became her fault that they had been played for fools. The charlatan had given them false hope but perhaps that was better than none at all.
Tianne knew that in the right hands magic was a gift but part of her was beginning to wonder if the people would ever view magic as a good thing. If she helped them, healed them and kept them safe, would it make a difference? How long would it be before they trusted her? How long before she could leave the palace by herself?
To make matters worse the rest of the cadre had gone to the other extreme. They proudly wore their facial tattoos and expected to be treated with respect because of who they served and what they could do. They wanted the people of Herakion to show them respect without first earning it. Tianne knew a storm was brewing. Much like her time at the Red Tower when Garvey entered a room, she was constantly walking on eggshells around the other mages.
Her mother's litany of false praise came to a sudden conclusion and the awkward atmosphere in the room became unbearable in the silence that followed. Everyone was clearly waiting for something and Tianne realised from the way her father's eyelid was twitching that she was supposed to respond.
"I'm very touched by this," said Tianne, focusing on the Regent as she couldn't bear to look at her parents. "I'm so surprised I think I'm still a little in shock."
Her laughter wasn't faked and it eased some of the tension in her chest. The Regent's grip on his glass eased and a real smile returned to his handsome face. Tianne couldn't believe she'd been so naïve. Buried beneath the charm and kind words she could see he was a vicious rat, biding his time. He'd kill and eat his own mother if it kept him on the throne a little longer. She was merely a means to an end for him.
"You do seem stunned," conceded the Regent and Tianne laughed again. She moved across the room and took her mother by the hand. For a second she felt her mother start to pull away but then Tianne tightened her grip until it must have been painful. Not a single muscle twitched on her mother's face to show her discomfort.
"Thank you for coming to see me. It's so good to see you both." She included her sweaty father in her too-wide smile. He flinched but to his credit managed not to run screaming from the room. "I hope you'll visit again soon, but the Regent is very busy and I have my duties as well."
Her mother took the hint and squeezed her hands before letting go and turning to face the Regent. "My deepest apologies, Regent. We didn't mean to keep you from important business."
"Nonsense. I'm delighted to oversee such a happy family reunion." Tianne could see him watching her closely for signs of discomfort. Tianne almost jumped out of her skin when her father rested a hand on her shoulder but she forced herself to relax.
"Well, I'll leave you three to catch up. You must have so much to talk about," said the Regent, moving towards the door.
The three of them stayed in exactly the same positions until the sound of his footsteps had receded down the corridor. When they were sure he was gone Tianne shook off her father's hand and moved across the room to put some distance between them. The fake smiles slipped and the fear that had been just under the surface became more apparent.
"They threatened us," gasped her father, speaking for the first time. Tianne thought he looked much older than the last time she'd seen him a few years ago. There was now a peppering of white in his hair and he was thinner than she remembered. It made him look frail. Growing up she'd not thought of her parents like other people. In her mind they never aged and would live for ever. Now she understood they were just as human and just as flawed as everyone else. "If we didn't come to the palace they suggested our house might burn down in a freak accident. We could have ended up as beggars living on the streets!"
"It's true. They've done that to others," lied Tianne. She had no desire to comfort him or quash his fears. Her father stared at Tianne with horror while her mother just sneered.
Once again all of this was somehow her fault.
Many times in the past Wren had told her that no matter what she did it was never good enough for her mother. It was an impossible standard to meet. Tianne would have preferred that instead of being ignored. At times it felt as if she'd been an accident, although they'd never said that to her face. She believed her parents resented her for being born. For intruding on their life and as such they had refused to change their ways to accommodate her. It was why from an early age she'd sought out others for companionship and guidance since there was none to be found at home. She'd placed too much trust in the wrong people and they had led her astray, filling her head with lies.
Tianne hadn't been sure how she'd feel about seeing her parents again. She hadn't expected a tearful reunion with apologies, but their continued blame was another reminder of why she'd been glad to leave. Just being in the same room with them again made her angry.
"Where are you going?" asked her mother as she opened the door.
"Stay here for an hour and then leave."
"But what if—"
"Stay here," said Tianne. Blue flames erupted on the palms of her hands as she vented some of her anger. Her father whimpered and hid behind a chair while her mother just stared at her with distaste. Unable to even look at their faces any more she left the room in a hurry.
Whatever the Regent had intended the reunion to achieve it had failed. More than ever before she resented her parents and now hated them on sight. Any illusions in her mind about the Regent being a benevolent saviour were also being eroded. As she mulled over the future Tianne didn't notice where her feet were taking her until she began to descend several flights of stairs. Pausing on the first level of cells she wondered if this was a good idea. The worst that could happen was that they put her back in a cell. Only this time if they tried she was determined not to be such an easy target.
It took a bit of dodging patrols, fast talking and at one point a threat to use her magic before she was finally admitted to the deepest cells beneath the palace. Tianne knew she'd have to deal with more of the same on the way back up, but right now it didn't matter.
Emotions were churning through her, making her reckless and angry. Normally she would never have lashed out with her magic but the guard had been in her way and she'd just snapped.
Part of her also needed someone to blame for all of this. For all of her problems but also the growing hatred towards mages. She needed to see him for herself. Part of her still didn't believe it was true.
The smell has been growing worse for a while and as she set foot in the lowest cell block Tianne couldn't help gagging. It was a horrific mix of rot, stale, sweaty bodies and rank piss that made her nose twitch. There were no lanterns outside the cells and only one pathetic torch beside the bottom step. It gave off enough light for her to see the winding staircase and little else. The cells were in absolute darkness but she could hear someone breathing in the heavy silence.
Tianne shivered and her breath frosted on the air. Her anger began to ebb away as she found herself alone, deep beneath the earth, surrounded by a dense blackness.
Even without looking in the cells she knew he was there. She could feel him. The loud echo of his magic pressed against her senses. It was just as strong as she remembered, making her question again why he'd let himself be taken prisoner.
"You've come all this way," said a harsh whisper in the darkness. "May as well take a look."
Taking a deep breath to steady her nerves Tianne summoned a small globe of light. The shadows reluctantly peeled back but not enough to see right to the back of the cells. She could only hear one person breathing so she purposefully avoided looking into the other cells. Out of the corner of her eyes she saw ugly, twisted shapes and heard the buzzing of flies. The further she went the worse the smell became until it was so ripe it made her eyes water.
In the last cell on the left she stopped and peered into the shadows. Apart from a moth-eaten blanket and a bucket the cell was empty of furniture. A thick coil of chain, with links as wide as her wrist, ran from the wall to one of his skinny ankles. His skin was pale and bruised, much like the rest of him, where it wasn't covered in filth or dried blood. He was sitting against the back wall and most of his face was hidden in shadow, for which she was grateful. Tianne had no desire to see his face again.
Part of her wanted to just turn around and run back up the stairs. She didn't have to prove anything to him. He wasn't her teacher and she wasn't a student any more.
"Come to gloat?" asked Garvey, his breath rattling in his chest. He'd lost a lot of weight since she'd last seen him. They were probably starving him until he agreed to make a public confession.
"I wanted to see if the stories were true. I was told they've been torturing you to try and get a confession."
Garvey's harsh laugh was just as she remembered. "They were very creative for a while but seem to have run out of ideas. I don't think they know what to do with me now."
Tianne wanted to hate him. To laugh at him for finally being caught and humbled. To hurt him with harsh words or even her magic, but instead she felt hollow. A part of her was also still afraid of Garvey despite him being such a pathetic creature now. Tianne couldn't help laughing at herself for that. The heavy drumbeat of his connection to the Source was almost as unbearable at this distance as the stench.
"Have we met before?" he asked.
"I'm Tianne."
"Ah," he said and smiled. "I hear you're first among the Regent's mages. You must be very special."
Tianne laughed. "I'm a prisoner, just like you, only my cell has a soft bed and a window."
"A window wouldn't be much use to me," said Garvey, leaning forward. Tianne gagged at the sight of his face and put a hand over her mouth to stop herself from screaming. Both of his eyes were gone. It looked as if they'd been burned out. The empty sockets were surrounded by pink and red scar tissue.
She turned her face away but it didn't matter. The image remained etched into her mind. "Why did you come here?" asked Garvey.
"I told you," she said.
"No, not my cell. To Zecorria. Why come back? Weren't you happy in your new life with Wren?"
"The Regent declared an amnesty. He wanted loyal magic users to protect him and the people from rogue mages. I came because of you!"
"That's a lie," said Garvey, settling back against the wall. Mercifully the top half of his face was in shadow again. "Don't blame me for your decision."
"You murdered people. You betrayed the Red Tower. Everything you told us was a lie." Tianne's voice echoed around the cells, over and over until it disappeared into the dark. "How could you do it?"
"The school was doomed. Something new needed to rise from the ashes." After everything that had happened to him and the school, he seemed without remorse. "But you didn't answer my question. Why did you come back?"
Another angry reply was on the tip of her tongue when Tianne stopped herself. What she'd told him was a lie. A small part of the reason for coming back had been about helping people, but the other reasons were selfish. She could have stayed in Shael and helped others there, but somehow she'd convinced herself coming home was more important. That if she was seen doing good work in Zecorria the people would see her as a patriot. She would be a hero. Then her old friends, and perhaps even her parents, would be full of regret and guilt about how they'd treated her.
"I wanted to prove them wrong. To show them I was special."
"You are special," said Garvey. "From the moment you felt the majesty of the Source. It set you apart from others."
"Magic doesn't make me better than anyone else." Tianne didn't know why she was telling him. Perhaps it was because she had to lie to everyone else about her true feelings.
"No, it doesn't. Magic is a tool, and like any other, it can be a dangerous weapon in the wrong hands." Tianne watched as a cherry-red mote of fire danced across his knuckles like a coin, moving from one hand to the other and then back again.
"I'm just as selfish and arrogant as you," she said. "I thought the Regent was creating a cadre that would help people, but so far all we've done is brutalise those with minor abilities. We're just a bunch of thugs."
The other young mages were nothing more than blunt instruments. They had no formal training, beyond what Tianne could show them, and once they'd learned control they stopped coming to her for help. To them magic was nothing more than the physical manifestation of will. She'd tried to explain that they could do so much more with magic. That with training a mage could heal people and that Talents gave them unique and wonderful abilities. They didn't care. With their magic under control they couldn't be brutalised, and with the Regent standing behind them they had been transformed from victims into bullies.
"You've had better training than them. So why don't you leave?"
"And go where?" said Tianne. He made it sound so simple.
"I heard about Wren's community. It sounded like she was helping people."
Tianne shook her head. "I can't abandon the others. They're not evil, they're just drunk on power."
"Are you their keeper? Their mother?" he asked. She wasn't either but Tianne still felt responsible for them.
"You made a mistake. Stop punishing yourself," said Garvey. "You don't need to pay penance for the rest of your life by staying here. You can just walk away."
"Why?" said Tianne. In all the time she'd been at the Red Tower he'd never spoken to her this way before. He'd endured much in the last few weeks but it seemed like a dramatic and sudden change. It was as if she were talking to a completely different person. "Why are you here?"
"I was captured."
"Now who's lying?" said Tianne, surprising herself. She would never have dared speak to him like this in the past. "I can feel your connection to the Source. It's just as strong. Why would you let yourself be subdued and locked in a cell? Why would you let someone blind you? Is this all part of some bigger plan?"
Garvey's smile showed too many teeth and even now he still had the power to unnerve her. "Those are the right questions." He turned his face away and coughed up something that he spat on the floor of his stinking cell. "Forgive yourself and leave Zecorria. Go back to Wren and help her create something new. She will welcome you back with open arms. You made a mistake, but you can choose something new. It's not too late."
"Is this your penance?" she asked, gesturing at the cell. "Are you punishing yourself for what you did?"
"Yes, but I never imagined what it would reveal."
"I don't understand."
"Neither did I," admitted Garvey. "Not until now."
In spite of everything she saw him grin. Tianne felt as confused as ever about him. She wanted to hate Garvey for what he'd done, murdering innocent people and his treatment towards all of the students at the school. But part of her was beginning to realise she'd never really known him at all.
Feeling overwhelmed, she hurried away from the cells and made the slow ascent back to her room. Just as she was rounding a corner Tianne ran into someone coming the other way.
"Are you all right?" asked Kalina.
Tianne didn't know how to explain what she was feeling. The guilt. The self-loathing and anger churning inside about her parents and the Regent. She tried to put some of it into words, but failed and found herself crying.
Kalina pulled her close. "What happened?"
"I went to see Garvey," she managed to say between sobs. Kalina swore under her breath, blaming him for her current state of mind. Tianne said nothing as it was far easier than telling her the truth. She couldn't trust what Garvey had said to her. He was an expert at lying and deception, but one fact remained. It had been a grave mistake coming back to Zecorria. She had to escape as soon as possible.
# CHAPTER 38
As Wren had expected, Boros's hatred for her meant she couldn't move on without getting revenge. Her pride wouldn't allow it. But after their previous encounters, Wren didn't presume that rage had made her enemy reckless or stupid.
After the destruction of her camp, Boros and the surviving raiders had fled, but Wren was confident they wouldn't have gone far. Once she and her friends had gathered up the horses they set off for home, taking the most direct route. Laila had noticed the wide trail they were leaving and had commented about it being easy to follow.
"That's the idea," said Wren.
At least fifty raiders were now standing in line waiting for the order to attack. Boros was at the centre of the line with a bow in one hand and a grim expression on her face. Wren wasn't sure how Boros expected this to be any different from their last battle, but she was ready for the unexpected.
Beside Wren were half a dozen young mages and Leonie the blacksmith.
As she'd expected the raiders had followed their tracks all the way back to their community. And now they were trapped at the mouth of their valley with no way out, except to retreat or to go through the raiders. Or so it seemed.
One raider struck flint and tinder, setting fire to a rag before moving down the line, lighting arrows. Even from where she stood Wren could feel the waves of hatred rolling off Boros. She was going to throw everything into this fight. There would be no retreat and no mercy.
"Ready," shouted Boros, raising her own bow with its flaming arrow. Half of the raiders followed her lead while the others drew their weapons. "Loose then shoot at will!" she shouted. Drawing back her bow, Boros sent her arrow high and more followed, arcing up into the sky. Wren and the others tracked their movement and when they reached their peak she tapped Kimme on the shoulder. She raised both hands and tightened her fists, instantly extinguishing the flames. Making a twisting motion with one hand Kimme shattered all the arrows as they began their descent. Laila wove a shield above their heads while around them bits of wood and metal began to rain down like a freak storm.
While Kimme was doing that half of the raiders began to charge with spears and swords held ready. The archers stayed back and sent more volleys as fast as they could. Boros had dropped her bow and now ran forward with the others. No doubt she wanted the pleasure of being the one to kill Wren herself.
"Can you manage the arrows?" said Wren.
"We'll be fine," said Kimme, smiling at Laila who was still nervous about using her magic. "You take care of the others."
"Toree, watch for anyone trying to throw something," Wren warned him. It was possible one of the raiders running towards them might throw a dagger, a spear or even have a crossbow. As the raiders approached Wren noticed they were all carrying a water pouch. Normally it wouldn't have been something that stood out in her mind but it was a strange thing to have when going into battle. And for every single raider to have one was even stranger.
She expected Boros and the others to charge until they were able to use their weapons. To prevent that Wren nudged the other young mages beside her to do as they had practised. Working together they wove a wide shield six feet in front that extended across the mouth of the valley. To the naked eye there was nothing to see. No disturbance in the air to show its presence, but if the raiders kept running they would rebound off it as if they had run straight into a wall. As predicted the first raider smashed into it face first, spraying blood and teeth across the invisible barrier. The others slowed and then stopped, feeling along the shield to find the edge. When they realised the shield extended to both sides of the valley entrance she thought they would retreat.
"Time for a drink," said Boros with a feral grin. All of the raiders beside her uncorked their waterskins and splashed the contents all over the shield. The thick viscous fluid made it difficult to see what they were doing and soon there was a solid black wall. They could drop the shield, rendering the sticky liquid useless but it would also mean they were open to attack.
"What's she doing?" asked Kimme.
A horrible thought started to creep into the back of Wren's mind. "Get ready to run," she yelled at those beside her.
A few more arrows rained down from overhead but Laila's shield kept them at bay. When flaming arrows fell they too were instantly destroyed upon impact, extinguishing the flames. Then one of the arrows struck the sticky black wall.
With a roar and a surge of bright yellow fire the combined shield burst into flames. The three mages beside Wren screamed as they felt part of the heat through their connection to the Source. Normally fire would rebound from a shield, but this was in permanent contact with an extension of their senses. The smoke and heat were also a problem, making everyone cough and splutter.
"It burns," said one of the young mages, rubbing the skin on her arms, looking for blisters.
"Drop the shield and run. All of you, go now," she ordered everyone.
The combined shield vanished instantly and the others ran. Without the shield to hold it upright the flames died down a little but not completely. Some of the black substance had been consumed but the rest fell to the ground in a flaming line. Wren summoned a gentle wind and sent the smoke back towards the raiders, aiding their retreat.
Boros had won the first round.
Boros sneered as the girl and her friends ran from the fire.
So far she'd only seen six mages and it was beginning to make her wonder how many there really were. Ten or twelve at most was her best guess. Despite the wind at her back the smoke blew into Boros's face, but she told her people to hold their position.
Caution. Especially now when it seemed as if victory was so close. She'd celebrate as hard as everyone else when the girl's head was mounted on a pike. Then she'd wave up at her lifeless eyes and raise a mug of ale.
The smoke continued to drift towards her and the others but eventually the fire burned itself out. The unnatural wind stopped and she signalled for her raiders to form up. Holding shields in front and weapons at the ready, they slowly walked down the path into the valley. Two groups of six went ahead. The rest stayed back with Boros in case it was a trap.
Before showing herself Boros had studied the valley. There was only one way in and one way out. If this next assault went badly she would pull back and starve out the girl and her friends. Mages or not, they still needed to eat. It wasn't the most heroic of victories but she didn't care and neither did her people. Once the girl and her friends were dead they could go back to collecting a tithe from every town and village in the west of Shael. Word was already beginning to spread about what she'd achieved. The law was tougher in other countries and Shael was looking more appealing all the time for bandits. With enough bodies she could expand her territory and push further east. But all of that was for tomorrow.
The first twelve went into the valley and didn't return. There were no cries of alarm or sounds of battle. After waiting a while Boros realised they weren't coming out. They were simply gone. It was a trap. The girl probably had all her people waiting in the valley below.
In the distance behind her a horn began to blare, over and over again. The ground started to shake and turning around she saw at least fifty riders coming towards her. Boros didn't recognise any of them but there were many young faces. She didn't believe all of them could be mages and intended to test her theory. If the girl expected her to run at their numbers she was going to be very disappointed.
"Archers, form up," she shouted, shoving those who moved too slowly. "Ready." She nocked an arrow and looked to her left and right, checking the line. They were scared but were still following her orders.
As the riders drew closer she judged the distance and then waited, her bow held ready. Just before they were in range the riders slowed and then stopped. At the centre of the line was a big woman with short blonde hair who seemed to be their leader. Oddly she wasn't carrying a weapon and neither were those beside her. Leaving the horses behind, the line of strangers started to walk towards her. They were making this too easy.
"Loose," shouted Boros, drawing and then releasing in one smooth motion. She nocked a second arrow and loosed again before stopping to see the impact. The big woman raised her arms and all the arrows in flight crumbled to dust. All along the line the enemy raised their hands and made strange twisting motions with their fists. Boros cried out in surprise as her bow snapped in three places. Beside her the others were all suffering the same fate as every bow was destroyed.
The mages continued to march forward and now Boros could see the expressions on their faces. Most of them were scared. They were just children playing at war. They knew nothing about suffering but she was happy to teach them.
"Prepare to charge," said Boros, drawing her sword and a dagger. With a great clattering of metal she heard others readying themselves.
"Fire!" someone shouted. Boros searched for the blaze but couldn't see anything. Then a six-foot wall of fire rose from the ground in front of the big woman at the front. The flames were bright blue but seemed like a normal fire as she could see it scorching the earth. Those beside her were waving their hands about as well and more fire appeared, creating a wall that began to stretch the full length of the line.
The collective heat from the flames reached Boros and she winced. The smell of burned grass and hot soil flooded her nostrils. Grey smoke rose up from the wall of fire as it burned the earth. The man beside her began to cough and splutter. Boros knew others would start to falter as well if she couldn't end the fight quickly. She needed to test the strength of the flames.
"Barker, break through the wall," she said to one of her men. He was big and strong and dumb as a rock. With a feral grin he hefted his axe and charged at the mages. The other raiders cheered and bashed their weapons together, creating a huge din.
Barker bellowed as he reached the fire and jumped. He passed through the fire and disappeared. Boros and the others fell silent and waited. Less than two heartbeats later he reappeared wreathed in flames. Screaming like a wounded pig he raced back towards them trailing black smoke. His weapon was forgotten as he tried to put out the flames with his hands before he burned to death.
Boros noted Barker was coming straight towards her and swung at him with her sword. She caught him on the temple with the flat of her blade and he dropped to the ground like a stone. She and several others tried to smother the flames with their coats but then something worse started to happen. The blue fire spread. It was far too sticky for normal fire and seemed to jump from one piece of clothing to another as if it had a mind of its own. Boros dropped her coat and tried her waterskin instead but the fire just hissed and continued to rage as if she'd poured lantern oil instead.
"Leave him," she told the others who stepped back from Barker. He'd stopped screaming now but his body continued to burn like a candle.
"Forward," shouted the big woman and the mages all moved six paces towards them. And with them came the wall of fire. It crawled across the ground, bending in places and occasionally showing gaps that were quickly plugged.
Creating the wall seemed a challenge in itself. Moving it was something else entirely. Those gaps suggested there were weak links among them and that was something she could use.
"Take three men and go right," she said, tapping one of her raiders. "Take three and go left," she said to someone else. "And make plenty of noise."
As her people split up Boros felt something slap her across the shoulders which sent her tumbling to her knees. Behind her, coming out of the valley, were the girl and the other five mages. All of them were using their magic as people all along her line started falling over for no apparent reason.
Those trying to get around the wall of fire were lifted off the ground by invisible hands and thrown backwards towards the rest of the group. In front the fire continued to creep forward. Behind Boros the girl and her friends were keeping her people off balance. Time was running out.
Boros reached under her shirt and passed a necklace to the man beside her. "Jarke, this necklace will protect you from the fire. I want you to charge through and kill the big woman in the middle. We'll be right behind you."
As she'd expected Jarke was dubious. It was a plain silver chain with a simple oval-shaped bronze locket. "Why? What's special about it?"
Boros leaned in closer and whispered. "It's magic. The locket itself is normal, but what's inside is special. Remember last year, when you asked me what I spent all my money on? This is it."
Some of his suspicion began to fade. "All of it? On that?"
"I swear by the Maker." Boros passed it across to him but held onto the chain. "I want it back after. You're not keeping it." His greedy little eyes focused on the locket and he licked his lips.
She waited until he agreed to return it before letting go. They were still losing the fight. Her people were being thrown off balance and knocked over like drunkards. No sooner had they regained their footing they were sent stumbling again.
Jarke slipped the chain over his head, took a deep breath and drew his sword. "I'm right behind you," said Boros, pulling two raiders close to her. "We all are." Jarke charged at the wall of flame screaming like a maniac. She waited a few seconds before following behind. As she'd expected the moment he touched the fire he began to scream and tried to move backwards. Boros hamstrung him from behind and he fell forward, temporarily blocking the fire and creating an opening. She jumped through and several others followed in her wake.
The mages were surprised and scared. This wasn't something they had anticipated. Some of them began to scream as she raced towards them with weapons drawn. Something struck Boros on her right shoulder, numbing her arm, but she held onto her dagger. With her left she hacked at the nearest person, cutting down a teenage boy, her blade biting into his neck. As blood spurted across her face the screaming intensified all around as her people went to work.
Something gripped Boros around the neck and she was lifted into the air. It felt like a rope but there was nothing to see. Behind her the fire continued to rage. Black spots danced in front of her eyes and she looked around to see who was doing this to her. One girl was staring at her with a fierce expression. Boros focused on her and threw her dagger. Her arm was still numb and her throw wide but the girl panicked and the pressure vanished.
Boros landed badly, twisting one ankle, but quickly scrambled to her feet. She was almost out of time and out of luck. A fist slammed into her jaw, spinning her head around. Before she could recover another struck her in the stomach, knocking the air from her body. The force was so strong she fell to her knees and began to retch, spitting bile and blood onto the ground. She wouldn't give up. This couldn't be the end. She tried to get up but her arms and legs wouldn't support her weight and she flopped down onto her face.
The heat from the fire dwindled and then faded. The screaming and sounds of battle had stopped. By the time Boros could breathe again she realised it was all over. Lying beside her on the ground were at least a dozen of her people. All of them were dead and she couldn't see any wounds. But there were also a few faces she didn't recognise which made her smile. They were bloody and gouged from steel, as they should be.
"You think this is funny," said a voice right before someone's fist hammered into the side of her head and the world turned black.
Wren stared down at the six dead people from her community and the bloody wounds they bore. Even Master Yettle had his limits and couldn't raise people from the dead. Six lives for sixty. That was how many raiders they had now captured.
The plan had been carefully put together and she'd been prepared for the need to adapt. It had all been going so well until Boros's final attack, which wasn't something she'd ever considered. For the raider to sacrifice one of her own people in such a merciless way was unimaginable. If not for the quick thinking of Leonie, who ordered everyone to drop the firewall, more lives would have been lost.
Boros and the others were being chained together and loaded into wagons that had been converted into prison carts. Many people from the community wanted to kill Boros and the others, to bring about a final end, but Wren knew it wasn't their place. Part of her wanted to do it as well to balance the scales. The urge quickly faded when she thought about the Red Tower and those who had died so that she and the others could escape. There had been enough killing.
Wren also realised that if she and the others in the community were going to have a future in Shael they could not put themselves above the law. Their magic did not make them better than anyone else. The raiders would be taken to the capital city and judged for their crimes.
"Are you ready?" asked Laila, once the prisoners were secure.
"Not really. I've never met a Queen before," said Wren. "But I'm looking forward to it."
# CHAPTER 39
Queen Morganse had just finished her evening meal when there was a knock at the door of her private dining room. She frowned and waited, expecting one of her Royal Guards to open it but nothing happened. There were two of them stationed at the end of the corridor and several more throughout the palace.
"Come in," she said.
Ben, her main contact in the Silent Order, entered the room. As ever, he was dressed in plain grey and black clothing and his shoes made no sound as he crossed the tiled floor.
"Majesty," he said with a deep bow which showed her that his grey hair was starting to go thin on top. Time seemed to be catching up with them both. "Given my news I thought it best if no one saw me."
Morganse thought she knew all of the hidden passageways in and out of the palace but he continued to surprise her. The thought of being alone with him in the room, when no one knew he was even there, was more than a little unsettling. If he was so inclined he could kill her and slip away without anyone knowing he'd been there. Thankfully that didn't seem to be her fate this evening.
"Please sit," she said, gesturing at the chair furthest away from her at the table. A little bit of prudence never hurt. "What's happened?"
Ben settled into his chair and rubbed his mouth as if trying to dislodge something sour. "It's not good news. The head of the Mining Guild was found dead this morning."
Morganse had met with the man on a couple of occasions and thought him as dense as the iron his miners dug out of the ground. But to his people he was a fair and effective leader. He didn't work for her but he was an important figure within the community. Yerskani steel might not be up to the standard of Seveldrom but it was an important commodity that was shipped around the world. "Was he murdered?"
"That's unclear at this time. However, I thought it prudent to investigate the man being considered to replace him. All of the miners seemed to be leaning towards one name in particular. Cal Hemsey. My people searched his home and found this."
Ben took something from his pocket and placed it on the table before sliding it towards her. Morganse caught the cloth pouch and tipped out its contents. A familiar and crudely made stone idol, of a benevolent mother holding a child, rolled onto the table. Akosh.
For almost two weeks Morganse had been wrestling with her decision. She'd asked the Silent Order to keep an eye on some of the people named in the list that Tammy had acquired. Her own agents were following the other less senior figures and were sending her regular reports of their activity. So far none of them had done anything untoward and were going about their daily lives as normal. The only anomaly, and the one trait all of Akosh's agents shared, was their ambition.
Until now she had thought the list acquired by the Guardians included all of Akosh's people in the city, but the death of the Mining Guild's leader seemed to prove otherwise. It made her wonder how many other followers Akosh had seeded around the city in positions adjacent to those in power. How many more agents should she be monitoring?
Ben's normally grave expression seemed distracted. "Is there something else?" she asked.
"I don't believe in coincidences," he said.
"Neither do I." Experience had taught her that even if she couldn't see the person pulling the strings it didn't mean they weren't there.
"This is the third death that struck me as unusual in two weeks. The first was an influential blacksmith and the second an important merchant. At first glance both deaths were not suspicious."
Morganse didn't like the sound of where this was going. "And now?"
"I made some thorough enquiries. It was difficult work," he said, rubbing his hands together. Morganse noted the dried blood under his nails and the swelling around his knuckles. She liked details but on this occasion was happy not to know what methods he'd used. "The thief who robbed the smith was quite skilled. It wasn't a random attack, although he didn't know who paid him. A very rare poison was used on the merchant, but once again the apothecarist who supplied it didn't have a name."
"And the people set to replace them? I take it you visited their homes as well?"
Ben reached into his pocket and placed two more identical idols on the table in front of him. Three murders in two weeks. Akosh was making a move on her city. Perhaps it was payback for the rededication of all her orphanages in Perizzi. Or perhaps that was merely a coincidence and her plan remained unchanged. Either way three murders in such a short space of time, in addition to the two previous ones Tammy had brought to her attention, indicated something was about to happen. If Morganse did nothing then the slow trickle effect of Akosh's people spreading across the city would continue.
Working alone they couldn't inflict significant harm, but if Akosh sent an order to even half a dozen of her people they could prove disruptive. Trade was the lifeblood of the city and if it was interrupted the knock-on effects would be far-reaching.
It was yet another problem she had to manage. This was in addition to the Regent and his continued demands that she ban all mages in Yerskania. The gall of the man was astonishing. Especially when everyone in the west knew about his amnesty for Zecorran mages. Her agents in the north also reported that his cadre was still small in number, and consisted of young people, which was both a blessing and a curse. While it meant they lacked significant training and experience it also suggested they were impressionable and naïve. Whatever else he was she knew Regent Choilan was a charismatic man who could be very persuasive. Either he or one of his three wives would find a way to bind the young mages to ensure their loyalty.
For the time being they had shown no signs of moving beyond the capital city but it was only a matter of time. Once all of Zecorria was secure his gaze would inevitably turn outwards. Before that could happen he, too, would have to contend with the will of the people who still loathed anything to do with magic.
In the meantime, she had to deal with the rogue mages who had fled south after the capture of their leader. Morganse still had no idea how that had happened or what to do with the few that Balfruss had already imprisoned. The idea of putting them on trial and then executing them for their crimes did not appeal. It would be right in the eyes of the law but she wasn't in the habit of murdering misguided children.
She also had yet to properly consider Tammy's proposal to set up magical schools in the country. The looming magical threat in the north made her consider it again, but her people's hatred of magic was still so raw she wondered at the wisdom of the idea. Yerskania would need some level of magical defence in the future, but the matter was not as pressing as Akosh and her agents. They could undermine everything she had worked so hard to build. Her life was dedicated to the safety of her people and she was not about to let a new cult destroy her legacy.
"Majesty?" asked Ben, interrupting her reverie.
"I was just considering my choices," she admitted. They were few and none were particularly appealing, but a decision was needed. So be it. She would make it and face the consequences of her actions. "This cannot continue."
Tomorrow more people could turn up dead and quickly be replaced by those loyal to Akosh.
"I agree, Majesty."
"The people you're watching, have you investigated those around them?"
"Yes, Majesty. We needed to know which were loyal and which are part of her network."
"How difficult would it be to find suitable replacements for all of those being watched on the list?" she asked.
"It would be relatively simple," said Ben. "There are several people vying for each role."
"That's good."
"What are you asking me to do, your Majesty?"
Morganse stared down at the idol and took a deep breath. When she felt calm she met Ben's gaze. "Eliminate them. Tonight. And make sure people know the Silent Order was responsible for a few. I want to send a clear message."
She'd given him orders before to take out certain targets but her decision made him pause. This was not one or two people. All of them had the potential to be dangerous targets, but so far none of them had done anything untoward. When Tammy had given her the list she'd hesitated. When the Dockmaster and Minister of Trade had died she'd hesitated.
She couldn't wait around any more to see what they did. It was too late to save those who had already been killed, but if she did nothing others could soon die in suspicious circumstances. Then her regret and compassion would mean nothing to those who suffered. Decisive action was needed.
"Are you certain?" asked Ben.
"Kill them all," said the Queen.
# CHAPTER 40
Tianne stared around at her room trying to find anything that she would truly miss. Her pack, containing all of her belongings, sat on the bed. It had been a lot easier and faster to gather everything up than when she'd left the Red Tower. Then she'd agonised over every item of clothing. This time she was only taking what was truly hers and would leave the rest behind. The only concessions were a new pair of boots and some warmer clothing for the journey south. Her experiences on the road last time had taught her to be ready for anything.
After shoving the bag under her bed she went for her last meal at the palace and then returned to her rooms to wait for midnight. When the building was silent and still she took a deep breath, wrapped her head and face in a long black scarf and retrieved her pack.
The sensible part of her mind was telling her to leave immediately. To find the shortest route outside, use her magic to climb over a wall and disappear into the streets. From there she had enough money to buy a horse, although sadly not the one on which she'd arrived. As part of his pretence of caring about her the Regent had attempted to find it, but unfortunately had not been successful. Tianne doubted he'd actually tried. It was yet another lie intended to make him seem like a compassionate man.
By bribing one of the stable boys she'd paid a different horse trader for a new mount, but had only given him half. The rest she would deliver in person tonight. If nothing else her recent experiences had made her a lot more cautious in all things.
Ignoring the sensible part of herself, Tianne followed her instincts. They were telling her to do something else. It was the part of herself that she wanted to ignore but it guided her feet down into the earth again. This time she had no need to argue or threaten any of the guards. Most of them were asleep at this hour and those who weren't she rendered unconscious from a distance with her magic. They never saw her face and would be unable to tell anyone which of the cadre had done it. For once not being the only mage in the city had its advantages.
This time when Tianne entered Garvey's cell block she was prepared for the stench. Even so the smell was so overpowering it still made her eyes water. The sputtering torch at the end of the cell block provided only meagre light, keeping the worst horrors in the shadows. A low hum filled several of the other cells as moving blankets of flies feasted on the rotting flesh of their dead occupants. She moved down to the last cell on the end and was grateful he remained wreathed in shadows. Only his feet were visible and she didn't summon a mage light to reveal more.
Garvey's breathing seemed incredibly loud in the dense silence this deep underground. Tianne's breath frosted on the air and she wondered how long he would make himself endure such horrors.
"Back again so soon," he whispered.
"I'm leaving. I came to say..." Tianne trailed off, not really sure why she'd come. Her instincts had told her she needed to see him one last time. To say something, but now she was here the words wouldn't come.
"Say what?"
"What did you mean the last time I was here?" It wasn't what she'd wanted to ask him, but it had been on her mind. "You said something had been revealed to you."
The echo of her words faded and the cloying silence returned. At first she thought that he wouldn't respond, but then he shuffled closer, the chains clinking with every move. Tianne braced herself for the grisly sight of his ruined face. Thankfully he'd wrapped a piece of cloth around his head, covering his eyes.
"Do you know how many Sorcerers there are in the world?" he asked. Tianne shook her head then realised he couldn't see her. "Four," he said, before she could respond. "And you met three of them at the Red Tower. Sorcerers are regarded as the most experienced and the learned mages in the world." Garvey's mocking laughter surprised her as it was so loud and bitter, echoing over and over again off the walls. It felt very out of place in this miserable hole deep underground.
"I don't understand."
"I can see so much now," he said, smiling ruefully at his choice of words. "As a Sorcerer I thought I understood the Source on a deeper level. In my arrogance I believed I knew the full potential of magic. I was so wrong."
"Is that why you're still here?" she said, gesturing at the filth around them.
"It's so quiet and there are no distractions. The peace has allowed me to clear my mind. Here I can focus on what is being revealed. Up there it's teeming with people. I can feel them all," he said, glancing at the ceiling. "Hundreds and thousands of them, scrabbling around in the city. They're like ants crawling across my skin. Don't you feel them?"
"I don't feel anything. We're too deep underground."
"Embrace the Source," he said, standing up and moving towards the bars of his cell. The chain on his ankle stopped him short and he glanced at it with irritation. Tianne felt a brief rush of power and then he simply touched the chain with two fingers. The metal chain dissolved and struck the floor as a liquid, splashing her on the face. Tianne wiped it away in disgust but then realised it had been transformed into water. That was impossible. In all the time she'd been a student at the Red Tower she'd never read or heard of such a Talent. Changing one thing into another was a fanciful myth that the ignorant used when talking about magic, like lead into gold.
"What do I do?" she asked.
"Open yourself to the Source," said Garvey, who was now standing at the bars of his cell. "Let it flow through you. Let it fill every corner of your body and mind."
Tianne focused and reached out towards the tide that always waited on the edge of her perception. Drawing power into her body from the Source was still a feeling that she couldn't put into words. Her senses became more acute, the shadows peeled back and the stench in the cells became even stronger, filling her nose with its putrid filth. Now she could hear the steady drip of water, see the pale green moss growing in the corner of Garvey's cell and the rodent-chewed corpse in the next cell. But all of it was insignificant compared to the warmth inside. It made her feel stronger, more confident, and with it she believed anything was possible.
"Reach out with your mind," said Garvey, his voice hypnotic in the gloom. "Let it drift up through the stone and beyond. Far above the city there's a hawk wheeling in slow circles. A murder of crows is watching, nervous about their chicks. Can you see them?"
Tianne tried to follow his instructions but all she could feel was the dense, immovable weight of all the stone above their heads. The earth around it was damp from a downpour and she sensed tiny specks of life as insects crawled and burrowed. Without channelling any power it felt as if she was trying to stretch a piece of string beyond its limit.
"I can't reach beyond the earth."
"Ah," said Garvey, but she didn't think he was speaking to her any more. His face was tilted towards the ceiling but she had the impression his mind was far away. A frown creased his forehead and Tianne felt a peculiar wave of nausea pass through her which made her stagger.
"What was that?"
"There's something here, in Herakion. A person. A being of immense power. It's old. So old and monstrous." Garvey gripped the bars of his cell with both hands and would have fallen as something invisible seemed to wrench him sideways. His knees buckled but he recovered and held himself upright. Garvey's smile was a mix of surprise and wonder. "I think it's aware of me. I can feel it searching."
The hairs on the back of Tianne's neck began to stand up and a primal urge to run started to build up in her chest. She released her connection to the Source but the awful feeling remained and there was a strange pressure in the air.
"Stop," she said, trying to swallow the lump in her throat. "Stop, stop, stop."
She was babbling but couldn't help it. Garvey had attracted the attention of something primal and dangerous. It was a predator and she was its prey. Her instincts were telling her to run far away if she wanted to live.
"What is it?" said Garvey.
"Stop!" shouted Tianne.
Garvey finally heard her and she felt him sever his connection to the Source. She was breathing heavily and sweat had soaked into her clothing. For a time neither of them spoke and merely listened to the silence. There was a strange itch between her shoulders and a strong feeling of being watched. The hairs on her arms were still standing upright and her heart thumped loudly in her chest. Slowly, so slowly, her sense of the other began to ebb away. Tianne fell to her knees, her whole body awash with relief.
They'd both come very close to attracting the attention of something powerful, malicious and far beyond their understanding. She should have ignored her instincts and listened to the sensible part of her mind. It seemed as if she hadn't learned. Garvey's expression was a reminder of everything she'd forgotten. While she was terrified by what had just happened he seemed elated at the discovery.
Garvey was dangerous. He didn't know when to stop and eventually it would be the death of him. She didn't belong here and had no intention of being caught up in his schemes.
Without saying another word Tianne ran from the cells, leaving him alone in the darkness. She never wanted to see him again in her life.
Tianne made it back to the ground floor without any problem and took a moment to catch her breath. The sooner she put some distance between her and this city the better off she would be. Now all she had to do was get out of the palace without being seen.
Just as she was creeping down a corridor a voice called out from the shadows sending her heart racing again.
"I knew something was wrong," said Kalina, moving into the light. She was fully dressed in her mage's uniform but so far hadn't embraced the Source. "Ever since you went to visit Garvey you've been different."
"It started long before that." There seemed no reason to lie at this point. "I don't want to fight you but I'm leaving Zecorria tonight," said Tianne.
"Tell me why? I need to understand."
Tianne sighed and leaned against the wall. She was just so damn tired. All she wanted to do was lie down and go to sleep. "The Regent doesn't care about us. The only reason he created the amnesty was to protect himself against Garvey and the other rogue mages. He said it was for the people, but he only cares about himself."
"What about the charlatans and the con men?" said Kalina. "They were hurting people."
"You're right, they were, but what do you think happened to them?" asked Tianne. "Do you think he let them go with a warning or a beating? I saw Frohake's beaten and bloody corpse. There's someone else rotting in the cell next to Garvey if you want to take a look."
A crack showed in Kalina's brave façade. "Why would he do that?"
Tianne shrugged. "Because he can, and who can stop him?"
"I can't believe the Regent would do that."
"He did." Tianne knew in her heart the Regent was a far worse con man than any of those they'd caught in the city. "There's already been too much violence against magic users. It needs to stop."
"You're running away."
"I'm surviving. He banned all Seekers and then, when it suited him, created the amnesty. If the wind blows south tomorrow he could change his mind again and ban all mages. You need to be careful."
"Stay. Help us build something different. Teach us how to fight. He can't stand up to all of us if we work together."
It was a noble idea and the sentiment appealed to her, but even Tianne could see it was naïve. If they stood up to the Regent he would wear them down or have them murdered in their sleep. The cadre was fumbling along with its magic and with only a couple of years' experience she wasn't the right person to teach them. They would lose if they ever came across a trained Battlemage or worse, a Sorcerer. Tianne knew that if Garvey really wanted to he could destroy the entire cadre by himself. There was also the real possibility he might bring doom to himself, and anyone nearby inside the palace, with his meddling. It was much safer to be far away from him.
"The Regent is cold and ruthless. They threw me into a water cell when I first arrived."
"I know, but that was just a mistake," said Kalina, making excuses for him. Her faith in him was admirable but misplaced.
"Was it?" asked Tianne. She'd thought about this a great deal since the Regent had apparently saved her. The more she went over it in her mind the more she believed it had been staged for her benefit.
"Come with me," said Tianne.
"What?"
"Tonight. Right now. We can leave together and build a new life somewhere else."
"Where would we go? How would we live?"
"I have a friend who can help us," said Tianne. She wanted to trust Kalina, and would tell her more about Wren and her community once they were on the road, but right now she couldn't tell if this was another of the Regent's ploys. "She's building a different kind of community."
Kalina considered it but eventually shook her head. "I can't. My father is here and this is my home. You should stay. We can find a way together to make it better."
"I'm sorry, I can't," said Tianne. "I should never have come back. I don't belong here."
"The Regent will be disappointed."
"Are you going to try and stop me?" asked Tianne, bracing herself in case she had to form a shield.
"No. You were right about one thing. There's been too much violence against mages. I'm not going to stop you."
"That's a relief," said Tianne with a smile. Kalina was perhaps the only thing she would miss about Zecorria. "Be careful. The Regent is not as kind as he seems. It would be safer if you pretended that you hadn't seen me."
Kalina nodded and turned away, heading back towards her room.
Tianne embraced the Source and crept through the corridors of the palace, listening for other people with her enhanced hearing, but she saw no one. She emerged into a courtyard and found the night was cool and crisp with faint grey clouds scudding by overhead. Taking a deep breath she tasted the air and wondered if she would ever return to Zecorria again.
Moving with purpose she crafted a crude set of stairs by freezing the air into blocks of ice. The surface of each was incredibly slippery but she took her time and eventually reached the top. By the time the sun came up the ice would have melted and she would be riding south. She glanced at the palace one final time and then turned her back on it and everyone inside.
# CHAPTER 41
Akosh gestured for Doggett to continue with his report but she wasn't really paying attention. She heard enough to pick up the main points but her mind was focused on a larger issue.
Doggett continued to tell her about the Regent. He'd now secured the capital city and all potential mages had been rounded up and either indoctrinated into his cadre or eliminated. Any charlatans had been beaten and were in hiding or they'd been murdered. Now he was setting his sights on expanding into nearby towns and cities. With twelve, previously thirteen, mages he'd begun to change the mood towards magic in Herakion. It was years away from a significant shift, but Zecorria was on the right path.
The thirteenth young mage had apparently run away, much to the Regent's annoyance. Attempts were being made to find her but Doggett said they weren't actually spending much time on it. He and Selina's other agents had more important matters to focus on, such as continuing to earn the Regent's trust and the respect of those closest to him. He and his first wife, Selina, were regularly relying on Doggett and the others which she would be able to use to her advantage in the future.
Akosh's mind kept drifting back to her meeting with Kai. She wondered if he knew about Selina's agents and that they were all loyal to her. Perhaps they could do some investigating to find out how many people he had in the city. Beyond the doctors and apothecarists she was willing to bet there were people hiding in plain sight just like some of hers. If she was going to make a move against him she would first need to secure the capital city.
"Mother?" asked Doggett, sensing her distraction.
"I'm listening," she said, gesturing for him to continue.
Kai had been so strong. Beyond anything she'd imagined. The only comparable experience she'd had was her first encounter with Nethun. The weight of his presence and vastness of his power had been humbling. One of her brethren had been driven to his knees. Part of her wondered how she could oppose someone almost as timeless and equally dangerous. Kai was worse in some ways as he was more devious.
He'd grown so powerful without the others noticing. But then they were always distracted by the mortals. They tended to focus on the larger issues of wars, the continual death of magic and political scheming between nations. And all the while Kai had been establishing a new following to grow his foundation, while gobbling up smaller gods and absorbing their power.
The image of her friends trapped inside Kai while he continually feasted on them still made her squirm. That was why she had to proceed with caution bordering on extreme paranoia. If he sensed what she was doing Akosh knew he wouldn't give her any kind of warning. She would go to sleep one night and wake up inside that abyss as he slowly drained the life from her. It would be a long, painful and very slow death. She would beg for the emptiness of the Void long before it found her.
Perhaps an alliance was her only chance of survival. Perhaps she should turn to her brethren for protection. He would never expect her to do that. Akosh couldn't believe she was even contemplating it, but in her desperation she was willing to try anything.
Despite the pretence of being a peculiar family, her kind rarely aided one another and many were in direct competition. Each was busy pursuing their own goals and it didn't profit them to help someone else become more powerful.
Every year there were more distractions for the mortals that took them away from religion. New pursuits created traditions of their own and sometimes this meant prayer was such a low priority it disappeared from their daily life. The mortals were always so busy chasing their ambitions, obtaining wealth or land, that faith became unnecessary.
It was why she continually saw new faces appearing at the banqueting table while others were forced to transform themselves in order to survive. She'd done it and had thought it made her powerful in comparison to her peers.
"Mother?" said Doggett. She realised he'd stopped talking a while ago. "Are you well? Can I help?"
"No. You can't. Be silent." As obedient as a trained hound he closed his mouth.
If she told Vargus the truth, or at least part of the truth, and begged for his protection then perhaps she could survive. She would not be a slave to Kai. He'd not given her any direct orders but had told her to continue as normal for now. Akosh knew it wouldn't last. Very soon he would send one of his people to her and ask for a favour. It would be something small and apparently insignificant but Akosh wouldn't be able to refuse. And if she said yes to him once then it would be increasingly difficult to say no after that. It would be the beginning of the end.
Would Vargus protect her? Or would he throw her to the wolves?
Despite her orders the sound of rapid footsteps in the corridor brought Doggett to his feet. His first instinct was still to protect her. He stood next to the door with a dagger held low as the runner approached. Someone frantically knocked on the door and Akosh could hear them breathing heavily.
"Yes?"
"Mother, I have urgent news," said a muffled voice.
"Come in," she said.
A red-faced woman she vaguely recognised stumbled into the room, wheezing and holding her sides while she tried to get her breathing under control. "A bird just came into the aviary. Bad news from Perizzi," she said.
Akosh had been expecting the opposite. Three more of her people were due to ascend to key positions of power in the city. It should have moved her one step closer to destabilising Yerskania and unseating Queen Morganse from the throne. "Take a moment, then tell me exactly what's happened."
Doggett had sheathed his dagger and handed the woman a glass of water. She sat down in the chair opposite and Akosh gave her a moment to compose herself.
"Something awful has happened, Mother," said the woman. Akosh was listening but couldn't help staring at the birdshit on the shoulders and one sleeve of the woman's jacket. That would be why she didn't recognise her. She'd never been in the aviary as it stank and she had no desire to be crapped on by a messenger bird.
"Did someone die? Was it one of my people?" she asked, refusing to call them children. It was a term she was starting to despise, much like when they called her Mother.
The woman began to cry and one of Akosh's hands twitched. She wanted to slap the woman hard across the face but that would only prolong the conversation. Instead she gripped her hand and gave it a squeeze she would no doubt interpret as comforting. "What has happened?" Akosh asked again, through gritted teeth.
"Everyone is gone in Perizzi, Mother. At least thirty-seven of your children are dead. They were all killed in one night."
"Who? Give me some names?"
The woman listed a dozen and Akosh held up a hand to silence her. Rohane had been her replacement for the Dockmaster and Tovin the new Minister of Trade. The others were all key figures spread out across the city, either in a position of power or due to inherit very soon.
"How did they die?" asked Akosh.
"Some had what seemed like accidents. They choked on their food. Three drowned and seven died in their sleep. It wouldn't have been unusual, except they all died on the same night."
It was possible Kai had done this but it seemed unlikely. It made no sense for him to tell her one thing only to do the exact opposite. He had an agenda of his own and for now it suited him to let her continue with her plans. That meant it was one of the human groups working against her. The Guardians wouldn't kill that many people. They would want them arrested and put on trial. Perhaps the mages from the Red Tower were moving against her and seeking revenge.
"Was there anything unusual about any of the murders?" said Akosh.
"At least eight were eliminated by the Silent Order. Their symbol was found beside the bodies."
The woman shuddered as she mentioned their name. The Silent Order. It was an ancient league of assassins that possessed a fierce reputation. Most humans were afraid of them as they seemed as elusive and difficult to catch as a shadow on the wall. It was rumoured they were responsible for the deaths of kings and queens and had shaped the course of history down through the centuries.
The reality behind the organisation was a lot more mundane. Akosh only knew the truth as, during her first incarnation as the deity of killers, she'd learned their secret. Despite the appearance of being an independent group who made their own decisions, the Silent Order had connections to Queen Morganse.
The group often carried out dirty work that left the hands of the Yerskani ruler clean. Their symbol was left beside a body when a clear message needed to be sent. At other times the murders were so carefully staged they were made to resemble accidents. Akosh wasn't fooled. The Silent Order had killed all thirty-seven of them.
"Why would they do it?" asked the woman.
"Why indeed?" said Akosh.
A few weeks ago she would have been distraught at the loss of so many of her children. She would have been crippled with grief, and raging. She would have gone on a drunken binge for days. Now, thanks to Kai putting the mortals and her true nature into perspective, she only felt irritated at their deaths. It was another serious setback to her plans in Yerskania but no more than that. She had other less prominent children in Perizzi and it would take her years to manoeuvre them into position of power, but she was not about to give up.
Her plans in Zecorria were continuing apace as her people made themselves indispensable to the Regent and his wife. Choilan would be the fulcrum she used to create a nation of her own, but this attack on her could not go unpunished. Especially when it was only a mere mortal she was dealing with.
"This was all Queen Morganse," said Akosh, thinking aloud. "She orchestrated it."
"Are you sure?" asked the woman.
Akosh ignored her question and gestured at Doggett to get rid of her. The sight of her was beginning to be a distraction. He escorted her from the room and returned alone a short time later. It had been a bold move by the Queen. It was one thing to find out someone was attempting to undermine your city from within every organisation with influence. It was something else entirely to cut them all out like gangrenous flesh. Sever the limb and with luck the infection wouldn't spread.
If those had been her only people in the city it might have worked. Akosh scribbled down a note and held it out.
"What do you want me to do, Mother?" asked Doggett, taking the message.
"Send this to Perizzi as soon as possible. A clear message needs to be sent to those who would interfere in my plans."
Until now she had worked hard to keep her name and identity a secret. It was starting to seem as if that no longer mattered. Both her brethren and the mortals were increasingly aware of her name and activities.
The Silent Order had left their mark beside some of the bodies. Now it was her turn.
# CHAPTER 42
Morganse was supposed to be reading the stack of reports waiting on her desk, but instead she was staring out of the window at the city below. It was still early in the evening but she had a half-empty glass of wine in her hand and it wasn't her first. Overhead the grey sky was turning black and spots of lights were appearing in the buildings as candles and lanterns were lit. The sea of glowing embers began to spread and snatches of music drifted through the air.
Despite the hour she was already tired. For once she just wanted to spend an evening sitting in the back of a tavern, drinking and singing along with the crowd. As a young woman, and not yet old enough to be recognised in public, she and some friends had sneaked out and done just that. Even though none of them had come to any harm the King, her father, had been furious. That night of revelry seemed like a long time ago.
She swirled the red liquid around the glass and drained the rest, not really savouring the flavour. It tasted too bitter and metallic, like blood. Perhaps she should have chosen a bottle of white instead.
The city seemed so quiet from up here. Everyone down there just wanted to live in peace. If only they knew the price of their freedom. She was contemplating another glass of wine when the sound of approaching footsteps drew her attention. There was only one person who walked like that who had access to her office. Morganse poured herself another glass and went back to the window.
As she'd expected Tammy came stomping into the room without being announced. "Do you know your assistant is asleep at his desk?" she asked.
Morganse glanced over her shoulder. "Let him sleep. He's been working late for several nights."
The Queen was expecting explosive anger from her new Khevassar but instead Tammy seemed deflated. "Are you not going to shout at me?"
"I'm working up to it," said Tammy with a wry smile.
"Drink?" said Morganse, lifting her glass.
"Never acquired a taste for wine." Tammy sat down with a long sigh that seemed to come from her boots. "I'm surprised to see you drinking."
"Isn't there something in the book of the Maker about raising a glass to the dead?"
Tammy shook her head. "I wouldn't know. I never had much time for religion."
"I used to visit the Maker's church every week with my children when they were young." That also seemed like a long time ago. She was a grandmother now, four times over and a fifth was on the way. Her eldest granddaughter was almost a teenager and already Morganse was looking towards her to take over the throne. But that was still several years away and the problems of today would not go away because she ignored them.
"Why?" said Tammy. "Why not imprison them?"
"I could not hold that many prominent figures in the city indefinitely without just cause."
"There could be others in the city. The names on the list might not be all of her agents," said Tammy.
"I'm sure you're right, but I'm safe here," said Morganse, gesturing at the building around her. She had several Royal Guards just down the corridor and more around the palace. After the events of the war additional precautions had been taken to ensure her safety. A clear message had been sent to Akosh. She knew there would be repercussions for such a bold attack but for now the city was back in the hands of people she could trust. A thorough search had been conducted into all the individuals who suddenly found themselves in line for a promotion. None of them were loyal to Akosh.
"We suspect Akosh has a few loyal mages as well," said Tammy. "What if she sends someone after you here? I'm not sure the Royal Guards would be able to defend you against a mage."
It was something she'd considered but right now didn't have an answer for. "We'll cross that bridge if we come to it."
"Have you considered my suggestion about asking Balfruss for protection and setting up a school?" asked Tammy.
"I have, but I don't think the people are ready. If we were to adopt such an approach it would have to be done in secret."
"Majesty, I would advise against that. Keeping it a secret was one of the problems with the Red Tower."
"It doesn't matter. It's a problem for another day. Has Balfruss returned?" asked Morganse.
"No, not yet."
Morganse had doubts that even if Balfruss was in the city he would be willing to protect her. She had once been instrumental in the introduction of monthly tests by the Seekers but had also banned them, putting more children at risk and heightening people's fear of magic.
"We will have to muddle on without Balfruss unless you know of another mage who's willing to help." Morganse said it as a joke but from Tammy's expression she could see the Khevassar was struggling with something. "Is there something you want to tell me?"
"Yes, your Majesty. Only that I would like one of my Guardians to patrol the palace. Just in case the Royal Guards miss something." They were the toughest and most skilled soldiers in the country, but she was aware that even they had their limits. A crudely trained mage could best the strongest and most skilled of warriors.
"I see. And did you have a particular Guardian in mind?"
Tammy winced. "Yes, your Majesty."
The Old Man had always given Morganse the impression that he knew more than she told him during their regular meetings. It seemed as if his replacement was equally adept at keeping secrets.
"Are you sure they're loyal?" she asked.
"I have no doubt, given his history."
"Very well," said the Queen. "Have him report to the palace from tomorrow."
"Thank you, Majesty. I think both of us will sleep a little better knowing that he's here."
"Do you think I made the right decision?"
Tammy took a long time before answering. "I don't know. Were I in your position, with the same pressures and responsibilities, then perhaps. A wise friend once told me that sometimes the only choices available are bad and worse."
"I see the Old Man has been sharing his wisdom," said Morganse. He'd said the same thing to her more than twenty-five years ago and had repeated it on occasion through the years. They shared a brief smile at the memory before Tammy departed, no doubt to return to her own duties.
Morganse stared out of the window again noting the sky was now completely dark. A few stars showed overhead, pinpricks of white in the endless black. Spread out below her, hundreds of yellow and amber lights carpeted the ground.
The door to her office opened again and Dorn shuffled in. He yawned and shook his head, trying to wake himself up. "Do I have another visitor?" she asked.
"No, Majesty, I wanted to speak to you about something. It's rather personal."
It was highly unusual but she gestured at one of the seats in front of her desk. Dorn was an able and highly organised secretary, if not a particularly thrilling conversationalist. She'd hoped for someone with initiative who would make suggestions, but he seemed content with doing exactly what he was told and nothing more. His loyalty and efficiency gave him some leeway if nothing else.
"What did you want to talk about?" she asked.
Dorn took a cloth from his pocket and mopped at his sweating brow. His thinning hair was getting long and she had the feeling he was trying to cover up the bald spot with volume.
"I'm struggling with your recent decision, your Majesty," he said, unable to meet her eye.
Morganse raised an eyebrow but said nothing at first. She was used to discussing her decisions with senior figures in her government, as well as the Khevassar, but never her secretary. Her patience was starting to wear thin. "Which one?" she asked, curious to know how much he'd been eavesdropping.
Dorn shook his head sadly. "You ordered the murders of almost forty innocent people."
The only other person in the room when she had given that order had been Ben, from the Silent Order. She was confident he hadn't told anyone and neither would other members of his group. Only a handful of the murders had been openly attributed to the Silent Order. The rest had been made to resemble accidents.
"If you are unable to carry out your duties any more, I will see that you're given a similar position elsewhere," said Morganse.
"How could you do it?" he asked, looking up at her. The rage simmering behind his eyes was so alien it surprised her. Until this point he'd never shown a hint of passion for anything besides his food.
"Leave now, or you'll make it worse for yourself."
Dorn remained in his seat and didn't seem intimidated by her threat. "They were loyal," he insisted.
"Get out!" said Morganse, but he continued to ignore her.
"Why did you do it?"
"I don't have to justify my decisions to you. This is your final warning."
"Tell me," he shouted, slamming a fist on the desk.
"This has gone on long enough." Her patience had run out. As she stood up to call for a Royal Guard Dorn drew a dagger from his sleeve.
Morganse froze. Dorn was still the slovenly, overweight man she'd seen every day for months but now there was an unfamiliar coldness to his face.
"You're right," said Dorn, standing up and kicking away his chair. They faced one another with the desk between them. "This has gone on long enough. You're not fit to be the Queen. You killed loyal servants."
"Their loyalty wasn't to me, or this country." Morganse looked around her office for a weapon while she kept him talking. The nearest item that might be of use was her glass of wine. She could reach it before he came around the desk. His arms weren't long enough to stab her from where he was standing. "They would've done whatever they were told by Akosh, even if it meant betraying this country."
Dorn twitched slightly and Morganse cursed herself for a fool. Her previous secretary had been ancient and had died of old age. He should have retired years ago but had stubbornly held on. When it happened she'd been upset but it hadn't come as a surprise. No one had suggested an investigation into his death, including her, but now she began to wonder if his demise had been natural. Dorn had been recommended to her by a number of trusted advisers who were probably unaware of his true loyalty.
"How old were you when Akosh found you?"
"Three," he said with an unsettling smile. "Mother saved me from a life of crime, begging or prostitution. I owe her everything."
"Ah, Captain," said Morganse, looking over his shoulder. "I want this man arrested."
As Dorn turned around Morganse leaned across her desk and smashed her glass across the side of his head. Wine splashed all over his face and clothes while the glass shattered, shards embedding themselves in his face and neck. Screeching in pain he reeled back, clawing at his face as Morganse ran towards the door.
Something caught one of her feet and she tripped, landing face down on the tiled floor. Blood ran from her nose but she scrambled to her hands and knees in time to see Dorn coming towards her. One of his eyes was a bloody mess and shards of glass stuck out of his face like a pin cushion. Despite his wounds he still clutched a dagger in one hand which he raised high above his head.
Morganse scrambled to one side, but felt the edge of the knife on her forearm, drawing a thin line of blood. Kicking out, she caught Dorn on the leg. He cried out in pain and fell over backwards, clipping the back of his head on the desk. Not waiting to see if he was stunned she kicked off her shoes and yanked open the door to her office.
The next set of doors was closed and when she tried to push them open she found they were locked. Dorn had broken the key in the lock sealing her in with him. She could hear him groaning and moving about. Pounding on the door, she shouted for the guards and then put her ear against the wood.
"Majesty?" said a muffled voice.
"He's trying to kill me. Break down the door!" she shouted and then stepped back.
Something heavy slammed into the door and Morganse heaved a sigh of relief. It wouldn't take them long to break it down.
"Murderer!" shrieked Dorn.
Morganse turned around in time to see the dagger coming down. She didn't feel it pierce her flesh and only noticed when she saw the patch of red spreading across the front of her dress.
Behind her the banging grew louder and she heard wood splintering, but she wasn't sure why. Dorn was shouting something and she saw him raise the blood-smeared dagger again. With a scream of her own she shoved a hand into his ruined face, driving the shards of glass deeper. Keening like a maimed animal he tripped and fell backwards. Morganse grabbed a heavy book from the nearest shelf and smashed Dorn over the head with it. With his face covered in blood he glared at her so she hit him again and again.
"Your Majesty!" shouted one of the Royal Guards from somewhere nearby.
Finally, he dropped the dagger but she brought the book down one more time on his face, smearing the cover with blood and glass.
A terrible weight settled on Morganse and she fell back suddenly feeling tired and cold. Part of her realised that closing her eyes was a mistake but as the cool surface of the tiled floor touched her face it was so difficult to stay awake. Her eyelids fluttered and then she fell into the black.
# CHAPTER 43
The tavern was busy when Akosh entered and for once she didn't mind the crowd. By expending a small amount of her power she was able to disguise herself as a plain-faced woman that no one really noticed. When she sat down at her contact's table he looked up from his ale in surprise.
"You've got the wrong table," he said. Akosh let her illusion slip momentarily and his expression transformed. "Apologies, Mother."
She replaced the illusion but his grovelling tone remained. "Sit up straight or people will get suspicious," she told him. He did as ordered and adopted a bored expression that was only partially successful. When the serving girl passed their table Akosh ordered herself a drink and waited until it had arrived before leaning forward.
"You have news from Yerskania?"
"Yes, Mother," he murmured, keeping his voice low but he need not have bothered. The table on her left was occupied by a raucous group of revellers telling jokes and laughing at regular intervals. On her other side a clutch of women were gossiping and beyond them two merchants were haggling loudly about a deal. The noise of the crowd around them almost swallowed his words but she was close enough to hear. She'd chosen this tavern on purpose because it was not one that she'd frequented before. Even her contact was not one she'd met in person until today.
Before her meeting with Kai she'd become a creature of habit, living a comfortable life as she believed herself safe in Herakion. Eating and drinking at the same bars. Sleeping in the same taverns and always taking the same route to bed through the city. Now she watched every face in the crowd for signs that they were serving another master. Her path here had been strangled and she was confident no one could have followed her. It paid to be cautious. He could have spies anywhere.
"What's your name?" she asked.
"Koyle, Mother." He bobbed his head and she gritted her teeth. So far no one had noticed his subservience, but it wouldn't last. She gestured at him to get on with it. "A bird came in this morning. Queen Morganse was attacked in the palace last night," he said.
Akosh sat back and took a long gulp of ale to cover her smile. It might take a few days for the news to trickle through to the north, but it would reach here eventually. She'd intended to destabilise Yerskania using her people on the inside, but it could work just as easily by removing the head of the snake. Chaos bred conflict and from that came murder and more orphans in need of a benevolent mother and teacher.
"Were there any more details?" she asked.
"Only that the Queen was injured, but no one knows how badly or if she will survive."
She might be dying. She might already be dead for that matter. Either option was acceptable.
The Queen had several daughters who had renounced their claims to the throne, which was why Morganse had been grooming her son for the position. That was until an unfortunate incident that left him castrated. With no clear successor what followed would be a mad scramble for power with lots of backstabbing and chaos. It was an assassin's dream come true. For the time being it would serve her purpose while she continued to strengthen her hold in the north.
In some ways Kai had done her a favour. She had become complacent and soft. Thinking of her followers as individuals and herself as human. Kai still terrified her and, if he really wanted to could snuff her out with little effort, but she would not live in fear. Until the time came when she had to face him Akosh would do as she'd always done. If he held up his part of the bargain then she would avoid the clutches of Vargus and the others. If not, there might be a deal to be made to ensure her continued survival. There were always possibilities.
"That's wonderful news," said Akosh, raising her mug to Koyle.
After finishing her drink she left the tavern with a big smile and decided to attend her next meeting. Part of her was tempted to spend the rest of the day drinking and celebrating. It would be a fun way to pass the time but it was an indulgence and she'd had too many of those lately. For the time being she would focus on her duties, even though she expected the next few hours to be an exercise in tedium.
As Bollgar had promised he had expanded her network of orphanages in the city. It was customary for her to visit each new orphanage within the first few months. The children would have been told a little about her by now but nothing solidified their belief more than a visit in person from their benevolent and loving god.
Fixing a caring smile on her face, Akosh pushed open the door of the first orphanage. The matron in charge was delighted to see her and made a point of introducing her to all members of staff before they went on a tour. The building was still in desperate need of repair but there were signs that the money was being put to good use. She could smell fresh paint and see that the floors had recently been scrubbed. A pair of builders were repairing a crumbling wall in one of the bedrooms and elsewhere she saw a carpenter building sets of bunk beds for the children.
As expected, when she first met the children they attempted to swarm all over her like locusts. Akosh braced herself for an assault of tiny, grabbing hands and screeching voices. She was almost knocked off her feet by the tide and forced herself to endure it for a while, answering an endless barrage of questions. Sooner than the children would have liked she signalled to the matron that she was ready for an extraction. The children were disappointed to see her leave but she made them all promise to be true to her for all their lives. As they solemnly swore Akosh felt a tingle of energy run across her skin and her smile stretched wider.
By the time Akosh walked into the third orphanage the tedious chore had become a valuable reminder of their importance. Without the orphanages and the children she would have disappeared years ago. While being close to so many children tested the limits of her endurance, Akosh bore all of it with a smile. Even so a headache was starting to form. There was a dull throb at the back of her head and it seemed to be growing worse. If she hurried through this last visit it might not be too bad.
The man in charge of the orphanage was more organised and efficient than the previous two. The building was already in a much better state with all repairs completed. The classrooms were busy with children and he went on to boast about the wonderful work they'd done in the garden.
"One of our members of staff has been spending a lot of time on it," he said with a hint of pride. "It's amazing."
As they passed down a corridor Akosh saw several children staring through doorways at her in open-mouthed wonder. A flurry of whispers followed in her wake and she graced the children with a brief smile and wave. The pain in her head was starting to get worse. She gritted her teeth and hoped that it would pass but, if anything, it seemed to be spreading.
"We've been telling the children for weeks that you might visit us," he said. "They're so excited to meet you. We're all so excited!" he admitted with a laugh.
Akosh chuckled at the startled look on his face. "Didn't you think I was real?"
"No, I mean, yes. Of course, but whenever I've asked people to describe you they're unable to tell me very much." He was looking directly at Akosh but she knew in a couple of hours he would struggle to tell others about her face, her build or her height. The only things he'd be able to remember clearly were the emotions she projected and the echo they created within.
Nothing strengthened a child's first impression of their god more than a strong memory of love, compassion and kindness. It rarely converted any of the adults to follow her path, but it did make them more open to her visits in the future. It required she expend a small portion of her power but it was something she always did on a first visit.
"Well, I'm here now," said Akosh. "When will I meet the children?"
"Soon. Their lessons are almost over. Would you like to meet the other members of staff?" he asked hopefully.
Akosh swallowed a sarcastic reply and inclined her head. She needed to leave but could endure this a little longer.
He led her into a sparsely furnished room where three women and one man were sitting talking and drinking tea. They rose to their feet and seemed almost as excited as the children to see her. Akosh extended her aura of euphoria as the administrator introduced her to all of them. She pretended to make a note of each one and mouthed their names, but made no real attempt to try and remember them.
"We have one more member of staff," he said. Just then a petite woman with dark, wavy hair came into the room brushing dirt off her hands. "Ah, here she is. I was just telling Akosh about the wonders you've been doing with the garden."
The woman stopped and stared at Akosh as if suddenly unable to move. She seemed utterly dumbstruck and barely seemed to be breathing. This happened from time to time and Akosh smiled indulgently at the woman.
"Akosh, this is Munroe," said the administrator.
"I've been waiting for this moment, for a long time," said Munroe. "I've been dreaming about it."
"I'm sure." It was probably the highlight of her boring little life. That was when Akosh noticed something unusual about the newcomer. The other members of staff were still staring at her with wide-eyed adoration but Munroe hadn't even smiled. In fact, Akosh could see rage building up behind her eyes. The air in the room suddenly felt close and the hairs on the back of Akosh's hands began to stand up. The others remained blissfully unaware and continued to stare with reverence.
Something made Akosh extend her senses and Munroe twitched as if she'd been pinched. She gasped in surprise as she realised the reason for her headache. The woman in front of her was a mage whose connection to the Source was so strong it set her teeth on edge. As Munroe started to draw power into her body Akosh felt the pressure of her will beginning to build.
"Gorell," said Munroe to the administrator. "Get everyone out of the building."
He looked at Munroe as if she was mad but something slapped him across the face and he came out of his trance. "What's happening?"
"You need to run," said Munroe, still drawing power into herself. It was impossible. She'd never seen any mortal that was so powerful. Akosh could see her skin beginning to glow with the build-up of energy. "Now!" hissed Munroe.
Gorell looked between her and Akosh and finally noticed something was terribly wrong. He didn't understand what was happening, only that it would be dangerous to remain. Shoving the others ahead of him, they hurried out of the room. Akosh could hear him shouting at others in the rest of the building but Munroe didn't wait.
With a feral scream Munroe lashed out with her magic. Something slammed into Akosh and she was thrown against the stone wall, which shattered upon impact.
# CHAPTER 44
Regent Choilan wanted to slap the girl for being so stupid, but instead he maintained a disappointed expression.
"And you had no idea that Tianne was thinking about leaving?" he asked Kalina.
"No. I didn't."
"Do you know where Tianne might go?" Kalina took a moment to think about it but then shook her head. "And you didn't see her leave the palace in the night?"
The girl shook her head again. Her face was the picture of innocence but even so he wondered. Selina's people all reported that the girl was loyal and that getting the tattoos had been her idea. To permanently mark her flesh and dedicate herself to his service was noble and patriotic, but it was also naïve, reminding him they were only children. At times he could see them as lost little lambs looking for their flock. But when he saw them practising their magic in the walled courtyard, a shiver of fear ran down his spine. The primal forces they commanded made him wonder if they were really wolves in disguise. A wolf wasn't a faithful hound that could be trained to obey commands. It was a wild beast and eventually it would revert to its true nature.
"Do you want to leave my service as well? Maybe go back home to your father's tavern?" he asked.
A hint of steel crept into Kalina's expression. "No." The way she said it told him many things about her past. Someone who'd been told always to be polite to the customer, no matter what they said or did. An only child with dreams that were bigger than serving drinks for the rest of her life. The fire in her belly made her ambitious but it also fuelled her anger. It was all in tune with what he'd read from his agents. "I belong here," she insisted.
"I'm glad to hear that. You are now first in my cadre," he said, holding up a second blue star for the front of her uniform. "Can I count on you?"
"Yes. Of course." She was on the verge of tears.
"Get some rest. You have a big day tomorrow." He dismissed her with a wave and she hurried out of the room, practically skipping.
"Deftly handled," said Selina, coming into the room from a side door. He suspected she'd been eavesdropping.
"Do you believe her?" he asked.
"Maybe," said Selina. "But it doesn't matter. The tattoos are hideous, but now there's nowhere she, or any of the others, can go without someone recognising them." Selina helped herself to a glass of watered-down wine and picked at the grapes beside him.
"True. That's why I'm sending them out to find other children."
Now that the capital city had been swept clean of all charlatans, and any youngsters with magic had been recruited, it was time to widen the net. Six mages from his cadre would soon begin a two-week journey to several of the larger towns and two cities to find more recruits. He wanted at least a hundred mages in his cadre by the end of the year, if not more. Then Zecorria would be secure against any invasion, whether or not they had magic of their own.
"I've been thinking, it's time we went to church," said Choilan. Selina raised an eyebrow, baffled by his suggestion. Choilan felt an extra thrill as he'd managed to surprise Selina. She was so rarely caught off balance.
"Why?" she asked with suspicion.
"We need to be seen as loyal followers of the Lady of Light, the true faith."
She still couldn't see where he was going with it. "And?"
"And, I think it would help the people if they saw the mages at prayer. Being a patriot and servant of Zecorria might not be enough for some. If they are seen as being dedicated to the faith, then it might ease some of the remaining tension."
"Perhaps, but you'll need a gesture," said Selina. "Something to make it stand out and generate gossip."
"I thought the High Priest Robella might personally bless them," said Choilan. "If she announced in public that they were noble and faithful, it would be remembered."
"She might object to that."
"I'm sure she can be persuaded," he mused. Bettina and the others had detailed personal information on almost everyone in key positions in the city and their vices. This included areas where pressure could be applied to make them more compliant.
He needed to shift public opinion. Children with magic were seen as dirty, dangerous and something to be hidden. Choilan imagined a future where parents would be proud to have such a child and would bring them forward to his people. A place where mages were seen to be as dedicated and loyal as his Royal Guards. It was going to take time, and a lot of patience, but a few large gestures would put them on the path. He was going to create a strong nation. One that could never be manipulated or controlled as it had been in the past.
"The High Priest will have to be very convincing for it to be effective," said Selina.
"I'm sure Bettina can find a way to motivate her," he said and they briefly shared a smile.
After Selina had left Choilan was alone for a short time before his next meeting. His mind drifted as he considered the possibilities of having his own army of mages. Seven mages had changed the course of the war and one had brought about its end. He wondered what fifty or a hundred mages who were loyal to him could accomplish. It was a remarkable and slightly terrifying idea.
They would have to be rigorously assessed to ensure they were true patriots. He didn't want any more of them running away. The earlier they could be recruited the better. Then they could be indoctrinated and made to feel important. Few people would find it easy to walk away from power, privilege and a form of authority.
A crisp knock on the door told him Bettina had arrived. She swept into the room in a pale yellow dress with a high neck and a trailing hem. Even the sleeves were uncommonly long. Her choice of clothing that showed as little bare flesh as possible had been noted and investigated. He was very aware of her secret and the marks on her flesh the dress was hiding. Everyone had their vices.
"I bring good news, my Regent," she said with a formal bow. It was exactly the right depth to show the appropriate level of respect. If only everyone who worked for him was so precise. "The parade seemed to work. People were pleased at seeing Garvey in chains."
Telling everyone in the city that they had captured the most notorious rogue mage was not enough. They needed to see it. And to believe that his cadre of mages were responsible. Another grand gesture to help tip the scales in their favour.
"Excellent. Has the inquisitor managed to extract a confession from him yet?"
Bettina's expression soured. "Not yet. He's exhausted all of his usual techniques and is now trying other methods." She didn't elaborate and he didn't really care. He just needed Garvey to admit what he'd done in public and beg forgiveness. It didn't matter if he really cared about his victims or not. He just had to say the words and make them sound convincing.
"Have they tried starving him?" he asked. Mages had to eat. For all their power they were still flesh and blood. As he'd seen in the last few months they could die like everyone else. The inquisitor had tested his theory on a number of those brought in with minor powers who wouldn't serve the throne. He'd assured the Regent that magic didn't change the inside of the body in any way.
"He's not been fed for six days now." When other people spoke about Garvey he could see they were angry. After all, hundreds of innocent people had died because of him and his group of rogue mages. Bettina's voice remained cold and dispassionate. "They've given him a little water to keep him alive, but nothing else. It shouldn't be long."
"I hope so. Failing that we'll just have to execute him with a gag. It won't be as powerful a message to the people, but it may be all he gives us." If only Garvey would do as he was told this would be much easier for everyone. Once he'd confessed they'd cut off his head and his suffering would end. It was really that simple. He was just prolonging his misery. Maybe he wanted to be punished for some reason. It seemed odd that he would suddenly develop a conscience, but it could happen. Either that or sometimes they went mad and were sent to an asylum like that poor fool Habreel. It seemed as if the pressure had proven too much and he'd cracked under the strain.
"Start making arrangements for Garvey's public execution," said Choilan. "The people have seen him in chains. Now they need to know he's paid the ultimate price."
"Yes, my Regent."
"We'll give the inquisitor another week. And make sure Garvey knows there's a deadline if he doesn't comply." Choilan thought it might motivate Garvey to confess if he knew his days were numbered.
The sound of heavy footsteps in the corridor made them both look up in surprise. The door flew open without announcement and a dozen Royal Guards burst into the room bearing their weapons.
"What is the meaning of this?" asked Choilan. For a moment he thought there'd been a coup and they'd come for him. But then the Guards formed a protective ring around the edge of the room, facing outwards.
Beyond them a wall of four more Royal Guards took up their positions outside the door to block the corridor. In addition, he could see more Guards posted at intervals in the corridor. The Captain of the Guards entered the room and bowed. Beside him a scraggly man with remarkably clean hands also bowed deeply. The stranger had lank greasy hair and a rather plain face, but when he straightened up Choilan saw his eyes were two different colours. One was a deep brown and the other bright blue.
"Apologies, my Regent, but Inquisitor Marsh has urgent news."
Choilan had never seen the inquisitor before but this weak-chinned man was not what he'd been expecting. "What has happened?"
The Captain nudged Marsh who bobbed his head and cleared his throat. "I went to check on the prisoner, to see if he was ready to confess, and found his cell was empty."
Choilan's mouth fell open. "Empty?"
"His chains were gone, the door was open and no one had seen him leave. He just disappeared."
"We're having the entire palace searched," said the Captain. "If he's still here we'll find him."
Marsh shook his head but said nothing. "You have something to say?" asked the Regent.
"No, my Regent."
"Spit it out. Tell me!" said Choilan in a shrill voice. Fear was tightening his stomach and making him sweat.
"You won't find him here," said Marsh. "He's gone."
"Where? Where is Garvey?" asked Choilan, but no one had an answer.
# CHAPTER 45
Munroe heard a loud crack as Akosh struck the wall hard enough to punch a hole in it, knocking her into the next room. With a snarl she slammed her will into the stones, gouging an opening large enough for her to step through. Akosh seemed a little stunned as she was still lying on the ground amid the rubble of a classroom. The room was empty except for the broken remains of desks and chairs which had shattered upon impact.
Akosh was still moving so it wasn't over yet.
This might be her one chance to kill Akosh for what she'd done. Munroe only intended to stop when she'd ripped Akosh's head clean away from her body. Drawing more energy into herself from the Source she forged a spear of molten fire. The cherry-red flames licked around her arms but didn't burn her skin while the tip started to glow white hot like the heart of the sun. As Akosh stumbled to her feet Munroe charged, stabbing her in the chest.
As the spear came into contact with Akosh's body there was a peculiar form of resistance. It wasn't magic like any she'd felt before, but there was definitely a barrier of sorts. She could feel something trying to divert the power from her weapon and redirect it around Akosh. Channelling more energy into the spear, she held it steady and drove it forward with both arms.
Akosh screamed in agony as the spear pierced her right side just under her ribs. Pressure against Munroe stopped her limbs abruptly, preventing her from driving the spear right through Akosh's body. She intended to pin Akosh to the wall then tear her apart, piece by piece. Munroe focused her will and pushed back against the barrier which was slick and flexible. She could feel it bending under pressure and the spear was driven a little further into Akosh's torso.
It became a battle of will as Munroe tried to impale her and Akosh's strange magic kept her at bay. She would not be denied. She would have revenge for her family, for every Seeker and all those murdered when the Red Tower had fallen.
Reaching out towards the Source, the heart of creation, Munroe drew more energy into herself, feeling it soaking into her entire body, infusing her being with its power. Her already sharpened senses became more acute, revealing a few peculiarities about Akosh. The way she smelled, like old blood and rot. The empty space behind her eyes where a soul should live. And the fear starting to creep in around the edges of her fierce expression.
Munroe grinned and thrust her arms forward with a scream of unbridled fury. The flaming spear burned a hole straight through Akosh's body and she howled in agony.
Something caught Munroe on the side of her head, breaking her concentration and then she was flying through the air. Working instinctively, she wove a shield around herself to cushion the impact. A second later she collided with a solid wall. Even through her shield the force was hard enough to rattle her teeth. Scrambling to her feet she was surprised to see that Akosh hadn't fled. She was holding a hand against her side but no blood was flowing from the cauterised wound. The skin around the edges was burned and blackened; however, there was a little blood on her hands.
"So you can bleed," said Munroe. Akosh tried to say something but the time for talking was over. There was nothing she could say that meant anything. Munroe forged a hammer of pure will in either hand and went to work, raining blows down on Akosh.
Akosh dodged the first few blows and the hammers struck the wall behind, tearing chunks from the stone fireplace. Cracks ran up the wall from the impact and the ceiling beams groaned and creaked.
Every time one of her weapons struck Akosh's raised forearm, or caught her on the side, there was some resistance. She was using her own form of magic, or life-force, to reduce the impact of Munroe's blows. Despite that she could see the damage being done as Akosh was bleeding. A normal human would have been crippled with shattered bones after taking one or two such attacks on their arms or torso. But Akosh wasn't normal. She was still standing as they struggled around the room. Ducking one blow aimed at her head, Akosh retaliated with an open palm to the shoulder, spinning Munroe around.
As she fell to one knee a huge weight fell on Munroe's back and something tight snaked around her neck, choking her. Grabbing a handful of Akosh's hair to keep her in place Munroe stood up and then fell backwards heavily, landing on top of her enemy. There was a loud crack and Akosh's arm loosened around her neck. The dancing black spots receded and she elbowed Akosh in the throat, making her choke.
A section of the stone wall had collapsed from where they'd punched through. Munroe lifted it with her magic and sent it hurtling at the prone figure of Akosh. Some of the impact was absorbed by her power but she still took the brunt of the collision on her head and shoulders. She should have been dead but was merely stunned.
"You can't kill me!" snarled Akosh, getting to her feet. "You are beneath me!"
Munroe thought about her husband and her son. She thought about her mother. She thought about the fact that she'd never see them again and that Akosh was responsible. Using those emotions to fuel her magic she lashed out with vicious abandon.
A brutal attack threw Akosh through the stone wall into the next room. Munroe scrambled through the gap and found they were now inside a huge kitchen.
Before Akosh could recover she lifted a section of wall and slammed it into her with so much force it broke apart on impact. Blood was trickling from Akosh's nose and ears but she still wasn't done. She wouldn't fall so Munroe drove her into the ground, hitting her again and again with her will, fuelling it with her boundless rage. With all of the anger she'd been holding in for so long. For all of the special moments she'd never have with her son. For the many years she'd been looking forward to sharing with her husband as they grew old together. For just one more day with her mother. Channelling all her fury into a scream, her voice was transformed into a weapon, tearing into Akosh's flesh, shredding her clothing and ripping chunks of meat from her bones.
Part of the ceiling fell into the room and a few stones struck Munroe on the shoulder. She wove a shield to keep the worst at bay but her assault didn't relent. Like a hammer striking the anvil she kept up the pressure on Akosh, throwing her one way and then the other. Gathering up a handful of knives she hurled them at her enemy. A few rebounded but the rest stabbed her in the torso, turning her into a pin cushion. It wasn't enough. It was too remote. She needed to feel the bones break.
Wreathing her fists in blue elemental fire Munroe clubbed Akosh across the face, scorching her flesh and driving her into the far wall which cracked. Splinters ran up the wall from the point of impact like a broken pane of glass and a section rained down into the room.
Someone was shouting but Munroe paid them no attention. It didn't matter. Nothing else did. She wouldn't let Akosh out of her sight. Not even for a second in case she tried to escape. When Akosh looked up at her Munroe noticed the burned skin on her face was already recovering as the blistered flesh repaired itself. The skin had not completely healed but it wouldn't be long.
As more stones fell from the ceiling Munroe inhaled some dust and started to cough, which made her eyes water. A tight band wrapped itself around her chest and began to squeeze. Akosh drew a pair of daggers and charged while the restraint around Munroe's chest tightened, driving all the air from her body. Instead of running or worrying about her chest she reached out towards Akosh, gripping her by the wrists.
As she struggled to breathe, and they fought over control of the daggers, Munroe knew she only had a few seconds before she lost consciousness. Reaching deep inside herself she instinctively used her Talent. Her oldest power, to manipulate the odds, and the first magic she'd ever wielded.
A section of the ceiling cracked and a huge chunk of stone and wood fell into the room landing exactly on top of Akosh, catching her on the shoulder. It ripped Akosh out of Munroe's grip as she was pinned to the floor by the weight of the furniture and wooden ceiling beams.
The pain in Munroe's chest vanished and she gulped in fresh air as a cloud of dust and debris began to fill the room making it difficult to see. Whirling both hands she summoned a strong wind to blow all of the dust away so she didn't lose sight of her enemy.
In the quietness that followed Munroe heard someone shouting for help. Looking up she saw half a dozen children clinging to the sloping floor of the room above. Other children were trying to reach them but they were too far away. "Help us!" screamed one of the children but she couldn't be distracted. They didn't matter. The only thing that mattered was killing her enemy.
With a groan Akosh made it to her hands and knees, shrugging off the massive weight of stone and wood across her back. She was bruised, bloody and burned, but far from done. The missing chunks of flesh on her face and neck had started to regrow, leaving fresh pink skin it its wake. It wouldn't be long before she was fully restored.
Shrieking with fury Munroe charged at Akosh. Grabbing her around the neck with both hands she lifted her off the ground and hammered her into the wall. Drawing deeper from the Source she fed power into her arms and out into her hands. Bright yellow and white light erupted from the pores of her skin, wreathing Akosh in swirling motes of energy that seemed alive. They moved in the air, dancing to an erratic beat, before digging into her skin with razor-sharp hooks.
Akosh screamed as they burrowed into her flesh, trailing wires of pure white light that was so bright they were difficult to look at. More and more tendrils flowed from Munroe's hands into Akosh, digging into her face and neck. With Akosh grabbing Munroe around the neck, the pair began to batter each other into the walls, breaking bones and bruising skin. Inside Akosh another war was raging as Munroe sought to destroy her core as power from the Source started to unravel her.
They struck another support beam and part of the floor above came tumbling down. The children had escaped that room but Munroe didn't notice. Her hands tightened around Akosh's neck and she smiled with delight as her enemy's face began to turn red and then purple.
Stones began to pelt them both, then larger chunks of stone and one caught Munroe a glancing blow on the temple. One of her hands loosened and Akosh gulped in fresh air. As a shadow fell over them, blotting out the light, Munroe looked up in time to see part of the building sliding towards her. With a hiss of frustration she dived aside and quickly wove a dense wedge-shaped shield above her head. Akosh tried to run but a section broke off landing across her legs and lower back, pinning her to the ground. More pieces of the building and furniture rained down all around Munroe. Objects struck her shield and fell to either side leaving her in a debris-free oasis amid the chaos.
"Help!" someone screamed but Munroe ignored them again. The voice was vaguely familiar but they would have to wait. The building was starting to settle and once it stopped she would finish this. Akosh's head was still attached to her body.
"Munroe, help me!"
The voice seemed to be coming from somewhere above her head and, turning in a circle, she saw Dox. The girl was two floors up and two rooms across. The only reason Munroe could see her was because huge sections of the floor and even the ceiling had fallen through. Dox was cradling one of the younger girls in her arms who appeared unconscious. Huddled beside her were half a dozen more children. All of them had cuts and bruises and were covered in dust.
"Get out of here. Run!" shouted Munroe.
"We're trapped," said Dox, gesturing at the doorway beside her. Through it should have been the stairs but Munroe could see it was blocked with broken beams and tiles from the roof that had collapsed. The section of floor they were huddled on creaked alarmingly and started to tip forward. The children screamed and all scrambled further up towards the blocked doorway. A fall from such a height might be lethal or they could just injure themselves.
"Climb down!" said Munroe.
"We can't," shouted Dox. "There are people trapped in the rubble." She gestured to where part of the building had collapsed. Munroe could see someone's arm poking out of the wreckage and she wondered if there were more buried underneath.
Behind her she heard the sound of rocks grating together as Akosh slowly began to pull herself free. A loud groaning began as more cracks ran through the remaining shell of the building and it started to come apart. The whole structure creaked and shook.
For the first time she and Akosh noticed the level of destruction they'd caused. It wouldn't take much for the rest of the building to fall apart. Munroe could see at least one dead body and knew there would be others buried beneath the ruins. These were Akosh's people, her orphans, and yet she showed no regard for them at all.
They both seemed to know what the other was thinking as a grin slowly spread across Akosh's face. As her bones popped back into place and her flesh slowly began to rebuild itself, she rested a hand against an outer wall. Munroe felt a strange distortion in the air. It was as if the weight of everything had suddenly increased as moving her limbs became difficult. Akosh was bringing her own power to bear on the building's skeleton. The grinding sound began again and stones started to rattle down from above. There was only a handful to begin with but more were falling all the time. If she kept up the pressure the whole structure would come tumbling down. And while she and Akosh might survive none of the others would stand a chance.
"It's time to choose," said Akosh, spitting out a wad of blood.
Dox and the others were screaming for help as the two of them faced off against one another.
"One day, I will find you again," Munroe promised her. "And I will finish what I started. I will tear your head from your body and piss on your corpse."
"We'll see," said Akosh.
With a heavy heart Munroe turned her back on Akosh, letting her escape, while she went to help the orphans.
# CHAPTER 46
As Danoph stared around at Balov, the village of his birth, he was surprised he didn't feel happier to see it again after so long.
Some parts of it had changed, with more houses than he remembered and different shops on the main street, but overall it was much the same. A tiny, nowhere village, surrounded by farmland, huddled up to the base of rolling hills that were covered with a forest of green.
As he stood at the end of the main street a few of the children running around at play gave him curious glances, but no more than that. Even in this remote place visitors were not uncommon. Three horse-drawn wagons laden with timber passed by, driven by surly merchants and guarded by masked Drassi. The rare wood in the hills would be taken to the capital where the finest carpenters would craft it into furniture for the Queen and others with money.
To the west he could see farmers busy at work in the fields and in the distance hear the faint sound of saws in the dense forest. It was almost midday and bright sunlight shone down from a crisp blue sky. Most people were busy at work so the main street was empty. There were a few small children but the older ones would be at school or at work themselves.
Danoph drifted down the street, pausing from time to time to peer into shop windows, a ghost in a place where he no longer belonged. No one seemed to recognise him as he walked about, which made him wonder. How much had he changed since his last visit? How long had it been?
He remembered learning his letters at school as a young boy. He remembered the kind face of the teacher, a handsome woman with curly golden hair. He vaguely remembered the names and faces of some former classmates. It made Danoph wonder where they were now. Working in the fields? Chopping down trees in the forest? Had any of them left the village and sought their fortune elsewhere?
At the centre of the village was the main crossroads. Danoph was pleased to see the Fat Goose hadn't changed much. It had been repainted and the sign straightened, but it was still the same old tavern with frosted windows. Sometimes at night in the summer, when it was hot and sticky, the owner would throw open the windows and doors in a vain attempt to keep the customers cool. On those nights music would drift to all corners of the village and Danoph would lie in bed and listen.
The jaunty tunes were amusing, but it was the more sombre tales that he remembered most clearly. Those that spoke of faraway places. They conjured images in his mind that were so clear it was as if he'd actually been there. Such was the power of the memory Danoph didn't realise how much he'd missed hearing music until now. Few students at the Red Tower had played an instrument and there hadn't been an opportunity to visit the nearby tavern. Perhaps he'd stop by the Fat Goose tonight and there would be some musicians.
Taking a path he'd walked countless times, Danoph wandered through the village towards his mother's house. It was a small cottage wedged between a number of larger homes, but it had been perfect for the two of them. From the outside it looked exactly the same. Herbs were drying in the rafters of the small porch at the front. The roof still sagged on the right side and the climbing vine had crept further up the west wall. A wealth of tiny yellow flowers was in bloom. They were so bright and cheery it more than made up for the peculiar smell they produced in the summer. But it kept the insects away and beneath the vine his mother was still growing fruit and sunflowers in clay pots.
As he approached the cottage Danoph was surprised to see the front door open and his mother emerge. He'd expected to find her at work in her shop. She seemed in a hurry to be somewhere and with the sun in her eyes didn't see him at first. When she passed into shade she paused and her mouth fell open.
They stared at each other in silence for a time, Danoph noting the slight changes. She seemed smaller than he remembered, or perhaps it was that he had grown that much taller. There was a touch of premature grey hair over her ears but he thought it made her look wiser. It was very much in keeping with her role as the local herbalist as people often expected her to have all of the answers to their problems.
"You've grown," said his mother. She made no move to embrace him and Danoph felt strangely shy about taking the initiative. "And put on weight. It suits you," she added quickly in case he misunderstood.
"They fed us very well," he said, trying to hide his anger about what had happened. The Red Tower was gone. Burned down by a rampaging, ignorant mob who had murdered those who'd chosen to stay behind. He owed his life to them.
Trying to hide anything from his mother was pointless. She could read him so easily. "I heard about what happened. I'm sorry about the school."
"They destroyed everything."
"Is that why you're here?" she asked, moving a little closer. "Have you come back to live here?"
"No. I came because I need some answers," he said. At first she seemed relieved by his reply but then fresh concerns surfaced.
"About what?"
"About why you sent me away. About my magic and also my father."
His mother grimaced as if she'd swallowed something bitter but then nodded, accepting the awkward questions. She must have known that one day he would ask.
"I need to get back to the shop. I'd run out of fresh mint so just came back for more." She hefted the basket and he caught a whiff. "Come back tonight and we'll talk."
"All right."
She came a bit closer and then stood just within arm's reach. Again he felt awkward and wasn't sure why. She was his mother. She was his blood. He'd not been home for years and yet this wasn't the tearful, happy reunion he'd imagined. Thankfully she took the initiative, carefully putting her arms around him and he held her as well. He'd barely closed his eyes when she pulled away and he was forced to let go. She hurried away towards her shop leaving him feeling puzzled and oddly bereft.
Danoph drifted around the village for the rest of the afternoon visiting all of his old haunts. In the woods not far from his mother's cottage the remnants of his treehouse were slowly being reclaimed by nature. Overgrown with weeds and flowering shrubs it was now home to a nest of birds that were making better use of it than he had. Growing up he'd sometimes come here to dream about the future. He'd imagined himself travelling all over the world as a soldier in the Queen's army. He'd wanted to be a hero whose brave deeds the bards sung about in taverns up and down the land.
After the war he never again imagined himself as a soldier. He had no desire to carry a weapon or go to war. He'd seen more than enough bloodshed and torture to last a lifetime. The treehouse then became his refuge where he'd spend hours by himself. The camps had been crowded and filthy, full of noise and other people. Here it was so quiet and peaceful. He was occasionally lonely after that but never felt uncomfortable in his own company.
By the time the afternoon had drained away Danoph realised why he'd hesitated coming home for so long. His early memories of glorious days full of wonder and imagination had been replaced with darker thoughts that lingered on what he'd endured during the war. The more time he spent exploring the streets and surrounding areas the more he realised why leaving had, in many ways, been a relief.
The Red Tower had been a chance to start afresh. The emergence of his magic had been unexpected, but it had presented him with an opportunity to build a new life. All of which brought Danoph back to thoughts of his mother and why she had sent him away. Something must have triggered it and he needed to know what had happened.
With sore feet and a slightly heavy heart he knocked on his mother's front door. Danoph realised he didn't even think about it as his home any more. It was her house. He had no home.
His mother answered and gestured for him to sit on the porch in the rocking chair while she brought out another seat. Danoph knew it was strange that she'd not invited him into her home, but part of him had been expecting it. It also made him wonder if she was trying to hide something or someone she didn't want him to see.
They sat together in silence for a while, listening to the distant drone of insects and the rustling of the trees in the wind. After a time she found the courage to turn towards him and speak.
"Ask your questions."
"Why did you send me away? Was it because of my visions?" he asked in a rush. The questions had been bottled up inside him for a long time. "Did I hurt someone?"
"Around here people have been afraid of magic for a long time. They still are today. But yours was something different," said his mother. "At first I thought they were just stories you'd made up. But the details were always so vivid."
"But they weren't stories," said Danoph.
"No, and they weren't just visions. They were glimpses of other places and other times. It was as if you'd been spying on people through their windows. Sometimes they were things in the past. Secrets from other families that I thought you'd overheard. Then you started telling me about things that hadn't happened, that later came true. That's when I knew you were different."
"Different?"
His mother sighed and ran a hand through her hair. "You weren't the first child born in our village with magic. Years ago there was a boy who could light fires without flint and tinder. Another could talk to dogs. He'd just stare and they obeyed him. They were both strange but, up to a point, people could understand their magic. Your visions were worrying, often predicting tragedies or crimes. Some I couldn't prove were real because you talked about places in other countries. I tried to hide your visions but other people in the village started to notice. If I hadn't sent you away I think you would've been lynched."
There was a hint of regret in her voice and hearing her reasons didn't sting as much as he'd expected.
Rather selfishly he'd not realised how difficult it must have been for her as well. To be the only woman in the village raising a child without a husband. Tragedies had been uncommon in their small community but when it happened widows were not shunned. Danoph had no memories of his father but he remembered the way other villagers stared at him and his mother. If she hadn't been the herbalist, and an important figure in the community, she might have been driven out. Danoph wondered if she'd found someone in the years since he'd left.
"Who was my father?" he asked.
His mother shook her head, not yet ready to answer the question. He'd thought the reason for sending him away would've been the difficult question to answer. As a small boy he'd daydreamed that his father had been a hero killed in battle. Or a member of the royal family who loved his mother but had been forced to leave by his wicked father and marry someone else. Now he suspected the truth was a lot more sinister. Even so, he needed to know.
"Did you know Talle and I were betrothed?" said his mother, breaking the tense silence.
"No."
"We grew up together. Did everything together. None of the other girls even tried to catch his eye. He only wanted me." She smiled wistfully but all too quickly it drained away. "We were married young and it lasted for three years. We visited the village Wise and several herbalists, but the answer was always the same. We couldn't have children."
"They were wrong," said Danoph.
"The local priest agreed to our unbinding and later he married Jodine. Now he's running a farm and they have four children."
"But they were all wrong," he said again, staring at his mother. "You can have children."
She stubbornly shook her head. "No. It's not what you think."
A cold prickle of fear ran across the back of his scalp. "Who was my father?"
"No one."
"You didn't know his name? Were you attacked?" he asked. It was far worse than he'd anticipated. Perhaps it would have been better not to know the truth.
"You don't understand. After Talle, I was alone. One day I wasn't pregnant and the next I was. Everyone assumed it was a passing merchant, and I never said otherwise. It was a lot easier to accept than the truth."
"I don't understand."
"Neither do I. I still don't, but I didn't care. You were my miracle."
It was impossible. It was ridiculous. She was lying to cover up something. "Was he already married? I'm not going to cause any trouble. I just want a name."
His mother took him by the hand and stared straight into his eyes. "You have no father."
Danoph didn't think she was lying and yet he had no other explanation. He didn't notice the man approaching the cottage until his shadow fell over them both. Danoph and his mother looked up in surprise at the tall, grizzled Seve with a sword on his back. At first Danoph thought this was his father. The man his mother claimed didn't exist until he saw the lack of recognition on her face.
"Danoph, my name is Vargus. I know you have many questions and I can help."
"Who are you?"
The old warrior smiled. "A friend."
The world shifted around him and Danoph found himself standing inside a huge banqueting hall. A massive wooden table ran down the centre of the room and arranged around it were dozens of chairs. Each looked identical and yet he instinctively knew they were unique. At the head of the table was a massive seat that dwarfed the others and without asking he knew who it belonged to and that its owner was still absent.
Images and pieces of memory swam to the surface but he couldn't focus on them. He'd never been to this place before and yet somehow he knew so much about it. Danoph should have felt scared to find himself in another place but for some reason he wasn't alarmed. It felt safe and so familiar.
Vargus stood beside one of the chairs towards the far end of the table. Danoph's instincts told him it belonged to Vargus. The longer he stared at the warrior the more familiar he seemed, although he didn't know why.
"For all things there is a season," said Vargus. "Over the years our star wanes, or the body breaks, and we pass into the Void. At other times we evolve, becoming something new in order to survive. Once, long ago, I had a different name and a different power. Now I am a Brother to all who carry a weapon into battle. Years ago my old mantle was reborn. And with it came the power to see the future and all of the possibilities it contains. To dream of tomorrow and see the choices that lay ahead for us all. To travel through the skein of time and know what's to come. This is the Weaver."
Vargus approached Danoph and put a hand on his shoulder. "Welcome home, brother."
_The story continues in book three of the Age of Dread._
The story continues in...
The Age of Dread: Book Three
Keep reading for a sneak peek!
# ACKNOWLEDGEMENTS
Many thanks to Juliet Mushens, my agent from CaskieMushens, for reading all the words. Thanks to Nathalie, for sorting out all the paperwork and making it all so easy for me.
I'm very grateful to everyone at Orbit for all of their hard work on my behalf to beat this book into shape, in particular Jenni, Brit and Joanna. Thanks also to Nazia for all the work she does organising events for me and all Orbit authors. Special thanks to Gemma and Tom for our regular "Two Authors and Tom" lunches out.
Finally, thanks to my family and friends for their continual support and enthusiasm.
# extras
# meet the author
_Photo Credit: Hannah Webster_
STEPHEN ARYAN was born in 1977 and was raised by the sea in northeast England. A keen podcaster, lapsed gamer and budding archer, when not extolling the virtues of _Babylon 5_ , he can be found drinking real ale and reading comics.
He lives in a village in West Midlands with his partner and two cats. You can find him at @SteveAryan or visit his website at www.stephen-aryan.com.
**if you enjoyed**
**MAGEFALL**
**look out for**
**The Age of Dread: Book Three**
**by**
**Stephen Aryan**
Kai sneered at the line of beggars that began to trail after him as he walked through Herakion, the capital city of Zecorria.
His sneer grew more intense as he passed the front doors of several large churches and temples dedicated to his older brethren. Huge stone buildings that spoke of permanence, giving mortals the illusion of comfort in their endless quest to confess their sins. But none were eternal, with perhaps the exception of the Maker, whom no one had seen in centuries and yet His faith endured. His followers were seemingly endless in number.
Kai knew the others dreamed of having as many followers so that they too might extend their miserable and empty existence for another century or so. They were sheep. And like all cattle, one day, they would be ripe for slaughter.
Somewhere deep inside he heard the faint whimpers and pleas of those being consumed and a wolfish smile spread across his face.
The beggars saw only a handsome, richly dressed man, striding down the street with purpose. A few cried out, asking for a coin to buy a crust of bread, which he completely ignored. One man, with blue stains at the corners of his mouth and open sores on his arms, made Kai smile. With nothing but the clothes on his back, not even his health, the man chose to spend his money on venthe, numbing himself to the world. The marks on his face were a clear sign of his drug addiction. Kai flicked the man a small coin, helping him along towards his imminent and painful death.
The mortals were even worse than his brethren. Greedy. Desperate to belong. Desperate to feel something to give their life meaning. They weren't sheep. They were ants, swarming around, searching for food and shelter.
Kai wasn't paying attention to where he was walking and almost tripped over another beggar. The blind man pulled in his legs while raising a cracked bowl in one grubby hand. Ignoring the wretched creature Kai was about to move on when he felt a familiar but insistent pull.
Part of him wanted to ignore it and keep walking, but as ever appearances had to be maintained. This wasn't a summons he could ignore without attracting attention to himself. Closing his eyes the world around him faded away. There was a brief moment of disorientation and then he was standing in the familiar banqueting hall.
At the far end of the table the huge chair of the Maker loomed over everyone in the room. Even in such a large space with a high vaulted ceiling, ribbed with beams like the innards of a vast beast, the chair drew everyone's attention. At some point every person glanced at it, half expecting it to be occupied by His indomitable presence. Perhaps, one day, it would be. That was the one thought that scared Kai.
As others began appearing out of thin air and the room began to fill up Kai noticed the pool of empty space around him as others kept their distance. He smiled at their fear and discomfort, while carefully studying a few of the new faces.
Vargus and the others paid little attention to them, probably didn't even know half of their names, which made sense. Even among their kind they were like moths. Here one day and gone the next. But some were stronger than others. Some flourished and grew. Some were lame, ready to be culled and others, on the cusp of greatness, were ready to be consumed. Licking his lips at the thought of feasting on the delicious treats that surrounded him, Kai moved towards his chair. The others moved out of the way without being asked.
Halfway down the table someone was blocking his path and refused to move aside. Looking up Kai saw that it was Elwei. Unlike most of his brethren, the Lord of the First People was inscrutable. Even now, as Elwei stood in the room with everyone, part of his attention remained elsewhere focused on distant events. His face was turned away from Kai and as ever most of his features were in shadow, partially hidden by a headscarf. The faded tattoos on his black skin were so ancient that even Kai didn't recognise the symbols. Powerful and mysterious were never a good combination. He skirted around the old Pilgrim, nodded politely to Summer and Winter, and then sat down.
Towards the head of the table the old sailor, Nethun, took his seat. Everyone else took that as a cue to cut short their conversations and sit down. Normally quick to smile Nethun's expression was as grim as those around him. The Blessed Mother seemed troubled and Vargus distracted, suggesting that both of them privy to what was about to be said. Kai maintained his air of ignorance, waiting to be told while working hard to keep the smile off his face.
"As you've noticed, a few of our number are absent," said Nethun, wasting no time on preamble. "But Akosh has not passed beyond the Veil. She has ignored several summonses and as we agreed, Vargus was tasked with finding out why."
"She has been dabbling in the affairs of mortals," said Vargus, drawing gasps of surprise from several around the table. Kai shook his head in disappointment, biting his lip to crush the mirth rising up inside. "Recently she was sighted in Zecorria, in Herakion, the capital city. Aren't you in the north at the moment?"
It took Kai a few seconds to realise the question was directed at him. As all eyes at the table turned his way, some reluctant even to look at him, the half-smile slid off his face. Lying and deception were second nature to him, but sometimes the truth, or at least a version of it, was better. It was also easier to remember under scrutiny.
"I am in Herakion at the moment. There was a huge disturbance last night," offered Kai.
Vargus continued to stare at him with an unreadable expression. Despite the aid Vargus had given him in the past Kai knew better than to trust his dear old friend. Vargus would try to snuff him out if he found out even a little of what he'd been doing over the last few years. Kai had promised to play by the rules. To be a good sheep, but he was fundamentally different from all of those around him at the table. They all knew it on some level. They felt it, deep down. It was why he unsettled them so much. In this place everyone wore a mask of flesh, but few had the bravery to look upon him as he truly was, stripped of all illusion. He belonged to another era that everyone wanted to forget.
"Akosh was partially responsible for what happened at the Red Tower," Vargus said eventually, breaking the silence. "One of the mages who survived found out that she was to blame. I'm told it was this mage who attacked Akosh last night, seeking vengeance for her murdered family. Their battle collapsed one building and several people died. Akosh fled the area and has not been spotted since. You told me she wasn't in the north when I asked."
Another arrow thrown his way. Vargus definitely had a boil that needed lancing and currently it seemed as if Kai was the pus-filled target. One of the reasons Akosh had remained hidden for so long was that he'd misdirected Vargus away from Zecorria and the capital city in particular. Her plans had been developing nicely, which he'd permitted to continue, but now that would have to change.
"She wasn't at the time. Perhaps she recently arrived in Zecorria," he suggested but Vargus didn't seem convinced. Kai couldn't tell if his old friend was angry because he could hear the lies, or he suspected Kai was somehow involved with Akosh.
"Vargus, where are you now?" asked Nethun.
"Travelling through Shael. It's going to take me a while to reach Herakion."
The old sailor didn't look pleased. Perhaps wishing he'd given the task to someone else, but this kind of work was always left to Vargus. Apparently no one else could be trusted. "Fine. Get there as fast as you can. Akosh broke the one rule he passed down," said Nethun. All eyes briefly turned to the empty chair at the head of the table. It amazed Kai that a piece of furniture could inspire so much fear and awe among his kind. The majority of those sat around the table had never even seen the Maker and yet they were absolutely terrified of him. "The Queen of Yerskania was recently attacked. My sources tell me it was in retaliation for something she did."
For all of his little birds, who whispered secrets into dark corners so that he might hear them, Kai's reach was limited. Nethun had followers in every port and on every ship in the world. They would be crawling all over Perizzi which explained how he knew so much about what went on in that city. It was one of the reasons Kai avoided travelling there. Another was that it stank of fish.
"Why do we care?" asked Kai. "The mortals have been killing each other since the beginning."
Nethun's frown deepened. "Because Akosh gave the order."
"Attempts by the humans have been made to dissolve Akosh's power by rededicating her orphanages," said Vargus, stepping in smoothly. "It was a good start, but it's not enough."
"We will ensure her end is final. We will rip her up, from root to stem," promised Nethun, clenching his ham-sized fists. "All of us will do this."
The Blessed Mother and a few others made noises of agreement which was a surprise.
They had been planning this. Vargus, Nethun and at least four or five others must have met earlier to discuss a plan of attack. Normally these meetings were a waste of time. Just an opportunity for the new faces to bask in the glory of their elders. To hear them speak wisely, make decisions without asking for their opinion, and be given warnings about not interfering. Asking everyone to get involved was new and unexpected. Moving forward Kai would have to be increasingly careful.
"What do you want us to do?" asked one of the youngest, eager to please.
"Find every orphanage belonging to Akosh, in every country, and make sure it is converted to another faith." Nethun's tone of voice left no room for discussion. In a hundred years she would cease to be, but she wouldn't receive such a period of grace. They intended to utterly destroy her much sooner than that. "She was also responsible for replacing a number of significant people in Perizzi with her own followers. We must ensure she's not done this in other cities. Report any such interference directly to me," said the old sailor.
"What will be done about Akosh in the meantime?" asked the Blessed Mother. "Kai will have to keep watch for her until I arrive," said Vargus.
"I will be happy to, brother," said Kai, forcing a smile. He knew exactly where she was at the moment, running scared from a mortal. It was so pathetic he almost laughed out loud.
"Is there anyone else in the Zecorran capital?" asked the Blessed Mother, turning towards the Lady of Light. After all the country was her stronghold but she sadly shook her head. Everything about her was sad. From her droopy mouth to her sad eyes, always so full of compassion and love. It was sickening.
Kai would have been offended by the Blessed Mother's lack of trust if not for the fact that he despised the old hag.
Of course, he was lying to all of them, but that was beside the point.
"I am in Shael," said the Lady of Light. "There are many here who are lost and dispossessed." Her benevolence made Kai want to vomit onto her face. She'd been scared into her new subservient role by Vargus after he'd destroyed her consort. It had been a mask to begin with, but now she had become that which she'd pretended to be in the past. She was a prisoner and didn't even realise.
"Anyone else?" asked Nethun.
Remarkably there were few in the country and no others in the city, a fact Kai knew very well. Those who had travelled to Herakion had mysteriously disappeared, a fact that no one had yet noticed.
"Should we travel to Herakion to lend our support in the search?" asked a desperate youngster. He was like a hungry puppy, begging for scraps from his master's table.
Nethun barely considered it. "No. It's not worth the risk."
Kai noticed he didn't specify who or what would put them at risk. Even if they destroyed Akosh's future she still had a large number of followers, particularly in the north, providing her with strength. A youngster bumbling into the city would be easily noticed and Akosh's followers would warn her that someone else was on her trail. Nethun was also probably worried that some of the mortals might be murdered during such a battle.
"I will do my best to keep you apprised of her whereabouts," said Kai, his smile bordering on a grimace. Ever a monument of witty banter the old sailor merely grunted.
"Is there any other business?" asked Summer.
"No, we're done," said Nethun, talking over one of the youngsters who'd raised his hand. With that they were dismissed. The majority of those assembled immediately vanished, returning to the mortal world.
"I'll see you soon," said Vargus, making it sound like both a promise and a threat. With that he too vanished. If Kai didn't know any better he would have said his old friend was distracted.
A few of his brethren had stayed behind and a group of four were having a frantic whispered conversation. They were too far away for Kai to overhear but he actually didn't care. Their petty concerns were of no interest to him. He'd lingered to ponder what to do about Akosh and how to manoeuvre Vargus when he eventually arrived. It was when the four youngsters concluded their discussion and finally vanished that Kai realised he wasn't alone.
Sat only a few seats from the head of the table was Elwei. He'd not spoken a word during their meeting and Kai had to admit he'd forgotten he was even there. His head was still turned away, staring at something in the distance, perhaps half a world away. Kai might have thought the old Pilgrim had lingered for him if not for the distracted stare.
Ignoring him Kai returned to the world, stepped around the blind beggar and hurried away down the street. It wouldn't take long for Vargus to arrive in the city. A few weeks at most. It might be possible to delay him for a few days, but Kai knew he was relentless. It was better to deal with Akosh now, make plans for when Vargus arrived, and hold a few plans in reserve in case those failed. Experience had taught him to prepare for the unexpected when his brethren were involved.
Garvey, the blind beggar had watched with his mouth agape, as the man-shaped being paused in front of him on the street. It moved like a man but it wasn't human and he doubted it was even mortal. It was more akin to a chalk outline of a man. Inside it was filled with a vast ocean of swirling energy that was both alien and somehow familiar. Even without the use of his eyes his remaining senses were being flooded by the creature in front of him. Energy radiated out from the being in waves, like ripples on a pond, which he translated into feelings. Darkness, despair and a sea of blood across time were the strongest impressions he received. The number of deaths connected to it seemed endless. There was so much blood he could taste it in the back of his mouth. Garvey would have screamed if his throat hadn't been so constricted with terror.
Everyone else on the street seemed oblivious to the weight of its presence, but he could feel a pressure against his mind. Its immense power made his teeth ache and his bones hum. Being so close it felt as if his skin felt were on fire. Thousands of hot needles were scratching across every part of his body.
It was also what he'd been searching for since escaping from the palace. The first time he'd sensed it had been his cell. And somehow it had noticed him reaching out across the city with his newly evolved senses. If not for Tianne's distress Garvey would've been discovered and he suspected torn to pieces. It was malicious and he knew it could crush him like an insect, but like a moth to the light he was drawn to it. Such a being was far beyond anything he'd encountered before. Its existence was both terrifying and intoxicating.
He'd expected the being to move away down the street, but something had happened. It had paused right in front of him, staring off into the distance. Even masking his own magic Garvey had sensed a peculiar shift in the air around the being. Energy unlike any he'd felt before saturated the area and a doorway had opened. The being of light remained immobile, staring into space, while the larger part seemed to travel elsewhere. He felt its focus move away from the street and decided to take a risk.
Reaching out to the Source he drew energy into his body. His fatigue and the pain in his muscles instantly vanished. His hunger became a distant niggle and the strain from being so close to the being also faded away.
In the rest of the city time seemed to be standing still. All sounds were muffled and stretched. Hawkers voices stretching on and on in an endless shout, never wavering. Overhead a seagull cried out, its mournful cry grating on the ears. Garvey seemed to be caught within a bubble as he could hear his heart beating normally.
Carefully, with delicate strands of power, he explored the surrounding area, noting the subtle changes. Only a few minutes had passed when Garvey's instincts began to scream at him to run. He instantly severed his connection to the Source and masked his power as the doorway to the other place reopened. The being returned to the present and marched away down the street, muttering under its breath.
Garvey was about to follow when the air in front of him flickered again. Time had resumed its normal pace and yet a schism remained. No one noticed as he moved towards it and reached out with one hand. The second he made contact the street and the whole world around him disappeared. His heart seemed to stop beating in his chest and Garvey found himself standing inside a huge building. Even without his eyes he could sense the vast space surrounding him and the high ceiling above his head. His breathing echoed loudly in the empty space, rebounding off bare stone walls suggesting the room held little or no soft furniture.
Something ancient and huge sat in the middle of the room. It held a distant echo of life. As soon as his fingers touched the surface of the table he knew the tree it came from had stood upon the world centuries before he was born. It was impossibly long and yet was a single piece of wood.
At first Garvey thought he was alone, but eventually became aware of a tall figure seated at the table. The stranger stood up and approached on sandaled feet that whispered across the tiled floor. His presence was as overwhelming as the other being, but Garvey sensed it was being masked, to make it more bearable for him.
"No mortal had set foot in this hall in over one thousand years," said the tall man, his voice deep and sonorous. The other had radiated malice but Garvey didn't feel afraid of the being in front of him, merely overwhelmed and intrigued. "And now, two Sorcerers have been here in only a handful of years."
"Balfruss," said Garvey. "Who are you?"
"A Pilgrim. More than that is not important."
As silence filled the hall Garvey thought the Pilgrim was waiting for him to speak. "Why am I here?"
"I sensed you were nearby."
"I was following someone like you," said Garvey. "But he was different."
"How?"
"He's coursing with malicious, dark energy. Blood and violence cling to him like a second skin. I've never felt anything like it."
"Tell me more," said the Pilgrim.
#
**if you enjoyed**
**MAGEFALL**
**look out for**
**YOU DIE WHEN YOU DIE**
**West of West: Book One**
**by**
**Angus Watson**
_You can't change your fate—so throw yourself into battle, because you'll either win or wake up drinking mead in the halls of your ancestors._
_When his settlement is massacred by a hostile empire, Finn and his clan must make their escape across an unforgiving land, battling animals and monsters, determined assassins, powerful tribes, and each other to fulfill a prophecy that is their only hope._
# Part One
# Hardwork, a Town by a Lake, and Calnia, a City by a River
# Chapter 1
# Finnbogi Is in Love
Two weeks before everyone died and the world changed for ever, Finnbogi the Boggy was fantasising about Thyri Treelegs.
He was picking his way between water-stripped logs with a tree stump on one shoulder, heading home along the shore of Olaf's Fresh Sea. No doubt, he reasoned, Thyri would fall in love with him the moment he presented her with the wonderful artwork he was going to carve from the tree stump. But what would he make? Maybe a racoon. But how would you go about...
His planning was interrupted by a wasp the size of a chipmunk launching from the shingle and making a beeline for his face.
The young Hardworker yelped, ducked, dropped the stump and spun to face his foe. Man and insect circled each other crabwise. The hefty wasp bobbed impossibly in the air. Finnbogi fumbled his sax from its sheath. He flailed with the short sword, but the wasp danced clear of every inept swipe, floating closer and louder. Finnbogi threw his blade aside and squatted, flapping his hands above his head. Through his terror he realised that this manoeuvre was exactly the same as his rabbit-in-a-tornado impression that could make his young adoptive siblings giggle so much they fell over. Then he noticed he could no longer hear the wasp.
He stood. The great lake of Olaf's Fresh Sea glimmered calmly and expansively to the east. To the west a stand of trees whispered like gossips who'd witnessed his cowardice in the face of an insect. Behind them, great clouds floated indifferently above lands he'd never seen. The beast itself—surely "wasp" was insufficient a word for such a creature—was flying southwards like a hurled wooden toy that had forgotten to land, along the beach towards Hardwork.
He watched until he could see it no longer, then followed.
Finnbogi had overheard Thyri Treelegs say she'd be training in the woods to the north of Hardwork that morning, so he'd donned his best blue tunic and stripy trousers and headed there in order to accidentally bump into her. All he'd found was the tree stump that he would carve into something wonderful for her, and, of course, the sort of wasp that Tor would have battled in a saga. He'd never seen its like before, and guessed it had been blown north by the warm winds from the south which were the latest and most pleasant phenomenon in the recent extraordinary weather.
If any of the others—Wulf the Fat, Garth Anvilchin or, worst of all, Thyri herself—had seen him throw away his sax and cower like Loakie before Oaden's wrath, they'd have mocked him mercilessly.
Maybe, he thought, he could tell Thyri that he'd killed the wasp? But she'd never believe how big it had been. What he needed to do was kill an animal known for its size and violence... That was it! That's how he'd win her love! He would break the Scraylings' confinement, venture west and track down one of the ferocious dagger-tooth cats that the Scraylings banged on about. It would be like Tor and Loakie's quest into the land of the giants, except that Finnbogi would be brawny Tor and brainy Loakie all rolled into one unstoppable hero.
The Scraylings were basically their captors, not that any Hardworker apart from Finnbogi would ever admit that.
Olaf the Worldfinder and the Hardworkers' other ancestors had arrived from the old world five generations before at the beginning of winter. Within a week the lake had frozen and the unrelenting snow was drifted higher than a longboat's mast. The Hardworkers had been unable to find food, walk anywhere or sail on the frozen lake, so they'd dug into the snow drifts and waited to die.
The local tribe of Scraylings, the Goachica, had come to their rescue, but only on two big conditions. One, that the Hardworkers learn to speak the universal Scrayling tongue and forsake their own language, and, two, that no Hardworker, nor their descendants, would ever stray further than ten miles in any direction from their landing spot.
It had been meant as a temporary fix, but some Scrayling god had decreed that Goachica continue to venerate and feed the Hardworkers, and the Hardworkers were happy to avoid foraging and farming and devote their days to sport, fighting practice, fishing, dancing, art or whatever else took their fancy.
Five generations later, still the Goachica gave them everything they needed, and still no Hardworker strayed more than ten miles from Olaf's landing spot. Why would they? Ten miles up and down the coast and inland from Olaf's Fresh Sea gave them more than enough space to do whatever they wanted to do. Few ever went more than a mile from the town.
But Finnbogi was a hero and an adventurer, and he was going to travel. If he were to break the confinement and track down a dagger-tooth cat... He'd be the first Hardworker to see one, let alone kill one, so if he dragged the monster home and made Thyri a necklace from its oversized fangs surely she'd see that he was the man for her? Actually, she'd prefer a knife to a necklace. And it would be easier to make.
A few minutes later Finnbogi started to feel as though he was being followed. He slowed and turned. There was nothing on the beach, but there was a dark cloud far to the north. For an alarming moment he thought there was another great storm on the way—there'd been a few groundshakers recently that had washed away the fishing nets and had people talking about Ragnarok ending the world—but then realised the cloud was a flock of crowd pigeons. One of the insanely huge flocks had flown over Hardwork before, millions upon millions of birds that had taken days to pass and left everything coated with pigeon shit. Finnbogi quickened his pace—he did not want to return to Hardwork covered in bird crap—and resumed his musings on Thyri.
He climbed over a bark-stripped log obstructing a narrow, sandy headland and heard voices and laughter ahead. Finnbogi knew who it was before he trudged up the rise in the beach and saw them. It was the gang of friends a few years older than he was.
Wulf the Fat ran into the sea, naked, waving his arms and yelling, and dived with a mighty splash. Sassa Lipchewer smiled at her husband's antics and Bodil Gooseface screeched. Bjarni Chickenhead laughed. Garth Anvilchin splashed Bodil and she screeched all the more.
Keef the Berserker stood further out in Olaf's Fresh Sea, his wet, waist-length blond hair and beard covering his torso like a sleeveless shirt. He swung his long axe, Arse Splitter, from side to side above the waves, blocking imaginary blows and felling imaginary foes.
Finnbogi twisted his face into a friendly smile in case they caught him looking. Up ahead their clothes and weapons were laid out on the shingle. Bodil and Sassa's neatly embroidered dresses were hanging on poles. Both garments would have been Sassa Lipchewer creations; she spent painstaking hours sewing, knitting and weaving the most stylish clothes in Hardwork. She'd made the blue tunic and stripy trousers that Finnbogi was wearing, for example, and very nice they were too.
The four men's clothes, tossed with manly abandon on the shingle, were leathers, plus Garth Anvilchin's oiled chainmail. Garth's metal shirt weighed as much as a fat child, yet Garth wore it all day, every day. He said that it would rust if the rings didn't move against each other regularly so he had to wear it, and also he wanted to be totally comfortable when he was in battle.
_In battle!_ Ha! The Hird's only battles were play fights with each other. The likelihood of them seeing real action was about the same as Finnbogi travelling west and taking on a dagger-tooth cat. He knew the real reason Garth wore the mail shirt all the time. It was because he was a prick.
Despite the pointlessness of it, many of the hundred or so Hardworkers spent much time learning to fight with the weapons brought over from the old world. All four of the bathing men were in the Hird, the elite fighting group comprising Hardwork's ten best fighters.
Finnbogi _had_ expected to be asked to join the Hird last summer when someone had become too old and left, but Jarl Brodir had chosen Thyri Treelegs. That had smarted somewhat, given that she was a girl and only sixteen at the time—two years younger than him. It was true that she had been making weapons, practising moves and generally training to be a warrior every waking hour since she was about two, so she probably wouldn't be a terrible Hird member. And he supposed it was good to see a woman included.
All Hardwork's children learnt the reasons that Olaf the Worldfinder and Hardwork's other founders had left the east, sailed a salty sea more vast than anyone of Finnbogi's generation could supposedly imagine, then travelled up rivers and across great lakes to establish the settlement of Hardwork. Unfair treatment of women was one of those reasons. So it was good that they were finally putting a woman in the Hird, but it was a shame that it had robbed Finnbogi of what he felt was his rightful place. Not that he wanted to be in the stupid Hird anyway, leaping about and waving weapons around all day. He had better things to do.
Out to sea, Wulf the Fat dived under—he could stay down for an age—and Garth Anvilchin caught sight of Finnbogi on the beach. "Hey, Boggy!" he shouted, "Don't even think about touching our weapons or I'll get one of the girls to beat you up!"
Finnbogi felt himself flush and he looked down at the weapons—Garth's over-elaborately inlaid hand axes the Biter Twins, Bjarni's beautiful sword Lion Slayer, Wulf's thuggish hammer Thunderbolt and Sassa's bow which wasn't an old world weapon so it didn't have a name.
"And nice outfit!" yelled Garth. "How lovely that you dress up when you go wanking in the woods. You have to treat your hand well when it's your only sexual partner, don't you, you curly-haired cocksucker?"
Finnbogi tried to think of a clever comeback based on the idea that if he sucked cocks then he clearly had more sexual partners than just his hand, but he didn't want to accept and develop the him-sucking-cocks theme.
"Fuck off then, Boggy, you're spoiling the view," Garth added before any pithy reply came to Finnbogi, curse him to Hel. Garth might be stupid but he had all the smart lines.
"Leave him alone," said Sassa Lipchewer. Finnbogi reddened further. Sassa was lovely.
"Yes, Garth," Bodil piped up. "Come for a wash, Finnbogi!"
"Yes, Boggy boy! Clean yourself off after all that wanking!" Garth laughed.
Wulf surfaced and smiled warmly at Finnbogi, the sun glinting off his huge round shoulders. "Come on in, Finn!" he called. Finally, somebody was calling him by the name he liked.
"Come in, Finn!" Bodil called. "Come in, Finn! Come in, Finn!" she chanted.
Sassa beckoned and smiled, which made Finnbogi gibber a little.
Behind them, Keef, who hadn't acknowledged Finnbogi's presence, continued to split the arses of imaginary enemies with his axe Arse Splitter.
"I can't swim now, I've got to... um..." Finnbogi nodded at the stump on his shoulder.
"Sure thing, man, do what you've got to do, see you later!" Wulf leapt like a salmon and disappeared underwater.
"Bye, Finn!" shouted Bodil. Sassa and Bjarni waved. Garth, towering out of the water, muscular chest shining, smiled and looked Finnbogi up and down as if he knew all about the wasp, why he was wearing his best clothes and what he had planned for the stump.
"I don't know why you give that guy any time..." he heard Garth say as he walked away.
He didn't know why the others gave any time to Garth Anvilchin. He was _such_ a dick. They were okay, the rest of them. Wulf the Fat had never said a mean word to anyone. Bjarni Chickenhead was friendly and happy, Sassa Lipchewer was lovely. And Bodil Gooseface... Bodil was Bodil, called Gooseface not because she looked like a goose, but because Finnbogi had once announced that she had the same facial expressions as a clever goose, which she did, and the name had stuck. Finnbogi felt a bit bad about that, but it wasn't his fault that he was so incisively observant.
He walked on, composing cutting replies to Garth's cock-sucking comments. The best two were "Why don't you swim out to sea and keep on swimming?" and "Spoiling the view am I? You're the only person here with a good view because you're not in it!"
He wished he'd thought of them at the time.
# By Stephen Aryan
#### THE AGE OF DREAD
_Mageborn_
_Magefall_
#### THE AGE OF DARKNESS
_Battlemage_
_Bloodmage_
_Chaosmage_
# Praise for Stephen Aryan
"[Stephen Aryan] enlivens his tale with abundant politics, intrigues, double-crossings, and plot twists to keep the pacing brisk and whet readers' appetites for future installments."
— _Publishers Weekly_ on _Mageborn_
"A propulsive combination of thrills, mystery, and magic."
_—B &N Sci-Fi & Fantasy Blog_ on _Mageborn_
"A vivid and rousing adventure with the kind of magic that punches you right in the face."
—Jen Williams on _Battlemage_
"This is epic fantasy for readers who appreciate extra helpings of carnage with their backstabbing."
— _Publishers Weekly_ on _Battlemage_
"Stephen Aryan puts the epic into Epic Fantasy. This is a ground-shaking debut, full of fiery promise."
