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\section{Introduction}
All the interactions of the Standard Model are known to arise from the behavior of quantum particles: photons, gluons, W/Z bosons, and Higgs bosons (e.g., see \cite{Weinberg}). There is clear experimental evidence for all these particles, along with all the fermions of the Standard Model. In contrast we do not have direct observations of the behavior of gravitons that underpin gravitation. Consistency between quantum mechanics and relativity implies that gravitons exist, and explains the structure of general relativity at long distances \cite{Weinberg:1964ew,Weinberg:1965rz,Deser:1969wk,Feynman,Hertzberg:2016djj,Hertzberg:2017abn,Hertzberg:2017nzl,Hertzberg:2020yzl,Hertzberg:2020gxu}. So it is a very worthwhile goal to search for observational consequences of quantum effects in gravitation. The inclusion of quantum effects can be done reliably at large distances, since general relativity is a well behaved effective theory for scales much larger than the Planck length.
Recent observations of gravitational waves (GWs) by LIGO are known to be broadly consistent with the predictions of classical general relativity \cite{LIGOScientific:2016aoc,LIGOScientific:2016lio,LIGOScientific:2016gtq,LIGO:2021ppb,McCuller:2021mbn}. Quantum corrections to the waves are ordinarily thought to be exceedingly small \cite{Rothman:2006fp,Dyson:2013hbl}. This is because the occupancy number of gravitons in a detectable wave is huge, and quantum corrections, or ``graviton shot noise", is suppressed. This conclusion is reliable under the assumption that the GW is in a coherent state, or similar, which are the most classical states. In such a case, we have essentially no chance to see any quantum behavior in the foreseeable future.
On the other hand, GWs that are detectable have arisen due to black hole mergers (and neutron stars). The quantum character of black holes remains mysterious. So, while it is very plausible that the resulting GW is indeed in a coherent state, or similar, we can have an open mind to the possibility that the wave produced is in a much more striking quantum state, such as a highly squeezed state. In fact, squeezed states are naturally produced when quantum degrees of freedom are affected by a time dependent background (e.g., see Ref.~\cite{Grishchuk:1993ds}). This is indeed the case when one considers quantum fluctuations in the gravitational field that are being acted on by the extreme spacetime evolution of merging black holes or neutron stars. Furthermore, it has been suggested that black holes may be highly quantum mechanical objects. We therefore think it is interesting to constrain the amount of squeezing that could have taken place in this process using existing data. As the wave propagates from the merger to the earth, it is possible that a highly quantum state will not undergo appreciable decoherence, since gravitation is so weak. (There are related issues for dark matter, which may only have gravitational interactions \cite{Allali:2020ttz,Allali:2020shm,Allali:2021puy}).
In this work, we shall build the relevant formalism to describe GWs in squeezed states, compute their correlation properties, and perform a direct comparison to LIGO data. We shall find a bound on the squeezing that seems rather weak; it only constrains a very large amount of squeezing. Nevertheless, if the merger produces squeezing at a rate that is analogous to how cosmic inflation produces extremely squeezed states \cite{Albrecht:1992kf,Polarski:1995jg}, then this may in fact be a useful bound. We note that in the context of cosmic inflation, this extreme ``squeezing" means the states are typically described as ``classical", since the field and momentum are closely correlated and matched well by stochastic methods.
However, in the present context, this squeezing would render the observed gravitational waves from a merger {\em different} than the classical general relativistic prediction, so we refer to it as ``quantum" (irrespective of whether some stochastic method might be able to reproduce it).
There has been very important earlier work on the topic of quantum fluctuations in gravitation. In particular, a sequence of very significant works appears in Refs.~\cite{Parikh:2020nrd,Parikh:2020kfh,Parikh:2020fhy}. Here the authors calculate in detail how quantum fluctuations in gravitational waves lead to corresponding fluctuations in the arms of detectors. They provide the equations for the geodesic motion of the detectors, which include a kind of stochastic term, as well as a kind of radiation reaction term. These authors in Refs.~\cite{Parikh:2020nrd,Parikh:2020kfh,Parikh:2020fhy}, along with others in Refs.~\cite{Kanno:2020usf,Kanno:2021gpt}, also make significant progress in computing correlation functions of the gravitational field and the response.
In this work, we build off the above foundational literature and provide a natural follow up.
Other interesting prior work includes Refs.~\cite{,Haba:2020jqs,Zurek:2020ukz,Verlinde:2019xfb,Guerreiro:2019vbq,Kuo:1993if,Ford:1994cr,Ford:1996qc,Coradeschi:2021szx,Cho:2021gvg,Guerreiro:2021qgk}.
In particular, our focus here is to compute specific details of the structure of a class of squeezed modes, the corresponding spacetime correlation functions, and a comparison to LIGO data.
The outline of this paper is the following: In Section \ref{Weak} we recap the form of the weak field metric for gravitational waves and the corresponding Hamiltonian.
In Section \ref{QGW} we construct a family of wave functions, including squeezed states.
In Section \ref{CST} we determine their correlations in space and time.
In Section \ref{DCS} we analyze the detector response for a coherent state.
In Section \ref{DSS} we analyze the detector response for a squeezed state and place an observational bound on the squeezing parameter.
In Section \ref{Conc} we discuss.
In the Appendix we provide the details of the conceptually simpler case of the single harmonic oscillator for pedagogical purposes.
\section{Weak Field Hamiltonian}\label{Weak}
Let us begin with a quick review of the basic of weak gravitational fields.
\subsection{Metric for Gravitational Waves}
We will write the metric perturbation $h_{\mu\nu}$ around flat spacetime $\eta_{\mu\nu}$ as
\begin{equation}
g_{\mu\nu}({\bf x},t)=\eta_{\mu\nu}+ h_{\mu\nu}({\bf x},t)
\end{equation}
We will use units $c=1$, and our signature is (+,-,-,-).
Although the gravitational field may be extreme near the merging black holes, once it is near the earth, we know that it has entered the weak field regime, with metric fluctuations $h_{\mu\nu}$ that are small, i.e., $|h_{\mu\nu}|\ll 1$.
For gravitational waves propagating through the vacuum, we can go to transverse-traceless gauge in which the metric fluctuations $h_{\mu\nu}$ are found to take the form $h_{0\mu}=0$ and the spatial components we denote
$h_{ij}$. In this gauge, we have $\partial_i h_{ij}=0$ (transverse) and $\delta^{ij}h_{ij}=0$ (traceless).
We will label the two gravitational wave polarizations by $p=(+,\times)$.
For example, for a wave traveling in the $z$-direction, the spatial metric is of the form
\begin{equation}
h_{ij}=\left(\begin{array}{ccc}
h_+(z,t) & h_\times(z,t) & 0 \\
h_\times(z,t) & -h_+(z,t) & 0 \\
0 & 0 & 0
\end{array}\right)
\end{equation}
\subsection{Energy in Gravitational Waves}
Consider a wave traveling through space. In this gauge we can define the local energy density $\rho_{\mbox{\tiny{GW}}}({\bf x},t)$.
We can write this as a sum over the 2 polarizations $p$ as
\begin{equation}
\rho_{\mbox{\tiny{GW}}}({\bf x},t) = \sum_{p=+,\times}{1\over 32\pi G}\left((\dot{h}_p)^2+(\nabla{h}_p)^2\right)
\end{equation}
The total energy is given by integrating the energy density over space as
\begin{equation}
E=\int \!d^3x\,\rho_{\mbox{\tiny{GW}}}({\bf x},t)
\end{equation}
By lifting the fields to operators, then the corresponding Schr\"odinger equation is
\begin{equation}
i\hbar{\partial\over\partial t}\Psi=\hat{H}\,\Psi
\end{equation}
where the Hamiltonian operator $\hat{H}$ is equal to the above energy $E$ under the replacement to conjugate variables $(\hat{h},\hat{\pi})$
\begin{equation}
h_p({\bf x})\to\hat{h}_p({\bf x}),\,\,\,\,\,\,\dot{h}_p({\bf x})\to(16\pi G)\,\hat{\pi}_p({\bf x})
\end{equation}
which obey standard commutation relations
\begin{equation}
[\hat{h}_p({\bf x}),\hat{\pi}_{p'}({\bf y})]=i\,\delta_{pp'}\,\delta^3({\bf x}-{\bf y})\,\hbar
\end{equation}
The corresponding probability density for a gravitational field configuration is $|\Psi|^2$.
\subsection{Energy in Each Mode }
It is convenient to discuss the properties of the waves in ${\bf k}$-space. Let us define the Fourier transform as
\begin{equation}
\tilde{h}_{{\bf k},p}(t) = \int\!d^3x\,h_p({\bf x},t)\,e^{-i{\bf k}\cdot{\bf x}}
\end{equation}
By writing the energy in terms of the Fourier transform of $h_p$, we have
\begin{equation}
E = \sum_{p=+,\times}\int\!{d^3k\over(2\pi)^3}\,{1\over 32\pi G}\left(|\dot{\tilde{h}}_{{\bf k},p}|^2+k^2|\tilde{h}_{{\bf k},p}|^2\right)
\end{equation}
It will also be convenient to define the theory in a finite size box of volume $V$. In this case, the modes become discrete. We can replace the integral over ${\bf k}$ by a discrete sum as
\begin{equation}
\int\!{d^3k\over(2\pi)^3} \to {1\over V}\sum_{\bf k}
\end{equation}
Then the energy can be written as the sum over modes and polarizations as
\begin{equation}
E = \sum_{\bf k}\sum_{p=+,\times} E_{{\bf k},p} \label{Eg}
\end{equation}
where
\begin{equation}
E_{{\bf k},p} = {1\over V32\pi G}\left(|\dot{\tilde{h}}_{{\bf k},p}|^2+k^2|\tilde{h}_{{\bf k},p}|^2\right)\label{EGWk}
\end{equation}
is the energy in each mode.
\section{Quantum Gravitational Wave}\label{QGW}
For a gravitational wave, the mathematics per mode is similar to the simple harmonic oscillator described in the Appendix. The reason being that the energy per mode of a gravitational wave of eq.~(\ref{EGWk}) is of the same structure of the energy of a simple harmonic oscillator of eq.~(\ref{ESHO}). The only difference is that the variable now is complex $\tilde{h}$, and we need to combine all the modes.
\subsection{Coherent and Squeezed States}
Of particular interest to us will be squeezed states, which can have enhanced fluctuations. While coherent states are the most classical, having minimal fluctuations that are too small to detect. Previously, Refs.~\cite{Parikh:2020nrd,Parikh:2020kfh,Parikh:2020fhy,Kanno:2020usf,Kanno:2021gpt,Guerreiro:2021qgk} made progress on studying these states. Our work here is to examine a particular class of squeezed states in more detail and its associated correlations.
To find the squeezed state wave function for a field, it is useful to compute in Fourier space with $\tilde{h}_{{\bf k},p}$. Since this is complex, it is useful to decompose in terms of its real $\tilde{h}_{1{\bf k},p}$ and imaginary $\tilde{h}_{2{\bf k},p}$ parts as
\begin{equation}
\tilde{h}_{{\bf k},p} = {\tilde{h}_{1{\bf k},p} + i\, \tilde{h}_{2{\bf k},p}\over\sqrt{2}},\,\,\,\,\,\,
\pi_{{\bf k},p} = {\pi_{1{\bf k},p} - i\, \pi_{2{\bf k},p}\over\sqrt{2}}
\end{equation}
A form of the squeezed state wave function for each component is
\begin{eqnarray}
\psi_s(h,t) \propto \prod_{a=1,2} \prod_{{\bf k}}\prod_{p=+,\times} &&\exp\!\Big{[} i\,\epsilon_{a {\bf k} ,p} + {i\over2\hbar}\pi_{ac, {\bf k} ,p}\tilde{h}_{a {\bf k} ,p} \nonumber\\
&&\!\!\!\!\!\!\!\!\!\!\!\!- {k \, S_{a {\bf k} ,p}(t) \over 64\pi V G \hbar}(\tilde{h}_{a{\bf k},p}-\tilde{h}_{ac,{\bf k},p}(t))^2\Big{]}\,\,\,\,\,\,\,\,\,\,\,
\end{eqnarray}
In this expression $\tilde{h}_{ac,{\bf k},p}(t)$ is a solution of the {\em classical} equation of motion, i.e.,
\begin{equation}
\ddot{\tilde{h}}_{ac,{\bf k},p}=-k^2 \tilde{h}_{ac,{\bf k},p}
\end{equation}
Note that back in position space, this is the classical wave equation
\begin{equation}
\ddot{h}_{c,p}=\nabla^2 h_{c,p}
\end{equation}
Note that if we take $S_{a{\bf k},p}(t)=1$ for all ${\bf k}$ and both polarizations, then this becomes a coherent state.
More generally, we can include a family of squeezing functions $S_{a{\bf k},p}$ for each mode ${\bf k}$ and polarization $p$, which can in principle be different between the real and imaginary parts $a$ (though we shall soon specialize to the case in which they are the same). By solving the Schr\"odinger equation, we find its time dependence is
\begin{equation}
S_{a{\bf k},p}(t) = \mbox{Tanh}\!\left(\mbox{Tanh}^{-1}(\beta_{a{\bf k},p}) + i\,k\,t\right)
\end{equation}
which are specified by the choice of initial squeezing parameters
\begin{equation}
S_{a{\bf k},p}(0) = \beta_{a{\bf k},p}
\end{equation}
which in principle can be different for each wave-vector ${\bf k}$ and each polarization $p=+,\times$. The wave function also includes the function
\begin{equation}
\epsilon_{a {\bf k} ,p}(t) = -{k\over 4} \int_0^t S_{a {\bf k} ,p}(\tau)d\tau - {1\over 4\hbar} \tilde{h}_{ac, {\bf k} ,p}(t) \pi_{ac, {\bf k} ,p}(t)
\end{equation}
Importantly, the conjugate momentum $\pi_{ {\bf k} ,p}$ is given from the Hamiltonian eq.\,(\ref{Eg}) as
\begin{equation}
\pi_{ {\bf k} ,p} = {\partial E \over \partial \dot{\tilde{h}}_{ {\bf k} ,p}} = {1\over 16\pi V G} \dot{\tilde{h}}^\dagger_{ {\bf k} ,p}
\end{equation}
and both obey the reality condition
\begin{eqnarray}
\tilde{h}_{ {\bf k} ,p} = \tilde{h}_{- {\bf k} ,p}^\dagger ~,~~~ \pi_{ {\bf k} ,p} = \pi_{- {\bf k} ,p}^\dagger.
\end{eqnarray}
while the real and imaginary components obey
\begin{eqnarray}
\tilde{h}_{1, {\bf k} ,p}&=&\tilde{h}_{1,- {\bf k} ,p},\,\,\,\,\,\,\tilde{h}_{2, {\bf k} ,p}=-\tilde{h}_{2,- {\bf k} ,p},\\
\pi_{1, {\bf k} ,p}&=&\pi_{1,- {\bf k} ,p},\,\,\,\,\,\,\pi_{2, {\bf k} ,p}=-\pi_{2,- {\bf k} ,p}.
\end{eqnarray}
\subsection{Equal Time Fluctuations}
If we take the continuum limit, then the above Gaussian distribution gives us the probability distribution for the field as $p(h,t)\propto|\psi_s(h,t)|^2$. For simplicity, let us report on results for a pair of identical squeezed functions $S_{ {\bf k} ,p}\equiv S_{1 {\bf k} ,p}=S_{2 {\bf k} ,p}$. In this case it is simplest to express results directly in terms of the complex fields $\tilde{h}_{{\bf k},p}$. From taking the absolute value squared of the above wave function, we have
\begin{eqnarray}
&&p(h,t) \propto \nonumber\\
&&\prod_{p=+,\times} \exp\!\left[-\int\!{d^3k\over(2\pi)^3}{k\,\mathbb{R}[S_{{\bf k},p}(t)] \over16\pi G\hbar}
|\tilde{h}_{{\bf k},p}-\tilde{h}_{c,{\bf k},p}(t)|^2\right]\,\,\,\,\,\,\,\,
\end{eqnarray}
where $\mathbb{R}[S]$ is the real part of $S$.
The mean and variance are given by
\begin{equation}
\langle \tilde{h}_{{\bf k},p}\rangle=\tilde{h}_{c,{\bf k},p}(t),\,\,\,\,\,\,
\sigma_{{\bf k},p}^2= {V 8\pi G\hbar\over k} f_{{\bf k},p}(t)
\end{equation}
where
\begin{equation}
f_{{\bf k},p}(t)\equiv \beta_{{\bf k},p}^{-1}\cos^2(k t)+\beta_{{\bf k},p}\,\sin^2(k t)
\end{equation}
In fact it is useful to define the departure from the mean as
\begin{equation}
\delta h_p\equiv h_p-\langle h_p\rangle
\end{equation}
We can then form the 2-point correlation function in ${\bf k}$-space as
\begin{equation}
\langle \delta \tilde{h}_{{\bf k},p} \, \delta \tilde{h}_{{\bf k}',p'}^* \rangle = {V 8\pi G\hbar\over k}f_{{\bf k},p}(t)\,\delta_{{\bf k},{\bf k}'}\delta_{p,p'}
\end{equation}
where $\delta_{{\bf k},{\bf k}'}$ is the Kronecker delta function ($=1$ if ${\bf k}={\bf k}'$ and $=0$ if ${\bf k}\neq {\bf k}'$) and similarly for $\delta_{p,p'}$.
In the continuum limit we can write this in terms of the Dirac delta function $\delta^3({\bf k}-{\bf k}')$ as
\begin{equation}
\langle \delta \tilde{h}_{{\bf k},p} \, \delta \tilde{h}_{{\bf k}',p'}^* \rangle =(2\pi)^3\,\delta^3({\bf k}-{\bf k}')\,\delta_{p,p'}\,P_{p}({\bf k},t)
\label{2ptpower}\end{equation}
where the ``power spectrum" is given by
\begin{equation}
P_{p}({\bf k},t)=P_v(k)\,f_{{\bf k},p}(t)
\end{equation}
where
\begin{equation}
P_v(k)={8\pi G\hbar\over k}
\label{Pvac}\end{equation}
is the power spectrum of vacuum fluctuations.
It is important to return to position space, since we are ultimately interested in the motion of mirrors in interferometers which are well localized in position space.
By taking the inverse Fourier transform we obtain
\begin{equation}
\langle \delta h_p({\bf x},t)\,\delta h_{p'}({\bf y},t)\rangle = \delta_{p,p'}\int\!{d^3 k\over(2\pi)^3}\,P_{p}({\bf k},t)\,e^{i{\bf k}\cdot({\bf x}-{\bf y})}
\end{equation}
Although this can be useful, to see correlations in space at a fixed time, the interferometer experiments are sensitive to something else. In particular, one watches a mirror swing back and forth over time. So therefore it is important to understand correlations in time as well, as we now compute.
\section{Correlations in Space and Time}\label{CST}
Here we report on the correlation functions at different times and space. It is convenient to perform the calculation in Fourier space, where we find an extension of Eq.~(\ref{2ptpower}) to
\begin{equation}
\langle \delta \tilde{h}_{{\bf k},p}(t) \, \delta \tilde{h}_{{\bf k}',p'}^*(t') \rangle =(2\pi)^3\,\delta^3({\bf k}-{\bf k}')\,\delta_{p,p'}\,Q_{p}({\bf k},t,t')
\end{equation}
where the mixed time power spectrum $Q$ is given by
\begin{equation}
Q_{p}({\bf k},t,t')=P_v(k)\,F_{{\bf k},p}(t,t')
\end{equation}
where $P_v$ is the power spectrum of vacuum fluctuations Eq.~(\ref{Pvac}). By using the Heisenberg equation of motion (an illustrative example is given in the Appendix), we find that $F$ is given by
\begin{eqnarray}
F_{{\bf k},p}(t,t')&\equiv& \beta_{{\bf k},p}^{-1}\cos(k t)\cos(k t')+\beta_{{\bf k},p}\,\sin(k t)\sin(k t')\nonumber\\
&&+i\,\sin(k(t'-t))
\end{eqnarray}
Returning to position space, this becomes
\begin{eqnarray}
\xi_p({\bf x},{\bf y},t,t') & = & \langle h_p({\bf x},t)\,h_p({\bf y},t')\rangle -\langle h_p({\bf x},t)\rangle\langle h_p({\bf y},t')\rangle \,\,\,\,\, \nonumber\\
& = & \delta_{p,p'}\int\!{d^3 k\over(2\pi)^3}\,Q_{p}({\bf k},t,t')\,e^{i{\bf k}\cdot({\bf x}-{\bf y})}
\end{eqnarray}
\subsection{Monochromatic Squeezing Function}
If, for simplicity, we assume there is only a single mode ${\bf k}^*$ that is significantly squeezed, then we can write
\begin{equation}
\beta_{{\bf k},p}=1+{e^{2\zeta_p}k^{*3}\!\over2}\,(2\pi)^3(\delta^3({\bf k}-{\bf k}^*)+\delta^3({\bf k}+{\bf k}^*))
\label{betadelta}\end{equation}
where $\zeta_p$ is the {\em dimensionless} strength of the squeezing. Note that we added a pair of delta-functions to ensure the reality condition is obeyed, i.e., we need $\beta_{{\bf k},p}=\beta_{-{\bf k},p}^*$. Also note that we added 1 to every mode, which corresponds to no-squeezing.
With this form for $\beta$, we have
\begin{eqnarray}
&&\xi({\bf x},{\bf y},t,t') \nonumber\\
&=& \delta_{p,p'}{1\over2\pi^2}\int_0^\infty dk\,k^2\,P_v(k){\sin(k|{\bf x}-{\bf y}|)\over k|{\bf x}-{\bf y}|} e^{-ik(t-t')}\nonumber\\
&+&\delta_{p,p'}{e^{2\zeta_p}k^{*3}\!\over2}\!\int\! d^3k\Big[P_v(k)(\delta^3({\bf k}-{\bf k}^*)+\delta^3({\bf k}+{\bf k}^*))\nonumber\\
&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,
\times\sin(kt)\sin(kt')e^{i{\bf k}\cdot({\bf x}-{\bf y})}\Big]\,\,\,\,\,\,\,\,\,
\end{eqnarray}
We can then use the following fact
\begin{equation}
\int_0^\infty dk\,k^2\,{1\over k}{\sin(k r)\over k r}e^{-ik(t-t')} = {1\over r^2-(t-t')^2}
\end{equation}
and we can trivially carry out the delta-function integrals.
Hence the full 2-point correlation function is
\begin{eqnarray}
&&\xi_p({\bf x},{\bf y},t,t') = \delta_{p,p'}{1\over 2\pi^2}{8\pi G\hbar\over|{\bf x}-{\bf y}|^2-(t-t')^2}\nonumber\\
&&+\delta_{p,p'}8\pi G\hbar \,e^{2\zeta_p}k^{*2}\sin(k^*t)\sin(k^*t')\cos({\bf k}^*\!\cdot\!({\bf x}-{\bf y}))\,\,\,\,\,\,\,\,\,\,
\label{2ptauto}\end{eqnarray}
Note the sinusoidal oscillations in both $t$ and $t'$; this is a property of the very restrictive monochromatic squeezing; this will be altered as we move to more realistic squeezing functions, as we turn to now.
\subsection{Smoothed Out Squeezing Function}
Let us consider squeezing a range of modes, rather than only a unique value ${\bf k}^*$. Since a gravitational wave involves a continuum of modes, this seems more realistic. Suppose the wave is heading in the (positive) $z$-direction, with its mean wavenumber of ${\bf k}^*=k^*\hat{z}$ and standard deviation $\kappa$. We smear out eq.~(\ref{betadelta}) to become
\begin{eqnarray}
\beta_{{\bf k},p}=1\,+\,&&{e^{2\zeta_p}k^{*2}k\!\over2}\,(2\pi)^3\delta(k_x)\delta(k_y)\times\nonumber\\
&&{1\over\sqrt{2\pi\kappa^2}}\left[e^{-(k_z-k^*)^2/2\kappa^2}+e^{-(k_z+k^*)^2/2\kappa^2}\right]\,\,\,\,\,\,\,\,\,
\label{betasmooth}\end{eqnarray}
Note that we also smoothed out the prefactor $k^{*3}\to k^{*2}k$ for convenience. By carrying out the above integrals, and taking the large $t$ and $t'$ limit, we obtain
\begin{eqnarray}
&&\xi_p({\bf x},{\bf x}',t,t') = \delta_{p,p'}{1\over 2\pi^2}{8\pi G\hbar\over|{\bf x}-{\bf x}'|^2-(t-t')^2}\nonumber\\
&&+\delta_{p,p'}2\pi G\hbar \,e^{2\zeta_p}k^{*2}\times\nonumber\\
&&\sum_{\mp}e^{-((z-z')\mp(t-t'))\kappa^2/2}\cos(k^*((z-z')\mp(t-t')))\,\,\,\,\,\,\,\,\,
\label{2ptautoSmooth}\end{eqnarray}
Note that having performed the smoothing, we have removed the oscillations in Eq.~(\ref{2ptauto}) and obtained a result with time translation invariance, being only a function of $t-t'$. A version whose fluctuations ``hit" in the region of the classical wave itself can be obtained, as we now discuss.
\subsection{Classical Wave Modulation}
A more realistic smoothing function should lead to the second line in Eq.~(\ref{2ptautoSmooth}) being appreciable at the center of the classical wave packet $h_c$, whose state one is taking to be squeezed. This can be accommodated by taking this modulation to be adiabatic, i.e., to suppose that the above high frequency modes are modulated by a relatively low frequency mode, whose corresponding wavelength is of the order of the size of the classical wave packet. So in this adiabatic approximation the second line should be re-scaled by an overall factor of $M_p(z,t)$, where
\begin{equation}
M_p(z,t) = \Bigg\{\begin{array}{c}
1,\,\,\,\, |z-t-\phi_c|\ll\lambda_c\\
0,\,\,\,\,|z-t-\phi_c|\gg\lambda_c\end{array}
\end{equation}
where $\phi_c$ is the phase of the center of the classical wave packet (i.e., $h_c(z=t+\phi,t)$ is large) and $\lambda_c$ is the overall size of the wavepacket. An example could be $M_p(z,t)=\exp(-(z-t-\phi_c)^2/\lambda_c^2)$.
\section{Detector Response for Coherent State}\label{DCS}
Let us first focus on the most classical possible state, i.e., a coherent state. So in this section we set
\begin{equation}
\beta_{{\bf k},p}=1
\end{equation}
(we consider $\beta_{{\bf k},p}\neq1$ in the next section).
Now despite the fact that this is essentially the ``most classical" state, nevertheless, the above result seems to indicate that as ${\bf x}\to{\bf y}$ the quantum fluctuations become infinite! However, we should note that this is only true if we really integrate the wave-numbers all the way up to $k\to\infty$. But this is unrealistic. The reason is that any detector, such as LIGO, cannot resolve arbitrarily high frequencies. The frequencies of the wave are related to the wave-number by
\begin{equation}
f={\omega\over 2\pi}={k\over 2\pi}
\end{equation}
Let's introduce a ``response" function $R(k)$, defined such that $R=1$ when the detector can resolve easily and $R=0$ when the detector cannot. We can insert this into our above result as follows
\begin{equation}
\xi({\bf x},{\bf y},t,t')_R = \delta_{p,p'}\int\!{d^3 k\over(2\pi)^3}\,P_v(k)\,e^{i{\bf k}\cdot({\bf x}-{\bf y})-ik(t-t')} R(k)
\end{equation}
where the subscript ``R" notation indicates we take into account the detector response.
If we consider the variance of fluctuations at a single spacetime point ${\bf x}\to {\bf y}$ we obtain the ``autocorrelation" function
\begin{equation}
\langle \delta h_p(t)\delta h_p(t')\rangle_R = \int\!{d^3 k\over(2\pi)^3}\,P_v(k)e^{-ik(t-t')}\,R(k)
\end{equation}
A simple choice to suppress high frequency modes is
\begin{equation}
R(k)
=\exp\left[-{k\over k_{max}}\right]
\end{equation}
where $k_{max}$ sets the maximum characteristic wavenumber the detector can resolve. Carrying out the above integral with this $R(k)$ leads to
\begin{equation}
\langle \delta h_p(t)\delta h(t')\rangle_R =
{4\over\pi}\left(k_{max}\over \omega_{Pl}\right)^2{1\over(1+i\,(t-t')\,k_{max})^2}
\end{equation}
where we have introduced the ``Planck frequency"
\begin{equation}
\omega_{Pl}\equiv{1\over\sqrt{G\hbar}}\approx 1.9\times10^{43}\,\mbox{sec}^{-1}
\end{equation}
Note that in general this autocorrelation function is complex, as the above is not a hermitian operator. However, to connect to a physical observable, we can symmetrize over the arguments to define a hermitian operator as follows
\begin{equation}
\xi({\bf x},{\bf y},t,t')_S\equiv (\xi({\bf x},{\bf y},t,t')_R+\xi({\bf y},{\bf x},t',t)_R)/2
\end{equation}
This gives
\begin{equation}
\langle \delta h_p(t)\delta h(t')\rangle_S = {4\over\pi}\left(k_{max}\over \omega_{Pl}\right)^2
{1-k_{max}^2(t-t')^2\over(1+ k_{max}^2(t-t')^2)^2}
\end{equation}
The standard deviation $(t\to t'$) in the fluctuations is therefore
\begin{equation}
\sigma_R=\sqrt{\langle (\delta h_p)^2\rangle_R}=\sqrt{4\over\pi}\left(k_{max}\over \omega_{Pl}\right)
\end{equation}
A plot of this symmetrized autocorrelation function is given in Figure \ref{AutoCorrelation}.
\begin{figure}[t!]
\centering
\includegraphics[width=\columnwidth]{Autocorrelation1.pdf}
\caption{(Normalized) autocorrelation function of vacuum fluctuations, defined with some cut off $k_{max}$.}
\label{AutoCorrelation}
\end{figure}
\subsection{Detector Limits and Comparison}
In the LIGO detector, the maximum frequency that the interferometer can respond to reliably is on the order of
\begin{equation}
{k_{max}\over2\pi}=f_{max}=\mathcal{O}(10^3)\,\mbox{Hz}
\end{equation}
This gives a standard deviation in quantum fluctuations on the order of
\begin{equation}
\sigma_R =\mathcal{O}(10^{-40})
\end{equation}
We should compare the size of these quantum fluctuations to the size of the classical gravitational waves detected at LIGO from merging binary black holes. From the LIGO paper,
we see that the measured amplitude of the wave is
\begin{equation}
h_c =\mathcal{O}(10^{-21})
\end{equation}
Putting this altogether we see that the relative size of the quantum fluctuations in a coherent state to the classical value is
\begin{equation}
{\sigma_R\over h_c}=\mathcal{O}(10^{-19})
\end{equation}
This is far too small to detect; as previously noted \cite{Parikh:2020nrd,Parikh:2020kfh,Parikh:2020fhy}. The current capability of LIGO is to detect fluctuations is about an order of magnitude below the classical value from mergers; certainly it cannot detect 19 orders of magnitude below.
For the {\em pure Minkowski vacuum state} fluctuations, there is a theoretical question of whether such fluctuations are detectable even in principle. More appropriately, since the world is actually built out of particles, one needs to construct the {\em dressed state} of the detector. Once this is constructed, it is unclear that any directly physical consequences of the vacuum fluctuations remain. After all, one needs to study interactions {\em between} materials (like the interactions between plates in the Casimir effect) to see physical consequences. This point seems to have been missed in some previous analyses of gravitational vacuum fluctuations in Minkowski space in the literature.
On the other hand, for the {\em coherent state}, this should manifest itself as physical shot noise. In any case, since the effect is so small, we do not pursue this further here.
\section{Detector Response for Squeezed State}\label{DSS}
Since the coherent state fluctuations are far too small, we can turn to the squeezed state, with strength of squeezing parameter $\zeta_p$.
In this case we only need to pay attention to the second term in eq.~(\ref{2ptauto}) or eq.~(\ref{2ptautoSmooth}).
Then the fluctuations are well behaved as ${\bf x}\to{\bf x}'$ and we expect to resolve these modes, which only apply for ${\bf k}={\bf k}^*$ since that is already anticipated to be a mode of the classical wave.
Focussing our attention on the case of the smooth squeezing function, the fluctuations are then
\begin{equation}
\langle \delta h_p(t) \delta h_p(t')\rangle
=A\,e^{-(t-t')\kappa^2/2}\cos(k^*(t-t'))\,M_p(z,t)\,\,\,\,\,\,\,\,\,
\label{2ptimeautoSmooth}\end{equation}
where the overall amplitude is defined as
\begin{equation}
A=4\pi G\hbar\, e^{2\zeta_p}k^{*2}
\end{equation}
At the center of the classical wave packet, where $M_p\to1$, the remaining shape
exhibits the nice features of time translation invariance, as it is only a function of $t-t'$.
The corresponding correlation is shown in Figure \ref{AutoCorrelation2}.
\begin{figure}[t!]
\centering
\includegraphics[width=\columnwidth]{Autocorrelation2.pdf}
\caption{(Normalized) autocorrelation function for squeezed modes from a smoothed distribution. Here we took $\kappa=k^*$ and evaluated $z$ at $t+\phi_c$; the center of the wave packet.}
\label{AutoCorrelation2}
\end{figure}
\subsection{Constraints from LIGO}
Let us consider the amplitude of fluctuations at each moment in time. To do so, we take $t\to t'$, and we evaluate $M_p\to1$ as we are interested in the maximum fluctuation. We wish to compare this to the noise seen at LIGO.
Writing the wave-number in terms of the frequency of the wave $k^*=2\pi f^*$, sending $t\to t'$, and taking a square root gives the standard deviation $\sigma_S =\sqrt{\langle (\delta h_p)^2\rangle}$ in the squeezed state of
\begin{equation}
\sigma_S = \sqrt{4\pi} \,e^{\zeta_p}\!\left(2\pi f^*\over \omega_{Pl}\right)
\label{sigmaS}\end{equation}
The scaling here is broadly consistent with the scalings estimated in prior works \cite{Parikh:2020kfh,Parikh:2020fhy,Kanno:2020usf,Guerreiro:2021qgk}.
Let us compare this to the first observation of merging black holes seen by LIGO GW150914 \cite{LIGOScientific:2016aoc}. As is well known, the response by the interferometer is in good agreement with the predictions of classical general relativity. There does exist a residual noise, i.e., a residual difference between observation and theoretical prediction. By running a statistical analysis of the LIGO data from Hanford (H) and Livingston (L), we find the standard deviation of the residual is
\begin{equation}
\sigma_{H}\approx\sigma_L\approx 0.16\times 10^{-21}
\end{equation}
Very reasonably, this residual can be mostly accounted for from various well known effects, such as thermal noise, photon shot noise, etc. So at the very least we can use this as a definite {\em upper bound} on the size of the quantum gravitational fluctuations $\sigma_S$ in our squeezed state. To evaluate $\sigma_S$ as above, we need a value of $f^*$, a central frequency of the (classical) wave. From GW150914 data, the frequencies of largest support in the wave occurred for
\begin{equation}
f^*\sim 200\,\mbox{Hz}
\end{equation}
By inserting this value into Eq.~(\ref{sigmaS}) and demanding
$\sigma_S<\sigma_H\approx\sigma_L$,
we obtain a bound on $\zeta_p$ of
\begin{equation}
\zeta_p<41
\end{equation}
(for each mode) which is our primary finding. By estimating residuals from known effects, one could improve this bound a little. We leave this for future work.
\subsection{Temporal Correlations}
The existing LIGO data does not exhibit any known unexplained correlation. So drawing from these correlated fluctuations, the bound should approximately reproduce the $\zeta_p\lesssim 41$ found above. The reason being that the above correlations in the squeezed state fall off beyond the inverse characteristic frequency of the signal (see Figure \ref{AutoCorrelation2}), so these are rather short ranged correlations. Nevertheless for further precision, one can run the autocorrelation function on the data to potentially improve the bound on $\zeta_p$ marginally.
\section{Discussion}\label{Conc}
At large distances, gravity is a consistent quantum effective theory. In this work we have computed the properties of a gravitational wave in a quantum mechanical squeezed state. We paid particular attention to the two-point correlation function of the gravitational wave in both space and time. By considering a smooth range of modes, we obtained the correlation function in Eq.~(\ref{2ptautoSmooth}) (along with the modulation function $M_p$), in which the fluctuations are nicely separated into a vacuum piece, which is not directly measurable, and an enhanced squeezed piece, which could in principle correct the motion of detectors in an interferometer. By using existing LIGO data, we placed a bound on the (exponential) squeezing parameter of $\zeta<41$. Although this is a relatively weak bound, it is interesting to be able to use existing data to place real constraints. Further detailed constraints from combining all LIGO data can be obtained in the future.
An important topic for future work is to compute from first principles the actual state set up by the merger of black holes. The usual assumption is that the state is close to classical, i.e., close to a coherent state, in which case the quantum fluctuations are predicted to be negligibly small. In this case, a future detection of quantum fluctuations would be unexpected and of profound significance as it would render gravitation incompatible with standard quantum mechanics with a universal uncertainty bound. Alternatively, if the black hole merger creates huge squeezing and/or if the individual black holes are intrinsically very quantum, as some speculative models have suggested, the state could be highly squeezed. This all deserves further analysis.
We are now in the era of gravitational wave astronomy, with several detectors, including LIGO, Virgo, GEO600, KAGRA. So any data that we can use to glean even the smallest clues about quantum gravity may be useful.
\section*{Acknowledgments}
M.~P.~H is supported in part by National Science Foundation grant PHY-2013953.
We would like to thank Eunice Beato, Andi Gray, and Erin Wilson for discussion.
\section*{Appendix: Simple Harmonic Oscillator}\label{AppSHO}
This appendix is for pedagogical purposes; for any reader who is new to this subject. By understanding the results here for the simple harmonic oscillator, one can extend them to the case of a quantum gravitational wave, as we did in the main part of the paper.
The standard simple harmonic oscillator is a body of mass $m$, oscillating on a spring with natural frequency $\omega_0$. The energy is a sum of kinetic and potential energy as
\begin{equation}
E_{\mbox{\tiny{SHO}}} = {1\over2}m\dot{x}^2+{1\over2}m\omega_0^2 x^2\label{ESHO}
\end{equation}
But this basic structure appears much more generically, including the form seen earlier for each mode of a gravitational wave in Eq.~(\ref{EGWk}).
\subsection{Ground State}
Classically, a harmonic oscillator would sit at rest at the bottom of the potential with minimal energy of zero. But this is not allowed by the Heisenberg uncertainty principle. Instead the quantum ground state wave function is given by
\begin{equation}
\Psi_g(x,t)\propto \exp\!\left[-{i}E_0 t/\hbar-{1\over2\hbar}m\omega_0 x^2\right]
\end{equation}
where $E_0={1\over2}\hbar\omega_0$ is the ground state energy.
The probability density distribution for where the particle can be found is
\begin{equation}
\rho_g(x,t)=|\Psi_{g}(x,t)|^2\propto \exp\!\left[-{1\over\hbar}m\omega_0 x^2\right]
\end{equation}
This is a type of Gaussian distribution as it fits the standard form
\begin{equation}
\rho(x,t)\propto \exp\!\left[-(x-\langle x\rangle)^2/(2\sigma^2)\right]
\end{equation}
Here the mean and variance of position is
\begin{equation}
\langle x\rangle = 0,\,\,\,\,\,\,\sigma_x^2={\hbar\over 2m\omega_0}
\end{equation}
While the mean and variance of momentum is
\begin{equation}
\langle p\rangle = 0,\,\,\,\,\,\,\sigma_p^2={\hbar m\omega_0\over 2}
\end{equation}
Note that the product of uncertainties is
\begin{equation}
\sigma_x\,\sigma_p={\hbar\over2}
\end{equation}
which is the minimum value allowed by the Heisenberg uncertainty principle.
\subsection{Coherent State}
A coherent state is considered the ``most classical state": Like the ground state, it minimizes the Heisenberg uncertainty principle at all times. However, unlike the ground state, it also has a mean value that undergoes familiar classical motion.
The wave function is given by
\begin{equation}
\psi_c(x,t)\propto \exp\!\left[i\,\epsilon(t)+ip_0(t)x/\hbar-{1\over2\hbar}m\omega_0 (x-x_0(t))^2\right]
\end{equation}
where the phase is given by
\begin{equation}
\epsilon(t)=-{1\over2}\omega_0\,t-{1\over2\hbar}x_0(t)p_0(t)
\end{equation}
Here $x_0(t)$ is a solution of the {\em classical} equation of motion, i.e.,
\begin{equation}
\ddot{x}_c=-\omega_0^2 x_c
\end{equation}
Its solutions are given by
\begin{equation}
x_0(t) = A \cos(\omega_0t-\varphi) \label{x0}
\end{equation}
where $A$ is the amplitude of oscillation and $\varphi$ is the phase. Also, $p_0(t)=m\dot{x}_0(t)$ is the classical momentum.
The corresponding probability distribution that is in fact the same as the ground state, except it is displaced as follows
\begin{equation}
\rho_c(x,t)\propto \exp\!\left[-{1\over\hbar}m\omega_0 (x-x_0(t))^2\right]
\end{equation}
Hence the coherent state is also a Gaussian distribution with mean and variance
\begin{eqnarray}
&&\langle x\rangle = x_0(t),\,\,\,\,\,\,\sigma_x^2={\hbar\over 2m\omega_0}\\
&&\langle p\rangle = p_0(t),\,\,\,\,\,\,\sigma_p^2={\hbar m\omega_0\over 2}
\end{eqnarray}
So just like the ground state, it too saturates the uncertainty principle
\begin{equation}
\sigma_x\,\sigma_p={\hbar\over2}
\end{equation}
while allowing for large oscillations. This makes it especially classical.
\subsection{Squeezed State}
A squeezed state is similar to a coherent state, except that the product of variances does {\em not} saturate the uncertainty principle limit, nor is it time independent. The initial wave function is taken to be
\begin{equation}
\psi_s(x,0)\propto \exp\!\left[{i\over\hbar}p_0(0)x-{\beta\over2\hbar}m\omega_0 (x-x_0(0))^2\right]
\end{equation}
where $\beta$ is the ``squeezing parameter". If $\beta=1$ then this returns to the above coherent state. While for $\beta\neq1$ we have a so-called squeezed state. By solving the time dependent Sch\"odinger equation, the time evolved state can be shown to be
\begin{equation}
\psi_s(x,t)\propto \exp\! \Big{[}
i\,\epsilon(t)+{i\over\hbar}p_0(t)x-{S(t)\over2\hbar}m\omega_0 (x-x_0(t))^2\Big{]}
\end{equation}
Here the function $\epsilon(t)$ can be represented as
\begin{equation}
\epsilon(t)=-{1\over2}\omega_0\!\int^t_0 dt'S(t')-{1\over2\hbar}x_0(t)p_0(t)
\end{equation}
Importantly, we now have the time evolved squeezing function $S(t)$. In general it is complex valued; it found to be given by
\begin{equation}
S(t) = \mbox{Tanh}\!\left(\mbox{Tanh}^{-1}(\beta) + i\,\omega_0\,t\right) \label{S}
\end{equation}
Note that initially ($t=0$) we have
\begin{equation}
S(0)=\beta
\end{equation}
The probability distribution is
\begin{equation}
\rho_s(x,t)\propto \exp\!\left[-{\mathbb{R}[S(t)]\over\hbar} m\omega_0(x-x_0(t))^2\right]
\end{equation}
where $\mathbb{R}[S(t)]$ means the real part of $S(t)$.
The mean of position and momentum is as usual: $\langle x\rangle = x_0(t),\,\langle p\rangle = p_0(t)$. However, the variances are not the usual values from the ground state. They are given by
\begin{eqnarray}
&&\sigma_x^2={\hbar\over 2m\omega_0}\!\left(\beta^{-1}\!\cos^2(\omega_0t)+\beta\sin^2(\omega_0t)\right)\,\\
&&\sigma_p^2={\hbar m\omega_0\over 2}\!\left(\beta\cos^2(\omega_0t)+\beta^{-1}\!\sin^2(\omega_0t)\right)\,\,\,\,\,\,\,\,\,\,
\end{eqnarray}
These are plotted in Figure \ref{VarianceVsTime} for the case of $\beta=4$. The product of the standard deviations does not saturate the uncertainty limit. Instead it is given by
\begin{equation}
\sigma_x\,\sigma_p={\hbar\over2}\sqrt{1+6\beta^2+\beta^4-(\beta^2-1)^2\cos(4\omega_0t)\over8\beta^2}
\end{equation}
This oscillates between the minimum and maximum values of
\begin{equation}
(\sigma_x\,\sigma_p)_{min}={\hbar\over2},\,\,\,\,\,\,(\sigma_x\,\sigma_p)_{max}={\hbar\over4}\left(\beta^{-1}+\beta\right)
\end{equation}
So by either taking $\beta\gg1$ or $\beta\ll1$ we obtain very large oscillations in the variances.
\subsection{Correlations in Time}
Here we report on the correlation functions in time. To compute this we operate in the Heisenberg picture with
\begin{eqnarray}
&&\hat{x}(t) = \hat{x}(0)\,\cos(\omega_0 t)+{\hat{p}(0)\over m\omega_0}\sin(\omega_0t)\\
&&\hat{p}(t) = \hat{p}(0)\,\cos(\omega_0 t)-m\omega_0\,\hat{x}(0)\sin(\omega_0t)
\end{eqnarray}
where $\hat{x}(0),\,\hat{p}(0)$ are standard operators evaluated at $t=0$.
We then define the temporal correlation function as
\begin{equation}
\xi(t,t') = \langle \hat{x}(t)\,\hat{x}(t')\rangle -x_0(t)x_0(t')
\end{equation}
By computing this expectation value with the above Heisenberg operator results, we obtain
\begin{eqnarray}
\xi(t,t')& = &{\hbar\over 2m\omega_0}\Big{(}\beta^{-1}\cos(\omega_0 t)\cos(\omega_0t') \nonumber\\
&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\beta\,\sin(\omega_0 t)\sin(\omega_0t') \nonumber\\
&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+i\,\sin(\omega_0(t'-t))\Big{)}
\label{xiONE}\end{eqnarray}
Note that by directly going from $t$ to $t'$, another way of writing this is
\begin{eqnarray}
\xi(t,t') &=&{\hbar \over 2m\omega_0 \mathcal{R}[S(t)]} \Big( \! \cos(\omega_0 (t'-t)) \nonumber\\
&&\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+ i \, S(t) \sin(\omega_0 (t'-t)) \Big)
\label{xiTWO}\end{eqnarray}
We note that in Eq.~(\ref{xiONE}) this is manifestly invariant under the interchange of $t \leftrightarrow t'$ and complex conjugation, though this fact becomes obscured in Eq.~(\ref{xiTWO}). This information is restored when $S(t)$ is written using Eq.~(\ref{S}).
\begin{figure}[b!]