—Den Patrick, on _Battlemage_
# We hope you enjoyed this book.
## Wondering what to read next?
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# Contents
1. COVER
2. TITLE PAGE
3. COPYRIGHT
4. TABLE OF CONTENTS
5. DEDICATION
6. CHAPTER 1
7. CHAPTER 2
8. CHAPTER 3
9. CHAPTER 4
10. CHAPTER 5
11. CHAPTER 6
12. CHAPTER 7
13. CHAPTER 8
14. CHAPTER 9
15. CHAPTER 10
16. CHAPTER 11
17. CHAPTER 12
18. CHAPTER 13
19. CHAPTER 14
20. CHAPTER 15
21. CHAPTER 16
22. CHAPTER 17
23. CHAPTER 18
24. CHAPTER 19
25. CHAPTER 20
26. CHAPTER 21
27. CHAPTER 22
28. CHAPTER 23
29. CHAPTER 24
30. CHAPTER 25
31. CHAPTER 26
32. CHAPTER 27
33. CHAPTER 28
34. CHAPTER 29
35. CHAPTER 30
36. CHAPTER 31
37. CHAPTER 32
38. CHAPTER 33
39. CHAPTER 34
40. CHAPTER 35
41. CHAPTER 36
42. CHAPTER 37
43. CHAPTER 38
44. CHAPTER 39
45. CHAPTER 40
46. CHAPTER 41
47. CHAPTER 42
48. CHAPTER 43
49. CHAPTER 44
50. CHAPTER 45
51. CHAPTER 46
52. ACKNOWLEDGEMENTS
53. EXTRAS
54. MEET THE AUTHOR
55. A PREVIEW OF _THE AGE OF DREAD: BOOK THREE_
56. A PREVIEW OF _YOU DIE WHEN YOU DIE_
57. BY STEPHEN ARYAN
58. PRAISE FOR STEPHEN ARYAN
59. ORBIT NEWSLETTER
# Navigation
1. Begin Reading
2. Table of Contents
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Title XLVIII
EARLY LEARNING-20 EDUCATION CODE Chapter 1013
EDUCATIONAL FACILITIES View Entire Chapter
F.S. 1013.38
1013.38 Boards to ensure that facilities comply with building codes and life safety codes.—
(1) Boards shall ensure that all new construction, renovation, remodeling, day labor, and maintenance projects conform to the appropriate sections of the Florida Building Code, Florida Fire Prevention Code, or, where applicable as authorized in other sections of law, other building codes, and life safety codes.
(a) For each proposed new facility and each proposed new facility addition exceeding 2,500 square feet, the board shall submit for review a minimum of one copy of the site plan to the local county, municipality, or independent special fire control district providing fire protection services to the facility.
(b) The local county, municipality, or independent special fire control district may review each site plan for compliance with the applicable provisions of the Florida Fire Prevention Code relating to fire department access roads, fire protection system connection locations, and fire hydrant spacing. Such site plans are not subject to local amendments to the Florida Fire Prevention Code or local ordinances as provided in s. 1013.371. Site plan reviews conducted pursuant to this section shall be performed at no charge to the school board or public college board.
(c) The site plan shall be deemed approved unless the local county, municipality, or independent special fire control district submits to the fire official appointed by the board, in writing, any deficiencies identified with reference to specific provisions of the Florida Fire Prevention Code within 15 days after receipt of the site plan. The fire official shall incorporate such comments into his or her review and subsequent inspections.
(d) If the local county, municipality, or independent special fire control district and the fire official appointed by the board do not agree on the requirements or application of the Florida Fire Prevention Code, either party may refer the matter to the State Fire Marshal, who shall have final administrative authority in resolving the matter.
(2) In addition to the submission of site plans, boards may provide compliance as follows:
(a) Boards or consortia may individually or cooperatively provide review services under the insurance risk management oversight through the use of board employees or consortia employees registered pursuant to chapter 471, chapter 481, or part XII of chapter 468 and firesafety inspectors certified under s. 633.216.
(b) Boards may elect to review construction documents using their own employees registered pursuant to chapter 471, chapter 481, or part XII of chapter 468 and firesafety inspectors certified under s. 633.216.
(c) Boards may submit phase III construction documents for review to the department.
(d) Boards or consortia may contract for plan review services directly with engineers and architects registered pursuant to chapter 471 or chapter 481 and firesafety inspectors certified under s. 633.216.
(3) The Department of Management Services may, upon request, provide facilities services for the Florida School for the Deaf and the Blind, the Division of Blind Services, and public broadcasting. As used in this section, the term "facilities services" means project management, code and design plan review, and code compliance inspection for projects as defined in s. 287.017(5).
(4)(a) Before the commencement of any new construction, renovation, or remodeling, the board shall:
1. Approve or cause to be approved the construction documents and evaluate such documents for compliance with the Florida Building Code and the Florida Fire Prevention Code.
2. Ensure compliance with all applicable firesafety codes and standards by contracting with a firesafety inspector certified by the State Fire Marshal under s. 633.216.
(b) A certificate of occupancy may not be issued until the board, through its designated certified building official, has determined that the building or structure and its site conditions comply with all applicable statutes and rules.
(c) The method of compliance as chosen by the board pursuant to subsection (2) shall be documented and maintained as part of the construction record file.
(d) Upon request by the local county, municipality, or independent special fire control district, the board shall provide reasonable access to all construction documents.
History.—s. 837, ch. 2002-387; s. 42, ch. 2010-151; s. 6, ch. 2011-79; s. 159, ch. 2013-183.
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Here's what REALLY happened after Kanye West ruined Taylor Swift's big VMA moment
The start of their famous feud began in 2013...
Kanye west ruins Taylor Swift's VMA speech
Updated 15:44, 21 Aug 2018
It was a defining pop culture moment of 2013.
But, while the world witnessed Kanye West storm the VMA stage during Taylor Swift's award speech, most of us didn't get to see the ugly fall-out backstage.
However, ex-MTV chief Van Toffler has now revealed all about the infamous moment, offering some behind-the-scenes vignettes which add extra, HD colour to the drama.
Specifically, that one of the world's biggest singers was left in tears over it all.
West had earlier been seen on the red carpet accompanied by his model girlfriend Amber Rose and a half-empty bottle of Hennessy Cognac (
Rex Features)
Swift and her mother were left in tears by the incident (
Speaking to The Hollywood Reporter , who asked what his best MTV story was, the business mogul said: "When Kanye walked up onstage with Taylor that year, it turned out that Taylor had to go onstage to do her song five minutes later.
"I ran out of the truck to see that everything was all right, and Taylor and her mom were crying hysterically. I'm not always wonderful with emotions. I didn't know what to say.
"Then I went backstage, and Beyonce was crying, too."
The incident happened when a then-19-year-old Swift won the Best Female Video award for You Belong With Me.
During her speech, Kanye jumped on stage and grabbed the microphone out of her hand, saying: "Yo, Taylor, I'm really happy for you and I'mma let you finish, but Beyonce had one of the best videos of all time."
His intervention was not well received, as an apparently horrified Beyonce invited Taylor back on stage with her later in the night to finish her speech and even then US president Barack Obama weighed in - dubbing West "a jackass".
Kanye takes the microphone from Taylor and speaks onstage (
WireImage)
A few days later Kanye made a tearful appearance on The Jay Leno Show, saying: "It was rude, period. I don't try to justify it, 'cause I was in the wrong.
"Dealing with the fact that I hurt someone or took anything away, you know, from a talented artist - or from anyone - because I only wanted to help people.
"My entire life, I've only wanted to do and give something that I felt was right and I immediately knew in this situation that it was wrong."
Meanwhile Taylor appeared on chat show The View to confirm Kanye had not been in touch to apologise. This prompted him to call her, with Tay saying: "He was very sincere in his apology, and I accepted that apology."
BeyonceTaylor SwiftKanye West | {
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Кан Джун Хо (; 22 июня 1928, Хэджу — 24 сентября 1990, Сеул) — корейский боксёр легчайшей весовой категории, в 1950-е годы выступал за сборную Южной Кореи. Бронзовый призёр летних Олимпийских игр в Хельсинки, участник многих международных турниров и национальных первенств. Также известен как тренер по боксу, долгое время возглавлял сборную своей страны.
Биография
Кан Джун Хо родился 22 июня 1928 года в городе Хэджу, провинция Хванхэ-Намдо. Активно заниматься боксом начал в 1949 году во время службы в армии и через год в полулёгком весе стал национальным чемпионом. Благодаря череде удачных выступлений удостоился права защищать честь страны на летних Олимпийских играх 1952 года в Хельсинки, где участвовал в программе соревнований легчайшей весовой категории. В четвертьфинале раздельным решением судей победил будущего чемпиона мира среди профессионалов американца Дэйви Мура, но в полуфинальном матче единогласным решением проиграл ирландцу Джону Макнелли.
Получив бронзовую олимпийскую медаль, Кан продолжил выходить на ринг в составе национальной сборной, принимая участие во всех крупнейших международных турнирах. Так, в 1954 и 1958 годах он боксировал на летних Азиатских играх, тем не менее, пробиться в число призёров в обоих случаях не смог.
После завершения спортивной карьеры работал тренером, в том числе возглавлял сборную Южной Кореи по боксу — возил команду на Олимпийские игры 1968 и 1972 годов, где его подопечные завоевали серебряную и бронзовую медали. В поздние годы занимался подготовкой нескольких известных боксёров-профессионалов, в частности, его учениками были чемпионы мира Ким Сан Хьон и Пак Чхан Хи. Умер от хронической болезни 24 сентября 1990 года в Сеуле.
Ссылки
Боксёры Республики Корея
Боксёры 1950-х годов
Боксёры легчайшей весовой категории
Боксёры на летних Олимпийских играх 1952 года
Бронзовые призёры летних Олимпийских игр 1952 года | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,567 |
\section{Introduction}
The widespread use of microblogging services, such as Twitter, which generate immense content has resulted in considerable research focusing on utilizing their counts and semantic content for many different practical applications. For example, researchers can use microblogging data to gain insight into events and how people behave when an event occurs. The change in microblogging behavior when an event occurs creates patterns that can aid in detecting events. Detecting an event is important as it allows local authorities to both respond to the event and inform the public in a timely manner \parencite{ozdikis2017survey}.
An event is defined as a real-world one-time occurrence that generates the interest of people and is based on specific spatial and temporal properties \parencite{atefeh2015survey,ozdikis2017survey}. Events have been classified as unexpected or expected \parencite{atefeh2015survey,ozdikis2017survey}. Unexpected events are rare or at least infrequent occurrences that are unpredictable, unidentified, unscheduled or unknown. Prior knowledge about event type, time and location may not be readily available until well after the event has occurred.
The purpose of this paper is to create a novel approach, called \textit{Twitter Behavior Agent-Based Model (TBAM)}, that can simulate microblogging behavior in an event. The necessity for creating the model is due to the limitations researchers have with the real world Twitter data. Such data are scarce and unreliable in terms of the delivery, knowledge of ground truth, and information content. Before using the real world content, further complicated processing of the data would be required so that it is suitable for event detection. The data generated from simulations can be used to understand patterns or to enrich this \textit{underdeveloped} data.
We define underdeveloped data under two dimensions. These two dimensions are \textit{reliability} and \textit{delivery slate}. Data can have high or low reliability and data delivery can be regular or sporadic. We can consider medical data from instruments (e.g. EKG data) to have high reliability and regular delivery slate. On the other hand, Twitter data has low reliability and low delivery slate.
Twitter content involves humans as source of the data which means that the data could intentionally or unintentionally be distorted and further only provides subjective information mixed with personal emotion. For example, microblogging data usually does not contain complete spatial information (like latitude and longitude) that is essential for accurate event detection. Use of location anonymization techniques for privacy preservation makes the latitude and longitude (\textit{geotags}) not readily available. Moreover, the data available is typically aggregated in space which reduces the event detection accuracy. Alternatively, researchers have used location names found in the message (also called place name) and user location found in their profiles to localize an event. But again, this information is not reliable as users may use multiple locations or may be slow in updating location information. This means that the location in the profile and the user location need not be consistent. Users may include incorrect location information which further reduces the data reliability \parencite{atefeh2015survey}. Twitter messages are short in length and can contain ambiguous words making it hard to obtain correct semantic information from the messages. Hence, Twitter data has low reliability. Another example of data with low reliability is mis-information data like fake news data \parencite{mcnair2017fake} because fake news data also involves humans as data sources.
The sporadic delivery slate of Twitter data is because there is no control over the delivery frequency and not all users are sending out event related data and even if they do, it may not be about an event and users may microblog only when it is convenient or of their interest. Factors like number of users who actively microblog, time of day, population density, significance of the microblog or event, etc. influence how frequently people may send out standard and event-related microblogs. Sensor data is another example of data with potentially sporadic delivery slates because of the battery life, duty cycle, random triggers, etc. For example, many sensors with limited battery life that cannot be replaced for long periods of time generate data only when events are detected and sometimes with long duty cycles. Other sensors only send out data when there is an external trigger (e.g. motion detection sensors only are triggered and send data when motion is detected). Thus, sensors may have unreliable delivery slate. Figure \ref{fig:data_domain} shows the placement of different data types according to their reliability and delivery slate.
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{iscram1.pdf}
\caption{Dimensions of Data}
\label{fig:data_domain}
\end{figure}
A consequence of the underdeveloped nature of data is that there might not be granular data or location information. These limitations reduce event detection accuracy. Data generated through models could not only be used as a replacement to real data to understand event change patterns but also complement and enrich the real data by providing information that the real data may not contain. As one example, the generated data may be used to train machine learning models to find event signatures. These machine learning models can then be applied to real data from Twitter to detect events. To create TBAM we use agent-based models (ABM). An ABM implements a top-down modeling approach where we can set different parameters that change the generation and distribution of tweets. An alternative approach for modelling could be through machine-learning, like generative adversarial networks (GAN) which would work as a bottom-up approach. In the bottom-up approach, instead of using parameters to generate data, the real data is directly used to train GAN and generate synthetic data. The limitation of the latter is the lack of explain-ability of the synthetic data.
To generate data using TBAM, we assume that there are users with known locations distributed throughout the (synthetic) world. There is a reference sensor (we call it a social sensor) placed at a known location that counts the number of tweets at radial distances from itself. In Figure \ref{fig:sim_world_comp} the sensor is placed at the origin $(0,0)$. We believe that counting the number of tweets can give us reasonable information about microblogging behavior and we use this rather than focusing on the messages within the tweets (which need further processing). The changes in the number of tweets can be used for event detection. For example, previous work has shown that peaks in a time series of the number of tweets is an indication of an event \parencite{Mehdi2020Sem}. We assume the spreading of information about an event is analogous to rumor-spreading \parencite{jin2013epidemiological}. The rumor spreading model assumes that information about an event spreads out gradually similar to the ripple effect when a stone is dropped in a puddle of water.
Figure \ref{fig:sim_world_comp} also shows different parameters like the probability that a user will tweet, distance and time from event, significance of an event, etc. By changing these parameters we have more control over the delivery slate. This allows generation of synthetic data that can match different scenarios. Finally, we validate our generated synthetic data by comparing it with data obtained from Twitter. Figures \ref{fig:virg_abm}, \ref{fig:stem_abm} and \ref{fig:gar_abm} show the comparison between the generated data using TBAM and the data obtained by scraping Twitter around three events. We describe the data sets later.
\begin{figure}[htp]
\centering
\includegraphics[width=0.80\textwidth]{tbam/netlogo_interface.png}
\caption{An example of TBAM's interface: the left side shows the parameters and the right side shows the simulation space}
\label{fig:sim_world_comp}
\end{figure}
\begin{figure}[htp]
\centering
\subfigure[Plot of VIRG Twitter Data vs TBAM generated data]{\includegraphics[width=0.45\textwidth]{tbam/virg0_tbam.png}\label{fig:virg_abm}}\hfill
\subfigure[Plot of STEM Twitter Data vs TBAM generated data]{\includegraphics[width=0.45\textwidth]{tbam/stem0_tbam.png}\label{fig:stem_abm}}\hfill
\subfigure[Plot of Garlic Festival Twitter Data vs TBAM generated data]{\includegraphics[width=0.45\textwidth]{tbam/gar0_tbam.png}\label{fig:gar_abm}}
\caption{Comparison of Real Twitter data with TBAM generated data}
\end{figure}
In summary, our goals and contributions in this paper are as follows:
\textbf{Formulation and Algorithm:} We propose a methodology called Twitter Behavior Agent-Based Model (TBAM) and build a simulation using Netlogo to generate data using agent based modeling. Our model is able to identify the major parameters that affect the microblogging behavior in users.
\textbf{Accuracy:} Based on our results, we are accurately able to generate data that are statistically significant to real data as seen in Figures \ref{fig:virg_abm}, \ref{fig:stem_abm} and \ref{fig:gar_abm}.
\section{Literature Review} \label{lit_rev}
There are numerous surveys that focus on event detection and how humans behave when an event occurs \parencite{steiger2015advanced,atefeh2015survey,cordeiro2016online,garg2016review, imran2015processing, ajao2015survey,hasan2018survey,ozdikis2017survey,zheng2018survey}. It is believed that whenever an event occurs, there will be a change in the user behavior which will be reflected in the change in the microblogging activity. These papers have also mentioned how unreliable Twitter data is for event detection and that the data require considerable pre-processing before they can be used.
A part of the enrichment process for underdeveloped data is to use data generated through models. Generated data has been used in prior literature for \textit{data augmentation} and \textit{data imputation}. Data augmentation and imputation are relatively recently developed techniques. Data augmentation has been used in previous literature for image (e.g., facial data augmentation \parencite{wang2020survey}), speech and natural language processing (NLP) \parencite{dai2020analysis} and time-series data to reduce over-fitting \parencite{shorten2019survey,wen2020time}. Augmentation increases the size of the training data set by geometric and color transformations and deep learning techniques like Generative Adversarial Networks (GAN). Augmentation also alleviates the issue of class imbalance, which is a data set with skewed majority to minority sample ratios \parencite{shorten2019survey}. The effect of different augmentation techniques on time-series data was evaluated in \citeauthor{iwana2020empirical} (\citeyear{iwana2020empirical}) where there is also a guide for researchers and developers to help select the appropriate data augmentation method for their applications. Generative adversarial networks (GAN) was one of the popular methods used to generate synthetic images in the medical domain \parencite{bowles2018gan,frid2018gan,han2018gan}. These works generated images of CT images of liver lesions \parencite{bowles2018gan,frid2018gan} and MR images \parencite{han2018gan} which were very close in comparison to the real data. Similarly, cycle-Consistent Generative Adversarial Networks (CycleGANs) were proposed as an image classification method to detect floods using images found in social media \parencite{pouyanfar2019unconstrained}. An agent-based model simulator called \textit{paysim} was created to simulate mobile money transaction and to create a synthetic data that is similar to the original data set \parencite{paysim}.
Data imputation is the task of estimating missing values in a data set. Data imputation is usually done to find missing values in traffic data arising from sensor damage, malfunction, or transmission errors, etc. using low-rank matrix decomposition. Most work on data imputation has focused on using GANs for data imputation by slightly varying its structure or the loss function \parencite{kim2020survey}. Two of the prominent works that have used GAN as a method for finding missing values in time-series data are found in \citeauthor{luo2018multivariate} (\citeyear{luo2018multivariate}) and \citeauthor{yoon2018gain} (\citeyear{yoon2018gain}).
However, there is little literature that has addressed the issue of using generated data to understand user microblogging behavior. The research studies have used Agent-Based modelling (ABM) to study information diffusion but none of the works focus on how user tweeting behavior changes when an event occurs. In \citeauthor{cui2013empirical} (\citeyear{cui2013empirical}) ABM was used to investigate how information was spread during the 2011 Wenzhou train crash through the Sina Weibo. They use the ABM framework to compare information diffusion through word-of-mouth and mass media and to determine which is a more significant means of spreading information when it comes to social media. ABM has been used to create an information propagation model to study how retweeting occurs \parencite{xiong2012information,pezzoni2013retweet}. In \citeauthor{pezzoni2013retweet} (\citeyear{pezzoni2013retweet}) a retweeting model was created based on two main parameters: the influence of the user (number of followers a user has) and the time at which the tweet was received. In \citeauthor{xiong2012information} (\citeyear{xiong2012information}) the retweeting model was based on the susceptible-infected-refractory (SIR) model. Similarly in \citeauthor{gatti2013large} (\citeyear{gatti2013large}), ABM was used to study user behavior in a social network. The model was created to predict the sentiment of users and whether they choose to forward, reply or do nothing about a topic.
\section{Background} \label{prelim}
In this section we look at how agent-based modeling and the Twitter network works. We design our agent-based model based on these definitions.
\subsection{Agent-Based Modeling} \label{abm}
ABM has been used in many different fields for analysis and understanding of the real world like biology, chemistry, cyber-security, social and economic modeling, etc. \parencite{allan2010survey}. Agent-based models (ABM) \parencite{wilensky2015introduction} have entities or \textit{agents}. An agent can be an individual or an object that has specific properties and actions. The agents may move around in a two dimensional grid called the \textit{world}. The interactions between the agents can be quite complex but can be defined according to a set of rules. An agent can be autonomous, flexible, adaptable, and self-learning \parencite{macal2005tutorial}. There may be other models that can simulate scenarios pertaining to human social behavior and social media information dispersion (like system dynamics). However, ABM is able to better represent complex and heterogeneous interactions \parencite{wilensky2015introduction,macal2005tutorial} which makes it suitable for creating our model. Further, the microblogging behavior of one human may be considered actions of an agent, that may be influenced by what the agent sees in the environment and the actions of other agents. We believe that this is best modeled using ABM.
\subsection{Twitter as a Microblogging Service} \label{twit}
Twitter is currently the fastest growing (and by far the most popular) microblogging service with a lot of research being done on the generated content to understand human behavior \parencite{atefeh2015survey}. A Twitter user can send out a standard Twitter message called a \textit{tweet} about a specific topic and can contain a short text, links, or images. Messages can be grouped together based on their topic or group by use of their \textit{hastags}. Tweets can also be forwarded by other users and they are called \textit{retweet}s. A retweet can only be received if a user is in the same network as the user who originally sent out the tweet. The tweets for research and analysis can be obtained from the Twitter API\footnote{https://dev.twitter.com/overview/api}. The Twitter API can provide past tweets as well as stream tweets. The Twitter API only allows tweets to be collected over the past two weeks and has restrictions in terms of the amount of number of tweets that can be collected.
\section{Twitter Behavior Agent-Based Model (TABM) Description} \label{method}
To generate synthetic data we developed the Twitter Behavior Agent-Based Model (TBAM) that uses Agent-Based Modelling (ABM) to simulate how users tweet and how microblogging behavior changes when an event occurs. In this section we provide a detailed overview of the model and the different parameters used to generate TBAM data.
\subsection{TBAM Design}
The scope of TBAM is to simulate user behavior when an event occurs, more specifically to investigate the change in number of tweets as time and distance from event changes. For our model we consider "local events" \parencite{ozdikis2017survey}, i.e., events restricted to a certain region. Our model simulates microblogging behavior of people similar to what may happen within a city or a few small neighborhoods and helps us examine how people's microblogging behavior changes when they have close spatial and temporal proximity to an event.
We use \textit{Netlogo} \parencite{Netlogo} to create our agent based model. In Netlogo there are four types of agents: turtles, patches, links and observer. The turtles are agents that move around in the \textit{world}. The world is sub-divided into smaller squares called \textit{patches} and each patch has a unique coordinate. Links are agents that connect two turtles. The observer observes the agents and their interactions. In Netlogo models, time passes in discrete steps called \textit{ticks}.
Figure \ref{fig:sim_world_comp} shows a snapshot of the synthetic world at a particular tick. In our model, the turtles are the Twitter users (people) who send out the tweets. A tweet can be a non-event related tweet (which is a standard or routine tweet indicated by green colored users), an event related tweet (indicated by users colored yellow) or tweets sent out during low Twitter activity (indication by users colored black). The patches represent the locations over which Twitter users lie and where an event can occur. Initially all patches are colored blue. Once an event occurs, the patches change color to red as the patches are influenced by the event. In a real world setting a patch could represent a geographical coordinate. A tick is a unit of time over which the total number of tweets are measured. Ticks could be in hours, minutes or seconds depending on the time granularity that is required.
\subsection{TBAM Parameter Description} \label{tbam_desc}
In order to generate data that may accurately reflect real world settings we define different parameters. The parameters are summarized in Table \ref{tab:synth_exp2a} and Table \ref{tab:synth_exp2b}. In this section, we provide an overview of these parameters and explain how our model simulates microblogging behavior and event generation. The model is made of two phases. In the first phase, also called the \textit{setup} phase, the synthetic world settings are created in which the users will tweet. In the second phase, also called the \textit{simulation} phase, the users tweet and once an event occurs, their microblogging behavior changes.
\begin{table*}[htp]
\caption{Fixed parameters for all TBAM data generation simulations}
\centering
\begin{tabular}{| p{.25\textwidth} | p{.55\textwidth} | p{.10\textwidth} |}
\hline
\textbf{Parameter} & \textbf{Description} & \textbf{Value} \\
\hline
\texttt{n-events?} & binary: chooses between one event or n-events & FALSE \\
\hline
\texttt{event-sources} & sets number of events. Only valid if n-events is true & 1 \\
\hline
\texttt{eight-mode?} & binary: chooses between spreading event to both diagonal and adjacent patches or only to adjacent patches & true \\
\hline
\texttt{twitter-network} & binary: chooses between Erdos-Renyii and random network & Erdos-Renyii \\
\hline
\texttt{num-links} & number of links in the random network & -NA- \\
\hline
\texttt{people} & number of people microblogging & 1000 \\
\hline
\texttt{probability} & probability of a link being created between two people in the Erdos-Renyii Network & 0.45 \\
\hline
\texttt{step} & distance between each layer & 7 \\
\hline
\texttt{num-clusters} & number of clusters of people & 9 \\
\hline
\texttt{cluster?} & binary: choose to cluster people (1) or distribute people uniformly (0) & 1 \\
\hline
\texttt{percentage-clustering} & percentage of people in clusters & 0.75 \\
\hline
\texttt{tweet-threshold} & used to generate random number that a user will tweet & 0.7 \\
\hline
\texttt{user-interest} & duration over which people remain interested about a tweet & 5 \\
\hline
\texttt{event-interest} & duration over which people remain interested about tweets related to an event & 5 \\
\hline
\texttt{night-mode} & to consider periodicity in tweets and separate users microblogging at day and night & True \\
\hline
\end{tabular}
\label{tab:synth_exp2a}
\end{table*}
The setup phase begins with the creation of $N$ users. The users are randomly distributed throughout the world. Some of the users are clustered together. The number of clusters are defined by the parameter \texttt{num-clusters}. The parameter \texttt{cluster?} determines if the users are clustered or not and \texttt{percentage-clustering} determines what percentage of users are clustered together randomly in each of the clusters. The setup phase also generates concentric circles around the central coordinate, i.e $(0,0)$. The central coordinate is the location of the sensor that counts the number of tweets. Each consequent circle increases its radius by the parameter \texttt{step}. These circles aim to provide a visual understanding of how tweets change with changing distance.
To simulate a Twitter network, some users are linked together with bi-directional links. The links are generated using \textit{Erdos-Renyi} model which has been used in previous literature to study social networks \parencite{erdHos1960evolution}. In the Erdos-Renyi model, each link between a user has a fixed probability of being present and being absent independent of the links in a network. The parameter \texttt{probability} can be varied to change the probability and create networks with a lot of links or with very few links between users. There is also an option for generating a network with random links between users. The \texttt{num-links} is a parameter specific to random networks which randomly creates \texttt{num-links} number of links between different users. The \texttt{twitter-network} can be set to true or false to choose between Erdos-Renyi or random model to generate the network.
In the simulation phase at each tick the total number of tweets sent out are counted. The total number of tweets are the sum of standard tweets, event related tweets, and tweets sent out during low Twitter activity. It should be noted that we are able to separate these in TBAM but it may not be possible to do so with scraped Twitter data. At each tick, a random number $z_i$ is generated for each user. The random number is used to create the random conditions where users may not choose to tweet at a specific time. Since it is hard to determine these random conditions, we assume that $z_i$ is normally distributed random number of mean \texttt{tweet-threshold} and variance $0.2$. The scraped twitter data also follows a rough normal distribution which is why we chose the random conditions to be normally distributed. Before an event occurs a user will only send out a routine tweet. A user will only tweet if $z_i < \texttt{tweet-chance}$ where $z_i$ is a random number generated for user $i$ and \texttt{tweet-chance} is probability of sending out a standard tweet (from Table \ref{tab:synth_exp2b}).
\begin{table*}
\caption{Variable parameters for different TBAM data generation simulations}
\centering
\resizebox{\textwidth}{!}{\begin{tabular}{| p{.20\textwidth} | p{.40\textwidth} | p{.08\textwidth} | p{.08\textwidth} | p{.08\textwidth} |}
\hline
\textbf{Parameter} & \textbf{Description} & \textbf{VIRG} & \textbf{STEM} & \textbf{GAR} \\
\hline
\texttt{tweet-chance} & probability of a person sending out a tweet & 0.33 & 0.29 & 0.22 \\
\hline
\texttt{event-duration} & length of time that event remains active & 31 & 48 & 8 \\
\hline
\texttt{event-tweet-chance} & probability of a person sending out a tweet about an event & 0.49 & 0.55 & 0.67 \\
\hline
\texttt{night-tweet-chance} & probability of sending out tweets during low Twitter activity & 0.17 & 0.16 & 0.12 \\
\hline
\texttt{night-duration} & the duration of low Twitter activity & 8 & 8 & 8 \\
\hline
\texttt{ndist} & scaling factor effecting decay for $q_i$ & 0.07 & 0.12 & 2 \\
\hline
\end{tabular}}
\label{tab:synth_exp2b}
\end{table*}
At a specific time (tick) and location (patch) the event occurs and with each tick spreads across the world. The rumor spreading model has been used as a basis to simulate spreading of an event influence (or information) \parencite{RumorMill}. There may be other models that can be used to simulate spreading of an event, like the susceptible-infected-refractory (SIR) model \parencite{xiong2012information}. In a manner similar to the rumor spreading model, immediately after an event occurs, the event influence starts spreading to all of the neighboring patches (shown by the red colored patches in Figure \ref{fig:sim_world_comp}). However, the rate at which the event influence spreads to its adjacent neighbors may not be uniform and may vary with time. Initially, as soon as the event occurs, the event influence immediately spreads to all patches within a fixed radius. The influence then spreads to adjacent neighboring patches with decreasing rate as more time elapses. This assumption is based on the observations made from collected Twitter data that show a sharp rise in the counts immediately after an event. The parameter that affects the spreading of an event is \texttt{eightmode?}. Setting \texttt{eightmode?} to true causes the event to spread to its diagonals and its adjacent neighbours but setting the \texttt{eightmode?} to false causes the event to only spread to its adjacent neighbours. It should be noted that when \texttt{eightmode?} is true, then the event spreads outwards more quickly.
Once an event occurs, a user can send out either an event related tweet or a routine tweet. A user will choose to send out a tweet about an event if $z_i < \frac{q_i}{(q_i + \texttt{tweet-chance})}$ where $z_i$ is a random number generated for user $i$ as described previously, $q_i$ is probability a user $i$ will tweet about an event and \texttt{tweet-chance} is from Table \ref{tab:synth_exp2b}. Once a user chooses to tweet about an event, then a user will only send out tweet about an event if they are on a patch where an event has spread to and $z_i < q_i$ where $z_i$ is a random number generated for user $i$ and $q_i$ is probability a user $i$ will tweet about an event. There are multiple methods of determining $q_i$. The value of $q_i$ could be fixed or vary with time and distance from event. For the model, we employ a hybrid approach. In the immediate vicinity of the event $q_i = \texttt{event-tweet-chance}$ where \texttt{event-tweet-chance} is one of the parameters from Table \ref{tab:synth_exp2b}. But as the distance and time from event increase, $q_i$ decreases according to Equation \ref{eq:01}.
\begin{equation}
q_i = event-tweet-chance*[ (t-t_{event})^{-\texttt{ndist}/\alpha} * (d_{event})^{-\texttt{ndist}/\beta} ]
\label{eq:01}
\end{equation}
The variable $t$ is the current time tick measured after the event occurs, $t_{event}$ is the time tick at which event occurred, $d_{event}$ is the distance of the user from the event, $\texttt{ndist}/\alpha$ and $\texttt{ndist}/\beta$ are scaling factors. A high \texttt{ndist} value means that \texttt{event-tweet-chance} decays less rapidly with changing time and distance. For our model we keep $\alpha$ fixed at $1$ and $\beta$ fixed at $20$. Since we are considering local events and users would generally be in close proximity to the event, the decay of \texttt{event-tweet-chance} with distance should be less rapid than decay due to time. Hence, we choose a larger value of $\beta$ than for $\alpha$. It should be noted that there are many different functions that could be used to simulate the decay of probability of microblogging about an event. But previous literature \parencite{pezzoni2013retweet,sakaki2010earthquake} have considered exponential distribution for tweets which can also be observed from the collected twitter data. Hence, we choose a simple exponential function to change how the probability of microblogging about an event decays with time and distance in our simulations. Figure \ref{qi} is a plot of the function showing how $q_i$ changes as distance and time from event changes when $\alpha=1$ and $\beta=20$.
During the simulation phase, users can also send out retweets. A user will send out a standard retweet if $z_i < \texttt{tweet-chance}$ AND there is a link with another user who has sent out a standard tweet. Consequently, a user will only send out an event related retweet, if $z_i < q_i$ and there is a link with another user who has sent out an event related tweet. We define the parameters \texttt{event-interest} and \texttt{user-interest} as the tick duration over which users will keep on talking about an event or a routine tweet. These parameters quantify the importance of standard or event related tweets and the higher these parameters are, the larger will be the number of retweets sent out. For our simulations, we keep these values constant for the simulation duration.
\begin{figure}[htp]
\centering
\includegraphics[width=8cm,height=6cm]{tbam/qi_plot2.png}
\caption{Changing $q_i$ with changing distance or ticks (with $\alpha=1$ and $\beta=20$)}
\label{qi}
\end{figure}
The event ends when \texttt{event-duration} ticks have elapsed. Once the event ends, just like the rumor spreading model, the patches loose the influence of the the events. No new tweets relating to an event are generated and the event related tweets gradually decrease until they eventually stop. A higher \texttt{event-duration} value signifies that users will continue to generate new tweets about an event for longer periods of time.
There is also the option of choosing multiple events which is done by setting \texttt{n-events?} true. If there are multiple events then \texttt{event-sources} sets the number of event sources. For this paper, we use one event source. In short, \texttt{event-duration}, \texttt{event-tweet-chance} and \texttt{event-interest} determine how significant an event is. If these values are set high then it indicates an event that has a high impact on users' lives and they will tweet and retweet more about the event and remain interested in the event for longer duration. These parameters can be changed to incorporate different types of events.
The data collected from Twitter reveals periods of time with very few tweets being sent out. To incorporate such behavior we introduce the parameter \texttt{night-mode} that enables or disables consideration of time when there is low Twitter activity. If \texttt{night-mode} is enabled, then there are two parameters that affect the low Twitter activity. One parameter \texttt{night-duration} effects how long the low activity period lasts. The other parameter \texttt{night-tweet-chance} is a measure of the probability of a user microblogging during the low Twitter time period. A user sends out tweets during this time only when $z_i < \texttt{night-tweet-chance}$. Usually \texttt{night-tweet-chance} would be less than \texttt{tweet-chance} which in turn is usually less than \texttt{event-tweet-chance}.
\section{TBAM validation} \label{twitter_real}
For our comparison we used three data sets, referred to as VIRG, STEM and GAR, collected directly from the Twitter API using the 'TwitteR' package in R \parencite{TwitteR}. The social sensor (reference point) coordinate was 2 miles from the event along the y-axis. It shows the number of tweets within a 2.8 mile radius changing with time. The data are related to three events and are summarized in Table \ref{tab:real_dataset}. Figures \ref{fig:virg_abm}, \ref{fig:stem_abm} and \ref{fig:gar_abm} represent the plots of the data. \textit{Real} indicates data obtained from Twitter and \textit{TBAM} indicates data generated through TBAM. Each tick represents the number of tweets sent out in an hour. The occurrence of an event is indicated by the vertical line. From the plots it can be clearly seen that after an event occurs, there is a sharp rise in the number of tweets which is similar to the real data.
\begin{table}
\caption{Summary of Real Data}
\centering
\begin{tabular}{| p{3cm} | p{1.5cm} | p{2cm} | p{3.5cm} | p{3.1cm} |}
\hline
\textbf{Event Name} & \textbf{Reference Name} & \textbf{Event Date} & \textbf{Event Location (latitude, longitude)} & \textbf{Social Sensor Location (latitude, longitude)} \\
\hline
Virginia Beach Shootings & VIRG & 05-31-2019 4:44pm & 36.7509,-76.0575 & 36.77974,-76.05750 \\
\hline
STEM School Shootings & STEM & 05-07-2019 1:53pm & 39.556,-104.9979 & 39.58482,-104.99790 \\
\hline
Garlic Festival Shootings & GAR & 07-28-2019 5:40pm & 36.997778,-121.585278 & 37.02661,-121.58528 \\
\hline
\end{tabular}
\label{tab:real_dataset}
\end{table}
To generate data using TBAM, we use the parameter values described in Table \ref{tab:synth_exp2a} and Table \ref{tab:synth_exp2b}. Table \ref{tab:synth_exp2a} shows the parameters that are kept fixed for all the simulations. Table \ref{tab:synth_exp2b} shows the parameters that are changed according to the Twitter data set they are meant to match. The parameters in Table \ref{tab:synth_exp2b} were estimated by inspection of the Twitter data. Table \ref{tab:synth_exp2c} summarizes how we estimated the different parameters from the Twitter data. The \texttt{event-duration} was estimated as the duration over which the number of tweets sent after the event were higher than tweets sent before the event. For example, in Figures \ref{fig:stem_abm} the number of tweets in the \textit{Real} data return to the value before the event after 48 ticks, hence, the TBAM \texttt{event-duration} parameter was set to 48 to generate the data in that figure.
Similarly, from the real data we calculate the values for \texttt{$tweets_{night}$}, \texttt{$tweets_{pre-event}$} and \texttt{$tweets_{post-event}$}. Then using these values we estimate the probabilities for the TBAM parameters of \texttt{tweet-chance}, \texttt{event-tweet-chance} and \texttt{night-tweet-chance} which are then used to generate TBAM data.
The heuristic analysis of the data from Twitter reveals how the different parameters vary for different areas and events. The difference in these parameters could be due to the difference in demographics, Twitter usage, and density of the Twitter network. For all three data sets we considered a similar event. VIRG and STEM had roughly similar parameters but GAR has very different parameters. This is because GAR refers to two events combined as one. GAR event is different from the other two events as it started off as a different event which was a festival but ended up as a shooting event. As a result there were more Twitter users compared to usual days and the parameters \texttt{event-tweet-chance}, \texttt{event-duration} and \texttt{ndist} are significantly different than the other two events. The parameter of \texttt{event-duration} is significantly shorter due to Twitter users leaving the event location and hence, the scaling factor is high to account for the high outflow of Twitter users.
\begin{table}[htp]
\centering
\begin{tabular}{| p{.35\textwidth} | p{.55\textwidth} |}
\hline
\textbf{Parameter} & \textbf{Description} \\
\hline
\texttt{$tweets_{night}$} & mean number of tweets sent in low Twitter activity hours \\
\hline
\texttt{$tweets_{pre-event}$} & mean number of tweets sent before the event (excluding low Twitter activity tweets) \\
\hline
\texttt{$tweets_{post-event}$} & mean number of tweets sent after the event (excluding low Twitter activity hour tweets) \\
\hline
\hline
\texttt{event-duration} & duration over which number of tweets sent after event are remain higher than number of tweets sent before event \\
\hline
\texttt{tweet-chance} & \Large $\frac{tweets_{pre-event}}{(tweets_{night})+tweets_{pre-event}+tweets_{post-event}}$ \\
\hline
\texttt{event-tweet-chance} & \Large $\frac{tweets_{post-event}}{(tweets_{night})+tweets_{pre-event}+tweets_{post-event}}$ \\
\hline
\texttt{night-tweet-chance} & \Large $\frac{tweets_{night}}{(tweets_{night})+tweets_{pre-event}+tweets_{post-event}}$ \\
\hline
\end{tabular}
\caption{Determining the probabilities from Twitter data for TBAM}
\label{tab:synth_exp2c}
\end{table}
\subsection{Model Validation}
In order to measure the accuracy of the TBAM generated data compared to the data collected from Twitter, we use the \textit{cross-correlation function (\textit{ccf})} \parencite{shumway2000time}. The cross-correlation function between two time series $x_t$ and $y_t$ is given by:
\begin{equation}
\rho_{xy}(s,t) = \frac{\gamma_{xy}(s,t)}{\sqrt{\gamma_{x}(s,s)\gamma_{y}(t,t)}}
\end{equation}
where
\begin{equation}
\gamma_{xy}(s,t) = cov(x_{s},y_{t}) = E[(x_{s}-\mu_{xs})(y_{s}-\mu_{yt})]
\end{equation}
$\mu_{xs}$ is the mean of time series $x_s$ and $\mu_{yt}$ is the mean of time series $y_t$.
The cross-correlation measures the dependence between two points on different time series observed at different times. In other words, \textit{ccf} measures the linear predictability of the series at time $s$, say $x_s$, using only
the value $y_t$. In our TBAM data we are trying to see if the trends and patterns in the original data match. Hence, \textit{ccf} will be a suitable metric and give an overview of the statistical significance between the two data sets.
Figures \ref{fig:ccf_virg1}, \ref{fig:ccf_stem1} and \ref{fig:ccf_gar1} shows the \textit{ccf} between VIRG, STEM and GAR data sets and the TBAM generated data respectively. It can be seen that the TBAM generated data and the real data have a very similar pattern as the \textit{ccf} is higher than the threshold for most lags. Another important observation is that the correlation is also high at $lag=0$. High correlation at $lag=0$ indicates a strong statistical significance and shows that the patterns in both the data match very closely. This also means that any events found in the real data could also be found in the same position in the TBAM data.
For comparison, to show that our method does generate reasonably accurate data, we measure the \textit{ccf} between data from Twitter and uniformly randomly generated data. The random numbers were generated between 1 and the maximum value in the number of tweets of the specific data set. Figures \ref{fig:ccf_virg2}, \ref{fig:ccf_stem2} and \ref{fig:ccf_gar2} shows the \textit{ccf} between VIRG, STEM and GAR data sets and uniformly randomly generated data. It is clearly seen from the plots that there is very low correlation at all lags. This shows that the data generated using TBAM is significantly better.
\begin{figure}[htp]
\centering
\subfigure[Cross Correlation between VIRG Twitter Data and TBAM data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_virg0_tbam.png}\label{fig:ccf_virg1}}\hfill
\subfigure[Cross Correlation between STEM Twitter Data and TBAM data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_stem0_tbam1.png}\label{fig:ccf_stem1}}\hfill
\subfigure[Cross Correlation between GAR Twitter Data and TBAM data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_gar0_tbam.png}\label{fig:ccf_gar1}}
\caption{CCF of Real Twitter data with TBAM generated data}
\end{figure}
\begin{figure}[htp]
\centering
\subfigure[Cross Correlation between VIRG Twitter Data and Uniform Random Data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_virg0_uni.png}\label{fig:ccf_virg2}}\hfill
\subfigure[Cross Correlation between STEM Twitter Data and Uniform Random Data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_stem_uni.png}\label{fig:ccf_stem2}}\hfill
\subfigure[Cross Correlation between GAR Twitter Data and Uniform Random Data]{\includegraphics[width=0.30\textwidth]{tbam/ccf_gar0_uni.png}\label{fig:ccf_gar2}}
\caption{CCF of Real Twitter data with randomly generated data}
\end{figure}
As shown above, TBAM reasonably reproduces microblogging behavior. Unlike real tweets, here we can (a) identify, control, and tune parameters which impact the tweet counts and microblogging behavioral patterns (b) separate event related tweets from standard tweets without looking at semantics (c) create aggregates in space or time (which we have not done here, but it is straightforward) which can reflect real world data scraping and provides different space and time granularity (d) intentionally, randomly, or using other models, introduce gaps or noise (e) add additional demographics - groups that tweet more or less (f) add system-wide or regional variations - all in a controlled manner. In this way, there is more control over the delivery slate and reliability of the microblogging data.
\section{Conclusion} \label{conc}
The result from our analysis indicates that the data generated using TBAM can be used to complement and possibly enrich the underdeveloped real-world data. The main application of our data generation model is in detecting and localizing events using crowd-sourced "social sensors" whose aggregate counts of event alerts are collected at reference sensors. The generated data can be used to enrich the data collected from Twitter. This can potentially improve event detection accuracy that may enable applications like first response during minor, yet consequential disasters such as road closures. Our model may also be used for data augmentation and imputation (estimation), for generating training data for machine learning models, testing event detection models and determining parameters that determine tweeting behavior of people.
An important method in event detection are machine learning methods (like long short-term memory (LSTM), classification, etc.) \parencite{atefeh2015survey}. The machine learning methods can be used to find event patterns in number of tweets. In case of event detection there might be the problem of class imbalance as there might be a single event signature in a long sequence of tweets. This can cause errors in event pattern detection when using machine learning methods. There might also be the problem of insufficient tweets to train the machine learning methods. In such cases the TBAM generated data can be used for data augmentation by creating additional synthetic data that can be used to train the machine learning methods.
Other previous works, such as \citeauthor{Mehdi2020Sem} (\citeyear{Mehdi2020Sem}) and \citeauthor{comito2017peak} (\citeyear{comito2017peak}), have considered peaks as indication of an event and have created models to find events using peaks. In fact a quick visual analysis does show that peaks in TBAM generated data and the data collected from Twitter have peaks in very close proximity to each other. We will perform detailed comparison of the peaks in future work. Nevertheless it does show that the data generated using TBAM can be used in lieu of Twitter data to find peaks and detect events.
Another application of the model could be to create a data base that would list different probabilities for different locations and different event-types. Our model quantified and identified different parameters that effect the microblogging behavior of users. These parameters could then be used to identify different events.
In our model we made simple assumptions for the parameters, some of which we estimated from the real data and some parameters, which could not be determined from the real data, were randomly generated. For example, the distribution of the people and their clusters was random which may not be the case in real world. Furthermore, each user is assigned a random number $z_i$ to reflect the inclination of a user to tweet. As a result, the magnitude of the number of tweets in the TBAM data and real data are different. As part of future work, we aim to design a method to better estimate these parameters. Different event spreading techniques and equations for decay of probability of microblogging about an event can be applied and tested. One way to better estimate the parameters would be to create an optimization problem that maximizes \textit{ccf} or use past Twitter data. But since Twitter data is underdeveloped, we could generate data using alternative methods like generative adversarial networks (GAN) and use GAN generated data to learn TBAM parameters. In this way both TBAM and GAN could work together to further enrich the data. Alternatively, we could also compare TBAM and GAN data generation techniques.
\printbibliography[heading=bibliography]
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,216 |
Home → Legal resources → Brain injury → When Can I Sue for Brain Injuries?
When Can I Sue for Brain Injuries?
Understand the types of brain injury and when you can sue
By Canaan Suitt, J.D. on August 19, 2022
According to the Center for Disease Control and Prevention (CDC), tens of thousands of people suffer a brain-related injury every year. Many traumatic brain injuries result in disability or death.
In addition to lifelong medical consequences, brain injuries can bring severe financial burdens due to medical expenses, lost wages, and lost earning potential.
If you or a loved one has suffered a brain injury, it's possible to get compensation. This article will give an overview of the types of brain injury and when speaking with an attorney is a good idea.
How Does a Brain Injury Happen?
Brain injuries can occur during many everyday activities. Some of the most common causes include:
Falls (learn more about slip and fall lawsuits)
Physical violence (including domestic abuse and gun injuries)
The cause of a brain injury will partly determine the kind of legal action you take to recover. For example:
If you are injured while working for your employer, you can pursue a workers' compensation claim or a personal injury lawsuit
If you or a family member were injured during surgery or another medical operation, you could pursue a medical malpractice claim
If a defective product (such as a defectively made tire causing a vehicle accident) was responsible for your head injuries, you could pursue a products liability claim
Regardless of the type of claim you bring, brain injury lawsuits generally involve proving someone acted negligently and their negligence was the cause of your injuries.
A "brain injury claim is no different from any other type of personal injury claim. It constitutes an injury that's no different in the eyes of the law than a fracture of a bone, an injury to the spine, scarring and disfigurement," says Pennsylvania personal injury lawyer Jason M. Lichtenstein.
As with other personal injury claims, "the elements of negligence have to be proven: there was a duty, there was a breach of that duty, and the breach caused an injury," he says.
Learn more about how to prove liability in brain injury lawsuits by reading this article.
What Are the Types of Brain Injury?
The most general brain injury category is "acquired brain injuries."
Acquired brain injuries are not hereditary or congenital and are due to some cause after birth.
Common causes of acquired brain injuries include:
Oxygen deprivation (anoxia)
Damage during brain surgery
The other major type of acquired brain injury is traumatic brain injury (TBI).
TBIs result from some external force or impact that causes head trauma. TBIs can result from hitting one's head on a stationary object (hitting the floor in a fall) or getting struck by a moving object (falling material on a job site).
TBIs can be divided into:
Mild TBI
Severe TBI
The difference in these types of TBI simply depends on how severe the injury is.
TBIs range from mild concussions in a fender bender to serious penetrative injuries that result from objects entering the skull and causing tissue damage.
Even though brain injuries are treated the same as other personal injury claims, Lichtenstein says they "can be much more complicated in determining values."
This is because "unlike a fractured bone, which is clearly defined in an X-ray, or a spinal issue that's clearly defined in a CT scan or MRI, very few brain injuries rise to the level of… a brain bleed or something that can be picked up by radiographic means," he says.
The "vast majority of brain injury cases are concussions and post-concussive syndrome. These are difficult because there's no definitive radiographic test to prove that you sustained a concussion," says Lichtenstein.
While "concussions are absolutely brain injuries," you "generally need a doctor who specializes in concussions… to give an opinion that the trauma in question caused the injury," he says.
Getting medical attention as soon as possible is therefore essential.
What Are the Symptoms of a Brain Injury?
Brain injuries can have immediate and long-term impacts depending on the type of injury.
Sometimes it can take months or years for the negative consequences of a brain injury to become apparent and for doctors to properly diagnose the injury.
Some of the more immediate symptoms of a brain injury include:
Drowsiness or extreme weakness
Confusion or dizziness
More permanent brain damage includes memory loss and cognitive impairments.
"The brain controls many different functions of your body," says Lichtenstein. "So, someone with a concussion might have intractable headaches; someone else may get very dizzy all the time; another may have sensitivity to loud noises or bright lights; another might have none of these symptoms but have emotional symptoms because their injury was in the area of the brain where emotions are controlled."
Some brain injury victims are "more prone to depression and anxiety," he says.
Because of the many problems that can result from brain injuries, "it's imperative to get to a medical specialist who concentrates on brain injuries as soon as possible," says Lichtenstein.
In some cases, brain injuries can result in death. In these cases, survivors may pursue a wrongful death claim depending on the circumstances of the injury.
Why You Should Speak With a Brain Injury Lawyer
If you or a loved one has experienced a brain injury, it's essential to seek legal advice from a personal injury attorney as soon as possible. There are a couple of main reasons why this is important:
Statute of Limitations. Every state has a law called a statute of limitations. These laws say how long someone has to bring a lawsuit after an injury. The exact timeframe varies from state to state and ranges from a year to several years. Once you miss the deadline, you are not allowed to file a lawsuit to recover money for your injuries. It's essential to speak with a lawyer to understand your state's statute of limitations.
Navigating the legal process. The process of filing a lawsuit and going to trial is very complex and time-consuming. This is especially true in brain injury cases, where medical experts and evidence will be needed. It is best to have an experienced attorney handling your case to ensure the best outcome.
Fortunately, many attorneys give free consultations. These meetings are an excellent resource for both attorney and client because they allow the attorney to hear the facts of the case while the client can determine if the attorney and law firm meets their needs.
Questions for a Brain Injury Lawyer
The best way to decide whether an attorney is the right fit is by asking informed questions. Here are some good questions to ask during your initial conversations:
What are your attorneys' fees?
What billing options do you offer?
What is the statute of limitations for a brain injury claim?
What is my brain injury claim worth?
Will my medical bills be covered?
What are the chances of a brain injury settlement?
Once you discuss your case with a lawyer, you can decide whether to hire them and begin an attorney-client relationship.
Finding the Right Attorney for Your Needs
It is essential to approach the right type of attorney—someone who can give you legal help through your entire case. You can visit the Super Lawyers directory and use the search box to find a lawyer based on your legal issue or location.
For brain injuries, look for a personal injury lawyer with experience in brain injury cases.
If you or a loved one has experienced a brain injury, it's essential to seek legal advice from a personal injury attorney as soon as possible.
What is Brain Injury Law?
Should you, or can you, pursue legal action?
How to Win a Brain Injury Lawsuit
Insight into the process of bringing a brain injury lawsuit
I Was Discriminated Against. How Do I Prove It?
Your options in a Michigan workplace discrimination lawsuit
View More Brain injury Articles » | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,591 |
\section{Introduction}
\textit{Spiders} were first introduced by Kuperberg in \cite{kup1} as a framework for the description and comparison of spherical monoidal categories. Using the spider formalism, Kuperberg provided a diagrammatic presentation for the category of finite dimensional representations of $U_q(\mathfrak{g})$, where $\mathfrak{g}$ is a simple Lie algebra of rank $2$. The diagrammatic presentation for a representation category has many advantages. For example, diagrammatic presentations lead naturally to the definition of skein modules. This in turn allows one to explore the topological information contained in the category.
Extending Kuperberg's work, Kim \cite{kim} proposed a presentation of the category of finite dimensional representations of $U_q(\mathfrak{sl_4})$ where the colors correspond to the exterior powers of the standard representation and its dual. Sikora in \cite{sik} provided a presentation for the braided spherical monoidal category coming from the representation theory of $U_q(\mathfrak{sl}_n)$ using the standard representation and its dual as objects. Further, Morrison proposed a complete set of generators and relations (conjecturally) in \cite{mor} for the spherical monoidal category, $\mathcal{R}ep(U_q(\mathfrak{sl}_n))$ where the colors correspond to the exterior powers of the standard representation and its dual. Later, Cautis, Kamnitzer and Morrison proved Morrison's conjecture in \cite{ckm} using skew-Howe duality.
The braided monoidal structure on $U_q(\mathfrak{sl}_n)$ was first explored by Murakami et al. in \cite{moy}. They provide web relations that align with the untagged relations (\ref{ckmb1}--\ref{boxrelationsckm}) in \cite{ckm}. However, they provide no discussion of a complete set of relations for this category. Later, Sikora \cite{sik} explained the connection between his presentation for $\mathcal{R}ep(U_q(\mathfrak{sl}_n))$ and generators and relations presented in \cite{moy}. Further, in his thesis \cite{mor}, Morrison states that he does not understand the relation between his conjecture and the work of Sikora. In this paper, we answer Morrison's question and also prove Conjecture \ref{lesikconjecture} \cite{lesik} which is related to the question posed by Morrison in his thesis.
There is a braided spherical category based on the HOMFLYPT skein relations. Early on it was realized \cite{TW} that by specializing the variables in HOMFLYPT one could obtain a category that mapped down to the categories of $U_q(\mathfrak{sl}_n)$ representations. One can build skeins that behave algebraically like Young symmetrizers \cite{Y, M, MA, Li, bla}. The category is missing both generators and relations that say that the $n$th exterior power of the of the standard representation and its dual are trivial. Sikora's model adds $n$-valent vertices that are sources and sinks corresponding to these invariant tensors and a relation for cancelling them. The CKM model adds tags that are sources and sinks and relations for moving them and cancelling them. The isomorphism in this paper shows that the two approaches are equivalent.
As in \cite{lesik}, let $\mathfrak{S}_n^b$ be a monoidal category with finite sequences of signs $\pm$ as objects and istopy classes of $n-$tangles (cf. \cite{sik}) as morphisms. The tensor product is given by horizontal concatenation and composition of morphisms is given by vertical stacking. Similarly, let $\mathcal{C}_n$ be the category of left $U_q(\mathfrak{sl}_n)$-modules isomorphic to finite tensor products of $V$ and $V^*$ where $V$ is the defining representation of $U_q(\mathfrak{sl}_n)$. Then, define a monoidal functor $RT_0: \mathfrak{S}_n^b \to \mathcal{C}_n$ which for any object $\eta = \{\eta_1, \cdots \eta_k\}\in \mathfrak{S}_n^b$, is defined as $RT_0(\eta) := V^\eta = V^{\eta_1} \otimes \cdots \otimes V^{\eta_k}$. Note that $V^+ = V$ and $V^- = V^*$. For any $n-$tangle, the functor takes caps and cups to evaluation and coevaluation maps respectively, crossings to the braid isomorphisms and an $n-$sink (resp. source) to a map from the $n-$fold tensor of $V$ (resp. ground ring) to the ground ring (resp. $n-$fold tensor of $V$). Also, a \textit{monoidal ideal} in a monoidal category, $\mathcal{C}$ is a subset $I\subset \Hom(\mathcal{C})$ such that for $x\in I$ and $y\in \Hom(\mathcal{C})$, we have $x\otimes y, y \otimes x \in I$ and $x\circ y, y\circ x \in I$ whenever such compositions are defined.
In this paper, we prove the Conjecture \ref{lesikconjecture} below by proving that Sikora's braided spherical category is equivalent (as a braided spherical category) to the full subcategory of the braided spherical category $\mathcal{S}p(SL_n)$ in \cite{ckm} which has as objects the standard representation and its dual.
\begin{conjecture}[\cite{lesik}] \label{lesikconjecture}
The kernel $\ker RT_0$ is the monoidal ideal generated by elements given in relations (\ref{homflysik}--\ref{unknotsik}).
\end{conjecture}
\subsection{Main results:}
The main results of this paper are:
\begin{itemize}
\item Theorem \ref{allckmrelationtheorem1} which provides a simpler topological criterion to obtain the list of relations in \cite{ckm}.
\item Theorem \ref{reducecolorthm} which shows that the full subcategory of the spider category of \cite{ckm} whose objects are finite tensor products of the standard representation and its dual is equivalent to its subcategory with same objects but with a smaller set of generators where the set of colors (appearing on the interior) is strictly smaller.
\item Theorem \ref{sikorackmequiv} which shows that the braided spherical category coming from \cite{sik} and the full subcategory of the spider category in \cite{ckm} with the standard representation and its dual as objects are equivalent to each other. This further provides the proof for the Conjecture \ref{lesikconjecture}.
\end{itemize}
\subsection{Outline}
In Section \ref{prelim}, we define the quantized integers (and binomial coefficients) along with the categorical structures that appear in our work. The notion of a free spider category and operations in this category are also introduced.
In Section \ref{ckmsikdef}, we define the two main categories in this paper: the CKM spider category and Sikora's spherical braided category.
In Section \ref{boxes}, the CKM box relations are derived in a diagrammatic fashion using the braided structure of the CKM spider category. We end this section with our first main result Theorem \ref{allckmrelationtheorem1}.
In Section \ref{fullsubcat}, we introduce and work with subcategories of the full subcategory of the CKM spider category generated by the standard representation on grading $0$. This section ends with our second main result (Theorem \ref{reducecolorthm}) regarding categorical equivalences between the subcategories introduced in this section.
In Section \ref{siktockmmain}, we prove that Sikora's spherical braided category is equivalent (as a spherical braided category) to the full subcategory of the CKM spider category monoidally generated by the standard representation and its dual in Theorem \ref{sikorackmequiv}. Further, using this result, we prove the Conjecture \ref{lesikconjecture}.
\section{Preliminaries}\label{prelim}
\subsection{Coefficients} Let $R$ be an integral domain with unit and suppose that $q\in R$ is a unit. The quantized integers in $R$ are defined to be the sums
\begin{equation} [k]=\sum_{i=0}^{n-1}q^{-k+1+2i}.\end{equation} The quantized factorials are defined recursively by $[0]!=1$ and $[n]!=[n][n-1]!$, and the quantum binomial coefficients
\begin{equation} \begin{bmatrix} n \\ k\end{bmatrix} =\frac{[n]!}{[k]![n-k]!}.\end{equation}
All the categories considered in this paper are categories of modules. We will assume that they are over a ring $R$ having a unit $q^{1/n}$ so that if the category is associated with $sl_n$ then the quantum integers $[1],\ldots,[n-1]$ are units. In the case where $q\in \mathbb{C}$ is a root of unity this will mean that the smallest prime divisor of the order of $q$ is greater than $n-1$.
\subsection{Categories}
A \textit{pivotal monoidal category}, $\mathcal{C}$, is a rigid monoidal category such that there exist a collection of isomorphisms (a pivotal structure) $a_X: X \xrightarrow{\sim} X^{**}$, natural in $X$, and satisfying $a_{X\otimes Y}=a_X \otimes a_Y$ for all objects $X,Y$ in $\mathcal{C}$.
For a pivotal monoidal category, $\mathcal{C}$, an object $X \in \mathcal{C}$, and morphisms $f\in \End(X)$, we define the \textit{left} and \textit{right quantum traces}, $Tr_l(f)$ and $Tr_r(f)$ respectively as follows (see \cite{Tur} for more details):
\begin{subequations}
\begin{equation}
Tr_l(f) = \ev_{X}\circ (\id_{X^*} \otimes f) \circ \coev'_X \in \End(\mathbf{1})
\end{equation}
\begin{equation}
Tr_r(f) =\ev'_{X}\circ (f \otimes \id_{X^*})\circ \coev_{X} \in \End(\mathbf{1})
\end{equation}
\end{subequations}
where (co)$\ev_X$ and (co)$\ev'_X$ are left and right \textit{(co)evaluations}, respectively defined as:
\begin{align*}
\ev_X:X^*\otimes X \to \mathbf{1} \hspace{1cm} \coev_X: \mathbf{1}\to X \otimes X^*\\
\ev'_X:X \otimes {}^*X\to \mathbf{1} \hspace{1cm} \coev'_X: \mathbf{1}\to {}^*X \otimes X
\end{align*}
Further, $\mathcal{C}$ is a \textit{spherical monoidal category} if it is a pivotal category such that the left and right quantum traces are the same. In a spherical monoidal category, the \textit{quantum dimension} $d_X$ of an object $X$ is defined to be the quantum trace of identity, $\id_X$. Further, note that $d_X=d_{X^*}$.
A \textit{braided monoidal category} $\mathcal{C}$ is a monoidal category such that there exist a collection of natural isomorphisms (\textit{braid isomorphisms}) $\beta_{X,Y}: X \otimes Y \to Y \otimes X$ for any pair of objects $X,Y\in \mathcal{C}$ that are compatible with the associativity isomorphisms. This compatibility with the associativity isomorphisms in the monoidal category is ensured by the hexagon axiom that the braid isomorphisms satisfy.
We refer the reader to \cite{Tur} for more details.
We will be working with spherical braided categories via generators and relations. The generators will be diagrams carrying labels, where the labels represent irreducible modules over some semisimple Lie algebra. The diagrams represent an element (a vector) in the morphism space (a vector space) of the corresponding category of representations of the Lie algebra. Further, each diagram is considered up to regular isotopy.
In the absence of relations this is called the \textit{free spider category} (on whatever the generators are). The operations are given by (as defined in \cite{kup1}) the following:\\
\textit{Join}: This operation simply allows one to tensor two diagrams (morphisms) by horizontally concatenating. \\
\textit{Stitch}: For any diagram in $\Hom(A,B)$, this means composing with an evaluation (or coevaluation) to attach a cap or a cup. So, as an example, a stitch could send $\Hom(A\otimes B,C)$ to $\Hom(A\otimes B \otimes B^*, C) \cong \Hom(A, C)$.\\
\textit{Rotation}: This allows one to apply a cyclic permutation on the tensor factors (up to sign). Diagrammatically, this amounts to attaching a cap and a cup to rotate the diagram.
\begin{center}
\def11cm}\input{CKMtoKV.pdf_tex{8.5cm}\input{stitchandrotate.pdf_tex}
\end{center}
\section{The braided categories}\label{ckmsikdef}
\subsection{The CKM braided category}\label{ckmcategory1}
As in \cite{ckm}, let $\mathcal{R}ep(SL_n)$ be the category of $U_q(\mathfrak{sl}_n)$-modules generated by tensor products of the fundamental representations. This is a \textit{braided spherical} monoidal category which is a full subcategory of the category of representations of $U_q(\mathfrak{sl}_n)$ where all the morphisms are generated by the wedge product and a version of its adjoint that embeds $\Lambda^{k+l}\mathbb{C}^n$ into $\Lambda^k \mathbb{C}^n \otimes \Lambda^l \mathbb{C}^n$:
\begin{align}
\Lambda^k \mathbb{C}^n \otimes \Lambda^l \mathbb{C}^n \to \Lambda^{k+l} \mathbb{C}^n \text{\hspace{1mm} and \hspace{1mm}} \Lambda^{k+l} \mathbb{C}^n \to \Lambda^k \mathbb{C}^n \otimes \Lambda^l \mathbb{C}^n
\end{align}
\\
\noindent \textit{The free spider category} $\mathcal{F}Sp(SL_n)$: Define the free spider category to be freely generated by the planar diagrams for morphisms in $\mathcal{R}ep(SL_n)$ as shown below. Objects in $\mathcal{F}Sp(SL_n)$ are subsequences of $\{1^{\pm}, \ldots , (n-1)^{\pm}\}$, where `+' denotes an arrow going upward and `-' denotes an arrow pointing downward. The morphisms are generated by the following:
\begin{figure}[H]
\centering
\includegraphics[scale=.5]{generatorsFSP.png}
\caption{Generators for $\mathcal{F}Sp(SL_n)$}
\label{generatorsfsp12}
\end{figure}
The spider category, $\mathcal{S}p(SL_n)$, is the quotient of $\mathcal{F}Sp(SL_n)$ by the following relations (together with their mirror reflections and arrow reversals) \cite{ckm}:
\begin{center}
\begin{align}
\vcenter{\includegraphics[scale=.5]{tagswitch.jpg}}\label{tagswitchckm}\\
\vcenter{\includegraphics[scale=.6]{movetag1.png}}\label{movetag1ckm}\\
\vcenter{\includegraphics[scale=.6]{movetag.png}}\label{movetagckm}\\
\vcenter{\includegraphics[scale=.6]{CKMB1.png}}\label{ckmb1}\\
\vcenter{\includegraphics[scale=.6]{CKMB2.png}}\label{ckmb2}\\
\vcenter{\includegraphics[scale=.6]{CKM6j.png}}\label{6jckm1}\\
\vcenter{\includegraphics[scale=.6]{CKMbox.png}} \label{boxrelationsckm}\\
\vcenter{ \includegraphics[scale=.6]{crossingckmnew.png}}\label{braiddecomp}\\
\vcenter{\includegraphics[scale=.4]{CKMReide.png}
\includegraphics[scale=.27]{Kauffmantrick.jpg}}\label{reidckm1}
\end{align}
\end{center}
Note, for a negative crossing, the RHS is obtained by changing $q$ to $q^{-1}$ in relation (\ref{braiddecomp}) above. Further, the Reidemeister relations have diagrams with unlabeled and unoriented edges as those hold for any admissible labels and orientation of edges, along with corresponding diagrams where undercrossings are changed to overcrossings and vice-versa. We will refer to the relations (\ref{tagswitchckm}, \ref{movetag1ckm}, \ref{movetagckm}) as ``tag relations", (\ref{ckmb1}) and (\ref{ckmb2}) as the ``bubble relations", (\ref{6jckm1}) as ``the 6j move" or ``the 6j relation", (\ref{boxrelationsckm}) as ``the box relation" and (\ref{braiddecomp}) as ``the braid relation".
\\
\begin{remark}
There is a natural grading on the spider category given by the difference in the number of tags appearing in sources and those appearing in sinks, i.e.
\begin{align}
\mathcal{S}p(SL_n) = \bigoplus_i \mathcal{S}p_i(SL_n), \text{ where } \hspace{2.5mm} i = |\text{no. of sources} - \text{no. of sinks}|
\end{align}
In a parenthetical remark \cite{ckm} it is noted that tags can be treated as where an edge labeled $n$ is attached. From this one can see that the braided spherical category in \cite{moy} (c.f. Section \ref{originalmoycat1}) maps onto the $0^{th}$ grading $\mathcal{S}p_0(SL_n)$. However, this (MOY) category does not include consequences of the tag relations (\ref{tagswitchckm} and \ref{movetag1ckm}) in $\mathcal{S}p_0(SL_n)$.
\end{remark}
\subsection{The Sikora category} \label{sikoracat}
The paper \cite{sik} is not couched in category theoretic terms. However, there is a natural way to describe his work in a category theoretic setting, which has been explicitly carried out in \cite{lesik}. In this paper, we present his work in \cite{sik} in terms of a quotient of a free spider category.
Consider a free spider category with objects sequences in $\{\pm\}$ where again `$+$' means edges going up and `$-$' means edges going down and the morphisms are generated by:
\begin{center}
\def11cm}\input{CKMtoKV.pdf_tex{6cm}\input{sikoragen.pdf_tex}\\
\end{center}
Note, the leftmost vertex is either a source or a sink and each morphism in this category is represented by a $n-$valent ribbon graph considered up to regular isotopy. Just as before, this is a braided spherical category which is a full subcategory of the category of $U_q(\mathfrak{sl}_n)$-modules whose objects are monoidal product of copies of the standard representation and its dual.
We call this category $\Tilde{\mathcal{S}}$ if the morphisms satisfy the following relations:
\begin{align}
\includegraphics[scale=.7]{hompflysik.png}\label{homflysik}\\
\includegraphics[scale=.7]{twistsik.png}\label{twistsik}\\
\includegraphics[scale=.7]{sourcesinksik.png}\label{sourcesink}\\
\includegraphics[scale=.7]{unknotsik.png}\label{unknotsik}
\end{align}
Here, for any permutation, $\sigma \in S_n$, $l(\sigma)$ denotes its length:
\[l(\sigma) = \#\{(i,j): 1\leq i < j \leq n, \sigma(i)>\sigma(j)\}
\]
The diagram with $\sigma$ as a coupon represents a positive braid with $l(\sigma)$ crossings representing $\sigma$. Note that along with these relations, this is also the category $\mathfrak{S}_n^b$ in \cite{lesik}.
Check \cite{sik, lesik} for more details.
\subsection{The MOY category}\label{originalmoycat1}
There is no attempt to establish a complete diagrammatic presentation of a category in \cite{moy}. However, the works \cite{mor,ckm} recapitulate the generators and relators given in \cite{moy}. Define a category $\mathcal{MOY}(SL_n)$ to be a spider category with objects sequences in $\{1^\pm, \cdots, (n-1)^\pm, n^\pm\}$ and morphisms generated by the trivalent vertices and crossings given in Figure \ref{generatorsfsp12}. The relators are given by all the relations in $\mathcal{S}p(SL_n)$ except the tag relations. Note that the conventions regarding the objects are the same as in $\mathcal{S}p(SL_n)$, however, in $\mathcal{MOY}(SL_n)$ edges with label $n$ are allowed and there are no tags.
\subsection{The HOMFLYPT category}
Define the HOMFLYPT category to be a spider category with objects sequences in $\{\pm\}$ as in the Sikora category $\Tilde{S}$ and the generators of morphisms given by edges and crossings. Below we show the relations in this category where $a, v, s$ and $s-s^{-1}$ are invertible elements in our integral domain $R$.
\begin{figure}[H]
\centering
\includegraphics[scale=.6]{homflyptrelation.png}
\caption{the HOMFLYPT relations}
\label{blanchethomfly}
\end{figure}
The specialized HOMFLYPT category $\mathcal{HMF}(SL_n)$ is obtained by setting $a=q^{-1/n}, s=q$ and $v = q^{-n}$.
\section{Understanding the CKM box relations}\label{boxes}
\noindent In this section, we derive the box relations (\ref{boxrelationsckm}) from Reidemeister invariance (\ref{reidckm1}), bubble (\ref{ckmb1} and \ref{ckmb2}) and 6j relations (\ref{6jckm1}).
\begin{lemma}\label{recursion1}
The following equation is a consequence of the bubble (\ref{ckmb1}, \ref{ckmb2}), $6j$ (\ref{6jckm1}), braid (\ref{braiddecomp}) and the Reidemeister (\ref{reidckm1}) relations.
\begin{align*}
\includegraphics[scale=.8]{Lemma1.png}
\end{align*}
\end{lemma}
\begin{proof}
Recalling the decomposition of braid isomorphism in terms of webs given in relation (\ref{braiddecomp}) and then applying Reidemeister II invariance gives us the following.\\
\begin{center}
\includegraphics[scale=.6]{lemma1a.png}\\
\includegraphics[scale=.6]{lemma1b.png}\\
\includegraphics[scale=.6]{lemma1c.png}
\end{center}
The claim follows from:
\begin{align*}
(-q-q^{-1})[j]+[j+1] = [j-1].
\end{align*}
\end{proof}
\begin{lemma}\label{generalizedrecursion1}
The following equation is a consequence of the bubble (\ref{ckmb1}, \ref{ckmb2}), the $6j$ (\ref{6jckm1}), braid (\ref{braiddecomp}) and the Reidemeister (\ref{reidckm1}) relations.
\begin{center}
\def11cm}\input{CKMtoKV.pdf_tex{14cm}\input{Lemma2.pdf_tex}
\end{center}
\end{lemma}
\begin{proof}
This follows by induction on $j-k$. \\
\textit{Base case:} when $j-k=1$, this follows from Lemma \ref{recursion1} above. Let this hold for all values up to $j-k=m$. Now, apply Lemma \ref{recursion1} with $j=k$ on LHS to get:
\includegraphics[scale=.65]{lemma2a.png}\\
\hspace*{4cm}\includegraphics[scale=.65]{lemma2b.png}\\
\hspace*{4cm}\includegraphics[scale=.65]{lemma2c.png}\\
Now the proof follows by Induction hypothesis on the box obtained on the last line by noticing that $j-k+1=m \implies j-k=m-1$.
\end{proof}
\begin{lemma}\label{boxrelationbasecase}
As a consequence of the bubble (\ref{ckmb1}, \ref{ckmb2}), the $6j$ (\ref{6jckm1}), braid (\ref{braiddecomp}) and the Reidemeister (\ref{reidckm1}) relations, we obtain:\\
\begin{center}
\def11cm}\input{CKMtoKV.pdf_tex{11cm}\input{Lemma3.pdf_tex}
\end{center}
\end{lemma}
\begin{proof}
As before, start from the box on the RHS to get \\
\includegraphics[scale=.7]{lemma3a.png}\\
\hspace*{3.45cm}\includegraphics[scale=.7]{lemma3b.png}\\
\hspace*{3.45cm}\includegraphics[scale=.7]{lemma3c.png}\\
\hspace*{3.45cm}\includegraphics[scale=.6]{lemma3d.png}\\
Above, we use Lemma \ref{recursion1} on the third equality and Lemma \ref{generalizedrecursion1} to obtain the fourth equality.
\end{proof}
\begin{theorem}\label{allckmrelationtheorem1}
The list of relations in $\mathcal{S}p(SL_n)$ (c.f. Section \ref{ckmcategory1}), not including the tag relations (\ref{tagswitchckm}, \ref{movetag1ckm}, and \ref{movetagckm}), follow from the Reidemeister invariance, the bubble (\ref{ckmb1} and \ref{ckmb2}) and the $6j$ relations (\ref{6jckm1}).
\end{theorem}
\begin{proof}
Following the remark in Section 2.2 in \cite{ckm}, Lemma \ref{boxrelationbasecase} gives us all the box relations. Since Lemma \ref{boxrelationbasecase} follows from assuming the Reidemeister II invariance, the bubble and the $6j$ relations, this gives us the result.
\end{proof}
\section{The full subcategory based on the standard representation}\label{fullsubcat}
Throughout this section, whenever $q$ is a root of unity, it is assumed that the smallest prime divisor of the order of $q$ is larger than $n$. In this section, our goal is to show the full subcategory of $\mathcal{MOY}(SL_n)$ with objects sequences in $\{1^\pm\}$ is equivalent, as a spherical briaded category, to the specialized HOMFLYPT category $\mathcal{HMF}(SL_n)$.
\subsection{Full subcategories of \(\mathcal{MOY}(SL_n)\)} Let $\mathcal{MOY}^i(SL_n)$ denote a subcategory of the full subcategory of \(\mathcal{MOY}(SL_n)\) with objects sequences in $\{1^\pm\}$ and whose morphisms are generated by trivalent vertices that do not contain any edge with a color `$x$' such that $x>i$.
There is a filtration on these subcategories by the number of colors as follows:
\begin{align*}
\mathcal{MOY}^1(SL_n) \subseteq \mathcal{MOY}^2(SL_n) \subseteq \mathcal{MOY}^3(SL_n) \subseteq \cdots \subseteq \mathcal{MOY}^i(SL_n)
\end{align*}
\\
Below, we construct a functor, $\phi_i$ from $\mathcal{MOY}^i(SL_n)$ to $\mathcal{MOY}^{i-1}(SL_n)$ explicitly.
\subsection{Constructing $\phi_i$} In order to define the map $\phi_i: \mathcal{MOY}^i(SL_n) \to \mathcal{MOY}^{i-1}(SL_n)$, we start with the following observation which follows from Lemma \ref{generalizedrecursion1}.\\
\begin{equation}\label{i.2a}
\def11cm}\input{CKMtoKV.pdf_tex{14cm}\input{colori-2.pdf_tex}
\end{equation}
where, going from the first to second equation, we use the $6j$ move. One can use the idea above to obtain a relation for a generic diagram with the color `$i$' in the middle.
Thus, define the functor $\phi_i: \mathcal{MOY}^i(SL_n) \to \mathcal{MOY}^{i-1}(SL_n)$ to be identity on $\mathcal{MOY}^{i-1}(SL_n) \subseteq \mathcal{MOY}^i(SL_n)$ and on $\mathcal{MOY}^i(SL_n) \setminus \mathcal{MOY}^{i-1}(SL_n)$, define the image of a morphism with a color `$i$' in its edge as
\begin{equation}\label{i.2}
\def11cm}\input{CKMtoKV.pdf_tex{14cm}\input{colori-3.pdf_tex}
\end{equation}
Note that using our observation in (\ref{i.2a}), one obtains a relation with LHS and RHS corresponding to the diagrams on (\ref{i.2}) which was the reason for defining $\phi_i$ in this manner in (\ref{i.2}) above.
\begin{lemma}\label{faithfulfunctorphi}
For $i\geq 3$, the functor $\phi_i:\mathcal{MOY}^i(SL_n) \to \mathcal{MOY}^{i-1}(SL_n)$ is fully faithful.
\end{lemma}
\begin{proof}
Let $\mathcal{R}el^i(SL_n)$ be the set of relations in $\mathcal{MOY}^i(SL_n)$. Since $\mathcal{R}el^{i-1}(SL_n) \subseteq \mathcal{R}el^iSL_n)$, and $\phi_i$ is a map between quotient categories, its well-definedness and faithfulness is established by showing that all the relations $\phi_i(\mathcal{R}el^i(SL_n)) \subseteq \mathcal{R}el^{i-1}(SL_n)$.To that end, recalling from Theorem \ref{allckmrelationtheorem1}, it is enough to check the two Reidemeister relations, the bubble and the $6j$ relations involving the color `$i$' and verify that their images under $\phi_i$ is contained in $\mathcal{R}el^{i-1}(SL_n)$.
\noindent\textit{The $6j$ relation}: In order to show that $\phi_i$ respects the $6j$ relation involving the color `$i$', we need to first show the following equality holds in $\mathcal{MOY}^{i-1}(SL_n)$.
\underline{Claim:}\\
\includegraphics[scale=.7]{6jreductionlemma0.png}
\begin{proof}[Proof of the claim]
Starting with the box on the LHS, and applying the relation from Lemma \ref{generalizedrecursion1} on the bottom `$i-1$' color gives us\\
\includegraphics[scale=.7]{6jreductionlemma1.png}\\
\hspace*{4cm}\includegraphics[scale=.7]{6jreductionlemma2.png}
Then, applying the Lemma \ref{generalizedrecursion1} on the leftmost box above gives us
\includegraphics[scale=.7]{6jreductionlemma3.png}\\
\newpage
\hspace*{4cm}\includegraphics[scale=.7]{6jreductionlemma4.png}\\
\hspace*{4cm}\includegraphics[scale=.7]{6jreductionlemma5.png}\\
Finally, the claim follows from applying the relation from Lemma \ref{boxrelationbasecase} to the lower box on the left diagram above and combining all the terms that we started with on the LHS.
\end{proof}
\noindent Note that all the other $6j$ relations involving the color `$i$' follow by applying induction using the method we showed above.
\noindent\textit{Reidemeister relations}: Consider the Reidemeister II relation involving color `$i$' in $\mathcal{R}el^i(SL_n)$. In order to see that its image under $\phi_i$ is contained in $\mathcal{R}el^{i-1}(SL_n)$ we proceed as shown below. Note that by $D_\alpha$, we mean the linear combination of trivalent oriented graphs obtained as the image of an edge with color `$i$' under $\phi_i$ shown in (\ref{i.2}) and $\gamma_\alpha$ are the corresponding coefficients. As each edge in $D_\alpha$ has label strictly less than `$i$', using a sequence of Reidemeister II's and III's coming from $\mathcal{R}el^{i-1}(SL_n)$, one obtains the result.
\begin{center}
\includegraphics[scale=.65]{R2forlemma.png}
\end{center}
Similarly, now consider the Reidemeister III relation involving the color `$i$'. In this case, one obtains the result by using the Kauffman Trick to observe that its image under $\phi_i$ is contained in $\mathcal{R}el^{i-1}(SL_n)$ by noticing that each edge in $D_\alpha$ has label strictly less than `$i$' as shown below:
\begin{center}
\includegraphics[scale=.55]{R3forlemma.png}
\end{center}
\noindent\textit{The bubble relation I:}
Take the general relation \ref{i.2} and stack them to get:\\
\begin{align}\label{crazybubble1}
\def11cm}\input{CKMtoKV.pdf_tex{18cm}\input{overlap1.pdf_tex}
\end{align}
\\
where, $A=\dfrac{1}{[j][k]}$ and $B = \dfrac{[i-2]}{[j][k]}$.\\
We analyze the first box from the RHS above. Start by applying the relation from Lemma (\ref{recursion1}) to the left edge colored `$j$' in the following manner.\\
\includegraphics[scale=.6]{Lemma2_1A.png}\\
\hspace*{4cm}\includegraphics[scale=.6]{Lemma2_1B.png}
Now going back to (\ref{crazybubble1}), apply the relation corresponding to (\ref{i.2}) again for the labels `$i-1$' appearing on the two (right) middle edges of the first diagram on RHS. Under applying $6j$ moves and the box relation (\ref{boxrelationsckm}), we get the following: \\
\def11cm}\input{CKMtoKV.pdf_tex{14cm}\input{Lemma2_2.pdf_tex}\\
where, $A'=A^2 [2]\begin{bmatrix} i-2 \\ i-j\end{bmatrix}$, \text{ }$A'' = A^2 \left(\begin{bmatrix} i-2 \\ i-3\end{bmatrix} -[j-2] \begin{bmatrix} i-1 \\ i-j\end{bmatrix}-[2][i-3]\right)[3-i]$ and $B' = A'[3-i]+A''$.
\\
Now, apply the relation corresponding to (\ref{i.2}) on the labels `$3$' on the left edges of the boxes, starting with the lower one first. This followed by applying the box relation \ref{boxrelationsckm} on the newly obtained interior box finally gives us the desired outcome once we note the following:
\def11cm}\input{CKMtoKV.pdf_tex{13.5cm}\input{Lemma2_3.pdf_tex}\\
Notice that we picked the most complicated diagram out of the four diagrams in the original expansion, but the other three diagrams on RHS are very similar (and simpler) to the diagram we worked out. Thus, the steps that led us to simplify the first diagram works for the rest of the diagrams as well. Finally, the result follows by combining the coefficients from the like terms.
\textit{The bubble relation II:} Use relation (\ref{boxrelationsckm}) again to get:
\begin{center}
\includegraphics[scale=.6]{bubbleforlemma.png}\\
\end{center}
where $E= \dfrac{1}{[k]^2}$ and $F=-\dfrac{[i-2]}{[k]^2}$.
Then, the result is obtained by applying the box relation below.\\
\includegraphics[scale=.7]{weirdbox.png}
\\
where $B' = \begin{bmatrix} n-k \\ i-k\end{bmatrix}$.
Note that the above coefficients can be computed using locality and the following relation:
\begin{center}
\includegraphics[scale=.65]{weirdtriangle.png}
\end{center}
Finally, surjectivity of $\phi_i$ is obtained by recalling the definition of $\phi_i$ and noting that $\mathcal{MOY}^{i-1}(SL_n) \subseteq \mathcal{MOY}^i(SL_n)$.
\end{proof}
\begin{theorem}\label{reducecolorthm}
For $n\geq i\geq 2$, $\mathcal{MOY}^i(SL_n)$ and $\mathcal{MOY}^{i-1}(SL_n)$ are equivalent as braided spherical categories.
\end{theorem}
\begin{proof}
This follows immediately from Lemma \ref{faithfulfunctorphi} and noting that any edge with label `2' in $\mathcal{MOY}^{2}(SL_n)$ can be written as a linear combination of diagrams (involving a crossing) with labels `1'.
\end{proof}
\begin{theorem}\label{MOYtoHOMFLY}
The category $\mathcal{MOY}^n(SL_n)$ is equivalent to $\mathcal{HMF}(SL_n)$ as a spherical braided category.
\end{theorem}
\begin{proof}
From Theorem \ref{reducecolorthm}, it suffices to look into $\mathcal{MOY}^1(SL_n)$. As for objects, one can identify the sequences in $\{1^\pm\}$ in $\mathcal{MOY}^1(SL_n)$ with the sequences in $\{\pm\}$ in $\mathcal{HMF}(SL_n)$.
Further, note that from \cite{moy}, we already know that $\mathcal{MOY}^1(SL_n)$ satisfies the HOMFLYPT relation. Now one can check that the bubble relations and the $6j$ relation in $\mathcal{MOY}^1(SL_n)$ can be derived from the kink, and Reidemeister II relations in $\mathcal{MOY}^1(SL_n)$ are the same as the ones in $\mathcal{HMF}(SL_n)$. The claim then follows.
\end{proof}
\vspace{.5in}
\section{From the Sikora Category to CKM}\label{siktockmmain}
\noindent In this section, we will define a functor: $\tau:\Tilde{\mathcal{S}} \to \mathcal{S}p^n(SL_n)$, where $\mathcal{S}p^n(SL_n)$ represents the full subcategory of the CKM spider category with objects \{$1^\pm$\}. Our goal is to show that this functor is fully faithful.
Note that $\mathcal{S}p^n(SL_n)$ does contain all the tag relations as the trivalent vertex given by the projection on (and inclusion of) the trivial representation $\Lambda^n \mathbb{C}^n$ is now one of the generators.
Also throughout this section, whenever $q$ is a root of unity, it is assumed that the smallest prime divisor of the order of $q$ is larger than $n$.
\subsection{On generators} We define $\tau$ as follows on the generators of morphisms:
\begin{center}\label{tauongens}
\includegraphics[scale=.75]{functor1.png}
\end{center}
Note, the assignment of the $n$-vertex from $\Tilde{\mathcal{S}}$ to the chosen (fusion) tree diagram above is unique upto $6j$ moves. Further, the tree diagram on the image is normalized so that it is $q^{n(n-1)/4}$ times the respective tree diagram in $\mathcal{S}p^n(SL_n)$.
Also note that the label `$n$' here shows the placement of the tag.
\subsection{On relations}
We start by recalling a result from \cite{bla}. Below, $H_j$ represents the Hecke algebra, i.e. the algebra isomorphic to the quotient of the braid group algebra $k[B_j]$ by the HOMFLYPT relation.
Let $\sigma_i \in H_n, i= 1,\cdots, n-1$ represent the standard generators of the braid group $B_n$ where the strand labeled $i$ crosses over the one labeled $i+1$. Further, let $f_j$ and $g_j$ be the deformation of Young symmetrizer and anti-symmetrizer, respectively, where $f_j$ satisfies the recursive relations (\ref{freln1}) and (\ref{freln2}), and $g_j$ satisfies the relation (\ref{antisym}) below.
\begin{align}
[2]f_2 &=s^{-1}\OIdma + a^{-1}\OPxa \label{freln1}\\
[n+1]f_{n+1}&=-[n-1]f_n\otimes 1_1 + [2][n](f_n\otimes 1_1)(1_{n-1}\otimes f_2)(f_n \otimes 1_1) \label{freln2}\\
g_j &= \frac{1}{[j]!}s^{j(j-1)/2}\sum_{\pi \in S_j}(-as)^{-l(\pi)}w_\pi\label{antisym}
\end{align}
where $l(\pi)$ is the length of $\pi$ and $w(\pi)$ is the positive braid associated with the permutation $\pi$. \\
Note that, just as $f_j$, $g_j$ can also be uniquely defined using the following recursive formulas \cite{bla}:
\begin{align}
g_1 &= 1_1 \label{antisymrecur1}\\
g_{j+1} &= 1_1 \otimes g_j - \frac{[2][j]}{[j+1]}(1_1 \otimes g_j)(f_2\otimes 1_{j-1})(1_1 \otimes g_j)\label{antisymrecur2}
\end{align}
\begin{proposition}[\cite{bla}]
If $[j]!$ is invertible in $k$, then there exists a unique idempotent $f_j\in H_j$ such that $\forall_i \sigma_if_j = a s f_j=f_j\sigma_i$, and a unique idempotent $g_j\in H_j$ such that $\forall_i \sigma_i g_j = -as^{-1}g_j=g_j\sigma_i$.
\end{proposition}
\begin{remark}
Setting $a=q^{-1/n}$ and $s=q$ on equation (\ref{antisym}) above, one sees that this resembles the relation (\ref{sourcesink}) where the source-sink diagram on the L.H.S. is equal to $[n]!q^{n(n-1/2)}\cdot g_n$.
\end{remark}
\begin{lemma}\label{antisymlemma2}
For each $1<j\leq n$, there exists an element in $\mathcal{S}p^n(SL_n)$ that satisfies the relation (\ref{antisym}) and is given by
\begin{align}\label{antisymlemmapic}
g_j = \frac{1}{[j]!}
\raisebox{-19mm}{\includegraphics[width=0.175\textwidth]{functor2}}
\end{align}
\end{lemma}
\begin{proof}
The proof will be done by showing that such an element satisfies the equivalent statements in equations (\ref{antisymrecur1}) and (\ref{antisymrecur2}) and by induction on $j$.
\noindent\textit{Base case ($j=1$):} Setting $j=1$ in equation (\ref{antisym}), we get that such an element has to be an identity on a single strand. Hence, the condition (\ref{antisymrecur1}) is satisfied. Next, to verify the condition (\ref{antisymrecur2}), use the two equations satisfied by $f_j$ and $g_j$ below, where the second equation follows from the relation (\ref{freln1}) by substituting $a=q^{-1/n}$ and $s=q$.
\begin{align}
1_2 &= f_2 + g_2\\
[2]f_2 &= q^{-1}\OIdma + q^{1/n}\OPxa
\end{align}
Using the two equations above to solve for $g_2$ after resolving the crossing proves the base case.
\noindent\textit{Induction step:} Assume the claim holds for all $g_j$ for $1<j\leq m$. We will show it's true for $j=m+1$.
Start with
\[g_{m+1} = 1_1 \otimes g_m - \frac{[2][m]}{[m+1]}(1_1 \otimes g_m)(f_2\otimes 1_{j-1})(1_1 \otimes g_m)
\]
Now use the induction hypothesis on the R.H.S.. Note that we have three diagrams stacked together in the term that is being subtracted on the RHS. Simplify this diagram by resolving the crossing obtained by substituting $f_2$ and applying the relation shown below.
\begin{align*}
\def11cm}\input{CKMtoKV.pdf_tex{12cm}\input{functor3.pdf_tex}
\end{align*}
Finally, combining the terms proves the claim.
\end{proof}
\begin{lemma}\label{tauwelldef}
The functor $\tau$ is well-defined.
\end{lemma}
\begin{proof}
By resolving the crossings, one can see that the relations (\ref{homflysik}, \ref{twistsik}, \ref{unknotsik}) get mapped to relations in $\mathcal{S}p^n(SL_n)$. Further, Lemma (\ref{antisymlemma2}) tells us that there exist elements in $\mathcal{S}p^n(SL_n)$ that satisfy the RHS of the relation (\ref{sourcesink}), after some normalization. Hence, with the assignment shown below, one sees that $\tau$ respects the relation (\ref{sourcesink}).
\begin{center}
\includegraphics[scale=.7]{functor3.png}
\end{center}
Thus, this shows that $\tau$ is well-defined.
\end{proof}
\begin{lemma}\label{tauonto}
The functor $\tau$ is surjective.
\end{lemma}
\begin{proof}
For any diagram in $\mathcal{S}p^n(SL_n)$, let us consider the two cases: subgraphs with tag and without tag.
For the latter case, from Theorem \ref{reducecolorthm}, we know any untagged diagram in $\mathcal{S}p^n(SL_n)$ can be written as a linear combination of diagrams in $\mathcal{S}p_0^3(SL_n)$. Further, from Lemma \ref{recursion1}, any such diagram can be written in terms of linear combination of diagrams with colors $\{1^\pm, 2^\pm\}$. Finally, any diagram with the color `$2$' can be replaced with a linear combination of diagrams with a crossing and parallel strands with color `$1$'. Recall that the preimage of a crossing with colors $\{1^\pm\}$ in $\mathcal{S}p^n(SL_n)$ is the same crossing in $\Tilde{\mathcal{S}}$.
Thus, any untagged diagram in $\mathcal{S}p^n(SL_n)$ can be obtained as an image of a combination of diagrams in $\Tilde{\mathcal{S}}$ under $\tau$.
Now, consider the case of tagged diagrams. Around each tag, we form a disk and proceed by creating bubbles on each of the two edges that meet at the tag. Then, using the definition of $\tau$, we obtain the preimage of a tagged diagram to be a diagram with a source or a sink. The procedure is demonstrated below.
\begin{align}\label{tagtosink}
\def11cm}\input{CKMtoKV.pdf_tex{11cm}\input{surjectivitytau1.pdf_tex}
\end{align}
For any vertices and edges that are not adjacent to the tag, we can identify those subgraphs (after applying the bubbling procedure as needed) as diagrams in $\mathcal{S}p^i_0(SL_n)$ whose preimage then lives in $\Tilde{\mathcal{S}}$ as discussed in the ``without tag" case above.
Thus, this shows that the functor $\tau$ is surjective.
\end{proof}
\subsection{Faithfulness of $\tau$}
Let us define a functor $\tau^{-1}: \mathcal{S}p^n(SL_n) \to \Tilde{\mathcal{S}}$ as a preimage functor, i.e. $\tau^{-1}(x)= y$ if $\tau(y)=x$.
Note that well-definedness of $\tau^{-1}$ proves faithfulness of $\tau$.
\begin{lemma}\label{taufaithful}
$\tau^{-1}$ is well-defined.
\end{lemma}
\begin{proof}
Let us again consider the two cases: relations with and without tags. \\
For the latter case, Theorem \ref{reducecolorthm} tells us it suffices to consider the relations in $\mathcal{S}p_0^3(SL_n)$. It is straightforward to check that the bubble relations and the $6j$ relation in $\mathcal{S}p_0^3(SL_n)$ follow from the Reidemeister II and III relations respectively. Hence, from Theorem \ref{allckmrelationtheorem1}, the image of all untagged relations in $\mathcal{S}p_0^3(SL_n)$ under $\tau^{-1}$ lie in the set of relations in $\Tilde{\mathcal{S}}$.
In the case of relations with tags, there are three types of relations to be considered. Consider one of the two `tag migration' relations: the one that is a $6j$ relation (c.f. (\ref{6jckm1})) involving the color `$n$'. Recall the definition of $\tau$ on the generators. In particular, $\tau$ maps an $n-$web that is a sink (similarly, source) to a left-adjoint tree with a tag that is a sink (accordingly, a source), c.f. (\ref{tauongens}). Note that the choice for the image of the $n-$web is unique upto $6j$ move involving the color `$n$'. Hence, by construction, $\tau^{-1}$ sends all diagrams that are related by $6j$ moves involving the color `$n$' to the corresponding $n-$web which is unique in $\Tilde{\mathcal{S}}$.
Now consider the `tag switch' relation (\ref{tagswitchckm}). In order to understand how this relation is obtained in $\Tilde{\mathcal{S}}$, first observe the following:
\begin{align}\label{tagswitchsik}
\def11cm}\input{CKMtoKV.pdf_tex{7cm}\input{tagswitchsik.pdf_tex}
\end{align}
The relation above follows from the relations (\ref{homflysik} - \ref{unknotsik}) in $\Tilde{\mathcal{S}}$. We refer the reader to \cite{sik} for more details. This relation tells us how the source (similarly, sink) moves past a strand labeled `$1$'. Using our definition of $\tau$ on generators, this tells us that $\tau^{-1}$ maps the relation (\ref{tagswitchckm}) with $k=1$ to the relation (\ref{tagswitchsik}) above. In order to obtain the general tag switch relation from this, one can proceed as in (\ref{tagtosink}) shown above by creating bubbles around the tag and migrating the tag to the strands with label `$1$'. Then repeatedly applying the relation (\ref{tagswitchsik}) above. It's worth noting that while doing this procedure, on the initial step, there is a choice to be made regarding which one of the two edges (labelled $k$ or $n-k$) to migrate the tag on. However, this doesn't make a difference since $(-1)^{k(n-k)}$ is always positive for $n$ odd and for $n$ even, it's enough to know the parity of either $k$ or $n-k$ as both $(-1)^k$ and $(-1)^{n-k}$ yield the same value. Thus the relations (\ref{homflysik} - \ref{unknotsik}) in $\Tilde{\mathcal{S}}$ imply the tag switch relation (\ref{tagswitchckm}).
Finally, consider the ``tag migration'' relation (\ref{movetagckm}). The following lemma will be used to prove this relation.
\begin{lemma}\label{addlemma1}
Given a trivalent vertex in $\mathcal{S}p^n(SL_n)$, its image under $\tau^{-1}$ is given by the following.
Below each label on the RHS represents the number of parallel bands.\\
\includegraphics[scale=.7]{Additionallemmafortag.png}
\end{lemma}
\begin{proof}
To begin with, recall the follwing fact using the antisymmetrizer relation in (\ref{antisymlemmapic}).
\begin{align}\label{antisymfortag1}
\includegraphics[scale=.7]{antisymfortag.png}
\end{align}
In order to use the relation above, we start with the diagram on the LHS of our claim and apply the bubbling procedure on each edge as observed in (\ref{tagtosink}). In order to relate this with the diagram on the RHS, we first observe the following fact from Lemma $25$ in \cite{sik}.
\begin{align}\label{sikoralemma1}
\includegraphics[scale=.7]{sikoralemma1.png}
\end{align}
Use induction on the number of strands being traced to the right on relation (\ref{sikoralemma1}) above, and make substitution using the relation (\ref{sourcesink}) to obtain the following equation (below, the labels on LHS represent the number of parallel strands):
\begin{align}\label{sikoralemma2}
\includegraphics[scale=.7]{sikoralemma2.png}
\end{align}
Finally, simplifying equation (\ref{sikoralemma2}) and comparing with the equation (\ref{antisymfortag1}) proves the claim.
\end{proof}
\noindent Make the following observation using Lemma \ref{tauonto} and Lemma \ref{addlemma1} from above.
\begin{align}
\raisebox{-15mm}{\includegraphics[width=0.12\textwidth]{movetaglhs.png}}
\longmapsto \dfrac{(-1)^{-n(n-1)}q^{-3n(n-1)/4}}{[k]![l]![k+l]![n-l]![n-k-l]!}
\raisebox{-19mm}{\includegraphics[width=0.27\textwidth]{LHStagrelation.png}}
\label{lhstagrel}\\
\raisebox{-15mm}{\includegraphics[width=0.175\textwidth]{movetagrhs.png}}
\longmapsto \dfrac{(-1)^{-n(n-1)}q^{-3n(n-1)/4}}{[k]![l]![k+l]![n-l]![n-k-l]!}
\raisebox{-21mm}{\includegraphics[width=0.23\textwidth]{RHStagrelation.png}}
\label{rhstagrel}
\end{align}
Then, notice that starting from the diagram on the image of $\tau^{-1}$ in (\ref{lhstagrel}), one obtains the diagram on (\ref{rhstagrel}) by applying the tag-switch relation twice on the two sinks connecting the edge labeled $n-k-l$. As the tag-switch relation on the same number of strands is applied twice, no negative sign appears. Hence, this shows that the tag migration relation (\ref{movetagckm}) is implied by the relations in $\Tilde{\mathcal{S}}$.
Thus, this shows $\tau^{-1}$ is well-defined.
\end{proof}
\begin{theorem}\label{sikorackmequiv}
$\Tilde{\mathcal{S}}$ and $\mathcal{S}p^n(SL_n)$ are equivalent as braided spherical tensor categories.
\end{theorem}
\begin{proof}
This follows immediately from Lemmas \ref{tauwelldef}, \ref{tauonto} and \ref{taufaithful}.
\end{proof}
\begin{corollary}\label{sikorapresentation1}
The categories $\Tilde{\mathcal{S}}$ and $\mathcal{C}_n$ are equivalent as braided spherical tensor categories.
\end{corollary}
\begin{proof}
First, define a functor $\Gamma^n: \mathcal{S}p^n(SL_n) \to \mathcal{C}_n$, where $\Gamma^n$ is a restriction of the functor to $\mathcal{S}p^n(SL_n)\subseteq \mathcal{S}p(SL_n)$ constructed in \cite{ckm} that goes from $\mathcal{S}p(SL_n) \to \mathcal{R}ep(SL_n)$.
Then, note that the main result from \cite{ckm} immediately implies that as a spherical tensor functor, this gives an equivalence of the two categories. In fact, fullness of $\Gamma^n$ as a braided tensor functor follows from the proof of fullness of their main result in \cite{ckm} along with the definition of braiding in Section 6 in \cite{ckm}. In order to check faithfulness of $\Gamma^n$ as a braided tensor functor, notice that from the final corollary in Section 6 of \cite{ckm}, it is known that the braiding can be expressed as a linear combination of boxes. Further, from Theorem \ref{allckmrelationtheorem1} it's known that the box relations are equivalent to the Reidemeister relations (check also for example \cite{moy}). Hence, this tells us that $\Gamma^n$ is faithful. Thus, $\Gamma^n$ gives an equivalence of $\mathcal{S}p^n(SL_n)$ with $\mathcal{C}_n$ as braided spherical tensor categories.
Now, define a functor $RT^n: \Tilde{\mathcal{S}} \to \mathcal{C}_n $ where, $RT^n:= \Gamma^n \circ \tau$. Then the fact that $\Gamma^n$ is an equivalence of braided spherical categories together with Theorem \ref{sikorackmequiv} implies that $RT^n$ is an equivalence of braided spherical tensor categories.
\end{proof}
\begin{theorem}[Proof of Conjecture \ref{lesikconjecture}]
\end{theorem}
\begin{proof}
From the Corollary \ref{sikorapresentation1}, we have that the category $\Tilde{\mathcal{S}}$ provides a presentation in terms of generators and relations of $\mathcal{C}_n$. Note that the full subcategory of $\mathcal{R}ep(SL_n)$ where the objects are finite tensor products of the standard representations is unique.
As the functor $RT_0: \Tilde{\mathcal{S}} \to \mathcal{C}_n$ defined in \cite{lesik}, and mentioned in the conjecture \ref{lesikconjecture}, is also a surjective functor between the same categories, we have that $ \Tilde{\mathcal{S}}/\ker(RT_0)$ is also equivalent as a braided tensor category to $\mathcal{C}_n$. Then, it follows from the Corollary \ref{sikorapresentation1} that $\ker(RT_0)$ is the monoidal ideal generated by elements given in relations (\ref{homflysik}--\ref{unknotsik}).
\end{proof}
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,072 |
Orlann Ombissa-Dzangue (born 26 May 1991) is a French sprinter who specializes in the 100 metres. As a relay runner she won a silver medal at the 2011 European U23 Championships, and competed without reaching the final at the 2017 World Championships in Athletics. Her personal best time is 11.06 seconds, achieved in July 2018 in Albi.
Personal life
Born in France, Ombizza-Dzangue is of Gabonese descent.
References
External links
1991 births
Living people
Sportspeople from Sens
French female sprinters
World Athletics Championships athletes for France
Athletes (track and field) at the 2018 Mediterranean Games
Mediterranean Games medalists in athletics
Mediterranean Games gold medalists for France
Mediterranean Games gold medalists in athletics
Athletes (track and field) at the 2020 Summer Olympics
Olympic athletes of France
French sportspeople of Gabonese descent | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,234 |
package com.dtolabs.rundeck.core.authorization;
import java.util.Map;
import java.util.Set;
/**
* A request to be evaluated
*/
public interface AuthorizationRequest {
/**
* @return resource map
*/
Map<String, String> getResource();
/**
* @return subject
*/
AclSubject getSubject();
/**
* @return action requested
*/
String getAction();
/**
* @return environment context
*/
Set<Attribute> getEnvironment();
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,217 |
Q: Get remote application pool state using Microsoft.Web.Administration I'm trying to get the state of an IIS 7.5 application pool using Microsoft.Web.Administration API, but get an exception:
System.Runtime.InteropServices.COMException was unhandled
ErrorCode=-2147020584
HResult=-2147020584
Message=The object identifier does not represent a valid object. (Exception from HRESULT: 0x800710D8)
Source=Microsoft.Web.Administration
I connect to a remote machine in a different domain using the following code:
string appHostConfigFile = "\\\\" + serverName + "\\c$\\windows\\system32\\inetsrv\\config\\applicationHost.config";
UNCAccess unc = new UNCAccess(@"\\" + serverName + "\\c$\\windows\\system32\\inetsrv\\config", <USER_NAME>, <DOMAIN>, <PASSWORD>);
server = new ServerManager(appHostConfigFile);
and then try to iterate through all application pools:
ApplicationPoolCollection applicationPools = server.ApplicationPools;
foreach (ApplicationPool pool in applicationPools)
{
Console.WriteLine("Name: " + pool.Name + " State: " + pool. State);
}
Now, the strange thing is that I do get the Name property correctly (and many other properties too) but the State property thoughts an exception.
Only when I tried connecting to the local machine (127.0.0.1), everything worked as expected.
So, can anyone tell me what I've been missing here? Is there any other way to connect to a remote IIS server on a machine outside of mine domain?
Thanks a lot!
A: I have successfully used Windows Impersonation to access a remote IIS instance using ServerManager.
using (ServerManager serverManager = new ServerManager($@"\\{computerName}\c$\windows\system32\inetsrv\config\applicationHost.config"))
{
ApplicationPoolCollection appPools = serverManager.ApplicationPools
}
This works with IIS 8 and IIS 7.5. I have not tested with other versions. I am using SimpleImpersonation (available via Nuget).
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,913 |
\section{Introduction}
Many signal and image processing problems, such as denoising, compressed sensing, or phase retrieval, can be formulated as inverse problems that aim to recover unknown signals from (noisy) observations. These ill-posed problems are, by definition, subject to many solutions under the given measurement model. Therefore, prior knowledge is required for a meaningful and physically plausible recovery of the original signal. Bayesian inference and maximum a posteriori (MAP) solutions incorporate both signal priors and observation likelihood models. Choosing an appropriate statistical prior is not trivial and is often dependent on both the application as well as the recovery task.
Before deep learning, sparsity in some transform domain has been the go-to prior in compressed sensing (CS) methods \citep{eldar2012compressed}, such as iterative thresholding \citep{beck2009fast} or wavelet decomposition \citep{mallat1999wavelet}.
At present, deep generative modeling has established itself as a strong mechanism for learning such priors for inverse problem-solving. Both generative adversarial networks (GANs) \citep{bora2017compressed} and normalizing flows (NFs) \citep{asim2020invertible, wei2022deep} have been applied as natural signal priors for inverse problems in image recovery. These data-driven methods are more powerful compared to classical methods, as they can accurately learn the natural signal manifold and do not rely on assumptions such as signal sparsity or hand-crafted basis functions.
Recently, diffusion models have shown impressive results for both conditional and unconditional image generation and can be easily fitted to a target data distribution using score matching \citep{vincent2011connection, song2020score}. These deep generative models learn the score of the data manifold and produce samples by reverting a diffusion process, guiding noise samples towards the target distribution. Diffusion models have achieved state-of-the-art performance in many downstream tasks and applications, ranging from state-of-the-art text-to-image models such as DALL-E 2 \citep{ramesh2022hierarchical} to medical imaging \citep{song2021solving, jalal2021robust, chung2022score}. Furthermore, understanding of diffusion models is rapidly improving and progress in the field is extremely fast-paced \citep{chung2022improving, bansal2022cold, daras2022score, karras2022elucidating, luo2022understanding}.
The iterative nature of the sampling procedure used by diffusion models renders inference slow compared to GANs and VAEs. However, many recent efforts have shown ways to significantly improve the sampling speed by accelerating the diffusion process.
Inspired by momentum methods in sampling, \citet{daras2022soft} introduces a momentum sampler for diffusion models, which leads to increased sample quality with fewer function evaluations.
\citet{chung2022come} offers a new sampling strategy, namely Come-Closer-Diffuse-Faster (CCDF), which leverages the conditional quality of inverse problems. The reverse diffusion can be initialized from the observation instead of a sample from the base distribution, which leads to faster convergence for conditional sampling.
\citet{salimans2021progressive} proposes a progressive distillation method that augments the training of the diffusion models with a student-teacher model setup. In doing this, they were able to drastically reduce the number of sampling steps.
Lastly, many methods aim to execute the diffusion process in a reduced space to accelerate the diffusion process. While \citet{jing2022subspace} restricts diffusion through projections onto subspaces, \citet{vahdat2021score} and \citet{rombach2022high} run the diffusion in the latent space.
Despite this promise, current score-based diffusion methods for inverse problems are limited to measurement models with unstructured noise.
In many image processing tasks, corruptions are however highly structured and spatially correlated. Relevant examples include interference, speckle, or haze. Nevertheless, current conditional diffusion models naively assume that the noise follows some basic tractable distribution (e.g. Gaussian or Poisson). Beyond the realm of diffusion models, \citet{whang2021solving} extended normalizing flow (NF)-based inference to structured noise applications. However, compared to diffusion models, NFs require specialized network architectures, which are computationally and memory expensive.
Given the promising outlook of diffusion models, we propose to learn score models for both the noise and the desired signal and perform joint inference of both quantities, coupled via the observation model. The resulting sampling scheme enables solving a wide variety of inverse problems with structured noise.
The main contributions of this work are as follows:
\begin{itemize}
\item We propose a novel joint conditional posterior sampling method to efficiently remove structured noise using diffusion models. Our formulation is compatible with many existing iterative sampling methods for score-based generative models.
\item We show strong performance gains across various challenging inverse problems involving structured noise compared to competitive state-of-the-art methods based on NFs and GANs.
\item We demonstrate improved robustness on out-of-distribution signals compared to baselines.
\end{itemize}
\section{Problem Statement}
\label{sec:inv_problems}
Many image reconstruction tasks can be formulated as an inverse problem with the basic form
\begin{equation}
{\mathbf y} = {\mathbf A}{\mathbf x} + {\mathbf n},
\label{eq:inverse_problem}
\end{equation}
where ${\mathbf y}\in{\mathbb R}^m$ is the noisy observation, ${\mathbf x}\in{\mathbb R}^d$ the desired signal or image, and ${\mathbf n}\in{\mathbb R}^m$ the additive noise. The linear forward operator ${\mathbf A}\in{\mathbb R}^{m\times d}$ captures the deterministic transformation of ${\mathbf x}$.
Maximum a posteriori (MAP) inference is typically used to find an optimal solution $\hat{{\mathbf x}}_{\text{MAP}}$ that maximizes posterior density $p_{X|Y}({\mathbf x}|{\mathbf y})$:
\begin{align}
\hat{{\mathbf x}}_{\text{MAP}} &= \argmax_{{\mathbf x}}{\log p_{X|Y}({\mathbf x}|{\mathbf y})}\\
&= \argmax_{{\mathbf x}}{\left[\log p_{Y|X}({\mathbf y}|{\mathbf x}) + \log p_{X}({\mathbf x})\right]},
\label{eq:map}
\end{align}
where $p_{Y|X}({\mathbf y}|{\mathbf x})$ is the likelihood according to the measurement model and $\log p_{X}({\mathbf x})$ the signal prior.
Assumptions on the stochastic corruption process ${\mathbf n}$ are of key importance too, in particular for applications for which this process is highly structured. However, most methods assume i.i.d. Gaussian distributed noise, such that the forward model becomes $p_{Y|X}({\mathbf y}|{\mathbf x}) \sim \mathcal{N}({\mathbf A}{\mathbf x},\sigma^{2}_{N} \mathbf{I})$. This naturally leads to the following simplified problem:
\begin{align}
\hat{{\mathbf x}}_{\text{MAP}} &= \argmin_{{\mathbf x}} \frac{1}{2\sigma^2_{N}}||{\mathbf y} - {\mathbf A}{\mathbf x}||_2^2 -\log p_X({\mathbf x}).
\end{align}
However, as mentioned, this naive assumption can be very restrictive as many noise processes are much more structured and complex. A myriad of problems can be addressed under the formulation of \eqref{eq:inverse_problem}, given the freedom of choice for the noise source ${\mathbf n}$. Therefore, in this work, our aim is to solve a more broad class of inverse problems defined by any arbitrary noise distribution ${\mathbf n} \sim p_N({\mathbf n}) \neq \mathcal{N}$ and signal prior ${\mathbf x} \sim p_X({\mathbf x})$, resulting in the following, more general, MAP estimator proposed by \citet{whang2021solving}:
\begin{align}
\hat{{\mathbf x}}_{\text{MAP}} &= \argmax_{{\mathbf x}} \log p_N({\mathbf y} - {\mathbf A}{\mathbf x}) -\log p_X({\mathbf x}).
\label{eq:ext_map}
\end{align}
In this paper, we propose to solve this class of problems using flexible diffusion models. Furthermore, diffusion models naturally enable posterior sampling, allowing us to take advantage of the benefits thereof \citep{jalal2021instance, kawar2021snips, daras2022score}.
\subsection{Related Work}
\subsubsection{Normalizing Flows}
\label{sec:nf}
\cite{whang2021solving} propose to use normalizing flows (NFs) to model both the data and the noise distributions. Normalizing flows are a special class of likelihood-based generative models that make use of an invertible mapping $G: {\mathbb R}^d\rightarrow{\mathbb R}^d$ to transform samples from a base distribution $p_Z({\mathbf z})$ into a more complex multimodal distribution ${\mathbf x} = G({\mathbf z}) \sim p_X({\mathbf x})$. The invertible nature of the mapping $G$ allows for exact density evaluation through the change of variables formula:
\begin{align}
\log p_X({\mathbf x}) = \log p_Z({\mathbf z}) + \log |\det J_{G^{-1}}({\mathbf x})|,
\end{align}
where $J$ is the Jacobian that accounts for the change in volume between densities. Since exact likelihood computation is possible through the flow direction $G^{-1}$, the parameters of the generator network can be optimized to maximize likelihood of the training data. Subsequently, the inverse task is solved using the MAP estimation in \eqref{eq:ext_map}:
\begin{equation}
\hat{{\mathbf x}} = \argmax_{{\mathbf x}} \left\{
\log p_{G_N}({\mathbf y} - {\mathbf A}{\mathbf x}) + \log p_{G_X}({\mathbf x})
\right\},
\end{equation}
where $G_N$ and $G_X$ are generative flow models for the noise and data respectively.
Analog to that, the solution can be solved in the latent space rather than the image space as follows:
\begin{equation}
\hat{{\mathbf z}} = \argmax_{{\mathbf z}} \left\{
\log p_{G_N}({\mathbf y} - {\mathbf A}(G_X({\mathbf z}))) + \lambda\log p_{G_X}(G_X({\mathbf z}))
\right\}.
\label{eq:latent_flow_opt}
\end{equation}
Note that in \eqref{eq:latent_flow_opt} a smoothing parameter $\lambda$ is added to weigh the prior and likelihood terms, as was also done in \citet{whang2021solving}.
\subsubsection{Generative Adversarial Networks}
\label{sec:gan}
Generative adversarial networks (GANs) are implicit generative models that can learn the data manifold in an adversarial manner \citep{goodfellow2020generative}. The generative model is trained with an auxiliary discriminator network that evaluates the generator's performance in a minimax game. The generator $G({\mathbf z}): {\mathbb R}^l\rightarrow{\mathbb R}^d$ maps latent vectors ${\mathbf z}\in{\mathbb R}^l\sim\mathcal{N}(\mathbf{0}, {\mathbf I})$ to the data distribution of interest. The structure of the generative model can also be used in inverse problem solving \citep{bora2017compressed}. The objective can be derived from \eqref{eq:map} and is given by:
\begin{equation}
\hat{{\mathbf z}} = \argmin_{{\mathbf z}} \left\{
||{\mathbf y} - AG_X({\mathbf z})|| + \lambda ||z||_2^2
\right\},
\end{equation}
where $\lambda$ weights the importance of the prior with the measurement error. The $\ell_2$ regularization term on the latent variable is proportional to negative log-likelihood under the prior defined by $G_X$, where the subscript denotes the density that the generator is approximating. While this method does not explicitly model the noise, it remains an interesting comparison, as the generator cannot reproduce the noise found in the measurement and can only recover signals that are in the range of the generator. Therefore, due to the limited support of the learned distribution, GANs can inherently remove structured noise. However, the representation error (i.e. observation lies far from the range of the generator \citep{bora2017compressed}) imposed by the structured noise comes at the cost of recovery quality.
\subsection{Background on Score-based Diffusion Models}
\label{sec:score_based_diff}
One class of deep generative models is known as diffusion models. These generative models have been introduced independently as score-based models \citep{song2019generative, song2020improved} and denoising diffusion probabilistic modeling (DDPM) \citep{ho2020denoising}. In this work, we will consider the formulation introduced in \citet{song2020score}, which unifies both perspectives on diffusion models by expressing diffusion as a continuous process through stochastic differential equations (SDE).
Diffusion models produce samples by reversing a corruption process. In essence these models are networks trained to denoise its input. Through iteration of this process, samples can be drawn from a learned data distribution, starting from random noise.
The diffusion process of the data $\left\{{\mathbf x}_t\in{\mathbb R}^{d}\right\}_{t\in[0,1]}$ is characterized by a continuous sequence of Gaussian perturbations of increasing magnitude indexed by time $t\in[0, 1]$. Starting from the data distribution at $t=0$, clean images are defined by ${\mathbf x}_0 \sim p({\mathbf x}_0)\equiv p({\mathbf x})$. Forward diffusion can be described using an SDE as follows:
\begin{equation}
\mathrm{d}{\mathbf x}_t = f(t){\mathbf x}_t\mathrm{d}t + g(t) \mathrm{d}\mathbf{w},
\end{equation}
where $\mathbf{w}\in{\mathbb R}^d$ is a standard Wiener process, $f(t): [0, 1]\rightarrow{\mathbb R}$ and $g(t): [0, 1]\rightarrow{\mathbb R}$ are the drift and diffusion coefficients, respectively. Moreover, these coefficients are chosen so that the resulting distribution $p_1({\mathbf x})$ at the end of the perturbation process approximates a predefined base distribution $p_1({\mathbf x})\approx\pi({\mathbf x})$.
Furthermore, the transition kernel of the diffusion process is defined as $q({\mathbf x}_t|{\mathbf x})\sim\mathcal{N}({\mathbf x}_t|\alpha(t){\mathbf x}, \beta^2(t)\mathbf{I})$, where $\alpha(t)$ and $\beta(t)$ can be analytically derived from the SDE.
Naturally, we are interested in reversing the diffusion process, so that we can sample from ${\mathbf x}_0 \sim p_0({\mathbf x}_0)$. The reverse diffusion process is also a diffusion process given by the reverse-time SDE \citep{anderson1982reverse, song2020score}:
\begin{equation}
\mathrm{d}{\mathbf x}_t =
\big[
f(t){\mathbf x}_t - g(t)^2\underbrace{\nabla_{{\mathbf x}_t} \log{p({\mathbf x}_t)}}_{\text{score}}
\big] \mathrm{d}t + g(t) \mathrm{d}\Bar{\mathbf{w}}_t
\label{eq:reverse_diff}
\end{equation}
where $\Bar{\mathbf{w}}_t$ is the standard Wiener process in the reverse direction. The gradient of the log-likelihood of the data with respect to itself, a.k.a. the \textit{score function}, arises from the reverse-time SDE. The score function is a gradient field pointing back to the data manifold and can intuitively be used to guide a random sample from the base distribution $\pi({\mathbf x})$ to the desired data distribution. Given a dataset $\mathcal{X} = \left\{{\mathbf x}^{(1)}, {\mathbf x}^{(2)}, \ldots, {\mathbf x}^{(|\mathcal{X}|)}\right\}\sim p({\mathbf x})$, scores can be estimated by training a neural network $s_\theta({\mathbf x}_t, t)$ parameterized by weights $\theta$, with score-matching techniques such as the denoising score matching (DSM) objective \citep{vincent2011connection}:
\begin{equation}
\theta^* = \argmin_\theta \mathbb{E}_{t\sim U[0, 1]}
\left\{
\mathbb{E}_{({\mathbf x}, {\mathbf x}_t)\sim p({\mathbf x})q({\mathbf x}_t|{\mathbf x})}
\left[
\norm{s_\theta({\mathbf x}_t, t) - \nabla_{{\mathbf x}_t}\log q({\mathbf x}_t|{\mathbf x})}_2^2
\right]
\right\}.
\label{eq:score_matching}
\end{equation}
Given a sufficiently large dataset $\mathcal{X}$ and model capacity, DSM ensures that the score network converges to $s_\theta({\mathbf x}_t, t)\simeq \nabla_{{\mathbf x}_t}\log p({\mathbf x}_t)$. After training the time-dependent score model $s_\theta$, it can be used to calculate the reverse-time diffusion process and solve the trajectory using numerical samplers such as the Euler-Maruyama algorithm. Alternatively, more sophisticated samplers, such as ALD \citep{song2019generative}, probability flow ODE \citep{song2020score}, and Predictor-Corrector sampler \citep{song2020score}, can be used to further improve sample quality.
These iterative sampling algorithms discretize the continuous time SDE into a sequence of time steps $\left\{0=t_0, t_1, \ldots, t_T=1 \right\}$, where a noisy sample $\hat{{\mathbf x}}_{t_i}$ is denoised to produce a sample for the next time step $\hat{{\mathbf x}}_{t_{i-1}}$. The resulting samples $\{\hat{{\mathbf x}}_{t_i}\}_{i=0}^T$ constitute an approximation of the actual diffusion process $\left\{{\mathbf x}_t\right\}_{t\in[0,1]}$.
\section{Method}
\subsection{Conditional Posterior Sampling under Structured Noise}
We are interested in posterior sampling under structured noise. We recast this as a joint optimization problem with respect to the signal ${\mathbf x}$ and noise ${\mathbf n}$ given by:
\begin{align}
({\mathbf x}, {\mathbf n}) \sim p_{X, N}({\mathbf x}, {\mathbf n}|{\mathbf y}) \propto \TSW{p_{Y|X,N}({\mathbf y}|{\mathbf x}, {\mathbf n}) \cdot p_X({\mathbf x}) \cdot p_N({\mathbf n}).}
\end{align}
\begingroup\abovedisplayskip=15pt \belowdisplayskip=15pt
Solving inverse problems using diffusion models requires conditioning of the diffusion process on the observation ${\mathbf y}$, such that we can sample from the posterior $p_{X|Y}({\mathbf x}, {\mathbf n}|{\mathbf y})$. Therefore, we construct a \textit{joint conditional} diffusion process $\left\{{\mathbf x}_t, {\mathbf n}_t|{\mathbf y}\right\}_{t\in[0,1]}$, in turn producing a \textit{joint conditional} reverse-time SDE:
\begin{equation}
\mathrm{d}({\mathbf x}_t, {\mathbf n}_t) =
\big[
f(t)\TSW{({\mathbf x}_t, {\mathbf n}_t)} - g(t)^2
\nabla_{{\mathbf x}_t, {\mathbf n}_t} \log{p({\mathbf x}_t, {\mathbf n}_t|\TSW{{\mathbf y}})}
\big] \mathrm{d}t + g(t) \mathrm{d}\Bar{\mathbf{w}_t}.
\label{eq:cond_reverse_diff}
\end{equation}
We would like to factorize the posterior using our learned \textit{unconditional} score model and tractable measurement model, given the joint formulation. Consequently, we construct two separate diffusion processes, defined by separate score models but entangled through the measurement model $p_{Y|X,N}({\mathbf y}|{\mathbf x}, {\mathbf n})$. In addition to the original score model $s_\theta({\mathbf x}, t)$, we introduce a second score model \TSW{$s_\phi({\mathbf n}_t, t)\simeq \nabla_{{\mathbf n}_t} \log p_N({\mathbf n}_t)$}, parameterized by weights $\phi$, to model the expressive noise component ${\mathbf n}$. \TSW{These two score networks can be trained independently on datasets for ${\mathbf x}$ and ${\mathbf n}$, respectively, using the objective in \eqref{eq:score_matching}.} The gradients of the posterior with respect to ${\mathbf x}$ and ${\mathbf n}$ are now given by:
\begin{align}
\nabla_{{\mathbf x}_t} \log{p({\mathbf x}_t, {\mathbf n}_t|{\mathbf y})} &\simeq \nabla_{{\mathbf x}_t} \log{p({\mathbf x}_t)} + \nabla_{{\mathbf x}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)} \nonumber\\
&\simeq s_{\theta^\star}({\mathbf x}_t, t) + \nabla_{{\mathbf x}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)},
\label{eq:approx_cond_x}
\end{align}
\begin{align}
\nabla_{{\mathbf n}_t} \log{p({\mathbf x}_t, {\mathbf n}_t|{\mathbf y})} &\simeq \nabla_{{\mathbf n}_t} \log{p({\mathbf n}_t)} + \nabla_{{\mathbf n}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)} \nonumber\\
&\simeq s_{\phi^\star}({\mathbf n}_t, t) + \nabla_{{\mathbf n}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)},
\label{eq:approx_cond_n}
\end{align}
where $\hat{{\mathbf y}}_t$ is a sample from $p({\mathbf y}_t|{\mathbf y})$, and $\left\{{\mathbf y}_t\right\}_{t\in[0,1]}$ is an additional stochastic process that essentially corrupts the observation along the SDE trajectory together with ${\mathbf x}_t$. As $p({\mathbf y}_t|{\mathbf y})$ is tractable, we can easily compute $\hat{{\mathbf y}}_t = \alpha(t){\mathbf y}+\beta(t){\mathbf A}{\mathbf z}$, using the reparameterization trick with ${\mathbf z}\in{\mathbb R}^d\sim\mathcal{N}(\mathbf{0}, {\mathbf I})$, see \citet{song2021solving}. Subsequently, the approximation in \eqref{eq:approx_cond_x} and \eqref{eq:approx_cond_n} can be substituted for the conditional score in \eqref{eq:cond_reverse_diff}, resulting in two entangled diffusion processes:
\begin{align}
\left\{
\begin{array}{rcl}
\mathrm{d}{\mathbf x}_t & = &
\big[
f(t){\mathbf x}_t - g(t)^2
\left\{
s_{\theta^\star}({\mathbf x}_t, t) + \nabla_{{\mathbf x}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)}
\right\}
\big] \mathrm{d}t + g(t) \mathrm{d}\Bar{\mathbf{w}}_{X, t} \\[2pt]
\mathrm{d}{\mathbf n}_t & = &
\big[
f(t){\mathbf n}_t - g(t)^2
\left\{
s_{\phi^\star}({\mathbf n}_t, t) + \nabla_{{\mathbf n}_t} \log{p(\hat{{\mathbf y}}_t|{\mathbf x}_t, {\mathbf n}_t)}
\right\}
\big] \mathrm{d}t + g(t) \mathrm{d}\Bar{\mathbf{w}}_{N,t}
\end{array}
\right.
\end{align}
which allows us to perform posterior sampling for both the signal, such that ${\mathbf x}\equiv{\mathbf x}_0\sim p_{X|Y}({\mathbf x}_0|{\mathbf y})$, as well as the structured noise, such that ${\mathbf n}\equiv{\mathbf n}_0\sim~p_{N|Y}({\mathbf n}_0|{\mathbf y})$.
To solve the approximated \textit{joint conditional} reverse-time SDE, we resort to the aforementioned iterative scheme in Section~\ref{sec:score_based_diff}, however, now incorporating the observation via a data-consistency step. This is done by taking gradient steps that minimize the $\ell_2$ norm between the true observation and its model prediction given current estimates of ${\mathbf x}$ and ${\mathbf n}$. Ultimately, this results in solutions that are consistent with the observation ${\mathbf y}$ and have high likelihood under both prior models. The data-consistency update steps for both ${\mathbf x}$ and ${\mathbf n}$ are derived as follows:
\begin{multicols}{2}
\noindent
\begin{align}
\hat{{\mathbf x}}_{t-\Delta t} &= \hat{{\mathbf x}}_{t} - \nabla_{{\mathbf x}_t} \log p(\hat{{\mathbf y}}_t|\hat{{\mathbf x}}_t, \hat{{\mathbf n}}_t) \nonumber\\
&= \hat{{\mathbf x}}_{t} - \nabla_{{\mathbf x}_t} ||\hat{{\mathbf y}}_t - ({\mathbf A}\hat{{\mathbf x}}_t + \hat{{\mathbf n}}_t)||_2^2 \nonumber\\
&= \hat{{\mathbf x}}_{t} - \lambda{\mathbf A}^{\mathsf{T}}({\mathbf A}\hat{{\mathbf x}}_t - \hat{\mathbf{y}}_t + \hat{{\mathbf n}}_t),
\label{eq:grad_step_x}
\end{align}
\begin{align}
\hat{{\mathbf n}}_{t-\Delta t} &= \hat{{\mathbf n}}_{t} - \nabla_{{\mathbf n}_t} \log p(\hat{{\mathbf y}}_t|\hat{{\mathbf x}}_t, \hat{{\mathbf n}}_t) \nonumber\\
&= \hat{{\mathbf n}}_{t} - \nabla_{{\mathbf n}_t} ||\hat{{\mathbf y}}_t - ({\mathbf A}\hat{{\mathbf x}}_t + \hat{{\mathbf n}}_t)||_2^2 \nonumber\\
&= \hat{{\mathbf n}}_{t} - \mu({\mathbf A}\hat{{\mathbf x}}_t - \hat{\mathbf{y}}_t + \hat{{\mathbf n}}_t),
\label{eq:grad_step_n}
\end{align}
\end{multicols}
where the time difference between two steps $\Delta t = 1/T$ and $\lambda$ and $\mu$ are weighting coefficients for the signal and noise gradient steps, respectively. An example of the complete sampling algorithm is shown in Algorithm~\ref{alg:joint_cond_sampler}, which adapts the Euler-Maruyama sampler \citep{song2020score} to jointly find the optimal data sample \textit{and} the optimal noise sample while taking into account the measurement model in line~\ref{alg:dc_x} and \ref{alg:dc_n} using the outcome of \eqref{eq:grad_step_x} and \eqref{eq:grad_step_n}, respectively. Although we show the Euler-Maruyama method, our addition is applicable to a large family of iterative sampling methods for score-based generative models.
\endgroup
\newpage
\input{algorithm}
\subsection{Training and Inference Setup}
\label{sec:setup}
For training the score models, we use the NCSNv2 architecture as introduced in \citet{song2020improved} in combination with the Adam optimizer and a learning rate of \num{5e-4} until convergence. For simplicity, no exponential moving average (EMA) filter on the network weights is applied. \TSW{Given two separate datasets, one for the data and one for the structured noise, two separate score models can be trained independently. This allows for easy adaptation of our method, since many existing trained score models can be reused. Only during inference, the two priors are combined through the proposed sampling procedure as described in Algorithm~\ref{alg:joint_cond_sampler}, using the adapted Euler-Maruyama sampler.} We use the variance preserving (VP) SDE ($\beta_0=0.1, \beta_1=7.0$) \citep{song2020score} to define the diffusion trajectory. During each experiment, we run the sampler for $T=600$ iterations.
\vspace{-1mm}
\section{Experiments}
All models are trained on the CelebA dataset \citep{liu2015faceattributes} and the MNIST dataset with 10000 and 27000 training samples, respectively. We downsize the images to $64\times64$ pixels. Due to computational constraints, we test on a randomly selected subset of 100 images. We use both the peak signal-to noise ratio (PSNR) and structural similarity index (SSIM) to evaluate our results.
\subsection{Baseline Methods}
The closest to our work is the flow-based noise model proposed by \citet{whang2021solving}, discussed in Section~\ref{sec:nf}, which will serve as our main baseline. To boost the performance of this baseline and to make it more competitive we moreover replace the originally-used RealNVP \citep{dinh2016density} with the Glow architecture \citep{kingma2018glow}. Glow is a widely used flow model highly inspired by RealNVP, with the addition of $1\times1$ convolutions before each coupling layer. We use the exact implementation found in \citet{asim2020invertible}, with a flow depth of $K=18$, and number of levels $L=4$\TSW{, which has been optimized for the same CelebA dataset used in this work and thus should provide a fair comparison with the proposed method.}
Secondly, GANs as discussed in Section~\ref{sec:gan} are used as a comparison. We train a DCGAN \citep{radford2015unsupervised}, with a generator latent input dimension of $l=100$. The generator architecture consists of 4 strided 2D transposed convolutional layers, having $4\times4$ kernels yielding feature maps of 512, 256, 128 and 64. Each convolutional layer is followed by a batch normalization layer and ReLU activation.
Lastly, depending on the reconstruction task, classical non-data-driven methods are used as a comparison. For denoising experiments, we use the block-matching and 3D filtering algorithm (BM3D) \citep{dabov2006image}, and in compressed sensing experiments, LASSO with wavelet basis \citep{tibshirani1996regression}.
Except for the flow-based method of \citet{whang2021solving}, none of these methods explicitly model the noise distribution. Still, they are a valuable baseline, as they demonstrate the effectiveness of incorporating a learned structured noise prior rather than relying on simple noise priors.
Automatic hyperparameter tuning for optimal inference was performed for all baseline methods on a small validation set of only 5 images. For both GAN and flow-based methods, we anneal the step size during inference based on stagnation of the objective.
\subsection{Results}
\subsubsection{Removing MNIST digits}
\label{sec:exp_mnist}
For comparison with \citet{whang2021solving}, we recreate an experiment introduced in their work, where MNIST digits are added to CelebA faces. Moreover, the experiment is easily reproducible as both CelebA and MNIST datasets are publicly available. The corruption process is defined by ${\mathbf y} = 0.5 \cdot {\mathbf x}_{\text{CelebA}} + 0.5 \cdot {\mathbf n}_{\text{MNIST}}$. \TSW{In this experiment, the score network $s_\phi$ is trained on the MNIST dataset.} Fig.~\ref{fig:metrics_celeba_mnist_1} shows a quantitative comparison of our method with all baselines. Furthermore, a random selection of test samples is shown in Fig.~\ref{fig:comparison_celeba_mnist} for qualitative analysis. Both our method and the flow-based method are able to recover the data, and remove most of the structured noise. However, more details are preserved using the diffusion method. In contrast, the flow-based method cannot completely remove the digits in some cases and is unable to reconstruct some subtle features present in the original images. Furthermore, we observe that for the flow-based method, initialization from the measurement is necessary to reproduce the results in \citet{whang2021solving} since random initialization does not converge.
The GAN method is also able to remove the digits, but cannot accurately reconstruct the faces as it is unable to project the observation onto the range of the generator. Similarly, the BM3D denoiser fails to recover the underlying signal, confirming the importance of prior knowledge of the noise in this experiment. The metrics in Fig.~\ref{fig:metrics_celeba_mnist_1} support these observations. See Table~\ref{tab:metrics} for the extended results.
Additionally, we expose the methods in a similar experiment to out-of-distribution (OoD) data. The images from this dataset not found in the CelebA dataset, which is the data used for training the models. In fact, the out-of-distribution data is generated using the stable-diffusion text-to-image model \cite{rombach2022high}. We use the exact same hyperparameters as during the experiment on the CelebA dataset. Quantitative and qualitative results are shown in Fig.~\ref{fig:metrics_celeba_mnist_2} and Fig.~\ref{fig:comparison_celeba_mnist_ood}, respectively. Similarly to the findings of \citet{whang2021solving} and \citet{asim2020invertible}, the flow-based method is robust to OoD data, due to their inherent invertibility. We empirically show that the diffusion method is also resistant to OoD data in inverse tasks with complex noise structures and even outperforms the flow-based methos. Unsurprisingly, the GAN method performs even more poorly when subjected to OoD data. More experiments, covering different inverse problem settings can be found in Appendix~\ref{app:experiments}.
\begin{figure}
\centering
\begin{subfigure}{0.49\textwidth}
\includegraphics[width=\textwidth]{figures/metrics_celeba_mnist.pdf}
\caption{CelebA}
\label{fig:metrics_celeba_mnist_1}
\end{subfigure}
\hfill
\begin{subfigure}{0.49\textwidth}
\includegraphics[width=\textwidth]{figures/metrics_celeba_mnist_ood.pdf}
\caption{Out-of-distribution data}
\label{fig:metrics_celeba_mnist_2}
\end{subfigure}
\caption{Quantitative results using PSNR (green) and SSIM (blue) for the removing MNIST digits experiment on $64\times64$ images of the (a) CelebA and (b) out-of-distribution datasets.}
\label{fig:metrics_celeba_mnist}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/comparison_celeba_mnist.pdf}
\vspace{-18pt}
\caption{Results for our diffusion-based method compared to the baselines; FLOW \citep{whang2021solving}, GAN \citep{bora2017compressed}, and BM3D \citep{dabov2006image} on the removing MNIST digits experiment on $64\times64$ images of the CelebA dataset.}
\label{fig:comparison_celeba_mnist}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\textwidth]{figures/comparison_celeba_mnist_ood.pdf}
\vspace{-18pt}
\caption{Results for our diffusion-based method on the removing MNIST digits experiment on an out of distribution dataset, generated using stable diffusion \citep{rombach2022high}.}
\label{fig:comparison_celeba_mnist_ood}
\end{figure}
\subsubsection{Performance}
To highlight the difference in inference time between our method and the baselines, benchmarks are performed on a single 12GBytes NVIDIA GeForce RTX 3080 Ti, see Table~\ref{tab:benchmark} in Appendix~\ref{app:perf}. Although this is not an extensive benchmark, a quick comparison of inference times reveals a $50\times$ difference in speed between ours and the flow-based method. All the deep generative models need approximately an equal amount of iterations $(T\approx 600)$ to converge. However, for the same modeling capacity, the flow model requires a substantial higher amount of trainable parameters compared to the diffusion method. This is mainly due to the restrictive requirements imposed on the architecture to ensure tractable likelihood computation. It should be noted that no improvements to speed up the diffusion process, such as CCDF \citep{chung2022come} are applied for the diffusion method, giving room for even more improvement in future work.
\section{Discussion and Conclusions}
In this work, we present a framework for removing structured noise using diffusion models. Our work provides an efficient addition to existing score-based conditional sampling methods incorporating knowledge of the noise distribution. We demonstrate our method on natural and out-of-distribution data and achieve increased performance over the state-of-the-art and \TSW{established conventional methods for complex inverse tasks. Additionally, the diffusion based method is substantially easier to train using the score matching objective compared to other deep generative methods and furthermore allows for posterior sampling.}
While our method is considerably faster and better in removing structured noise compared to the flow-based method \citep{whang2021solving}, it is not ready (yet) for real-time inference and still slow compared to GANs \citep{bora2017compressed} and classical methods. Luckily, research into accelerating the diffusion process are well on their way. In addition, although a simple sampling algorithm was adapted in this work, many more sampling algorithms for score-based diffusion models exist, each of which introduces a new set of hyperparameters. For example, the predictor-corrector (PC) sampler has been shown to improve sample quality \citep{song2020score}. Future work should explore this wide increase in design space to understand limitations and possibilities of more sophisticated sampling schemes in combination with the proposed joint diffusion method. Furthermore, the range of problems to which we can apply the proposed method, can be expanded into non-linear likelihood models and extend beyond the additive noise models.
Lastly, the connection between diffusion models and continuous normalizing flows through the neural ODE formulation \citep{NEURIPS2021_0a9fdbb1} is not investigated, but greatly of interest given the comparison with the flow-based method in this work.
\section{Reproducibility Statement}
\TSW{All code used to train and evaluate the models as presented in this paper can be found at \url{https://anonymous.4open.science/r/iclr2023-joint-diffusion}. Essentially, the codebase in \url{https://github.com/yang-song/score_sde_pytorch} of \citet{song2020score} is used to train the score-based diffusion networks, for both data and structured noise, independently. To implement the proposed inference scheme, the lines in Algorithm~\ref{alg:joint_cond_sampler} should be adapted to create a sampler that includes both trained diffusion models. Details regarding the training and inference settings used to reproduce the results in this work can be found in Section~\ref{sec:setup}.}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,955 |
package com.turbomanage.httpclient;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.net.HttpURLConnection;
import java.net.URL;
/**
* Default {@link RequestHandler} used by {@link BasicHttpClient}. It is
* intended to be used for simple requests with small amounts of data only (a
* few kB), as it does no buffering, chunking, streaming, etc. Only character
* set supported is UTF-8. Only {@link String} content is supported. All
* responses are treated as {@link String}s. This class is abstract so that
* it can be easily extended in an anonymous inner class when constructing
* a client.
*
* @author David M. Chandler
*/
public abstract class BasicRequestHandler implements RequestHandler {
private final RequestLogger logger;
/**
* Constructs a handler with default logger.
*/
public BasicRequestHandler() {
this(new ConsoleRequestLogger());
}
/**
* Constructs a handler with supplied logger.
*
* @param logger
*/
public BasicRequestHandler(RequestLogger logger) {
this.logger = logger;
}
@Override
public HttpURLConnection openConnection(String urlString) throws IOException {
URL url = new URL(urlString);
HttpURLConnection uc = (HttpURLConnection) url.openConnection();
return uc;
}
@Override
public void prepareConnection(HttpURLConnection urlConnection, HttpMethod httpMethod,
String contentType) throws IOException {
// Configure connection for request method
urlConnection.setRequestMethod(httpMethod.getMethodName());
urlConnection.setDoOutput(httpMethod.getDoOutput());
urlConnection.setDoInput(httpMethod.getDoInput());
if (contentType != null) {
urlConnection.setRequestProperty("Content-Type", contentType);
}
// Set additional properties
urlConnection.setRequestProperty("Accept-Charset", UTF8);
}
@Override
public OutputStream openOutput(HttpURLConnection urlConnection)
throws IOException {
return urlConnection.getOutputStream();
}
@Override
public void writeStream(OutputStream out, byte[] content) throws IOException {
out.write(content);
}
@Override
public InputStream openInput(HttpURLConnection urlConnection)
throws IOException {
return urlConnection.getInputStream();
}
@Override
public byte[] readStream(InputStream in) throws IOException {
int nRead;
byte[] data = new byte[16384];
ByteArrayOutputStream buffer = new ByteArrayOutputStream();
while ((nRead = in.read(data)) != -1) {
buffer.write(data, 0, nRead);
}
buffer.flush();
return buffer.toByteArray();
}
@Override
public boolean onError(HttpRequestException e) {
HttpResponse res = e.getHttpResponse();
if (logger.isLoggingEnabled()) {
logger.log("BasicRequestHandler.onError got");
e.printStackTrace();
}
if (res != null) {
int status = res.getStatus();
if (status > 0) {
// Perhaps a 404, 501, or something that will be fixed later
return true;
}
}
// Connection refused, host unreachable, etc.
return false;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,954 |
Forestry, Parks & Recreation
Campgrounds & Parks
ADVANCE RESERVATIONS FOR campsites BEgins February 1st at 9 am
for the standard season
- PLEASE SEE BELOW FOR CAMPGROUND SEASON DATES -
The Douglas County Forest offers three developed campgrounds each offering unique amenities and attractions; Lucius Woods County Park, Gordon Dam County Park, and Mooney Dam County Park. Each campground is located on a large body of water and all three offer excellent sportfishing opportunities. No more than one (1) camping unit (tent, trailer, RV or other similar type of shelter) may occupy each site. Camping rates are subject to change. All campsites available for advance reservations and same day check-in as long as sites are available at time of check-in and do not interfere with upcoming reservations.
Campground Opening and closing dates
Standard Season: from two Fridays before Memorial Day to Monday after Labor Day (full service and amenities provided). Advance reservation and first come first serve basis.
Extended Season: earliest opening May 1st and latest closing October 31st (full service and amenities provided). At the complete discretion of Department staff dependent on weather and available staffing. NO advance reservation, only first come first serve basis.
Off-Season: Only offered at Gordon Dam. Day after the Standard Season and/or Extended Season closing date until the campground is inaccessible by highway vehicles due to snow conditions on the access road (electric service provided at electric sites, NO other service or amenities provided). NO advance reservation, only first come first serve basis.
Mooney Dam County Park
(location map)
14293 South Fowlers Circle, Gordon, WI 54838
Located on Lower Eau Claire Lake in the town of Gordon, this park offers visitors 10 electric and 4 non-electric campsites, containing fire rings, picnic tables, and benches. There is a boat launch with excellent fishing opportunities, newer vault toilets, picnic and grill areas. Mooney Dam is located on Lower Eau Claire Lake, 13 miles east of Gordon on County Road Y.
Camping Rates:
Electric site: $25.00/night
Non-electric site: $20.00/night
Firewood: $5.00/armload
Groups of more than 5: Additional $2.00/person
Off-Season Camping:
Mooney Dam County Park Brochure
Printed brochures are available by contacting the Forestry Department.
Gordon Dam County Park
7201 East County Highway Y, Gordon, WI 54838
Located on the St. Croix Flowage (Gordon Flowage) in the town of Gordon, this park offers visitors 33 total camping sites: 22 with electric hook-up and 11 non-electric campsites, containing fire rings, picnic tables, and benches. The park has opportunities for picnicking, boating, swimming, hiking, wildlife viewing, and excellent fishing opportunities.
Other amenities include a fish cleaning house, canoe and boat launch with a handicap accessible dock, children's playground, newer vault toilets, several picnic sites with grills, and an official "Watchable Wildlife" viewing area.
The park is located at the headwaters of the St. Croix Scenic River, seven miles west of Gordon on County Road Y, which is approximately 37 miles south of Superior on US Highway 53.
Offered following the standard and extended camping season, until snow covers the road on a first-come, first-served self-registration basis. Upper restrooms are open but not stocked or serviced, no garbage pickup provided (100% carry-in carry-out), no firewood delivery provided, and the fish cleaning house is closed. Water hand pumps are available for use.
Off-Season access to the park is 100% weather dependent and no snow removal or vehicle recovery services will be provided. Access at your own risk. The park access road serves as a winter snowmobile trail during the winter months and is actively groomed for snowmobile use. Use of the road during this time of year by highway vehicles is prohibited.
Off-Season Camping Rates:
$20.00/night at any site. Electric will remain on during off-season.
Gordon Dam Park Brochure
Printed brochures are available by contacting the Douglas County Forestry Department.
Lucius Woods County Park
9231 East Marion Avenue, Solon Springs, WI 54873
Located on Upper St. Croix Lake in the village of Solon Springs, this park offers visitors 29 total sites: 23 with electrical and water hook-ups and, 9 non-electric campsites, containing fire rings, picnic tables, and benches. Lucius Woods amenities include showers, flush toilets, a sanitary dump station, opportunities for picnicking, swimming, hiking, the Music in the Park concert series, and excellent fishing opportunities.
The park has many hiking trails, a bateau shelter, children's playground, a beautiful swimming beach, a large log pavilion with a fieldstone fireplace, many picnic areas with grills, and an open-air performing arts amphitheater. The amphitheater is home to Music in the Park, an annual outdoor concert series on the shore of Lake St. Croix. The Giesen Concert Shell is the backdrop for the performances on Saturday evenings throughout the summer. The schedule changes annually. To view a schedule of the concerts, visit Lucius Woods Performing Arts Center.
Lucius Woods County Park Brochure
Include a non-refundable $5.00 Reservation Service Fee in addition to the camping fee.
Campsites in all 3 campgrounds may be reserved in advance for the Standard Season (from two Fridays before Memorial Day to Monday after Labor Day). Advance reservation is NOT offered for Extended Season or Off-Season dates, campsites will only be available on first come first serve basis.
Campsite reservations may be made online starting February 1st and up to the date of occupancy for the current year standard camping season. Changes to existing reservations can be made by contacting the Forestry Department Office in Solon Springs at (715) 378-2219 during open business hours. By submitting a reservation, the individual expressly agrees to ensure compliance with State/local laws and park use rules and regulations by themselves and all of their guests.
Campsite Check-In at 2:00 PM and Check-Out at NOON (12:00 PM).
All cancellations must be made by calling the Forestry Department Office in Solon Springs during open business hours at (715) 378-2219. A full refund less the Reservation Service Fee will be provided when a reservation is cancelled 24 hours or more in advance of check-in time (2:00 PM) on the first day of the scheduled reservation. For reservations cancelled less than 24 hours in advance of check-in time (2:00 PM) on the first day of the scheduled reservation, the first night camping fee plus the Reservation Service Fee will be forfeited.
Total camping fees plus the Reservation Service Fee will be forfeited for any scheduled reservation where the site has not been occupied by check-in time (2:00 PM) on the second day of the reservation.
Non-reserved, unoccupied campsites are available anytime on a first come first served basis.
Douglas County Wildlife Area
Day-Use Parks | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,055 |
#include "squid.h"
#include "base/StringArea.h"
#include "HttpHeader.h"
#include "HttpHeaderFieldStat.h"
#include "HttpHeaderStat.h"
#include "HttpHeaderTools.h"
#include "HttpHdrCc.h"
#include "StatHist.h"
#include "Store.h"
#include "StrList.h"
#if HAVE_MAP
#include <map>
#endif
/* a row in the table used for parsing cache control header and statistics */
typedef struct {
const char *name;
http_hdr_cc_type id;
HttpHeaderFieldStat stat;
} HttpHeaderCcFields;
/* order must match that of enum http_hdr_cc_type. The constraint is verified at initialization time */
static HttpHeaderCcFields CcAttrs[CC_ENUM_END] = {
{"public", CC_PUBLIC},
{"private", CC_PRIVATE},
{"no-cache", CC_NO_CACHE},
{"no-store", CC_NO_STORE},
{"no-transform", CC_NO_TRANSFORM},
{"must-revalidate", CC_MUST_REVALIDATE},
{"proxy-revalidate", CC_PROXY_REVALIDATE},
{"max-age", CC_MAX_AGE},
{"s-maxage", CC_S_MAXAGE},
{"max-stale", CC_MAX_STALE},
{"min-fresh", CC_MIN_FRESH},
{"only-if-cached", CC_ONLY_IF_CACHED},
{"stale-if-error", CC_STALE_IF_ERROR},
{"Other,", CC_OTHER} /* ',' will protect from matches */
};
/// Map an header name to its type, to expedite parsing
typedef std::map<const StringArea,http_hdr_cc_type> CcNameToIdMap_t;
static CcNameToIdMap_t CcNameToIdMap;
/// used to walk a table of http_header_cc_type structs
http_hdr_cc_type &operator++ (http_hdr_cc_type &aHeader)
{
int tmp = (int)aHeader;
aHeader = (http_hdr_cc_type)(++tmp);
return aHeader;
}
/// Module initialization hook
void
httpHdrCcInitModule(void)
{
/* build lookup and accounting structures */
for (int32_t i = 0; i < CC_ENUM_END; ++i) {
const HttpHeaderCcFields &f=CcAttrs[i];
assert(i == f.id); /* verify assumption: the id is the key into the array */
const StringArea k(f.name,strlen(f.name));
CcNameToIdMap[k]=f.id;
}
}
/// Module cleanup hook.
void
httpHdrCcCleanModule(void)
{
// HdrCcNameToIdMap is self-cleaning
}
void
HttpHdrCc::clear()
{
*this=HttpHdrCc();
}
bool
HttpHdrCc::parse(const String & str)
{
const char *item;
const char *p; /* '=' parameter */
const char *pos = NULL;
http_hdr_cc_type type;
int ilen;
int nlen;
/* iterate through comma separated list */
while (strListGetItem(&str, ',', &item, &ilen, &pos)) {
/* isolate directive name */
if ((p = (const char *)memchr(item, '=', ilen)) && (p - item < ilen)) {
nlen = p - item;
++p;
} else {
nlen = ilen;
}
/* find type */
const CcNameToIdMap_t::const_iterator i=CcNameToIdMap.find(StringArea(item,nlen));
if (i==CcNameToIdMap.end())
type=CC_OTHER;
else
type=i->second;
// ignore known duplicate directives
if (isSet(type)) {
if (type != CC_OTHER) {
debugs(65, 2, "hdr cc: ignoring duplicate cache-directive: near '" << item << "' in '" << str << "'");
++CcAttrs[type].stat.repCount;
continue;
}
}
/* special-case-parsing and attribute-setting */
switch (type) {
case CC_MAX_AGE:
if (!p || !httpHeaderParseInt(p, &max_age) || max_age < 0) {
debugs(65, 2, "cc: invalid max-age specs near '" << item << "'");
clearMaxAge();
} else {
setMask(type,true);
}
break;
case CC_S_MAXAGE:
if (!p || !httpHeaderParseInt(p, &s_maxage) || s_maxage < 0) {
debugs(65, 2, "cc: invalid s-maxage specs near '" << item << "'");
clearSMaxAge();
} else {
setMask(type,true);
}
break;
case CC_MAX_STALE:
if (!p || !httpHeaderParseInt(p, &max_stale) || max_stale < 0) {
debugs(65, 2, "cc: max-stale directive is valid without value");
maxStale(MAX_STALE_ANY);
} else {
setMask(type,true);
}
break;
case CC_MIN_FRESH:
if (!p || !httpHeaderParseInt(p, &min_fresh) || min_fresh < 0) {
debugs(65, 2, "cc: invalid min-fresh specs near '" << item << "'");
clearMinFresh();
} else {
setMask(type,true);
}
break;
case CC_STALE_IF_ERROR:
if (!p || !httpHeaderParseInt(p, &stale_if_error) || stale_if_error < 0) {
debugs(65, 2, "cc: invalid stale-if-error specs near '" << item << "'");
clearStaleIfError();
} else {
setMask(type,true);
}
break;
case CC_PRIVATE: {
String temp;
if (!p) {
// Value parameter is optional.
private_.clean();
} else if (/* p &&*/ httpHeaderParseQuotedString(p, (ilen-nlen-1), &temp)) {
private_.append(temp);
} else {
debugs(65, 2, "cc: invalid private= specs near '" << item << "'");
}
// to be safe we ignore broken parameters, but always remember the 'private' part.
setMask(type,true);
}
break;
case CC_NO_CACHE: {
String temp;
if (!p) {
// On Requests, missing value parameter is expected syntax.
// On Responses, value parameter is optional.
setMask(type,true);
no_cache.clean();
} else if (/* p &&*/ httpHeaderParseQuotedString(p, (ilen-nlen-1), &temp)) {
// On Requests, a value parameter is invalid syntax.
// XXX: identify when parsing request header and dump err message here.
setMask(type,true);
no_cache.append(temp);
} else {
debugs(65, 2, "cc: invalid no-cache= specs near '" << item << "'");
}
}
break;
case CC_PUBLIC:
Public(true);
break;
case CC_NO_STORE:
noStore(true);
break;
case CC_NO_TRANSFORM:
noTransform(true);
break;
case CC_MUST_REVALIDATE:
mustRevalidate(true);
break;
case CC_PROXY_REVALIDATE:
proxyRevalidate(true);
break;
case CC_ONLY_IF_CACHED:
onlyIfCached(true);
break;
case CC_OTHER:
if (other.size())
other.append(", ");
other.append(item, ilen);
break;
default:
/* note that we ignore most of '=' specs (RFCVIOLATION) */
break;
}
}
return (mask != 0);
}
void
HttpHdrCc::packInto(Packer * p) const
{
// optimization: if the mask is empty do nothing
if (mask==0)
return;
http_hdr_cc_type flag;
int pcount = 0;
assert(p);
for (flag = CC_PUBLIC; flag < CC_ENUM_END; ++flag) {
if (isSet(flag) && flag != CC_OTHER) {
/* print option name for all options */
packerPrintf(p, (pcount ? ", %s": "%s") , CcAttrs[flag].name);
/* for all options having values, "=value" after the name */
switch (flag) {
case CC_MAX_AGE:
packerPrintf(p, "=%d", (int) maxAge());
break;
case CC_S_MAXAGE:
packerPrintf(p, "=%d", (int) sMaxAge());
break;
case CC_MAX_STALE:
/* max-stale's value is optional.
If we didn't receive it, don't send it */
if (maxStale()!=MAX_STALE_ANY)
packerPrintf(p, "=%d", (int) maxStale());
break;
case CC_MIN_FRESH:
packerPrintf(p, "=%d", (int) minFresh());
break;
default:
/* do nothing, directive was already printed */
break;
}
++pcount;
}
}
if (other.size() != 0)
packerPrintf(p, (pcount ? ", " SQUIDSTRINGPH : SQUIDSTRINGPH),
SQUIDSTRINGPRINT(other));
}
void
httpHdrCcUpdateStats(const HttpHdrCc * cc, StatHist * hist)
{
http_hdr_cc_type c;
assert(cc);
for (c = CC_PUBLIC; c < CC_ENUM_END; ++c)
if (cc->isSet(c))
hist->count(c);
}
void
httpHdrCcStatDumper(StoreEntry * sentry, int idx, double val, double size, int count)
{
extern const HttpHeaderStat *dump_stat; /* argh! */
const int id = (int) val;
const int valid_id = id >= 0 && id < CC_ENUM_END;
const char *name = valid_id ? CcAttrs[id].name : "INVALID";
if (count || valid_id)
storeAppendPrintf(sentry, "%2d\t %-20s\t %5d\t %6.2f\n",
id, name, count, xdiv(count, dump_stat->ccParsedCount));
}
#if !_USE_INLINE_
#include "HttpHdrCc.cci"
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,259 |
\section{Introduction}
Since the pioneering work of Madelung and Ewald,\cite{Mad+Ewa} a huge
amount of experimental and theoretical work has been devoted to alkali
halides which are the simplest and most representative ionic solids. The
interest in the high-pressure properties of these materials has been
recently renewed by the introduction of the diamond anvil cell
technology\cite{diamond-anvil} which has opened the way to exploring
previously unaccessible portions of their phase diagram. CsI is the
softest among alkali halides and it has the smallest optical gap. For
these reasons it is an ideal candidate to display a pressure-induced
band-overlap metallization which is actually found at a pressure
$P\approx 110\,\rm GPa$.\cite{Metallo} Looking for this effect, new and
unexpected crystal phases have been found to be stable in the pressure
range of a few tens GPa.
The first systematic studies of the high-pressure phases of Cesium
halides date back to 1984. From energy-dispersive X-ray diffraction
experiments Huang {\it et al.}\cite{Huang} and Knittle {\it et
al.}\cite{Knittle} were able to observe that CsI and CsBr (whose
low-pressure stable phase is the cubic B2), undergo a transition which
lowers their cubic symmetry when an applied pressure reduces their
residual volume to $v = V/V_0 \approx 0.54$, $V_0$ being the
equilibrium volume. The observed transition pressures are of $\approx
39$ and 53~GPa for CsI and CsBr respectively.\cite{Knittle} A similar
instability has been also reported in CsCl, at about 65 GPa.\cite{Huang}
This symmetry lowering manifests itself through the splitting of the
(110) X-ray diffraction line into two peaks which are interpreted as
corresponding to the (101) and (110) inequivalent reciprocal-lattice
vectors of a tetragonal structure. These authors did not observe any
detectable discontinuity in any physical observable, and they
conjectured therefore that the phase transition was of second order.
However, general group-theoretical considerations indicate that a
transition from a cubic to a tetragonal phase in which the only order
parameter is the unit cell shape, {\it i.e.} strain, cannot be of second
order.\cite{Anderson} We conclude therefore that a weak first-order
character of the transition must have escaped the analysis of the
experimental data. Claims that this tetragonal phase would undergo a
further transition to an orthorhombic structure\cite{asaumi} (space
group $D_{2h}^1$) were not confirmed by subsequent theoretical
work\cite{Born-Meyer,Christensen,Noi}.
The first-order character of the cubic-to-tetragonal transition in
Cesium halides was confirmed by the very first theoretical
investigations performed by Vohra {\it et al.}\cite{Born-Meyer} within a
Born-Meyer semiempirical approach. According to these authors, the
instability of the CsCl crystal structure is related to the softening of
the shear constant, $c_s=\frac{1}{2} (c_{11} - c_{12})$, due to the
competition between the long-range Coulomb attraction and the
short-range repulsive energy which becomes more and more important as
the pressure increases. They also found that the tetragonal structure
is stable against further orthorhombic distortions of symmetry
corresponding to the space group $D_{2h}^1$; i.e., for any given value
of $a$ and $c/a$, the minimum of the lattice energy was always found at
$b/a=1$ in the whole pressure range explored. Some investigations on CsI
have also been carried out from first principles. The work of
Christensen and Satpathy\cite{Christensen}---performed within the Linear
Muffin-Tin Orbital approximation---and that of Baroni and
Giannozzi\cite{Noi}---in which ab-initio pseudopotentials were
used---confirmed the overall picture proposed by Vohra {\it et
al}.\cite{Born-Meyer}.
In 1989, new and unexpected features emerged from the X-ray diffraction
experiments performed by Mao {\it et al.} \cite{Mao} on CsI. Using a
sophisticated experimental set-up based on a synchrotron radiation
source, they were able to identify a distortion of CsI from the cubic B2
to the hexagonal closed-packed structure passing through an intermediate
orthorhombic phase whose assigned symmetry ($C_{2v}^1$), however is
different from that guessed in Ref. \onlinecite{asaumi}. It was
observed that the (110) peak splits into three components, whereas two
additional lines appear on the low- and high-energy sides of the
triplet, corresponding to two diffraction peaks which are forbidden in
the B2 structure. This diffraction pattern can be explained by assuming
a $2\times 1$ reconstruction of the cubic cell characterized by the
gliding of one (110) plane, as depicted in Fig. 1. The onset of the
phase transition, characterized by the broadening of the diffraction
lines of the cubic structure, is observed at pressures as low as 15~GPa.
The observed splittings and peak intensities evolve continuously from 15
to 100~GPa, showing a single orthorhombic phase with variable
parameters. However, below 45~GPa the splittings are not large enough to
allow an unequivocal identification of the orthorhombic structure The
transition from the cubic to the orthorhombic phase was observed to be
continuous within the experimental resolution.
In a recent paper\cite{PRL} we have shown that the distortion leading to
the orthorhombic structure observed by Mao {\it et al.}\cite{Mao} is
driven by the softening of an $M^-_5$ phonon at the $M$ point of the
Brillouin zone (BZ). This softening is related to the ferroelastic
instability responsible for the previously assumed cubic-to-tetragonal
transition. The shear constant is in fact proportional to the square of
the sound velocity along the $(110)$ direction for vibrations polarized
along $(1\bar 1 0)$. This observation suggests that a large reduction of
the magnitude of the shear constant could favour the softening of a
transverse phonon along the (110) direction. In fact, the gliding of the
(110) plane depicted in Fig. 1 represents a lattice distortion which is
very similar (but not strictly equal) to one of the two degenerate ionic
displacement patterns of the $M^-_5$ acoustic phonon mode. We are thus
led to identify the amplitude of this mode as the order parameter of the
transition, in Landau's sense.
In this paper we present a complete account of our previous work on the
high-pressure phases of CsI,\cite{PRL} and its extension to other Cesium
halides, CsBr and CsCl. Our approach is based on a combined use of the
Landau theory of phase transitions to classify the possible low-symmetry
phases and to determine the form of the interactions which can lead to
them, and on first-principles calculations of the relevant interaction
constants and energy differences as functions of the applied pressure.
Our calculations are based on density-functional theory to determine
crystal energies and their first derivatives with respect to atomic
displacements (forces) and macroscopic strain (stress), and on
density-functional perturbation theory to determine the second
derivatives (essentially, the phonon frequencies). In Sec. II we present
our theoretical framework and computational details. Sec. III contains
our results. Sec. IV contains the conclusions.
\section{Theory}
\subsection{Landau theory of phase transitions} In the Landau theory of
phase transitions, the relevant thermodynamical potential, $\cal F$,
describing the relative stability of two phases is expressed as a power
series of the so called order parameter, $u$, whose value is different
from zero in the low-symmetry (high-pressure, in the present case)
phase, while $u$ vanishes in the high-symmetry (low-pressure) phase:
\begin{equation} {\cal F} (u) = {\cal F}_0 + A_2 u^2 + A_3 u^3 + A_4 u^4
+ \cdots, \label{eq:landau} \end{equation} where the linear term in $u$
is missing to ensure the stability of the low-pressure phase. Let us
suppose for the moment that the fourth-order coefficient, $A_4$, is
positive so that it can ensure the global stability of the system, and
let us neglect all higher-order terms. If
$A_2 > 0$, the relative stability of the low- and high-symmetry phases
is determined by the sign of the discriminant $\Delta_6 = A_3^{~2}-4
A_2A_4$. If $\Delta_6 <0$ the high-symmetry ($u=0$) phase is stable,
while for $\Delta_6>0$ Eq. (1) has a minimum for $u\ne 0$ and the
low-symmetry phase prevails. In this case, the transition from the high-
to the low-symmetry phase is discontinuous, and it is said to be {\em
first-order}. Continuous {\em second-order} transitions are possible if,
because of symmetry, the third-order coefficient vanishes identically:
$A_3 \equiv 0$. In this case the high- or low-symmetry phases are stable
according to whether the second-order coefficient, $A_2$, is positive or
negative. Suppose now that $A_4$ is negative in the region of the phase
diagram where $A_2$ softens and that $A_5\equiv 0$. In this case, the
global stability of the system must be ensured by the sixth- and
higher-order terms and a first-order transition to the low-symmetry
phase would then occur when $\Delta_8 \equiv A_4^{~2}-4A_2A_6=0$.
For structural transitions where the order parameter is the amplitude of
a lattice distortion, $A_2$ is essentially the square of the phonon
frequency associated to that distortion. In the present case, the phonon
which goes soft is the $M^-_5$ mode at the $M$ point of the BZ. The
small group of the $M$ point---whose coordinates are $({1 \over 2}{1
\over 2} 0)$---is $D_{4h}$ and its star is made of three equivalent
points. $M_5^-$ transforms according to a doubly degenerate irreducible
representation of $D_{4h}$, so that the order parameter associated with
this mode is six-dimensional: ${\bf u}\equiv \{ {u}_i \}_{i=1,6}$. The
$M^-_5$ representation is odd with respect to inversion, so that no
third-order (or, more generally, odd-order) terms must be present in Eq. (1)
in order to ensure invariance with respect to the (cubic) symmetry group
of the low-pressure phase. Following Landau's argument, we conclude that
$A_3\equiv 0$, and $A_5\equiv 0$. Assuming that the sixth- and
higher-order terms in Eq. (1) are positive in the neighborhood of the
transition, this is then first- or second-order, according to whether
the fourth-order coefficient is negative or positive, respectively.
\subsection{First-principles techniques} In this paper we will ignore
any entropy effects and restrict ourselves to zero temperature. In this
condition, the implementation of the above phenomenological scheme
requires the knowledge of the system energy as a function of the atomic
displacements (phonon amplitudes) and unit-cell distortions (strain).
Density-Functional Theory (DFT) is a very reliable and computationally
viable tool for the study of the energetics of simple materials. We
refer the reader to the many available review papers on this
subject\cite{DFT-reviews} and we summarize here the main points. The
local-density approximation (LDA) to DFT provides a practical, though
approximate, way to map the ground-state properties of a system of
interacting electrons onto those of a system of noninteracting
electrons, subject to an effective external field which depends
self-consistently on the ground-state electronic density. DFT-LDA
allows to calculate in a rather accurate and efficient way the energies
of materials within the Born-Oppenheimer approximation, along with their
first derivatives with respect to external parameters, such as e.g.
nuclear coordinates (i.e. atomic forces)\cite{HF} and unit-cell shape
and volume (i.e. stress).\cite{Nielsen} By linearizing the DFT-LDA
equations with respect to the strenght of an external perturbation, the
second derivatives of the energy can be conveniently obtained by solving
a suitable set of linear equations.\cite{DFPT,DFPT-sega} This is the essence of
the Density-Functional Perturbation Theory (DFPT) approach to lattice
dynamics, which we will employ to determine the phonon spectra of the
system considered, as functions of the crystal volume, i.e. of the
applied pressure.
Our calculations are performed in the framework of the plane-wave
pseudopotential method.\cite{DFT-reviews} For Cs and I we have used the same
pseudopotentials as in Ref. \onlinecite{Noi}.
Pseudopotentials for Br and Cl have been generated
using the method originally proposed by von
Barth and Car.\cite{pap_pasquale} For Cs, electrons up to $4d$ have been
treated as frozen in the core. The inclusion of the Cs $5s$ and $5p$
states into the valence shell is necessary to obtain sensible results.
In fact we found that a Cs pseudopotential which sustains only the $6s$
electron as a valence electron yields a monotonic decrease of the
crystal energy at decreasing volume, with no stability at all. An
explicit account for the non-linear core-corrections,\cite{Louie-NLCC}
suggested by the large size of the Cs core, does not substantially
improve the results. The inclusion of Cs $5s$ and $5p$ orbitals in the
valence does not increase dramatically the numerical burden. In fact,
the spatial extension of these orbitals is comparable to those of the
anion $s$ and $p$ valence wavefunctions, so that the plane-wave basis
set necessary to describe the latter is also adequate for the former.
Plane waves up to a kinetic energy cutoff of 25 Ry were included in the
basis set. The electron-gas exchange-correlation energy and potential
used to implement LDA are those determined by Ceperley and Alder
\cite{Ceperley} as interpolated by Perdew and Zunger.\cite{Perdew}
Brillouin-zone integrations have been performed using sets of special
points corresponding to the (666) Monkhorst-Pack mesh.\cite{MP}
This mesh---which corresponds to 10, 12, and 24
points in the cubic, tetragonal, and orthorombic structures
respectively---has been explicitly checked for convergence for all the
relevant structural properties of interest here.
\section{Results}
\subsection{Zero-pressure properties} The low-pressure structural
properties of the materials investigated have been determined by fitting
the calculated crystal energies to the Murnaghan equation of
state.\cite{Murnaghan} DFPT allows a straightforward determination of
the electronic contribution to the static dielectric constants and Born
effective charges.\cite{DFPT} The theoretical predictions for these data
are compared with experiments in Table \ref{t:parret}. The resulting
accuracy on the predicted equilibrium lattice constants and bulk moduli
is of the order of $3\%$ and 10\% respectively, i.e. in the typical
range of DFT-LDA calculations. Dielectric constants are systematically
overestimated by $\approx 20\%$, a well known drawback of the
LDA.\cite{eps-LDA} Using the theoretically determined equilibrium
lattice parameters, the phonon dispersions of the three salts have been
calculated by DFPT along the main symmetry directions. In Fig.
\ref{f:fig2} we display the calculated dispersion of CsI and compare
them with neutron-diffraction data. Selected frequencies for CsI, CsBr,
and CsCl are reported and compared with experiments in Table
\ref{t:phonon}. The agreement is quite satisfactory and gives us
confidence in the predictive power of our calculations.
\subsection{Phonons at high pressure} In order to substantiate the
hypothesis of a mode softening occurring upon increasing pressure along
the (110) acoustic branch, we have calculated the corresponding phonon
dispersion for several values of the crystal residual volume, $v$.
In Fig. \ref{f:fig3} we display our results for CsI. The $M_5^-$
acoustic phonon softens at $v^* = 0.638$, corresponding to a
pressure $P^* \approx 23~ \rm GPa$, as a consequence of the incipient
softening of the sound velocity of one of the transverse branches. The
same behavior is observed in CsBr at $v^* = 0.520$ while CsCl does not
display any tendency to softening upon increasing pressure. The
dependence of the $M_5^-$ acoustic phonon frequency upon the residual
volume is displayed in Fig. \ref{f:fig4} for CsI, CsBr and CsCl.
\subsection{High-pressure phases} \subsubsection{Tetragonal phase} As a
first step we have reinvestigated the cubic-to-tetragonal transition
described in the introduction. In
Fig. \ref{f:tet1} we display the zero-temperature enthalpies {\it vs.}
the $c/a$ cell parameter calculated at constant pressure for CsI, CsBr
and CsCl. In CsI and in CsBr the existence of a first-order transition
is clearly visible with a second minimum occurring at $c/a > 1$ above
some critical pressure, $P_{tet}$, and separated from the high-simmetry phase
by a well defined enthalpy barrier. The transition pressures are $P_{tet} =
44$ and $58$ GPa for CsI and CsBr respectively, with a very small volume
discontinuity ($\approx 0.5\%$ and $\approx 0.7\%$ respectively). In
Fig. \ref{f:tet2} we report the $c/a$ parameter {\it vs.} $P/P_{tet}$ for
CsI and CsBr. In CsCl the stability of the low-simmetry phase cannot be
unambiguously established within our present accuracy. An instability
towards the tetragonal phase is signalled by the flatness of the
enthalpy as a function of $c/a$ for pressures $\approx 70~\rm GPa$. At
higher pressures, however, this instability seems to weaken, and
calculations for pressures as high as 100 GPa do not give any evidence
of a stable tetragonal phase.
\subsubsection{Orthorhombic phase} As we have seen in Sec. IIA, the
vanishing of the $M^-_5$ phonon frequency signals the onset of a phase
transition whose order parameter is the phonon amplitude and which can
be second-order because no third-order terms are present in the
expansion of the crystal energy in powers of the order parameter. In
order to investigate the character of the transition and determine the
possible low-symmetry phases, it is necessary to find out the expression
of the crystal energy in powers of $u$ to the lowest
meaningful order, i.e. $n=4$. In Table \ref{t:phonq} we display the
wavevectors and the polarizations corresponding to one possible choice
for the components of the six-dimensional order parameter. The
corresponding fourth-order invariant polynomials can be obtained by
using standard group theoretical techniques. The $u$'s realize an irreducible
representation of the symmetry group of the high-symmetry phase (space
group $O_h^1$). The number of fourth-order invariants is equal to the
number of times the identical representation of $O_h$ is contained in
the symmetric part of $[ M^-_5]^4$. A simple exercise shows that this
number is equal to four. A straightforward way to obtain them is to
symmetrize all the possible translationally invariant fourth-order
monomials with respect to $O_h$. In order to satisfy translational
invariance, the starting monomials, $u_iu_ju_ku_l$ must satisfy the
relation: $ {\bf q}_i + {\bf q}_j + {\bf q}_k + {\bf q}_l = {\bf G}$,
where ${\bf q}_i$ is the wavevector associated to the $i$-th component of the
order parameter, and {\bf G} is a reciprocal-lattice vector of the cubic
phase. The four independent invariants are summarized in Table
\ref{t:inv}. The resulting expansion of the crystal energy
reads: \begin{equation} {\cal F}({\bf u}) = {\cal F}_0 + A_2
\sum_{i=1,6} u_i^{~2} + \sum_{i=1,4}A_4^i\,P_4^i({\bf u}) + {\cal
O}(u^6). \label{eq:free_en} \end{equation}
The possible low-symmetry stable phases compatible with this expression
for the crystal energy have been worked out in Ref. \onlinecite{Kim}.
Following the notation of Ref. \onlinecite{Kim}, these stable phases can
be classified as in Table \ref{t:P}, where each configuration
corresponds to a particular direction in the six-dimensional order
parameter space, {\it i.e.} to a particular combination of phonon
displacements. In the specific case of CsI, the four fourth-order
coefficients appearing in Eq. (2) have been fitted to the results of
DFT-LDA calculations performed for lattice distortions along some of the
order-parameter directions listed in Table \ref{t:P}. In fact, the
coefficients of the crystal energy expansion are easily obtained through
total energy and stress calculations. With the numerical values so
obtained, we have verified that at the crystal volume where the $M^-_5$
phonon frequency softens, the only minimum of the energy given by Eq.
(2) occurs along the $P11$ direction, whereas directional minima along
all the other directions are actually saddle points. This observation
seems to suggest that a second-order transition to a phase of
tetrahedral symmetry ($T^5$) would occur at the softening pressure of
the $M^-_5$ phonon. This finding is at variance with experimental data
which indicate that the high-pressure phase has an orthorhombic
symmetry, compatible with a distortion along the $P1$ line.
The above considerations hold in the hypothesis that the strain state of
the crystal is constant across the transition, except for the isotropic
compression due to the application of a hydrostatic pressure. We have
seen, however, that the softening of the $M^-_5$ phonon mode is closely
related to the softening of the shear constant of the crystal, so that a
strong coupling between the soft mode and macroscopic strain (i.e.,
between zone-center and zone-border acoustic phonons) is to be expected.
Let us consider now the expression of the Landau crystal energy up to
fourth order in the phonon amplitude, including the coupling with the
anisotropic components of the strain tensor, $\epsilon$:
\begin{equation} {\cal F}({\bf u},\epsilon) = {\cal F}({\bf
u},\epsilon=0) + Q(u,\epsilon), \label{eq:strain} \end{equation} where
$Q(u,\epsilon)$ is a polynomial in $u$ and the components of the strain
tensor containing all the possible products up to the fourth order:
$\epsilon^2$, $u^2\epsilon$, $u^2\epsilon^2$, $\epsilon^3$, and
$\epsilon^4$. All odd terms in $u$ must vanish by symmetry. Up to fourth
order only $u^2\epsilon$ must be considered; in fact the actual value of
$\epsilon$ is the one which minimizes Eq. (\ref{eq:strain}) for a given
value of $u$, i.e. $\epsilon \propto u^2$ so that $u^2\epsilon^2$ and
$\epsilon^3$ are actually of sixth order in $u$ while $\epsilon^4$ is of
eighth order. To find the form of the $u^2\epsilon$ invariants we have
first determined all the second order monomials, $u_iu_j$, such that
${\bf k}_i + {\bf k}_j = {\bf G}$. There are nine such monomials which
realize a reducible representation of the $O_h$ point group. The
decomposition of this reducible representation into irreducible
components is displayed in Table \ref{t:irrep}. The six independent
components of the strain tensor split into three irreducible
representation of the cubic group, as indicated in Table
\ref{t:irrep_strain}. The desired invariants are finally obtained by
coupling each irreducible representation from the $uu$ set (Table
\ref{t:irrep}), with an equal irreducible representation from the
$\epsilon$ set (Table \ref{t:irrep_strain}), and listed in Table
\ref{t:inv_strain}. The resulting expression for the crystal energy
including the coupling with the strain reads: \begin{eqnarray} \quad
{\cal F}&(&{\bf u},\epsilon) = {\cal F}_0 + A_2 \sum_{i=1,6}u_i^{~2}
+\sum_{i,j=1}^6 c_{ij}\epsilon_i\epsilon_j \nonumber \\ && \quad+
\sum_{i=1,4}A_4^i\,P_4^i({\bf u}) + \sum_{i=1,4} B^i Q^i_4({\bf
u},\epsilon) + {\cal O}(u^6), \label{eq:phon_strain} \end{eqnarray}
where $c_{ij}$ are the elastic constants, $\epsilon_i$ components of the
strain tensor, and the $Q_4^i$ are the polynomials listed in Table
\ref{t:inv_strain}.
Numerical values of the $B$ coefficients have been determined along
lines similar to those used to determine the $A_4$'s. The $P11$ minimum
previously found to be stable ignoring the phonon-coupling strain is
unaffected by such a coupling, while the minima along four out of the
remaining six directions of Table \ref{t:P} are slightly modified, still
maintaining the saddle-point character they had in absence of such a
coupling. The coupling to the strain changes instead the character of
the directional minima along $P1$ and $P2$. Let us consider the simpler
case of the P1 minimum. Projecting Eq. (\ref{eq:phon_strain}) along $P1$
one obtains: \begin{eqnarray}{\cal F}^{P1}(u,\epsilon_s,\epsilon_4) &=&
A_2 u^2 + A^{P1}_4 u^4 + {1\over 2} c_s \epsilon_s^2 + {1\over 2} c_{44}
\epsilon_4^2 + \nonumber \\ &&\quad ( B^{P1}_s \epsilon_s + B^{P1}_4
\epsilon_4 ) u^2 + {\cal O}(u^6), \label{H_u_eps} \end{eqnarray} where
$u=u_1$ is the amplitude of the phonon displacement along $(1\bar 10)$,
$B^{P1}_s ={1\over 4}B^1 -2B^2$, $B^{P1}_4 = B^4$,
$\epsilon_s=\frac{1}{2}(\epsilon_{xx}+ \epsilon_{yy} -2 \epsilon_{zz})$,
and $\epsilon_4=\epsilon_{xy}$. By eliminating $\epsilon_1$ and
$\epsilon_2$ from Eq. (\ref{H_u_eps}) by the equilibrium condition
$\partial {\cal F}^{P1}/\partial\epsilon_s = \partial {\cal
F}^{P1}/\partial\epsilon_4 = 0$, one obtains: \begin{equation}
\epsilon_s = -\frac{B^{P1}_s u^2}{c_s};\quad \epsilon_4 =
-\frac{B^{P1}_4 u^2}{c_{44}}, \label{e:eps_u} \end{equation}
\begin{eqnarray} \quad \widetilde {\cal F}^{P1}(u) &=& A_2 u^2 +
\nonumber\\ \quad &+& \left ( A_4^{P1} -\frac{{B^{P1}_s}^2}{2c_s} -
\frac{{B^{P1}_4}^2}{2c_{44}} \right )u^4 + {\cal O} (u^6).
\label{H_of_u} \end{eqnarray} Eq. (\ref{H_of_u}) shows that the coupling
between the soft phonon and macroscopic strain renormalizes the
fourth-order coefficient, making it large and {\it negative}, whenever
$c_s$ or $c_{44}$ are small enough. Due to the ongoing softening of the
shear constant, $c_s$, we find that at the softening pressure the
fourth-order coefficient is negative, and we conclude that the
transition must then be first-order, occurring at a somewhat lower
pressure (see the discussion at the end of Sec. IIA). A similar
behaviour is observed along P2. A thorough study of the transition might
be performed by considering the expansion of the crystal energy up to
sixth order in the order parameter, and by fitting the relevant
coefficients to first-principles calculations, as it was done when the
coupling to the strain was neglected. However the presence of many
sixth-order invariants and the smallness of the computed energy
differences make such a procedure unpractical. We have preferred instead
to concentrate on the $P1$ line which is geometrically simpler and whose
symmetry is compatible with the observed x-ray diffraction pattern of
the high-pressure phase. For this direction we have performed straight
energy minimizations with respect to $u$ and $\epsilon$. By repeating
such a minimization for different volumes, one directly obtains the
equation of state of the crystal in the low-symmetry phase.
\subsubsection{Relative stability} CsI and CsBr both display a softening
of the $M^-_5$ phonon frequency and the ferroelastic instability
responsible for the cubic-to-tetragonal transition, whereas CsCl does
not show any tendency to phonon softening and a very weak tendency
towards the ferroelastic instability. We conclude that the
high-pressure stable phase of CsCl in the pressure range up to $\approx
100\,\rm GPa$ is cubic B2, whereas the relative stability of the
tetragonal and orthorhombic phases must be checked for CsBr.
We have performed complete energy minimizations with respect to atomic
displacements and strain parameters for both the tetragonal and the
newly determined orthorhombic structure. The structural parameters of
the orthorombic phase of CsI as functions of pressure/volume are shown
in Fig. \ref{f:fig5}. All these, including volume, are discontinuous at
the transition pressure as a consequence of its first-order character.
The volume discontinuity is however very weak ($\approx 0.1\%$) and it
is not visible on the scale of the figure. Note also the different
magnitude of Cesium and Iodine displacements and the weak
dependence of $b/a$ upon applied pressure. The different behavior of
$c/a-1$ and $b/a-1$ with respect to pressure is due to the fact that the
former is inversely proportional to the nearly vanishing shear constant,
$c_s$, whereas the latter depends on $c_{44}$ which is regular in this
pressure range. We remark that, due to the different amplitude of Cs and
I displacements in the unit cell, the space group of our final structure
is $D_{2h}^5$, different from the $C_{2v}^1$ originally proposed by Mao
{\it et al.} \cite{Mao}. However, the diffraction pattern corresponding
to the two groups is the same, and our proposed structure is
compatible with the experimental data.
We have compared the enthalpies of the various phases and identified the
transition pressures through the Maxwell construction. Results of this
procedure are shown in Fig. \ref{f:fig6} where the enthalpies of CsI and
CsBr are shown for the tetragonal and orthorhombic phases relative to
the cubic one. In agreement with experimental findings the high-pressure
stable phase of CsI is the orthorhombic one (for pressures larger than
$\approx 21\,\rm GPa$). At variance with the case of CsI, in CsBr the
tetragonal structure turns out to be more stable all over the explored
pressure range. The phonon softening is preceeded by the
cubic-to-tetragonal transformation at $P_{tet} = 58\,\rm GPa$, and we have
verified that the tetragonal phase is always favored.
So we can definitely
assign the high-pressure phase of CsBr to be tetragonal.
The cubic-to-tetragonal transition has been
experimentally observed in CsBr at $53\pm 2\,\rm GPa$ corresponding to
a residual
volume $v_{tet} \approx 0.54$.\cite{Huang}
As we have
seen, CsCl does not manifest any phonon softening upon increasing
pressure. This compound shows only a weak tendency to
a tetragonal instability at $P_{tet} \approx
69\,\rm GPa$, but the tetragonal phase seems not to be stable at higher
pressures.
Our results are in agreement with this
measurement. In CsCl, a weak tetragonal instability has been observed
experimentally at $65 \pm 5$ GPa, but an extensive study at higher
pressure is still lacking.
\section{Conclusions}
In this paper we have shown that a combined use of the Landau theory of
phase transitions and accurate first-principles calculations based of
DFT-LDA provide a reliable scheme for predicting the structural
properties of ionic systems at high pressures. In the specific case of
Cesium halides, we have observed a trend in the high-pressure phases
which can be related with the polarizability of the anion. Our results
indicate that the more polarizable is the anion the larger is the
tendency towards a tetragonal instability of the cubic B2 structure
(passing from CsCl to CsBr) and, for even larger polarizability towards
an orthorombic structure (from CsBr to CsI). Some investigations which
we have performed also for other alkali halides indicate that when the
cation is lighter (and hence less polarizable) than Cs, the stable
high-pressure phase seems always to be the cubic B2 one.
\section{Acknowledgements}
We would like to thank S. de Gironcoli and P. Pavone for valuable
discussions. Most of this work was completed while MBN was at SISSA.
| {
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I have been a WOC nurse for the past 24 years in the acute care setting. In my clinical position, I am responsible for all aspects of pressure injury management including pressure injury risk assessment. As a clinical researcher, I have a program of research which focuses on pressure injury risk in the critical care population. | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/trace-and-determinant.288414\/","text":"# Trace and Determinant\n\n1. Jan 29, 2009\n\n### alle.fabbri\n\nHi,\ncan anyone give me an hint to proof the relation\n\ndet(I + x A) = 1 + x tr A + O(x^2)\n\nthank you.\n\n2. Jan 29, 2009\n\n### Ben Niehoff\n\nWrite out the general form of (I+xA). The determinant must be some polynomial in x, right? So, carefully pick out the constant- and linear-order terms of this polynomial by choosing the appropriate factors in the determinant.\n\n3. Jan 29, 2009\n\n### alle.fabbri\n\nok that's the idea behind....but what about some explicit calculations? Are them possible? I thought i can use the general determinant expansion in terms of the total antisymmetric tensor which, for a nxn matrix A must be something like\n\n$$det A = \\frac{1}{n!} \\sum_{i_1, i_2, ... , i_n = 1}^{n} \\epsilon_{i_1\\;i_2\\;...\\;i_n} A_{1\\;i_1} A_{2\\;i_2} A_{3\\;i_3} ... A_{n\\;i_n}$$\n\nthe expression of the fact that the determinant is the average of all possible products of the elements picked one per column keeping them in different rows, thanks to totally antisymmetric tensor.\n\nAny idea to be a bit formal?\n\n4. Jan 29, 2009\n\n### Ben Niehoff\n\nThere should be no 1\/n! in there. The determinant is the anti-symmetrized sum of all the products; not the average.\n\nIf you want to do the proof formally, the simplest way would be to diagonalize A. Or in general, bring A to upper-triangular form by a similarity transformation. Note that the identity matrix is invariant under similarity transformations. The determinant and trace are also invariant.","date":"2017-12-13 01:49:33","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\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8277006149291992, \"perplexity\": 778.6720678510586}, \"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-2017-51\/segments\/1512948520218.49\/warc\/CC-MAIN-20171213011024-20171213031024-00259.warc.gz\"}"} | null | null |
var $ = require('jquery');
import React from 'react';
import reactDOM from 'react-dom';
import Backbone from 'backbone';
import todoModel from 'pages/todoReact/todoModel';
import TodoItemView from 'pages/todoReact/todoView';
import dispatcher from 'pages/todoReact/todoDispatcher';
var TodoListView = Backbone.View.extend({
el: '.todo-container',
model: todoModel,
events: {
'click .btn-add': 'addTodoItem'
},
initialize: function(){
this.model.fetch();
this.model.on('change', this.render, this);
},
render: function(){
// render the todo items
var todos = this.model.get('todos');
var $ul = this.$el.find('.list-group');
$ul.html('');
todos.forEach(function(todo){
var $li = $('<li class="list-group-item row"></li>');
$ul.append($li);
reactDOM.render(
<TodoItemView data={todo} />,
$li[0] // react does not recognize jQuery selector, get original DOMnode from jQuery object
);
});
},
addTodoItem: function(){
var $input = this.$el.find('.input-name');
var newTitle = $input.val();
dispatcher.addTodo(newTitle);
$input.val('');
}
});
module.exports = TodoListView;
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,535 |
from django.contrib import admin
# Register your models here.
from .models import Bot, MatchResult, Match
admin.site.register(Bot)
admin.site.register(Match)
admin.site.register(MatchResult)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,640 |
Q: Automatic test input causes end of file error with python I am currently writing a program that is supposed to return certain values when it completes, but the system that tests it is a black box (don't know how it tests the program), and even though I think it would work if I ran the program by itself, the automated tester always raises an end of file error when it encounters the first input prompt. This the part that is in the main portion of the python code (kind of the first thing that runs).
y=list(input("Enter numbers separated by commas and spaces"))
x=list(input("Do the same as above but for other list"))
The tester raises the end of file error on the first prompt. Any idea what may cause that?
A: It is quite possible that the tester is not supplying any input at all. In which case, you (I) have to supply the values in the program itself, not as input but as defined values.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,272 |
Table of Contents
Title Page
Dedication
Copyright Page
Introduction
Part 1 - Fundamentals of Fast Food
Chapter1 - Kitchen Efficiency
Chapter 2 - Skill Builds
Part 2 - Beginning Hors d'Oeuvres and Appetizers
Chapter 3 - Dippity-Do
Chapter 4 - Nibbles and Noshes: Hors d'Oeuvres for All Occasions
Chapter 5 - Appealing Appetizers
Chapter 6 - The Bountiful Bowl: Sou6ps
Part 3 - Casual Cuisine
Chapter 7 - Sunny Starts: Breakfast
Chapter 8 - Convertible Cooking: Casual Meals for Brunch or Supper
Chapter 9 - Crusty Creations: Hot Sandwiches and Quiches
Chapter 10 - A Potpourri of Pasta and Pizza
Part 4 - Salad Daze
Chapter 11 - On the Side: Small Vegetable Salads
Chapter 12 - Cold Carb Salads
Chapter 13 - The Main Event: Entrée Salads
Part 5 - Redefining Fast Food
Chapter 14 - Sensational Seafood
Chapter 15 - Poultry Pals
Chapter 16 - Grazing Greats
Part 6 - Great Grills
Chapter 17 - Ready, Set, Grill!
Chapter 18 - Burger Bonanza
Chapter 19 - Flavor Without Fuss: Marinated Grilled Dishes
Part 7 - Desserts on a Deadline
Chapter 20 - Fruity Favorites
Chapter 21 - The Best Baked Goods
Chapter 22 - Chocolate Cravings
Appendix A - Glossary
Appendix B - Metric Conversion Tables
Appendix C - Common Ingredient Yields
Index
_This book is dedicated to the memory of my father, who introduced me to the tantalizing world of foods with childhood trips to Chinatown._
**ALPHA BOOKS**
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**Copyright © 2007 by Ellen Brown**
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**Introduction**
We seem to have gotten away from the idea of eating fresh food. At one time, though, that's all there was. People ate whatever crops the land around them yielded. And everything available—from eggs and chickens to vegetables to fish—was organic. (Of course, this was before twentieth-century pesticides, herbicides, and other dangerous chemicals were invented.) At that time, the definition of _convenience food_ could be found in the cupboards: jars of jams, jellies, and pickles that were "put up" during the summer for later enjoyment.
But during the last century, "progress" was viewed as getting as far away from fresh food as possible. After World War II, the country's dependence on canned food was supplemented by the ever-growing options of frozen food. The size of refrigerators shrank as appliance manufacturers lured customers by promising enough freezer space so the average household would only have to shop once every few weeks. The food groups seemed to evolve into take-out, eat-out, frozen, and canned.
But today that seems to be changing for the better. In this century, we're taking pleasure in turning back the clock by eating food in season and reveling in the joys of fresh foods. In the past 10 years, the trend toward the expansion of space given to frozen foods in supermarkets has been halted. The section now gaining space the most rapidly is the produce section. And that's the way it should be.
The dishes in this book are "real food." They're not made with tons of convenience products that list more chemicals on their labels than words recognizable as foods; you won't find a can of cream-of-something soup anywhere. They're made with healthful vegetables and vivid fresh fruits—the foods we should be eating to fulfill the 5 to 9 servings a day recommended for our overall good health.
There are times that using minimally processed ingredients can save time, and not diminish the quality of the completed dish. I do give such foods as canned tomatoes and preroasted red bell peppers as alternatives to starting from scratch with many recipes, and the beans in all recipes are canned to save the long amount of time it takes to begin a dish with dried beans. In the same way if you don't have a fresh herb on hand, there's no reason to eliminate a recipe; just use a dried version.
But there's another need in today's fast-paced life, and these recipes acknowledge it. We want fresh food, but we want it fast. Time is our most precious commodity, even though commodities take time to prepare. And as you'll see when cooking the recipes in this book, fresh and fast can be joined, and joined deliciously.
You'll notice that there's no time frame given as part of this book's title. I'm not promising that you can have dinner on the table in less time than it takes to watch the evening news. But I do promise you that the recipes are straightforward so your actual involvement with cooking is less than 30 minutes in all cases.
What underpins this book is my 30 years as a food writer, knowing what foods cook fast. There aren't any recipes for beets, although they're one of my favorite vegetables. They take too long to cook properly. Nor are there any slowly braised stews.
What you will find is a wide range of cooking methods, all of which are fast because they utilize high heat. There are sautées, stir-fries, and grilled dishes. But there are not any fried foods, although that's another high-heat cooking method. While there are high-fat foods in the book that use cheese or cream, the goal is to trim fat when possible.
If you're one of the vast majority of Americans who want to eat a more healthful diet, this book is for you!
# **How This Book Is Organized**
The book is divided into seven parts:
In **Part 1, "Fundamentals of Fast Food,"** I give you information on equipment as well as cooking skills to make you a more efficient cook. I offer tips for choosing equipment to make life in the kitchen easier and knife skills and ways to speed up the chopping and dicing that are part and parcel of fresh cooking.
**Part 2, "Beginning Hors d'Oeuvres and Appetizers,"** contains a kaleidoscope of small dishes that give any meal a delicious start. There are chapters on dips and hors d'oeuvres, many of which start out as big batches to minimize labor. Also featured are recipes for small appetizers and soups for all seasons.
**Part 3, "Casual Cuisine,"** includes recipes to make everyday meals special at all times of day. You'll find recipes for breakfast and brunch dishes, many of which would also work as a supper. Also in Part 3 is a chapter on hot sandwiches and quiches, and one on pastas and pizzas.
**Part 4, "Salad Daze,"** encompasses everything cold and crunchy. There's a chapter on small side salads and some distinctive dressings to elevate the basic tossed green salad to new levels of elegance. You'll also find ways to satisfy a carb craving with the small pasta, rice, and potato salads in Chapter 12. Part 4 ends main dish salads, often featuring cooked protein with raw vegetables and some fruits, too.
**Part 5, "Redefining Fast Food,"** gives you ways to have a great dinner on the table fast. The chapters include recipes for seafood, poultry, and meats, prepared with the herbs and spices of Asia, the Mediterranean, and most of the remainder of the world.
**Part 6, "Great Grills,"** is simply that. Here you'll find recipes for foods that are quickly seasoned and then topped with delicious relishes and sauces. You'll also find marinated dishes, and burgers made with everything from lentils to lamb.
**Part 7, "Desserts on a Deadline,"** is full of quick and easy recipes to end meals with a sweet finale and flourish, whether you crave fresh fruits, anything chocolate, or baked goods like homey cobblers and creative cookies.
In the appendixes, you'll find a glossary to expand your knowledge of food words. That's followed by an appendix of charts to help you convert measurements to or from the metric system, and one giving weights and measures of ingredients to ease your shopping.
# **Extras**
In every chapter you'll find boxes that give you extra bits of information:
**Fast Talk**
Cooking has a language all its own. Look to these boxes for quick definitions.
**Fresh Ways**
Look here to find tips about specific recipes or to boost your general cooking knowledge.
**Speedy Solutions**
Check these boxes for timesaving tips on shopping, food prep, cooking, or kitchen cleanup.
**Stale Stuff**
Be sure to check out these warning boxes to be alerted to potential problems in advance.
# **A Note on "Active Time" and "Start to Finish"**
You'll notice that the times given with each recipe are broken into two segments. Cooking is like sports; there are participants and spectators, and these two time measurements are similar.
The first is the "active time." That's the time you actually have to be in the kitchen chopping, sautéing, or stirring. In all cases, this time 30 minutes or less. You're not going to be spinning swans from sugar or boning tiny quail. When you're the cook, this is the measurement you need to factor into your day.
The second measurement is simple enough to understand—"start to finish" means just that. It's the combination of the active time with the cooking time and then any additional time that's needed for marinating before cooking or chilling after cooking. But during most of this time you can be reading a book in the living room. The start to finish time is so you know when to begin a dish so you can have it ready by a particular time.
# **Acknowledgments**
Writing a book is a solitary endeavor, but its publication is always a team effort. My thanks go to...
Michele Wells of Alpha Books and Ed Claflin, my agent, for proposing this project.
Christy Wagner, Megan Douglass, and Ross Patty for their eagle-eyed editing.
Karen Konopelski for her nutritional analysis and culinary insights.
Grace Skinger Lefrancois for her editorial assistance.
Tigger and Patches, my furry companions, who personally approved all seafood recipes.
# **Special Thanks to the Technical Reviewer**
_The Complete Idiot's Guide to Fast and Fresh Meals_ was reviewed by an expert who double-checked the accuracy of what you'll learn here, to help us ensure that this book gives you everything you need to know about creating dishes chock full of fresh foods—fast! Special thanks are extended to Karen Konopelski.
# **Trademarks**
All terms mentioned in this book that are known to be or are suspected of being trademarks or service marks have been appropriately capitalized. Alpha Books and Penguin Group (USA) Inc. cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark.
**Part 1**
**Fundamentals of Fast Food**
The chapters in Part 1 set the scene for the recipes in the rest of the book. In this case the scene is your kitchen, and you learn how to equip it and become more efficient when you're cooking in it.
In the first chapter, you learn the rules for food safety and how to streamline your trips to the supermarket, because time saved. The second chapter is your lesson in fast and fresh cooking. It begins by helping you use knives more efficiently and then gives you pointers on cutting and selecting fresh produce.
**Chapter1**
**Kitchen Efficiency**
**In This Chapter**
• Necessary kitchen equipment
• Tips on organizing your kitchen
• Savvy food shopping
• Understanding and practicing good food safety
Efficiency is as important in cooking as it is in any other aspect of your life—maybe even more so when you and your family are hungry and waiting on dinner! In this chapter, I give you several pointers on saving time, even before you start cooking. You learn the equipment you need to cook not just the recipes in this book, but in all books. Plus, I give you tricks for arranging your kitchen to enhance your efficiency and ways to make trips to the supermarket less stressful.
Food safety is a cornerstone to every aspect of eating, so this chapter ends with guidelines to keep your food healthful and healthy at all times.
# **A Panoply of Pans**
Many cooks often make the mistake of just grabbing any size pan, but using the correct size pot or pan listed in a recipe is important to the success of the dish. It's easy to know if a pot is too small: the food won't fit in it! But don't overcompensate and use the largest pan you have, either. If you're sautéing one shallot in a 12-inch skillet, you can't control the food well and keep it stirring. A 6-inch skillet works better for this.
When it comes to selecting pots and pans, consider the thickness and kind of metal used. I prefer enameled iron, but stainless-steel and anodized cast aluminum are other good choices. One thing to keep in mind when selecting pots and pans is whether or not you plan to wash them in the dishwasher. Such upscale brands as Calphalon should not be washed in the dishwasher. You also shouldn't wash pots with wooden handles in the dishwasher because the handles will eventually rot and break off.
Here's the list of pots I think you need, along with some suggestions for what you'll do with them:
**Skillets** Ideally, you should have a 6- or 7-inch skillet for sautéing small amounts of vegetables, a 10-inch skillet for browning food, and a 12-inch skillet with a tight-fitting cover and sloping sides to cook all the recipes referred to as "skillet meals." Skillets now come with nonstick coatings, and should you choose one of these, it's important to use only plastic utensils. Metal utensils can scratch off the nonstick coating.
**Dutch oven** These heavy, squat pots usually hold between 6 and 8 quarts. Because they have a large surface area that sits on the burner, you can use Dutch ovens for frying and sautéing as well as for simmering. It's important that the Dutch oven be sturdy and that the cover fits tightly.
**Stale Stuff**
When it comes to pots and pans, being penny-wise is being pound-foolish. You only buy them a few times in a lifetime, and while the quality of your can opener doesn't matter so much, the quality of your pots does. Flimsy pans have "hot spots" that can cause food to stick and burn.
**Saucepans** You'll need a small, 1-quart pan for making white sauces, a 2-quart for general boiling, and a 4-quart for soups and pasta. As with the other pots detailed in this section, a key to performance is a tight-fitting lid, especially when cooking foods such as rice. When it comes to nonstick coating, the same cautions apply as with skillets.
**Stockpot** A good stockpot should be at least 12 quarts and have a lid in case you're cooking lobsters or boiling a lot of corned beef. However, it can be made of thinner metal and less expensive than other pots.
**Roasting pans** You need a 9×13-inch glass or metal baking pan for roasting meats and vegetables as well as baking, and a 10×14-inch pan for larger cuts of meat and whole chickens. You also need a ½-size sheet pan with 1-inch sides for toasting nuts and general baking.
**Metal colanders** You need a handheld colander for small jobs and one with feet that sits firmly in the sink for draining pasta.
**Mixing bowls** No kitchen is complete without a set of stainless-steel or glass mixing bowls in graduated sizes from 2 cups to 2 quarts. Stainless steel is more durable, but glass can go into the microwave for reheating.
**Fresh Ways**
If you frequent yard sales and thrift shops, you might uncover treasure troves of inexpensive kitchen items. I don't trust used electrical equipment, as it could lead to fires, but a mixing bowl is a mixing bowl.
# **The Pots' Pals**
Pots and pans don't exist in a vacuum, and any cook who has had to improvise a soup ladle from a mug or try to do without a slotted spoon knows it's the inexpensive equipment that makes cooking efficient.
Here's a list of miscellaneous odds and ends to complete your kitchen list:
• Measuring spoons, graduated from ¼ teaspoon to 1 tablespoon
• Dry measuring cups, graduated from ¼ cup to 1 cup
• 2-cup liquid glass measuring cup
• A few plastic cutting boards
• Glass and stainless-steel mixing bowls
• Some long-handled cooking spoons
• Heatproof rubber spatula
• 8-inch tongs
• 12-inch tongs
• Slotted spatula
• Offset spatula
• Slotted spoon
• Sturdy meat fork
• Large and small balloon whisks
• Flat-bottom whisk
• Soup ladle
• Garlic press
• Vegetable peeler
• Instant-read meat thermometer
• Wire mesh strainer (can double as a sifter)
• Four-sided box grater
• Puncture bottle opener (for opening cans of liquid)
• Manual can opener
• Corkscrew
**Fresh Ways**
A corkscrew comes in handy even if you don't drink wine. They're great for opening bottles of vinegar and fancy olive oils, too. And an instant-read thermometer should be mandatory in every kitchen. Just stick it in the thickest part of food and leave it in for 20 seconds.
# **The Cutting Edge**
Knives are so important to cooking that some chefs travel with their own sets. It's important that the knife is made from carbon steel and that the blade goes the entire way to the end of the handle. That's called full tang, and it makes knives sturdier.
You don't have to go nuts and buy a huge knife set with a wooden block to take up counter space. Here's a list of the basic cutlery you need:
• At least one paring knife with a 4-inch blade for peeling, slicing, and dicing small foods
• A chef's knife with an 8- to 12-inch blade for chopping, mincing, dicing, etc.
• A serrated knife with a 12- to 14-inch blade for slicing bread, tomatoes, and meats
• A sharpening steel to keep the knives razor-sharp
Be sure you've got some way of keeping knives sharp. People cut themselves with poorly sharpened knives much more often than with a sharp knives, and dull knives make cutting harder and can detract from the appearance of the food. A steel rod or sharpening stone is much less expensive than the electric knife-sharpening gizmos and serves the same function with the aid of a little elbow grease. (In Chapter 2, you learn tricks on how to best use your knives.)
**Stale Stuff**
Don't skimp on knives; they're a once-in-a-lifetime purchase, but they are dear. A set of three knives from Sabatier, Wüsthof, or Henckels—the three market leaders—cost in the $200 and up range.
# **The Electric Aisle**
You also need a few small appliances in the kitchen. The most important is a food processor. The food processor's on-and-off action has revolutionized formerly laborious cutting and chopping tasks. When testing these recipes, I do the chopping by hand to calculate the active time, and I'm always amazed at how long it takes without a food processor! Even if you're shopping off the salad bar, chances are you might have to do additional dicing, mincing, and fine chopping.
My food processor has a permanent spot in the dishwasher because I use it every day. I start by chopping foods that leave a residue that's easy to rinse out such as parsley or nuts. Then I finish with foods like garlic or onions, after which the work bowl really needs soap and water.
**Speedy Solutions**
Don't bother spending money on a toaster; you can toast anything your heart desires underneath the oven broiler. The same is true for a blender. While they might make smoothies better than a food processor, they can't chop and dice for you, so if you're only going to buy one appliance, make it a food processor.
Here are some other good additions to your electric arsenal:
**Immersion blender with whisk attachment** If you like puréed soups, you've got to get one of these. Just place it into the pot, and there's no need to take the time to transfer the solids to the food processor (or risk the spills!). The whisk is excellent for beating egg whites or cream, too, and for small quantities of batter that would get lost in the beaters of an electric mixer.
**Handheld electric mixer** Unless you're a serious baker who makes large cakes or needs a dough hook to knead bread dough, this is the only mixer you'll need. Such mixers are inexpensive and easy to store.
**Hinged-top grill** These are the new kids on the block, the most prominent of which is the George Foreman Grill. These grills are great for making pressed sandwiches and for indoor grilling, and they come in a variety of sizes to fit your household.
# **Divine Disposables**
Next to the food processor, the roll of heavy-duty aluminum foil is my best kitchen friend. Any time you can cover a baking sheet or line a roasting pan with foil, you save clean-up time. The only time you can't use foil for baking and roasting is when food might have a tendency to stick. You don't want bits of foil on your crusty chicken!
The heavy resealable plastic bag is one of the most useful items in a kitchen. This bag revolutionized marinating, and there's no dish or bowl to wash, either!
# **Shopping Savvy**
Supermarkets charge a premium price for items in those chilled bins in the salad bar, but the amount of time you can save by letting the supermarket to do your prepping makes shopping the salad bar an appealing alternative. The salad bar has done all the vegetable prep work for you, which means you can substantially decrease the active time you spend chopping, slicing, etc. Carrots? Already peeled and sliced! Onions? Prechopped—and tear free! Spinach? Already rinsed and stemmed!
**Stale Stuff**
One fear of shopping from—and eating from—salad bars is that the produce might have been sprayed with chemicals to prevent discoloration and wilting. Question the supermarket about this practice.
But the salad bar isn't limited to produce. Want to make egg salad? You'll find hard-cooked eggs already peeled. Want just a few beans rather than a 15-ounce can? Most salad bars offer garbanzo beans, sometimes kidney beans, and frequently other bean-y options as well.
## **Other Produce Department Options**
For quantities larger than what you can get at the salad bar, shop in the preprepped vegetables section of the produce department. This section is constantly growing, and now includes everything from preshredded cabbage for coleslaw to preshredded carrots and prechopped onions.
All the stir-fried recipes in this book call for individual vegetables, but remember that recipes are guidelines and not laws. If you see an appealing mix of vegetables preprepped for you, it's likely the right volume for these recipes.
## **I Love Farmers' Markets!**
The hints thus far in this chapter have been geared to supermarket shopping. But there's an alternative at least during the summer months, even in large cities—the farmers' market. I'm addicted to farmers' markets. Here you can find an incredible variety of the freshest possible ingredients. You won't find plastic-wrapped bunches of carrots; you get lovely individual carrots sold by the pound!
In many larger cities, especially in downtown areas, you can shop at the farmers' markets' first cousins: sidewalk vendors. One great advantage to buying fruit from sidewalk vendors is that their fruit is always ripe and ready to eat or cook.
**Fresh Ways**
Since 1994, the U.S. Department of Agriculture (USDA) has published the National Directory of Farmers' Markets. In 1994, the number was less than 2,000; today it's double that! To find a farmers' market near you, go to www.ams.usda.gov/farmersmarkets.
# **Safety First**
Speaking of safe, the first—and most important—requirement for good cooking is knowing the basic rules of food safety. This begins with trips to the supermarket and ends after leftovers are refrigerated or frozen at the end of a meal. The sections that follow might seem like common sense, but after many decades as a food writer who has heard horror stories about very sick people, please believe me, they're not.
## **Safe Shopping and Transport**
I mentioned earlier in the chapter that you should hit the seafood and meat counters last before the checkout. Here are some other food safety tips:
• Never buy meat or poultry in a package that's torn and leaking.
• Place all meats and poultry in the disposable plastic bags available in the produce department to keep them from contaminating other foods in your basket.
• Check the "sell by" and "use by" dates, and never purchase food that exceeds them.
• For the trip home, carry an insulated cooler in the back of your car if it's hot outside or if the perishable items will be out of refrigeration for more than 1 hour.
• In really hot weather, ask your seafood department or meat counter for some crushed ice in a separate bag to keep your fish and meat cool.
## **Banishing Bacteria**
All fruits and vegetables should be rinsed before eating or cooking them unless they're peeled such as apples or potatoes. Even salad greens that proclaim they're prewashed should still be rinsed again for the sake of safety.
Fruits and vegetables can contain some bacteria, but it's far more likely that the culprits will grow on meat, poultry, and seafood. Store these foods on the bottom shelves of your refrigerator so their juices cannot accidentally drip on other foods. And keep these foods refrigerated until just before they go into the dish.
**Fresh Ways**
If you have questions about food safety, the USDA—specifically the Food Safety and Inspection Service—is the place to go for answers. The website, www.fsis.usda.gov, provides a wealth of information in a very user-friendly format.
Bacteria multiply at room temperature, in a so-called "danger zone" between 40° and 140°F. As food cooks, it's important for it to pass through this zone as quickly as possible.
If you want to get a jump-start on dinner by browning meats or poultry or cutting up vegetables in advance, that's fine. Just refrigerate all foods separately until it's time to combine them and cook the finished dish. Like all rules, this one has exceptions: raw eggs—you can make batters in advance and refrigerate them.
## **Avoiding Cross-Contamination**
Cleanliness is not only next to godliness, it's also the key to food safety. Wash your hands often while you're cooking, and never touch cooked food if you haven't washed your hands after handling raw food. The "cooked food and raw food shall never meet" precept extends beyond the cook's hands. Clean cutting boards, knives, and kitchen counters often. If you have the space, section off your countertops for raw foods and cooked foods, as many restaurant kitchens do. Don't place cooked foods or raw foods that will remain uncooked (such as salad) on cutting boards that have been used to cut raw meat, poultry, or fish. Bacteria from raw animal proteins can contaminate the other foods.
**Fresh Ways**
A good way to prevent food-borne illness is by selecting the right cutting board. Wooden boards might be attractive, but you can never get them as clean as plastic boards that can be run through the dishwasher. Even with plastic boards, it's best to use one for only cooked food and foods such as vegetables that are not prone to contain bacteria, and another one devoted to raw meats, poultry, and fish.
## **The Least You Need to Know**
• It's important to use high-quality pots and pans to avoid burning food.
• The best knives are made from carbon steel and have blades that go all the way to the end of the handle.
• Buying precut vegetables from supermarket salad bars is more expensive but can save considerable time and you're not left with leftovers.
• The same utensils, serving dishes, cutting boards, etc. should not be used for raw foods and then cooked food without being thoroughly washed first.
**Chapter 2**
**Skill Builds**
**In This Chapter**
• Tips for safe and efficient knife handling
• A mini-glossary of cutting terms
• Perfect produce pointers
Cooking fresh food fast requires some culinary skills—none of which are difficult to master. In this chapter, I give you tips to make you more efficient in the kitchen. When you're more efficient, you're also speedier! You learn in this chapter the difference between _dice, mince, and slice_ , along with knife-holding tips that will have you dicing, mincing, and slicing like a pro.
I end the chapter with some tips on how to select, store, and cut popular produce.
# **Careful Cutting**
Learning how to hold a knife is a little like learning to hold a tennis racket or a golf club. Once you've mastered it, you're good for life. You want to be sure you're holding a knife for comfort, control, and safety, all with minimum stress on your hand.
To do this, grip the knife by its bolster. The bolster is your knife's balance point, and it serves as a finger guard. Only your last three fingers should rest on the handle. Your thumb and index finger should be on opposite sides of the blade. When you hold a knife at its balance point, it becomes an extension of your hand.
Regardless of what you're cutting, the hand not holding the knife serves a vital role. It stabilizes the food you're cutting and guides the knife to determine the size of your cuts. Be sure your fingers are curled inward with your thumb tucked underneath the palm of your hand. The side of the knife—and _never_ the blade—should rest against your knuckles.
**Fresh Ways**
The best way to cut food is with a forward cutting motion. If you cut back to front, the knife is doing the work. If you cut up and down, your arm is doing the work.
**Stale Stuff**
Take it slow at first, and don't try to imitate a TV chef with great speed or bravado. Your speed increases naturally as you become more confident and sure about your knife skills.
For slicing, begin by initiating the cut with the tip of the knife and pushing the knife forward across the food until you reach the knife's heel. If you find you have to push down with the knife, your knife probably needs sharpening. If you reach the heel and haven't finished your cut, bring the knife back to the tip and repeat the motion.
For large items that sit high on the cutting board like potatoes or carrots, start with the tip of the blade on the food. For smaller foods like celery or herbs, start with the tip on the cutting board.
For fine mincing and chopping, you use your knife in a different way. When food is cut into small pieces, and you want to make the pieces yet smaller, your guiding hand should be placed on top of the blade. This hand helps the one holding the knife pivot repeatedly along its curved edge in a rocking motion. You never lift your knife off the cutting board except to scrape the food you're cutting into a pile.
# **Sizing the Situation**
There are many traditional ways of cutting food, many of which can be done quickly in the food processor, using the steel blade for chopping and using special discs for shredding and cutting. The use of one cut rather than another is determined by how the ingredient functions in a recipe. If the food must cook quickly in a sauté or stir-fry, the pieces have to be smaller than if they're going into a stew that will simmer for hours. And if a food is intended as a garnish, chances are it'll be cut in a manner to make it attractive.
One constant for all cutting methods is to make the pieces uniform; this is important for both cooking and appearance. Here is a list of cutting methods used frequently in recipes:
**Coarse chopping** Coarse chopping is usually used for foods such as vegetables added to stews or foods such as cooked potatoes or chicken that form the basis for cold salads.
**Speedy Solutions**
Many supermarkets stock packages of prechopped onion or trimmed broccoli or cauliflower florets. The time saved might be worth the additional money to buy these convenience foods.
**Mincing** This is an even, very fine cut that's especially appropriate for herbs, garlic, and shallots. Gather herbs or roughly chopped garlic or shallots in a pile on a cutting board and position the knife above the pile. Keeping the tip of the blade against the cutting board, lower the knife firmly and rapidly, repeatedly chopping through the herbs or vegetables. Continue chopping until the desired fineness is attained.
**Julienne and batonnets** These are long, rectangular cuts used for vegetables and for any ingredient that's to be finely cut, like the julienne of prosciutto used to top a pizza. For hard vegetables like carrots or potatoes, trim them so the sides are straight, which makes it easier to create even cuts. Slice the vegetable length-wise, using parallel cuts of the proper thickness. Stack the slices, aligning the edges, and make parallel cuts of the same thickness through the stack. Batonnet cuts should be thick. To make a fine julienne, the cuts should be very thin. For soft foods like cooked meats, it's easier to slice it thinly, trim the slices into a neat shape, and then make the thin cuts.
**Stale Stuff**
Meats should be cut into a julienne _with_ the grain because they'll fall apart if cut _against_ it.
**Dice** The results of dicing are cube-shaped pieces, and a recipe usually specifies the size of the dice (¼-inch dice, etc.). Everything from vegetables to meats, cheeses to chocolate are diced.
To dice, trim and cut the food as for julienne or batonnet. Gather the julienne or batonnets, and cut through them cross-wise at evenly spaced intervals.
# **Help for Handling**
Cooking is at best an inexact science because every piece of food has a unique composition. Perhaps "a rose is a rose is a rose," but a swordfish steak was cut from a fish of a certain size that was caught on a specific date and cut to a certain thickness. There is no such thing as two chickens that are exactly alike, nor are carrots grown in the soil of California identical in flavor to those grown in New Jersey. And even different brands of all-purpose flour contain differing amounts of protein so they perform differently when used in baking.
The following sections help you select and handle produce and give you other tips for storing or efficient handling.
**Fresh Ways**
If you do need to core an apple to make fanned slices for an apple tart, a melon baller is the best instrument to use. Cut the apple in half, and use the large side of the instrument to remove the core and seeds, leaving an even, circular hole.
## **Apples**
Look for large apples that have good color, are free of bruises, and are firm to the touch. The bruised cells of apples release an enzyme, polyphenoloxidase, that hastens the oxidation or decay of the flesh. Overripe apples feel soft, and the flesh feels mushy. To check apples in a plastic bag, turn it upside down and examine the apples on the bottom.
While traditional slicing methods call for first quartering and coring apples, these steps are unnecessary. After you peel the apple, start shaving off slices from the outside with a paring knife, turning the apple in quarter turns. Continue slicing until you reach the core and then discard the core.
## **Asparagus**
Look for asparagus with rich green color; firm and straight stalks; and closed, compact tips. Its appearance should be crisp and firm, not limp or wrinkled. For ease of cooking, it's best to select same-diameter stalks.
Rinse all stalks under cold water. Then break or cut the spears at the point where the stem turns woody. This will be easy to determine because it's where the stem naturally snaps. For thick stalks, use a small paring knife or a vegetable peeler to peel almost up to the base of the tip. Wrap peeled asparagus in a damp towel and refrigerate until ready to cook, but don't peel them more than a few hours in advance of cooking.
## **Bell Peppers**
The best bell peppers are plump; have a vibrant color; and have long, fresh-looking green stems. Peppers should look crisp and be firm when purchased. Flimsy stems, cracks, and bruises or soft spots are signs of an old pepper.
Most recipes with bell peppers specify "seeds and ribs removed." Here's a quick way to do this: cut a slice off the bottom of the pepper so it stands firmly on the cutting board. You can see the ribs indenting the contour of the pepper. Holding the cap with your free hand, slice down the natural curve of the pepper in sections. You're left with all the pepper and none of the seeds and ribs. You can then chop the flesh, or cut as indicated in the recipe.
Achieving perfect roasted peppers is a two-part process: you have to heat them and then cool them to separate the skin from the flesh. For all peppers, cut a small slit near the stem end with the tip of a paring knife to insure they won't explode. For a large number of peppers, and to retain the most texture, lower them gently into 375°F oil and fry until the skin blisters. Turn them with tongs when one side is blistered, because they'll float on the surface of the oil. You could also place the peppers 6 inches from the broiler element or grill, turning them with tongs until all surfaces are charred. The fastest way to cool peppers is to plunge them into ice water. This stops the cooking action immediately and cools them enough to peel them within a minute.
**Speedy Solutions**
Like canned tomatoes for cooking, jarred already-roasted and peeled peppers can provide great time savings. Try to buy an imported brand in a glass jar, and look to see if bits of charred skin are attached. That means they were really roasted and not just heated and peeled.
## **Cabbage**
A head of cabbage should be heavy for its size, free of brown spots or streaks, and have crisp leaves. In green cabbage, look for cabbage with dark green leaves still attached; many markets pull these off because they're the first to turn yellow. Black edges in red cabbage is a sign of age.
To clean cabbage, discard outer leaves or any leaves that are discolored or wilted. Halve the head, and cut out the tough core with a knife. For shredded cabbage or leaves, remove the entire core; for wedges to be boiled, leave some of the core in place to keep the wedges from falling apart. To shred cabbage, put it cut side down on a board and cut crosswise in very fine slices. (For best appearance on the plate, cut or shred cabbage just before cooking or serving.)
## **Carrots**
It's best to buy carrots that still have the green tops attached. Look for firm, bright orange-yellow carrots with fresh, crisp, green tops. Trim off the green tops before you store carrots, because the leafy tops will wilt and rot long before the sturdy root.
Rather than time-consuming peeling, you can preserve better color if you cover the carrots with boiling water for 5 minutes and then place them in ice water. The skins will then slip right off. Cross-slices of carrots are always appropriate, but they look more decorative if they're cut on the bias. Hold the knife at a 20-degree angle to the carrot and slice, beginning with the small end.
**Fresh Ways**
If celery is wilted, soak the ribs in ice water for 2 to 3 hours. Or wash the celery and stand it vertically for 2 hours in a pitcher of cold water plus 1 teaspoon salt in the refrigerator.
## **Celery**
Select a medium-size stalk that has a solid, rigid feel and a glossy surface of light to medium green. The leaves should be green and fresh, and the ribs should be crisp.
Rinse the ribs, and trim off the bottom; save these pieces for making stock later. Cut the ribs lengthwise into the size pieces you want. Then pile the thin strips and slice across them. If using ribs whole, slice them with the curved side up so they'll sit firmly on the cutting board.
## **Cucumbers**
Select smaller cucumbers because they tend to have fewer seeds. Look for cucumbers that have a clean break at the stem end. An uneven stem means the cucumber was harvested from the vine before it was ready.
While no organic cucumbers are waxed, many conventional ones are coated with a shiny wax to prevent dehydration during transport, and all waxed cucumbers should be peeled. That's why English cucumbers are wrapped in plastic as an alternative to waxing. Use a vegetable peeler or paring knife to remove the dark, waxy coating.
To seed cucumbers, halve them lengthwise and spoon out the seedy centers with a melon baller, or use the tip of a teaspoon or measuring spoon.
## **Eggplants**
The freshest eggplants are plump, have shiny skins and a bright green cap, and should not weigh more than 1 pound or they might be old and bitter. Eggplants should be firm and heavy for their size. Avoid damaged, bruised, or soft eggplants, because even slightly soft eggplants are bitter. Eggplants turn brown easily, so slice them just prior to cooking.
About two-thirds of an eggplant's weight is water, and the flesh is also porous, which is why eggplants seem to drink up oil when fried. For these reasons, most eggplants should be salted and pressed before cooking to compact the flesh so it won't absorb as much fat. This also works to extract the bitter juices in some types of eggplants.
Although you can avoid this step when dealing with most Asian or tiny Italian eggplants, salting is needed to extract the bitter juices found in mature eggplants. Slice or dice the eggplant as specified in the recipe, and sprinkle the pieces liberally with salt. Place the salted eggplant in a colander in the sink or in a mixing bowl. Place a plate on top the salted eggplant, and top the plate with some cans. Drain for 30 minutes and then rinse the pieces thoroughly to remove the salt and bitter juices. Dry well on paper towels, especially if the eggplant is to be sautéed, to remove excess water.
## **Garlic**
Look for whole heads with no cloves broken off, tightly packed large cloves, and no sign of green sprouts at the tips. The clove skin should be tight and snug, because loose cloves indicate deterioration. When the cloves are pressed, they should feel firm and solid. Papery skin or skin that's pulling away from the cloves is a sign of old garlic. Keep garlic in a cool, dark, dry space with fresh, circulating air. Fresh garlic should keep from 3 to 6 months if properly stored.
**Fresh Ways**
Raw garlic is always stronger than cooked garlic, and the finer garlic is processed, the stronger it is. Adding raw garlic during a dish's cooking process results in a stronger flavor than if you sautée the garlic in oil prior to adding other ingredients.
Separate the cloves from the head as needed. For a few cloves, you can easily pry off the outer cloves with your thumb. To quickly separate the entire head, hit the base firmly onto a counter or cutting board; the cloves will easily pull apart.
To peel a clove, place the side of a heavy knife over the clove and bring your fist down hard on the blade (be careful not to cut yourself!). This is the easiest method and is best to use if the clove is to be pounded or minced. You can easily pull off the skin with your fingers. For several cloves, it's easier to drop the cloves into boiling water for 10 to 20 seconds. Refresh them under cold water and then use your fingers to slip off the skins.
To mince garlic, cut the peeled clove lengthwise with a very sharp knife. Keeping the garlic together, make a quarter turn and slice again. Continue to chop the garlic, using a rocking motion with your knife. Hold the tip end of the knife with your other hand, and use quick, small strokes. As the garlic spreads out, use the knife to push it back to the center. Keep chopping until the garlic is very fine.
## **Ginger**
You can find ginger in pieces from a few inches to a foot long. The freshest ginger is plump and very firm, and the skin should be tan, shiny, smooth, and unwrinkled. Try to buy the largest knobs possible without many small bumps; you'll have to remove those, and they're virtually useless for cooking. Store ginger refrigerated for up to 2 weeks, wrapped in paper towels to absorb moisture, inside a plastic bag or store in a paper bag. After the ginger has been peeled, you can cover it in dry sherry and refrigerate it for up to 3 months.
If the ginger is to be used to flavor a marinade or dish and then discarded, there's no need to peel it. Scrub it with a vegetable brush under cold running water and then slice or dice it as specified. In most cases, however, ginger should be peeled not only for aesthetic reasons, but because the peel never softens.
Using a sharp paring knife, trim the small stubs off the knobs. Then peel with the curve of the knobs, along the grain rather than across it. Cut the ginger into slices, and crush them with the flat side of a large knife; the crushing separates the fibers, which makes it easier to chop or slice further. To grate ginger, use the tiny-hole side of a box grater, or drop cubes through the feed tube of a food processor with the motor running.
## **Mangoes**
Look for mangoes that yield slightly to finger pressure but are not mushy. Smell the stem end; the aroma should be faintly sweet and floral. Because the soft, pulpy, juicy flesh clings so tightly to the flat stone,
mangoes are one of the most difficult fruits to cut neatly. Cut away the mango peel with a vegetable peeler or sharp paring knife. Slice the mango flesh until you reach the central stone. Continue slicing on the other side of the stone and then cut away, in chunks, any flesh that remains on the stone.
**Fresh Ways**
Place unripe mangoes in a paper bag and keep them in a dark, warm place until they ripen. If you have too many ripe mangoes becoming ripe at once, peel and purée the flesh. It can be frozen for up to 6 months.
## **Mushrooms**
White mushrooms grow from a stem and have a cap and a veil (a membrane between the stem and the cap). Fresh mushrooms are firm, smooth, plump, and have a consistent color that ranges from creamy white to light brown. The caps should be spongy and tightly closed, hiding the gills. In small, delicate mushrooms, look for mushrooms with the veil still attached to the mushroom cap. Mushrooms should be slightly moist, but with no damp patches. Avoid slimy mushrooms or those with some yellow underneath.
Store mushrooms in their unopened packages in the refrigerator until ready to use (they're packaged with ventilation holes for air). Once the package is opened or if you purchase loose mushrooms, refrigerate them where they can get good air circulation in a paper bag poked with a few holes. You could also cover them with wax paper, a damp cloth, or a damp paper towel to help them retain moisture.Mushrooms bruise easily, so handle them gently. If mushrooms are pristine, simply rub them gently with a damp paper towel and trim the stem. Never soak mushrooms because they absorb water.
Slice mushrooms just before cooking, as oxidation causes the mushrooms to turn an unattractive purplish brown. If the recipe calls for mushroom caps without the stem, loosen the stem with the tip of a knife or teaspoon, or twist until loosened, and then remove. Cultivated mushrooms never need peeling due to their soft, thin skin.
**Speedy Solutions**
White mushrooms all taste the same regardless of size. If you're chopping them, it makes sense to buy the largest ones possible, as it takes less time to clean them.
_To slice:_ Cut a mushroom in half, and place the cut side on the cutting board. Slice with a sharp paring knife, using a front-to-back motion. Do not press straight down, or you can bruise the mushroom.
_To dice:_ Slice the stem so it's level with the mushroom cap. Cut the mushroom horizontally into medium to thick slices. Arrange the slices, or stack them on top of each other, and cut into medium-size sticks. Gather the mushroom slices together, and cut across.
Wild mushrooms should be firm with a wholesome odor. Brown, shiny, or slimy spots or a strange smell is an indication of decay. Check mushrooms for worm holes or gills that are fragmenting. Store as you would white mushrooms.
Clean wild mushrooms about 30 minutes before you plan to use them to allow them to dry. Use as little water as possible, and never soak mushrooms in water. If they don't appear dirty, it's best to just wipe them with a damp cloth. Unless necessary, do not wet underneath the caps of fresh wild mushrooms.
## **Onions**
Choose onions that are firm and nicely shaped. The skins should appear tight and healthy. Sprouting is a sign of age, and sprouting onions should be avoided. Also avoid onions with soft spots, a dried appearance, or black or powdery spots, all of which are signs of internal decay. For green onions and leeks, look for perky green stems with no signs of wilt, limpness, marks, or bruises on the bulb.
**Fresh Ways**
Buy loose onions in a number of different sizes rather than a bag. You can choose the onion depending on the quantity needed and not have as much, if any, leftovers.
If you store onions in a cool, dry area with good air circulation, they should keep for 3 or 4 weeks. At cooler temperatures (55° to 60°F), they could keep for several months. Refrigerate onions only after they've been cut, wrapped tightly in plastic wrap to avoid the odor affecting other foods. If you only need part of an onion for a recipe, slice off only that much, leaving the remainder of the onion in its skin.
_To peel onions:_ Take a small slice off the top and root ends using a stainless-steel paring knife (iron can cause the onion to discolor). Pull away the papery skin with the blade of the paring knife or with your fingers if possible.
_To slice and dice onions:_ Place the onion on a chopping board, and slice it in half lengthwise. Cut down at regular intervals, holding the onion by its root end with the hand not holding the knife. To dice it, place the onion cut side down, and slice lengthwise at intervals from ¼ to ½ inch, depending on the size pieces you need. Slice to—but not through—the root end. Next, hold the knife horizontal, and slice at the same intervals from bottom to top. Then slice down vertically, and the onion will be diced. To chop more finely, use a chef's knife to chop the onion into smaller pieces by rolling the blade back and forth over the diced onion.
**Stale Stuff**
While both onions and potatoes should be stored at cool room temperature, they shouldn't be stored together. Potatoes give off moisture and produce a gas that causes onions to deteriorate more quickly.
## **Peaches**
Look for peaches that have a consistent creamy or golden color all over. (The blush is an indication of variety, not of ripeness.) Avoid wrinkled peaches, or peaches with any trace of green, blemishes, or brown spots. Because peaches ripen so easily at home, it's best to buy peaches that are still a bit firm. The fruit's ripe when it's slightly soft. Store firm peaches at room temperature; to speed ripening, place them in a brown paper bag. Keep the soft fruit in the refrigerator, and use it within a few days.
_To peel peaches:_ You can peel firm peaches using a vegetable peeler just as you'd peel a potato. Or you can place ripe peaches in boiling water for 30 seconds and then the skins will slip right off. You can also microwave a peach on high for 10 seconds and then let it stand for 5 minutes before peeling.
**Fresh Ways**
Rub cut peaches with a cut lemon or toss with lemon juice to prevent discoloration.
## **Tomatoes**
Tomatoes should be smooth and heavy for their size with firm flesh. Avoid any that appear watery. Avoid bruised tomatoes, as many times damaged tomatoes are rotten inside. Mold growing around the stem is a bad sign, and the mold may be toxic or poi- sonous. Vine-ripened varieties often have the green stems attached. Press these tomatoes gently between your palms; they should give slightly.
**Speedy Solutions**
If using canned tomatoes, which are already partially cooked, subtract about 5 minutes from the cooking time listed in a recipe. If canned tomatoes taste acidic, add 1 teaspoon sugar to the recipe.
Never refrigerate unripe tomatoes; they won't ripen in the refrigerator. Store unripe tomatoes in a cool spot, out of direct sunlight, which could encourage tomatoes to turn to mush and may also destroy vitamins A and C. Store them between 60° and 75°F. For quicker ripening, place unripe tomatoes in a closed paper bag. Refrigerate only fully ripe tomatoes, and use them within 3 to 5 days after ripening.
_To peel tomatoes:_ Cut out the core from the stem end, and with a knife, lightly cross-hatch over the bottom of the tomato. Plunge tomatoes in boiling water and boil for exactly 10 seconds. Remove with slotted spoon to a bowl of cold water. This change in temperature damages the layer of cells just below the skin, allowing the skin to easily slip off.
_To remove the seeds:_ Slice the tomato in half through the middle. Squeeze gently over a bowl and the seeds should loosen and drop. Remove any clinging seeds with the tip of a paring knife or your finger.
_To dice a tomato:_ Cut the tomato in half, slice it into strips, and cut the strips crosswise into a dice.
Once you've become familiar with how to handle produce, your cooking will become faster when you enter the kitchen. But do keep in mind that no two pieces of food are identical, so there will always be some variation as to color, flavor, and texture.
## **The Least You Need to Know**
• The goals for holding a knife are comfort, control, and safety.
• Knowing what various cutting instructions mean can save you precious time in the kitchen.
• By following proper selection, storage, and preparation steps, you can cook confidently with fresh fruits, vegetables, and other foods.
**Part 2**
**Beginning Hors d'Oeuvres and Appetizers**
Because the recipes in this book are so quick to make, they're ideal to consult when you're entertaining. That's where the chapters in Part 2 fit in.
Whether it's a small dinner party or a large cocktail party, you'll probably want to start off the evening with hors d'oeuvres. Two chapters are devoted to finger foods, one for hot and cold dips and the other for individual nibbles.
The next two chapters are for small dishes to start your meal. Some are light and luscious vegetable and fish appetizers and some are soups, including chilled soups to cool you in the summer and hot soups to warm you in the winter.
**Chapter 3**
**Dippity-Do**
**In This Chapter**
• Easy bean dips
• Gooey cheese dips
• Hearty meat and seafood dips
Dips are part and parcel of nearly every party. They're easy on hosts, they require no last-minute hors d'oeuvres assembly, and there's no need to pass anything during the party. After the party is over, there's no mountain of small plates stacked up like the Leaning Tower of Pisa awaiting washing in the kitchen.
And dips are easy on guests. Your friends and family can eat dips with one hand, eliminating the need for a juggling lesson to learn how to simultaneously handle glasses, forks, and plates. Dips encourage people to talk and mingle because they're a gathering point of a party.
In this chapter, you'll find recipes for a wide range of dips, both hot and cold, inspired by cuisines as varied as Chinese and Mexican. Most are vegetarian, some are vegan, and a few contain seafood or meat.
# **Dip Diversification**
Sure, you know what to do with a dip. You stick something crunchy—a tortilla chip or a carrot stick maybe—into it and then chomp down on dip and dipper. But that's not the only way many of these dips can be served.
Thick cold dips can be transformed into _canapés_ (that's a fancy French word for "nibble"). Place the dip in a pastry bag fitted with a large fluted tip, and pipe a rosette onto anything from a slice of cucumber to a piece of melba toast.
Thick cold dips can also be served as spreads for breads. Many chic Italian and French restaurants serve small ramekins of savory spreads along with butter and bread. These dips are far lower in fat than butter, plus they add more flavor to the bread.
Both hot and cold dips can be used as toppings for grilled or broiled foods. Spread thin dips over the food, and place a dollop of thick dips off to the side. A bite of chicken breast or steak can be just as good for dipping as a celery stick!
# **Tuscan White Bean Dip**
Flecks of roasted red pepper and parsley enliven this garlicky dip that also makes a great bread spread.
**2 red bell peppers 1 TB. fresh thyme or 1 tsp.**
**2 (15-oz.) cans white cannel- dried**
**lini beans, drained and rinsed Salt and freshly ground black**
**⅓ cup extra-virgin olive oil pepper to taste**
**¼ cup freshly squeezed lemon**
**juice**
**3 garlic cloves, peeled**
**½ cup chopped fresh parsley**
1. Preheat the oven broiler. Place red peppers on the rack of a broiler pan and broil 4 inches from the broiler element until skin is charred and black. Turn peppers with tongs to char all sides.
2. Plunge peppers into ice water, and when cool enough to handle, remove and discard the cap, skin, and seeds. Cut peppers into 1-inch dice and set aside.
3. Combine beans, olive oil, lemon juice, and garlic in a food processor fitted with a steel blade. Purée until smooth.
4. Add parsley, thyme, and red peppers. Chop finely, using on-and-off pulsing. Season to taste with salt and pepper.
5. Serve immediately, or refrigerate for up to 2 days, tightly covered.
Serves: 10
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
173 calories
70 calories from fat
8 g fat
1 g saturated fat
6.5 g protein
21 g carbohydrates
**Speedy Solutions** f you opt for
jarred roasted red peppers rather than roasting them yourself, you can reduce the active time this recipe takes to 5 minutes.
# **Sun-Dried Tomato Dip**
This intensely flavored dip is a wonderful topping for grilled foods, too.
Serves: 10
**Active time:** 10 minutes
**Start to finish:** 10 minutes
**Each serving contains:**
196 calories
176 calories from fat
19.5 g fat
8 g saturated fat
2.5 g protein
3 g carbohydrates
**1 (8-oz.) pkg. cream cheese,**
**softened**
**½ cup mayonnaise**
**½ cup sour cream**
**3 garlic cloves, peeled**
**2 tsp.** _**Herbes de Provence**_
**½ cup sun-dried tomatoes**
**packed in oil, drained**
**4 scallions, rinsed, trimmed,**
**and cut into 1-inch sections**
**Salt and freshly ground black**
**pepper to taste**
1. Combine cream cheese, mayonnaise, sour cream, garlic, and Herbes de Provence in a food processor fitted with a steel blade. Purée until smooth.
2. Add sun-dried tomatoes and scallions, and chop finely by using on-and-off pulsing. Season to taste with salt and pepper.
3. Serve immediately, or refrigerate for up to 2 days, tightly covered.
**Fast Talk**
Herbes de Provence, found in the spice section of many supermarkets and gourmet stores, is a dried blend of many herbs associated with the sunny cuisine of that part of France, including basil, thyme, fennel, rosemary, sage, and marjoram.
# **Guacamole**
This classic version of Mexican avocado dip is a perennial favorite.
**4 ripe avocados 1 tsp. ground cumin**
**1 small red onion, peeled and 2 TB. freshly squeezed lime**
**finely diced juice**
**1 jalapeño chili, seeds and Salt and freshly ground black**
**ribs removed and finely diced pepper to taste**
**½ cup chopped fresh cilantro**
1. Place avocados, red onion, and jalapeño in a medium mixing bowl. Use a table fork to mash mixture together, leaving some avocado in chunks.
2. Add cilantro, cumin, and lime juice, and season to taste with salt and pepper. Mix well, and serve immediately. (You can make this dip up to 8 hours in advance. Push a piece of plastic wrap directly into the surface to prevent discoloration, and then refrigerate.)
**Fresh Ways**
An easy and efficient way to remove the flesh from avocadoes is to run a rubber spatula under the skin after the avocado is cut in half and the pit has been discarded. You can then pop out the flesh without scraping the skin.
Serves: 10
**Active time:** 10 minutes
**Start to finish:** 10 minutes
**Each serving contains:**
121 calories
95 calories from fat
10.5 g fat
1 g saturated fat
2 g protein
8 g carbohydrates
# **Mexican Black Bean Dip**
This hearty dip can be served in place of refried beans with any Mexican meal.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
155 calories
85 calories from fat
9.5 g fat
2 g saturated fat
4.5 g protein
14 g carbohydrates
**⅓ cup olive oil**
**1 small red onion, peeled and**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**2 (15-oz.) cans black beans,**
**drained and rinsed**
**½ cup crème fraîche**
**¼ cup freshly squeezed lime**
**juice**
**1 tsp. ground coriander**
**1 tsp. ground cumin**
**1 TB. chopped fresh oregano**
**or 1 tsp. dried**
**Hot red pepper sauce to taste**
**½ cup chopped pimiento**
**¼ cup chopped fresh cilantro**
**Salt and freshly ground black**
**pepper to taste**
1. Heat olive oil in a large skillet over medium heat. Add onion and garlic, and cook, stirring constantly, for 3 minutes or until onion is translucent. Scrape mixture into a mixing bowl and set aside.
2. Combine beans, crème fraîche, lime juice, coriander, cumin, oregano, and red pepper sauce in a food processor fitted with a steel blade. _Purée_ until smooth, and scrape mixture into the mixing bowl. Stir in pimiento and cilantro, and season to taste with salt and pepper.
3. Serve immediately or refrigerate for up to 2 days, tightly covered.
**Fast Talk**
Purée means to turn foods to a thick, creamy texture resembling thick baby food. The most efficient way to do this is with a food processor. Unless there's a lot of liquid, a blender isn't really up to the job.
# **Spinach Dip with Feta and Dill**
This dip is right out of the Greek islands with flavors of tangy cheese, aromatic dill, and lemon.
**1 lb. fresh baby spinach**
**2 TB. unsalted butter**
**1 medium onion, peeled and**
**chopped**
**1 garlic clove, peeled and**
**minced**
**2 cups crumbled** _**feta cheese**_
**1 (3-oz.) pkg. cream cheese,**
**softened**
**¼ cup chopped fresh dill or 3**
**TB. dried**
**2 TB. chopped fresh oregano**
**or 2 tsp. dried**
**3 TB. freshly squeezed lemon**
**juice**
**Salt and freshly ground black**
**pepper to taste**
1. Place spinach in a large bowl of cold water. Rinse spinach in water and then remove it from the top of the water and place it in a colander to drain. Remove stems, if large.
2. Place a large skillet over high heat. Add spinach by the handfuls, and toss until spinach wilts, adding additional spinach until all is wilted. Drain spinach in a colander, and chop coarsely.
3. Heat butter in the skillet over medium-high heat. Add onion and garlic, and cook, stirring frequently, for 3 minutes or until onion is translucent.
4. Stir spinach, feta cheese, cream cheese, dill, oregano, and lemon juice into the skillet. Reduce heat to low, and cook, stirring frequently, until mixture comes to a boil. Simmer for 3 minutes, stirring occasionally. Season to taste with salt and pepper.
5. Transfer dip to a fondue pot or other heated serving dish, and serve immediately.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
145 calories
108 calories from fat
12 g fat
8 g saturated fat
7 g protein
4 g carbohydrates
**Fast Talk**
Feta cheese is a classic Greek cheese traditionally made from sheep's or goat's milk, although today it's often made with cow's milk. White, crumbly, and rindless, feta is usually pressed into square cakes. It has a rich, tangy flavor and can range in texture from soft to semidry.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
250 calories
143 calories from fat
16 g fat
10 g saturated fat
15 g protein
3 g carbohydrates
# **Classic Cheese Fondue**
This Swiss favorite doubles as a dinner for 4. Serve it with a tossed salad.
**1 garlic clove, peeled and**
**halved crosswise**
**1** **½ cups dry white wine**
**2 cups Emmenthal cheese,**
**coarsely grated**
**2 cups Gruyère cheese,**
**coarsely grated**
**2 TB.** _**kirsch**_
**1 TB. cornstarch**
1. Rub the inside of a heavy 2-quart saucepan with the cut sides of garlic. Discard garlic. Add wine to the pot and bring to a simmer over medium heat.
2. Add Emmenthal and Gruyère cheeses to wine by ½ cup measures, stirring constantly with a whisk in a figure-eight pattern. Add additional cheese only after the previous addition is melted.
3. Combine kirsch and cornstarch in a small bowl, and stir to dissolve cornstarch. Add cornstarch mixture to fondue, and bring to a simmer, stirring constantly. Cook over low heat for 1 or 2 minutes or until fondue has thickened.
4. Transfer fondue to a fondue pot or other pot with a heat source, and serve immediately.
**Fast Talk**
Kirsch, also labeled _kirschwasser,_ is a clear, tart cherry brandy distilled from cherry juice and cherry pits. In addition to the characteristic flavor in cheese fondue, kirsch is what's used to flame cherries jubilee.
# **Brie, Stilton, and Wild Mushroom Dip**
This hearty dip is a great sauce for grilled or broiled meats or poultry.
**1 garlic clove, peeled and**
**halved crosswise**
**2 TB. dried porcini mushrooms,**
**finely chopped**
**2 tsp. fresh thyme or** **¾ tsp.**
**dried**
**1** **½ cups dry white wine**
**¼ lb. fresh shiitake mushrooms**
**2 TB. unsalted butter**
**2 TB. olive oil**
**2 cups Brie cheese, at room**
**temperature**
**1 cup coarsely grated Stilton**
**cheese**
**1 TB. cold water**
**1 TB. cornstarch**
**Salt and freshly ground black**
**pepper to taste**
1. Rub the inside of a heavy 2-quart saucepan with cut sides of garlic. Discard garlic. Add porcini mushrooms, thyme, and wine to the pan, and bring to a simmer over medium heat. Reduce heat to low, and simmer for 1 minute. Turn off heat and allow mixture to _steep_ for 10 minutes.
2. While mixture is steeping, wipe mushrooms with a damp paper towel. Discard stems, and chop mushrooms finely.
3. Heat butter and olive oil in a medium skillet over medium-high heat. When butter foam begins to subside, add chopped shiitake mushrooms. Cook, stirring constantly, for 3 minutes or until mushrooms are soft and browned. Add cooked mushrooms to the pan with wine.
4. Scrape the top rind off Brie, and scoop out interior cheese using a spoon. Discard bottom and side rinds.
5. Bring wine back to a simmer over medium heat. Add Brie and Stilton cheeses to wine by ½ cup measures, stirring constantly with a whisk in a figure-eight pattern. Add additional cheese only after the previous addition is melted.
6. Combine water and cornstarch in a small bowl, and stir to dissolve cornstarch. Add to fondue, and bring to a simmer, stirring constantly. Cook over low heat for 1 or 2 minutes or until fondue has thickened. Season to taste with salt and pepper.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
244 calories
163 calories from fat
18 g fat
10 g saturated fat
10 g protein
4 g carbohydrates
**Fast Talk**
To steep means to soak dry ingredients such as dried mushrooms, tea leaves, and dried herbs and spices in hot liquid until the food's flavor is transferred into the liquid.
7. Transfer fondue to a fondue pot or other pot with a heat source, and serve immediately.
**Variation:** You can substitute Camembert or Explorateur cheese for the Brie, and Gorgonzola or blue cheese can be used in place of the Stilton.
Serves: 10
**Active time:** 10 minutes
**Start to finish:** 30 minutes, including 20 minutes for chilling
**Each serving contains:**
172 calories
102 calories from fat
11 g fat
3 g saturated fat
11 g protein
6 g carbohydrates
# **Smoked Trout Dip**
Bits of sweet pickle balance the saltiness of the fish in this creamy dip.
**1 cup sweet pickle slices,**
**drained**
**1 lb. smoked trout fillets,**
**skinned and broken into 1-**
**inch pieces**
**⅓ cup mayonnaise**
**¼ cup heavy cream**
**¼ cup freshly squeezed lemon**
**juice**
**½ tsp. cayenne or to taste**
1. Place pickle slices in a food processor fitted with a steel blade. Chop finely, using on-and-off pulsing. Scrape chopped pickles into a mixing bowl and set aside.
2. Place smoked trout, mayonnaise, cream, lemon juice, and cayenne in the work bowl of the food processor and purée until smooth. Scrape trout mixture into the mixing bowl, and stir well to combine. Refrigerate until well chilled.
**Variation:** Substitute smoked salmon, smoked whitefish, or smoked bluefish for the trout.
**Fresh Ways**
A pretty way to serve this dip—or any very thick dip—is to line a small bowl or mold with plastic wrap and pack the dip into the plastic-wrapped bowl. To serve, invert the mold onto a platter, discard the plastic wrap, and decorate with herbs.
# **Two-Salmon Dip**
Delicate fresh salmon is joined with bits of succulent smoked salmon in this colorful dip.
**1 (** **½-lb.) salmon fillet**
**1 tsp.** _**Old Bay**_ **seasoning**
**2 (8-oz.) pkg. cream cheese,**
**softened**
**3 TB. freshly squeezed lemon**
**juice**
**2 TB. white horseradish**
**¼ lb. smoked salmon, finely**
**chopped**
**3 scallions, rinsed, trimmed,**
**and chopped**
**3 TB. chopped fresh dill or**
**2 tsp. dried**
**Freshly ground black pepper**
**to taste**
1. Sprinkle salmon fillet with Old Bay seasoning and place it in a microwave-safe dish. Cover the dish with plastic wrap, and microwave salmon fillet on high (100 percent) for 3 minutes or until cooked through. Refrigerate salmon until cold. Remove and discard skin, and break salmon into 1-inch chunks.
2. Place salmon, cream cheese, lemon juice, and horseradish in a food processor fitted with a steel blade, and purée until smooth. Scrape mixture into a mixing bowl, and stir in chopped smoked salmon, scallions, and dill. Season with pepper, and refrigerate for at least 45 minutes or until chilled. (You can make this dip up to 2 days in advance and refrigerate, tightly covered.)
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 1 hour,
including 45 minutes for
chilling
**Each serving contains:**
218 calories
169 calories from fat
19 g fat
11 g saturated fat
10 g protein
2.5 g carbohydrates
**Fast Talk**
Old Bay is a seasoning mix developed for Chesapeake Bay's prized steamed crabs. It contains celery salt, mustard, cayenne, bay leaves, cloves, allspice, ginger, and paprika.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
133 calories
100 calories from fat
11 g fat
8 g saturated fat
6.5 g protein
3 g carbohydrates
**Speedy Solutions**
A fast way to soften cream cheese is to cut it into cubes, place it on a microwave-safe dish, and microwave for 10 seconds. Repeat, if necessary.
# **Crab Rangoon Dip**
Hints of ginger, garlic, and other Asian flavors enliven this creamy hot dip.
**½ lb. crabmeat**
**3 scallions**
**1 (8-oz.) pkg. cream cheese,**
**softened**
**½ cup coconut milk**
**2 garlic cloves, peeled and**
**minced**
**2 TB. soy sauce**
**2 TB. grated fresh ginger**
**1 TB. Worcestershire sauce**
**2 TB. chopped fresh cilantro**
**Salt and freshly ground black**
**pepper to taste**
1. Place crabmeat on a dark-colored plate. Rub it gently with your fingertips, and discard any bits of shell or cartilage you uncover. Set crabmeat aside.
2. Rinse and trim scallions. Discard all but 2 inches of green tops, and chop scallions.
3. Combine scallions, cream cheese, coconut milk, garlic, soy sauce, ginger, and Worcestershire sauce in a heavy 2-quart saucepan. Cook over medium-low heat, stirring frequently, for 5 minutes or until mixture is hot and bubbly. Stir in crabmeat and cilantro, and season to taste with salt and pepper.
4. Transfer dip to a fondue pot or other heated serving dish, and serve immediately.
**Variation:** Substitute chopped shrimp or finely chopped cooked chicken for the crabmeat.
# **Mexican Beef and Chili Dip (** _ **Chili con Queso**_ **)**
This hearty dish is like nacho topping just awaiting the dipping.
**8 ripe plum tomatoes or**
**1 (14.5-oz.) can petite diced**
**tomatoes, drained**
**2 TB. olive oil**
**1 onion, peeled and diced**
**3 garlic cloves, peeled and**
**minced**
**1 lb. lean ground beef**
**1 (4-oz.) can chopped mild**
**green chilies, drained**
**½ cup heavy cream**
**2 cups Monterey Jack cheese,**
**coarsely grated**
**2 cups mild cheddar cheese,**
**coarsely grated**
**1 TB. cold water**
**1 TB. cornstarch**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse, core, and seed tomatoes. Chop tomatoes finely, and set aside.
2. Heat olive oil in a large heavy skillet over medium-high heat. Add onion, garlic, and ground beef. Cook, breaking up lumps with a fork, for 3 to 5 minutes or until beef is brown and no pink remains. Add tomatoes and green chilies, and cook for an additional 3 minutes. Remove contents of the skillet with a slotted spoon, and discard grease from the skillet.
3. Return contents to the skillet, and add cream and Monterey Jack and cheddar cheeses. Cook over medium heat, stirring frequently, for 3 minutes or until cheese is melted and bubbly.
4. Combine water and cornstarch in a small bowl, and stir to dissolve cornstarch. Add cornstarch mixture to dip, and bring to a simmer, stirring constantly. Cook over low heat for 1 or 2 minutes or until dip has thickened. Season to taste with salt and pepper. (This can be done up to 4 hours ahead. Reheat over medium heat until boiling.)
5. Transfer dip to a fondue pot or other heated serving dish, and serve immediately.
**Variation:** Use Mexican chorizo sausage instead of ground beef, and for a spicier dish, try jalapeño Jack cheese instead of the Monterey Jack.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
321 calories
215 calories from fat
24 g fat
13 g saturated fat
22 g protein
5 g carbohydrates
**Speedy Solutions**
Petite cut tomatoes, a relative new-comer to the market, are great for dips. Regular diced tomatoes should really be cut into smaller pieces or someone's dip into the bowl could yield nothing but tomato. The petite cut ones are preferable and save time.
Serves: 10
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
209 calories
129 calories from fat
14 g fat
7 g saturated fat
16 g protein
4 g carbohydrates
# **Sausage Pizza Dip**
If your favorite part of a pizza is the gooey topping, here's all the flavors you love in a dip.
**1 TB. olive oil**
**¾ lb. mild or hot Italian bulk**
**sausage**
**1 cup spaghetti sauce**
**1 TB. chopped fresh oregano**
**or 1 tsp. dried**
**1 TB. chopped fresh basil or**
**1 tsp. dried**
**2 tsp. fresh thyme or** **½ tsp.**
**dried**
**4 cups whole milk mozzarella**
**cheese, coarsely grated**
**Salt and freshly ground black**
**pepper to taste**
1. Heat olive oil in a large skillet over medium-high heat. Add sausage and cook, breaking up lumps with a fork, for 3 to 5 minutes or until sausage is no longer pink. Remove sausage from the skillet with a slotted spoon, and discard grease from the pan.
2. Return sausage to the pan and add spaghetti sauce, oregano, basil, and thyme. Bring to a boil, reduce heat to low, and simmer 10 minutes or until slightly thickened. Stir in mozzarella and cook until cheese is melted. Season to taste with salt and pepper. (This can be done up to 4 hours ahead. Reheat over medium heat until boiling.)
3. Transfer dip to a fondue pot or other heated serving dish, and serve immediately.
**Variation:** Personalize this recipe using your favorite pizza toppings. Try ground beef or diced pepperoni in place of the sausage, or make this a vegetarian dip by removing sausage and adding sautéed onion, green pepper, or mushrooms.
**Fresh Ways**
If you can't find bulk sausage for recipes, add a few minutes to the prep time for removing the sausage meat from its casings (the casing turns into nasty rubber bands when cooked). Just push on one end like a tube of toothpaste.
**Chapter 4**
**Nibbles and Noshes: Hors d'Oeuvres for All Occasions**
**In This Chapter**
• Fun finger foods
• Roll-ups and wraps
• Seafood starters
Maybe your standard hors d'oeuvres are a bowl of sesame sticks or a handful of cherry tomatoes while you're cooking dinner (or waiting for dinner to be cooked for you!). But chances are, when you're entertaining, you want to enjoy foods a bit more elegant with your predinner beverage. That's when the recipes in this chapter come in handy.
Hors d'oeuvres should be simple to make and simple to eat, and all the dishes here qualify as both. In these pages, you'll find recipes that produce crunchy textures; those are the sort of dressed-up chips of one type or another. And you'll also find some elegant seafood nibbles and various types of wraps that are quick to make and easy to slice into individual portions.
# **Assembly Line Logic**
I'm not one for ditsy hors d'oeuvres. And I pride myself on telling you that I've never stuffed a snow pea. All the individual hors d'oeuvres in this chapter start out as a big batch of something. You do the individual portioning of the hors d'oeuvre either before or after baking, but it's basically an assembly line process. When you're reading through the recipes here, note how far in advance dishes can be prepared up to a certain point. Then start a countdown from the time your party starts.
# **Fresh Tomato Bruschetta**
Luscious rosy tomatoes flavored with herbs and garlic make a great toast topper.
**1 French baguette, cut into**
**½-inch-thick slices**
**4 TB. olive oil**
**6 ripe plum tomatoes, rinsed,**
**cored, seeded, and finely**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh basil**
**2 TB. chopped fresh parsley**
**2 TB. balsamic vinegar**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven broiler and cover a baking sheet with aluminum foil. Brush both sides of bread slices very lightly with 3 tablespoons olive oil. Broil bread 6 inches from the broiler element for 1 minute per side or until browned. Remove and set aside.
2. Combine tomatoes, garlic, basil, parsley, and vinegar in a mixing bowl. Add remaining 1 tablespoon olive oil. Season to taste with salt and pepper, and stir well.
3. To serve, place 1 tablespoon tomato mixture on each toast slice, and serve immediately. (The toasts can be made up to 1 day in advance and kept at room temperature, tightly covered. The tomato mixture can be made up to 2 hours in advance and kept at room temperature. Do not top toasts until just before serving.)
**Variation:** Reduce the number of tomatoes to 4 and add ½ cup canned white beans, drained and rinsed, and ¼ cup chopped pitted kalamata olives.
Yield: 24 toasts
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
78 calories
26 calories from fat
3 g fat
1 g saturated fat
2 g protein
11 g carbohydrates
**Fast Talk**
Bruschetta (pronounced _broo-SKEH-tah_ ) comes from the Italian word _bruscare,_ meaning "to cook over the coals." Or it's the fancy Italian word for toast. While traditional bruschetta is grilled, broiling in the oven is just fine.
# **Herbed Goat Cheese and Roasted Pepper Spirals**
Tart cheese is a perfect foil for sweet peppers in these colorful spirals.
Yield: 36 spirals
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
29 calories
20 calories from fat
2 g fat
1.5 g saturated fat
1.5 g protein
1 g carbohydrates
**Stale Stuff**
You'll see precrumbled goat cheese next to the precrumbled blue and feta cheese in supermarkets. Avoid them all. Cheese loses flavor quickly when it's exposed to air that way.
**3 red bell peppers, or 3 jarred**
**roasted red peppers**
**½ lb. (1 cup) mild goat**
**cheese, softened**
**2 TB. heavy cream**
**2 garlic cloves, peeled**
**8 sprigs parsley, rinsed and**
**stemmed**
**2 tsp. Herbes de Provence**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven broiler. Place red peppers on the rack of a broiler pan and broil 4 inches from the broiler element until skin is charred and black. Turn peppers with tongs to char all sides. Plunge peppers into ice water, and when cool enough to handle, remove and discard cap, skin, and seeds. Cut peppers in half and set aside.
2. Combine goat cheese, cream, garlic, parsley, and Herbes de Provence in a food processor fitted with a steel blade. Purée until smooth and then scrape mixture into a mixing bowl. Season to taste with salt and pepper.
3. Spread herbed cheese onto pepper halves, and roll peppers lengthwise into cylinders. Refrigerate peppers for 3 hours, tightly wrapped with plastic wrap. To serve, slice each roll into 6 slices. (Peppers can be stuffed 1 day in advance and refrigerated, tightly covered. Slice rolls just before serving.)
# **Cheddar Crackers**
Crushed potato chips are the "secret ingredient" that makes these cheese crackers extra crunchy.
**1 (5.5-oz.) bag potato chips**
**1½ cups grated sharp cheddar**
**cheese**
**5 TB. unsalted butter, melted**
**⅓ cup all-purpose flour**
**½ tsp. cayenne or to taste**
1. Preheat the oven to 350°F. Place potato chips in a food processor fitted with a steel blade. Chop chips coarsely, using on-and-off pulsing.
2. Scrape potato chip crumbs into a large mixing bowl and add cheese, butter, flour, and cayenne. Stir until mixture is combined and holds together when pressed in the palm of your hand.
3. Form mixture into 1 tablespoon balls. Place balls on an ungreased baking sheet and flatten into circles with the bottom of a floured glass or with your fingers. Repeat with remaining dough, leaving 1 inch between circles.
4. Bake for 15 to 18 minutes or until browned. Cool crackers on the baking sheet for 2 minutes and then transfer to a cooling rack with a spatula to cool completely. Serve at room temperature. (The crackers can be made 2 days in advance and kept at room temperature in a tightly sealed container.)
**Variation:** Substitute Gruyère or jalapeño Jack for the cheddar.
**Fresh Ways** f you're grating cheese by hand rather than with a food
processor, spray the grater with vegetable oil spray before grating. It will be much easier to clean.