\centering
\includegraphics[width=\columnwidth]{Autocorrelation3SHO.pdf}
\caption{Variances vs time for a squeezed state with squeezing parameter $\beta=4$. Red curve is $\sigma_x^2(m\omega_0/\hbar$), blue curve is $\sigma_p^2/(\hbar m\omega_0)$, and green curve is $\sigma_x\,\sigma_p/\hbar$.}
\label{VarianceVsTime}
\end{figure}
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Al-Ahli () (cunoscut și cu numele de Al-Thaghar) este un club sportiv din Jeddah, Arabia Saudită. A câștigat Campionatul de fotbal din Arabia Saudită patru anotimpuri, în 1968, 1978,1984 Și 2016
Al-Ahli a fost primul club din Arabia Saudită care a câștigat competiția în 1968 și este singurul club din Arabia Saudită care a câștigat de 13 ori Cupa Regelui.
Palmares
Campionatul de fotbal din Arabia Saudită: 4
Campioni : 1968/69, 1978, 1984, 2016
Cupa Prințului: 6
Campioni : 1957, 1970, 1998, 2002, 2007, 2015
Cupa Regelui: 13
Campioni : 1962, 1965, 1969, 1970, 1971, 1972, 1977, 1978, 1979, 1983, 2011, 2012, 2016
Cupa Federației Arabiei Saudite: 5
Campioni : 2001, 2002, 2007, 2012, 2013
Supercupa Saudită 1: 2016
Cupa clubului de golf 3: 1985, 2002, 2008
Cupa Cluburilor Arabe 1: 2003
Cupa internațională a prieteniei 2: 2001, 2002
Cupa Ligii Campionilor Al Masif 3: 1966, 1974, 1982
Cupa Campionatului EPIC 1: 2014
Campionatul Regiunii Vest 10: 1962, 1965, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1976
Campionatul Ligii Orașului Jeddah 2: 1961, 1962
Cupa regiunii Mecca 1: 1967
Performanțe în competițiile AFC
Liga Campionilor Asiei: 14 prezențe
1985-86 - Finalist
2002-03 - Calificare Western - Runda a treia
2005 - sferturi de finală
2008 - Etapa grupelor
2010 - Etapa grupelor
2012 - Finalist
2013 - sferturi de finală
2015 - optimi
2016 - Etapa grupelor
2017 - sferturi de finală
2018 - optimi
2019 - optimi
2020 - sferturi de finală
2021 - Etapa grupelor
Lot actual
Jucători notabili
Antrenori notabili
Valdir Pereira (Didi) 1978 - 1981
Telê Santana 1983 - 1985
Mahmoud El-Gohary 1985
Luiz Felipe Scolari 1990 - 1991
Carlos Roberto Cabral 1993 - 1994
Moscofetch Nebosha 2007 - 2008
Leandro Mendel 2008
Stoycho Mladenov 2008 - 2009
Gustavo Alfaro 2009
Sergio Farias 2010 - prezent
Legături externe
Site oficial
Fondări în 1937
Cluburi de fotbal din Arabia Saudită
|
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| 245
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The Strathearn Pipe Band is a non profit organisation with Charitable Status. Our instructors and teachers give their tuition free. Donations from our functions and funding from grants go to equipment and clothing.
Our band meets on a Monday evening in the Moray Institute in Blackford. Feel free to drop in and hear us play or discuss joining or supporting us.
More information is available on Strathearn Pipe Band's website.
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{"url":"https:\/\/socratic.org\/questions\/is-hcn-cyanic-acid-or-hydrocyanic-acid","text":"# Is HCN cyanic acid or hydrocyanic acid?\n\n$\\text{H}$, hydrogen and $\\text{CN}$ which is cyanide put together is Hydrogen Cyanide although it is sometimes referred to as prussic acid","date":"2019-11-22 13:00:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 2, \"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\": 0.9114151000976562, \"perplexity\": 10925.18287508951}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-47\/segments\/1573496671260.30\/warc\/CC-MAIN-20191122115908-20191122143908-00285.warc.gz\"}"}
| null | null |
Q: CMake with Qt UI file not found I have a C++ project using Qt with CMAKE that is organized in the following folders:
├── app
│ ├── CMakeLists.txt
│ └── main.cpp
├── CMakeLists.txt
├── include
│ └── MainWindow
│ └── MainWindow.h
└── src
├── CMakeLists.txt
├── MainWindow.cpp
└── MainWindow.ui
In the different CMakeLists.txt I have the following information:
CMakeLists.txt
cmake_minimum_required(VERSION 3.23)
project(prj VERSION 0.0.1 LANGUAGES CXX)
add_subdirectory(app)
add_subdirectory(src)
app/CMakeLists.txt
add_executable(app main.cpp)
target_link_libraries(app PRIVATE MainWindow)
src/CMakeLists.txt
# Configure AUTO
set(CMAKE_AUTOMOC ON)
set(CMAKE_AUTORCC ON)
set(CMAKE_AUTOUIC ON)
# Generar librería para la interfaz gráfica.
add_library(MainWindow MainWindow.cpp MainWindow.ui)
target_include_directories(MainWindow PUBLIC ../include)
target_compile_features(MainWindow PUBLIC cxx_std_14)
# Load QT files
set(CMAKE_PREFIX_PATH "/opt/Qt/5.15.2/gcc_64/lib/cmake")
find_package(Qt5 COMPONENTS Core Gui Widgets REQUIRED)
target_link_libraries(MainWindow Qt5::Core Qt5::Gui Qt5::Widgets)
What modifications or additions do I have to make in the different CMake files so that with a similar folder distribution I can get the application to work correctly without having errors?
The exact error, after all the modificications, is the following one:
FAILED: app/app
: && /usr/bin/c++ -g app/CMakeFiles/app.dir/main.cpp.o -o app/app -Wl,-rpath,/opt/Qt/5.15.2/gcc_64/lib src/libMainWindow.a /opt/Qt/5.15.2/gcc_64/lib/libQt5Widgets.so.5.15.2 /opt/Qt/5.15.2/gcc_64/lib/libQt5Gui.so.5.15.2 /opt/Qt/5.15.2/gcc_64/lib/libQt5Core.so.5.15.2 && :
/usr/bin/ld: src/libMainWindow.a(MainWindow.cpp.o): in function `MainWindow::MainWindow(QWidget*)':
/home/developer/CLionProjects/qtTest_v0/src/MainWindow.cpp:12: undefined reference to `vtable for MainWindow'
/usr/bin/ld: /home/developer/CLionProjects/qtTest_v0/src/MainWindow.cpp:12: undefined reference to `vtable for MainWindow'
/usr/bin/ld: src/libMainWindow.a(MainWindow.cpp.o): in function `MainWindow::~MainWindow()':
/home/developer/CLionProjects/qtTest_v0/src/MainWindow.cpp:16: undefined reference to `vtable for MainWindow'
/usr/bin/ld: /home/developer/CLionProjects/qtTest_v0/src/MainWindow.cpp:16: undefined reference to `vtable for MainWindow'
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{"url":"https:\/\/plainmath.net\/18700\/find-limit-exists-discuss-continuity-function-lim_-rightarrow-frac-plus","text":"Question\n\n# Find the limit (if it exists) and discuss the continuity of the function. \\lim_(x, y)\\rightarrow (1, 1)\\frac{xy}{x\u00b2 + y\u00b2}\n\nLimits and continuity\nFind the limit (if it exists) and discuss the continuity of the function. $$\\displaystyle\\lim_{{{x},{y}}}\\rightarrow{\\left({1},{1}\\right)}{\\frac{{{x}{y}}}{{{x}\u00b2+{y}\u00b2}}}$$\n\n2021-06-29\nthe function is continuous everywhere except the origin - the origin sets the denominator to 0\nsubstitute (1,1) into the function, and we obtain the limit is $$\\displaystyle{\\frac{{{1}}}{{{2}}}}$$ - by continuity of the function.","date":"2021-07-31 03:35:39","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\": 0.9125238060951233, \"perplexity\": 498.7810099794912}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"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-2021-31\/segments\/1627046154042.23\/warc\/CC-MAIN-20210731011529-20210731041529-00506.warc.gz\"}"}
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\section*{Acknowledgements}
This work received the funding from the European Research Council under the European Union's Seventh Framework Programme FP7/2007–2013/ERC grant agreement number [306292]. We acknowledge Prof. Barend Thijsse for useful discussions on this work.
\section*{Contributions}
Authors declare no conflict of interest. SK, JS, and MS designed the research. SK and AE prepared the initial simulation systems. SK carried out the MD simulations and wrote the initial manuscript. All authors contributed to the analysis of the simulations and preparation of the final manuscript.
\bibliographystyle{ActaMatnew-2}
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{"url":"http:\/\/www.ck12.org\/book\/CK-12-Chemistry---Intermediate\/r12\/section\/4.1\/","text":"<meta http-equiv=\"refresh\" content=\"1; url=\/nojavascript\/\"> Atoms | CK-12 Foundation\nYou are reading an older version of this FlexBook\u00ae textbook: CK-12 Chemistry - Intermediate Go to the latest version.\n\n# 4.1: Atoms\n\nCreated by: CK-12\n\n## Lesson Objectives\n\n\u2022 Explain the law of conservation of mass, the law of definite proportions, and the law of multiple proportions.\n\u2022 Describe John Dalton\u2019s atomic theory.\n\n## Lesson Vocabulary\n\n\u2022 atom\n\u2022 law of conservation of mass\n\u2022 law of definite proportions\n\u2022 law of multiple proportions\n\n## Early Atomic Models\n\nDemocritus was a Greek philosopher who lived from 460 B.C. until 370 B.C. He was among the first known individuals to suggest the idea of the atom as the basic unit of matter. The word atom comes from the Greek word atomos, meaning \u201cindivisible.\u201d Democritus (see Figure below) was indeed ahead of his time, but his ideas were not useful at that time in describing chemical behavior because there was no experimental evidence to support it. His approach was a philosophical one rather than a truly scientific one. Many centuries would pass before the notion of atoms was merged with modern scientific experimentation and thought.\n\nDemocritus believed that all matter consisted of tiny, indestructible particles called atoms.\n\n### Beginnings of Atomic Theory\n\nBy the late 1700s, chemists had accepted the definition of an element as a substance that cannot be broken down into simpler substances by ordinary chemical means. It was also clear that elements combine with one another to form more complex substances called compounds. The chemical and physical properties of these compounds are different than the properties of the elements from which they were formed. There was some disagreement, however, about whether elements always combined in exactly the same ratio when forming a particular compound.\n\nIn the 1790s, a greater emphasis began to be placed on the quantitative analysis of chemical reactions. Accurate and reproducible measurements of the masses of reacting elements and the compounds that they form led to the formulation of several basic laws. One of these is called the law of conservation of mass, which states that during a chemical reaction, the total mass of the products must be equal to the total mass of the reactants. In other words, mass cannot be created or destroyed during a chemical reaction, but must always be conserved.\n\nThe law of conservation of mass is demonstrated in this video: http:\/\/www.youtube.com\/watch?v=J5hM1DxaPLw (1:05).\n\nThe discovery that mass is always conserved in chemical reactions was soon followed by the law of definite proportions, which states that a given chemical compound always contains the same elements in the exact same proportions by mass. As an example, any sample of pure water contains 11.19% hydrogen and 88.81% oxygen by mass. It does not matter where the sample of water came from or how it was prepared. Its composition, like that of every other compound, is fixed (Figure below).\n\nRegardless of its source or its form (solid, liquid, or gas), water always has the exact same elemental composition: 11.19% of its mass is hydrogen and 88.81% of its mass is oxygen.\n\nExperiments also began to demonstrate that the same pairs of certain elements could combine to form more than one compound. Consider the elements carbon and oxygen. Combined in one way, they form the familiar compound called carbon dioxide. In every sample of carbon dioxide, there is 32.0 g of oxygen present for every 12.0 g of carbon. By dividing 32.0 by 12.0, this simplifies to an oxygen\/carbon mass ratio of 2.66 to 1. Another compound that forms from the combination of carbon and oxygen is called carbon monoxide. Every sample of carbon monoxide contains 16.0 g of oxygen for every 12.0 g of carbon, which simplifies to an oxygen\/carbon mass ratio of 1.33 to 1. In other words, a given mass of carbon needs to combine with exactly twice as much oxygen to make carbon dioxide as it would to produce carbon monoxide. Figure below illustrates the law of multiple proportions. Whenever the same two elements form more than one compound, the different masses of one element that combine with the same mass of the other element are in the ratio of small whole numbers.\n\nCarbon monoxide, on the left, contains 1.333 g of oxygen for every 1 g of carbon. Carbon dioxide, on the right, contains 2.666 g of oxygen for every gram of carbon. The ratio of oxygen in these two compounds is 1:2, which is a ratio of small whole numbers.\n\nSample Problem 4.1: Calculating Mass Ratios\n\nCopper reacts with chlorine to form two compounds. Compound A contains 4.08 g of copper for every 2.28 g of chlorine. Compound B contains 7.53 g of copper for every 8.40 g of chlorine. What is the lowest whole number mass ratio of copper that combines with a given mass of chlorine?\n\nStep 1: List the known quantities and plan the problem.\n\nKnown\n\n\u2022 Compound A = 4.08 g Cu and 2.28 g Cl\n\u2022 Compound B = 7.53 g Cu and 8.40 g Cl\n\nApply the law of multiple proportions to the two compounds. For each compound, find the grams of copper that combine with 1.00 g of chlorine by dividing the mass of copper by the mass of chlorine. Then, find the ratio of the masses of copper in the two compounds by dividing the larger value by the smaller value.\n\nStep 2: Calculate.\n\n$&\\text{Compound A} & \\dfrac{4.08 \\ \\text{g Cu}}{2.28 \\ \\text{g Cl}} &= \\dfrac{1.79 \\ \\text{g Cu}}{1.00 \\ \\text{g Cl}} \\\\&\\text{Compound B} & \\dfrac{7.53 \\ \\text{g Cu}}{8.40 \\ \\text{g Cl}} &= \\dfrac{0.896 \\ \\text{g Cu}}{1.00 \\ \\text{g Cl}} \\\\$\n\nCompare the masses of copper per gram of chlorine in the two samples.\n\n$\\dfrac{1.79 \\ \\text{g Cu (in compound A)}} {0.896 \\ \\text{g Cu (in compound B)}} = \\dfrac{2.00}{1} = 2:1$\n\nThe mass ratio of copper per gram of chlorine in the two compounds is 2:1.\n\nThe ratio is a small whole-number ratio. For a given mass of chlorine, compound A contains twice the mass of copper as does compound B.\n\n### Dalton's Atomic Theory\n\nIn 1808, an English chemist and schoolteacher named John Dalton (1766-1844) formulated an atomic theory based on the law of conservation of mass, the law of definite proportions, and the law of multiple proportions. His theory can be summarized in the following statements, illustrated in Figure below.\n\n1. All matter is composed of extremely small particles called atoms.\n2. Atoms of the same element are identical in terms of size, mass, and other properties. Atoms of one element are different from the atoms of any other element.\n3. Atoms of different elements can chemically combine with one another in simple whole-number ratios to form chemical compounds.\n4. Chemical reactions can be described as the separation, combination, or rearrangement of atoms. Atoms of one element cannot be changed into atoms of a different element as a result of a chemical reaction.\n\nDalton\u2019s atomic theory states that chemical reactions are due to rearrangements of atoms. On the left, hydrogen molecules are shown as two H atoms, while oxygen molecules are shown as two O atoms. The chemical reaction forms water as the atoms rearrange. There are identical numbers of hydrogen and oxygen atoms before and after the reaction.\n\n## Sizes of Atoms\n\nThe graphite in your pencil is composed of the element carbon. Imagine taking a small piece of carbon and grinding it until it is a fine dust. Each speck of carbon would still have all of the physical and chemical properties of carbon. Now imagine that you could somehow keep dividing the speck of carbon into smaller and smaller pieces. Eventually, you would reach a point where your carbon sample is as small as it could possibly be. This final particle is called an atom, which is defined as the smallest particle of an element that retains the properties of that element.\n\nAtoms, as you probably know, are extremely small. In fact, the graphite in an ordinary pencil contains about 5 \u00d7 1020 atoms of carbon. This is an almost incomprehensibly large number. The population of the entire Earth is about 7 \u00d7 109 people, meaning that there are about 7 \u00d7 1010 times as many carbon atoms in your pencil as there are people on the Earth! For this to be true, atoms must be extremely small. Can we see atoms? It\u2019s not easy, but a modern instrument called a scanning tunneling microscope allows scientists to visualize the atom, as shown in Figure below.\n\nImages of individual gold atoms can be seen on the surface of a smooth sheet of gold metal using scanning tunneling microscopy.\n\n## Lesson Summary\n\n\u2022 The Greek philosopher Democritus believed that matter is composed of indivisible and indestructible building blocks, which he called atoms.\n\u2022 John Dalton transformed the ideas of Democritus into a scientific atomic theory, which began to explain the law of conservation of mass, the law of definite proportions, and the law of multiple proportions.\n\u2022 Matter cannot be created or destroyed in chemical reactions.\n\u2022 Elements react to form compounds in fixed proportions by mass.\n\u2022 Elements combine with one another in simple whole-number ratios.\n\u2022 An atom is the smallest unit of an element that retains the properties of that element.\n\n## Lesson Review Questions\n\n### Recall\n\n1. Describe the contribution of Democritus to modern atomic theory.\n2. What happens to the total mass of a system during a chemical reaction?\n3. What does \u201cfixed composition\u201d mean with regard to chemical compounds?\n4. What law explains the relationships between different chemical compounds that contain only the elements carbon and oxygen?\n5. What are the four essential points of Dalton\u2019s atomic theory?\n\n### Apply Concepts\n\n1. Alchemy is an ancient tradition that predated the modern science of chemistry. One goal of the alchemist was to change base metals such as iron or lead into valuable metals such as gold or silver. Explain, using Dalton\u2019s theory, why alchemists were unable to do this.\n\n### Think Critically\n\n1. If an atom of element A has a mass of 2 units, while an atom of element B has a mass of 5 units, what would be the ratio of element A to element B in a compound that had a mass of 11 units?\n2. Sulfur reacts with oxygen to form two compounds. Compound A consists of 1.89 g of sulfur for every 1.89 g of oxygen. Compound B consists of 3.72 g of sulfur for every 5.57 g of oxygen. What is the lowest whole number mass ratio of sulfur that combines with a given mass of oxygen?\n3. Hydrocarbons are a class of organic compounds that contain only carbon and hydrogen. Methane, an important hydrocarbon fuel, has a carbon\/hydrogen mass ratio of 3:1. An 80-g sample of a hydrocarbon compound is analyzed and found to contain 64 g of carbon. Is the hydrocarbon sample methane? Explain.\n4. The mass of 6.02 \u00d7 1023 atoms of iron is 55.85 g. What is the mass of one atom of iron?\n\nAug 02, 2012\n\nAug 02, 2014","date":"2014-09-02 07:57:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 2, \"texerror\": 0, \"math_score\": 0.5822798609733582, \"perplexity\": 905.1102348224243}, \"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-2014-35\/segments\/1409535921869.7\/warc\/CC-MAIN-20140901014521-00164-ip-10-180-136-8.ec2.internal.warc.gz\"}"}
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XXX (ou xXx selon la graphie de la jaquette) est un jeu vidéo d'action développé par Digital Eclipse et édité par Activision, sorti en 2002 sur Game Boy Advance. Il est adapté du film xXx.
Système de jeu
Accueil
Jeux vidéo Magazine : 10/20
Notes et références
Notes
Références
Jeu vidéo sorti en 2002
Jeu Game Boy Advance
Jeu d'action
Jeu vidéo développé aux États-Unis
Jeu Activision
Jeu Digital Eclipse
Adaptation d'un film en jeu vidéo
XXX (série de films)
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Appear TV, a leading global provider of next-generation headends for broadcast and IP television, will showcase its modular headend supporting top transmission functions at the SCTE Cable-Tec Expo 13 (Booth 1368). On display will be modules providing encoding/transcoding/multiscreen, descrambling, powerful video processing, multiplexing with IP streaming and modulation support.
Broadcast Pix today announced that Mica, its new cost-effective live video production system, is now shipping. Powered by native HD technology fromBroadcast Pix Granite systems and Broadcast Pix Fluent software that tightly integrates video and file-based content, Mica allows even single operators to create compelling live productions. The company also announced its Powerful Punch Tour, which is stopping at a number of dealers and trade shows in cities worldwide this fall to demonstrate its Mica and Granite systems.
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The B&B Hotel DIE BERGQUELLE in the Salzburger Land is the ideal starting point for an active summer holiday. Starting out from our bed & breakfast, make Flachau the high point of your holiday. Blessed with lovely views, not too rugged and with many quaint and cosy lodges along the way, the Flachau mountains in Austria are waiting to be discovered.
Whether you choose to go on foot or by bike, the focus is on an experience of nature and sociable times in good company. So "auffi" is the cry – get cracking and scale the pinnacles of fun!
Enjoy your summer family active holiday in Flachau Austria!
From 13 June to 15 September 2019 numerous included services and benefits as well as a varied programme of activities await you with the Flachau Summer Card! The Flachau Summer Card is available free for you at our reception, if you stay 2 or more nights at the bed & breakfast Hotel "DIE BERGQUELLE".
Simply switch off, take a deep breath and take a time out in a holiday for a few days. Welcome to a world of feeling good, of generosity and enjoyment.
Pure mountain experience! Let yourself be carried away – we will show you the Flachau mountain world in all its diversity!
Whether on foot or by bike, nature and pleasant times together take centre stage.
Pretty promising, not too harsh, and many cosy chalets - the Flachau mountains are waiting to be discovered.
The first step to your holiday with us in Flachau!
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{"url":"https:\/\/fractalforums.org\/off-topic\/29\/memory-saving-tricks-in-software-of-the-80s\/3526\/0;wap2","text":"Community > Off Topic\n\nMemory-saving tricks in software of the 80's\n\n(1\/2) > >>\n\nmarcm200:\nI recently learned about some tricks, software developers employed for the Amstrad game Elite in the early 80's when memory was a concern back then.\n(from a german podcast: https:\/\/www.stayforever.de\/2014\/09\/folge-37-elite\/\n\nDoes anyone know of further such brilliant ideas from other software?\n\nElite is one of my favourite games from the 80s. You're a starship pilot, flying the universe, trading goods and shooting enemies to climb the rating ladder of traders.\n\nTrick 1\nThe developers use a system of 2-letter syllables that - in any combination - sound like alien planetary names. With that method they could just store a short bit pattern for every planet instead of a longer character string (La-ve, Le-eh-ti).\n\nTrick 2\nFor the galaxies, the planets and where which goods are tradable and to what price, they use a (system of) equations, where, when a different seed is entered, a different bit string results that is interpreted as the desired planet (I haven't figured that part out yet). Sounds almost like a compression method to me.\n\nIt would be interesting to use the classic quadratic Mandelbrot equation to form such a planetary system - with different seeds and different max it resulting in different alien systems :)\n\nLinkback: https:\/\/fractalforums.org\/index.php?topic=3526.0\n\ngerrit:\nReminds me of the SMTP greeting: HELO\n\nhobold:\nElite was procedurally generated. It was not the first game to do this. Pitfall was procedural, M.U.L.E.'s maps were procedural, too, for example. It was a common technique to work around the limited amounts of mass storage and main memory. It wasn't called \"procedural\" back then. And it isn't called \"procedural\" today, because today that word implies the (frequent) generation of fresh game content. Back then games re-generated a fixed set of game content, pre-selected by the game makers.\n\nInitially, the procedural generators were flawed. They would sometimes create unplayable or otherwise buggy game content. That's why the game designers restricted their games to a small, hand picked subset of possible creations.\n\nLater, in the 16 bit home computer era, procedural generators could be more sophisticated. They started to generate content with guarantees of playability and variety. I remember \"Seven Cities of Gold\" as my first encounter with a game that could create an entire new game world from scratch after you had played through the initial campaign (which was a manually created map of South America, if I remember correctly).\n\nBut most of the experimentation and exploration of possibilities was done outside the commercial video game industry. Rogue, Hack (and particularly Nethack) were all about procedurally generated dungeons as their core game mechanic. Some really weird experimentation continues until this day - I believe it was here on FractalForums that I was made aware of \"Hyperrogue\", which is set on the hyperbolic plane.\n\nData compression techniques are being employed, too. One of Sony's God of War games did some really heroic feats internally to let the Playstation shine in its brightest light. For example, it encoded a few extra bits of information by making intentional choices about the order in which they stored the three vertices of each surface facet. It is no coincidence that the end credits roll several hundred names. The Cell Processor was powerful, but a lot of ingenuity was necessary to overcome its limitations.\n\nmarcm200:\nVery interesting, thanks for the explanation. I wasn't aware that this method was so widespread and had never heard of it before.\n\nBut back in the 80s, my programming skills were at the beginner's state. I remember being very proud having managed to stop a text adventure from loading from datasette and look at the BASIC code lines to see which commands to enter where actually understood by the parser (I think the game's name was Thor trilogy with a guy named Llywenhuf or so), but it didn't help solvin the task :)\n\nmarcm200:\nA little computer experiment I'm conducting right now.\n\nThe \"hello world\" polynomial:\n\n$f(x) = x^6+3x^5+394x^4+416x^3+234x^2+293x+258$\n\n$$f(466) = 10324913503655364$$ which can be interpreted to represent \"hello world\" by considering the binary bit string of the function value, split into groups of 5 bits taken as an entry to an alphabet. In a sense this is a procedural method, as there is another text hidden in the formula.\n\n$$f(1262) = 4050368722319510032$$ which reads \"cykl_tiffanyy\" containing the name of an 80's female singer.\n\nThe latter was put there by rearranging the alphabet as the two words are disjoint, so after constructing the polynomial with \"hello world\" I could freely move the alphabet at some points around to fit the desired letter shape without changing hello world's function value.\n\nMy goal here is to construct a polynomial for galac's minuscule Mandelbrot code https:\/\/fractalforums.org\/programming\/11\/small-mandelbrot-set-in-c\/2658\/msg13599#msg13599 which only has 165 characters. I hope to get a function with not too many coefficients. For that I have to find an easy (or best not-to)-install BigInt library or try to write a maxima script to get the desired precision.\n\nNavigation\n\n[#] Next page\n\nGo to full version\nPowered by Advanced Topic Prefix Pro\nPowered by SMFPacks Rates (Facepunch) Mod\nPowered by SMFPacks Advanced Attachments Uploader Mod","date":"2020-08-14 04:37:54","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\": 0.308681845664978, \"perplexity\": 2264.348546914305}, \"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-2020-34\/segments\/1596439739177.25\/warc\/CC-MAIN-20200814040920-20200814070920-00386.warc.gz\"}"}
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Neogene pictus is a moth of the family Sphingidae. It is known from Paraguay and northern Argentina.
References
Neogene (moth)
Moths described in 1931
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Japanese and German broadcasters plan to jointly create a TV drama series that will be aimed at worldwide broadcast and also be pitched to Internet streaming services such as Netflix, Hulu and Amazon.
Japan's Fuji Television Network Inc. plans to produce a soccer-related drama series as a jointly funded project with ZDF Enterprises, a subsidiary of German public broadcaster ZDF.
The drama series "The Window," delving into the behind-the-scenes jockeying of professional soccer, will detail 10 weeks of conflict over huge contracts involved in a transfer window for England's Premier League.
A production company in Britain will start shooting the series next year, to air by the start of 2020. The series will be shot in English, and a British scriptwriter will be hired. Actors from Hollywood will be hired and an audition for Japanese actors is scheduled.
Fuji Television sought to secure large-scale production costs by working with foreign companies. Fuji is trying to compete on a global basis by making programming intended for the world market.
In addition to offering the series to broadcasters around the world, it will also be marketed to Internet streaming services.
The two companies teamed up because they have common subjects to be shared.
The future of the respective domestic markets in Japan and Germany is uncertain with the declining birthrate and the fact that fewer young people are watching TV.
The Japanese government has been trying to market Japanese TV programs overseas as part of its "Cool Japan" initiative. But the effort has been primarily limited to pitching Japanese programming to only other Asian countries.
In the midst of this, leading Internet entertainment services have appeared.
For a Japanese broadcaster, the project, costing about 2 billion yen ($18 million) for 10 episodes in total, is on an extraordinarily massive scale.
In the world market, Netflix and other entertainment services have joined in production of drama programming in rapid succession. Hulu and other online services broadcast "The Walking Dead," a popular U.S. TV drama series.
Netflix created the original series "House of Cards," which was the first drama series aired online to win an Emmy Award. The series was later broadcast on cable TV in some parts of the world.
The circulation of content beyond the borders between commercial TV and the Internet has just begun.
"I think that this joint project can be a steppingstone to improving the current situation for Japanese broadcasters, which have faced a sluggish growth of their audiences," Ota said. "While marketing the drama to broadcasters in Asia, Europe and North America, we also have to challenge in the global market by teaming with other services such as Netflix and Amazon."
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Group Health Insurance | AllDirect Insurance Services, Inc. | Insurance Agency in San Antonio, Texas.
There is safety in numbers and this principle applies in every office setting. When your business has employees running the operations, you will want to keep them safe, to make them feel valued and protected. The best way to compensate your employees for their hard work is to enroll your team/staff in a Group Health Insurance.
Group Health Insurances at AllDirect Insurance Services, Inc. are derived from a number of carriers each with their own version of health insurance coverage for a group of insurance holders. You will have a comparative view of your health insurance options and the advice of our staff to help you make a sound decision.
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{
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| 7,008
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Alexander Goldin (* 27. února 1964) je americký šachový velmistr ruského původu.
V roce 1981 vyhrál mistrovství SSSR šachistů do 18 let. Mezi jeho další úspěchy patří vítězství na World Open ve Philadelphii v letech 1998 a 2001. V roce 2003 vyhrál Goldin americký kontinentální šampionát v Buenos Aires, když v tiebreaku porazil brazilského Giovanni Vescovi.
Celkem třikrát se s americkým týmem účastnil šachové olympiády. V roce 2004 se svým týmem skončil v Calvià na čtvrtém místě, přičemž Goldinova úspěšnost na tomto turnaji dosáhla 65 procent.
Reference
Externí odkazy
Američané ruského původu
Američtí šachisté
Sovětští šachisté
Ruští šachisté
Šachoví velmistři
Žijící lidé
Narození v roce 1965
Muži
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{
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| 9,677
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\section{Introduction}
There is compelling evidence that the universe is currently undergoing a phase of accelerated expansion \cite{scp, riess, planck, wmap9, sdss, boss, wigglez}. This indicates some new physics at cosmological scales (``dark energy") \cite{de} that can give rise to repulsive gravity resulting the universe to accelerate. The cosmological constant with $w = \frac{p}{\rho} = -1$ is the simplest example of repulsive gravity and is consistent with the majority of cosmological observations. But the observational data at present is also consistent with dark energy behavior which is strictly not constant but evolves slowly throughout the cosmological history. Moreover the cosmological constant comes with its own baggage of problems like cosmic coincidence problem which can be avoided using dynamical dark energy.
Scalar fields are the most widely used dynamical dark energy models where late time acceleration can be obtained by adjusting the slope of the scalar field potential around suitable epoch \cite{quint}. But the cosmological evolution of these models is severely constrained by very accurate cosmological observations. From the measurements of temperature anisotropy in the cosmic microwave background (CMB) radiation, the distance to last scattering is very well determined. This restricts the equation of state for the scalar field to be very close to $w=-1$ at present. The type-Ia supernovae observations as well as Baryon Acoustic Oscillation (BAO) measurement in the large scale structures also give similar constraint on the scalar field equation of state. On the other hand CMB measurements also restricts the scalar field contribution to the total energy density of the universe during recombination to be less than $1\%$. All these constraints disfavor \cite{linder} the original ``tracker" kind of quintessence model\cite{lindcald} where the scalar field initially has a fast roll phase before settling to the cosmological constant behavior at present. Just recently, analysis of the spectrum from a distant quasar finds no evidence of deviation in molecular lines produced around 12 billion years ago. This confirms no change in the mass ratio of the proton to the electron. The results also indicate that a dark energy scalar field—if it exists—has not evolved appreciably over $90\%$ the age of the Universe \cite{Bagdon}, thereby putting doubt on the tracker kind of models as a possible candidate for dark energy.
The other scalar field behavior that is consistent with the present observational data is the ``thawing" one \cite{lindcald}. Currently there are many types of scalar field models that can give rise to thawing behavior. Examples are quintessence \cite{quint}, tachyons \cite{tach} as well as Galileon \cite{gal} models. In all these thawing models, the thawing nature does not depend crucially on the form of the potential. Once the initial conditions are chosen in such way that the scalar field starts in a nearly frozen state with $w\approx -1$, the thawing behavior is ensured. Fine tuning this initial condition is an issue in all thawing type of models. In a recent investigation, attempt has been made to relate this initial condition to inflationary dynamics \cite{raghu}.
Given the fact that thawing models are observationally promising as a possible candidate for dynamical dark energy models, we need to have a combined setup to investigate the cosmological evolution for different thawing scalar field models. In this work, we present such a setup in a Python environment. We name this setup as ``ScalPy" which solves the autonomous system with a given scalar field model by providing suitable initial conditions and calculates the observables like normalized Hubble parameter, angular diameter distance, luminosity distance, growth function, growth rate, linear matter power spectrum etc. We consider two simple potentials , the power-law and exponential for all the different versions of the scalar fields as these are the two most widely used potentials for dark energy in the literature. But one can easily incorporate the other potentials in this package. We also combine the package with the publicly available MCMC sampler ``emcee" \cite{ForemanMackey:2012ig} to do the statistical analysis of different scalar fields with observational data.
Given the promise of thawing scalar field models as possible candidate for the dark energy, there are several investigations related to the thawing model for different types of scalar field. All these works are related to individual scalar field models and there are not many attempts to study the different thawing scalar field model in a combined approach. This is the first such combined approach in python environment.
This paper is structured as follows. In the section II, we describe the autonomous system of equations for different scalar field models and also the method to fix the initial conditions to solve these systems; in section III, we describe different cosmological observable that ScalPy calculates for different scalar field models; in section IV, we describe different data sets that are used to put observational constraints on different models and the results of the data analysis; finally we summarizes our results in the conclusion section. In the Appendix part of the manuscript, we briefly describe how to install and to use ScalPy.
\section{Dynamics of cosmological scalar fields}
In the present investigation, we confine ourselves to flat FRW universe with scale factor $a(t)$ and given by the line element
\begin{equation}
ds^2 = -dt^2 + a^2(t)(dr^2 + r^2d\Omega^2),
\end{equation}
\noindent
where $d\Omega^2 = (d\theta^2 + sin^2(\theta)d\phi^2)$. The scale factor at present is set to be $a_{0} =1$. In the late time evolution of the universe, the dominant contribution to the energy budget of the universe is from the non-relativistic matter (baryons+dark matter) and from the dark energy. In the present paper we are interested in studying various forms of scalar field models as the dark energy component in the universe..
In following subsection we will look at quintessence, tachyon and Galileon fields and see how we make autonomous systems in these frameworks.
\subsection{Quintessence}
We consider a minimally coupled scalar field and Lagrangian for such a field is given by
\begin{equation}
\mathcal{L} = \frac{1}{2}\partial_\mu\phi\partial^\mu\phi - V(\phi),
\end{equation}
\noindent
where $V(\phi)$ is the given potential. One can calculate the energy momentum tensor and by considering perfect fluid, the energy density and pressure of quintessence field is given by
\begin{eqnarray}
\rho_\phi &=& \frac{1}{2}\dot{\phi}^2 + V(\phi),\\
P_\phi &=& \frac{1}{2}\dot{\phi}^2 - V(\phi).
\end{eqnarray}
\noindent
The equation of motion for scalar field obtained by variation of action with respect to field $\phi$ is
\begin{equation}
\ddot{\phi} + 3H\dot{\phi} + V_\phi = 0.
\end{equation}
\noindent
where the subscript $\phi$ denotes the derivative with respect to field $\phi$. The Hubble equation is given by
\begin{equation}
H^2 = \frac{1}{3 M^2_{\rm{pl}}}\rho,
\end{equation}
\noindent
where $\rho = \rho_m + \rho_\phi$ is the total density of matter and scalar field. We define the variables $x$, $y$, and $\lambda$ as \cite{quint}
\begin{align}
x&=\frac{\phi^\prime}{\sqrt{6} M_{\rm{pl}}}\,,\quad y=\frac{\sqrt{V}}{\sqrt{3} H M_{\rm{pl}}},\\
\lambda &= -M_{\rm{pl}} \frac{V_\phi}{V}\,, \quad \Gamma = V\frac{V_{\phi\phi}}{V_{\phi}^2}.
\end{align}
\noindent
Here the prime denote the derivative with respect to the e-folding $N$ (= $\ln a$) i.e. $\phi^\prime \equiv a(d\phi/da)$ and subscript `$\phi$' denote the derivative with respect to field $\phi$. In terms of these variables
\begin{equation}
\Omega_\phi = x^2 + y^2,\\
\gamma \equiv 1+w = \frac{2x^2}{x^2 + y^2},
\end{equation}
\noindent
where $\Omega_\phi$ is the density parameter for scalar field and $w = \frac{P}{\rho}$ is the equation of state. We can construct an autonomous system using variables $x$, $y$ and $\lambda$
\begin{eqnarray}
x^\prime &=& -3x + \lambda\sqrt{\frac{3}{2}}y^2 + \frac{3}{2}x[1 + x^2-y^2]\label{quint1}\\
y^\prime &=& -\lambda\sqrt{\frac{3}{2}}xy + \frac{3}{2}y[1+x^2-y^2] \label{quint2}\\
\lambda^\prime &=& - \sqrt{6} \lambda^2(\Gamma - 1) x. \label{quint3}
\end{eqnarray}
In terms of $\Omega_{\phi}$, $\gamma$ and $\lambda$, the above equations becomes \cite{ss},
\begin{eqnarray}
\gamma^\prime &=& -3\gamma(2-\gamma) + \lambda(2-\gamma)\sqrt{3 \gamma
\Omega_\phi},\label{quint4}\\
\Omega_\phi^\prime &=& 3(1-\gamma)\Omega_\phi(1-\Omega_\phi),\label{quint5}\\
\lambda^\prime &=& - \sqrt{3}\lambda^2(\Gamma-1)\sqrt{\gamma \Omega_\phi}. \label{quint6}
\end{eqnarray}
\subsection{Tachyons}
Cosmological dynamics for tachyonic field can be obtained by the Dirac-Born-Infeld (DBI) type action \cite{tach}
\begin{equation}
S_{tachyon} = -\int d^4x V(\phi) \sqrt{-g} \sqrt{1 - \partial^\mu\phi\partial_\mu\phi}.
\end{equation}
In natural units, the dimension of the tachyon field is $[Mass]^{-1}$. The energy density, pressure and equation of state of the tachyon field is given by
\begin{eqnarray}
\rho_\phi &=& \frac{V(\phi)}{\sqrt{1 - \dot{\phi}^2}},\\
P_\phi &=& -V(\phi) \sqrt{1 - \dot{\phi}^2},\\
w &=& - (1 - \dot{\phi}^2).
\end{eqnarray}
\noindent
The equation of motion for Tachyon field is
\begin{equation}
\ddot{\phi} + 3H\dot{\phi}(1-\dot{\phi}^2) + \frac{V'}{V}(1-\dot{\phi}^2).
\end{equation}
\noindent
Again we define following dimensionless variables
\begin{align}
x &=H\phi' \,,\quad y =\frac{\sqrt{V}}{\sqrt{3}H M_{\rm{pl}}},\\
\lambda &=-M_{\rm{pl}}\frac{V_\phi}{V^{3/2}} \,,\quad \Gamma = V \frac{V_{\phi\phi}}{V_{\phi}^2}.
\end{align}
\noindent
In terms of these variables, equation of state $w_\phi$ and density parameter $\Omega_\phi$ for the tachyon field is
\begin{equation}
\gamma = (1+w_\phi) = x^2 \, , \quad \Omega_\phi = \frac{y^2}{\sqrt{1 - x^2}}.
\end{equation}
\noindent
We construct the autonomous system for tachyon field \cite{Ali:2009mr}
\begin{align}
\gamma' &= -6\gamma(1-\gamma) + 2\sqrt{3\gamma\Omega_\phi}\lambda(1 - \gamma)^{5/4}, \label{tachyon1}\\
\Omega_\phi' &= 3\Omega_\phi(1-\gamma)(1 - \Omega_\phi),\label{tachyon2}\\
\lambda' &= -\sqrt{3\gamma\Omega_\phi}\lambda^2(1 - \gamma)^{1/4}(\Gamma - 3/2),\label{tachyon3}.
\end{align}
\subsection{Galileon}
The large scale modification of gravity which involves an effective scalar field $\pi$ can explain late time acceleration of the Universe. This field $\pi$ is called ``Galileon" and its Lagrangian respects the shift symmetry in the Minkowski background satisfying $\pi \rightarrow \pi + c$ and $\partial_\mu\phi \rightarrow \partial_\mu\pi + b_\mu$ where $c$ and $b_\mu$ are constants \cite{gal}. The action for Galileon field up to third order is \cite{wali}
\begin{equation}
S=\int d^4x\sqrt{-g}\Bigl [\frac{M^2_{\rm{pl}}}{2} R - \frac{1}{2}(\nabla \pi)^2\Bigl(1+\frac{\alpha}{M^3}\Box \pi\Bigr) - V(\pi) \Bigr] + \mathcal{S}_m,
\label{1.1}
\end{equation}
where $M_{\rm{pl}} = \sqrt{\frac{1}{8\pi G}}$ is reduced Planck Mass. $\alpha$ is the dimensionless constant and setting it equal to zero givers the standard quintessence action. $M$ is the constant with mass dimension and it can be fixed to $M_{\rm{pl}}$ by redefining $\alpha$. Again by defining following dimensionless variables,
\begin{align}
x&=\frac{\dot{\pi}}{\sqrt{6}H M_{\rm{pl}}}\,,\quad y=\frac{\sqrt{V}}{\sqrt{3} H M_{\rm{pl}}},\\
\epsilon &=-6\frac{\alpha}{M_{\rm{pl}}^3}H\dot \pi\,, \quad \lambda=-M_{\rm{pl}}\frac{V_\pi}{V} \, , \quad \Gamma= V \frac{V_{\pi\pi}}{V_{\pi}^2},
\end{align}
we construct the autonomous system \cite{wali}
\begin{widetext}
\begin{align}
x'&=\frac{3 x^3 \left(2+5 \epsilon +\epsilon ^2\right)-3 x \left(2-\epsilon +y^2 (2+3 \epsilon )\right)+2 \sqrt{6} y^2 \lambda -\sqrt{6} x^2 y^2 \epsilon \lambda }{4+4 \epsilon +x^2 \epsilon ^2}, \label{galileon1}\\
y'&=-\frac{y \left(12 \left(-1+y^2\right) (1+\epsilon )-6 x^2 \left(2+4 \epsilon +\epsilon ^2\right)+\sqrt{6} x^3 \epsilon ^2 \lambda +2 \sqrt{6} x \left(2+\left(2+y^2\right) \epsilon \right) \lambda \right)}{8+8 \epsilon +2 x^2 \epsilon ^2},\label{galileon2}\\
\epsilon' &=-\frac{\epsilon \left(-3 x \left(-3+y^2\right) (2+\epsilon )+3 x^3 \left(2+3 \epsilon +\epsilon ^2\right)-2 \sqrt{6} y^2 \lambda -\sqrt{6} x^2 y^2 \epsilon \lambda \right)}{x \left(4+4 \epsilon +x^2 \epsilon ^2\right)},\label{galileon3}\\
\lambda' &=\sqrt{6}x\lambda^2(1-\Gamma),\label{galileon4}.
\end{align}
\end{widetext}
\noindent
For $\epsilon=0$ we recover the autonomous system for the standard quintessence \eqref{quint1}-\eqref{quint3}.
\noindent
The density parameter $\Omega_m$ and equation of state for the $\pi$ field is given by:
\begin{align}
\Omega_m &=1-x^2 (1+\epsilon)-y^2, \label{galileon5}\\
\omega_{\pi}&=\frac{-12 y^2 (1+\epsilon )+3 x^2 \left(4+8 \epsilon +\epsilon ^2\right)-2 \sqrt{6} x y^2 \epsilon \lambda }{3 \left(4+4 \epsilon +x^2 \epsilon ^2\right) \left(y^2+x^2 (1+\epsilon )\right)}. \label{galileon6}
\end{align}
\subsection{Solving the dynamical systems}
To solve a cosmological dynamical system, we have to choose a point in time where we set the appropriate initial conditions and then let the system evolve till present day. We give initial conditions at around decoupling ($a \approx 10^{-3}$).
In case of quintessence and tachyons, we solve the autonomous system of equations in terms of $\gamma$, $\Omega_{\phi}$ and $\lambda$ given by equations \eqref{quint4}-\eqref{quint6} and \eqref{tachyon1}-\eqref{tachyon3}for quintessence and tachyon respectively. We have to provide initial conditions for $\gamma_{i}$, $\Omega_{\phi i}$ and $\lambda_{i}$ where ``i'' represents the initial value. As we are considering the thawing class of models, the scalar field is initially nearly frozen due to large Hubble friction and hence we choose $\gamma_{i}$ to be close to zero. Throughout rest of the paper, we fix $\gamma_{i} = 10^{-4}$. $\lambda_{i}$ is the initial slope of the potential and $\lambda_{i} = 0$ gives an exact cosmological constant behavior. So values for $\lambda_{i}$ different from zero, gives the deviation from cosmological constant. In our subsequent calculations, we choose $\lambda_{i}$ to be a parameter of the model. As the contribution of dark energy to be negligible in the early time, $\Omega_{\phi i}$ should be close to zero initially. But it has to be fixed initially in such a way that for a given $\gamma_{i}$ and $\lambda_{i}$, the system evolves to present day with the appropriate value of $\Omega_{\phi 0}$ where ``0'' stands for present day value. We check that $\Omega_{\phi i}$ around $10^{-9}$ gives suitable values for $\Omega_{\phi 0}$. So in our calculations, we choose $\Omega_{\phi i}$ to be the second parameter and varies it between $1 \times 10^{-9}$ to $10 \times 10^{-9}$.