Yield: 24 crackers
**Active time:** 5 minutes
**Start to finish:** 30 minutes, including 10 minutes for cooling
**Each serving contains:**
93 calories
66 calories from fat
7 g fat
4 g saturated fat
2 g protein
5 g carbohydrates
Yield: 24 pinwheels
**Active time:** 15 minutes
**Start to finish:** 1¼
hours, including 1 hour
for chilling
**Each serving contains:**
65 calories
23 calories from fat
2.5 g fat
1 g saturated fat
3 g protein
7 g carbohydrates
**Stale Stuff**
Do not try to substitute bottled salsa for the fresh, refrigerated salsa you find in the produce section. The success of this dish requires the texture and flavor of the fresh vegetables.
# **Southwest Smoked Salmon Pinwheels**
A core of salad greens in the center of layers of smoked salmon and salsa cream cheese makes this a stunning hors d'oeuvre.
**1 cup good-quality refrigerated**
**salsa**
**1 (3-oz.) pkg. cream cheese,**
**softened**
**¼ cup chopped fresh cilantro**
**4 (10-in.) flour tortillas**
**½ lb. sliced smoked salmon**
**2 cups mesclun salad mix or**
**other baby greens, rinsed and**
**dried**
1. Drain salsa in a strainer, pressing to extract as much liquid as possible. Combine salsa, cream cheese, and cilantro in a mixing bowl, and stir well.
2. Wrap tortillas in plastic wrap and microwave on high (100 percent) for 10 to 20 seconds or until soft and pliable.
3. Place tortillas on a counter, and spread each with cream cheese mixture. Arrange salmon slices on the bottom half of each tortilla. Place ½ cup mesclun at the bottom edge of tortilla on top of salmon. Roll tortillas firmly but gently, starting at the filled edge. Place rolls, seam side down, on a platter or ungreased baking sheet, and refrigerate for 1 hour.
4. Trim end off each roll by cutting on the diagonal to remove the portion of tortilla that does not meet and form a log. Slice each tortilla into 6 slices, and serve chilled. (Tortillas can be filled up to 4 hours in advance and refrigerated, tightly covered. Slice just before serving.)
**Variation:** You can use thinly sliced smoked turkey, roast beef, or ham instead of the smoked salmon.
# **Salmon Tartare on Cucumber Slices**
If you **'** re a fan of sushi or shashimi **,** you **'** ll love this seasoned salmon canapé served on crunchy cucumber slices.
**1 (1-lb.) salmon fillet, skinned**
**1 bunch fresh parsley, rinsed**
**and stemmed**
**4 anchovy fillets**
**2 shallots, peeled and quartered**
**3 TB. capers, drained and**
**rinsed**
**2 TB. white horseradish**
**2 TB. grainy mustard**
**3 TB. freshly squeezed lemon**
**juice**
**Salt and freshly ground black**
**pepper to taste**
**2 medium cucumbers**
1. Rinse salmon and pat dry on paper towels. Cut into ½-inch dice and chop finely by hand. Place salmon in a mixing bowl.
2. Combine parsley, anchovies, and shallots in a food processor fitted with a steel blade. Chop finely using on-and-off pulsing. Scrape mixture into the mixing bowl and add capers, horseradish, mustard, and lemon juice. Stir well, and season to taste with salt and pepper.
3. Rinse cucumbers, and _score_ each with the tines of a fork. Slice each cucumber into 18 slices.
4. To serve, top each cucumber slice with 2 teaspoons salmon mixture. (Salmon can be chopped and the remaining mixture can be prepared up to 4 hours in advance. Do not combine them or top cucumber slices until just before serving.)
**Variation:** Substitute fresh tuna or chopped sea scallops for the salmon. You could also place the mixture on the stem end of Belgian endive spears instead of cucumber slices.
Yield: 36 slices
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
24 calories
6 calories from fat
1 g fat
0 g saturated fat
3.5 g protein
1 g carbohydrates
**Fast Talk**
To score a food is to make shallow cuts at regular intervals. Scoring cucumbers makes them more decorative on a platter, but foods such as flank steak are scored to prevent them from curling when cooked.
Yield: 24 cakes
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
36 calories
16 calories from fat
2 g fat
0 g saturated fat
3 g protein
2 g carbohydrates
**Stale Stuff**
Don't automatically reach for the salt and pepper! Seasoning mixtures such as Old Bay or Cajun seasoning contain both seasonings, so you don't need to add more when using them in recipes.
# **Southwest Miniature Crab Cakes**
Aromatic fresh cilantro gives these seafood cakes a Hispanic accent.
**4 scallions**
**¾ lb. crabmeat**
**1 large egg**
**3 TB. mayonnaise**
**3 TB. cracker meal**
**1 to 2 tsp. Old Bay seasoning**
**2 red bell peppers, seeds and**
**ribs removed, and very finely**
**chopped**
**3 TB. chopped fresh cilantro**
**Vegetable oil spray**
1. Heat the oven to 450°F. Cover a baking sheet with heavy duty aluminum foil, and spray the foil with vegetable oil spray.
2. Rinse and trim scallions, discarding all but 2 inches of green tops. Chop scallions finely.
3. Place crabmeat on a dark-colored plate. Rub it gently with your fingertips, and discard any bits of shell or cartilage you uncover. Set crabmeat aside.
4. Combine egg, mayonnaise, cracker meal, and Old Bay in a mixing bowl, and whisk until well blended. Gently fold in crabmeat, red bell peppers, scallions, and cilantro.
5. Using a tablespoon, form mixture into balls and then flatten them on the baking sheet into patties. Spray tops of patties with vegetable oil spray.
6. Bake for 10 to 12 minutes, or until lightly brown on top. Serve immediately. (The crabmeat mixture can be made 1 day in advance and refrigerated, tightly covered with plastic wrap. Do not form or bake until just before serving.)
**Variation:** Larger versions of this hors d'oeuvre can serve 4 as an entrée. Form mixture into 8 patties, and bake them at 400°F for 15 to 20 minutes. Also, you can use finely chopped shrimp or lobster instead of crabmeat.
# **Baked Shrimp Toast Rolls**
These baked rolls are a more healthful version of traditional Chinese shrimp toast.
**12 slices white sandwich**
**bread**
**¾ lb. raw shrimp, peeled and**
_**deveined**_
**2 TB. chopped fresh ginger**
**1 TB. Asian sesame oil**
**1 large egg white**
**1 TB. dry sherry**
**2 TB. cornstarch**
**1 TB. soy sauce**
**2 scallions, rinsed, trimmed,**
**and sliced into 2-inch sections**
**⅓ cup finely chopped canned**
**water chestnuts**
**Salt and freshly ground black**
**pepper to taste**
**Vegetable oil spray**
1. Preheat the oven to 425°F. Cover a baking sheet with heavy-duty aluminum foil and spray foil with vegetable oil spray.
2. Remove crusts from bread slices using a serrated bread knife. Roll each slice with a rolling pin (or a large glass or a wine bottle) until bread is thin but still pliable. Set aside.
3. Combine shrimp, ginger, sesame oil, egg white, sherry, cornstarch, and soy sauce in a food processor fitted with a steel blade. Purée until smooth, stopping a few times to scrape the sides of the work bowl. Add scallions and chop finely using on-and-off pulsing. Scrape mixture into a mixing bowl and stir in water chestnuts. Season to taste with salt and pepper.
4. Spread bread slices out on a counter, and place 1 heaping tablespoon filling in a line across the long side of each slice. Roll bread around filling so the edges meet, and place rolls, seam side down, on the prepared baking sheet. Spray tops with vegetable oil spray.
5. Bake rolls 5 minutes, turn them over gently with tongs, and bake 4 more minutes or until browned. Cut each roll into 3 sections with a serrated knife, and serve immediately. (Filling can be prepared 1 day in advance and refrigerated, tightly covered. Fill bread and bake the rolls just before serving.)
**Variation:** Any firm-fleshed white fish such as cod, snapper, or sole will work instead of the shrimp.
Yield: 36 rolls
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
40 calories
7 calories from fat
1 g fat
0 g saturated fat
3 g protein
5 g carbohydrates
**Fast Talk**
Deveining is the process of removing the dark vein (actually the intestinal tract) from the top of shrimp after they are shelled. This is done with a paring knife or with a special gadget called a deveiner.
Yield: 24 spears
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
39 calories
24 calories from fat
3 g fat
2 g saturated fat
2.5 g protein
2 g carbohydrates
**Fresh Ways**
Submerging vegetables in ice water performs a number of functions: it stops the vegetables from continuing to cook with residual heat, it cools them down in a jiffy so you can save time, and it sets the green color of vegetables such as asparagus and snow peas.
# **Asparagus Wrapped in Herbed Cheese and Prosciutto**
Asparagus moves from the dinner plate to the hors d'oeuvre tray when wrapped in ham spread with cream cheese.
**24 thick asparagus spears**
**(about 2 1b.)**
**1 (3-oz.) pkg. cream cheese,**
**softened**
**2 TB. unsalted butter, softened**
**3 garlic cloves, peeled and**
**minced**
**2 TB. chopped fresh parsley**
**1 TB. chopped fresh oregano**
**or ½ tsp. dried**
**1 TB. chopped fresh basil or**
**½ tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**¼ lb. thinly sliced prosciutto**
1. Rinse asparagus spears, discard woody stem end, and peel ⅓ the way up the stalk with a vegetable peeler. Steam asparagus for 5 to 7 minutes or until crisp-tender. Plunge asparagus into ice water to stop the cooking action. Drain, and pat dry with paper towels.
2. While asparagus is steaming, combine cream cheese, butter, garlic, parsley, oregano, and basil in a mixing bowl. Stir well, and season to taste with salt and pepper.
3. Trim visible fat off prosciutto slices, and cut prosciutto into 2-inch-wide strips.
4. Spread prosciutto slices with cheese mixture and wrap around asparagus spears, beginning at the stem end and wrapping only to the tip. Serve immediately. (Asparagus can be steamed up to 1 day in advance and refrigerated, tightly covered, and they can be wrapped up to 4 hours in advance and refrigerated, tightly covered.)
**Variation:** If you're not a fan of asparagus, try this recipe with sugar snap peas or broccoli florets.
# **Vietnamese Spring Rolls (** _ **Cha Gio**_ **)**
Delicate rice paper pancakes hold a filling of pork and vegetables in these crispy rolls.
**5 large dried shiitake mushrooms**
**1 oz.** _**bean thread noodles**_
**½ lb. ground pork**
**1 cup bean sprouts, rinsed**
**and cut into 1-inch lengths**
**½ cup shredded carrot**
**½ cup chopped scallions,**
**white part and 4 inches of**
**green tops**
**4 garlic cloves, peeled and**
**minced**
**3 TB. fish sauce (** _ **nam pla**_ **)**
**2 large eggs, lightly beaten**
**½ cup granulated sugar**
**Salt and freshly ground black**
**pepper to taste**
**18 rice paper pancakes**
**Vegetable oil spray**
Yield: 36 pieces
**Active time:** 30 minutes
**Start to finish:** 1 hour
**Each serving contains:**
58 calories
15 calories from fat
2 g fat
1 g saturated fat
1 g protein
9 g carbohydrates
**Fast Talk**
Bean thread noodles—sometimes called cellophane noodles, glass noodles, or bean thread vermicelli—are translucent strands made from the starch of green mung beans. While they should be soaked before adding to most dishes, they don't need to be soaked if added to soups.
1. Soak dried mushrooms and bean thread noodles in separate bowls of very hot tap water for 15 minutes. Remove mushrooms, and squeeze well to extract as much water as possible. Discard stems, and finely chop mushrooms. Drain bean thread noodles. Place on a cutting board in a long log shape, and cut into 1-inch pieces. Measure out ½ cup, and discard any additional noodles.
2. Preheat the oven to 400°F. Cover a baking sheet with heavy-duty aluminum foil, and spray foil with vegetable oil spray.
3. Place mushrooms and noodles in a mixing bowl and add pork, bean sprouts, carrot, scallions, garlic, fish sauce, eggs, and 1 teaspoon sugar. Season to taste with salt and pepper.
4. Fill a wide mixing bowl with very hot tap water, and stir in remaining sugar.
5. Place a damp tea towel in front of you on the counter. Place rice paper pancakes on a plate, and cover with a barely damp towel.
6. Fill 1 rice paper pancake at a time, keeping the remainder covered. Totally immerse pancake in hot water for 2 seconds. Remove, and place it on the damp tea towel; it will become pliable within a few seconds. Gently fold front pancake edge ⅓ of the way to the top. Place about 2 tablespoons filling on the folded-up portion, and shape it into a log, leaving a 2-inch margin on each side. Lightly spray the unfilled pancake with vegetable oil spray. Fold the sides over filling, and roll tightly but gently, beginning with filled side. Place roll on the baking sheet, and fill remaining rice paper pancakes.
7. Spray tops and sides of rolls with vegetable oil spray. Bake for 12 minutes, turn rolls gently with tongs, and bake an additional 10 to 12 minutes or until rolls are browned. Remove the pan from the oven, and blot rolls with paper towels. Slice each in half on the diagonal, and serve immediately. (Rolls can be made up to 2 days in advance and refrigerated, tightly covered. Reheat in a 375°F oven for 8 to 10 minutes or until crisp.)
**Variation:** You can use ground turkey or finely chopped raw shrimp for the ground pork in this recipe.
**Chapter 5**
**Appealing Appetizers**
**In This Chapter**
• Hot and cold clam and mussel appetizers
• Succulent shrimp dishes
• Elegant veggie treats
The dishes in the previous chapter were all finger foods. In this chapter, you'll find recipes for plated appetizers to start a meal. Appetizers are so popular that many restaurants have adopted appetizer-size portions, a.k.a. "little plates," for their entire menu. It's these fast and easy recipes that you'll find in this chapter.
The emphasis in this chapter is on seafood appetizers with a few vegetable dishes in the mix. I think meals should start on a light note. Fish before meat became the norm in classic dining for just that reason. But _light_ is hardly synonymous with _dull_. As you'll see, these dishes are vibrantly flavored and draw inspiration from cuisines around the world.
# **Mad for Mollusks**
Mollusks, along with crustaceans, are a large family of seafood that ranges from tiny cockles to massive abalone. But what they all have in common is that they protect their soft bodies with hard shells.
Oysters are identified by their place of origin and have names such as Blue Point (for the waters off New York's Long Island) and Olympia (native to the Pacific Northwest). Clams and scallops are graded by size.
**Speedy Solutions**
Removing bivalves from their shells is a labor-intensive process referred to as _shucking_. Increasingly, fish processors are doing this for us. Pints of shucked oysters, scallops by the pound, and minced fresh clams are becoming the rule rather than the exception, so look for preshucked mollusks when you're shopping.
Littleneck clams are the smallest, followed in size by cherrystone clams and quahogs. Sea scallops are about four times the size of bay scallops and can be cut into quarters for a recipe calling for the tiny bay scallops.
When selecting mollusks, the most critical consideration is whether they are alive. The shells should be closed or should close tightly when handled. To test a mollusk, with your forefinger above and thumb underneath, gently squeeze the mollusk, as if to push the top shell forward. If the shell does not firmly close, the mollusk should be immediately discarded.
# **Mussel-ing In**
While some cultures eat raw mussels, we eat them cooked, so opening them is not a problem. (That happens naturally when they're steamed.) But mussels do require some specialized preparation prior to that trip to the pot.
To clean mussels, first wash and remove the beards. The easiest way is to grasp the mussel between your thumb and a dull knife blade and give the beard a tug to pull it free. Scrape or pull away any that remains. Using a stiff brush or scouring pad, continue to scrub the shell of each mussel to remove every bit of grass and mud. You don't have to remove scales and barnacles, except when the shells are going to be served with the dish.
# **Black Bean Cakes**
These sautéed cakes are flavored with herbs and spices, and they double as a side dish for Mexican or Southwestern meals.
**6 TB. olive oil**
**1 medium onion, peeled and**
**coarsely chopped**
**3 garlic cloves, peeled and**
**minced**
**2 serrano chilies, seeds and**
**ribs removed, and diced**
**2 TB. chili powder**
**1½ TB. ground cumin**
**2 (15-oz.) cans black beans,**
**drained and rinsed**
**½ cup chopped fresh cilantro**
**½ cup water**
**Salt and freshly ground black**
**pepper to taste**
**1 cup sour cream**
**1 cup good-quality refrigerated**
**tomato salsa**
1. Heat 2 tablespoons olive oil in a large, heavy skillet over medium-high heat. Add onion, garlic, and serrano chilies, and cook, stirring frequently, for 3 minutes or until onion is translucent. Add chili powder and cumin, and cook, stirring constantly, for 1 minute. Add black beans, cilantro, and water. Bring mixture to a boil and simmer, stirring frequently, for 3 minutes.
2. Transfer mixture to a food processor fitted with a steel blade and purée. Scrape mixture into a mixing bowl, and season to taste with salt and pepper.
3. Roll enough mixture into a ball the size of a golf ball. Flatten between two sheets of plastic wrap until patty is ¼ inch thick. Repeat with remaining mixture.
4. Heat remaining 4 tablespoons olive oil in a large, heavy skillet over high heat. Add bean cakes and cook for 1 or 2 minutes per side or until crisp, turning gently with a slotted spatula. Drain cakes on paper towels, and continue until all cakes are cooked.
5. To serve, place 1 or 2 cakes on a plate and top each with 1 tablespoon sour cream and 1 tablespoon salsa. Serve immediately. (Bean mixture can be made up to 1 day in advance and refrigerated, tightly covered. Fry cakes just prior to serving.)
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
282 calories
194 calories from fat
22 g fat
6 g saturated fat
6 g protein
17 g carbohydrates
**Stale Stuff**
You might think it's not necessary to dice and chop ingredients that are destined to become a purée, but it really is important. If the pieces are too large, they won't cook properly and your finished dish will taste like your raw ingredients.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
253 calories
66 calories from fat
7 g fat
4 g saturated fat
9 g protein
39 g carbohydrates
# **Deviled Leeks**
This elegant appetizer conveys the subtle flavor of leeks, the mild member of the onion family.
**12 to 16 small leeks**
**2 TB. unsalted butter**
**½ cup chicken or vegetable**
**stock**
**⅓ cup dry white wine**
**2 TB. chopped fresh** _**marjoram**_
**or 1 tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**3 TB. Dijon mustard**
**½ cup plain breadcrumbs**
**½ cup freshly grated**
**Parmesan cheese**
1. Preheat the oven to 375°F.
2. Trim off the root end of leeks and discard all but 1 inch of green tops. Split leeks lengthwise, and rinse well under cold running water.
3. Melt butter in a large skillet over medium heat. Add leeks, and cook 5 minutes or until leeks begin to soften, turning them gently with tongs. Add stock, wine, marjoram, salt, and pepper, and bring to a boil. Cover the pan, reduce the heat to low, and cook for 10 minutes, rolling leeks over occasionally.
4. Arrange leeks in a 9×13-inch baking dish, and pour liquid from the skillet over them. Spread leeks evenly with Dijon mustard and sprinkle with breadcrumbs and Parmesan cheese. Bake, uncovered, for 10 minutes. Serve immediately. (Leeks can be prepared for baking up to 6 hours in advance and kept at room temperature. Bake just prior to serving.)
**Fast Talk**
Marjoram ( _MAHR-jur-umm_ ) is a member of the mint family. The flavor from the long, pale-green leaves is similar to that of oregano but sweeter. If you can't find marjoram, use oregano, but only use half as much as you would marjoram.
# **Baked Clams Casino**
Sautéed onion, sweet red bell pepper, and garlic flavor the bread topping that crowns the clams.
**5 TB. unsalted butter**
**4 garlic cloves, peeled and**
**minced**
**1 medium onion, peeled and**
**chopped**
**1 red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**1½ cups** _**Italian breadcrumbs**_
**¼ cup freshly grated**
**Parmesan cheese**
**Salt and freshly ground black**
**pepper to taste**
**24 littleneck or small cherrystone**
**clams**
1. Preheat the oven to 425°F.
2. Melt butter in a large skillet over medium heat. Add garlic and onion and cook, stirring frequently, for 3 minutes or until onion is translucent. Add red bell peppers and cook, stirring frequently, for 5 to 7 minutes or until peppers are soft. Add breadcrumbs and cheese, and stir to combine. Season to taste with salt and pepper. Set aside.
3. Scrub clams well under cold running water with a stiff brush. Discard any clams that do not shut tight while being scrubbed. Place clams in a mixing bowl, and cover them with hot tap water. Within about 2 minutes, the shells will be slightly apart. Insert a clam knife or paring knife between the shells at one corner, and sever the muscles holding the shells together. Discard one shell, release clams from the bottom shell by scraping under meat with a paring knife, and leave meat in the shell.
4. Mound topping on raw clams, using about 1 tablespoon per clam. Bake for 5 to 8 minutes, depending on the size of clam, or until clams are hot and topping is brown. Serve immediately. (Topping can be made up to 2 days in advance and refrigerated in a container or heavy plastic bag.)
**Variation:** You can use oysters instead of clams for this dish. They bake in the same amount of time.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
394 calories
178 calories from fat
20 g fat
11 g saturated fat
16 g protein
38 g carbohydrates
**Fast Talk**
Italian breadcrumbs are toasted breadcrumbs that are then seasoned with parsley, other herbs, garlic, and Parmesan cheese. To replicate the flavor if you only have plain breadcrumbs, add 1 teaspoon Italian seasoning, ½ teaspoon garlic powder, and 3 tablespoons Parmesan cheese to each 1 cup plain breadcrumbs.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
115 calories
66 calories from fat
7 g fat
1 g saturated fat
7.5 g protein
3 g carbohydrates
# **Garlic-Steamed Clams**
This is a very easy dish to make because the clams open during the cooking process, and their juice creates the flavorful broth.
**3 dz. littleneck or small cherrystone**
**clams**
**3 TB. olive oil**
**6 garlic cloves, peeled and**
**minced**
**¼ cup water**
**¼ cup white wine**
**¼ cup chopped fresh parsley**
**Salt and freshly ground black**
**pepper to taste**
1. Scrub clams well under cold running water with a stiff brush. Discard any that do not shut tightly while being scrubbed.
2. Heat olive oil in a Dutch oven over medium heat. Add garlic and cook, stirring frequently, for 2 minutes. Raise the heat to high and add water, wine, and clams. Cover the pot and steam clams for 6 to 8 minutes, depending on the size of clams. Shake the pan a few times, without opening it, to redistribute clams.
3. Remove clams from the pan with a slotted spoon, discarding any that did not open. Stir in parsley, salt, and pepper.
4. To serve, place clams in shallow bowls and ladle broth on top. Serve with soup spoons as well as seafood forks.
**Variation:** If you prefer, you can use fresh mussels instead of clams.
**Fresh Ways**
Leftover broth from a recipe for steamed mollusks is a treasure trove of flavor for saucing future fish dishes. Freeze it, and be sure to note what dish it's from so you know what flavors you're adding.
# **Oysters with Green Chili Cilantro Pesto**
There's a delicate Southwestern flavor in the cheese topping on these baked oysters.
**2 dz. fresh oysters ½ cup firmly packed cilantro**
**6 mild green Anaheim chilies, leaves**
**seeds and ribs removed, and ¼ lb. (1 cup) Parmesan**
**cut into 1-inch pieces cheese, cut into ½-inch cubes**
**3 garlic cloves, peeled 3 TB. olive oil**
**½ cup pine nuts Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven to 400°F.
2. Scrub oysters well with a stiff brush under cold running water, and discard any that are not firmly closed. Place oysters on a baking sheet and bake for 5 minutes. Remove oysters and transfer to a bowl of ice water. Pry oysters open, and cut underneath oyster to release the muscle. Discard one shell, arrange oysters on the baking sheet in the remaining shell, and set aside.
3. Increase the oven heat to 500°F.
4. Combine Anaheim chilies, garlic, pine nuts, cilantro, Parmesan cheese, and olive oil in a food processor fitted with a steel blade. Purée until smooth, scraping the sides of the work bowl with a rubber spatula a few times.
5. Spread 1 tablespoon pesto on top of each oyster. Bake oysters for 3 to 5 minutes or until topping is bubbly. Serve immediately. (Pesto can be prepared 1 day in advance and refrigerated, tightly covered.)
**Speedy Solutions**
It's worth a few dollars to find a fishmonger to open oysters for you but then you should cook them within a few hours. An alternative is to buy preshucked oysters and arrange them in ovenproof gratin dishes (round or oval dishes with low sides). They'll taste just the same, and it saves time and work.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
385 calories
222 calories from fat
25 g fat
6 g saturated fat
3 g protein
13 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 45 minutes, including 30 minutes for chilling
**Each serving contains:**
309 calories
181 calories from fat
20 g fat
3 g saturated fat
25 g protein
6 g carbohydrates
# **Creole Marinated Shrimp**
The sweet shrimp are joined with perky Italian pickled vegetables that create a colorful dish.
**1½ lb. extra-large (16 to**
**20 per lb.) cooked shrimp,**
**peeled and deveined**
**2 celery ribs, rinsed,**
**trimmed, and finely chopped**
**1 cup pickled Italian** _**gardiniera**_
**vegetables, drained and**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**½ cup chopped fresh parsley**
**½ cup white wine vinegar**
**2 TB. freshly squeezed lemon**
**juice**
**2 TB. chopped fresh oregano**
**Salt and freshly ground black**
**pepper to taste**
**½ cup extra-virgin olive oil**
**3 to 4 cups salad greens or 6**
**to 8 large leaves Boston lettuce**
1. Remove tails from shrimp, if necessary, and place shrimp in a large mixing bowl. Add celery, gardiniera vegetables, garlic, and parsley. Set aside.
2. Combine vinegar, lemon juice, oregano, salt, and pepper in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again. Add dressing to the bowl, and mix it with shrimp and vegetables. Refrigerate for 30 minutes.
3. To serve, divide mixed greens or lettuce leaves among small plates, and mound shrimp in the center. Serve immediately.
**Variation:** You could also use cooked bay scallops or 1-inch cubes of cooked halibut, cod, or sole instead of shrimp.
**Fast Talk**
Gardiniera ( _jar-din-YAIR-ah_ ) vegetables are a mélange of cauliflower, olives, and pepperoncini peppers all pickled together in a jar. They're part of a traditional antipasti spread and can be found in the Italian section of supermarkets.
# **Bourbon Shrimp**
A tomato cream sauce is laced with heady bourbon and scented with aromatic dill in this easy appetizer.
**1 ½ lb. extra large (16 to 20**
**per lb.) raw shrimp, peeled**
**and deveined**
**3 TB. unsalted butter**
**2 TB. olive oil**
**½ cup bourbon**
**2 tsp. tomato paste**
**1 cup heavy cream**
**1 TB. chopped fresh dill**
**Salt and freshly ground black**
**pepper to taste**
**6 dill sprigs for garnish**
**(optional)**
1. Rinse shrimp and pat dry with paper towels.
2. Heat butter and oil in a large, heavy skillet over medium-high heat. Add shrimp and cook, stirring constantly, for 1 minute or until shrimp just begin to turn pink.
3. Add bourbon, raise the heat to high, and cook for 1 minute or until liquid is reduced to 2 tablespoons.
4. Add tomato paste and cream, and continue to cook for 1 minute. Remove shrimp from the pan with a slotted spoon, and set aside. Raise the heat to high, and reduce sauce by ½. Add chopped dill and season to taste with salt and pepper.
5. To serve, spoon sauce over shrimp and garnish with additional dill sprigs (if using).
**Variation:** Sea scallops or 1-inch cubes of firm-fleshed whitefish such as cod, halibut, or sea bass work well instead of shrimp.
**Stale Stuff**
While much of the alcohol is burned off this dish or any dish containing liquor or wine, some residual remains. It's not enough for anyone to feel its effects, but do keep this in mind if you're serving this dish to children.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
400 calories
246 calories from fat
27 g fat
14 g saturated fat
24 g protein
3 g carbohydrates
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
702 calories
566 calories from fat
63 g fat
28 g saturated fat
22 g protein
10 g carbohydrates
**Fresh Ways**
Butter sauces are always made at the last minute to keep them emulsified, but here's a trick for some advance preparation: fill an insulated bottle with very hot tap water, drain it, and fill it with the sauce. It will "hold" for up to 2 hours.
# **Crab Cakes with Mustard Sauce**
Delicate scallops hold these cakes together, and the sauce is sparked with grainy, sharp mustard.
**¾ lb. crabmeat**
**10 oz. raw scallops, well**
**chilled**
**1 egg white**
**¾ cup heavy cream**
**Salt and freshly ground black**
**pepper to taste**
**½ cup cracker crumbs**
**½ cup dry white wine**
**2 large shallots, peeled and**
**chopped**
**4 sprigs fresh thyme**
**½ lb. (2 sticks) unsalted butter,**
**cut into 1-TB. pieces**
**3 TB. grainy mustard**
**½ cup vegetable oil for frying**
1. Place crabmeat on a dark-colored plate. Rub it gently with your fingertips, and discard any bits of shell or cartilage you uncover. Set aside.
2. Purée scallops in a food processor fitted with a steel blade until a paste is formed. Slowly add egg white and ½ cup cream through the feed tube, and process until smooth. Season to taste with salt and pepper, and gently fold in crabmeat.
3. Form mixture into 6 to 8 patties, and coat patties in cracker crumbs. Refrigerate cakes loosely covered with plastic wrap.
4. Combine wine, shallots, and thyme in a small saucepan. Cook over high heat until 2 tablespoons remain. Add remaining ¼ cup cream, and cook again until 2 tablespoons remain. Strain sauce and return it to the pan.
5. Place the pan over very low heat, and add pieces of butter, one at a time, swirling with a whisk until a piece is completely incorporated before adding the next. Stir in mustard, and season to taste with salt and pepper.
6. Heat oil in a large skillet over medium-high heat. Add patties and cook for 2 minutes or until lightly brown. Turn gently and cook the other side.
7. To serve, spoon sauce on small plates and top sauce with one crab cake. (Patties can be prepared up to cooking 1 day in advance and refrigerated, tightly covered with plastic wrap.)
# **Chicken in Lettuce Cups**
These Chinese rolls are a healthful version of tacos because the filling is rolled in crunchy lettuce leaves.
**2 TB. sesame oil**
**2 garlic cloves, peeled and**
**minced**
**1 TB. grated fresh ginger**
**4 scallions, rinsed, trimmed,**
**and thinly sliced**
**1 lb. ground chicken**
**1 (8-oz.) can water chestnuts,**
**drained, rinsed, and chopped**
**¼ cup soy sauce**
**2 TB.** _**hoisin sauce**_
**1 TB. cider vinegar**
**1 tsp. cornstarch**
**Salt and freshly ground black**
**pepper to taste**
**12 to 16 Boston or iceberg**
**lettuce leaves, rinsed and**
**dried**
**2 scallions, rinsed, trimmed,**
**and thinly sliced for garnish**
**(optional)**
1. Heat sesame oil in a large skillet over medium-high heat. Add garlic, ginger, and scallions. Stir-fry for 30 seconds, stirring constantly. Add chicken, and stir-fry for 3 or 4 minutes, breaking up lumps with a fork or until chicken has lost all its pink color and is white and beginning to brown. Stir in water chestnuts, and stir-fry 1 minute.
2. Mix soy sauce, hoisin sauce, vinegar, and cornstarch in a small bowl. Add to the pan, and when mixture boils and thickens, reduce heat to low and simmer for 1 minute, stirring frequently. Season to taste with salt and pepper.
3. Spoon mixture into lettuce leaves, and garnish with scallions (if using). Serve immediately.
**Variation:** Instead of ground chicken, try ground pork or turkey.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
228 calories
135 calories from fat
15 g fat
1 g saturated fat
14.5 g protein
8 g carbohydrates
**Fast Talk**
Hoisin ( _hoy-ZAN_ ) sauce is the ketchup of Chinese cooking. This thick, sweet, and spicy reddish-brown sauce is a mixture of soybeans, garlic, chilies, Chinese five-spice powder, and sugar. Like ketchup, it's used both as a condiment and an ingredient.
**Chapter 6**
**The Bountiful Bowl: Sou6ps**
**In This Chapter**
• Chilled summer soups
• Creamy chowder creations
• Hearty winter soups
Soups aid emotional well-being immeasurably. On a hot summer day, a bowl of frosty soup cools like an ocean breeze, and on a chilly winter night, a bowl of steaming soup warms like nothing else. It's easy to see the truth in the old Spanish proverb, "between love and soup, soup is best."
You'll find a potpourri of soups in this chapter, united by the short amount of time it takes to create them. They range from light uncooked summer soups to hearty chowders, perfect for whatever suits your mood or the season.
# **Taking Stock**
Want to know a secret? The reason why so many people think that soups and sauces taste better in restaurants is because they're based on slowly simmered stocks. These stocks form the structure of the soup or sauce and add a depth of flavor.
The _word_ fast in the title of this book is antithetical to watching a pot simmer for 8 hours on the stove. But there is a middle ground. If you have the time to make the Quick Chicken Stock in this chapter and have it handy in the freezer, you're much closer to that long-simmered taste.
# **Quick Chicken Stock**
Enriching canned stock quickly with vegetables and herbs replicates the flavor of homemade stock.
**2 qt. canned chicken stock**
**4 celery ribs, rinsed and**
**sliced**
**1 large onion, peeled and**
**diced**
**2 carrots, trimmed, scrubbed,**
**and sliced**
**12 black peppercorns**
**6 garlic cloves, peeled**
**4 sprigs parsley**
**4 sprigs thyme or 1 tsp. dried**
**2 bay leaves**
1. Combine stock, celery, onion, carrots, peppercorns, garlic, parsley, thyme, and bay leaves in a large stockpot. Bring to a boil over high heat, reduce heat to low, cover the pan, and simmer for 20 minutes.
2. Strain stock, pressing with the back of a spoon to extract as much liquid as possible. Refrigerate when cool. The stock can be refrigerated and used within 3 days, or it can be frozen for up to 6 months.
**Fresh Ways**
If you've got some limp carrots or celery ribs in the refrigerator, don't throw them out. They're still good for making stock.
Makes: 2 quarts
**Active time:** 5 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
289 calories
11 calories from fat
1 g fat
0 g saturated fat
29.5 g protein
47 g carbohydrates
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 45 minutes, including 30 minutes for chilling
**Each serving contains:**
113 calories
64 calories from fat
7 g fat
1 g saturated fat
2 g protein
12 g carbohydrates
# **Gazpacho**
Gazpacho is a traditional Spanish vegetable soup flavored with garlic, chilies, and vinegar.
**1 medium Bermuda or other 3 garlic cloves, peeled**
**sweet white onion, peeled 1½ cups tomato juice**
**and quartered**
**1 medium cucumber, rinsed, ¼ cup olive oil**
**seeded, and cut into 1-inch 1 jalapeño chili, seeds and**
**sections ribs removed**
**1 red bell pepper, seeds and** ¼ **cup balsamic vinegar**
**ribs removed, and diced** ¼ **cup chopped fresh cilantro**
**3 medium to large ripe toma- Salt and freshly ground black**
**toes, rinsed, cored, seeded, pepper to taste**
**and diced**
1. Finely chop onion, cucumber, red pepper, and 1 tomato in a food processor fitted with a steel blade using on-and-off pulsing. Scrape mixture into a large mixing bowl.
2. Purée remaining 2 tomatoes with garlic, tomato juice, olive oil, jalapeño, and balsamic vinegar. Stir purée and cilantro into vegetables, and season to taste with salt and pepper. Chill for at least 30 minutes, or until cold. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
**Speedy Solutions**
If you start with all your ingredients chilled, any of these noncooked soups are ready to serve as soon as they're assembled.
# **Dilled Cream of Cucumber Soup**
Aromatic dill makes delicate cucumbers more interesting in this soup that can be served either hot or cold.
**2 TB. unsalted butter 1 cup half-and-half**
**1 leek, white part only, Salt and freshly ground black**
**trimmed, sliced, and rinsed pepper to taste**
**well 6 to 8 TB. finely chopped**
**2 large or 3 small cucumbers, cucumber for garnish**
**rinsed, seeded, and sliced (optional)**
**4 TB. chopped fresh dill or 1 6 to 8 fresh dill sprigs for**
**TB. dried garnish (optional)**
**5 cups chicken or vegetable**
**stock**
1. Melt butter in a heavy 4-quart saucepan over medium heat. Add leek, cucumbers, and 2 tablespoons dill. Cook, stirring frequently, for 5 minutes or until leek is translucent.
2. Add stock and bring to a boil over high heat. Reduce heat to low, and simmer, partially covered, for 25 minutes.
3. Transfer mixture to a blender or food processor fitted with the steel blade. Purée until smooth, and refrigerate soup until chilled, at least 2 hours.
4. Stir in half-and-half and remaining 2 tablespoons dill, and season to taste with salt and pepper. Serve immediately, garnishing each serving with 1 tablespoon cucumber and 1 sprig dill, if using. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
**Fresh Ways**
Although most herbs don't freeze or thaw well, you can freeze leafy herbs such as dill, cilantro, and parsley if you'll later add them to dishes that cook. They'll lose their texture once thawed, but you won't notice it as much in the final dish. Rinse small bundles and freeze wrapped in plastic wrap. "Chop" the frozen herbs using the blunt side of a knife.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 1 hour if
served hot or 3 hours to
allow for chilling
**Each serving contains:**
94 calories
60 calories from fat
7 g fat
4 g saturated fat
3.5 g protein
6 g carbohydrates
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 3 hours,
including 2 hours for
chilling
**Each serving contains:**
185 calories
76 calories from fat
8 g fat
5 g saturated fat
6 g protein
24 g carbohydrates
**Fresh Ways**
A huge variation exists in the flavor and composition of canned stocks, with the best-known national brands not very high on the list. Whenever possible, buy organic stocks. The sodium content is much lower, and stocks found in whole foods markets usually have a better flavor.
# **Leek and Potato Soup (** _ **Vichyssoise**_ **)**
Although this creamy soup has a French name, it was actually invented in New York in the early twentieth century.
**3 TB. unsalted butter**
**6 leeks, white part only,**
**trimmed, chopped, and**
**rinsed well**
**1 lb. boiling potatoes, peeled**
**and thinly sliced**
**6 cups chicken or vegetable**
**stock**
**1 cup half-and-half**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 TB. snipped fresh**
**chives for garnish (optional)**
1. Melt butter in a heavy 4-quart saucepan over medium heat. Add leeks and cook, stirring frequently, for 5 minutes or until leeks are translucent.
2. Add potatoes and stock, and bring to a boil over high heat. Reduce heat to low and simmer soup, partially covered, for 25 minutes or until potatoes are tender.
3. Transfer mixture to a blender or food processor fitted with the steel blade and purée. (This may have to be done in several batches.)
4. Refrigerate, covered, until cold, at least 2 hours, and then stir in half-and-half. Season to taste with salt and pepper, and serve immediately, garnished with chives, if using. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
**Variation:** This soup can also be served hot, and when served this way, it's frequently not puréed. If serving it hot, omit the half-and-half.
# **Cream of Celery Soup with Tarragon**
Adding rice to the soup as it cooks gives this luxurious dish its thick texture.
**8 celery ribs, rinsed,**
**trimmed, and cut into 1-inch**
**lengths**
**4 cups chicken or vegetable**
**stock**
**⅓** cup white rice
**2 TB. chopped fresh** _**tarragon**_
**or 2 tsp. dried**
**1 cup half-and-half**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 sprigs tarragon for**
**garnish (optional)**
1. Combine celery, stock, rice, and tarragon in a heavy 4-quart saucepan. Bring to a boil over high heat, and simmer soup, partially covered, over low heat for 30 minutes.
2. Place soup in a blender or food processor fitted with the steel blade and purée until smooth. Return soup to the pan, stir in half-and-half, and simmer 2 minutes.
3. Season to taste with salt and pepper, and serve immediately, garnished with tarragon, if using. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
**Fast Talk**
**Tarragon** is an aromatic herb used extensively in French cooking. It has long, pointed, dark-green leaves and adds a distinctive aniselike flavor to foods.
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 50 minutes
**Each serving contains:**
126 calories
45 calories from fat
5 g fat
3 g saturated fat
6 g protein
14 g carbohydrates
Serves: 8
**Active time:** 25 minutes
**Start to finish:** 55 minutes
**Each serving contains:**
208 calories
81 calories from fat
9 g fat
4.5 g saturated fat
7 g protein
30 g carbohydrates
**Speedy Solutions**
The most time-consuming part of this recipe is grilling the corn, so there's no reason not to fill the grill with more ears than you'll need for one batch of this chowder. Cut the kernels off the extra cobs and freeze for future batches.
# **Grilled Corn Chowder**
The smoky flavor that comes from grilling the corn over aromatic mesquite makes this soup special.
**1 cup mesquite chips**
**4 garlic cloves, unpeeled**
**8 to 10 medium ears of fresh**
**corn, unshucked**
**3 TB. unsalted butter**
**¼ cup yellow cornmeal**
**1 (4-oz.) can mild green chilies,**
**drained**
**2 cups chicken or vegetable**
**stock**
2 cups whole milk
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven to 350°F. Light a charcoal or gas grill and soak mesquite chips covered in cold water for 20 minutes.
2. Bake garlic cloves for 15 minutes or until soft. When cool enough to handle, remove pulp and discard skins. Set aside.
3. Remove all but 1 layer of husks from corn, and pull out corn silks. Soak corn covered in cold water for 5 minutes.
4. Drain mesquite chips and place on the fire. Grill corn for 10 to 15 minutes, turning with tongs occasionally. When cool enough to handle, discard husks and cut kernels off cobs using a sharp serrated knife.
5. Melt butter in a large saucepan over low heat. Add kernels and cook for 5 minutes, stirring occasionally. Remove 1 cup kernels and set aside. Purée remaining corn, roasted garlic, cornmeal, chilies, and stock in a food processor fitted with a steel blade or in a blender.
6. Combine purée with milk, and heat to a boil over medium heat, stirring occasionally. Add reserved corn kernels, and season with salt and pepper. Simmer for 5 minutes over low heat, stirring occasionally. Serve immediately. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
# **Nantucket Clam Chowder**
This version of the New England classic, made with celery and thyme, won contests when I lived on the island!
**1** **¼ lb. red-skinned potatoes,**
**scrubbed and cut into** **½-inch**
**dice**
**3 celery ribs, rinsed,**
**trimmed, and diced**
**2 (8-oz.) bottles clam juice**
**2 pt. fresh minced clams,**
**drained with all clam juice**
**reserved**
**¼ cup chopped fresh parsley**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**1 bay leaf**
**3 TB. unsalted butter**
**2 medium onions, peeled and**
**diced**
**¼ cup all-purpose flour**
**3 cups whole milk or half-and-half**
**Salt and freshly ground black**
**pepper to taste**
1. Combine potatoes, celery, clam juice, reserved clam juice, parsley, thyme, and bay leaf in a heavy 2-quart saucepan. Bring to a boil over high heat. Reduce heat to medium, and cook for 15 minutes or until potatoes are tender and liquid is reduced by half.
2. While potatoes are boiling, melt butter in a small saucepan over medium heat. Add onions and cook, stirring frequently, for 5 minutes or until onions are soft. Reduce heat to low.
3. Stir in flour and cook for 2 minutes, stirring constantly. Whisk in milk, and bring to a boil over medium heat, stirring constantly. Simmer for 2 minutes. Set aside until potatoes are tender.
4. Add cream mixture to potato mixture, and bring to a boil over medium heat. Stir in clams, and simmer for 5 minutes, stirring occasionally. Remove and discard bay leaf. Season to taste with salt and pepper, and serve immediately. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
**Variation:** Many versions of chowder include either corn kernels, crisp crumbled bacon, or both. For this size batch ½ cup corn kernels and 3 tablespoons crumbed bacon would be good additions.
Serves: 8
**Active time:** 25 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
255 calories
71 calories from fat
8 g fat
5 g saturated fat
13.5 g protein
32.5 g carbohydrates
**Stale Stuff**
It's important to use the additional clam juice for the chowder rather than cooking the potatoes and celery in water. It's this reduction of the clam juice that adds great flavor after the milk is added.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 35 minutes
**Each serving contains:**
252 calories
111 calories from fat
12 g fat
7 g saturated fat
10.5 g protein
28.5 g carbohydrates
**Fresh Ways**
Bisque and chowder both contain seafood, but that's where the similarity ends. A bisque is always a puréed cream soup, while chowders are always chunky and can be made with or without cream.
# **Dilled Corn and Oyster Bisque**
Sweet corn and aromatic dill are the perfect foils for the briny taste of oysters in this elegant soup.
**10 ears fresh corn (or 4 cups**
**frozen corn, thawed)**
**1 pt. fresh oysters**
**4 TB. unsalted butter**
**4 cups whole milk**
**3 TB. chopped fresh dill**
**or 1 TB. dried**
**1 tsp. hot red pepper sauce**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 sprigs dill for garnish**
**(optional)**
1.Shuck corn and discard silks. Cut corn off cobs with a sharp serrated knife.
2.Drain oysters, reserving oyster liquor. Refrigerate oysters, and strain liquor through cheesecloth or a paper coffee filter. Set aside.
3.Melt butter in a heavy 4-quart saucepan. Add corn and cook for 5 minutes, stirring occasionally. Add milk and reserved oyster liquor. Bring to a boil over medium heat, stirring occasionally. Reduce heat to low, and simmer soup uncovered for 15 minutes. Purée soup in a blender or food processor fitted with a steel blade. (Soup can be made up to 2 days in advance and refrigerated, tightly covered.)
3.Before serving, reheat soup to a simmer and add oysters and dill. Bring to a boil, and simmer over low heat, stirring occasionally, for 3 minutes or until edges of oysters start to curl. Stir in hot red pepper sauce, and season to taste with salt and pepper. Serve immediately, garnished with dill sprigs (if using).
**Variation:** You could use 1 pint minced fresh clams instead of the oysters in this recipe.
# **Greek Lemon Egg Soup with Chicken and Orzo (** _ **Avgolemono**_ **)**
The luxurious texture of this soup comes from being thickened with eggs like a custard.
**2 (6-oz.) boneless, skinless**
**chicken breast halves**
**7 cups chicken stock**
**⅔ cup orzo**
**1 large carrot, peeled and**
**grated**
**2 celery ribs, rinsed,**
**trimmed, and finely chopped**
4 large eggs
**⅓ cup freshly squeezed lemon**
**juice**
**1 tsp. grated lemon zest**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut into ½-inch cubes.
2. Combine chicken stock, chicken, orzo, carrot, and celery in a heavy 2-quart saucepan. Bring to a boil over high heat, stirring occasionally. Reduce heat to low and simmer, covered, for 10 to 12 minutes or until orzo is tender.
3. While soup is simmering, whisk together eggs and lemon juice. When orzo is tender, remove soup from heat and stir constantly for 1 minute. It should no longer be bubbling at all. Stir in lemon mixture, cover the pan, and allow soup to sit for 5 minutes to thicken.
4. Season to taste with salt and pepper, and serve immediately. (Soup can be made up to 2 days in advance and refrigerated, tightly covered. Reheat over low heat, stirring frequently, until hot. Do not let soup boil.)
Serves: 8
**Active time:** 10 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
160 calories
36 calories from fat
4 g fat
1 g saturated fat
17 g protein
14 g carbohydrates
**Fresh Ways**
You want to cool the liquid by stirring before adding the egg to prevent the egg from curdling and turning this into a Greek version of Chinese Egg Drop Soup. Eggs thicken at 160°F, while the boiling point of liquid is 212°F. Be sure to stir!
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
335 calories
62 calories from fat
7 g fat
3 g saturated fat
26 g protein
44 g carbohydrates
**Fresh Ways**
Save the rinds from Parmesan cheese and use them for flavoring dishes such as soups and sauces. The rind won't melt into the dishes, but it will impart flavor. Remove and discard it before serving.
# **Tuscan White Bean Soup with Sausage**
This thick and hearty soup is a perfect starter on a cold winter night. Swiss chard gives it added color and flavor.
**1 lb. bulk Italian sausage**
**(sweet or hot)**
**2 large onions, peeled and**
**diced**
**4 garlic cloves, peeled and**
**minced**
**4 celery ribs, rinsed,**
**trimmed, and diced**
**2 carrots, peeled and diced**
**4 cups chicken stock**
**3 (15-oz.) can white beans,**
**drained and rinsed**
**¼ cup chopped fresh parsley**
**1½ tsp. dried thyme**
**1 bay leaf**
**1 cup water**
**¾ lb. (8 firmly packed cups)**
**Swiss chard, rinsed, stemmed,**
**and thinly sliced**
**½ cup freshly grated**
**Parmesan cheese**
**Salt and freshly ground black**
**pepper to taste**
1. Place a heavy 2-quart saucepan over medium-high heat. Add sausage, breaking up lumps with a fork. Cook, stirring occasionally, for 3 minutes or until sausage is browned and no longer pink. Remove sausage from the pan with a slotted spoon, and set aside. Discard all but 1 tablespoon sausage fat from the pan.
2. Add onions, garlic, celery, and carrots to the pan. Cook, stirring occasionally, for 3 minutes or until onion is translucent. Add stock, ½ of beans, parsley, thyme, and bay leaf. Bring to a boil over medium heat. Simmer, partially covered, for 20 minutes or until carrots are soft.
3. While soup begins simmering, combine reserved beans and water in a blender or food processor fitted with a steel blade. Purée until smooth. Stir mixture into soup.
4. Add Swiss chard to soup, and simmer for 5 minutes. Remove and discard bay leaf, and stir Parmesan cheese into soup. Season to taste with salt and pepper, and serve immediately. (You can do this up to 2 days in advance and refrigerate soup, tightly covered. Reheat over low heat, stirring occasionally, until soup comes to a simmer.)
**Part 3**
**Casual Cuisine**
Sure you might want to cook a fancy dinner with candles lit and silver gleaming a few nights a week. But what about Sunday brunch? What about those nights when a crusty sandwich or steaming bowl of pasta is what will hit the spot? These are the times you'll turn to the recipes in Part 3.
Here you'll find a chapter with goodies for breakfast and brunch—but don't relegate them to the morning. Many of them can do double duty as a light supper, too. The other chapters in this part contain recipes for those great stalwarts of casual cooking—sandwiches, pastas, and pizza. But do look closely. While the categories are casual, the dishes are sophisticated as well as delicious.
**Chapter 7**
**Sunny Starts: Breakfast**
**In This Chapter**
• Sweet and savory pancakes
• Fancy frittatas
• Exotic egg dishes
Nutritionists are quick to point out that breakfast is the most important meal of the day, but we all know that the morning is also the most hectic part of the day. The recipes in this chapter are here to solve that dilemma.
Foods like pancakes can be on the table in a matter of minutes. And it's much more efficient to cook one frittata that serves the whole table rather than worrying about individual omelets. So breakfast need not be a reason for stress, and these recipes start the day with a treat.
# **Pancake Pointers**
Pancakes couldn't be easier to make, and nearly everyone loves them. To save time in the morning, start the pancake-making process the night before by combining the dry ingredients in one bowl and whisking the wet ingredients in another. In the morning, all you have to do is stir them together as the griddle heats. (Don't over mix the batter or whisk it. Pancake batters _should_ be somewhat lumpy.)
Getting your griddle or skillet to the proper temperature is important. The ideal pancake-cooking temperature is 375°F. To test and see if it's 375°F, drop a few drops of water onto it. If they "dance" across the griddle as they turn to steam, then you're ready to cook.
If you use a ¼-cup measure, your pancakes will all be relatively the same size. If you're really particular about perfectly round pancakes, use a bulb baster filled with batter.
Pancakes are ready to turn when you see bubbles appearing on the surface and the edges turn brown. It's at this time that you can add some additional ingredients like chocolate chips, dried fruit, or granola. Use a wide spatula when flipping pancakes so the whole bottom of the pancake is supported.
# **The Fine Points of Frittatas**
Frittatas are Italian-style omelets. Unlike their French counterparts, which are cooked in single portions entirely on the stove, frittatas start on the stovetop and finish in the oven. It's much easier to make one frittata for two people rather than two individual omelets, and frittatas don't require the careful turning that can lead to omelets becoming scrambled eggs with other ingredients folded in. Plus you only have the one skillet to wash.
**Fresh Ways**
Only have skillets with plastic handles? Wrap the handle in a double layer of aluminum foil before you place the skillet into the oven to prevent the plastic from cracking or even melting.
# **Cutting Cholesterol**
Eggs have gotten a bad nutritional reputation because of the fat and cholesterol in the yolk. But the white is the "good egg." The white, made up primarily of protein and water, is what gives eggs their ability to bind.
**Stale Stuff**
Never rinse eggs before using them. The water makes the shells porous and can cause the eggs to spoil faster and allow bacteria to enter.
If you want to be judicious about cutting cholesterol, you can use an egg substitute product. (The best-known one is Egg Beaters.) These products are essentially egg whites tinted yellow. But you can also make your own by using 2 egg whites for each whole egg, or if a recipe calls for several eggs, use 2 egg whites and 1 whole egg for every 2 whole eggs listed.
# **Oven-Baked Apple Pancakes**
These puffy pancakes are like small apple cakes—children adore them!
**6 TB. unsalted butter**
**2 Golden Delicious apples,**
**peeled, cored, and thinly**
**sliced**
**⅓ cup firmly packed dark**
**brown sugar**
**¼ tsp. ground cinnamon**
**3 TB. freshly squeezed lemon**
**juice**
**6 large eggs, lightly beaten**
**1 cup whole milk**
**1 cup all-purpose flour**
**Pinch salt**
**Maple syrup or apple butter**
**for serving**
1. Preheat the oven to 425°F. Place 6 (1-cup) custard cups on a baking sheet.
2. Melt butter in a small saucepan over low heat. Pour 1 tablespoon butter into each custard cup.
3. Toss apples with brown sugar and cinnamon and drizzle with lemon juice. Combine eggs, milk, flour, and salt in a mixing bowl, and stir until just blended. Divide batter among cups on top of butter. Arrange apple slices on top of batter.
4. Bake for 15 minutes or until pancakes are puffed and golden. Unmold the pancakes onto plates, and serve immediately with maple syrup or apple butter.
**Variation:** You could also try pears or peaches instead of apples.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
354 calories
169 calories from fat
19 g fat
10 g saturated fat
10 g protein
37 g carbohydrates
**Stale Stuff**
Don't use 2 percent or skim milk here. This is one recipe that really does require whole milk. The fat is necessary to make the pancakes puff.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
636 calories
258 calories from fat
29 g fat
12 g saturated fat
11 g protein
85 g carbohydrates
**Fresh Ways**
Although it's a shelf-stable product, baking powder does have an expiration date; check it before buying. And because you use so little of it for any recipe, hunt for the cans with the date farthest in the future.
# **Gingerbread Pancakes**
If you love the flavor of gingerbread cookies, these are the way to start your day.
**3 cups all-purpose flour**
**1 cup firmly packed dark**
**brown sugar**
**1 TB. baking powder**
**1** **½ tsp. baking soda**
**¾ tsp. salt**
**1 tsp. ground cinnamon**
**1 tsp. ground ginger**
**½ tsp. grated nutmeg**
**½ cup water**
**½ cup brewed coffee, cold or**
**at room temperature**
**4 large eggs**
**¼ lb. (1 stick) unsalted butter,**
**melted and cooled**
**¼ cup vegetable oil**
**Maple syrup or sweetened**
**whipped cream for serving**
1. Preheat the oven to 200°F, and cover a baking sheet with aluminum foil.
2. Combine flour, brown sugar, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg in a large mixing bowl, and whisk well. Combine water, coffee, eggs, and butter in another mixing bowl, and whisk well. Pour liquid mixture into flour mixture, and stir until just combined. Allow batter to sit for 10 minutes.
3. Place a griddle or 12-inch skillet over medium heat. Brush with oil. Pour ¼ cup measures of batter into the skillet, and cook for 1 or 2 minutes or until bubbles appear on the surface. Turn pancakes with a spatula and cook for 1 or 2 more minutes or until pancakes are cooked through. Place pancakes on a baking sheet and keep warm in the oven. Repeat with remaining batter, brushing the griddle with oil between batches.
4. Serve immediately, topping pancakes with maple syrup or sweetened whipped cream.
# **Whole-Wheat Blueberry Pancakes**
The inclusion of whole-wheat flour makes these blueberry pancakes hardier than most.
**¾ cup all-purpose flour**
**½ cup whole-wheat flour**
**¼ cup wheat germ**
**¼ cup granulated sugar**
**2 tsp. baking powder**
**1** **½ tsp. baking soda**
**½ tsp. salt**
**2 cups buttermilk, well**
**shaken**
**3 large eggs**
**6 TB. unsalted butter, melted**
**and cooled**
**2 cups blueberries, rinsed**
**¼ cup vegetable oil**
**Maple syrup or blueberry**
**syrup for serving**
1. Preheat the oven to 200°F, and cover a baking sheet with aluminum foil.
2. Combine all-purpose flour, whole-wheat flour, wheat germ, sugar, baking powder, baking soda, and salt in a large mixing bowl, and whisk well. Combine buttermilk, eggs, and butter in another mixing bowl, and whisk well. Pour liquid into flour mixture, and stir until just combined. Stir in blueberries.
3. Place a griddle or 12-inch skillet over medium heat. Brush with oil. Pour ¼ cup measures of batter into the skillet, and cook for 1 or 2 minutes or until bubbles appear on the surface. Turn pancakes with a spatula and cook 1 or 2 more minutes or until pancakes are cooked through. Place pancakes on a baking sheet and keep warm in the oven. Repeat with remaining batter, brushing the griddle with oil between batches.
4. Serve immediately, topping pancakes with maple or blueberry syrup.
**Variation:** Feel free to substitute sliced strawberries or raspberries for the blueberries.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
426 calories
229 calories from fat
25 g fat
10 g saturated fat
10 g protein
42 g carbohydrates
**Stale Stuff**
All the "butter" of buttermilk tends to rise to the top of the carton, it's important to shake it vigorously. And shake it often if you're using it at different times when preparing a recipe.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
907 calories
352 calories from fat
39 g fat
19 g saturated fat
18 g protein
124 g carbohydrates
**Fresh Ways**
If you have bananas that are past their prime, toss them into the freezer still in their peels. Defrosted, they're perfect for any recipe calling for mashed bananas such as this one or banana bread.
# **Banana Pancakes with Banana Syrup**
These pancakes are rich and luscious. In fact, on occasion, I serve them for dessert with vanilla ice cream.
**12 TB. (1** **½ sticks) unsalted**
**butter, melted**
**1 cup firmly packed dark**
**brown sugar**
**½ cup water**
**¾ tsp. pure vanilla extract**
**4 large very ripe bananas**
**4 cups all-purpose flour**
**⅔ cup granulated sugar**
**2 tsp. baking powder**
**1 tsp. baking soda**
**½ tsp. ground cinnamon**
**½ tsp. salt**
**3 cups buttermilk, well**
**shaken**
**4 large eggs**
**¼ cup vegetable oil**
1. Preheat the oven to 200°F, and cover a baking sheet with aluminum foil.
2. Combine 8 tablespoons butter, brown sugar, water, and vanilla extract in a medium saucepan. Bring to a boil over medium-high heat and simmer mixture, stirring occasionally, for 5 minutes.
3. While syrup is simmering, peel bananas. Cut 2 bananas into ¼-inch slices, and mash remaining 2 bananas in a large mixing bowl. Stir sliced bananas into syrup, and set aside.
4. Combine flour, granulated sugar, baking powder, baking soda, cinnamon, and salt in a large mixing bowl. Whisk well. Add buttermilk, eggs, and remaining 4 tablespoons butter to bowl with mashed bananas, and whisk well. Pour liquid into flour mixture, and stir until just combined.
5. Place a griddle or 12-inch skillet over medium heat. Brush with oil. Pour ¼ cup measures of batter into the skillet, and cook for 1 or 2 minutes or until bubbles appear on the surface. Turn pancakes with a spatula and cook 1 or 2 more minutes or until pancakes are cooked through. Place pancakes on a baking sheet and keep warm in the oven. Repeat with remaining batter, brushing the griddle with oil between batches.
6. Serve immediately, topping pancakes with banana syrup.
# **Raspberry French Toast with Raspberry Sauce**
This dish takes French toast to the next level by filling slices with fruity cream cheese.
12 slices _challah_ or other egg
bread, sliced ½-inch thick
4 large eggs
2½ cups whole milk
¾ cup granulated sugar
½ tsp. pure vanilla extract
¼ tsp. salt
1 (8-oz.) pkg. cream cheese,
well chilled
3 cups fresh raspberries,
rinsed
2 TB. unsalted butter, or as
necessary
1. Trim crusts from challah, and cut slices into a uniform shape. Arrange bread slices in a 9×13-inch baking pan, and set aside.
2. Whisk eggs in a large mixing bowl until frothy. Add milk, ½ cup sugar, vanilla extract, and salt. Whisk again, and pour liquid over bread slices in baking pan. Allow bread to soak for 5 minutes, turning slices occasionally with a slotted spatula.
3. While bread is soaking, cut cream cheese into 12 slices, and set aside.
4. Purée 1½ cups raspberries with remaining ¼ cup sugar in a blender or food processor fitted with a steel blade. Set aside.
5. Heat 2 tablespoons butter in a large, heavy skillet over medium heat. Remove 6 bread slices from liquid, and allow excess to drain back into the pan. Add slices to the skillet, and cook for 3 minutes or until lightly browned. Place 2 cream cheese slices on each bread slice, and top cream cheese with ¼ cup raspberries. Place remaining bread slices on top of raspberries, and press gently to enclose filling. Turn gently with a slotted spatula, and cook for an additional 3 minutes or until browned. (This may have to be done in batches if 6 slices cannot fit into the skillet. If so, keep the first batch warm in a 200°F oven while the second batch cooks.) Serve immediately.
**Variation:** No raspberries? Try blueberries, blackberries, or sliced strawberries instead.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
630 calories
261 calories from fat
29 g fat
15 g saturated fat
19 g protein
75.5 g carbohydratesI
**Fast Talk**
Challah is an egg-rich ceremonial Jewish bread served on the Sabbath and holidays. It has a light, airy texture and is traditionally braided into an oval loaf that tapers at the ends.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
513 calories
335 calories from fat
37 g fat
19 g saturated fat
21 g protein
22 g carbohydrates
**Speedy Solutions**
If you have trouble separating individual slices of bacon when they're cold, here's an easy solution: peel off the total number of slices you need, and place the block into the hot pan. Within a few minutes, the slices will naturally separate due to the heat and then you can pull them apart with a meat fork.
# **Potato, Onion, and Bacon Frittata**
This combination of omelet additions comes from the Lyon region of France, and all the elements add great flavor to the dish.
1 ½ lb. bacon, cut into 1-inch
lengths
2 large red-skinned potatoes,
scrubbed and cut into ¼-inch
dice
1 large onion, peeled and
diced
1 garlic clove, peeled and
minced
8 large eggs
¼ cup half-and-half
2 TB. chopped fresh parsley
Salt and freshly ground black
pepper to taste
1. Preheat the oven to 425°F.
2. Place bacon in a 12-inch ovenproof skillet over medium-high heat. Cook for 5 to 7 minutes or until bacon is crisp. Remove bacon from the pan with a slotted spoon and set aside.
3. Discard all but 3 tablespoons bacon fat from the skillet. Add potatoes, and cook until tender, scraping them occasionally with a heavy spatula. Add onion and garlic to the skillet and cook for 5 minutes, stirring occasionally, or until onion is soft.
4. Whisk eggs with half-and-half and parsley, and season to taste with salt and pepper. Pour egg mixture into the skillet. Cook for 4 minutes over medium heat.
5. Transfer the skillet to the oven, and bake for 10 minutes or until top is browned. Remove the skillet from the oven, and run a spatula around the sides of the skillet and underneath frittata to release it from the pan. Slide frittata onto a platter, and cut it into wedges. Serve immediately.
**Variation:** You can substitute ham or sausage for the bacon, and ½ cup diced red bell pepper works well cooked along with the onion and garlic.
# **Western Frittata**
This is an easier version of a Western omelet—filled with a combination of ham, onions, and bell peppers—to feed a crowd in a hurry.
3 **TB.** unsalted butter
1 large onion, peeled and cut
into ½-inch dice
1 red bell pepper, seeds and
ribs removed, and cut into
½-inch dice
½ lb. baked ham, trimmed
of all visible fat, and cut into
½-inch dice
8 large eggs
¼ cup half-and-half
Salt and freshly ground black
pepper to taste
1. Preheat the oven to 425°F.
2. Heat butter in a 12-inch ovenproof skillet over medium heat. Add onion and red bell pepper, and cook, stirring frequently, for 3 minutes or until onion is translucent. Add ham and cook for 2 minutes, stirring frequently. Remove the pan from the heat.
3. Whisk eggs with half-and-half, and season to taste with salt and pepper. Pour egg mixture into the skillet. Cook for 4 minutes over medium heat.
4. Transfer the skillet to the oven, and bake for 10 minutes or until top is browned. Remove the skillet from the oven, and run a spatula around the sides of the skillet and underneath frittata to release it from the pan. Slide frittata onto a platter, and cut it into wedges. Serve immediately.
**Variation:** Instead of ham, try it with cooked and crumbled bacon, sausage, or poultry sausage. You can sub mushrooms for the bell pepper, too.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
321 calories
204 calories from fat
23 g fat
11 g saturated fat
23 g protein
7 g carbohydrates
**Speedy Solutions**
To save time when dicing ham, ask the deli clerk to cut the meat into ½-inch-thick slices. When you get home, all you have to do is stack them and they're ready to dice.
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 35 minutes
**Each serving contains:**
514 calories
247 calories from fat
27 g fat
8 g saturated fat
26 g protein
41 g carbohydrates
**Fast Talk**
Al dente is Italian for "against the teeth" and refers to pasta (or another ingredient such as rice) that is neither soft nor hard, but just slightly firm when you bite it.
# **Vegetable Frittata with Pasta**
This dish can easily be served room temperature on a picnic or at a brunch with a tossed salad.
1 (6-oz.) pkg. fresh angel hair
pasta, cut into 2-inch sections
4 scallions
3 TB. olive oil
2 small zucchini, trimmed
and thinly sliced
1 garlic clove, peeled and
minced
2 ripe medium tomatoes,
cored, seeded, and finely
chopped
3 **TB.** chopped fresh basil
or 2 tsp. dried
1 **TB.** chopped fresh oregano
or ½ tsp. dried
¼ cup sliced green olives
Salt and freshly ground black
pepper to taste
8 large eggs
¾ cup freshly grated
Parmesan cheese
2 TB. half-and-half
1. Preheat the oven to 425°F.
2. Cook pasta according to package directions until _al dente_. Drain and set aside to cool.
3. Rinse and trim scallions, discarding all but 2 inches of green tops. Cut scallions into thin slices.
4. Heat olive oil in a heavy 12-inch skillet over medium-high heat. Add zucchini, scallions, and garlic. Cook, stirring frequently, for 3 minutes or until zucchini is tender. Add tomatoes, basil, oregano, and olives. Cook, stirring occasionally, for 5 minutes or until liquid from tomatoes has evaporated. Season to taste with salt and pepper, and let cool for 10 minutes. (You can prepare this a day in advance and refrigerate, tightly covered. Before baking, reheat vegetables to room temperature in a microwave-safe dish or over low heat.)
5. Whisk eggs with Parmesan and half-and-half, and season to taste with salt and pepper. Stir in pasta, and pour egg mixture into the skillet. Cook for 4 minutes over medium heat.
6. Transfer the skillet to the oven, and bake for 10 minutes or until top is browned. Remove the skillet from the oven, and run a spatula around the sides of the skillet and underneath frittata to release it from the pan. Slide frittata onto a platter, and cut it into wedges. Serve immediately.
# **Baked Eggs with Herbed Cheese**
Shirred eggs were the epitome of elegance in the Victorian era, and this easy recipe is an updated version.
**3 TB. unsalted butter**
½ cup heavy cream
12 large eggs
½ cup herbed chèvre or
Boursin cheese
3 **TB.** chopped fresh chives
or parsley
Salt and freshly ground black
pepper to taste
1. Preheat the oven to 450°F, and bring a kettle of water to a boil.
2. Divide butter and cream into the bottom of 12 (6-ounce) ovenproof ramekins. Break 1 egg into the center of each ramekin, and dot the top of each egg with 2 teaspoons cheese. Sprinkle eggs with chives, salt, and pepper.
3. Arrange ramekins in a baking pan, and pour boiling water into the pan so it comes halfway up the sides of the ramekins for a _bain marie_. Bake eggs for 7 to 10 minutes or until whites are set. Serve immediately.
**Variation:** Grated cheddar, dilled Havarti, or jalapeño Jack work well in this dish, too.
**Fast Talk**
Bain marie is the French term for a simmering water bath that cooks food gently. The water temperature is actually lower than the oven temperature, as water only reaches 212°F, so delicate egg dishes and custards set without getting rubbery.
Serves: 6
**Active time:** 5 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
304 calories
235 calories from fat
26 g fat
13 g saturated fat
15 g protein
2 g carbohydrates
**Chapter 8**
**Convertible Cooking: Casual Meals for Brunch or Supper**
**In This Chapter**
• Hearty hashes
• Fancy pancakes
• Filling pepper and other veggie dishes
• Egg additions
After you've cooked a recipe and liked the results, you're likely to want to cook it again. You've come to the right place, because the recipes in this chapter serve double duty on the brunch table or as a casual supper.
_Brunch_ is the composite word for "breakfast and lunch" and is most often a savory dish that might or might not contain eggs. The same definition holds true for a casual supper. What changes are the side dishes for different times of the day.
Many dishes in this chapter are some sort of hash. _Hash_ comes from the French _hacher,_ which means "to chop." And what's chopped can range from standards such as corned beef and grilled chicken to succulent smoked salmon.
# **Brunch Bonuses**
Think about the breakfast part of the day when planning for tag-alongs for brunch. Fruit salads are always welcomed, and beverages can be either fruit juices or juices blended with sparkling wine for a mimosa or wine and fruit for a version of sangria.
Breads and other side dishes should also carry on the early morning theme. Muffins, croissants, quick breads, and Danish pastries pair with coffee following or during the meal to anchor the dish to the early part of the day.
Don't feel obligated to make anything other than the main course yourself. After all, it's early in the day and there's bound to be a good bakery within a few miles.
# **Sides for Supper**
The crunchy dinner side dishes could be a tossed salad or some sort of raw or cooked vegetable salad. Take a peek at the recipes for small salads in Chapter 11 for inspiration.
What to serve to drink? It is supper time, so the same wine or beer you'd serve with other meals would work here, too.
For dessert, anything goes. It can be a light fruit dessert from Chapter 20 or a rich chocolate concoction found in the pages of Chapter 21.
# **Southwest Sweet Potato Pancakes with Salsa Cream**
Potato pancakes go from homey to haute when they're made with sweet potatoes and topped with spicy salsa.
**4 large sweet potatoes (about**
**3** **½ lb. total), scrubbed and**
**cut into 1-inch dice**
**1 medium onion, peeled and**
**cut into 1-inch dice**
**2 large eggs**
**3 TB. all-purpose flour**
**½ cup chopped fresh cilantro**
**1 jalapeño chili, seeds and**
**ribs removed, and finely**
**chopped**
**1 TB. ground cumin**
**Salt and freshly ground black**
**pepper to taste**
**½ cup vegetable oil**
**1 cup crème fraîche**
**2 cups Three Tomato Salsa**
**(recipe in Chapter 18) or**
**good-quality refrigerated**
**salsa**
**6 sprigs cilantro for garnish**
**(optional)**
1. Preheat the oven to 200°F, and line a baking sheet with aluminum foil.
2. Place 1 cup sweet potato cubes in a food processor fitted with the steel blade. Chop finely using on-and-off pulsing. Scrape potatoes into a colander, and repeat until all sweet potatoes and onion are finely chopped. (You can also do this through the large holes of a box grater.) Press on sweet potatoes and onion with the back of a heavy spoon to extract as much liquid as possible.
3. Whisk eggs, flour, cilantro, jalapeño, cumin, salt, and pepper in a large mixing bowl. Add sweet potato and onion mixture, and stir well.
4. Heat oil in a heavy 12-inch skillet over medium-high heat. Add batter by ¼-cup measures and flatten with a slotted spatula. Cook for 4 minutes or until browned and crisp. Turn gently with a slotted spatula and fry other side. Remove pancakes from the skillet and drain on paper towels. Place pancakes in the warm oven with the door ajar, and repeat with remaining batter.
5. To serve, spread tops of pancakes with crème fraîche and top with salsa. Garnish with cilantro sprigs (if using) and serve immediately.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
432 calories
318 calories from fat
35 g fat
12 g saturated fat
6 g protein
26 g carbohydrates
**Stale Stuff**
When using a food processor for puréeing food, never fill it more than ⅔ way up so there's room for the food to move. When you're chopping food finely, it needs a lot more space than that. Don't fill it more than ¼ full.
Serves: 6
**Active time:** 18 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
416 calories
290 calories from fat
32 g fat
12 g saturated fat
22 g protein
11 g carbohydrates
**Fresh Ways**
When buying mushrooms, it's best to choose loose ones rather than prepackaged. Look for tightly closed mushrooms. If the brown gills on the bottom are showing, the mushrooms are past their prime.
# **Summertime Baked Eggs**
A mélange of fresh vegetables form the base for baked eggs. Feel free to experiment with different vegetables.
**½ lb. white mushrooms**
**¼ cup olive oil**
**2 TB. unsalted butter**
**6 scallions, rinsed, trimmed,**
**and thinly sliced**
**1 red bell pepper, seeds and**
**ribs removed, and chopped**
**3 garlic cloves, peeled and**
**minced**
**6 ripe plum tomatoes, rinsed,**
**cored, seeded, and chopped**
**2 tsp. Herbes de Provence**
**Salt and freshly ground black**
**pepper to taste**
**12 large eggs**
**1** **½ cups grated Monterey**
**Jack cheese**
1. Preheat the oven to 350°F, and grease a 9×13-inch baking dish.
2. Wipe mushrooms with a damp paper towel. Discard stems, and slice mushrooms thinly.
3. Heat olive oil and butter in a medium skillet over medium heat. Add scallions, red bell pepper, mushrooms, and garlic. Cook, stirring frequently, for 3 minutes or until scallions are translucent. Add tomatoes and Herbes de Provence, raise the heat to medium-high, and cook, stirring frequently, for 5 minutes or until mixture has slightly thickened and liquid has almost evaporated. Season vegetables to taste with salt and pepper.
4. Spread vegetables in the baking dish in an even layer. Make 12 depressions in the vegetables with the back of a spoon, and break an egg into each. Sprinkle eggs with salt and pepper and sprinkle cheese over the top of eggs and vegetables.
5. Bake for 12 to 15 minutes or until eggs are just set. Serve immediately. (Vegetable mixture can be prepared 1 day in advance and refrigerated, tightly covered. Reheat over low heat before adding eggs and baking.)
# **Smoked Salmon Hash with Poached Eggs**
"Cheating" by using frozen hash-brown potatoes gets this dish on the table fast—a boon to morning meals.
**½ lb. sliced smoked salmon,**
**cut into** **½-in. strips**
**1 small red onion, peeled and**
**finely chopped**
**¼ cup capers, drained and**
**rinsed**
**⅓ cup sour cream**
**2 TB. prepared white horse-radish**
**2 TB. Dijon mustard**
**3 TB. unsalted butter**
**2 TB. olive oil**
**½ lb. (2 cups) frozen hash-brown**
**potatoes**
**Salt and freshly ground black**
**pepper to taste**
**12 large eggs, cold**
**2 TB. distilled white vinegar**
1. Combine smoked salmon, onion, capers, sour cream, horseradish, and Dijon mustard in a mixing bowl and set aside.
2. Heat butter and oil in a large, heavy skillet over medium-high heat. Add potatoes and cook for 10 to 12 minutes or until golden brown. Reduce heat to low, and stir in salmon mixture. Cook, stirring gently, for 2 minutes or until heated through. Season to taste with salt and pepper.
3. While potatoes are cooking, poach eggs. Bring a saucepan of water to a simmer and add vinegar. Break eggs, one at a time, into a custard cup or saucer. Holding the dish close to water's surface, slip egg into water. Cook eggs for 3 to 5 minutes, depending on desired doneness, keeping water at just a bare simmer. Remove eggs with a slotted spoon and place them in a bowl of cold water for 10 seconds to remove vinegar and stop the cooking. Place eggs gently on a kitchen towel to drain.
4. To serve, place a portion of hash onto each plate and top with 2 poached eggs. (Hash can be prepared 3 hours in advance and reheated gently over low heat. If you're not serving eggs immediately, leave them in cold water for up to 3 hours. Reheat eggs by holding them in simmering water in a slotted spoon for 20 seconds.)
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
355 calories
222 calories from fat
25 g fat
9 g saturated fat
22 g protein
12 g carbohydrates
**Fresh Ways**
If you're not sure about the freshness of your eggs, float them in a bowl of cold water. Fresh eggs sink to the bottom of the bowl, because as eggs age, air pockets form that cause them to float. If the eggs are floating high on the surface of the water, it's best to get a fresh dozen.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 1 hour,
including 30 minutes for
marinating
**Each serving contains:**
436 calories
214 calories from fat
24 g fat
8 g saturated fat
27.5 g protein
28 g carbohydrates
**Speedy Solutions**
The smaller the cubes of hard foods like potatoes or carrots, the faster they cook. If you want to rush a recipe and it specifies potatoes that are quartered, feel free to cut them into smaller pieces.
# **Grilled Chicken Hash**
The smoky nuances from the grilled chicken meld with the sweet flavor of caramelized onions to create a memorable dish.
**4 (6-oz.) boneless, skinless**
**chicken breast halves**
**⅓ cup olive oil**
**3 garlic cloves, peeled and**
**minced**
**1 TB. herbes de Provence**
**Salt and freshly ground black**
**pepper to taste**
**4 TB. unsalted butter**
**2 large sweet onions, such as**
**Vidalia or Bermuda, peeled**
**and diced**
**1 tsp. granulated sugar**
**1** **½ lb. red-skinned potatoes,**
**scrubbed and cut into** **½-inch**
**dice**
1. Light a charcoal or gas grill.
2. Trim any visible fat off chicken breasts and pound chicken between 2 sheets of plastic wrap to an even thickness of ½ inch using the flat side of a meat mallet or the bottom of a heavy skillet.
3. Place 3 tablespoons olive oil in a mixing bowl and add garlic, herbes de Provence, salt, and pepper. Add chicken breasts, turning them to coat with mixture. Marinate chicken for 30 minutes. Grill chicken for 3 or 4 minutes on each side or until cooked through and no longer pink. When cool, dice chicken into ½-inch pieces and set aside.
4. While chicken is marinating, heat butter and remaining olive oil in a large saucepan over low heat. Add onions, toss to coat with fats, and cover the pan. Cook over low heat for 10 minutes, stirring occasionally. Uncover the pan, raise the heat to medium, sprinkle with salt, and stir in sugar. Cook for 15 to 20 minutes, stirring frequently, until onions are medium brown.
5. Preheat the oven to 450°F, and grease a 9×13-inch baking pan.
6. While onions are cooking, place potato cubes in a large saucepan of salted water. Bring to a boil over high heat, and boil for 10 to 12 minutes or until potatoes are very tender when tested with the tip of a paring knife. Drain potatoes and mash roughly with a potato masher. Set aside.
7. Add chicken and onions to potatoes and mix well. Season to taste with salt and pepper. Spread hash into prepared pan, and bake for 10 minutes or until top is lightly brown. Serve immediately. (Hash can be prepared 2 days in advance and refrigerated, tightly covered. Reheat covered with aluminum foil for 10 minutes and then remove foil and bake for 10 more minutes.)
**Variation:** You can substitute diced cooked ham or roast beef for the grilled chicken—or any leftover roasted chicken.
# **Welsh Rarebit with Tomatoes and Bacon**
Welsh rarebit is a traditional "high tea" meal for British laborers; it was their evening meal because lunch was the heavy meal of the day.
**1 lb. bacon**
**3 large ripe tomatoes, rinsed,**
**cored, seeded, and thinly**
**sliced**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 slices white or whole-wheat**
**bread**
**1 (12-oz.) can lager beer**
**1 TB. prepared mustard,**
**preferably English**
**2 tsp. paprika**
**½ tsp. cayenne**
**1 lb. (4 cups) sharp cheddar**
**cheese, coarsely grated**
**1 TB. cold water**
**1 TB. cornstarch**
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
779 calories
543 calories from fat
60 g fat
27.5 g saturated fat
31 g protein
24 g carbohydrates
1. Place bacon in a large heavy skillet. Cook over medium-high heat, turning as necessary with tongs, for 5 to 7 minutes or until bacon is crisp. Remove bacon from the pan with a slotted spoon, and drain on paper towels.
2. While bacon is cooking, sprinkle tomatoes with salt and pepper, and set aside. Toast bread slices, and set aside.
3. Combine beer, mustard, paprika, and cayenne in a heavy 2-quart saucepan, and stir well. Bring to a simmer over medium heat.
4. Add cheddar cheese to beer by ½-cup measures, stirring constantly with a whisk in a figure-eight pattern. Add additional cheese only after the previous addition is melted.
5. Combine water and cornstarch in a small bowl, and stir to dissolve cornstarch. Add to cheese mixture, and bring to a simmer, stirring constantly. Cook over low heat for 1 or 2 minutes or until thickened. Season to taste with salt and pepper.
6. To serve, place toast slices on individual plates and top with sliced tomatoes and bacon. Spoon cheese mixture over all, and serve immediately.
**Fresh Ways**
Sprinkling tomatoes with salt and pepper in advance of eating them, even by a few minutes, increases the taste of the tomato. The salt absorbs into the fruit so it tastes succulent but not salty.
**Variation:** Sliced turkey, roast beef, or ham can be used in place of bacon.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 50 minutes
**Each serving contains:**
818 calories
354 calories from fat
39 g fat
24 g saturated fat
48 g protein
67 g carbohydrates
# **Baked Macaroni and Cheese with Ham**
If you omit the ham, this creamy mac and cheese becomes a side dish for 10 for any simple entrée.
**1 (1-lb. pkg.) elbow macaroni**
**4 TB. unsalted butter**
**4 TB. all-purpose flour**
**1 tsp. paprika**
**¼ tsp. cayenne**
**1 cup chicken stock**
**2 cups whole milk**
**1 lb. (4 cups) grated sharp**
**cheddar cheese**
**1 TB. Dijon mustard**
**Salt and freshly ground black**
**pepper to taste**
**1 lb. cooked ham, trimmed of**
**fat and cut into** **½-inch cubes**
1. Preheat the oven to 400°F, and grease a 10×14-inch baking pan.
2. Bring a large pot of salted water to a boil. Add macaroni, and cook for 2 minutes less than the package directions indicate. Drain and set aside.
3. Melt butter in a saucepan over low heat. Stir in flour, paprika, and cayenne, and stir constantly for 2 minutes. Whisk in chicken stock, and bring to a boil over medium-high heat, whisking constantly. Reduce heat to low, and simmer for 2 minutes. Stir in whole milk and all but ½ cup grated cheese, stirring until cheese is melted. Stir in Dijon mustard, and season to taste with salt and pepper.
4. Stir ham and macaroni into sauce, and transfer mixture to the prepared baking pan. Cover with aluminum foil and bake for 10 minutes. Remove foil, sprinkle with remaining ½ cup cheese, and bake for 15 to 20 more minutes or until bubbly. Allow to sit for 5 minutes before serving.
**Variation:** Replace the ham with cooked sausage, chicken, or turkey, or make this dish vegetarian by using sautéed mushrooms and peppers instead of the ham and vegetable stock instead of the chicken stock.
**Fresh Ways**
When pasta is going to be baked in a sauce after its initial boiling it's best to undercook it by a few minutes. It will absorb moisture from the sauce and finish cooking in the oven without overcooking.
# **Sausage and Pepper Hash**
A dramatic way to serve this dish individually is in halved bell peppers that are blanched for 5 minutes before baking.
**1** **½ lb. bulk pork sausage**
**10 shallots, peeled and**
**minced**
**6 garlic cloves, peeled and**
**minced**
**2 yellow bell peppers, seeds**
**and ribs removed, and finely**
**chopped**
**2 red bell peppers, seeds**
**and ribs removed, and finely**
**chopped**
**2 green bell peppers, seeds**
**and ribs removed, and finely**
**chopped**
**1 jalapeño chili, seeds and**
**ribs removed, finely chopped**
**½ cup chopped fresh parsley**
**1 TB. chopped fresh sage or**
**1 tsp. dried**
**1 TB. fresh thyme leaves**
**or 1 tsp. dried**
**1 TB. chopped fresh rose-**
**mary leaves or 1 tsp. dried**
**2 tsp. chopped fresh oregano**
**or** **½ tsp. dried**
**3 bay leaves**
**Salt and freshly ground black**
**pepper to taste**
**12 large eggs**
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
580 calories
413 calories from fat
46 g fat
16 g saturated fat
31 g protein
11 g carbohydrates
**Stale Stuff**
Bay leaves have an extremely bitter flavor and should always be removed from a dish before serving. They're left whole when included in a recipe because it makes them easier to spot at the end.
1. Preheat the oven to 350°F.
2. Place a large skillet over medium-high heat. Add sausage, breaking up any lumps with a fork, and brown sausage for 5 minutes or until no pink remains. Remove sausage from the pan with a slotted spoon and set aside. Discard all but 2 tablespoons sausage fat from the skillet.
3. Add shallots, garlic, yellow bell peppers, red bell peppers, green bell peppers, and jalapeño to the pan. Cook over medium-high heat, stirring frequently, for 3 minutes or until shallots are translucent. Return sausage to the pan, and add parsley, sage, thyme, rosemary, oregano, and bay leaves. Simmer mixture over low heat, stirring occasionally, for 15 to 20 minutes or until vegetables are soft. Remove and discard bay leaves. Tilt the pan and skim off as much grease as possible. Season mixture to taste with salt and pepper.
4. Spread sausage mixture in a 9×13-inch baking dish. Make 12 indentations in mixture with the back of a spoon, and break 1 egg into each. Sprinkle eggs with salt and pepper, and bake for 12 to 15 minutes or until egg whites are set. Serve immediately. (Sausage mixture can be made 2 days in advance and refrigerated, tightly covered. Reheat over low heat or in a microwave oven before adding eggs and baking.)
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 35 minutes
**Each serving contains:**
302 calories
159 calories from fat
18 g fat
5 g saturated fat
22 g protein
15 g carbohydrates
# **Stuffed Peppers**
Sausage in tomato sauce sits beneath a baked egg when these are brought to the table.
**6 small red, yellow, or orange**
**bell peppers that sit evenly**
**when placed on a flat surface**
**2 TB. olive oil**
**¼ cup Italian breadcrumbs**
**1 lb. bulk sweet Italian sausage**
**½ cup marinara sauce**
**1 TB. chopped fresh parsley**
**1 TB. chopped fresh basil**
**or** **½ tsp. dried**
**6 large eggs**
**Salt and freshly ground black**
**pepper to taste**
**3 TB. freshly grated**
**Parmesan cheese**
1. Bring a large pot of salted water to a boil over high heat. Preheat the oven to 375°F, and grease a 9×13-inch baking pan.
2. Cut tops off peppers. Discard tops and seeds, and pull out ribs with your fingers. Boil peppers for 4 minutes. Remove from water with tongs and place upside down on paper towels to drain.
3. While peppers are blanching, heat olive oil in a heavy skillet over medium heat. Add breadcrumbs and cook, stirring constantly, for 2 minutes or until brown. Scrape crumbs into a small bowl, and set aside.
4. In the same pan, cook sausage over medium-high heat, breaking up lumps with a fork. Cook, stirring frequently, for 5 minutes or until brown with no trace of pink. Remove sausage from the pan with a slotted spoon, and drain on paper towels. Discard all grease from the pan. Return sausage to the pan, and add marinara sauce, parsley, and basil. Bring to a boil and simmer, stirring occasionally, for 2 minutes.
5. Place peppers in the baking dish. Evenly divide sausage mixture into the bottom of each pepper. Break 1 egg on top of sausage, and sprinkle eggs with salt and pepper, toasted breadcrumbs, and Parmesan cheese. Bake for 20 minutes, or until egg whites are set. Serve immediately. (Peppers can be prepared for cooking up to 2 hours in advance and kept at room temperature. Bake them just before serving.)
**Stale Stuff**
Green peppers are immature red bell peppers; they're less expensive because they're not as perishable to ship. Green peppers have a harsher flavor than their brightly colored cousins and should not be substituted.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
455 calories
368 calories from fat
41 g fat
14 g saturated fat
18 g protein
3.5 g carbohydrates
# **Bacon, Egg, and Arugula Salad**
Soft-scrambled eggs and crunchy bacon are tossed along with greens for this all-in-one meal.
**¾ lb. bacon 6 cups arugula leaves, rinsed**
**2 TB. unsalted butter and stemmed**
**10 large eggs** **⅓ cup Balsamic Vinaigrette**
**⅓ cup sour cream (recipe in Chapter 11)**
**Salt and freshly ground black**
**pepper to taste**
1. Place bacon in a large, heavy skillet, and cook over medium-high heat for 5 to 7 minutes or until bacon is crisp. Drain and crumble bacon. Set aside. Pour bacon grease out of the skillet.
2. Melt butter in the same skillet over low heat.
3. Whisk eggs with sour cream, salt, and pepper. When butter has melted, pour eggs into the skillet and then cover the pan. After 3 minutes, stir eggs and cover the pan again. Cook for another 2 or 3 minutes or until eggs are ¾ set.
4. While eggs are cooking, place arugula in a salad bowl. Toss with Balsamic Vinaigrette. Add reserved bacon and hot eggs to salad bowl, and toss gently. Serve immediately. (Balsamic Vinaigrette can be made 2 days in advance and refrigerated, tightly covered.)
**Speedy Solutions**
An alternative to frying bacon is to bake it on a baking pan in a 325°F oven for 15 minutes or until crisp. The baking time depends on the thickness of the bacon.
# **Corned Beef Hash with Baked Eggs**
Buying the corned beef precooked from the supermarket makes this hash that much easier to prepare.
**1** **½ lb. red-skinned potatoes,**
**scrubbed and cut into** **½-inch**
**dice**
**1 TB. unsalted butter**
**2 TB. vegetable oil**
**1 large sweet onion, such as**
**Bermuda or Vidalia, peeled**
**and diced**
**1 red bell pepper, seeds and**
**ribs removed, and chopped**
**2 garlic cloves, peeled and**
**minced**
**1** **½ lb. cooked corned beef,**
**coarsely chopped**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 large eggs**
1. Preheat the oven to 350°F. Grease a 9×13-inch baking pan.
2. Place potato cubes in a large saucepan of salted water. Bring to a boil over high heat, and boil for 10 to 12 minutes or until potatoes are very tender when tested with a knife. Drain potatoes and mash roughly with a potato masher. Set aside.
3. While potatoes are cooking, heat butter and oil in a large skillet over medium heat. Add onion, red bell pepper, and garlic. Cook, stirring frequently, for 10 minutes or until vegetables are soft. Add corned beef, mashed potatoes, and thyme, and mix well. Season to taste with salt and pepper. (You can do this a day in advance and refrigerate, tightly covered. Add 15 minutes to the initial covered baking if chilled.)
4. Spread hash in the prepared baking pan, and create 6 to 8 evenly spaced indentations in top of hash. Break 1 egg into each indentation, and sprinkle eggs with salt and pepper. Bake for 12 to 15 minutes or until whites are set. Serve immediately.
**Stale Stuff**
When making a dish that contains corned beef, ham, prosciutto, sausage, or any cured or spiced meat, use salt sparingly, if at all, because all these foods already have a high salt content. In a dish such as this one with potatoes, chances are you'll need to add additional salt, but that's not usually the case.
Serves: 6
**Active time:** 28 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
535 calories
309 calories from fat
34 g fat
11 g saturated fat
31 g protein
25 g carbohydrates
**Chapter 9**
**Crusty Creations: Hot Sandwiches and Quiches**
**In This Chapter**
• Creative quesadillas
• Panini with panache
• Quick-cooking quiches
There's something so appealing about crunchy textures, be it from a sandwich or an actual crust. And those are the recipes you'll find in this chapter. Hot sandwiches elevate everyone's favorite finger food into a more elegant meal, and you'll find ones made crisp by grilling and others that top toast with luscious sauces.
Egg custard tarts are usually lumped under the "quiche" moniker. They bake quickly and can be flavored in myriad ways. You'll find classic and contemporary fillings for quiches here, too.
# **Great Grill!**
One of the greatest small appliances to come on the market in the past decade is the sloping double-sided grill. Boxing great George Foreman is famous in this field, although many companies now manufacture such grills. I love these grills for indoor cooking because they cook both sides at the same time, which cuts down on cooking time.
I've recently discovered how great these grills are for making sandwiches. There are some expensive panini presses on the market, but they're really superfluous unless you want every gadget in the aisle
# **Sophisticated Sandwiches**
It used to be that quesadillas ( _case-ah-DEE-yas_ ) were only found on Mexican menus; the word _quesadilla_ comes from the Spanish word _queso,_ which means "cheese." But that's all changed today. Quesadillas now mean any hot sandwich made in a flour tortilla.
While some recipes are fried, I prefer to bake them to cut back on the fat. If you don't want to wait for the stove to preheat, heat 2 tablespoons vegetable oil in a heavy 12-inch skillet over medium-high heat. Add the quesadillas, and cook for 2 minutes per side or until browned and the cheese has melted. Turn the quesadillas gently with a slotted spatula, and blot them with paper towels before serving.
If you've never heard of panini ( _pah-NEE-nee_ ), you're missing out! You must acquaint yourself with these grilled Italian sandwich snacks that traditionally have stripe marks on both sides from the grill.
# **Quiche Quickie**
Quiche ( _KEESH_ ) originated in the Alsace-Lorraine region in northeastern France. The only common denominator to call something a quiche is that the base is an egg and cream custard and it's baked as an open-faced tart. Other than that, it's all up to you.
**Fresh Ways**
While quiches can be fully baked in advance and reheated, they look so pretty coming to the table lightly puffed right from the oven that it's a shame to miss that visual part of the experience.
One step you should not skip when making quiches is partially baking the crust before adding the filling. This ensures a crispy crust. You can pre-bake the pie shell and make the filling in advance, and relax during the final 30-minute-or-less baking time.
Quiches are done when the egg mixture no longer jiggles in any way and a knife inserted into the center comes out clean, without any egg particles clinging to it.
# **Eggplant and Red Pepper Panini**
This healthful sandwich is reminiscent of eggplant Parmesan, with melted cheese layered with vegetables.
**6 red bell peppers (or 6**
**jarred roasted red peppers)**
**6 Italian eggplant, rinsed,**
**trimmed, and cut into** **¼-inch**
**slices**
**Salt and freshly ground black**
**pepper to taste**
**½ cup olive oil**
**12 slices Italian bread,** **¼ inch**
**thick and 8 inches wide**
**¾ lb. thinly sliced fontina**
**cheese**
Serves: 6
**Active time:** 30 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
661 calories
349 calories from fat
39 g fat
14 g saturated fat
25 g protein
59 g carbohydrates
1. Preheat an oven broiler. Place red peppers on the rack of a broiler pan and broil 4 inches from the broiler element until skin is charred and black. Turn peppers with tongs to char all sides. Plunge peppers into ice water, and when cool enough to handle, remove and discard cap, skin, and seeds. Slice peppers into thin slices, and set aside.
2. Season eggplant slices to taste with salt and pepper. Arrange slices on the rack of the broiler pan, and brush slices with olive oil. Broil eggplant for 3 minutes per side, turning gently with a slotted spatula. (You might have to do this in batches.) Remove eggplant from the broiler and set aside.
3. Preheat a two-sided grill (if using). Brush one side of bread slices with remaining olive oil. Place bread slices, oiled sides down, on the counter or a plate. Place half of eggplant slices on a slice of bread, and top with half of cheese, roasted peppers, remaining cheese, and remaining 2 bread slices, oiled sides up.
4. Grill sandwiches in a two-sided grill for 3 or 4 minutes or until bread is brown and cheese is melted. Alternately fry sandwiches for 3 minutes per side in a ridged grill pan or any large skillet, turning it once, weighted down by a pan. Cut sandwiches in half, and serve immediately.
**Fresh Ways**
Like all fruits, eggplants have male and female gender, and the males are preferable because they are less bitter and have fewer seeds. To tell a male from a female, look at the stem end. The male is rounded and has a more even hole, and the female hole is indented.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 50 minutes, including 15 minutes for marinating
**Each serving contains:**
728 calories
360 calories from fat
40 g fat
12 g saturated fat
55 g protein
35 g carbohydrates
**Speedy Solutions**
As long as you're pounding chicken breasts, do a few extra. Freeze them flat, wrapping each one in plastic wrap and placing the group into a heavy resealable plastic bag. Pounded breasts defrost very quickly.
# **Grilled Chicken, Sun-Dried Tomato, and Mozzarella Panini**
Sun-dried tomatoes are a miracle food in the way they give foods an intense flavor without juice, so they're perfect for this sandwich.
**6 (6-oz.) boneless, skinless**
**chicken breast halves**
**Salt and freshly ground black**
**pepper to taste**
**½ cup olive oil**
**4 garlic cloves, peeled and**
**minced**
**3 TB. chopped fresh rose-mary**
**or 2 tsp. dried**
**12 slices Italian bread,** **¼ inch**
**thick and 8 inches wide**
**¾ cup sun-dried tomatoes**
**packed in olive oil, drained**
**and chopped**
**¾ lb. fresh mozzarella,**
**drained and sliced**
1. Rinse chicken, pat dry with paper towels, and trim of all visible fat. Place chicken between two sheets of plastic wrap and pound to an even ¼-inch thickness. Place chicken on a platter, and season both sides to taste with salt and pepper. Combine ¼ cup olive oil, garlic, and 1 tablespoon rosemary in a small bowl. Rub mixture on both sides of chicken. Let chicken sit at room temperature for 15 minutes, covered with plastic wrap.
2. Preheat a grill or oven broiler. Grill or broil chicken for 4 minutes on a side, turning it gently with tongs, or until chicken is cooked through and no longer pink. Set aside.
3. Preheat a two-sided grill (if using). Brush one side of bread slices with remaining olive oil. Place bread slices, oiled sides down, on the counter or a plate. Place 1 chicken breast on a slice of bread, and top with ⅙ of sun-dried tomatoes, ⅙ of mozzarella, and remaining 6 bread slices, oiled sides up.
4. Grill sandwiches in a two-sided grill for 3 or 4 minutes or until bread is brown and cheese is melted. Alternately fry sandwiches for 3 minutes per side in a ridged grill pan or any large skillet, turning them once, weighted down by a pan. Cut sandwiches in half, and serve immediately.
**Variation:** This recipe works equally well with leftover roast chicken or a thin fish fillet such as sole or tilapia.
# **Cuban Quesadillas**
The traditional combination of ham, pork, pickles, mustard, and Swiss cheese is the filling for these crispy sandwiches.
**6 (10-in.) flour tortillas**
**6 TB.** _**Dijon mustard**_
**1 lb. thinly sliced roast pork**
**1 lb. baked ham**
**1 cup thinly sliced dill pickles**
**3 cups grated Swiss cheese**
**Vegetable oil spray**
1. Preheat the oven to 450°F. Cover 2 baking sheets with heavy-duty aluminum foil, and spray foil with vegetable oil spray.
2. Place tortillas on a counter. Spread Dijon mustard on each tortilla. Layer roast pork, baked ham, and pickle slices on one half of each tortilla. Sprinkle Swiss cheese over filling. Fold blank side of tortillas over filling, and press closed with the palm of your hand or a spatula. Arrange tortillas on prepared baking sheets, and spray tops with vegetable oil spray.
3. Bake quesadillas for 10 minutes. Turn them gently with a spatula, and press them down if the top has separated from the filling. Bake for an additional 5 minutes or until crispy.
4. Allow quesadillas to sit for 3 minutes and then cut each in half and serve immediately. (You can do this up to 6 hours in advance and refrigerate the quesadillas, covered with plastic wrap. Add 3 minutes to the baking time if chilled.)
**Variation:** Try thinly sliced chicken or roast beef instead of roast pork.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
662 calories
262 calories from fat
29 g fat
15 g saturated fat
49 g protein
52 g carbohydrates
**Fast Talk**
Dijon mustard, known for its clean, sharp flavor, was actually invented in Dijon, France. It is made from a combination of brown and black mustard seeds, and the essential ingredients are white wine and unfermented grape juice.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
576 calories
238 calories from fat
26.5 g fat
13 g saturated fat
37 g protein
48 g carbohydrates
**Speedy Solutions**
If you don't have any hard-cooked eggs in the house, pick some up at the supermarket salad bar. The salad bar is also a great place if all you need is a small amount of any ingredient contained in its bins.
# **Springtime Quesadillas**
Have ham, hard-cooked eggs, and asparagus left over from Easter dinner? Here's a great way to use them up!
**1 lb. fresh asparagus spears**
**6 (10-in.) flour tortillas**
**4 oz. Boursin cheese with**
**garlic and herbs, softened**
**1 lb. baked ham, thinly sliced**
**6 hard-cooked eggs, peeled**
**and cut into 6 slices each**
**3 ripe plum tomatoes, rinsed,**
**cored, seeded, and thinly**
**sliced**
**Freshly ground black pepper**
**to taste**
**1** **½ cups grated sharp cheddar**
**Vegetable oil spray**
1. Preheat the oven to 450°F. Cover 2 baking sheets with heavy-duty aluminum foil, and spray the foil with vegetable oil spray. Have a bowl of ice water handy.
2. Break woody stems off asparagus, and place spears in a microwave-safe dish. Sprinkle with water, and cover dish tightly with plastic wrap. Microwave on high (100 percent) for 1 minute. Remove asparagus, cut slit in plastic wrap to allow steam to escape, and plunge asparagus into ice water to stop the cooking action. Drain, and set aside.
3. Place tortillas on the baking sheets, and spread Boursin on half of each tortilla. Layer ham, eggs, tomatoes, and asparagus on top of cheese. Season with pepper, and spread ¼ cup cheddar on each quesadilla. Fold empty half of tortillas over filled sides, pressing with the palm of your hand to seal tightly. Spray tops with vegetable oil spray.
4. Bake quesadillas for 5 minutes, turn gently with a spatula, and bake for 4 or 5 minutes more or until browned. Allow quesadillas to sit for 3 minutes and then cut into 2 or 3 wedges. Serve immediately. (Quesadillas can be prepared for baking up to 1 day in advance and refrigerated, tightly covered.)
**Variation:** Instead of ham, try this recipe with sliced turkey, chicken, or roast beef. Instead of cheddar, try Gruyère.
# **Tuna Melt with Olives**
Mellow kalamata olives added to the tuna salad make this fast meal special.
**3 (6-oz.) can light tuna,**
**drained and flaked**
**¾ cup mayonnaise**
**3 celery ribs, rinsed,**
**trimmed, and chopped**
**¾ cup pitted kalamata or**
**other pitted brine-cured**
**black olives, chopped**
**3 TB. chopped fresh parsley**
**2 TB. freshly squeezed lemon**
**juice**
**Freshly ground black pepper**
**to taste**
**6 slices rye bread, lightly**
**toasted**
**1** **½ cups grated sharp cheddar**
**cheese**
1. Preheat an oven broiler, and cover a baking sheet with heavy-duty aluminum foil. Combine tuna, mayonnaise, celery, olives, parsley, lemon juice, and pepper in medium mixing bowl. Stir well.
2. Place toast slices on the baking sheet, and divide tuna mixture among them. Spread tuna evenly, and top with grated cheese.
3. Broil sandwiches 6 inches from the broiling element for 2 minutes or until cheese is melted and bubbly. Serve immediately.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 17 minutes
**Each serving contains:**
520 calories
315 calories from fat
35 g fat
11 g saturated fat
32 g protein
18 g carbohydrates
**Stale Stuff**
Due to the high amount of salt in canned tuna, plus the salt added to commercial mayonnaise, you shouldn't add salt to a tuna salad—at least before tasting it.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
548 calories
287 calories from fat
32 g fat
18.5 g saturated fat
41 g protein
24 g carbohydrates
**Fast Talk**
Roux (pronounced _ROO,_ like in kangaroo) is a French term for a mixture of fat and flour used as a thickening agent for soups and sauces. The first step in all roux preparation is to cook the flour so the dish doesn't taste like library paste.
# **Kentucky Hot Brown Sandwich**
This is a knife-and-fork sandwich with ham, turkey, and asparagus topped with a cheddar cheese sauce.
**6 slices thick white bread**
**1 lb. fresh asparagus spears**
**3 TB. unsalted butter**
**3 TB. all-purpose flour**
**1** **½ cups half-and-half**
**2 cups grated sharp or mild**
**cheddar cheese**
**Salt and cayenne to taste**
**⅓ lb. smoked ham, sliced**
**3 cups shredded cooked**
**turkey**
**3 ripe tomatoes, rinsed,**
**cored, seeded, and sliced**
**¼ cup freshly grated**
**Parmesan cheese**
1. Preheat the oven broiler, and cover a baking sheet with heavy-duty aluminum foil. Have a bowl of ice water handy.
2. Toast bread slices and set aside.
3. Break woody stems off asparagus, and place spears in a microwave-safe dish. Sprinkle with water, and cover dish tightly with plastic wrap. Microwave on high (100 percent) for 1 minute. Remove asparagus, cut slit in plastic wrap to allow steam to escape, and plunge asparagus into ice water to stop the cooking action. Drain, and set aside.
4. Melt butter in a saucepan over low heat. Stir in flour, and cook _roux_ for 2 minutes, stirring constantly. Whisk in half-and-half and bring to a boil. Simmer, stirring frequently, for 2 minutes. Stir in cheddar cheese until melted, and season to taste with salt and cayenne. Set aside.
5. Arrange toast slices on the baking sheet. Layer ham, turkey, tomatoes, and asparagus on top of toast. Ladle sauce over asparagus, and sprinkle with Parmesan cheese.
6. Broil 8 inches from the broiler element for 5 minutes or until bubbly and Parmesan is browned. Serve immediately.
**Variation:** Not a fan of asparagus? Try broccoli or cauliflower florets or green beans instead. Love Gruyère? Used it instead of cheddar.
# **Grilled Reuben Sandwich**
The combination of corned beef, sauerkraut, Swiss cheese, and Russian dressing is what defines a classic Reuben, named for a deli in New York.
**1** **½ cups sauerkraut, drained**
**3 TB. unsalted butter, softened**
**12 slices rye bread or pumpernickel**
**¾ cup Russian or Thousand**
**Island dressing**
**¾ lb. thinly sliced Swiss**
**cheese**
**1 lb. thinly sliced corned beef**
1. Place sauerkraut in a large mixing bowl of cold water, and swirl it around well. Drain and repeat three more times. Press dry after the last draining, and set aside.
2. Preheat a two-sided grill (if using). Butter one side of each slice of bread. Spread Russian dressing on the nonbuttered sides. Layer the sauerkraut, Swiss cheese, and corned beef on 2 slices. Enclose filling by topping it with remaining bread slices, buttered side up.
3. Grill sandwiches in a two-sided grill for 3 or 4 minutes or until bread is brown and cheese is melted. Alternately, fry sandwiches for 3 minutes per side in a ridged grill pan or any large skillet, turning it once, weighted down by a pan. Cut sandwiches in half and serve immediately.
**Fresh Ways**
What most people find objectionable about sauerkraut is the salty brine in which it's pickled. By repeatedly rinsing it, you wash away most of this brine.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 18 minutes
**Each serving contains:**
717 calories
399 calories from fat
44 g fat
20 g saturated fat
41 g protein
40 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
564 calories
407 calories from fat
45 g fat
24 g saturated fat
21 g protein
18.5 g carbohydrates
**Stale Stuff**
Stay away from dried chives. Like parsley and cilantro, chives lose all flavor when dried. If you don't have fresh chives, you can always substitute finely chopped green scallion tops, but don't use dried chives.
# **Crab Quiche**
The sweet flavor of fresh crab is enhanced with fresh herbs in this easy and elegant recipe.
**1 (9-in.) pie shell, thawed if**
**frozen**
**3 scallions**
**2 TB. unsalted butter**
**½ lb. crabmeat**
**3 large eggs**
**1** **¼ cups heavy cream**
**2 TB. chopped fresh chives**
**2 TB. chopped fresh cilantro**
**1 TB. chopped fresh rose-mary**
**or 1 tsp. dried**
**1** **½ cups grated Swiss cheese**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven to 400°F. Prick pie shell all over with the tines of a fork, and bake for 8 or 9 minutes or until pastry is set and just starting to brown. Remove crust from the oven, and set aside.
2. While crust is baking, rinse and trim scallions, discarding all but 2 inches of green tops. Slice scallions thinly. Heat butter in a small skillet over medium-high heat. Add scallions and cook, stirring frequently, for 4 minutes or until scallions are soft. Cool for 5 minutes.
3. Place crabmeat on a dark-colored plate. Rub it gently with your fingertips, and discard any bits of shell or cartilage you uncover. Set aside.
4. Reduce the oven temperature to 375°F. Whisk eggs with cream and add chives, cilantro, rosemary, and Swiss cheese. Season to taste with salt and pepper. Stir in crabmeat, fill pie shell, and bake quiche for 25 to 30 minutes or until it's browned and eggs are set. Serve immediately. (Filling can be prepared 1 day in advance and refrigerated, tightly covered. Add 5 to 7 minutes to the baking time if filling is chilled.)
**Variation:** Substitute diced cooked shrimp or chicken for the crab.
# **Herbed Sausage and Tomato Quiche**
Now here's a hearty quiche with aromatic herbs, sweet tomatoes, and your choice of sausage that's sure to please any carnivore for supper as well as lunch.
**1 (9-in.) pie shell, thawed if**
**frozen**
**¾ lb. bulk pork sausage**
**3 garlic cloves, peeled and**
**minced**
**2 shallots, peeled and minced**
**6 ripe plum tomatoes, rinsed,**
**cored, seeded, and finely**
**chopped, or 1 (14.5-oz.) can**
**petite cut canned tomatoes,**
**drained**
**1 TB. herbes de Provence**
**3 large eggs**
**1** **¼ cups heavy cream**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven to 400°F. Prick pie shell all over with the tines of a fork and bake for 8 or 9 minutes or until pastry is set and just starting to brown. Remove crust from the oven, and set aside.
2. While crust is baking, place a large skillet over medium-high heat and crumble sausage into it, breaking up any lumps with a fork. Cook sausage, stirring occasionally, for 5 minutes or until sausage is brown and no pink remains. Add garlic and shallots, and cook, stirring frequently, for 3 minutes or until shallots are translucent. Add tomatoes and herbes de Provence, and cook, stirring occasionally, for 5 to 7 minutes or until tomato juice has evaporated. Cool mixture for 5 minutes.
3. Reduce the oven temperature to 375°F. Whisk eggs with cream, and season to taste with salt and pepper. Stir in sausage mixture, fill pie shell, and bake quiche for 25 to 30 minutes or until it's browned and eggs are set. Serve immediately. (Filling can be prepared 1 day in advance and refrigerated, tightly covered. Add 5 to 7 minutes to the baking time if filling is chilled.)
**Variation:** Try chopped ham or poultry sausage instead of pork sausage.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
588 calories
443 calories from fat
49 g fat
21 g saturated fat
15 g protein
22.5 g carbohydrates
**Fresh Ways**
All the quiche fillings in this chapter can also be used to make about 4 dozen mini-quiches for hors d'oeuvres. Use Athens Foods' prebaked phyllo shells (found in the freezer section of supermarkets), and bake the mini-quiches for 12 to 15 minutes or until the tops are browned.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
625 calories
496 calories from fat
55 g fat
25 g saturated fat
17 g protein
16 g carbohydrates
# **Classic Quiche Lorraine**
This bacon and cheese quiche is the one that started it all in France centuries ago.
**1 (9-in.) pie shell, thawed if**
**frozen**
**½ lb. thick sliced bacon, cut**
**into** _**lardons**_
**3 large eggs**
**1** **¼ cups heavy cream**
**1 cup grated Gruyère**
**Pinch ground nutmeg**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat the oven to 400°F. Prick pie shell all over with the tines of a fork, and bake for 8 or 9 minutes or until pastry is set and just starting to brown. Remove crust from the oven, and set aside.
2. While crust is baking, place a skillet over medium-high heat. Cook bacon for 5 to 7 minutes or until crisp. Remove bacon from the pan with a slotted spoon, and drain on paper towels.
3. Reduce the oven temperature to 375°F. Whisk eggs with cream, Gruyère, and nutmeg and season to taste with salt and pepper. Stir in bacon, fill pie shell, and bake quiche for 25 to 30 minutes or until it's browned and eggs are set. Serve immediately. (Filling can be prepared 1 day in advance and refrigerated, tightly covered. Add 5 to 7 minutes to the baking time if filling is chilled.)
**Fast Talk**
**Lardons** ( _LAHR-don_ ) is the French term for bacon that's been cut into pieces about the size of matchsticks. It's easiest to do if you buy thick-sliced bacon and then just cut it into very thin slices.
**Chapter 10**
**A Potpourri of Pasta and Pizza**
**In This Chapter**
• Lightning-fast pasta recipes
• Easy vegetarian pastas
• Pizzas with panache
As long as you've got a few boxes of dried pasta in the pantry, dinner is a certainty. There's always something around in the cupboard or in the refrigerator to use as a sauce or toss. And as you'll see by the recipes in this chapter, sauces need not take hours to simmer away.
And then there's pizza. Making pizza at home is becoming almost as common as boiling a pot of pasta. And what you top your pizza with can be homey or haute—the choice is up to you. In this chapter, I give you some recipes that are sure to get you thinking about what else you can top your pie with.
# **Pasta Power**
Good-quality dried pasta is made with a high percentage of high-gluten semolina, the inner part of the grain of hard durum wheat. The gluten gives the pasta resilience and allows it to cook while remaining somewhat firm, thus reaching the state of al dente.
Pasta is merely flour and water, so it's high in carbohydrates. The higher a pasta's semolina content, the more protein it contains. The protein in pasta is an incomplete protein, like that of rice, which can be completed by eating it with foods such as beans.
Eggless pasta contains little fat, and other nutrients are added if spinach or tomato flour is used. Each ounce of pasta is approximately 100 calories.
# **Perfect Pasta Tips**
As a general rule, pasta imported from Italy is superior to American factory-made products due to its higher semolina content. Try to purchase pasta you can see through a cellophane window in the box. The pasta should be smooth and shiny, not crumbly.
**Fresh Ways**
Store pasta in a sealed plastic bag after you open the box, and it will stay fresh for at least 6 months. You can still use pasta if it's stale; just add a few minutes to the cooking time.
Traditional dried Italian pastas are named according to their shape. For example, fusilli are twists, and fiochetti are bows. You could fill an entire kitchen with boxes of different-shaped pasta if you wanted a complete selection. Not many people have such a pantry luxury, so instead look at the cooking times and sizes in the following table to determine alternatives you might have on hand to make a recipe.
While the table serves as a guideline, each brand of pasta can vary slightly both in pasta composition and size. It's best to take the manufacturer's advice as to how long to cook each one.
# **Fresh from the Refrigerator Case**
Until the past few years, it was rare to find fresh dough in supermarkets. Some pizza parlors might sell you a ball, or you could find frozen shells, which never really delivered the product you wanted.
But that's all changed today. In almost all cities, you can now purchase ready-to-bake balls of pizza dough. They're right there in the dairy case. Look for a brand made locally, and look at the condition of the ball. It should be shiny but not too puffy. If it shows signs of liquid inside the plastic bag, it means the dough might have been frozen, so don't purchase it.
With a few balls of pizza dough handy, any pizza can be on the table in less time than it takes to have one delivered!
**Fresh Ways**
Pizzas are best if baked on pizza stones that have been heated in the oven as it preheats. A pizza pan that has holes in the bottom so the heat penetrates also yields a crispy crust.
Serves: 8
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
481 calories
164 calories from fat
18 g fat
3 g saturated fat
14.5 g protein
65 g carbohydrates
**Fast Talk**
Escarole is a member of the endive family of vegetables. It has broad, pale green leaves that are slightly curved, and it's more mild in flavor than Belgian or curly endive.
# **Spaghetti with Escarole, Pine Nuts, and Raisins**
Bitter greens, sweet raisins, and crunchy nuts blend masterfully in this quickly prepared dish.
**1** **¼ lb. spaghetti**
**½ cup golden raisins**
**1 lb.** _**escarole**_
**⅓ cup olive oil**
**½ cup pine nuts**
**4 garlic cloves**
**¼ cup dry white wine**
**¼ cup water**
**Salt and freshly ground black**
**pepper to taste**
**¾ cup freshly grated**
**Parmesan cheese**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente _._ Drain, reserving ½ cup cooking liquid, and set aside.
2. Soak raisins in very hot tap water for 15 minutes and then drain and set aside.
3. Rinse escarole well, discard the core, and cut it into thin shreds. Set aside.
4. While water is heating, heat olive oil in a large, heavy skillet over medium heat. Add pine nuts and cook, stirring constantly, for 1 minute or until nuts are browned. Remove nuts from the skillet with a slotted spoon and set aside. Add garlic to the skillet and cook, stirring constantly, for 1 minute. Add escarole, wine, and water to the skillet. Stir well, cover the skillet, and cook, stirring occasionally, for 10 minutes or until escarole is soft. Season to taste with salt and pepper.
5. Add drained pasta to the skillet, and add some reserved cooking water if mixture seems dry. Cook for 2 minutes. Serve immediately, sprinkled with pine nuts. Pass Parmesan cheese separately.
**Variation:** For a little something extra, try adding about 1 pound sautéed Italian sausage or ground turkey to this recipe. Add it to the oil along with the garlic, and it will continue to cook from that point.
# **Pasta with Garlic and Oil (** _ **Pasta Aglio e Olio**_ **)**
This is a classic Italian recipe, and if you're a garlic fan, it's a natural for your repertoire.
**1** **¼ lb. spaghetti or linguine**
**⅔ cup olive oil**
**10 garlic cloves, peeled and**
**minced**
**2 to 3 tsp. crushed red pepper**
**flakes**
**Salt to taste**
**¾ cup freshly grated**
**Parmesan cheese**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente _._ Drain, reserving ½ cup cooking liquid, and set aside.
2. While pasta is cooking, heat olive oil in a heavy 12-inch skillet over medium-high heat. Add garlic and red pepper flakes. Reduce heat to low, and cook, stirring constantly, for 1 minute or until garlic is golden brown.
3. Remove the pan from the heat and add pasta. Toss well, adding some reserved cooking liquid if mixture seems dry. Season to taste with salt, and serve immediately, offering Parmesan cheese separately.
**Speedy Solutions**
Reserving some of the pasta cooking water is a traditional step in Italian cooking for pastas cooked in relatively dry sauces. It can moisten the sauce with the same innate flavor without making the dish taste "watery."
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
462 calories
193 calories from fat
21 g fat
4 g saturated fat
12 g protein
55 g carbohydrates
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
413 calories
89 calories from fat
10 g fat
2 g saturated fat
15 g protein
68 g carbohydrates
**Fresh Ways**
Any food that comes in a tube like anchovy paste or tomato paste can be hard to extract fully, even if you roll up the tube. One way to be sure you're getting it all out is to use a rolling pin on the metal tube before turning the tube forward.
# **Fusilli with Porcini Puttanesca Sauce**
There's a spicy bite to this hearty tomato sauce from Southern Italy.
**1** **¼ lb. fusilli**
**½ cup dried porcini mushrooms,**
**chopped**
**1 cup boiling water**
**3 TB. olive oil**
**1 large onion, peeled and**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**3 lb. ripe plum tomatoes,**
**rinsed, cored, and chopped,**
**or 2 (14.5-oz.) cans diced**
**tomatoes, undrained**
**½ cup Niçoise olives, pitted**
**and chopped**
**2 TB. tomato paste**
**2 TB. capers, drained and**
**rinsed**
**2 TB. anchovy paste (optional)**
**2 tsp. dried oregano**
**2 tsp. dried basil**
**¼ tsp. red pepper flakes or to**
**taste**
**Salt to taste**
**¾ cup freshly grated**
**Parmesan cheese**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente _._ Drain and set aside.
2. Soak mushrooms in boiling water for 10 minutes, pushing them down into the water with the back of a spoon. Drain mushrooms, reserving soaking liquid. Strain soaking liquid through a sieve or coffee filter and set aside.
3. While mushrooms are soaking, heat olive oil in a heavy 2-quart saucepan over medium-high heat. Add onion and garlic, and cook, stirring frequently, for 3 minutes or until onion is translucent. Add tomatoes, olives, tomato paste, capers, anchovy paste (if using), oregano, basil, and red pepper flakes. Bring to a boil over medium-high heat.
4. Add mushrooms and strained soaking liquid to the saucepan when available. Reduce heat to low, and simmer sauce, uncovered, for 20 minutes or until slightly thickened. Season to taste with salt.
5. To serve, top pasta with sauce and pass Parmesan cheese separately.
# **Linguine with White Clam Sauce**
Garlic, herbs, and tomatoes join with clams and white wine in this light sauce.
**1** **¼ lb. linguine**
**2 pt. fresh minced clams**
**¼ cup olive oil**
**2 large shallots, peeled and**
**minced**
**6 garlic cloves, peeled and**
**minced**
**1 (8-oz.) bottle clam juice**
**¾ cup dry white wine**
**¼ cup chopped fresh parsley**
**¼ cup chopped fresh basil**
**½ tsp. red pepper flakes or to**
**taste**
**4 ripe plum tomatoes, rinsed,**
**cored, seeded, and diced**
**Salt and freshly ground black**
**pepper to taste**
**¾ cup freshly grated**
**Parmesan cheese**
1.Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente _._ Drain, and set aside.
2.Place clams in a colander over a mixing bowl. Press with the back of a spoon to extract as much liquid as possible. Refrigerate clams if not using immediately. Reserve clam juice, and refrigerate it also if not cooking immediately.
3.Heat olive oil in a heavy 2-quart saucepan over medium-high heat. Add shallots and garlic, and cook, stirring frequently, for 3 minutes or until shallots are translucent. Add reserved clam juice, bottled clam juice, wine, parsley, basil, and red pepper flakes. Bring to a boil, stirring occasionally. Simmer sauce uncovered for 20 minutes or until reduced by half.
3.Add tomatoes and clams to sauce. Bring to a boil and simmer for 5 minutes. Season to taste with salt and pepper. Add pasta to sauce, and serve immediately, offering Parmesan cheese separately.
**Variation:** For red clam sauce, use red wine in place of white.
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
456 calories
94 calories from fat
10.5 g fat
2 g saturated fat
21 g protein
65 g carbohydrates
**Fresh Ways**
Clams cook so quickly that they should be added to dishes at the end of cooking time. However, a sauce should not be seasoned until after the clams are cooked because they give off liquid into the food.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
706 calories
337 calories from fat
37 g fat
14 g saturated fat
31 g protein
59 g carbohydrates
# **Spaghetti with Egg and Bacon (** _ **Pasta Carbonara**_ **)**
Recipes don't get any faster than this! And there's a lot of black pepper and Parmesan cheese, too.
**1 lb. spaghetti**
**¾ lb. bacon, sliced into**
**½-inch strips**
**6 garlic cloves, peeled and**
**minced**
**Freshly ground black pepper**
**to taste (at least 1** **½ tsp.)**
**6 large eggs, beaten**
**1** **½ cups freshly grated**
**Parmesan cheese**
**Salt to taste**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente _._ Drain and set aside.
2. Place bacon in a heavy 12-inch skillet over medium-high heat. Cook, stirring occasionally, for 5 to 7 minutes or until crisp. Remove bacon from the skillet with a slotted spoon and set aside.
3. Discard all but 2 tablespoons bacon grease from the pan. Add garlic and black pepper, and cook for 30 seconds. Return bacon to the pan and turn off heat.
4. Add drained pasta, and cook over medium heat for 1 minute. Remove the pan from the stove, and stir in eggs. Allow eggs to thicken, but do not put the pan back on the stove or they will scramble. Add cheese, and season to taste with salt and additional pepper. Serve immediately.
**Stale Stuff**
Don't pour bacon grease down the kitchen sink! Bacon grease is notorious for clogging kitchen plumbing, even if it's put down the sink with the hot water running. To better dispose of it, pour it in empty cans or half-pint cream containers after it's cool and dispose of it in the container.
# **Basic Pizza Dough**
This is my favorite recipe, given to me years ago by famed chef Wolfgang Puck, and it's foolproof.
**3 cups all-purpose flour**
**1 (** **¼-oz.) pkg. dry or fresh**
**yeast**
**1 tsp. salt**
**1 TB. honey**
**2 TB. olive oil**
**¾ cup water**
**2 TB. yellow cornmeal**
1. Place flour and yeast in a mixing bowl or the bowl of an electric mixer fitted with a dough hook. Add salt, honey, olive oil, and water, and mix well until dough forms a soft ball.
2. Transfer dough to a lightly floured surface and _knead_ for 5 minutes or until smooth. Place dough in a buttered deep bowl and allow dough to rest, covered with a clean dry towel, for 30 minutes.
3. Preheat the oven to 450°F, and if using a baking stone or tiles, place them in the oven now.
4. Divide dough into 4 equal parts for individual pizzas, and roll each piece into a smooth, tight ball. Place them on a flat dish, covered with a damp towel, and refrigerate until baking time. For 1 large pizza, leave dough as a large ball. (This can be done up to 6 hours in advance, but dough should be removed from the refrigerator 1 hour before baking to reach room temperature.)
5. Lightly flour a work surface, and using the fleshy part of your fingertips, flatten each dough ball into a circle, approximately 6 inches in diameter, leaving the outer edge thicker than the center. Lift dough from the work surface and gently stretch the edges, working clockwise, to form 8-inch circles.
6. Sprinkle cornmeal on pizza paddles or baking sheets, and place pizza on cornmeal. Brush surface with olive oil, and top as desired.
7. Bake pizzas for 10 to 12 minutes, or as directed, until crust is golden brown and topping is bubbly.
Makes: dough for 4
(8-inch) pizzas
**Active time:** 15 minutes
**Start to finish:** 50 minutes, including 30 minutes for rising
**Each serving contains:**
411 calories
69 calories from fat
8 g fat
1 g saturated fat
10 g protein
76 g carbohydrates
**Fast Talk**
To knead is to work dough to make it pliable so it holds the gas bubbles from the leavening agent and expands when heated. Kneading is done with a pressing-folding-turning action. Press down into the dough with the heels of both hands and then push your hands away from your body. Fold the dough in half, give it a quarter turn, and repeat the process.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
386 calories
252 calories from fat
28 g fat
10 g saturated fat
16 g protein
22 g carbohydrates
# **Pizza Margherita**
This is a authentic Italian combination of mozzarella, fresh basil, and tomatoes.
**1 batch Basic Pizza Dough**
**(recipe on previous page) or**
**purchased pizza dough**
**½ lb. whole milk mozzarella**
**cheese, thinly sliced**
**8 ripe plum tomatoes, rinsed,**
**cored, seeded, and chopped**
**½ cup firmly packed fresh**
**basil leaves**
**Salt and freshly ground black**
**pepper to taste**
**4 TB. extra-virgin olive oil**
**2 TB. yellow cornmeal**
1. Make Basic Pizza Dough according to recipe instructions.
2. Preheat the oven to 450°F, and if using a baking stone or tiles, place them in the oven now.
3. Shape pizza dough into 1 large round or 4 individual rounds. Cover with mozzarella and then tomatoes. Scatter basil over the top. Season to taste with salt and freshly ground black pepper, and drizzle 3 tablespoons oil over the top.
4. Sprinkle cornmeal on the baking sheet. Bake pizza for 10 minutes. Reduce the oven temperature to 400°F and bake for an additional 10 minutes or until crust is golden. Drizzle with remaining 1 tablespoon oil, and serve immediately.
**Variation:** Either fresh oregano or fresh chopped rosemary can be substituted for basil.
**Fresh Ways**
To ensure that the tomatoes don't create a soggy pizza crust, spin them in a salad spinner before placing them on the unbaked pie.
# **Smoked Salmon Pizza**
This prebaked pizza crust is topped with a combination of succulent smoked salmon nestled on creamy sour cream. Try cutting it into small pieces for an hors d'oeuvre.
**1 batch Basic Pizza Dough**
**(recipe earlier in this chapter)**
**or purchased dough**
**6 oz. sliced smoked salmon**
**3 TB. minced fresh chives**
**4 TB. extra-virgin olive oil**
**2 TB. yellow cornmeal**
**6 TB. sour cream**
**4 TB. golden** _**caviar**_
**4 TB. salmon caviar**
1. Make Basic Pizza Dough according to recipe instructions.
2. Preheat the oven to 500°F, and if using a baking stone or tiles, place them in the oven now.
3. Slice smoked salmon into thin strips, and set aside.
4. Knead 2 tablespoons minced chives into pizza dough. Shape pizza dough into 1 large round or 4 individual rounds. Brush center with olive oil.
5. Sprinkle cornmeal on baking sheet, and bake crusts for 8 to 10 minutes or until golden. Transfer pizzas to 4 serving plates. (Crusts can be baked up to 6 hours in advance. Reheat in a 400°F oven for 5 minutes.)
6. Spread crust with sour cream, and arrange salmon slices decoratively over top of sour cream. Place 1 tablespoon golden caviar in the center of each pizza, sprinkle salmon caviar around circumference, and sprinkle remaining chives over top of salmon. Serve immediately.
**Fast Talk**
Caviar is just fish roe (eggs from female fish) that's been pressed through a sieve and salted. When most people think of caviar, they're thinking of the eggs from three species of Caspian Sea sturgeon—beluga, osetra, and sevruga. But American golden whitefish caviar and the bright red eggs of salmon caviar are also authentic for those species.
Serves: 4 **Active time:** 10 minutes **Start to finish:** 20 minutes **Each serving contains:** 332 calories 233 calories from fat 26 g fat 6 g saturated fat 17 g protein 11.5 g carbohydrates
Serves: 4 **Active time:** 15 minutes **Start to finish:** 30 minutes **Each serving contains:** 895 calories 616 calories from fat 68.5 g fat 28 g saturated fat 48 g protein 25 g carbohydrates
**Fresh Ways**
You can greatly reduce garlic's pungency if you blanch it a few minutes or roast it in the oven. Both methods of taming it render it sweet. With a few cloves it's easier to blanch; a whole head can be roasted in a 375°F oven for 30 to 45 minutes.
# **Prosciutto Pizza**
This is a robust recipe, with red bell peppers, basil, and two cheeses added to the Italian meat topping.
**1 batch Basic Pizza Dough**
**(recipe earlier in this chapter)**
**or purchased pizza dough**
**4 garlic cloves, peeled**
**½ cup olive oil**
**2 red bell peppers, seeds**
**and ribs removed, and thinly**
**sliced**
**1 TB. crushed red pepper**
**flakes**
**¾ lb. (3 cups) fresh whole-milk**
**mozzarella, grated**
**¼ lb. (1 cup) fontina cheese,**
**grated**
**½ cup chopped fresh basil**
**6 ripe plum tomatoes, rinsed,**
**cored, and thinly sliced**
**6 oz. prosciutto, cut into fine**
**julienne strips**
**1 medium red onion, peeled**
**and thinly sliced**
**4 oz. (1 cup) fresh goat**
**cheese, crumbled**
1. Make Basic Pizza Dough according to recipe instructions.
2. Preheat the oven to 450°F, and if using a baking stone or tiles, place them in the oven now.
3. Bring a small saucepan of water to a boil over high heat. Add garlic cloves and blanch for 3 minutes. Drain, slice, and set aside.
4. Heat ¼ cup olive oil in a large skillet over medium-high heat. Add red bell peppers and cook, stirring frequently, for 5 minutes or until peppers are soft.
5. Mix remaining ¼ cup oil with crushed red pepper flakes, and set aside.
6. Combine mozzarella and fontina cheeses, and set aside.
7. Brush dough with pepper oil. Spread mixed cheeses on top, reserving 1 cup cheese and leaving a ½-inch margin. Sprinkle with basil, top with tomatoes, prosciutto, red peppers, red onion, and garlic. Dot with goat cheese, and finish by sprinkling with reserved cheese.
8. Sprinkle cornmeal on baking sheets. Bake pizzas for 15 to 17 minutes or until crust is golden brown and toppings are bubbly. Serve immediately.
**Part 4**
**Salad Daze**
_Salad_ is synonymous with "fast and fresh cooking." In fact, _cooking_ might be a misnomer; it's often fast and fresh _slicing_ and _dicing!_
Two chapters in this part are for small salads that serve as an elegant touch if your entrée is something that's simple. There are small salads that could be served as appetizers or as a side dish, and there's a chapter of chilled salads made from carbohydrates, including new twists on old-fashioned pasta and potato salads.
The last chapter in this part is for main dish salads, which continue to grow in popularity because they combine so many colors, textures, and flavors of produce with proteins. You'll find options featuring all types of aquatic species as well as meats and poultry.
**Chapter 11**
**On the Side: Small Vegetable Salads**
**In This Chapter**
• Cooked and raw salads
• Crispy slaws
• Distinctive dressings
When the entrée is a simple grilled or broiled food, it's the little touches—like the salad—that give the meal style. You'll find recipes for just such salads in this chapter.
While we think of salads as a mélange of raw vegetables, that need not be the case. Some of the salads in this chapter are cooked and served either warm or at room temperature. Some star a certain food like cucumbers or cabbage, and a number mix a cornucopia of vegetables.
The chapter ends with some simple dressings that have delicious flavor and a fraction of the fat of conventional dressings. They're the salad equivalent of having your cake and eating it, too!
# **Olive Oil Savvy**
Olive oil is made from ripe, crushed olives. Two types of olive oil are available commercially—extra virgin and pure. Extra-virgin olive oil is made from the first pressing of the olives, which have been cold pressed (no heat added) with no chemicals added to the mixture. Olive oil must have less than 1 percent acidity in most countries to be called extra-virgin.
Pure olive oil is a blend of virgin and refined olive oil, which is oil that's been extracted from the olives by means other than mechanical or physical. Olives that are damaged—bruised or too ripe—are mixed with chemicals such as caustic soda which generates heat and "cooks" the olives to remove characteristic bitterness and soften them.
**Stale Stuff**
Extra-virgin olive oil is sensitive to light and heat and should be in dark bottles, ideally with a coating. Do not buy olive oil that's been sitting on a shelf near a window exposed to light.
Extra-virgin olive oil is primarily a condiment and is used for dressings and other cold dishes. It is a waste of money to use it for cooking, plus some extra-virgin oils burn at a lower temperature than pure oils if they contain olive particles.
Store all olive oil in a cool, dark place away from heat. If a bottle is unopened, a wine cellar is the perfect storage spot. Refrigerating olive oil can extend its life, but the oil will become cloudy and solidify. It will liquefy again when warmed to room temperature.
# **Warm Vegetable Salad**
A cornucopia of fresh vegetables are blanched and served warm in a light vinaigrette dressing.
**2 medium tomatoes, rinsed,**
**cored, seeded, and finely**
**chopped**
**2 shallots, peeled and finely**
**chopped**
**2 garlic cloves, peeled and**
**minced**
**¼ cup freshly squeezed lemon**
**juice**
**2 TB. chopped fresh parsley**
**1 TB. chopped fresh tarragon**
**or 1 tsp. dried**
**1 TB. chopped fresh basil or**
**1 tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**½ cup extra-virgin olive oil**
**¼ lb. green beans, rinsed,**
**stemmed, and cut into 1-in.**
**sections**
**1 carrot, peeled and cut into**
_**julienne**_ **strips**
**¼ lb. asparagus, rinsed,**
**woody stems discarded, and**
**cut into 1-in. sections**
**1 cup cauliflower florets**
**1 cup broccoli florets**
**6 leaves Boston or iceberg**
**lettuce**
Serves: 6 **Active time:** 10 minutes **Start to finish:** 15 minutes **Each serving contains:** 199 calories 171 calories from fat 19 g fat 3 g saturated fat 2 g protein 9 g carbohydrates
1. Bring a large pot of salted water to a boil, and have a bowl of ice water handy.
2. Combine tomatoes, shallots, garlic, lemon juice, parsley, tarragon, basil, salt, and pepper in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again. Set aside.
3. Add green beans, carrot, asparagus, cauliflower, and broccoli to boiling water. Cook for 3 to 5 minutes or until vegetables are crisp-tender. Drain, and plunge vegetables into ice water to stop the cooking action. Drain again, and toss with dressing. Arrange lettuce leaves on plates, and divide vegetable mixture into leaves. Serve immediately.
**Fast Talk**
Julienne ( _julie-EN_ ) is the French word for very thin sticks of vegetables that can cook very quickly. To cut a vegetable julienne style, first cut into long, thin slices, about ⅛ inch thick or smaller. Stack these layers, and cut into thin strips. Then cut the strips into any length, as determined by the recipe.
Serves: 6 **Active time:** 15 minutes **Start to finish:** 30 minutes, including 15 minutes for chilling **Each serving contains:** 169 calories 113 calories from fat 12.5 g fat 2 g saturated fat 5 g protein 11 g carbohydrates
**Fresh Ways**
Store wild mushrooms, such as fresh shiitakes, in a paper bag rather than a plastic bag. Plastic causes mushrooms to become moist and soggy. You could also line a bowl with paper towels, add the mushrooms, and then cover the bowl with more paper towels.
# **Stir-Fried Vegetable Salad**
This salad has all the flavors of a traditional Chinese stir-fry including sesame, scallions, ginger, and soy sauce.
**¼ cup sesame seeds**
**1 bunch bok choy**
**½ lb. snow peas**
**½ lb. fresh shiitake mushrooms**
**2 TB. vegetable oil**
**2 TB. Asian sesame oil**
**3 garlic cloves, peeled and**
**minced**
**2 TB. finely minced fresh**
**ginger**
**4 scallions, rinsed, trimmed,**
**and thinly sliced**
**½ cup oyster sauce**
**¼ cup vegetable stock**
**2 TB. soy sauce**
**2 TB. dry sherry**
1. Place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes, or until browned, shaking the pan frequently. Set aside.
2. Trim root end off bok choy, and separate head into ribs. Rinse ribs under cold running water and pat dry with paper towels. Slice ribs on the diagonal into ½-inch slices, and set aside.
3. Remove tips from snow peas, rinse in a colander, and set aside.
4. Trim and discard stems from shiitake mushrooms. Wipe mushroom caps with a damp paper towel, and set caps aside.
5. Heat vegetable oil and sesame oil in a wok or large skillet over medium-high heat. Add garlic, ginger, and scallions. Stir-fry 30 seconds or until fragrant. Add mushroom caps, and stir-fry for 2 minutes or until caps are soft. Add bok choy, and stir-fry for 1 minute. Add snow peas, and stir-fry for 1 minute. Add oyster sauce, stock, soy sauce, and sherry. Stir well and bring to a boil. Boil for 1 minute and then remove pan from heat.
6. Transfer vegetables to a mixing bowl or serving dish with a slotted spoon. Chill for at least 15 minutes to reach room temperature, or refrigerate, tightly covered, and serve chilled. Sprinkle vegetables with toasted sesame seeds just before serving. (Salad can be prepared up to 1 day in advance and refrigerated, tightly covered.)
# **Green Bean and Tomato Salad**
Here, bright green beans and vivid red tomatoes are tossed with a creamy dressing. This salad can also be served for summer picnics.
**2 garlic cloves, peeled and**
**minced**
**½ cup sour cream**
**2 TB. freshly squeezed lemon**
**juice**
**1 TB. dry mustard**
**1 tsp. granulated sugar**
**Salt and freshly ground black**
**pepper to taste**
**1 lb. green beans, rinsed,**
**stemmed, and cut into 2-in.**
**segments**
**1 pt. cherry tomatoes, rinsed,**
**stemmed, and halved**
1. Bring a large pot of salted water to a boil, and have a bowl of ice water handy.
2. Combine garlic, sour cream, lemon juice, mustard, sugar, salt, and pepper in a jar with a tight-fitting lid. Shake well, and set aside.
3. Add green beans to boiling water. Cook for 3 to 5 minutes or until crisp-tender. Drain and plunge vegetables into ice water to stop the cooking action. Drain again, and place beans in a mixing bowl. Add tomatoes, toss with dressing, and serve immediately.
**Variation:** For a dish lower in fat and calories, use plain nonfat yogurt instead of sour cream.
Serves: 6 **Active time:** 15 minutes **Start to finish:** 15 minutes **Each serving contains:** 80 calories 33 calories from fat 4 g fat 2 g saturated fat 3 g protein 11 g carbohydrates
**Fresh Ways**
To make this salad into a kaleidoscope of color, use yellow and orange cherry tomatoes as well as red ones. These bright tomatoes are becoming more available in supermarkets as well as farmers' markets.
Serves: 4 **Active time:** 10 minutes **Start to finish:** 25 minutes **Each serving contains:** 316 calories 263 calories from fat 29 g fat 4 g saturated fat 4 g protein 14 g carbohydrates
**Stale Stuff**
Don't use salt in a dressing that contains soy sauce. The soy sauce is very high in sodium and serves the same purpose.
# **Asian Eggplant Salad**
Baked eggplant is moistened with a sesame seed dressing in this easy salad.
**4 to 6 Japanese eggplants**
**(about 1** **¼ lb. total)**
**3 TB. vegetable oil**
**Salt and freshly ground black**
**pepper to taste**
**¼ cup sesame seeds**
**2 TB. soy sauce**
**2 garlic cloves, peeled and**
**minced**
**1 tsp. granulated sugar**
**2 TB. Asian sesame oil**
**2 TB. extra-virgin olive oil**
**¼ tsp. hot red pepper sauce**
**4 to 6 cups salad greens,**
**rinsed and dried**
1. Preheat the oven to 400°F, and cover 2 baking sheets with heavy-duty aluminum foil.
2. Cut eggplants into ¼-inch slices. Spread vegetable oil on baking sheets, and arrange eggplant slices. Sprinkle with salt and pepper. Bake eggplants for 15 to 20 minutes or until soft.
3. While eggplants are baking, place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes or until browned, shaking the pan frequently. Set aside.
4. Combine soy sauce, garlic, and sugar in a jar with a tight-fitting lid. Shake well, add sesame oil, olive oil, and hot red pepper sauce and shake well again. Set aside.
5. Arrange salad greens on serving plates, and top with warm eggplant slices. Drizzle with dressing, sprinkle with sesame seeds, and serve immediately.
# **Tomato and Mozzarella Salad with Oregano**
This salad with aromatic oregano, delicate cheese, and vivid tomatoes is a variation on the Italian classic _caprese_ and is great for a buffet, as it uses small cherry tomatoes.
**2 pt. cherry tomatoes, rinsed,**
**stemmed, and halved**
**Salt and freshly ground black**
**pepper to taste**
**1 lb. fresh mozzarella cheese,**
**drained and cut into** **½-inch**
**dice**
**3 TB. chopped fresh oregano**
**2 TB. capers, drained and**
**rinsed**
**¼ cup balsamic vinegar**
**¼ cup extra-virgin olive oil**
1. Place cherry tomatoes in a mixing bowl and sprinkle with salt and pepper. Refrigerate for 10 minutes. Drain tomatoes and return them to the mixing bowl.
2. Add mozzarella, oregano, and capers to tomatoes. Sprinkle salad with vinegar and oil, and toss well. Serve immediately.
**Variation:** The traditional way to make this salad is with basil, and it can be substituted for oregano.
**Fresh Ways**
Fresh mozzarella is very perishable, and the best way to keep it fresh is to change the water that covers it daily. The same process will prolong the freshness of tofu.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 20 minutes, including 10 minutes for chilling
**Each serving contains:**
348 calories
239 calories from fat
27 g fat
11 g saturated fat
18 g protein
10.5 g carbohydrates
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 10 minutes
**Each serving contains:**
134 calories
113 calories from fat
12.5 g fat
2 g saturated fat
1 g protein
7 g carbohydrates
# **Fennel Salad**
Fresh fennel has the crunch of celery with a light taste of licorice, and it's dressed simply in this easy salad.
**2 fennel bulbs, well chilled**
**¼ cup chopped fresh parsley**
**⅓ cup extra-virgin olive oil**
**3 TB. freshly squeezed lemon**
**juice**
**2 tsp. anchovy paste, or** **½ tsp.**
**salt**
**2 garlic cloves, peeled and**
**minced**
**Freshly ground black pepper**
**to taste**
1. Trim stalks and root ends from fennel bulbs. Slice fennel using a thin slicing disc of a food processor, or a very sharp knife. Place fennel in a salad bowl, and toss with parsley.
2. Place olive oil, lemon juice, anchovy paste, garlic, and pepper in a jar with a tight-fitting lid and shake well.
3. Toss dressing with fennel, and serve immediately.
**Fresh Ways**
This salad uses the bulb of the fennel, so save the stalks and use them as an alternative to celery in chicken and tuna salad.
# **Three-Pepper Gazpacho Salad**
Imagine all the healthful vegetables used to make gazpacho soup tossed in a salad bowl.
**2 red bell peppers, seeds**
**and ribs removed, and thinly**
**sliced**
**2 yellow bell peppers, seeds**
**and ribs removed, and thinly**
**sliced**
**1 green bell pepper, seeds**
**and ribs removed, and thinly**
**sliced**
**⅓ cup chopped red onion**
**2 medium cucumbers, rinsed,**
**seeded, and thinly sliced**
**1 pt. cherry tomatoes, rinsed,**
**stemmed, and halved**
**2 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh cilantro**
**¼ cup balsamic vinegar**
**Salt and cayenne to taste**
**⅓ cup extra-virgin olive oil**
1. Combine red bell peppers, yellow bell peppers, green bell pepper, onion, cucumbers, and tomatoes in a large mixing bowl.
2. Combine garlic, cilantro, vinegar, salt, and cayenne in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again.
3. Toss salad with dressing, and refrigerate for 15 minutes. Serve well chilled.
**Speedy Solutions**
Save time by buying English cucumbers rather than conventional ones. The seeds are so small that seeding them isn't really necessary. They're larger, so 1 English cucumber is the equivalent of 1½ to 2 conventional ones.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 30 minutes, including 15 minutes for chilling
**Each serving contains:**
178 calories
116 calories from fat
13 g fat
2 g saturated fat
2 g protein
16 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
258 calories
114 calories from fat
13 g fat
2 g saturated fat
6 g protein
32 g carbohydrates
**Fast Talk**
Jicama ( _HEE-KAM-AH_ ) is a root vegetable with crunchy flesh that tastes reminiscent of an apple. It's covered with a thin brown skin that should be peeled just prior to cutting it.
# **Black Bean and Papaya Salad**
Colorful, sweet ripe papaya and earthy black beans are a great combination in a dressing with Caribbean flavors.
**2 (15-oz.) cans black beans,**
**drained and rinsed**
**1 ripe papaya, peeled, seeded,**
**and cut into** **½-inch dice**
**1 medium** _**jicama,**_ **peeled and**
**cut into** **½-inch dice**
**½ red bell pepper, seeds and**
**ribs removed, and cut into**
**½-inch dice**
**¼ cup chopped fresh cilantro**
**3 garlic cloves, peeled and**
**minced**
**3 shallots, peeled and**
**chopped**
**1 tsp. ground cumin**
**¼ tsp. ground cinnamon**
**⅓ cup freshly squeezed**
**orange juice**
**3 TB. freshly squeezed lime**
**juice**
**3 TB. sherry vinegar**
**Salt and cayenne to taste**
**⅓ cup olive oil**
1. Combine beans, papaya, jicama, red bell pepper, and cilantro in a mixing bowl.
2. Combine garlic, shallots, cumin, cinnamon, orange juice, lime juice, vinegar, salt, and cayenne in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again.
3. Toss salad with dressing, and refrigerate salad for at least 15 minutes before serving. (Salad can be made 1 day in advance and refrigerated, tightly covered.)
**Variation:** For some substitutions, try mango instead of papaya and white beans instead of black beans.
# **Gingered Asian Red Cabbage Slaw**
This colorful slaw is dotted with golden raisins in an easy sweet and sour dressing.
**½ cup golden raisins**
**1 (2-lb.) head red cabbage,**
**cored and shredded**
**2 carrots, peeled and grated**
**½ red onion, peeled and**
**thinly sliced**
**2 TB. grated fresh ginger**
**¾ cup cider vinegar**
**2 TB. honey**
**3 TB. vegetable oil**
**Salt and freshly ground black**
**pepper to taste**
**3 scallions, rinsed, trimmed**
**with all but 2 inches of green**
**tops discarded, and thinly**
**sliced**
1. Place raisins in a mixing bowl and cover with very hot tap water. Allow raisins to plump for 15 minutes. Drain, and set aside.
2. Combine cabbage, carrots, and onion in a vegetable steamer over boiling water. Steam for 5 minutes, drain, and place in a glass or stainless-steel bowl.
3. Combine ginger, vinegar, honey, oil, salt, and pepper in a jar with a tight-fitting lid. Shake well, and pour dressing over steamed vegetables. Add raisins and scallions, and marinate at room temperature for at least 30 minutes, tossing occasionally. (Slaw can be made 1 day in advance and refrigerated, tightly covered.)
**Fresh Ways**
Slaw always tastes better if the cabbage has been wilted in some way to lose its bitterness. In this case, it's steamed and then tossed with a room temperature dressing, but an alternative, as in the next recipe, is to pour hot dressing over cold cabbage.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 45 minutes, including 30 minutes for marinating
**Each serving contains:**
183 calories
67 calories from fat
7.5 g fat
1 g saturated fat
4 g protein
29 g carbohydrates
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 2 hours,
10 minutes, including 2
hours for marinating
**Each serving contains:**
66 calories
2 calories from fat
0 g fat
0 g saturated fat
11 g protein
13 g carbohydrates
# **Dilled Cucumbers**
Mild rice wine vinegar creates a delicate pickling for these healthful cucumbers.
**3 medium cucumbers, rinsed,**
**seeded, and thinly sliced**
**½ large sweet onion, such as**
**Vidalia or Bermuda, peeled**
**and thinly sliced**
**1 cup rice wine vinegar**
**3 TB. chopped fresh dill**
**2 TB. granulated sugar**
**Salt and freshly ground white**
**pepper to taste**
1. Combine cucumbers and onion in a heavy resealable plastic bag.
2. Combine vinegar, dill, sugar, salt, and pepper in a jar with a tight-fitting lid. Shake well to dissolve sugar.
3. Add cucumbers and onion to dressing, and marinate for at least 2 hours, refrigerated.
4. Drain salad from marinade, and serve chilled. (Salad can be made up to 2 days in advance and refrigerated, tightly covered.)
**Variation:** You can use zucchini or yellow squash in place of cucumbers. They need to marinate for 3 hours.
**Stale Stuff**
All rice wine vinegar is not created equal. Some have been seasoned and are sometimes referred to as "sushi vinegar." That's not what you want. Always be sure you see "unseasoned" on the label if you plan on cooking with it.
# **Thai Cucumber Salad**
If you like spicy food, this is the dish for you, with lots of red pepper in the pickling liquid.
**¾ cup distilled white vinegar**
**¼ cup firmly packed light**
**brown sugar**
**1 TB. fish sauce (** _ **nam pla**_ **)**
**1 to 2 tsp. crushed red pepper**
**3 medium cucumbers, rinsed,**
**halved, seeded, and thinly**
**sliced**
**3 plum tomatoes, cored,**
**seeded, and diced**
1. Combine vinegar, brown sugar, fish sauce, and red pepper in a heavy resealable plastic bag. Mix well to dissolve sugar.
2. Add cucumbers, and marinate for 2 hours, refrigerated. Add tomatoes, and marinate an additional 20 minutes.
3. Drain salad from marinade, and serve chilled. (Salad can be made up to 2 days in advance and refrigerated, tightly covered.)
**Variation:** Instead of cucumbers, try zucchini or yellow squash. And then up the marinade time to 3 hours.
**Fast Talk**
Fish sauce (nam pla), a salty sauce with an extremely pungent odor, is made from fermented fish. It's used as a dipping sauce/condiment and seasoning ingredient throughout Southeast Asia. _Nam pla_ is the Thai term; it's known as _nuoc nam_ in Vietnam and _shottsuru_ in Japan.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 2½
hours, including 2 hours,
20 minutes for marinating
**Each serving contains:**
73 calories
4 calories from fat
0 g fat
0 g saturated fat
2 g protein
17.5 g carbohydrates
Makes: 8 (2-ounce) servings
**Active time:** 10 minutes
**Start to finish:** 10 minutes
**Each serving contains:**
175 calories
147 calories from fat
16 g fat
2 g saturated fat
1 g protein
8 g carbohydrates
# **Pear Dressing**
Luscious ripe pears and cashew nuts give this dressing a creamy appearance.
**2 ripe pears, peeled, cored,**
**and diced**
**¼ cup unsalted cashews**
**5 TB. raspberry vinegar**
**⅓ cup vegetable oil**
**3 TB. walnut oil**
**1 TB. Dijon mustard**
**2 sprigs parsley**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**Salt and freshly ground black**
**pepper to taste**
1. Combine pears, cashews, vinegar, vegetable oil, walnut oil, Dijon mustard, parsley, thyme, salt, and pepper in a blender or food processor fitted with a steel blade. Purée until smooth.
2. Transfer dressing to a container, and refrigerate for up to 5 days.
**Fresh Ways**
While pears, like apples and bananas, discolor when exposed to the air, there's no need to rub them with lemon juice for use in this recipe. The vinegar in the dressing serves that purpose.
# **Balsamic Vinaigrette**
Sweet fresh orange juice cuts the acidity of the vinegar in this great all-purpose dressing.
**½ cup freshly squeezed**
**orange juice**
**6 TB.** _**balsamic vinegar**_
**4 TB. freshly squeezed lemon**
**juice**
**1 TB. chopped fresh oregano**
**or** **½ tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**⅓ cup extra-virgin olive oil**
1. Combine orange juice, vinegar, lemon juice, oregano, salt, and pepper in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again. Refrigerate for up to 5 days.
**Fast Talk**
Balsamic vinegar is traditionally made from white Trebbiano grapes grown in the Modena region of Italy. It gets its rich, dark color and mellow flavor from being aged for many years in wooden barrels, similar to aging a wine.
Makes: 6 (2-ounce) servings
**Active time:** 5 minutes
**Start to finish:** 5 minutes
**Each serving contains:**
131 calories
105 calories from fat
12 g fat
2 g saturated fat
0 g protein
7 g carbohydrates
# **Sesame Ginger Dressing**
This flavorful dressing can also be used as a marinade for meats, chicken, or seafood.
**¼ cup sesame seeds**
**½ cup rice wine vinegar**
**3 TB. grated fresh ginger**
**2 garlic cloves, peeled and**
**minced**
**2 TB. soy sauce**
**2 TB. hoisin sauce**
**1 TB. dry sherry**
**Red pepper flakes to taste**
**¼ cup Asian sesame oil**
**3 TB. vegetable oil**
1. Place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes, or until browned, shaking the pan frequently. Set aside.
Makes: 6 (2-ounce) servings
**Active time:** 8 minutes
**Start to finish:** 8 minutes
**Each serving contains:**
206 calories
173 calories from fat
19 g fat
3 g saturated fat
2 g protein
6 g carbohydrates
2. Combine sesame seeds, vinegar, ginger, garlic, soy sauce, hoisin sauce, sherry, and red pepper flakes in a jar with a tight-fitting lid. Shake well, add sesame oil and vegetable oil, and shake well again. Refrigerate for up to 5 days.
**Fresh Ways**
An easy way to peel fresh ginger without losing a lot of its flesh is with the edge of a measuring spoon. The thin brown skin scrapes off easily.
Makes: 6 (2-ounce) servings
**Active time:** 5 minutes
**Start to finish:** 5 minutes
**Each serving contains:**
185 calories
115 calories from fat
13 g fat
2 g saturated fat
1 g protein
18 g carbohydrates
# **Celery Seed Dressing**
The distinctive flavor of celery seeds blends well with fruity raspberry vinegar and honey in this dressing.
**½ cup raspberry vinegar**
**⅓ cup vegetable stock**
**¼ cup honey**
**2 TB. celery seed**
**Salt and freshly ground black**
**pepper to taste**
**⅓ cup vegetable oil**
1. Combine vinegar, stock, honey, celery seed, salt, and pepper in a jar with a tight-fitting lid. Shake well, add oil, and shake well again. Refrigerate for up to 5 days.
**Speedy Solutions**
If you coat a measuring spoon or measuring cup with vegetable oil spray, sticky ingredients like honey or molasses won't stick to it.
**Chapter 12**
**Cold Carb Salads**
**In This Chapter**
• Chilly pastas
• Cold Asian rice dishes
• Super spuds
Salads don't only encompass leafy green things, as you see when cooking the recipes in this chapter. All these frosty side dishes are made with carbohydrates flavored in myriad ways. For example, potato salad is an all-American summer favorite, but it can be made with European flair as well. And rice, native to Asia, takes on Asian seasonings for this group of yummy recipes. And of course, no roster of cold carbs would be complete without some pastas added.
Whether you're looking for a salad to take to a pitch-in or something for your dinner table, you'll find the salad in this chapter.
# **Rice Size Specifics**
Rice is classified by the length of individual grains. Perhaps the most popular is white long-grain rice, in which the length of the grain is four or five times the size of the width. When cooked, it produces light, dry grains that separate easily.
Along with white long-grain rice, other species are popular:
_Basmati_ and _jasmine rice_ are both long-grain varieties from Asia and produce an aromatic fragrance when cooked. The aroma is created by a high concentration of acetyl pyroline, a compound naturally found in all rice.
_Brown rice_ is the entire grain with only the inedible outer husk removed. The nutritious, high-fiber bran coating gives it a light tan color, nutlike flavor, and chewy texture. The presence of the bran means brown rice is subject to rancidity, which limits its shelf life to only about 6 months. It also takes slightly longer to cook (up to 50 minutes total) than regular white long-grain rice.
_Arborio rice,_ almost all of which is imported from Italy, is a medium-grain rice (a softer rice that is two to three times as long as it is wide). Arborio rice has a high starch content. This natural carbohydrate is released as the rice is stirred to create a creamy texture in risotto dishes.
# **Potato Pointers**
Potatoes are tubers, which are the swellings of the root of the plant, which is why they're so nutritious. It's in the roots that the plant's valuable nutrients are stored.
**Fresh Ways**
Always choose firm, well-shaped potatoes free of blemishes, bruises, discolorations, or sprouting eyes. Especially avoid those with green spots, which indicate the presence of a toxic alkaloid called solanine that results from exposure to light.
Broadly speaking, potatoes are divided into "bakers," "boilers," and "all-purpose." Baking potatoes have more starch so they're light and fluffy when cooked. In addition to baking, they're wonderful for mashing and french fries. "Boilers" have less starch but more moisture. That's why they're the ones to use for potato salads and sautéeing. They have thin skin yet hold their shape quite well when sliced. "All-purpose" potatoes can be either baked or boiled and are generally white or red.
# **Sesame Noodles with Asian Vegetables**
In addition to sesame, the dressing for this salad contains peanut butter and Asian seasonings.
**1 lb. linguine, broken into**
**2-in. sections**
**¼ cup sesame seeds**
**¼ cup peanut butter**
**¼ cup very hot tap water**
**4 TB. Asian sesame oil**
**2 TB. soy sauce**
**2 TB. rice wine vinegar**
**2 TB. firmly packed dark**
**brown sugar**
**3 garlic cloves, peeled and**
**minced**
**2 TB. grated fresh ginger**
**2 TB. chopped fresh cilantro**
**1 to 2 TB.** _**Chinese chili paste**_
_**with garlic**_
**6 scallions, rinsed, trimmed,**
**and thinly sliced**
**1 medium cucumber, rinsed,**
**halved lengthwise, seeded,**
**and thinly sliced**
**1 carrot, peeled and thinly**
**sliced**
**1 cup bean sprouts, rinsed**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente. Drain pasta, and rinse under cold running water until pasta is cool. Drain and refrigerate.
2. Place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes or until browned, shaking the pan frequently. Set aside.
3. Combine peanut butter and water in a mixing bowl, and whisk until smooth. Add sesame oil, soy sauce, vinegar, brown sugar, garlic, ginger, cilantro, and Chinese chili paste. Whisk well again.
4. Add sauce, scallions, cucumber, carrot, and bean sprouts to pasta. Mix well and serve immediately, sprinkled with toasted sesame seeds.
**Variation:** Add cold shredded chicken or pork to make this a main dish salad that will serve 4 to 6.
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
377 calories
128 calories from fat
14 g fat
2 g saturated fat
11 g protein
52 g carbohydrates
**Fast Talk**
Chinese chili paste with garlic is a fiery thick paste made from fermented fava beans, red chilies, and garlic. It's available in jars in the Asian aisle of supermarkets.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
433 calories
165 calories from fat
18 g fat
6 g saturated fat
17.5 g protein
51 g carbohydrates
**Fresh Ways**
You don't mix the vegetables in step 2 because while salt adds to the flavor of tomatoes, it draws moisture out of the other vegetables.
# **Rigatoni with Vegetables and Mozzarella**
This is a cooling salad that's perfect for summer when tomatoes and herbs are all grown locally.
**1 lb. rigatoni**
**1 lb. ripe plum tomatoes,**
**rinsed, cored, and chopped**
**Salt and freshly ground black**
**pepper to taste**
**1 orange or yellow bell pepper,**
**seeds and ribs removed,**
**and chopped**
**2 small zucchini, rinsed,**
**trimmed, and chopped**
**1 small cucumber, rinsed,**
**seeded, and chopped**
**6 scallions, rinsed, trimmed,**
**and chopped**
**1 cup chopped fresh basil**
**leaves**
**½ lb. fresh mozzarella,**
**drained and cut into** **½-inch**
**dice**
**⅓ cup extra-virgin olive oil**
**½ cup freshly grated**
**Parmesan cheese**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente. Drain pasta and rinse under cold running water until pasta is cool. Drain and refrigerate.
2. While pasta is cooking, place tomatoes in a large mixing bowl and season to taste with salt and pepper. Add orange bell pepper, zucchini, cucumber, and scallions to the bowl but _do not mix_.
3. Add chilled pasta, basil, mozzarella, olive oil, and Parmesan. Toss to mix, season to taste with salt and pepper, and serve immediately.
# **Gemelli with White Beans, Tomatoes, and Sage**
The pungent and musky taste of fresh sage melds with the sweetness of the tomatoes in this hearty salad.
**1 lb. gemelli**
**⅓ cup extra-virgin olive oil**
**4 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh sage or**
**2 TB. dried**
**1** **½ lb. ripe plum tomatoes,**
**rinsed, cored, and chopped**
**1 (15-oz.) can cannellini**
**beans, drained and rinsed**
**Salt and freshly ground black**
**pepper to taste**
1. Bring a large pot of salted water to a boil. Add pasta and cook according to package directions until al dente. Drain pasta and rinse under cold running water until pasta is cool. Drain and refrigerate.
2. While water is heating, heat olive oil in a large skillet over medium-high heat. Add garlic and sage, and cook, stirring constantly, for 1 minute. Scrape mixture into a large mixing bowl, and add tomatoes and beans.
3. Add pasta to mixing bowl, season to taste with salt and pepper, and serve at room temperature or chilled.
**Fresh Ways**
The purpose of cooking the garlic and herbs in oil for a minute is to infuse the oil with the herb and garlic flavors. And it also mellows the garlic flavor and makes it less pungent.
Serves: 8
**Active time:** 10 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
162 calories
87 calories from fat
10 g fat
1 g saturated fat
5 g protein
16 g carbohydrates
Serves: 8
**Active time:** 30 minutes
**Start to finish:** 2½
hours, including 2 hours
for chilling
**Each serving contains:**
290 calories
133 calories from fat
15 g fat
7 g saturated fat
5 g protein
36.5 g carbohydrates
**Fresh Ways**
If you're cutting back on fat in your diet, use light coconut milk. It delivers the same flavor but has less fat.
# **Coconut Rice and Vegetable Salad**
Here, aromatic jasmine rice is cooked in coconut milk and Asian seasonings and then tossed with crunchy vegetables.
**½ cup unsweetened shredded**
**coconut**
**2** **¾ cups water**
**Salt and freshly ground black**
**pepper to taste**
**1** **½ cups jasmine rice**
**1 cup chopped fresh cilantro**
**¾ cup coconut milk**
**4 tsp. grated fresh ginger**
**1 TB. freshly squeezed lime**
**juice**
**2 garlic cloves, peeled and**
**minced**
**1 TB. Asian sesame oil**
**1 TB. vegetable oil**
**6 scallions, rinsed, trimmed,**
**and thinly sliced**
**1 tsp. ground cumin**
**½ tsp. crushed red pepper**
**flakes or to taste**
**¼ lb. snow peas, rinsed and**
**stemmed**
**1 pt. cherry tomatoes, rinsed,**
**stemmed, and halved**
**½ cup salted peanuts, coarsely**
**chopped**
1. Stir shredded coconut in a small nonstick skillet over medium heat for 5 minutes or until light golden. Set aside.
2. Bring water, salt, and pepper to boil in a saucepan. Stir in rice, and bring to a boil. Reduce heat to low, cover the saucepan, and simmer for about 18 minutes or until water is absorbed and rice is tender.
3. While rice is cooking, combine cilantro, ½ cup coconut milk, 1 teaspoon ginger, lime juice, and ½ of the garlic in a blender. Purée until smooth, and stir purée and toasted coconut into rice. Set aside.
4. Heat sesame oil and vegetable oil in a large skillet over medium-high heat. Add remaining garlic, remaining ginger, ½ scallions, cumin, and red pepper flakes. Cook, stirring constantly, for 1 minute. Stir in snow peas and remaining coconut milk. Cover and cook for 1 minute or until snow peas are bright green.
5. Stir vegetables into rice, and season to taste with salt and pepper. Chill for at least 2 hours or until cold. (Salad can be prepared up to 1 day in advance and refrigerated, tightly covered.) Stir in remaining scallions and tomatoes, and sprinkle with peanuts before serving.
**Variation:** Add cold shredded chicken or diced shrimp to make this a main dish salad that will serve 4 to 6.
# **Thai Rice Salad**
This sweet and sour rice salad contains a confetti of vegetables.
**1** **½ cups jasmine rice**
**6 TB. vegetable oil**
**4 garlic cloves, peeled and**
**minced**
**1 large shallot, peeled and**
**minced**
**3 cups water**
**Salt and freshly ground black**
**pepper to taste**
**½ cup rice wine vinegar**
**¼ cup firmly packed dark**
**brown sugar**
**2 TB. fish sauce (** _ **nam pla**_ **)**
**1 to 2 tsp. Chinese chili paste**
**with garlic**
**1 large carrot, peeled and**
**shredded**
**1 red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**6 scallions, rinsed, trimmed,**
**and finely chopped**
1. Rinse rice in a colander under cold running water.
2. Heat 2 tablespoons oil in a large saucepan over medium heat. Add garlic and shallot, and cook, stirring frequently, for 3 minutes or until shallot is translucent. Add rice, water, salt, and pepper and cover the pan. Bring rice to a boil over high heat. Reduce heat to low, and simmer rice for 20 minutes or until liquid is absorbed. Remove the pan from heat. Allow rice to rest, covered, for 10 minutes, and then fluff with a fork.
3. While rice is cooking, combine vinegar, brown sugar, fish sauce, and Chinese chili paste in a jar with a tight-fitting lid. Shake well until sugar is dissolved. Add remaining 4 tablespoons oil, and shake well again.
4. Place rice in a mixing bowl or serving dish. Pour dressing over hot rice. Add carrot, red bell pepper, and scallions. Mix well to combine. Refrigerate salad for at least 2 hours or until chilled, tightly covered with plastic wrap. (Salad can be made up to 2 days in advance.)
**Variation:** If you want, replace the carrot and red bell pepper with sliced raw celery or cooked asparagus.
Serves: 8
**Active time:** 30 minutes
**Start to finish:** 2 hours,
including 1½ hours for
chilling
**Each serving contains:**
258 calories
95 calories from fat
11 g fat
1.5 g saturated fat
2 g protein
38 g carbohydrates
**Speedy Solutions**
Burning rice is a common problem. To get rid of the burnt taste—and save the rice—scoop it out into a clean pot, leaving the burnt layer behind. Then cover the top of the rice with a layer of onion skins, and cover the pot for 10 minutes. Discard the onion peels, and your rice won't taste burnt.
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 45 minutes, including 30 minutes for chilling
**Each serving contains:**
252 calories
61 calories from fat
7 g fat
1 g saturated fat
7 g protein
42 g carbohydrates
**Fast Talk**
Tamari, like soy sauce, is a dark sauce made from soybeans, but its flavor is more mellow and less salty than that of soy sauce.
# **Spicy Asian Brown Rice Salad**
While brown rice might not be Asian, its nutty flavor takes well to the assertive seasonings in this salad.
**¼ lb. fresh shiitake mushrooms**
**3 TB. Asian sesame oil**
**3 garlic cloves, peeled and**
**minced**
**4 TB. grated fresh ginger**
**2 carrots, peeled and thinly**
**sliced**
**2 medium zucchini, rinsed,**
**trimmed, and thinly sliced**
**¼ lb. snow peas, rinsed,**
**stemmed, and halved lengthwise**
**⅓ cup** _**tamari**_
**¼ cup water**
**2 TB. hoisin sauce**
**1 tsp. Chinese chili paste**
**with garlic or to taste**
**6 cups cold cooked brown**
**rice**
**Freshly ground black pepper**
**to taste**
**3 scallions, rinsed, trimmed,**
**and thinly sliced**
1. Wipe mushrooms with a damp paper towel. Discard stems, and cut mushrooms into thin strips.
2. Heat oil in a large skillet over high heat. Add garlic and ginger, and stir-fry 1 minute. Add carrots, zucchini, shiitake mushrooms, and snow peas, and cook, stirring frequently, for 2 minutes or until vegetables are crisp-tender. Add tamari, water, hoisin sauce, and Chinese chili paste, and cook for 1 minute. Scrape mixture into a large mixing bowl.
3. Stir in rice, and season to taste with pepper. Chill for at least 30 minutes. Serve sprinkled with scallions.
# **Tabbouleh with Feta**
This lemony bulgur salad with chopped cucumber, tomato, and onion is a staple in the Middle East.
**1 lb. bulgur wheat**
**¾ cup freshly squeezed lemon**
**juice**
**3 cups hot water**
**1 medium cucumber, rinsed,**
**seeded, and chopped**
**4 ripe plum tomatoes, rinsed,**
**cored, seeded, and chopped**
**1 small red onion, peeled and**
**minced**
**2 garlic cloves, peeled and**
**minced**
**1 cup chopped fresh parsley**
**3 TB. chopped fresh mint**
**1 cup crumbled feta cheese**
**½ cup olive oil**
**Salt and freshly ground black**
**pepper to taste**
1. Place bulgur in a large mixing bowl, and add lemon juice and hot water. Let stand for 30 minutes or until bulgur is tender. Drain off any excess liquid.
2. Add cucumber, tomatoes, onion, garlic, parsley, mint, and feta to bulgur, and toss to combine. Add olive oil a few tablespoons at a time to make salad moist but not runny. Season to taste with salt and pepper.
3. Refrigerate _tabbouleh_ for at least 1 hour. Serve cold or at room temperature.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 1½
hours, including 1 hour
for chilling
**Each serving contains:**
395 calories
173 calories from fat
19 g fat
5 g saturated fat
12 g protein
49.5 g carbohydrates
**Fast Talk**
Tabbouleh ( _ta-BOOL-a_ ) is a salad dish of the Middle East; it's served as an accompaniment to almost everything. The characteristic ingredients are bulgur, parsley, and lemon juice. From that base, it's open to interpretation.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 2 hours,
including 1½ hours for
chilling
**Each serving contains:**
200 calories
101 calories from fat
11 g fat
2 g saturated fat
3 g protein
22 g carbohydrates
**Fresh Ways**
To keep onions from overpowering other ingredients in a salad after a few hours, before adding them to a salad, soak the cut onions for about 10 minutes in a bowl of cold water with a few tablespoons of vinegar added.
# **Janet's Potato Salad**
The inclusion of delicate and crunchy cucumber is a welcomed addition to this classic summer potato salad.
**2 lb. small red-skinned potatoes,**
**scrubbed**
**1 medium cucumber, peeled**
**1 green bell pepper, seeds**
**and ribs removed**
**1 small red onion, peeled**
**3 celery ribs, rinsed and**
**trimmed**
**½ cup mayonnaise**
**2 TB. white wine vinegar**
**Salt and freshly ground black**
**pepper to taste**
1. Place potatoes in a large saucepan of cold, salted water. Bring to a boil over high heat, and boil potatoes for 10 to 20 minutes or until they're tender when pierced with the tip of a paring knife. Drain potatoes and chill well. Cut potatoes into 1-inch cubes, and place them in a large mixing bowl.
2. Cut cucumber in half lengthwise and scrape out seeds with a teaspoon. Slice cucumber into thin arcs, and add to potatoes.
3. Cut green bell pepper into 1-inch sections, and slice each section into thin strips. Add peppers to the mixing bowl.
4. Cut onion in half through the root end, and cut each half into thirds. Cut into thin slices, and add to the mixing bowl.
5. Cut each celery rib in half lengthwise, and thinly slice celery. Add to the mixing bowl.
6. Toss potato salad with mayonnaise and vinegar, and season to taste with salt and pepper. Serve well chilled. (Salad can be made 1 day in advance and refrigerated, tightly covered.)
# **Garlicky Potato Salad**
The dressing for this salad dotted with colorful vegetables is an aïoli from Provence.
**2 lb. small red-skinned potatoes,**
**scrubbed**
**3 carrots, peeled and cut into**
**¼-inch dice**
**1 cup fresh green peas (or**
**frozen peas, thawed)**
**1 red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**6 garlic cloves, peeled**
**2 egg yolks, at room temperature**
**¾ cup extra-virgin olive oil**
**1 TB. freshly squeezed lemon**
**juice**
**Salt and freshly ground black**
**pepper to taste**
1. Place potatoes in a large saucepan of cold, salted water. Bring to a boil over high heat, and boil potatoes for 10 to 20 minutes or until they're tender when pierced with the tip of a paring knife. After 5 minutes, add carrots to the pan. When potatoes are almost tender, add peas to the pan. Drain vegetables and chill well. Cut potatoes into 1-inch cubes, and add red bell pepper to the mixing bowl.
2. Combine garlic and egg yolks in a food processor fitted with a steel blade or in a blender. Purée and then very slowly add olive oil through the feed tube of the food processor or the top of the blender. When sauce has thickened, add lemon juice, and season to taste with salt and pepper.
3. Combine sauce and vegetables, and serve chilled. (Salad can be made 1 day in advance and refrigerated, tightly covered.)
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 2 hours,
including 1½ hours for
chilling
**Each serving contains:**
306 calories
202 calories from fat
22 g fat
3.5 g saturated fat
4 g protein
51 g carbohydrates
**Speedy Solutions**
Potatoes cooked whole rather than chopped retain their shape better in salads such as this. If you don't want to take the time to cook whole potatoes, add some white distilled vinegar to the salted water and boil the potatoes cubed.
Serves: 8
**Active time:** 20 minutes
**Start to finish:** 35 minutes, including 15 minutes for cooling
**Each serving contains:**
210 calories
122 calories from fat
14 g fat
2 g saturated fat
2 g protein
21 g carbohydrates
# **Sweet Potato Salad with Mustard Dressing**
Sweet pickles balance the Dijon mustard in the dressing for this colorful sweet potato salad.
**1** ½ **lb. sweet potatoes,**
**scrubbed**
**3 TB. white wine vinegar**
**2 TB. Dijon mustard**
**Salt and freshly ground black**
**pepper to taste**
**1 shallot, peeled and finely**
**chopped**
**2 garlic cloves, peeled and**
**minced**
½ **cup olive oil**
¼ **small red onion, peeled and**
**finely chopped**
½ **red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
¼ **cup finely chopped sweet**
**pickles**
1. Quarter sweet potatoes lengthwise, and cut quarters into 2-inch sections. Place sweet potatoes in a saucepan of cold, salted water. Bring potatoes to a boil over high heat, and boil for 10 minutes or until potatoes are tender. Drain well and peel potatoes when cool enough to handle. Cut potatoes into 1-inch cubes, and place in a mixing bowl.
2. Combine vinegar, Dijon mustard, salt, pepper, shallots, and garlic in a jar with a tight-fitting lid, and shake well. Add oil and shake well again.
3. Add dressing to potatoes along with onion, red bell pepper, and pickles. Toss gently, and season to taste with salt and pepper. Serve at room temperature or chilled. (Salad can be made 1 day in advance and refrigerated, tightly covered with plastic wrap.)
**Speedy Solutions**
It's much faster to peel potatoes after they're cooked rather than when they're raw. That's why these sweet potatoes were cooked and then peeled. (And that's why red-skinned potatoes are such a time-saver; they don't need peeling at all!)
**Chapter 13**
**The Main Event: Entrée Salads**
**In This Chapter**
• Salads with hot toppings
• Fruity salads
• New life for leftovers
Salads are a great way to give second life to cooked foods. Maybe that's the reason why the entrée salad is one category that continues to grow in popularity, especially during the warm summer months. These visually attractive and colorful mixtures of raw lettuces and other greens with cooked chicken, seafood, or meats are refreshing as well as healthful to eat. Those are the recipes you'll find in this chapter.
Entrée salads are also a delicious way to ensure you're getting all nine daily servings of fruits and vegetables in your diet. As a bonus, they can be on the table in a matter of minutes.
# **Savvy Greens Subbing**
Making substitutions for some ingredients is difficult if you want to retain the character of the finished dish, but this is hardly a problem with lettuces. It's more important to have the freshest lettuce than a specific one. Use the following table to pick a lettuce that has the same characteristics as the one specified in a recipe.
# **Thai Shrimp Salad**
This salad is emblematic of Thai cuisine; it uses both fiery chilies and aromatic basil.
**8 oz. thin** _**rice noodles**_
⅓ **cup freshly squeezed lime**
**juice**
¼ **cup fish sauce (** _ **nam pla**_ **)**
¼ **cup vegetable oil**
**2 TB. granulated sugar**
**2 (** ¼ **-inch-thick) slices fresh**
**ginger, about the size of a**
**quarter**
**2 to 3 jalapeño chilies,**
**stemmed and seeded**
**3 cloves garlic, peeled**
¾ **cup firmly packed basil**
**leaves**
**1** ½ **lb. cooked shrimp, peeled**
**and deveined**
**1 English cucumber, rinsed,**
**trimmed, halved lengthwise,**
**and thinly sliced**
**1 small red onion, peeled and**
**thinly sliced**
**10 oz. baby spinach, rinsed**
**and dried**
1. Cook rice noodles according to package directions and chill.
2. Combine lime juice, fish sauce, oil, sugar, ginger, jalapeños, garlic, and basil in a food processor fitted with a steel blade or in a blender. Purée until smooth. Refrigerate dressing.
3. Combine shrimp with cooked rice noodles, cucumber, and red onion in a mixing bowl. Toss with dressing, and chill 30 minutes.
4. To serve, arrange spinach on individual plates or on a platter. Mound salad in the center.
**Variation:** Instead of shrimp, try cooked lobster, chicken, turkey, or pork.
Serves: 6
**Active time:** 30 minutes
**Start to finish:** 1 hour,
including 30 minutes for
chilling
**Each serving contains:**
379 calories
100 calories from fat
11 g fat
2 g saturated fat
28 g protein
42 g carbohydrates
**Fast Talk**
Rice noodles are Asian noodles made from rice flour, so they are a boon to people who are gluten-intolerant. They have a delicate flavor and are very quick-cooking.
Serves: 6
**Active time:** 30 minutes
**Start to finish:** 45 minutes, including 15 minutes for chilling
**Each serving contains:**
204 calories
54 calories from fat
6 g fat
1 g saturated fat
23 g protein
16 g carbohydrates
# **Scallop and Asparagus Salad**
Citrus flavors and herbs are the subtle seasonings in this delicate and colorful salad.
**1** ½ **lb. bay scallops or sea**
**scallops, cut into quarters and**
**rinsed**
**Water or fish stock**
**1** ½ **lb. fresh asparagus spears,**
**rinsed** ¼ **small red onion,**
**peeled and finely chopped**
½ **cup freshly squeezed**
**orange juice**
**2 TB. white wine vinegar**
**2 TB. chopped fresh parsley**
**1 TB. grated lemon zest**
**1 TB. grated orange zest**
**2 tsp. fresh thyme or** ½ **tsp.**
**dried**
**1 tsp. granulated sugar**
**Salt and freshly ground black**
**pepper to taste**
**2 TB. extra-virgin olive oil**
**6 to 8 cups baby salad greens,**
**rinsed and dried**
**1 large cucumber, rinsed and**
**sliced**
½ **pt. cherry tomatoes, rinsed**
**and stemmed**
1. Place scallops in a small saucepan with water or fish stock to cover. Bring to a boil over high heat, cover the pan, and remove the pan from heat. Allow scallops to sit undisturbed in the covered pan for 5 minutes. Drain, place scallops in a mixing bowl, and chill for at least 15 minutes.
2. Bring a large pot of salted water to a boil, and have a bowl of ice water handy. Break woody stems off asparagus spears, and cut asparagus into 1-inch sections on the diagonal. Blanch asparagus for 3 to 5 minutes or until crisp-tender. Drain and plunge asparagus into ice water to stop the cooking action. Drain again, and add asparagus to the mixing bowl with scallops along with red onion.
3. Combine orange juice, vinegar, parsley, lemon zest, orange zest, thyme, sugar, salt, and pepper in a jar with a tight-fitting lid. Shake well, add oil, and shake well again. Set aside. Combine dressing with salad 5 minutes before serving.
4. Arrange greens, cucumber, and tomatoes on individual plates or a serving platter, and mound salad in the center. Serve immediately. (Salad can be prepared 1 day in advance and refrigerated, tightly covered. Do not add dressing until just prior to serving.)
**Variation:** You can substitute cooked shrimp, ½-inch cubes of cooked chicken, turkey, or pork for the scallops.
**Stale Stuff**
If you buy organic cucumbers, there's no reason to peel them. This saves time, plus the peel contains many nutrients. If you're using a conventional cucumber, it should be peeled because there's a good chance it's been waxed.
# **Salmon and Cucumber Salad**
Poached salmon with dill sauce is a classic combination that's transformed to a salad in this recipe.
**2 cups water or fish stock**
**1** ½ **lb. salmon fillets, skinned**
**3 medium cucumbers**
**1 cup sour cream**
**2 scallions, rinsed, trimmed,**
**and cut into 1-inch segments**
**Salt and freshly ground black**
**pepper to taste**
¼ **cup chopped fresh dill**
**or 1 TB. dried**
**6 to 8 cups baby salad greens,**
**rinsed and dried**
**1 pt. cherry tomatoes, rinsed**
**and stemmed**
1. Bring water or fish stock to a boil in a large skillet. Add salmon fillets, reduce heat to a simmer, and _poach_ fillets for 7 to 10 minutes, depending on the size. Remove fillets from the pan with a slotted spatula, and break fillets with a fork into 1-inch chunks. Place salmon chunks in a mixing bowl, and chill until cold, at least 50 minutes.
2. Rinse cucumbers, cut them in half lengthwise, scrape out seeds, and cut cucumbers into ¼-inch slices. Set aside ⅓ cup cucumber slices, and add remaining slices to the mixing bowl with salmon.
3. Combine sour cream, scallions, and remaining cucumber in a blender or food processor fitted with the steel blade. Purée until smooth. Scrape dressing into a bowl, season to taste with
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 1¼
hours, including 50 minutes for chilling
**Each serving contains:**
363 calories
201 calories from fat
22 g fat
8 g saturated fat
29 g protein
12 g carbohydrates
salt and pepper, and stir in dill. Gently toss salmon and cucumbers with dressing.
4. Arrange greens and tomatoes on individual plates or a serving platter, and mound salad in the center. Serve immediately. (Salad can be prepared 1 day in advance and refrigerated, tightly covered.)
**Variation:** To lower the fat content of this salad, you can use plain nonfat yogurt instead of sour cream.
**Fresh Ways**
Certain herbs, such as the chopped dill in this recipe, add visual interest to the finished dish. That's the reason they're not puréed along with the other dressing ingredients.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes, including 10 minutes for chilling
**Each serving contains:**
444 calories
157 calories from fat
17 g fat
3 g saturated fat
41 g protein
32 g carbohydrates
# **Gazpacho Chicken Salad**
All the crisp vegetables comprising gazpacho soup are represented in this refreshing chicken salad.
**1** ½ **lb. cooked chicken, cut**
**into** ½ **-inch dice**
**2 red bell peppers, seeds and**
**ribs removed, and cut into** ½ **-**
**inch dice**
**2 cucumbers, rinsed, seeded,**
**and cut into** ½ **-inch dice**
**1 small red onion, peeled and**
**cut into** ½ **-inch dice**
**3 large ripe tomatoes, rinsed,**
**cored, seeded, and cut into**
½ **-inch dice**
⅓ **cup chopped fresh cilantro**
**1 jalapeño chili, seeds and**
**ribs removed, and finely**
**chopped**
**3 garlic cloves, peeled and**
**minced**
¼ **cup balsamic vinegar**
**Salt and freshly ground black**
**pepper to taste**
**6 to 8 cups baby salad greens,**
**rinsed and dried**
⅓ **cup extra-virgin olive oil**
**6 to 8 cups baby salad greens,**
**rinsed and dried**
1. Combine chicken, red bell peppers, cucumbers, red onion, and tomatoes in a large mixing bowl.
2. Combine cilantro, jalapeño, garlic, vinegar, salt, and pepper in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again. Pour dressing over salad, and refrigerate 10 minutes.
3. Arrange greens on individual plates or a serving platter, and mound salad in the center. Serve immediately. (Salad can be prepared 1 day in advance and refrigerated, tightly covered. Do not add dressing until 10 minutes before serving.)
**Variation:** You could substitute cooked shrimp or turkey for the chicken.
**Stale Stuff** Don't add the
dressing until a recipe says to. Some salads are only dressed at the last minute to ensure that the assertive flavors in the dressing don't overpower the delicate flavors of the salad.
# **Stir-Fried Chicken and Papaya Salad**
Warm chicken in a citrus dressing is contrasted with buttery avocado and luscious tropical fruit in this recipe.
**6 (6-oz.) boneless skinless**
**chicken breast halves**
**3 navel oranges**
**6 TB. sesame seeds**
**3 shallots, peeled**
**3 garlic cloves, peeled**
⅓ **cup sherry vinegar**
**2 TB. fresh ginger, peeled**
**and sliced**
**Salt and freshly ground black**
**pepper to taste**
**1 cup vegetable oil**
**2 or 3 heads Boston lettuce,**
**rinsed, dried, and broken into**
**1-inch pieces**
**3 ripe avocadoes, peeled and**
**sliced**
**2 ripe papayas, peeled, seeds**
**discarded, and thinly sliced**
**3 red bell peppers, seeds**
**and ribs removed, and thinly**
**sliced**
**3 TB. soy sauce**
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
808 calories
518 calories from fat
57.5 g fat
8 g saturated fat
46 g protein
35 g carbohydrates
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and slice chicken into ¼-inch slices against the grain.
2. Cut all rind and white pith off oranges, and cut between the sections to free orange segments from membranes.
3. Place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes, or until browned, shaking the pan frequently. Set aside.
4. Place orange segments, shallots, garlic, sherry vinegar, ginger, salt, and pepper in a blender or food processor fitted with a steel blade. Purée until smooth. Add ¾ cup vegetable oil, and blend again. Set aside.
5. Arrange lettuce, avocadoes, and papayas on individual plates or a large platter.
6. Add remaining ¼ cup oil to the skillet, and heat over medium-high heat. Add chicken and red bell peppers, and cook, stirring constantly, for 3 minutes or until chicken is cooked through and no longer pink. Add soy sauce and stir well. Turn off heat, and add dressing to the skillet. Stir to warm dressing, but do not let mixture boil.
7. To serve, mound chicken mixture on top of greens and fruits, and sprinkle with toasted sesame seeds. Serve immediately.
**Fresh Ways**
Always add granular seasonings like salt or sugar to a salad dressing before adding the oil. These ingredients dissolve in liquid but not in oil.
**Variation:** Instead of chicken, you could use 1½ pounds of extra large (16 to 20 per pound) shrimp, peeled and deveined. The shrimp will take the same time. Instead of papaya, try mango.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
412 calories
185 calories from fat
21 g fat
3 g saturated fat
31 g protein
30 g carbohydrates
# **Smoked Turkey Salad**
Eggs, beans, and a barbecue-flavored dressing join turkey in this quick and easy salad.
**1** ½ **lb. smoked turkey, cut**
**into** ½ **-inch dice**
**4 hard-cooked eggs, peeled**
**and diced**
**1 cup cooked corn kernels**
**1 (15-oz.) can red kidney**
**beans, drained and rinsed**
**1 small red onion, peeled and**
**chopped**
**2 celery ribs, rinsed,**
**trimmed, and thinly sliced**
½ **cup barbecue sauce**
**2 garlic cloves, peeled and**
**minced**
**2 TB. chopped fresh cilantro**
⅓ **cup mayonnaise or to taste**
**6 to 8 cups baby greens,**
**rinsed and dried**
**3 to 4 ripe beefsteak tomatoes,**
**rinsed, cored, and sliced**
1. Combine turkey, eggs, corn, beans, onion, and celery in a mixing bowl.
2. Whisk together barbecue sauce, garlic, cilantro, and mayonnaise. Toss dressing with salad and refrigerate.
3. Arrange greens and tomatoes on individual plates or a serving platter, and mound salad in the center. Serve immediately. (Salad can be prepared 1 day in advance and refrigerated, tightly covered.)
**Variation:** Smoked chicken or roasted turkey or chicken can be substituted for the smoked turkey.
**Speedy Solutions**
The large celery ribs around the outside of a bunch can be tough and fibrous. Starting at the tip, break off the top inch. It will be attached to the strings, which you can then easily pull off.
# **Asian Chicken Salad**
Aromatic sesame oil adds its flavor to this simple salad made with crunchy Chinese cabbage.
⅓ **cup soy sauce**
⅓ **cup rice wine vinegar**
⅓ **cup vegetable oil**
**3 TB. Asian sesame oil**
**3 TB. Dijon mustard**
**3 TB. grated fresh ginger**
¾ **tsp. dried hot red pepper**
**flakes**
**1** ½ **lb. cooked chicken,**
**coarsely shredded**
**6 cups shredded Napa cabbage**
**3 medium cucumbers, rinsed,**
**quartered lengthwise, seeded,**
**and thinly sliced**
**9 scallions, rinsed, trimmed,**
**and finely chopped**
¾ **cup chopped fresh cilantro**
1. Combine soy sauce, rice vinegar, vegetable oil, sesame oil, Dijon mustard, ginger, and hot red pepper flakes in a jar with a tight-fitting lid. Shake well and set aside.
2. Combine chicken, Napa cabbage, cucumbers, scallions, and cilantro in a large mixing bowl. Toss salad with dressing, and serve immediately.
**Variation:** Try shredded cooked beef or pork instead of chicken for something different.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
427 calories
212 calories from fat
24 g fat
4 g saturated fat
40 g protein
15 g carbohydrates
**Speedy Solutions**
Many a cook has suffered a scraped knuckle when grating fresh ginger. To avoid this, peel only a small portion of the rhizome and then hold on to the unpeeled portion as a handle.
Serves: 6
**Active time:** 30 minutes
**Start to finish:** 50 minutes, including 20 minutes for chilling
**Each serving contains:**
434 calories
119 calories from fat
13 g fat
2.5 g saturated fat
40 g protein
37 g carbohydrates
# **Jambalaya Salad**
Like a traditional Louisiana jambalaya, this salad contains tomato-flavored rice, shrimp, ham, and chicken.
**2 cups Bloody Mary mix**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**1 cup long-grain rice**
**1** ½ **cups fresh green peas or**
**1 (10-oz.) pkg. frozen peas,**
**thawed**
**1 lb. cooked chicken, cut into**
½ **-inch dice**
½ **lb. cooked shrimp, peeled,**
**deveined, and cut in half**
**lengthwise**
¼ **lb. baked ham, cut into** ½ **-**
**inch dice**
**6 scallions, rinsed, trimmed,**
**and thinly sliced**
**2 celery ribs, rinsed,**
**trimmed, and thinly sliced**
½ **red bell pepper, seeds and**
**ribs removed, and chopped**
¼ **cup freshly squeezed lemon**
**juice**
**3 garlic cloves, peeled and**
**minced**
**Salt and cayenne to taste**
¼ **cup olive oil**
**6 to 8 large Boston lettuce**
**leaves, rinsed and dried**
1. Bring Bloody Mary mix and thyme to a boil in a saucepan over high heat. Add rice, reduce heat to low, and cook, covered, for 15 to 20 minutes or until rice is soft. Spread hot rice on a baking sheet, and chill for at least 20 minutes.
2. While rice is cooking, cook peas in boiling salted water for 5 minutes. Drain and plunge peas into ice water to stop the cooking action. Drain and chill well.
3. Place rice and peas in a large bowl and add chicken, shrimp, ham, scallions, celery, and red bell pepper.
4. Combine lemon juice, garlic, salt, and cayenne in a jar with a tight-fitting lid. Shake well, add olive oil, and shake well again.
5. Toss dressing with salad, and serve chilled, mounded on lettuce leaves. (Salad and dressing can be prepared 1 day in advance and refrigerated, tightly covered. Do not toss salad with dressing until ready to serve.)
**Speedy Solutions**
Cooking rice in flavored liquid rather than water is an easy way to give it flavor without any fuss. Cooking in stock is common and the way to turn rice into pilaf, but let your imagination run wild.
# **Pork, Peach, and Orange Salad**
Lean pork tenderloin is the perfect foil for fruit with an herbed dressing made with sweet raspberry vinegar.
**1** ½ **lb. pork tenderloin**
**1 tsp. ground ginger**
**1 tsp. dry mustard**
**1 tsp. ground coriander**
**Salt and cayenne to taste**
**3 ripe peaches**
**3 navel oranges**
¼ **cup raspberry vinegar**
**2 TB. chopped fresh cilantro**
**2 TB. snipped fresh chives**
**1 TB. chopped fresh rose-mary**
**or 1 tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
⅓ **cup olive oil**
½ **lb. baby spinach, rinsed and**
**dried**
**1 medium cucumber, rinsed**
**and sliced**
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
334 calories
166 calories from fat
18.5 g fat
4 g saturated fat
27 g protein
16 g carbohydrates
1. Preheat the oven to 450°F, and line a baking pan with heavy-duty aluminum foil.
2. Rinse pork and pat dry with paper towels. Scrape off all fat and iridescent silverskin with a sharp paring knife.
3. Combine ginger, mustard, coriander, salt, and cayenne in a small bowl. Rub mixture onto all sides of pork.
4. Roast pork for 20 minutes or until an instant-read thermometer inserted into the center registers 140°F. Remove pork from the oven, and allow it to rest for 15 minutes. (Pork can be roasted up to 4 hours in advance and kept at room temperature.)
5. While pork is roasting, bring a medium saucepan of water to a boil. Add whole peaches and allow them to boil for 30 seconds. Remove peaches with a slotted spoon and place under cold running water. The peel should then slide right off. Discard stones, and slice peach thinly.
6. Cut all rind and white pith off oranges, and slice thinly.
7. Combine vinegar, cilantro, chives, rosemary, salt, and pepper in a jar with a tight-fitting lid. Shake well, add oil, and shake well again.
8. Slice pork thinly.
9. To serve, arrange spinach and cucumber on individual plates or a large platter. Arrange pork, peaches, and oranges on top, and drizzle with dressing. Serve immediately.
**Speedy Solutions**
Plunging peaches or tomatoes into boiling water for 30 seconds is the fastest way to peel them. And it makes sense if you're going to be using a number of either fruit within a few days to peel them at one time and then refrigerate the peeled fruit.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
449 calories
287 calories from fat
32 g fat
7 g saturated fat
34 g protein
7 g carbohydrates
# **Vietnamese Beef Salad**
Using precooked roast beef from the deli department means this salad tossed with lime dressing is on the table in minutes.
**1** ½ **lb. thinly sliced cooked**
**roast beef**
**1 head romaine, rinsed, dried,**
**and thinly sliced**
**12 scallions, rinsed, trimmed,**
**and thinly sliced**
**12 radishes, rinsed, trimmed,**
**and thinly sliced**
⅓ **cup freshly squeezed lime**
**juice**
¼ **cup fish sauce (** _ **nam pla**_ **)**
**1 TB. grated lime** _**zest**_
**Salt and freshly ground black**
**pepper to taste**
⅓ **cup Asian sesame oil**
¼ **cup vegetable oil**
1. Trim roast beef of all visible fat and cut it into ½-inch strips. Place beef in a large mixing bowl, and add romaine, scallions, and radishes.
2. Combine lime juice, fish sauce, lime zest, salt, and pepper in a jar with a tight-fitting lid. Shake well, add sesame oil and vegetable oil, and shake well again.
3. Toss salad with dressing, and serve immediately.
**Variation:** Not in the mood for beef? Try turkey, chicken, or roast pork instead.
**Fast Talk**
Zest is the thin, colored outer portion of the citrus skin that contains all the aromatic oils. Remove the zest using a zester, a vegetable peeler, a paring knife, or the fine holes of a box grater. Be careful to get just the colored portion; the white pith underneath is very bitter.
# **Warm Lamb Salad**
Rosy rich lamb is frequently paired with sharp Dijon mustard, and that's true for this salad.
**1** ½ **lb. boneless leg of lamb,**
**rinsed and patted dry with**
**paper towels**
**9 garlic cloves, peeled and**
**minced**
½ **cup Dijon mustard**
**2 TB. chopped fresh rose-mary**
**or 2 tsp. dried**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**Salt and freshly ground black**
**pepper to taste**
⅓ **cup red wine vinegar**
¾ **cup extra-virgin olive oil**
**3 bunches arugula, rinsed and**
**dried**
**3 cups sliced romaine, rinsed**
**and dried**
½ **cup sun-dried tomatoes**
**packed in oil, drained and**
**finely chopped**
¾ **cup freshly grated**
**Parmesan cheese**
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
597 calories
465 calories from fat
52 g fat
14 g saturated fat
29 g protein
9 g carbohydrates
1. Preheat oven to 450°F. Cover a baking sheet with heavy-duty aluminum foil, and place lamb in the center.
2. Combine 6 garlic cloves, 5 tablespoons Dijon mustard, rosemary, thyme, salt, and pepper in small bowl. Rub mixture on all sides of lamb. Bake lamb for 15 to 20 minutes or until an instant-read thermometer registers 135°F for medium-rare. Remove lamb from oven and allow it to rest for 10 minutes.
3. While lamb is roasting, combine remaining garlic, remaining Dijon mustard, and red wine vinegar in a jar with a tight-fitting lid. Season to taste with salt and pepper, and shake well. Add olive oil, and shake well again.
4. Combine arugula, romaine, sun-dried tomatoes, and Parmesan in salad bowl. Drizzle with half dressing, toss well, and divide salad onto individual plates.
5. Carve lamb against the grain into thin slices, and arrange lamb on top of salad. Drizzle with additional dressing, and serve immediately.
**Fresh Ways**
Save the oil you've drained from the sun-dried tomatoes. It's a great addition to salad dressings or drizzled over foods.
**Part 5**
**Redefining Fast Food**
You'll be taking an around-the-world tour while cooking the recipes in Part 5—most of which are ready in less time than it would take to have a pizza delivered!
Stir-fried dishes and sautéed foods are healthful, low-fat cooking methods. We associate stir-fries with Asian food, but any food cut into small pieces qualifies regardless of seasoning. Dishes that qualify as sautés are in larger pieces, but the same quick cooking takes place.
The chapters are divided by the type of food being starred so it's easy to locate the perfect dish for a meal. Some cuts of meat like lean pork tenderloin or rosy rack of lamb roast in a very short amount of time. You'll find recipes for them, too.
**Chapter 14**
**Sensational Seafood**
**In This Chapter**
• Asian fish dishes
• Saucy seafood delights
• Easy stove-top recipes
It's a chicken-and-egg situation: are we eating more fresh fish because it's more widely available, or is the fish department growing because we're eating more fish?
Regardless of the reason, more countries border on an ocean or major lake than are land-locked, so the majority of the world's cuisines include great fish dishes. Those are the recipes you'll find in this chapter. In addition to recipes for fin fish you'll find international options for preparing shrimp—the favorite crustacean of many people.
# **Choosing the Choicest**
When making your fish selection, keep a few simple guidelines in mind: above all, do not buy any fish that actually smells fishy, indicating that it is no longer fresh or hasn't been cut or stored properly. Fresh fish has the mild, clean scent of the sea—nothing more.
**Fresh Ways**
If possible, select a whole fish and then have it cut to your specifications, such as fillets or steaks, because there are more signs to judge the freshness of a whole fish than any of the parts comprising it.
Look for bright, shiny colors in the fish scales, because as a fish sits, its skin becomes more pale and dull looking. Then peer into the eyes; they should be black and beady. If they're milky or sunken, the fish has been dead too long. And if the fish isn't behind glass, gently poke its flesh. If the indentation remains, the fish is old.
Fish fillets or steaks should look bright, lustrous, and moist, with no signs of discoloration or drying.
# **Fish Families**
Although the recipes in this chapter call for specific fish, it's more important to use the freshest fish in the market rather than the particular species. All fin fish fall into three basic families, and you can easily substitute one species for another. Use the following table to make life at the fish counter easier.
**A Guide to Fish**
# **Shrimp: Sizing Up the Situation**
Shrimp are sorted by "count," which means their size and the number that comprises 1 pound, and the smaller the number of shrimp in a pound, the higher the price. Here are the general size categories into which shrimp fall:
_Colossal_ (less than 10 per pound) These are sometimes referred to as U8s as well.
_Jumbo_ (11 to 15 per pound) These yield the highest proportion of meat to shell.
_Extra large_ (16 to 20 per pound) These are frequently called "cocktail shrimp."
_Large_ (21 to 30 shrimp per pound) This is the most common size for shrimp found in the supermarket, both cooked and raw.
_Small_ (36 to 45 per pound) and _miniature_ (more than 45 per pound) These are usually sold as "salad shrimp." Unless they're cooked and peeled, stay away, because the labor involved in preparing them for cooking or eating is monumental.
Regardless of the color of the shell, raw shrimp are termed "green shrimp." Raw shrimp should smell of the sea with no hint of ammonia. Cooked, shelled shrimp should look plump and succulent.
**Fresh Ways**
If you're a fan of shrimp, it makes good sense to keep a bag of raw large shrimp in the freezer. Cooked shrimp are a great snack but are not as useful for cooking.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
268 calories
90 calories from fat
10 g fat
1.5 g saturated fat
27 g protein
14 g carbohydrates
**Fresh Ways**
An easy way to rehydrate mushrooms (or any dry ingredient), is in a French press pot coffee maker. Place the ingredients and liquid in the pot and lower the top to keep the ingredients submerged. If you're saving the soaking liquid for any reason, the mesh on the top will also serve as a strainer.
# **Asian Shrimp and Stir-Fried Vegetables**
Both fresh and dried mushrooms are used in this classic Chinese preparation.
**1** ½ **lb. extra large (16 to 20**
**per lb.) shrimp**
¼ **lb. fresh shiitake mushrooms**
**12 dried shiitake mushrooms**
**1 cup boiling water**
½ **cup dry sherry**
**3 TB. soy sauce**
**3 TB. freshly squeezed lime**
**juice**
**2 tsp. granulated sugar**
**2 TB. cold water**
**1 TB. cornstarch**
**2 TB. Asian sesame oil**
**1 TB. vegetable oil**
**2 TB. grated fresh ginger**
**4 garlic cloves, peeled and**
**minced**
**4 scallions, rinsed, trimmed,**
**and cut into 1-in. lengths**
**2 celery ribs, rinsed,**
**trimmed, and sliced**
**1 red bell pepper, seeds and**
**ribs removed, cut into julienne**
⅓ **lb. snow peas, rinsed and**
**stringed**
**Salt and freshly ground black**
**pepper to taste**
1. Peel and devein shrimp. Rinse shrimp and pat dry with paper towels.
2. Wipe fresh shiitake mushrooms with a damp paper towel. Discard stems and slice mushrooms. Set aside.
3. Soak dried shiitake mushrooms in boiling water, pushing them down with the back of a spoon, for 10 minutes. Drain mushrooms, squeezing to remove excess water. Stem mushrooms and chop coarsely. Set aside.
4. Combine sherry, soy sauce, lime juice, and sugar in a small bowl. Stir well, and set aside.
5. Combine cold water and cornstarch in a small bowl. Stir well, and set aside.
6. Heat sesame oil and vegetable oil in a heavy wok or skillet over high heat. Add ginger and garlic, and stir-fry, stirring constantly, for 30 seconds or until fragrant. Add shrimp and cook for 1 minute. Remove shrimp from the pan with a slotted spoon, and add scallions, celery, red bell pepper, and fresh and dried shiitake mushrooms.
7. Stir-fry vegetables for 2 minutes, stirring constantly, and return shrimp to the pan. Add snow peas and sauce mixture. Bring to a boil, and simmer for 2 minutes. Stir in cornstarch mixture. Simmer 1 minute or until lightly thickened. Serve immediately.
**Variation:** Instead of shrimp, try substituting bay scallops or ¾-inch cubes of firm-fleshed whitefish such as grouper or swordfish.
# **Prawns in Garlic Sauce with Fettuccine**
By the time the pasta is cooked the creamy tomato and garlic-sauced shrimp are ready to top it!
**1** ½ **lb. prawns or jumbo (11**
**to 15 per lb.) shrimp**
½ **cup olive oil**
**4 garlic cloves, peeled and**
**minced**
**1 cup dry white wine**
**2 ripe tomatoes, rinsed,**
**cored, seeded, and diced**
**2 TB. chopped fresh basil**
**or 1** ½ **tsp. dried**
**1** ½ **cups light cream**
**Salt and freshly ground black**
**pepper to taste**
**1** ½ **lb. fresh fettuccine,**
**cooked al dente**
**6 TB. freshly grated Romano**
**cheese**
**6 sprigs fresh basil for garnish**
**(optional)**
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
649 calories
353 calories from fat
39 g fat
15 g saturated fat
37 g protein
29 g carbohydrates
1. Peel and devein prawns. Rinse prawns and pat dry with paper towels. Heat olive oil in a large skillet over medium-high heat. Add prawns and garlic, and cook, stirring constantly, for 1 minute or until prawns begin to turn pink.
2. Add wine, tomatoes, basil, and cream and bring to a boil. Cook over medium heat for 3 minutes or until prawns are cooked through. Remove prawns from the pan with a slotted spoon, and _reduce_ sauce over medium heat for 3 minutes or until it coats the back of a spoon. Season to taste with salt and pepper.
3. Toss pasta and prawns with sauce to heat through. Garnish each serving with 1 tablespoon cheese and 1 sprig basil (if using).
**Fast Talk**
To reduce in cooking is to make something thicker. The term means to boil a liquid until the volume is decreased through evaporation, thereby intensifying the flavor. The resulting liquid is called a _reduction_.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
382 calories
249 calories from fat
28 g fat
9 g saturated fat
21 g protein
7 g carbohydrates
# **Scallops with Pine Nuts**
Succulent and sweet scallops are glorified with a simple butter sauce and pine nuts add a crunchy accent to this dish.
**1** **½ 1b. fresh bay scallops or**
**sea scallops cut into quarters**
**3 TB. olive oil**
**½ cup** _**pine nuts**_
**2 garlic cloves, peeled and**
**minced**
**2 large shallots, peeled and**
**minced**
**1 cup dry white wine**
**¼ cup freshly squeezed lemon**
**juice**
**6 TB. unsalted butter, cut**
**into thin slices**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse scallops, pat dry on paper towels, and set aside.
2. Heat olive oil in a heavy 12-inch skillet over high heat. Add scallops and pine nuts, and cook, stirring constantly, for 1 minute or until pine nuts are golden.
3. Remove scallops and nuts from the pan with a slotted spoon and reserve. Add garlic and shallots to the pan, and cook for 30 seconds. Add wine and lemon juice, and continue cooking until liquid is reduced to ¼ cup. Add any juice rendered from scallops.
4. Reduce heat to low. Add bits of butter to the pan, whisking constantly, allowing bits to melt but not letting sauce come to a boil or it will separate and thin out. Return scallops and pine nuts to the pan to reheat briefly. Season to taste with salt and pepper, and serve immediately.
**Fast Talk**
Pine nuts, also called _piñon_ in the American Southwest or _pingnoli_ in Italy, don't actually fall from pine trees. They are found inside pinecones, and the cones have to be heated to release them. This labor-intensive process is the reason behind their high cost.
# **Pan-Fried Flounder with Black Walnut Butter**
The slightly bitter flavor of all-American black walnuts is a great match for the delicate fish.
**6 (6- to 8-oz.) flounder fillets**
**4 cups black walnut pieces**
**1** **½ cups yellow cornmeal**
**½ cup all-purpose flour**
**Salt and freshly ground black**
**pepper to taste**
**¾ cup whole milk**
**2 large eggs**
**½ tsp. hot red pepper sauce**
**½ cup vegetable oil**
**¼ lb. (1 stick or** **½ cup)**
**unsalted butter, sliced into**
**thin slices**
**⅓ cup freshly squeezed lemon**
**juice**
**1 cup chopped fresh parsley**
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
1251 calories
857 calories from fat
95 g fat
17.5 g saturated fat
60 g protein
56 g carbohydrates
1. Rinse flounder fillets and pat dry with paper towels.
2. Place 2 cups black walnut pieces in a food processor fitted with a steel blade. Chop finely using on-and-off pulsing.
3. Combine chopped nuts, cornmeal, flour, salt, and pepper in a shallow dish and mix well.
4. Combine milk, eggs, and red pepper sauce in a mixing bowl and whisk well.
5. Heat vegetable oil in a large skillet over medium-high heat. Dip fillets in milk mixture and then _dredge_ fillets in black walnut flour, coating them evenly. Add fillets to the skillet, and cook for 2 to 3 minutes per side or until browned, turning fillets gently with a slotted spatula. Remove fillets from the skillet and pat with paper towels. Keep warm.
6. Pour grease out of the skillet, and wipe the skillet clean with paper towels. Return the skillet to the stove over medium heat. Add butter and remaining 2 cups black walnut pieces, and cook, stirring frequently, for 2 minutes or until black walnuts are browned. Add lemon juice and parsley, and cook for 1 minute. Season sauce to taste with salt and pepper.
7. To serve, place flounder fillets on six plates, and spoon sauce across center of each fillet. Serve immediately.
**Fast Talk**
To dredge means to completely coat a food with some sort of dry mixture before cooking it. It can be as simple as seasoned flour for cubes of meat to be browned before braising, or it can be a flavorful mixture such as this one.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
339 calories
162 calories from fat
18 g fat
8 g saturated fat
31 g protein
7 g carbohydrates
# **Scrod with Red Onion Marmalade**
Red wine and red currant jelly create a sweet and sour flavor for the onion garnish in this easy fish entrée.
**6 (6- to 8-oz.) scrod fillets**
**Salt and freshly ground black**
**pepper to taste**
**5 TB. unsalted butter**
**5 medium red onions, peeled**
**and thinly sliced**
**¾ cup dry red wine**
**1 tsp. grated orange zest**
**2 TB. beach plum or red currant**
**jelly**
**3 TB. olive oil**
1. Rinse scrod fillets and pat dry with paper towels. Season fillets to taste with salt and pepper, and set aside.
2. Melt 3 tablespoons butter in a large skillet over medium heat. Add onions, toss to coat, cover the pan, and cook over low heat for 10 minutes. Uncover the pan and cook onions over medium heat until soft, about 15 minutes, stirring frequently. Add wine, orange zest, and jelly, and boil over medium-high heat until liquid has almost evaporated. Season to taste with salt and pepper, and keep warm. (You can do this up to 2 days in advance and refrigerate, tightly covered. Reheat over low heat, stirring occasionally, until hot.)
3. Heat oil and remaining 2 tablespoons butter in a large skillet over medium-high heat. When butter foam begins to subside, add fillets. Cook fillets for 2 to 3 minutes on a side, turning gently with a slotted spatula.
4. To serve, divide onion mixture among 6 plates, and place a fish fillet on top.
**Variation:** Fillets of halibut or any firm-fleshed whitefish or salmon fillets can be substituted for the flounder in this recipe without changing the cooking time.
**Speedy Solutions**
Cooking the onions takes the most time in this recipe, so it makes sense to spend a few more minutes cooking a double or triple batch and freezing the remainder for future use.
# **Roast Monkfish in Plum Wine Sauce**
A host of Asian flavors from fruity plum wine to ginger create the sauce for this treatment of the fish dubbed "poor man's lobster."
**2 lb. thick monkfish fillets**
**3 TB. sliced fresh ginger**
**3 garlic cloves, peeled and**
**minced**
**1 cup plum wine**
**¾ cup dry sherry**
**½ cup rice wine vinegar**
**¼ cup freshly squeezed lemon**
**juice**
**2 tsp. grated lemon zest**
**2 TB. soy sauce**
**3 dried Chinese chilies**
**1 TB. coriander seed**
**2 TB. chopped fresh cilantro**
**or parsley**
**½ tsp. cayenne pepper**
**½ cup dried shiitake mushrooms**
**2 celery ribs, rinsed,**
**trimmed, and thinly sliced**
**2 carrots, peeled and thinly**
**sliced**
**1 cup fresh bean sprouts,**
**rinsed**
**8 scallions, rinsed, trimmed,**
**and thinly sliced**
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 1 hour,
including 30 minutes for
marinating
**Each serving contains:**
212 calories
24 calories from fat
3 g fat
1 g saturated fat
24 g protein
13 g carbohydrates
1. If monkfish fillets are not trimmed, use a sharp paring knife and remove the shiny membrane covering fillets. Trim to an even thickness, rinse, and pat dry with paper towels. Cut monkfish into 6 equal serving pieces.
2. Combine ginger, garlic, plum wine, sherry, rice wine vinegar, lemon juice, lemon zest, soy sauce, Chinese chilies, coriander seed, cilantro, and cayenne in a heavy resealable plastic bag (or a glass or stainless-steel mixing bowl). Add monkfish and marinate at room temperature for 30 minutes, turning the bag occasionally.
3. Soak dried shiitake mushrooms in boiling water to cover for 10 minutes, pushing them down with the back of a spoon to absorb water. Drain, stem, and slice.
4. Preheat the oven to 450°F. Remove monkfish from marinade, reserving marinade. Place monkfish in a 9×13-inch baking dish, and bake for 10 to 12 minutes or until flesh springs back to the touch. Remove and keep warm.
5. While monkfish is roasting, boil down marinade in a small saucepan until reduced by half. Strain sauce, and return it to the pan. Add shiitake, celery, and carrots and simmer for 5 minutes. Add bean sprouts, and simmer 2 minutes.
6. To serve, place a monkfish fillet on each plate and top with vegetables and sauce. Scatter chopped scallions over fillets.
**Stale Stuff**
Resealable plastic bags have revolutionized marinating because it's so easy to just turn the bag a few times to marinate foods evenly, but you might not always have one available. A glass or stainless-steel mixing bowl works fine, but don't use an aluminum one. The acid in the marinade will react with the metal and give the food a metallic flavor.
Serves: 6
**Active time:** 40 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
305 calories
129 calories from fat
14 g fat
3 g saturated fat
33 g protein
13 g carbohydrates
# **Fish Steamed in Napa Cabbage with Red Pepper Sauce**
This dish is stunning when it comes to the table with a combination of salmon and sole in vivid red sauce.
**2 red bell peppers or 2 jarred**
**roasted red peppers, rinsed**
**12 leaves Napa or savoy cabbage**
**1 lb. salmon fillets, skinned**
**1 lb. sole fillets**
**1 TB. vegetable oil**
**1 TB. Asian sesame oil**
**3 scallions, rinsed, white part**
**only, finely minced**
**1 TB. plus 1** **½ tsp. freshly**
**squeezed lemon juice**
**1 TB. soy sauce**
**1** **½ cups fish stock**
**1 TB. grated fresh ginger**
**Salt and freshly ground black**
**pepper to taste**
1. Preheat an oven broiler. Place red bell peppers on the rack of a broiler pan and broil 4 inches from the broiler element until skin is charred and black. Turn peppers with tongs to char all sides. Plunge peppers into ice water, and when cool enough to handle, remove and discard cap, skin, and seeds.
2. Bring a large pot of water to a boil. Add cabbage leaves and cook for 2 minutes or until leaves are pliable. Drain and set aside.
3. Rinse salmon and sole fillets, and pat dry with paper towels. Cut salmon and sole into ½-inch cubes and set aside.
4. Heat vegetable oil and sesame oil in a small skillet over medium heat. Add scallions and cook, stirring frequently, for 3 minutes or until scallions are translucent. Add to fish along with 1 tablespoon lemon juice and soy sauce.
5. Lay out 2 cabbage leaves so they overlap slightly, and divide fish mixture in the center of leaves. Roll cabbage, tucking in the sides to enclose filling, and secure rolls with toothpicks. Place rolls in a bamboo steamer, and steam over boiling water for 10 minutes.
6. While rolls are steaming, purée stock, peppers, remaining 1½ teaspoons lemon juice, ginger, salt, and pepper in a blender or food processor fitted with the steel blade. Pour into a small saucepan, and bring to boil over medium heat. Reduce by half, stirring frequently.
7. To serve, place a pool of sauce on the plate and top with a cabbage roll.
**Speedy Solutions**
Skinning fish is an easy task. Using an 8-inch chef's knife, start at one end of the fillet by pulling the skin away from the fillet with your fingers. Then hold on to the skin and push the knife away from you. It will scrape the fish away from the skin so you can then discard the skin.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
283 calories
82 calories from fat
9 g fat
2 g saturated fat
33 g protein
14 g carbohydrates
**Fast Talk**
To poach is to cook food gently in liquid that's just at the boiling point and barely simmering. This way of cooking preserves the tenderness of what's being cooked, be it an egg or a fish steak.
# **Creole Swordfish**
The "Creole Trinity" of celery, onion, and green bell pepper is joined with herbs in this dynamically flavored dish.
**2 lb. swordfish steaks,**
**approximately 1 in. thick, cut**
**into 6 equal serving pieces**
**1 TB. olive oil**
**1 large onion, peeled and**
**finely chopped**
**2 celery ribs, rinsed,**
**trimmed, and finely chopped**
**3 garlic cloves, peeled and**
**minced**
**1 green bell pepper, seeds**
**and ribs removed, finely**
**chopped**
**½ cup seafood stock**
**½ cup dry white wine**
**2 lb. ripe plum tomatoes,**
**rinsed, cored, and finely**
**chopped**
**1 (8-oz.) can tomato sauce**
**½ to 1 tsp. hot red pepper**
**sauce**
**¼ cup chopped fresh parsley**
**2 tsp. chopped fresh thyme**
**or** **½ tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse swordfish steaks and pat dry with paper towels. Set aside.
2. Heat oil in a large skillet over medium-high heat. Add onion, celery, garlic, and green bell pepper. Cook, stirring frequently, for 3 minutes or until onion is translucent.
3. Add swordfish steaks, stock, wine, tomatoes, tomato sauce, hot red pepper sauce, parsley, and thyme. Bring to a boil over medium heat. _Poach_ swordfish, partially covered, for 5 to 7 minutes, depending on thickness. Turn swordfish gently with a slotted spatula, and poach an additional 5 to 7 minutes or until cooked through.
4. Remove swordfish from the pan with a slotted spatula and keep warm. Raise the heat to high, and reduce sauce by ⅓, stirring frequently. Season sauce to taste with salt and pepper. To serve, spoon sauce over swordfish steaks. (Swordfish can be served either hot or at room temperature.)
**Variation:** Thick fillets of halibut or salmon can be substituted for the swordfish without changing the cooking time; however, if you're using flounder, tilapia, or sole, reduce the cooking time to no more than a total of 5 minutes.
# **Salmon with Basil Cream Sauce**
Delicate pink salmon is paired with an equally delicate cream sauce for this elegant dinner option.
**6 (6- to 8-oz.) salmon fillets**
**2 TB. unsalted butter**
**3 shallots, peeled and minced**
**1 garlic clove, peeled and**
**minced**
**1** **½ cups firmly packed**
**chopped fresh basil**
**¼ cup chopped fresh parsley**
**¾ cup dry white wine**
**⅔ cup light cream**
**1 TB. freshly squeezed lemon**
**juice**
**Salt and freshly ground black**
**pepper to taste**
1. Skin salmon (if necessary), rinse, and pat dry on paper towels.
2. Melt butter in a large skillet over medium-high heat. Sear salmon on both sides for about 2 to 3 minutes, keeping the center slightly rare. Remove fish from the pan with a slotted spatula and keep warm. Reduce heat to low, and add shallots and garlic to the pan. Cook, stirring frequently, for 3 minutes or until shallots are translucent.
3. Add basil, parsley, wine, cream, and lemon juice to the pan and cook over medium heat, stirring frequently, until mixture is reduced by ½. Return fish to the skillet and cook for 2 minutes. Season sauce to taste with salt and pepper. Serve immediately.
**Variation:** You could use thick fillets of halibut or swordfish instead of salmon without changing the cooking time. If you're using flounder, tilapia, or sole, reduce the cooking time to no more than a total of 5 minutes.
**Fresh Ways**
Certain ingredients are always packed firmly into mixing cups for accurate measurement. Brown sugar is one because it ranges from dense to fluffy depending on the brand. Herbs such as basil and vegetables such as lettuce or watercress are other foods that should always be packed down.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
459 calories
278 calories from fat
31 g fat
11.5 g saturated fat
35 g protein
3 g carbohydrates
Serves: 6
**Active time:** 17 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
323 calories
75 calories from fat
8 g fat
1 g saturated fat
30 g protein
30 g carbohydrates
# **Halibut in White Wine with Pearl Onions and Oranges**
This is a fabulous dish to serve guests who shy away from assertive seasoning. It's delicate but also colorful and flavorful.
**3 scallions**
**2 TB. olive oil**
**1 celery rib, trimmed and**
**sliced**
**3 garlic cloves, peeled and**
**minced**
**1 (16-oz.) pkg. frozen pearl**
**onions, thawed**
**2 lb. ripe plum tomatoes,**
**rinsed, cored, seeded, and**
**chopped, or 1 (14.5-oz.) can**
**diced tomatoes, drained**
**¼ cup chopped fresh parsley**
**1** **½ cups fish or chicken stock**
**½ cup dry white wine**
**1 cup freshly squeezed**
**orange juice**
**1 bay leaf**
**Salt and freshly ground black**
**pepper to taste**
**1** **½ to 2 1b. halibut fillets, cut**
**into 6 pieces, rinsed**
**2 navel oranges, rind and**
**white pith removed, and cut**
**into** **½-inch cubes**
**¾ lb. sugar snap peas, rinsed**
**and stemmed**
**Speedy Solutions**
One of the worst jobs in the kitchen is peeling tiny pearl onions. There's really no reason to use fresh ones, though. They're always cooked in recipes, and frozen pearl onions are even a better thing than sliced bread.
1. Rinse and trim scallions. Discard all but 2 inches of green tops, and slice scallions thinly.
2. Heat olive oil in a large skillet over medium heat. Add scallions, celery, and garlic, and cook, stirring frequently, for 3 minutes. Add pearl onions, tomatoes, parsley, fish stock, white wine, orange juice, and bay leaf. Season to taste with salt and pepper. Bring to a boil, and simmer, uncovered, for 3 minutes.
3. Add halibut and orange pieces to the skillet. Cover, bring to a boil, reduce heat to low, and cook for 5 minutes. Turn halibut gently with a slotted spatula, add sugar snap peas, and cook for an additional 5 minutes.
4. To serve, place halibut on plates and surround each portion with vegetables. Serve immediately.
**Variation:** Also try thick fillets of salmon or swordfish instead of the halibut without changing the cooking time. If you're using flounder, tilapia, or sole, reduce the cooking time to no more than a total of 5 minutes.
# **Tuna Steaks with Tomato Relish**
Baking tuna is a way to avoid the pitfall of overcooking, and the fresh vegetable relish contrasts with the meatiness of the fish.
**3 TB. olive oil**
**6 (6- to 8-oz.) tuna steaks,**
**about** **¾-inch thick**
**Salt and freshly ground black**
**pepper to taste**
**2 garlic cloves, peeled and**
**minced**
**2 large ripe beefsteak tomatoes,**
**rinsed, cored, seeded,**
**and chopped**
**4 scallions, rinsed, trimmed,**
**and sliced**
**3 TB. chopped fresh chives**
**½ cup refrigerated salsa**
**3 TB. freshly squeezed lime**
**juice**
1. Preheat the oven to 350°F. Line a baking sheet with heavy-duty aluminum foil, and spread 1 tablespoon olive oil on the foil.
2. Rinse tuna and pat dry with paper towels. Sprinkle on both sides with salt and pepper, and rub with garlic.
3. Heat remaining 2 tablespoons olive oil in a large skillet over high heat. Add tuna, and _sear_ for 1 minute per side. Remove tuna from the skillet and arrange on the baking sheet. Bake tuna for 10 to 12 minutes or until still rare in the center when probed with the tip of a paring knife.
4. While tuna is baking, combine tomatoes, scallions, chives, salsa, lime juice, and remaining 1 tablespoon olive oil in a mixing bowl. Stir well, and season to taste with salt and pepper.
5. Remove tuna steaks from the oven, and spoon sauce over. Serve immediately.
**Variation:** You can also use thick fillets of salmon, swordfish, or halibut instead of tuna. Increase the baking time to 15 to 17 minutes unless you want the fish as rare as tuna.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
262 calories
77 calories from fat
9 g fat
1 g saturated fat
41 g protein
4 g carbohydrates
**ast Talk**
To sear is to cook food over high heat to brown the exterior and seal in the juices. Searing meat prior to braising it produces a richness in the sauce, while moisture retention is the goal of searing fish.
**Chapter 15**
**Poultry Pals**
**In This Chapter**
• Asian stir-fries
• European flavors
• Homey turkey treats
The versatility of the boneless, skinless chicken breast knows no bounds. There's hardly a cuisine in the world that doesn't have a way to treat these quick-cooking, lean chicken parts, as you'll see by the recipes in this chapter. Chicken breasts take to every sort of seasoning. In addition, when crunchy, vibrantly colored vegetables are added to the mix, the dishes are as visually pleasing as they are delicious.
This chapter ends with two homey recipes that utilize ground turkey, although you can substitute turkey cutlets or ground turkey for chicken in the other recipes, too. These two birds are interchangeable at all times. Chicken has a more delicate flavor, but to some people that's a negative rather than a positive quality. The two foods also cook in the same amount of time, so it's personal preference.
# **Stir-Fry Strategy**
Advance planning, speed, and control are the keys to a successful stir-fry. But stir-frying isn't just for Asian dishes anymore; many other recipes are now utilizing the technique. It's quick, requires little fat, and leaves food with a lovely crisp-tender texture.
Because the final cooking is a quick process, the prepared ingredients must be ready and waiting in bowls or dishes within arm's reach. Cut all pieces of the same ingredient the same size, have your seasonings at hand, and be sure any vegetables requiring partial cooking—such as blanching broccoli—have gotten it.
**Stale Stuff**
Never place too much food in the wok or skillet at one time. The food must be able to be seared on all sides, without steaming from being buried under a layer of food.
The best pan to use for a stir-fry is an Asian wok because the rounded bottom facilitates keeping the food moving constantly. But if all you have is a large skillet, you can use that, too.
To cook, place the wok or skillet over a high flame and heat it to very hot. Listen for the sound of sizzles; if a few drops of water evaporate immediately, the pan is ready to cook in. Add the required amount of oil to the pan, and swirl it around gently to coat all sides.
# **Mock Mu Shu Chicken**
Easy-to-find flour tortillas take the place of Chinese pancakes for these roll-ups.
**8 large dried shiitake mushrooms**
**1 oz. dried** _**wood ear mushrooms**_
**1 cup boiling water**
**¼ cup soy sauce**
**1 TB. dry sherry**
**2 TB. cornstarch**
**1 1b. boneless, skinless**
**chicken breast**
**2 TB. vegetable oil**
**6 scallions, rinsed, trimmed,**
**and sliced**
**3 garlic cloves, peeled and**
**minced**
**5 large eggs, lightly beaten**
**Salt and freshly ground black**
**pepper to taste**
**½ cup plum sauce**
**12 (6-in.) flour tortillas**
1. Place dried shiitake mushrooms and wood ear mushrooms in a small mixing bowl. Pour boiling water over mushrooms, pressing them into water with the back of a spoon. Soak mushrooms for 10 minutes and then drain, squeezing out as much liquid as possible. Discard stems, and slice mushrooms thinly. Set aside.
2. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut chicken into thin slivers by cutting into thin slices and then cutting slices lengthwise.
3. Combine soy sauce, sherry, and cornstarch in a mixing bowl. Stir well, and add chicken. Toss to coat chicken evenly.
4. Heat oil in a heavy wok or large skillet over medium-high heat. Add scallions and garlic, and stir-fry for 30 seconds, stirring constantly. Add chicken mixture and stir-fry for 2 minutes or until chicken is cooked through and no longer pink. Add mushrooms and eggs to the pan and stir. Cook for 1 minute and then scrape the bottom of the pan to dislodge cooked egg. Cook for an additional 1 or 2 minutes or until eggs are just set. Season to taste with salt and pepper.
5. To serve, spread plum sauce on the surface of each tortilla. Place a portion of filling in the center. Tuck one edge over filling, and roll tortillas firmly to enclose filling. Serve immediately.
**Variation:** No chicken? Try this with pork tenderloin.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
486 calories
136 calories from fat
15 g fat
3.5 g saturated fat
30 g protein
56 g carbohydrates
**Fast Talk**
Wood ear mushrooms, also called _cloud ear mushrooms,_ are a form of Asian dried mushroom with a slightly crunchy texture and very delicate flavor. They're almost brownish black and expand to five times their size when rehydrated.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
279 calories
101 calories from fat
11 g fat
2 g saturated fat
28 g protein
15 g carbohydrates
**Fast Talk**
Chinese five-spice powder is perhaps the oldest blend of spices around. Used in traditional Chinese cooking for centuries, it's made up of equal parts cinnamon, cloves, fennel seed, star anise, and Szechwan peppercorns. It's available in most supermarkets, found either with spices or with Asian food.
# **Chicken with Plum Sauce**
This easy stir-fry has the popular sweet and sour flavor, and the vegetables make it colorful.
**1** **½ 1b. boneless, skinless**
**chicken breast halves**
**2 TB. cornstarch**
**2 TB. dry sherry**
**2 TB. soy sauce**
**1 TB. rice wine vinegar**
**6 scallions**
**1 cup chicken stock**
**⅓ cup plum sauce**
**1 tsp.** _**Chinese five-spice powder**_
**¼ cup vegetable oil**
**4 garlic cloves, peeled and**
**minced**
**2 TB. grated fresh ginger**
**2 celery ribs, rinsed,**
**trimmed, and thinly sliced**
**on the diagonal**
**1 red bell pepper, seeds and**
**ribs removed, and thinly**
**sliced**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut chicken into ½-inch cubes. Place chicken in a mixing bowl, and sprinkle with cornstarch. Toss to coat evenly, and add sherry, soy sauce, and rice wine vinegar, tossing again to coat evenly.
2. Rinse and trim scallions. Cut into 1-inch lengths and then slice lengthwise into thin strips. Set aside.
3. Combine chicken stock, plum sauce, and Chinese five-spice powder in a small bowl. Stir well, and set aside.
4. Heat vegetable oil in a heavy wok or large skillet over high heat, swirling to coat the pan. Add scallions, garlic, and ginger, and stir-fry for 30 seconds or until fragrant, stirring constantly. Add chicken and cook for 1 minute, stirring constantly. Add celery and red bell pepper, and stir-fry vegetables for 2 minutes more, stirring constantly.
5. Add sauce mixture and cook, stirring constantly, for 2 minutes or until chicken is cooked through and no longer pink and sauce is slightly thickened. Season to taste with salt and pepper, and serve immediately.
**Variation:** Instead of chicken, try this with boneless pork chops, trimmed of all fat and cut into ½-inch cubes.
# **Chicken Fajitas**
Colorful red bell pepper, sweet red onion, and fiery jalapeño are cooked along with the chicken in this colorful Mexican favorite.
**1** **½ lb. boneless, skinless**
**chicken breast halves**
**¼ cup olive oil**
**1 large red onion, peeled and**
**thinly sliced**
**1 large red bell pepper, seeds**
**and ribs removed, and thinly**
**sliced**
**2 jalapeño chilies, seeds and**
**ribs removed, and finely**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**2 medium ripe tomatoes,**
**rinsed, cored, seeded, and diced**
**¼ cup freshly squeezed lime**
**juice**
**2 tsp. ground** _**cumin**_
**¼ cup chopped fresh cilantro**
**Salt and freshly ground black**
**pepper to taste**
**8 (6-in.) flour tortillas**
**Sour cream (optional)**
**Salsa (optional)**
**Guacamole (recipe in**
**Chapter 3; optional)**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat. Place chicken between 2 sheets of plastic wrap, and pound to an even ½-inch thickness. Cut chicken into strips 2 inches long and ¾ inch wide.
2. Heat 2 tablespoons olive oil in a heavy 12-inch skillet over medium-high heat. Add chicken and cook, stirring frequently, for 4 or 5 minutes or until chicken is cooked through and no longer pink. Remove chicken from the skillet with a slotted spoon and set aside.
3. Add remaining olive oil to the skillet, and heat over medium-high heat. Add onion, red bell pepper, jalapeño, and garlic. Cook, stirring frequently, for 4 to 6 minutes, or until onion is soft. Add tomatoes, and cook for 1 minute. Add lime juice, cumin, cilantro, and chicken. Cook for 2 minutes, stirring frequently. Season to taste with salt and pepper.
4. Roll up filling in tortillas, and serve with small bowls of sour cream, salsa, and guacamole (if using) for garnish. Serve immediately.
**Variation:** You could use flank steak or pork loin cut to the same size as the chicken strips. Cook beef to the desired doneness, and cook pork for the same amount of time as the chicken.
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
555 calories
191 calories from fat
21 g fat
4 g saturated fat
46 g protein
44 g carbohydrates
**Fast Talk**
Cumin ( _KOO-men_ ) is frequently found in markets under its Spanish name, _comino_. The seeds from which it's ground are the dried fruit from a very aromatic plant in the parsley family. Cumin is one of the major ingredients in commercial chili powder, so you can always substitute chili powder if necessary.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
442 calories
251 calories from fat
28 g fat
10 g saturated fat
40 g protein
6 g carbohydrates
# **Chicken with Garlic and Parsley**
This Italian dish balances pungent garlic with fragrant parsley, and it's great on top of pasta.
**1** **½ 1b. boneless, skinless**
**chicken breast halves**
**3 TB. all-purpose flour**
**Salt and freshly ground black**
**pepper to taste**
**¼ cup olive oil**
**4 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh parsley**
**4 TB. unsalted butter**
**3 TB. freshly squeezed lemon**
**juice**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut chicken into ½-inch cubes. Toss chicken with flour, salt, and pepper in a bowl.
2. Heat oil in a 12-inch skillet over high heat, add chicken cubes, and cook, stirring frequently, for 3½ minutes or until chicken is cooked through and no longer pink.
3. Add garlic, parsley, and butter to the skillet and cook for 1 minute, shaking the skillet occasionally to coat the chicken. Add lemon juice, and season to taste with salt and pepper. Serve immediately.
**Variation:** For a seafood slant, use extra-large (16 to 20 per pound) raw shrimp, peeled and deveined, or 1-inch cubes of a firm-fleshed whitefish like cod or halibut instead of the chicken.
**Speedy Solutions**
Especially if you're cutting chicken into small cubes for a crowd, an alternative method is to pound the breasts to an even ½-inch thickness and then dice.
# **Poached Chicken with Balsamic Vinegar**
Zesty dried currants and orange juice add fruity sweetness to the sauce on this lean dish.
**4 (6-oz.) boneless, skinless**
**chicken breasts**
**1 cup dry white wine**
**½ cup freshly squeezed**
**orange juice**
**½ cup balsamic vinegar**
**½ cup golden raisins**
**½ cup dried currants**
**2 TB. extra-virgin olive oil**
**1 TB. grated lemon zest**
**2 TB. grated orange zest**
**2 tsp. chopped fresh tarragon**
**or** **½ tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat. Place chicken between 2 sheets of plastic wrap, and pound to a uniform ½-inch thickness. Set aside.
2. Pour wine into a large skillet, and bring to a boil over medium-high heat. Add chicken, reduce heat to a simmer, and poach chicken for 5 to 7 minutes or until chicken is cooked through and no longer pink. Remove chicken from the skillet with a slotted spoon, and set aside.
3. While wine is heating, bring orange juice and vinegar to a boil in a small saucepan. Remove the pan from the heat and add raisins and currants. _Plump_ fruit for 10 minutes.
4. Add reserved wine, olive oil, lemon zest, orange zest, and tarragon to the saucepan. Bring to a boil over high heat. Reduce the heat to medium-high, and boil sauce for 5 to 10 minutes or until the mixture is reduced by ½.
5. Cut chicken into ½-inch slices. Pour sauce over chicken, and serve immediately.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
448 calories
84 calories from fat
9 g fat
2 g saturated fat
41 g protein
40 g carbohydrates
**Fast Talk**
To plump is to rehydrate dried food, especially dried fruit, so it softens. Foods are plumped in hot liquid, which speeds up the process.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
562 calories
270 calories from fat
30 g fat
18 g saturated fat
46 g protein
20 g carbohydrates
**Fresh Ways**
While the green tops of leeks are not used very often in cooking, save them if you're making a stock and use them in place of onion. They give stocks a rich color as well as an improved flavor.
# **Tarragon Chicken with Spring Vegetables**
While it can still be classified as "comfort food," the creamy wine sauce is lighter than ones for red meats.
**4 (6-oz.) boneless, skinless**
**chicken breast halves**
**Salt and freshly ground black**
**pepper to taste**
**½ lb. fresh asparagus spears**
**2 large leeks, white part only**
**4 TB. unsalted butter**
**2 garlic cloves, peeled and**
**minced**
**1 cup chicken stock**
**⅔ cup dry white wine**
**⅔ cup heavy cream**
**¼ cup chopped fresh tarragon**
**or 2 tsp. dried**
**2 medium carrots, peeled and**
**thinly sliced**
**2 small zucchini, rinsed,**
**trimmed, and sliced**
**⅔ cup green peas**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut chicken into 1-inch cubes. Sprinkle chicken with salt and pepper to taste.
2. Rinse asparagus and discard woody stems. Cut asparagus into 1-inch lengths. Set aside.
3. Trim leeks, cut in half lengthwise, slice thinly, and rinse slices well in a colander. Set aside.
4. Heat butter in a heavy 12-inch skillet over medium heat. Add chicken cubes, and cook for 3 minutes or until chicken is opaque. Add leeks and garlic, and cook, stirring occasionally, for 3 minutes or until leek is translucent.
5. Stir chicken stock, wine, cream, tarragon, and carrots into the skillet. Bring to a boil, reduce the heat to medium-low, and simmer for 5 minutes. Add zucchini, asparagus, and peas, and simmer for an additional 5 minutes or until chicken is cooked through and no longer pink. Season to taste with salt and pepper. Serve immediately.
# **Chicken Marsala with Mushrooms and Sage**
Woodsy sage adds a more complex flavor to this classic Italian dish.
**1** **½ 1b. boneless, skinless**
**chicken breast halves**
**¼ cup all-purpose flour**
**Salt and freshly ground black**
**pepper to taste**
**½ lb. white mushrooms**
**⅓ cup olive oil**
**1 small onion, peeled and**
**diced**
**5 garlic cloves, peeled and**
**minced**
**1 cup dry marsala wine**
**1 cup chicken stock**
**¼ cup chopped fresh parsley**
**2 TB. chopped fresh sage or**
**2 tsp. dried**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut chicken into 1-inch cubes. Season flour to taste with salt and pepper. Dust chicken with seasoned flour, shaking off any excess.
2. Wipe mushrooms with a damp paper towel. Discard stems, and thinly slice mushrooms.
3. Heat olive oil in a heavy 12-inch skillet over medium high heat. Add chicken pieces, and cook, stirring frequently, for 3 minutes or until chicken is opaque. Remove chicken from the pan with a slotted spoon, and set aside.
4. Add onion, garlic, and mushrooms to the skillet. Cook, stirring frequently, for 3 minutes or until onion is translucent. Return chicken to the skillet, and add marsala, chicken stock, parsley, and sage. Bring to a boil, stirring occasionally.
5. Reduce heat to medium, and simmer mixture, uncovered, for 10 minutes or until chicken is cooked through and no longer pink. Season to taste with salt and pepper. Serve immediately.
**Variation:** Instead of chicken, you can use veal scallops pounded to an even ½-inch thickness. The cooking time does not change.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
454 calories
191 calories from fat
21 g fat
3 g saturated fat
43 g protein
13 g carbohydrates
**Speedy Solutions**
If you have leftover stock and don't think you'll use it within a few days, freeze it in ice cube trays. Measure the capacity of your ice cube tray with a measuring tablespoon, and when the cubes are frozen, transfer them to a resealable plastic bag. If you need a few tablespoons of stock later, you're all set.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
394 calories
181 calories from fat
20 g fat
3 g saturated fat
42 g protein
11 g carbohydrates
# **Italian Chicken with Lemon and Capers (** _ **Pollo Piccata**_ **)**
The light lemon sauce on this chicken is punctuated by piquant capers.
4 (6-oz.) boneless, skinless
chicken breast halves
⅓ cup all-purpose flour
Salt and freshly ground black
pepper to taste
⅓ cup olive oil
1½ cups chicken stock
**½ cup freshly squeezed lemon**
**juice**
⅓ cup chopped fresh parsley
¼ cup _capers,_ drained and
rinsed
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat. Place chicken between two sheets of plastic wrap, and pound to an even ½-inch thickness.
2. Season flour to taste with salt and pepper. Dust chicken with seasoned flour, shaking off any excess.
3. Heat olive oil in a heavy 12-inch skillet over medium high heat. Add chicken and cook for 2 minutes per side, turning with a slotted spatula.
4. Add chicken stock, lemon juice, parsley, and capers to the skillet. Bring to a boil, reduce the heat to low, cover the pan, and simmer chicken for 5 minutes. Turn chicken over and simmer for an additional 5 minutes or until chicken is cooked through and no longer pink. Season to taste with salt and pepper. Serve immediately.
**Variation:** Instead of chicken, you can substitute veal scallops pounded to an even ¼-inch thickness. Cook the veal for 2 minutes per side.
**Fast Talk**
Capers are the flower bud of a low bush native to he Mediterranean. After harvest, they're sun-dried and pickled in vinegar. The best capers are the tiny ones from France, and while they are customarily packed in brine, they are also sometimes packed in coarse salt. However, you buy them, rinse them well before using.
# **Turkey Chili**
Ground turkey is lighter than hearty beef, but there's still a lot of flavor in this traditionally seasoned dish.
**3 lb. ripe plum tomatoes, or**
**2 (14.5-oz.) cans diced tomatoes,**
**drained**
¼ cup vegetable oil
**1 large onion, peeled and**
**chopped**
**3 garlic cloves, peeled and**
**minced**
**1 red bell pepper, seeds and**
**ribs removed, and chopped**
**1 green bell pepper, seeds**
**and ribs removed, and**
**chopped**
1½ lb. ground turkey
**2 TB. all-purpose flour**
**3 TB. chili powder**
**2 TB. ground cumin**
**2 tsp. powdered cocoa**
Salt and cayenne to taste
2 (15-oz.) cans kidney beans,
drained and rinsed
1. Rinse, core, and seed tomatoes. Chop tomatoes finely, and set aside.
2. Heat oil in a Dutch oven over medium-high heat. Add onion, garlic, red bell pepper, and green bell pepper. Cook, stirring frequently, for 3 minutes or until onion is translucent. Add turkey and cook, stirring constantly, for 5 minutes, breaking up lumps with a fork.
3. Stir in flour, chili powder, cumin, cocoa, salt, and cayenne. Cook over low heat, stirring frequently, for 3 minutes. Add tomatoes and bring to a boil over medium heat. Simmer chili, stirring occasionally, for 30 to 40 minutes or until thick. Add beans and cook for an additional 5 minutes.
**Variation:** No turkey? Use ground beef or ground pork instead.
Serves: 6 **Active time:** 20 minutes **Start to finish:** 55 minutes **Each serving contains:** 469 calories 190 calories from fat 21 g fat 4 g saturated fat 31 g protein 42 g carbohydrates
**Fresh Ways**
You cook the flour and spices before adding other ingredients so the flour cooks in the accumulated fat and the dish doesn't get a "floury" taste.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 55 minutes
**Each serving contains:**
413 calories
191 calories from fat
21 g fat
5 g saturated fat
24 g protein
31 g carbohydrates
**Fast Talk**
Contrary to its name, chili sauce is closer to a chunky ketchup than a fiery sauce. This tomato-based condiment contains onions, green peppers, vinegar, sugar, and spices.
# **Turkey Meatloaf**
Crushed corn flakes create a crispy topping for this loaf that incorporates cheese and well as vegetables.
¼ cup olive oil
1 medium onion, peeled and
chopped
3 garlic cloves, peeled and
minced
2 medium carrots, peeled and
grated
1¼ lb. ground turkey
2 large eggs, lightly beaten
½ cup grated mozzarella
cheese
½ cup Italian breadcrumbs
**5 TB. whole milk**
½ cup _chili sauce_ or ketchup
1 **TB.** Worcestershire sauce
1 TB. fresh thyme or 1 tsp.
dried
Salt and freshly ground black
pepper to taste
3 cups cornflakes
1. Preheat the oven to 375°F, and line a baking sheet with heavy-duty aluminum foil.
2. Heat olive oil in a medium skillet over medium-high heat. Add onion, garlic, and carrots. Cook, stirring frequently, for 3 minutes or until onion is translucent. Scrape mixture into a mixing bowl.
3. Add ground turkey, eggs, mozzarella, breadcrumbs, milk, ¼ cup chili sauce, Worcestershire sauce, thyme, salt, and pepper to the mixing bowl. Mix well. (Mixture can be made up to 1 day in advance and refrigerated, tightly covered.)
4. Form meat into a log 10 inches long and 3 inches wide on a baking sheet. Spread top with remaining chili sauce.
5. Place cornflakes in a heavy resealable plastic bag. Crush into coarse crumbs with the flat side of a meat mallet or the bottom of a skillet. Press crumbs into top and sides of meatloaf. Bake for 40 minutes or until an instant-read thermometer inserted into the center of loaf registers 180°F. Serve immediately.
**Variation:** Instead of turkey, try ground beef or a combination of pork and beef.
**Chapter 16**
**Grazing Greats**
**In This Chapter**
• Quick-cooking pork and veal
• Sautéed beef
• Luscious lamb
You probably know that it's fast to grill a steak—after the grill heats, that is—but you might not know that you can fulfill your carnivore cravings in the same short amount of time at the stove or in the oven. Those are the recipes you'll find in this chapter.
In these pages you'll find delicious recipes for beef stir-fried with Asian flair or sautéed with European style. And then there are other recipes for cuts of meat like lean pork tenderloins and rich and rosy rack of lamb that bake to perfection within minutes.
# **Sauté Savvy**
_Sauté_ is another cooking term we've adopted from the French; it means literally "to jump." What this means for the dishes in this chapter is quick cooking with just a little fat over moderate to high heat.
**Fresh Ways**
Stir-frying and sautéing are first cousins. The main difference is that foods to be stir-fried are cut into small pieces and stirred continually to keep them moving, while sautéed food can be larger and is left alone for longer periods of time. And like a stir-fry, these dishes produce a meal in very little time and in one pan. (To learn more about stir-frying, see Chapter 15.)
Like broiling, sautéing is reserved for relatively thin and tender pieces of protein. It's not for "stewing meat" that needs both time and moisture to get tender. Nor is it suited to large pieces, because the outer portions would become dry—and possibly burnt—before the interior cooked properly.
# **Subbing with Success**
I list variations for many recipes in this chapter. But you can also improvise on your own. To help with that, here's a chart of what cuts of different meats can be sautéed successfully.
**Meat Choices for Sautéing**
# **Pork Scaloppine**
Pork is incredibly tender when quickly cooked after coating with breadcrumbs, and fresh mushrooms complete the dish.
**1 lb. white mushrooms**
**2 (12- to 16-oz.) pork tender-loins**
**Salt and freshly ground black**
**pepper to taste**
**2 large eggs**
2 cups Italian breadcrumbs
⅓ cup freshly grated
Parmesan cheese
**2 tsp. Italian seasoning**
⅓ cup olive oil
3 TB. unsalted butter
2 shallots, peeled and
chopped
⅓ cup freshly squeezed lemon
juice
2 TB. chopped fresh parsley
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
804 calories
409 calories from fat
45 g fat
13.5 g saturated fat
55 g protein
46 g carbohydrates
**Fast Talk**
Silverskin is the iridescent membrane covering tenderloins of any animal. It should be removed before cooking because it becomes tough gristle when the meat is cooked.
1. Preheat the oven to 150°F.
2. Wipe mushrooms with a damp paper towel. Discard stems, and slice mushrooms. Set aside.
3. Rinse tenderloins and pat dry with paper towels. Trim each tenderloin by cutting off all visible fat and then scrape off the iridescent silverskin. Cut each tenderloin crosswise into 6 slices. Pound slices between two sheets of plastic wrap to an even ¼-inch thickness, and sprinkle with salt and pepper.
4. Beat eggs with a fork in a shallow bowl. Combine breadcrumbs, cheese, and Italian seasoning in another shallow bowl. Dip meat slices into egg, letting any excess drip off, and then dip meat into crumb mixture, pressing crumbs into meat on both sides.
5. Heat ¼ cup olive oil in a large, heavy skillet over medium-high heat. Cook pork for 1½ minutes or until nicely browned. Turn gently with tongs, and cook the second side for 1½ minutes. Transfer pork to a baking sheet, and place it in the oven to keep warm.
6. Wipe the skillet with paper towels. Heat remaining olive oil and butter over medium-high heat. Add shallots and cook, stirring frequently, for 3 minutes or until shallots are translucent. Add mushrooms and cook for 3 to 5 minutes, stirring frequently, or until mushrooms are lightly browned and most of their liquid has evaporated. Stir in lemon juice and parsley, and season to taste with salt and pepper.
7. Remove pork from the oven. Spoon mushrooms over pork, and serve immediately.
**Variation:** Instead of pork, you can use chicken breasts pounded to the same ¼-inch thickness. Cook the chicken for 2 minutes per side or until cooked through and no longer pink.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
453 calories
210 calories from fat
23 g fat
11 g saturated fat
55 g protein
3 g carbohydrates
**Fresh Ways**
For small quantities of foods, like a few slices of prosciutto, it's best to visit your supermarket's deli department. Even the smallest package of prepackaged meats are 4 to 6 ounces—more than you probably need.
# **Pork with Prosciutto, Mozzarella, and Sage (** _ **Porchetta Saltimbocca**_ **)**
This dish is cooked in two steps so the pork remains moist after being layered with the cheese, ham, and herbs.
**2 (12- to 16-oz.) pork tender-loins**
**Salt and freshly ground black**
**pepper to taste**
**4 garlic cloves, peeled and**
**minced**
**1 tsp. Italian seasoning**
16 to 20 fresh sage leaves
**8 slices imported prosciutto,**
**trimmed of visible fat**
**½ 1b. whole milk mozzarella**
**cheese, thinly sliced**
1. Preheat the oven to 450°F, and line a 10×14-inch baking pan with heavy-duty aluminum foil.
2. Rinse pork and pat dry with paper towels. Trim off all visible fat and iridescent silverskin. Sprinkle pork with salt and pepper, and rub with garlic and Italian seasoning. Tuck thin tail under pork to form an even-size roll, and tie tail section with kitchen string or pin it with wooden toothpicks.
3. Place pork in the baking pan and bake for 10 minutes. Remove pork from the oven, and discard string or toothpicks. Allow pork to rest 5 minutes. Slice pork into ½-inch slices. Pork will still be rare.
4. Arrange pork slices in the baking pan in 4 columns, slightly overlapping slices. Top each with ¼ sage leaves, 2 slices prosciutto, and ¼ cheese slices. Bake for 5 to 7 minutes or until cheese is melted and bubbly. Serve immediately.
# **Herb-Crusted Pork Tenderloin**
Rather than stuffing the pork on the inside, crumbled herbed corn muffins become the basis for a coating patted on the outside of the tenderloins.
**2 (12- to 16-oz.) pork tender-loins**
Salt and freshly ground black
**pepper to taste**
**2 TB. olive oil**
**2 TB. unsalted butter**
**3 garlic cloves, peeled and**
minced
**2 large corn muffins, crumbled**
**(2 cups crumbs)**
**2** **TB.** **chopped fresh parsley**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**1 TB. chopped fresh rose-mary**
**or 1 tsp. dried**
**2 tsp. chopped fresh sage or**
**½ tsp. dried**
**¼ cup Dijon mustard**
1. Preheat the oven to 425°F, and line a 10×14-inch baking pan with heavy-duty aluminum foil.
2. Rinse pork and pat dry with paper towels. Trim off all visible fat and iridescent silverskin. Sprinkle pork with salt and pepper. Tuck thin tail under pork form an even-size roll , and tie tail section with kitchen string or pin it with wooden toothpicks.
3. Heat oil in a large, heavy skillet over high heat. Sear pork on all sides, turning gently with tongs, for 3 minutes or until browned. Remove pork from the pan, and transfer to the baking pan. Discard string or toothpicks.
4. Reduce the heat to low, and add butter to the skillet. Add garlic and cook, stirring constantly, for 30 seconds or until fragrant. Remove the pan from the heat and stir in corn muffin crumbs, thyme, rosemary, and sage. Season to taste with salt and pepper.
5. Spread mustard over pork and pat seasoned crumbs onto mustard. Roast pork for 10 to 15 minutes or until an instant-read thermometer inserted into the center registers 150°F. Allow pork to rest for 5 minutes, slice, and serve immediately.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
455 calories
220 calories from fat
24 g fat
9 g saturated fat
42 g protein
17 g carbohydrates
**Fresh Ways** et roasted and
sometimes grilled food rest to allow the juices to be reabsorbed into the fiber of the meat, thus making it juicier when sliced. During this resting period, the internal temperature continues to rise and finish the cooking process.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
358 calories
182 calories from fat
20 g fat
5 g saturated fat
37 g protein
7 g carbohydrates
**Fast Talk**
Star anise is a spice native to China that has a more distinct licorice flavor than European anise seed. It's one of the ingredients used in Chinese five-spice powder.
# **Japanese Sautéed Beef with Scallions (** _ **Negimaki**_ **)**
This dish is stunning on a plate, with a core of bright green scallions surrounded by succulent tender beef.
**1 (2-lb.) beef tenderloin, well**
**trimmed**
**18 to 24 scallions, rinsed,**
**trimmed, with all but 2**
i **nches of green tops discarded**
**½ cup soy sauce**
**1 TB. grated fresh ginger**
**2 garlic cloves, peeled and**
**minced**
**¼ tsp. Chinese five-spice**
**powder**
**2 TB. Asian sesame oil**
**1 cup beef stock**
**2 TB.vegetable oil**
**1 small piece _star anise_**
**Salt and freshly ground black**
**pepper to taste**
1. Rinse beef and pat dry with paper towels. Trim off all visible fat and iridescent silverskin. Slice into 12 (½-inch-thick) slices, and place them well apart between 2 sheets of plastic wrap. Pound into ¼-inch-thick ovals.
2. Place 1½ to 2 scallions along the edge of each beef slice, and roll tightly. Secure rolls with toothpicks, or tie with string.
3. Mix soy sauce, ginger, garlic, Chinese five-spice powder, and Asian sesame oil in a small bowl and set aside.
4. Bring beef stock to a boil in a small saucepan over high heat. Boil for 5 minutes or until reduced by ½. Set aside.
5. Heat vegetable oil over high heat in a heavy 12-inch skillet. Brush beef rolls with soy mixture and sear, turning with tongs, until brown on all sides. Lower the heat to medium, and continue to cook and turn beef rolls for 5 minutes. Remove and repeat with remaining beef. Place cooked rolls on a heated platter to keep warm.
6. Add reduced stock, star anise, and remaining brushing sauce to the pan. Deglaze the pan by stirring to loosen brown bits. Season to taste with salt and pepper.
7. Slice beef rolls into medallions on the diagonal and arrange them in a circle on a platter or on individual plates. Spoon sauce over medallions, and serve immediately.
**Variation:** Try chicken breasts instead of the beef. Cook chicken to a temperature of 160°F on an instant-read thermometer or until cooked through and no longer pink.
# **Pan-Seared Filet Mignon with Red Wine Sauce**
Deglazing a pan with red wine to create a sauce—as done in this dish—is a classic of French cooking, and it's always delicious.
**4 (6-oz.) filet mignons**
**Salt and freshly ground black**
**pepper to taste**
**3 TB. olive oil**
3 **TB.** unsalted butter
3 large shallots, peeled and
chopped
3 garlic cloves, peeled and
minced
1½ cups dry red wine
⅔ cup beef stock
3 TB. chopped fresh parsley
1 TB. fresh thyme or 1 tsp.
dried
1. Preheat the oven to 150°F.
2. Rinse steaks and pat dry with paper towels. Trim to remove any excess fat, season to taste with salt and pepper, and set aside.
3. Heat oil in a heavy 12-inch skillet over high heat. Add steaks and sear on each side for 1 minute. Reduce the heat to medium-high and cook steaks for 2 to 3 minutes on a side for rare or to desired doneness. Remove steaks from the pan with tongs and place them on a serving platter. Place steaks in the oven to keep warm.
4. Pour oil out of the pan, and place the pan over medium heat. Heat butter, and add shallots and garlic. Cook, stirring frequently, for 3 minutes, or until shallots are translucent.
5. Raise the heat to medium-high, and add red wine, beef stock, parsley, and thyme. Cook, stirring occasionally, until sauce is reduced by ½. Season to taste with salt and pepper, and pour sauce over steaks. Serve immediately.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
460 calories
206 calories from fat
23 g fat
8 g saturated fat
41 g protein
5 g carbohydrates
**Fresh Ways**
Meat is rare and ready to turn when the meat begins to feel soft and spongy. It's medium when drops of juice begin to appear and the meat resists when pressed. When it's well done, the meat is firm when pressed.
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
635 calories
436 calories from fat
49 g fat
18 g saturated fat
37 g protein
12 g carbohydrates
**Stale Stuff**
Sour cream adds a luscious richness and tangy flavor to sauces, but it curdles if boils and then your sauce is ruined, so watch it carefully. You can substitute crème fraîche, which does not curdle.
# **Beef Stroganoff**
Slices of tender beef are cooked with mushrooms and then served in a sauce finished with tangy sour cream in this comfort food dish.
1 (1¼ lb.) beef tenderloin
**Salt and freshly ground black**
**pepper to taste**
**4 TB. unsalted butter**
**2 TB. all-purpose flour**
1½ cups beef stock
**2 TB. tomato paste**
**4 TB. olive oil**
**3 large shallots, peeled and**
**thinly sliced**
**1 lb. crimini mushrooms,**
**wiped with a damp paper**
**towel, stemmed, and sliced**
⅓ cup sour cream
**2 tsp. Dijon mustard**
**2 TB. chopped fresh parsley**
1. Rinse tenderloin and pat dry with paper towels. Trim off all visible fat, and scrape off iridescent silverskin. Cut tenderloin into ½-inch-thick slices. Pound between two sheets of plastic wrap to an even thickness of ¼ inch. Season to taste with salt and pepper, and set aside.
2. Melt 2 tablespoons butter in a heavy 1-quart saucepan over medium heat. Stir in flour, and cook, stirring constantly, for 1 minute. Add beef stock in a slow stream, whisking constantly, and bring to a boil. Whisk in tomato paste. Reduce the heat and simmer, whisking occasionally, for 3 minutes. Remove the pan from the heat, and cover to keep warm.
3. While sauce is simmering, heat 2 tablespoons olive oil in a heavy 12-inch skillet over medium-high heat. Add beef and cook, turning gently with tongs, until browned on both sides but still pink inside, about 1 minute total time. Remove meat from the skillet.
4. Add remaining butter and olive oil to the skillet and heat over medium high heat. Add shallots and cook, stirring frequently, for 3 minutes or until shallots are translucent. Add mushrooms and cook, stirring occasionally, for 5 to 7 minutes or until liquid mushrooms give off has evaporated.
5. Return meat to the skillet, along with any juices that accumulated. Add sauce and whisk in sour cream, Dijon mustard, and parsley. Do not let sauce boil. Season to taste with salt and pepper, and serve immediately.
# **Mustard-Crusted Rack of Lamb**
This is one of the most elegant entrées you can serve, with its dramatic and flavorful topping over a rack of rosy lamb.
2 (1½-1b.) racks of lamb,
trimmed
Salt and freshly ground black
**pepper to taste**
**2 TB. vegetable oil**
**4 TB. Dijon mustard**
**6 garlic cloves, peeled and**
**minced**
**½ cup Italian breadcrumbs**
**¼ cup freshly grated**
**Parmesan cheese**
**2 TB. chopped fresh rose-mary**
1. Preheat the oven to 450°F, and line a 10×14-inch baking pan with heavy-duty aluminum foil.
2. Season racks of lamb well on all sides with salt and pepper. Heat oil in a large skillet over high heat. Add 1 rack of lamb and brown well on all sides. Transfer lamb to the baking pan. Repeat with second rack of lamb.
3. Spread Dijon mustard evenly over all sides of lamb racks. Combine garlic, breadcrumbs, Parmesan cheese, and rosemary in a small bowl. Press mixture onto the top of lamb with your hands.
4. Bake lamb for 13 to 15 minutes for medium rare or until it registers 130°F on an instant-read thermometer. Allow lamb to rest for 5 minutes and then carve into individual chops. Serve immediately.
**Stale Stuff**
Most racks of lamb are trimmed when you buy them, but if yours isn't, here's how you do it. Cut between the rib bones and scrape off the meat, exposing the bottom few inches of bone. Be sure the rack is cut through at the thick end so the individual chops can be carved off.