For Galileon field, we solve autonomous systems in terms of variables $x$, $y$, $\epsilon$ and $\lambda$ given by the equations \eqref{galileon1}-\eqref{galileon4} and hence we have to provide four initial conditions for $x_i$, $y_i$, $\epsilon_i$ and $\lambda_i$ respectively. As here also, we consider the thawing behavior only, the Galileon field is initially nearly frozen and hence $x_{i} \approx 0$. We set $x_i = 10^{-7}$ in our calculations. For $\Omega_{\phi i}$ to be the same as in quintessence and tachyon, $\epsilon_{i}$ and $y_{i}$ are now related by equation \eqref{galileon5}. So we vary $\epsilon_{i}$ and $\Omega_{\phi i}$ as two parameters and $y_{i}$ is fixed subsequently by equation \eqref{galileon5}. We also consider $\lambda_{i}$ as our third parameter as it gives the deviation from cosmological constant. So in Galileon models, we have three parameters, $\Omega_{\phi i}, \epsilon_{i}$ and $\lambda_{i}$.
For power law and exponential potential, $\Gamma$ is a constant while for other potentials, $\Gamma$ evolve as a function of $\lambda$ in equations \eqref{quint3},\eqref{tachyon3} and \eqref{galileon4}.
\begin{figure*}[t]
\centering
\subfigure
{
\includegraphics[scale=0.4]{eqn_state_scalar.eps}
}
\\
\subfigure
{
\includegraphics[scale=0.4]{eqn_state_tachyon.eps}
}
\subfigure
{
\includegraphics[scale=0.4]{eqn_state_galileon.eps}
}
\caption{Equation of state $w$ as a function of redshift z for quintessence field (top), tachyon field (bottom left) and Galileon field (bottom right). Solid lines corresponds to exponential potential while dashed, dotted-dashed and dotted lines corresponds to power law potential with $n = 1,2$ and $-1$ respectively.}
\end{figure*}
\section{cosmological Observables}
Following David Hogg \cite{Hogg:1999ad} we define observable quantities such as Hubble distance, luminosity distance, angular diameter distance and lookback time. The Hubble distance is defined as $D_H = \frac{c}{H_0}$ where c is the speed of light and $H_0$ is the Hubble constant. Since we have assumed a flat FLRW metric, the line of sight comoving distance is defined as
\begin{equation}
D_c = \frac{c}{H_0}\int_{0}^{z}\frac{dz'}{h(z')},
\end{equation}
\noindent
where $h(z)=H(z)/H_0$ is normalized Hubble parameter. The angular diameter distance $D_A$ and luminosity distance $D_L$ are related to comoving distance as
\begin{equation}
D_L = (1+z)D_m = (1+z)^2D_A,
\end{equation}
\noindent
where $D_m$ is transverse comoving distance which is equal to $D_c$ for the flat Universe.
\noindent
We also define lookback time $t_L$ to an object as the difference between age of the Universe and the time when the light was emitted from that object:
\begin{equation}
t_L = \frac{1}{H_0}\int_0^{z}\frac{dz'}{(1+z')h(z')}.
\end{equation}
\noindent
The age of the Universe is given by,
\begin{equation}
t = \frac{1}{H_0}\int_0^{\infty} \frac{dz'}{(1+z')h(z')}.
\end{equation}
\noindent
We also define Om diagnostic \cite{Sahni:2008xx} in our package :
\begin{equation}
Om(x) = \frac{h^2(x) - 1}{x^3 -1} ;\quad x = 1+z.
\end{equation}
\noindent
The time delay distance used in gravitational lensing cosmography is also included in the package. It is defined as \cite{Suyu:2012aa}
\begin{equation}
D_{\vartriangle t} = (1 + z_d)\frac{D_d D_s}{D_{ds}}.
\end{equation}
Where $D_d$ is the angular diameter distance to the deflector or lens at redshift $z_d$ and $D_s$ is the angular diameter distance to the source. $D_{ds}$ is the angular diameter distance between source and deflector.
In figure 1 we plotted equation of state, $w$ as a function of redshift for each type of scalar field (quintessence, tachyon and Galileon) with power law potential ($n = 1,2,-1$) and for exponential potential. The initial conditions we choose for quintessence and tachyon fields are ($\Omega_{\phi i},\lambda_i$) $\sim$ ($2.5\times10^{-9}, 0.9$) and for Galileon field we choose ($\Omega_{\phi i}, \epsilon_i,\lambda_i$) $\sim$ ($2.5\times10^{-9}, 2.0, 0.9$). The value of $\gamma_i$ for all three types of field is taken to be $10^{-4}$.
\begin{figure*}[t]
\centering
\subfigure
{
\includegraphics[scale=0.4]{fsigma8_scalar.eps}
}
\\
\subfigure
{
\includegraphics[scale=0.4]{fsigma8_tachyon.eps}
}
\subfigure
{
\includegraphics[scale=0.4]{fsigma8_galileon.eps}
}
\caption{$f\sigma_8$ redshift z for scalar field (top), tachyon field (bottom left) and Galileon field (bottom right). Solid lines corresponds to exponential potential while dashed, dotted-dashed and dotted lines corresponds to power law potential with $n = 1,2$ and $-1$ respectively..}
\end{figure*}
\subsection{Growth of inhomogeneities}
We consider perturbation in matter part only and scalar field is homogeneous. We are interested in structure formation to scale much smaller than the Hubble radius so the Newtonian approximation is valid. The density contrast of matter field $\delta_m = \frac{\overline{\rho}_m - \rho_m}{\overline{\rho}_m}$ follows the equation at sub-horizon approximation
\begin{equation}
\ddot{\delta}_m + 3H\dot{\delta}_m + 4\pi G\rho_m \delta_m = 0.
\end{equation}
Taking Fourier transform of above equation and defining the linear growth function $D$ and the linear growth rate $f$ as
\begin{eqnarray}
\delta_{k}^{lin} (a) &\equiv& D(a)\delta_{k}^{ini},\\
f &=& \frac{d \ln{D}}{d \ln{a}}.
\end{eqnarray}
We calculate the linear matter power spectrum defined as
\begin{equation}
P_{lin}(z,k) = A_0 k^{n_s} T^2(k) D^2_{n}(z).
\end{equation}
\noindent
Here $A_0$ is the normalization constant, $n_{s}$ is spectral index for the primordial density fluctuations generated through inflation, $D_n(z)$ is growth function normalized such as it is equal to unity at $z=0$ i.e. $D_n(z)=\frac{D(z)}{D(0)}$ and $T(k)$ is the transfer function as prescribed by Eisenstein and Hu \cite{eisenhu}
for a mixture of CDM and baryons:
\begin{equation}
T(k) = \left(\frac{\Omega_{b0}}{\Omega_{m0}}\right)T_{b}(k) + \left(\frac{\Omega_{c0}}{\Omega_{m0}}\right)T_{c}(k),
\end{equation}
\noindent
where $\Omega_{c0}$ is density parameter for CDM and $\Omega_{m0} = \Omega_{c0}+\Omega_{b0}$.
The form for $T_{b}(k)$ and $T_{c}(k)$ are given by Eisenstein and Hu \cite{eisenhu}. An important quantity $\sigma_8$ is defined as the fluctuation of mass within the boxes of $8h^{-1}$ Mpc when we move from place to place in present day universe.:
\begin{equation}
\sigma^{2}(a,R) = \int^{\infty}_{0} \Delta^{2}(k,a) W^{2}(k,R) d \ln{k},
\end{equation}
\noindent
where the window function $W(k,R)$ is defined as $W(k,R) = 3\left( \frac{\sin(KR)}{(kR)^3} + \frac{\cos(kR)}{(kr)^2}\right)$ and for $\sigma_{8}$, one puts $ R = 8h^{-1}$ Mpc.
Using definition of $\sigma_8$ and window function, we fix the normalization constant $A_0$ as \cite{Knobel:2012wa}
\begin{equation}
A_0 = 2\pi^2\sigma_8^2\left(\int k^{n_s + 2} T^2(k) W^2(k,R) dk \right)^{-1},
\end{equation}
\noindent
where we take $R = 8h^{-1}$ Mpc. Fig 2 shows the behavior of $f\sigma_8$ as a function of z for quintessence, tachyons and Galileon fields with exponential as well as power law potential. We used the same initial conditions as used for plotting equation of state in figure 1.
\begin{figure*}[t]
\centering
\subfigure
{
\includegraphics[scale=0.4]{contour_om_w_scalar_linear.eps}
}
\\
\subfigure
{
\includegraphics[scale=0.4]{contour_om_w_tachyon_linear.eps}
}
\subfigure
{
\includegraphics[scale=0.4]{contour_om_w_galileon_linear.eps}
}
\caption{1$\sigma$, 2$\sigma$ and 3$\sigma$ contours obtained for $JLA+BAO+Shift(from CMB)$ for quintessence field (top), tachyon (bottom left) and Galileon field (bottom right) with linear potential.}
\end{figure*}
\section{Data Analysis}
We used our ScalPy package and MCMC hammer `emcee' \cite{ForemanMackey:2012ig} to constrained model parameters of quintessence, tachyon and Galileon fields as well as $w$CDM, $w_0w_a$CDM and $GCG$ models(See Appendix). We used following data sets for our analysis:
\begin{itemize}
\item 31 binned distance modules fitted to JLA sample given by by M. Betoule et al. \cite{Betoule:2014frx}
\item Combined BAO/CMB constraints on the angular scales of the BAO oscillations in the matter power spectrum measured by SDSS survey, 6dF Galaxy survey and the Wiggle-z survey. We used covariance matrix for this provided by Giostri et al \cite{Giostri:2012ek}.
\item We also used measurement of shift parameter of CMB as given in Shafer et al \cite{Shafer:2013pxa}.
\item Measurements for $f\sigma_{8}$ by various Galaxy surveys like 2dF, SDSS, 6dF, BOSS and Wiggle-Z. A compilation of different measurements for $f\sigma_{8}$ has been provided by Basilakos et al.\cite{Basilakos:2013nfa}
\end{itemize}
The results for data analysis for quintessence, tachyon field and Galileon field with linear potential are shown in figure (3). We used $h=0.7$ in our analysis. We show the 1$\sigma$, 2$\sigma$ and 3$\sigma$ contours in $\Omega_{\phi}-w$ plane. The $\Lambda$CDM behavior ($w = -1$) is allowed for all these types of scalar fields within 1$\sigma$ region with considerable range of $\Omega_{m0}$ values. One can also see that the constraints on present day equation of state $w_0$ and density parameter for matter $\Omega_{m0}$ are same for all three type of scalar fields with linear potential. This result also holds for other power law potentials.
In figure (4) and (5) we show the constraints on model parameters for $w_0w_a$CDM and $w$CDM models respectively. The concordance $\Lambda$CDM model is within $1\sigma$ error bar when we combine all the four data sets used. The constraints on the model parameters of GCG model is shown in figure (6). The parameter $A_s$ is related to present day equation of state $w_0$ as $w_0 = -A_s$. We see that $w_0 = -1$ is again allowed within $1\sigma$ region for GCG as well.
\begin{figure}
\begin{center}
\begin{tabular}{cc}
& \\
{\includegraphics[width=2.6in,height=2.4in,angle=0]{contour-om-w0.eps}}&
{\includegraphics[width=2.6in,height=2.4in,angle=0]{contour-w0-wa.eps}}
\\
\end{tabular}
\caption{1$\sigma$, 2$\sigma$ and 3$\sigma$ contours obtained for $JLA+BAO+CMB~Shift$ (dashed) and $JLA+BAO+CMB~Shift+f\sigma_8$ (solid) on model parameters for $w_0w_aCDM$ model.}
\end{center}
\end{figure}
\section{Conclusion}
To summarize, we present a python package ScalPy to study the late time cosmology with different kind of scalar field models. To begin with, we consider only the minimally coupled scalar field and a flat FRW universe. We also neglect the radiation component as it will not affect the results in the late time. But one can trivially incorporate radiation component in ScalPy. As thawing models of scalar fields are more consistent with different observational data, we confine ourselves only to the thawing class of fields where the scalar field is initially frozen due to large Hubble friction and starts very close to $w=-1$. ScalPy solves the autonomous system of equations for different kind of scalar field models with power-law and exponential potentials. It calculates various observables related to background expansion as well as to the growth of structures in universe. In this paper, we consider only the linear regime in the sub-horizon scales where effect of dark energy perturbation is negligible. Finally we integrate it with MCMC sampler ``emcee" to constrain various scalar field models with presently available data.
To conclude, we present a python package to study various scalar field dark energy models. This is probably the first package exclusively for the scalar field case. At present, we confine only to the canonical scalar fields and flat FRW models. But in near future, we shall incorporate various other scalar field models like coupled quintessence, scalar tensor models as well as non-flat FRW models. We shall also include the observables related to super-horizon scales where dark energy perturbation can play an important role.
\begin{figure}
{\includegraphics[scale=0.4]{contour_wcdm-om-w0.eps}}
\caption{1$\sigma$, 2$\sigma$ and 3$\sigma$ contours obtained for $JLA+BAO$(dotted),$JLA+BAO+CMB~Shift$ (dashed) and $JLA+BAO+CMB~Shift+f\sigma_8$ (solid) on model parameters for $w$CDM model.}
\end{figure}
\begin{figure}
\begin{center}
\begin{tabular}{cc}
& \\
{\includegraphics[width=2.6in,height=2.4in,angle=0]{gcg_As_alpha.eps}}&
{\includegraphics[width=2.6in,height=2.4in,angle=0]{gcg_om_As.eps}}
\\
\end{tabular}
\caption{1$\sigma$, 2$\sigma$ and 3$\sigma$ contours obtained for $JLA+BAO+CMB~Shift$ (solid) and $JLA+BAO+CMB~Shift+f\sigma_8$ (dashed) on model parameters for GCG model. Present day equation of state $w_0$ is equal to $-A_s$ in GCG model.}
\end{center}
\end{figure}
\section{Acknowledgements}
AJ thank Centre for Theoretical Physics, Jamia Millia Islamia for kind hospitality where this work was initiated. AJ also acknowledges Indian Academy of Sciences for funding through Summer Research Fellowship Program. SK is funded by University Grants Commission, Govt. of India through SRF scheme. AJ and SK thank Md Wali Hossain for useful discussions.
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Now ISIS jihadis use BOULDERS to crush a prisoner to death in shocking new propaganda video filmed in Yemen
ISIS executed a prisoner by crushing him to death with a large rock
Two other prisoners, accused of being in the Yemeni army, were also killed
A Dutch jihadi is also shown carrying out a suicide bomb attack in Aden
WARNING: GRAPHIC CONTENT
By Tom Wyke for MailOnline
ISIS have released a shocking new video showing a prisoner being crushed to death by a large boulder in Yemen.
In the appalling propaganda video, several masked ISIS fighters dressed in matching military fatigues and tactical vests are shown executing three prisoners in cold blood.
Titled 'Crush your enemies,' the footage shows each prisoner, dressed in blue jumpsuits, being murdered using different methods.
Scroll down for video:
In the appalling propaganda video, several masked ISIS fighters dressed in matching military fatigues and tactical vests are shown executing three prisoners in cold blood
ISIS have released a shocking new video showing a prisoner being crushed to death by a large rock in Yemen
The video also features archived video of the Yemeni army before close up footage of a line of six ISIS fighters standing in a mountainous part of the country.
The prisoners are accused of being members of the Yemeni government army fighting against the jihadi group.
The first victim is beheaded while the second prisoner is tied a chair and gunned down. Graphic closeup footage of their bodies is also shown in the sickening video.
Were EgyptAir passengers alive for three minutes as smoke... Did Paris attackers also plan EgyptAir disaster? Jihadis...
A Dutch student, known only as Mazen, is also shown carrying out a suicide bomb mission near the presidential palace in Yemen.
Calling himself Abu Hanifa al-Holandi, the student is understood to have told his family in Holland that he was studying Arabic in Yemen.
The prisoners are accused of being members of the Yemeni government army fighting against the jihadi group
All of the Yemeni prisoners appears to have been forced to wear matching blue uniforms
One of the prisoners appeals for mercy before he is horrifically gunned down in the Yemeni desert
Unaware of his decision to secretly join ISIS, his distraught father described his shock upon seeing his son's death photo.
'He liked playing football and had friends. He's a good boy, everyone knows that. When it happened, his friends all came here. They didn't believe it either,' Mazen's father said.
There have also been reports that a notorious ISIS executor, nickname the Bulldozer due to his colossal weight, appears in the video.
A chunky fighter is featured standing in the middle of a group of ISIS fighters but appears to be too slim to be the Bulldozer.
A Dutch student, known only as Mazen, is also shown carrying out a suicide bomb mission near the presidential palace in Yemen
There have also been reports that a notorious ISIS executor, nickname the Bulldozer due to his colossal weight, appears in the video
Parts of the video are too graphic to describe, particularly the moment one of the prisoners is beaten to death with a huge rock
ISIS jihadis use BOULDERS to crush a prisoner to death in Yemen video
The comments below have been moderated in advance.
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Код АТХ-C () «Препараты для лечения заболеваний сердечно-сосудистой системы» — раздел система буквенно-цифровых кодов Анатомо-терапевтическо-химической классификации, разработанных Всемирной организацией здравоохранения для классификации лекарств и других медицинских продуктов.
Коды для применения в ветеринарии (ATCvet коды) могут быть созданы путём добавления буквы Q в передней части человеческого Код ATC: QC.
Из-за различных национальных особенностей в классификацию АТС могут включаться дополнительные коды, которые отсутствуют в этом списке, который составлен Всемирной организацией здравоохранения.
АТХ код C01 Препараты для лечения заболеваний сердца
АТХ код C02 Антигипертензивные препараты
АТХ код C03 Диуретики
АТХ код C04 Периферические вазодилататоры
АТХ код C05 Ангиопротекторы
АТХ код C07 Бета-адреноблокаторы
АТХ код C08 Блокаторы кальциевых каналов
АТХ код C09 Препараты, влияющие на ренин-ангиотензиновую систему
АТХ код C10 Гиполипидемические препараты
Примечания
Коды АТХ
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ROMANS
MACARTHUR BIBLE STUDIES
© 2007, John F. MacArthur, Jr.
All rights reserved. No portion of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, scanning, or other—except for brief quotations in critical reviews or articles, without the prior written permission of the publisher.
John MacArthur
"Unleashing God's Truth, One Verse at at a Time®"
"Unleashing God's Truth, One Verse at a Time" is a trademark of Grace to You. All rights reserved.
Published in Nashville, Tennessee, by Nelson Books, an imprint of Thomas Nelson. Nelson Books and Thomas Nelson are registered trademarks of HarperCollins Christian Publishing, Inc.
Nelson Books titles may be purchased in bulk for education, business, fundraising, or sales promotional use. For information, please email SpecialMarkets@ThomasNelson.com
Published in association with the literary agency of Wolgemuth & Associates, Inc.
Produced with the assistance of the Livingstone Corporation. Project staff include Jake Barton, Betsy Todt Schmitt, and Andy Culbertson.
Project editors: Mary Horner Collins, Amber Rae, and Len Woods
Scripture quotations marked NKJV are taken from the The New King James Version®.
© ww1982 by Thomas Nelson, Inc. Used by permission. All rights reserved.
"Keys to the Text" material taken from the following sources:
_Galatians_. MacArthur New Testament Commentary Series. © 1987, 1996 by John MacArthur.
Published by Moody Press, Chicago, Illinois. Used by permission.
_The Gospel According to Jesus._ © 1997, 1988 by John MacArthur. (Electronic ed.). Published by Zondervan, Grand Rapids, Michigan. Used by permission.
_The MacArthur Study Bible_ (electronic ed.), John MacArthur, General Editor. © 1997 by Word Publishing. All rights reserved. Used by permission.
_Nelson's New Illustrated Bible Dictionary, Rev. ed._ R. F. Youngblood, F. F. Bruce, R. K. Harrison, editors. © 1995 by Thomas Nelson Publishers. Used by permission.
_Romans_. MacArthur New Testament Commentary Series. © 1994, 1996 by John MacArthur.
Published by Moody Press, Chicago, Illinois. Used by permission.
Cover Art by Holly Sharp Design
Interior Design and Composition by Joel Bartlett, Livingstone Corporation
ISBN 978-0-7180-3506-8
ISBN 978-0-7180-3525-9 (eBook)
15 16 17 18 19 RRD 6 5 4 3 2 1
CONTENTS
_Introduction to Romans_
1 The Good News
_Romans 1:1–17_
2 The Bad News
_Romans 1:18–3:20_
3 By Faith Alone
_Romans 3:21–4:25_
4 Grace through One Man
_Romans 5:1–21_
5 Dead and Alive!
_Romans 6:1–23_
6 Delivered from the Law
_Romans 7:1–25_
7 In the Spirit
_Romans 8:1–39_
8 Israel and God's Eternal Plan
_Romans 9:1–11:36_
9 Supernatural Living
_Romans 12:1–21_
10 Living in the World
_Romans 13:1–14_
11 The Strong and the Weak
_Romans 14:1–15:13_
12 Ministering Together
_Romans 15:14–16:27_
INTRODUCTION TO ROMANS
This epistle's name comes from its original recipients: the members of the church in Rome, the capital of the Roman Empire.
AUTHOR AND DATE
No one disputes that the apostle Paul wrote Romans. Like his namesake, Israel's first king ( _Saul_ was Paul's Hebrew name; _Paul_ his Greek name), Paul was from the tribe of Benjamin (Phil. 3:5). He was also a Roman citizen (Acts 16:37; 22:25). Paul was born about the time of Christ's birth, in Tarsus, an important city (Acts 9:11; 21:39) in the Roman province of Cilicia located in Asia Minor (modern Turkey). He spent much of his early life in Jerusalem as a student of the celebrated rabbi Gamaliel (Acts 22:3). Like his father before him, Paul was a Pharisee (Acts 23:6), a member of the strictest Jewish sect (Phil. 3:5).
Miraculously converted while on his way to Damascus (ca. AD 33–34) to arrest Christians in that city, Paul immediately began proclaiming the gospel message (Acts 9:20). After narrowly escaping from Damascus with his life (Acts 9:23–25; 2 Cor. 11:32–33), Paul spent three years in Nabatean Arabia, south and east of the Dead Sea (Gal. 1:17–18). During that time, he received much of his doctrine as direct revelation from the Lord (Gal. 1:11–12).
More than any other individual, Paul was responsible for the spread of Christianity throughout the Roman Empire. He made three missionary journeys through much of the Mediterranean world, tirelessly preaching the gospel that he had once sought to destroy (Acts 26:9). After Paul returned to Jerusalem bearing an offering for the needy in the church there, he was falsely accused by some Jews (Acts 21:27–29), savagely beaten by an angry mob (Acts 21:30–31), and arrested by the Romans. Although two Roman governors, Felix and Festus, as well as Herod Agrippa, did not find him guilty of any crime, pressure from the Jewish leaders kept Paul in Roman custody. After two years, the apostle exercised his right as a Roman citizen and appealed his case to Caesar. Through a harrowing trip (Acts 27–28), including a violent, two-week storm at sea that culminated in a shipwreck, Paul reached Rome. Eventually Paul was released for a brief period of ministry, but he was later arrested again. Paul suffered martyrdom at Rome in ca. AD 65–67 (2 Tim. 4:6).
Though physically unimpressive (2 Cor. 10:10; Gal. 4:14), Paul possessed an inner strength granted him through the Holy Spirit's power (Phil. 4:13). The grace of God proved sufficient to provide for his every need (2 Cor. 12:9–10), enabling this noble servant of Christ to successfully finish his spiritual race (2 Tim. 4:7).
Paul wrote Romans from Corinth, as indicated by the references to Phoebe (Rom. 16:1, Cenchrea was Corinth's port), Gaius (Rom. 16:23), and Erastus (Rom. 16:23)—all of whom were associated with Corinth. The apostle wrote the letter toward the close of his third missionary journey (most likely in AD 56), as he prepared to leave for Palestine with an offering for the poor believers in the Jerusalem church (Rom. 15:25). Phoebe was given the great responsibility of delivering this letter to the Roman believers (16:1–2).
BACKGROUND AND SETTING
Rome was the capital and most important city of the Roman Empire. It was founded in 753 BC, but is not mentioned in Scripture until New Testament times. Rome is located along the banks of the Tiber River, about fifteen miles from the Mediterranean Sea. Until an artificial harbor was built at nearby Ostia, Rome's main harbor was Puteoli, some hundred and fifty miles awa _y._ In Paul's day, the city had a population of over one million people, many of whom were slaves. Rome boasted magnificent buildings, such as the Emperor's palace, the Circus Maximus, and the Forum, but its beauty was marred by the slums in which so many lived. According to tradition, Paul was martyred outside Rome on the Ostian Way during Nero's reign (AD 54–68).
Some of those converted on the Day of Pentecost probably founded the church at Rome (Acts 2:10). Paul longed to visit the Roman church, but had been prevented from doing so (1:13). In God's providence, Paul's inability to visit Rome gave the world this inspired masterpiece of gospel doctrine.
Paul's primary purpose in writing Romans was to teach the great truths of the gospel of grace to believers who had never received apostolic instruction. The letter also introduced him to a church where he was personally unknown but hoped to visit soon for several important reasons: to edify the believers (1:11), to preach the gospel (1:15), and to get to know the Roman Christians so they could encourage him (1:12; 15:32), better pray for him (15:30), and help him with his planned ministry in Spain (15:28).
Unlike Paul's other epistles (for example, 1 Corinthians, 2 Corinthians, and Galatians), his purpose for writing Romans was not to correct aberrant theology or rebuke ungodly living. The Roman church was doctrinally sound, but, like all churches, it was in need of the rich doctrinal and practical instruction this letter provides.
HISTORICAL AND THEOLOGICAL THEMES
Since Romans is primarily a work of doctrine, it contains little historical material. Paul does use such familiar Old Testament figures as Abraham (chapter 4), David (4:6–8), Adam (5:12–21), Sarah (9:9), Rebekah (9:10), Jacob and Esau (9:10–13), and Pharaoh (9:17) as illustrations. He also recounts some of Israel's history (chapters 9–). Chapter 16 provides insightful glimpses into the nature and character of the first-century church and its members.
The overarching theme of Romans is the righteousness that comes from God: the glorious truth that God justifies guilty, condemned sinners by grace alone through faith in Christ alone. Chapters 1– present the theological truths of that doctrine, while chapters 12–16 detail its practical outworking in the lives of individual believers and the life of the whole church. Some specific theological topics include principles of spiritual leadership (1:8–15); God's wrath against sinful humankind (1:18–32); principles of divine judgment (2:1–16); the universality of sin (3:9–20); an exposition and defense of justification by faith alone (3:21–4:25); the security of salvation (5:1–11); the transference of Adam's sin (5:12–21); sanctification (chapters 6–); sovereign election (chapter 9); God's plan for Israel (chapter 11); spiritual gifts and practical godliness (chapter 12); the believer's responsibility to human government (chapter 13); and principles of Christian liberty (14:1–15:12).
INTERPRETIVE CHALLENGES
As the preeminent doctrinal work in the New Testament, Romans naturally contains a number of difficult passages. Paul's discussion of the perpetuation of Adam's sin (5:12–21) is one of the deepest, most profound theological passages in all of Scripture. The nature of humanity's union with Adam and how Adam's sin was transferred to the human race has always been the subject of intense debate. Bible students also disagree on whether 7:7–25 describes Paul's experience as a believer or unbeliever or is a literary device and not intended to be autobiographical at all. The closely related doctrines of election (8:28–30) and the sovereignty of God (9:6–29) have confused many believers. Others question whether chapters 9– teach that God has a future plan for the nation of Israel. Some have ignored Paul's teaching on the believer's obedience to human government (13:1–7) in the name of Christian activism, while others have used it to defend slavish obedience to totalitarian regimes. Some of these interpretive challenges are addressed in the lessons that follow.
NOTES
**1**
THE GOOD NEWS
_Romans 1:1–17_
DRAWING NEAR
When and where did you first hear the gospel—the good news that Jesus loves you and died for your sins?
What is so "good" about this good news of the gospel?
As you begin this study, what do want to learn about the book of Romans? How do you want to grow in your faith?
THE CONTEXT
Newspapers and television news shows contain constant reminders that most news is bad and seems to be getting worse. What happens on a national and worldwide scale, however, is simply the magnification of what is occurring on an individual level. As personal problems, animosities, and fears increase, so do their counterparts in society at large. A terrifying power grips human beings at the very core of their being. Left unchecked, it pushes them to self-destruction in one form or another. That power is _sin_ , and that is always bad news. The tidbits of good news are often merely brief respites from the bad. And sometimes what appears to be good merely masks an evil. One cynic commented that peace treaties merely provide time for both sides to reload.
The essence of Paul's letter to the Romans, however, is that there is good news that is truly good! The apostle was, in fact, "a minister of Jesus Christ to the Gentiles, ministering the gospel of God" (Rom. 15:16). He brought the good news that, in Christ, sin can be forgiven, selfishness can be overcome, guilt can be removed, anxiety can be alleviated, and people can, indeed, have hope and eternal glory.
The entire thrust of the book of Romans is distilled in the first seven verses. The apostle apparently was so overjoyed by his message of good news that he could not wait to introduce his readers to the gist of what he had to say. He burst into it immediately.
KEYS TO THE TEXT
_Apostle:_ "One who is sent with a commission." An apostle chosen and trained by Jesus Christ to proclaim His truth during the formative years of the church. In its primary usage, the term applied to the original twelve disciples who were chosen at the beginning of Jesus' earthly ministry, and were set aside to lay the foundation of the early church. They were also given power to perform healings and to cast out demons as verifying signs of their divine authority. Because Paul was not among the original twelve, he needed to defend his apostleship. One of the qualifications was witnessing the risen Christ (Acts 1:22). Paul explained to the Corinthian church that between His resurrection and ascension Jesus "was seen by Cephas [Peter], then by the twelve. . . . After that He was seen by James, then by all the apostles. Then last of all He was seen by me also" (1 Cor. 15: 5–8 NKJV). Paul witnessed the resurrected Christ in a unique way as he was traveling to Damascus to arrest Christians there (Acts 9). Further personal appearances of the Lord to Paul are recorded in Acts 18:9; 22:17–21; 23:11; and 2 Corinthians 12:1–4.
In a wider sense, the term _apostle_ is also used of men like Barnabas, Silas, and Timothy (Rom. 16:7). Such men are more specifically called messengers ( _apostoloi_ ) of the churches, whereas the Twelve and Paul were "apostles of Jesus Christ." Neither group was perpetuated. Except for Judas (who was replaced by Matthias), there is no record of an apostle in either the primary or secondary group being replaced after he died.
UNLEASHING THE TEXT
Read 1:1–17, noting the key words and definitions next to the passage.
**Romans 1:1–17 (NKJV)**
**1** _Paul, a bondservant of Jesus Christ, called to be an apostle, separated to the gospel of God_
**_bondservant_** (v. 1)—the Greek word for servant or slave, but given a Hebrew sense here by Paul to imply willing service for a beloved, respected master
**_separated to_** (v. 1)—Paul had been set apart (that is, specially selected) by God for his ministry to the Gentiles.
**_gospel of God_** (v. 1)—The word _gospel_ means "good news."
**2** _which He promised before through His prophets in the Holy Scriptures,_
**3** _concerning His Son Jesus Christ our Lord, who was born of the seed of David according to the flesh,_
**4** _and declared to be the Son of God with power according to the Spirit of holiness, by the resurrection from the dead._
**_declared_** (v. 4)—Literally, "to distinguish, or mark off," this is the Greek word from which the English word "horizon" comes; as the horizon marks clearly the boundary between earth and sky, the resurrection marks Christ as the Son of God come in the flesh.
**5** _Through Him we have received grace and apostleship for obedience to the faith among all nations for His name,_
**_obedience to the faith_** (v. 5)—True saving faith always produces obedience and submission to the Lordship of Christ.
**6** _among whom you also are the called of Jesus Christ;_
**7** _To all who are in Rome, beloved of God, called to be saints: Grace to you and peace from God our Father and the Lord Jesus Christ._
**8** _First, I thank my God through Jesus Christ for you all, that your faith is spoken of throughout the whole world._
**9** _For God is my witness, whom I serve with my spirit in the gospel of His Son, that without ceasing I make mention of you always in my prayers,_
**_serve with my spirit_** (v. 9)—The word translated "serve" can also be translated "worship."
**10** _making request if, by some means, now at last I may find a way in the will of God to come to you._
**11** _For I long to see you, that I may impart to you some spiritual gift, so that you may be established—_
**_spiritual gift_** (v. 11)—The Greek word for "gift" is _charisma,_ meaning a "gift of grace," a divine enablement.
**12** _that is, that I may be encouraged together with you by the mutual faith both of you and me._
**13** _Now I do not want you to be unaware, brethren, that I often planned to come to you (but was hindered until now), that I might have some fruit among you also, just as among the other Gentiles._
**14** _I am a debtor both to Greeks and to barbarians, both to wise and to unwise._
**_debtor_** (v. 14)—under obligation to fulfill his ministry because of God's calling and the Gentiles' great need
**15** _So, as much as is in me, I am ready to preach the gospel to you who are in Rome also._
**16** _For I am not ashamed of the gospel of Christ, for it is the power of God to salvation for everyone who believes, for the Jew first and also for the Greek._
**_salvation_** (v. 16)—deliverance or rescue, in this case from lostness—that is, separation from God
**_believes_** (v. 16)—trusts, relies on, or has faith in
**17** _For in it the righteousness of God is revealed from faith to faith; as it is written, "The just shall live by faith."_
1) What does this passage reveal about the promise of the good news (v. 2) and the Person of the good news (vv. 3–4)?
2) Verses 8–15 provide interesting insights into Paul's character and motives, as well as the kind of behavior that should mark all true spiritual leaders. What admirable qualities are described in these verses?
_(Verses to consider: 1 Thess. 2:1–3:13)_
3) What reasons does Paul give for not being ashamed of the gospel?
GOING DEEPER
Read about Paul's own experience with the gospel and his commissioning by Christ to go to the Gentiles. This testimony is from Acts 26.
**Acts 26:1–18 (NKJV)**
**1** _Then Agrippa said to Paul, "You are permitted to speak for yourself." So Paul stretched out his hand and answered for himself:_
**2** _"I think myself happy, King Agrippa, because today I shall answer for myself before you concerning all the things of which I am accused by the Jews,_
**3** _especially because you are expert in all customs and questions which have to do with the Jews. Therefore I beg you to hear me patiently._
**4** _"My manner of life from my youth, which was spent from the beginning among my own nation at Jerusalem, all the Jews know._
**5** _They knew me from the first, if they were willing to testify, that according to the strictest sect of our religion I lived a Pharisee._
**6** _And now I stand and am judged for the hope of the promise made by God to our fathers._
**7** _To this promise our twelve tribes, earnestly serving God night and day, hope to attain. For this hope's sake, King Agrippa, I am accused by the Jews._
**8** _Why should it be thought incredible by you that God raises the dead?_
**9** _"Indeed, I myself thought I must do many things contrary to the name of Jesus of Nazareth._
**10** _This I also did in Jerusalem, and many of the saints I shut up in prison, having received authority from the chief priests; and when they were put to death, I cast my vote against them._
**11** _And I punished them often in every synagogue and compelled them to blaspheme; and being exceedingly enraged against them, I persecuted them even to foreign cities._
**12** _"While thus occupied, as I journeyed to Damascus with authority and commission from the chief priests,_
**13** _at midday, O king, along the road I saw a light from heaven, brighter than the sun, shining around me and those who journeyed with me._
**14** _And when we all had fallen to the ground, I heard a voice speaking to me and saying in the Hebrew language, 'Saul, Saul, why are you persecuting Me? It is hard for you to kick against the goads.'_
**15** _So I said, 'Who are You, Lord?' And He said, 'I am Jesus, whom you are persecuting._
**16** _But rise and stand on your feet; for I have appeared to you for this purpose, to make you a minister and a witness both of the things which you have seen and of the things which I will yet reveal to you._
**17** _I will deliver you from the Jewish people, as well as from the Gentiles, to whom I now send you,_
**18** _to open their eyes, in order to turn them from darkness to light, and from the power of Satan to God, that they may receive forgiveness of sins and an inheritance among those who are sanctified by faith in Me.'_
EXPLORING THE MEANING
4) How did Paul's encounter with the risen Christ alter his life and purpose?
5) Read Philippians 3:1–7. What about Paul's life before Christ would have caused him to see the message of Christ as "good news"?
6) What was behind Paul's eagerness to travel widely and minister to others?
TRUTH FOR TODAY
Some people object to terms such as _salvation_ and _being saved_ , claiming that the ideas they convey are out of date and meaningless to contemporary men and women. But salvation is God's term, and there is no better one to describe what He offers fallen humankind through the sacrifice of His Son. Through Christ and Christ alone, people can be saved from sin, from Satan, from judgment, from wrath, and from spiritual death.
REFLECTING ON THE TEXT
7) The dying words of one ancient saint were, "Grace is the only thing that can make us like God. I might be dragged through heaven, earth, and hell and I would still be the same sinful, polluted wretch unless God Himself should cleanse me by His grace." How would you answer someone who asked: "I keep hearing about 'the grace of God.' What does that mean, and why is it such a good thing?"
8) Paul was bowled over, quite literally, by the love of God, and he never seemed to get over God's amazing grace. How can lukewarm Christians recapture a sense that the gospel is good news—the very best news ever announced?
9) Who in your life needs to hear and embrace God's good news of salvation by grace through faith in Christ? Take some time to pray for them right now.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
**2**
THE BAD NEWS
_Romans 1:18–3:20_
DRAWING NEAR
How would you respond to a sincere, concerned friend who observed: "We don't need to try to scare people into heaven with all this talk of hell, fire, and brimstone. Christians should be more positive and tolerant—emphasizing all the blessings of the Christian life, not threatening people with damnation. It just gives us—and God—a bad name!"
THE CONTEXT
After stating the thesis of his epistle—a righteous God is able to make sinners righteous through faith (1:16–17)—Paul expounds on the wretchedness of the human heart, and the divine wrath that this rebelliousness elicits.
For Paul, knowledge of eternal condemnation was one motivation he offered for coming to belief. He was determined that they understand that God is holy and just, and that we are all sinners under God's wrath. This approach makes both logical and theological sense. We cannot appreciate the wonder of God's grace and love until we truly understand God's righteous anger against sin. We cannot appreciate God's forgiveness until we appreciate the eternal consequences of sin.
Paul says that everyone—Gentiles and Jews, indeed all of humankind—stands guilty before a holy God. Human nature is corrupt. Human motives are impure. By the time Paul is finished with his divine indictment, every mouth has been shut (3:19–20). We are without excuse. We are incapable of saving ourselves. This "bad" news is a necessary part of the good news, called the gospel.
KEYS TO THE TEXT
_Human Depravity:_ The basic meaning of the Greek word, _adokimos,_ "depraved," ("debased" in NKJV) is that of "not standing the test." The term was commonly used of metals that were rejected by refiners because of impurities. The impure metals were discarded, and _adokimos_ therefore came to include the ideas of worthlessness and uselessness. In relation to God, the rejecting mind becomes a rejected mind and thereby becomes spiritually depraved, worthless, and useless. Because fallen humanity did not see fit to acknowledge God any longer, God gave them over, in this case here in Romans, to a depraved mind. The God-less mind is a depraved mind, whose predetermined and inevitable disposition is to do those things that are not proper. The mind that finds God worthless becomes worthless itself. It is debauched, deceived, and deserving only of God's divine wrath. Although God-less people think they are wise, they are supremely foolish (Rom. 1:22).
_Divine Revelation:_ God testifies through Paul that all people have evidence of God, and what their physical senses can perceive of Him, their inner senses can understand to some extent. All men know something and understand something of the reality and the truth of God. They are responsible for a proper response to that revelation. Any wrong response is "inexcusable." God has made Himself known to all people everywhere in the marvels of nature and in the human conscience, which is able to distinguish right from wrong. Because this knowledge is universal and continuous, by it God has displayed His glory to everyone.
UNLEASHING THE TEXT
Read 1:18–3:20, noting the key words and definitions next to the passage.
**Romans 1:18–3:20 (NKJV)**
**18** _For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness,_
**_wrath of God_** (v. 18)—not a capricious, impulsive, arbitrary outburst of anger, but the settled determined response of a holy God against sin
**19** _because what may be known of God is manifest in them, for God has shown it to them._
**_manifest in them_** (v. 19)—God's sovereignly implanted evidence of His own existence in the heart of every person
**20** _For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse,_
**21** _because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened._
**_although they knew God_** (v. 21)—Every person is conscious of God's existence, power, and divine nature via general revelation.
**_glorify_** (v. 21)—honor; We were created for no other reason than to exalt God, the failure or refusal to do so is the ultimate affront to our Creator.
**22** _Professing to be wise, they became fools,_
**23** _and changed the glory of the incorruptible God into_ _an image made like corruptible man—and birds and four-footed animals and creeping things._
**_changed the glory . . . into an image_** (v. 23)—the worship of idols
**24** _Therefore God also gave them up to uncleanness, in the lusts of their hearts, to dishonor their bodies among themselves,_
**_gave them up_** (vv. 24, 26) **_gave them over_** (v. 28)—a Greek judicial term meaning to lord over a prisoner to his sentence; it conveys the sense of abandonment
**25** _who exchanged the truth of God for the lie, and worshiped and served the creature rather than the Creator, who is blessed forever. Amen._
**_the lie_** (v. 25)—the denying of God's existence
**26** _For this reason God gave them up to vile passions. For even their women exchanged the natural use for what is against nature._
**_vile passions_** (v. 26)—disgrace-ful or degrading perversions (for example, in this context, homosexuality)
**27** _Likewise also the men, leaving the natural use of the woman, burned in their lust for one another, men with men committing what is shameful, and receiving in themselves the penalty of their error which was due._
**28** _And even as they did not like to retain God in their knowledge, God gave them over to a debased mind, to do those things which are not fitting;_
**29** _being filled with all unrighteousness, sexual immorality, wickedness, covetousness, maliciousness; full of envy, murder, strife, deceit, evil-mindedness; they are whisperers,_
**30** _backbiters, haters of God, violent, proud, boasters, inventors of evil things, disobedient to parents,_
**31** _undiscerning, untrustworthy, unloving, unforgiving, unmerciful;_
**32** _who, knowing the righteous judgment of God, that those who practice such things are deserving of death, not only do the same but also approve of those who practice them._
**2:1** _Therefore you are inexcusable, O man, whoever you are who judge, for in whatever you judge another you condemn yourself; for you who judge practice the same things._
**2** _But we know that the judgment of God is according to truth against those who practice such things._
**3** _And do you think this, O man, you who judge those practicing such things, and doing the same, that you will escape the judgment of God?_
**4** _Or do you despise the riches of His goodness, forbearance, and longsuffering, not knowing that the goodness of God leads you to repentance?_
**_despise_** (2:4)—to think down on, to treat with contempt
**_repentance_** (v. 4)—the act of turning from sin to Christ for forgiveness
**5** _But in accordance with your hardness and your impenitent heart you are treasuring up for yourself wrath in the day of wrath and revelation of the righteous judgment of God,_
**_hardness_** (v. 5)—the Greek word from which we get "sclerosis," that is, a hardening of one's heart
**6** _who "will render to each one according to his deeds":_
**7** _eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality;_
**_eternal life_** (v. 7)—not just quantity but an endless quality of existence
**8** _but to those who are self-seeking and do not obey the truth, but obey unrighteousness—indignation and wrath,_
**9** _tribulation and anguish, on every soul of man who does evil, of the Jew first and also of the Greek;_
**10** _but glory, honor, and peace to everyone who works what is good, to the Jew first and also to the Greek._
**11** _For there is no partiality with God._
**_partiality_** (v. 11)—literally, to "receive a face," that is, to give consideration to someone simply because of position, wealth, appearance, and so forth
**12** _For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law_
**13** _(for not the hearers of the law are just in the sight of God, but the doers of the law will be justified;_
**14** _for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves,_
**_by nature_** (v. 14) **_. . . conscience_** (v. 15)—our God-given instinctive or innate sense of what is right and wrong
**15** _who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves their thoughts accusing or else excusing them)_
**16** _in the day when God will judge the secrets of men by Jesus Christ, according to my gospel._
**17** _Indeed you are called a Jew, and rest on the law, and make your boast in God,_
**18** _and know His will, and approve the things that are excellent, being instructed out of the law,_
**19** _and are confident that you yourself are a guide to the blind, a light to those who are in darkness,_
**20** _an instructor of the foolish, a teacher of babes, having the form of knowledge and truth in the law._
**21** _You, therefore, who teach another, do you not teach yourself? You who preach that a man should not steal, do you steal?_
**22** _You who say, "Do not commit adultery," do you commit adultery? You who abhor idols, do you rob temples?_
**23** _You who make your boast in the law, do you dishonor God through breaking the law?_
**24** _For "the name of God is blasphemed among the Gentiles because of you," as it is written._
**25** _For circumcision is indeed profitable if you keep the law; but if you are a breaker of the law, your circumcision has become uncircumcision._
**26** _Therefore, if an uncircumcised man keeps the righteous requirements of the law, will not his uncircumcision be counted as circumcision?_
**27** _And will not the physically uncircumcised, if he fulfills the law, judge you who, even with your written code and circumcision, are a transgressor of the law?_
**28** _For he is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh;_
**29** _but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God._
**_he is a Jew_** (v. 29)—The true child of God has a heart separated from sin unto God.
**3:1** _What advantage then has the Jew, or what is the profit of circumcision?_
**2** _Much in every way! Chiefly because to them were committed the oracles of God._
**_oracles_** (3:2)—important supernatural sayings or messages
**3** _For what if some did not believe? Will their unbelief make the faithfulness of God without effect?_
**4** _Certainly not! Indeed, let God be true but every man a liar. As it is written: "That You may be justified in Your words, And may overcome when You are judged."_
**5** _But if our unrighteousness demonstrates the righteousness of God, what shall we say? Is God unjust who inflicts wrath? (I speak as a man.)_
**_I speak as a man_** (v. 5)—Paul is paraphrasing the weak, unbiblical logic of his opponents.
**6** _Certainly not! For then how will God judge the world?_
**7** _For if the truth of God has increased through my lie to His glory, why am I also still judged as a sinner?_
**8** _And why not say, "Let us do evil that good may come"?—as we are slanderously reported and as some affirm that we say. Their condemnation is just._
**9** _What then? Are we better than they? Not at all. For we have previously charged both Jews and Greeks that they are all under sin._
**_we_** (v. 9)—the Christians in Rome
**_under sin_** (v. 9)—enslaved and dominated by sin
**10** _As it is written: "There is none righteous, no, not one;_
**11** _There is none who understands; There is none who seeks after God._
**12** _They have all turned aside; They have together become unprofitable; There is none who does good, no, not one."_
**_unprofitable_** (v. 12)—useless, worthless; the Hebrew equivalent was used to describe milk that had become rancid
**13** _"Their throat is an open tomb; With their tongues they have practiced deceit"; "The poison of asps is under their lips";_
**14** _"Whose mouth is full of cursing and bitterness."_
**_cursing_** (v. 14)—caustically, derisively wishing the worst for someone
**15** _"Their feet are swift to shed blood;_
**16** _Destruction and misery are in their ways;_
**17** _And the way of peace they have not known."_
**18** _"There is no fear of God before their eyes."_
**19** _Now we know that whatever the law says, it says to those who are under the law, that every mouth may be stopped, and all the world may become guilty before God._
**_every mouth may be stopped_** (v. 19)—People are silent and speechless before God's righteous judgment.
**20** _Therefore by the deeds of the law no flesh will be justified in His sight, for by the law is the knowledge of sin._
1) What reasons does Paul give for the wrath of God against humanity?