Serves: 4
**Active time:** 12 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
986 calories
655 calories from fat
73 g fat
30 g saturated fat
67 g protein
15 g carbohydrates
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
349 calories
177 calories from fat
20 g fat
6 g saturated fat
38 g protein
6 g carbohydrates
**Stale Stuff**
Never season a sauce that's going to reduce with salt and pepper prior to the reduction, or the sauce could be too salty. When the water evaporates during reduction, it intensifies flavors, including that of salt.
# **Veal Scaloppine with Fresh Shiitake Mushrooms**
Tender veal sautéed with a variety of woodsy mushrooms is napped with a simple sauce for this delicate dish.
**1½ lb. veal scallops**
**¼ lb. fresh shittake mushrooms**
**¼ lb. white mushrooms**
**2 TB. walnut oil**
**2 TB. unsalted butter**
**4 shallots, peeled and**
**chopped**
**2 garlic cloves, peeled and**
**minced**
**2 cups veal or chicken stock**
**2 tsp. chopped fresh thyme or**
**½ tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**2 tsp. cornstarch**
**1 TB. cold water**
1. Rinse veal and pat dry with paper towels. Place veal between two sheets of plastic wrap and pound to an even ⅛-inch thickness.
2. Wipe fresh shiitake and white mushrooms with a damp paper towel. Discard stems, and slice mushrooms. Set aside.
3. Heat walnut oil in a 12-inch skillet over medium-high heat. Sear veal on both sides, turning quickly. Remove veal with a slotted spatula to a platter and repeat until all veal is seared.
4. Add butter to the pan, and add shiitake mushrooms, white mushrooms, shallots, and garlic. Cook, stirring frequently, for 5 minutes or until shallots and mushrooms are soft.
5. Add veal stock and thyme, and bring to a boil over medium heat. Simmer until stock is reduced by ½ and season to taste with salt and pepper.
6. Combine cornstarch and water in a small bowl and stir well. Stir mixture into sauce, and simmer for an additional minute or until slightly thickened.
7. Return veal to the pan, and bring back to a boil to heat veal through. Do not let veal cook further, or it will toughen. Serve immediately.
**Variation:** Thin slices of filet mignon can be substituted for the veal.
**Part 6**
**Great Grills**
Everything tastes better when it's cooked outdoors, and those are the recipes in Part 6. Perhaps you grill year-round, or maybe you save this quick-cooking method for bucolic summer evenings. Regardless, you'll find recipes that are ready in minutes.
One chapter contains dishes that get grilled as soon as the grill is heated up. Those recipes are then dressed up with toppings and sauces you make while the food cooks. Then I give you a chapter devoted to all manner of burgers, extending far beyond traditional beef burgers.
Part 6 ends with a chapter on marinated foods. They do need a few hours to absorb flavor from the marinade, but that's all time you're doing something else.
**Chapter 17**
**Ready, Set, Grill!**
**In This Chapter**
• Seafood with relishes
• Poultry with stuffings
• Meats with sauces
Ahhh, the grill. Nothing says summer like grilling out, and in the winter, having a grilled dinner is a special treat (well, except maybe for the cook, who has to stand outside in the cold ). Whether the grill is Dad's bastion or Mom takes a turn manning the coals (or gas), whoever holds the title of "Grill Master" will enjoy the recipes in this chapter.
All these dishes have been formulated to be ready to grill by the time the grill is hot. There's no marinating involved. You will find some flavorful herb and spice rubs as well as sauces to top the food after it's whisked from the grill. Yum!
# **Gas vs. Charcoal**
I'm sure there's a debate among grillers about which is better, charcoal grills or gas grills: "Charcoal gives better flavor!" "Gas is so much more convenient!" "Charcoal is messy!" "Gas kills the flavor!"
I'll not get into that debate here, and besides, chances are you already have a grill or at least an idea which is better for your needs and tastes. For our purposes, I'll assume you have a grill already and know how to use it—or know where you put the instruction manual that came with it!
# **Where There's Smoke**
Whether you use them with gas or charcoal, wood chips made from aromatic woods like hickory, mesquite, and cherry add immeasurably to the flavor of grilled foods, as well as giving the skin of poultry a rich mahogany color.
For charcoal grills, the secret is to cover the chips in water to soak for at least 30 minutes. When the coals just begin to form white ash but are still somewhat red, drain the chips and scatter them over the charcoal.
**Fresh Ways**
You can also soak woody herb sprigs like rosemary or grape vines, or try whole garlic cloves and pieces of citrus peel. All add flavor.
Even though it's not as pronounced a flavor, you can also use wood chips on a gas grill. Place about 2 cups dry wood chips in the center of a large (12×18-inch) piece of heavy-duty aluminum foil. Bring up the foil on all sides and roll the ends together to seal the pouch. Poke several small holes in the top of the packet. When the grill is hot, place the wood chip pouch under the grate across the burner shields. Smoke will eventually come out from the holes.
# **Taking Your Grill's Temperature**
Ignore the thermometer sticking out of the grill's lid. All that's going to tell you is the temperature of the air in the upper part of the grill lid, and not the temperature at the grate level where the food is grilling.
The best way to judge your grill's surface temperature is with the palm of your hand. After the coals have a light coating of ash place your hand, palm side down, about 4 to 5 inches above the cooking rack. Here are your readings:
Hot grill: 2 seconds
Medium-hot grill: 3 to 4 seconds
Medium grill: 5 to 6 seconds
Medium-low grill: 7 seconds
Grilling is a high-heat cooking method, so if you can hold your hand over the coals for more than 7 seconds it means you should be adding more coals or preheating the gas burners longer.
# **Play It Safe**
Grilling might be man's oldest cooking method, but tried-and-true doesn't necessarily mean safe. You're dealing with live flames, after all. Safety is important:
• There's a reason why grill tools have long handles—to keep your fingers (hands, arms, body) away from the flame and heat. Use them.
• Use charcoal lighter fluid only as directed, and _never_ use it again once charcoal has been initially lit.
• Keep the grill a safe distance from the walls of the house or any deck railing. If the grill is on wood, place a layer of bricks or a metal plate underneath it.
• When you need to oil the grill rack so foods don't stick, _never_ use vegetable oil spray on a grill rack while it's on the grill. The oil can explode. If you want to spray the rack, remove it from the grill first.
• Charcoal can carry residual heat for at least a day; don't remove any ashes until the day after you've grilled, and even then they shouldn't go into paper or plastic. Use a can or some other metal container instead.
• Don't store charcoal next to the grill or anything else that produces heat. Keep it in a cool, dry place.
• Do you know where your instruction manual is? Be sure to study how to change the propane tank, or ask someone experienced to show you how to do it.
• Overall, remember safety first. You're cooking with fire or high heat. Children and pets should be kept far from the grill at all times. You don't want to risk a little one knocking over or getting burned on a hot grill.
_*Note:_ In all the recipes in this chapter, the "Start to finish time" includes 30 minutes for the grill to heat.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 45 minutes*
**Each serving contains:**
599 calories
350 calories from fat
39 g fat
10g saturated fat
47 g protein
12.5 g carbohydrates
# **Salmon with Tomatillo Sauce**
Delicate salmon is topped with a bright green sauce made with Mexican green tomatoes and aromatic cilantro.
4 (8-oz.) salmon fillets,
skinned
2 TB. olive oil
**Salt and freshly ground black**
**pepper to taste**
1¼ lb. _tomatillos_
2 TB. unsalted butter
2 garlic cloves, peeled and
minced
1 jalapeño chili, rinsed, seeds
and ribs removed, and diced
2 TB. white wine vinegar
**2 TB. white wine**
1 TB. granulated sugar
¼ cup firmly packed cilantro
leaves
Cilantro sprigs for garnish
(optional)
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
2. Rinse salmon and pat dry with paper towels. Rub salmon with olive oil, sprinkle with salt and pepper, and set aside.
3. Discard papery husks from tomatillos and then rinse, core, and dice tomatillos.
4. Heat butter in a medium saucepan over medium heat. Add tomatillos, garlic, jalapeño, vinegar, wine, and sugar. Bring to a boil, and cook, stirring frequently, for 10 minutes or until tomatillos are soft.
5. Pour mixture into a food processor fitted with a steel blade or a blender. Add cilantro, and purée until smooth. Return mixture to the pan, season to taste with salt and pepper, and keep warm.
6. Grill salmon for 3 to 5 minutes per a side, turning gently with a wide spatula. Edges should be opaque, but the center should still be slightly translucent.
7. To serve, ladle some sauce onto each plate, and place salmon top. Garnish with cilantro sprigs (if using).
**Variation:** Instead of salmon, try swordfish, halibut, or boneless chicken breasts pounded to an even ½-inch thickness. Cook the chicken to an internal temperature of 160°F.
**Fast Talk**
Tomatillos ( _tohm-aah-TEE-os_ ) are green tomatoes, popular in Mexican and Southwestern cooking. They're covered in a thin, parchmentlike husk that must be pulled off and discarded before cooking. You can use tomatillos raw in salsa, but their distinctive tangy flavor with hints of lemon and herbs is released when they're cooked.
# **Tuna with Ginger Vinaigrette**
The Asian flavors in this easy dressing moisten tender tuna steaks seared until just rare.
4 (8-oz.) fresh tuna steaks, at
least 1 in. thick
¾ cup olive oil
Salt and freshly ground black
pepper to taste
¼ cup sesame seeds
½ cup rice wine vinegar
**Juice of 2 limes**
**2 TB. soy sauce**
**3 shallots, peeled and**
**chopped**
**2 TB. grated fresh ginger**
**2 TB. chopped fresh cilantro**
**3 TB. Asian sesame oil**
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
775 calories
520 calories from fat
58 g fat
8 g saturated fat
56 g protein
6 g carbohydrates
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is very hot.
2. Rinse tuna and pat dry with paper towels. Rub tuna with 2 tablespoons olive oil, and sprinkle with salt and pepper. Place tuna on a sheet of plastic wrap on a platter and place in the freezer while the grill heats.
3. Place sesame seeds in a small dry skillet over medium heat. Toast seeds for 2 minutes, or until browned, shaking the pan frequently. Set aside.
4. Combine vinegar, lime juice, soy sauce, shallots, ginger, cilantro, and salt and pepper to taste in a jar with a tight-fitting lid. Shake well. Add remaining olive oil and sesame oil, and shake well again. Set aside.
5. Sear tuna for 2 minutes per side; the interior should be very rare. Remove tuna from the grill, drizzle with dressing, and sprinkle with sesame seeds. Serve immediately.
**Fresh Ways**
Deep-chilling the tuna in the freezer for a short time is a way to ensure that it won't become overcooked when grilled.
**Variation:** Any thick fish steak such as cod, salmon, or halibut can be substituted for the tuna, but unless you like all fish very raw, increase the cooking time to a total of 10 minutes per inch of thickness.
# **Sea Scallops with Mango Salsa and Chili Vinaigrette**
A colorful mango salsa enlivened with chili oil tops succulent and tender grilled sea scallops in this dish.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 50 minutes*
**Each serving contains:**
414 calories
257 calories from fat
29 g fat
4 g saturated fat
26 g protein
13 g carbohydrates
**12 bamboo or 6 metal skewers**
**1 red bell pepper or 1 jarred**
**roasted red pepper**
**2 lb. sea scallops**
1 large, ripe mango, peeled,
seeded, and cut into ¼-inch
dice
½ small cucumber, rinsed and
finely chopped
½ small red onion, peeled and
finely chopped
**3 TB. chopped fresh cilantro**
¾ cup olive oil
2 **TB.** freshly squeezed lime
juice
Salt and freshly ground black
pepper to taste
⅓ cup cider vinegar
¼ to ¾ tsp. Chinese chili oil
or to taste
1. If using bamboo skewers, cover them in water to soak for at least 30 minutes.
2. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
3. Place red bell pepper on the hot grill rack, and grill until skin is charred and black. Turn pepper with tongs to char all sides. Plunge pepper into ice water, and when cool enough to handle, remove and discard cap, skin, and seeds.
4. Rinse scallops and pat dry with paper towels. Thread scallops onto skewers, and refrigerate until ready to grill.
5. Combine mango, cucumber, onion, cilantro, 1 tablespoon olive oil, and lime juice in a glass or stainless-steel mixing bowl. Stir gently and season to taste with salt and pepper. Allow salsa to sit at room temperature for at least 15 minutes to blend flavors.
6. Combine roasted red pepper and vinegar in a food processor fitted with a steel blade or in a blender. With the motor running, slowly add remaining olive oil and Chinese chili oil through the feed tube to emulsify dressing. Season to taste with salt and pepper, and set aside. (Salsa and dressing can be made up to 1 day in advance and refrigerated, tightly covered. Allow both to reach room temperature before serving.)
7. Season scallops with salt and pepper, and brush with vinaigrette. Grill skewers for 1½ to 2 minutes per side. To serve, drizzle vinaigrette over skewers and place salsa next to them on the plate.
**Variation:** You could use extra-large (16 to 20 per pound) shrimp or cubes of firm-fleshed whitefish like cod or swordfish instead of the scallops.
**Speedy Solutions**
Metal skewers have a flat back so food isn't likely to spin when you turn it, but that's not the case with bamboo skewers. Try this trick: skewer food with two bamboo skewers parallel to one another. That makes food easier to turn.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
938 calories
639 calories from fat
71 g fat
34 g saturated fat
65 g protein
8 g carbohydrates
**Stale Stuff**
Thin fish fillets such as sole or flounder should never be grilled; they fall apart. Save them for more delicate cooking methods like baking or sautéing. Be sure any fish you grill is at least ⅔ inch thick.
# **Swordfish with Smoked Cheddar Sauce**
The smoky nuances from the cheese and bacon in the sauce are the perfect complement for this grilled fish.
½ **lb.** bacon, cut into small
pieces
3 shallots, peeled and
**chopped**
**2 garlic cloves, peeled and**
**minced**
**1 cup chicken stock**
**1 cup heavy cream**
**2 tsp. cornstarch**
1½ cups grated smoked cheddar
**cheese**
**1 ripe plum tomato, rinsed,**
**cored, seeded, and finely**
**chopped**
**Salt and freshly ground black**
**pepper to taste**
**4 (8-oz.) swordfish steaks**
**4 to 6 TB. fresh tomato salsa**
**(your favorite; optional)**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Cook bacon in a heavy skillet over medium-high heat for 5 to 7 minutes or until crisp. Remove bacon from the pan with a slotted spoon and set aside.
3. Discard all but 2 tablespoons bacon fat from the pan. Add shallots and garlic, and cook over medium heat, stirring frequently, for 3 minutes or until shallots are translucent. Add ¾ cup stock and cream. Bring to a boil, and simmer for 5 minutes.
4. Mix cornstarch with remaining stock, and stir mixture into sauce. Simmer for 1 to 2 minutes or until sauce is lightly thickened. Stir in grated cheese, and stir until melted. Add tomato and bacon, and season to taste with salt and pepper. (Sauce can be prepared up to 2 days in advance and refrigerated, tightly covered. Reheat it in a saucepan over low heat, stirring frequently.)
5. Sprinkle swordfish with salt and pepper, and grill fish for 2 to 4 minutes per side, depending on thickness, or until fish is still slightly translucent in the center. To serve, ladle sauce onto the center of a plate, and top with a fish steak. Garnish with a mound of salsa (if using).
**Variation:** No swordfish? Try thick fillets of cod, halibut, or sea bass instead.
# **Ham and Cheese-Stuffed Chicken**
The flavorful stuffing keeps the chicken moist as it grills and can be personalized in myriad ways.
4 (10-oz.) chicken breast
halves, with skin and bones
Salt and freshly ground black
pepper to taste
¼ **lb.** (1 cup) Gruyère cheese,
grated
¼ **lb.** cooked ham, cut into
¼-inch dice
1 **TB.** fresh thyme or 1 tsp.
dried
3 **TB**. unsalted butter, melted
**2 TB. freshly squeezed lemon**
**juice**
**2 TB. Worcestershire sauce**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
2. Rinse chicken and pat dry with paper towels. Insert a sharp paring knife into the thicker side of chicken breasts, and cut a lengthwise pocket, being careful not to puncture the skin. Sprinkle chicken with salt and pepper, and set aside.
3. Combine cheese, ham, and thyme in a small bowl. Gently stuff mixture into chicken pocket, and secure opening with a toothpick or skewer.
4. Combine butter, lemon juice, and Worcestershire sauce in a small bowl, and set aside.
5. Grill chicken for 10 to 12 minutes per side, basting frequently with sauce. Do not baste for final 2 minutes of cooking, and discard any unused sauce. Chicken is cooked when it registers 160°F on an instant-read thermometer inserted into the thickest part. Serve immediately.
**Variation:** For a different taste, try cheddar cheese and cooked sausage instead of Gruyère and ham. Either stuffing can also be used for pork chops.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 55 minutes*
**Each serving contains:**
727 calories
408 calories from fat
45 g fat
19 g saturated fat
73 g protein
3 g carbohydrates
**Stale Stuff**
When you start basting a raw or partially cooked chicken with a sauce, the sauce comes into contact with the natural bacteria on the chicken and must be discarded. Cross-contamination is one of the leading causes of food illness.
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 50 minutes*
**Each serving contains:**
672 calories
435 calories from fat
48 g fat
10.5 g saturated fat
33 g protein
31 g carbohydrates
**Fast Talk**
Mole ( _MOH-LAY_ ) is an ancient Mexican spicy sauce that dates from the Aztec era. Unsweetened chocolate adds to its richness, and it always includes some sort of nut or legume for thickening.
# **Mexican Chicken with Mole Sauce**
Unsweetened chocolate and peanut butter are the "secret ingredients" that give this sauce its rich flavor.
4 to 8 chicken pieces (your
choice: breasts, thighs, legs),
with skin and bones
5 TB. olive oil
**6 garlic cloves, peeled and**
**minced**
**4 TB. chili powder**
Salt and cayenne to taste
2 medium onions, peeled and
chopped
**2 tsp. ground cumin**
**2 cups chicken stock**
**3 ripe plum tomatoes, rinsed,**
**cored, seeded, and chopped**
**¼ cup peanut butter**
**¼ cup raisins**
**1 TB. granulated sugar**
**1 TB. unsweetened cocoa**
**powder**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
2. Rinse chicken and pat dry with paper towels.
3. Combine 3 tablespoons oil, 2 garlic cloves, and 2 tablespoons chili powder in a small bowl. Season to taste with salt and cayenne. Mix well, and rub mixture on chicken. Set aside.
4. Heat remaining 2 tablespoons oil in a heavy saucepan over medium-high heat. Add onions and remaining garlic, and cook, stirring frequently, for 3 minutes or until onions are translucent. Stir in remaining chili powder and cumin, and cook, stirring constantly, for 1 minute.
5. Add chicken stock, tomatoes, peanut butter, raisins, sugar, and cocoa powder. Stir well, and bring to a boil over high heat. Reduce the heat to low, and simmer _mole_ sauce for 15 minutes or until lightly thickened. Season to taste with salt and cayenne.
6. Grill chicken starting with skin side down for 8 to 10 minutes per side or until white meat registers 160°F and dark meat registers 180°F on an instant-read thermometer. Remove chicken from the grill, and serve immediately, passing sauce on the side.
**Variation:** Pork chops can be substituted for the chicken pieces.
# **Sweet and Hot Chicken Skewers**
You can make these skewers basted with a sweet and hot Asian sauce smaller and serve them as an hors d'oeuvre, too.
**12 bamboo skewers**
**4 (6-oz.) boneless, skinless**
**chicken breast halves**
**⅓ cup unsweetened applesauce**
**¼ cup hoisin sauce**
**2 TB. firmly packed dark**
**brown sugar**
**3 TB. ketchup**
**1 TB. honey**
**1 TB. rice wine vinegar**
**1 TB. soy sauce**
**2 tsp. Chinese chili paste**
**with garlic or to taste, or hot**
**red pepper sauce**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Cover bamboo skewers in water to soak for 30 minutes.
3. Rinse chicken, pat dry with paper towels, and trim of all visible fat. Cut chicken into strips 2 inches long and ½ inch wide.
4. Combine applesauce, hoisin sauce, brown sugar, ketchup, honey, rice wine vinegar, soy sauce, and Chinese chili paste in a mixing bowl. Whisk until smooth, and divide sauce into two small bowls.
5. Thread chicken onto skewers. Grill chicken, basting with sauce every 2 minutes, for 3 to 5 minutes per side. Do not baste for the last 2 minutes, and discard basting sauce. Remove chicken from the grill, and serve immediately, passing extra sauce separately.
**Variation:** Not in the mood for chicken? Cubes of pork loin or pork tenderloin or extra-large (16 to 20 per pound) shrimp can grilled instead.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
288 calories
24 calories from fat
3 g fat
1 g saturated fat
40 g protein
24 g carbohydrates
**Speedy Solutions**
To save time when making a recipe with many liquid ingredients, measure them into the same large cup, calculating what the level should be after each addition.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
342 calories
144 calories from fat
16 g fat
2.5 g saturated fat
41 g protein
8 g carbohydrates
**Fresh Ways**
Food has to be at least ¾-inch thick for an instant-read thermometer to be effective. For thinner food, you can judge by eye or poke it with the tip of a paring knife.
# **Chicken with Three-Tomato Salsa**
This dish is the epitome of summer eating, when you can find tomatoes right from the field.
**4 (6-oz.) boneless, skinless**
**chicken breasts**
**¼ cup olive oil**
**4 garlic cloves, peeled and**
**minced**
**Salt and freshly ground black**
**pepper to taste**
**1 red tomato, rinsed, cored,**
**seeded, and finely chopped**
**1 orange tomato, rinsed,**
**cored, seeded, and finely**
**chopped**
**1 yellow tomato, rinsed,**
**cored, seeded, and finely**
**chopped**
**½ red onion, peeled and**
**finely chopped**
**½ red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**1 jalapeño chili, rinsed, seeds**
**and ribs removed, and finely**
**chopped**
**3 TB. chopped fresh cilantro**
**1 TB. chopped fresh oregano**
**or 1 tsp. dried**
**1 TB. chopped fresh basil or**
**1 tsp. dried**
**¼ cup red wine vinegar**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
2. Rinse chicken, pat dry with paper towels, and trim of all visible fat. Place chicken between 2 sheets of plastic wrap, and pound to an even ½-inch thickness.
3. Combine 2 tablespoons olive oil and 2 garlic cloves in a small bowl. Spread mixture on chicken, and sprinkle chicken with salt and pepper to taste.
4. Combine red tomato, orange tomato, yellow tomato, red onion, red bell pepper, jalapeño, cilantro, oregano, basil, vinegar, remaining 2 tablespoons olive oil, and remaining 2 garlic cloves in a large bowl. Season to taste with salt and pepper, and stir well. Set aside.
5. Grill chicken for 3 to 4 minutes per side, uncovered, or until cooked through and no longer pink. To serve, place chicken on plates and top with salsa. Serve immediately.
**Variation:** Veal scallops can be used instead of the chicken.
# **Caribbean Pork Chops**
The paste that's rubbed on these pork chops have all the hallmark flavors of Jamaican "jerk" seasonings.
**4 (8-oz.) pork loin chops**
**1 large onion, peeled and**
**diced**
**4 garlic cloves, peeled**
**1 TB. dried thyme**
**1 TB. granulated sugar**
**1** **½ tsp. cayenne**
**1 tsp. freshly ground black**
**pepper**
**1 tsp. ground** _**allspice**_
**½ tsp. ground cinnamon**
**Salt to taste**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Rinse pork chops, and pat dry with paper towels. Trim chops of excess fat, and set aside.
3. Combine onion, garlic, thyme, sugar, cayenne, black pepper, allspice, cinnamon, and salt in a blender, and purée.
4. Rub pork chops on both sides with the spice paste and grill for 5 to 6 minutes per side or until an instant-read thermometer registers 150°F. Serve immediately.
**Variation:** Try boneless, skinless chicken breasts instead of the pork chops. Cook them over a medium-hot fire for 4 to 6 minutes on a side or until an instant-read thermometer registers 160°F.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
392 calories
171 calories from fat
19 g fat
6.5 g saturated fat
44 g protein
9 g carbohydrates
**Fast Talk**
**Allspice** comes from small berries of a pimiento tree native to the West Indies. The spice got its English name because its flavor is like a combination of cinnamon, nutmeg, and cloves.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 45 minutes*
**Each serving contains:**
994 calories
570 calories from fat
63 g fat
29 g saturated fat
62 g protein
11 g carbohydrates
**Speedy Solutions**
Many classic French recipes include a step for igniting liquor such as cognac, but it's not really necessary. The alcohol cooks off as the sauce cooks, although there is a minute trace left.
# **Steak with Shiitake Cognac Sauce**
Steak takes on new elegance when topped with a creamy sauce laced with potent cognac.
**1 lb. fresh shiitake mushrooms**
**4 (10-oz.) boneless rib-eye,**
**New York strip, or filet**
**mignon steaks**
**Salt and freshly ground black**
**pepper to taste**
**5 TB. unsalted butter**
**½ cup cognac**
**1** **½ cups dry red wine**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**18 scallions, rinsed, trimmed,**
**with all but 2 inches of green**
**tops discarded**
**4 TB. water**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Wipe shiitake mushrooms with a damp paper towel. Discard stems, slice mushrooms, and set aside.
3. Season both sides of steaks with salt and pepper to taste.
4. Heat 3 tablespoons butter in a heavy 12-inch skillet over medium-high heat. Add mushrooms, and cook, stirring frequently, for 3 minutes or until mushrooms begin to brown. Season to taste with salt and pepper, and continue to cook, stirring frequently, until liquid has evaporated. Remove mushrooms from the pan with a slotted spoon, and set aside.
5. Add cognac to the skillet, and cook over high heat until only 2 tablespoons remain. Add wine and thyme, and cook until liquid is ¾ cup. Return mushrooms to the skillet, season to taste with salt and pepper, and keep warm.
6. While sauce is reducing, heat remaining 2 tablespoons butter in a medium skillet and add scallions and water. Cook over high heat until mixture comes to a boil, shaking the pan to distribute butter. Lower heat to medium, and continue to cook until water has evaporated and scallions are glazed. Set aside.
7. Grill steaks to desired doneness. To serve, place steaks on plates and top with sauce and scallions. Serve immediately.
**Variation:** Rib lamb chops can be substituted for the steak.
# **Steak with Southwest Corn Sauce**
The sweet flavor of fresh corn in this creamy sauce is balanced by chili and vegetables.
**4 (10-oz.) boneless rib-eye or**
**New York strip steaks**
**1 TB. Herbes de Provence**
**1 TB. dry mustard**
**4 garlic cloves, peeled and**
**minced**
**Salt and freshly ground black**
**pepper to taste**
**4 ears fresh corn, shucked**
**2 TB. olive oil**
**1 small onion, peeled and**
**diced**
**1 red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**3 TB. chili powder**
**½ cup dry red wine**
**2 cups beef stock**
**½ cup heavy cream**
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 45 minutes*
**Each serving contains:**
714 calories
299 calories from fat
33 g fat
15 g saturated fat
70 g protein
30 g carbohydrates
**Fresh Ways** he carbohydrates
in corn create a natural thickening agent for the sauce, so no roux or cornstarch is necessary. If you want the sauce thicker, add a few tablespoons cornmeal.
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Rinse steak, pat dry with paper towels, and trim of excess fat.
3. Combine Herbes de Provence, mustard, garlic, salt, and pepper in a small bowl. Rub mixture on both sides of steaks, and set aside.
4. Cut kernels from corn using a sharp serrated knife. Place ¼ kernels in a food processor fitted with a steel blade or in a blender, and purée until smooth.
5. Heat oil in a saucepan over low heat. Add onion and red bell pepper, and cook, stirring frequently, for 3 minutes or until onion is translucent. Add chili powder, and cook over low heat, stirring constantly, for 1 minute.
6. Add wine, stock, and puréed corn, and bring to a boil over medium-high heat, stirring occasionally. Cook, stirring occasionally, for 15 minutes or until sauce is reduced by ½.
7. Add cream and remaining corn kernels to sauce, and cook over medium heat, stirring occasionally, for 5 minutes. Season to taste with salt and pepper, and keep sauce hot. (Sauce can be prepared up to 2 days in advance and refrigerated, tightly covered. Reheat over low heat, stirring occasionally.)
8. Grill steaks to desired doneness. Top steaks with sauce, and serve immediately.
**Variation:** Chicken breasts can be substituted for the steaks. If cooking chicken, use chicken stock rather than beef stock in the sauce.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 50 minutes*
**Each serving contains:**
319 calories
116 calories from fat
13 g fat
5 g saturated fat
47 g protein
1 g carbohydrates
# **Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon**
Garlic and rosemary are the classic Aegean way to flavor lamb, and I find that lemon zest is a good addition to cut some of the meat's richness.
**1 (3-1b.) boneless and butterflied**
**leg of lamb**
**5 garlic cloves, peeled and**
**minced**
**Zest of 1 lemon**
**3 TB. fresh chopped rose-mary**
**or 1 TB. dried**
**Salt and freshly ground black**
**pepper to taste**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Rinse lamb and pat dry with paper towels.
3. Combine garlic, lemon zest, rosemary, salt, and pepper in a small bowl. Rub mixture on lamb, and allow it to sit at room temperature until the grill is ready.
4. Sear lamb over a hot fire, uncovered, for 5 minutes per side or until exterior is browned. Move lamb to medium heat, and grill for an additional 5 to 8 minutes per side or until an instant-read thermometer registers 125°F for medium-rare or until desired doneness. Remove lamb from the grill, and allow lamb to _rest_ for 5 minutes before carving. Carve against the grain, and serve immediately.
**Fast Talk**
To rest is to allow thick pieces of meat to sit for anywhere from 5 to 15 minutes during which time the juices are reabsorbed into the fiber of the meat, making the food juicier when carved.
**Chapter 18**
**Burger Bonanza**
**In This Chapter**
• Lean fish burgers
• Flavorful poultry burgers
• Marvelous meaty burgers
_Burger_ is synonymous with _grilling_. And as you'll discover when cooking the recipes in this chapter, the definition of _burger_ goes far beyond beef. The only common denominator to these yummy burgers is that the basic food is ground and they're served between two pieces of some type of bread. But that's where the similarity stops.
In these pages, you'll find burgers made with succulent shrimp and rich tuna as well as burgers with lean ground turkey. And of course, I've included beef burgers, too. But they're not your run-of-the-mill burgers. Mine are flavored with international spice.
# **Between the Bread**
The bread that transforms your burger from a patty to a sandwich is an important part of the finished dish and can harmonize with other flavors. Choose a sturdy bread or bun that will stand up to the burgers' juice or wet condiments. Use crusty buns, and be sure to grill your buns, too, to create additional crust. I've given some suggestions for buns in the recipes, but don't feel you're limited to those. Look around your bakery and use whatever bun appeals to you.
# **Classy Condiments**
The condiments that top your burger should always be of top quality. Ketchup, mustard, and mayonnaise are the classics, but you can add additional options by shopping the supermarket's other aisles. Here are some ideas to vary the fare:
• Any dip you'd use with a potato chip or tortilla chip is perfect for burger topping, such as ranch dip, blue cheese dip, or our old friend onion dip. Or try some of the dip recipes you'll find in Chapter 3!
• Hummus, the Middle Eastern dip made from garbanzo beans, is now a refrigerated standard. It comes with many flavor additions, from roasted garlic to lemon.
• Thick salad dressings such as creamy Italian or Thousand Island work well.
• Use barbecue sauces and chutneys straight from the bottle.
_*Note:_ In most recipes in this chapter, the "Start to finish time" includes 30 minutes for the grill to heat.
# **Middle Eastern Lentil Burgers**
Seasonings like aromatic cumin and coriander flavor these healthful meatless burgers.
**2 cups** _**lentils,**_ **picked over,**
**washed, and drained**
**1 qt. water**
**1 tsp. salt**
**¾ cup pine nuts**
**2 TB. vegetable oil**
**1 medium onion, peeled and**
**chopped**
**2 garlic cloves, peeled and**
**minced**
**2 tsp. ground coriander**
**1 tsp. ground cumin**
**Salt and freshly ground black**
**pepper to taste**
**6 sesame buns, sliced in half**
**Lettuce, tomato, and mayonnaise**
**for serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Place lentils in a 2-quart saucepan, and cover with 1 quart water and at least 1 teaspoon salt. Bring to a boil over medium-high heat, reduce heat to low, and simmer, covered, for 20 to 25 minutes or until cooked. Drain lentils, and place in a mixing bowl.
3. While lentils are simmering, place pine nuts in a small dry skillet over medium-high heat. Toast nuts, shaking pan frequently, for 2 to 3 minutes or until browned. Set aside.
4. While lentils are cooking, heat oil in a small skillet over medium-high heat. Add onion and garlic, and cook, stirring frequently, for 3 minutes or until onion is translucent. Add coriander and cumin, and cook, stirring constantly, for 1 minute. Add onion mixture to lentils, and stir well.
5. Purée ½ cup pine nuts and 1 cup lentil mixture in a food processor fitted with a metal blade. Scrape mixture back into the mixing bowl, and add remaining pine nuts. Season to taste with salt and pepper. Form mixture into 6 (¾-inch-thick) burgers.
6. Grill buns cut side down until toasted. Grill burgers for 3 minutes per side, turning gently with a spatula. Serve immediately on buns with lettuce, tomato, and mayonnaise.
Serves: 6
**Active time:** 30 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
513 calories
171 calories from fat
19 g fat
2 g saturated fat
23 g protein
64 g carbohydrates
**Fast Talk**
Lentils are tiny lens-shape pulses and one of the oldest foods in the world. We commonly find brownish-gray lentils, but they also come in bright red, green, and yellow.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 45 minutes*
**Each serving contains:**
665 calories
163 calories from fat
18 g fat
3 g saturated fat
46 g protein
79 g carbohydrates
# **Creole Shrimp Burgers**
This is a burger version of the New Orleans po' boy sandwich, with vegetables included in the patties.
**2 TB. vegetable oil**
**1** **½ lb. large (21 to 30 per lb.)**
**raw shrimp**
**1 small onion, peeled and**
**chopped**
**2 garlic cloves, peeled and**
**minced**
**1 celery rib, rinsed, trimmed,**
**and chopped**
**1 red bell pepper, seeds and**
**ribs removed, and finely**
**chopped**
**3 TB. chopped fresh chives**
**3 TB. chopped fresh parsley**
**½ tsp. hot red pepper sauce**
**or to taste**
**Cajun seasoning to taste**
**4 long submarine rolls, split**
**in half**
**Lettuce, tomato, and tartar**
**sauce for serving**
**Speedy Solutions**
While they're a bit more expensive, you can save a lot of time by buying prepeeled shrimp. Or try Easy Peel shrimp. These have already been deveined, and the peels slip right off.
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Peel and devein shrimp. Rinse shrimp, and set aside.
3. Heat oil in a large skillet over medium-high heat. Add onion, garlic, celery, and red bell pepper. Cook, stirring frequently, for 5 to 7 minutes or until vegetables are soft. Scrape mixture into a mixing bowl.
4. Finely chop ½ pound shrimp, and add to the mixing bowl. Purée remaining 1 pound shrimp in a food processor fitted with a steel blade. Add to the bowl, along with chives, parsley, hot red pepper sauce, and Cajun seasoning. Form mixture into 8 (¾-inch-thick) burgers.
5. Grill rolls cut side down until toasted. Sear shrimp burgers for 2 minutes per side over hot heat and then cook for an additional 3 or 4 minutes per side over medium heat or until cooked through. Serve immediately placing 2 patties on each roll, with lettuce, tomato, and tartar sauce.
**Variation:** You can use scallops or a firm-fleshed whitefish such as cod or tilapia instead of shrimp.
# **Dilled Salmon Burgers**
Dill and salmon are a timeless combination, and those foods are sparked by some Dijon mustard for these moist burgers.
**1 (1** **¼-lb.) salmon fillet**
**¼ cup Dijon mustard**
**¼ cup chopped fresh dill**
**Salt and freshly ground black**
**pepper to taste**
**¼ cup mayonnaise**
**¼ cup sour cream**
**2 TB. vegetable oil**
**4 rolls (your choice), split in**
**half**
**Lettuce, tomato, and thinly**
**sliced red onion for serving**
1. Rinse salmon, pat dry with paper towels, and cut into 1-inch pieces. Chop salmon in a food processor fitted with a steel blade using on-and-off pulsing. Place salmon in a mixing bowl and add 2 tablespoons Dijon mustard and 2 tablespoons dill. Season to taste with salt and pepper.
2. Form salmon mixture into 4 (1-inch-thick) burgers. Cover burgers with plastic wrap, and refrigerate for at least 1½ hours. (Mixture can be made up to 1 day in advance and refrigerated, tightly covered.)
3. After 1 hour, light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
4. While burgers are chilling, combine mayonnaise and sour cream with remaining Dijon mustard and dill. Stir well, and refrigerate until ready to use.
5. Grill rolls cut side down until toasted. Rub burgers with oil, and grill on a hot grill for 3 minutes per side for medium-rare or to desired doneness. Serve immediately on rolls with sauce, lettuce, tomato, and onion slices.
**Variation:** Instead of salmon, try this with tuna or a firm-fleshed whitefish like cod or halibut.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 2 hours,
including 1½ hours for
chilling
**Each serving contains:**
615 calories
334 calories from fat
37 g fat
7 g saturated fat
37 g protein
33 g carbohydrates
**Stale Stuff**
Don't skip refrigerating the burgers. The chilling time gives the burgers time to solidify so there's no fear they'll fall apart on the grill.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
841 calories
318 calories from fat
35 g fat
10 g saturated fat
55 g protein
79 g carbohydrates
**Fresh Ways**
The dark meat of poultry should be cooked to an internal temperature of 165°F to ensure it's cooked properly at the bone, and burgers should be cooked to the same temperature.
# **Italian Turkey Burgers**
These lean turkey burgers are seasoned with herbs and spices and then topped with mozzarella cheese and marinara sauce.
**2 TB. olive oil**
**½ small red onion, peeled and**
**chopped**
**3 garlic cloves, peeled and**
**minced**
**1** **½ lb. ground turkey**
**¼ cup freshly grated**
**Parmesan cheese**
**3 TB. chopped fresh parsley**
**2 TB. chopped fresh basil or**
**2 tsp. dried**
**1 TB. chopped fresh oregano**
**or 1 tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
**4 Italian rolls, split in half**
**¼ lb. whole milk mozzarella**
**cheese, sliced**
**½ cup marinara sauce**
**Lettuce and thinly sliced red**
**onion for serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Heat olive oil in a small skillet over medium-high heat. Add onion and garlic, and cook, stirring frequently, for 5 minutes or until onion is soft. Scrape mixture into a mixing bowl.
3. Add turkey, Parmesan cheese, parsley, basil, and oregano. Season to taste with salt and pepper. Mix thoroughly, and form mixture into 4 (¾-inch-thick) burgers.
4. Grill rolls cut side down until toasted. Sear burgers over high heat for 2 minutes per side and then place burgers over medium heat. Continue to cook for 3 to 5 minutes per side or until burgers register 165°F on an instant-read thermometer and are cooked through.
5. Top burgers with mozzarella slices, cover grill, and cook for 2 minutes or until cheese is melted. Place burgers on rolls, top with marinara sauce, and serve immediately with lettuce and onion slices.
**Variation:** No turkey? Try ground pork or ground veal.
# **New England Turkey Burgers**
Dried cranberries and maple are two of the flavors topping these burgers made moister with grated apple.
**1** **¼ lb. ground turkey**
**1 Golden Delicious apple,**
**peeled, cored, and grated**
**2 tsp. dry mustard**
**½ tsp. dried thyme**
**Salt and freshly ground black**
**pepper to taste**
**½ cup barbecue sauce**
**½ cup pure maple syrup**
**½ cup cider vinegar**
**¼ cup dried cranberries**
**1 tsp. lemon zest**
**½ tsp. ground cinnamon**
**½ tsp. ground ginger**
**4 rolls (your choice), sliced**
**in half**
**Lettuce, tomato, and thinly**
**sliced red onion for serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Combine turkey, apple, 1 teaspoon dry mustard, and thyme in a mixing bowl. Season to taste with salt and pepper. Form mixture into 4 (1-inch thick) burgers.
3. Combine barbecue sauce, maple syrup, cider vinegar, dried cranberries, lemon zest, cinnamon, ginger, and remaining 1 teaspoon dry mustard in a small saucepan. Bring to a boil over medium-high heat, stirring occasionally. Reduce heat to low and simmer sauce for 3 minutes. Divide sauce into 2 small bowls.
4. Grill rolls cut side down until toasted. Sear burgers over high heat for 2 minutes per side and then place burgers over medium heat. Continue to cook, basting with sauce every 2 minutes, for 3 to 5 minutes per side or until burgers register 165°F. Do not baste for the last 2 minutes, and discard basting sauce. Serve immediately on rolls with lettuce, tomato, and red onion slices. Pass second bowl of sauce separately.
**Variation:** Instead of turkey, try ground pork or ground veal.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
507 calories
119 calories from fat
13 g fat
3 g saturated fat
34 g protein
65 g carbohydrates
**Fresh Ways**
Apple adds moisture as well as a sweet flavor to foods. These burgers cook so quickly that the apple retains its texture and makes the burgers juicier.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
983 calories
670 calories from fat
74 g fat
23 g saturated fat
48 g protein
28 g carbohydrates
**Fast Talk**
Chorizo ( _chore-EAT-zoh_ ) is a highly seasoned pork sausage flavored with garlic, chili powder, and other spices and used in Mexican and Spanish cooking. The best substitute is linguiça.
# **Mexican Burgers**
Spicy chorizo sausage enlivens the taste of the beef in these cheese-filled burgers.
**½ lb.** _**chorizo**_
**1 lb. ground chuck**
**2 shallots, peeled and finely**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**3 TB. chopped fresh cilantro**
**2 TB. chili powder**
**2 tsp. ground cumin**
**1 tsp. dried oregano**
**Salt and cayenne to taste**
**1 cup grated jalapeño Jack**
**cheese**
**¾ cup mayonnaise**
**2 TB. diced canned green**
**chilies, drained**
**1 TB. freshly squeezed lime**
**juice**
**4 rolls (your choice), sliced**
**in half**
**Lettuce, tomato slices, and**
**thinly sliced red onion for**
**serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Remove casings from chorizo, if necessary, and chop chorizo finely in a food processor fitted with a steel blade using on-and-off pulsing. Combine chorizo, ground chuck, shallots, 3 garlic cloves, cilantro, chili powder, cumin, and oregano in a mixing bowl. Season to taste with salt and cayenne. Mix well, and form mixture into 8 (½-inch-thick) patties. Place ¼ cup grated cheese on 4 burgers, and top with remaining 4 patties. Press together gently to enclose cheese.
3. Combine mayonnaise, remaining garlic, green chilies, and lime juice in a small bowl. Season with salt and cayenne, and stir well. Set aside.
4. Grill rolls cut side down until toasted. Grill burgers for a total time of 4 to 6 minutes per side or to an internal temperature of 125°F for medium-rare or to desired doneness. To serve, place burgers on bottom half of rolls and top each with mayonnaise. Serve immediately with lettuce, tomato, and red onion slices.
**Variation:** Try ground turkey instead of beef. Cook burgers to an internal temperature of 160°F on an instant-read thermometer or until cooked through and no longer pink.
# **Caribbean Burgers**
Curry and aromatic spices flavor these beef burgers.
**1** **½ lb. ground chuck**
**3 TB. chopped fresh cilantro**
**4 garlic cloves, peeled and**
**minced**
**1 TB. freshly squeezed lime**
**juice**
**2 tsp. curry powder**
**2 tsp. ground cumin**
**1 tsp. ground allspice**
**3 to 5 dashes hot red pepper**
**sauce**
**Salt to taste**
**4 rolls (your choice), split in**
**half**
**½ cup jarred mango chutney**
**Lettuce, tomato, and thinly**
**sliced red onion for serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Combine ground chuck, cilantro, garlic, lime juice, curry powder, cumin, allspice, and red pepper sauce in a mixing bowl. Season to taste with salt. Form mixture into 4 (1-inch-thick) burgers.
3. Grill rolls cut side down until toasted. Grill burgers for a total time of 4 to 6 minutes per side or to an internal temperature of 125°F for medium-rare or to desired doneness. To serve, place burgers on bottom half of rolls and top each with chutney. Serve immediately with lettuce, tomato, and red onion slices.
**Variation:** Ground pork or turkey can be substituted for the beef. Cook pork to an internal temperature of 150°F or to desired doneness. Cook turkey to an internal temperature of 165°F on an instant read thermometer or until cooked through and no longer pink.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
486 calories
175 calories from fat
19 g fat
7 g saturated fat
39 g protein
37 g carbohydrates
**Fresh Ways**
Small quantities of lemon and lime juice are added to many recipes not for their flavor, but to boost the other flavors in the dish. In the same way, they're drizzled on sweet fresh fruit to enliven the taste.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 45 minutes*
**Each serving contains:**
660 calories
348 calories from fat
39 g fat
14 g saturated fat
36 g protein
39 g carbohydrates
**Stale Stuff**
When a sauce contains a high percentage of sugar, like this one made with hoisin sauce, you should only baste food for the last few minutes of cooking, especially when cooking over anything but low heat. Otherwise, you'll burn the sugar in the sauce.
# **Chinese Pork Burgers**
Crunchy water chestnuts, scallions, and ginger give a decidedly Asian accent to these delicate pork burgers.
**1** **½ lb. ground pork**
**12 scallions, rinsed, trimmed,**
**and thinly sliced**
**4 TB. grated fresh ginger**
**¼ cup chopped fresh cilantro**
**4 garlic cloves, peeled and**
**minced**
**3 TB. soy sauce**
**2 TB. dry sherry**
**½ cup chopped water chestnuts**
**Freshly ground black pepper**
**to taste**
**½ cup Dijon mustard**
**¼ cup hoisin sauce**
**4 sesame rolls, split in half**
**Lettuce and tomato slices for**
**serving**
1. Light a gas or charcoal grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
2. Combine ground pork, 6 scallions, ginger, cilantro, garlic, soy sauce, sherry, water chestnuts, and pepper in a mixing bowl. Mix well and form into 4 (¾-inch-thick) burgers.
3. Combine Dijon mustard and hoisin sauce in a bowl, whisk well, and set aside.
4. Grill rolls cut side down until toasted. Grill burgers for a total of 4 or 5 minutes per side or until burgers are cooked to 150°F on an instant-read thermometer. Baste burgers with sauce for last 4 minutes of grilling.
5. Add remaining scallions to remaining sauce. Serve immediately on rolls with lettuce and tomato slices. Pass sauce separately.
**Variation:** Ground turkey or ground veal can be used instead of the pork.
# **Bombay Lamb Burgers**
Succulent dried apricots and curry flavor these yogurt-topped lamb patties.
**½ pt. plain** _**yogurt**_
**2 TB. vegetable oil**
**1 medium onion, peeled and**
**finely chopped**
**2 garlic cloves, peeled and**
**minced**
**1** **½ lb. ground lamb**
**½ cup finely chopped dried**
**apricots**
**¼ cup chopped fresh cilantro**
**1 TB. curry powder**
**Salt and freshly ground black**
**pepper to taste**
**2 tsp. ground cumin**
**4 pita bread**
**Cucumber and tomato slices**
**for serving**
1. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
2. Place yogurt in a strainer set over a mixing bowl. Shake strainer gently a few times, and allow yogurt to drain for at least 30 minutes at room temperature or up to 6 hours refrigerated. Discard whey from mixing bowl, and place yogurt in the bowl. Set aside.
3. Heat oil in a small skillet over medium-high heat. Add onion and garlic, and cook, stirring frequently, for 5 minutes or until onion is soft. Scrape mixture into a mixing bowl, and add ground lamb, dried apricots, cilantro, and curry powder. Season to taste with salt and pepper. Mix well, and form mixture into 4 (1-inch-thick) burgers.
4. Grill burgers for a total time of 4 to 6 minutes per side or to an internal temperature of 130°F for medium-rare or to desired doneness.
5. While burgers are grilling, combine drained yogurt and cumin in a small bowl.
6. To serve, split pita bread and place burgers inside. Top each with yogurt and cucumber and tomato slices. Serve immediately.
**Variation:** Ground beef can be substituted for the ground lamb.
Serves: 4
**Active time:** 30 minutes
**Start to finish:** 40 minutes*
**Each serving contains:**
800 calories
433 calories from fat
48 g fat
18.5 g saturated fat
38 g protein
52 g carbohydrates
**Fast Talk**
Yogurt is a dairy product usually made from cow's milk, but it can be made from either goat's milk or sheep's milk. It coagulates into a soft custard texture from being invaded by friendly bacteria that give it a slightly tart taste. When drained, it becomes firmer as the watery whey drips off.
**Chapter 19**
**Flavor Without Fuss: Marinated Grilled Dishes**
**In This Chapter**
• Exciting Asian approaches
• Lusty Latin flavors
• Subtle European seasoning
There are many times that you anticipate hours—or even days—in advance using the grill to cook a delicious dinner, and those are the times when you'll be leafing through the recipes in this chapter. These are all for foods that need a leisurely few hours to marinate before their trip to the grill.
While the length of time from start to finish is measured in hours instead of minutes, your actual time in preparing the food is never more than 25 minutes. Marinades are quick to make and easy to use, and their flavors are drawn from cuisines around the world.
# **The Soaking Solutions**
The secret to all the recipes in this chapter is that they're soaked for a time period in a marinade to give them flavor, and in some cases to tenderize the food as well. This process of soaking foods in the marinade is called marinating.
Most marinades contain some sort of acid. It can be citrus juice or juices, any sort of vinegar, liquor, or any type of wine. Generally the rule holds true that you'll use
**Stale Stuff**
While the resealable plastic bag is the perfect choice for marinating foods, marinating can also be done in a mixing bowl or roasting pan. Just be sure the pan is glass, ceramic, or stainless steel and _not_ aluminum. Aluminum makes the food taste metallic.
white wine for white foods like chicken and fish and red wine for red meats. The liquid is the key to a marinade, but other ingredients run the gamut from garlic and onions to puréed olives and herbs.
The length of time you marinate food depends on the food. Delicate fish should not be marinated for more than a few hours, while dense beef or lamb could be marinated overnight. Check individual recipes for the correct amount of time, and don't exceed that time.
# **Combination Cooking**
Certain cuts of meat, such as a butterflied leg of lamb or a thick steak, can be started on a grill and then finished in the oven. Using this method enables you get the perfect heating throughout. The center is rare while the exterior is done but not overly done and dry. How does this work? The heat transferred by the high heat of the grill starts to heat through to the center and then the oven's more gentle heat finishes the process.
Begin by grilling the meat over a hot grill for 4 minutes on a side and then place the meat in a 375°F oven for the time shown in the following table.
**Times for Combination Grilling and Roasting**
This method of cooking is ideal if you're grilling for a large group. You can sear thick steaks or chops early in the day and then arrange them on a number of baking sheets for completion right before dinner is served.
# **Salmon Provençale**
Heady balsamic vinegar is joined with wine and herbs to give this fish the sunny flavors of Southwestern France.
**4 (6-oz.) salmon fillets**
**¼ cup balsamic vinegar**
**1 cup dry white wine**
**3 TB. Dijon mustard**
**4 garlic cloves, peeled and**
**minced**
**2 TB. chopped fresh parsley**
**1 TB. Herbes de Provence**
**Salt and freshly ground black**
**pepper to taste**
**¼ cup olive oil**
**1 cup mesquite or applewood**
**chips**
1. Rinse salmon and pat dry with paper towels. Skin salmon by running the blade of a boning knife between the meat and skin.
2. Combine vinegar, wine, Dijon mustard, garlic, parsley, Herbes de Provence, salt, and pepper in a heavy resealable plastic bag, and mix well. Add olive oil and mix well again. Add salmon and marinate, refrigerated, for 3 to 8 hours, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions. If you're using a charcoal grill, soak mesquite chips in water to cover for 30 minutes. When the fire is hot, drain wood chips and scatter them on the fire. If you're using a gas grill, create a tinfoil packet for the chips and poke holes in the top. Place packet on grill.
4. Drain salmon, and discard marinade. Cook salmon on a medium grill, covered, for 6 to 8 minutes, turning gently with a wide spatula, or until fish it is opaque at the edges and slightly translucent in the center. Serve immediately.
**Variation:** Cod, halibut, or sea bass can be used instead of salmon.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 3½
hours, including 3 hours
for marinating
**Each serving contains:**
549 calories
302 calories from fat
33.5 g fat
6 g saturated fat
36.5 g protein
15 g carbohydrates
**Speedy Solutions**
Although it's against traditional wisdom, I find it easier to fillet fish starting at the head rather than the tail end. Cut around the gills, and use the backbone of the fish as guide. Slice along the backbone, and you'll get the fillet off in one piece.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 2¼
hours, including 2 hours
for marinating
**Each serving contains:**
521 calories
326 calories from fat
36 g fat
6 g saturated fat
45 g protein
2 g carbohydrates
# **Aegean Swordfish**
Lemon and oregano are hallmarks of grilled fish in Greece, and they're part of this marinade, too.
**4 (8-oz.) swordfish steaks**
**¼ cup freshly squeezed lemon**
**juice**
**Zest of 1 lemon**
**6 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh parsley**
**2 TB. dried oregano**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**Salt and freshly ground black**
**pepper to taste**
**½ cup olive oil**
1. Rinse swordfish steaks and set aside.
2. Combine lemon juice, lemon zest, garlic, parsley, oregano, thyme, salt, and pepper in a heavy resealable plastic bag, and mix well. Add olive oil, and mix well again. Add swordfish and marinate, refrigerated, for 2 to 3 hours, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions.
4. When the fire is hot, remove fish from marinade and discard marinade. Grill fish for 3 or 4 minutes on each side or until slightly translucent in the center. Serve immediately.
**Variation:** Other firm-fleshed fish such as sea bass, halibut, or scrod can be substituted for the swordfish.
**Stale Stuff**
When marinating in a strong acid such as lemon juice, it's important to marinate food for only the amount of time specified. Otherwise the acid will "cook" the food and you end up with food that has an unappealing color or texture.
# **Caribbean Shrimp**
A combination of citrus juices, rum, and herbs give these shrimp an island accent.
**2 1b. jumbo (11 to 15 per 1b.)**
**raw shrimp**
**2 shallots, peeled and**
**chopped**
**2 garlic cloves, peeled and**
**minced**
**Juice of 1 lime**
**½ cup freshly squeezed**
**orange juice**
**½ cup white wine**
**2 TB. dark rum**
**2 TB. soy sauce**
**2 TB. chopped fresh parsley**
**1 TB. chopped fresh rose-mary**
**or 1 tsp. dried**
**Salt and freshly ground black**
**pepper to taste**
1. Peel and devein shrimp. Place shrimp in a heavy resealable plastic bag. Add shallots, garlic, lime juice, orange juice, wine, rum, soy sauce, parsley, and rosemary. Season to taste with salt and pepper. Mix well, and add shrimp. Marinate shrimp, refrigerated, for a minimum of 1 or up to 4 hours, turning the bag occasionally.
2. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
3. Remove shrimp from marinade, reserving marinade. Grill shrimp uncovered, for 3 minutes per side or until cooked through.
4. White shrimp are grilling, boil down marinade until it is reduced by ½. Spoon a few tablespoons over each portion of shrimp. Serve immediately or at room temperature.
**Variation:** Any firm-fleshed whitefish fillet, such as halibut, whitefish, or snapper can be used in place of the shrimp. The cooking time is the same.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 2½
hours, including 2 hours
for marinating
**Each serving contains:**
205 calories
24 calories from fat
3 g fat
0.5 g saturated fat
31 g protein
6 g carbohydrates
**Fresh Ways**
When grilling small foods like shrimp it's easier to turn them if they've been skewered with two skewers. Insert the skewers as parallel lines, and you can use tongs to turn the food evenly.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 4¾
hours, including 4 hours
for marinating
**Each serving contains:**
932 calories
615 calories from fat
68 g fat
13 g saturated fat
62 g protein
14 g carbohydrates
# **Middle Eastern Chicken**
Aromatic spices like cumin and coriander give this grilled chicken its regional flavor.
**4 to 8 chicken pieces (breasts,**
**thighs, legs), with bones and**
**skin**
**¼ cup balsamic vinegar**
**1 small onion, peeled and**
**chopped**
**3 garlic cloves, peeled and**
**minced**
**¼ cup chopped fresh parsley**
**3 TB. ground cumin**
**2 TB. ground coriander**
**1 TB. granulated sugar**
**1 tsp. ground cinnamon**
**½ tsp. cayenne or to taste**
**Salt to taste**
**¾ cup olive oil**
1. Rinse chicken and pat dry with paper towels.
2. Combine vinegar, onion, garlic, parsley, cumin, coriander, sugar, cinnamon, cayenne, and salt in a heavy resealable plastic bag. Mix well, add olive oil, and mix well again. Add chicken and marinate for a minimum of 4 hours, refrigerated, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
4. Remove chicken from marinade and discard marinade. Grill chicken for 12 minutes per side or until white meat registers 160°F and dark meat registers 180°F on an instant-read thermometer. Serve immediately.
**Variation:** You could also use pork chops instead of chicken pieces.
**Speedy Solutions**
I like to mince the marinade ingredients because the pieces then cling to the food when it's grilled, but if you want to save time, combine all the marinade ingredients in a food processor fitted with a steel blade or in a blender and purée. It'll taste the same.
# **Chicken Satay with Spicy Peanut Sauce**
This easy peanut sauce can also be used as a dressing for chicken salad or cold noodles.
**4 (6-oz.) boneless, skinless**
**chicken breasts**
**¾ cup soy sauce**
**1 cup firmly packed dark**
**brown sugar**
**⅔ cup freshly squeezed lime**
**juice**
**4 TB. Chinese chili paste**
**with garlic**
**10 garlic cloves, peeled and**
**minced**
**3 TB. Asian sesame oil**
**8 to 12 (8-in.) bamboo skewers**
**1 cup chunky peanut butter**
**½ cup very hot tap water**
**3 scallions, rinsed, trimmed,**
**and chopped**
**¼ cup chopped fresh cilantro**
1. Rinse chicken and pat dry with paper towels. Trim chicken of all visible fat, and cut into 1-inch cubes.
2. Combine ½ cup soy sauce, ½ cup brown sugar, ⅓ cup lime juice, 2 tablespoons Chinese chili paste, 4 cloves garlic, and 1 tablespoon sesame oil in a heavy resealable plastic bag. Mix well and add chicken. Marinate chicken for a minimum of 3 hours, refrigerated, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions. Cover bamboo skewers in water to soak. Begin cooking when the fire is hot.
4. Combine peanut butter, water, scallions, cilantro, remaining ¼ cup soy sauce, remaining ½ cup brown sugar, remaining ⅓ cup lime juice, remaining 2 tablespoons chili paste, remaining 6 garlic cloves, and remaining 2 tablespoons sesame oil in a mixing bowl. Whisk well, and set aside.
5. Drain chicken from marinade and discard marinade. Thread chicken on soaked skewers. Grill chicken for 3 minutes per side, turning it in quarter turns to grill all 4 sides, until chicken registers 160°F on an instant-read thermometer. Serve immediately accompanied by peanut sauce.
**Variation:** Try this recipe with pork or beef cubes or extra-large shrimp instead of chicken.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 3½
hours, including 3 hours
for marinating
**Each serving contains:**
916 calories
400 calories from fat
44 g fat
7 g saturated fat
59 g protein
78 g carbohydrates
**Stale Stuff**
When skewering food for grilling, don't just jam the pieces together on the sticks. Food cooks at a slower rate if it's pressed together. You want the pieces to be just touching.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 6½
hours, including 6 hours
for marinating
**Each serving contains:**
936 calories
643 calories from fat
71 g fat
26 g saturated fat
49 g protein
21 g carbohydrates
**Stale Stuff**
While it was a luxury even a few decades ago, it's now easy to find authentic maple syrup in most supermarkets. So there's no reason to ever use anything else—and certainly not "pancake syrup" or any artificially flavored product.
# **Cranberry-Maple Spareribs**
Here, cranberry and orange flavor the ribs and then maple syrup adds to the succulent glaze.
**1 cup cranberry juice**
**2 TB. orange juice concentrate**
**4 garlic cloves, peeled and**
**minced**
**1 shallot, peeled and minced**
**1 TB. fresh thyme or 1 tsp.**
**dried**
**½ tsp. ground allspice**
**Salt and freshly ground black**
**pepper to taste**
**2 (2-1b.) racks baby back ribs,**
**cut into 6 servings**
**⅓ cup pure maple syrup**
1. Combine cranberry juice, orange juice concentrate, garlic, shallot, thyme, allspice, salt, and pepper in a heavy resealable plastic bag. Mix well, and add ribs. Marinate ribs, refrigerated, for a minimum of 6 hours and up to 18 hours, turning the bag occasionally.
2. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is medium-hot.
3. Remove ribs from marinade, and reserve marinade. Grill ribs over medium-hot fire, covered, turning occasionally, for 20 minutes or until almost cooked through.
4. While ribs are grilling, combine reserved marinade and maple syrup in a small saucepan, and boil over medium heat until mixture is reduced to ⅓ cup.
5. Brush underside of ribs with the glaze, and grill for 2 minutes. Turn ribs, brush the top side, and grill for 2 minutes more. (Ribs can be grilled 1 day in advance and reheated, uncovered, in a 375°F oven for 10 to 12 minutes or until hot.)
**Variation:** You could also use pork chops or pieces of chicken with bones in place of the ribs. Cook chicken to an internal temperature of 165°F on an instant-read thermometer and pork chops to an internal temperature of 155°F.
# **Stuffed Flank Steak**
This dish looks stunning when it's brought to the table, with a colorful filling of sautéed vegetables in the center of each slice.
**1 (1** **½-lb.)** _**flank steak,**_ **cut**
**from the thick end**
**1 cup dry red wine**
**1 shallot, peeled and chopped**
**4 garlic cloves, peeled and**
**minced**
**1 TB. Herbes de Provence**
**Salt and freshly ground black**
**pepper to taste**
**¼ cup olive oil**
**2 TB. unsalted butter**
**1 green bell pepper, seeds**
**and ribs removed, and**
**chopped**
**1 red bell pepper, seeds and**
**ribs removed, and chopped**
**1 large onion, peeled and**
**chopped**
**2 TB. beef stock**
**¼ cup freshly grated**
**Parmesan cheese**
**½ cup Italian breadcrumbs**
**2 TB. chopped fresh parsley**
**1 TB. chopped fresh oregano**
**or 1 tsp. dried**
**1 TB. fresh thyme or 1 tsp.**
**dried**
Serves: 4
**Active time:** 25 minutes
**Start to finish:** 3¾
hours, including 3 hours
for marinating
**Each serving contains:**
631 calories
334 calories from fat
37 g fat
13 g saturated fat
42 g protein
21 g carbohydrates
**Fast Talk**
To score is to make shallow cuts in food, frequently in a diamond pattern. In the case of flank steak, it keeps the meat from curling as it grills, but it can also be used as a way to speed absorption of the flavors in a marinade.
1. Rinse flank steak and pat dry with paper towels. _Score_ steak lightly in a diamond pattern on both sides. Cut a deep pocket in the center of flank steak from the side of steak that extends to within ½ inch of sides of meat.
2. Combine wine, shallot, 2 garlic cloves, and Herbes de Provence in a heavy resealable plastic bag. Season to taste with salt and pepper. Mix well, add olive oil, and mix well again. Add steak, and marinate, refrigerated, for a minimum of 3 hours and up to 8 hours.
3. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
4. Melt butter in a 12-inch skillet over medium heat. Add green bell pepper, red bell pepper, onion, and remaining garlic. Cook, stirring frequently, for 10 minutes or until vegetables are soft. Remove the pan from the heat and stir in stock, Parmesan cheese, breadcrumbs, parsley, oregano, and thyme. Season to taste with salt and pepper, and mix well.
5. Gently stuff vegetable mixture into steak pocket and skewer the opening closed with turkey-trussing skewers or wooden toothpicks soaked in water. Sprinkle meat with salt and pepper.
6. Grill steak uncovered for 3 to 4 minutes per side for medium-rare or to desired doneness. Allow steak to rest for 5 minutes and then carve into slices. Serve immediately.
Serves: 4
**Active time:** 20 minutes
**Start to finish:** 3½
hours, including 3 hours
for marinating
**Each serving contains:**
956 calories
597 calories from fat
66 g fat
14 g saturated fat
66 g protein
9 g carbohydrates
# **Mexican Steaks with Chipotle Mayonnaise**
The smoky flavor of chipotle chilies underscores the grilled taste of these spicy steaks.
**4 (10-oz.) New York strip or**
**boneless rib-eye steaks**
**1 cup dry red wine**
**¼ cup red wine vinegar**
**1 small onion, peeled and**
**chopped**
**4 garlic cloves, peeled and**
**minced**
**1 large jalapeño chili, rinsed,**
**seeds and ribs removed, and**
**finely chopped**
**2 TB. ground cumin**
**1 TB. dried oregano, preferably**
**Mexican**
**Salt to taste**
**½ cup olive oil**
**½ cup mayonnaise**
**1** _**chipotle chili in adobo sauce,**_
**finely chopped**
**2 tsp. adobo sauce**
1. Rinse steaks and pat dry with paper towels.
2. Combine wine, vinegar, onion, 3 garlic cloves, jalapeño, cumin, and 2½ teaspoon oregano in a heavy resealable plastic bag. Add salt to taste, and mix well. Add olive oil, and mix well again. Add steaks and marinate, refrigerated, for 3 to 5 hours, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions. Begin cooking when the fire is hot.
4. Combine mayonnaise, chipotle chili, adobo sauce, remaining garlic, and remaining oregano in a mixing bowl. Whisk well.
5. Remove steaks from marinade and discard marinade. Grill steaks uncovered for 3 to 4 minutes per side for medium rare or to desired doneness. To serve, slice steaks into ¾-inch slices and top with sauce. Serve immediately.
**Variation:** Lamb chops can be substituted for the steak.
**Fast Talk**
Chipotle chilies are dried jalapeño chilies that have been smoked. They're canned in a spicy sauce similar to a hot red pepper sauce made from chilies, vinegar, and salt.
# **Korean Steak**
In this authentic Korean dish, the grilled steak is topped with a spicy sauce flavored with cilantro and garlic.
**4 (10-oz.) New York strip**
**or boneless rib-eye steaks**
**1 cup soy sauce**
**¼ cup sweet sherry**
**3 TB. granulated sugar**
**7 garlic cloves, peeled and**
**minced**
**2 TB. Asian sesame oil**
**1 tsp. red pepper flakes**
**or to taste**
**½ cup firmly packed cilantro**
**leaves**
**⅓ cup vegetable oil**
**2 TB. freshly squeezed lime**
**juice**
**½ jalapeño or serrano**
**chili, rinsed, seeds and ribs**
**removed, and diced**
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 3½
hours, including 3 hours
for marinating
**Each serving contains:**
590 calories
207 calories from fat
23 g fat
7 g saturated fat
70 g protein
19 g carbohydrates
1. Rinse steaks and pat dry with paper towels.
2. Combine ¾ cup soy sauce, sherry, sugar, 4 garlic cloves, 1 tablespoon Asian sesame oil, and red pepper flakes in a heavy resealable plastic bag. Mix well, and add steaks. Marinate steaks, refrigerated, for a minimum of 3 hours, turning the bag occasionally.
3. Light a charcoal or gas grill according to the manufacturer's instructions.
4. Combine remaining ¼ cup soy sauce, remaining 3 garlic cloves, remaining 1 tablespoon sesame oil, cilantro, vegetable oil, lime juice, and jalapeño in a food processor fitted with a steel blade or in a blender. Purée until smooth, and set aside.
5. Remove steaks from marinade and discard marinade. Grill steaks uncovered for 3 to 4 minutes per side for medium-rare or to desired doneness. To serve, slice steaks into ¾-inch slices and top with sauce. Serve immediately.
**Fresh Ways** ou can increase
the number of servings from 4 to 6 for any recipe without increasing the amount of marinade. When you get to 8 servings, though, you should double the marinade.
**Variation:** Thick pork chops can be substituted for the beef steaks. Cook them to an internal temperature of 150°F.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 2 hours,
including 1½ hours for
marinating
**Each serving contains:**
721 calories
299 calories from fat
33 g fat
10.5 g saturated fat
96 g protein
2 g carbohydrates
**Fresh Ways** f you have an
aversion to anchovies, feel free to pass them over in this recipe. But then do add salt to taste to the marinade to compensate.
# **Rosemary Lamb Chops**
While there's not a lot of liquid in this marinade, it still enters the meat well via slits cut in the chops.
**8 (1** **½-in.) loin lamb chops**
**3 garlic cloves, peeled**
**3 anchovy fillets**
**¼ cup fresh rosemary leaves**
**¼ cup fresh parsley leaves**
**½ tsp. dried thyme**
**Freshly ground black pepper**
**to taste**
**3 TB. olive oil**
**2 TB. dry red wine**
1. Rinse lamb chops and pat dry with paper towels.
2. Combine garlic, anchovies, rosemary, parsley, thyme, pepper, oil, and wine in a food processor fitted with the steel blade. Purée until smooth.
3. Using a small sharp knife, make several shallow incisions in both sides of each lamb chop. Rub marinade generously over both sides of chops, and press it into incisions. Place chops on a platter, and marinate chops at room temperature for 1½ to 2 hours or refrigerated for up to 8 hours.
4. Light a charcoal or gas grill according to the manufacturer's instructions. Grill chops over a hot fire for 5 or 6 minutes per side for medium-rare or to desired doneness.
**Variation:** No lamb chops? Try boneless rib-eye or strip sirloin steaks instead, each about 10 ounces.
**Part 7**
**Desserts on a Deadline**
Ahhh... dessert. That delicious ending to a meal. Those are the recipes in this part.
The first chapter features fresh fruits from all seasons. You'll find ways to quickly glorify summer's ripest berries and ways to use apples for dessert quesadillas. The next chapter also contains a lot of fruit. These become the stars of baked goods, joined by a number of rich cookies.
The last chapter contains everything chocolate—from rich and gooey fondues to frozen delights. For those of us who consider _chocolate_ and _dessert_ to be synonymous, it doesn't get any better than that.
**Chapter 20**
**Fruity Favorites**
**In This Chapter**
• Yummy cooked fruit combinations
• Dressed-up berries
• Fruity tropical treats
Come summer, there's nothing better than ripe fresh fruit straight from a farmers' market, and in this chapter, you'll find recipes that put those fantastic fruits to work! These simple dishes glorify the vivid color and luscious flavor of ripe fruits.
Berries are good sources of vitamins and are on the list of foods high in disease-fighting antioxidants—not to mention there's nothing better than berries for a fast dessert. But berries aren't the only fruit. Also in this chapter you'll find recipes for some stalwarts like bananas and pineapples, ripe at any time of the year.
# **The Fruit Family**
The common factor that unites fruit botanically as a group is a seed (or many seeds). That seed is more obvious in some fruits than in others, but it's always present in fruit. Here's some tips on choosing some of the fruits featured in this chapter:
**Fresh Ways**
There are two basic types of peaches: clingstone and free-stone. They taste similar, and the only difference is whether or not the flesh clings to the pit. Regardless of which you pick, choose the ripest peach you can find.
**Blueberries** Look for plump (not shriveled) berries with a slight grayish patina.
**Peaches** Peaches, high in beta-carotene, are ripe if they're soft when gently pressed. The easiest way to peel peaches is to drop them into boiling water for 30 seconds. Remove them from the water with a slotted spoon, and the skins will slip right off when you rub the fruit.
**Raspberries** When choosing fresh raspberries, look at the bottom of the container, and choose a package that has the least amount of juice pooled in the bottom—a sign that the berries are not damaged or moldy.
**Strawberries** Strawberries do not ripen once they've been picked, so what you buy is what you get. Because most companies "top dress" the packages with the "hero berries" on the top, check out the bottom of the package.
Regardless of the species of bright berry, they're treated the same way. Do not rinse berries prior to storing them, but always rinse them prior to eating them. Cut the green caps off of strawberries right before they're rinsed.
# **Fig and Raspberry Gratin**
The vivid fruits in this dessert are enhanced by a flavorful topping.
**2 (** **½-pt.) containers fresh**
**raspberries**
**1 (1-pt.) container fresh figs**
**¾ cup sour cream**
**3 TB. whole milk**
**5 TB. firmly packed dark**
**brown sugar**
1. Preheat an oven broiler.
2. Gently rinse raspberries and pat dry. Place berries in an ovenproof 7×12-inch gratin dish or 9×9-inch baking dish.
3. Rinse and stem figs, and cut into ⅓-inch slices.
4. Mix sour cream with milk, and spread mixture over raspberries. Top with sliced figs, and sprinkle with brown sugar.
5. Broil for 2 to 3 minutes or until sugar is melted and fruit is warm. Serve immediately.
**Variation:** You can use blueberries instead of raspberries and thinly sliced peeled peaches instead of figs.
**Fresh Ways**
Fruits are always more flavorful if they're warm or at room temperature and not chilled. You can take the chill off any fruit quickly using the microwave set at medium (50 percent). The amount of time depends on the size of the fruit and how many you're warming at once.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 12 minutes
**Each serving contains:**
317 calories
78 calories from fat
9 g fat
5 g saturated fat
4 g protein
62 g carbohydrates
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
432 calories
121 calories from fat
13 g fat
5 g saturated fat
4 g protein
83 g carbohydrates
# **Blueberry Shortbread Gratin**
Crumbled cookies create a crunchy topping for this easy and fast dessert.
**2 qt. fresh blueberries, rinsed**
**and picked over**
**¼ cup fruit-only blueberry**
**preserves**
**2 TB. instant** _**tapioca**_
**1 tsp. grated lemon zest**
**2 cups crumbled shortbread**
**cookies**
**¼ cup granulated sugar**
**½ tsp. ground cinnamon**
**3 TB. unsalted butter, diced**
**into 12 pieces**
**1** **½ cups vanilla ice cream**
**(optional)**
1. Preheat the oven to 400°F.
2. Place blueberries in a greased 9×13-inch baking pan. Mix with preserves, tapioca, and lemon zest.
3. Combine cookie crumbs, sugar, and cinnamon in a mixing bowl. Sprinkle mixture evenly over berries, and dot with butter. Bake for 20 to 25 minutes or until top is browned and berries are bubbling. Serve immediately or at room temperature, topped with ice cream (if using).
**Variation:** Don't care for blueberries? Try raspberries or blackberries instead with the appropriate fruit jam.
**Fast Talk**
Tapioca ( _tap-ee-OH-kah_ ) is a starch that comes from the roots of the cassava plant. It's used like cornstarch as a thickening agent.
# **Mixed Berry Compote**
Various fresh berries create a flavorful hot syrup to top ice cream.
**1 cup fresh strawberries**
**1 cup fresh blueberries**
**1 cup fresh raspberries**
**½ cup granulated sugar**
**½ cup water**
**2 TB. crème de cassis**
**3 TB. unsalted butter, cut**
**into small pieces**
**2 cups vanilla ice cream**
1. Rinse strawberries, blueberries, and raspberries, keeping them in separate dishes. Discard green tops from strawberries, and slice strawberries, if large.
2. Combine sugar, water, and crème de cassis in a heavy 2-quart saucepan. Bring to a boil over high heat, reduce the heat to medium, and simmer mixture for 10 minutes. Add strawberries and blueberries, and cook for 2 minutes, stirring gently a few times. Add raspberries and butter, heating just until butter melts.
3. To serve, divide ice cream into serving dishes and top each with berries.
**Stale Stuff**
It's important to take the time to reduce the sugar syrup in this recipe; otherwise, it won't be as intensely flavored if the water has not evaporated. You don't have to worry about it being dry, though. The fruit adds its own moisture back to the dish.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
437 calories
194 calories from fat
22 g fat
13 g saturated fat
4 g protein
56 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 27 minutes
**Each serving contains:**
229 calories
60 calories from fat
7 g fat
4 g saturated fat
3 g protein
41 g carbohydrates
# **Dumpling-Topped Berry Grunt**
Grunts (or slumps) are steamed dumplings on top of fruits, dating from the Colonial era.
**⅔ cup freshly squeezed**
**orange juice**
**1 cup fresh blackberries,**
**rinsed**
**1 cup fresh blueberries,**
**rinsed**
**1 cup fresh strawberries,**
**rinsed, capped, and halved**
**2 tsp. grated orange zest**
**½ cup granulated sugar**
**1 TB. cornstarch**
**2 TB. cold water**
**¾ cup all-purpose flour**
**1 tsp. baking powder**
**¼ tsp. ground cinnamon**
**Pinch salt**
**3 TB. unsalted butter, cut**
**into small pieces**
**⅓ cup whole milk**
**Vanilla ice cream (optional)**
1. Combine orange juice, blackberries, blueberries, strawberries, orange zest, and ¼ cup sugar in a large skillet with a lid. Bring to a boil over medium-high heat, stirring occasionally. Cover, reduce heat to medium, and simmer for 5 minutes. Mix cornstarch into water, and stir to dissolve. Uncover the skillet, stir cornstarch mixture into fruit, and simmer for 2 minutes or until lightly thickened.
2. Combine flour, remaining ¼ cup sugar, baking powder, cinnamon, and salt. Cut in butter with a pastry blender, two knives, or your fingertips until mixture resembles coarse meal. Add milk to flour mixture, and mix just until moist dough forms. Spoon 6 mounds of dough on top of fruit in skillet.
3. Cover and simmer for 15 minutes or until a toothpick inserted in topping comes out clean. Serve hot with vanilla ice cream (if using).
**Fresh Ways**
Pastry blenders have three or four wire half-moon-shaped blades attached to a handle. Rocking it back and forth through a bowl with flour and butter breaks up the butter into tiny pieces similar to a coarse meal. Pastry blenders were once a part of every cook's kitchen, but today, more people make pie crust with the aid of a food processor instead.
# **Fresh Berries with Lemon Mousse**
The tangy flavor of lemon in this light mousse enhances the fruit it tops.
**6 large egg yolks**
**¾ cup granulated sugar**
**½ cup freshly squeezed lemon**
**juice**
**2 tsp. grated lemon zest**
**2 TB. Grand Marnier**
**1** **½ cups heavy cream**
**4 cups assorted fresh berries**
**(blueberries, raspberries,**
**blackberries, or sliced strawberries)**
1. Beat egg yolks with sugar in a saucepan with an electric mixer at medium speed until thick and light colored. Beat in lemon juice and lemon zest, and place the pan over low heat. Heat, stirring constantly, until mixture is thick enough to coat the back of the spoon. Remove the pan from the heat, and beat in Grand Marnier. Scrape mixture into a pie plate, and chill for at least 20 minutes or until cold. While mixture is chilling, chill a mixing bowl and electric beaters in the freezer.
2. Beat cream in the chilled bowl until stiff peaks form. Fold custard mixture into whipped cream.
3. To serve, divide berries into dishes and spoon mousse on top.
**Variation:** For a twist, try lime juice and lime zest instead of lemon juice and lemon zest.
Serves: 6
**Active time:** 20 minutes
**Start to finish:** 45 minutes, including 20 minutes for chilling
**Each serving contains:**
417 calories
244 calories from fat
27 g fat
15 g saturated fat
5 g protein
40 g carbohydrates
**Fresh Ways**
Don't waste all the egg whites from a recipe like this one that requires just the yolks. Use them along with whole eggs for omelets or scrambled eggs that will be lower in cholesterol. Or make them into meringue cookies.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
277 calories
128 calories from fat
14 g fat
8 g saturated fat
11 g protein
26 g carbohydrates
# **Peach Skillet Cake**
The creamy topping on this cake is browned under the broiler for a dramatic presentation.
**3 TB. unsalted butter**
**3 ripe peaches, peeled,**
**seeded, and cut into 8 wedges**
**each**
**3 TB. granulated sugar**
**1 cup cottage cheese**
**¾ cup sour cream**
**1 tsp. pure vanilla extract**
**¾ cup all-purpose flour**
**3 large eggs**
**1 TB. confectioners' sugar**
**Sweetened whipped cream**
**for serving (optional)**
1. Preheat the oven broiler.
2. Melt butter in a 12-inch ovenproof skillet. Arrange peach wedges in one layer in the skillet and sprinkle with 1 tablespoon sugar. Cook over medium heat for 5 minutes, turn wedges over with a slotted spatula, and cook for 3 more minutes.
3. While peaches are cooking, combine cottage cheese, sour cream, vanilla extract, flour, eggs, and remaining 2 tablespoons sugar in a food processor fitted with a steel blade or in a blender. Purée until smooth.
4. Pour batter over peaches in the skillet. Cover and cook over low heat on top of the stove for 6 minutes. Uncover the skillet and broil 6 inches from the broiler element for 6 to 8 minutes or until browned.
5. Invert cake onto a serving plate, sprinkle with confectioners' sugar, cut into wedges, and serve immediately, passing whipped cream separately (if using).
**Variation:** No peaches? Try Golden Delicious apples instead.
**Speedy Solutions**
Traditionally peaches are peeled by dropping them into boiling water for 30 seconds and then using a paring knife to slip off the skin. This method works, but I find it's faster to peel them with a paring knife or vegetable peeler.
# **Easy Berry Trifle**
A trifle is a traditional English dessert combining berries and some sort of creamy custard, and this one is so easy because the custard doesn't need cooking.
**1 cup** _**mascarpone**_ **cheese**
**1 cup sour cream**
**⅓ cup granulated sugar**
**1 tsp. pure vanilla extract**
**1 cup puréed raspberries**
**2 TB. framboise or any raspberry**
**flavored liqueur**
**12 or 24 ladyfingers (depending**
**on size)**
**2 (** **½-pt.) containers fresh**
**raspberries, rinsed**
1. Combine mascarpone, sour cream, ¼ cup sugar, and vanilla extract in a mixing bowl, and whisk until smooth.
2. In another bowl, combine remaining sugar, puréed raspberries, and Framboise. Arrange ⅓ ladyfingers in one layer in a baking dish, and pour syrup evenly over them.
3. Spoon ¼ cream filling into a 4-cup glass bowl, and add ⅓ raspberries. Add ⅓ ladyfingers, pushing them into filling. Repeat with remaining cream, fruit, and ladyfingers, ending with a layer of cream. Cover the bowl with plastic wrap, and refrigerate for at least 45 minutes.
4. To serve, spoon onto serving plates, digging the spoon in vertically to give each diner many layers.
**Variation:** This trifle is also great with strawberries or blackberries if you don't have raspberries.
**Fast Talk**
**Mascarpone** is a rich double or triple cream cheese made from milk and famous in the Lombardy region of Italy. It resembles cream cheese but has a far higher butter content. If you can't find any, use half cream cheese and half unsalted butter instead.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 1 hour,
including 45 minutes for
chilling
**Each serving contains:**
482 calories
298 calories from fat
33 g fat
20 g saturated fat
7 g protein
41 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
324 calories
235 calories from fat
26 g fat
16 g saturated fat
4 g protein
20 g carbohydrates
# **Lemon Curd Mascarpone Fondue**
This creamy dessert is not too sweet, and the warm temperature makes it special.
**3 large eggs**
**½ cup granulated sugar**
**⅔ cup freshly squeezed lemon**
**juice**
**1 TB. grated lemon zest**
**6 TB. unsalted butter, cut**
**into** **¼-inch dice**
**1 TB. cornstarch**
**½ cup mascarpone**
1. Combine eggs and sugar in a heavy 1-quart saucepan, and whisk until thick and lemon colored. Add ½ cup lemon juice, lemon zest, and butter. Place the pan over medium-low heat, and cook, whisking frequently, for 5 to 6 minutes or until _curd_ is thick and small bubbles begin to appear on the surface.
2. Combine remaining lemon juice and cornstarch in a small bowl, and stir to dissolve cornstarch. Add to fondue, and bring to a simmer, stirring constantly. Cook over low heat for 1 to 2 minutes or until fondue has thickened. Remove the pan from the heat, and whisk in mascarpone.
3. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), clementine segments, donut holes, waffle squares, angel food cake cubes, pound cake cubes, coconut macaroons, or sugar cookies.
**Variation:** Try this with lime juice and lime zest in place of lemon juice and zest.
**Fast Talk**
Curd is most often refers to cheese (e.g., separating the curd from the liquid whey), but it's also the name of a family of thick fruit spreads, especially popular in England, made from sugar, butter, fruit juice, and eggs. When the curd is cool, it's spread on breakfast pastries.
# **Bananas Foster Fondue**
Bananas Foster is the signature dessert from famed Brennan's in New Orleans, and this fondue is a liquid version.
**2 very ripe bananas**
**½ cup heavy cream**
**4 TB. unsalted butter**
**½ cup firmly packed dark**
**brown sugar**
**¼ cup crème de banana**
**2 tsp. cornstarch**
1. Place bananas and cream in a food processor fitted with a steel blade or in a blender. Purée until smooth, and set aside.
2. Melt butter in a heavy 1-quart saucepan over medium heat, and add brown sugar. Cook for 3 minutes, stirring occasionally. Add banana purée, and bring to a boil over medium heat, stirring occasionally. Reduce the heat to low, and simmer for 3 minutes, stirring occasionally.
3. Combine crème de banana and cornstarch in a small bowl, and stir to dissolve cornstarch. Add to fondue, and bring to a simmer, stirring constantly. Cook over low heat for 1 to 2 minutes or until fondue has thickened.
4. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), donut holes, waffle squares, butter cookies, angel food cake cubes, pound cake cubes, brownie cubes, coconut macaroons, or sugar cookies.
**Speedy Solutions**
If you have bananas that are getting overly ripe, freeze them right in the peels. Once thawed, the bananas are ready to peel and all set to go in any dish that requires mashed banana such as this fondue or banana bread.
Serves: 6
**Active time:** 10 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
290 calories
141 calories from fat
16 g fat
10 g saturated fat
1 g protein
33 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
205 calories
125 calories from fat
14 g fat
12 g saturated fat
2 g protein
10 g carbohydrates
# **Piña Colada Fondue**
Pineapple and coconut are the dominant flavors in this rum-laced fondue.
**2 cups diced fresh pineapple**
**or 2 cups crushed pineapple**
**packed in pineapple juice,**
**drained**
**1 cup sweetened cream**
**of coconut (such as Coco**
**López)**
**½ cup rum**
**1 TB. freshly squeezed lime**
**juice**
**1 TB. cornstarch**
1. Place 1 cup pineapple in a food processor fitted with a steel blade or in a blender. Purée until smooth. Finely chop remaining 1 cup pineapple.
2. Combine all pineapple, cream of coconut, and rum in a heavy 1-quart saucepan. Bring to a boil over medium heat, stirring occasionally. Reduce the heat to low, and simmer mixture for 5 minutes, stirring occasionally.
3. Combine lime juice and cornstarch in a small bowl, and stir to dissolve cornstarch. Add to fondue, and bring to a simmer, stirring constantly. Cook over low heat for 1 to 2 minutes or until fondue has thickened.
4. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), banana chunks, clementine segments, dried coconut slices, crystallized ginger, donut holes, angel food cake cubes, pound cake cubes, coconut macaroons, or sugar cookies.
**Fresh Ways**
Any dessert fondue can instantly become a dessert sauce to top berries or a slice of pound cake. You don't have to limit these fondue recipes to occasions on which you'll be dipping.
**Chapter 21**
**The Best Baked Goods**
**In This Chapter**
• Homey fruit desserts
• Quick cakes
• Creative cookies
If you think baking is too time-consuming, wait until you try the recipes in this chapter! These recipes for homey cakes, cobblers, and cookies are on the table in a matter of minutes.
Most of these baked goods contain luscious fresh fruit, which makes them healthful as well as delicious. And there's a lot of room to improvise and substitute whatever fruits are the prettiest and freshest at your market.
# **Procedural Matters**
While cooking is a form of art, when it comes to baking, science class enters the equation as well. Before you put on your apron, you should know some general pointers on procedures to be used for all genre of baked goods.
**Fresh Ways**
Planning ahead also applies to preheating the oven. Some ovens can take up to 25 minutes to reach a high temperature, such as 400°F. The minimum heating time should be 15 minutes, and most cookie doughs and batters do not take that long to prepare. If you turn your oven on and then start preparing your dough or batter, you should be in good shape.
Be sure to use the correct measuring cups for the ingredient: measure dry ingredients in dry measure cups; measure liquids in liquid measure cups. Spoon dry ingredients from the container or canister into the measuring cup and then sweep the top with a straight edge such as the back of a knife or a spatula to measure it properly. _Do not_ dip the cup into the canister or tap it on the counter to produce a level surface.
Level tablespoons and teaspoons, too; a rounded ½ teaspoon can really measure almost 1 teaspoon. If the box or can doesn't have a straight edge built in, level the excess in the spoon back into the container with the back of a knife.
# **Careful Creaming**
Perhaps the most vital step in the creation of a cookie dough or cake batter is the "creaming" of the butter and sugar. During this process, air is beaten in and trapped in the butter's crystalline structure. It's the number and size of the air bubbles (which then become enlarged by the carbon dioxide produced by baking soda or baking powder) that leavens a dough or batter to produce a high, finely textured product.
**Speedy Solutions**
If you're in a hurry to begin a batter, you can grate the butter through the large holes of a box grater. _Do not_ soften butter in a microwave oven. It will become too soft.
For successful creaming, start with butter at the correct temperature: approximately 70°F. Remove butter from the refrigerator and cut each stick into approximately 30 slices. Allow them to sit at room temperature for 15 to 20 minutes to soften.
Begin creaming by beating the butter alone with a mixer on medium speed until it has broken into small pieces. Then add the sugar a few tablespoons at a time, scraping the bowl frequently. When properly creamed, the texture of the butter and sugar mixture will be light and fluffy.
# **Caramel Apple Quesadillas**
This dessert has all the flavors and textures of a great apple pie, but it's ready in minutes!
**8 (6-in.) flour tortillas**
**24 caramel candies,**
**unwrapped**
**¼ cup whole milk**
**½ tsp. ground cinnamon**
**2 Golden Delicious apples,**
**peeled, cored, and thinly**
**sliced**
**3 TB. unsalted butter, melted**
**⅓ cup granulated sugar**
1. Preheat the oven to 400°F, and cover 2 baking sheets with heavy-duty aluminum foil.
2. Soften tortillas by wrapping them in plastic wrap and heating them in a microwave oven on high (100 percent) for 10 to 15 seconds or until pliable.
3. Place caramel candies and milk in a small microwave-safe bowl, and microwave for 45 seconds on medium (50 percent). Stir, and repeat as necessary until caramel is smooth. Stir in cinnamon.
4. Spread caramel mixture on tortillas to about ½ inch from the edge. Arrange apple slices over half of each tortilla, and fold over the other half. Press down with the palm of your hand.
5. Place quesadillas on the baking sheet, brush each with 1 tablespoon butter and sprinkle with 2 tablespoons sugar. Bake for 10 minutes, turn with a spatula, brush with remaining butter, and sprinkle with remaining sugar. Bake for an additional 10 minutes or until quesadillas are browned. Allow to sit for 3 minutes, cut in half, and serve immediately.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
619 calories
177 calories from fat
20 g fat
9 g saturated fat
9 g protein
106 g carbohydrates
**Stale Stuff**
Dessert quesadillas aren't the norm, so it's really important to buy plain flour tortillas rather than flavored ones.
Serves: 6
**Active time:** 9 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
361 calories
107 calories from fat
12 g fat
6 g saturated fat
10.5 g protein
54 g carbohydrates
# **Cherry Clafouti**
This French dessert is like a popover studded with bits of luscious fresh fruit.
**1 cup granulated sugar**
**6 TB. all-purpose flour**
**6 large eggs**
**2 cups whole milk**
**2 tsp. pure vanilla extract**
**2 tsp. grated orange zest**
**½ tsp. salt**
**3 cups dark sweet cherries,**
**halved and pitted**
**2 TB. unsalted butter, cut**
**into bits**
**Vanilla ice cream (optional)**
1. Preheat the oven to 400°F. Grease a 9×13-inch baking pan.
2. Reserve 3 tablespoons sugar, and combine remaining sugar, flour, eggs, whole milk, vanilla extract, orange zest, and salt in a food processor fitted with a steel blade or in a blender. Purée until smooth.
3. Arrange cherries in a single layer in the prepared baking pan, and pour custard over them. Bake for 20 to 25 minutes or until top is puffed and springy to the touch. Remove from the oven and increase the oven temperature to broil.
4. Sprinkle _clafouti_ with remaining 3 tablespoons sugar, dot with butter, and broil under the broiler about 3 inches from the heat for 1 minute or until it is browned. Serve immediately with ice cream (if using).
**Variation:** No cherries? Try raspberries, blueberries, or chopped peaches or apricots instead.
**Fast Talk**
Clafouti originated in the Limousin region of France. It's basically a dessert that combines fruit and a batter. Any fruit that holds its shape while baking, such as cherries, plums, or peaches, can be used.
# **Blueberry Crème Fraîche Tart**
The tangy taste of crème fraîche, similar to that of sour cream, is the perfect foil for vividly flavored berries.
**1 (9-in.) pie shell (homemade**
**or purchased)**
**3 large eggs**
½ **cup granulated sugar**
**1 tsp. pure vanilla extract**
**1** ¼ **cups** _**crème fraîche**_
**1 pt. fresh blueberries, rinsed**
1. Preheat the oven to 375°F.
2. Prick bottom and sides of piecrust with a fork, press in a sheet of parchment paper, and fill pie plate with dried beans, rice, or metal pie stones. Bake for 10 to 15 minutes. Remove weights and parchment, and bake an additional 15 minutes or until golden brown. Set aside, and reduce the oven temperature to 350°F.
3. While crust is baking, whisk eggs and sugar in the top of a double boiler for 2 minutes or until thick and lemon colored. Add vanilla extract and crème fraîche, and stir well. Place mixture over water that's simmering in the bottom of the double boiler. Heat, stirring constantly, until mixture is hot and starting to thicken.
4. Place blueberries in the bottom of piecrust and pour warm custard over. Bake for 10 minutes or until custard is set. Chill for at least 2 hours before serving. (The pie can be baked 1 day in advance and refrigerated, tightly covered.)
**Variation:** You could also use raspberries or blackberries instead of blueberries.
**Fast Talk**
Crème fraîche is a thickened cream with the texture and flavor of sour cream; however, it does not curdle when boiled. You can make it at home by adding 2 tablespoons buttermilk to 1 cup heavy cream and allowing the mixture to sit at room temperature for 8 to 12 hours or until thickened.
Serves: 8
**Active time:** 15 minutes
**Start to finish:** 2½
hours, including 2 hours
for chilling
**Each serving contains:**
282 calories
165 calories from fat
18 g fat
8 g saturated fat
4 g protein
26 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 40 minutes
**Each serving contains:**
475 calories
161 calories from fat
18 g fat
8 g saturated fat
6 g protein
76 g carbohydrates
# **Gingered Pear Crisp**
Pears are one of the glories of fall, and they are enhanced in this easy recipe by a crunchy topping flavored with aromatic ginger.
**6 medium ripe pears, peeled,**
**cored, and sliced**
¾ **cup firmly packed dark**
**brown sugar**
⅓ **cup all-purpose flour**
**2 TB. finely chopped** _**crystallized**_
_**ginger**_
¾ **tsp. ground cinnamon**
½ **tsp. ground ginger**
**1 tsp. pure vanilla extract**
**1** ½ **cups granola cereal**
**5 TB. unsalted butter, melted**
**Vanilla ice cream or sweetened**
**whipped cream**
**(optional)**
1. Preheat the oven to 375°F. Grease a 9×13-inch baking pan.
2. Combine pears, ⅓ cup brown sugar, ¼ cup flour, crystallized ginger, ¼ teaspoon cinnamon, ginger, and vanilla extract. Spread mixture into the prepared baking pan.
3. Combine remaining brown sugar, remaining flour, remaining cinnamon, granola cereal, and melted butter. Mix well, and sprinkle mixture over pears. Bake for 25 minutes or until pear mixture is bubbly and topping is golden brown. Serve hot or warm with sweetened whipped cream or vanilla ice cream (if using).
**Variation:** You can personalize this recipe in myriad ways with the topping. Visit the bulk food section of your market and select the granola flavor combination that appeals to you. You can also add nuts, more spices, or dried fruits.
**Fast Talk**
Crystallized ginger is fresh ginger that's preserved by being candied in sugar syrup. It's then tossed with coarse sugar. It's very expensive in little bottles in the spice aisle, but most whole foods markets sell it in bulk.
# **Strawberry-Rhubarb Cobbler**
Cobblers are as at home on the breakfast or brunch table as a treat as they are after dinner.
**1 cup granulated sugar**
**2 TB. Grand Marnier or**
**Cointreau**
**1** ½ **lb. (3 cups) rhubarb,**
**rinsed and thinly sliced**
**1 TB. cornstarch**
**2 TB. cold water**
**1 cup all-purpose flour**
**1** ½ **tsp. baking powder**
**4 TB. unsalted butter, cut**
**into** ½ **-inch pieces**
**1 large egg, lightly beaten**
**2 TB. whole milk**
**1 pt. fresh strawberries,**
**rinsed, capped, and halved**
1. Preheat the oven to 400°F. Grease a 9×13-inch baking pan.
2. Reserve 2 tablespoons sugar, and set aside. Combine remaining sugar, Grand Marnier, and rhubarb in a saucepan. Bring to a boil over medium heat, stirring occasionally. Cook, stirring occasionally, for 12 minutes or until rhubarb is soft. Stir cornstarch into water, and stir cornstarch mixture into rhubarb. Simmer for 2 minutes or until thick and bubbly. Remove from heat, and keep warm.
3. While rhubarb is cooking, stir together flour, remaining 2 tablespoons sugar, and baking powder in a medium bowl. Cut in butter using a pastry blender, two knives, or your fingertips until mixture resembles coarse meal. Stir together egg and milk, and add to flour mixture, stirring just to moisten until a moist dough forms.
4. Turn out dough onto lightly floured surface, and knead five or six times. Roll dough to a rectangle 14 inches long. Cut lengthwise into ½-inch-wide strips.
5. Stir strawberries into rhubarb mixture. Transfer mixture to the prepared baking pan. Weave dough strips over fruit mixture to make a lattice top by placing alternate strips horizontally and vertically across the pan. Trim the strips to fit the baking pan. Place the baking pan on a foil-lined baking sheet. Bake for 20 to 25 minutes or until fruit is tender and lattice top is golden. Serve hot or at room temperature.
Serves: 6
**Active time:** 25 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
352 calories
86 calories from fat
10 g fat
5.5 g saturated fat
5 g protein
61 g carbohydrates
**Speedy Solutions**
There's a fine line between a cobbler that's full enough to support the crust and one that's spilling hot juices into the oven. That's why it's important to always use a baking sheet under it; it saves a lot of oven-cleaning time.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 40 minutes, including 10 minutes for cooling
**Each serving contains:**
985 calories
551 calories from fat
61 g fat
38 g saturated fat
9 g protein
95 g carbohydrates
**Fast Talk**
Cream of tartar comes from the acid deposited inside wine barrels. It's used in conjunction with baking soda to produce the same chemical reaction as that caused by baking powder.
# **Strawberry Shortcake**
Rich biscuits, luscious berries, and whipped cream are a time-honored combination for good reason—it's delicious!
**3 cups all-purpose flour**
¾ **cup granulated sugar**
**1 TB.** _**cream of tartar**_
**2** ¼ **tsp. baking soda**
¼ **tsp. salt**
½ **lb. (1 cup) unsalted butter**
**2 cups heavy cream**
**1 qt. strawberries**
⅓ **cup crème de cassis or**
**Chambord**
⅓ **cup confectioners' sugar**
1. Preheat the oven to 375°F and grease 2 baking sheets.
2. Combine flour, ⅓ cup sugar, cream of tartar, baking soda, and salt in a medium mixing bowl.
3. Melt 3 tablespoons butter in a small saucepan over low heat or in a microwave-safe dish on medium (50 percent) for 45 seconds or until melted, and set aside.
4. Cut remaining butter into ¼-inch cubes. Cut butter into flour mixture using a pastry blender, two knives, or your fingertips until mixture resembles coarse meal. Add 1 cup cream, and blend until just blended.
5. Scrape dough onto a floured surface and knead lightly. Roll dough ¾ inch thick, cut out 6 (4-inch) rounds, and place them on the baking sheet. Brush rounds with melted butter. Cut out 6 (2½-inch) rounds, and place them on top of larger rounds. Brush tops with butter. Bake for 15 to 17 minutes or until shortcakes are golden brown. Cool for at least 10 minutes on a wire rack.
6. While shortcakes are baking, rinse strawberries, discard green caps, and slice. Toss strawberries with crème de cassis. Set aside.
7. Just prior to serving, whip remaining cream with confectioners' sugar until stiff peaks form. To serve, separate the top and bottom rounds. Mound strawberries on larger round, and top with whipped cream and smaller round. Serve immediately.
**Variation:** You can substitute any berry for the strawberries. Peeled peach slices work nicely, too.
# **Oatmeal Cranberry Cookies**
These homey cookies are scented with cinnamon and have crunchy nuts for texture and vivid dried cranberries for flavor.
**1 cup chopped walnuts**
**1 cup all-purpose flour**
**1 tsp. ground cinnamon**
½ **tsp. baking soda**
**Pinch salt**
**6 TB. unsalted butter, softened**
½ **cup granulated sugar**
½ **cup firmly packed dark**
**brown sugar**
**2 large eggs, at room temperature**
**1 tsp. pure vanilla extract**
**1** ¼ **cups quick-cooking or**
**old-fashioned oats (not**
**instant)**
**1 cup dried cranberries**
1. Preheat the oven to 350°F, and grease 2 baking sheets.
2. Toast walnuts in a single layer on an ungreased baking sheet for 5 to 7 minutes or until browned, and set aside. Increase the oven temperature to 375°F.
3. While the oven is preheating, sift together flour, cinnamon, baking soda, and salt.
4. Place butter, granulated sugar, and brown sugar in a large mixing bowl. Beat with an electric mixer on low speed to combine, raise the speed to high, and beat for 2 minutes or until light and fluffy. Add eggs and vanilla extract, and beat for 2 minutes more. Reduce the speed to low and add flour mixture until just blended in. Stir in oats, cranberries, and toasted walnuts.
5. Drop batter by rounded tablespoon measures onto the baking sheets, spacing them 2 inches apart. Bake for 12 minutes for chewy cookies and 15 minutes for crisp cookies. Move cookies with a spatula to a cooling rack and cool completely.
**Variation:** Instead of cranberries, try raisins, dried blueberries, or dried currants. Out of cinnamon? Substitute with ground ginger.
**Speedy Solutions**
An easy way to warm eggs to room temperature is to place them in a cup of hot tap water for 5 minutes while you gather the rest of the ingredients.
Yield: 24 cookies
**Active time:** 15 minutes
**Start to finish:** 40 minutes, including 12 minutes for cooling
**Each serving contains:**
165 calories
65 calories from fat
7 g fat
2 g saturated fat
4 g protein
23 g carbohydrates
Yield: 24
**Active time:** 15 minutes
**Start to finish:** 35 minutes, including 15 minutes for cooling
**Each serving contains:**
196 calories
76 calories from fat
8.5 g fat
5 g saturated fat
2 g protein
28.5 g carbohydrates
# **Chocolate Malted Cookies**
If you're a fan of chocolate malts, you'll love these homey cookies with the same flavor.
**2 cups all-purpose flour**
**1 tsp. baking soda**
½ **tsp. salt**
**1** ¾ **sticks (** ¾ **cup) unsalted**
**butter, cut into small pieces**
**1 cup firmly packed light**
**brown sugar**
½ **cup granulated sugar**
**2 large eggs, at room temperature**
**1 tsp. pure vanilla extract**
½ **cup malt powder**
**2 cups semisweet chocolate**
**chips**
1. Preheat the oven to 350°F, and grease 2 baking sheets.
2. While the oven is preheating, sift together flour, baking soda, and salt.
3. Place butter, brown sugar, and granulated sugar in a large mixing bowl. Beat with an electric mixer on low speed to combine, raise the speed to high, and beat for 2 minutes or until light and fluffy. Add eggs and vanilla extract, and beat for 2 minutes more. Reduce the speed to low and add flour mixture and malt powder until just blended in. Stir in chocolate chips.
4. Drop batter by rounded tablespoon measures onto the baking sheets, spacing them 2 inches apart. Bake for 10 minutes for chewy cookies and 12 minutes for crisp cookies. Move cookies with a spatula to a cooling rack and cool completely.
**Variation:** Any sort of chips—from white chocolate to butterscotch or peanut butter—work in place of the semisweet chips.
**Fresh Ways**
If you don't have enough cooling racks for cookies, start them on the rack and then transfer them to sheets of plastic wrap onto which granulated sugar has been sprinkled. The sugar keeps the bottoms from sticking.
# **Carrot Cookie Sandwiches**
These cookies are a hand-holdable version of classic carrot cake, complete with the creamy icing.
**1 cup chopped walnuts**
**1** ¼ **cups all-purpose flour**
½ **tsp. ground cinnamon**
½ **tsp. ground ginger**
½ **tsp. baking soda**
¼ **tsp. salt**
**10 TB. unsalted butter**
½ **cup firmly packed light**
**brown sugar**
½ **cup granulated sugar**
**1 large egg, at room temperature**
¾ **tsp. pure vanilla extract**
**1 cup firmly packed grated**
**carrot**
¼ **cup sweetened coconut**
¼ **cup finely chopped fresh**
**pineapple**
¼ **cup raisins**
**1 (3-oz.) pkg. cream cheese,**
**softened**
**1 cup confectioners' sugar**
Yield: 12 cookies
**Active time:** 15 minutes
**Start to finish:** 45 minutes, including 20 minutes for cooling
**Each serving contains:**
260 calories
87 calories from fat
10 g fat
2.5 g saturated fat
5 g protein
40 g carbohydrates
**Speedy Solutions**
When you need just a small amount of a fruit, like the pineapple in this recipe, it makes sense to pay more per pound and buy a precut slice at the supermarket. That way there's no waste and it's easier to chop.
1. Preheat the oven to 350°F, and grease 2 baking sheets.
2. Toast walnuts in a single layer on an ungreased baking sheet for 5 to 7 minutes or until browned, and set aside. Increase the oven temperature to 375°F.
3. While the oven is preheating, sift together flour, cinnamon, ginger, baking soda, and salt.
4. Place 8 tablespoons butter, brown sugar, and granulated sugar in a large mixing bowl. Beat with an electric mixer on low speed to combine, raise the speed to high, and beat for 2 minutes or until light and fluffy. Add egg and ½ teaspoon vanilla extract, and beat for 2 minutes more. Reduce the speed to low and add flour mixture until just blended in. Stir in carrot, coconut, pineapple, raisins, and toasted walnuts.
5. Drop batter by rounded tablespoon measures onto the baking sheets, spacing them 2 inches apart (you should have 24 cookies). Bake for 12 to 14 minutes or until lightly browned. Cool cookies for 1 minute and then transfer cookies with a spatula to a cooling rack and cool completely.
**Fresh Ways**
Store soft cookies and crisp cookies in different containers to keep the crisp ones crisp, and always store cookies at room temperature.
6. While cookies are cooling, combine cream cheese, confectioners' sugar, remaining 2 tablespoons butter, and remaining ¼ teaspoon vanilla extract in a food processor fitted with a steel blade. Blend until smooth, and scrape mixture into a mixing bowl.
7. Create cookie sandwiches by spreading frosting on the flat side of 1 cookie and topping it with the flat side of a second cookie. Store at room temperature.
# **Fudgy Brownies**
These brownies are incredibly moist and chewy and deliver an intense chocolate flavor.
**4 oz. (4 squares) unsweetened**
**chocolate**
**1 stick (** ½ **cup) unsalted butter**
**1 cup chopped walnuts**
½ **tsp. pure vanilla extract**
**2 large eggs, at room temperature**
**1** ¼ **cups granulated sugar**
**Pinch salt**
½ **cup all-purpose flour**
Yield: 16 brownies
**Active time:** 15 minutes
**Start to finish:** 1½
hours, including 30 minutes for cooling
**Each serving contains:**
217 calories
133 calories from fat
15 g fat
6 g saturated fat
4 g protein
21 g carbohydrates
1. Preheat the oven to 350°F, and grease and flour an 8×8-inch baking pan.
2. Melt chocolate and butter in a heavy saucepan over low heat, stirring frequently until mixture is melted and smooth. Remove the pan from the heat, and set aside for 5 to 7 minutes to cool.
3. Toast walnuts in a single layer on an ungreased baking sheet for 5 to 7 minutes or until browned, and set aside.
4. Combine vanilla extract, eggs, sugar, and salt in a bowl, and whisk well. Stir in cooled chocolate mixture, and beat well. Add flour, mix well, and stir in toasted walnuts. Scrape batter into the prepared pan, and smooth the top. Bake for 45 minutes or until top is dry and a toothpick inserted in the center comes out almost clean. Remove brownies from the oven and cool on a rack. Cut into squares when cool. (Brownies can be baked up to 2 days in advance and kept at room temperature, tightly covered.)
**Chapter 22**
**Chocolate Cravings**
**In This Chapter**
• Gooey chocolaty fondues
• Frozen chocolaty treats
• Baked chocolaty treasures
Chocolate might be the Americas' most delicious contribution to the cuisines of the world. Some folks—me included—can justly call ourselves "chocoholics" and think _all_ desserts should be chocolate. You folks are in luck, because chocolate dessert recipes are all you'll find in this chapter.
Chocolate can take a wide range of dessert forms, from luscious fondues that can be on the table in a matter of minutes to some sophisticated options like individual cakes or an elegant soufflé that takes just a little longer. Now on to the sweet stuff!
# **Chocolate 101**
The key to the success for all chocolate desserts is to use a high-quality product. Here's a quick guide to the various types of chocolate used for the desserts in this chapter:
**Unsweetened** Also referred to as _baking_ or _bitter_ chocolate, this is the purest of all cooking chocolate and it contains no sugar.
**Bittersweet** This chocolate is slightly sweetened with sugar, and the amount varies depending on the manufacturer. You can use it interchangeably with semisweet chocolate.
**Stale Stuff**
It's important (with noted exceptions) to use the type of chocolate specified in the recipe because the amount of additional sugar and other ingredients are calculated according to the sweetness level of the chocolate.
**Semisweet** This chocolate is sweetened with sugar, but unlike bittersweet, it also can have added flavorings such as vanilla. It's available in bar form as well as chips and pieces.
**Unsweetened cocoa powder** This is powdered chocolate that has had a portion of the cocoa butter removed. Cocoa keeps indefinitely in a cool place.
**White** Actually ivory in color, white chocolate is technically not chocolate at all; it's made from cocoa butter, sugar, and flavoring.
# **Handle with Care**
Except when you're eating chocolate out of your hand or folding chips into cookie dough, chocolate needs a bit of special handling. Use these tips when handling the sweet stuff:
Chopping chocolate into fine pieces makes melting easier. You can do this in a food processor fitted with a steel blade. Begin by breaking it with a heavy knife rather than breaking it with your hands. Body heat is sufficiently high enough to soften the chocolate so it won't chop evenly.
Most chocolate needs careful melting because it scorches easily. You can melt it in a number of ways:
• Melt chunks in the top of a double boiler placed over barely simmering water.
• Melt chopped chocolate in a microwave-safe bowl on high (100 percent) for 20 seconds. Stir and repeat as necessary.
• Preheat the oven to 250°F. Place chopped chocolate in the oven and immediately turn off the heat. Stir after 3 minutes, and return to the warm oven if necessary.
# **Classic Chocolate Fondue**
Desserts don't get any easier or more luscious than dipping food into a vat of liquid chocolate!
½ **cup heavy cream**
**10 oz. bittersweet chocolate,**
**chopped**
**2 or 3 TB. liquor or liqueur**
**(rum, bourbon, tequila,**
**Cognac, brandy, triple sec,**
**Grand Marnier, Chambord,**
**kirsch,** _**amaretto,**_ **Frangelico,**
**crème de cacao, crème de**
**banana, Irish cream liqueur,**
**or Kahlúa)**
1. Combine cream and chocolate in a heavy 1-quart saucepan. Stir over very low heat to melt chocolate. When mixture is smooth and chocolate is melted, stir in liquor. (This can be done up to 4 hours ahead. Reheat over very low heat or in a microwave.)
2. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), banana chunks, clementine segments, apple slices, donut holes, waffle squares, butter cookies, angel food cake cubes, cake cubes, brownie cubes, biscotti, or sugar cookies.
**Variation:** If you're serving the fondue to children or adults who cannot tolerate alcohol, you can substitute ¼ to ½ teaspoon pure almond, coconut, or peppermint extract for the liquor or liqueur.
**Fast Talk**
Amaretto is a liqueur that has the flavor of almonds but is frequently distilled from the kernels of apricot pits as well. It was invented in Saronno, Italy, but now many varieties are made in the United States.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
331 calories
215 calories from fat
24 g fat
14.5 g saturated fat
3 g protein
30.5 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 15 minutes
**Each serving contains:**
417 calories
300 calories from fat
33 g fat
23 g saturated fat
5 g protein
30 g carbohydrates
# **Bittersweet Chocolate Coconut Cream Fondue**
This is like a molten version of an Almond Joy candy bar with both chocolate and coconut sharing star billing.
**9 oz. bittersweet chocolate,**
**chopped**
**1 oz. unsweetened chocolate,**
**chopped**
**1 cup sweetened cream**
**of coconut (such as Coco**
**López)**
½ **cup heavy cream**
¼ **cup dark rum**
¼ **tsp. pure coconut extract**
1. Combine bittersweet chocolate, unsweetened chocolate, cream of coconut, and cream in a heavy 1-quart saucepan. Stir over very low heat to melt chocolate. When mixture is smooth and chocolate is melted, stir in rum and coconut extract. (This can be done up to 4 hours ahead. Reheat over very low heat or in a microwave.)
2. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), banana chunks, _clementine_ segments, apple slices, dried coconut slices, dried apricots, crystallized ginger, donut holes, waffle squares, butter cookies, angel food cake cubes, cake cubes, brownie cubes, coconut macaroons, or sugar cookies.
**Fast Talk**
Clementines are a member of the Mandarin orange family and are identified by their loose skin that peels right off. Clementines are about the size of a golf ball, and they are usually seedless with tangy orange flavor.
# **White Chocolate Cranberry Orange Fondue**
Hints of orange flavor this pale mixture dotted with vivid dried cranberries.
**1 cup freshly squeezed**
**orange juice**
½ **cup heavy cream**
**10 oz. white chocolate,**
**chopped**
**1 TB. grated orange zest**
½ **cup dried cranberries,**
**coarsely chopped**
**2 TB. triple sec or other**
**orange-flavored liqueur**
1. Place orange juice in a heavy 1-quart saucepan. Bring to a boil over high heat and cook, stirring occasionally, 10 minutes or until liquid is reduced by ¾. Add cream, chocolate, and orange zest, and reduce heat to very low. Stir over very low heat to melt chocolate. When mixture is smooth and chocolate is melted, stir in dried cranberries and liqueur. (This can be done up to 4 hours ahead. Reheat over very low heat or in a microwave.)
2. Transfer fondue to a fondue pot or other pot with a heat source, and serve with hulled strawberries (halved if large), banana chunks, clementine segments, apple slices, donut holes, waffle squares, butter cookies, angel food cake cubes, cake cubes, brownie cubes, biscotti, or sugar cookies.
**Variation:** Substitute dried blueberries or dried cherries for the dried cranberries in this if you like.
**Speedy Solutions**
If you need to grate a lot of citrus zest, save time by using a vegetable peeler to separate the colored zest from the bitter white pith beneath it. Then place the strips in a mini-food processor. Chop the strips finely into zest at high speed.
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
406 calories
205 calories from fat
23 g fat
15 g saturated fat
4 g protein
42 g carbohydrates
Serves: 4
**Active time:** 7 minutes
**Start to finish:** 20 minutes
**Each serving contains:**
819 calories
441 calories from fat
49 g fat
28 g saturated fat
12.5 g protein
84 g carbohydrates
**Stale Stuff**
Be careful when buying unsalted butter. Many packages are labeled "sweet butter" because all butter is made from sweet cream and not sour cream. But the term "sweet butter" is not an indication that salt has not been added.
# **Candy Bar Quesadillas**
This crispy dessert is like a fast version of a turnover; personalize it with your choice of candy.
**8 (6-in.) flour tortillas**
**1 (8-oz.) pkg. cream cheese,**
**softened**
**4 (1.5- to 2-oz.) candy bars**
**(plain or flavored chocolate**
**bars with or without additional**
**ingredients: Snickers,**
**Three Musketeers, or**
**Almond Joy), each cut into**
**thin slices**
**4 TB. unsalted butter, melted**
⅓ **cup granulated sugar**
1. Preheat the oven to 450°F, and cover a baking sheet with heavy-duty aluminum foil.
2. Soften tortillas by wrapping them in plastic wrap and heating them in a microwave oven on high (100 percent) for 10 to 15 seconds or until pliable.
3. Spread tortillas out on a counter, and divide cream cheese amongst them. Spread cream cheese over ½ of each tortilla, and top with equal amounts of candy bar slices. Press quesadillas together gently into half circles, and place them on the baking sheet. Brush tops with melted butter, and sprinkle with ½ sugar.
4. Bake quesadillas for 5 minutes. Turn with a spatula, brush other side with butter, and sprinkle with remaining sugar. Bake an additional 3 or 4 minutes, or until quesadillas are browned. Remove from the oven, and serve immediately.
# **Mini-Molten Chocolate Tortes**
These easy tortes have a center that remains soft so they create their own sauce.
**10 TB. unsalted butter**
⅓ **cup granulated sugar**
¼ **lb. semisweet chocolate,**
**chopped**
**2 large eggs**
**2 large egg yolks**
⅓ **cup confectioners' sugar**
¾ **tsp. pure vanilla extract**
**4 TB. all-purpose flour**
**2 TB. unsweetened cocoa**
**powder**
**Sweetened whipped cream**
**(optional)**
**Fresh raspberries (optional)**
1. Preheat the oven to 400°F. Grease 4 (6-ounce) custard cups with 2 tablespoons butter, and sprinkle with 2 tablespoons granulated sugar. Place in a shallow baking pan, and set aside.
2. Combine remaining 8 tablespoons butter and chopped semisweet chocolate in a small saucepan, and melt over low heat, stirring constantly. Remove the pan from the heat and cool.
3. Beat eggs, egg yolks, confectioners' sugar, and vanilla extract with a mixer on high for 5 minutes or until mixture is thick and pale yellow. Reduce speed to medium and beat in chocolate mixture. Sift flour and cocoa powder over chocolate mixture, and beat on low speed just until blended. Spoon batter into the prepared custard cups. (You can do this up to 2 hours in advance. Keep at room temperature.)
4. Bake for 12 to 14 minutes or until cakes rise slightly and feel firm at the edges and softer in the center when pressed gently. Cool in custard cups for 5 minutes. Invert with pot holders onto dessert plates, and serve with sweetened whipped cream and top with fresh raspberries (if using).
**Variation:** If you want to make this a sinfully rich dessert, place a chocolate truffle in the center of each cup before baking. The short bake time will just melt the center.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 30 minutes
**Each serving contains:**
602 calories
372 calories from fat
41 g fat
24 g saturated fat
7 g protein
52 g carbohydrates
**Stale Stuff**
Always use pure extracts in cooking. They may cost a bit more, but you only use them in minute quantities, and they last for up to 2 years after they're opened. The flavor of extracts is intense, and the chemical taste from artificial extracts is unpleasant.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 1 hour,
including 50 minutes for
freezing
**Each serving contains:**
536 calories
254 calories from fat
28 g fat
17 g saturated fat
5 g protein
52 g carbohydrates
# **White Chocolate Strawberry Sundaes**
This frozen treat uses purchased ice cream as the base and can be personalized in myriad ways.
**1 pt. strawberry ice cream**
**6 oz. white chocolate,**
**chopped**
**1⅓ cup sliced strawberries**
**½ cup Chambord or other**
**berry-flavored liqueur**
**⅔ cup heavy cream**
**4 TB. confectioners' sugar**
1. Place ice cream in a microwave oven, and microwave for 15 seconds on high (100 percent). Repeat, if necessary, until ice cream softens.
2. Scoop ice cream into a mixing bowl, and stir in white chocolate, strawberries, and ¼ cup Chambord. Refreeze ice cream mixture for at least 50 minutes.
3. While mixture is freezing, combine cream and confectioners' sugar in a chilled mixing bowl. Beat with an electric mixer until soft peaks form.
4. To serve, divide ice cream into 4 bowls and drizzle with remaining Chambord. Top with whipped cream, and serve immediately.
**Variation:** This recipe is open to endless variations; the only constant is the proportion of ice cream to chocolate. You can use any ice cream flavor, any type of chocolate, and any additions from fruits to nuts.
**Fresh Ways**
n addition to providing flavor, the inclusion of liquor or a liqueur in a recipe means the mixture won't freeze rock-solid. (Alcohol doesn't freeze.)
# **Quick Mocha Soufflé**
You might think soufflés are difficult to make, but this one is really easy, and it rises every time!
**1 TB. unsalted butter, softened**
**4 TB. granulated sugar**
**4 oz. bittersweet chocolate,**
**chopped**
¼ **cup strong coffee**
¼ **cup heavy cream**
**4 large eggs, separated**
**2 large egg whites**
1. Preheat the oven to 400°F. Prepare a 6-cup soufflé dish by rubbing it with butter and dusting it well with 2 tablespoons granulated sugar. Knock out any excess sugar.
2. Combine chocolate, coffee, and cream in a small saucepan, and place it over low heat, stirring occasionally, until melted. Remove pan from the heat, and beat mixture until thick and glossy. Add egg yolks, one at a time, beating well after each addition.
3. Beat egg whites at medium speed with an electric mixer until frothy, increase the speed to high, and whip until stiff peaks form, gradually adding remaining 2 tablespoons sugar. Fold in chocolate mixture, and scrape mixture into the soufflé dish.
4. Place the dish in the center of the oven, and immediately turn the oven down to 375°F. Bake for 30 minutes or until puffed, and serve immediately.
**Variation:** You can substitute 2 tablespoons Grand Marnier or amaretto and 2 tablespoons water for the coffee.
Serves: 4
**Active time:** 15 minutes
**Start to finish:** 45 minutes
**Each serving contains:**
346 calories
211 calories from fat
23.5 g fat
13 g saturated fat
10 g protein
29 g carbohydrates
**Stale Stuff**
Always be sure a bowl in which you're beating egg whites is totally free from grease. Even a speck will keep the egg whites from beating properly.
Serves: 4
**Active time:** 9 minutes
**Start to finish:** 10 minutes
**Each serving contains:**
765 calories
354 calories from fat
39 g fat
23 g saturated fat
11.5 g protein
103 g carbohydrates
# **Chocolate Pudding**
This homey pudding is thick and rich; it's the quintessential chocolate comfort food.
**1 cup granulated sugar**
**4 TB. cornstarch**
½ **lb. bittersweet chocolate,**
**chopped**
**Pinch salt**
**2** ⅔ **cups whole milk**
**2 large egg yolks, lightly**
**beaten**
**2 TB. unsalted butter**
½ **tsp. pure vanilla extract**
**1 cup vanilla ice cream**
1. Combine sugar, cornstarch, chocolate, and salt in a heavy 2-quart saucepan. Add milk and egg yolks, and whisk well. Place the saucepan over medium heat and bring to a boil, whisking constantly. Simmer 1 minute, whisking constantly. Remove the pan from the heat, and whisk in butter and vanilla extract.
2. Serve immediately, topped with ice cream, or chill and serve cold.
**Variation:** For mocha pudding, add 1 tablespoon instant coffee powder to the pudding. You can also use any flavor of ice cream instead of vanilla.
**Fresh Ways**
Cornstarch prevents eggs from scrambling when they come to a boil. That's why this pudding can simmer while a custard cannot.
# **Chocolate Peanut Butter Turnovers**
These pastries join crispy puff pastry with sensuous chocolate and crunchy peanut butter.
**4 oz. bittersweet chocolate,**
**chopped**
¼ **cup chunky peanut butter**
¼ **tsp. pure vanilla extract**
**1 large egg**
**2 tsp. water**
**1 (17.25-oz.) pkg. frozen puff**
**pastry sheets, thawed**
**2 TB. granulated sugar**
1. Preheat the oven to 425°F, and lightly grease a baking sheet.
2. Combine chocolate, peanut butter, and vanilla extract in a small bowl. Stir well.
3. Combine egg and water in another small bowl, and whisk well.
4. Trim uneven edges from pastry sheets, and cut each into 4 squares. Place ⅛ chocolate mixture in the center of each square, and fold squares on the diagonal into triangles. Seal edges by _crimping_ with the tines of a fork.
5. Brush tops of turnovers with egg wash and sprinkle with sugar. Cut 3 small steam vents into each turnover with a sharp paring knife. Bake turnovers for 12 minutes or until golden brown. Remove turnovers from the oven and cool for 3 minutes. Serve immediately or at room temperature.
**Fast Talk**
Crimping, also called _fluting,_ means pinching or pressing two pastry edges together with your fingers or a fork, sealing the dough while forming a decorative edge.
Serves: 4
**Active time:** 10 minutes
**Start to finish:** 25 minutes
**Each serving contains:**
948 calories
591 calories from fat
66 g fat
19 g saturated fat
16 g protein
81 g carbohydrates
Serves: 6
**Active time:** 15 minutes
**Start to finish:** 50 minutes
**Each serving contains:**
926 calories
441 calories from fat
49 g fat
20 g saturated fat
19 g protein
102 g carbohydrates
**Stale Stuff** _
The thinner the pieces of bread, the faster they absorb custard for a bread pudding. But you can't slice the bread too thinly or it will fall apart.
# **Chocolate Bread Pudding with Easy Bourbon Caramel Sauce**
Hot bread pudding topped with a bourbon-laced sauce elevates this New Orleans' classic to new levels.
**1 cup chopped pecans**
**1** ¼ **cups whole milk**
**1** ¼ **cups light cream**
½ **cup granulated sugar**
½ **lb. semisweet chocolate,**
**chopped**
**8 large eggs**
¾ **tsp. pure vanilla extract**
**Pinch salt**
½ **lb. (about an 8-inch loaf)**
**egg bread, such as challah,**
**thinly sliced**
**1 cup jarred caramel sauce**
¼ **cup bourbon**
¼ **tsp. ground cinnamon**
1. Preheat the oven to 375°F. Grease a 10×14-inch baking pan.
2. Place pecans on a baking sheet, and toast in the oven for 4 to 6 minutes or until browned. Remove nuts from the oven and set aside.
3. Combine milk, cream, and sugar in a large, heavy saucepan over medium-high heat. Stir until sugar dissolves and mixture comes to boil. Remove the pan from the heat. Add chocolate, and stir until smooth.
4. Beat eggs, vanilla extract, and salt in a large bowl to blend. Gradually whisk in chocolate mixture. Add bread slices. Let stand, stirring occasionally, for about 10 minutes or until bread absorbs some of custard and breaks into pieces.
5. Transfer mixture to the prepared baking pan, and cover with aluminum foil. Bake for 20 minutes, remove foil, and bake for an additional 10 minutes or until a knife inserted in the center comes out clean. Cool for 5 minutes before serving. (You can bake pudding 1 day in advance and refrigerate, tightly covered. Heat in a 350°F oven, covered with aluminum foil, for 30 minutes or until hot.)
6. While pudding is baking, combine caramel sauce, toasted pecans, bourbon, and cinnamon in a small saucepan. Heat, stirring occasionally, until hot. To serve, spoon sauce on top of warm bread pudding.
**Appendix A**
**Glossary**
_**al dente**_ Italian for "against the teeth." Refers to pasta or rice that's neither soft nor hard, but just slightly firm against the teeth.
**all-purpose flour** Flour that contains only the inner part of the wheat grain. Usable for all purposes from cakes to gravies.
**allspice** Named for its flavor echoes of several spices (cinnamon, cloves, nutmeg), allspice is used in many desserts and in rich marinades and stews.
**amaretto** A popular almond liqueur.
**anchovies** (also **sardines** ) Tiny, flavorful preserved fish that typically come in cans. Anchovies are a traditional garnish for Caesar salad, the dressing of which contains anchovy paste.
**arugula** A spicy-peppery garden plant with leaves that resemble a dandelion and have a distinctive—and very sharp—flavor.
_**bain marie**_ A water bath that cooks food gently by surrounding it with simmering water.
**bake** To cook in a dry oven. Dry-heat cooking often results in a crisping of the exterior of the food being cooked.
**balsamic vinegar** Vinegar produced primarily in Italy from a specific type of grape and aged in wood barrels.
**basil** A flavorful, almost sweet, resinous herb delicious with tomatoes and used in all kinds of Italian or Mediterranean-style dishes.
**baste** To keep foods moist during cooking by spooning, brushing, or drizzling with a liquid.
**bean thread noodles** Thin translucent strands made from the starch of green mung beans.
**beat** To quickly mix substances.
**Belgian endive** A plant that resembles a small, elongated, tightly packed head of romaine lettuce.
**bisque** A creamed seafood soup that's puréed.
**black pepper** A biting and pungent seasoning made from crushing whole peppercorns.
**blanch** To place a food in boiling water for about 1 minute (or less) to partially cook the exterior.
**blend** To completely mix something, usually with a blender or food processor, more slowly than beating.
**blue cheese** A blue-veined cheese that crumbles easily and has a somewhat soft texture, usually sold in a block.
**boil** To heat a liquid to a point where water is forced to turn into steam, causing the liquid to bubble.
**bok choy** (also **Chinese cabbage** ) A member of the cabbage family with thick stems, crisp texture, and fresh flavor. It's perfect for stir-frying.
**braise** To cook with the introduction of some liquid, usually over an extended period of time.
**breadcrumbs** Tiny pieces of crumbled dry bread, often used for topping or coating.
**Brie** A creamy cow's milk cheese from France with a soft, edible rind and a mild flavor.
**broil** To cook in a dry oven under the overhead high-heat element.
**broth** _See_ stock.
**brown** To cook in a skillet, turning, until the food's surface is seared and brown in color, to lock in the juices.
**brown rice** Whole-grain rice including the germ with a characteristic pale brown or tan color.
**bruschetta** (or **crostini** ) Slices of toasted or grilled bread with garlic and olive oil, often with other toppings.
**bulgur** A wheat kernel that's been steamed, dried, and crushed and is sold in fine and coarse textures.
**canapés** Bite-size hors d'oeuvres usually served on a small piece of bread or toast.
**capers** Flavorful buds of a Mediterranean plant, ranging in size from _nonpareil_ (about the size of a small pea) to larger, grape-size caper berries produced in Spain.
**caramelize** To cook sugar over low heat until it develops a sweet caramel flavor or to cook vegetables develop a caramel color.
**caviar** Salted and sieved fish roe (eggs) from any species of fish. The best known is from sturgeon from the Caspian Sea.
**cayenne** A fiery spice made from (hot) chili peppers, especially the cayenne chili, a slender, red, and very hot pepper.
**challah** An egg-rich ceremonial Jewish bread served on the Sabbath and holidays.
**cheddar** The ubiquitous hard cow's milk cheese with a rich, buttery flavor that ranges from mellow to sharp.
**chevre** French for "goat milk cheese," chevre is a typically creamy-salty soft cheese.
**chili powder** A seasoning blend that includes chili pepper, cumin, garlic, and oregano. Proportions vary among different versions, but they all offer a warm, rich flavor.
**chili sauce** A chunky sweet condiment similar to ketchup in flavor.
**chilis** (or **chiles** ) Any one of many different "hot" peppers, ranging in intensity from the relatively mild ancho pepper to the blisteringly hot habañero.
**Chinese chili paste with garlic** A fiery thick paste made from fermented fava beans, red chilies, and garlic.
**Chinese five-spice powder** A seasoning blend of cinnamon, anise, ginger, fennel, and pepper.
**chipotle chilies in adobo sauce** Smoked jalapeño chilies packed in a thick spicy sauce similar to hot red pepper sauce.
**chives** A member of the onion family, chives grow in bunches of long leaves that resemble tall grass.
**chop** To cut into pieces, usually qualified by an adverb such as " _coarsely_ chopped," or by a size measurement such as "chopped into ½-inch pieces."
**chorizo** A spiced pork sausage eaten alone and as a component in many recipes.
**cider vinegar** Vinegar produced from apple cider, popular in North America.
**cilantro** A member of the parsley family and used in Mexican cooking (especially salsa) and some Asian dishes.
**cinnamon** A sweet, rich, aromatic spice commonly used in baking or desserts.
**clafouti** A French dessert that combines fruit and a batter that's baked in the oven and browned under the broiler.
**clementine** A member of the Mandarin orange family with a loose skin.
**coriander** A rich, warm, spicy seed used in all types of recipes, from African to South American.
**crème fraîche** A thickened cream with the texture and flavor of sour cream that does not curdle when it boils.
**crimp** To press or pinch pastry edges together to seal a pie or turnover.
**crudités** Fresh vegetables served as an appetizer, often all together on one tray.
**crystallized ginger** Fresh ginger preserved by being candied in sugar syrup and usually coated with coarse sugar.
**cumin** A fiery, smoky-tasting spice popular in Middle Eastern, Latin American, and Indian dishes.
**curd** A gelatinous substance resulting from coagulated milk used to make cheese. Curd also refers to dishes of similar texture, such as dishes make with egg (lemon curd).
**curry powder** A ground blend of rich and flavorful spices used as a basis for curry and many other Indian-influenced dishes.
**custard** A cooked mixture of eggs and milk popular as base for desserts.
**dash** A few drops, usually of a liquid, released by a quick shake of, for example, a bottle of hot sauce.
**deglaze** To scrape up the bits of meat and seasoning left in a pan or skillet after cooking by adding liquid.
**devein** The removal of the dark vein from the back of a large shrimp with a sharp knife.
**dice** To cut into small cubes about ¼-inch square.
**Dijon mustard** Hearty, spicy mustard made in the style of the Dijon region of France.
**dill** A herb perfect for eggs, salmon, cheese dishes, and, of course, vegetables (pickles!).
**dollop** A spoonful of something creamy and thick, like sour cream or whipped cream.
**dredge** To cover a piece of food with a dry substance such as flour or corn meal.
**drizzle** To lightly sprinkle drops of a liquid over food, often as the finishing touch to a dish.
**fennel** In seed form, a fragrant, licorice-tasting herb. The bulbs have a much milder flavor and a celerylike crunch and are used as a vegetable in salads or cooked recipes.
**fermented black beans** Small black soybeans with a pungent flavor preserved in salt.
**feta** A white, crumbly, sharp, and salty cheese popular in Greek cooking and on salads.
**fillet** A piece of meat or seafood with the bones removed.
**flake** To break into thin sections, as with fish.
**floret** The flower or bud end of broccoli or cauliflower.
**flour** Grains ground into a meal. Wheat is perhaps the most common flour. Flour is also made from oats, rye, buckwheat, soybeans, etc. _See also_ all-purpose flour; cake flour; whole-wheat flour.
**fold** To combine a dense and light mixture with a circular action from the middle of the bowl.
_**fraises du bois**_ Tiny French strawberries.
**frittata** A skillet-cooked mixture of eggs and other ingredients.
**fry** _See_ sauté.
**garbanzo beans** (or **chickpeas** ) A yellow-gold, roundish bean used as the base ingredient in hummus.
**gardiniera** A combination of pickled vegetables including cauliflower, carrots, and peppers.
**garlic** A member of the onion family, a pungent and flavorful element in many savory dishes. A garlic bulb contains multiple cloves.
**garnish** An embellishment not vital to the dish but added to enhance visual appeal.
**ginger** Available in fresh root or dried, ground form, ginger adds a pungent, sweet, and spicy quality to a dish.
**grate** To shave into tiny pieces using a sharp rasp or grater.
**grind** To reduce a large, hard substance, often a seasoning such as peppercorns, to the consistency of sand.
**Gruyère** A rich, sharp cow milk cheese made in Switzerland that has a nutty flavor.
**Herbes de Provence** A seasoning mix including basil, fennel, marjoram, rosemary, sage, and thyme, common in the south of France.
**hoisin sauce** A sweet Asian condiment similar to ketchup made with soybeans, sesame, chili peppers, and sugar.
**horseradish** A sharp, spicy root that forms the flavor base in many condiments from cocktail sauce to sharp mustards.
**infusion** A liquid in which flavorful ingredients such as herbs have been soaked to extract flavor.
**Italian seasoning** A blend of dried herbs, including basil, oregano, rosemary, and thyme.
**jicama** A juicy, crunchy, sweet, large, round Central American vegetable. **julienne** A French word meaning "to slice into very thin pieces."
**kalamata olives** Traditionally from Greece, these medium-small long black olives have a smoky rich flavor.
**kirsch** A clear tart liqueur made from cherries used in cheese fondue and desserts.
**knead** To work dough to make it pliable so it holds gas bubbles as it bakes.
**lardons** Thin slices of bacon used to flavor foods like quiche and salads.
**lentils** Tiny lens-shape pulses used in European, Middle Eastern, and Indian cuisines.
**marinate** To soak meat, seafood, or other food in a seasoned sauce, called a marinade, which is high in acid content.
**mascarpone** A thick, creamy, spreadable cheese, traditionally from Italy.
**medallion** A small round cut, usually of meat or vegetables such as carrots or cucumbers.
**meld** To allow flavors to blend and spread over time.
**mesclun** Mixed salad greens, usually containing lettuce and assorted greens such as arugula, cress, endive, and others.
**mince** To cut into very small pieces smaller than diced pieces, about ⅛ inch or smaller.
**molé** A thick spicy Mexican sauce made with unsweetened chocolate and chilies.
**nutmeg** A sweet, fragrant, musky spice used primarily in baking.
**Old Bay** A seasoning mix containing celery salt, mustard, cayenne, bay leaves, cloves, allspice, ginger, and paprika.
**olive oil** A fragrant liquid produced by crushing or pressing olives.
**olives** The green or black fruit of the olive tree commonly grown on all sides of the Mediterranean.
**oregano** A fragrant, slightly astringent herb used in Greek, Spanish, and Italian dishes.
**orzo** A rice-shape pasta used in Greek cooking.
**oxidation** The browning of fruit flesh that happens over time and with exposure to air.
**paprika** A rich, red, warm, earthy spice that also lends a rich red color to many dishes.
**Parmesan** A hard, dry, flavorful cheese primarily used grated or shredded as a seasoning for Italian-style dishes.
**parsley** A fresh-tasting green leafy herb, often used as a garnish.
**pecans** Rich, buttery nuts, native to North America, that have a high unsaturated fat content.
**peppercorns** Large, round, dried berries ground to produce pepper.
**pesto** A thick spread or sauce made with fresh basil leaves, garlic, olive oil, pine nuts, and Parmesan cheese.
**pinch** An unscientific measurement term, the amount of an ingredient—typically a dry, granular substance such as an herb or seasoning—you can hold between your finger and thumb.
**pine nuts** (also **pignoli** or **piñon** ) Nuts grown on pine trees, that are rich (read: high fat), flavorful, and a bit pine-y. Pine nuts are a traditional component of pesto and add a wonderful hearty crunch to many other recipes.
**pizza stone** Preheated with the oven, a pizza stone cooks a crust to a delicious, crispy, pizza-parlor texture.
**plump** To rehydrate food, especially dried fruits, in hot liquid.
**poach** To cook a food in simmering liquid, such as water, wine, or broth.
**porcini mushrooms** Rich and flavorful mushrooms used in rice and Italian-style dishes.
**portobello mushrooms** A mature and larger form of the smaller crimini mushroom, portobellos are brownish, chewy, and flavorful.
**preheat** To turn on an oven, broiler, or other cooking appliance in advance of cooking .
**prosciutto** Dry, salt-cured ham that originated in Italy.
**purée** To reduce a food to a thick, creamy texture, usually using a blender or food processor.
**reduce** To boil or simmer a broth or sauce to remove some of the water content, resulting in more concentrated flavor.
**reserve** To hold a specified ingredient for another use later in the recipe.
**rest** To allow food to sit for a short period of time before carving so juices will be reabsorbed into the fibers.
**rice vinegar** Vinegar produced from fermented rice or rice wine, popular in Asian-style dishes. Different from rice wine vinegar.
**roast** To cook something uncovered in an oven, usually without additional liquid.
**rosemary** A pungent, sweet herb used with chicken, pork, fish, and especially lamb. A little of it goes a long way.
**roux** A mixture of butter or another fat and flour, used to thicken sauces and soups.
**sage** An herb with a musty yet fruity, lemon-rind scent and "sunny" flavor.
**salsa** A style of mixing fresh vegetables or fresh fruit in a coarse chop.
**satay** (also **sate** ) A popular Southeast Asian dish of broiled skewers of fish or meat, often served with peanut sauce.
**sauté** To pan-cook over lower heat than used for frying.
**score** To cut food in a shallow diamond pattern.
**sear** To quickly brown the exterior of a food, especially meat, over high heat to preserve interior moisture.
**sesame oil** An oil, made from pressing sesame seeds, that's tasteless if clear and aromatic and flavorful if brown.
**shallot** A member of the onion family that grows in a bulb somewhat like garlic and has a milder onion flavor.
**shellfish** A broad range of seafood, including clams, mussels, oysters, crabs, shrimp,
and lobster. Some people are allergic to shellfish, so take care with its inclusion in recipes.
**shiitake mushrooms** Large, dark brown mushrooms with a hearty, meaty flavor that are sold both fresh and dried.
**shred** To cut into many long, thin slices.
**silverskin** The iridescent membrane covering tenderloins that must be scraped off before cooking.
**simmer** To boil gently so the liquid barely bubbles.
**skewers** Thin wooden or metal sticks, usually about 8 inches long.
**skim** To remove fat or other material from the top of liquid.
**slice** To cut into thin pieces.
**star anise** A spice native to China with a distinct licorice flavor that's part of Chinese five-spice powder.
**steep** To let sit in hot water, as in steeping tea in hot water for 10 minutes.
**stir-fry** To cook small pieces of food in a wok or skillet over high heat, moving and turning the food quickly to cook all sides.
**stock** A flavorful broth made by cooking meats and/or vegetables with seasonings with water.
**tamari** A dark sauce made from soybeans with a more mellow and less salty flavor than soy sauce.
**tapioca** A starch made from the root of a cassava plant used for thickening in a way similar to cornstarch.
**tarragon** A sweet, rich-smelling herb perfect with seafood, vegetables (especially
asparagus), chicken, and pork.
**thyme** A minty, zesty herb.
**toast** To heat something, usually bread, so it's browned and crisp.
**tofu** A cheeselike substance made from soybeans and soy milk.
**tomatillo** A small, round green fruit in a papery husk with a distinctive spicy flavor.
**veal** Meat from a calf, generally characterized by mild flavor and tenderness.
**vinegar** An acidic liquid widely used as dressing and seasoning, often made from fermented grapes, apples, or rice. _See also_ balsamic vinegar; cider vinegar; rice vinegar; white vinegar; wine vinegar.
**walnuts** A rich, slightly woody flavored nut.
**wasabi** Japanese horseradish, a fiery, pungent condiment used with many Japanese-style dishes.
**water chestnut** A crunchy tuber, popular in many types of Asian-style cooking.
**whisk** To rapidly mix, introducing air to the mixture.
**white mushrooms** Button mushrooms. When fresh, they have an earthy smell and an appealing "soft crunch."
**white vinegar** The most common type of vinegar, produced from grain.
**whole-wheat flour** Wheat flour that contains the entire grain.
**wine vinegar** Vinegar produced from red or white wine.
**wok** A pan with a rounded bottom for quick-cooking.
**wood ear mushrooms** A form of Asian dried mushroom with a slightly crunchy texture and very delicate flavor.
**Worcestershire sauce** Originally developed in India and containing tamarind, this spicy sauce is used as a seasoning for many meats and other dishes.
**yeast** Tiny fungi that, when mixed with water, sugar, flour, and heat, release carbon dioxide bubbles, which, in turn, cause the bread to rise.
**yogurt** A dairy product made from cow's milk coagulated into a soft tart custard from being invaded by friendly bacteria.
**zest** Small slivers of peel, usually from a citrus fruit such as lemon, lime, or orange.
**zester** A kitchen tool used to scrape zest off a fruit. A small grater also works well.
**Appendix B**
**Metric Conversion Tables**
The scientifically precise calculations needed for baking are not necessary when cooking conventionally. The tables in this appendix are designed for general cooking. If making conversions for baking, grab your calculator and compute the exact figure.
# **Converting Ounces to Grams**
The numbers in the following table are approximate. To reach the exact amount of grams, multiply the number of ounces by 28.35.
# **Converting Quarts to Liters**
The numbers in the following table are approximate. To reach the exact amount of liters, multiply the number of quarts by 0.95.
# **Converting Pounds to Grams and Kilograms**
The numbers in the following table are approximate. To reach the exact amount of grams, multiply the number of pounds by 453.6.
# **Converting Fahrenheit to Celsius**
The numbers in the following table are approximate. To reach the exact temperature, subtract 32 from the Fahrenheit reading, multiply the number by 5, and then divide by 9.
# **Converting Inches to Centimeters**
The numbers in the following table are approximate. To reach the exact number of centimeters, multiply the number of inches by 2.54.
**Appendix C**
**Common Ingredient Yields**
**Table of Weights and Measures of Common Ingredients**
**Table of Liquid Measurements**
**Index**
## **A**
Aegean Swordfish
al dente pasta
all-purpose potatoes
allspice
amaretto
appetizers
Black Bean Cakes
Chicken in Lettuce Cups
Deviled Leeks
dips
Brie, Stilton, and Wild Mushroom Dip
Classic Cheese Fondue
Crab Rangoon Dip
Guacamole
Mexican Beef and Chili Dip
Mexican Black Bean Dip
Sausage Pizza Dip
Smoked Trout Dip
Spinach Dip with Feta and Dill
Sun-Dried Tomato Dip
Tuscan White Bean Dip
Two-Salmon Dip
finger foods
Asparagus Wrapped in Herbed Cheese and Prosciutto
Baked Shrimp Toast Rolls
Cheddar Crackers
Fresh Tomato Bruschetta
Herbed Goat Cheese and Roasted Pepper Spirals
Salmon Tartare on Cucumber Slices
Southwest Miniature Crab Cakes
Southwest Smoked Salmon Pinwheels
Vietnamese Spring Rolls
seafood appetizers
Baked Clams Casino
Bourbon Shrimp
Crab Cakes with Mustard Sauce
Creole Marinated Shrimp
Garlic-Steamed Clams
Oysters with Green Chili Cilantro Pesto
apples
Caramel Apple Quesadillas
safe-handling
appliances
arborio rice
Asian Chicken Salad
Asian Eggplant Salad
Asian Shrimp and Stir-Fried
Vegetables
Asian woks
asparagus, safe-handling
Asparagus Wrapped in Herbed Cheese and Prosciutto
Avgolemono (Greek Lemon Egg Soup with Chicken and Orzo)
## **B**
Bacon, Egg, and Arugula
Salad
bacon grease
bacteria, food safety
Bain marie
Baked Clams Casino
Baked Eggs with Herbed
Cheese
baked goods
Blueberry Crème Fraîche Tart
Caramel Apple Quesadillas
Carrot Cookie Sandwiches
Cherry Clafouti
Chocolate Malted Cookies
creaming
Fudgy Brownies
Gingered Pear Crisp
Oatmeal Cranberry Cookies
Strawberry Shortcake
Strawberry-Rhubarb Cobbler
Baked Macaroni and Cheese
with Ham
Baked Shrimp Toast Rolls
baked potatoes
baking powder
Balsamic Vinaigrette
Banana Pancakes with Banana Syrup
Bananas Foster Fondue
Basic Pizza Dough
basmati rice
bay leaves
beans
Black Bean and Papaya Salad
Black Bean Cakes
dips
Mexican Black Bean Dip
Tuscan White Bean Dip
green mung beans
thread noodles
thread vermicelli
Tuscan White Bean Soup with Sausage
beef recipes
Beef Stroganoff
Cranberry-Maple Spareribs
Japanese Sautéed Beef with Scallions
Korean Steak
Mexican Beef and Chili Dip
Mexican Steaks with Chipotle Mayonnaise
Pan-Seared Filet Mignon with Red Wine Sauce
Stuffed Flank Steak
bell peppers
safe-handling
Stuffed Peppers
bisques, Dilled Corn and Oyster Bisque
bittersweet chocolate
Bittersweet Chocolate Coconut Cream Fondue
bivalves, removing from shell
Black Bean and Papaya Salad
Black Bean Cakes
blanching garlic
blueberries
Blueberry Crème Fraîche Tart
Blueberry Shortbread Gratin
boiler potatoes
bolster (part of knife)
Bombay Lamb Burgers
Bourbon Shrimp
bowls, mixing
breadcrumbs, Italian
bread pudding, Chocolate Bread Pudding with Easy Bourbon Caramel Sauce
breakfast recipes
Baked Eggs with Herbed Cheese
Banana Pancakes with Banana Syrup
brunch dishes
Bacon, Egg, and Arugula Salad
Baked Macaroni and Cheese with Ham
Corned Beef Hash with Baked Eggs
Grilled Chicken Hash
Sausage and Pepper Hash
Smoked Salmon Hash with Poached Eggs
Southwest Sweet Potato Pancakes with Salsa Cream
Stuffed Peppers
Summertime Baked Eggs
Welsh Rarebit with Tomatoes and Bacon
cholesterol reduction
frittata tips
Gingerbread Pancakes
Oven-Baked Apple Pancakes
pancake tips
Potato, Onion, and Bacon Frittata
Raspberry French Toast with Raspberry Sauce
Vegetable Frittata with Pasta
Western Frittata
Whole-Wheat Blueberry Pancakes
Brie, Stilton, and Wild Mushroom Dip
brownies
brown rice
brown sugar measurements
brunch recipes
Bacon, Egg, and Arugula Salad
Baked Macaroni and Cheese with Ham
Classic Quiche Lorraine
Corned Beef Hash with Baked Eggs
Crab Quiche
Grilled Chicken Hash
Herbed Sausage and Tomato Quiche
quiches
Sausage and Pepper Hash
Smoked Salmon Hash with Poached Eggs
Southwest Sweet Potato Pancakes with Salsa Cream
Stuffed Peppers
Summertime Baked Eggs
Welsh Rarebit with Tomatoes and Bacon
bruschetta, Fresh Tomato Bruschetta
burgers
Bombay Lamb Burgers
breads
Caribbean Burgers
Chinese Pork Burgers
condiments
Creole Shrimp Burgers
Dilled Salmon Burgers
Italian Turkey Burgers
Mexican Burgers
Middle Eastern Lentil Burgers
New England Turkey Burgers
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
buttermilk
butter sauces
## **C**
cabbage, safe-handling
cakes, Peach Skillet Cake
canapés
Candy Bar Quesadillas
canned stocks
capers
Caramel Apple Quesadillas
carb salads
Coconut Rice and Vegetable Salad
Garlicky Potato Salad
Gemelli with White Beans, Tomatoes, and Sage
Janet's Potato Salad
Rigatoni with Vegetables and Mozzarella
Sesame Noodles with Asian Vegetables
Spicy Asian Brown Rice Salad
Sweet Potato Salad with Mustard Dressing
Tabbouleh with Feta
Thai Rice Salad
Caribbean Burgers
Caribbean Pork Chops
Caribbean Shrimp
Carrot Cookie Sandwiches
carrots, safe-handling
caviar
celery, safe-handling
Celery Seed Dressing
cellophane noodles
Cha Gio (Vietnamese Spring Rolls)
Challah
charcoal grills
Cheddar Crackers
cheese dips Brie, Stilton, and Wild
Mushroom Dip
Classic Cheese Fondue
cherries, Cherry Clafouti
chicken recipes
Chicken in Lettuce Cups
Chicken Marsala with Mushrooms and Sage
Chicken Satay with Spicy Peanut Sauce
Chicken with Garlic and Parsley
Chicken with Three-Tomato Salsa
Grilled Chicken Hash
Ham and Cheese-Stuffed Chicken
Italian Chicken with Lemon and Capers
Mexican Chicken with Mole Sauce
Middle Eastern Chicken
Poached Chicken with Balsamic Vinegar
stir-frys
Chicken Fajitas
Chicken with Plum Sauce
Mock Mu Shu Chicken
Sweet and Hot Chicken Skewers
Tarragon Chicken with Spring Vegetables
chili
sauce
Turkey Chili
Chili con Queso
chilies
Chinese chili paste with garlic
Chinese five-spice powder
Chinese Pork Burgers
chipotle chilies
chocolate
Bittersweet Chocolate Coconut Cream Fondue
Candy Bar Quesadillas
Chocolate Bread Pudding with Easy Bourbon Caramel Sauce
Chocolate Malted Cookies
Chocolate Peanut Butter Turnovers
Chocolate Pudding
Classic Chocolate Fondue
Mini-Molten Chocolate Tortes
Quick Mocha Soufflé
special handling of chocolate
types of chocolate
White Chocolate Cranberry Orange Fondue
White Chocolate Strawberry Sundaes
cholesterol-reducing tips
chorizo
chowders
Dilled Corn and Oyster Bisque
Grilled Corn Chowder
Nantucket Clam Chowder
clafouti (Cherry Clafouti)
clams
Baked Clams Casino
Garlic-Steamed Clams
Nantucket Clam Chowder
Classic Cheese Fondue
Classic Chocolate Fondue
Classic Quiche Lorraine
cleaning mussels
clementines
cloud ear mushrooms
cobblers, Strawberry-Rhubarb Cobbler
Coconut Rice and Vegetable Salad
colanders
cole slaws, Gingered Asian Red Cabbage Slaw
colossal shrimp
compote, Mixed Berry Compote
condiments
cookies
Carrot Cookie Sandwiches
Chocolate Malted Cookies
Oatmeal Cranberry Cookies
storage
corkscrews
Corned Beef Hash with Baked Eggs
cornstarch
crab
Crab Cakes with Mustard Sauce
Crab Quiche
Crab Rangoon Dip
Southwest Miniature Crab Cakes
crackers, Cheddar Crackers
Cranberry-Maple Spareribs
crème fraîche
creaming
Cream of Celery Soup with Tarragon
cream of tartar
Creole Marinated Shrimp
Creole Shrimp Burgers
Creole Swordfish
crimping
cross-contamination, food safety
crystallized ginger
Cuban Quesadillas
cucumbers
Dilled Cucumbers
safe-handling
Thai Cucumber Salad
cumin
curd
cured meats
cuts, knife safety
## **D**
desserts
baking tips
Bananas Foster Fondue
Blueberry Crème Fraîche Tart
Caramel Apple Quesadillas
Carrot Cookie Sandwiches
Cherry Clafouti
chocolate
Bittersweet Chocolate Coconut Cream Fondue
Candy Bar Quesadillas
Chocolate Bread Pudding with Easy Bourbon Caramel Sauce
Chocolate Peanut Butter Turnovers
Chocolate Pudding
Classic Chocolate Fondue
Mini-Molten Chocolate Tortes
Quick Mocha Soufflé
special handling of chocolate
types of chocolate
White Chocolate Cranberry Orange Fondue
White Chocolate Strawberry Sundaes
Chocolate Malted Cookies
creaming
Easy Berry Trifle Cake
Fudgy Brownies
Gingered Pear Crisp
Lemon Curd Mascarpone Fondue
Oatmeal Cranberry Cookies
Peach Skillet Cake
Piña Colada Fondue
Strawberry Shortcake
Strawberry-Rhubarb
Cobbler
deveining shrimp
Deviled Leeks
dicing foods
Dijon mustard
Dilled Corn and Oyster Bisque
Dilled Cream of Cucumber Soup
Dilled Cucumbers
Dilled Salmon Burgers
dips
Brie, Stilton, and Wild Mushroom Dip
Classic Cheese Fondue
Crab Rangoon Dip
Guacamole
Mexican Beef and Chili Dip
Mexican Black Bean Dip
Sausage Pizza Dip
Smoked Trout Dip
Spinach Dip with Feta and Dill
Sun-Dried Tomato Dip
Tuscan White Bean Dip
Two-Salmon Dip
disposables
dough, pizza
dredging foods
dressings
Balsamic Vinaigrette
Celery Seed Dressing
Pear Dressing
Sesame Ginger Dressing
Dumpling-Topped Berry Grunt
Dutch ovens
## **E**
Easy Berry Trifle
Easy Peel shrimp
Egg Beaters
Eggplant and Red Pepper Panini
eggplants, safe-handling eggs
Baked Eggs with Herbed Cheese
cholesterol reduction
Corned Beef Hash with Baked Eggs
freshness
Smoked Salmon Hash with Poached Eggs
Summertime Baked Eggs
electric appliances
entrées
beef
Beef Stroganoff
Cranberry-Maple Spareribs
Japanese Sautéed Beef with Scallions
Korean Steak
Mexican Steaks with Chipotle Mayonnaise
Pan-Seared Filet Mignon with Red Wine Sauce
Stuffed Flank Steak
burgers
Bombay Lamb Burgers
breads
Caribbean Burgers
Chinese Pork Burgers
condiments
Creole Shrimp Burgers
Dilled Salmon Burgers
Italian Turkey Burgers
Mexican Burgers
Middle Eastern Lentil Burgers
New England Turkey Burgers
chicken
Chicken Fajitas
Chicken in Lettuce Cups
Chicken Marsala with Mushrooms and Sage
Chicken Satay with Spicy Peanut Sauce
Chicken with Garlic and Parsley
Chicken with Plum Sauce
Chicken with Three-Tomato Salsa
Grilled Chicken Hash
Ham and Cheese- Stuffed Chicken
Italian Chicken with Lemon and Capers
Mexican Chicken with Mole Sauce
Middle Eastern Chicken
Mock Mu Shu Chicken
Poached Chicken with Balsamic Vinegar
Sweet and Hot Chicken Skewers
Tarragon Chicken with Spring Vegetables
grilled foods
Aegean Swordfish
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Caribbean Pork Chops
Caribbean Shrimp
Chicken Satay with Spicy Peanut Sauce
Chicken with Three-Tomato Salsa
Cranberry-Maple Spareribs
gas versus charcoal
grill safety
grill temperature
Ham and Cheese- Stuffed Chicken
Korean Steak
marinated grilled dishes
Mexican Chicken with Mole Sauce
Mexican Steaks with Chipotle Mayonnaise
Middle Eastern Chicken
Rosemary Lamb Chops
Salmon Provençale
Salmon with Tomatillo Sauce
Sea Scallops with Mango Salsa and Chili Vinaigrette
Steak with Shiitake Cognac Sauce
Steak with Southwest Corn Sauce
Stuffed Flank Steak
Sweet and Hot Chicken Skewers
Swordfish with Smoked Cheddar Sauce
Tuna with Ginger Vinaigrette
wood chips
lamb
Bombay Lamb Burgers
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Mustard-Crusted Rack of Lamb
Rosemary Lamb Chops
pork
Herb-Crusted Pork Tenderloin
Pork Scaloppine
Pork with Prosciutto, Mozzarella, and Sage
salads
Asian Chicken Salad
Gazpacho Chicken Salad
Jambalaya Salad
Pork, Peach, and Orange Salad
Salmon and Cucumber Salad
Scallop and Asparagus Salad
Smoked Turkey Salad
Stir-Fried Chicken and Papaya Salad
Thai Shrimp Salad
Vietnamese Beef Salad
Warm Lamb Salad
turkey
Turkey Chili
Turkey Meatloaf
Veal Scaloppine with Fresh Shiitake Mushrooms
equipment
disposables
knives
pots and pans
small appliances
escarole
extra-virgin olive oil
extracts
## **F**
farmers' markets
Fennel Salad
feta cheese
Fig and Raspberry Gratin
finger foods
Asparagus Wrapped in Herbed Cheese and Prosciutto
Baked Shrimp Toast Rolls
Cheddar Crackers
Fresh Tomato Bruschetta
Herbed Goat Cheese and Roasted Pepper Spirals
Salmon Tartare on Cucumber Slices
Southwest Miniature Crab Cakes
Southwest Smoked Salmon Pinwheels
Vietnamese Spring Rolls
fish
Aegean Swordfish
Creole Swordfish
Fish Steamed in Napa Cabbage with Red Pepper Sauce
guide
Halibut in White Wine with Pearl Onions and Oranges
Pan-Fried Flounder with Black Walnut Butter
Roast Monkfish in Plum Wine Sauce
Salmon with Basil Cream Sauce
sauce
Scrod with Red Onion Marmalade
seafood dips
Smoked Trout Dip
Two-Salmon Dip
selection
skinning
Swordfish with Smoked Cheddar Sauce
Tuna Steaks with Tomato Relish
five-spice powder
fluting
fondues
Bananas Foster Fondue
Bittersweet Chocolate Coconut Cream Fondue
Classic Cheese Fondue
Classic Chocolate Fondue
Lemon Curd Mascarpone Fondue
Piña Colada Fondue
White Chocolate Cranberry Orange Fondue
food-borne illnesses
food processors
food safety
Food Safety and Inspection Service (USDA)
french toast, Raspberry French Toast with Raspberry Sauce
Fresh Berries with Lemon Mousse
freshness of eggs
Fresh Tomato Bruschetta
frittatas
Potato, Onion, and Bacon Frittata
tips
Vegetable Frittata with Pasta
Western Frittata
fruit recipes
Bananas Foster Fondue
Blueberry Crème Fraîche Tart
Blueberry Shortbread Gratin
Caramel Apple Quesadillas
Cherry Clafouti
Chocolate Malted Cookies
Dumpling-Topped Berry Grunt
Easy Berry Trifle
Fig and Raspberry Gratin
Fresh Berries with Lemon Mousse
Gingered Pear Crisp
Lemon Curd Mascarpone Fondue
Mixed Berry Compote
Oatmeal Cranberry Cookies
Peach Skillet Cake
Piña Colada Fondue
Strawberry Shortcake
Strawberry-Rhubarb Cobbler
Fudgy Brownies
Fusilli with Porcini Puttanesca Sauce
## **G**
gadgets
Gardiniera vegetables
garlic
roasting and blanching
safe-handling
Garlic-Steamed Clams
Garlicky Potato Salad
gas grills
Gazpacho
Gazpacho Chicken Salad
Gemelli with White Beans, Tomatoes, and Sage
ginger
crystallized
safe-handling
Gingerbread Pancakes
Gingered Asian Red Cabbage Slaw
Gingered Pear Crisp
glass noodles
Greek Lemon Egg Soup with Chicken and Orzo (Avgolemono)
Green Bean and Tomato Salad
green mung beans
green shrimp
Grilled Chicken, Sun-Dried Tomato, and Mozzarella Panini
Grilled Chicken Hash
Grilled Corn Chowder
grilled foods
burgers
Bombay Lamb Burgers
breads
Caribbean Burgers
Chinese Pork Burgers
condiments
Creole Shrimp Burgers
Dilled Salmon Burgers
Italian Turkey Burgers
Mexican Burgers
Middle Eastern Lentil Burgers
New England Turkey Burgers
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Caribbean Pork Chops
Chicken with Three-Tomato Salsa
gas versus charcoal
grill safety
grill temperature
Grilled Reuben Sandwich
Ham and Cheese-Stuffed Chicken
marinated grilled dishes
Aegean Swordfish
Caribbean Shrimp
Chicken Satay with Spicy Peanut Sauce
combination cooking
Cranberry-Maple Spareribs
Korean Steak
Mexican Steaks with Chipotle Mayonnaise
Middle Eastern Chicken
Rosemary Lamb Chops
Salmon Provençale
Stuffed Flank Steak
Mexican Chicken with Mole Sauce
Salmon with Tomatillo Sauce
Sea Scallops with Mango Salsa and Chili Vinaigrette
Steak with Shiitake Cognac Sauce
Steak with Southwest Corn Sauce
Sweet and Hot Chicken Skewers
Swordfish with Smoked Cheddar Sauce
Tuna with Ginger Vinaigrette
wood chips
grills
panini presses
grocery-shopping tips
grunt, Dumpling-Topped Berry Grunt
Guacamole
## **H**
Halibut in White Wine with Pearl Onions and Oranges
Ham and Cheese-Stuffed Chicken
handheld electric mixers
handling produce
apples
asparagus
bell peppers
cabbage
carrots
celery
cucumbers
eggplants
garlic
ginger
mangoes
mushrooms
onions
peaches
tomatoes
Herb-Crusted Pork Tenderloin
Herbed Goat Cheese and Roasted Pepper Spirals
Herbed Sausage and Tomato Quiche
Herbes de Provence hinged-grills
hinged-top grills hoisin sauce
hors d'oeuvres
Black Bean Cakes
Chicken in Lettuce Cups
Deviled Leeks
dips
Brie, Stilton, and Wild Mushroom Dip
Classic Cheese Fondue
Crab Rangoon Dip
Guacamole
Mexican Beef and Chili Dip
Mexican Black Bean Dip
Sausage Pizza Dip
Smoked Trout Dip
Spinach Dip with Feta and Dill
Sun-Dried Tomato Dip
Tuscan White Bean Dip
Two-Salmon Dip
finger foods
Asparagus Wrapped in Herbed Cheese and Prosciutto
Baked Shrimp Toast Rolls
Cheddar Crackers
Fresh Tomato Bruschetta
Herbed Goat Cheese and Roasted Pepper Spirals
Salmon Tartare on Cucumber Slices
Southwest Miniature Crab Cakes
Southwest Smoked Salmon Pinwheels
Vietnamese Spring Rolls
seafood appetizers
Baked Clams Casino
Bourbon Shrimp
Crab Cakes with Mustard Sauce
Creole Marinated Shrimp
Garlic-Steamed Clams
Oysters with Green Chili Cilantro Pesto
hummus
## **I**
immersion blenders
Italian breadcrumbs
Italian Chicken with Lemon and Capers (Pollo Piccata)
Italian Turkey Burgers
## **J**
Jambalaya Salad
Janet's Potato Salad
Japanese Sautéed Beef with Scallions (Negimaki)
jasmine rice
jicama
julienned foods
jumbo shrimp
## **K**
Kentucky Hot Brown Sandwich
kirsch
kirschwasser
kitchen equipment
disposables
knives
pots and pans
small appliances
kneading dough
knives
Korean Steak
## **L**
lamb
Bombay Lamb Burgers
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Mustard-Crusted Rack of Lamb
Rosemary Lamb Chops
Lardons
large shrimp
Leek and Potato Soup (Vichyssoise)
leeks
Lemon Curd Mascarpone Fondue
lentils
lettuces
Linguine with White Clam Sauce
liqueur, amaretto lunch recipes
brunch recipes
Bacon, Egg, and Arugula Salad
Baked Macaroni and Cheese with Ham
Classic Quiche Lorraine
Corned Beef Hash with Baked Eggs
Crab Quiche
Grilled Chicken Hash
Herbed Sausage and Tomato Quiche
quiches
Sausage and Pepper Hash
Smoked Salmon Hash with Poached Eggs
Southwest Sweet Potato Pancakes with Salsa Cream
Stuffed Peppers
Summertime Baked Eggs
Welsh Rarebit with Tomatoes and Bacon
quesadillas quiches
Classic Quiche Lorraine
Crab Quiche
Herbed Sausage and Tomato Quiche
sandwiches
Eggplant and Red Pepper Panini
Grilled Chicken, Sun-Dried Tomato, and
Mozzarella Panini Grilled Reuben Sandwich
Kentucky Hot Brown Sandwich
Tuna Melt with Olives
## **M**
macaroni and cheese, Baked Macaroni and Cheese with Ham
mangoes, safe-handling
maple syrup
marinated grilled dishes
Aegean Swordfish
Caribbean Shrimp
Chicken Satay with Spicy Peanut Sauce
combination cooking
Cranberry-Maple Spareribs
Korean Steak
Mexican Steaks with Chipotle Mayonnaise
Middle Eastern Chicken
Rosemary Lamb Chops
Salmon Provençale
Stuffed Flank Steak
marjoram
mascarpone
meatloaf, Turkey Meatloaf
metal colanders
Mexican Beef and Chili Dip
Mexican Black Bean Dip
Mexican Burgers
Mexican Chicken with Mole Sauce
Mexican Steaks with Chipotle Mayonnaise
Middle Eastern Chicken
Middle Eastern Lentil Burgers
mincing
Mini-Molten Chocolate Tortes
Mixed Berry Compote mixing bowls
Mock Mu Shu Chicken mole
mollusks
mozzarella
mung beans
mushrooms
rehydrating
safe-handling
storage
wood ear
mussels
Mustard-Crusted Rack of Lamb
mustards, Dijon mustard
## **N**
Nantucket Clam Chowder
National Directory of Farmers Markets
Negimaki (Japanese Sautéed Beef with Scallions)
New England Turkey Burgers
## **O**
Oatmeal Cranberry Cookies
Old Bay
olive oil
onions
organic stocks
Oven-Baked Apple Pancakes
ovens, Dutch
oysters
Dilled Corn and Oyster Bisque
Oysters with Green Chili Cilantro Pesto
## **P**
Pan-Fried Flounder with Black Walnut Butter
Pan-Seared Filet Mignon with Red Wine Sauce
pancakes
Banana Pancakes with Banana Syrup
Gingerbread Pancakes
Oven-Baked Apple Pancakes
tips
Whole-Wheat Blueberry Pancakes
panini sandwiches
Eggplant and Red Pepper Panini
Grilled Chicken, Sun-Dried Tomato, and Mozzarella Panini
presses
pans and pots
pasta, al dente
Pasta Aglio e Olio (Pasta with Garlic Oil)
Pasta Carbonara (Spaghetti with Egg and Bacon)
pasta recipes
contents of pasta
Fusilli with Porcini Puttanesca Sauce
Gemelli with White Beans, Tomatoes, and Sage
Linguine with White Clam Sauce
Pasta with Garlic and Oil
Rigatoni with Vegetables and Mozzarella
shopping tips
Spaghetti with Egg and Bacon
Spaghetti with Escarole, Pine Nuts, and Raisins
Pasta with Garlic and Oil (Pasta Aglio e Olio)
pastry blenders
peaches
Peach Skillet Cake
Pear Dressing
pearl onions
pears, Gingered Pear Crisp
Piña Colada Fondue
piñon
pine nuts
pizza recipes
Basic Pizza Dough
pizza dough
Pizza Margherita
Prosciutto Pizza
Smoked Salmon Pizza
plumped foods
Poached Chicken with Balsamic Vinegar
poached foods
Pollo Piccata (Italian Chicken with Lemon and Capers)
Porchetta Saltimbocca (Pork with Prosciutto, Mozzarella, and Sage)
Pork, Peach, and Orange Salad
pork recipes
Caribbean Pork Chops
Herb-Crusted Pork Tenderloin
Pork Scaloppine
Pork with Prosciutto, Mozzarella, and Sage
Potato, Onion, and Bacon Frittata
potatoes
Garlicky Potato Salad
Janet's Potato Salad
Sweet Potato Salad with Mustard Dressing
pots and pans
Prawns in Garlic Sauce with Fettuccine
produce
apples
asparagus
bell peppers
cabbage
carrots
celery
cucumbers
eggplants
garlic
ginger
mangoes
mushrooms
onions
peaches
tomatoes
Prosciutto Pizza
pudding
Chocolate Bread Pudding with Easy Bourbon Caramel Sauce
Chocolate Pudding
puréed foods
pure extracts
pure olive oil
## **Q**
quesadillas
Candy Bar Quesadillas
Caramel Apple Quesadillas
Cuban Quesadillas
Springtime Quesadillas
quiches
Classic Quiche Lorraine
Crab Quiche
Herbed Sausage and Tomato Quiche
Quick Chicken Stock
Quick Mocha Soufflé
## **R**
raspberries
Raspberry French Toast with Raspberry Sauce
raw mussels
recipes
appetizers
Asparagus Wrapped in Herbed Cheese and Prosciutto
Baked Clams Casino
Baked Shrimp Toast Rolls
Black Bean Cakes
Bourbon Shrimp
Cheddar Crackers
Chicken in Lettuce Cups
Crab Cakes with Mustard Sauce
Creole Marinated Shrimp
Deviled Leeks
Fresh Tomato Bruschetta
Garlic-Steamed Clams
Herbed Goat Cheese and Roasted Pepper Spirals
Oysters with Green Chili Cilantro Pesto
Salmon Tartare on Cucumber Slices
Southwest Miniature Crab Cakes
Southwest Smoked Salmon Pinwheels
Vietnamese Spring Rolls
beef
Beef Stroganoff
Cranberry-Maple Spareribs
Japanese Sautéed Beef with Scallions
Korean Steak
Mexican Steaks with Chipotle Mayonnaise
Pan-Seared Filet Mignon with Red Wine Sauce
Stuffed Flank Steak
breakfast
Baked Eggs with Herbed Cheese
Banana Pancakes with Banana Syrup
cholesterol reduction frittata tips
Gingerbread Pancakes
Oven-Baked Apple Pancakes
pancake tips
Potato, Onion, and Bacon Frittata
Raspberry French Toast with Raspberry Sauce
Vegetable Frittata with Pasta
Western Frittata
Whole-Wheat Blueberry Pancakes
brunch recipes
Bacon, Egg, and Arugula Salad
Baked Macaroni and Cheese with Ham
Classic Quiche Lorraine
Corned Beef Hash with Baked Eggs
Crab Quiche
Grilled Chicken Hash
Herbed Sausage and Tomato Quiche
quiches
Sausage and Pepper Hash
Smoked Salmon Hash with Poached Eggs
Southwest Sweet Potato Pancakes with Salsa Cream
Stuffed Peppers
Summertime Baked Eggs
Welsh Rarebit with Tomatoes and Bacon
burgers
Bombay Lamb Burgers
breads
Caribbean Burgers
Chinese Pork Burgers
condiments
Creole Shrimp Burgers
Dilled Salmon Burgers
Italian Turkey Burgers
Mexican Burgers
Middle Eastern Lentil Burgers
New England Turkey Burgers
chicken
Chicken Fajitas
Chicken Marsala with Mushrooms and Sage
Chicken with Garlic and Parsley
Chicken with Plum Sauce
Italian Chicken with Lemon and Capers
Mock Mu Shu Chicken
Poached Chicken with Balsamic Vinegar
stir-frys
Tarragon Chicken with Spring Vegetables
desserts
Bittersweet Chocolate Coconut Cream Fondue
Blueberry Crème Fraîche Tart
Candy Bar Quesadillas
Caramel Apple Quesadillas
Carrot Cookie Sandwiches
Cherry Clafouti
Chocolate Bread Pudding with Easy Bourbon Caramel Sauce
Chocolate Malted Cookies
Chocolate Peanut Butter Turnovers
Chocolate Pudding
Classic Chocolate Fondue
Fudgy Brownies
Gingered Pear Crisp
Mini-Molten Chocolate Tortes
Oatmeal Cranberry Cookies
Quick Mocha Soufflé
Strawberry Shortcake
Strawberry-Rhubarb Cobbler
White Chocolate Cranberry Orange Fondue
White Chocolate Strawberry Sundaes
dips
Brie, Stilton, and Wild Mushroom Dip
Classic Cheese Fondue
Crab Rangoon Dip
Guacamole
Mexican Beef and Chili Dip
Mexican Black Bean Dip
Sausage Pizza Dip
Smoked Trout Dip
Spinach Dip with Feta and Dill
Sun-Dried Tomato Dip
Tuscan White Bean Dip
Two-Salmon Dip
fruit
Bananas Foster Fondue
Blueberry Crème Fraîche Tart
Blueberry Shortbread Gratin
Caramel Apple Quesadillas
Cherry Clafouti
Chocolate Malted Cookies
Dumpling-Topped Berry Grunt
Easy Berry Trifle
Fig and Raspberry Gratin
Fresh Berries with Lemon Mousse
Gingered Pear Crisp
Lemon Curd Mascarpone Fondue
Mixed Berry Compote
Oatmeal Cranberry Cookies
Peach Skillet Cake
Piña Colada Fondue
Strawberry Shortcake
Strawberry-Rhubarb Cobbler
grilled foods
Aegean Swordfish
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Caribbean Pork Chops
Caribbean Shrimp
Chicken Satay with Spicy Peanut Sauce
Chicken with Three-Tomato Salsa
Cranberry-Maple Spareribs
Ham and Cheese- Stuffed Chicken
Korean Steak
marinated grilled dishes
Mexican Chicken with Mole Sauce
Mexican Steaks with Chipotle Mayonnaise
Middle Eastern Chicken
Rosemary Lamb Chops
Salmon Provençale
Salmon with Tomatillo Sauce
Sea Scallops with Mango Salsa and Chili Vinaigrette
Steak with Shiitake Cognac Sauce
Steak with Southwest Corn Sauce
Stuffed Flank Steak
Sweet and Hot Chicken Skewers
Swordfish with Smoked Cheddar Sauce
Tuna with Ginger Vinaigrette
lamb
Bombay Lamb Burgers
Butterflied Leg of Lamb with Garlic, Rosemary, and Lemon
Mustard-Crusted Rack of Lamb
Rosemary Lamb Chops
pasta
Fusilli with Porcini Puttanesca Sauce
Linguine with White Clam Sauce
Pasta with Garlic and Oil
Spaghetti with Egg and Bacon
Spaghetti with Escarole, Pine Nuts, and Raisins
pizza
Basic Pizza Dough
Pizza Margherita
Prosciutto Pizza
Smoked Salmon Pizza
pork
Herb-Crusted Pork Tenderloin
Pork Scaloppine
Pork with Prosciutto, Mozzarella, and Sage
quesadillas
quiches
Classic Quiche Lorraine
Crab Quiche
Herbed Sausage and Tomato Quiche
salad dressings
Balsamic Vinaigrette
Celery Seed Dressing
Pear Dressing
Sesame Ginger Dressing
salads
Asian Chicken Salad
Asian Eggplant Salad
Black Bean and Papaya Salad
Coconut Rice and Vegetable Salad
Dilled Cucumbers
Fennel Salad
Garlicky Potato Salad
Gazpacho Chicken Salad
Gemelli with White Beans, Tomatoes, and Sage
Gingered Asian Red Cabbage Slaw
Green Bean and Tomato Salad
Jambalaya Salad
Janet's Potato Salad
Pork, Peach, and Orange Salad
Rigatoni with Vegetables and Mozzarella
Salmon and Cucumber Salad
Scallop and Asparagus Salad
Sesame Noodles with Asian Vegetables
Smoked Turkey Salad
Spicy Asian Brown Rice Salad
Stir-Fried Chicken and Papaya Salad
Stir-Fried Vegetable Salad
Sweet Potato Salad with Mustard Dressing
Tabbouleh with Feta
Thai Cucumber Salad
Thai Rice Salad
Thai Shrimp Salad
Three-Pepper Gazpacho Salad
Tomato and Mozzarella Salad with Oregano
Vietnamese Beef Salad
Warm Lamb Salad
Warm Vegetable Salad
sandwiches
Eggplant and Red Pepper Panini
Grilled Chicken, Sun-Dried Tomato, and Mozzarella Panini
Grilled Reuben Sandwich
Kentucky Hot Brown Sandwich
Tuna Melt with Olives
seafood
Asian Shrimp and Stir-Fried Vegetables
Creole Swordfish
Fish Steamed in Napa Cabbage with Red Pepper Sauce
Halibut in White Wine with Pearl Onions and Oranges
Pan-Fried Flounder with Black Walnut Butter
Prawns in Garlic Sauce with Fettuccine
Roast Monkfish in Plum Wine Sauce
Salmon with Basil Cream Sauce
Scallops with Pine Nuts
Scrod with Red Onion Marmalade
Tuna Steaks with Tomato Relish
soups
Cream of Celery Soup with Tarragon
Dilled Corn and Oyster Bisque
Dilled Cream of Cucumber Soup
Gazpacho
Greek Lemon Egg Soup with Chicken and Orzo
Grilled Corn Chowder
Leek and Potato Soup
Nantucket Clam Chowder
Quick Chicken Stock
Tuscan White Bean Soup with Sausage
turkey
Veal Scaloppine with Fresh Shiitake Mushrooms
reductions
rehydration of mushrooms
resting meats
rice dishes
Spicy Asian Brown Rice Salad
Tabbouleh with Feta
Thai Rice Salad
rice noodles
Rigatoni with Vegetables and Mozzarella
roasting garlic
roasting pans
Roast Monkfish in Plum Wine Sauce
Rosemary Lamb Chops
roux
## **S**
safety (food safety)
salad dressings
Balsamic Vinaigrette
Celery Seed Dressing
Pear Dressing
Sesame Ginger Dressing
salads
Asian Chicken Salad
Asian Eggplant Salad
Bacon, Egg, and Arugula Salad
Black Bean and Papaya Salad
Coconut Rice and Vegetable Salad
Dilled Cucumbers
Fennel Salad
Garlicky Potato Salad
Gazpacho Chicken Salad
Gemelli with White Beans, Tomatoes, and Sage
Gingered Asian Red Cabbage Slaw
Green Bean and Tomato Salad
Jambalaya Salad
Janet's Potato Salad
lettuce choices
Pork, Peach, and Orange Salad
Rigatoni with Vegetables and Mozzarella
Salmon and Cucumber Salad
Scallop and Asparagus Salad
Sesame Noodles with Asian Vegetables
Smoked Turkey Salad
Spicy Asian Brown Rice Salad
Stir-Fried Chicken and Papaya Salad
Stir-Fried Vegetable Salad
Sweet Potato Salad with Mustard Dressing
Tabbouleh with Feta
Thai Cucumber Salad
Thai Rice Salad
Thai Shrimp Salad
Three-Pepper Gazpacho Salad
Tomato and Mozzarella Salad with Oregano
Vietnamese Beef Salad
Warm Lamb Salad
Warm Vegetable Salad
salmon
Dilled Salmon Burgers
Salmon and Cucumber Salad
Salmon Provençale
Salmon Tartare on Cucumber Slices
Salmon with Basil Cream Sauce
Salmon with Tomatillo Sauce
Smoked Salmon Hash with Poached Eggs
Smoked Salmon Pizza
Southwest Smoked Salmon Pinwheels
Two-Salmon Dip
sandwiches
Eggplant and Red Pepper Panini
Grilled Chicken, Sun-Dried Tomato, and Mozzarella Panini
Grilled Reuben Sandwich
Kentucky Hot Brown Sandwich
panini presses
Tuna Melt with Olives
saucepans
sauces
chili sauce
fish sauce
Hoisin
mole
tamari
sausage
Sausage and Pepper Hash
Sausage Pizza Dip
sautéing foods
Scallop and Asparagus Salad
scallops
Scallop and Asparagus Salad
Scallops with Pine Nuts
sea scallops
Sea Scallops with Mango Salsa and Chili Vinaigrette
scoring foods
Scrod with Red Onion Marmalade
seafood
appetizers
Baked Clams Casino
Baked Shrimp Toast Rolls
Bourbon Shrimp
Crab Cakes with Mustard Sauce
Creole Marinated Shrimp
Garlic-Steamed Clams
Oysters with Green Chili Cilantro Pesto
Asian Shrimp and Stir-Fried Vegetables
clams
Creole Swordfish
dips
Crab Rangoon Dip
Smoked Trout Dip
Two-Salmon Dip
fish guide
fish selection
Fish Steamed in Napa Cabbage with Red Pepper Sauce
Halibut in White Wine with Pearl Onions and Oranges
mollusks
mussels
oysters
Pan-Fried Flounder with Black Walnut Butter
Prawns in Garlic Sauce with Fettuccine
Roast Monkfish in Plum Wine Sauce
Salmon with Basil Cream Sauce
scallops
Scallop and Asparagus Salad
Scallops with Pine Nuts
Sea Scallops with Mango Salsa and Chili Vinaigrette
Scrod with Red Onion Marmalade
shrimp choices
Tuna Steaks with Tomato Relish
searing foods
sea scallops
Sea Scallops with Mango Salsa and Chili Vinaigrette
semisweet chocolate
Sesame Ginger Dressing
Sesame Noodles with Asian Vegetables
shrimp
Asian Shrimp and Stir-Fried Vegetables
Baked Shrimp Toast Rolls
Bourbon Shrimp
Caribbean Shrimp
Creole Marinated Shrimp
Creole Shrimp Burgers
deveining
Prawns in Garlic Sauce with Fettuccine
selection
Thai Shrimp Salad
shucking bivalves
silverskin
skillets
skinning fish
slaws, Gingered Asian Red Cabbage Slaw
slumps, Dumpling-Topped Berry Grunt
small appliances
Smoked Salmon Hash with Poached Eggs
Smoked Salmon Pizza
Smoked Trout Dip
Smoked Turkey Salad
solanine
soups
Cream of Celery Soup with Tarragon
Dilled Corn and Oyster Bisque
Dilled Cream of Cucumber Soup
Gazpacho
Greek Lemon Egg Soup with Chicken and Orzo
Grilled Corn Chowder
Leek and Potato Soup
Nantucket Clam Chowder
Quick Chicken Stock roux
Tuscan White Bean Soup with Sausage
Southwest Miniature Crab Cakes
Southwest Smoked Salmon Pinwheels
Southwest Sweet Potato Pancakes with Salsa Cream
Spaghetti with Egg and Bacon (Pasta Carbonara)
Spaghetti with Escarole, Pine Nuts, and Raisins
spiced meats
spices
allspice
cumin
Herbes de Provence
marjoram
star anise
tarragon
Spicy Asian Brown Rice Salad
Spinach Dip with Feta and Dill
Springtime Quesadillas
star anise
steaks
Korean Steak
Mexican Steaks with Chipotle Mayonnaise
Pan-Seared Filet Mignon with Red Wine Sauce
Steak with Shiitake Cognac Sauce
Steak with Southwest Corn Sauce
Stuffed Flank Steak
steeping ingredients
stews
stir-fry recipes
Chicken Fajitas
Chicken with Plum Sauce
Mock Mu Shu Chicken
Stir-Fried Chicken and Papaya Salad
Stir-Fried Vegetable Salad
stockpots
stocks
canned
Quick Chicken Stock
storage
cookies
mozzarella
mushrooms
olive oil
strawberries
Strawberry Shortcake
Strawberry-Rhubarb Cobbler
White Chocolate Strawberry Sundaes
Stuffed Flank Steak
Stuffed Peppers
substitutions, meats
Summertime Baked Eggs
Sun-Dried Tomato Dip
sushi vinegar
Sweet and Hot Chicken Skewers
Sweet Potato Salad with Mustard Dressing
Swordfish with Smoked Cheddar Sauce
## **T**
Tabbouleh with Feta
tamari
tapioca
tarragon
Tarragon Chicken with Spring Vegetables
temperature, grills
Thai Cucumber Salad
Thai Rice Salad
Thai Shrimp Salad
Three-Pepper Gazpacho Salad
tomatillos
Tomato and Mozzarella Salad with Oregano
tomatoes, safe-handling
trout, Smoked Trout Dip
Tuna Melt with Olives
Tuna Steaks with Tomato Relish
Tuna with Ginger Vinaigrette
Turkey Chili
Turkey Meatloaf
turkey recipes
Italian Turkey Burgers
New England Turkey Burgers
Turkey Chili
Turkey Meatloaf
Tuscan White Bean Dip
Tuscan White Bean Soup with Sausage
Two-Salmon Dip
## **U**
U.S. Department of Agriculture (USDA)
unsweetened chocolate
unsweetened cocoa powder
USDA (U.S. Department of Agriculture)
## **V**
Veal Scaloppine with Fresh Shiitake Mushrooms
Vegetable Frittata with Pasta vegetables
appetizers
Asparagus Wrapped in Herbed Cheese and Prosciutto
Deviled Leeks
Vietnamese Spring Rolls
escarole
Gardiniera salads
Asian Eggplant Salad
Black Bean and Papaya Salad
Dilled Cucumbers
Fennel Salad
Gingered Asian Red Cabbage Slaw
Green Bean and Tomato Salad
Salmon and Cucumber Salad
Scallop and Asparagus Salad
Stir-Fried Vegetable Salad
Thai Cucumber Salad
Three-Pepper Gazpacho Salad
Tomato and Mozzarella Salad with Oregano
Warm Vegetable Salad
vegetarian recipes
Asian Eggplant Salad
Black Bean and Papaya Salad
Dilled Cucumbers
Fennel Salad
Gingered Asian Red Cabbage Slaw
Green Bean and Tomato Salad
Middle Eastern Lentil Burgers
Stir-Fried Vegetable Salad
Thai Cucumber Salad
Three-Pepper Gazpacho Salad
Tomato and Mozzarella Salad with Oregano
Warm Vegetable Salad
Vichyssoise (Leek and Potato Soup)
Vietnamese Beef Salad
Vietnamese Spring Rolls
vinaigrettes, Balsamic
Vinaigrette
## **W-X-Y-Z**
Warm Lamb Salad
Warm Vegetable Salad
Welsh Rarebit with Tomatoes and Bacon
Western Frittata
white chocolate White Chocolate
Cranberry Orange Fondue
White Chocolate Strawberry Sundaes
white long-grain rice
Whole-Wheat Blueberry Pancakes
woks
wood chips
wood ear mushrooms
yogurt
zest
| {
"redpajama_set_name": "RedPajamaBook"
} | 8,596 |
title: A Red Hat Journey to Linux.conf.au 2016
date: 2016-02-15 15:25 UTC
author: sellis
tags: Linux.conf.au events
published: true
comments: true
---
Every year a (relatively) large number of Red Hatters descend upon a town/city in Australia or New Zealand for linux.conf.au. This is a blog of my week and a brain dump of sessions I attended or feel would be of value to my colleagues at Red Hat and in the broader open source community.
As a nomadic and volunteer-run event, [linux.conf.au](http://lcabythebay.org.au/) moves location each year around Australia and NZ, with a new team and a new focus. For 2016, the location was Geelong Australia from 1-5 February, with around 600 attendees from over 30 countries.
READMORE
The conference runs over five days with a wide range of open source presentations, labs, and keynotes. This year, we had a number of local, regional, and international Red Hat presenters, more details of which can be found on the [Red Hat Community page](http://community.redhat.com/events/2016/#linuxconfau).
Unlike other more commercial Open Source conferences, keynotes are selected by the conference team and aim to inspire, rather than push the products or focus of the top-tier sponsors.
* [Chair of Internet Australia George Fong](https://linux.conf.au/news/georgefong)
* [OpenMaterials and EverywhereTech Founder Catarina Mota](https://linux.conf.au/news/catarinamota)
* [Jono Bacon - Community Manager GitHub](https://linux.conf.au/news/jonobacon)
* [Intel Fellow and cultural anthropologist Genevieve Bell](https://linux.conf.au/news/genevievebell)
I highly recommend the session by Genevieve Bell, plus anyone with an interest in community will appreciate Jono Bacon's talk on Community 3.0. Jono is now a regular contributor to [Opensource.com](https://opensource.com/).
Another highlight of this conference was the quality of the session recordings generated by the volunteer team using open source technologies (hdmi2usb)
* [Linux.conf.au 2016—Geelong, Australia - Conference Videos - YouTube](https://www.youtube.com/user/linuxconfau2016)
* [hdmi2usb](https://hdmi2usb.tv/home/)
* [Conference Recording 2.0: Building a Better System](https://www.youtube.com/watch?v=ezikdeVWT84)
With the breadth of content running across five sessions, hallway tracks, social events, and birds of a feather sessions it isn't an easy event to write up. I'll present a perspective on sessions I attended, or heard good feedback on and intend to catch up on video later. I also suggest taking a look at the blogs of Rodger Donaldson and Simon Lyall, who regularly attend LCA and provide a great deal of coverage of the conference, amongst others.
* [LCA 2016 Day 1—Rodger Donaldson](http://rodger.donaldson.gen.nz/conferences/lca-2016-day-1/)
* [Linux.conf.au—Simon Lyall's Blog](http://blog.darkmere.gen.nz/category/tech/lca/)
* [linux.conf.au 2016—Monday & Tuesday—Jack Scott's Blog](http://jackscott.id.au/2016/02/linux-conf-au-2016-monday-tuesday/)
In addition, Jonathan Corbet from Linux Weekly News is a regular attendee and you'll find numerous articles over at [LWN](http://lwn.net).
* [Protecting systems with the TPM](http://lwn.net/Articles/674751/)
* [Whole-house audio with free hardware and software](http://lwn.net/Articles/674191/)
## Day 0—Sunday 31st Jan
 There is a bit of an linux.conf.au tradition that a newbie introduction session, plus a speaker briefing, are held on the Sunday afternoon before the conference. Normally Rusty Russell runs the newbie session but this year he was awaiting the arrival of his latest offspring, so [Bdale Garbee](https://en.wikipedia.org/wiki/Bdale_Garbee) and Hugh Blemings (the new Linux Australia President) stepped in.
## Day 1—Monday 1st Feb
* [Monday Schedule—linux.conf.au 2016](http://lcabythebay.org.au/programme/schedule/monday)
My personal focus was the "Open Cloud Symposium" in Costa Hall, where I was also speaking on ManageIQ that afternoon.
* [Cloud Crafting—Public / Private / Hybrid](https://www.youtube.com/watch?v=WQ7eU2mVL0o)
Casey West from Pivotal gave two talks that weren't Pivotal- or CloudFoundry-specific and I highly recommend them for anyone working around DevOps or containers.
The Live Migration of Containers session was a touch LXC/LXD-specific and several people wondered why you'd bother, given the service driven approach to container workloads.
* [The Twelve-Factor Container](https://www.youtube.com/watch?v=aPv12drmIqg)
* [Cloud Anti-Patterns](https://www.youtube.com/watch?v=fV3epaFUEmk)
* [Live Migration of Linux Containers](https://www.youtube.com/watch?v=ol85OJxDaHc)
### Recommended Sessions I'll Catch Later
* [Continuous Delivery using blue-green deployments and immutable infrastructure](https://www.youtube.com/watch?v=KD1JHpzKW3Q)
### Special Mentions
 Thanks to Zac Dover for running the Documentation Mini-Conf and the large number of Red Hatter's who attended from Brisbane. It helped to balance up the Rackspace presence in the room.
There was a new Open Source and Bio-informatics mini-conf this year that gathered a lot of interest, and I might try and catch some of their sessions on video at a later date, based on feedback.
Monday closed with the [Linux Australia](https://linux.org.au/) AGM, where their recent election results mean a 4:3 ratio in favor of females on the council (including my wife Cherie).
## Day 2—Tuesday 2nd Feb
* [Tuesday Schedule—linux.conf.au 2016](http://lcabythebay.org.au/programme/schedule/tuesday)
 After an interesting [keynote from George Fong](https://www.youtube.com/watch?v=5E589-0kK20), my focus was the System Administrator Mini-Conf, which has been running for over 10 years as part of LCA.
 I was (un)lucky to be the opening speaker at the Sys Admin mini-conf, providing a re-work of an internal talk I gave at Red Hat Tech Exchange APAC last year
* [Is that a data-center in your pocket?](https://www.youtube.com/watch?v=4ZnvjJSmbO4)
Tim Serong from SuSE gave a 101 session on Ceph, and I sadly missed Jamie Bainbridge's session on Network Performance Tuning which had terrific feedback. A special mention for Eric Burgueno from Plant and Food Research, a Red hat NZ Customer, who talked about his operational challenges.
* [A Gentle Introduction to Ceph](https://www.youtube.com/watch?v=5xoYFGkFTkM)
* [Network Performance Tuning](https://www.youtube.com/watch?v=ZYCKSN4xf84)
* [The life of a sysadmin in a research environment](https://www.youtube.com/watch?v=SiSY1b0am5w)
### Recommended Sessions I'll Catch Later
* [Site Reliability Engineering at Dropbox](https://www.youtube.com/watch?v=ggizCjUCCqE) by Tammy Butow
### Special Mentions
* The amazing Donna Benjamin ran a Community Leadership Summit with Jono Bacon in attendance
* Fraser Tweedale ran a functional programming mini-conf.
The day finished with the Professional Delegates Networking session out at Little Creatures Brewery. Great to catch old friends and make new ones.
## Day 3—Wednesday 3rd Feb
* [Wednesday Schedule—linux.conf.au 2016](http://lcabythebay.org.au/programme/schedule/wednesday)
 Quite a different [keynote from Catarina Mota](https://www.youtube.com/watch?v=CpYsrpnDtsE) started our day, including how to build an Open Source House, before we dived into the main conference program.
This year the Papers Committee had 300 submissions for the 75 slots spread across five streams, so the pedigree of talks is generally very high.
### Sessions Attended
* [Using Linux features to make a hacker's life hard](https://www.youtube.com/watch?v=vNNuJve459o) Kayne Naughton was a terrific presenter and a great one for anyone who deals with security.
* [Embrace the Atomic (Display) Age](https://www.youtube.com/watch?v=LjiB_JeDn2M)
* [Adventures in OpenPower Firmware](https://www.youtube.com/watch?v=a4XGvssR-ag) Stewart Smith is a great speaker and having Linux as your firmware to bootstrap Linux on Open Power is simply awesome. Plus I'm a bit of a Power and PowerPC geek.
* [Improving thread synchronization in GlusterD (Daemon for Gluster) using Userspace RCU (Read-copy-update)](http://lcabythebay.org.au/schedule/30007/view_talk?day=wednesday) by Atin Mukherjee. No video online yet, and one for serious Gluster fans.
* [Melvin: A new implementation of LVM in Rust](https://www.youtube.com/watch?v=JYSqVyxlBBE). Spent a lot of time hacking on LVM so this was really interesting, plus Andy Grover covered the reasons on why you'd implement this in Rust.
### Recommended Sessions I'll Catch Later
* [Going Faster: Continuous Delivery for Firefox](https://www.youtube.com/watch?v=IaH1BN71fkw)
* [What Happens When 4096 Cores All Do synchronize_rcu_expedited?](https://www.youtube.com/watch?v=1nfpjHTWaUc) Especially for HPC fans and Paul is a fantastic speaker.
* [Welcoming Everyone: Five Years of Inclusion and Outreach Programmes at PyCon Australia](https://www.youtube.com/watch?v=6jusW1PqL-4) One I'd recommend to any current or potential conference organisers.
* [Tutorial: Identity Management with FreeIPA](https://www.youtube.com/watch?v=VLhNcirKFDs) Follow up on Fraser Tweedale's FreeIPA talk from last year.
* [Challenges when Scaling: Adventures in Swift's Sharding](https://www.youtube.com/watch?v=MFPNA3tnWcM)
The day ended with the annual Penguin Dinner at the end of Geelong's Pier. A great opportunity to socialize and network over dinner.
## Day 4—Thursday 4 Feb
* [Thursday Schedule - linux.conf.au 2016](http://lcabythebay.org.au/programme/schedule/thursday)
 Jono Bacon last attended linux.conf.au back in 2007 in Sydney, which was my first LCA. I've bumped into Jono at various conferences in the US since then and I have to say his [Keynote on Community 3.0](https://www.youtube.com/watch?v=LToxpzWcMxc) was one of his best. As former community manager at Canonical, and current Director of Community at GitHub, he presented his perspective on how we should be building and maintaining communities today. Overall, this was a hard day due to numerous conflicting sessions.
### Sessions Attended
* [Using Persistent Memory for Fun and Profit](https://www.youtube.com/watch?v=8CIskyAaSpY) Ultimately not something I need in my day job, but very interesting issues when dealing with RAM than can persist like Flash.
* [Dropbox Database Infrastructure](https://www.youtube.com/watch?v=71VryWiEw2A) Tammy Butow is very energetic and passionate about her role at Dropbox. Some useful nuggets on how they manage and scale their backend.
* [Builds, dependencies and deployment in the modern multiplatform world](https://www.youtube.com/watch?v=CTJtKtQ8R5k) Looking at a different approach from RPM and Software Collections in managing application dependencies.
* [Open Source Tools for Distributed Systems Administration](https://www.youtube.com/watch?v=yu0PFfbldNU) Elizabeth Joseph is an incredibly well respected Sys Admin running the Open Stack build infrastructure.
* [Record and replay debugging with "rr"](https://www.youtube.com/watch?v=4hSIrjL7IR8) Robert O'Callahan from Mozilla provided some awesome quote worthy moments, and terrific content for testers and developers.
* [Playing to lose: making sensible security decisions by assuming the worst](https://www.youtube.com/watch?v=K8p0gvOgQ_c) Tom Eastman is a great friend and a terrific public speaker. Not just for security specialists, all developers and operators should take a look at this talk.
Thursday also featured the [Jobs BoF](https://linux.conf.au/wiki/Jobs_Page) during afternoon tea, where together with Nick Coghlan, we promoted the currently open roles in Australia and Globally. There was quite a lot of interest with a number of one-on-one follow up conversations.
### Recommended Sessions I'll Catch Later
* [Tutorial: The Power of Open Data with ELK](https://www.youtube.com/watch?v=k8bpxxR0Ws0) Elastic came back as a sponsor this year and this session on ELK was recommended by a number of fellow attendees.
* [Hardware and Software Architecture of The Machine](https://www.youtube.com/watch?v=S--Kgseuy0Q) Regular LCA presenter Keith Packard is always watchable, and this session had a number of jaws dropping.
* [Linux driven microwave](https://www.youtube.com/watch?v=R3DADx5z-XY) A lot of great feedback, and a bit of IoT in practice—just possibly don't do this at home.
* [Machine Ethics and Emerging Technologies](https://www.youtube.com/watch?v=9snMlhCU5ug) Paul Fenwick is another crowd pleaser and one to watch.
* [What I've learned as the kernel docs maintainer](https://www.youtube.com/watch?v=gsJXf6oSbAE) Jonathan Corbet seldom disappoints as a speaker.
* [A Detailed Look at Erasure Codes in OpenStack Swift](https://www.youtube.com/watch?v=9YHvYkcse-k)
* [SubPos - A "Dataless" Wi-Fi Positioning System](https://www.youtube.com/watch?v=m3yo97_1XFI)
* [Speaking their language: How to write for technical and non-technical audiences](https://www.youtube.com/watch?v=DcsfDpEWG88) Great to see Rikki Endsley join us in Geelong this year, and I hope she returns despite the lack of warm water at her accommodation.
* [Computer Performance Microscopy with SHIM](https://www.youtube.com/watch?v=iDEIHkwgaUc) Not a talk I was going to see, but very highly recommended by a couple of attendees.
 The day finished with the Speakers Dinner for main conference speakers, where I believe a couple of the speakers persuaded the strings to "[Rick Roll](https://www.youtube.com/watch?v=dQw4w9WgXcQ)" the event, and also play [The Rains of Castamere](http://gameofthrones.wikia.com/wiki/The_Rains_of_Castamere_%2528song%2529).
## Day 5—Friday 5 Feb
* [Friday Schedule - linux.conf.au 2016](http://lcabythebay.org.au/programme/schedule/friday)
 By this point if you haven't paced yourself then you're likely to miss the opening keynote, which would be a shame as Genevieve Bell (Intel Fellow and cultural anthropologist) was [simply amazing and totally engaged her audience](https://www.youtube.com/watch?v=QqADuKyBNMc). A key part of her role is to help Intel better understand their customers. I particularly liked the part where she decided to treat her team at Intel as another "Tribe."
Friday, like Thursday, had multiple session clashes, so the is plenty for me to catch up on later.
### Sessions Attended
* [Helicopters and rocket-planes](https://www.youtube.com/watch?v=kifraO9yMrk) Andrew Tridgell could read the Yellow Pages and give an interesting and inspiring talk. Sadly, I missed the end as I had to jump on some customer calls.
* [Copyleft For the Next Decade: A Comprehensive Plan](https://www.youtube.com/watch?v=5mnHebVSUb0) I'm so pleased we brought Bradley Kuhn to Auckland for last years conference as again his talk on GPL and Free Software was a highlight of the conference. Anyone and everyone in Red Hat should watch this session as well as last year's.
* [Considering the Future of Copyleft: How Will The Next Generation Perceive GPL?](https://www.youtube.com/watch?v=-ItFjEG3LaA)
* [Troublesome Privacy Measures: using TPMs to protect users](https://www.youtube.com/watch?v=rML5DfYUh_k) Former Red Hatter Matthew Garrett is always interesting as he relates the pain of his most recent work. The potential of using TPM in conjunction with OTP to validate the authenticity of a system boot was intriguing.
* [Life is better with Rust's community automation](https://www.youtube.com/watch?v=dIageYT0Vgg) Emily Dunham's talk on community *should* be watched by all of our OSAS community leads and those of us working within Open Source communities.
* [Lightning Talks and Conference Closing](https://www.youtube.com/watch?v=KERsn72QESE)
There are always some interesting Lightning talks at LCA including
* [My Own "Call to ARM"](https://youtu.be/KERsn72QESE?t=1m7s)
* [Plus a rather unexpected song](https://youtu.be/KERsn72QESE?t=31m10s)<br>
* and then we closed the conference out until next year.
### Recommended Sessions I'll Catch Later
* [Accessibility and Security](https://www.youtube.com/watch?v=0ijIzUUXdTM) Ever considered how disabled people can interact with security measures like captcha?
* [Open Source Two-Way Radio](https://www.youtube.com/watch?v=xDeMT7eUf4c) I love David Rowe's talks, especially where Open Hardware can enable underprivileged communities.
* [Raspberry Pi Hacks](https://www.youtube.com/watch?v=22dKTGyuRrc) Ruth Suehle had a total hardware failure just before presenting so had to wing a lot of this without her notes, and a copy of her slides from LCA 2014.
## Summary
And that is it until Linux.conf.au 2017 from 16-20 January in Hobart Tasmania. Each LCA is an opportunity to see what the early adopters are up to and perhaps predict future trends for the Enterprise. My first conferences were focused on configuration management (Puppet/Chef) and file systems (xfs vs ext vs btrfs). We then moved onto cloud technologies like OpenStack while last year had a lot of Container technology.
Every year we see lots more on Open Hardware and IoT. I'm pleased to see that both  Documentation and Community are increasingly important over the last two years with areas like DevOps and Security picking up momentum.
I've had the privilege to speak at the mini-confs again this year and had some great feedback on ManageIQ from attendees who'd previously been unaware of the project, some of whom might become CloudForms customs in the future.
Please excuse an errors/omissions. I've hopefully caught all of the sessions with Red Hat speakers or organizers. I'll also try and update video links and add additional recommendations as I watch recordings. Also if you have a chance catch Brett James's [time-lapse video](https://youtu.be/HrABSseB4F0) of the conference.
A huge thank you to the LCA 2016 team. After running LCA2015 in Auckland, I understand what a massive undertaking this volunteer-run event is and they did an amazing job.
| {
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Third business to open up in Sleaford '˜pop-up shop' scheme
A photographic business has been selected to be the next business to benefit from North Kesteven's '˜Pop-up Shop' initiative in Sleaford.
21st Feb 2017, 6:44am
Updated 28th Feb 2017, 12:47pm
Charlotte Frisyby is opening her photographic business as a pop-up shop. EMN-170220-142325001
Little and Loud Photography has been selected as the third business to open a pop up shop, moving into unit 6 in Navigation Yard, off Carre Street, on Saturday specialising in photo shoots with families and children.
On the same day, Gills2Gems - the second pop up business selected - will be opening their pop up shop next door in unit 7.
Charlotte Frisby, who owns Little and Loud Photography, said: "I have been working with the Prince's Trust to build up my business plan and my business idea.
"I have learnt lots in the build up to this point and I am very excited about opening my own business and premises within Sleaford.
"I am a newborn and family photographer offering studio and outdoor shoots and I am really looking forward to capturing precious memories to keep forever."
Neighbouring Gills2Gems will sell a range of different handbags and purses.
Owner Gill Allenby said: "I can't wait to open and welcome customers into the store.
"I'm really looking forward to trying the store out and learning lots of things along the way."
Partnership NK, of which North Kesteven District Council is a member, is running the pop up shop initiative to give new or expanding businesses the chance to test the marketplace with easy in, easy out terms so there's no commitment to a long-term contract.
Having started life in 2014 through Facebook, the business evolved into stalls at a number of events including pamper days, craft and school fairs and Christmas fairs.
Anyone wanting to register interest in Pop Up NK can fill in a form online at www.n-kesteven.gov.uk/popup
Once the form has been received, an officer will be in touch to find out more about your business, identifying if any additional support or advice is needed. | {
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Movie Review: "Judy" (2019)
Movie: "Judy"
Director: Rupert Goold
With a waning career, in financial ruin, with few prospects, and in danger of losing her kids, famous actress and singer Judy Garland heads to England to perform in a house show which she hopes will give her the financial stability to find a permanent home for her and her children.
"I'm only Judy Garland for an hour a night." (Image Source)
"Judy" is directed by Rupert Goold, who has directed movies like "True Story" and the made-for-TV film "King Charles III." The screenplay is written by Tom Edge, who is best known for creating the Netflix series "Love Sick," and it is based on the biography "End of the Rainbow" by Peter Quilter. This feature takes place during the last few months of Judy Garland's (Renée Zellweger) life. At the start of the film, it has been years since Judy has had a role in a feature-length picture. She is deep in debt and is trying her best to make ends meet by doing small club gigs here and there, dragging her kids along for the ride. When she gets locked out of the hotel they have been living in, Judy breaks down and drops her kids off with her ex-husband, Sid Luft (Rufus Sewell). Desperate to earn some money so she can once again be with her children, Judy takes a well-paying gig in England where she is still a smash hit. Taking this job means getting money so she can gain some form of stability for her and her family, but it also means being away from her kids as well. Just as things seem to be brightening up for her, Judy's past demons start to take a toll, putting her career in jeopardy once again.
"Frank is great, but he's no Judy Garland. I bet it kills him." (Image Source)
Most people who know anything about "the pictures" know who Judy Garland is. Whether you've seen the majority of her filmography or just "The Wizard of Oz," you know her name and probably, more so, her iconic voice. What some people may not know is the tragic end of the star's life and the events in her childhood that led to her untimely, unfortunate fate. If you're one of the people who don't know anything about Garland, "Judy" is the kind of biopic film that may detrimentally damage your perception of old Hollywood and the previously mentioned all-time classic "The Wizard of Oz." Her experiences sure put her through the wringer. Via flashbacks, this film explores how Garland's treatment as a child star where she was fed uppers and downers, forced to work long days for MGM, and told not to eat anything but black coffee and thin chicken soup led to a life full of an addiction to pills, the abuse of alcohol, a slew of illnesses, yo-yo dieting, the inability to sleep, and more. These flashbacks are juxtaposed with Judy's sold-out "comeback" gigs in London where she desperately tried to reclaim her former glory in a haze of pills, booze, depression, adoration, and sometimes disappointment.
As a whole, "Judy" is a rather basic, by-the-numbers biopic about a star fallen from grace that burned too bright and was extinguished too soon. What is anything but basic, however, is Renée Zellweger's performance as Judy Garland. We think Zellweger is magnificent in the titular role. She does a terrific job and goes all-in, capturing both the spirit and the struggles of the famed actress with Oscar-worthy ease. Zellweger also showcases her impressive singing chops again (we thought she did a great job in the Oscar-winning "Chicago"), emulating and capturing the wobbliness and runs and cracks of Garland's trill. If nothing else, "Judy" is worth watching for her performance alone. The rest of the cast is good, but, much like Garland upstaged pretty much anyone else, this is basically Zellweger's show from start to finish. There are also some fabulous costumes, wigs, and make-up work, all of which aid in bringing Judy's dynamic look to life in ways that make Zellweger nearly unrecognizable from some angles.
"I'm coming straight back for you." (Image Source)
Rupert Goold's "Judy" doesn't add any new insight for those familiar with Garland's storied life, but it was compelling enough for us to recommend it.
RT Rating: 83%
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Posted by Lolo at Sunday, November 10, 2019
Labels: 2010's, 2019, biography, drama, history, movie review | {
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\section{Introduction}
The link between operator semigroups and abstract Cauchy problems
through the infinitesimal behaviour of the semigroup is a classic question
in the theory of partial differential equations. A fundamental result is that
strongly continuous semigroups of bounded linear operators on Banach
spaces are uniquely characterized by their infinitesimal generator. In a
nonlinear setting, Alvarez et al.\ \cite{Alvarez93} provide an axiomatic
foundation for viscosity solutions to fully nonlinear second-order partial
differential equations based on monotone semigroups which are defined
on the space of bounded uniformly continuous functions and satisfy suitable
regularity and locality assumptions. This approach was picked up later
by Biton~\cite{Biton01} for semigroups on more general spaces of continuous
functions with a certain behaviour at infinity. While these works mainly focus
on the existence and axiomatization of second-order differential operators
through semigroups, the uniqueness of the associated semigroups in terms
of their generator is not yet fully clarified, cf.\ the discussion
in~\cite[Section 5]{Biton01}. The key ideas of viscosity solutions are local
comparisons with smooth functions and regularizations by introducing
additional viscosity terms. We refer to Fleming and
Soner~\cite[Chapter~II.3]{Fleming-Soner06} for an intuitive discussion
on viscosity solutions in an operator-theoretic setting based on abstract
dynamic programming principles. In the present paper we follow a different
approach which is closer to the theory of linear semigroups and based on
invariant sets which are suitable domains for a weaker definition of the
generator. In order to provide uniqueness results for semigroups based on
their infinitesimal behaviour, it is crucial that the domain of the generator
is invariant under the semigroup. If we drop the linearity, the invariance may
fail, see \cite[Example~5.2]{DKN21+}.\ Additionally, the domain might be even
empty, see Crandall and Liggett~\cite[Section~4]{Crandall-Liggett71}.
For convex semigroups, the invariance can, in general, only be guaranteed
for spaces with order continuous norm, see~\cite{DKN2021}. In contrast to
$L^p$-spaces and Orlicz hearts, which might be too large to handle the
nonlinearity, spaces of continuous functions lack this property. Hence, we
are looking for an invariant set on which we can define the generator in a
weaker form such that the semigroup still represents the unique solution to
the associated abstract Cauchy problem. Similar to Rademacher's theorem,
it turns out that Lipschitz continuous paths of the semigroup are differentiable
in a weaker sense, i.e., the generator can be defined with respect to
$\Gamma$-convergence.
Let $S:=(S(t))_{t\geq 0}$ be a strongly continuous semigroup of convex
monotone operators on a suitable space of continuous functions. On
the so-called upper Lipschitz, which is invariant under the semigroup,
we can define the upper $\Gamma$-generator
\[ A_\Gamma^+ f:=\Glimsup_{h\downarrow 0}\frac{S(h)f-f}{h}. \]
Likewise we define the $\Gamma$-generator $A_\Gamma f$ if the limes superior
in the previous equation can be replaced by a $\Gamma$-limit. Since the
function $A_\Gamma^+ f$ is merely upper semicontinuous, an extension of $S$
to the set of all upper semicontinuous functions is necessary in order to
define the term $S(t)A_\Gamma^+ f$. For that purpose, we follow the ideas of
Beer~\cite{Beer1978}. Under the assumption that $S$ is continuous from
above, there exists a unique extension which is upper semicontinuous with
respect to $\Gamma$-convergence. The latter property is crucial for our
work. Moreover, on the set of upper semicontinuous functions, the concept
of $\Gamma$-convergence satisfies desirable stability properties, see, e.g.,
Dal Maso~\cite{DalMaso} and Rockafellar and Wets~\cite{RW}.
Our first main result is a comparison principle which implies, in particular,
that convex monotone semigroups are uniquely determined by their upper
$\Gamma$-generator on their upper Lipschitz set, see Theorem~\ref{thm:comp}
and Corollary~\ref{cor:comp}. Second, under additional assumptions,
we show that $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n$ if $(f_n)_{n\in\mathbb{N}}$
is a suitable approximating sequence for $f$, see Theorem~\ref{thm:lb}.
Typically, the approximating sequence can be constructed via convolutions
with mollifiers or sup-inf-convolutions. In particular, we obtain an explicit
description of $A_\Gamma f$ if, for smooth functions, the $\Gamma$-generator
is given as a convex functional of certain partial derivatives. It was shown in
Alvarez et al.~\cite{Alvarez93} and Biton~\cite{Biton01} that this is the case
for typical fully nonlinear PDEs. Third, we study approximation schemes of
the form
\[ S(t)f=\lim_{l\to\infty}\big(I(2^{-{n_l}}t)\big)^{2^{n_l} t}f \]
which are known as Chernoff approximations~\cite{chernoff1968, chernoff1974}
or Trotter formulae~\cite{trotter1958, trotter1959}. In this case, key
properties of $S$ can be obtained from the corresponding properties
of $I$, see Theorem~\ref{thm:I} and Theorem~\ref{thm:I3}.
The semigroups we consider are upper semicontinuous with respect to
$\Gamma$-convergence and sequentially continuous in buc\footnote{A
sequence converges buc if and only if it is bounded and converges
uniformly on compacts. On Polish spaces, a sequence converges buc if
and only if it converges in the strict topology, see~\cite{sentilles}.}, see
Lemma~\ref{lem:usc} and Lemma~\ref{lem:uniform}. The idea of weakening
topological properties of the semigroup is already present in the literature.
Goldys and Kocan~\cite{Goldys}, van Casteren~\cite{vanCasteren},
Kunze~\cite{Kunze} and Kraaij~\cite{kraaij19strict} study linear semigroups
in strict topologies, see also Kraaij~\cite{Kraaij16} and Yosida~\cite{Yoshida}
for semigroups in locally convex spaces. Furthermore, equi-continuity in the
strict topology is suitable for stability results.\ Kraaij~\cite{Kraaij22}
provides convergence results for nonlinear semigroups based on the
connection between viscosity solutions to Hamilton--Jacobi equations and
pseudo-resolvents and, in~\cite{Kraaij19}, $\Gamma$-convergence of
functionals on path-spaces is established.
A classical approach to nonlinear semigroups concentrates on the study
of maximal monotone or m-accre\-tive operators, see, e.g., Barbu~\cite{Barbu10},
B\'enilan and Crandall~\cite{Benilan-Crandall91}, Br\'ezis~\cite{Brezis71},
Kato~\cite{Kato67} and the references therein. However, there exist
simple examples of operators which are accretive but not m-accretive,
see, e.g.,~\cite[Example~5.2]{DKN21+}. This obstacle was one of the
motivations for the study of viscosity solutions to fully nonlinear equations,
cf.\ Lions~\cite{Lions}, Crandall et.al.~\cite{Crandall-Ishii-Lions92} and
Evans~\cite[Section~4]{Evans87}.
In Section~\ref{sec:examples}, the abstract results are applied to several
classes of examples. In Subsection~\ref{sec:control}, we show that dynamic
stochastic optimal control problems for drift and volatility controlled diffusions
can be approximated by iterating a corresponding static control problem,
where we only take simple deterministic controls. Moreover, the study of the
so-called symmetric Lipschitz set yields a regularity result for the corresponding
PDE even in the degenerate case. In Subsection~\ref{sec:infdim}, we show that,
in the sublinear case, the previous approximation result can be lifted to an
infinite-dimensional setting. In Subsection~\ref{sec:wasserstein}, we show that
non-parametric Wasserstein perturbations of transition semigroups asymptotically
coincide with perturbations which have a finite-dimensional parameter space.
As a byproduct, we recover the Talagrand $T_2$ inequality for the normal distribution.
\section{Comparison of convex monotone semigroups on Lipschitz sets}
\label{sec:compare}
\subsection{Setup and $\Gamma$-convergence}
Let $(X,d)$ be a complete separable metric space and denote by
$B(x,r):=\{y\in X\colon d(x,y)\leq r\}$ the closed ball with radius
$r\geq 0$ around $x\in X$. We endow the set of all functions with the
pointwise order, i.e., $f\leq g$ if and only if $f(x)\leq g(x)$ for all
$f,g\colon X\to\Rinf$ and $x\in X$. All order-related notions
(sup, inf, max, min, $\limsup$, etc.) for such functions are understood
with respect to this order. We define $f\vee g:=\max\{f,g\}$,
$f\wedge g:=\min\{f,g\}$, $f ^+:=f\vee 0$ and $f^-:=-(f\wedge 0)$
for all $f,g\colon X\to\Rinf$, where $f^-(x):=\infty$ if $f(x)=-\infty$.
We slightly relax the supremum norm in order to include unbounded
functions with controlled growth behaviour at infinity. For this, we fix
a bounded continuous function $\kappa\colon X\to (0,\infty)$ and
consider the $\kappa$-weighted supremum norm
\[ \|f\|_\kappa:=\sup_{x\in X}|f(x)|\kappa(x)\in [0,\infty]
\quad\mbox{for all } f\colon X\to\Rinf. \]
Let ${\rm C}_\kappa$ be the space of all continuous functions $f\colon X\to\mathbb{R}$ with
$\|f\|_\kappa<\infty$ and ${\rm U}_\kappa$ be the set of all upper semicontinuous
functions $f\colon X\to[-\infty,\infty)$ with $\|f^+\|_\kappa<\infty$. If $\kappa\equiv 1$,
then $\|\cdot\|_\kappa$ is the usual supremum norm $\| \cdot \|_\infty$, ${\rm C}_\kappa$
coincides with the space ${\rm C}_{\rm b}$ of all bounded continuous functions and
${\rm U}_\kappa$ is the set ${\rm U}_{\rm b}$ of all upper semicontinuous functions which are
bounded above by a real constant. Since the mapping
\[ {\rm C}_\kappa\to{\rm C}_{\rm b},\; f\mapsto f\kappa \]
is an order-preserving linear isometric isomorphism, the space ${\rm C}_\kappa$ is
a Banach lattice. Note that
\[ {\rm U}_\kappa=({\rm C}_\kappa)_\delta
:=\Big\{\inf_{n\in \mathbb{N}} f_n\colon (f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa\Big\}.
\footnote{It holds
$f(x)=\inf_{n\in\mathbb{N}}\sup_{y\in X}\frac{1}{\kappa(x)}
\big(\max\{(f\kappa)(y),-n\}-n^2 d(x,y)\big)$
for all $f\in{\rm U}_\kappa$ and $x\in X$.} \]
Let $(f_n)_{n\in\mathbb{N}}\subset{\rm U}_\kappa$ be a sequence and $f\in{\rm U}_\kappa$. We write
$f_n\downarrow f$ if $(f_n)_{n\in\mathbb{N}}$ decreases pointwise to $f$. If
$f_n$ and $f$ are real-valued, we say that $f_n\to f$ uniformly on
compacts if $\sup_{x\in K}|f(x)-f_n(x)|\to 0$ for every compact set
$K\subset X$. Furthermore, a set $F\subset {\rm U}_\kappa$ is called bounded
if $\sup_{f\in F}\|f\|_\kappa<\infty$ and bounded above if
$\sup_{f\in F}\|f^+\|_\kappa<\infty$.
\begin{definition}
For every sequence $(f_n)_{n\in\mathbb{N}}\subset {\rm U}_\kappa$, which is bounded above,
we define
\[ \Big(\Glimsup_{n\to\infty}f_n\Big)(x)
:=\sup\Big\{\limsup_{n\to\infty}f_n(x_n)\colon
(x_n)_{n\in\mathbb{N}}\subset X\mbox{ with } x_n\to x\Big\}\in\Rinf \]
for all $x\in X$. Moreover, we say that $f=\Glim_{n\to\infty}f_n$ with
$f\in{\rm U}_\kappa$ if, for every $x\in X$,
\begin{itemize}
\item $f(x)\geq\limsup_{n\to\infty}f_n(x_n)$ for every sequence
$(x_n)_{n\in\mathbb{N}}\subset X$ with $x_n\to x$,
\item $f(x)=\lim_{n\to\infty}f_n(x_n)$ for some sequence
$(x_n)_{n\in\mathbb{N}}\subset X$ with $x_n\to x$.
\end{itemize}
For every $t\geq 0$ and $(f_s)_{s\geq 0}\subset{\rm U}_\kappa$, which bounded
above, we define
\[ \Glimsup_{s\to t}f_s
:=\sup\Big\{\Glimsup_{n\to\infty}f_{s_n}\colon s_n\to t\Big\}\in{\rm U}_\kappa. \]
Furthermore, we say that $f=\Glim_{s\to t}f_s$ with $f\in{\rm U}_\kappa$ if
$f=\Glim_{n\to\infty}f_{s_n}$ for all sequences $(s_n)_{n\in\mathbb{N}}\subset [0,\infty)$
with $s_n\to t$.
\end{definition}
For further details and a summary of basic results on $\Gamma$-convergence,
we refer to Appendix~\ref{app:gamma}. The following geometric characterization
of the $\Glimsup$ is based on the work of Beer~\cite{Beer1978}. We will use
it throughout this work to link $\Gamma$-convergence with monotone
convergence and $\Gamma$-upper semicontinuity with continuity from above.
\begin{remark} \label{rem:fe}
For every $f\in{\rm U}_\kappa$, there exists a family $(\overline{f}^\epsilon)_{\varepsilon>0}\subset{\rm U}_\kappa$ with
\[ \overline{f}^\epsilon\downarrow f \quad\mbox{as } \varepsilon\downarrow 0
\quad\mbox{and}\quad
-\tfrac{1}{\varepsilon}\leq\overline{f}^\epsilon\kappa\leq\|f^+\|_\kappa+\varepsilon
\quad\mbox{for all } \varepsilon>0.\]
Furthermore, let $(f_n)_{n\in\mathbb{N}}\subset{\rm U}_\kappa$ be bounded above. Then, it holds
$\Glimsup_{n\to\infty}f_n\leq f$ if and only if, for every
$\varepsilon>0$ and $K\subset X$ compact, there exists $n_0\in\mathbb{N}$ such that
\[ f_n(x)\leq\overline{f}^\epsilon(x) \quad\mbox{for all } x\in K \mbox{ and } n\geq n_0.\]
The family $(\overline{f}^\epsilon)_{\varepsilon>0}$ is explicitly constructed in Appendix~\ref{app:gamma}.
\end{remark}
\subsection{Convex monotone semigroups on Lipschitz sets}
Let $S:=(S(t))_{t\geq 0}$ be a family of operators $S(t)\colon{\rm C}_\kappa\to{\rm U}_\kappa$.
The \emph{norm generator} is defined by
\[ A\colon D(A)\to{\rm C}_\kappa,\; f\mapsto\lim_{h\downarrow 0}\frac{S(h)f-f}{h}, \]
where the domain $D(A)$ consists of all $f\in{\rm C}_\kappa$ such that $S(t)f\in{\rm C}_\kappa$
for all $t\geq 0$, the previous limit exists with respect to the norm
$\|\cdot\|_\kappa$ and $S(s+t)f=S(s)S(t)f$ for all $s,t\geq 0$. As previously
discussed, the assumption $S(t)\colon D(A)\to D(A)$ for all $t\geq 0$ is, in
general, too restrictive. We point out that this problem can not be avoided
by restricting the semigroup and the generator to a subspace of ${\rm C}_\kappa$.
Hence, instead of considering the largest set on which the right derivative
of the trajectories $t\mapsto S(t)f$ exists with respect to the norm, we
consider the largest set on which the trajectories are merely (upper)
Lipschitz continuous. For these trajectories the right derivative can still
be defined as a limes superior. This brings us to the following crucial
definition.
\begin{definition} \label{def:Lset}
The \emph{upper Lipschitz set} $\mathcal{L}^S_+$ consists of all $f\in{\rm C}_\kappa$
such that
\begin{enumerate}
\item $S(t)f\in{\rm C}_\kappa$ for all $t\geq 0$,
\item $S(s+t)f=S(s)S(t)f$ for all $s,t\geq 0$,
\item there exist $h_0>0$ and $c\geq 0$ with $\big(S(h)f-f\big)\kappa\leq ch$
or all $h\in [0,h_0]$.
\end{enumerate}
Furthermore, we define \emph{the upper $\Gamma$-generator} by
\[ A_\Gamma^+ f:=\Glimsup_{h\downarrow 0}\frac{S(h)f-f}{h}\in{\rm U}_\kappa
\quad\mbox{for all } f\in\mathcal{L}^S_+. \]
\end{definition}
By definition, it holds $D(A)\subset\mathcal{L}^S_+$ and $Af=A_\Gamma^+ f$ for all
$f\in D(A)$. Furthermore, we will see in Section~\ref{sec:approx} that,
under additional assumptions, the limes superior in the previous definition
can be replaced by a limit. The invariance of the upper Lipschitz set, i.e.,
$S(t)\colon\mathcal{L}^S_+\to\mathcal{L}^S_+$ for all $t\geq 0$, does not require further
assumptions and is shown in Remark~\ref{rem:Lset} below. While $Af\in{\rm C}_\kappa$
holds by definition, $A_\Gamma^+ f$ is not necessarily continuous and may take
the value $-\infty$. Hence, in order to to give the term $S(t)A_\Gamma^+ f$ a
meaning, an extension of $S$ from ${\rm C}_\kappa$ to ${\rm U}_\kappa$ is necessary. Moreover,
the argumentation in this article relies heavily on the fact that the extension
is $\Gamma$-upper semicontinuous in time and continuous from above.
This can be achieved under the following assumption which holds throughout
the rest of this section. Let $B_{{\rm C}_\kappa}(r):=\{f\in{\rm C}_\kappa\colon\|f\|_\kappa\leq r\}$
and $B_{{\rm U}_\kappa}(r):=\{f\in{\rm U}_\kappa\colon\|f\|_\kappa\leq r\}$ be the closed balls
with radius $r\geq 0$ around zero in ${\rm C}_\kappa$ and ${\rm U}_\kappa$, respectively.
\begin{assumption} \label{ass:S}
The family $S:=(S(t))_{t\geq 0}$ of operators $S(t)\colon{\rm C}_\kappa\to{\rm U}_\kappa$
satisfies the following conditions:
\begin{enumerate}[label=(S\arabic*)]
\item \label{S1} The operator $S(t)$ is convex and monotone,\footnote{The
mapping ${\rm C}_\kappa\to\Rinf,\; f\mapsto (S(t)f)(x)$ is convex and monotone for all
$x\in X$.} and $S(t)0=0$ for all $t\geq 0$.
\item \label{S2} For every $t\geq 0$, the operator $S(t)$ is continuous
from above, i.e., $S(t)f_n\downarrow S(t)f$ for all sequences
$(f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa$ and $f\in{\rm C}_\kappa$ with $f_n\downarrow f$.
\item \label{S3} $\Glimsup_{s\to t}S(s)f\leq S(t)f$ and $S(0)f=f$ for all
$t\geq 0$ and $f\in{\rm C}_\kappa$.
\item \label{S4} $\sup_{s\in [0,t]}\sup_{f\in B_{{\rm C}_\kappa}(0,r)}\|S(s)f\|_\kappa<\infty$
for all $r,t\geq 0$.
\end{enumerate}
\end{assumption}
Since ${\rm C}_\kappa$ is a Banach lattice and $S(t)$ is convex, it is sufficient to require
condition~\ref{S2} for some $f\in{\rm C}_\kappa$, e.g., $f=0$. Although, in many examples,
$S$ is a priori only defined on a closed subspace $\mathcal{C}\subset{\rm C}_\kappa$, we assume
that $S$ is defined on the whole space ${\rm C}_\kappa$. The reason behind this is the fact
that the property ${\rm U}_\kappa=({\rm C}_\kappa)_\delta$ together with condition~\ref{S2} ensures
the existence of a pointwise extension to ${\rm U}_\kappa$ which is again continuous from
above and satisfies the conditions~\ref{S1}-\ref{S4} for all $f\in{\rm U}_\kappa$. If
${\rm U}_\kappa=\mathcal{C}_\delta$, it is sufficient to state Assumption~\ref{ass:S} with $\mathcal{C}$
instead of ${\rm C}_\kappa$. We conclude this subsection with the crucial observation
that $S$ is simultaneously upper semicontinuous in the variables $t$ and $f$,
see Lemma~\ref{lem:usc} below. Moreover, we state some further comments
about Definition~\ref{def:Lset} and Assumption~\ref{ass:S}. Let ${\rm B}_\kappa$ be the
space of all Borel measurable functions $f\colon X\to\Rinf$ with
$\|f^+\|_\kappa<\infty$.
\begin{remark} \label{rem:S}
We discuss the extension of $S$ from ${\rm C}_\kappa$ to ${\rm U}_\kappa$. For a proof, we
refer to Corollary~\ref{cor:ext}.
\begin{enumerate}
\item Fix $t\geq 0$. Since $S(t)\colon{\rm C}_\kappa\to{\rm U}_\kappa$ is continuous from above and
${\rm U}_\kappa=({\rm C}_\kappa)_\delta$, there exists a unique extension $S(t)\colon{\rm U}_\kappa\to{\rm U}_\kappa$ which
is continuous from above. The family of extended operators satisfies the
conditions~\ref{S1}-\ref{S4} with ${\rm U}_\kappa$ instead of ${\rm C}_\kappa$. In addition, for every
$x\in X$, the functional
\[ {\rm U}_\kappa\to\Rinf,\; f\mapsto (S(t)f)(x) \]
can even be extended to ${\rm B}_\kappa$ in such a way that, for every $\varepsilon>0$
and $c\geq 0$, there exists a compact set $K\subset X$ with
$\big(S(t)\big(\frac{c}{\kappa}\mathds{1}_{K^c}\big)\big)(x)\leq\varepsilon$.
Here, $K^c:=X\backslash K$.
\item Fix $t\geq 0$ and $K\subset X$ compact. Let $(f_n)_{n\in\mathbb{N}}\subset{\rm U}_\kappa$
be a sequence with $f_n\downarrow 0$. By part~(i), the mapping
\[ [0,t]\times K\to\mathbb{R},\; (s,x)\mapsto \big(S(s)f_n\big)(x) \]
is upper semicontinuous for all $n\in\mathbb{N}$ and decreases pointwise to zero as
$n\to\infty$. It thus follows from Dini's theorem that
\[ \sup_{(s,x)\in [0,t]\times K}\big(S(s)f_n\big)(x)\downarrow 0
\quad\mbox{as } n\to\infty. \]
Moreover, for every $\varepsilon>0$ and $c\geq 0$, there exists a compact set
$K_1\subset X$ with
\[ \sup_{(s,x)\in [0,t]\times K}\big(S(s)
\big(\tfrac{c}{\kappa}\mathds{1}_{K_1^c}\big)\big)(x)\leq\varepsilon. \]
\end{enumerate}
\end{remark}
\begin{lemma} \label{lem:usc}
Let $(f_n)_{n\in \mathbb{N}}\subset {\rm U}_\kappa$ be bounded above and
$(t_n)_{n\in\mathbb{N}}\subset [0,\infty)$ a convergent sequence. Define
$f:=\Glimsup_{n\to\infty}f_n$ and $t:=\lim_{n\to\infty}t_n$. Then,
\[ \Glimsup_{n\to \infty}S(t_n)f_n\leq S(t)f. \]
\end{lemma}
\begin{proof}
Let $\varepsilon\in (0,1]$ and $K\subset X$ compact. By Remark~\ref{rem:fe},
there exists $n_0\in\mathbb{N}$ with $f_n(x)\leq\overline{f}^\epsilon(x)$ for all $x\in K$ and $n\geq n_0$.
We use the fact that $\overline{f}^\epsilon\geq-\nicefrac{1}{\varepsilon\kappa}$ together with
the monotonicity of $S(t_n)$ to come up with
\[ S(t_n)f_n\leq S(t_n)\big(\overline{f}^\epsilon+\tfrac{c_\varepsilon}{\kappa}\mathds{1}_{K^c}\big)
\quad\mbox{for all } n\geq n_0, \]
where $c_\varepsilon:=\sup_{n\in\mathbb{N}}\|f_n^+\|_\kappa+\nicefrac{1}{\varepsilon}<\infty$.
For all $\lambda\in (0,1)$, the convexity of $S(t_n)$ implies
\[ S(t_n)\big(\overline{f}^\epsilon+\tfrac{c_\varepsilon}{\kappa}\mathds{1}_{K^c}\big)
\leq \lambda S(t_n)\big(\tfrac{1}{\lambda}\overline{f}^\epsilon\big)
+(1-\lambda)S(t_n)\Big(\tfrac{c_\varepsilon}{\kappa (1-\lambda)}\mathds{1}_{K^c}\Big). \]
Hence, it follows from Lemma~\ref{lem:gamma}(iv) and Remark~\ref{rem:S}(i)
that
\[ \Glimsup_{n\to\infty}S(t_n)f_n\leq\lambda S(t)\big(\tfrac{1}{\lambda}\overline{f}^\epsilon\big)
+(1-\lambda)\sup_{n\in \mathbb{N}}S(t_n)\Big(\tfrac{c_\varepsilon}{\kappa (1-\lambda)}\mathds{1}_{K^c}\Big). \]
Since $K\subset X$ is arbitrary, we can use Remark~\ref{rem:S}(ii) to conclude that
\[ \Glimsup_{n\to\infty}S(t_n)f_n\leq\lambda S(t)\big(\tfrac{1}{\lambda}\overline{f}^\epsilon\big). \]
Furthermore, $\overline{f}^\epsilon\kappa\leq\|f^+\|_\kappa+\varepsilon\leq c_\varepsilon$ and the
monotonicity of $S(t)$ yield
\[ \Glimsup_{n\to\infty}S(t_n)f_n\leq\lambda S(t)\big(\tfrac{1}{\lambda}\overline{f}^\epsilon\big)
\leq\lambda S(t)\Big(\overline{f}^\epsilon+\big(\tfrac{1}{\lambda}-1\big)\tfrac{c_\varepsilon}{\kappa}\Big). \]
Since $S(t)$ is continuous from above, the right-hand side converges to
$S(t)\overline{f}^\epsilon$ as $\lambda\uparrow 1$. Thus, it follows from $\overline{f}^\epsilon\downarrow f$
that
\[ \Glimsup_{n\to\infty}S(t_n)f_n\leq S(t)\overline{f}^\epsilon\downarrow S(t)f
\quad\mbox{as } \varepsilon\downarrow 0. \qedhere \]
\end{proof}
\begin{lemma} \label{lem:uniform}
Let $(f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa$ be a bounded sequence and $f\in{\rm C}_\kappa$
with $f_n\to f$ uniformly on compacts. Then, $S(t)f_n\to S(t)f$
uniformly on compacts for all $t\geq 0$.
\end{lemma}
\begin{proof}
Let $K\subset X$ be compact and $\varepsilon>0$. Choose $\delta,\lambda\in (0,1)$
with
\begin{equation} \label{eq:uniform}
(1-\lambda)\|S(t)f\|_\kappa<\tfrac{\varepsilon}{3} \quad\mbox{and}\quad
c\|(1-\lambda)f+\delta\|_\kappa<\tfrac{\varepsilon}{3},
\end{equation}
where the constant $c\geq 0$ will be fixed later. By Remark~\ref{rem:S}(ii),
there exists a compact set $K_1\subset X$ with $K\subset K_1$ such that
\[ \sup_{x\in K}\left((1-\lambda)S(t)
\big(\tfrac{c}{(1-\lambda)\kappa}\mathds{1}_{K_1^c}\big)\right)(x)
<\tfrac{\varepsilon}{3}. \]
Since $f_n\to f$ uniformly on compacts, there exists $n_0\in\mathbb{N}$ with
$f_n\leq f+\delta+\frac{c_1}{\kappa}\mathds{1}_{K_1^c}$ for all $n\geq n_0$,
where $c_1:=\sup_{n\in\mathbb{N}}2\|f_n\|_\kappa$. Monotonicity and convexity of
$S(t)$ imply
\[ S(t)f_n\leq\lambda S(t)\big(\tfrac{f+\delta}{\lambda}\big)
+(1-\lambda)S(t)\Big(\tfrac{c_1}{(1-\lambda)\kappa}\mathds{1}_{K_1^c}\Big)
\quad\mbox{for all } n\geq n_0. \]
By Lemma~\ref{lem:lip}(ii), there exists a constant $c_2\geq 0$ such that
\[ \left\|\lambda S(t)\big(\tfrac{f+\delta}{\lambda}\big)-S(t)f\right\|_\kappa
\leq c_2\|(1-\lambda)f+\delta\|_\kappa+(1-\lambda)\|S(t)f\|_\kappa. \]
Now, choose $\delta,\lambda\in (0,1)$ such that condition~\eqref{eq:uniform}
is satisfied with $c:=c_1\vee c_2$. Then,
\[ \big(S(t)f_n\big)(x)\leq\big(S(t)f\big)(x)+\varepsilon
\quad\mbox{for all } n\geq n_0 \mbox{ and } x\in K. \]
Since $(f_n)_{n\in\mathbb{N}}$ is bounded, we can change the role of $f$ and $f_n$
in the previous considerations in order to obtain the reverse estimate.
\end{proof}
The following lemma shows that the upper Lipschitz set is invariant.
\begin{lemma} \label{lem:inv}
It holds $S(t)\colon\mathcal{L}^S_+\to\mathcal{L}^S_+$ for all $t\geq 0$.
\end{lemma}
\begin{proof}
Let $f\in\mathcal{L}^S_+$. Choose $h_0\in (0,1]$ and $c\geq 0$ such that
$\big(S(h)f-f\big)\kappa\leq ch$ for all $h\in [0,h_0]$. We use
$S(h)S(t)f=S(h+t)=S(t+h)=S(t)S(h)f$, Lemma~\ref{lem:lambda},
the monotonicity of $S(t)$ and Lemma~\ref{lem:lip} to estimate
\begin{align*}
\left(\frac{S(h)S(t)f-S(t)f}{h}\right)\kappa
&\leq \left(S(t)\left(f+\frac{(S(h)f-f)^+}{h}\right)-S(t)f\right)\kappa \\
&\leq c'\left\|\frac{(S(h)f-f)^+}{h}\right\|_\kappa\leq c'ch
\quad\mbox{for all } h\in (0,h_0],
\end{align*}
where $c'\geq 0$ is a constant independent of $h\in (0,h_0]$.
\end{proof}
In the next remark, we give an outlook on stronger versions of the Lipschitz
set. Furthermore, we discuss some results about the Lipschitz set from the
theory of linear semigroups. Most of these results rely on the reflexivity of
the underlying Banach space, a property which ${\rm C}_\kappa$ does not have.
\begin{remark} \label{rem:Lset} {\rule{0mm}{1mm}\\[-3.25ex]\rule{0mm}{1mm}}
\begin{enumerate}
\item Similar to $\mathcal{L}^S_+$, one can define the \emph{Lipschitz set} $\mathcal{L}^S$,
consisting of all $f\in{\rm C}_\kappa$ with
\begin{itemize}
\item $S(t)f\in{\rm C}_\kappa$ for all $t\geq 0$,
\item $S(s+t)f=S(s)S(t)f$ for all $s,t\geq 0$,
\item there exists $h_0>0$ and $c\geq 0$ with $\|S(h)f-f\|_\kappa\leq ch$
for all $h\in [0,h_0]$.
\end{itemize}
Furthermore, we define the \emph{symmetric Lipschitz set}
$\mathcal{L}^S_{\sym}:=\{f\in\mathcal{L}^S\colon -f\in\mathcal{L}^S\}$. While $S(t)\colon\mathcal{L}^S\to\mathcal{L}^S$
for all $t\geq 0$ follows by a similar argumentation as in the proof of
Lemma~\ref{lem:inv}, the invariance of $\mathcal{L}^S_{\sym}$ can, in general, not be
guaranteed. However, in several examples, the symmetric Lipschitz set is
invariant and can, in contrast to $\mathcal{L}^S_+$ and $\mathcal{L}^S$, be determined
explicitly. This leads to regularity results for the associated semigroup,
see~\cite{BK20, BK21} and Subsection~\ref{sec:control}.
\item Let $T:=(T(t))_{t\geq 0}$ be a be a strongly continuous semigroup of
bounded linear operators on a Banach space $\mathcal{X}$. For simplicity,
we assume that the growth bound of $T$ is negative, i.e., there exist $c\geq 0$
and $\omega<0$ with $\|T(t)x\|\leq c e^{\omega t}\|x\|$ for all $x\in\mathcal{X}$.
Then, the set
\[ F_1:=\Big\{x\in\mathcal{X}\colon\sup_{h>0}\Big\|\frac{T(h)x-x}h\Big\|<\infty\Big\} \]
is called the \emph{Favard space} or the \emph{saturation class} of $T$, a notion
coming from approximation theory, see, e.g.,~\cite[Section~2.1]{Butzer-Nessel71}
and~\cite[Section~II.5.b]{Engel-Nagel00}. Denoting by $A$ the norm generator
of $T$, it is known that $F_1=D(A)$ holds if $\mathcal{X}$ is reflexive,
see~\cite[Theorem~2.1.2]{Butzer-Nessel71}. If $T$ is even holomorphic, then
$F_1=(\mathcal{X},D(A))_{1,\infty}$, see~\cite[Proposition~2.2.2]{Lunardi95}.
Here, $(\cdot,\cdot)_{1,\infty}$ stands for the real interpolation functor. However,
for non-reflexive $\mathcal{X}$, an explicit description of $F_1$ seems to be
unknown in many cases.
\end{enumerate}
\end{remark}
\subsection{Comparison and uniqueness}
Based on the preliminary work of the previous two subsections, we can
now prove the following comparison principle which is the main result
of Section~\ref{sec:compare}. Basically, a semigroup satisfying
Assumption~\ref{ass:S} can be seen as the minimal $\Gamma$-supersolution
of the associated abstract Cauchy problem. Furthermore, the semigroup
is uniquely determined by its upper $\Gamma$-generator. In the next
section, we will prove approximation results which show that, in many
examples, the evaluation of the generator at smooth functions is
sufficient to determine the $\Gamma$-generator and thus the semigroup.
\begin{theorem} \label{thm:comp}
Fix $T\geq 0$ and $f\in\mathcal{L}^S_+$. Let $u\colon [0,T]\to\mathcal{L}^S_+$ be a bounded
function with $u(0)=f$ and $\Glimsup_{s\to t} u(s)\leq u(t)$ for all $t\in [0,T]$.
Assume that, for all $t\in [0,T)$,
\begin{align}
\limsup_{h\downarrow 0} \Big\|\Big(\frac{u(t+h)-u(t)}{h}\Big)^-\Big\|_\kappa &<\infty,
\label{eq:comp} \\
\Glimsup_{h\downarrow 0}\Big(A_\Gamma^+ u(t)-\frac{u(t+h)-u(t)}{h}\Big) &\leq 0.
\label{eq:comp2}
\end{align}
Then, it holds $S(t)f\leq u(t)$ for all $t\in [0,T]$.
\end{theorem}
\begin{proof}
Fix $t\in [0,T]$. We prove that the function $v\colon [0,t]\to\mathcal{L}^S_+,\; s\mapsto S(t-s)u(s)$
satisfies $v(0)\leq v(s)$ for all $s\in [0,t]$. First, we show that
\begin{equation} \label{eq:v}
\liminf_{h\downarrow 0}\frac{v(s+h)-v(s)}{h}\geq 0
\quad\mbox{for all } s\in [0,t).
\end{equation}
Let $s\in [0,t)$. Because of $u(s)\in\mathcal{L}^S_+$ and condition~\eqref{eq:comp},
there exists $h_0>0$ with
\begin{equation} \label{eq:c}
c:=\sup_{h\in (0,h_0]}\max\left\{\Big\|\Big(\frac{S(h)u(s)-u(s)}{h}\Big)^+\Big\|_\kappa,
\Big\|\Big(\frac{u(s+h)-u(s)}{h}\Big)^-\Big\|_\kappa\right\}<\infty.
\end{equation}
For every $h\in (0,h_0]$, we define
\[ f_h:=\max\left\{\frac{S(h)u(s)-u(s)}{h},-\frac{c}{\kappa}\right\}
\quad\mbox{and}\quad
g_h:=\max\left\{-\frac{u(s+h)-u(s)}{h},-\frac{c}{\kappa}\right\}. \]
It follows from Lemma~\ref{lem:gamma}(vi) that
\[ f:=\Glimsup_{h\downarrow 0} f_h=\max\left\{A_\Gamma ^+ u(s),-\frac{c}{\kappa}\right\}. \]
Furthermore, we can use inequality~\eqref{eq:comp2}, equation~\eqref{eq:c}
and Lemma~\ref{lem:gamma}(vi) to estimate
\begin{equation} \label{eq:0}
\Glimsup_{h\downarrow 0}\, (f+g_h)\leq 0.
\end{equation}
Let $\varepsilon>0$. By the boundedness of $u$ and condition~\ref{S4}, there exists
$\lambda\in (0,1]$ such that
\begin{equation} \label{eq:epsilon}
\sup_{a,b\in [0,t]}\lambda\|S(a)u(b)\|_\kappa<\varepsilon.
\end{equation}
Lemma~\ref{lem:lambda} and inequality~\eqref{eq:epsilon} imply
\begin{align*}
&-\liminf_{h\downarrow 0}\frac{v(s+h)-v(s)}{h}
=\limsup_{h\downarrow 0}\frac{v(s)-v(s+h)}{h} \\
&=\limsup_{h\downarrow 0}\frac{S(t-s-h)S(h)u(s)-S(t-s-h)u(s+h)}{h} \\
&\leq\limsup_{h\downarrow 0}\lambda\left(S(t-s-h)\left(\frac{S(h)u(s)-u(s+h)}{\lambda h}
+u(s+h)\right)-S(t-s-h)u(s+h)\right) \\
&\leq\limsup_{h\downarrow 0}\lambda S(t-s-h)\left(\frac{f_h+g_h}{\lambda}+u(s+h)\right)
+\frac{\varepsilon}{\kappa}. \\
\end{align*}
Furthermore, the boundedness of $(g_h)_{h\in (0,h_0]}$, $(f_h)_{h\in (0,h_0]}$,
and $u$ together with condition~\ref{S1}, condition~\ref{S4} and Remark~\ref{rem:S}(ii)
ensure that we can apply Lemma~\ref{lem:limsup} to estimate
\[ \limsup_{h\downarrow 0} \lambda S(t-s-h)\left(\frac{f_h+g_h}{\lambda}+u(s+h)\right)
\leq\limsup_{h\downarrow 0} \lambda S(t-s-h)\left(\frac{f+g_h}{\lambda}+u(s+h)\right). \]
Lemma~\ref{lem:usc}, inequality~\eqref{eq:0}, Lemma~\ref{lem:gamma}(iv),
$\Glimsup_{h\downarrow 0}u(s+h)\leq u(s)$ and inequality~\eqref{eq:epsilon}
yield
\[ \limsup_{h\downarrow 0} \lambda S(t-s-h)\left(\frac{f+g_h}{\lambda}+u(s+h)\right)
\leq\lambda S(t-s)u(s)\leq\frac{\varepsilon}{\kappa}. \]
We combine the previous estimates and let $\varepsilon\downarrow 0$ to obtain
the inequality in~\eqref{eq:v}.
Second, we adapt the proof of~\cite[Lemma~1.1 in Chapter~2]{pazy} to show
$v(0)\leq v(s)$ for all $s\in [0,t]$. Let $x\in X$ and $\varepsilon >0$. Define
$v(s,x):=(v(s))(x)$ and
\[ v_\varepsilon(\cdot,x)\colon [0,t]\to\mathbb{R},\; s\mapsto v(s,x)+\varepsilon s.\]
Moreover, let $s_0:=\sup\{s\in [0,t]\colon v_\varepsilon(0,x)\leq v_\varepsilon(s,x)\}$.
From $\Glimsup_{r\to s} u(r)\leq u(s)$ and Lemma~\ref{lem:usc}, we obtain
that $v_\varepsilon(\cdot,x)$ is upper semicontinuous. In particular, it holds
$v_\varepsilon(0,x)\leq v_\varepsilon(s_0,x)$. By contradiction, we assume that
$s_0<t$. Let $(s_n)_{n\in\mathbb{N}}\subset (s_0,t]$ be a sequence with
$s_n\downarrow s_0$. It follows from
$v_\varepsilon(s_n,x)<v_\varepsilon(0,x)\leq v_\varepsilon(s_0,x)$ and
inequality~\eqref{eq:v} that
\[ 0\geq\limsup_{n\to\infty}\frac{v_\varepsilon(s_n,x)-v_\varepsilon(s_0,x)}{s_n-s_0}
=\limsup_{n\to\infty}\frac{v(s_n,x)-v(s_0,x)}{s_n-s_0}+\varepsilon\geq\varepsilon>0. \]
This implies $v_\varepsilon(0,x)\leq v_\varepsilon(t,x)$ and therefore
$v(0,x)\leq v(t,x)$ as $\varepsilon\downarrow 0$. In particular, we
obtain $S(t)f=v(0)\leq v(t)=u(t)$.
\end{proof}
Having a close look at the proof of the previous theorem, it seems natural to
replace the conditions~\eqref{eq:comp} and~\eqref{eq:comp2} by the
assumption that
\[ \limsup_{h\downarrow 0}\Big\|\Big(\frac{S(h)u(t)-u(t+h)}{h}\Big)^+\Big\|_\kappa<\infty
\quad\mbox{and}\quad
\Glimsup_{h\downarrow 0}\frac{S(h)u(t)-u(t+h)}{h}\leq 0. \]
Indeed, the previous theorem remains valid and the proof simplifies. In particular,
we do not need the technical Lemma~\ref{lem:limsup}. However, in examples, this
assumption is not verifiable. Lemma~\ref{lem:gamma}(iv) implies that
condition~\eqref{eq:comp2} is satisfied if
\[ A_\Gamma^+ u(t)\le{\Gliminf}_{h\downarrow 0}\frac{u(t+h)-u(t)}{h}
:=-\Big(\Glimsup_{h\downarrow 0}-\frac{u(t+h)-u(t)}{h}\Big).\]
Furthermore, it follows from Remark~\ref{rem:fe} that condition~\eqref{eq:comp2}
is satisfied if
\[ \lim_{h\downarrow 0}\Big(A_\Gamma^+ u(t)-\frac{u(t+h)-u(t)}{h}\Big)^+=0 \]
uniformly on compacts. We conclude this subsection with a comparison
result for convex monotone semigroups and a remark on the concept
of a $\Gamma$-supersolution.
\begin{corollary} \label{cor:comp}
Let $(T(t))_{t\geq 0}$ be another family of operators $T(t)\colon{\rm C}_\kappa\to{\rm U}_\kappa$
with Lipschitz set $\mathcal{L}^T$ and upper $\Gamma$-generator $B_\Gamma^+$.
Suppose that $T$ satisfies Assumption~\ref{ass:S}. Furthermore, let
$\mathcal{D}\subset\mathcal{L}^T\cap\mathcal{L}^S_+$ satisfy $T(t)\colon\mathcal{D}\to\mathcal{D}$ for all $t\geq 0$
and
\begin{equation} \label{eq:AB}
A_\Gamma^+ f\leq B_\Gamma^+ f \quad\mbox{for all } f\in\mathcal{D}.
\end{equation}
Then, it holds $S(t)f\leq T(t)f$ for all $t\geq 0$ and $f\in\mathcal{D}$ such that
the limit
\[ B_\Gamma^+ f=\lim_{h\downarrow 0}\frac{T(h)f-f}{h}\in{\rm C}_\kappa \]
exists uniformly on compacts.
\end{corollary}
\begin{proof}
Define $u(t):=T(t)f$ for all $t\geq 0$ and $f\in\mathcal{D}$. Assumption~\ref{ass:S}
and the invariance of $\mathcal{D}\subset\mathcal{L}^S_+$ imply that $u\colon [0,\infty)\to\mathcal{L}^S_+$
is a well-defined mapping with $u(0)=0$ which is bounded on compact
intervals and satisfies $\Glimsup_{s\to t} u(s)\leq u(t)$ for all $t\geq 0$.
Condition~\eqref{eq:comp} also holds due to the invariance of
$\mathcal{D}\subset\mathcal{L}^T$.
It remains to verify condition~\eqref{eq:comp2}. For every $t\geq 0$ and
$h>0$, we use $u(t)\in\mathcal{D}$ and inequality~\eqref{eq:AB} to estimate
\[ A_\Gamma^+ u(t)-\frac{u(t+h)-u(t)}{h}\leqB_\Gamma^+ u(t)-\frac{u(t+h)-u(t)}{h}. \]
Let $(h_n)_{n\in\mathbb{N}}\subset (0,\infty)$ be a sequence with $h_n\downarrow 0$.
For every $n\in\mathbb{N}$, we have
\begin{equation} \label{eq:BG}
B_\Gamma^+ u(t)-\frac{u(t+h_n)-u(t)}{h_n}
=B_\Gamma^+ u(t)-g_n+g_n-\frac{u(t+h_n)-u(t)}{h_n},
\end{equation}
where $g_n:=\frac{1}{h_n}\big(T(t)(f+h_nB_\Gamma^+ f)-T(t)f\big)$. It follows
from Lemma~\ref{lem:lambda} that
\begin{align*}
&T(t)(f+h_nB_\Gamma^+ f)-T(t)\left(\frac{T(h_n)f-f}{h_n}-B_\Gamma^+ f+f+h_nB_\Gamma^+ f\right) \\
&\leq g_n-\frac{u(t+h_n)-u(t)}{h_n}
=\frac{T(t)(f+h_nB_\Gamma^+ f)-T(t)T(h_n)f}{h_n} \\
&\leq T(t)\left(-\left(\frac{T(h_n)f-f}{h_n}-B_\Gamma^+ f\right)+T(h_n)f\right)
-T(t)T(h_n)f.
\end{align*}
Combining the previous estimate with Lemma~\ref{lem:uniform} yields
\[ g_n-\frac{u(t+h_n)-u(t)}{h_n}\to 0 \]
uniformly on compacts. Furthermore, since $T(t)$ is convex, the sequence
$(g_n)_{n\in\mathbb{N}}$ is non-increasing. Hence, there exists a function $g\in{\rm U}_\kappa$
with $g_n\downarrow g$. We use Lemma~\ref{lem:gamma}(iii) and~(v)
to conclude $g=B_\Gamma^+ u(t)$. It follows from inequality~\eqref{eq:BG},
$B_\Gamma^+ u(t)-g_n\leq 0$ and Lemma~\ref{lem:gamma}(iv) that
condition~\eqref{eq:comp2} is satisfied. Theorem~\ref{thm:comp}
yields $S(t)f\leq T(t)f$.
\end{proof}
\begin{remark}
Let $T\geq 0$ and $f\in\mathcal{L}^S_+$. A function $u\colon [0,T]\to \mathcal{L}^S_+$
can be seen as a $\Gamma$-supersolution of the equation
\begin{equation}\label{eq:cauchy}
\partial_t u(t) = A_\Gamma^+ u(t) \quad\mbox{for all } t\in [0,T],
\quad u(0)=f,
\end{equation}
if $u$ satisfies the conditions from Theorem~\ref{thm:comp}. Let $f\in\mathcal{L}^S$
such that the limit
\[ A_\Gamma^+ f=\lim_{h\downarrow 0}\frac{S(h)f-f}{h}\in{\rm C}_\kappa \]
exists uniformly on compacts. Define $u_0(t) := S(t)f$ for all $t\in[0,T]$.
It follows from the proof of Corollary~\ref{cor:comp} with $T:=S$ and
Theorem~\ref{thm:comp} that $u_0$ is the smallest $\Gamma$-supersolution
of equation~\eqref{eq:cauchy}. In this way, for a large class of fully
nonlinear equations, we obtain a solution concept which is directly
related to the idea of semigroups and their generators.
\end{remark}
\section{Approximation of the $\Gamma$-generator}
\label{sec:approx}
Throughout this section, let $S:=(S(t))_{t\geq 0}$ be a family of operators
$S(t)\colon{\rm C}_\kappa\to{\rm U}_\kappa$ satisfying Assumption~\ref{ass:S}. A priori it is not
clear how the upper $\Gamma$-generator can be computed and whether
the limes superior in the definition of $A_\Gamma^+$ can be replaced by a limit.
In many examples, the norm generator can be computed explicitly for
smooth functions as a differential operator. Furthermore, we want to recall
that linear differential operators are typically closed and uniquely determined
by the evaluation at smooth functions. Here, we do not claim that $A_\Gamma$ is
closed, i.e., that the graph of $A_\Gamma$ is a closed subset of ${\rm C}_\kappa\times{\rm U}_\kappa$.
However, under additional assumptions, we obtain approximation results
for the $\Gamma$-generator.
\begin{definition}
The \emph{$\Gamma$-generator} is defined by
\[ A_\Gamma\colon D(A_\Gamma)\to{\rm U}_\kappa,\; f\mapsto\Glim_{h\downarrow 0}\frac{S(h)f-f}{f}, \]
where the domain $D(A_\Gamma)$ consists of all $f\in\mathcal{L}^S_+$ such that the previous
limit exists.
\end{definition}
In the sequel, we denote by $S$ the family of extended operators
$S(t)\colon{\rm U}_\kappa\to{\rm U}_\kappa$ satisfying condition~\ref{S1}-\ref{S4} with ${\rm U}_\kappa$
instead of ${\rm C}_\kappa$, see Remark~\ref{rem:S}. For every $t\geq 0$,
$f\in{\rm U}_\kappa$ and $x\in X$, we define the pointwise integral
\[ \left(\int_0^t S(s)f\,{\rm d} s\right)(x):=\int_0^t \big(S(s)f\big)(x)\,{\rm d} s. \]
\subsection{General approximation results}
The goal of this subsection is to prove an approximation result of the
following form: for every $f\in\mathcal{L}^S_+$ and $(f_n)_{n\in\mathbb{N}}\subset D(A_\Gamma)$,
which is bounded above such that $(A_\Gamma f_n)_{n\in\mathbb{N}}$ is also bounded
above and $f_n\to f$ uniformly on compacts, it holds
$A_\Gamma^+ f=\Glimsup_{n\to\infty}A_\Gamma f_n$. While the inequality
$A_\Gamma^+ f\leq\Glimsup_{n\to\infty}A_\Gamma f_n$ is always satisfied, the reverse
inequality only holds under an additional assumption on $S$ and for
special choices of the sequence $(f_n)_{n\in\mathbb{N}}$. This is, for example,
the case if $S$ is translation invariant and $(f_n)_{n\in\mathbb{N}}$ is generated
by convolution, see Subsection~\ref{sec:conv}. We need the following
auxiliary estimate.
\begin{lemma} \label{lem:ub}
For every $r,t_0\geq 0$ and $\varepsilon>0$, there exists $\lambda_0\in (0,1]$
such that
\[ S(t)f-f\leq\lambda\int_0^t S(s)\Big(\frac{1}{\lambda}A_\Gamma^+ f+f\Big){\rm d} s
+\frac{\varepsilon t}{\kappa} \]
for all $t\in [0,t_0]$, $f\in B_{{\rm C}_\kappa}(0,r)\cap\mathcal{L}^S_+$ and $\lambda\in (0,\lambda_0]$.
\end{lemma}
\begin{proof}
Fix $r,t_0\geq 0$ and $\varepsilon>0$. By condition~\ref{S4} we can choose
$\lambda_0\in (0,1]$ such that
\begin{equation} \label{eq:ub}
\sup_{s\in [0,t_0]}\sup_{f\in B_{{\rm C}_\kappa}(0,r)}\lambda_0\|S(s)f\|_\kappa\leq\varepsilon
\quad\mbox{and}\quad \lambda_0 t_0\leq 1.