2) Circle all the words and descriptive phrases in this passage for man's rebellion against God.
3) Other than long-term judgment, what short-term consequences of rebelliousness does Paul cite in this extended passage?
4) According to this passage, why are not even "moral" and religious people exempted from God's widespread judgment?
GOING DEEPER
Read Psalm 14 and note how it relates to the above passage in Romans.
**Psalm 14 (NKJV)**
**1** _The fool has said in his heart,"There is no God." They are corrupt, They have done abominable works, There is none who does good._
**2** _The L ORD looks down from heaven upon the children of men, To see if there are any who understand, who seek God._
**3** _They have all turned aside, They have together become corrupt; There is none who does good, No, not one._
**4** _Have all the workers of iniquity no knowledge, Who eat up my people as they eat bread, And do not call on the L ORD?_
**5** _There they are in great fear, For God is with the generation of the righteous._
**6** _You shame the counsel of the poor, But the L ORD is his refuge._
**7** _Oh, that the salvation of Israel would come out of Zion! When the L ORD brings back the captivity of His people, Let Jacob rejoice and Israel be glad._
EXPLORING THE MEANING
5) How do these passages from both Old and New Testaments answer the popular, modern-day belief that "human beings are basically good"?
6) What specific evidence do you see in this passage to suggest that God is not impressed by mere "religious activity"?
7) Read Galatians 3:19–25. Why did God give sinful human beings a perfect law code to follow?
TRUTH FOR TODAY
The final verdict, then, is that unredeemed humankind has no defense whatever and is guilty of all charges. The defense must rest, as it were, before it has opportunity to say anything, because the omniscient and all-wise God has infallibly demonstrated the impossibility of any grounds for acquittal. Absolute silence is the only possible response just as there will be utter silence in heaven when the Lord Jesus Christ will one day break the seventh seal and release the seven trumpet judgments upon the condemned earth (see Rev. 8:1–6).
REFLECTING ON THE TEXT
8) R. A. Torrey observed: "When we see sin in all its hideousness and enormity, the holiness of God in all its perfection, and the glory of Jesus Christ in all its infinity, nothing but a doctrine that those who persist in . . . the rejection of the Son of God shall endure everlasting anguish will satisfy the demands of our own moral intuitions." How can you come to a deeper understanding of the depravity of the human heart and the holiness of our God?
9) What in this study convicts you most? challenges you most? compels you to action the most? Why?
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**3**
BY FAITH ALONE
_Romans 3:21–4:25_
DRAWING NEAR
What does _faith_ mean to you? How would you explain it to a child?
THE CONTEXT
In Homer's _Iliad_ , the great Trojan warrior, Hector, was preparing to fight Achilles and the invading Greeks. As he was about to leave home, Hector wanted to hold his young son Astayanax in his arms and bid him farewell. But Hector's armor so frightened the infant that he shrank back to his nurse's caress. The father, laughing out loud, then removed his bronze helmet and took up his little child in his arms. The boy discovered his loving father behind all that armor.
That is similar to what Paul does here in Romans. Having shown God as holy judge, he now shows the God of love, who reaches out with open arms to sinful people in the hope that they will come to Him and be saved. After conclusively proving the universal sinfulness of humanity and their desperate need for righteousness (1:18–3:20), Paul shifts gears and demonstrates that God alone can provide that righteousness. To illustrate this truth, Paul devotes the entire fourth chapter to Abraham. This godly Old Testament saint is a shining example of the central biblical truth that a person can become right with God only by faith in response to His grace, never by works.
KEYS TO THE TEXT
_Justification:_ The words _justify_ and _justification_ occur some thirty times in Romans and are concentrated in 2:13–5:1. This legal or forensic term comes from the Greek word for "righteous" and means "to declare righteous." This verdict includes: pardon from the guilt and penalty of sin, and the imputation of Christ's righteousness to the believer's account, which provides for the positive righteousness man needs to be accepted by God. God declares a sinner righteous solely on the basis of the merits of Christ's righteousness. God imputed a believer's sin to Christ's account in His sacrificial death. The sinner receives this gift of God's grace by faith alone. Justification is a gracious gift God extends to the repentant, believing sinner, wholly apart from human merit or work.
_Abraham:_ Paul uses the model of Abraham to prove justification by faith alone because the Jews held him up as the supreme example of a righteous man (John 8:39), and because it clearly showed that Judaism with its works-righteousness had deviated from the faith of the Jews' patriarchal ancestors. In a spiritual sense, Abraham was the forerunner of the primarily Gentile church in Rome, as well.
UNLEASHING THE TEXT
Read 3:21–4:25, noting the key words and definitions next to the passage.
**Romans 3:21–4:25 (NKJV)**
**21** _But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets,_
**_But_** (v. 21)—an adversative, contrasting humanity's total depravity and inability to please God, and God's own provision of a way to Himself
**22** _even the righteousness of God, through faith in Jesus Christ, to all and on all who believe. For there is no difference;_
**23** _for all have sinned and fall short of the glory of God,_
**24** _being justified freely by His grace through the redemption that is in Christ Jesus,_
**25** _whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed,_
**_propitiation_** (v. 25)—appease-ment or satisfaction; Christ's death satisfied the offended holiness of God
**_passed over_** (v. 25)—a temporary withholding of judgment
**26** _to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus._
**27** _Where is boasting then? It is excluded. By what law? Of works? No, but by the law of faith._
**28** _Therefore we conclude that a man is justified by faith apart from the deeds of the law._
**29** _Or is He the God of the Jews only? Is He not also the God of the Gentiles? Yes, of the Gentiles also,_
**30** _since there is one God who will justify the circumcised by faith and the uncircumcised through faith._
**31** _Do we then make void the law through faith? Certainly not! On the contrary, we establish the law._
**4:1** _What then shall we say that Abraham our father has found according to the flesh?_
**2** _For if Abraham was justified by works, he has something to boast about, but not before God._
**3** _For what does the Scripture say? "Abraham believed God, and it was accounted to him for righteousness."_
**_accounted_** (4:3)—a word used in legal and financial settings; here to take something that belongs to someone and credit it to the account of another
**4** _Now to him who works, the wages are not counted as grace but as debt._
**5** _But to him who does not work but believes on Him who justifies the ungodly, his faith is accounted for righteousness,_
**_justifies the ungodly_** (v. 5)—Only those who freely admit their unworthiness are candidates for salvation.
**6** _just as David also describes the blessedness of the man to whom God imputes righteousness apart from works:_
**_David_** (v. 6)—King David's sin with Bathsheba is another Old Testament example of imputed righteousness.
**7** _"Blessed are those whose lawless deeds are forgiven, And whose sins are covered;_
**8** _Blessed is the man to whom the Lord shall not impute sin."_
**9** _Does this blessedness then come upon the circumcised only, or upon the uncircumcised also? For we say that faith was accounted to Abraham for righteousness._
**10** _How then was it accounted? While he was circumcised, or uncircumcised? Not while circumcised, but while uncircumcised._
**11** _And he received the sign of circumcision, a seal of the righteousness of the faith which he had while still uncircumcised, that he might be the father of all those who believe, though they are uncircumcised, that righteousness might be imputed to them also,_
**_the sign of circumcision_** (v. 11)—the physical, racial mark of identity for the Jewish people
**12** _and the father of circumcision to those who not only are of the circumcision, but who also walk in the steps of the faith which our father Abraham had while still uncircumcised._
**_walk in the steps_** (v. 12)—those non-Jews who emulate Abraham's faith
**13** _For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith._
**14** _For if those who are of the law are heirs, faith is made void and the promise made of no effect,_
**_faith is made void and the promise made of no effect_** (v. 14)—Paul is demonstrating that if adherence to the Law could save, then faith in God's promise would be worthless.
**15** _because the law brings about wrath; for where there is no law there is no transgression._
**16** _Therefore it is of faith that it might be according to grace, so that the promise might be sure to all the seed, not only to those who are of the law, but also to those who are of the faith of Abraham, who is the father of us all_
**17** _(as it is written, "I have made you a father of many nations") in the presence of Him whom he believed—God, who gives life to the dead and calls those things which do not exist as though they did;_
**18** _who, contrary to hope, in hope believed, so that he became the father of many nations, according to what was spoken, "So shall your descendants be."_
**19** _And not being weak in faith, he did not consider his own body, already dead (since he was about a hundred years old), and the deadness of Sarah's womb._
**_weak in faith_** (v. 19)—to allow doubt to erode and undermine belief
**20** _He did not waver at the promise of God through unbelief, but was strengthened in faith, giving glory to God,_
**21** _and being fully convinced that what He had promised He was also able to perform._
**22** _And therefore "it was accounted to him for righteousness."_
**23** _Now it was not written for his sake alone that it was imputed to him,_
**24** _but also for us. It shall be imputed to us who believe in Him who raised up Jesus our Lord from the dead,_
**25** _who was delivered up because of our offenses, and was raised because of our justification._
**_delivered up_** (v. 25)—to be crucified as punishment for human beings' sins
1) Why does Paul argue that when it comes to one's standing before God, no one has the right to boast or be filled with religious pride?
2) Circle every word or phrase in this passage that describes what God has done.
3) Paul goes to some lengths to demonstrate that Abraham was justified in the sight of God long before he was ever circumcised. Why was this an important argument for him to make to his Roman audience?
4) Underline every reference in the passage to God's law. What is the purpose or effect of God's law (4:13–15)?
GOING DEEPER
Read Galatians 3:6–25, noting the parallels with Romans 3:21–4:25.
**Galatians 3:6–25 (NKJV)**
**6** _just as Abraham "believed God, and it was accounted to him for righteousness."_
**7** _Therefore know that only those who are of faith are sons of Abraham._
**8** _And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel to Abraham beforehand, saying, "In you all the nations shall be blessed."_
**9** _So then those who are of faith are blessed with believing Abraham._
**10** _For as many as are of the works of the law are under the curse; for it is written, "Cursed is everyone who does not continue in all things which are written in the book of the law, to do them."_
**11** _But that no one is justified by the law in the sight of God is evident, for "the just shall live by faith."_
**12** _Yet the law is not of faith, but "the man who does them shall live by them."_
**13** _Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, "Cursed is everyone who hangs on a tree"),_
**14** _that the blessing of Abraham might come upon the Gentiles in Christ Jesus, that we might receive the promise of the Spirit through faith._
**15** _Brethren, I speak in the manner of men: Though it is only a man's covenant, yet if it is confirmed, no one annuls or adds to it._
**16** _Now to Abraham and his Seed were the promises made. He does not say, "And to seeds," as of many, but as of one, "And to your Seed," who is Christ._
**17** _And this I say, that the law, which was four hundred and thirty years later, cannot annul the covenant that was confirmed before by God in Christ, that it should make the promise of no effect._
**18** _For if the inheritance is of the law, it is no longer of promise; but God gave it to Abraham by promise._
**19** _What purpose then does the law serve? It was added because of transgressions, till the Seed should come to whom the promise was made; and it was appointed through angels by the hand of a mediator._
**20** _Now a mediator does not mediate for one only, but God is one._
**21** _Is the law then against the promises of God? Certainly not! For if there had been a law given which could have given life, truly righteousness would have been by the law._
**22** _But the Scripture has confined all under sin, that the promise by faith in Jesus Christ might be given to those who believe._
**23** _But before faith came, we were kept under guard by the law, kept for the faith which would afterward be revealed._
**24** _Therefore the law was our tutor to bring us to Christ, that we might be justified by faith._
**25** _But after faith has come, we are no longer under a tutor._
EXPLORING THE MEANING
5) What points in Galatians 3 underscore Paul's argument in Romans 3–4?
6) What incidents from the life of Abraham and Sarah does Paul use to make the case that salvation is by divine power, not human effort?
7) Read 2 Corinthians 5:21. If God's wrath is directed toward unrighteousness, and His favor is directed toward righteousness, what are the wonderful implications of this verse for believers?
TRUTH FOR TODAY
Scripture makes it clear that there is indeed a way to God, but that it is not based on anything men can do to achieve or merit it. Man can be made right with God, but not on his own terms or in his own power. In that basic regard Christianity is distinct from every other religion. As far as the way of salvation is concerned, there are therefore only two religions the world has ever known or will ever know—the religion of divine accomplishment, which is biblical Christianity, and the religion of human achievement, which includes all other kinds of religion, by whatever names they may claim.
REFLECTING ON THE TEXT
8) Some Christians view God's law and His grace as contradictory. Based on what you have seen in this study, how would you harmonize these two truths?
9) What's the problem with trying to _do_ things in order to earn favor with God? Why is that never sufficient?
10) If salvation were by human effort, we could boast. Since salvation is all of grace, what is the proper response of the redeemed?
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**4**
GRACE THROUGH ONE MAN
_Romans 5:1–21_
DRAWING NEAR
Have you ever experienced doubts about your salvation? In what way?
Why is it sometimes hard to believe that you are secure in Christ forever?
THE CONTEXT
After describing the appalling sin and lostness of all humankind, Paul revealed how Christ, by His death on the cross, has provided the way of salvation for everyone who comes to God in faith. Next, Paul moves to answer two important questions that were, no doubt, on the minds of his readers. First, how complete, or how secure is this salvation provided by Christ? Can we really be certain? What happens if we sin after turning to Christ in faith? Paul addresses this query in 5:1–11.
The second issue addressed here by Paul is, "How can what one man did at one time in history have such an absolute effect on humankind?" Paul concisely answers this question by comparing the reign of death that Adam's sin engendered with the reign of life made possible by Christ's perfect sacrifice. Though many people consider the latter half of Romans 5 to be one of the most enigmatic passages in the New Testament, when looked at carefully, this chapter is a source of great comfort and genuine awe in a God who is able and willing to provide such an extraordinary salvation.
KEYS TO THE TEXT
_Imputed:_ Used in both financial and legal settings, the Greek word means to take something that belongs to someone and credit to another's account. It is a one-sided transaction. As in the case of Abraham, Abraham did nothing to accumulate it; God simply credited it to him. God took His own righteousness and credited it to Abraham as if it were actually his. God did this because Abraham believed in Him. This is the heart of the doctrine of justification, whereby God declares the repentant sinner righteous the moment he places wholehearted faith in Christ and His sacrificial death. Christ made atonement by shedding His own blood on the cross. This provides forgiveness. And just as our sins were put to His account when He bore them on the cross, so now His righteousness is reckoned as our own. His perfect righteousness thus becomes the ground on which we stand before God.
_Types:_ A figure, representation, or symbol of something to come, as an event in the Old Testament foreshadows another in the New Testament. Types generally find their fulfillment in the person and ministry of Christ, but they sometimes relate to God, His people, or some other reality. For instance, Melchizedek, the king-priest of Salem (Gen. 14:18–20 and Ps. 110:4), is said to be typical of Christ (Heb. 6:20). Jesus said the bronze serpent in the wilderness (Num. 21:4–9) was in some sense typical of His own crucifixion (John 3:14–15). The writer of Hebrews (Heb. 9–10) pointed out that the tabernacle typically foreshadowed the person and work of Jesus Christ. The NKJV uses the word "type" in Romans 5:14, where Paul mentions Adam as "a type of Him [Jesus] who was to come." ( _Nelson's New Illustrated Bible Dictionary_ )
UNLEASHING THE TEXT
Read 5:1–21, noting the key words and definitions next to the passage.
**Romans 5:1–21 (NKJV)**
**1** _Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ,_
**_having been justified_** (v. 1)—The Greek construction of this verb indicates a one-time legal declaration with ongoing results.
**_we have_** (v. 1)—we presently possess
**_peace with God_** (v. 1)—an external, objective reality, not a subjective, internal sense of serenity and calm
**2** _through whom also we have access by faith into this grace in which we stand, and rejoice in hope of the glory of God._
**_access_** (v. 2)—introduction
**_stand_** (v. 2)—the idea of permanence, of being fixed and immovable
**_hope_** (v. 2)—a certainty not yet realized; not a wishful, uncertain dream
**3** _And not only that, but we also glory in tribulations, knowing that tribulation produces perseverance;_
**_tribulations_** (v. 3)—extreme pressure, as in the pressure exerted to extract oil from an olive
**4** _and perseverance, character; and character, hope._
**_perseverance_** (v. 4)—remaining under tremendous weight without succumbing; endurance
**_character_** (v. 4)—literally "proof," a term used in the testing of precious metals to determine their purity
**5** _Now hope does not disappoint, because the love of God has been poured out in our hearts by the Holy Spirit who was given to us._
**_poured out_** (v. 5)—God's love is lavished on His children.
**6** _For when we were still without strength, in due time Christ died for the ungodly._
**_without strength_** (v. 6)—liter-ally "helpless," because of their spiritual deadness
**_ungodly_** (v. 6)—a proof that Christ's love was never based on human merit
**7** _For scarcely for a righteous man will one die; yet perhaps for a good man someone would even dare to die._
**8** _But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us._
**9** _Much more then, having now been justified by His blood, we shall be saved from wrath through Him._
**10** _For if when we were enemies we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life._
**11** _And not only that, but we also rejoice in God through our Lord Jesus Christ, through whom we have now received the reconciliation._
**12** _Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned—_
**_because all sinned_** (v. 12)—All humanity existed in the loins of Adam and have through procreation inherited his fallenness and depravity. Thus it can be said that all sinned in him.
**13** _(For until the law sin was in the world, but sin is not imputed when there is no law._
**14** _Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come._
**_a type of Him . . . to come_** (v. 14)—Adam and Christ were similar in that their acts affected many others.
**15** _But the free gift is not like the offense. For if by the one man's offense many died, much more the grace of God and the gift by the grace of the one Man, Jesus Christ, abounded to many._
**16** _And the gift is not like that which came through the one who sinned. For the judgment which came from one offense resulted in condemnation, but the free gift which came from many offenses resulted in justification._
**17** _For if by the one man's offense death reigned through the one, much more those who receive abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.)_
**_death reigned_** (v. 17)—Adam's sinful act brought universal death.
**18** _Therefore, as through one man's offense judgment came to all men, resulting in condemnation, even so through one Man's righteous act the free gift came to all men, resulting in justification of life._
**19** _For as by one man's disobedience many were made sinners, so also by one Man's obedience many will be made righteous._
**20** _Moreover the law entered that the offense might abound. But where sin abounded, grace abounded much more,_
**21** _so that as sin reigned in death, even so grace might reign through righteousness to eternal life through Jesus Christ our Lord._
1) Circle all the verbs in verses 1–11, noting especially their tenses.
2) How does Paul refute the erroneous notion that we receive salvation by faith but must preserve it by good works? What evidences does he give that salvation is unconditional?
3) What word picture does Paul use to drive home the truth that unbelievers are actually at war with God?
4) How did Adam's actions affect the human race? What were the effects of Christ's actions?
GOING DEEPER
Read the following passage and consider what the author has to say about the law's inability to save us, Christ's perfect sacrifice, and the possibilities this creates for relating to God.
**Hebrews 10:1–4, 12–14, 19–23 (NKJV)**
**1** _For the law, having a shadow of the good things to come, and not the very image of the things, can never with these same sacrifices, which they offer continually year by year, make those who approach perfect._
**2** _For then would they not have ceased to be offered? For the worshipers, once purified, would have had no more consciousness of sins._
**3** _But in those sacrifices there is a reminder of sins every year._
**4** _For it is not possible that the blood of bulls and goats could take away sins._
**12** _But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God,_
**13** _from that time waiting till His enemies are made His footstool._
**14** _For by one offering He has perfected forever those who are being sanctified._
**19** _Therefore, brethren, having boldness to enter the Holiest by the blood of Jesus,_
**20** _by a new and living way which He consecrated for us, through the veil, that is, His flesh,_
**21** _and having a High Priest over the house of God,_
**22** _let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience and our bodies washed with pure water._
**23** _Let us hold fast the confession of our hope without wavering, for He who promised is faithful._
EXPLORING THE MEANING
5) In what way was Jesus's sacrifice different from the old sacrificial system?
6) Why do you think both of these passages (Romans 4; Hebrews 10) emphasize our access to God?
7) In what ways does this Hebrews passage echo the idea that salvation is permanent?
TRUTH FOR TODAY
Jesus Christ broke the power of sin and death, but the converse is not true. Sin and death cannot break the power of Jesus Christ. The condemnation of Adam's sin is reversible, the redemption of Jesus Christ is not. The effect of Adam's act is permanent only if not nullified by Christ. The effect of Christ's act, however, is permanent for believing individuals and not subject to reversal or nullification. We have the great assurance that once we are in Jesus Christ, we are in Him forever.
REFLECTING ON THE TEXT
8) A. W. Pink said the following about our eternal security in Christ: "It is utterly and absolutely impossible that the sentence of the divine Judge should ever be revoked or reversed. Sooner shall the lightnings of omnipotence shiver the Rock of Ages than those sheltering in Him again be brought under condemnation." How does knowing that your salvation is eternally secure affect your life on a daily basis? How does it make you feel?
9) When have you experienced God's love being "poured out" (v. 5)?
10) What new things about God have you learned from this passage?
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**5**
DEAD AND ALIVE!
_Romans 6:1–23_
DRAWING NEAR
Think of an area in which you have struggled with sin in your life. How has God helped you overcome these struggles?
THE CONTEXT
Like a skillful lawyer building an airtight case, the apostle Paul has been laying out the remarkable facts of the gospel. After an extensive discussion of human beings' sin and inability to please God, Paul announced the doctrine of justification, which is God's declaration of believing sinners as righteous. Next he moves to the subject of the believer's _holiness_ —living in obedience to God's Word through the power of His Spirit. In short, Paul sets out to demonstrate the practical ramifications of salvation for those who have been justified. He specifically begins a lengthy discussion on the doctrine of sanctification, which is the process of becoming holy.
Paul also addresses the logical conclusion of his readers: If the old self is dead, why is there continually a struggle with sin, and how can the new self become dominant? His exhortation is contained in two key words: _reckon_ (vv. 11b–12) and _present_ (vv. 13–14). The final section of chapter 6 continues Paul's discussion of sanctification by reminding his readers of their past slavery to sin and their new slavery to righteousness. He wants them to live in submission to their new master, Jesus Christ, and not to be entangled again with the sins that characterized their old life, sins which no longer have any claim over them.
KEYS TO THE TEXT
_To Reckon:_ While it literally means "to count or number something," this phrase was often used metaphorically to refer to having an absolute, unreserved confidence in what one's mind knows to be true—the kind of heartfelt confidence that affects his actions and decisions. Paul is not referring to mind games in which we trick ourselves into thinking a certain way. Rather he is urging us to embrace by faith what God has revealed to be true.
_Dead to Sin:_ Not a reference to the believer's ongoing daily struggle with sin, but to a one-time event completed in the past. Because we are "in Christ" (Rom. 6:11; 8:1) and He died in our place (5:6–8), we are counted dead with Him. This is the fundamental premise of chapter 6, and Paul spends the remainder of the chapter explaining and supporting it.
_Not Under Law But Under Grace (6:14)._ This does not mean God has abrogated His moral law. The law is good, holy, and righteous; but it cannot be kept, so it curses. Since it cannot assist anyone to keep God's moral standard (see Rom. 7:7–11), it can only show the standard and thus rebuke and condemn those who fail to keep it. But the believer is no longer under the law as a condition of acceptance with God—an impossible condition to meet and one designed only to show man his sinfulness—but under grace, which enables him to truly fulfill the law's righteous requirements. See chapter 7 for Paul's complete commentary on this crucial expression.
UNLEASHING THE TEXT
Read 6:1–23, noting the key words and definitions next to the passage.
**Romans 6:1–23 (NKJV)**
**1** _What shall we say then? Shall we continue in sin that grace may abound?_
**_Shall we continue in sin . . ._** (v. 1)—Paul anticipated that skeptics might reason, "If salvation is based entirely upon grace, won't this encourage them to sin even more?"
**2** _Certainly not! How shall we who died to sin live any longer in it?_
**_Certainly not!_** (v. 2)—literally, "may it never be, by no means"; a strong Greek idiom of repudiation
**3** _Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death?_
**_baptized into Christ Jesus_** (v. 3)—Not a literal water baptism, but a metaphorical immersion of a person into the work of Christ; that is, completely united and identified with Him, "so as to alter [a person's] condition or relationship to [his or her] previous environment or condition" (Wuest).
**4** _Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life._
**_newness of life_** (v. 4)—In the same way that we were united with Christ in His death and burial, so too in His resurrection; this speaks of regeneration.
**5** _For if we have been united together in the likeness of His death, certainly we also shall be in the likeness of His resurrection,_
**6** _knowing this, that our old man was crucified with Him, that the body of sin might be done away with, that we should no longer be slaves of sin._
**_our old man_** (v. 6)—a believer's unregenerate self, worn out and useless
**_crucified_** (v. 6)—not merely made to suffer but put to death
**_body of sin_** (v. 6)—essentially a synonym for the "old man"
**7** _For he who has died has been freed from sin._
**_freed from sin_** (v. 7)—no longer under sin's domination
**8** _Now if we died with Christ, we believe that we shall also live with Him,_
**9** _knowing that Christ, having been raised from the dead, dies no more. Death no longer has dominion over Him._
**_dominion_** (v. 9)—mastery, control, or domination
**10** _For the death that He died, He died to sin once for all; but the life that He lives, He lives to God._
**11** _Likewise you also, reckon yourselves to be dead indeed to sin, but alive to God in Christ Jesus our Lord._
**12** _Therefore do not let sin reign in your mortal body, that you should obey it in its lusts._
**_mortal body_** (v. 12)—the only remaining repository where sin finds the believer vulnerable
**13** _And do not present your members as instruments of unrighteousness to sin, but present yourselves to God as being alive from the dead, and your members as instruments of righteousness to God._
**_present_** (v. 13)—refers to a decision of the will
**_your members_** (v. 13)—the parts of the physical body from which sin operates in the life of a believer
**14** _For sin shall not have dominion over you, for you are not under law but under grace._
**15** _What then? Shall we sin because we are not under law but under grace? Certainly not!_
**16** _Do you not know that to whom you present yourselves slaves to obey, you are that one's slaves whom you obey, whether of sin leading to death, or of obedience leading to righteousness?_
**17** _But God be thanked that though you were slaves of sin, yet you obeyed from the heart that form of doctrine to which you were delivered._
**18** _And having been set free from sin, you became slaves of righteousness._
**19** _I speak in human terms because of the weakness of your flesh. For just as you presented your members as slaves of uncleanness, and of lawlessness leading to more lawlessness, so now present your members as slaves of righteousness for holiness._
**_weakness of your flesh_** (v. 19)—the human difficulty in grasping divine truth
**20** _For when you were slaves of sin, you were free in regard to righteousness._
**21** _What fruit did you have then in the things of which you are now ashamed? For the end of those things is death._
**22** _But now having been set free from sin, and having become slaves of God, you have your fruit to holiness, and the end, everlasting life._
**23** _For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord._
1) How would you summarize Paul's response to the idea that believers in Christ will continue to live as they did when they were unbelievers?
2) What does Paul say happened to our old selves?
3) What things do believers need to "know"? How does this "knowing" differ from the "reckoning" (v. 11) that believers are commanded to do?
4) What three things are part of the process of sanctification (vv. 6, 11, 13)?
GOING DEEPER
Note the parallels in Colossians 3 with what you've been studying in chapter 6.
**Colossians 3:1–11**
**1** _If then you were raised with Christ, seek those things which are above, where Christ is, sitting at the right hand of God._
**2** _Set your mind on things above, not on things on the earth._
**3** _For you died, and your life is hidden with Christ in God._
**4** _When Christ who is our life appears, then you also will appear with Him in glory._
**5** _Therefore put to death your members which are on the earth: fornication, uncleanness, passion, evil desire, and covetousness, which is idolatry._
**6** _Because of these things the wrath of God is coming upon the sons of disobedience,_
**7** _in which you yourselves once walked when you lived in them._
**8** _But now you yourselves are to put off all these: anger, wrath, malice, blasphemy, filthy language out of your mouth._
**9** _Do not lie to one another, since you have put off the old man with his deeds,_
**10** _and have put on the new man who is renewed in knowledge according to the image of Him who created him,_
**11** _where there is neither Greek nor Jew, circumcised nor uncircumcised, barbarian, Scythian, slave nor free, but Christ is all and in all._
EXPLORING THE MEANING
5) Why are Christians to "put off " and "put on" certain things?
6) If Christians really are dead to sin and alive to God, why do we still struggle so with temptation?
7) These passages teach two truths: (1) _God_ is the One who changes us—sanctification is by His grace; and (2) in the sanctification process _we_ are to do certain things and not do certain things. How do you reconcile these facts?
TRUTH FOR TODAY
Jesus Christ is not looking for people who want to add Him to their life as an insurance against hell. He is not looking for people who want to apply His high moral principles to their unregenerate lives. He is not looking for those who want only to be outwardly reformed by having their old nature improved. Jesus Christ calls to Himself those who are willing to be inwardly transformed by Him, who desire an entirely new nature that is created in His own holy likeness. He calls to Himself those who are willing to die with Him in order to be raised with Him, who are willing to relinquish slavery to their sin for slavery to His righteousness. And when people come to Him on His terms, He changes their destiny from eternal death to eternal life.
REFLECTING ON THE TEXT
8) What do you think it means to come to Jesus "on His own terms"? Are you willing to relinquish your sinful inclinations and be transformed from the inside out?
9) The noble theologian Charles Hodge summarized: "There can be no participation in Christ's life without a participation in his death, and we cannot enjoy the benefits of his death unless we are partakers of the power of his life. We must be reconciled to God in order to be holy, and we cannot be reconciled without thereby becoming holy." What are some barriers in your life to becoming holy? What are some things in your life that contribute to becoming more holy?
10) In the three-part process of sanctification described in this passage (that is, "know," "reckon," and "present"), in what area do you struggle the most? Is it in understanding God's salvation truths and really being convinced by them, or choosing to live them out? Explain.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**6**
DELIVERED FROM THE LAW
_Romans 7:1–25_
DRAWING NEAR
Would you describe yourself as a rigid "rule keeper"? Why or why not?
Ask God to show you new truths in this study about His power over sin and His love for you.
THE CONTEXT
In this doctrinal masterpiece, Paul, the consummate theologian, has first established the sad, sinful state of human beings. All are under _condemnatio_ n. However, the good news includes the miracle of _justificatio_ n—a righteousness from God available by grace through faith. But the gospel received from God and preached by Paul doesn't stop there. It also includes _sanctificatio_ n—that truth of absolute identification with Christ (in His death, burial, and resurrection), by which God transforms redeemed sinners into the very likeness of Christ.
Knowing that his readers—especially Jewish ones—would have many questions about how the Old Testament laws relate to their faith in Christ, Paul sets out to explain that law convicts unbelievers (and believers) of sin, but it cannot deliver anyone from sin. He also addresses the issue of why believers still struggle with sinful desires.
KEYS TO THE TEXT
_The Law:_ In the Bible, particularly the Old Testament, a unique law code was established by direct revelation from God to direct His people in their worship, in their relationship to Him, and in their social relationships with one another. Israel was not the only nation to have a law code. Such collections were common among the countries of the ancient world. The biblical law code, or the Mosaic Law, was different from other ancient Near Eastern law codes in several ways. Biblical law was different, first of all, in its origin. Throughout the ancient world, the laws of most nations were believed to originate with the gods, but they were considered intensely personal and subjective in the way they were applied. By contrast, the biblical concept was that law comes from God, issues from His nature, and is holy, righteous, and good. Furthermore, at the outset of God's ruling over Israel at Sinai, God the great King gave His laws. These laws were binding on His people, and He upheld them. Furthermore, His laws were universal and an expression of His love for His people (Exod. 19:5–6). If salvation has always been by faith and never by works, and if the covenant of promise to Abraham was fulfilled in Jesus Christ, what purpose did the Law have? Paul's answer is direct and sobering: The purpose of the Law was to demonstrate to man his total sinfulness, his inability to please God by his own works, and his need for mercy and grace. ( _Nelson's New Illustrated Bible Dictionary_ )
UNLEASHING THE TEXT
Read 7:1–25, noting the key words and definitions next to the passage.
**Romans 7:1–25 (NKJV)**
**1** _Or do you not know, brethren (for I speak to those who know the law), that the law has dominion over a man as long as he lives?_
**_dominion_** (v. 1)—jurisdiction
**2** _For the woman who has a husband is bound by the law to her husband as long as he lives. But if the husband dies, she is released from the law of her husband._
**3** _So then if, while her husband lives, she marries another man, she will be called an adulteress; but if her husband dies, she is free from that law, so that she is no adulteress, though she has married another man._
**4** _Therefore, my brethren, you also have become dead to the law through the body of Christ, that you may be married to another—to Him who was raised from the dead, that we should bear fruit to God._
**_become dead_** (v. 4)—literally "you were made to die"; in response to a sinner's faith, God makes the sinner forever dead to the condemnation and penalty of law
**_married to another_** (v. 4)—united with Christ in a permanent relationship
**_fruit_** (v. 4)—a transformed life that manifests new attitudes and actions
**5** _For when we were in the flesh, the sinful passions which were aroused by the law were at work in our members to bear fruit to death._
**_flesh_** (v. 5)—people's unredeemed humanness, that is, that remnant of the old man that will remain with each believer until each receives his or her glorified body
**_sinful passions_** (v. 5)—the overwhelming impulses to think and do evil
**_aroused by the law_** (v. 5)—The unbeliever's rebellious nature is awakened when restrictions are placed on him or her.
**_fruit to death_** (v. 5)—Sin brings a harvest of eternal judgment in the life of an unbeliever.
**6** _But now we have been delivered from the law, having died to what we were held by, so that we should serve in the newness of the Spirit and not in the oldness of the letter._
**_delivered from the law_** (v. 6)—Because we died in Christ, we are no longer subject to the condemnation and penalties of the law.
**_oldness of the letter_** (v. 6)— the external, written law code that produced only condemnation
**7** _What shall we say then? Is the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, "You shall not covet."_
**_Is the law sin?_** (v. 7)—Paul wanted to make sure his readers understood that the law was not imperfect or evil but rather only a beacon to point out evil.
**8** _But sin, taking opportunity by the commandment, produced in me all manner of evil desire. For apart from the law sin was dead._
**_opportunity_** (v. 8)—a starting point or base of operations
**_dead_** (v. 8)—that is, dormant
**9** _I was alive once without the law, but when the commandment came, sin revived and I died._
**10** _And the commandment, which was to bring life, I found to bring death._
**11** _For sin, taking occasion by the commandment, deceived me, and by it killed me._
**_sin . . . deceived me_** (v. 11)—by causing people to think they could find life in keeping the law
**12** _Therefore the law is holy, and the commandment holy and just and good._
**13** _Has then what is good become death to me? Certainly not! But sin, that it might appear sin, was producing death in me through what is good, so that sin through the commandment might become exceedingly sinful._
**14** _For we know that the law is spiritual, but I am carnal, sold under sin._
**_carnal_** (v. 14)—Literally, "of flesh"; that is, incarcerated in unredeemed humanness; Paul is not in the flesh, but the flesh is in him.
**15** _For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do._
**16** _If, then, I do what I will not to do, I agree with the law that it is good._
**17** _But now, it is no longer I who do it, but sin that dwells in me._
**_sin that dwells in me_** (v. 17)—Paul's sin flowed not from his new, redeemed nature but from his unredeemed humanness or flesh.
**18** _For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find._
**19** _For the good that I will to do, I do not do; but the evil I will not to do, that I practice._
**20** _Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me._
**21** _I find then a law, that evil is present with me, the one who wills to do good._
**22** _For I delight in the law of God according to the inward man._
**23** _But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members._
**_law of my mind_** (v. 23)—equiv-alent to the new inner self
**24** _O wretched man that I am! Who will deliver me from this body of death?_
**_deliver_** (v. 24)—to rescue from danger, as in a soldier pulling his wounded comrade from the battlefield
**25** _I thank God—through Jesus Christ our Lord! So then, with the mind I myself serve the law of God, but with the flesh the law of sin._
1) What illustration does Paul use to explain the manner in which believers are dead to the law?
2) Underline every reference to the law in this passage. Circle words and phrases that speak about sin.
3) What does Paul say we will wrestle with the rest of our lives (v. 1)?
4) How do you reconcile Paul's discussion of the believer as an entirely new creation, dead to sin, in chapter 6 with his admission of a huge struggle with sin in chapter 7?
GOING DEEPER
Note the psalmist's high view of God's law in Psalm 19:7–11.
**Psalm 19:7–11**
**7** _The law of the Lord is perfect, converting the soul; The testimony of the Lord is sure, making wise the simple;_
**8** _The statutes of the Lord are right, rejoicing the heart; The commandment of the Lord is pure, enlightening the eyes;_
**9** _The fear of the Lord is clean, enduring forever; The judgments of the Lord are true and righteous altogether._
**10** _More to be desired are they than gold, Yea, than much fine gold; Sweeter also than honey and the honeycomb._
**11** _Moreover by them Your servant is warned, And in keeping them there is great reward._
EXPLORING THE MEANING
5) What are the benefits of knowing and obeying God's Word?
6) Is there a contradiction between Paul's observation that the Law is a demanding, unyielding code of condemnation and David's obvious affection for the Law in Psalm 19? Why or why not?
7) Read 1 Peter 2:11. How does this command echo the internal struggle described by Paul in this passage?
8) Where did Paul ultimately find hope in his struggle to live as God commands?
TRUTH FOR TODAY
Sin is so wretched and powerful that, even in a redeemed person, it hangs on and contaminates his living and frustrates his inner desire to obey the will of God.
REFLECTING ON THE TEXT
9) In what areas are you frustrated by your sinful inclinations? Based on chapter 7, how effective is legalism in fighting the flesh?
10) What have you learned in this passage that convicts you? Comforts you? Why?
11) Think about one thing in your life you should be doing. Think about one thing in your life that you should not be doing. Write those items in the space below and make them a source of prayer in the week to come.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**7**
IN THE SPIRIT
_Romans 8:1–39_
DRAWING NEAR
Jesus promised the Holy Spirit would come to His followers. When you think about the Holy Spirit, what comes to mind? What questions do you have?
THE CONTEXT
In the first seven chapters of Romans, God's Holy Spirit is mentioned only once. In chapter 8, Paul mentions the Spirit almost twenty times. It is the Spirit who frees us from sin and death, enables us to fulfill God's law, changes our nature, gives us the ability to overcome the desires of our unredeemed flesh, confirms our adoption as God's children, and guarantees our eternal glory. In short, there can be no success or progress in the Christian life apart from an utter dependence on the third Person of the Trinity.
Paul closes the chapter with profound teaching about the believer's absolute security. Not only are we saved by the blood of Christ and indwelt by the Spirit, but we also are safe in the Father's love. The God who is in control of all things, who has graciously saved us from sin and death and who has begun the process of transformation in us, will never let us go.
KEYS TO THE TEXT
_Holy Spirit:_ The Holy Spirit is the divine agent who creates, sustains, and preserves spiritual life in those who place their trust in Jesus Christ. The Holy Spirit is not merely an influence or an impersonal power emanating from God. He is a person, the third member of the Trinity, equal in every way to God the Father and God the Son. Among the many characteristics of personhood that the Holy Spirit manifests are: He functions with mind, emotion, and will; He loves the saints, He communicates with them, teaches, guides, comforts, and chastises them; He can be grieved, quenched, lied to, tested, resisted, and blasphemed. He is called God, Lord, the Spirit of God, the Spirit of the Lord, the Spirit of Yahweh (or Jehovah), the Spirit of the Father, the Spirit of the Son, the Spirit of Jesus, and the Comforter and Advocate for believers.
Since Pentecost, the Holy Spirit has indwelt all believers, illuminating their understanding and application of God's Word. He fills them, seals them, communes with them, fellowships with them, intercedes for them, comforts them, admonishes them, sanctifies them, and enables them to resist sin and to serve God.
UNLEASHING THE TEXT
Read 8:1–39, noting the key words and definitions next to the passage.
**Romans 8:1–39 (NKJV)**
**1** _There is therefore now no condemnation to those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit._
**_therefore_** (v. 1)—Here Paul summarizes the ramifications of the truths presented in chapters 1–7.
**_condemnation_** (v. 1)—a judicial term meaning a guilty verdict; the opposite of justification
**2** _For the law of the Spirit of life in Christ Jesus has made me free from the law of sin and death._
**_the law of the Spirit of life_** (v. 2)—the gospel, the law of faith
**_the law of sin and death_** (v. 2)—God's perfect law that, because of the weakness of the flesh, produces only condemnation.
**3** _For what the law could not do in that it was weak through the flesh, God did by sending His own Son in the likeness of sinful flesh, on account of sin: He condemned sin in the flesh,_
**_in the likeness of sinful flesh_** (v. 3)—Christ was fully man, but without the unredeemed humanness or fleshly nature of sinners.
**4** _that the righteous requirement of the law might be fulfilled in us who do not walk according to the flesh but according to the Spirit._
**_walk_** (v. 4)—one's manner of living
**5** _For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit._
**_set their minds_** (v. 5)—a basic orientation or disposition of the mind that is set on satisfying the cravings of the flesh
**6** _For to be carnally minded is death, but to be spiritually minded is life and peace._
**_spiritually minded_** (v. 6)—focused on the things of the Spirit
**7** _Because the carnal mind is enmity against God; for it is not subject to the law of God, nor indeed can be._
**8** _So then, those who are in the flesh cannot please God._
**9** _But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His._
**_dwells_** (v. 9)—makes one's home
**10** _And if Christ is in you, the body is dead because of sin, but the Spirit is life because of righteousness._
**11** _But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ from the dead will also give life to your mortal bodies through His Spirit who dwells in you._
**12** _Therefore, brethren, we are debtors—not to the flesh, to live according to the flesh._
**13** _For if you live according to the flesh you will die; but if by the Spirit you put to death the deeds of the body, you will live._
**_put to death the deeds of the body_** (v. 13)—the ongoing, lifelong process of relying on the Spirit's strength to resist fleshly urges and to carry out God's commands
**14** _For as many as are led by the Spirit of God, these are sons of God._
**_led by the Spirit_** (v. 14)—usual-ly by illuminating the Scripture so that our sinful, finite minds can grasp God's will
**15** _For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out, "Abba, Father."_
**_spirit of bondage . . . to fear_** (v. 15)—The unredeemed have no lasting peace because of the effects of sin and the prospect of punishment.
**16** _The Spirit Himself bears witness with our spirit that we are children of God,_
**_bears witness with our spirit_** (v. 16)—by fruitfulness and power, not mystical voices
**17** _and if children, then heirs—heirs of God and joint heirs with Christ, if indeed we suffer with Him, that we may also be glorified together._
**_heirs_** (v. 17)—We stand to inherit all that God is and has.
**18** _For I consider that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us._
**19** _For the earnest expectation of the creation eagerly waits for the revealing of the sons of God._
**20** _For the creation was subjected to futility, not willingly, but because of Him who subjected it in hope;_
**_futility_** (v. 20)—a reference to the effects of the curse (Gen. 3:17–19)
**21** _because the creation itself also will be delivered from the bondage of corruption into the glorious liberty of the children of God._
**22** _For we know that the whole creation groans and labors with birth pangs together until now._
**23** _Not only that, but we also who have the firstfruits of the Spirit, even we ourselves groan within ourselves, eagerly waiting for the adoption, the redemption of our body._
**_creation eagerly waits . . . groans_** (vv. 19–23)—the universal longing for the removal of the curse
**_firstfruits of the Spirit_** (v. 23)—The changes God works in us are evidence of the truth that we will one day be like Christ.
**24** _For we were saved in this hope, but hope that is seen is not hope; for why does one still hope for what he sees?_
**25** _But if we hope for what we do not see, we eagerly wait for it with perseverance._
**26** _Likewise the Spirit also helps in our weaknesses. For we do not know what we should pray for as we ought, but the Spirit Himself makes intercession for us with groanings which cannot be uttered._
**_groanings which cannot be uttered_** (v. 26)—divine articulations within the Trinity; profound appeals for the welfare of God's people
**27** _Now He who searches the hearts knows what the mind of the Spirit is, because He makes intercession for the saints according to the will of God._
**28** _And we know that all things work together for good to those who love God, to those who are the called according to His purpose._
**_all things work together for good_** (v. 28)—Our sovereign God orchestrates every event in life to bring glory to Himself and benefit (temporal or eternal) His children.
**29** _For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren._
**_foreknew_** (v. 29)—not omniscience, but the divine choice to set His love on us and establish a relationship with us
**30** _Moreover whom He predestined, these He also called; whom He called, these He also justified; and whom He justified, these He also glorified._
**_predestined_** (v. 30)—literally, "to mark out," "appoint," or "determine beforehand"
**31** _What then shall we say to these things? If God is for us, who can be against us?_
**_If_** (v. 31)—since
**32** _He who did not spare His own Son, but delivered Him up for us all, how shall He not with Him also freely give us all things?_
**33** _Who shall bring a charge against God's elect? It is God who justifies._
**34** _Who is he who condemns? It is Christ who died, and furthermore is also risen, who is even at the right hand of God, who also makes intercession for us._
**35** _Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword?_
**36** _As it is written: "For Your sake we are killed all day long; We are accounted as sheep for the slaughter."_
**37** _Yet in all these things we are more than conquerors through Him who loved us._
**38** _For I am persuaded that neither death nor life, nor angels nor principalities nor powers, nor things present nor things to come,_
**39** _nor height nor depth, nor any other created thing, shall be able to separate us from the love of God which is in Christ Jesus our Lord._
1) List the various names for the Spirit that Paul uses.
2) According to this chapter, what acts/ministries does the Holy Spirit perform in us, through us, and for us?
3) How does the Spirit's presence and work change our very nature?
4) What does Paul mean by the references to "groaning" in this chapter (vv. 22–23)?
GOING DEEPER
Consider Christ's promise of the Spirit to His followers, given in the Upper Room.