\end{equation}
In the sequel, we fix $t\in [0,t_0]$, $f\in B_{{\rm C}_\kappa}(0,r)\cap\mathcal{L}^S_+$ and
$\lambda\in (0,\lambda_0]$. Define $h_n:=2^{-n}t$ and $t_n^k:=k2^{-n}t$
for all $k,n\in\mathbb{N}_0$. For every $n\in\mathbb{N}$, it follows from the semigroup property
of $S$ on $\mathcal{L}^S_+$, inequality~\eqref{eq:ub} and Lemma~\ref{lem:lambda} that
\begin{align*}
S(t)f-f
&=\sum_{k=1}^{2^n} \big(S(t_n^k)f-S(t_n^{k-1})f\big)
=\sum_{k=1}^{2^n} \big(S(t_n^{k-1})S(h_n)f-S(t_n^{k-1})f\big) \\
&\leq\lambda h_n\sum_{k=1}^{2^n} \left(S(t_n^{k-1})\left(\frac{S(h_n)f-f}{\lambda h_n}+f\right)
-S(t_n^{k-1})f\right) \\
&\leq\lambda h_n\sum_{k=1}^{2^n} S(t_n^{k-1})\left(\frac{S(h_n)f-f}{\lambda h_n}+f\right)
+\frac{\varepsilon t}{\kappa} \\
&=\lambda\int_0^t \sum_{k=1}^{2^n} S(t_n^{k-1})\left(\frac{S(h_n)f-f}{\lambda h_n}+f\right)
\mathds{1}_{[t_n^{k-1},t_n^k)}(s)\,{\rm d} s+\frac{\varepsilon t}{\kappa}.
\end{align*}
We use Fatou's lemma and Lemma~\ref{lem:usc} to conclude that
\begin{align*}
S(t)f-f
&\leq\lambda\int_0^t \limsup_{n\to\infty}\sum_{k=1}^n S(t_n^{k-1})
\left(\frac{S(h_n)f-f}{\lambda h_n}+f\right)
\mathds{1}_{[t_n^{k-1},t_n^k)}(s)\,{\rm d} s+\frac{\varepsilon t}{\kappa} \\
&\leq\lambda\int_0^t S(s)\Big(\frac{1}{\lambda}A_\Gamma^+ f+f\Big){\rm d} s
+\frac{\varepsilon t}{\kappa}.
\end{align*}
Note that the sequence inside the integral, to which we apply Fatou's
lemma, is bounded from above, because of $f\in\mathcal{L}^S_+$ and condition~\ref{S4}.
\end{proof}
\begin{theorem} \label{thm:ub}
Let $(f_n)_{n\in\mathbb{N}}\subset\mathcal{L}^S_+$ be a bounded sequence and $f\in{\rm C}_\kappa$
with $f_n\to f$ uniformly on compacts and $(A_\Gamma^+ f_n)_{n\in\mathbb{N}}$
bounded above. Then,
\[ f\in\mathcal{L}^S_+ \quad\mbox{and}\quad
A_\Gamma^+ f\leq\Glimsup_{n\to\infty}A_\Gamma^+ f_n.\]
\end{theorem}
\begin{proof}
Let $\varepsilon>0$. Choose $\lambda_0\in (0,1]$ such that Lemma~\ref{lem:ub}
holds with $r:=\sup_{n\in\mathbb{N}}\|f_n\|_\kappa$ and $t_0:=1$. For every
$h\in (0,1]$ and $\lambda\in (0,\lambda_0]$, we use Lemma~\ref{lem:uniform},
Fatou's lemma, Lemma~\ref{lem:usc} and Lemma~\ref{lem:gamma}(iv)
to conclude that
\begin{align*}
\frac{S(h)f-f}{h}
&=\lim_{n\to\infty}\frac{S(h)f_n-f_n}{h} \\
&\leq\limsup_{n\to\infty}\frac{\lambda}{h}\int_0^h
S(s)\Big(\frac{1}{\lambda}A_\Gamma^+ f_n+f_n\Big){\rm d} s +\frac{\varepsilon}{\kappa} \\
&\leq\frac{\lambda}{h}\int_0^h \limsup_{n\to\infty}
S(s)\Big(\frac{1}{\lambda}A_\Gamma^+ f_n+f_n\Big){\rm d} s +\frac{\varepsilon}{\kappa} \\
&\leq\frac{\lambda}{h}\int_0^h S(s)\Big(\frac{1}{\lambda}g+f\Big){\rm d} s
+\frac{\varepsilon}{\kappa},
\end{align*}
where $g:=\Glimsup_{n\to\infty}A_\Gamma^+ f_n$. In particular, condition~\ref{S4} implies
$f\in\mathcal{L}^S_+$. Moreover, it follows from Lemma~\ref{lem:gamma}(iv),
Lemma~\ref{lem:usc} and $S(0)=\id_{{\rm U}_\kappa}$ that
\[ A_\Gamma^+ f
\leq\Glimsup_{h\downarrow 0}\frac{\lambda}{h}\int_0^h
S(s)\Big(\frac{1}{\lambda}g+f\Big){\rm d} s +\frac{\varepsilon}{\kappa}
\leq g+\lambda f+\frac{\varepsilon}{\kappa}. \]
Letting $\varepsilon\downarrow 0$ and $\lambda\downarrow 0$, we obtain
$A_\Gamma^+ f\leq\Glimsup_{n\to\infty}A_\Gamma^+ f_n$.
\end{proof}
Under additional assumptions on the approximating sequence $(f_n)_{n\in\mathbb{N}}$,
we also obtain the reverse estimate for the upper $\Gamma$-generator and
that $f\in D(A_\Gamma)$.
\begin{theorem} \label{thm:lb}
Let $(f_n)_{n\in\mathbb{N}}\subset D(A_\Gamma)$ be a bounded sequence and $f\in{\rm C}_\kappa$
with $f_n\to f$ uniformly on compacts and $(A_\Gamma f_n)_{n\in\mathbb{N}}$ is
bounded above. Assume that, for every $\varepsilon>0$, there exists a sequence
$(r_n)_{n\in\mathbb{N}}\subset (0,\infty)$ with $r_n\to 0$ such that
\begin{equation} \label{eq:lb}
\left(\frac{S(h)f_n-f_n}{h}\right)(x)
\leq\sup_{y\in B(x,r_n)}\left(\frac{S(h)f-f}{h}\right)(y)+\frac{\varepsilon}{\kappa(x)}
\end{equation}
for all $h\in (0,1]$, $n\in\mathbb{N}$ and $x\in X$. Then, $f\in D(A_\Gamma)$ and
$A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n$.
\end{theorem}
\begin{proof}
First, let $(h_m)_{m\in\mathbb{N}}\subset (0,1]$ be a sequence with $h_m\to 0$.
By Theorem~\ref{thm:ub} and Lemma~\ref{lem:gamma}(i), there exists a
subsequence, which is still denoted by $(h_m)_{m\in\mathbb{N}}$, such that
\begin{equation} \label{eq:g1}
g_1:=\Glim_{m\to\infty}\frac{S(h_m)f-f}{h_m}\in{\rm U}_\kappa \quad\mbox{exists}.
\end{equation}
Moreover, since $(A_\Gamma f_n)_{n\in\mathbb{N}}$ is bounded above and due to
Lemma~\ref{lem:gamma}(i), every subsequence $(f_{n_k})_{k\in\mathbb{N}}$ has
a further subsequence $(f_{n_{k_l}})_{l\in\mathbb{N}}$ such that
\begin{equation} \label{eq:g2}
g_2:=\Glim_{l\to\infty}A_\Gamma f_{n_{k_l}}\in{\rm U}_\kappa \quad\mbox{exists}.
\end{equation}
To simplify the notation, we subsequently write $f_l:=f_{n_{k_l}}$.
Theorem~\ref{thm:ub} implies
\[ g_1\leqA_\Gamma^+ f\leq\Glim_{l\to\infty}A_\Gamma f_l=g_2. \]
Second, we show that $g_1\geq g_2$. To do so, let $x\in X$ and $\varepsilon>0$.
By definition of the $\Gamma$-limit, we can choose a sequence $(x_l)_{l\in\mathbb{N}}\subset X$
with $x_l\to x$ such that
\[ \Big(\Glim_{l\to\infty}A_\Gamma f_l\Big)(x)=\lim_{l\to\infty}A_\Gamma f_l(x_l).\]
In addition, there exist sequences $(m_l)_{l\in\mathbb{N}}$ and $(y_l)_{l\in\mathbb{N}}$ with
$d(x_l,y_l)\to 0$ such that
\[ A_\Gamma f_l(x_l)
\leq\left(\frac{S(h_{m_l})f_l-f_l}{h_{m_l}}\right)(y_l)+\varepsilon
\quad\mbox{for all } l\in\mathbb{N}. \]
Let $(r_l)_{l\in\mathbb{N}}\subset (0,\infty)$ be a sequence satisfying condition~\eqref{eq:lb}.
Then, for every $l\in\mathbb{N}$,
\begin{align*}
A_\Gamma f_l(x_l)
&\leq\sup_{z\in B(y_l,r_l)}\left(\frac{S(h_{m_l})f-f}{h_{m_l}}\right)(z)
+\frac{\varepsilon}{\kappa(y_l)}+\varepsilon \\
&\leq\sup_{z\in B(x,\delta_l)}\left(\frac{S(h_{m_l})f-f}{h_{m_l}}\right)(z)
+\sup_{l\in\mathbb{N}}\frac{\varepsilon}{\kappa(y_l)}+\varepsilon,
\end{align*}
where $\delta_l:=d(x,y_l)+r_l\to 0$. Since $\kappa>0$ is continuous,
we have $\inf_{l\in\mathbb{N}}\kappa(y_l)>0$. It follows from Lemma~\ref{lem:gamma}(vii)
that
\[ g_2(x)=\Big(\Glim_{l\to\infty}A_\Gamma f_l\Big)(x)=\lim_{l\to\infty}A_\Gamma f_l(x_l)
\leq\left(\Glim_{l\to\infty}\frac{S(h_{m_l})f-f}{h_{m_l}}\right)(x)=g_1(x).\]
Third, we show that $f\in D(A_\Gamma)$ with $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n$. From
the first part, we know that every sequence $(h_m)_{m\in\mathbb{N}}\subset(0,\infty)$
with $h_m\to 0$ has a subsequence which satisfies equation~\eqref{eq:g1}. A
priori the choice of the subsequence and the limit $g_1$ depend on the choice
of the sequence $(h_m)_{m\in\mathbb{N}}$. However, we have $g_1=g_2$ and the function
$g_2$ is independent of $(h_m)_{m\in\mathbb{N}}$. Hence, Lemma~\ref{lem:gamma}(ii)
implies
\[ g_1=\Glim_{h\downarrow 0}\frac{S(h)f-f}{h}, \]
i.e., $f\in D(A_\Gamma)$ with $A_\Gamma f=g_1$. Since the limit in equation~\eqref{eq:g2}
is also independent of the choice of of subsequence, we obtain
$A_\Gamma f=\lim_{n\to\infty}A_\Gamma f_n$.
\end{proof}
\subsection{Convolution}
\label{sec:conv}
In this subsection, we study two particular convolution schemes to generate
approximating sequences $(f_n)_{n\in\mathbb{N}}$ which satisfy condition~\eqref{eq:lb}.
The first one, convolution with probability measures, works particularly well if
$X=\mathbb{R}^d$ and the measure has a smooth density with respect to the
Lebesgue measure. In this case, $(f_n)_{n\in\mathbb{N}}$ is a sequence of smooth
functions and the generator can be a differential operator of arbitrary order.
However, the condition $f_n\in D(A_\Gamma)$ is no longer verifiable if $X$ is
infinite-dimensional. The second one, sup-inf-convolution, is restricted to
first-order equations but can be applied in separable Hilbert spaces.
\subsubsection{Convolution with mollifiers}
\label{sec:conv2}
Let $X$ be a separable Banach space. Suppose that there exists
$\delta_0>0$ with
\begin{equation} \label{eq:kappa}
c:=\sup_{x\in X}\sup_{y\in B(x,\delta_0)}\frac{\kappa(x)}{\kappa(y)}<\infty.
\end{equation}
To simplify the notation, we assume, w.l.o.g., that $\delta_0:=1$.
In the sequel, we fix a sequence $(\mu_n)_{n\in\mathbb{N}}$ of probability measures
on the Borel $\sigma$-algebra $\mathcal{B}(X)$ of $X$ which concentrate in the
sense that
\begin{equation} \label{eq:conv}
\mu_n\big(B(0,\nicefrac{1}{n})^c\big)=0\quad\mbox{for all }n\in\mathbb{N}.
\end{equation}
For every $n\in\mathbb{N}$, $f\in{\rm U}_\kappa$ and $x\in X$, we define the convolution by
\[ (f*\mu_n)(x):=\int_X f(x-y)\mu_n({\rm d} y)\in\Rinf. \]
Condition~\eqref{eq:kappa} ensures that the previous integral is
well-defined.
\begin{lemma} \label{lem:conv}
For every $n\in\mathbb{N}$, the mapping ${\rm U}_\kappa\to{\rm U}_\kappa,\; f\mapsto f*\mu_n$ is
well defined and upper semicontinuous, i.e., for every sequence
$(f_m)_{m\in\mathbb{N}}\subset{\rm U}_\kappa$, which is bounded above,
\[ \Glimsup_{m\to\infty}\, (f_m*\mu_n)
\leq\Big(\Glimsup_{m\to\infty}f_m\Big)*\mu_n. \]
Furthermore, it holds $\Glimsup_{n\to\infty}\,(f*\mu_n)\leq f$ for all $f\in{\rm U}_\kappa$.
\end{lemma}
\begin{proof}
First, we show that ${\rm U}_\kappa\to{\rm U}_\kappa,\; f\mapsto f*\mu_n$ is well defined. Let
$n\in\mathbb{N}$, $f\in{\rm U}_\kappa$ and $x\in X$. It follows from condition~\eqref{eq:kappa}
and condition~\eqref{eq:conv} that
\[ (f*\mu_n)(x)\kappa(x)
=\int_{B(0,1)} f(x-y)\kappa(x-y)\frac{\kappa(x)}{\kappa(x-y)}\,\mu_n({\rm d} y)
\leq c\|f^+\|_\kappa.\]
Moreover, let $(x_m)_{m\in\mathbb{N}}\subset X$ be a sequence with $x_m\to x$.
Fatou's lemma implies
\[ \limsup_{m\to\infty}\,(f*\mu_n)(x_m)
\leq\int_X \limsup_{m\to\infty}f(x_m-y)\,\mu_n({\rm d} y)
\leq\int_X f(x-y)\,\mu_n({\rm d} y) \]
Second, we show that, for fixed $n\in\mathbb{N}$, the convolution is upper semicontinuous.
Let $(f_m)_{m\in\mathbb{N}}\subset{\rm U}_\kappa$ be bounded above, $x\in X$ and
$(x_m)_{m\in\mathbb{N}}\subset X$ with $x_m\to x$. Since
$\sup_{m\in\mathbb{N}}\|f_m^+\|_\kappa<\infty$ and $\nu(A):=\int_A\frac{1}{\kappa}\,{\rm d}\mu_n$
defines a finite Borel measure, we can apply Fatou's lemma to conclude that
\begin{align*}
&\limsup_{m\to \infty}\,(f*\mu_n)(x_m)
=\limsup_{m\to \infty}\int_X f_m(x_m-y)\,\mu_n({\rm d} y) \\
&\leq\int_X \limsup_{m\to \infty}f_m(x_m-y)\,\mu_n({\rm d} y)
\leq \int_X \Big(\Glimsup_{m\to\infty}f_m\Big)(x-y)\,\mu_n({\rm d} y).
\end{align*}
Third, we show that $\Glimsup_{n\to\infty}\,(f*\mu_n)\leq f$ for all $f\in{\rm U}_\kappa$.
Let $x\in X$ and $(x_n)_{n\in\mathbb{N}}\subset X$ with $x_n\to x$. Since $f$ is upper
semicontinuous, for every $\varepsilon>0$, there exists $n_0\in\mathbb{N}$ such that
$f(x_n-y)\leq f(x)+\varepsilon$ for all $n\geq n_0$ and $y\in B(0,\nicefrac{1}{n})$.
Hence,
\[ (f*\mu_n)(x_n)=\int_{B(0,\nicefrac{1}{n})}f(x_n-y)\,\mu_n({\rm d} y)
\leq f(x)+\varepsilon \quad\mbox{for all } n\geq n_0. \]
Letting $\varepsilon\downarrow 0$ yields $\limsup_{n\to\infty}(f*\mu_n)(x_n)\leq f(x)$.
\end{proof}
For every $x\in X$, we define the shift operator $\tau_x\colon{\rm U}_\kappa\to{\rm U}_\kappa$ by
\[ (\tau_x f)(y):=f(x+y) \quad\mbox{for all } y\in X. \]
Condition~\eqref{eq:trans} in the following lemma is clearly satisfied
if $S$ is translation invariant, i.e., $\tau_x S(t)f=S(t)(\tau_x f)$. Moreover,
in many examples, the condition holds at least for Lipschitz continuous
functions.
\begin{lemma} \label{lem:conv2}
Let $f\in\mathcal{L}^S_+$ such that $f_n:=f*\mu_n\in D(A_\Gamma)$ for all $n\in\mathbb{N}$.
Assume that, for every $\varepsilon>0$, there exists $\delta>0$ such that
\begin{equation} \label{eq:trans}
\|\tau_x S(t)f-S(t)(\tau_x f)\|_\kappa\leq\varepsilon t
\quad\mbox{for all } t\in[0,1] \mbox{ and } x\in B(0,\delta).
\end{equation}
Then, it holds $f\in D(A_\Gamma)$ and $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n$.
\end{lemma}
\begin{proof}
We verify the assumptions of Theorem~\ref{thm:lb}. First, we show that the
sequence $(f_n)_{n\in\mathbb{N}}$ is bounded and converges to $f$ uniformly on
compacts. It follows from condition~\eqref{eq:kappa} that
$\|f_n^+\|_\kappa\leq c\|f^+\|_\kappa$ for all $n\in\mathbb{N}$. Moreover, for every
compact set $K\subset X$, continuity of $f$ implies
\[ \sup_{x\in K}|f_n(x)-f(x)|
\leq\sup_{x\in K}\int_{B(0,\nicefrac{1}{n})} |f(x-y)-f(x)|\,\mu_n({\rm d} y)
\to 0\quad\mbox{as } n\to\infty.\]
Second, we verify condition~\eqref{eq:lb}. To do so, let $\varepsilon>0$.
By condition~\eqref{eq:trans}, there exists $n_0\in\mathbb{N}$ such that
\[ S(t)(\tau_{-y}f)\leq\tau_{-y}S(t)f+\tfrac{\varepsilon t}{\kappa}
\quad\mbox{for all } t\in [0,1] \mbox{ and } y\in B\big(0,\tfrac{1}{n_0}\big).\]
For every $h\in [0,1]$, $n\geq n_0$ and $x\in X$, we use Jensen's inequality
and the monotonicity of $S(h)$ to estimate
\begin{align*}
&(S(h)f_n)(x)
=\left(S(h)\left(\int_{B(0,\nicefrac{1}{n})}(\tau_{-y}f)(\,\cdot\,)\,\mu_n({\rm d} y)\right)\right)(x) \\
&\leq\int_{B(0,\nicefrac{1}{n})}\big(S(h)(\tau_{-y}f)\big)(x)\,\mu_n({\rm d} y)
\leq\int_{B(0,\nicefrac{1}{n})}\Big(\big(\tau_{-y}S(h)f\big)(x)
+\tfrac{\varepsilon h}{\kappa(x)}\Big)\,\mu_n({\rm d} y) \\
&=\Big(S(h)f_n+\tfrac{\varepsilon h}{\kappa}\Big)(x).
\end{align*}
It follows from the linearity of the convolution and condition~\eqref{eq:conv}
that
\begin{equation} \label{eq:conv2}
\frac{S(h)f_n-f_n}{h}
\leq\left(\frac{S(h)f-f}{h}\right)*\mu_n+\frac{\varepsilon}{\kappa}
\leq\sup_{y\in B(\,\cdot\,,\nicefrac{1}{n})}\Big(\frac{S(h)f-f}{h}\Big)(y)
+\frac{\varepsilon}{\kappa}.
\end{equation}
Third, we show that the sequence $(A_\Gamma f_n)_{n\in\mathbb{N}}$ is bounded above.
By inequality~\eqref{eq:conv2} with $\varepsilon:=1$, Jensens's inequality
and condition~\eqref{eq:conv}, there exists $n_0\in\mathbb{N}$ with
\[ \|(S(h)f_n-f_n)^+\|_\kappa\leq\|(S(h)f-f)^+*\mu_n\|_\kappa+h
\leq c\|(S(h)f-f)^+\|_\kappa+h. \]
for all $h\in [0,1]$ and $n\geq n_0$. Since $f\in\mathcal{L}^S_+$, we can choose
$h_0>0$ and $c'\geq 0$ such that
\[ \sup_{n\in\mathbb{N}}\|(S(h)f_n-f_n)^+\|_\kappa
\leq c\|(S(h)f-f)^+\|_\kappa+h\leq (cc'+1)h
\quad\mbox{for all } h\in (0,h_0]. \]
This shows that $(A_\Gamma^+ f_n)_{n\in\mathbb{N}}$ is bounded above. Now,
Theorem~\ref{thm:lb} yields the claim.
\end{proof}
To discuss the assumption $f*\mu_n\in D(A_\Gamma)$, we consider only
the finite-dimensional case and convolution with mollifiers. Denote by
${\rm Lip}_{\rm b}$ the space of all bounded Lipschitz continuous functions
$f\colon\mathbb{R}^d\to\mathbb{R}$ and by ${\rm C}_{\rm b}^\infty$ the space of all bounded
infinitely differentiable functions $f\colon\mathbb{R}^d\to\mathbb{R}$ such that all
derivatives are bounded. Moreover, let ${\rm C}_{\rm c}^\infty$ be the set of all
infinitely differentiable functions $f\colon\mathbb{R}^d\to\mathbb{R}$ with compact
support.
\begin{remark} \label{rem:conv}
Let $X:=\mathbb{R}^d$. Moreover, let $\eta\in{\rm C}_{\rm c}^\infty$ with $\eta\geq 0$,
$\supp(\eta)\subset B(0,1)$ and $\int_{\mathbb{R}^d}\eta(x)\,{\rm d} x=1$. Define
$\eta_n(x):=n^d\eta(nx)$ for all $n\in\mathbb{N}$ and $x\in\mathbb{R}^d$. For the
measure $\mu_n(A):=\int_A \eta_n(y)\,{\rm d} y$, the convolution
$f*\mu_n$ is given by
\[ (f*\eta_n)(x)=\int_{\mathbb{R}^d} f(x-y)\eta_n(y)\,{\rm d} y. \]
We have $f*\eta_n\in{\rm C}_{\rm b}^\infty$ for all $f\in{\rm Lip}_{\rm b}$ and $n\in\mathbb{N}$.
Assume that $S(t)\colon{\rm Lip}_{\rm b}\to{\rm Lip}_{\rm b}$ for all $t\geq 0$,
${\rm C}_{\rm b}^\infty\subset D(A_\Gamma)$ and that condition~\eqref{eq:trans} is
satisfied for all $f\in{\rm Lip}_{\rm b}$. Lemma~\ref{lem:conv2} yields $f\in D(A_\Gamma)$
and $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma(f*\eta_n)$ for all $f\in\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}$.
In particular, the $\Gamma$-generator is uniquely determined by
the evaluation at smooth functions. Hence, the uniqueness result,
Corollary~\ref{cor:comp}, can be improved accordingly, i.e., equality
of the generator on ${\rm C}_{\rm b}^\infty$ ensures equality of the semigroups
on ${\rm Lip}_{\rm b}$. Furthermore, Lemma~\ref{lem:uniform} implies equality on
${\rm C}_\kappa$.
\end{remark}
\subsubsection{Regularization with sup-inf-convolution}
Let $X$ be a separable Hilbert space with norm $|\cdot|$. We fix
$\kappa\equiv 1$ and denote by ${\rm BUC}$ the space of all bounded
uniformly continuous functions $f\colon X\to\mathbb{R}$. For every $n\in\mathbb{N}$
and $f\in{\rm BUC}$, we define the sup-inf-convolution
\begin{equation} \label{eq:si}
\big(\theta_n f\big)(x):=\sup_{y\in X}\inf_{z\in X}
\Big(f(z)+\tfrac{n}{2}|y-z|^2-n|y-x|^2\Big).
\end{equation}
It is shown in~\cite{lasry} that $\theta_n f\in{\rm Lip}_{\rm b}^1$ for all $n\in\mathbb{N}$,
and $\lim_{n\to\infty}\|\theta_n f-f\|_\infty=0$ for all $f\in{\rm BUC}$.
Here, ${\rm Lip}_{\rm b}^1$ denotes the space of all differentiable functions
$f\in{\rm Lip}_{\rm b}$ such that the first derivative is again bounded and
Lipschitz continuous.
\begin{lemma}\label{lem:si}
For every $r>0$, $f,g\in B_{{\rm BUC}}(0,r)$, $n\in\mathbb{N}$ and $x\in X$,
\[ (\theta_n f-\theta_n g)(x)\leq\sup_{y\in B(x,r_n)}(f-g)(y),
\quad\mbox{where}\quad r_n:=(\sqrt{2}+2)\sqrt{\tfrac{r}{n}}. \]
\end{lemma}
\begin{proof}
In equation~\eqref{eq:si}, the supremum can be taken over the ball
$B(x,\sqrt{2r/n})$ and the infimum over the ball $B(y,\sqrt{4r/n})$.
Hence, we can estimate
\begin{align*}
&(\theta_n f-\theta_n g)(x)
\leq\sup_{y\in B(x,\sqrt{2r/n})}\sup_{z\in B(y,\sqrt{4r/n})}\big(F(y,z)-G(y,z)\big) \\
&\leq\sup_{y\in B(x,\sqrt{2r/n})}\sup_{z\in B(y,\sqrt{4r/n})}\big(f(z)-g(z)\big)
=\sup_{z\in B(x,r_n)}\big(f(z)-g(z)\big),
\end{align*}
where $F(y,z):=f(z)+\frac{n}{2}|y-z|^2-n|y-x|^2$ and
$G(y,z):=g(z)+\frac{n}{2}|y-z|^2-n|y-x|^2$.
\end{proof}
As an application of Theorem~\ref{thm:lb}, we obtain the following result.
Condition~(i) is typically satisfied for first order equations, where we have
${\rm Lip}_{\rm b}^1\subset D(A_\Gamma)$.
\begin{lemma} \label{lem:si2}
Assume that $S(t)\colon{\rm BUC}\to{\rm BUC}$ for all $t\geq 0$. Let
$f\in\mathcal{L}^S_+\cap{\rm BUC}$ with
\begin{enumerate}
\item $\theta_n f\in D(A_\Gamma)$ for all $n\in\mathbb{N}$,
\item $S(t)(\theta_n f)\leq\theta_nS(t)f$ for all $n\in\mathbb{N}$ and $t\geq 0$.
\end{enumerate}
Then, it holds $f\in D(A_\Gamma)$ and $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma(\theta_n f)$.
\end{lemma}
\begin{proof}
We verify the assumptions of Theorem~\ref{thm:lb}. Define $f_n:=\theta_n f$
for all $n\in\mathbb{N}$. By definition and~\cite{lasry}, it holds
$\sup_{n\in\mathbb{N}}\|f_n\|_\infty\leq\|f\|_\infty$ and $\|\theta_n f-f\|_\infty\to 0$.
Moreover, we use condition~(ii), condition~\ref{S4} and Lemma~\ref{lem:si} to
choose a sequence $(r_n)_{n\in\mathbb{N}}\subset (0,\infty)$ with $r_n\to 0$
such that
\[ S(h)f_n-f_n\leq\theta_n S(h)f-f_n
\leq\sup_{y\in B(\,\cdot\,, r_n)}\big(S(h)f-f\big)(y)
\quad\mbox{for all } h\in[0,1]. \]
Hence, condition~\eqref{eq:lb} is satisfied. Furthermore, since $f\in\mathcal{L}^S_+$,
there exist $h_0\in (0,1]$ and $c\geq 0$ with
\[ \frac{S(h)f_n-f_n}{h}
\leq\sup_{y\in B(\,\cdot\,, r_n)}\frac{S(h)f-f}{h}\leq ch
\quad\mbox{for all } h\in (0,h_0]. \]
This shows that $(A_\Gamma^+ f_n)_{n\in\mathbb{N}}$ is bounded above.
Theorem~\ref{thm:lb} yields the claim.
\end{proof}
\subsection{Connection to distributional derivative}
Let $X:=\mathbb{R}^d$. Moreover, let $\eta\in{\rm C}_{\rm c}^\infty$ with $\eta\geq 0$,
$\supp(\eta)\subset B(0,1)$ and $\int_{\mathbb{R}^d}\eta(x)\,{\rm d} x=1$. Denote
by $f*\eta_n$ the convolution, where $\eta_n(x):=n^d\eta(nx)$.
Let $I\subset\mathbb{N}_0^d$ be an index set and $H\colon\mathbb{R}^I\to\mathbb{R}$ be a convex
function. Our goal is to identify $A_\Gamma f$ with $g:=H((D^\alpha f)_{\alpha\in I})$
if the partial derivatives $D^\alpha f$ exist as regular distributions for all
$\alpha\in I$ and $g$ is locally integrable. Since $A_\Gamma f$ is, in contrast to $g$,
upper semicontinuous, we want to replace $g$ by its upper semicontinuous
hull $\overline{g}$. To do so, we have to choose a suitable representative of $g$.
Let $f\colon\mathbb{R}^d\to\mathbb{R}$ be a locally integrable function. We define $X_f$
as the set of all $x\in\mathbb{R}^d$ such that the limit
\[ \tilde{f}(x):=\lim_{r\downarrow 0}\fint_{B(x,r)}f(y)\,{\rm d} y \]
exists.\footnote{Denoting by $\lambda$ the Lebesgue measure, the
normalized integral is given by
\[ \fint_{B(x,r)}f(y)\,{\rm d} y:=\frac{1}{\lambda(B(x,r))}\int_{B(x,r)}f(y)\,{\rm d} y.\]}
We remark that the Lebesgue set of a function $f$, consisting of all $x\in\mathbb{R}^d$ with
$\tilde{f}(x)=f(x)$, depends on the choice of the representative, while the
set $X_f$ does not. Furthermore, by the Lebesgue differentiation theorem,
the complement of the Lebesgue set has measure zero,
see~\cite[Corollary~3.1.6]{Stein-Shakarchi05}. This implies
$\lambda(X_f^c)=0$ and therefore $X_f$ is dense in $\mathbb{R}^d$.
\begin{theorem} \label{thm:dist}
Let $I\subset\mathbb{N}_0^d$ be an index set and $H\colon\mathbb{R}^I\to\mathbb{R}$ be a convex
function. Let $f\in\mathcal{L}^S_+$ satisfy condition~\eqref{eq:trans}. For every
$n\in\mathbb{N}$, we define $f_n:=f*\eta_n$ and assume that
\begin{enumerate}
\item $D^\alpha f$ and $D^\alpha f_n$ exist as regular distributions for all
$\alpha\in I$,
\item $H((D^\alpha f)_{\alpha\in I})$ and $H((D^\alpha f_n)_{\alpha\in I})$
are locally integrable,
\item $f_n\in D(A_\Gamma)$ and $A_\Gamma f_n=H((D^\alpha f_n)_{n\in\mathbb{N}})$.
\end{enumerate}
Furthermore, we define the functions
\begin{align*}
g(x) &:=H\big((D^\alpha f(x))_{\alpha\in I}\big) \quad\mbox{for all } x\in\mathbb{R}^d, \\
\tilde{g}(x) &:=\lim_{r\downarrow 0}\fint_{B(x,r)}g(y)\,{\rm d} y \quad\mbox{for all } x\in X_g, \\
\overline{g}(x) &:=\limsup_{y\in X_g,y\to x}\widetilde g(y) \quad\mbox{for all } x\in\mathbb{R}^d.
\end{align*}
Then, it holds $f\in D(A_\Gamma)$ and $(A_\Gamma f)(x)=\overline{g}(x)$ for all
$x\in\mathbb{R}^d$. In particular, we have $\overline{g}(x)<\infty$ for all $x\in\mathbb{R}^d$.
\end{theorem}
\begin{proof}
It follows from Lemma~\ref{lem:conv2} that $f\in D(A_\Gamma)$ and
$A_\Gamma f=\Glim_{n\to\infty}Af_n$. First, we show $\overline{g}\leqA_\Gamma f$.
Define $F:=(D^\alpha f)_{\alpha\in I}$ and $F_n:=(D^\alpha f_n)_{\alpha\in I}$
for all $n\in\mathbb{N}$. It holds $F_n=F*\eta_n$ for all $n\in\mathbb{N}$, where the
convolution of the vector valued-function $F$ with $\eta_n$ is
understood componentwise. Hence, we can use condition~(i)
and~\cite[Theorem~3.2.1]{Stein-Shakarchi05} to obtain $F_n\to F$
almost everywhere. Continuity of $H$ and condition~(iii) imply
\[ g=H(F)=\lim_{n\to\infty}H(F_n)=\lim_{n\to\infty}A_\Gamma f_n
\leq\Glimsup_{n\to\infty}A_\Gamma f_n=A_\Gamma f \]
almost everywhere. This yields the estimate
\[ \fint_{B(x,r)} g(y)\,{\rm d} y\leq\fint_{B(x,r)}(A_\Gamma f)(y)\,{\rm d} y
\quad\mbox{for all } x\in\mathbb{R}^d \mbox{ and } r>0. \]
For every $x\in X_g$, it follows from the upper semicontinuity of $A_\Gamma f$
that
\[ \tilde{g}(x)=\lim_{r\downarrow 0}\fint_{B(x,r)} g(y)\,{\rm d} y
\leq\limsup_{r\downarrow 0}\fint_{B(x,r)}(A_\Gamma f)(y)\,{\rm d} y
\leq (A_\Gamma f)(x). \]
In particular, $\tilde{g}$ is bounded above and therefore $\overline{g}(x)<\infty$
for all $x\in\mathbb{R}^d$. We use again that $A_\Gamma f$ is upper semicontinuous
in order to conclude that
\[ \overline{g}(x)=\limsup_{y\in X_g,y\to x}\tilde{g}(y)
\leq\limsup_{y\in X_g,y\to x}(A_\Gamma f)(y) \leq (A_\Gamma f)(x)
\quad\mbox{for all } x\in\mathbb{R}^d. \]
Second, we show $A_\Gamma f\leq\overline{g}$. Let $x\in\mathbb{R}^d$ and
$\varepsilon>0$. Because of $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n$, there
exists a sequence $(x_n)_{n\in\mathbb{N}}\subset\mathbb{R}^d$ with $x_n\to x$ and
$(A_\Gamma f_n)(x_n)\to (A_\Gamma f)(x)$. In addition, since $\overline{g}$ is
upper semicontinuous, there exists $\delta>0$ such that
$\overline{g}(y)<\overline{g}(x)+\varepsilon$ for all $y\in B(x,\delta)$.
Choose $n_0\in\mathbb{N}$ with $B(x_n,\nicefrac{1}{n})\subset B(x,\delta)$
for all $n\geq n_0$. Since $g$ is locally integrable, it holds
$H(F)=g=\tilde{g}\leq\overline{g}$ almost everywhere. It follows from
the previous considerations and Jensen's inequality that
\begin{align*}
\big(A_\Gamma f_n\big)(x_n)=H\big(F_n(x_n)\big)
&=H\left(\int_{B(0,\nicefrac{1}{n})} F(x_n-y)\eta_n(y)\,{\rm d} y\right) \\
&\leq\int_{B(0,\nicefrac{1}{n})}H\big(F(x_n-y)\big)\eta_n(y)\,{\rm d} y \\
&\leq\int_{B(0,\nicefrac{1}{n})}\overline{g}(x_n-y)\eta_n(y)\,{\rm d} y
\leq\overline{g}(x)+\varepsilon.
\end{align*}
We obtain $(A_\Gamma f)(x)=\lim_{n\to\infty}A_\Gamma f_n(x_n)\leq\overline{g}(x)$
for all $x\in\mathbb{R}^d$.
\end{proof}
In several examples, the set $\mathcal{L}^S_{\sym}\cap{\rm Lip}_{\rm b}$ is invariant under
$S$ and has an explicit representation by means of Sobolev spaces.
In addition, it holds ${\rm C}_{\rm b}^\infty\subset D(A_\Gamma)$ and
$A_\Gamma f=H((D^\alpha f)_{\alpha\in I})$ for all $f\in{\rm C}_{\rm b}^\infty$. Hence,
for every $f\in\mathcal{L}^S_{\sym}\cap{\rm Lip}_{\rm b}$, the previous theorem yields
that $u(t):=S(t)f$ solves the equation
\[ \Glim_{h\downarrow 0}\frac{u(t+h)-u(t)}{h}
=H\big((D^\alpha u(t))_{\alpha\in I}\big)
\quad\mbox{for all } t\geq 0. \]
These ideas can be carried out by using quite elementary calculations,
see Subsection~\ref{sec:control}. Nonetheless, we want to mention a
general result that locality of the generator implies the existence of a
function $H$ with $Af=H((D^\alpha f)_{\alpha\in I})$ for sufficiently
smooth $f$.
\begin{remark}
Fix $\kappa:=1$ and assume that $S$ restricted to ${\rm BUC}$ is a strongly
continuous semigroup. Furthermore, let $H\colon\mathbb{R}^I\to\mathbb{R}$ be a convex
function satisfying
\begin{equation} \label{eq:local}
Af=H((D^\alpha)_{\alpha\in I}) \quad\mbox{for all } f\in{\rm BUC}^\infty,
\end{equation}
where $I:=\{\alpha\in\mathbb{N}_0^d\colon |\alpha|\leq 2\}$ and ${\rm BUC}^\infty$
denotes the space of all infinitely differentiable functions $f\in{\rm BUC}$
such that all partial derivatives are again in ${\rm BUC}$. Then, $A$ is local
in sense that, for fixed $x\in\mathbb{R}^d$, it holds $A f(x)=A g(x)$ if $f,g\in{\rm BUC}^\infty$
coincide on an open neighbourhood of $x$. On the other hand, it was
shown in~\cite{Biton01} that locality and some (technical) regularity
of the semigroup already imply the existence of a convex function $H$
satisfying equation~\eqref{eq:local}.
To formulate the conditions from \cite{Biton01}, we denote by $C^\infty$
the space of all infinitely differentiable functions $f\colon\mathbb{R}^d\to\mathbb{R}$.
For every sequence $r:=(r_n)_{n\in\mathbb{N}}\subset [0,\infty)$, let $Q_r$ be the
set of all $f\in{\rm C}_{\rm c}^\infty$ such that $\|D^\alpha f\|_\infty\leq r_n$ for all
$n\in\mathbb{N}$ and $|\alpha|\leq n$. We call $S$ \emph{regular} if the following
holds: Let $(r_n)_{n\in\mathbb{N}}\subset [0,\infty)$, $f\in {\rm BUC}\cap C^\infty$ and
$K\subset\mathbb{R}^d$ compact. Then, for every $T\geq 0$ and $\varepsilon>0$,
there exists $\delta_0>0$ such that, for all $t\in [0,T]$, $\delta\in (0,\delta_0]$,
$g\in Q_r$ and $x\in K$
\[ \big|\big(S(t)(f+\delta g)\big)(x)-\big(S(t))(x)-\delta g(x)\big|\leq\varepsilon t.\]
Moreover, we call $S$ \emph{local} if the following holds: Let $x\in\mathbb{R}^d$
and $f,g\in{\rm BUC}\cap C^\infty$ which coincide on an open neighbourhood
of $x$. Then, for all $\varepsilon>0$, there exists $h_0>0$ with
\[ |S(h)f-S(h)g|(x)<\varepsilon h \quad\mbox{for all } h\in [0,h_0]. \]
In particular, this condition implies that $Af(x)=Ag(x)$ if $f,g\in D(A)$.
In the sequel, let $S$ be regular and local. Then, by~\cite[Theorem~3.1]{Biton01},
there exists a continuous function $H\colon\mathbb{R}^d\times\mathbb{R}^I\to\mathbb{R}$ such that
\[ Af(x) = H\big(x, (D^\alpha f(x))_{\alpha\in I}\big)
\quad\mbox{for all } f\in{\rm BUC}^\infty \mbox{ and } x\in\mathbb{R}^d. \]
It follows from the proof of~\cite[Theorem~3.1]{Biton01} that convexity of
$S$ implies convexity of the mapping $H(x,\,\cdot\,)\colon\mathbb{R}^I\to\mathbb{R}$ for all
$x\in\mathbb{R}^d$. Furthermore, if $S$ is translation invariant, i.e.,
$S(t)(\tau_x f)=\tau_x S(t)f$, then $H$ does not depend on $x\in\mathbb{R}^d$,
see~\cite[Proposition~4.1]{Biton01}.
\end{remark}
\section{Generating families}
\label{sec:gen}
In many examples, the semigroup $S$ can be approximated by iterating another
family $I:=(I(t))_{t\geq 0}$ of operators which do not form a semigroup but have
(in contrast to $S$) an explicit representation. This leads to approximation schemes
of the form
\begin{equation} \label{eq:IS}
S(t)f=\lim_{l\to\infty}\big(I(h_{n_l})\big)^{t h_{n_l}^{-1}}f,
\quad\mbox{where } h_n\downarrow 0.
\end{equation}
Furthermore, they can be used in order to construct nonlinear semigroups, see~\cite{BK20}.
In this case, we call $I$ a \emph{generating family} and $S$ an \emph{associated semigroup}.
In view of the previous results, we expect, in particular, that two generating families with
the same infinitesimal behaviour lead to the same associated semigroup.
In the sequel, we fix a family of operators $I(t)\colon{\rm C}_\kappa\to{\rm C}_\kappa$ and a sequence
$(h_n)_{n\in\mathbb{N}}\subset (0,1]$ with $h_n\to 0$. For every $t\geq 0$ and $n\in\mathbb{N}$,
we define the iterated operators
\[ I(\pi^t_n):=I(h_n)^{k_n^t} I(t-k_n^t h_n), \]
where $k_n^t:=\max\{k\in\mathbb{N}_0\colon kh_n\leq t\}$ and $\pi^t_n:=\{kh_n\wedge t\colon k\in\mathbb{N}_0\}$
denotes the equidistant partition of $[0,t]$ with mesh size $h_n$.
The Lipschitz set $\mathcal{L}^I$ consists of all $f\in{\rm C}_\kappa$ such that there exist $t_0>0$ and $c\geq 0$
with
\[ \|I(t)f-f\|_\kappa\leq ct \quad\mbox{for all } t\in [0,t_0].\]
For $f\in\mathcal{L}^I$ such that the following limit exists uniformly on compacts we define the derivative
of the mapping $t\mapsto I(t)f$ at zero by
\[ I'(0)f:=\lim_{h\downarrow 0}\frac{I(h)f-f}{h}\in{\rm C}_\kappa. \]
Moreover, let $\mathbb{R}_+:=\{x\in\mathbb{R}\colon x\geq 0\}$.
\begin{assumption} \label{ass:I}
Suppose that $I$ satisfies the following conditions:
\begin{enumerate}
\item $I(0)=\id_{{\rm C}_\kappa}$.
\item The operator $I(t)$ is convex and monotone with $I(t)0=0$ for all $t\geq 0$.
\item There exists a function $\alpha\colon\mathbb{R}_+\times\mathbb{R}_+\to\mathbb{R}_+$, which is
non-decreasing in the second argument, such that, for all $r,s,t\geq 0$,
\[ I(t)\colon B_{{\rm C}_\kappa}(r)\to B_{{\rm C}_\kappa}(\alpha(r,t)) \quad\mbox{and}\quad
\alpha(\alpha(r,s),t)\leq\alpha(r,s+t). \]
\item For every $r\geq 0$, there exists $\omega_r\geq 0$ with
\[ \|I(t)f-I(t)g\|_\kappa\leq e^{t\omega_r}\|f-g\|_\kappa
\quad\mbox{for all } t\in [0,1] \mbox{ and } f,g\in B_{{\rm C}_\kappa}(r). \]
W.l.o.g., we can assume that the mapping $r\mapsto\omega_r$ is non-decreasing.
\item There exists a countable set $\mathcal{D}\subset\mathcal{L}^I$ such that the sequence
$(I(\pi_n^t)f)_{n\in\mathbb{N}}$ is uniformly equicontinuous for all $(f,t)\in\mathcal{D}\times\mathcal{T}$. Moreover,
for every $f\in{\rm C}_\kappa$, there exists a sequence $(f_n)_{n\in\mathbb{N}}\subset\mathcal{D}$ with
$\|f_n\|_\kappa\leq\|f\|_\kappa$ for all $n\in\mathbb{N}$ and $f_n\to f$ uniformly on compacts.
\item For every $t\geq 0$, $K\subset X$ compact and $(f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa$
with $f_n\downarrow 0$,
\[ \sup_{(s,x)\in [0,t]\times K}\sup_{n\in\mathbb{N}}\big(I(\pi_n^s)f_k\big)(x)\downarrow 0
\quad\mbox{as } k\to\infty. \]
\end{enumerate}
\end{assumption}
For every $(f,t)\in\mathcal{D}\times\mathcal{T}$, it follows from the conditions~(iii) and~(v) and
Lemma~\ref{lem:AA}, that the sequence $(I(\pi_n^t)f)_{n\in\mathbb{N}}$ has a subsequence
which convergences uniformly on compacts. Hence, we can define $S(t)f$ by
equation~\eqref{eq:IS} for all $(f,t)\in\mathcal{D}\times\mathcal{T}$ and then extend to ${\rm C}_\kappa\times\mathbb{R}_+$.
In many examples, the uniform equicontinuity required in condition~(v) is ensured
for Lipschitz continuous functions, see Assumption~\ref{ass:I2}(iii) below.
By construction, properties of $I$ transfer to $S$. However, since we only have
uniform convergence on compacts in equation~\eqref{eq:IS}, the semigroup property
is rather delicate and requires an additional assumption which is given by condition~(vi).
Another possibility to ensure the semigroup property is to assume norm convergence
or monotone convergence, see~\cite{BK20, NR21+, FKN21, BEK}.
\begin{remark} \label{rem:I}
We mention two sufficient conditions for Assumption~\ref{ass:I}(vi).
\begin{enumerate}
\item Let $\tilde{\kappa}\colon X\to (0,\infty)$ be another bounded continuous function
such that, for every $\varepsilon>0$, there exists a compact set $K\subset X$ with
$\sup_{x\in K^c}\frac{\tilde{\kappa}(x)}{\kappa(x)}\leq\varepsilon$.
Furthermore, we assume that there exists a function
$\tilde{\alpha}\colon\mathbb{R}_+\times\mathbb{R}_+\to\mathbb{R}_+$, which is non-decreasing
in the second argument, such that, for all $r,s,t\geq 0$ and $f\in{\rm C}_\kappa$ with
$\|f\|_{\tilde{\kappa}}\leq r$,
\begin{equation} \label{eq:tilde}
\|I(t)f\|_{\tilde{\kappa}}\leq\tilde{\alpha}(r,t)
\quad\mbox{and}\quad
\tilde{\alpha}(\tilde{\alpha}(r,s),t)\leq\tilde{\alpha}(r,s+t).
\end{equation}
For every sequence $(f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa$ with $f_n\downarrow 0$, Dini's theorem
implies uniform convergence on compact sets and therefore $\|f_n\|_{\tilde{\kappa}}\to 0$.
It follows from Assumption~\ref{ass:I}(ii), equation~\eqref{eq:tilde},~\cite[Lemma~2.7]{BK20}
and Lemma~\ref{lem:lip}(ii) that
\[ \sup_{s\in [0,t]}\sup_{n\in\mathbb{N}}\|I(\pi_n^s)f_k\|_{\tilde{\kappa}}
\leq\tilde{\alpha}(3\|f_1\|_{\tilde{\kappa}},t)\|f_k\|_{\tilde{\kappa}}\to 0
\quad\mbox{as } k\to\infty. \]
Since $\inf_{x\in K}\kappa(x)>0$ for every compact subset $K\subset X$, we obtain
that Assumption~\ref{ass:I}(vi) is satisfied.
\item Assume that there exists a family $J$ of operators $J(t)\colon{\rm C}_\kappa\to{\rm C}_\kappa$, which
are continuous from above, such that, for all $s,t\geq 0$ and $f\in{\rm C}_\kappa$,
\[ I(t)f\leq J(t)f \quad\mbox{and}\quad J(s)J(t)f\leq J(s+t)f. \]
In addition, we suppose that the mapping
\[ \mathbb{R}_+\times X\to\mathbb{R},\; (t,x)\mapsto (J(t)f)(x) \]
is upper semicontinuous for all $f\in{\rm C}_\kappa$. By induction, we obtain
\[ I(\pi_n^t)f\leq J(t)f \quad\mbox{for all } t\geq 0, n\in\mathbb{N} \mbox{ and } f\in{\rm C}_\kappa.\]
For every $t\geq 0$, $K\subset X$ compact and sequence $(f_n)_{n\in\mathbb{N}}\subset{\rm C}_\kappa$
with $f_n\downarrow 0$, Dini's theorem implies
\[ \sup_{(s,x)\in [0,t]\times K}\sup_{n\in\mathbb{N}}\big(I(\pi_n^s)f_k\big)(x)
\leq\sup_{(s,t)\in [0,t]\times K}(J(t)f_k)(x)\downarrow 0 \quad\mbox{as } k\to\infty. \]
\end{enumerate}
\end{remark}
The next statement is a consequence of the results in~\cite{BK20}
and Appendix~\ref{app:ext}. For the reader's convenience, we provide
a proof in Appendix~\ref{app:I}. Subsequently, we define
\[ \|f\|_{\infty,Y}:=\sup_{x\in Y}|f(x)|
\quad\mbox{for all } f\colon X\to\mathbb{R} \mbox{ and } Y\subset X. \]
\begin{theorem} \label{thm:I}
Suppose that Assumption~\ref{ass:I} is satisfied and let $\mathcal{T}\subset\mathbb{R}_+$ be
a countable dense set including zero. Then, there exist a family $S$ of
operators $S(t)\colon{\rm C}_\kappa\to{\rm C}_\kappa$ and a subsequence $(n_l)_{l\in\mathbb{N}}\subset\mathbb{N}$ such
that, uniformly on compacts,
\begin{equation} \label{eq:IS2}
S(t)f=\lim_{l\to\infty}I(\pi_{n_l}^t)f \quad\mbox{for all } (f,t)\in{\rm C}_\kappa \times\mathcal{T}.
\end{equation}
Furthermore, the following statements hold:
\begin{enumerate}
\item $S(0)=\id_{{\rm C}_\kappa}$ and $S(s+t)f=S(s)S(t)f$ for all $s,t\geq 0$ and $f\in{\rm C}_\kappa$.
\item $S(t)$ is convex and monotone with $S(t)0=0$ for all $t\geq 0$.
\item For every $r,t\geq 0$ and $f,g\in B_{{\rm C}_\kappa}(r)$, we have
\[ \|S(t)f\|_\kappa\leq\alpha(r,t) \quad\mbox{and}\quad
\|S(t)f-S(t)g\|_\kappa\leq e^{t\omega_{\alpha(r,t)}}\|f-g\|_\kappa. \]
\item For every $\varepsilon>0$, $r,t\geq 0$ and compact set $K\subset X$, there exist another
compact set $K'\subset X$ and a constant $c\geq 0$ with
\[ \|S(s)f-S(s)g\|_{\infty,K}\leq c\|f-g\|_{\infty,K'}+\varepsilon \]
for all $s\in [0,t]$ and $f,g\in B_{{\rm C}_\kappa}(r)$.
\item For every $t\geq 0$, $f\in{\rm C}_\kappa$ and compact set $K\subset\mathbb{R}^d$,
\[ \lim_{s\to t}\sup_{x\in K}|(S(s)f)(x)-(S(t)f)(x)|=0. \]
\item It holds $\mathcal{L}^I\subset\mathcal{L}^S$. Moreover, for every $f\in\mathcal{L}^I$ such that $I'(0)f\in{\rm C}_\kappa$
exists,
\[ I'(0)f=\lim_{h\downarrow 0}\frac{S(h)f-f}{h},\]
where the limit on the right-hand side exists uniformly on compacts.
\end{enumerate}
In particular, $S$ satisfies Assumption~\ref{ass:S}.
\end{theorem}
If the sequence $(I(\pi_n^t)f)_{n\in\mathbb{N}}$ is non-decreasing, which is for instance the
case for Nisio semigroups~\cite{Nisio, NR21+}, it holds $S(t)f=\sup_{n\in\mathbb{N}}I(\pi_n^t)f$.
Hence, the limit in equation~\eqref{eq:IS2} exists without choosing a convergent
subsequence. Under mild additional assumptions, one can further show that
$S(t)f=\sup_{\pi\in\mathcal{P}_t}I(\pi)f$, where $\mathcal{P}_t$ consists of all finite partitions of the
interval $[0.t]$. For details we refer to~\cite[Lemma~2.15]{BK20}.
In the sequel, we focus on the case $X:=\mathbb{R}^d$ in order to apply the approximation
results from Subsection~\ref{sec:conv2}. Furthermore, we assume that there exists
$\delta_0>0$ with
\begin{equation} \label{eq:kappa2}
\sup_{x\in\mathbb{R}^d}\sup_{y\in B(x,\delta_0)}\frac{\kappa(x)}{\kappa(y)}\leq 1.
\end{equation}
To simplify the notation, we subsequently fix $\delta_0:=1$. For every $r\geq 0$, let
${\rm Lip}_{\rm b}(r)$ be the space of all $r$-Lipschitz functions $f\colon X\to\mathbb{R}$ with
$\|f\|_\infty\leq r$.
\begin{assumption} \label{ass:I2}
Suppose that $I$ satisfies the following conditions:
\begin{enumerate}
\item There exist $L\geq 0$ and $\delta\in (0,1]$ with
\[ \| I(t)(\tau_x f)-\tau_x I(t)f\|_\kappa\leq Lrt|x| \]
for all $t\in [0,1]$, $r\geq 0$, $f\in{\rm Lip}_{\rm b}(r)$ and $x\in B_{\mathbb{R}^d}(\delta)$.
\item It holds ${\rm C}_{\rm b}^\infty\subset\mathcal{L}^I$ and $I'(0)f\in{\rm C}_\kappa$ exists for all $f\in{\rm C}_{\rm b}^\infty$.
\item There exists a function $\beta\colon\mathbb{R}_+\times\mathbb{R}_+\to\mathbb{R}_+$,
which is non-decreasing in the second argument, such that, for all
$r,s,t\geq 0$,
\[ I(t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(\beta(r,t)) \quad\mbox{and}\quad
\beta(\beta(r,s),t)\leq\beta(r,s+t). \]
\end{enumerate}
\end{assumption}
By Theorem~\ref{thm:I}, there exists an associated semigroup $S$. Let
$\eta\colon\mathbb{R}^d\to\mathbb{R}_+$ be an infinitely differentiable function with
$\supp(\eta)\subset B_{\mathbb{R}^d}(1)$ and
$\int_{\mathbb{R}^d}\eta(x)\,{\rm d} x=1$. For every $n\in\mathbb{N}$ and $x\in\mathbb{R}^d$, we define
$\eta_n(x):=n^d\eta(nx)$ and
\[ (f*\eta_n)(x):=\int_{\mathbb{R}^d} f(x-y)\eta_n(y)\,{\rm d} y,\]
where $f\colon\mathbb{R}^d\to\mathbb{R}$ is locally integrable.
\begin{theorem} \label{thm:I2}
Suppose that $I$ satisfies Assumption~\ref{ass:I} and Assumption~\ref{ass:I2}.
Then, it holds $\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}\subset D(A_\Gamma)$ and, for every $f\in\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}$,
\[ A_\Gamma f=\Glim_{n\to\infty}A_\Gamma(f*\eta_n)=\Glim_{n\to\infty}I'(0)(f*\eta_n). \]
In addition, for every $r,t\geq 0$, it holds $S(t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(\beta(r,t))$ and
\[ \|S(t)(\tau_x f)-\tau_x S(t)f\|_\kappa\leq Lt\beta(r,t)e^{t\omega_{\alpha(r,t)}}|x| \]
for all $f\in B_{{\rm C}_\kappa}(r)\cap{\rm Lip}_{\rm b}(r)$ and $x\in B_{\mathbb{R}^d}(\delta)$.
\end{theorem}
\begin{proof}
By induction, one can show that
\[ I(\pi_n^t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(\beta(r,t))
\quad\mbox{for all } r,t\geq 0 \mbox{ and } n\in\mathbb{N}. \]
We use equation~\eqref{eq:IS2} and Theorem~\ref{thm:I}(v) to conclude
\[ S(t)\colon{\rm Lip}_{\rm b}(r)\colon{\rm Lip}_{\rm b}(\beta(r,t)) \quad\mbox{for all } r,t\geq 0. \]
Next, we show by induction that
\begin{equation} \label{eq:shift}
\|I(2^{-n})^k(\tau_x f)-\tau_x I(2^{-n})^k f\|_\kappa
\leq L\beta(r,k2^{-n})e^{k2^{-n}\omega_{\alpha(r,k2^{-n})}}k2^{-n}|x|
\end{equation}
for all $k,n\in\mathbb{N}$, $r\geq 0$ $f\in B_{{\rm C}_\kappa}(r)\cap{\rm Lip}_{\rm b}(r)$ and $x\in B_{\mathbb{R}^d}(\delta)$.
For $k=1$ the previous estimate holds by Assumption~\ref{ass:I2}(i). Suppose
that inequality~\eqref{eq:shift} holds for some fixed $k\in\mathbb{N}$. For every $r\geq 0$
and $f\in B_{{\rm C}_\kappa}(r)\cap{\rm Lip}_{\rm b}(r)$, it follows from Assumption~\ref{ass:I}(iii),
Assumption~\ref{ass:I2}(iii) and condition~\eqref{eq:kappa2} that
\[ I(2^{-n})f, I(2^{-n})(\tau_x f),\tau_x I(2^{-n})f
\in B_{{\rm C}_\kappa}(\alpha(r,2^{-n}))\cap{\rm Lip}_{\rm b}(\beta(r,2^{-n})).\]
We use~\cite[Lemma~2.7]{BK20}, Assumption~\ref{ass:I2}(i) and inequality~\eqref{eq:shift}
to conclude
\begin{align*}
&\|I(2^{-n})^{k+1}(\tau_x f)-\tau_x I(2^{-n})^{k+1}f\|_\kappa \\
&\leq\|I(2^{-n})^k I(2^{-n})(\tau_x f)-I(2^{-n})^k(\tau_x I(2^{-n})f)\|_\kappa \\
&\quad\; +\|I(2^{-n})^k(\tau_x I(2^{-n})f)-\tau_x I(2^{-n})^k I(2^{-n})f\|_\kappa \\
&\leq e^{k2^{-n}\omega_{\alpha(\alpha(r,2^{-n}),k2^{-n})}}
\|I(2^{-n})(\tau_x f)-\tau_x I(2^{-n})f\|_\kappa \\
&\quad\; +L\beta(\beta(r,2^{-n}),k2^{-n})e^{k2^{-n}
\omega_{\alpha(\alpha(r,2^{-n}),k2^{-n})}}k2^{-n}|x| \\
&\leq e^{k2^{-n}\omega_{\alpha(r,(k+1)2^{-n})}}Lr2^{-n}|x|
+L\beta(r,(k+1)2^{-n})e^{k2^{-n}\omega_{\alpha(r,(k+1)2^{-n})}}k2^{-n}|x| \\
&\leq L\beta(r,(k+1)2^{-n})e^{(k+1)2^{-n}\omega_{\alpha(r,(k+1)2^{-n}}}(k+1)2^{-n}|x|.
\end{align*}
Due to Equation~\eqref{eq:IS2} and Theorem~\ref{thm:I}(v), inequality~\eqref{eq:shift}
transfers to $S$, i.e.,
\[ \|S(t)(\tau_x f)-\tau_x S(t)f\|_\kappa
\leq Lt\beta(r,t)e^{t\omega_{\alpha(r,t)}}|x| \]
for all $r, t\geq 0$, $f\in B_{{\rm C}_\kappa}(r)\cap{\rm Lip}_{\rm b}(r)$ and $x\in B_{\mathbb{R}^d}(\delta)$. In particular,
condition~\eqref{eq:trans} is satisfied for all $f\in{\rm Lip}_{\rm b}$. Moreover, for every $f\in{\rm C}_{\rm b}^\infty$,
it follows from Assumption~\ref{ass:I2}(ii) and Theorem~\ref{thm:I}(vi) that $f\in D(A_\Gamma)$
with $A_\Gamma f=I'(0)f$. Hence, Lemma~\ref{lem:conv2} implies $\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}\subset D(A_\Gamma)$
and $A_\Gamma f=\Glim_{n\to\infty}A_\Gamma(f*\eta_n)$ for all $f\in\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}$.
\end{proof}
To conclude this section, we address the initial question of whether two generating
families with the same infinitesimal behaviour lead to the same associated semigroup.
The upper Lipschitz set $\mathcal{L}^I_+$ consists of all $f\in{\rm C}_\kappa$ such that there exist $t_0>0$
and $c\geq 0$ with
\[ \|(I(t)f-f)^+\|_\kappa\leq ct \quad\mbox{for all } t\in [0,t_0].\]
We further introduce the symmetric Lipschitz set $\mathcal{L}^I_{\sym}:=\{f\in\mathcal{L}^I\colon -f\in\mathcal{L}^I\}$
which can be, in many examples, determined explicitly, see Subsection~\ref{sec:control}.
Moreover, in~\cite[Section~5]{BK20}, the authors provide conditions which guarantee that
$\mathcal{L}^I_{\sym}=\mathcal{L}^S_{\sym}$ and $S(t)\colon\mathcal{L}^S_{\sym}\to\mathcal{L}^S_{\sym}$ for all $t\geq 0$.
Under the assumption that $I(t)$ is globally Lipschitz continuous one can show that
$\mathcal{L}^I_+\subset\mathcal{L}^S_+$ and if, in addition,
\[ I(t)f\leq S(t)f \quad\mbox{for all } t\geq 0 \mbox{ and } f\in{\rm C}_\kappa, \]
we obtain the equality $\mathcal{L}^I_+=\mathcal{L}^S_+$. For further research, it would be desirable to
find general conditions that do not involve inequalities between $I$ and $J$, but still
guarantee the equality $\mathcal{L}^I_+=\mathcal{L}^S_+$.
\begin{theorem} \label{thm:I3}
Let $I$ and $J$ be two families of operators which satisfy Assumption~\ref{ass:I} and
Assumption~\ref{ass:I2}. Denote by $S$ and $T$, respectively, the associated semigroups
which exist due to Theorem~\ref{thm:I}. Let $\mathcal{C}\subset\mathcal{L}^T\cap\mathcal{L}^S_+\cap{\rm Lip}_{\rm b}$
such that $T(t)\colon\mathcal{C}\to\mathcal{C}$ for all $t\geq 0$ and assume that
\[ I'(0)f\leq J'(0)f \quad\mbox{for all } f\in{\rm C}_{\rm b}^\infty.\]
Then, it holds $S(t)f\leq T(t)f$ for all $t\geq 0$ and $f\in{\rm C}_\kappa$.
\end{theorem}
\begin{proof}
It follows from Theorem~\ref{thm:I}(vi) and Assumption~\ref{ass:I2}(ii) that
\[ A_\Gamma f=I'(0)f\leq J'(0)f=B_\Gamma f \quad\mbox{for all }f\in{\rm C}_{\rm b}^\infty, \]
where $A_\Gamma$ and $B_\Gamma$ denote the $\Gamma$-generators of $S$ and $T$, respectively.
Hence, Theorem~\ref{thm:I2} and Lemma~\ref{lem:gamma}(iv) imply
\[ A_\Gamma f=\Glim_{n\to\infty}A_\Gamma(f*\eta_n)\leq\Glim_{n\to\infty}B_\Gamma(f*\eta_n)=B_\Gamma f
\quad\mbox{for all } f\in\mathcal{C}. \]
We apply Corollary~\ref{cor:comp} to conclude $S(t)f\leq T(t)f$ for all $t\geq 0$ and
$f\in{\rm C}_{\rm b}^\infty$. In order to generalize this inequality to the whole space ${\rm C}_\kappa$, let
$f\in B_{{\rm C}_\kappa}(r)$ for some $r\geq 0$. By multiplication with a smooth cutting
function and convolution with a smooth molifier, we can construct a sequence
$(f_n)_{n\in\mathbb{N}}\subset B_{{\rm C}_\kappa}(r)\cap{\rm C}_{\rm c}^\infty$ with $f_n\to f$ uniformly on
compacts. Theorem~\ref{thm:I}(iv) implies, uniformly on compacts,
\[ S(t)f=\lim_{n\to\infty}S(t)f_n\leq\lim_{n\to\infty}T(t)f_n=T(t)f. \qedhere \]
\end{proof}
\section{Examples}
\label{sec:examples}
\subsection{Control problems and upper semigroup envelopes}
\label{sec:control}
In this subsection, we show that value functions of stochastic optimal control
problems can be approximated by a sequence of static optimization problems
over increasingly finer partitions. The latter corresponds to the construction
of so-called upper semigroup envelopes, cf. Nisio~\cite{Nisio}
and Nendel and R\"ockner~\cite{NR21+}. For a
representative class of optimal control problems, we thus show that
the value function coincides with the upper envelope of a suitable family
of penalized linear semigroups.
Let $(W_t)_{t\geq 0}$ be a $d$-dimensional standard Brownian motion on
a complete filtered probability space $(\Omega,\mathcal F,(\mathcal F_t)_{t\geq 0},\mathbb{P})$
satisfying the usual conditions. Denote by $\mathbb{S}^d_+$ the set of all symmetric
positive semidefinite $d\times d$-matrices. Throughout this subsection,
we fix a measurable function $L\colon\mathbb{S}^d_+\times \mathbb{R}^d\to [0,\infty]$
satisfying the following assumption.
\begin{assumption} \label{ass:L}
Suppose that $L$ satisfies the following conditions:
\begin{enumerate}
\item There exists $(a^*,b^*)\in\mathbb{S}^d_+\times\mathbb{R}^d$ with $L(a^*,b^*)=0$.
\item $L$ grows superlinearly, i.e.,
\[ \lim_{|a|+|b|\to\infty}\frac{L(a,b)}{|a|+|b|}=\infty.\]
\end{enumerate}
\end{assumption}
\noindent
In order to apply It\^o's isometry, we endow $\mathbb{R}^{d\times d}$ with
the Frobenius norm
\[ |a|:=\sqrt{\sum_{i,j=1}^d |a_{ij}|^2}
\quad\mbox{for all } a\in\mathbb{R}^{d\times d}. \]
Let $\mathcal{A}$ be the set of all predictable processes
$(a,b)\colon\Omega\times\mathbb{R}_+\to\mathbb{S}^d_+\times\mathbb{R}^d$ with
\[ \mathbb{E}\left[\int_0^t |a_s|+|b_s|\,{\rm d} s\right]<\infty
\quad \mbox{for all } t\geq 0. \]
For every $t\geq 0$, $f\in{\rm C}_{\rm b}$ and $x\in\mathbb{R}^d$, we define
\begin{align*}
(S(t)f)(x):=\sup_{(a,b)\in\mathcal{A}}
\left(\mathbb{E}\Big[f\Big(x+\int_0^t\sqrt{a_s}\,{\rm d} W_s+\int_0^t b_s\,{\rm d} s\Big)\Big]
-\mathbb{E}\Big[\int_0^t L(a_s,b_s)\,{\rm d} s\Big]\right),
\end{align*}
where $\mathbb{E}[X]$ denotes the expectation of a random variable
$X\colon\Omega\to\mathbb{R}$. Note that $S(t)f$ is the value function of a
dynamic optimal control problem with finite time horizon $t\geq 0$.
In addition, for every $t\geq 0$, $f\in{\rm C}_{\rm b}$ and $x\in\mathbb{R}^d$, we define
the value function of the related static control problem
\[ (J(t)f)(x):=\sup_{(a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d}
\big(\mathbb{E}[f(x+\sqrt{a}W_t+bt)]-L(a,b)t\big). \]
Subsequently, we use the following notations:
\begin{align*}
X_t^{a,b} &:=\int_0^t \sqrt{a_s}\,{\rm d} W_s+\int_0^t b_s\,{\rm d} s
\quad\mbox{for all } (a,b)\in\mathcal{A} \mbox{ and } t\geq 0, \\
c_L &:=\sup_{(a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d}\frac{|a|+|b|}{1+L(a,b)}, \\
L^*(c) &:=\sup_{(a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d}\big(c(|a|+|b|)-L(a,b)\big)
\quad\mbox{for all } c\geq 0, \\
B_{a,b}f &:=\frac{1}{2}\tr(a D^2 f)+\langle\nabla f,b\rangle
\quad\mbox{for all } f\in{\rm BUC}^2 \mbox{ and } (a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d,
\end{align*}
where ${\rm BUC}^2$ denotes the space of all twice differentiable
$f\in{\rm BUC}$ such that the first and second derivative are in ${\rm BUC}$.
Assumption~\ref{ass:L}(ii) implies $c_L<\infty$ and $L^*(c)\to 0$
as $c\downarrow 0$. The proof of the following auxiliary estimates
consists of straightforward but lengthy calculations, see
Appendix~\ref{app:control}.
\begin{lemma} \label{lem:control} {\rule{0mm}{1mm}\\[-3.25ex]\rule{0mm}{1mm}}
\begin{enumerate}
\item For every $c,t\geq 0$, $r>0$ and $(a,b)\in\mathcal{A}$,
\[ c\mathbb{P}(|X_t^{a,b}|\geq r)-\mathbb{E}\left[\int_0^t L(a_s,b_s)\,{\rm d} s\right]
\leq\frac{c}{r}+L^*\Big(\frac{c}{r}\Big)t. \]
In particular, $S$ is continuous from above.
\item For every $c,t\geq 0$, $\delta\in (0,1]$, $x\in\mathbb{R}^d$, $(a,b)\in\mathcal{A}$
and $f\in{\rm Lip}_{\rm b}(c)$,
\[ \mathbb{E}\left[\int_0^t f(x+X_s^{a,b})\,{\rm d} s\right]
\leq\big(f(x)+c\delta\big)t
+\frac{cc_L}{\delta^2}\mathbb{E}\left[\int_0^t \int_0^s 1+L(a_u,b_u)\,{\rm d} u\,{\rm d} s\right].\]
\item Let $t\geq 0$, $x\in\mathbb{R}^d$, $f\in{\rm BUC}^2$ and $(a,b)\in\mathcal{A}$ with
\[ (S(t)f)(x)\leq t+\mathbb{E}\big[f(x+X_t^{a,b})\big]
-\mathbb{E}\left[\int_0^t L(a_s,b_s)\,{\rm d} s\right]. \]
Then, for
$c_f:=2\big(1+\|B_{a^*,b^*}f\|_\infty\big)
+L^*\big(\|D^2 f\|_\infty\vee 2\|\nabla f\|_\infty\big)$, it holds
\[ \mathbb{E}\left[\int_0^t L(a_s,b_s)\,{\rm d} s\right]\leq c_f t.\]
\end{enumerate}
\end{lemma}
The next theorem is a consequence of the results in Section~\ref{sec:gen}
and a generalization of the example presented in~\cite[Section~6.1]{BK20}.
For the reader's convenience, we provide a proof in Appendix~\ref{app:control}.
Denote by $L^\infty$ the set of all bounded measurable functions
$f\colon\mathbb{R}^d\to\mathbb{R}$ and by $W^{1,\infty}$ the corresponding first order
Sobolev space. For $f\in W^{1,\infty}$ and $a\in\mathbb{S}^d_+$, we say that
$\Delta_a f$ exists in $L^\infty$ if there exists a function $g\in L^\infty$
with
\[ \int_{\mathbb{R}^d}g\phi\,{\rm d} x
=-\int_{\mathbb{R}^d}\langle\sqrt{a}\nabla f,\sqrt{a}\nabla\phi\rangle\,{\rm d} x
\quad\mbox{for all } \phi\in{\rm C}_{\rm c}^\infty \]
In this case, since $g$ is unique almost everywhere, we define $\Delta_a f:=g$.
Clearly, it holds $\Delta_a f=\sum_{i,j=1}^n a_{ij}\partial_{ij}f$ for all $f\in{\rm BUC}^2$.
Moreover, let $\nabla_b f:=\langle b,\nabla f\rangle$ for all $f\in W^{1,\infty}$
and $b\in\mathbb{R}^d$. Define
\[ \mathbb{S}_L:=\Big\{a\in\mathbb{S}^d_+\colon\inf_{b\in\mathbb{R}^d}L(a,b)<\infty\Big\}.\]
\begin{theorem} \label{thm:control}
There exists a family $S$ of operators $S(t)\colon{\rm C}_{\rm b}\to{\rm C}_{\rm b}$, which satisfy
Assumption~\ref{ass:S}, such that, uniformly on compacts,
\[ T(t)f=\lim_{n\to\infty}J(\pi_n^t)f=\sup_{n\in\mathbb{N}}J(\pi_n^t)f
\quad\mbox{for all } f\in{\rm C}_{\rm b} \mbox{ and } t\geq 0. \]
Furthermore, $T$ is a strongly continuous convex monotone semigroup
on ${\rm BUC}$. Denoting by $B$ the norm generator of $T$, it holds
${\rm BUC}^2\subset D(B)$ with
\[ Bf=\sup_{(a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d}
\Big(\frac{1}{2}\Delta_a f+\nabla_b f-L(a,b)\Big)
\quad\mbox{for all } f\in{\rm BUC}^2. \]
It holds $T(t)\colon\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}\to\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}$
for all $t\geq 0$ and $\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}$ has the explicit
characterization
\begin{align*}
\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}
&=\Big\{f\in\bigcap_{a\in\mathbb{S}_L}D(\Delta_a)\cap W^{1,\infty}\colon
\sup_{(a,b)\in\mathbb{S}_L\times\mathbb{R}^d}
\big(\|B_{a,b}f\|_\infty-L(a,b)\big)<\infty\Big\}
\end{align*}
Furthermore, we have $T(t)f\leq S(t)f$ for all $t\geq 0$ and $f\in{\rm C}_{\rm b}$.
\end{theorem}
We do not assume that the matrices $a\in\mathbb{S}_L$ are positive definite
which is a common assumption for parabolic PDEs. Moreover, in the
completely degenerate case $\mathbb{S}_L=\{0\}$, we have
$\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}={\rm Lip}_{\rm b}$ and $T$ is a shift semigroup corresponding
to a first order PDE. If there exists a positive definite matrix $a\in\mathbb{S}_L$,
then~\cite[Theorem~3.1.7]{Lunardi95} implies
\[ \mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}\subset D(\Delta)
=\bigcap_{p\geq 1} \{f\in W^{2,p}_{\loc}\cap{\rm BUC}\colon \Delta f\in L^\infty\}. \]
In particular, if the function
\[ H\colon\mathbb{R}^{d\times d}\times\mathbb{R}^d,
(x,y)\mapsto\sup_{(a,b)\in\mathbb{S}^d_+\times\mathbb{R}^d}
\Big(\frac{1}{2}\sum_{i,j=1}^d a_{ij}x_{ij}+\sum_{i=1}^d b_i y_i\Big) \]
has at most polynomial growth, we can apply Theorem~\ref{thm:dist}.
Note that the operator $B$ can still be degenerate, since positive
definiteness is not required for all $a\in\mathbb{S}_L$. We also remark that
if there exist $a\in\mathbb{S}^d_+$ and $\varepsilon>0$ with
\[ \sup_{\{b\in\mathbb{R}^d\colon |b|=\varepsilon\}}L(a,b)<\infty, \]
then one can show $\mathcal{L}^T_{\sym}\subset{\rm Lip}_{\rm b}$. For details we refer to the
proof of~\cite[Theorem~6.3]{BK20}. However, without this additional
assumption on $L$, the intersection with ${\rm Lip}_{\rm b}$ is necessary. To our
knowledge, an explicit description of $\mathcal{L}^T_{\sym}$ seems to be
unknown even in the linear case $B=\Delta$, where $\mathcal{L}^T_{\sym}$
coincides with the Favard space which has been discussed in
Remark~\ref{rem:Lset}.
Denote by ${\rm Lip}_{\rm b}^2$ the space of all twice differentiable functions
$f\in{\rm Lip}_{\rm b}$ such that the first and second derivative are in ${\rm Lip}_{\rm b}$.
Moreover, we denote by $A$ the norm generator of $S$.
\begin{theorem} \label{thm:control2}
The family $S$ satisfies Assumption~\ref{ass:S}. Furthermore, we
have ${\rm Lip}_{\rm b}^2\subset D(A)$, $Af=Bf$ for all $f\in{\rm Lip}_{\rm b}^2$ and
$\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}\subset\mathcal{L}^S_+$. Hence,
\[ S(t)f=T(t)f \quad\mbox{for all } (f,t)\in{\rm C}_{\rm b}\times\mathbb{R}_+. \]
\end{theorem}
\begin{proof}
First, we note that $S(t)$ is convex and monotone with $S(t)0=0$
for all $t\geq 0$. By Lemma~\ref{lem:control}(i), $S$ is continuous
from above. It holds $\|S(t)f-S(t)g\|_\infty\leq\|f-g\|_\infty$ for all
$t\geq 0$ and $f,g\in{\rm C}_{\rm b}$. Thus, we obtain $S(t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(r)$
for all $r,t\geq 0$, since $S(t)$ is translation invariant. It follows that
$S(t)\colon{\rm BUC}\to{\rm BUC}$ and $S(t)\colon{\rm C}_{\rm b}\to{\rm U}_{\rm b}$, because
${\rm Lip}_{\rm b}\subset{\rm BUC}$ is dense and ${\rm U}_{\rm b}=({\rm BUC})_\delta$.
Moreover, the dynamic programming principle, see, e.g., Fabbri et
al.~\cite[Theorem~2.24]{Fabbri} or Pham~\cite[Theorem~3.3.1]{Pham},
yields that $S$ is a semigroup on ${\rm BUC}$. Hence, in order to verify
condition~\ref{S3}, it suffices to show that $\lim_{t\downarrow 0}\|S(t)f-f\|_\infty$
for a dense subset of ${\rm BUC}$.
Second, we show that ${\rm Lip}_{\rm b}^2\subset D(A)$ and $Af=Bf$ for all
$f\in{\rm Lip}_{\rm b}^2$. Let $f\in{\rm Lip}_{\rm b}^2$, $\varepsilon\in (0,1]$, $t>0$ and
$x\in \mathbb{R}^d$. Choose $(a,b)\in \mathcal{A}$ with
\[ (S(t)f)(x)\leq\frac{\varepsilon t}{2}+\mathbb{E}\big[f(x+X_t^{a,b})\big]
-\mathbb{E}\left[\int_0^t L(a_s,b_s)\,{\rm d} s\right]. \]
By Theorem~\ref{thm:control} and Assumption~\ref{ass:L}(ii),
there exists $c>0$ with $Bf\in{\rm Lip}_{\rm b}(c)$. Define
$\delta:=\nicefrac{\varepsilon}{2c}$. We use It\^o's formula,
Theorem~\ref{thm:control} and Lemma~\ref{lem:control}(ii) and~(iii)
to obtain
\begin{align*}
\left(\frac{S(t)f-f}{t}\right)(x)
&\leq\frac{\varepsilon}{2}+\mathbb{E}\left[\frac{1}{t}\int_0^t
B_{a_s,b_s}f(x+X_s^{a,b})-L(a_s,b_s)\,{\rm d} s\right] \\
&\leq\frac{\varepsilon}{2}+\mathbb{E}\left[\frac{1}{t}\int_0^t Bf(x+X_s^{a,b})\,{\rm d} s\right] \\
&\leq Bf(x)+\varepsilon+\frac{cc_L}{\delta^2}
\mathbb{E}\left[\frac{1}{t}\int_0^t \int_0^s 1+L(a_u,b_u)\,{\rm d} u\,{\rm d} s\right] \\
&\leq Bf(x)+\varepsilon+\frac{cc_L}{\delta^2}\frac{(1+c_f)t}{2}.
\end{align*}
It follows from $T(t)f\leq S(t)f$ and Theorem~\ref{thm:control} that
\begin{align*}
0=\lim_{t\downarrow 0}\sup_{x\in\mathbb{R}^d}\left(\frac{T(t)f-f}{t}-Bf\right)(x)
\leq\lim_{t\downarrow 0}\sup_{x\in\mathbb{R}^d}\left(\frac{S(t)f-f}{t}-Bf\right)(x)
\leq\varepsilon.
\end{align*}
Letting $\varepsilon\downarrow 0$ yields $f\in D(A)$ and $Af=Bf$.
Third, we show that $\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}\subset\mathcal{L}^S_+$. Let
$f\in\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}$. Theorem~\ref{thm:control} implies
$f\in\bigcap_{a\in\mathbb{S}_L}D(\Delta_a)\cap W^{1,\infty}$ and
\[ C:=\sup_{(a,b)\in\mathbb{S}_L\times\mathbb{R}^d}
\big(\|B_{a,b}f\|_\infty-L(a,b)\big)<\infty. \]
Let $\eta\in{\rm C}_{\rm c}^\infty$ with $\eta\geq 0$, $\supp(\eta)\subset B(0,1)$,
and $\int_{\mathbb{R}^d}\eta(x)\,{\rm d} x=1$. Let $\eta_n(x):=n^d\eta(nx)$ and
$f_n:=f*\eta_n$ for all $n\in\mathbb{N}$ and $x\in\mathbb{R}^d$. For every $(a,b)\in\mathcal{A}$,
$t\geq 0$ and $x\in\mathbb{R}^d$, we use It\^o's formula and
$\|B_{a_s,b_s}f_n\|_\infty\leq\|B_{a_s,b_s}f\|_\infty$ to estimate
\begin{align*}
&\mathbb{E}\big[f(x+X_t^{a,b})\big]-f(x)-\mathbb{E}\left[\int_0^t L(a_s,a_s)\,{\rm d} s\right] \\
&=\lim_{n\to\infty}\big(\mathbb{E}\big[f_n(x+X_t^{a,b})\big]-f_n(x)\big)
-\mathbb{E}\left[\int_0^t L(a_s,b_s)\,{\rm d} s\right] \\
&=\lim_{n\to\infty}\mathbb{E}\left[\int_0^t B_{a_s,b_s}f_n(x+X_s^{a,b})
-L(a_s,b_s)\,{\rm d} s\right] \\
&=\lim_{n\to\infty}\mathbb{E}\left[\int_0^t \Big(B_{a_s,b_s}f_n(x+X_s^{a,b})
-L(a_s,b_s\Big)\mathds{1}_{\{a_s\in\mathbb{S}_L\}}\,{\rm d} s\right]
\leq Ct.
\end{align*}
We obtain $S(t)f-f\leq Ct$ for all $t\geq 0$. It follows from
Theorem~\ref{thm:control} and Corollary~\ref{cor:comp} that $S(t)f=T(t)f$
for all $t\geq 0$ and $f\in{\rm Lip}_{\rm b}^2$. Now, let $f\in{\rm C}_{\rm b}$ by arbitrary. Choose
a bounded sequence $(f_n)_{n\in\mathbb{N}}\subset{\rm Lip}_{\rm b}^2$ with $f_n\to f$
uniformly on compacts. Lemma~\ref{lem:uniform} implies
$S(t)f=\lim_{n\to\infty}S(t)f_n=\lim_{n\to\infty}T(t)f_n=T(t)f$.
\end{proof}
\subsection{Trace class Wiener processes with drift}
\label{sec:infdim}
Let $X$ be a real separable Hilbert space with inner product
$\langle\,\cdot,\cdot\,\rangle$ and norm $|\cdot|$. Denote by
$\mathscr{S}_1(X)$ the space of all trace class operators endowed with the
trace class norm $\|\cdot\|_{\mathscr{S}_1(X)}$.
\begin{assumption} \label{ass:Q}
Let $B\times\mathcal{Q}\subset X\times\mathscr{S}_1(X)$ satisfy the following conditions:
\begin{enumerate}
\item $Q$ is selfadjoint and positive semidefinite for all $Q\in\mathcal{Q}$.
\item $Q_1Q_2= Q_2Q_1$ for all $Q_1,Q_2\in\mathcal{Q}$.
\item $B\times\mathcal{Q}$ is bounded.
\end{enumerate}
\end{assumption}
By the previous assumption and~\cite[Corollary~3.2.5]{Zimmer90},
there exists a joint orthonormal basis of eigenvectors
$(e_k)_{k\in\mathbb{N}}\subset X$, i.e., for every $Q\in\mathcal{Q}$ and $k\in\mathbb{N}$,
there exists $\mu_{Q,k}\geq 0$ with $Qe_k = \mu_{Q,k} e_k$.
For every $Q\in\mathcal{Q}$ and $x\in X$,
\[ Qx = \sum_{k\in\mathbb{N}}\mu_{Q,k} \,\langle x,e_k\rangle e_k. \]
Hence, every $Q\in\mathcal{Q}$ can be identified with the sequence
$\mu_Q=(\mu_{Q,k})_{k\in\mathbb{N}}\in\ell^1$ satisfying
$\tr(Q)=\|Q\|_{\mathscr{S}_1(X)}=\|\mu_Q\|_{\ell^1}$.
Assumption~\ref{ass:Q}(iii) implies that
$\Lambda:=B\times\mu(\mathcal{Q})\subset X\times\ell^1$ is bounded,
where $\mu(\mathcal{Q}):=\{\mu_Q\colon Q\in\mathcal{Q}\}$.
Let $(\xi^k)_{k\in\mathbb{N}}$ be a sequence of independent one-dimensional
standard Brownian motions on a complete filtered probability
space $(\Omega,\mathcal F,(\mathcal F_t)_{t\geq 0},\mathbb{P})$ satisfying
the usual conditions. For every $\lambda:=(b,\mu)\in\Lambda$,
the semigroup $(T_\lambda(t))_{t\geq 0}$ associated to the
$Q$-Wiener process with $\mu=\mu_Q$ and drift term $b$ is given by
\[ (T_\lambda(t)f)(x)
:=\mathbb{E}\left[f\left(x+tb+\sum_{k\in\mathbb{N}}\sqrt{\mu_k}\xi^k_t e_k\right)\right] \]
for all $t\geq 0$, $f\in{\rm BUC}$ and $x\in X$. Furthermore, we define
\[ J(t)f:=\sup_{\lambda\in\Lambda}T_\lambda(t)f
\quad\mbox{for all } t\geq 0 \mbox{ and } f\in{\rm BUC}. \]
Let $\mathcal{A}$ be the set of all predictable processes
\[ (b,\mu)\colon\Omega\times [0,\infty)\to\Lambda,\;
(\omega,t)\mapsto (b_t(\omega), (\mu^k_t(\omega))_{k\in\mathbb{N}}). \]
For every $t\geq 0$, $f\in {\rm BUC}$ and $x\in X$, we define
\[ (S(t)f)(x):=\sup_{(b,\mu)\in\mathcal{A}}
\mathbb{E}\left[f\left(x+\int_0^t b_s\,{\rm d} s
+\sum_{k\in\mathbb{N}}\Big(\int_0^t\sqrt{\mu_s^k}\,{\rm d}\xi^k_s\Big)e_k\right)\right]. \]
\begin{theorem}
There exists a strongly continuous convex monotone semigroup
$T$ on ${\rm BUC}$ such that, uniformly on compacts,
\[ T(t)f=\lim_{n\to\infty}J(\pi_n t)=\sup_{n\in\mathbb{N}}J(\pi_n^t)f
\quad\mbox{for all } f\in{\rm BUC} \mbox{ and } t\geq 0. \]
Furthermore, it holds $S(t)f=T(t)f$ for all $t\geq 0$ and $f\in{\rm BUC}$ such that
there exist a compact linear operator $K\colon X\to X$ and $g\in{\rm BUC}$ with
$f(x):=g(Kx)$ for all $x\in X$.
\end{theorem}
\begin{proof}
First, we show the existence of the associated semigroup $T$.
Since
\[ \sup_{(b,\mu)\in\Lambda}\big(|b|+\|\mu\|_{\ell^1}\big)<\infty, \]
we can apply the results from~\cite[Section~2 and Example~7.2]{NR21+}.
Hence, there exists a strongly continuous convex monotone semigroup
$T$ on ${\rm BUC}$ such that $J(\pi_n^t)f\uparrow T(t)f$ for all $t\geq 0$
and $f\in{\rm BUC}$. Dini's theorem implies uniform convergence on compacts.
For every $t\geq 0$ and $f\in{\rm BUC}$, it holds $J(t)f\leq S(t)f$ and thus
$T(t)f\leq S(t)f$ by construction.
Second, we show that $S(t)f=T(t)f$ for all $t\geq 0$ and $f\in{\rm BUC}$
depending only on finitely many coordinates, i.e., there exists $n\in\mathbb{N}$
such that
\[ f(x)=f\left(\sum_{k=1}^n \langle x,e_k\rangle e_k\right)
\quad\mbox{for all } x\in X. \]
Fix $n\in\mathbb{N}$ and define $X_n:=\Span\{e_1,\ldots, e_n\}\subset X$.
For every $t\geq 0$, $f_n\in{\rm C}_{\rm b}(X_n)$ and $x\in X_n$, we define
\begin{align*}
(S_n(t)f_n)(x)
:=\sup_{(b,\mu)\in\mathcal{A}_n}\mathbb{E}\left[f_n\left(x+\int_0^t b_s\,{\rm d} s
+\sum_{k=1}^n \Big(\int_0^t \sqrt{\mu_s^k}\,{\rm d}\xi^k_s\Big) e_k\right)\right],
\end{align*}
where $\mathcal{A}_n$ denotes the set of all predictable processes
$(b,\mu)\colon\Omega\times [0,\infty)\to\Lambda_n$ with
\[ \Lambda_n:=\Big\{\big((\langle b,e_k\rangle)_{k=1,\dots,n},
(\mu_k)_{k=1,\dots,n}\big)\colon (b,\mu)\in\Lambda\Big\}
\subset\mathbb{R}^n\times\mathbb{R}^n_+. \]
In addition, for every $t\geq 0$, $f_n\in{\rm C}_{\rm b}(X_n)$ and $x\in X_n$,
we define
\begin{align*}
(T_{\lambda,n}(t)f_n)(x)
&:=\mathbb{E}\left[f_n\left(x+tb+\sum_{k=1}^n \sqrt{\mu_k}\xi^k_t e_k\right)\right]
\quad\mbox{for all } \lambda:=(b,\mu)\in\Lambda_n, \\
(I_n(t)f_n)(x) &:=\sup_{\lambda\in\Lambda_n}(T_{\lambda,n}(t)f_n)(x).
\end{align*}
Note that Assumption~\ref{ass:L} is satisfied with
$L:=\infty\cdot\mathds{1}_{\Lambda_n^c}$. Hence, by Theorem~\ref{thm:control},
there exists a semigroup $T_n$ on ${\rm C}_{\rm b}(X_n)$ associated to $I_n$.
Furthermore, Theorem~\ref{thm:control2} implies
\[ S_n(t)f_n=T_n(t)f_n
\quad\mbox{for all } t\geq 0 \mbox{ and } f_n\in{\rm C}_{\rm b}(X_n). \]
Let $f\in{\rm BUC}$ such that there exists $f_n\in{\rm BUC}(X_n)$ with
\[ f(x)=f_n\left(\sum_{k=1}^n \langle x,e_k\rangle e_k\right)
\quad\mbox{for all } x\in X. \]
It follows from the definition of $S_n$ and the construction of
$T_n$ that
\[ S(t)f=S_n(t)f_n=T_n(t)f_n=T(t)f \quad\mbox{for all } t\geq 0. \]
Third, we show that $S(t)f=T(t)f$ for all $t\ge 0$ and all $f\in {\rm BUC}$
such that there exist a compact linear operator $K\colon X\to X$ and
$g\in{\rm BUC}$ with $f(x):=g(Kx)$ for all $x\in X$. Since the finite rank
operators are dense in the space of all compact linear operators w.r.t.
the operator norm $\|\cdot\|_{L(X)}$, there exists a sequence
$(K_n)_{n\in\mathbb{N}}$ of finite rank operators with $\|K-K_n\|_{L(X)}\to 0$.
Let $f_n(x) := g(K_n x)$ for all $x\in X$ and $n\in\mathbb{N}$. It holds
$\|f_n\|_\infty\leq\|g\|_\infty$ for all $n\in\mathbb{N}$ and
\[ \lim_{n\to\infty}\sup_{x\in B(0,r)}|f(x)-f_n(x)|=0
\quad\mbox{for all } r\geq 0. \]
Moreover, the boundedness of $\Lambda$ yields
\[ c:=\sup_{(b,\mu)\in\mathcal{A}}\mathbb{E}\left[\left|\int_0^t b_s\,{\rm d} s
+\sum_{k=1}^\infty \Big(\int_0^t \sqrt{\mu_s^k}\,{\rm d}\xi^k_s\Big) e_k
\right|\right]<\infty. \]
For every $r>0$ and $x\in X$, we use Chebyshev's inequality to
estimate
\begin{align*}
&\big(S(t)|f-f_n|\big)(x) \\
&\leq\sup_{y\in B(0,r)}|f(y)-f_n(y)| \\
&\quad\; +2\|g\|_\infty\sup_{(b,\mu)\in\mathcal{A}}
\mathbb{P}\left(\left|x+\int_0^t b_s\,{\rm d} s
+\sum_{k=1}^\infty\Big(\int_0^t \sqrt{\mu_s^k}\,{\rm d}\xi^k_s\Big)e_k\right|>r\right) \\
&\leq\sup_{y\in B(0,r)}|f(y)-f_n(y)|+\frac{2\|g\|_\infty}{r}\sup_{(b,\mu)\in\mathcal{A}}
\mathbb{E}\left[\left| x+\int_0^t b_s\,{\rm d} s
+\sum_{k=1}^\infty\Big(\int_0^t \sqrt{\mu_s^k}\,{\rm d}\xi^k_s\Big)e_k\right|\right] \\
&\leq\sup_{y\in B(0,r)}|f(y)-f_n(y)|+\frac{2\|g\|_\infty(|x|+c)}{r}.
\end{align*}
By choosing first $r>0$ and then $n\in\mathbb{N}$ sufficiently large, we obtain
\begin{align*}
&\max\{|S(t)f-S(t)f_n|(x), |T(t)f-T(t)f_n|(x)\} \\
&\leq\max\{(S(t)|f-f_n|)(x),(T(t)|f-f_n|)(x)\}
=(S(t)|f-f_n|)(x)\to 0.
\end{align*}
Hence, the second part implies $S(t)f=T(t)f$.
\end{proof}
\subsection{Wasserstein perturbation of linear transition semigroups}
\label{sec:wasserstein}
Let $X:=\mathbb{R}^d$ and $\kappa\equiv 1$. Moreover, for a fixed
$p\in (1,\infty)$, we denote by $\mathcal{P}_p$ the set of all probability
measures on the Borel-$\sigma$-algebra $\mathcal{B}(\mathbb{R}^d)$ with finite
$p$-th moment. Let $(\mu_t)_{t\geq 0}\subset\mathcal{P}_p$ and
$(\psi_t)_{t\geq 0}$ be a family of functions $\psi_t\colon\mathbb{R}^d\to\mathbb{R}^d$.
Following the setting in~\cite{FKN21, BEK}, for every $t\geq 0$, $f\in{\rm C}_{\rm b}$
and $x\in\mathbb{R}^d$, we define
\[ (R(t)f)(x):=\int_{\mathbb{R}^d} f(\psi_t(x)+y)\,{\rm d} \mu_t( y). \]
Typical examples include Koopman semigroups and transition semigroups
of L\'evy and Ornstein--Uhlenbeck processes, see~\cite{FKN21}.
Denote by $\mathcal{L}^R$ the Lipschitz set of $R$. Let ${\rm C}_0^\infty$ be
the space of all infinitely differentiable functions $f\in{\rm C}_0$ such
that all derivatives are in ${\rm C}_0$, where ${\rm C}_0$ consists of all
continuous functions $f\colon\mathbb{R}^d\to\mathbb{R}$ with $\lim_{|x|\to\infty}f(x)=0$.
\begin{assumption} \label{ass:R}
Suppose that $R$ forms a semigroup. Furthermore, let $(\mu_t)_{t\geq 0}$
and $(\psi_t)_{t\geq 0}$ satisfy the following conditions:
\begin{enumerate}
\item $\lim_{t\downarrow 0} \int_{\mathbb{R}^d} |y|^p\,{\rm d}\mu_t(y)=0$.
\item There exist $r>0$ and $c\geq 0$ such that
$\mu_t(B(0,r)^c)\leq ct$ for all $t\in[0,1]$.
\item $\psi_t(0)=0$ for all $t\ge 0$.
\item There exists $c\geq 0$ such that, for all $x,y\in\mathbb{R}^d$ and $t\in [0,1]$,
\[ |\psi_t(x)-\psi_t(y)-(x-y)|\leq ct|x-y|. \]
\item For every $f\in{\rm C}_0^\infty\cap\mathcal{L}^R$, the limit
\[ R'(0) f:=\lim_{h\downarrow 0}\frac{R(h)f-f}{h}\in{\rm C}_{\rm b} \]
exists uniformly on compacts.
\end{enumerate}
\end{assumption}
For every $x,y\in \mathbb{R}^d$ and $t\in[0,1]$, the conditions~(iii) and~(iv) imply
\begin{equation} \label{eq:psi}
|\psi_t(x)-x|\leq ct|x| \quad\mbox{and}\quad
|\psi_t(x)-\psi_t(y)|\leq e^{ct}|x-y|.
\end{equation}
\begin{lemma} \label{lem:LsetR}
It holds ${\rm C}_{\rm c}^\infty\subset \mathcal{L}^R$.
\end{lemma}
\begin{proof}
Let $f\in{\rm C}_{\rm c}^\infty$. Choose $c,r\geq 0$ such that Assumption~\ref{ass:R}(ii)
and~(iv) are satisfied. In addition, let $\supp(f)\subset B(0,r)$. By
Assumption~\ref{ass:R}(v), there exist $t_0\in(0,\nicefrac{1}{2c}]$
and $c'\geq 0$ with
\[ \sup_{x\in B(0,4r)}|(R(t)f-f)(x)|\leq c't \quad\mbox{for all } t\in [0,t_0]. \]
Inequality~\eqref{eq:psi} implies $|\psi_t(x)+y|\geq r$ for all $x\in B(0,4r)^c$,
$y\in B(0,r)$ and $t\in [0,t_0]$. Hence, for every $x\in B(x,4r)^c$ and
$t\in [0,t_0]$, it follows from Assumption~\ref{ass:R}(ii) that
\[ |(R(t)f)(x)-f(x)|\leq\|f\|_\infty\mu_t\big(B(0,r)^c\big)
\leq c\|f\|_\infty t. \]
We obtain $\|R(t)f-f\|_\infty\leq\max\{c',c\|f\|_\infty\}t$ for all $t\in [0,t_0]$.
\end{proof}
In the sequel, we consider a perturbation of the linear transition semigroup
$R$, where we take the supremum over all probabilities which are sufficiently
close to the reference measure $\mu_t$. Recall that, in Subsection~\ref{sec:control},
we considered a Brownian motion with uncertain drift and volatility,
where the uncertainty was parametrized by a finite-dimensional parameter space.
Here, the non-parametric uncertainty is instead given by an infinite-dimensional
ball of probability measures. We define the $p$-Wasserstein distance by
\[ W_{p}(\mu,\nu):=\left(\inf_{\pi \in\Cpl(\mu,\nu)}
\int_{\mathbb{R}^d\times\mathbb{R}^d}|y-z|^p\,{\rm d}\pi(y, z)\right)^\frac{1}{p}
\quad\mbox{for all } \mu,\nu\in\mathcal{P}_p,
\end{equation*}
where $\Cpl(\mu,\nu)$ consists of all probability measures on $\mathcal{B}(\mathbb{R}^d\times \mathbb{R}^d)$
with first marginal $\mu$ and second marginal $\nu$.
Let $\varphi\colon [0,\infty)\to [0,\infty]$ be a convex lower semicontinuous
function with $\varphi(0)=0$ and $\varphi(v)>0$ for some $v>0$. Furthermore,
we assume that that the mapping
$[0,\infty)\to [0,\infty],\; v\mapsto\varphi\big(v^{1/p}\big)$
is convex. The previous assumptions ensure that
\[ \varphi^*(w):=\sup_{v\geq 0}\big(vw-\varphi(v)\big)<\infty
\quad\mbox{for all } w\geq 0. \]
For every $t\geq 0$, $f\in{\rm C}_{\rm b}$ and $x\in\mathbb{R}^d$, we define
\[ (I(t)f)(x):=\sup_{\nu\in\mathcal{P}_p}\left(\int_{\mathbb{R}^d} f(\psi_t(x)+z)\, {\rm d}\nu(z)
-\varphi_t\big(\mathcal{W}_p(\mu_t,\nu)\big)\right), \]
where $\varphi_t\colon [0,\infty)\to [0,\infty]$ denotes the rescaled function
\[ \varphi_t(v):=\begin{cases}
t\varphi\big(\tfrac{v}{t}\big), & t>0,\, v\geq 0, \\
0, & t=v=0, \\
+\infty, & t=0, \,v\neq 0.
\end{cases} \]
The following result is a consequence of~\cite[Theorem 3.13]{FKN21}
and Lemma~\ref{lem:conv2}.
\begin{theorem} \label{thm:WS}
There exists a semigroup $S$ on ${\rm C}_{\rm b}$, which satisfies Assumption~\ref{ass:S},
such that, uniformly on compacts,
\begin{equation} \label{eq:WS}
S(t)f=\lim_{n\to\infty}I(\pi_n)f=\inf_{n\in\mathbb{N}}I(\pi_n)f
\quad\mbox{for all } f\in{\rm C}_{\rm b} \mbox{ and } t\geq 0.
\end{equation}
Denoting by $A_\Gamma$ the $\Gamma$-generator of $S$, it holds
${\rm C}_0^\infty\cap\mathcal{L}^R\subset D(A_\Gamma)$ and
\[ A_\Gamma f=R'(0)f+\varphi^*(|\nabla f|)=\lim_{h\downarrow 0}\frac{S(h)f-f}{h} \]
uniformly on compacts for all $f\in{\rm C}_0^\infty\cap\mathcal{L}^R$.
Condition~\eqref{eq:trans} is satisfied for all $f\in{\rm Lip}_{\rm b}$.
Furthermore, it holds $S(t)\colon{\rm Lip}_{\rm b}\to{\rm Lip}_{\rm b}$ and $S(t)\colon{\rm C}_0\to{\rm C}_0$
for all $t\geq 0$.
\end{theorem}
\begin{proof}
By~\cite[Theorem~3.13 and Remark~3.14]{FKN21}, there exists
a semigroup $S$ on ${\rm C}_{\rm b}$ which satisfies equation~\eqref{eq:WS},
Assumption~\ref{ass:S} and the statement about the $\Gamma$-generator.
Choose $c\geq 0$ such that Assumption~\ref{ass:R}(iv) is satisfied.
It follows from the proof of Theorem~\ref{thm:I2} that
condition~\eqref{eq:trans} holds for all $f\in{\rm Lip}_{\rm b}$ if we verify the
following conditions:
\begin{itemize}
\item $I(t)\colon B_{{\rm C}_{\rm b}}(0,r)\to B_{{\rm C}_{\rm b}}(0,r)$ for all $r,t\geq 0$,
\item $\|I(t)f-I(t)g\|_\infty\leq\|f-g\|_\infty$ for all $t\geq 0$ and
$f,g\in{\rm C}_{\rm b}$,
\item $I(t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(e^{ct}r)$ for all $r,t\geq 0$,
\item $\|\tau_x(I(t)f)-I(t)(\tau_x f)\|_\infty\leq crt|x|$ for all $r,t\geq 0$,
$f\in{\rm Lip}_{\rm b}(r)$ and $x\in\mathbb{R}^d$.
\end{itemize}
The first two statements follow immediately from the definition of $I$.
For every $r,t\geq 0$, $f\in{\rm Lip}_{\rm b}(r)$ and $x,y\in\mathbb{R}^d$, inequality~\eqref{eq:psi}
implies
\begin{align}
|(I(t)f)(x)-(I(t)f)(y)|
&\leq\sup_{\nu\in\mathcal{P}_p}\int_{\mathbb{R}^d}|f(\psi_t(x)+z)-f(\psi_t(y)+z)|\,{\rm d}\nu(z)
\nonumber \\
&\leq e^{ct}r|x-y|. \label{eq:Lip}
\end{align}
Furthermore, we use Assumption~\ref{ass:R}(iv) to estimate
\begin{align*}
|(\tau_x(I(t)f)-I(t)(\tau_x f)|(y)
&\leq\sup_{\nu\in\mathcal{P}_p}\int_{\mathbb{R}^d}|f(\psi_t(x+y)+z)-f(\psi_t(y)+x+z)|\,{\rm d}\nu(z) \\
&\leq r|\psi_t(x+y)-\psi_t(y)-x|\leq crt|x|.
\end{align*}
It remains to show $S(t)\colon{\rm C}_0\to{\rm C}_0$ for all $t\geq 0$. Since $S$ is
semigroup, it suffices to show $S(t)f\in{\rm C}_0$ for all $t\in [0,\nicefrac{1}{2c}]$
and $f\in{\rm C}_0$. Since $S(t)$ is monotone and convex with $S(t)0=0$, it holds
$|S(t)f|\leq S(t)|f|\leq I(t)|f|$. By~\cite[Lemma~3.4]{FKN21}, there exists
a constant $c'\geq 0$ with
\[ \big(I(t)|f|\big)(x)
\leq\sup_{\{v\in\mathcal{P}_p\colon\mathcal{W}_p(\mu_t,\nu)\leq c'\}}
\int_{\mathbb{R}^d}|f(\psi_t(x)+y)|{\rm d}\nu(y). \]
Let $\varepsilon>0$. Since $f\in{\rm C}_0$ and the Wasserstein ball
$\{v\in\mathcal{P}_p\colon\mathcal{W}_p(\mu_t,\nu)\leq c'\}$ is tight, we can
choose $r\geq 0$ with
\[ \sup_{x\in B(0,r)^c}|f(x)|\leq\frac{\varepsilon}{2}
\quad\mbox{and}\quad
\sup_{\mathcal{W}_p(\mu_t,\nu)\leq c'}\nu(B(0,r)^c)\|f\|_\infty
\leq\frac{\varepsilon}{2}. \]
For every $x\in B(0,4r)^c$ and $y\in B(0,r)$, inequality~\eqref{eq:psi}
implies $|\psi_t(x)+y|\geq r$. Thus,
\begin{align*}
\big(I(t)|f|\big)(x)
&\leq\sup_{\mathcal{W}_p(\mu_t,\nu)\leq c'}
\left(\int_{B(0,r)}|f(\psi_t(x)+y)|{\rm d}\nu(y)
+\int_{B(0,r)^c}|f(\psi_t(x)+y)|{\rm d}\nu(y)\right) \\
&\leq\sup_{\mathcal{W}_p(\mu_t,\nu)\leq c'}
\left(\frac{\varepsilon}{2}+\nu(B(0,r)^c)\|f\|_\infty\right)\leq\varepsilon.
\end{align*}
We obtain $S(t)\colon{\rm C}_0\to{\rm C}_0$ for all $t\geq 0$.
\end{proof}
In addition to the Wasserstein perturbation, we consider a perturbation
which is parametrized only by drifts $b\in\mathbb{R}^d$. For every $t\geq 0$,
$f\in{\rm C}_{\rm b}$ and $x\in\mathbb{R}^d$, we define
\[ (J(t)f)(x):=\sup_{b\in\mathbb{R}^d}
\left(\int_{\mathbb{R}^d} f(\psi_t(x)+y+b)\, {\rm d}\mu_t(y)-\varphi_t(|b|t)\right). \]
We remark that $\mathcal{W}_p(\mu_t,\nu_b)=|b|t$ for all $b\in\mathbb{R}^d$ and
$t\geq 0$, where
\[ \nu_b(A):=\int_{\mathbb{R}^d}\mathds{1}_A(b+y)\,{\rm d}\mu_t(y)
\quad\mbox{for all } A\in\mathcal{B}(\mathbb{R}^d). \]
Furthermore, the previous definition of $J$ is consistent with the one
in Subsection~\ref{sec:control} if we fix the volatility matrix $a$
and choose $\mu_t:=\mathbb{P}\circ (\sqrt{a}W_t)^{-1}$ and $L(b):=\varphi(|b|)$.
Note that uncertainty in the volatility is not included in the setting of
this subsection. Define ${\rm Lip}_0:={\rm Lip}_{\rm b}\cap{\rm C}_0$.
\begin{theorem} \label{thm:WT}
There exists a family $T$ of operators $T(t)\colon{\rm C}_{\rm b}\to{\rm C}_{\rm b}$, which
satisfy Assumption~\ref{ass:S}, such that, uniformly on compacts,
\begin{equation} \label{eq:JT}
T(t)f=\lim_{n\to\infty}J(\pi_n^t)f
\quad\mbox{for all } (f,t)\in{\rm C}_{\rm b}\times\mathcal{T}.
\end{equation}
Furthermore, $T$ is a strongly continuous convex monotone
semigroup on ${\rm C}_0$.
Denoting by $B_\Gamma$ the $\Gamma$-generator of $T$, it holds
${\rm C}_0^\infty\cap\mathcal{L}^R\subset D(B_\Gamma)$ and
\[ B_\Gamma f=R'(0)f+\varphi^*(|\nabla f|)=\lim_{h\downarrow 0}\frac{T(h)f-f}{h} \]
uniformly on compacts for all $f\in{\rm C}_0^\infty\cap\mathcal{L}^R$. Condition~\eqref{eq:trans}
is satisfied for all $f\in{\rm Lip}_0$. Furthermore, we have $T(t)\colon{\rm Lip}_0\to{\rm Lip}_0$
for all $t\geq 0$.
\end{theorem}
\begin{proof}
First, we verify Assumption~\ref{ass:I}. Clearly, the conditions~(i)-(iv) are
satisfied. Choose $c\geq 0$ such that Assumption~\ref{ass:R}(iv) is satisfied.
Similar to inequality~\eqref{eq:Lip}, one can show that $J(t)\colon{\rm Lip}_{\rm b}(r)\to{\rm Lip}_{\rm b}(e^{ct}r)$
for all $r,t\geq 0$. In particular, the sequence $(J(\pi_n^t)f)_{n\in\mathbb{N}}$ is
uniformly Lipschitz continuous for all $t\geq 0$ and $f\in{\rm Lip}_{\rm b}$.
Assumption~\ref{ass:I}(vi) follows from Remark~\ref{rem:I}(ii), since
$J(t)f\leq S(t)f$ for all $t\geq 0$ and $f\in{\rm C}_{\rm b}$. Next, we show that
$J(t)\colon{\rm C}_{\rm b}\to{\rm C}_{\rm b}$ for all $t\geq 0$. Let $t\geq 0$ and $f\in{\rm C}_{\rm b}$.
Choose a bounded sequence $(f_n)_{n\in\mathbb{N}}\subset{\rm Lip}_{\rm b}$ with
$f_n\to f$ uniformly on compacts. Lemma~\ref{lem:uniform} yields
$J(t)f_n\to J(t)f$ uniformly on compacts. Indeed, the corresponding
proof only relies on the fact that $J(t)$ is convex, monotone and
continuous from above. Since $J(t)f_n\in{\rm Lip}_{\rm b}\subset{\rm C}_{\rm b}$ for all
$n\in\mathbb{N}$, we obtain $J(t)f\in{\rm C}_{\rm b}$. Moreover, it holds
$|J(t)f|\leq J(t)|f|\leq S(t)|f|$ and thus $|J(\pi_n^t)f|\leq S(t)|f|\in{\rm C}_0$
for all $t\geq 0$, $n\in\mathbb{N}$ and $f\in{\rm C}_0$. It remains to show that $\mathcal{L}^J\subset{\rm C}_0$
is dense. For every $c,t\geq 0$ and $f\in{\rm Lip}_{\rm b}(c)$, it follows
from~\cite[Equation~(3.7)]{FKN21} that
\begin{equation} \label{eq:IJR}
0\leq J(t)f-R(t)f\leq I(t)f-R(t)f\leq t\varphi^*(c).
\end{equation}
Hence, Lemma~\ref{lem:LsetR} implies ${\rm C}_{\rm c}^\infty\subset\mathcal{L}^R\subset\mathcal{L}^J$.
By Theorem~\ref{thm:I}, there exists a family $T$ of operators
$T(t)\colon{\rm C}_{\rm b}\to{\rm C}_{\rm b}$ and a subsequence $(n_l)_{l\in\mathbb{N}}$, which
satisfy Assumption~\ref{ass:S}, such that, uniformly on compacts,
\[ T(t)f=\lim_{l\to\infty}J(\pi_{n_l}^t)f \quad\mbox{for all } (f,t)\in{\rm C}_{\rm b}\times\mathcal{T}. \]
Since $(J(\pi_n^t)f)_{n\in\mathbb{N}}$ is non-decreasing, the convergence holds
without choosing a subsequence. In addition, $T$ is a strongly continuous
convex monotone semigroup on ${\rm C}_0$ and it holds
$T(t)\colon{\rm Lip}_0\to{\rm Lip}_0$ for all $t\geq 0$.
Second, we show that ${\rm C}_0^\infty\cap\mathcal{L}^R\subset D(B_\Gamma)$ and
\[ B_\Gamma f=R'(0)f+\varphi^*(|Df|)=\lim_{h\downarrow 0}\frac{T(h)f-f}{h} \]
uniformly on compacts for all $f\in{\rm C}_0^\infty\cap\mathcal{L}^R$. For every
$h>0$ and $b,x,y\in\mathbb{R}^d$, we use Taylor's formula to obtain
\[ |f(\psi_h(x)+y+bh)-f(\psi_h(x)+y)-\langle\nabla f(\psi_h(x)+y),bh\rangle|
\leq\|D^2 f\|_\infty|b|^2h^2. \]
As seen in the proof of~\cite[Lemma~3.6]{FKN21}, it holds
$\lim_{h\downarrow 0}|R(h)g-g|(x)=0$ for all $g\in{\rm Lip}_{\rm b}$. Hence,
we can estimate
\begin{align*}
\liminf_{h\downarrow 0}\left(\frac{J(h)f-R(h)f}{h}\right)(x)
&\geq \liminf_{h\downarrow 0}
\int_{\mathbb{R}^d}\langle\nabla f(\psi_h(x)+y,b\rangle{\rm d}\mu_h(y)-\varphi(|b|) \\
&=\liminf_{h\downarrow 0}R(h)\big(\langle\nabla f,b\rangle\big)(x)
-\varphi(|b|) \\
&=\langle\nabla f(x),b\rangle-\varphi(|b|).
\end{align*}
Taking the supremum over all $b\in\mathbb{R}^d$ yields
\[ \liminf_{h\downarrow 0}\left(\frac{J(h)f-R(h)f}{h}\right)(x)\geq\varphi^*(|\nabla f|). \]
We use the previous inequality, $J(h)f\leq T(h)f\leq S(h)f$, Assumption~\ref{ass:R}(v)
and Theorem~\ref{thm:WS} to conclude
\[ \lim_{h\downarrow 0}\frac{T(h)f-f}{h}=R'(0)f+\varphi^*(|\nabla f|) \]
uniformly on compacts.
Third, we remark that the verification of condition~\eqref{eq:trans}
for all $f\in{\rm Lip}_0$ is similar to the proof of Theorem~\ref{thm:WS}.
Moreover, it follows from $J(t)\colon{\rm Lip}_0(r)\to{\rm Lip}_0(e^{ct}r)$ and
the construction of $T$ that $T(t)\colon{\rm Lip}_0(r)\to{\rm Lip}_0(e^{ct}r)$
for all $r,t\geq 0$.
\end{proof}
\begin{theorem} \label{thm:WST}
It holds $S(t)f=T(t)f$ for all $t\geq 0$ and $f\in{\rm C}_{\rm b}$.
\end{theorem}
\begin{proof}
By construction, it holds $0\leq T(t)f-R(t)f\leq S(t)f-R(t)f\leq I(t)f-R(t)f$
for all $t\geq 0$ and $f\in{\rm Lip}_0$. Hence, inequality~\eqref{eq:IJR} implies
\[ \mathcal{L}^R\cap{\rm Lip}_0=\mathcal{L}^S\cap{\rm Lip}_0=\mathcal{L}^T\cap{\rm Lip}_0. \]
Let $\mathcal{D}:=\mathcal{L}^R\cap{\rm Lip}_0$. It follows from Remark~\ref{rem:Lset}(i) and
Theorem~\ref{thm:WT} that $T(t)\colon\mathcal{D}\to\mathcal{D}$ for all $t\geq 0$.
Next, we show that $A_\Gamma f=B_\Gamma f$ for all $f\in\mathcal{D}$. Let
$\eta\in{\rm C}_{\rm c}^\infty$ with $\eta\geq 0$, $\supp(\eta)\subset B(0,1)$,
and $\int_{\mathbb{R}^d}\eta(x)\,{\rm d} x=1$. Define $\eta_n(x):=n^d\eta(nx)$
and $f_n:=f*\eta_n$ for all $n\in\mathbb{N}$ and $x\in\mathbb{R}^d$. Then, it holds
$f_n\in{\rm C}_0^\infty$ for all $n\in\mathbb{N}$. Choose $c,r\geq 0$ such that
Assumption~\ref{ass:R}(iv) is satisfied and $f\in{\rm Lip}_0(r)$. For every
$t\geq 0$, $n\in\mathbb{N}$ and $x\in\mathbb{R}^d$, we use Fubini's theorem to
estimate
\begin{align*}
&|R(t)f_n-(R(t)f)*\eta_n|(x) \\
&\leq\int_{B(0,1)}\left(\int_{\mathbb{R}^d}|f(\psi_t(x)+y-z)-f(\psi_t(x-z)+y)|
\,{\rm d}\mu_t(y)\right)\eta_n(z)\,{\rm d} z
\leq crt.
\end{align*}
We obtain $\|R(t)f_n-f_n\|_\infty\leq\|R(t)f-f\|_\infty+crt$ and,
therefore, $f_n\in\mathcal{L}^R$. It follows from Lemma~\ref{lem:conv2},
Theorem~\ref{thm:WS} and Theorem~\ref{thm:WT} that
\[ A_\Gamma f=\Glim_{n\to\infty}A_\Gamma f_n=\Glim_{n\to\infty}B_\Gamma f_n=B_\Gamma f. \]
Hence, Corollary~\ref{cor:comp} implies $S(t)f\leq T(t)f$ for all
$t\geq 0$ and $f\in{\rm C}_0^\infty\cap\mathcal{L}^R$ while the inequality $S(t)f\geq T(t)f$
holds by construction. Now, let $f\in{\rm C}_{\rm b}$ be arbitrary and choose a
bounded sequence $(f_n)_{n\in\mathbb{N}}\subset{\rm C}_{\rm c}^\infty$ with $f_n\to f$
uniformly on compacts. We use Lemma~\ref{lem:uniform} and
Lemma~\ref{lem:LsetR} to conclude
\[ S(t)f=\lim_{n\to\infty}S(t)f_n=\lim_{n\to\infty}T(t)f_n=T(t)f.
\qedhere \]
\end{proof}
In the particular case that $S$ coincides with the entropic semigroup,
as a byproduct of Theorem~\ref{thm:WST}, we recover that $\mu_t$
satisfies the Talagrand $T_2$ inequality, see~\cite[Chapter~22]{Villani}
and~\cite{Talagrand}. Denote by $\mathcal{N}(0,t\mathds{1})$ the $d$-dimensional
normal distribution with mean zero and covariance matrix $t\mathds{1}$,
where $\mathds{1}\in\mathbb{R}^{d\times d}$ is the identity matrix.
\begin{corollary}
It holds $\mathcal{W}_2(\nu,\mu_t)\leq\sqrt{2t H(\nu|\mu_t)}$ for all $t\geq 0$
and $\nu\in\mathbb{P}_2$, where $H(\nu|\mu_t)$ denotes the relative entropy of
$\nu$ w.r.t. $\mu_t:=\mathcal{N}(0,t)$.
\end{corollary}
\begin{proof}
Choose $\psi_t:=\id_{\mathbb{R}^d}$, $\mu_t:=\mathcal{N}(0,t\mathds{1})$ and
$\varphi(v):=\nicefrac{v^2}{2}$ for all $t,v\geq 0$. Moreover, let
$(W_t)_{t\geq 0}$ be a $d$-dimensional standard Brownian
motion on a complete filtered probability space
$(\Omega,\mathcal F,(\mathcal F_t)_{t\geq 0},\mathbb{P})$ satisfying the
usual conditions. We show that
\[(T(t)f)(x)=(\tilde{S}(t)f)(x)
:=\tfrac{1}{2}\log\big(\mathbb{E}[\exp(2f(x+W_t))]\big) \]
for all $t\geq 0$, $f\in{\rm C}_{\rm b}$ and $x\in\mathbb{R}^d$. By elementary calculation,
see~\cite[Lemma~4.4]{BK21} and the proof of~\cite[Theorem~4.5]{BK21},
one can show that $J(t)f\leq\tilde{S}(t)f$ and thus $T(t)f\leq\tilde{S}(t)f$
for all $t\geq 0$ and $f\in{\rm C}_{\rm b}$. To show the reverse inequality, we want to
apply Corollary~\ref{cor:comp}. By straightforward computations, one can
show that $\tilde{S}$ satisfies Assumption~\ref{ass:S} and
${\rm BUC}^2\subset D(\tilde{A})$ with
\[ \tilde{A}f=\tfrac{1}{2}\big(\Delta f+|\nabla f|^2\big)
\quad\mbox{for all } f\in{\rm BUC}^2. \]
Moreover, it follows from It\^o's formula and Theorem~\ref{thm:control}
that $\mathcal{D}:=\mathcal{L}^T_{\sym}\cap{\rm Lip}_{\rm b}\subset\mathcal{L}^{\tilde{S}}_+$. Since $\tilde{S}$
and $T$ are translation invariant, Lemma~\ref{lem:conv2} yields
$\tilde{A_\Gamma}f=B_\Gamma f$ for all $f\in\mathcal{D}$. Hence, Corollary~\ref{cor:comp}
implies $\tilde{S}(t)f=T(t)f$ for all $t\geq 0$ and $f\in{\rm BUC}^2$. For
arbitrary $f\in{\rm C}_{\rm b}$, the equality follows by approximation. In addition,
it follows from Theorem~\ref{thm:WST} that $\tilde{S}(t)f=S(t)f\leq I(t)f$
for all $t\geq 0$ and $f\in{\rm C}_{\rm b}$. Fenchel--Moreaus's theorem yields
\begin{align*}
\frac{\mathcal{W}_2(\nu,\mu_t)^2}{2t}
&=\sup_{f\in{\rm C}_{\rm b}}\left(\int_{\mathbb{R}^d} f\,{\rm d}\nu-(I(t)f)(0)\right) \\
&\leq\sup_{f\in{\rm C}_{\rm b}}\left(\int_{\mathbb{R}^d} f\,{\rm d}\nu-(\tilde{S}(t)f)(0)\right)
=H(\nu|\mu_t). \qedhere
\end{align*}
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,898 |
Q: Can someone explain how a dictionary can hold different input values under one key I have this simple looping code that takes in a line of user input and (after making this into a list) puts the individual words into a dictionary as keys, with the lineCount number being the value. Can someone explain how to adjust this so that if the same word is entered on a different line, it doesn't replace the dictionary value but instead just adds to it?
import string
lineCount = 1
q = raw_input("enter something")
d = {}
while q != "no":
q = q.split()
for word in q:
d[word] = lineCount
lineCount += 1
q = raw_input("enter something")
print d
For example, if the input is "x y" on line 1, and "x n" on line 2, the dictionary should print as "x: 1,2 y:1 n:2" but currently it would only print "x:2 y:1 n:2" as the original lineCount value associated with key x is replaced. If possible, please avoid importing collections in the solution, as I would rather understand the longest way possible first.
Many thanks in advance.
A: You can use get if a default value like in the code below:
lineCount = 1
q = raw_input("enter something")
d = {}
while q != "no":
q = q.split()
for word in q:
d[word] = d.get(word, 0) + 1
lineCount += 1
query = raw_input("enter something")
When you add the word for the first time, the get won't find the word and will return 0 (the default value). So you add this with 1 to update the result.
A: Using lists for your dictionary values, you can have the following solution:
line_count = 1
q = raw_input("enter something: ")
d = {}
while q != "no":
words = q.split()
for word in words:
if word in d and line_count not in d[word]:
d[word].append(line_count)
else:
d[word] = [line_count]
line_count += 1
q = raw_input("enter something: ")
print d
Example of output:
>>> python word_lines.py
enter something: hello world
enter something: hello
enter something: world
enter something: sof
enter something: no
{'world': [1, 3], 'hello': [1, 2], 'sof': [4]}
A: If you really want to use a Dictionary instead of a list as suggested by ettanany, I would suggest you use the lines as the keys and the words as values since lines are unique and words are not. I'm sure you can figure this out without a code sample :)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,071 |
Corporate wellbeing provider, Let's Get Healthy has been appointed to deliver bespoke resilience training to Enza Zaden UK's employees.
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With this goal in mind, Let's Get Healthy has developed a bespoke training programme called 'Buzz Resilience', which aims to build team and individual resilience, both at work and at home – giving staff the confidence to make changes that will enhance their lives.
Let's Get Healthy, which was recently named Gold Winner Employee Experience Awards for the category of Health & Wellbeing 2018, was chosen by Enza Zaden to support its UK employees through what is a turbulent time for the industry, with Brexit highlighted as a key contributing factor. The Leeds-based company boasts very diverse sector experience, and currently operates as corporate wellbeing providers to the likes of The Co-op, G's Fresh, Travis Perkins, Arriva and Virgin Media.
"We've had a great time meeting the team and designing a fun, interactive learning campaign that will have a positive impact on each and every one of them. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,181 |
Les herbes de Provence sont une sélection de plantes aromatiques traditionnelles de la cuisine provençale, sauvages, fraîches, ou séchées, originaires de Provence, ou des régions méditerranéennes.
Histoire
Ce terme regroupe à l'origine une variété de plantes aromatiques sauvages provençales, dont le thym, le serpolet, la marjolaine, l'origan, le romarin, le basilic, le cerfeuil, l'estragon, la livèche, la sarriette, la sauge, le laurier-sauce et le fenouil...
Une partie de ces plantes entre dans la composition du bouquet garni.
Cueillette et production
Le terme commercial « herbes de Provence » est un terme générique de mélange d'herbes séchées. L'expression, qui n'est pas une appellation, a été créée avec un important succès par une entreprise agroalimentaire française dans les années 1960. Ce mélange n'est donc pas protégé.
Ces plantes ont pendant longtemps fait uniquement l'objet d'une cueillette à l'état sauvage. Elles sont à ce jour de plus en plus cultivées par l'industrie agroalimentaire. À côté d'une production de jardin potager familiale, ou en pots sur les balcons, cette production organisée représente la moitié du marché.
Seulement 10 % des herbes de Provence séchées (ou lyophilisées) vendues en France sont à ce jour produites en France. 95 % des mélanges dits « Herbes de Provence » proviennent à ce jour des pays d'Europe centrale et orientale (Pologne et Albanie en tête), du Maghreb, ou de Chine.
Leur négoce est le fait de sociétés marseillaises qui approvisionnent les usines de conditionnement et de distribution comme Ducros, Gyma ou le Dijonnais Amora Maille. Deux groupements de producteurs se sont constitués dans la région Provence-Alpes-Côte d'Azur.
La totalité de la récolte régionale, essentiellement concentrée en Haute-Provence, est absorbée par les usines de transformation qui commercialisent les herbes, soit séchées, soit congelées sous vide. Il n'existe aucun chiffre pour la commercialisation de ces herbes fraîches, mais leur présence massive sur les marchés provençaux, comtadins et niçois, a assuré la réputation de ceux-ci.
Label rouge
La production d'herbes de Provence Label rouge de l'Institut national de l'origine et de la qualité (INAO), est une recette composée de de romarin, d'origan, de sarriette, de thym.
Usage culinaire
Les herbes de Provence accompagnent grillades, sauces, ragoûts, rôtis, poissons, marinades, pâtes, et plats à base de tomates...
Variantes
Aromate
Persillade
Fines herbes
Bouquet garni
Plante aromatique
Liste d'épices et aromates
Liste de mélanges d'épices
Épice et graine aromatique
Herbes et aromates de cuisine
Assaisonnements et condiments
Bibliographie
Jacques Marseille (dir.), Dictionnaire de la Provence et de la Côte d'Azur, Éd. Larousse, Paris, 2002 .
Notes et références
Voir aussi
Articles connexes
Cuisine occitane
Cuisine provençale
Plante médicinale
Liste de plantes médicinales de France
Liens externes
sur Météo à la carte de France 3
Cuisine provençale
Plante aromatique
Épice ou aromate
Label rouge | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 316 |
{"url":"http:\/\/math.stackexchange.com\/questions\/255451\/every-sequence-has-at-least-one-limit-point\/255461","text":"# Every sequence has at least one limit point\n\nThis is, of course, easily proven with the help of the Bolzano-Weierstrass theorem. However, going through the lecture notes in my class, the B-W theorem is only introduced after the claim\n\nEvery sequence has at least one limit point\n\nis introduced, which itself is introduced as a corollary of:\n\nTheorem:\n\n1) The element $a\\in\\mathbb R\\cup\\{{-\\infty,\\infty}\\}$ is a limit point of a sequence $\\{X_n\\}$ iff exists its subsequence $\\{X_{k_n}\\}$ converging to $a$.\n\n2) Limit inferior of $\\{X_n\\}$ is the lowermost limit point of the sequence.\n\n3) Limit superior of $\\{X_n\\}$ is the uppermost limit point of the sequence.\n\n(Hopefully the idea is clear, this is only my own translation as the text is not english)\n\nI don't quite see how does that imply that \"every sequence has at least one limit point\" and therefore would be grateful for any help, thanks.\n\n-\n\n@DahnJahn Yes, the limit superior and limit inferior of a sequence always exist, because they are defined to be the limits of $a_n=\\sup_{k\\geq n} \\{ x_k \\}$ and $b_n=\\inf_{k\\geq n} \\{ x_k \\}$ respectively, and both $a_n$ and $b_n$ are monotone (make sure you think about why) thus their limits exist. \u2013\u00a0Ragib Zaman Dec 10 '12 at 13:32","date":"2016-04-30 01:30:26","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\": 0.9882966876029968, \"perplexity\": 104.67388981542949}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-18\/segments\/1461860111581.11\/warc\/CC-MAIN-20160428161511-00201-ip-10-239-7-51.ec2.internal.warc.gz\"}"} | null | null |
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