**John 14:15–17**
**15** _"If you love Me, keep My commandments._
**16** _And I will pray the Father, and He will give you another Helper, that He may abide with you forever—_
**17** _the Spirit of truth, whom the world cannot receive, because it neither sees Him nor knows Him; but you know Him, for He dwells with you and will be in you._
EXPLORING THE MEANING
5) What more do you learn here about the Spirit?
6) How does the promise in John 14:17 relate to the promise of Romans 8:35–39?
7) Read Galatians 5:22–23. How can the presence of these qualities in your life bring a sense of hope and expectation?
TRUTH FOR TODAY
The Spirit-filled life does not come through mystical or ecstatic experiences, but from studying and submitting oneself to Scripture. As a believer faithfully and submissively saturates his mind and heart with God's truth, his Spirit-controlled behavior will follow as surely as night follows day. When we are filled with God's truth and led by His Spirit, even our involuntary reactions—those that happen when we don't have time to consciously decide what to do or say—will be godly.
REFLECTING ON THE TEXT
8) According to the statement above, why is it important to read and know God's Word? How is that related to being led by the Spirit?
9) The Holy Spirit was not given so that believers could enjoy ecstatic, feel-good experiences. The Spirit lives in us to change us. The Scottish theologian David Brown stated, "If you don't kill sin, sin will kill you." How, practically speaking, can God's indwelling Spirit empower you for victory over sin today?
10) On a scale of 1–10, with 1 being "carnal" and 10 being "Christlike," how would you evaluate your "life in the Spirit" right now? What needs to change?
11) Meditate on Romans 8:35–39. How does this benediction about God's love encourage you?
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
**8**
ISRAEL AND GOD'S ETERNAL PLAN
_Romans 9:1–11:36_
DRAWING NEAR
In this study we will look at Israel's part in God's plan. Many professed Christians through the centuries have fanned the flames of anti-Semitism, leading to horrendous persecution of the Jewish people. Other Christians have been Israel's biggest supporters. What do you think is the reason for so many conflicting responses over the centuries to the Jewish people?
THE CONTEXT
Romans 9–11 is one of the most fascinating passages in the New Testament, filled with essential and very practical doctrine and focused on Israel, God's chosen people. Some people have argued that these chapters are a parenthetical body of teaching, largely unrelated to the rest of the epistle. Clearly if Paul had left out chapters 9–, the overall argument and flow of the letter would be unbroken. His beautiful song of praise, hope, and assurance at the end of chapter 8 flows naturally into chapter 12.
This Jewish apostle to the Gentiles, however, needed to clarify some truths regarding Israel, as well as contradict some prevailing falsehoods that many early Jewish believers accepted as truth. Paul addresses the question of whether, in light of Christ's offer of salvation to all Gentiles, the Jews have been forsaken by God as a people. Did they still have a unique place or purpose in God's plan of redemption? Why, if they were God's chosen people, did they so stubbornly reject His Messiah?
With profound wisdom and holy reason, Paul demonstrates that our sovereign God will be faithful to keep all His promises and that Israel still has a future in the purposes of God.
KEYS TO THE TEXT
_Covenant:_ A covenant is a legally binding promise, agreement, or contract. Three times in the New Testament the word "covenants" is used in the plural (Gal. 4:24; Eph. 2:12). All but one of God's covenants with man are eternal and unilateral—that is, to the end of time, and God promised to accomplish something based on His own character and not on the response or actions of the promised beneficiary. The six biblical covenants include: (1) the covenant with Noah (Gen. 9:8–17); (2) the covenant with Abraham (Gen. 12:1–3); (3) the covenant of law given through Moses at Sinai (Exod. 19–31); (4) the priestly covenant (Num. 25:10–13); (5) the covenant of an eternal kingdom through David's greatest Son (2 Sam. 7:8–16); and (6) the new covenant (Jer. 31:31–34; Ezek. 37:26; cf. Heb. 8:6–13). All but the Mosaic Covenant are eternal and unilateral. It is neither, since Israel's sin abrogated it and it has been replaced by the new covenant (cf. Heb. 8:7–13).
_God's Sovereignty:_ A theological term that refers to the unlimited power of God, who has sovereign control over the affairs of nature and history. The Bible declares that God is working out His sovereign plan of redemption for the world and that the conclusion is certain. The story of redemption from Genesis to Revelation is possible only because the sovereign God loves the created world, fallen though it is, and is able to do something about it. Without the sovereign love of the Father ministered to us through the Son and the Holy Spirit, there would be no real human freedom and no hope of everlasting life. God's sovereignty is not the sovereignty of a tyrant, but the loving providence of a gracious God. The believer who doesn't live in the confidence of God's sovereignty will lack God's peace and be left to the chaos of a troubled heart. But our confident trust in the Lord will allow us to thank Him in the midst of trials because we have God's peace on duty to protect our hearts. ( _Nelson's New Illustrated Bible Dictionary_ )
UNLEASHING THE TEXT
Read 9:1–11:36, noting the key words and definitions next to the passage.
**Romans 9:1–11:36 (NKJV)**
**1** _I tell the truth in Christ, I am not lying, my conscience also bearing me witness in the Holy Spirit,_
**2** _that I have great sorrow and continual grief in my heart._
**3** _For I could wish that I myself were accursed from Christ for my brethren, my countrymen according to the flesh,_
**_accursed_** (v. 3)—The Greek word is _anathema,_ meaning "to devote to destruction in eternal hell."
**4** _who are Israelites, to whom pertain the adoption, the glory, the covenants, the giving of the law, the service of God, and the promises;_
**_glory_** (v. 4)—the Shekinah, a cloud signifying God's presence in the Holy of Holies or among His people
**_covenants_** (v. 4)—legally binding agreements or contracts, used here of the promises between God and His people
**5** _of whom are the fathers and from whom, according to the flesh, Christ came, who is over all, the eternally blessed God. Amen._
**_fathers_** (v. 5)—Israel's patriarchs
**6** _But it is not that the word of God has taken no effect. For they are not all Israel who are of Israel,_
**7** _nor are they all children because they are the seed of Abraham; but, "In Isaac your seed shall be called."_
**8** _That is, those who are the children of the flesh, these are not the children of God; but the children of the promise are counted as the seed._
**_children of the flesh_** (v. 8)—Abraham's children through Hagar and Keturah
**9** _For this is the word of promise: "At this time I will come and Sarah shall have a son."_
**10** _And not only this, but when Rebecca also had conceived by one man, even by our father Isaac_
**11** _(for the children not yet being born, nor having done any good or evil, that the purpose of God according to election might stand, not of works but of Him who calls),_
**_not of works, but of Him who calls_** (v. 11)—God chose Jacob before he was born and apart from any possible human merit to demonstrate that election is the prerogative of God.
**12** _it was said to her, "The older shall serve the younger."_
**13** _As it is written, "Jacob I have loved, but Esau I have hated."_
**14** _What shall we say then? Is there unrighteousness with God? Certainly not!_
**15** _For He says to Moses, "I will have mercy on whomever I will have mercy, and I will have compassion on whomever I will have compassion."_
**16** _So then it is not of him who wills, nor of him who runs, but of God who shows mercy._
**_who wills_** (v. 16)—Salvation is not of human initiative.
**17** _For the Scripture says to the Pharaoh, "For this very purpose I have raised you up, that I may show My power in you, and that My name may be declared in all the earth."_
**18** _Therefore He has mercy on whom He wills, and whom He wills He hardens._
**19** _You will say to me then, "Why does He still find fault? For who has resisted His will?"_
**20** _But indeed, O man, who are you to reply against God? Will the thing formed say to him who formed it, "Why have you made me like this?"_
**21** _Does not the potter have power over the clay, from the same lump to make one vessel for honor and another for dishonor?_
**22** _What if God, wanting to show His wrath and to make His power known, endured with much longsuffering the vessels of wrath prepared for destruction,_
**_vessels of wrath_** (v. 22)—those allowed to incur the just penalty for their sin
**23** _and that He might make known the riches of His glory on the vessels of mercy, which He had prepared beforehand for glory,_
**24** _even us whom He called, not of the Jews only, but also of the Gentiles?_
**25** _As He says also in Hosea: "I will call them My people, who were not My people, And her beloved, who was not beloved."_
**26** _"And it shall come to pass in the place where it was said to them, 'You are not My people,' There they shall be called sons of the living God."_
**27** _Isaiah also cries out concerning Israel: "Though the number of the children of Israel be as the sand of the sea, The remnant will be saved._
**28** _For He will finish the work and cut it short in righteousness, Because the Lord will make a short work upon the earth."_
**29** _And as Isaiah said before: "Unless the Lord of Sabaoth had left us a seed, We would have become like Sodom, And we would have been made like Gomorrah."_
**_Lord of Sabaoth_** (v. 29)—Lord of hosts or armies, a reference to God's all-encompassing sovereignty
**30** _What shall we say then? That Gentiles, who did not pursue righteousness, have attained to righteousness, even the righteousness of faith;_
**31** _but Israel, pursuing the law of righteousness, has not attained to the law of righteousness._
**32** _Why? Because they did not seek it by faith, but as it were, by the works of the law. For they stumbled at that stumbling stone._
**33** _As it is written: "Behold, I lay in Zion a stumbling stone and rock of offense, And whoever believes on Him will not be put to shame."_
**10:1** _Brethren, my heart's desire and prayer to God for Israel is that they may be saved._
**2** _For I bear them witness that they have a zeal for God, but not according to knowledge._
**_zeal for God_** (10:2)—fierce attempts to live out God's law; fervent opposition to Judaism's opponents
**3** _For they being ignorant of God's righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God._
**4** _For Christ is the end of the law for righteousness to everyone who believes._
**_Christ is the end of the law_** (v. 4)—That is, trusting in Christ is the end of the futile quest of trying to fulfill the law in hopes of being seen as righteous in the sight of God.
**5** _For Moses writes about the righteousness which is of the law, "The man who does those things shall live by them."_
**6** _But the righteousness of faith speaks in this way, "Do not say in your heart, 'Who will ascend into heaven?'" (that is, to bring Christ down from above)_
**7** _or, " 'Who will descend into the abyss?' " (that is, to bring Christ up from the dead)._
**8** _But what does it say? "The word is near you, in your mouth and in your heart" (that is, the word of faith which we preach):_
**9** _that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved._
**10** _For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation._
**_confession_** (v. 10)—literally, "to say the same thing," thus to agree with God the Father's declaration that Jesus is Savior and Lord
**11** _For the Scripture says, "Whoever believes on Him will not be put to shame."_
**12** _For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him._
**13** _For "whoever calls on the name of the Lord shall be saved."_
**14** _How then shall they call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher?_
**15** _And how shall they preach unless they are sent? As it is written: "How beautiful are the feet of those who_ _preach the gospel of peace, Who bring glad tidings of good things!"_
**16** _But they have not all obeyed the gospel. For Isaiah says, "L ORD, who has believed our report?"_
**17** _So then faith comes by hearing, and hearing by the word of God._
**_the word of God_** (v. 17)—more accurately, "the word of Christ"—that is, the message about Christ, the gospel
**18** _But I say, have they not heard? Yes indeed: "Their sound has gone out to all the earth, And their words to the ends of the world."_
**19** _But I say, did Israel not know? First Moses says: "I will provoke you to jealousy by those who are not a nation, I will move you to anger by a foolish nation."_
**20** _But Isaiah is very bold and says: "I was found by those who did not seek Me; I was made manifest to those who did not ask for Me."_
**21** _But to Israel he says: "All day long I have stretched out My hands To a disobedient and contrary people."_
**11:1** _I say then, has God cast away His people? Certainly not! For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin._
**_cast away_** (11:1)—to thrust away from one's self
**2** _God has not cast away His people whom He foreknew. Or do you not know what the Scripture says of Elijah, how he pleads with God against Israel, saying,_
**3** _"L ORD, they have killed Your prophets and torn down Your altars, and I alone am left, and they seek my life"?_
**4** _But what does the divine response say to him? "I have reserved for Myself seven thousand men who have not bowed the knee to Baal."_
**5** _Even so then, at this present time there is a remnant according to the election of grace._
**_remnant_** (v. 5)—Though the national leadership had spurned Christ, thousands of individual Jews had believed in Him (Acts 2:41 and 4:4).
**6** _And if by grace, then it is no longer of works; otherwise grace is no longer grace. But if it is of works, it is no longer grace; otherwise work is no longer work._
**7** _What then? Israel has not obtained what it seeks; but the elect have obtained it, and the rest were blinded._
**8** _Just as it is written: "God has given them a spirit of stupor, Eyes that they should not see And ears that they should not hear, To this very day."_
**9** _And David says: "Let their table become a snare and a trap, A stumbling block and a recompense to them._
**10** _Let their eyes be darkened, so that they do not see, And bow down their back always."_
**11** _I say then, have they stumbled that they should fall? Certainly not! But through their fall, to provoke them to jealousy, salvation has come to the Gentiles._
**12** _Now if their fall is riches for the world, and their failure riches for the Gentiles, how much more their fullness!_
**13** _For I speak to you Gentiles; inasmuch as I am an apostle to the Gentiles, I magnify my ministry,_
**14** _if by any means I may provoke to jealousy those who are my flesh and save some of them._
**15** _For if their being cast away is the reconciling of the world, what will their acceptance be but life from the dead?_
**16** _For if the firstfruit is holy, the lump is also holy; and if the root is holy, so are the branches._
**_root_** (v. 16)—the patriarchs Abraham, Isaac, and Jacob
**_branches_** (v. 16ff.)—the patriarch's descendants, that is, the nation of Israel
**17** _And if some of the branches were broken off, and you, being a wild olive tree, were grafted in among them, and with them became a partaker of the root and fatness of the olive tree,_
**18** _do not boast against the branches. But if you do boast, remember that you do not support the root, but the root supports you._
**19** _You will say then, "Branches were broken off that I might be grafted in."_
**20** _Well said. Because of unbelief they were broken off, and you stand by faith. Do not be haughty, but fear._
**21** _For if God did not spare the natural branches, He may not spare you either._
**22** _Therefore consider the goodness and severity of God: on those who fell, severity; but toward you, goodness, if you continue in His goodness. Otherwise you also will be cut off._
**_goodness and severity_** (v. 22)—God's attributes are not at odds.
**23** _And they also, if they do not continue in unbelief, will be grafted in, for God is able to graft them in again._
**24** _For if you were cut out of the olive tree which is wild by nature, and were grafted contrary to nature into a cultivated olive tree, how much more will these, who are natural branches, be grafted into their own olive tree?_
**25** _For I do not desire, brethren, that you should be ignorant of this mystery, lest you should be wise in your own opinion, that blindness in part has happened to Israel until the fullness of the Gentiles has come in._
**26** _And so all Israel will be saved, as it is written: "The Deliverer will come out of Zion, And He will turn away ungodliness from Jacob;_
**27** _For this is My covenant with them, When I take away their sins."_
**28** _Concerning the gospel they are enemies for your sake, but concerning the election they are beloved for the sake of the fathers._
**29** _For the gifts and the calling of God are irrevocable._
**_the gifts . . . are irrevocable_** (v. 29)—God's sovereign election of Israel is unconditional and unchangeable.
**30** _For as you were once disobedient to God, yet have now obtained mercy through their disobedience,_
**31** _even so these also have now been disobedient, that through the mercy shown you they also may obtain mercy._
**32** _For God has committed them all to disobedience, that He might have mercy on all._
**_God has committed them all to disobedience_** (v. 32)—God is not the author of sin, but He allows sinful inclinations so that He can receive glory in both mercy and judgment.
**33** _Oh, the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments and His ways past finding out!_
**34** _"For who has known the mind of the Lord? Or who has become His counselor?"_
**35** _"Or who has first given to Him And it shall be repaid to him?"_
**36** _For of Him and through Him and to Him are all things, to whom be glory forever. Amen._
1) What is Paul's tone in this passage? What is his feeling about his own people?
2) What main characters and events in Israel's history does Paul mention?
3) How does Paul argue in chapter 9 that Israel's unbelief is consistent with God's plan?
4) What agricultural imagery does Paul use in chapter 11 to demonstrate that God's setting aside of Israel is not a permanent condition?
GOING DEEPER
Notice how this passage in the Old Testament book of Jeremiah foreshadows the theme of chapters 9–—that God is sovereign and can do as He wishes with His creatures (without violating His goodness or mercy).
**Jeremiah 18:1–10 (NKJV)**
**1** _The word which came to Jeremiah from the Lord, saying:_
**2** _"Arise and go down to the potter's house, and there I will cause you to hear My words."_
**3** _Then I went down to the potter's house, and there he was, making something at the wheel._
**4** _And the vessel that he made of clay was marred in the hand of the potter; so he made it again into another vessel, as it seemed good to the potter to make._
**5** _Then the word of the Lord came to me, saying:_
**6** _"O house of Israel, can I not do with you as this potter?" says the Lord. "Look, as the clay is in the potter's hand, so are you in My hand, O house of Israel!_
**7** _The instant I speak concerning a nation and concerning a kingdom, to pluck up, to pull down, and to destroy it,_
**8** _if that nation against whom I have spoken turns from its evil, I will relent of the disaster that I thought to bring upon it._
**9** _And the instant I speak concerning a nation and concerning a kingdom, to build and to plant it,_
**10** _if it does evil in My sight so that it does not obey My voice, then I will relent concerning the good with which I said I would benefit it._
EXPLORING THE MEANING
5) What does God want Israel to know about Him? Why?
6) How does Jeremiah express the concept of God's sovereignty? Does this help you understand it better? Why?
7) Read Revelation 7:1–12. What does this suggest about the future relationship between Jews and Gentiles?
TRUTH FOR TODAY
God cannot be finished with the nation of Israel—for the obvious reason that all of His promises to her have not yet been fulfilled. If God were through with His chosen nation, His Word would be false and His integrity discredited.
REFLECTING ON THE TEXT
8) Given what you've seen in these chapters, what should be the modern-day Christian's attitude toward the Jews?
9) Paul's love and concern for his countrymen was such that he wished he could trade places with them, literally that he could go to hell so that they might be saved. How can you develop more compassion for those who do not know the good news of Jesus?
10) Paul ends his reflection on God's faithfulness and mercy with a magnificent doxology. If you were to write a four-sentence tribute of praise to God for including you in His eternal plan of salvation, what would it say?
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**9**
SUPERNATURAL LIVING
_Romans 12:1–21_
DRAWING NEAR
On a scale of 1 to 10 (1= "Virtually nonexistent"; 10= "Almost perfect"), how would you rate your church's "body life"—how people serve and relate to each other in the body of Christ? Why?
What do you wish was different in your church body?
THE CONTEXT
After pages of rich theological truth, Paul spends the balance of his letter to the Romans explaining how these doctrines should look in a believer's or congregation's daily life. This is a repeated theme in Paul's writings: Theology can _never_ be divorced from life; it _always_ has practical ramifications and implications.
Paul's description here is nothing short of supernatural living! Paul demonstrates that when believers give themselves fully to God and then, in the power of the Spirit, live out in experience what is true of them theologically in Christ, the result is staggering. Such an other-worldly life will be like a bright neon sign in a dark culture.
Christians who are living sacrifices in the service of God are godly, not worldly; transformed, not conformed; humble, not proud; helpful and generous, not stingy; unified with others, not divided from them; loving, not hypocritical and hateful; other-centered, not self-absorbed; enthusiastic, not blah; forgiving, not vengeful. To find out more about this kind of supernatural life, read on.
KEYS TO THE TEXT
_Spiritual Gifts:_ A spiritual gift is a graciously given supernaturally designed ability granted to every believer by which the Holy Spirit ministers to the body of Christ. Spiritual gifts are divine enablements for ministry that the Holy Spirit gives in some measure to all believers. They are to be completely under His control and used for the building of the church to Christ's glory. The Greek word ( _charisma_ ) emphasizes the freeness of the gift. A spiritual gift cannot be earned, pursued, or worked up. It is merely "received" through the grace of God. The categories of spiritual gifts are given in Romans 12:3–8 and 1 Corinthians 12:4–10. Each believer has one specific gift, often a combination of the various categories of gifts blended together uniquely for each Christian. Spiritual gifts are not for the exaltation of the one with the gift, but to be used in loving concern for the benefit of others in the church.
UNLEASHING THE TEXT
Read 12:1–21, noting the key words and definitions next to the passage.
**Romans 12:1–21 (NKJV)**
**1** _I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service._
**_beseech_** (v. 1)—urge, admonish, encourage; from the same Greek word that means to call alongside for help
**_therefore_** (v. 1)—Since all things were created for the glory of God (11:36), we should live our lives for the same purpose.
**_mercies of God_** (v. 1)—a phrase summarizing the gracious, extravagant work of God on behalf of sinners that Paul had discussed in chapters 1–
**_present your bodies_** (v. 1)—Believers are called to devote or offer themselves completely and unreservedly to the Lord. This is the only way we can honor God with our unredeemed bodies.
**_reasonable service_** (v. 1)—Reasonable means logical; in light of all God has done for us, this is what we should do for Him.
**2** _And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God._
**_conformed_** (v. 2)—to assume an external appearance that does not match the internal reality
**_this world_** (v. 2)—literally, "this age"; the system of beliefs and values that comprise the spirit of the times in which we live
**_transformed_** (v. 2)—The Greek term is the source of the English term "metamorphosis"; the meaning is to change in appearance (because of the inner changes that have and are taking place).
**_renewing of your mind_** (v. 2)—to be made new in the way one thinks by being saturated with the Word of God and controlled by the Spirit of God
**3** _For I say, through the grace given to me, to everyone who is among you, not to think of himself more highly than he ought to think, but to think soberly, as God has dealt to each one a measure of faith._
**_soberly_** (v. 3)—the exercise of sound judgment
**_measure of faith_** (v. 3)—the correct proportion of the spiritual gift needed to fulfill one's role in the body of Christ
**4** _For as we have many members in one body, but all the members do not have the same function,_
**_many members . . . one body_** (v. 4)—The church is a unified diversity.
**5** _so we, being many, are one body in Christ, and individually members of one another._
**6** _Having then gifts differing according to the grace that is given to us, let us use them: if prophecy, let us prophesy in proportion to our faith;_
**_prophecy_** (v. 6)—literally, "speaking forth" the truth of God, not necessarily predicting the future
**7** _or ministry, let us use it in our ministering; he who teaches, in teaching;_
**_ministry_** (v. 7)—service, from the Greek word from which we get our word "deacon"
**_teaching_** (v. 7)—the ability to interpret, clarify, systematize, and explain God's truth clearly
**8** _he who exhorts, in exhortation; he who gives, with_ _liberality; he who leads, with diligence; he who shows mercy, with cheerfulness._
**_liberality_** (v. 8)—simplicity, single-mindedness, and openhearted generosity
**_leads_** (v. 8)—literally, "standing before"
**9** _Let love be without hypocrisy. Abhor what is evil. Cling to what is good._
**10** _Be kindly affectionate to one another with brotherly love, in honor giving preference to one another;_
**_in honor giving preference_** (v. 10)—showing genuine appreciation and admiration for fellow believers by putting them first
**11** _not lagging in diligence, fervent in spirit, serving the Lord;_
**_fervent in spirit_** (v. 11)—literally, "to boil in spirit"—that is, to have an inner enthusiasm that results in productive labor
**12** _rejoicing in hope, patient in tribulation, continuing steadfastly in prayer;_
**13** _distributing to the needs of the saints, given to hospitality._
**_given to hospitality_** (v. 13)—Literally "pursuing the love of strangers"; this kind of openness and generosity should be the hallmark of believers.
**14** _Bless those who persecute you; bless and do not curse._
**15** _Rejoice with those who rejoice, and weep with those who weep._
**16** _Be of the same mind toward one another. Do not set your mind on high things, but associate with the humble. Do not be wise in your own opinion._
**17** _Repay no one evil for evil. Have regard for good things in the sight of all men._
**_Repay no one evil for evil_** (v. 17)—a ban on individual application of the "eye for an eye" principle of justice
**18** _If it is possible, as much as depends on you, live peaceably with all men._
**19** _Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, "Vengeance is Mine, I will repay," says the Lord._
**20** _Therefore "If your enemy is hungry, feed him; If he is thirsty, give him a drink; For in so doing you will heap coals of fire on his head."_
**_heap coals of fire on his head_** (v. 20)—a reference to an Egyptian custom of demonstrating shame and contrition by carrying a pan of burning coals on one's head; kindness to hateful, undeserving enemies produces shame
**21** _Do not be overcome by evil, but overcome evil with good._
1) Paul begins chapter 12 with a call for believers to give themselves fully and completely—body, mind, and will—to God. According to Paul, what is involved in doing this?
2) What evidence do you find here that the Christian life is not to be lived out in isolation?
3) What has God given each of us to use in service to others?
4) If keeping God's law is impossible (as Paul has already argued in this letter), how can you expect to live out the list of commands Paul gives in verses 9–21?
GOING DEEPER
Read 1 Peter 4:7–11 for more insight about spiritual gifts.
**1 Peter 4:7–11 (NKJV)**
**7** _But the end of all things is at hand; therefore be serious and watchful in your prayers._
**8** _And above all things have fervent love for one another, for "love will cover a multitude of sins."_
**9** _Be hospitable to one another without grumbling._
**10** _As each one has received a gift, minister it to one another, as good stewards of the manifold grace of God._
**11** _If anyone speaks, let him speak as the oracles of God. If anyone ministers, let him do it as with the ability which God supplies, that in all things God may be glorified through Jesus Christ, to whom belong the glory and the dominion forever and ever. Amen._
EXPLORING THE MEANING
5) What insights does Peter add to the doctrine of spiritual gifts presented in Romans 12? Who has the gifts and what is their purpose?
_(Verses to consider: 1 Cor. 12:1–31; Eph. 4:7–16)_
6) According to Paul, what attitudes and actions glorify God and build up the body? What attitudes and actions dishonor God and tear down the body of Christ?
7) Why is the metaphor of a human body a good one for the church?
TRUTH FOR TODAY
Supernatural living is conforming our outer lives to our inner lives, living out the redeemed, purified, and holy nature we have in Jesus Christ, becoming in practice what Christ has made us—new creations. Supernatural living is not a mystical, undefined life based on elusive good impulses and sincere intentions. It is practical living that results from conscious obedience to God's standards of righteousness, a life lived within divinely-ordained parameters. It is thinking, speaking, and acting in daily conformity with God's Word and will.
REFLECTING ON THE TEXT
8) The nineteenth-century Englishman Robert C. Chapman wrote, "Seeing that so many preach Christ and so few live Christ, I will aim to live Him." What principle or truth have you learned from this passage that you want to stop talking about and start living?
9) Based on your experiences and the evaluations of Christian leaders and friends, what do you think your spiritual gifts are? How are you using these God-given abilities to serve the body of Christ?
10) Write out a verse from chapter 12 that you will memorize and meditate upon this week to help you renew your mind.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**10**
LIVING IN THE WORLD
_Romans 13:1–14_
DRAWING NEAR
Do you think it's important to be a good citizen? Why?
Is there ever a time you would not obey the law? Explain.
THE CONTEXT
The first eleven chapters of this epistle (in particular chapters 1–) explain in marvelous detail what it means to be saved—justified by God's grace working through faith. This monumental miracle of salvation impacts every relationship of the believer. When we are saved, our initial response should be to fully present our "bodies a living sacrifice, holy, acceptable to God, which is [our] spiritual service of worship." The apostle's next concern is for having right relationships in the church with brothers and sisters in Christ, and even with enemies.
After dealing with these matters, Paul focuses on the need to have right relationships in the world. First, we must demonstrate respect for governing authorities. Second, we must love our neighbors and live holy lives that will stand out against the dark backdrop of a world without God.
KEYS TO THE TEXT
_Taxes:_ The Greek word referred specifically to taxes paid by individuals, particularly those living in a conquered nation to their foreign rulers—which makes the tax even more onerous. That tax was usually a combined income and property tax. In this context, however, Paul uses the term in the broadest possible sense to speak of all kinds of taxes. Jesus explicitly taught that taxes are to be paid—even to the pagan Roman government (Matt. 22:17–21). He also set an example by willingly paying the temple tax (Matt. 17:24–27).
_Cast Off Darkness/Put On the Lord Jesus Christ:_ This phrase summarizes sanctification, the continuing spiritual process in which those who have been saved by faith are transformed into Christ's image and likeness. The image Paul uses to describe that process is taking off and putting on clothing, which is symbolic of thoughts and behavior. Like one who removes his dirty clothes at day's end, believers must discard the filthy garments of their old, sinful lives, and dress themselves in Christ's righteousness.
UNLEASHING THE TEXT
Read 13:1–14, noting the key words and definitions next to the passage.
**Romans 13:1–14 (NKJV)**
**1** _Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God._
**_be subject_** (v. 1)—used elsewhere of a soldier's absolute obedience to his superior officer
**_no authority except from God_** (v. 1)—As the Sovereign of the universe, God established the various authority structures (government, family, church, employer).
**2** _Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves._
**_resists the ordinance of God_** (v. 2)—To disobey the government is to disregard that which has been ordained of God.
**_judgment_** (v. 2)—temporal, at the hands of the human authorities
**3** _For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same._
**_Do what is good . . . have praise_** (v. 3)—Law-abiding citizens do not normally need to fear punishment.
**4** _For he is God's minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God's minister, an avenger to execute wrath on him who practices evil._
**_God's minister . . . for good_** (v. 4)—to restrain evil and promote domestic peace
**_bear the sword_** (v. 4)—Government has a divine right to execute justice on lawbreakers, even capital punishment.
**5** _Therefore you must be subject, not only because of wrath but also for conscience' sake._
**6** _For because of this you also pay taxes, for they are God's ministers attending continually to this very thing._
**7** _Render therefore to all their due: taxes to whom taxes are due, customs to whom customs, fear to whom fear, honor to whom honor._
**_Render_** (v. 7)—A Greek word signifying the payment of something owed; not a voluntary contribution, but something due.
**_customs_** (v. 7)—tolls or taxes on goods
**8** _Owe no one anything except to love one another, for he who loves another has fulfilled the law._
**_Owe no one anything_** (v. 8)— _not_ a prohibition against borrowing altogether, but an exhortation to pay debts in a timely fashion
**_love one another_** (v. 8)—non-Christians as well as fellow believers
**9** _For the commandments, "You shall not commit adultery," "You shall not murder," "You shall not_ _steal," "You shall not bear false witness," "You shall not covet," and if there is any other commandment, are all summed up in this saying, namely, "You shall love your neighbor as yourself."_
**10** _Love does no harm to a neighbor; therefore love is the fulfillment of the law._
**11** _And do this, knowing the time, that now it is high time to awake out of sleep; for now our salvation is nearer than when we first believed._
**_sleep_** (v. 11)—spiritual lethargy and apathy; non-responsiveness to the things of God
**_our salvation is nearer_** (v. 11)—Not the element of justification (a present possession), but the time of our glorification; that is, Christ is coming back.
**12** _The night is far spent, the day is at hand. Therefore let us cast off the works of darkness, and let us put on the armor of light._
**_cast off_** (v. 12)—an exhortation to repent and get rid of sins
**13** _Let us walk properly, as in the day, not in revelry and drunkenness, not in lewdness and lust, not in strife and envy._
**_revelry_** (v. 13)—wild parties, sexual orgies, brawls, riots
**14** _But put on the Lord Jesus Christ, and make no provision for the flesh, to fulfill its lusts._
**_make no provision_** (v. 14)—Do not plan ahead or give forethought to sin.
1) What contrasts does Paul make between Christians and the world?
2) What are the God-ordained consequences of defying government authority?
3) How does Paul use some of the Ten Commandments to demonstrate that love is the fulfillment of the law?
4) What facts does Paul use to motivate the believers in Rome to forsake sin and live righteously? Why are we to submit?
GOING DEEPER
In the Old Testament the Israelites were taken captive by the Assyrian empire. Three devout Jewish men, Shadrach, Meshach, and Abed-Nego, refused to serve or worship the golden idol the king had set up. Read what happened.
**Daniel 3:14–30 (NKJV)**
**14** _Nebuchadnezzar spoke, saying to them, "Is it true, Shadrach, Meshach, and Abed-Nego, that you do not serve my gods or worship the gold image which I have set up?_
**15** _Now if you are ready at the time you hear the sound of the horn, flute, harp, lyre, and psaltery, in symphony with all kinds of music, and you fall down and worship the image which I have made, good! But if you do not worship, you shall be cast immediately into the midst of a burning fiery furnace. And who is the god who will deliver you from my hands?"_
**16** _Shadrach, Meshach, and Abed-Nego answered and said to the king, "O Nebuchadnezzar, we have no need to answer you in this matter._
**17** _If that is the case, our God whom we serve is able to deliver us from the burning fiery furnace, and He will deliver us from your hand, O king._
**18** _But if not, let it be known to you, O king, that we do not serve your gods, nor will we worship the gold image which you have set up."_
**19** _Then Nebuchadnezzar was full of fury, and the expression on his face changed toward Shadrach, Meshach, and Abed-Nego. He spoke and commanded that they heat the furnace seven times more than it was usually heated._
**20** _And he commanded certain mighty men of valor who were in his army to bind Shadrach, Meshach, and Abed-Nego, and cast them into the burning fiery furnace._
**21** _Then these men were bound in their coats, their trousers, their turbans, and their other garments, and were cast into the midst of the burning fiery furnace._
**22** _Therefore, because the king's command was urgent, and the furnace exceedingly hot, the flame of the fire killed those men who took up Shadrach, Meshach, and Abed-Nego._
**23** _And these three men, Shadrach, Meshach, and Abed-Nego, fell down bound into the midst of the burning fiery furnace._
**24** _Then King Nebuchadnezzar was astonished; and he rose in haste and spoke, saying to his counselors, "Did we not cast three men bound into the midst of the fire?" They answered and said to the king, "True, O king."_
**25** _"Look!" he answered, "I see four men loose, walking in the midst of the fire; and they are not hurt, and the form of the fourth is like the Son of God."_
**26** _Then Nebuchadnezzar went near the mouth of the burning fiery furnace and spoke, saying, "Shadrach, Meshach, and Abed-Nego, servants of the Most High God, come out, and come here." Then Shadrach, Meshach, and Abed-Nego came from the midst of the fire._
**27** _And the satraps, administrators, governors, and the king's counselors gathered together, and they saw these men on whose bodies the fire had no power; the hair of their head was not singed nor were their garments affected, and the smell of fire was not on them._
**28** _Nebuchadnezzar spoke, saying, "Blessed be the God of Shadrach, Meshach, and Abed-Nego, who sent His Angel and delivered His servants who trusted in Him, and they have frustrated the king's word, and yielded their bodies, that they should not serve nor worship any god except their own God!_
**29** _Therefore I make a decree that any people, nation, or language which speaks anything amiss against the God of Shadrach, Meshach, and Abed-Nego shall be cut in pieces, and their houses shall be made an ash heap; because there is no other God who can deliver like this."_
**30** _Then the king promoted Shadrach, Meshach, and Abed-Nego in the province of Babylon._
EXPLORING THE MEANING
5) How did the public stance of the three God-fearing Jews enhance God's reputation?
6) Read Acts 5:28–29. What exception, if any, is there to the divine command to "be subject to the governing authorities" (13:1)?
7) What does it mean to "put on the Lord Jesus Christ" (13:14)?
TRUTH FOR TODAY
Believers are to be model citizens, known as law abiding, not rabble-rousing, obedient rather than rebellious, respectful of government rather than demeaning of it. We must speak against sin, against injustice, against immorality and ungodliness with fearful dedication, but we must do it within the framework of civil law and with respect for civil authorities. We are to be a godly society, doing good and living peaceably within an ungodly society, manifesting our transformed lives so that the saving power of God is seen clearly.
REFLECTING ON THE TEXT
8) What happens to the message of the gospel and the reputation of God and His people when Christians are belligerent and disrespectful in the public sector?
9) When you consider your current set of elected officials (federal, state, and local), is it easy for you to want to subject yourself to their authority? Do you resent paying taxes to the current administration? Why or why not?
10) What if an official is corrupt, unlikable, or disreputable? What are our options as believers?
11) Write down the names of three government officials for whom you can pray this week. If you wish, write them a note expressing your support and gratitude.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**11**
THE STRONG AND THE WEAK
_Romans 14:1–15:13_
DRAWING NEAR
Paul didn't mince words when he discussed the relationships we are to have with fellow-believers. We'll see in this study how to deal with tricky situations. Have you ever been truly offended by another Christian? How did you handle it? What was the result?
THE CONTEXT
A major theme of the New Testament is that of sin's power to destroy the spiritual and moral character of the church. But outright, blatant sin is not the only danger to a church's spiritual health and unity. Certain attitudes and behavior can destroy fellowship and fruitfulness, and they have crippled the work, the witness, and the unity of countless congregations throughout church history. These problems are caused by differences between Christians over matters that are neither commanded nor forbidden in Scripture. They are matters of personal preference and historic tradition, which, when imposed on others, inevitably cause confusion, strife, ill will, abused consciences, and disharmony.
The diversity of the church displays Christ's power to bring together dissimilar people in genuine unity. Yet Satan often works to create division and threaten that unity. The threat to unity Paul addresses in this passage arises when mature (strong) believers—both Jews and Gentiles—conflict with immature (weak) believers. The strong Jewish believers understood their freedom in Christ and realized the ceremonial requirements of the Mosaic Law were no longer binding. The mature Gentiles understood that idols are not gods and, therefore, that they could eat meat that had been offered to them. But in both cases the weaker brothers' consciences were troubled, and they were even tempted to violate their consciences (a bad thing to train oneself to do), become more legalistic under the feelings of guilt, or even to sin. Knowing that the mature Jews and Gentiles would be able to understand these struggles, Paul addresses most of his comments to them.
This section is extremely helpful to all who find themselves worshiping in a congregation of diverse believers, and who struggle to accept those who are different. And isn't that all of us?
KEYS TO THE TEXT
_Idol Worship and Practices:_ The Greeks and Romans were polytheistic (worshiping many gods) and polydemonistic (believing in many evil spirits). They believed that evil spirits would try to invade human beings by attaching themselves to food before it was eaten, and that the spirits could be removed only by the food's being sacrificed to a god. The sacrifice was meant not only to gain favor with the god, but also to cleanse the meat from demonic contamination. Such decontaminated meat was offered to the gods as a sacrifice. That which was not burned on the altar was served at wicked pagan feasts. What was left was sold in the market. After conversion, believers resented eating such food bought out of idol markets, because it reminded sensitive Gentile believers of their previous pagan lives and the demonic worship. Paul and mature believers knew better than to be bothered by such food offered once to idols and then sold in the marketplace. They knew the deities didn't exist and that evil spirits did not contaminate the food. Knowledge mingled with love prevents a believer from exercising freedoms that offend weaker believers and, rather, builds the others up in truth and wisdom.
UNLEASHING THE TEXT
Read 14:1–15:13, noting the key words and definitions next to the passage.
**Romans 14:1–15:13 (NKJV)**
**1** _Receive one who is weak in the faith, but not to disputes over doubtful things._
**_weak in the faith_** (v. 1)—a reference to believers' inability to let go of the religious ceremonies and rituals of the past
**2** _For one believes he may eat all things, but he who is weak eats only vegetables._
**_only vegetables_** (v. 2)—the strict diet of conscience-stricken Jewish and Gentile believers who could not bring themselves to eat meat that had been sacrificed to idols
**3** _Let not him who eats despise him who does not eat, and let not him who does not eat judge him who eats; for God has received him._
**_despise_** (v. 3)—to have contempt or disdain
**_judge_** (v. 3)—to condemn
**4** _Who are you to judge another's servant? To his own master he stands or falls. Indeed, he will be made to stand, for God is able to make him stand._
**_To his own master he stands or falls._** (v. 4)—Christ is the ultimate judge of our motives and actions.
**5** _One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind._
**_Let each be fully convinced_** (v. 5)—In matters not dictated by Scripture, believers must follow their Spirit-led conscience (regardless of what others say or do).
**6** _He who observes the day, observes it to the Lord; and he who does not observe the day, to the Lord he does not observe it. He who eats, eats to the Lord, for he gives God thanks; and he who does not eat, to the Lord he does not eat, and gives God thanks._
**_to the Lord_** (v. 6)—Whether weak or strong in conscience, our decision must be with a view to bring honor and pleasure to God.
**7** _For none of us lives to himself, and no one dies to himself._
**8** _For if we live, we live to the Lord; and if we die, we die to the Lord. Therefore, whether we live or die, we are the Lord's._
**9** _For to this end Christ died and rose and lived again, that He might be Lord of both the dead and the living._
**10** _But why do you judge your brother? Or why do you show contempt for your brother? For we shall all stand before the judgment seat of Christ._
**_judgment seat of Christ_** (v. 10)—a future day of accounting before God's throne in which our decisions as believers will be examined
**11** _For it is written: "As I live, says the L ORD, Every knee shall bow to Me, And every tongue shall confess to God."_
**12** _So then each of us shall give account of himself to God._
**13** _Therefore let us not judge one another anymore, but rather resolve this, not to put a stumbling block or a cause to fall in our brother's way._
**_stumbling block_** (v. 13)—anything a believer does—even biblically permissible things—that causes another to sin
**14** _I know and am convinced by the Lord Jesus that there is nothing unclean of itself; but to him who considers anything to be unclean, to him it is unclean._
**15** _Yet if your brother is grieved because of your food, you are no longer walking in love. Do not destroy with your food the one for whom Christ died._
**_grieved_** (v. 15)—to cause pain or distress; that is, a weak believer seeing a stronger believer enjoy a freedom that the weak believer is convinced is sin
**_destroy_** (v. 15)—in this context, not damnation, but devastation
**16** _Therefore do not let your good be spoken of as evil;_
**_your good_** (v. 16)—one's rightful exercise of Christian liberty
**17** _for the kingdom of God is not eating and drinking, but righteousness and peace and joy in the Holy Spirit._
**_eating and drinking_** (v. 17)—trivial, nonessentials
**18** _For he who serves Christ in these things is acceptable to God and approved by men._
**_approved by men_** (v. 18)—suggests approval after careful examination; here, it suggests that our righteous behavior and love for one another would be seen as genuine by a skeptical world
**19** _Therefore let us pursue the things which make for peace and the things by which one may edify another._
**20** _Do not destroy the work of God for the sake of food. All things indeed are pure, but it is evil for the man who eats with offense._
**21** _It is good neither to eat meat nor drink wine nor do anything by which your brother stumbles or is offended or is made weak._
**22** _Do you have faith? Have it to yourself before God. Happy is he who does not condemn himself in what he approves._
**23** _But he who doubts is condemned if he eats, because he does not eat from faith; for whatever is not from faith is sin._
**15:1** _We then who are strong ought to bear with the scruples of the weak, and not to please ourselves._
**_bear_** (15:1)—literally, "to pick up and carry a weight"; the strong believer is to not just tolerate the weaker brother, but is to show consideration and love by shouldering their burdens
**2** _Let each of us please his neighbor for his good, leading to edification._
**3** _For even Christ did not please Himself; but as it is written, "The reproaches of those who reproached You fell on Me."_
**_Christ did not please Himself_** (v. 3)—Christ's goal was always to please the Father.
**4** _For whatever things were written before were written for our learning, that we through the patience and comfort of the Scriptures might have hope._
**_written before_** (v. 4)—the Old Testament Scriptures
**5** _Now may the God of patience and comfort grant you to be like-minded toward one another, according to Christ Jesus,_
**6** _that you may with one mind and one mouth glorify the God and Father of our Lord Jesus Christ._
**7** _Therefore receive one another, just as Christ also received us, to the glory of God._
**_receive_** (v. 7)—to warmly accept and embrace, even with differences
**8** _Now I say that Jesus Christ has become a servant to the circumcision for the truth of God, to confirm the promises made to the fathers,_
**9** _and that the Gentiles might glorify God for His mercy, as it is written: "For this reason I will confess to You among the Gentiles, And sing to Your name."_
**_the promises made to the fathers, and . . . the Gentiles_** (vv. 8–9)—God's plan has always been to bring both Jews and Gentiles into His kingdom.
**10** _And again he says: "Rejoice, O Gentiles, with His people!"_
**11** _And again: "Praise the L ORD, all you Gentiles! Laud Him, all you peoples!"_
**12** _And again, Isaiah says: "There shall be a root of Jesse; And He who shall rise to reign over the Gentiles, In Him the Gentiles shall hope."_
**13** _Now may the God of hope fill you with all joy and peace in believing, that you may abound in hope by the power of the Holy Spirit._
1) What was the situation in the church at Rome? Why do you think there was so much judging of each other?
2) In areas where the Scripture neither prescribes nor prohibits behavior, what counsel does Paul give for determining a course of action?
3) Behind all the different convictions and behaviors, what does Paul suggest should be our ultimate goals when we confront issues not addressed by the Word of God?
GOING DEEPER
The Roman church wasn't the only congregation in Paul's time that suffered tension due to differences in the body. Consider the apostle's instruction to the church at Corinth.
**1 Corinthians 8:1–9 (NKJV)**
**1** _Now concerning things offered to idols: We know that we all have knowledge. Knowledge puffs up, but love edifies._
**2** _And if anyone thinks that he knows anything, he knows nothing yet as he ought to know._
**3** _But if anyone loves God, this one is known by Him._
**4** _Therefore concerning the eating of things offered to idols, we know that an idol is nothing in the world, and that there is no other God but one._
**5** _For even if there are so-called gods, whether in heaven or on earth (as there are many gods and many lords),_
**6** _yet for us there is one God, the Father, of whom are all things, and we for Him; and one Lord Jesus Christ, through whom are all things, and through whom we live._
**7** _However, there is not in everyone that knowledge; for some, with consciousness of the idol, until now eat it as a thing offered to an idol; and their conscience, being weak, is defiled._
**8** _But food does not commend us to God; for neither if we eat are we the better, nor if we do not eat are we the worse._
**9** _But beware lest somehow this liberty of yours become a stumbling block to those who are weak._
EXPLORING THE MEANING
4) The struggle in the church at Corinth was over meat that had been sacrificed to idols and then was sold in the nearby marketplace. "Should a Christian eat such meat or not?"—this was the big debate. Some concluded that the meat was fine since idols are manmade and not truly divine. Others could not, in good conscience, enter into this practice. What was Paul's solution?
5) Read Galatians 5:13. We are free in Christ, but for what purpose does Paul say our freedom is to be used?
6) Consider the twelve men Jesus chose to be his closest followers (Mark 3:13–19). We know from the biblical record that these men were from a wide range of backgrounds, political persuasions, and occupations. How does this diverse group serve as a model for the kind of unity that modern-day congregations can enjoy?
TRUTH FOR TODAY
To accept one another, just as Christ also accepted us, is a sure mark of godliness, and failure to do so is just as surely a mark of carnality. Failure to accept one another in love and compassion is an affront to the Savior who accepted us. A congregation that is divisive, quarrelsome, contentious, and judgmental gives the world reason to ridicule Christ's church and to reject the One who is their only hope of salvation.
REFLECTING ON THE TEXT
7) What biblical command or principle from this passage is most helpful to you as you think about relating to others in your local church?
8) When dealing with differences between people, four things are necessary: _recognizing_ the differences; _working to understand_ the differences; _learning to appreciate_ the differences; and _wisely utilizing_ the differences. Which of these steps do you have the most difficulty with and why?
9) What particular behaviors in today's culture are okay or not okay for a Christian to participate in? Ask God to give you wisdom to honor Him and love others in all that you do.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
**12**
MINISTERING TOGETHER
_Romans 15:14–16:27_
DRAWING NEAR
Think back over the truths you studied in Romans. What is one new thing you've learned about God? About yourself?
THE CONTEXT
After completing the major doctrinal treatise of this letter, Paul now begins what amounts to an epilogue, which comprises comments about his ministry, his plans for future service, personal greetings from himself and others, and a closing benediction.
Because Paul had spoken so forcefully on so many issues to a church he did not found and had never visited, he wants to make sure he does not seem insensitive, presumptuous, or unloving. He commends them corporately for their involvement in the work of the gospel. He shares a bit of information about his own ministry and future plans. He reiterates his heart's desire to minister in Rome and to fellowship with the church there.
We get a rare glimpse into Paul's working relationships and close friendships. He mentions by name more than two dozen colleagues and coworkers. In this extended passage we sense the deep affection that Paul had for those with whom and to whom he ministered. We also get to see the sincere gratitude the apostle felt for those who had been such a help and encouragement to him in life and ministry. As the faces of redeemed and transformed Jews and Gentiles flashed through Paul's mind, he closed his epistle with a hymn of praise: "To God, alone wise, be glory through Jesus Christ forever. Amen."
KEYS TO THE TEXT
_Deacon/Deaconess /Servant:_ From a word group meaning "to serve." Originally referring to menial tasks such as waiting on tables (Acts 6:1–4), "deacon" came to denote any service in the church. Deacons serve under the leadership of elders, helping them exercise oversight in the practical matters of church life. Scripture defines no official or specific responsibilities for deacons; they are to do whatever the elders assign them or whatever spiritual ministry is necessary. Phoebe was named here as a "servant of the church." In the early church, these women cared for sick believers, the poor, strangers, and those in prison. They also instructed the women and children.
_Rome:_ The capital city of the Roman Empire. It is likely the church at Rome had been founded by a group of Jewish Christians who came there from Judea. It is possible that there had been Christians in Rome for many years, converts from among the "visitors from Rome, both Jews and proselytes" at Pentecost. The apostle Paul's first known connection with Rome was when he met Aquila and Priscilla at Corinth (Acts 18:2). They had left Rome when Claudius expelled all the Jews from the city. Some few years after meeting Aquila and Priscilla, Paul decided that he "must also see Rome." When he wrote this letter to the Christians at Rome, it was obvious how much he longed to meet them. His plan was to visit friends in the city on his way to Spain.
When he finally came to Rome, however, it was at the expense of the Roman government, due to his insistence that he be tried before Caesar concerning the charges brought against him by the Jewish leaders in Jerusalem (Acts 25:2, 11). His ministry in Rome was therefore as a prisoner, and it was during that imprisonment that he wrote the epistle to the Philippians. It was also likely that Paul wrote Ephesians, Colossians, and Philemon from Rome. According to tradition, Paul was martyred during Nero's reign (AD 54–68).
UNLEASHING THE TEXT
Read 15:14–16:27, noting the key words and definitions next to the passage.
**Romans 15:14–16:27 (NKJV)**
**14** _Now I myself am confident concerning you, my brethren, that you also are full of goodness, filled with all knowledge, able also to admonish one another._
**_knowledge_** (v. 14)—deep, intimate knowledge; doctrinal soundness
**_admonish_** (v. 14)—encourage, warn, advise; that is, a comprehensive term for counseling
**15** _Nevertheless, brethren, I have written more boldly to you on some points, as reminding you, because of the grace given to me by God,_
**16** _that I might be a minister of Jesus Christ to the Gentiles, ministering the gospel of God, that the offering of the Gentiles might be acceptable, sanctified by the Holy Spirit._
**_minister_** (v. 16)—one who serves God in some form of public worship
**17** _Therefore I have reason to glory in Christ Jesus in the things which pertain to God._
**_glory_** (v. 17)—boast; Paul never boasted of his accomplishments, only of what Christ had done through him
**18** _For I will not dare to speak of any of those things which Christ has not accomplished through me, in word and deed, to make the Gentiles obedient—_
**19** _in mighty signs and wonders, by the power of the Spirit of God, so that from Jerusalem and round about to Illyricum I have fully preached the gospel of Christ._
**_signs and wonders_** (v. 19)—miracles that authenticated true teaching and preaching
**20** _And so I have made it my aim to preach the gospel, not where Christ was named, lest I should build on another man's foundation,_
**_another man's foundation_** (v. 20)—As one with the gift of evangelism, Paul's goal and desire was to minister to those who had never heard.
**21** _but as it is written: "To whom He was not announced, they shall see; And those who have not heard shall understand."_
**22** _For this reason I also have been much hindered from coming to you._
**_hindered from coming_** (v. 22)—an ongoing, providential prevention from getting to Rome
**23** _But now no longer having a place in these parts, and having a great desire these many years to come to you,_
**24** _whenever I journey to Spain, I shall come to you. For I hope to see you on my journey, and to be helped on my way there by you, if first I may enjoy your company for a while._
**_helped on my way_** (v. 24)—Paul's tactful way of requesting assistance in his proposed evangelistic campaign to Spain
**25** _But now I am going to Jerusalem to minister to the saints._
**26** _For it pleased those from Macedonia and Achaia to make a certain contribution for the poor among the saints who are in Jerusalem._
**_contribution_** (v. 26)—The Greek word indicates sharing and is usually translated "fellowship" or "communion"; that is, minister and financial supporters are partners.
**27** _It pleased them indeed, and they are their debtors. For if the Gentiles have been partakers of their spiritual things, their duty is also to minister to them in material things._
**28** _Therefore, when I have performed this and have sealed to them this fruit, I shall go by way of you to Spain._
**29** _But I know that when I come to you, I shall come in the fullness of the blessing of the gospel of Christ._
**30** _Now I beg you, brethren, through the Lord Jesus Christ, and through the love of the Spirit, that you strive together with me in prayers to God for me,_
**31** _that I may be delivered from those in Judea who do not believe, and that my service for Jerusalem may be acceptable to the saints,_
**32** _that I may come to you with joy by the will of God, and may be refreshed together with you._
**33** _Now the God of peace be with you all. Amen._
**16:1** _I commend to you Phoebe our sister, who is a servant of the church in Cenchrea,_
**2** _that you may receive her in the Lord in a manner worthy of the saints, and assist her in whatever business she has need of you; for indeed she has been a helper of many and of myself also._
**3** _Greet Priscilla and Aquila, my fellow workers in Christ Jesus,_
**4** _who risked their own necks for my life, to whom not only I give thanks, but also all the churches of the Gentiles._
**5** _Likewise greet the church that is in their house. Greet my beloved Epaenetus, who is the firstfruits of Achaia to Christ._
**6** _Greet Mary, who labored much for us._
**_labored_** (16:6)—suggests hard work to the point of exhaustion
**7** _Greet Andronicus and Junia, my countrymen and my fellow prisoners, who are of note among the apostles, who also were in Christ before me._
**8** _Greet Amplias, my beloved in the Lord._
**9** _Greet Urbanus, our fellow worker in Christ, and Stachys, my beloved._
**10** _Greet Apelles, approved in Christ. Greet those who are of the household of Aristobulus._
**11** _Greet Herodion, my countryman. Greet those who are of the household of Narcissus who are in the Lord._
**12** _Greet Tryphena and Tryphosa, who have labored in the Lord. Greet the beloved Persis, who labored much in the Lord._
**13** _Greet Rufus, chosen in the Lord, and his mother and mine._
**14** _Greet Asyncritus, Phlegon, Hermas, Patrobas, Hermes, and the brethren who are with them._
**15** _Greet Philologus and Julia, Nereus and his sister, and Olympas, and all the saints who are with them._
**16** _Greet one another with a holy kiss. The churches of Christ greet you._
**_holy kiss_** (v. 16)—a show of affection for friends, on the forehead, cheek, or beard; carried over from Jewish tradition
**17** _Now I urge you, brethren, note those who cause divisions and offenses, contrary to the doctrine which you learned, and avoid them._
**18** _For those who are such do not serve our Lord Jesus Christ, but their own belly, and by smooth words and flattering speech deceive the hearts of the simple._
**_serve . . . their own belly_** (v. 18)—false teachers driven by self-interest and self-gratification
**19** _For your obedience has become known to all. Therefore I am glad on your behalf; but I want you to be wise in what is good, and simple concerning evil._
**20** _And the God of peace will crush Satan under your feet shortly. The grace of our Lord Jesus Christ be with you. Amen._
**21** _Timothy, my fellow worker, and Lucius, Jason, and Sosipater, my countrymen, greet you._
**22** _I, Tertius, who wrote this epistle, greet you in the Lord._
**23** _Gaius, my host and the host of the whole church, greets you. Erastus, the treasurer of the city, greets you, and Quartus, a brother._
**_the whole church_** (v. 23)—the congregation that met in Gaius' house
**24** _The grace of our Lord Jesus Christ be with you all. Amen._
**25** _Now to Him who is able to establish you according to my gospel and the preaching of Jesus Christ, according to the revelation of the mystery kept secret since the world began_
**_establish_** (v. 25)—to make firm, stable, fast; that is, being rooted in the truth of the gospel
**26** _but now made manifest, and by the prophetic Scriptures made known to all nations, according to the commandment of the everlasting God, for obedience to the faith—_
**27** _to God, alone wise, be glory through Jesus Christ forever. Amen._
1) What specifically did Paul ask his friends to pray about? What ministry plans and dreams did Paul have as he awaited his release?
2) Underline the numerous verbs and descriptive phrases Paul uses in 15:14–33 to refer to his labor for the Lord.
3) Circle the names Paul mentions in chapter 16. What insights into the work and structure of the first-century church can we glean from Paul's personal greetings?
4) In the middle of this warm benediction, Paul includes a brief, but grave, warning against harmful teachings and practices. What specific instruction does he give?
GOING DEEPER
Consider Luke's record of Paul's difficult, but much longed for, arrival at Rome in Acts 28:11–16.
**Acts 28:11–16 (NKJV)**
**11** _After three months we sailed in an Alexandrian ship whose figurehead was the Twin Brothers, which had wintered at the island._
**12** _And landing at Syracuse, we stayed three days._
**13** _From there we circled round and reached Rhegium. And after one day the south wind blew; and the next day we came to Puteoli,_
**14** _where we found brethren, and were invited to stay with them seven days. And so we went toward Rome._
**15** _And from there, when the brethren heard about us, they came to meet us as far as Appii Forum and Three Inns. When Paul saw them, he thanked God and took courage._
**16** _Now when we came to Rome, the centurion delivered the prisoners to the captain of the guard; but Paul was permitted to dwell by himself with the soldier who guarded him._
EXPLORING THE MEANING
5) How does this passage illustrate the mutual affection between Paul and his brothers and sisters in Christ at Rome?
6) Read 2 Timothy 1:16–18. For what is Onesiphorus remembered?
7) Read 2 Corinthians 8:2–4. What instructions or principles for giving does Paul share with the church at Corinth?
TRUTH FOR TODAY
The people God uses to accomplish His will are His instruments, and no Christian should take personal credit for what God does through him. No brush takes credit for a masterpiece it was used to paint. No violin takes credit for the beautiful music the musician makes with it. Neither should a Christian deny or belittle what God has done through him because that would be to deny and belittle God's own work.
REFLECTING ON THE TEXT
8) A modern-day Christian says, "Why should I get involved in ministry? That's what we pay the church staff for! And all these appeals for money—I'd like to help, but I've got bills to pay. Besides, the church seems to get by nicely whether I give or not." How do you think the believers listed in Romans 16 would respond?
9) Imagine yourself sitting among the believers at Rome as Paul's letter was being read for the first time. How might the words of this final chapter have affected you and your brothers and sisters? Why?
10) Now that you've completed this study of Romans, skim back over some of the passages. Write a short doxology of your own, expressing your thanks to God for all He has done in your life through Christ.
PERSONAL RESPONSE
Write out additional reflections, questions you may have, or a prayer.
ADDITIONAL NOTES
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"redpajama_set_name": "RedPajamaBook"
}
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\section{Introduction}
\label{sec:intro}
A Markov chain Monte Carlo (MCMC) method is a powerful numerical tool
to study a wide variety of statistical mechanical
problems\,\cite{LandauB2005,NewmanB1999}. Many kinds of non-trivial
phases and phase transitions, both in classical and quantum systems,
have been uncovered as its applications. The essence of the method is
to construct a transition kernel as a series of {\em local} kernels
acting on local state variables and to achieve eventual sampling from
an arbitrary target distribution even in a huge number of dimensions
(or degrees of freedom) of a state space.
Because next state (sample) is generated from the previous state, one
has to care correlation of samples, which can be described by an
autocorrelation function\,\cite{LandauB2005,NewmanB1999}:
\begin{equation}
A_{\hat{\mathcal O}} (t) = \frac{\langle {\mathcal O}_{i+t}{\mathcal O}_i \rangle - \langle \hat{\mathcal O} \rangle^2}{\langle \hat{\mathcal O}^2
\rangle - \langle \hat{\mathcal O} \rangle^2},
\label{A}
\end{equation}
where ${\mathcal O}_s$ is an observable, or a realization of a random
variable, at the $s$-th Monte Carlo step, the bracket $\langle \cdot
\rangle$ denotes the Monte Carlo average, and $\hat{\mathcal O}$ is an
estimator of physical quantity ${\mathcal O}$, e.g., energy or
susceptibility.
The autocorrelation function eventually becomes independent of $i$ in
Eq.~(\ref{A}) after distribution convergence (thermalization or
burn-in). In many cases, the function dumps exponentially for large
$t$:
\begin{equation}
A_{\hat{\mathcal O}}(t) \sim e^{ - t / \tau_{{\rm exp}, {\hat{\mathcal O}}}} \label{A_dump},
\end{equation}
where
\begin{equation}
\tau_{{\rm exp},{{\hat{\mathcal O}}}} = \limsup_{t \to \infty} \frac{ t }{ - \log | A_{\hat{\mathcal O}}(t)| }
\end{equation}
is the exponential autocorrelation time. Here we assume $\tau_{{\rm
exp}, {\hat{\mathcal O}}}$ is finite, which is the case for finite
size systems we study in the present paper. A thermalization period in
a Monte Carlo simulation should be, at least, several times as long as
the exponential autocorrelation time.
Meanwhile, autocorrelation reduces the effective number of Monte Carlo
samples to $M_{\rm eff} \approx M / 2 \tau_{{\rm int},{\hat{\mathcal
O}}}$, where $M$ is the number of samples in simulation and
\begin{equation}
\tau_{{\rm int}, {\hat{\mathcal O}}}= \frac{1}{2} + \sum_{t=1}^{\infty} A_{\hat{\mathcal O}} (t) \label{tau_int}
\end{equation}
is the integrated autocorrelation time. The constant $\frac{1}{2}$
comes from the discrete nature of Monte Carlo steps. Then needed
computational time is proportional to these autocorrelation times:
$\tau_{{\rm exp}, {\hat{\mathcal O}}}$ and $\tau_{{\rm int},
{\hat{\mathcal O}}}$, which may differ among estimators and update
methods.
MCMC methods can be applied to many kinds of phase transitions in
principle, but distribution-convergence rate and sampling efficiency
can become quite poor in some cases, such as critical slowing
down\,\cite{HohenbergH1977,Sokal1997}. For example, in the case of the
Ising model on the square lattice, the Metropolis algorithm for the
single spin update suffers from the rapid growth of the
autocorrelation times: $\tau_{\rm exp} \sim \tau_{\rm int} \sim \xi^z
\sim L^{z}$ with $z \approx
2.17$\,\cite{WangH1997,NightingaleB2000,MuraseI2008,LiuPS2014}, where
$L$ is the system length. Here $z$ is called the dynamic critical
exponent, which may differ between $\tau_{\rm exp}$ and $\tau_{\rm
int}$ depending on estimator. Nevertheless, the exponent is expected
to be universal among many types of updates used for MCMC
sampling\,\cite{NightingaleB2000}. This slowing down hampers accurate
or precise analysis of phase transition. It is thus crucial to devise
an efficient update method that alleviates or avoids the slowing down.
In the case of unfrustrated models, the cluster update, such as the
Swendsen-Wang\,\cite{SwendsenW1987} and the Wolff\,\cite{Wolff1989}
algorithm, reduces the dynamic critical exponents
significantly\,\cite{TamayoBK1990,CoddingtonB1992,LiuPS2014}: for
example, $z \approx 0.3$ for the Ising model in two dimensions.
The size of a cluster corresponds to the correlation length in
systems, and the flip of clusters, which can be performed with
probability one, achieves an efficient global (non-local) spin
update. Forming such an efficient cluster, however, is non-trivial or
impractical in general cases. Application of a non-local update is
thus limited to specific cases so far.
In the meantime, the worm algorithm has been one of the most versatile
techniques in the worldline quantum Monte Carlo
method\,\cite{ProkofievST1998,SyljuasenS2002}. In quantum cases, a
naive local update is often not allowed because of a certain
conservation law; for example, the total magnetization is conserved in
the $XXZ$ quantum spin model including the $XY$ and Heisenberg models
as special cases. The worm algorithm works well especially for systems
with such a conservation law. The key point of the algorithm is to
extend physical state space and allow configurations with kinks
breaking the conservation law, a pair of which is called a worm.
A whole procedure of the worm algorithm is described by the repetition
of the following processes: (i) A pair of kinks is inserted at a
randomly chosen position of a system. (ii) These kinks move on the
system in a stochastic way and update configurations. (iii) When the
kinks meet each other, the conservation law is again satisfied and an
original physical configuration is sampled. Although each worm move is
local, a non-local update is achieved in terms of the original state
space after a worm update (from insertion to removal of a worm). We
review the detail of the algorithm in Sec.~\ref{alg1}.
The worm algorithm has been proposed also for classical
systems\,\cite{ProkofievS2001}. It aims at a random walk of kinks on
sites of a lattice. Remarkably, in spite of the local nature of the
update, the worm algorithm greatly reduces the dynamic critical
exponents in the case of the Ising models and other classical
models\,\cite{DengGS2007,LiuDG2011}.
It is critical to optimize the stochastic worm update for efficient
computation. The original algorithm (hereafter called the classical
algorithm) uses the simple Metropolis algorithm; the next site is
chosen at random among nearest sites and the site shifting process is
accepted or rejected according to the distribution weights. The
detailed balance is satisfied in every worm shifting process.
Meanwhile, the efficient directed-loop algorithm was proposed in the
worldline quantum Monte Carlo method\,\cite{SyljuasenS2002}. The
directed worm does not satisfy the detailed balance for each worm
scattering process but does for one worm update from insertion to
removal. Here the worm backscattering process canceling the previous
update, which is thus a rejection process, should be averted for
efficient sampling.
In the present paper, we propose a modified worm update moving on
bonds instead of sites. The worm scattering probability is optimized
using the geometric allocation\,\cite{SuwaT2010,Suwa2014}, which is a
universal approach for probability optimization under the
non-negativity condition. One can find solutions satisfying global
balance even without detailed balance. In our modified worm update, we
minimize the worm backscattering rate and maximize the probability of
going {\em straight} on lattices for reducing the diffusive nature of
worm random walk. The reduction of the diffusive behavior is confirmed
in the probability distribution of worm position. The present
algorithm is detailed in Sec.~\ref{alg2}.
We demonstrate, in Sec.~\ref{result}, that the computational efficiency
quantified by exponential autocorrelation time and an asymptotic variance
is approximately 25 times as high as that of the classical worm for
the simple-cubic-lattice Ising model at the critical temperature. Our
algorithm is even more efficient than the Wolff algorithm. We stress
that sampling efficiency of an MCMC method should be compared in
asymptotic variance, which is discussed in Sec.~\ref{mc}. There is no
extra computational cost in the present algorithm, compared with the
classical algorithm. Our approach is applicable to generic classical
models, such as the $| \phi|^4$ model, the Potts
model\,\cite{MercadoEG2012}, the O($n$) loop
model\,\cite{JankeNS2010,LiuDG2011,ShimadaJK2014}, and the lattice
QCD\,\cite{AdamsC2003}. The present paper is summarized in
Sec.~\ref{sd}.
\section{Classical Algorithm}
\label{alg1}
We review the classical, or conventional, worm
algorithm\,\cite{ProkofievS2001} for the Ising model in this
section. Let the model be represented by $-H/T=K\sum_{\langle ij \rangle}
\sigma_i \sigma_j$, where $H$ is the Hamiltonian, $T$ is a
temperature, and $\sigma_i = \pm 1$ is the Ising spin variable at site
(vertex) $i$ of the lattice (graph). The partition function of the
canonical ensemble is expanded into the Taylor series as
\begin{align}
Z&=\sum_{\sigma_i = \pm 1} e^{K \sum_{\langle ij \rangle} \sigma_i \sigma_j}=\sum_{\sigma_i = \pm 1} \prod_{b=\langle ij \rangle} e^{K \sigma_i \sigma_j} \nonumber \\
&= \sum_{\sigma_i= \pm 1} \prod_{b=\langle ij \rangle} \cosh(K) \sum_{n_b=0,1} [\sigma_i \sigma_j \tanh K]^{n_b} \nonumber \\
&= 2^{N} \cosh(K)^{N_b^{tot}}\sum_{\{n_b\}}^{loops} [\tanh K]^{\ell} ,
\label{Z}
\end{align}
where $n_b$ denotes the bond variable on bond $b$, the identity $e^{K
\sigma_i \sigma_j}= \cosh(K) \sum_{n_b=0,1}[ \sigma_i \sigma_j \tanh
K]^{n_b}$ is used in the second line, and $N$ and $N_b^{tot}$ are
the total number of sites and bonds of a lattice, respectively. In the
last line, the sum runs over bond configurations forming loops whose
total length is denoted by $\ell \equiv \sum_{b} n_b$. The terms of
other (non-loop) configurations cancel with each others in tracing out
the spin degrees of freedom. Then the bond variables on the constraint
of loop structure are sampled by means of the MCMC method. Any set of
bond variables can be used as the initial state in a simulation as
long as the loop constraint is satisfied. We choose the state with all
bond variables deactivated ($n_b=0$ $\forall b$) as the initial one.
The worm algorithm is an efficient update method to sample under such
a constraint or a conservation law. The main idea is to extend the
sampled state space and allow configurations with kinks breaking the
constraint. Let us consider inserting two kinks, and move one of them
in a stochastic way. The moving kink is called the head of a worm and
the other is the tail of it. The classical worm algorithm is then
described as follows:
\begin{enumerate}
\item Choose a site $i_0$ at random as the starting point and set $i \leftarrow i_0$. Insert the head and tail of the worm at $i_0$. Go to step 2.
\item Choose a nearest neighbor site, $j$, at random among nearest
neighbor sites of site $i$ and shift the head of the worm from $i$
to $j$ with probability $p=[\tanh K]^{1-n_b}$, where $n_b=0,1$ is
the bond variable on $b=\langle i j \rangle$ before shifting. If the shift
is accepted, update $n_b$ as $0 \leftrightarrow 1$ and set $i
\leftarrow j$. If $j = i_0$, go to step 3. Otherwise, repeat step
2.
\item Measure observables. Go to step 1 after removing the worm with probability $p_{\rm move}$, or go to step 2 with probability $1-p_{\rm move}$.
\end{enumerate}
The probability $p_{\rm move}$ can be set an arbitrary value in
$(0,1]$: $p_{\rm move}=1/2$ in Ref.\,\citenum{ProkofievS2001}.
As for measurement, energy can be measured by the total number of
activated bonds:
\begin{align}
E &= - d \log Z / d\beta \nonumber \\
&= - N_b^{total} - N \left( \frac{1}{\tanh K} - \tanh K \right) \langle \ell \rangle, \label{e}
\end{align}
where $\beta=1/T$ is the inverse temperature. The correlation
function, $G_{ij} \equiv {\rm tr} [\sigma_i \sigma_j e^{-\beta H}] /
Z$, can be calculated by $\langle N_{ij} \rangle / \langle N_j \rangle$, where
$N_{ij}$ is the number of times when the head is at $i$ and the tail
is at $j$ in the interval between measurements (at above Step 3), and
$N_j$ is the number of times when both the head and tail are at $j$ at
Step 3. Susceptibility, $\chi \equiv \frac{\beta}{N}\sum_{ij}G_{ij}$,
can be calculated by $\beta \langle \ell_{\rm worm} \rangle$, where $\ell_{\rm
worm}$ is the worm length, or the total number of worm shifting
processes (Step 2) in the interval between measurements. It is
straightforward to calculate the Fourier transformed (or the Fourier
series of) correlation function and the correlation length by use of
the moment method\,\cite{SuwaT2015}, where one only needs to consider
a phase factor depending on worm position.
In several cases, the worm update produces a much smaller dynamic
critical exponent than a naive local spin update does: in
Ref.\,\citenum{DengGS2007}, $z \approx 0.379 $ and $0.174$ for the
Ising model on the square and the cubic lattices, respectively. The
worm algorithm is efficient not only for the Ising model but for many
fundamental physical systems: the Potts model\,\cite{MercadoEG2012},
the $| \phi |^4$ model, the O($n$) loop
model\,\cite{JankeNS2010,LiuDG2011,ShimadaJK2014}, the Lattice
QCD\,\cite{AdamsC2003}, and so on.
Meanwhile, one can use the worm algorithm for dual variables on a dual
lattice\,\cite{ProkofievS2001,HitchcockSA2004,Wang2005,RakalaD2017}. The
dual worm algorithm samples domain walls of original spin variables;
in other words, it samples ``unsatisfied'' bonds increasing
energy. While the classical worm explained above is formulated in the
high-temperature expansion, the dual worm is in the low-temperature
expansion with dual inverse temperature $\beta' = - \frac{1}{2} \ln
\tanh \beta$\,\cite{KramersW1941,Kogut1979}. One of the advantages of
the dual worm is that it is applicable also to frustrated cases while
the original worm suffers from the negative sign
problem\,\cite{Wang2005,RakalaD2017}.
Contrary to the high-temperature expansion, dual variables have the
constraint that the winding numbers of unsatisfied bonds are even in
the case of the periodic boundary condition. If the constraint is
ignored, nevertheless, the free energy difference between the periodic
and the antiperiodic boundaries can be calculated from the winding
number histogram\,\cite{HitchcockSA2004}: $e^{-\beta ( F_{\rm AP} -
F_{\rm P} )} = Z_{\rm AP} / Z_{\rm P} = \langle N_{\rm AP} \rangle / \langle
N_{\rm P} \rangle$, where $F_{\rm AP}$ and $F_{\rm P}$ are the free
energies, $Z_{\rm AP}$ and $Z_{\rm P}$ are the partition functions,
and $N_{\rm AP}$ and $N_{\rm P}$ are the numbers of times when the
winding numbers are even (odd) in one (the other) direction, and both
are even, respectively. Since the square lattice has the self-duality,
the dual worm update at the critical temperature is exactly the same
with the original update except for the winding number constraint. The
free energy difference is then available in both the formalisms.
\section{Present Approach}
\label{alg2}
We present a modified directed-worm update in this section. The worm
backscattering (rejection) probability is minimized using the
geometric allocation approach, and our algorithm is indeed free from
rejection at the critical temperature of the Ising model on the square
and the cubic lattices. As a result, the random walk behavior of the
kink is successfully suppressed, which is evident in the probability
distribution of worm position. We also explain how to measure relevant
physical quantities, such as energy and susceptibility.
\subsection{Worm on Bonds}
\label{bw}
We adopt the same representation of the partition function
[Eq.~(\ref{Z})] with the classical worm algorithm. Our goal is to
sample bond variables $\{n_b\}$ efficiently under the loop
constraint. We insert a worm, namely a pair of kinks, at a bond of a
lattice, and move the head, namely one of the pair, in a stochastic
way. When the head meets a site, it scatters onto another (or possibly
same) bond with a certain probability. This scattering process
continues until the head comes back to the tail, namely the other of
the pair.
In the case of the square lattice, a typical example of configurations
with the present worm after several scattering processes is
illustrated in Fig.~\ref{fig:example}. In our algorithm, the head and
tail breaking the loop constraint are located at the {\em center} of
bonds, or edges, of a lattice. As a result, bond variables can take
$n_b=0, \frac{1}{2}$, or $1$. The head has a moving direction in the
same sense of the directed-loop algorithm\,\cite{SyljuasenS2002}.
\begin{figure}
\begin{center}
\includegraphics[width=5cm]{fig-1.jpg}
\caption{Example of a configuration with the present worm on the
square lattice. The solid lines show activated bonds with $n_b=1$
and the broken lines show deactivated bonds with $n_b=0$. The solid
circles indicate the head ($h$) and the tail ($t$) of the worm
breaking the loop constraint of activated bonds.}
\label{fig:example}
\end{center}
\end{figure}
Let us move the head in Fig.~\ref{fig:example} upward and scatter it
around the next vertex. The head is going to scatter onto a bond
connecting to the vertex, which we define as a worm scattering
process. The four candidate states after scattering are shown as $b$,
$c$, $d$, and $e$ in Fig.~\ref{fig:ws}. The next state is chosen with
a certain (optimized) probability, which we will discuss in
Sec.~\ref{go}. After the worm scattering, the bond variables are
updated as shown in Fig.~\ref{fig:ws}; the halves of bonds are updated
($n_b=0,\frac{1}{2},1$) since the kink is assumed at the center of a
bond. We repeat this worm scattering process until the head comes back
to the tail.
The whole algorithm of the present method is described as follows:
\begin{enumerate}
\item Choose a bond $b_0$ at random as a starting point and $b
\leftarrow b_0$. Insert the head and tail of the worm at
$b_0$. Choose a moving direction at random. Go to step 2.
\item Choose the next bond $c$ according to a set of probabilities (optimized using the geometric allocation). If $b \neq c$, update bond variables $n_b$ and $n_c$, and set $b \leftarrow c$. if $b = b_0$, go to step 3. Otherwise, repeat step 2.
\item Measure observables and go to step 1 after removing the worm.
\end{enumerate}
Compared with the classical worm algorithm, we simply set $p_{\rm move}=1$ in our procedure.
As an advantage of our approach, it is straightforward to optimize the
worm scattering probability and improve efficiency. In the MCMC
method, transition probabilities are set under global balance. The
worm shifting probability at a site, in the classical algorithm, is
determined by other shifting processes at the nearest neighboring
sites. The processes at the nearest neighboring sites are then
affected by the next nearest sites. Thus, it is non-trivial to write
down the balance condition in a closed form. The Metropolis scheme
reduces the condition to a local form, but no room for optimization is
left except for increasing candidate states. In our approach, on the
other hand, the balance condition of the worm scattering process is
represented in a closed form. This simple structure of the balance
condition leaves much room for optimization we discuss in the next
subsection, compared to the previous directed-loop
approaches\,\cite{HitchcockSA2004}.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fig-2.jpg}
\caption{Example of the worm scattering process on the square lattice
in the present approach. The solid circles show the worm head, and
the arrows show the direction of the head. When the head meets a
vertex (state $a$), the next state is chosen with a certain
probability between $b$, $c$, $d$, and $e$.}
\label{fig:ws}
\end{center}
\end{figure}
\subsection{Geometric Optimization}
\label{go}
We detail the transition-probability optimization in the geometric
allocation approach\,\cite{SuwaT2010,Suwa2014}. To satisfy the global
balance or the detailed balance, raw stochastic flow is allocated in a
geometric way instead of solving simultaneous algebraic equations. Let
us denote a raw stochastic flow from state $i$ to $j$ as
$v_{ij}:=\pi_i \, p_{i\to j}$, where $\pi_i$ is the weight, or the
measure, of state $i$ apart from the normalization of a target
distribution, and $p_{i \to j}$ is the transition probability from $i$
to $j$. The law of probability conservation and the global balance
condition are expressed by
\begin{equation}
\pi_i = \sum_{j=1}^n v_{ij} \qquad \forall i
\label{pc}
\end{equation}
and
\begin{equation}
\pi_j = \sum_{i=1}^n v_{ij} \qquad \forall j ,
\label{bc}
\end{equation}
respectively, where $n$ is the number of candidate states. The average
rejection (worm backscattering) rate is written as $\sum_i v_{ii} /
\sum_i \pi_i$.
We optimize the flows so that the average rejection rate is
minimized. To reduce further the worm diffusive behavior, we maximize
the average probability that the worm head goes {\em straight} on the
square or the cubic lattice under the condition of rejection
minimization. This preference at local transition is expected to
reduce the variance of the worm length, namely the variance of return
time for the head to come back to the same position.
\begin{figure}[t]
\begin{center}
\includegraphics[width=8cm]{fig-3.jpg}
\caption{(Color online) Geometric allocation for one case of the
square lattice. In the upper panel, the solid (broken) lines show
the activated (deactivated) bonds, and the solid circles show the
worm head. In the lower panel, the weight, or the measure, of each
state is denoted by $\pi_i$ ($i=1,2,3,4$) apart from the
normalization of the target distribution, and allocated raw
stochastic flow from $i$ to $j$ is denoted by $v_{ij}$. Although the
ratio of the weights, $\pi_4 / \pi_1$, varies according to
temperature in a simulation, it is possible to allocate flows in a
similar way for $T < 2 / \ln 2$.}
\label{fig:go1}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fig-4.jpg}
\caption{(Color online) Geometric allocation for the other case of the
square lattice. The notations are the same with Fig.~\ref{fig:go1}.}
\label{fig:go2}
\end{center}
\end{figure}
In our approach, raw stochastic flows are optimized using the
geometric allocation. The optimized flows in the case of the square
lattice are illustrated in Figs.~\ref{fig:go1} and~\ref{fig:go2}. It
is easy to confirm that Eqs.~(\ref{pc}) and~(\ref{bc}) are both
satisfied: the area of each weight (color) is conserved, which is
nothing but the probability conservation, and the whole {\em box}
shape is intact after the allocation, which ensures the global
balance. As for the probability that the head goes straight, the value
$v_{12}+v_{21}+v_{34}+v_{43}$ is maximized. The ratio of the weights,
$\pi_4 / \pi_1=\tanh K$, varies according to temperature in
simulation. The rejection free condition is, in general, $\pi_1 \leq
\sum_{i=2}^n \pi_i$: that is, $\tanh K \geq 1/3 \iff T \leq 2 / \ln 2
\simeq 2.88539$ in the case of Fig.~\ref{fig:go1}. This condition is
always satisfied in the case of Fig.~\ref{fig:go2}. Thus, our update
is rejection free at the critical temperature, $T_{\rm
c}=2/\ln(1+\sqrt{2}) \simeq 2.269$\,\cite{KramersW1941}.
In our implementation, we calculate all transition probabilities $p_{i
\to j}= v_{ij} / \pi_i$ before sampling, and prepare a look-up table
storing probabilities. We then choose the next state at each worm
scattering by using the Walker's method of alias in $O(1)$
computational time\,\cite{FukuiT2009,HoritaST2017}. The advantage of
this method is that the computational cost does not increase with the
number of candidates $n$, while the binary search does in $O(\log
n)$. There is no extra computational cost in our algorithm, compared
with the classical worm algorithm.
We choose a set of flows satisfying detailed balance, which is
expressed by $v_{ij}=v_{ji}$ in the allocation approach. It is easy to
find many, or actually infinite, solutions to satisfy the required
conditions [Eqs.~(\ref{pc}) and~(\ref{bc})] thanks to the geometric
picture. Even solutions without detailed balance can be readily
found\,\cite{SuwaT2010}, but the performance is not different much as
far as we checked for the Ising model, compared with the present
choice of flows.
\begin{figure}
\begin{center}
\includegraphics[width=8.2cm]{fig-5.jpg}
\caption{(Color online) Geometric allocations for the simple-cubic-lattice
case in three dimensions. The six candidate states are indexed so
that (1,\,2), (3,\,4), and (5,\,6) are pairs of states before and
after worm going straight in a similar way to the square-lattice
case. It is possible to allocate flows likewise for $T <
2/\ln(3/2)$.}
\label{fig:go3}
\end{center}
\end{figure}
In the simple-cubic-lattice case, we choose a set of flows
as illustrated in Fig.~\ref{fig:go3}. The six candidate states are
indexed so that (1,\,2), (3,\,4), and (5,\,6) are pairs of states
where the worm head is on a bond in the same direction; that is, the
pairs are states before and after worm going straight in a similar way
to the square-lattice case. All possible cases of the simple cubic lattice
are shown in Fig.~\ref{fig:go3}. The rejection-free condition is
satisfied for $T \leq 2/\ln(3/2) \simeq 4.9326$ including the critical
temperature, $T_{\rm c} \approx 4.511$\,\cite{DengB2003}. In addition
to the conditions of the rejection minimization and the
going-straight-probability maximization, we here put a further
condition to find the unique solution; the variance of the going
straight flow, which is $\sum_{k=1,3,5} ( v_{k \, k+1} -
\overline{v})^2$, where $\overline{v}= \frac{1}{3} \sum_{k=1,3,5} v_{k
\, k+1}$, is minimized. Other solutions, nevertheless, are expected
to work as well as our choice as long as the rejection rate is
minimized and the going straight flow is maximized. Our worm update
optimized by the geometric allocation can be generalized to many
classical models, such as the $|\phi|^4$ model, the Potts model, and
the O($n$) loop model. It is promising to improve computational
efficiency, in general, as well as the case of the Ising model in the
present paper.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig-6.eps}
\caption{(Color online) Probability distribution of the distance
between two kinks of the worm (head and tail) for the square-lattice
model with $L=128$ in the classical (upper panel) and the present
(lower panel) approaches. The distance was measured after 256 worm
shifting or scattering processes. The contours show the coordinates
where $P(x,y)=0.5, 1.0, 1.5, 2.0$, and $2.5 \times 10^{-4}$. Because
the worm is removed when the two kinks meet each other, the
distribution is lowered around the center, which is more significant
in the case of the classical algorithm. Removed worms are not shown
here but counted in the distribution normalization.}
\label{fig:P}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig-7.eps}
\caption{(Color online) Tails of the probability distributions of the
distance between two kinks for the square-lattice model with $L=128$
in the classical (open) and the present (solid) algorithms after 64
(triangles), 128 (squares), and 256 (circles) worm shifting or
scattering processes. The distribution was measured at $r=|{\mathbf
r}|$, where ${\mathbf r = (x,y)}$ and $|x|=|y|$. The tails are
fitted to Gaussian distributions: $ P(r) \propto e^{-r^2 / 2
\sigma^2 }$, where $\sigma^2$ is a parameter. The inset shows the
linear scaling of the estimated parameter in the case of the
classical (circles) and the present (squares) algorithms as a
function of the number of worm shifting or scattering processes
($s$). The variance in the present algorithm is approximately 6
times as large as that in the classical algorithm.}
\label{fig:P_r}
\end{center}
\end{figure}
\subsection{Reduction of Diffusive Behavior}
\label{dist}
We demonstrate here that the present worm algorithm indeed reduces the
diffusive behavior of worm position. Figure~\ref{fig:P} shows the
probability distribution of the distance between two kinks (the head
and tail of the worm) for the square-lattice case with $L=128$ after
256 worm shifting or scattering processes since the insertion. The
present worm exhibits the much broader distribution than the classical
worm does. Worms removed at $(x,y)=(0,0)$ before 256 worm processes
are not shown in Fig.~\ref{fig:P} but counted in the distribution
normalization.
The tail of the distribution of kink distance is well approximated by
a Gaussian distribution. We estimate the variance of the Gaussian
distribution after 64, 128, and 256 worm shifting or scattering
processes for $L=128$ on the square lattice, and find the linear
growth of the variance as a function of the number of processes, as
shown in Fig.~\ref{fig:P_r}: $\sigma^2 \propto s$, where $\sigma^2$ is
the estimated variance and $s$ is the number of processes. In
Fig.~\ref{fig:P_r}, although some faster decay is seen in the
distribution after 64 scattering processes of the present worm, the
tails of the distributions after 128 and 256 processes are well fitted
to the Gaussian form until longer distance. The distribution of
distance in the present algorithm is much broader: the variance in the
present approach grows approximately 6 times as fast as that in the
classical approach does, as a function of the number of worm shifting
or scattering processes. These observations clearly show that the
present method successfully reduces the diffusive nature of the worm
random walk, which is expected to make sampling more efficient.
\subsection{Estimators}
\label{obs}
The present worm can measure all physical quantities accessible by the
classical worm. Energy can be calculated by the same
formula~(\ref{e}). Meanwhile, quantities related to worm position are
measured in a different way. We explain how to measure the spin
correlation function and the susceptibility here.
In the classical worm algorithm, the sampled configuration space is
extended including configurations with two kinks on sites of a
lattice. Then the number of times when the two kinks are at sites $i$
and $j$ naturally becomes an estimator of the spin correlation between
$i$ and $j$, as mentioned in Sec.~\ref{alg1}. On the other hand, the
present worm never visits sites, so we need a different estimator for
measuring the correlation.
Let us here consider a {\it virtual} Monte Carlo step to shift two
kinks from bonds to sites. There are four choices of sites because
each bond connects two sites. Let us then choose a pair of sites at
random and consider the Metropolis algorithm for accepting or
rejecting the virtual shift. Since we assume the kink is at the center
of a bond in the present algorithm, the weight of configurations will
be changed by this kink shift according to the change in $\ell =
\sum_b n_b$. If this virtual shift would be accepted, we would count
one for measuring the corresponding spin correlation in a similar way
to the classical worm algorithm. Thus, we can use the acceptance
probability as the reweighting factor from bond-kink configurations to
site-kink configurations. To calculate the susceptibility, we simply
need to sum up the reweighting factor during the one-time worm update
from insertion to removal.
To sum up the argument of the above virtual shift, the susceptibility
estimator in the present algorithm is expressed by
\begin{equation}
\hat{\chi} = \frac{2 \beta}{4z} \sum_{\rm worm} f_{\rm rew}, \label{chi}
\end{equation}
where $\beta$ is the inverse temperature, $z$ is the coordination
number (the number of bonds connecting to a site, which is four on the
square lattice and six on the cubic lattice),
\begin{equation}
f_{\rm rew} = \left( s + \frac{1}{s} \right) f_h \label{f-rew}
\end{equation}
is the reweighting factor after a worm scattering process, and $s
\equiv \sqrt{\tanh K}$. In Eq.~(\ref{f-rew}), $f_h$ is $2/s$ if the
head is on an activated bond, $2s$ on a deactivated bond, and
$s+\frac{1}{s}$ on a half-activated and half-deactivated bond. In
other words, $f_h$ takes $2/s$ or $2s$ if the head comes back to the
tail, $s+\frac{1}{s}$ otherwise. The summation in Eq.~(\ref{chi})
means that $f_{\rm rew}$ is calculated after each worm scattering
process and summed in the interval between measurements. Note that
\begin{equation}
\hat{\chi} \sim \frac{ \beta }{ 2z } \left( s + \frac{1}{s} \right)^2 \ell_{\rm worm} ,
\label{chi-sim-ell}
\end{equation}
where $\ell_{\rm worm}$ is the worm length, because $f_h$ takes
$s+\frac{1}{s}$ except for the case where the head comes back to the
tail.
Regarding the prefactor in Eq.~(\ref{chi}), we assume the present worm
has the extra weight, $1/2$, for accepting the worm insertion and
removal with probability one, and need to consider it for estimators
related to the extended configuration. The value of the extra weight
comes from the fact that there are two possible directions for the
worm head to go in. Then, in the susceptibility estimator~(\ref{chi}),
the reweighting factor is multiplied by two, which is the inverse of
the extra weight the worm carries. In addition, it is divided by four
because we need the average of four reweighting factors, and divided
by the coordination number because of multiple counts caused by the
virtual shift from bonds to sites. It is straightforward to calculate
other quantities, such as the Fourier transformed correlation function
and the correlation length. Note that while the extra weight worm
carries is two in the case of the Ising model, it depends on model and
worm variant used in simulation.
\subsection{Possible Bias}
\label{cwa}
Before closing this section on the methodology, we note possible bias
caused by fixed-time computation of the worm algorithm as well as the
Wolff cluster algorithm\,\cite{Wolff1989}. In these methods,
computational time cost in a Monte Carlo step fluctuates depending on
worm length, or cluster size. The mean worm length, which corresponds
to susceptibility, is usually a decreasing function of
temperature. Energy, on the other hand, is an increasing
function. Thus, when a configuration is at a higher energy, the
computational time spent at the subsequent Monte Carlo step will be
shorter on average. As a result, given a simulation time, say, one
hour, high-energy configurations tend to be sampled more times than
low-energy configurations. Therefore, such a fixed-time computation
causes bias. For example, if parallel simulations are run using
different random numbers and the average among them is naively
calculated after some run-time, the estimator has a bias. To avoid it,
we have to fix the number of Monte Carlo steps instead of run-time and
calculate the average among runs of the same number of Monte Carlo
steps. The bias we discuss here is caused in quantum Monte Carlo
simulations\,\cite{ProkofievST1998,SyljuasenS2002} as well as
classical simulations. Although the systematic error might be
negligible compared to statistical error, our simulations are
carefully done avoiding the bias.
\section{How to Compare MCMC Samplers}
\label{mc}
We discuss how to quantify the computational efficiency of an MCMC
sampler. There are two points to care\,\cite{Suwa2014}: thermalization
(namely distribution convergence or burn-in) and sampling
efficiency. On the former, since Monte Carlo samples are taken after
thermalization process, faster distribution convergence to a target
one allows for sampling from an earlier Monte Carlo step; on the
latter, more efficient sampling yields a smaller statistical
error. The mean squared error of an estimator in an MCMC method is
proportional to the inverse of the number of samples (Monte Carlo
steps) according to the central limit
theorem\,\cite{RobertC2004}. Efficiency then should be compared in the
prefactor of the scaling, that is, the asymptotic
variance\,\cite{Suwa2014}. We explain here how to measure these
quantities.
Thermalization rate is quantified by exponential autocorrelation
time. An autocorrelation function exponentially decays in large Monte
Carlo steps as shown in Eq.~(\ref{A_dump}), which is the case for
finite-size systems we study in the present paper. We calculate the
function by running independent simulations and estimate the
exponential autocorrelation time as a fitting parameter. The error of
an estimate is calculated by
bootstrapping\,\cite{DavisonH1997,SenSS2015}. We simply choose a
single exponential function as the fitting function.
In the worm algorithm, we consider a Monte Carlo step in a simulation
to be a one-time worm update. In other words, the number of Monte
Carlo steps is equal to the number of times when the head comes back
to the tail. Here, one Monte Carlo step should be renormalized in
units of the number of sites. Then an autocorrelation time
($\tau'_{\rm exp}$) estimated by regression is rescaled:
\begin{align}
\tau_{\rm exp} = \tau'_{\rm exp} \frac{ \langle \ell_{\rm worm} \rangle }{N} ,
\label{tau_exp_worm}
\end{align}
where $ \langle \ell_{\rm worm} \rangle$ is the mean worm length, and $N$ is
the number of sites. The mean worm length differs between the
classical and the present algorithms since the sampled space is
extended in different manners.
Sampling efficiency is, on the other hand, related to an integrated
autocorrelation time. It can be estimated by
\begin{equation}
\tau_{\rm int}' = \frac{\sigma^2}{2 \bar{\sigma}^2} ,
\label{tau_int_est}
\end{equation}
where $\sigma^2$ is a mean squared error, namely the square of a
statistical error, calculated by the binning analysis using a much
larger bin size than the exponential autocorrelation time, and
$\bar{\sigma}^2$ is calculated without binning. The above
estimator~(\ref{tau_int_est}) will give an exact integrated
autocorrelation time in the large Monte-Carlo-step
limit\,\cite{LandauB2005}. In a similar way to
Eq.~(\ref{tau_exp_worm}), it is also rescaled as
\begin{align}
\tau_{\rm int} = \tau'_{\rm int} \frac{ \langle \ell_{\rm worm} \rangle }{N}
\label{tau_int_worm}
\end{align}
for comparison.
Although the integrated autocorrelation time is useful to study Monte
Carlo dynamics, we stress that sampling efficiency should be compared
in asymptotic variance that is the prefactor of the scaling:
\begin{equation}
\sigma_{\hat{\mathcal O}}^2 \approx \frac{ v_{{\rm asymp},{\hat{\mathcal O}}} }{M} \label{clt},
\end{equation}
where $\sigma_{\hat{\mathcal O}}^2$ is the mean squared error of an
estimator $\hat{\mathcal O}$, $v_{{\rm asymp}, {\hat{\mathcal O}}}$ is
the asymptotic variance of $\hat{\mathcal O}$, and $M$ is the number
of Monte Carlo steps used for sampling. Here we assume $\hat{\mathcal
O}$ is an unbiased estimator of a physical quantity ${\mathcal O}$:
$\langle \hat{\mathcal O} \rangle = {\mathcal O}$. Then the asymptotic
variance is represented by:
\begin{equation}
v_{{\rm asymp},{\hat{\mathcal O}}} = 2 \tau_{{\rm int}, {\hat{\mathcal O}}} v_{\hat{{\mathcal O}}} \label{v_asymp},
\end{equation}
where $v_{\hat{\mathcal O}}= \langle \hat{\mathcal O}^2 \rangle - \langle
\hat{\mathcal O} \rangle ^2$ is the variance of $\hat{\mathcal O}$. In
other words, if $M$ Monte Carlo samples are all independent with each
others, the mean squared error of $\hat{\mathcal O}$ is estimated to
be $\sigma_{\hat{\mathcal O}}^2 \approx v_{\hat{\mathcal O}} / M$. In
actual MCMC simulations, samples are correlated, so $ v_{{\rm
asymp},{\hat{\mathcal O}}} \neq v_{\hat{\mathcal O}}$; the
effective number of samples are reduced to $M_{\rm eff} \approx M / 2
\tau_{\rm int, {\hat{\mathcal O}}}$. Note $2\tau_{\rm int,
{\hat{\mathcal O}}}>1$ in most cases: $2\tau'_{\rm int,
{\hat{\mathcal O}}}>1$ in the present paper. Because different
estimators may have different variances, an integrated autocorrelation
time may not be adequate for comparison of sampling efficiency between
MCMC methods. We, therefore, use asymptotic variances to compare MCMC
samplers.
In the present paper, according to Eqs.~(\ref{tau_int_est}),
(\ref{tau_int_worm}), (\ref{clt}) and~(\ref{v_asymp}), we estimate the
variances by using the jackknife method\,\cite{Berg2004} in the
following ways:
\begin{align}
v_{{\rm asymp},\hat{\mathcal O}} &= M \frac{\sigma_{\hat{\mathcal O}}^2}{\mu_{\hat{\mathcal O}}^2} \frac{ \langle \ell_{\rm worm} \rangle }{N} \label{v_asymp_est}\\
v_{\hat{\mathcal O}} &= M \frac{\bar{\sigma}_{\hat{\mathcal O}}^2}{\mu_{\hat{\mathcal O}}^2}, \label{v_obs_est}
\end{align}
where $M$ is the number of Monte Carlo steps used for sampling,
$\mu_{\hat{\mathcal O}}$ is the average, and $\sigma_{\hat{\mathcal
O}}^2$ and $\bar{\sigma}_{\hat{\mathcal O}}^2$ are the mean
squared errors of an estimator $\hat{\mathcal O}$ with and without
binning, respectively. The squared coefficient of variation
($\sigma^2/\mu^2$) is used here for avoiding the dependence of the
definition of estimator: for example, an asymptotic variance estimated
by Eq.~(\ref{v_asymp_est}) is the same for total energy and energy
density. Note that the rescaling factor $\langle \ell_{\rm worm} \rangle / N$
in Eqs.~(\ref{tau_exp_worm}), (\ref{tau_int_worm}), and
(\ref{v_asymp_est}) is necessary for the worm and also the Wolff
algorithms, but not for the single spin update.
\section{Results}
\label{result}
We investigate the performance of our worm algorithm for the Ising
model on the simple cubic lattice, focusing on the critical
slowing down at the transition temperature.
We compare the present algorithm to the classical worm
algorithm\,\cite{ProkofievS2001} and the Wolff cluster
algorithm\,\cite{Wolff1989}.
The ensemble used in simulations is represented by the Boltzmann
distribution at the critical temperature: $1/T_{\rm c} \approx
0.22165455$\,\cite{DengB2003}. The boundary condition is periodic in
all the spatial directions. We optimize the worm scattering
probability as illustrated in Fig.~\ref{fig:go3}. More than $2^{24}$
Monte Carlo samples were taken, in total, after $2^{16}$
thermalization steps.
For fair comparison, autocorrelation times are rescaled in units of
the number of sites as shown in Eqs.~(\ref{tau_exp_worm})
and~(\ref{tau_int_worm}). In the case of the Wolff algorithm, we
rescale integrated autocorrelation time by using cluster size:
$\tau_{\rm int} = \tau'_{\rm int} \langle \ell_{\rm cl} \rangle / N$, where
$\tau'_{\rm int}$ is estimated using Eq.~(\ref{tau_int_est}), $\langle
\ell_{\rm cl} \rangle$ is the mean cluster size, and $N$ is the number of
sites. The mean worm length of the classical algorithm is proportional
to the susceptibility: $\langle \ell_{\rm classical worm} \rangle = \chi /
\beta \propto L^{\gamma/\nu}$, where $\gamma$ and $\nu$ are the
critical exponents of the susceptibility and the correlation length,
respectively\,\cite{LandauB2005}. We found the relation of the worm
length between the present and the classical algorithms: $\langle
\ell_{\rm present \ worm} \rangle \approx 1.765 \langle \ell_{\rm classical
\ worm} \rangle$ for $L \geq 16$.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fig-8.eps}
\caption{(Color online) Integrated autocorrelation time (top panel),
variance (middle panel), and asymptotic variance (bottom panel) of
the energy estimator for the Ising model on the simple cubic lattice,
calculated by the Wolff (triangles), the classical worm (circles),
or the present worm algorithm (squares). The dynamic critical
exponents are estimated to be $z \approx 0.28$, $0.31$, and $0.27$
for $\tau_{{\rm int}, \hat{E}}$, $z \approx -2.75$ in common for
$v_{\hat{E}}$, and $z \approx -2.44$, $-2.35$, and $-2.46$ for
$v_{{\rm asymp}, \hat{E}}$, in the use of the Wolff, the classical
worm, and the present worm algorithms, respectively. The inset of
the bottom panel shows the asymptotic variances of the classical
worm (diamonds) and the Wolff algorithm (pentagons) in units of the
asymptotic variance of the present algorithm, which are
approximately 27 and 2.2 for relatively large system sizes,
respectively.}
\label{fig:e-3D}
\end{center}
\end{figure}
The integrated autocorrelation time, the variance, and the asymptotic
variance of the energy estimator are shown in
Fig.~\ref{fig:e-3D}. These quantities were calculated in the manner
explained above in Sec.~\ref{mc}. In the Wolff algorithm, energy is
simply calculated from spin configuration. In Fig.~\ref{fig:e-3D}, the
present algorithm gives the shortest integrated autocorrelation time
and the smallest asymptotic variance. Meanwhile, the variance of the
estimator is almost the same for the three algorithms. It is
interesting that the variance decays fast as the system size
increases, which is sort of a self-averaging effect. The shorter
correlation time of the present algorithm allowed us to calculate the
larger system size.
By fitting data to a power-law form ($\propto L^z$), we estimate the
dynamic critical exponents to be $z \approx 0.28$, $0.31$, and $0.27$
for $\tau_{{\rm int}, \hat{E}}$, $z \approx -2.75$ in common for
$v_{\hat{E}}$, and $z \approx -2.44$, $-2.35$, and $-2.46$ for
$v_{{\rm asymp}, \hat{E}}$, in the use of the Wolff, the classical
worm, and the present worm algorithms, respectively. We expect three
algorithms produce the same exponent asymptotically. Nevertheless, the
present algorithm yields approximately 27 and 2.2 times as small
asymptotic variance as the classical worm and the Wolff algorithm do,
respectively, as shown in the inset of the bottom panel of
Fig.~\ref{fig:e-3D}.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{fig-9.eps}
\caption{(Color online) Integrated autocorrelation time (top panel),
variance (middle panel), and asymptotic variance (bottom panel) of
the susceptibility estimator for the Ising model on the simple cubic
lattice, calculated by the Wolff (triangles), the classical
(circles), or the present worm algorithm (squares). In the Wolff
algorithm, two estimators using spins (upper triangles) or cluster
size (lower triangles) are compared (see the main text for the
detail of the estimators). The dynamic critical exponents are
estimated to be $z=0.150(9)$, $-0.50(1)$, $-0.731(7)$, and
$-0.679(4)$ for $\tau_{{\rm int}, \hat{\chi}}$, $z \approx 0.01$,
$0.58$, $0.92$, $0.85$ for $v_{\hat{\chi}}$, and $z \approx 0.18$,
$0.18$, $0.22$, and $0.18$ for $v_{{\rm asymp}, \hat{\chi}}$, in the
use of spins in the Wolff, cluster size in the Wolff, the classical
worm, and the present algorithm, respectively. The inset of the
bottom panel shows the asymptotic variances of the classical worm
(diamonds) and the Wolff algorithm (pentagons) in units of the
asymptotic variance of the present algorithm, which are
approximately 23 and 1.6 for relatively large system sizes,
respectively.}
\label{fig:sus-3D}
\end{center}
\end{figure}
The quantities of the susceptibility estimator are shown in
Fig.~\ref{fig:sus-3D} in a similar way to the energy estimator. In the
case of the Wolff algorithm, we compare two estimators: $\hat{\chi} =
\beta M_z^2 /N$, where $M_z$ is the total magnetization of spins, and
$\hat{\chi} = \beta \ell_{\rm cl} $, where $\ell_{\rm cl} $ is cluster
size. The dynamic critical exponents are estimated to be
$z=0.150(9)$, $-0.50(1)$, $-0.731(7)$, and $-0.679(4)$ for $\tau_{{\rm
int}, \hat{\chi}}$; $z \approx 0.01$, $0.58$, $0.92$, and $0.85$
for $v_{\hat{\chi}}$; and $z \approx 0.18$, $0.18$, $0.22$, and $0.18$
for $v_{{\rm asymp}, \hat{\chi}}$, in the use of spins in the Wolff,
cluster size in the Wolff, the classical worm, and the present
algorithms, respectively. The numbers in parentheses hereafter
indicate statistical uncertainty, one standard deviation, on the
preceding digit. Interestingly, while the scalings of $\tau_{{\rm
int}, \hat{\chi}}$ and $v_{\hat{\chi}}$ are quite different
between the estimators and algorithms, the dynamic critical exponent
of $v_{{\rm asymp}, \hat{\chi}}$ is likely common. Particularly, in
the case of the Wolff algorithm, $v_{{\rm asymp}, \hat{\chi}}$ is
almost the same between the estimators using spins and cluster
size. The present worm, nonetheless, yields approximately 23 and 1.6
times as small asymptotic variance as the classical worm and the Wolff
cluster do, respectively, as shown in the inset of the bottom panel of
Fig.~\ref{fig:sus-3D}.
We emphasize sampling efficiency should be compared in asymptotic
variance. The integrated autocorrelation time of the susceptibility
estimator in the classical worm algorithm is orders of magnitude
shorter than that measured by spins in the Wolff algorithm, showing
the quite different size scaling. However, the asymptotic variances of
the two estimators show almost the same scaling. In fact, the
asymptotic variance is much larger in the classical worm algorithm
because of the different scalings of the estimator variances. If you
only look at integrated autocorrelation time, it may lead to an
incorrect conclusion about efficiency.
Compared to the classical worm, the variance of the susceptibility
estimator is significantly reduced by the present worm update as shown
in the middle panel of Fig.~\ref{fig:sus-3D}. Because the worm length
is, exactly in the case of the classical worm and almost in the case
of the present worm as shown in Eq.~(\ref{chi-sim-ell}), proportional
to the susceptibility estimator, also the variance of the worm length
is reduced by the present algorithm in a similar way to the middle
panel of Fig.~\ref{fig:sus-3D}. We expect the performance improvement
to be attributed to the variance reduction of the worm length.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig-10.eps}
\caption{(Color online) Autocorrelation functions of the energy (left
panel) and the susceptibility (right panel) estimators for $L=4$
(open) and $8$ (solid) on the simple cubic lattice in the use of the
classical worm (circles) and the present algorithm (squares). The
horizontal axis is the renormalized number of Monte Carlo steps in
units of $L^3$ worm shifting or scattering processes.}
\label{fig:A}
\end{center}
\end{figure}
We compare not only sampling efficiency but also thermalization
rate. The autocorrelation functions~(\ref{A}) of the energy and the
susceptibility estimators for $L=4$ and $8$ are shown in
Fig.~\ref{fig:A}, calculated from more than $2^{30}$ independent
Markov chains (sample paths). The function of the energy estimator
shows the almost single exponential decay.
As for the susceptibility estimator, on the other hand, some fast and
slow decays are observed. While $\tau_{{\rm int}, \hat{\chi}}$
decreases with $L$ as shown in the top panel of Fig.~\ref{fig:sus-3D},
the autocorrelation function for $L=8$ clearly has slower decay than
that for $L=4$ does, in the case of the classical algorithm, as shown
in the right panel of Fig.~\ref{fig:A}. The reason why $\tau_{{\rm
int}, \hat{\chi}}$ decreases with $L$ is that the prefactor of the
slowly decaying mode decreases, which is also seen in
Fig.~\ref{fig:A}.
The scaling of the exponential autocorrelation time is shown in
Fig.~\ref{fig:tau_exp-3D}, calculated by bootstrapping as mentioned in
Sec.~\ref{mc}. We found $\tau_{{\rm exp}, \hat{\chi}} \approx
\tau_{{\rm exp}, \hat{E}}$, which is also seen in Fig.~\ref{fig:A}.
Since the autocorrelation function of the energy estimator is well
approximated by a single exponential function, it is expected that
$\tau_{{\rm exp}, \hat{E}} \approx \tau_{{\rm int}, \hat{E}}$, which
we indeed confirmed. Therefore, we expect the asymptotic scaling:
$\tau_{{\rm exp}, \hat{\chi}} \approx \tau_{{\rm exp}, \hat{E}}
\approx \tau_{{\rm int}, \hat{E}} \propto L^{0.27}$, where the power
was estimated from the plots in Fig.~\ref{fig:e-3D}.
The ratio of the exponential autocorrelation times between the
classical and the present algorithms is approximately 26 as shown in
the inset of Fig.~\ref{fig:tau_exp-3D}, which is consistent with the
ratio regarding the integrated autocorrelation time or the asymptotic
variance of the energy estimator. Note that the summation of the
autocorrelation function with respect to the renormalized time is
somewhat different from the renormalized integrated autocorrelation
time~(\ref{tau_int_worm}) because of the constant $1/2$ in the
definition~(\ref{tau_int}). Nonetheless, the asymptotic scaling with
respect to system size should be the same for the two quantities.
A lesson to learn from these analyses is that we must be careful for
estimating $\tau_{\rm exp}$ and needed thermalization (burn-in)
period. Because $\tau_{\rm int}$ is usually easier to estimate than
$\tau_{\rm exp}$, people roughly estimate $\tau_{\rm exp}$ from
$\tau_{\rm int}$ in some (or maybe many) cases. Assume that an
autocorrelation function is approximated by a single exponential
function and $\tau_{\rm exp} \gg 1$, then $\tau_{\rm int} \sim
\tau_{\rm exp}$. When an autocorrelation function has a slow decay
with prefactor $c$, $\tau_{\rm int} \sim c \, \tau_{\rm exp}$. Thus
$\tau_{\rm exp}$ can be much larger than $\tau_{\rm int}$ possibly in
orders of magnitude as we have estimated $\tau_{{\rm int}, \hat{\chi}}
\propto L^{-0.731}$, but $\tau_{{\rm exp}, \hat{\chi}} \propto
L^{0.27}$ for the classical algorithm.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig-11.eps}
\caption{(Color online) Size dependence of the exponential
autocorrelation time of the energy (solid) and the susceptibility
(open) estimators in the use of the classical (circles) and the
present (squares) algorithms for the Ising model on the simple cubic
lattice. The inset shows the ratio of the times of the energy
estimators between the two algorithms.}
\label{fig:tau_exp-3D}
\end{center}
\end{figure}
\section{Summary}
\label{sd}
We have proposed the modified worm algorithm for classical models and
demonstrated the performance improvement for the Ising model at the
critical temperature. The kinks of the present worm are located on
bonds instead of sites on a lattice. The probabilities at worm
scattering are optimized using the directed-loop framework and the
geometric allocation approach so that the bounce (rejection)
probability is minimized and indeed reduced to zero in a wide range of
temperature including the critical point. Furthermore, the probability
for the worm head to go straight is maximized to reduce the diffusive
nature of worm position.
The reduction of the diffusive behavior is confirmed in the
probability distribution of worm position as the rapid growth of the
variance of the distribution as a function of scattering processes in
Figs.~\ref{fig:P} and~\ref{fig:P_r}. As a result, the variance of worm
length, as well as the variance of the susceptibility estimator, is
significantly reduced as seen in the middle panel of
Fig.~\ref{fig:sus-3D}, which is expected to lead to efficient
sampling.
We have discussed how to compare Monte Carlo samplers and measure
relevant quantities. While thermalization rate is quantified by
exponential autocorrelation time, sampling efficiency, as we have
stressed, should be compared in asymptotic variance.
The exponential autocorrelation time and the asymptotic variance in
the present method are approximately only 4\% as large as those in the
classical algorithm for the Ising model on the simple cubic lattice, shown in
Figs.~\ref{fig:e-3D},~\ref{fig:sus-3D}, and~\ref{fig:tau_exp-3D}. Our
algorithm is remarkably even more efficient than the Wolff cluster
algorithm. The compared algorithms likely produce the same dynamic
critical exponents of the exponential autocorrelation time and the
asymptotic variance. The exponent of the longest time scale in the
worm update is estimated to be $ z \approx 0.27$, which is somewhat
larger than the previous estimate in the classical worm algorithm, $z
\approx 0.174$\,\cite{DengGS2007}, but consistent with the recent
estimate in the Wolff update, $z=0.24(2)$\,\cite{LiuPS2014}. This
agreement suggests that the worm and the Wolff algorithms share the
same exponent of the exponential autocorrelation time as well as the
asymptotic variance.
Meanwhile, we observed the integrated autocorrelation time of the
susceptibility estimator shows the quite different scaling from the
exponential autocorrelation time: $\tau_{{\rm exp}, \hat{E}} \approx
\tau_{{\rm int}, \hat{E}} \approx \tau_{{\rm exp}, \hat{\chi}} \gg
\tau_{{\rm int}, \hat{\chi}}$. These findings clearly indicate that
asymptotic variance is more adequate than integrated autocorrelation
time for comparison of sampling efficiency.
The present approach can be generalized to a wide range of physical
models, such as the $| \phi|^4$ model, the Potts
model\,\cite{MercadoEG2012}, the O($n$) loop
model\,\cite{JankeNS2010,LiuDG2011,ShimadaJK2014}, and the lattice
QCD\,\cite{AdamsC2003}. The directed-loop framework and the geometric
allocation approach are expected to reduce computational cost
significantly for many kinds of systems. In particular, it is
promising to apply to frustrated models in combination with the dual
worm formalism\,\cite{RakalaD2017}. The performance of the present
worm algorithm in the case of other models needs to be investigated in
the future.
\acknowledgements {The author is grateful to Synge Todo for discussion
on measurement and the distribution of worm position. Some
simulations have been done using computational resources of the
Supercomputer Center at the Institute for Solid State Physics, the
University of Tokyo. The author acknowledges support by KAKENHI
under Grant No.\,16K17762 from JSPS.}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,871
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What a lineup of speakers and topics!
The 2016 Vermont Agronomy Plus meetings, scheduled for seven Vermont locations in February, will give farmers an opportunity to learn from state and nationally recognized experts on a range of important topics.
Registration for the University of Vermont (UVM) Extension-hosted meetings is $25, and includes lunch, if received at least three days prior to the meeting. Farmers may attend in person or remotely from home using GoToMeeting. As content varies for each meeting, all registrants will be able to access other sessions at no additional cost through a high-speed Internet connection.
Registrations will be accepted online or by mail. Go tohttp://go.uvm.edu/agronomyplus2016 for information.
To request a disability-related accommodation or special dietary needs, contact Brent Passut at (800) 545-8920, ext. 351 (toll-free inVermont) or (802) 751-8307, ext. 351, two weeks prior to the meeting date.
Event sponsors include Ben and Jerry's Caring Dairy, U.S. Department of Agriculture's Risk Management Agency, Barenbrug USA, Resource Management, Incorporated and Agri-Mark.
Register for the event closest to you, or come and join a location that has the content you want. OR, register for one meeting, and have access to any/all of the meetings from the comfort of your home, (provided you have high-speed internet).
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,508
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Thivencelle es una población y comuna francesa, en la región de Norte-Paso de Calais, departamento de Norte, en el distrito de Valenciennes y cantón de Condé-sur-l'Escaut.
Demografía
Enlaces externos
INSEE
Localidades de Norte
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,760
|
On Saturday, March 30, 2019, A person has died after a CSX train struck a car on the railroad tracks that crossed Snowden Street in Chesapeake late Saturday night. Most people do not see the yield or stop sign. The yield sign is blocked by a bush and the stop sign isn't even facing the road. To prevent another crash like this happening again, we need lights and/or crossing arms to let people know that a train is coming. Keep people safe and sign this petition. This young woman lost her life and her family lost a loved one.
Jennifer Shrader needs your help with "Chesapeake City Counsil: Railroad Cross arms installed". Join Jennifer and 12,250 supporters today.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,529
|
Join us and be part of something great!
At Publica we put our customers first. We provide excellent service to our local communities, the councils and clients we support and our colleagues. Our aim is to have a reputation for service that is second to none, and we do that by staying true to our shared values. This is the way we work and how we make our customers smile.
At Publica we want to be an organisation where great people want to work, our approach to reward plays a big part in that. We consider the whole you and not just the bit of you that comes to work, so we take a total reward approach. We always try to be open, fair and consistent, clear about what we expect from you and what you can expect in return.
We know that everyone is different, so we provide flexibility and choice so that you can make your reward meaningful to you. It is aligned to our business, our values, strategy and commitments, so we are all working together with common goals.
Publica offices are based across Gloucestershire and West Oxfordshire in some of the most beautiful British countryside. We have charming stone cottages, festivals for those with four legs or two, historic woodland, gliding and hot air ballooning, art and craft, fine dining, the meandering River Severn and River Wye, together with a sprinkling of global superstars and royalty who call our region home. We feel our area has it all and is quite simply the best place to live and work in the UK.
But don't take our word for it, come and find out for yourself.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,964
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Olšovec (Duits: Olspitz) is een Tsjechische gemeente in de regio Olomouc, en maakt deel uit van het district Přerov.
Olšovec telt 463 inwoners.
Gemeente in Přerov
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 532
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Q: Adding seconds to timestamp in python I have tons of timestamp strings like this one 2017-04-18 05:03:40.966084 and the script needs to add seconds to the timestamp. I have been trying to turn the string into a legit timestamp object and then add seconds to it with timedelta but for some reason it isn't working.
This is what I have so far:
duration = "150.100"
timestamp = datetime.strptime(timestamp, "%Y-%m-%d %H:%M:%S.%f")
timestamp_e = timestamp+timedelta(seconds=duration)
Am I going at this the right way?
A: Yes timedelta is a good way to adjust a timestamp. However note that your duration variable is a string. As per the documentation it should be an integer or float:
All arguments are optional and default to 0. Arguments may be integers or floats, and may be positive or negative.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,859
|
# cardinal-spline
A cardinal spline is a sequence of individual curves joined to form a larger curve. The spline is specified by an array of points and a tension parameter. A cardinal spline passes smoothly through each point in the array; there are no sharp corners and no abrupt changes in the tightness of the curve. The following illustration shows a set of points and a cardinal spline that passes through each point in the set.
## Install
[](https://nodei.co/npm/cardinal-spline/)
`npm install cardinal-spline`
or with bower:
`bower install cardinal-spline`
## Use
```js
var cSpline = require('cardinal-spline');
var splinePoints = cSpline(points[, tension, numOfSeg, close]);
//-> splinePoints is a flat Float32Array, [x1, y1, x2, y2, ..., xn, yn]
```
### Options
```js
/**
* @param {Array} points - (flat) point array: [x1, y1, x2, y2, ..., xn, yn]
* @param {Number} [tension=0.5] - tension. Typically between [0.0, 1.0] but can be exceeded
* @param {Number} [numOfSeg=25] - number of segments between two points (line resolution)
* @param {Boolean} [close=false] - Close the ends making the line continuous
* @returns {Float32Array} - the spline points.
*/
```
#### tension
The formulas for mathematical splines are based on the properties of flexible rods, so the curves produced by mathematical splines are similar to the curves that were once produced by physical splines. Just as physical splines of different tension will produce different curves through a given set of points, mathematical splines with different values for the tension parameter will produce different curves through a given set of points.
A tension of 0 corresponds to infinite physical tension, forcing the curve to take the shortest way (straight lines) between points. A tension of 1 corresponds to no physical tension, allowing the spline to take the path of least total bend. With tension values greater than 1, the curve behaves like a compressed spring, pushed to take a longer path.
## License
MIT
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 5,484
|
Chernobyl contaminating cow milk 30 years after nuclear meltdown – study
More than 30 years after its catastrophic meltdown, the Chernobyl nuclear power plant is being blamed for high radiation levels discovered in local cow's milk.
Sampling milk from private farms in the Ukraine's Rivne region, scientists from Exeter University and the National University of Life and Environmental Sciences made a startling find – radioactive material from more than three decades ago has leached into the livestock.
The lingering nuclear fallout from 1986 means farmers are unwittingly producing milk with radioactive caesium levels above the Ukraine safety standard of 100 becquerel per litre. The becquerel is a unit of radioactivity, with the new report documenting how some farms had milk with a radioactivity concentration of around 500 becquerel per litre.
One of the researchers, Dr Iryna Labunska, of the University of Exeter, believes the issue warrants government intervention. She said that while soil contamination in the Rivne region is not particularly high, the milk study shows how nuclear accidents have a long lasting legacy.
"More than 30 years after the Chernobyl disaster, people are still routinely exposed to radioactive caesium when consuming locally produced staple foods, including milk, in Chernobyl-affected areas of Ukraine," said Dr Labunska, of Greenpeace Research Laboratories at the University of Exeter.
On April 25, 1986, the reactor core at Chernobyl nuclear power plant near the now desolate town of Pripyat went into meltdown. Considered to be one of the worst nuclear accidents in history, Chernobyl's radioactive exposure could end up claiming the lives of up to 4,000 people through various diseases, according to the World Health Organisation.
The US-Neocon project of a world war against Russia and China and its implications for Europe
The area surrounding the former power plant is not expected to be habitable again from another 150 to 300 years.
"Many people in the area we studied keep cows for milk, and children are the main consumers of that milk. Government and international monitoring needs to take place, along with help for people affected by this radiation," Dr Labunska added.
"Without adequate countermeasures, what may now seem a purely historical event will remain a daily reality for those communities impacted."
Published at https://www.rt.com/news/429279-ukraine-radioactive-chernobyl-milk/
Move Over Chernobyl, Fukushima is Now Officially the…
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Radiation from Fukushima spreads off US coast – monitor
Fukushima Darkness
Mysterious Radioactive Leak Detected Across Europe
SOURCEwww.rt.com
Radioactive Pollution
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 2,818
|
Latest in Robert The Bruce
'Robert The Bruce' Movie With 'Braveheart' Actor Angus Macfadyen Boarded By Metro International, First Look — EFM
EXCLUSIVE: UK sales outfit Metro International has boarded international sales rights to historical action-drama Robert The Bruce, in which Angus Macfadyen reprises his role from Mel Gibson's Braveheart as the iconic Scottish warrior. Metro will be screening the film this week at the EFM in Berlin. We can also reveal…
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EXCLUSIVE: Angus Macfadyen who played the renowned warrior and king Robert the Bruce in Braveheart is portraying the historical hero again in what is turning out to be an epic Scottish drama Robert the Bruce from Aussie director Richard Gray (Sugar Mountain). Macfadyen and Eric Belgau scripted the story that continues…
Aaron Taylor-Johnson Is Scottish Legend James Douglas In Netflix's 'Outlaw King'
EXCLUSIVE: Aaron Taylor-Johnson is being set to co-star as James Douglas in Outlaw King, the David Mackenzie-directed Netflix feature that stars Chris Pine as Robert the Bruce in the War for Scottish Independence. Pine reunites with his Hell or High Water helmer in a package Netflix landed in April for its burgeoning…
Netflix Lands 'Outlaw King'; David Mackenzie Directs Chris Pine As Robert The Bruce In Scottish Epic
EXCLUSIVE: In one of the first major deals coming together as Scott Stuber takes the reins as head of Netflix feature films, the director and stars of Hell Or High Water are in final talks to re-team in Outlaw King, an epic period drama that will tell a different version than Braveheart did on Robert The Bruce, the…
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,891
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Marianne Thieme: Adventist Animal Rights Politician
This interview with Adventist legislator Marianne Thieme is the kind of thing you have come to expect from Adventist Today. Since this week is our Spring Fundraising drive, I invite you to click here to support our ministry of independent Adventist journalism! —Loren Seibold, AT Executive Editor.
Marianne Thieme is a young Dutch Seventh-day Adventist animal rights activist who has thrown herself into her country's political arena to campaign, very successfully, for what she believes in.
Thieme (pronounced TEE-mah) is ambitious and savvy but she's also fueled by a bold sense of idealism. It seems a winning combination as she has led her political party from being a non-player to one of international renown in the space of a decade.
The movement she leads, Party for the Animals (Partij voor de Dieren), boasts the unique accolade of being the first political party worldwide with a primary focus on animals, nature and the environment.
When Adventist Today reached out to her, Party for the Animals was just coming off a very successful election season. Her party more than doubled their presence in Holland's parliament: winning five seats, up from the two they had before the March 15 election.
The party currently has 53 seats spread over different levels of Dutch government. They occupy five out of 150 seats in the National Parliament, two seats in the country's Senate and one seat in the European Parliament.
In an email interview, Thieme revealed more about her thoughts on politics, religion and why she believes Adventists just aren't doing enough.
Not Your Average Adventist
Thieme, 45, isn't your average Adventist.
She came to the faith 10 years ago, after becoming a politician.
It's a bit of a wonder that she discovered Adventism as she had an allergy to religion for several reasons.
Raised a Roman Catholic, Thieme was an animal lover from a very young age and was shocked that the church blessed bull fights and hunting.
She noted that disregard for the welfare of animals wasn't just restricted to the Catholic Church.
The fact that many Orthodox Christians owned Dutch farms where livestock were raised in dismal conditions further turned Thieme off Christianity.
She became a vegetarian during her time at university. Thieme studied at Duno College in Doorwerth, Holland before continuing her studies at the prestigious Sorbonne University in Paris. Later she pursued law at Erasmus University Rotterdam.
Her rejection of religion continued as she launched into a series of jobs relating to animal rights advocacy.
It wasn't until a little over 10 years ago that Thieme learned of the Adventist Church and found a fit for both her spiritual views and her staunchly vegetarian lifestyle.
She was baptized in 2006, the same year Dutch voters elected members of Party for the Animals to the national parliament for the first time.
Thieme's pioneering party has generated enthusiasm across the globe. There are currently 18 parties with similar platforms internationally.
A Belief in Sustainability
Thieme co-founded Party of the Animals in 2002. She assumed her role as Parliamentary Leader for Party for the Animals in 2006.
According to Thieme, one of the biggest misconceptions about Party of the Animals is that it is a single-issue party.
She explained to Adventist Today that the Dutch public has begun to understand that "a good Party for the Animals is also a good party for people.
"In this world dominated with crises like the food crisis, the economic crisis, the biodiversity crisis, and climate change, people become aware that we have lived as though we have three planets to use, to harvest from, and more and more we realise that we can't eat money. That we have to re-value the things that really matter. Clean air and water, compassion not only for our own kind but also for other living beings."
It is this focus on sustainability and an up-ending of the status quo that seems to drive interest in Thieme's party.
"People in our country are really fed up with politics and do not trust any politician," said Thieme.
"The Party for the Animals has attracted not only people who care about animals and the environment but also people who have wanted to protest against the political establishment and have chosen for new politics led by principles of compassion, sustainability, personal freedom and personal responsibility."
Thieme urges lawmakers to widen their policy considerations, shifting them from an obsessive focus on economic growth.
"Economic growth isn't a guarantee for happiness or a better quality of life. On the contrary, more production and more consumption is bad for our planet. GDP measures everything except the things that are really important to us such as clean air, safety, social cohesion, justice, welfare, biodiversity etc."
Thieme is adamant about the importance of the separation of Church and State. She never preaches on the job and has built an entirely secular platform.
When we asked her if there was a tie between her faith and her political party her answer was direct: "No, there isn't."
"Our animal rights party is a progressive, secular political party. I am in favour of a strict separation of Church and State."
She says that voters that backed her party and members of the party are from all kinds of different backgrounds, "atheist, humanists, Buddhists, Christian, Muslim, agnostic, young, old, liberal, socialistic, conservative, but they all share a common goal: to create a society where compassion, sustainability, personal freedom and responsibility are the leading principles in everything people do."
Thieme's refusal to mix politic with religion didn't stop accusations of ulterior motives being leveled against her when the press got wind of her Adventist faith in 2006.
"I have experienced that we live in a time when the secular inquisition strongly distrusts everyone with a Christian background. A lot of religion fighters see Christians as people with a hidden agenda, and the bad thing is, that they are often reinforced in this view by the actions of politicians from religious parties that promote or justify, with the Bible in hand, unsustainable, unemancipated behaviour and behaviour with a lack of solidarity," said Thieme.
"This is sad because it stigmatizes people. I also believe that Christian politics play a harmful role in the perception of people, and it's one of the reasons that I chose with conviction for the establishment of a progressive, secular political party."
Challenging Adventists
Just as Thieme is campaigning for a shift in political thinking, she is a sharp critic of her own faith community's apathy about sharing long-held views about the benefits of vegetarianism.
"It's unbelievable that Adventists aren't visible in the discussion about the meat impact on climate change, obesity, animal welfare and the food crisis. Now is the time, I should say! More than ever!"
As an Adventist, Thieme is especially interested in the female co-founder of the Adventist Church, Ellen White.
But the reasons for her interest and her view of White can raise eyebrows in Adventist circles: "I dare say she was an animal rights activist."
She quotes an Ellen White passage from the book "Ministry of Health" to back up her assertion:
"Animals are often transported long distances and subjected to great suffering in reaching a market. Taken from the green pastures and traveling for weary miles over the hot, dusty roads, or crowded into filthy cars, feverish and exhausted, often for many hours deprived of food and water, the poor creatures are driven to their death, that human beings may feast on the carcasses."
It's impossible not to feel the sense of urgency in Thieme's words. She urges Adventists to be bolder about the health message they have as a heritage.
"Now is the time to stand up and show that you're involved and you have such practical solutions to make this world a better place. To let people know what stewardship really means."
Thieme is a determined opponent of President Donald Trump:
"Trump is a danger to all the emancipation movements and a major obstruction to fight climate change. Fortunately a lot of American states did not stop their environmental policy and countries like China seem to be more ambitious since the Paris (climate change) agreement," she said.
Thieme, whose husband owns a business that produces plant-based meat substitutes, sees responsible business practices as key to a sustainable future.
"Let's not forget: a lot of consumers and companies are committed to solving all the environmental problems. It's not only politics in terms of parliaments and presidents that change the world. It's also our daily choices in terms of buying sustainable and ethical whether as a consumer, as an employee or as an entrepreneur."
Thieme's enthusiasm about the future is palpable:
"We are on a threshold of a new era: the US Humane Party (a sister party of the Party for the Animals) and people like Bernie Sanders and Elizabeth Warren should be able to conquer old politics and populists. It takes courage and perseverance. It reminds me of a great quote of Margaret Mead in the 1940s:
'Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has.'
"And she is so right. Think about other social movements that changed the world: it all started with just a few people."
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namespace dacron {
enum class ContextState { kSame, kDifferent };
// A stranded execution context.
class Context {
public:
// Default construct a context, it gets its own io_service.
Context()
: io_service_(std::make_shared<boost::asio::io_service>()),
strand_(
std::make_shared<boost::asio::io_service::strand>(*io_service_)) {}
// Copy a context, specify whether the context shares the parent's
// strand, or gets a different one.
Context(const Context& context, ContextState state)
: io_service_(context.io_service_) {
switch (state) {
case ContextState::kSame:
strand_ = context.strand_;
break;
case ContextState::kDifferent:
strand_ =
std::make_shared<boost::asio::io_service::strand>(*io_service_);
break;
}
}
Context(const Context& context) = default;
Context& operator=(const Context& context) = default;
Context(Context&& context) = default;
Context& operator=(Context&& context) = default;
template <typename Function>
void Post(Function&& f) {
strand_->post(std::forward<Function>(f));
}
void ResetAndRun() {
Reset();
Run();
}
// Run the io_service until it is out of work.
// subsequent calls to Run. See io_service::reset() docs.
size_t Run() { return io_service_->run(); }
// Reset the Context's io_service. This should be invoked before
// subsequent calls to Run. See io_service::reset() docs.
void Reset() { io_service_->reset(); }
boost::asio::io_service::strand& GetStrand() const { return *strand_; }
boost::asio::io_service& GetIoService() const { return *io_service_; }
private:
// A class invariant is that io_service_, and strand_ are never
// null. These are shared_ptr so that they may be aliased between
// copies of the same context.
std::shared_ptr<boost::asio::io_service> io_service_;
std::shared_ptr<boost::asio::io_service::strand> strand_;
public:
// Returns a wrapped function object which when invoked posts itself
// to the context's strand. The wrapped function object should have
// the same signature as the f.
//
// NOTE: This needs to go at the bottom, so that the compiler has enough
// type information to for the auto return type.
template <typename Function>
auto Wrap(Function&& f)
-> decltype(this->strand_->wrap(std::forward<Function>(f))) {
return strand_->wrap(std::forward<Function>(f));
}
};
} // namespace dacron
#endif // DACRON_CONTEXT_H_
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\section{Our Implementation}
We implemented our solution in MP-SPDZ \cite{mp-spdz}. It features
fixed-point computation, that is, the fractional number $x$ is
represented as an integer near $x \cdot 2^k$ for some $k$. Addition and
subtraction are straight-forward due to linearity while
multiplication is implemented as integer multiplication followed by
truncation. This truncation can either mean rounding to the nearest
integer or the more efficient probabilistic truncation where rounding
down is the more likely the closer the input number is to the
floor. See Catrina and Saxena~\cite{FC:CatSax10} for more details.
Standard logistic regression uses the sigmoid function based on the
exponential, and computing the loss requires the logarithm
function. Our implementation of these is based on the code provided in
SCALE-MAMBA \cite{scale-mamba} by Aly and Smart \cite{ACNS:AlySma19}.
A particular helpful feature of MP-SPDZ in some protocols including
the one used here is the implementation of dot products of fixed-point
numbers with constant communication. See Dalskov et
al. \cite{cryptoeprint:2019:131} for more details. Due to this
optimization, we decided not to use mini-batches but the whole training
set at once for simplicity.
The benefit of the optimization increases with the size of the batch.
Our implementation can be straightforwardly generalized to mini-batch training.
Given the decisions above, we ran our implementation with a few
parameters on AWS \texttt{c5.9xlarge}, namely the precision of
fixed-point truncation and the duration. For the former, there is a
choice of probabilistic and exact truncation.
Considering the latter, we saw that
it takes about 100 epochs for the loss to get close to zero without
using mini-batches. Therefore, we ran our implementation either for
100 or for 200 epochs, or until the loss was below $10^{-4}$.
Table \ref{table:results} shows the five-fold cross-validation accuracy
and running time
for each combination of parameters and dataset. Each values is
averaged over 100 runs. Note that the running times are taken from the
same run as the accuracies and therefore use only 80\% of the
respective dataset.
\begin{table}
\centering
\begin{tabular}{@{}lllcc@{}}
\toprule
Dataset & Duration & Truncation
& $F_1$
& Time (sec) \\
\midrule
\multirow{6}{*}{GSE2034} & \multirow{2}{*}{100} & Probabilistic
& $0.670 \pm 0.070$
& 8 \\
&& Exact
& $0.666 \pm 0.068$
& 20 \\
& \multirow{2}{*}{200} & Probabilistic
& $0.674 \pm 0.063$
& 14 \\
&& Exact
& $0.670 \pm 0.066$
& 38 \\
& \multirow{2}{*}{Variable} & Probabilistic
& $0.657 \pm 0.091$
& 6 \\
&& Exact
& $0.650 \pm 0.091$
& 22 \\
\midrule
\multirow{6}{*}{BC-TCGA} & \multirow{2}{*}{100} & Probabilistic
& $0.994 \pm 0.007$
& 21 \\
&& Exact
& $0.994 \pm 0.008$
& 43 \\
& \multirow{2}{*}{200} & Probabilistic
& $0.994 \pm 0.007$
& 38 \\
&& Exact
& $0.994 \pm 0.009$
& 77 \\
& \multirow{2}{*}{Variable} & Probabilistic
& $0.995 \pm 0.010$
& 8 \\
&& Exact
& $0.994 \pm 0.011$
& 17 \\
\bottomrule
\end{tabular}
\caption{Five-fold cross-validation accuracy and running times of our
implementation}
\label{table:results}
\end{table}
The implementation used for these timings is different to the
submitted version in two points: The submitted version would only use
a single thread because the evaluation criterion was changed from a
single host to several shortly before the deadline. Furthermore, the
improved version uses the dot product optimization more
consequently. We have seen that this reduces the running time by about one
third.
Given the result, one would choose 200 epochs with probabilistic
rounding for the best accuracy and variable duration with
probabilistic rounding for faster inference at the cost of accuracy.
However, we did not have
time to run these evaluations before the deadline. From the limited
information we had at the time, we decided to submit the training with
200 epochs and exact rounding.
We achieved slightly better accuracy than logistic regression with plaintext
computation, because a limited precision helps improve generalization on these two datasets.
\section{Introduction}
In this section, we summarize the
task.\footnote{\url{http://www.humangenomeprivacy.org/2019/competition-tasks.html}}
Participants were invited to implement machine learning (ML) training in
multi-party computation (MPC). MPC allows a set of parties to
jointly compute on data hold among each other without revealing anything other
than the result of the computation. In the current context this means
that a set of healthcare providers holding measurements about cancer
patients and healthy individuals can jointly compute a ML model
detecting cancer without sharing the measurements.
The training algorithm must be suitable to the GSE2034 \cite{gse2034}
and BC-TCGA \cite{BC-TCGA} breast cancer datasets. The organizers provided a subset of both. For GSE2034, this
contains 142 positive (recurrence tumor)
and 83 negative (no recurrence normal) samples,
each with 12,634 features. On the other hand, the subset of BC-TCGA
contains 422 positive (breast cancer tissue)
and 48 negative (normal tissue) samples
of 17,814 features each. The organizers
provided a reference model, and the submissions were expected to perform similarly.
In terms of security, the competition asked for three-party computation
with one semi-honest corruption. This security model has received
widespread attention because it does not require relatively
expensive cryptographic primitives such as oblivious transfer or
homomorphic encryption. Instead, so-called replicated secret sharing
suffices, where every party holds two out of three random shares which
sum up to a secret value~\cite{CCS:AFLNO16}. Furthermore, semi-honest
security requires that even corrupted parties follow the protocol,
which allows the creation of optimized protocols for specific
purposes, for example probabilistic truncation
\cite{cryptoeprint:2019:131}.
For the evaluation, the organizers asked for Docker containers that
would be run on three hosts in a local cluster. The submissions were
required to finish within 24 hours, and they were ranked on accuracy,
performance, and communication.
\section{The Model}
\renewcommand{\P}{\mathrm{P}}
\newcommand{\mathrm{N}}{\mathrm{N}}
\newcommand{\mathrm{TP}}{\mathrm{TP}}
\newcommand{\mathrm{TN}}{\mathrm{TN}}
\newcommand{\mathrm{FP}}{\mathrm{FP}}
\newcommand{\mathrm{FN}}{\mathrm{FN}}
We evaluated the performance of the following baseline models using plaintext computation
\begin{description}
\item[Logistic] Logistic regression based on mini-batch stochastic gradient
descent (SGD) with constant learning rate and momentum.
The model is trained for a fixed number of 100 epochs. In each mini-batch of 16 samples,
we re-balance the positive and negative classes by re-sampling the same number of
samples from these two classes;
\item[MLP] A multilayer perceptron with two hidden layers of 256+64 ReLU~\cite{relu} neurons.
We apply dropout~\cite{dropout} with probability 0.5 to the hidden layers to avoid over-fitting. The
model is trained by SGD for 100 epochs using the same mini-batches as Logistic;
\item[Linear SVM] A linear SVM classifier with $L_2$ regularization and typical settings.
We use scikit-learn's~\cite{sklearn} implementation with a stopping tolerance of
$10^{-3}$ and other default settings;
\item[Random Forest] A random forest classier~\cite{tin95} with 100 trees
based on scikit-learn's~\cite{sklearn} implementation;
\item[Reference] The reference model provided by the iDASH committee, which is a
deep 1D convolutional network composed of Residual blocks~\cite{resnet}.
We train the model using the Adam optimizer~\cite{adam} with a fixed learning rate of
$10^{-4}$ for 30 epochs.
\end{description}
In these models, both Logistic and Linear SVM correspond to a single-neuron model.
The main difference between these two methods is the loss function:
Logistic minimizes the cross-entropy between the target label and the prediction,
while Linear SVM minimizes the squared Hinge loss.
The detailed hyper-parameter configurations are omitted for brevity. We tried to
achieve a representative accuracy score for each method. Further tuning these
methods can give marginal improvement. We tried to compare all methods using
similar settings such as how the mini-batches are constructed and how the
performance is evaluated.
Denote $\mathrm{TP}$ (true positive), $\mathrm{FN}$ (false negative) to be the
population of the ground truth positive class; denote $\mathrm{TN}$ (true negative), and
$\mathrm{FP}$ (false positive) to be the negative class. Then the $F_1$ score
of these two classes are given by the harmonic mean of the precision and recall,
that is,
\begin{equation}
F^{\P}_1 = \frac{2}{\frac{1}{\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}}} + \frac{1}{\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}}} = \frac{2\mathrm{TP}}{2\mathrm{TP} + \mathrm{FP} + \mathrm{FN}},
\quad
F^{\mathrm{N}}_1 = \frac{2\mathrm{TN}}{2\mathrm{TN} + \mathrm{FP} + \mathrm{FN}}.
\end{equation}
Then we evaluate the classification performance based on the weighted $F_1$ score
\begin{equation}
F_1 = \frac{\mathrm{TP}+\mathrm{FN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}} F^{\P}_1 + \frac{\mathrm{TN}+\mathrm{FP}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}} F^{\mathrm{N}}_1,
\end{equation}
which is a population-weighted mean of $F^{\P}_1$ and $F^{\mathrm{N}}_1$.
See Table~\ref{table:models} for our cross-validation accuracy scores and timing results.
Observe that MLP does not improve over Logistic, because the training data is
linearly separable and prone to over-fitting.
The poor performance of the reference model, despite its expensive training
cost, is due to over-fitting. One may improve further its performance with
a carefully designed optimization procedure, e.g., based on dynamic learning rates.
However, the benefit is quite limited in light of the high complexity to implement it.
Eventually, we decided to go ahead with logistic regression because
its accuracy comes close the
other models while its simplicity promised a more efficient
implementation.
In the next section, we will show that our MPC implementation
slightly surpasses the plaintext implementation of logistic regression and
comes even closer to the linear SVM classifier in terms of accuracy.
\begin{table}
\centering
\begin{tabular}{@{}r|cc|cc}
\toprule
& \multicolumn{2}{c|}{GSE2034} & \multicolumn{2}{c}{BC-TCGA} \\
Model & $F_1$ & Time (sec) & $F_1$ & Time (sec) \\
\midrule
Logistic & $0.666\pm0.062$ & 3 & $0.995\pm0.006$ & 8 \\
MLP & $0.664\pm0.066$ & 35 & $0.994\pm0.007$ & 39 \\
Linear SVM & $0.677\pm0.058$ & 1 & $0.996\pm0.006$ & 0.3\\
Random Forest & $0.592\pm0.055$ & 0.6 & $0.988\pm0.011$ & 0.8\\
Reference & $0.650\pm0.075$ & 68$^\star$ & $0.987\pm0.008$ & $139^\star$ \\
\bottomrule
\end{tabular}
\caption{Weighted $F_1$ score and computational time in seconds with plaintext computation.
All reported number are averages over 20 runs of five-fold cross validation (100 folds in total).
The reported time in seconds is measured on an Intel~Core~i5-7300U CPU.
The upper-script ``$^\star$'' means that the timing is performed instead on a NVidia Tesla P100
because the experiments could not finish in reasonable time.}
\label{table:models}
\end{table}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,953
|
For information about customs, import duties, etc., visit: Ministry of Finance – Poland, Taxation and Customs Union.
Inpost: Duties, Taxes, and Fees Prepaid! All duties taxes, and import fees are pre-collected at the time of checkout to expedite customs clearance; no further payments are required at the time of delivery.
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|
{
"redpajama_set_name": "RedPajamaC4"
}
| 3,933
|
Q: Partially Transparent Panels in WinForms app showing up black on Windows XP Preface:
Pardon for the partial images - This has to do with a work-in progress for my company.
I have tested this on several fully updated Windows XP SP3 laptops using both .NET4.0 and .NET3.5. The end result is the same.
I have a WinForms application. On the first screen of the application I have several panels that are a partially transparent black. I set this color by manually typing it into the properties editor.
The resulting designer code if it helps is
this.pnlMain.BackColor = System.Drawing.Color.FromArgb(((int)(((byte)(125)))), ((int)(((byte)(0)))), ((int)(((byte)(0)))), ((int)(((byte)(0)))));
The visual end result is (corner of my main panel, the main form has an image background):
When I open my application on the problematic Windows XP machines, this is the result (the panel is solid black, sorry for the camera phone):
The application looks as expected on Windows Vista -> Windows 8.
The curious thing is that on Windows XP if I click and drag the application to where it is almost completely off-screen and then drag it back into visual range, the partial transparency renders properly.
I believe there is some weird paint/invalidation issue happening. Does anyone have any ideas? I have looked at many of the "transparency turns black" issues on StackOverflow and most mention custom controls, however it doesn't feel like that is a solution for my problem. Thanks in advance!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,249
|
Q: CSS transform transition layout flash in WebKit (possibly caused by layout caching?) I have been trying to use CSS transforms on a element to center an absolutely positioned image, so that I can transition position from center to left. This is the basic code (with vendor prefixes in all of the combinations) I have been using.
position: absolute;
left: 50%;
height: 100%;
transform: translateX(-50%);
transition: transform 1s, left 1s;
And then on hover, the following properties are changed.
left: 0;
transform: translateX(0%);
This all works perfectly, but the problem starts when the height of the wrapper also changes during transition. WebKit appears to cache the width of the element from what it was before while transitioning the element, and because the width/height change during transition, once it reaches the end of the transition, it jumps to where it belongs. Here is a JSFiddle that shows my problem. It works perfectly in Firefox and IE10, but WebKit based browsers Chrome, Safari, and Opera, have a layout flash at the end of the hover out.
JSFiddle Example
I have spent the past few days trying everything I could think of to trick WebKit into behaving correctly, from adding additional CSS properties, transitions, animations, and even triggering a reflow on the element using requestAnimationFrame and timers, but nothing seems to help. I would be very grateful to anyone who can offer a solution.
A: This was apparently a bug in the vendor-prefixed implementation of CSS transitions where it pre-computes the target and does not update it after a reflow. It's no longer resent in the un-prefixed version in newer versions of WebKit.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,601
|
Q: Content Type vs MIME Type Can someone explain to me what's the difference between Content-Type and the MIME Type? I can't find a clear answer on the net.
If Content-Type usually used inside the Browser.
And MIME type is used by the os?
A: In Content-Type=text/plain, Content-Type is a MIME header, text/plain is MIME Type.
Here are more MIME Headers (https://msdn.microsoft.com/en-us/library/ms526943(v=exchg.10).aspx):
MIME-Version
Content-Type
Content-Transfer-Encoding
Content-ID
Content-Description
Content-Disposition
Here are more MIME Types (https://developer.mozilla.org/en-US/docs/Web/HTTP/Basics_of_HTTP/MIME_types. ):
text/plain
text/html
image/jpeg
image/png
audio/mpeg
audio/ogg
audio/*
video/mp4
More, you can specify an encoding for Content-Type
text/html; charset=UTF-8
A: The Content-Type indicates the media type, where media types are defined as MIME types.
Content Type in RFC 7231
The "Content-Type" header field indicates the media type of the associated representation: [...]
Content-Type = media-type
Media Type in RFC 7231
HTTP uses Internet media types [RFC2046] in the Content-Type
(Section 3.1.1.5) and Accept (Section 5.3.2) header fields in order
to provide open and extensible data typing and type negotiation.
Where RFC 2046 specifies MIME Types.
A: MIME (Multipurpose Internet Mail Extensions)
MIME was originally designed to solve problems encountered in moving messages between different electronic mail systems.
Content-type
Header value defined in a HTTP response, the browser can open the file with the proper extension/plugin.
Example:Content-type: image/jpeg
This format is inspired form MIME format.
Content-type: main_mime_type(image)/mime_subtype(jpeg)
or HTTP adopted it to describe and label its own multimedia content.
Outside from question: MIME sniffing:-is used by some web browsers, in an attempt to help web sites which do not correctly signal the MIME type of web content display.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,877
|
Dreizack steht für:
Dreizack, eine Waffe
Dreizack (Heraldik), Symbol der Wappenkunde
Pflanzengattung der Dreizacke (Triglochin), Familie der Dreizackgewächse
Siehe auch:
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,221
|
"""Common test utilities"""
import os
import tempfile
def get_test_tmpdir():
"""Get default test temp dir."""
tmpdir = os.environ.get('TEST_TMPDIR', tempfile.gettempdir())
return tmpdir
def mkdtemp():
"""mkdtemp wrapper that respects TEST_TMPDIR"""
return tempfile.mkdtemp(dir=get_test_tmpdir())
def temp_file(contents, suffix=''):
"""Create a self-deleting temp file with the given content"""
tmpdir = get_test_tmpdir()
t = tempfile.NamedTemporaryFile(suffix=suffix, dir=tmpdir)
t.write(contents)
t.flush()
return t
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 794
|
{"url":"http:\/\/mathhelpforum.com\/math-topics\/98461-arithmetic-mean-geometric-mean-print.html","text":"# Arithmetic mean and Geometric mean\n\n\u2022 August 18th 2009, 07:18 AM\na69356\nArithmetic mean and Geometric mean\nQ) A and B are two numbers such that there G.M is 20% lower than their A.M .Find the ratio between the two numbers.\n\nThanks,\nAshish\n\u2022 August 18th 2009, 07:38 AM\nmr fantastic\nQuote:\n\nOriginally Posted by a69356\nQ) A and B are two numbers such that there G.M is 20% lower than their A.M .Find the ratio between the two numbers.\n\nThanks,\n\nAshish\n\n$\\sqrt{a b} = \\frac{4}{5} \\left( \\frac{a + b}{2} \\right)$\n\n$\\Rightarrow ab = \\frac{4}{25} (a + b)^2 \\Rightarrow 25 ab = 4a^2 + 8 ab + 4 b^2 \\Rightarrow 25 = 4 \\left( \\frac{a}{b}\\right) + 8 + 4 \\left(\\frac{b}{a}\\right)$.\n\nLet the ratio be $x = \\frac{a}{b}$. Then:\n\n$25 = 4x + 8 + \\frac{4}{x}$.\n\nYour job is to solve for x.\n\u2022 August 18th 2009, 08:06 AM\nSoroban\nHello, Ashish!\n\nMy solution is similar to Mr. F's . . .\n\nQuote:\n\n$A$ and $B$ are two numbers such that there G.M is 20% lower than their A.M.\nFind the ratio between the two numbers.\n\nLet $a$ and $b$ be the two numbers.\n\nWe have: . $\\sqrt{ab} \\:=\\:\\frac{4}{5}\\left(\\frac{a+b}{2}\\right) \\quad\\Rightarrow\\quad 5\\sqrt{ab} \\:=\\:2(a+b)$\n\nSquare both sides: . $25ab \\;=\\;4a^2 + 8ab + 4b^2 \\quad\\Rightarrow\\quad 4x^2 - 17ab + 4b^2 \\:=\\:0$\n\n. . which factors: . $(a - 4b)(4a - b) \\:=\\:0$\n\nHence, we have: . $\\begin{Bmatrix}a - 4b \\:=\\:0 & \\Rightarrow & \\dfrac{a}{b} \\:=\\: 4 \\\\ \\\\[-2mm] 4a - b \\:=\\:0 & \\Rightarrow & \\dfrac{a}{b} \\:=\\:\\dfrac{1}{4} \\end{Bmatrix}$","date":"2014-07-11 17:58:12","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\": 12, \"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\": 0.959376335144043, \"perplexity\": 1727.9291847738746}, \"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-2014-23\/segments\/1404776428349.3\/warc\/CC-MAIN-20140707234028-00079-ip-10-180-212-248.ec2.internal.warc.gz\"}"}
| null | null |
{"url":"http:\/\/mathoverflow.net\/questions\/10509\/goldbach-type-theorems-from-dense-models\/10558","text":"# Goldbach-type theorems from dense models?\n\nI'm not a number theorist, so apologies if this is trivial or obvious.\n\nFrom what I understand of the results of Green-Tao-Ziegler on additive combinatorics in the primes, the main new technical tool is the \"dense model theorem,\" which -- informally speaking -- is as follows:\n\nIf a set of integers $S \\subset N$ is a dense subset of another \"pseudorandom\" set of integers, then there's another set of integers $S' \\subset N$ such that $S'$ has positive density in the integers and $S, S'$ are \"indistinguishable\" by a certain class of test functions.\n\nThey then use some work of Goldston and Yildirim to show that the primes satisfy the given hypothesis, and note that if the primes failed to contain long arithmetic\/polynomial progressions and $S'$ did, they'd be distinguishable by the class of functions. Applying Szemeredi's theorem, the proof is complete.\n\nObviously I'm skimming over a great deal of technical detail, but I'm led to believe that this is a reasonably accurate high-level view of the basic approach.\n\nMy question(s), then: Can one use a similar approach to obtain \"Goldbach-type\" results, stating that every sufficiently large integer is the sum of at most k primes? Is this already implicit in the Goldston-Yildirim \"black box?\" If we can't get Goldbach-type theorems by using dense models, what's the central obstacle to doing so?\n\n-\n\n## 1 Answer\n\nYes, this can be done, provided that k is at least 3. A typical example is given in this paper: http:\/\/arxiv.org\/abs\/math\/0701240 . (This uses a slightly older Fourier-based method of Ben that predates his work with me, but is definitely in the same spirit - Ben's paper was very inspirational for our joint work.)\n\nFor k=2, unfortunately, the type of indistinguishability offered by the dense model theorem is not strong enough to say anything. The k=2 problem is very similar to the twin prime conjecture (in both cases, one is trying to seek an additive pattern in the primes with only one degree of freedom). If one deletes all the twin primes from the set of primes, one gets a new set which is indistinguishable from the set of primes in the sense of the dense model theorem (because the twin primes have density zero inside the primes, by Brun's theorem), but of course the latter set has no more twins. One can pull off a similar trick with representations of N as the sum of two primes. But one can't do it with sums of three or more primes - there are too many representations to delete them all just by removing a few primes.\n\n-","date":"2015-08-29 17:31:58","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\": 0.7999125123023987, \"perplexity\": 333.6518194277365}, \"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-2015-35\/segments\/1440644064517.22\/warc\/CC-MAIN-20150827025424-00081-ip-10-171-96-226.ec2.internal.warc.gz\"}"}
| null | null |
Q: understanding this javascript function code function isBlank(s){
var len = s.length
var i
for(i=0; i<len; ++i) {
if(s.charAt(i)!= " ") return false
}
return true
}
I am totally new to JavaScript and coding. Please can someone explain me how is this code working.
I know that it is being used to check whether a input box has some value or not, but I know no further.
question update....
See, in the above code, the for loop runs and if the string is not blank it returns false.
Now for loop ends and browser reads the next line which is-- returns true--. So is not the function finally returning true. No matter if there was a return false in the middle.
A: It is looping through the string s and checking if each character is a space. If there are characters other than spaces, then the function returns false, because the string is not blank. If the string is empty or only contains spaces, then it returns true because the string is blank.
A: function isBlank(s){ // it is a function named 'isBlank' that accept one parameter, that the parameter is something passed from the outside
var len = s.length // Assign the length of parameter 's' into a local variable 'len'
var i // Declare a new local variable 'i'
for(i=0;i<len;++i) { // This is a 'loop', you can google it
if(s.charAt(i)!= " ") return false // if any character inside the parameter 's' is not an empty space, that means it isn't blank, so return false
}
return true; // If code reach this line that means 's' is either with 0 length or all characters of it are an empty space
}
By using the above function:
alert(isBlank("123")); // false
alert(isBlank("")); // true
alert(isBlank(" ")); //true
A: The function checks whether the string is empty or not.
for(i=0;i<len;++i) { // iterates through the string
if(s.charAt(i)!= " ") // checks whether character at index i of string s is not equal to " ".
return false
}
It iterates through the string and returns false if any character is not equal to " ".s.charAt(i) returns the character at index i of the string s.
If the condition is not satisfied for every character then it returns true.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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| 2,025
|
Some of us have the best of intentions when it comes to our plans to complete our advance directives or start the advance care planning process with our families. But, our intentions to plan for the medical unknown are often waylaid by our fears or what we perceive to be our loved ones' fears of discussing such things.
Or perhaps it seems like we'd be planning for the worst rather than hoping for the best–a rationale I've often heard used to condemn people who are adamant about advance care planning (myself included). If we are stopped in our tracks by the fear of offending our loved ones, it can be incredibly hard to convince ourselves to move forward with the advance care planning process. That is until you hear a story about how not planning affected someone else's family. I ran across this most touching news story about one wife's regrets after the passing of her husband (that remain with her some five years later) and just had to share it. I hope that it will serve as inspiration to all of you out there who have stalled your advance care planning process to kick it back into high gear and 'have the talk' with your family today!
|
{
"redpajama_set_name": "RedPajamaC4"
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| 8,791
|
NHS Forth Valley
A Century and a Half of NHS Service
12/06/2017 Forth Valley Royal Hospital, Media Release
Four members of staff who worked in NHS Forth Valley's Physiotherapy Department recently retired, after notching up a total of 150 years of service between them.
Mary Ferguson who worked for NHS Forth Valley for 43 years, started her health service career in the catering department at the former Stirling Royal Infirmary in 1974. She worked in a number of departments within the hospital including domestic services, the maternity unit as a nursing assistant and casualty as a nursing assistant. She then moved to the physiotherapy department in 1990 to be a physiotherapy assistant, a role she held for the next 27 years both in Stirling and at Forth Valley Royal Hospital. Mary was also a trade union representative for many years.
Liz Smith joined NHS Forth Valley as a new physiotherapy graduate in 1975 and worked in the former Falkirk and District Royal Infirmary, the Royal Scottish National Hospital and Denny Health Centre. She became a physiotherapy superintendent in 1990 and in 2011 was appointed as Physiotherapy Co-ordinator with responsibility for all outpatient physiotherapists and clinics across Forth Valley. With an MSc in physiotherapy, her final five years were spent implementing the redesign of the musculoskeletal service to give local patients a better service.
Margaret Godsman spent 20 years working as a clerical assistant in the physiotherapy departments in Alloa Health Centre, Clackmannanshire Community Healthcare Centre and Stirling Community Hospital. Known for her cheerful friendly nature, she was able to put patients at ease with her welcoming manner.
Linda Thomson, who recently retired after more than 40 years service, started her health service career in the former NHS Board headquarters in Spittal Street in Stirling as a junior clerkess before moving in 1982 to the physiotherapy department in the former Stirling Royal Infirmary to work as a clerical assistant. In her 34 years working in the department office, Linda was a hardworking colleague, who kept the team together and was the first to organise any social event.
Pictured: Front Left – Liz Smith, Front Right – Mary Ferguson, Back Left – Linda Thomson, Back Right – Margaret Godsman.
Enter your email address to receive the latest news and regular updates from NHS Forth Valley. You can unsubscribe at any time.
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Step on Stress Course
|
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| 8,562
|
\section{Introduction}
Black holes (BHs) are a basic component of galaxies, and the existence of a
tight correlation between the stellar velocity dispersion of bulges
(\ensuremath{\sigma_{\ast}}) and the
BH mass (the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation; Gebhardt et al.\ 2000a; Ferrarese \&
Merritt 2000) suggests that the growth of the BH plays a fundamental
role in the growth of the bulge, although exactly how remains unclear
(e.g.,~Silk \& Rees 1998; Kauffmann \& Haehnelt 2000; Di~Matteo et al.\ 2005).
The \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation for inactive galaxies, in so far as it
represents the final state of the BH-bulge system, represents a
boundary condition for various evolutionary scenarios, and some clues
are embedded in the scatter and possible skewness in the local
\ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation (Robertson et al.\ 2005). Unfortunately, the number
of available points in the relation for inactive galaxies is limited, and
statistics are poor. Currently, our only recourse is to rely on BH
masses from active galactic nuclei (AGNs). To the extent that the BHs
in AGNs continue to gain mass, the relation of BH masses in AGNs to
their host bulges may carry additional information about the
establishment of the relation for inactive sources. Since the majority of BH
mass was assembled at high redshift (e.g.,~Yu \& Tremaine 2002), we
might expect to find the strongest evidence for evolution in the
\ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation at large cosmological distances (Shields et al.\
2003; Treu et al.\ 2004; Walter et al.\ 2004; Peng et al.\ 2005).
While undoubtedly this
is a vital direction to pursue, there are a number of compelling
reasons to study the local AGN \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation as well.
For one thing, while various methods are available to characterize the
bulge potential, virial mass estimation (e.g.,~Ho 1999; Wandel et al.\ 1999;
Kaspi et al.\ 2000), where the dense broad-line region (BLR) gas
is assumed to be on Keplerian orbits around the central BH, is currently
the most widely utilized tracer of BH mass.
In the absence of a detailed
model of the BLR, the zeropoint for the virial BH mass scale is set
through a direct comparison with stellar velocity dispersions for a
small sample of local AGNs (Gebhardt et al.\ 2000b; Ferrarese et al.\
2001; Nelson et al.\ 2004; Onken et al.\ 2004). The virial BH masses
considered in these studies are remarkably consistent with the
\ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation of inactive galaxies, suggesting virial masses are
reliable. But we must be cautious. For instance, there are compelling
reasons to believe the BLR is actually a disk-wind (e.g.,~Murray \&
Chiang 1997; Proga et al. 2000; Proga \& Kallman 2004)
whose kinematics depend on both the mass and the accretion rate onto
the BH. In this scenario, the virial mass calibration would depend
systematically on BH mass and luminosity. We require objects spanning
a wide range of AGN properties to properly calibrate the primary
rung in our AGN BH ``mass ladder.'' At the same time, we may hope to
learn about evolution of the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation by looking at the full
distribution of local BHs (Robertson et al.\ 2005), and AGNs in
particular (e.g.,~Yu \& Lu 2004), in the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ plane.
\section{Sample Selection and Methodology}
Our goal is to directly compare \ensuremath{M_\mathrm{BH}}\ with \ensuremath{\sigma_{\ast}}\ for a large
sample of AGNs. As outlined in Greene \& Ho (2005c), we selected
spectroscopically identified AGNs from the Third Data Release of the
Sloan Digital Sky Survey (SDSS DR3; Abazajian et al.\ 2005) with $z
\leq 0.05$ and signal-to-noise (S/N) ratios per pixel $\geq 18$ in the
region surrounding the \ion{Ca}{2} $\lambda \lambda$8498, 8542, 8662
triplet (CaT). Here we consider the 32 objects from Greene \& Ho
(2005c) with resolved \ensuremath{\sigma_{\ast}}\ measurements and robust H\ensuremath{\alpha}\
line widths. To increase the sample, we have relaxed the $z$
requirement and included an additional 24 galaxies to satisfy the
criteria established by Greene \& Ho for use of the ``Fe region''
(5250--5820 \AA): S/N $\geq 20$ ($\langle$ S/N $\rangle=40 \pm 8$),
estimated Eddington ratios [\ensuremath{L_{\mathrm{bol}}/L{\mathrm{_{Edd}}}}, where $L_{\mathrm{Edd}} \equiv
1.26 \times 10^{38}$~(\ensuremath{M_\mathrm{BH}}/\ensuremath{M_{\odot}}) ergs s$^{-1}$] $\lesssim 0.5$, and AGN
contamination $< 80 \%$.
In addition to the 56 objects from the SDSS,
we include 15 intermediate-mass BHs (IMBHs; \ensuremath{M_\mathrm{BH}}\ $\leq$ $10^6$~\ensuremath{M_{\odot}})
from Greene \& Ho (2004) with \ensuremath{\sigma_{\ast}}\ measurements from Barth
et al.\ (2005), resulting in a total of 71 objects
(see Table 1).
The stellar velocity dispersions are measured using a
\psfig{file=table1_sh_v4.epsi,width=9cm,angle=0}
\vskip +3mm
\noindent
direct pixel-fitting algorithm described in detail in Greene \& Ho
(2005c). The uncertainties are derived from simulations in which the
AGN contamination and S/N ratio are varied for a grid of model galaxy spectra.
Virial masses are based on reverberation mapping (Blandford \& McKee
1982), which uses the measured lag between variability in the
photoionizing continuum and emission lines to estimate BLR radii.
Currently there are 35 reverberation-mapped AGNs in the literature
(Peterson et al.\ 2004). These, in turn, are used to calibrate the
radius-luminosity relation, \ensuremath{R_{\mathrm{BLR}}} $\propto$ \ensuremath{L_{5100}}$^{0.64}$ (Greene \& Ho
2005b; see also Kaspi et al.\ 2005), from which it is possible to infer
a radius from the AGN luminosity.
Combining the radius with an estimate of the velocity dispersion of the BLR
yields a virial mass estimate for the BH, \ensuremath{M_\mathrm{BH}}=$fR~v^2/G$, where $f$ is
a factor that accounts for the geometry of the BLR. We
assume $f=0.75$ for a spherical BLR (Netzer 1990). Because our
sample is selected to have strong stellar continua, virial BH mass
estimation requires special care. Under these circumstances the most
robust virial mass estimator is that based on the width and luminosity
of the broad H\ensuremath{\alpha}\ emission line, as advocated by Greene \& Ho (2005b).
The emission-line fitting is described in Greene \& Ho
(2004, 2005b). Briefly, the stellar continuum is modeled and removed
using a principal component analysis designed for the SDSS data by Lei Hao
(Hao et al.\ 2005). We then construct a multi-component Gaussian model
of the [\ion{S}{2}]~$\lambda \lambda$6716, 6731 doublet, which is shifted and
scaled to fit the narrow H\ensuremath{\alpha}+[\ion{N}{2}]~$\lambda\lambda$6548, 6583
complex. The remaining (broad) H\ensuremath{\alpha}\ flux is fit with as many
Gaussian components as needed to provide a statistically acceptable
fit, although we attach no physical significance to the individual
components. As described in Greene \& Ho (2005b), we measure both
\ensuremath{\mathrm{FWHM}_\mathrm{H{\alpha}}}\ and the true second moment (\ensuremath{\sigma_{\mathrm{H\alpha}}}) from the multi-component
Gaussian fits. The uncertainties in the luminosities and line widths
are derived using simulations, although we set a minimum uncertainty
of $\sim 5 \%$ on the line width.
\section{Results}
We present the largest single collection of \ensuremath{\sigma_{\ast}}\ measurements
in active galaxies. The single-epoch \ensuremath{M_\mathrm{BH}}\ values for the SDSS and
Barth et al.\ (2005) samples are estimated using \ensuremath{\mathrm{FWHM}_\mathrm{H{\alpha}}}\ (rather
than \ensuremath{\sigma_{\mathrm{H\alpha}}}; e.g.,~Peterson et al.\ 2004). In our full sample, we also
include the 15 reverberation-mapped AGNs considered by either Onken
et al.\ (2004) or Nelson et al.\ (2004), using the weighted-mean
\ensuremath{\sigma_{\ast}}\ from the two works. Weighted-mean virial products for
this sample are computed using the H\ensuremath{\beta}\ lag and FWHM measurements
presented in Peterson et al.\ (2004; the weights are calculated taking
into account the asymmetric error bars), and BH masses
are derived assuming $f=0.75$. Finally, we include the
well-
\hskip -8mm
\psfig{file=msigma_qn_newmass.epsi,width=9cm,angle=0}
\vskip -1mm
\figcaption[]
{ The \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation for active and inactive galaxies.
Open circles are measurements from this work using CaT, open squares
are measurements using the 5250--5820 \AA\ Fe region (see Greene \& Ho
2005c), and open triangles represent the Keck data from Barth et al.\
(2005) but with \ensuremath{M_\mathrm{BH}}\ recalculated using \ensuremath{\mathrm{FWHM}_\mathrm{H{\alpha}}}\ values from DR3.
Literature data include those of Onken et al.\ (2004) and Nelson et al.\
(2004; crosses; BH masses from Peterson et al.\ 2004), NGC 4395 and POX
52 (Filippenko \& Ho 2003; Peterson et al. 2005; Barth et al.\ 2004;
asterisks), and the primary sample of inactive galaxies with
dynamically determined values of \ensuremath{M_\mathrm{BH}}\ (Tremaine et al. 2002; filled
squares). Representative error bars are shown in the upper left for
the SDSS and Keck measurements. The dashed line represents the fit
for the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation of inactive galaxies as given by Tremaine
et al.\ (2002). The solid line is our best fit for the AGN sample with
a fixed slope of $\beta = 4.02$ and $\alpha = 7.96 \pm 0.03$;
the dotted lines show the measured
intrinsic scatter of 0.4 dex. We display histograms of
the \ensuremath{\sigma_{\ast}}\ ({\it top}) and \ensuremath{M_\mathrm{BH}}\ ({\it right}) distributions for
the Keck (shaded), SDSS (open), literature (filled), and inactive
(dash-dot line) samples.
\label{msigma}}
\vskip 2mm
\noindent
studied intermediate-mass BHs in NGC 4395 (reverberation mass
\ensuremath{M_\mathrm{BH}}$= 3.6 \times 10^5$~\ensuremath{M_{\odot}}, Peterson et al.\ 2005; virial mass
\ensuremath{M_\mathrm{BH}}$=1.4 \times 10^4$~\ensuremath{M_{\odot}}, Filippenko \& Ho 2003) and in POX 52
(virial mass \ensuremath{M_\mathrm{BH}}$=1.6 \times 10^5$~\ensuremath{M_{\odot}}, Barth et al.\ 2004).
The full sample of 88 objects
covers a range in mass of $10^{5}-10^{8.5}$ \ensuremath{M_{\odot}}, and a
corresponding range in \ensuremath{\sigma_{\ast}}\ of $30 - 268$ km~s\ensuremath{^{-1}}\ (see
Table 1). Consistent with
previous work, Figure 1 shows that active galaxies apparently follow
the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation defined by inactive systems, even with a sample
size increased by a factor of nearly 6. In detail, however, we do
find significant differences in zeropoint and slope compared to the
inactive sample, which we describe below.
Assuming a log-linear form for the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation,
log(\ensuremath{M_\mathrm{BH}}/\ensuremath{M_{\odot}}) = $\alpha+\beta$log(\ensuremath{\sigma_{\ast}}/$\sigma_0$), with
$\sigma_0$ = 200 km~s\ensuremath{^{-1}}, we can formally quantify deviations of AGNs
from the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation of inactive systems.
We use the Levenberg-Marquardt algorithm as implemented by
{\it mpfit} to minimize \ensuremath{\chi^2}, defined, following Tremaine et al. (2002), as
\begin{equation}
\ensuremath{\chi^2} \equiv \sum_{i=1}^N \frac{(y_i-\alpha-\beta
x_i)^2}{\epsilon^2_{yi}+\beta^2\epsilon^2_{xi}},
\end{equation}
where $x_i$ correspond to \ensuremath{\sigma_{\ast}}$_{,i}$, $y_i$ to \ensuremath{M_\mathrm{BH}}$_{,i}$, and
$\epsilon_i$ to the formal uncertainties in each measurement. In
order to account for asymmetric uncertainties in each parameter, at
each iteration $\epsilon_i$ is selected to reflect the sign of
$y_i-\alpha-\beta x_i$. In the simplified case of symmetric errors,
we recover the results of the Numerical Recipes routine {\it fitexy}
(Press et al. 1992) as implemented in IDL. We begin by fixing the
slope $\beta$ to the best-fit value of 4.02 from Tremaine et al. and
investigate potential offsets in zeropoint. We find, for our sample
alone, a best-fit $\alpha = 7.96 \pm 0.03$, which corresponds to an
offset of $-0.17 \pm 0.07$ from the value of $\alpha=8.13 \pm 0.06$ of
Tremaine et al.\ (consistent with Gebhardt et al.\ 2000b; Nelson et al.\
2004; Onken et al.\ 2004; see summary in Table 2).
The offset increases to $-0.21 \pm 0.06$
when the literature values are included (using either the
reverberation-mapped or virial mass for NGC 4395). Note that we are
using formal uncertainties in \ensuremath{M_\mathrm{BH}}, while the true uncertainties are
probably dominated by our ignorance of the BLR geometry and the
corresponding uncertainty in how to extract the velocity dispersion of
the virialized BLR from the observed line profile.
Following Tremaine et al.\ and Gebhardt et al.\ (2000a), we
estimate the intrinsic scatter as the value $\epsilon_0$ that, when
added to $\epsilon_y$, results in a minimum \ensuremath{\chi^2_r}\ of 1. For both
our sample alone and including the literature sample, we find an
intrinsic scatter\footnote{The intrinsic scatter increases to 0.5 dex
when \ensuremath{\sigma_{\mathrm{H\alpha}}}, rather than \ensuremath{\mathrm{FWHM}_\mathrm{H{\alpha}}}\ is used to estimate \ensuremath{M_\mathrm{BH}}, partly
because of the difficulty of measuring the low-contrast line wings.
We therefore consider only masses derived using \ensuremath{\mathrm{FWHM}_\mathrm{H{\alpha}}}\ in the
following. We estimate that disk rotation contributes at most a small
error to \ensuremath{\sigma_{\ast}}\ since we find no correlation between galaxy
inclination angle and deviation from \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ ($78 \%$ probability of
no correlation with Kendall's $\tau$), and typically only the inner
$\sim 20 \%$ of the galaxy light enters the fiber. See further
arguments in Greene \& Ho (2005a).} of \ensuremath{\epsilon_0}=0.4 (dotted lines in
Fig. 1). This is to be compared with the estimated scatter of 0.25-0.3
dex for the inactive sample (Tremaine et al.\ 2002).
While there is probably intrinsic scatter in the underlying
\ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation, we conservatively adopt 0.4 dex as the systematic
uncertainty in the single-epoch \ensuremath{M_\mathrm{BH}}\ measurements, so that we bracket
the full range in possible uncertainty.
If we repeat the fitting above increasing the uncertainties in the
single-epoch BH masses by 0.4 dex in quadrature, the results for our sample
alone are virtually unchanged, while we find $\alpha = 7.86 \pm 0.04$ for the
full sample, which corresponds to an offset of $-0.27 \pm 0.07$. This
offset is similar to that advocated by Onken et al., but it is
statistically much more robust, being based on a final sample that is
nearly 6 times larger.
When we fit both the zeropoint and slope, we obtain $\alpha=7.84 \pm
0.04$ and $\beta=3.65 \pm 0.13$ ($\alpha=7.89 \pm 0.05$, $\beta=3.74
\pm 0.17$) if we include (exclude) literature values, corresponding to
slopes flatter than the value of $\beta = 4.02 \pm 0.32$ for inactive
sources by $-0.37 \pm 0.35$ ($-0.28 \pm 0.36$). Including the 0.4 dex
scatter to the single-epoch measurements yields an even flatter slope,
with $\alpha=7.79 \pm 0.04$ and $\beta = 3.49 \pm 0.18$ ($\alpha=7.68
\pm 0.10$, $\beta= 2.95 \pm 0.32$).
It appears that much of the flattening is driven
by objects with BH masses $< 10^6$~\ensuremath{M_{\odot}}, which rely on an
extrapolation of the radius-luminosity relation and thus may be
suspect. [As pointed out by Barth et al.\ (2005), these objects also
may be biased by selection toward large \ensuremath{M_\mathrm{BH}}\ at a given \ensuremath{\sigma_{\ast}}.]
When we remove the Barth et al.\ objects, as well as POX 52 and NGC
4395, but include all other data, we find $\beta = 4.19 \pm 0.22$ with
the formal errors, or $\beta = 3.85 \pm 0.25$ with the additional 0.4
dex uncertainty added. The fact that the slope is still shallower when
the (more realistic) uncertainties are included gives us some
confidence that the flattening is real.
\section{Implications and Conclusions}
We have established, with statistical confidence for the first time,
that the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation of local AGNs, while generally similar to
that of inactive galaxies, shows some significant differences. We
find evidence for a lower zeropoint, shallower slope, and (probably)
larger scatter. There are many competing effects,
relating both to BLR physics and galaxy evolution,
\hskip 10mm
\psfig{file=table2_v2.epsi,width=6cm,angle=0}
\vskip +3mm
\noindent
that may contribute
to the observed differences. If we posit that AGNs obey the relation
of inactive galaxies exactly, then the scatter and zeropoint offset
may be attributed to variations in the geometry of the BLR. This is
the assumption made by Onken et al.\ (2004), who derive a statistical
offset in the factor $f$ that scales all BH masses upwards relative to
the case of a spherical BLR. If, however, as suggested by disk-wind
models (e.g.,~Proga \& Kallman 2004), the geometry of the BLR depends
on physical properties of the AGN such as the BH mass and the
Eddington ratio, then virial mass estimates will not scatter randomly
about one fixed value of $f$. Rather, $f$ will change systematically
with the state of the system, and its average value for any given
sample will depend on the range of parameter space spanned by the
objects used to derive it. It is important to recognize that all work
so far---including ours---has considered a rather limited range in
\ensuremath{M_\mathrm{BH}}\ and \ensuremath{L_{\mathrm{bol}}/L{\mathrm{_{Edd}}}}, and so may lead to a biased value of $f$. Apart from
the Greene \& Ho (2004) objects studied by Barth et al.\ (2005), the
practical challenge of detecting stellar absorption features to
measure \ensuremath{\sigma_{\ast}}\ inevitably biases the final sample toward
relatively low Eddington ratios and BH masses. Excluding the Barth et
al. objects, the sample summarized in Figure 1 has a median \ensuremath{L_{\mathrm{bol}}/L{\mathrm{_{Edd}}}}\ =
$6\times10^{-2}$ and $10^6$ {$\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}$}\ \ensuremath{M_\mathrm{BH}}\ {$\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}$}\ $10^8$~\ensuremath{M_{\odot}}. While we
expect that secondary parameters (e.g., \ensuremath{L_{\mathrm{bol}}/L{\mathrm{_{Edd}}}}) may ultimately help to
account for the overall scatter in the AGN \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation, we
refrain from discussing this issue here because we believe that a
proper analysis would require a larger and more complete sample than
is currently available.
Apart from systematic uncertainties in virial masses, evolution of the
\ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation with cosmic time (e.g.,~Shields et al.\ 2003; Treu
et al.\ 2004; Walter et al.\ 2004; Peng et al.\ 2005) also imprints
scatter and skewness into the local relation as a function of \ensuremath{M_\mathrm{BH}}\
(Robertson et al.\ 2005). However, it is unclear at this stage how
much scatter can be attributed to the fact that BHs in AGNs, in so far
as they are radiating and thus accreting, are still gaining mass.
Any differential growth between BHs and bulges
will introduce additional scatter to the AGN \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation
if AGN accretion and star formation are not precisely synchronized (Ho
2005; Kim et al. 2005). If we
ascribe all the observed scatter to differential growth (taking the
observed scatter of $\sim 0.27$ dex in the relation for inactive
objects from Tremaine et al.), there can be no more than $\sim$0.3 dex
scatter (factor of 2) introduced by relative BH-bulge growth.
This level of growth has only modest fuel requirements that are easy
to sustain in nearby galaxies;
a $10^6$ \ensuremath{M_{\odot}}\ BH requires only
$0.022$~\ensuremath{M_{\odot}}\ yr$^{-1}$ to double its mass in a Saltpeter time ($4.5
\times 10^{7}$ yr).
Finally, taking our entire data set at face value, we do find evidence
for a shallower slope than the inactive \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation. Whether
this is the result of flattening at low mass or a different slope in
AGNs is difficult to determine at the present time, in the absence of
more AGNs with \ensuremath{M_\mathrm{BH}}\ $> 10^8$~\ensuremath{M_{\odot}}. In this regard, Wyithe (2005)
argues that the slope for the inactive sample steepens considerably
when the four smallest \ensuremath{\sigma_{\ast}}\ values are removed, independently
suggesting flattening at low mass. Flattening at low mass may be a
result of the changing efficiency in AGN feedback in low-mass halos.
For instance, the formalism of Vittorini et al.\ (2005) finds that a
combination of decreased optical depth (proportional to galaxy radius)
and cooling times shorter than a dynamical time (small, dense halos)
allows these BHs to grow to larger relative masses without feedback
limitations. Alternatively, different growth modes between spheroidal
and disk-dominated systems may result in a different final position on
the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ plane. On the other hand, we cannot preclude the
possibility that a change in slope in the BLR radius-luminosity
relation at low luminosity is responsible for the change in slope in
the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation. However, we note that a radius-luminosity
slope closer to the theoretically preferred value of 0.5 (e.g.,~Kaspi
et al.\ 2000) would only increase the observed discrepancy in slope.
Reverberation mapping of low-mass BHs would be required to address
this issue.
In summary, although we have increased the population of AGNs with \ensuremath{\sigma_{\ast}}\
measurements by a factor of nearly 6, we do not yet have a large enough
sample, or adequate coverage of parameter space, to uniquely identify the
cause or causes responsible for the observed differences between
the \ensuremath{M_{\mathrm{BH}}-\ensuremath{\sigma_{\ast}}}\ relation of local active and inactive galaxies. Future effort
should focus on (1) further enlarging the sample of AGNs with robust
\ensuremath{\sigma_{\ast}}\ measurements, (2) pushing the samples to the extremes of the
mass distribution, particular above $10^8$~\ensuremath{M_{\odot}}, (3) extending the
luminosity coverage to include objects with a wider range in Eddington
ratios, and (4) better characterizing the BLR radius-luminosity relation
over a broader range of AGN properties than is currently available.
\acknowledgements
We thank L. Hao for providing her PCA code, D.~Proga
for useful discussion, and the SDSS collaboration for providing the
extraordinary database and processing tools that made this work
possible. We thank an anonymous referee for a prompt and positive
review.
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{
"redpajama_set_name": "RedPajamaArXiv"
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About The GFG
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Accreditation: About
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Planning the Funeral
Do it all Yourself
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Recommended Directory
Book Review: R.I.P. Off! By Ken West
Charles Cowling No Comments Like
RIP Off! is Ken West's thinly-fictionalised account of his pioneering introduction of natural burial to Carlisle in 1993. It contrasts the enthusiastic reception his invention received in the media and among the public with the fear and loathing it stirred up in local undertakers.
They didn't understand it. They saw it as a threat to their commercial interests and their professional status. They didn't like Ken's mission to empower the bereaved with information. They didn't like his advocacy of low-cost funerals and his imputation that undertakers charge too much. They were infuriated by his charm, his humour and his success in creating publicity for his revolutionary way of disposing of the dead. They conspired to undermine and discredit him.
Considering the battering Ken took in real life from the Dismal Trade, you'll not be surprised to see him settle scores in RIP Off!. He does. But his weapon of choice is not invective but satire. He debunks but he doesn't put the boot in. He is gracious in victory. This is not how some undertakers may see it. If so, they may console themselves that it could have been a lot worse.
I suspect Ken has cause to feel much angrier than he lets on, but he refuses to cast himself as victim and he rises serenely above rancour. This is descriptive, I think, of the strength of character he must have needed, as a local authority officer, to steer his innovative scheme through all manner of committeedom all the way to implementation. It is rare to see the public service at the cutting edge of anything. In addition to zeal, persuasiveness and perseverance, there must have been cunning, too – of the most ethical sort, of course.
RIP Off! reads more like a thinly fictionalised memoir than a novel because, though it has conflict a-plenty, it doesn't have a conventional plot which concludes, after a period of suspense, in a resolution. It begins as story, then becomes more episodic and anecdotal. That's not meant as a criticism. There're plenty of insights into the hidden world of the funerals business to keep you turning the pages, together with some cracking stories reworked, they have to be, from personal experience; many of them are much stranger than fiction. As for resolution, well, in real time, we've still some way to go.
Ken sets out his stall early. He characterises undertakers as a "mafia" as early as page 2. He pinpoints with deadly accuracy their insecurities and vanities: "all Round Table and moral rectitude". He has a go at their disposition to think too well of themselves. A great many people who work in crematoria will cheer when they read:
"The measure of a dominant funeral director was his belief that he could call the tune at all the local cemeteries and crematoria; that he could act as the top dog, as if he owned the entire facility and its staff."
Okay, Ken can occasionally be cruel: "Brian said he could always get work because he had an O level, and this made the more cynical funeral directors refer to him as the professor." But he can be kind, too. The portrayals of Roger, the cut-price undertaker, and Graham, who ends up working for a corporate, are not unsympathetic.
The undertakers' trade association, BALU, embodies the pomposity and secretiveness of its members, viewing them as "the only ones who could judge what people really needed. They were convinced that too much information would confuse and upset the bereaved; that they can be told too much." Not much change there, then.
If the independents are nothing to write home about, the corporates are worse. When one undertaker sells up to a corporate based in Manchester of all places, "it stuck in [his] craw that although he had not provided cheap funerals, he had never been this greedy."
It is the settled view of the undertakers in RIP Off! that the hero, Ben West (see what I mean about thinly disguised) is "an isolated green weirdo" and a "fucking smartarse." Worse, he is "an advocate of change and this … was intolerable." The story is an account of the undertakers' fightback. Each side enjoys victories. Or, rather, the undertakers win some skirmishes but Ben is in the business not of picking a fight with them but of campaigning in the public arena for cheaper, greener, more authentic funerals. Everyone is left standing at the end, by which time, the record shows, natural burial has gone global.
Not necessarily in the form Ben West originally envisages, though. West is an environmentalist and, appealing as natural burial is to those who would tread lightly on the Earth, and it is one of the undertakers who comes to understand what natural burial comes to mean to most people: "Graham realised that Ben had got it wrong all those years ago. Sure, there were a few people wanting to save the planet but the majority were seeking something else, here and now, something that enabled the soul to go on."
Briefly, the future isn't green, it's spiritual.
It is Graham, too, who reflects at the end of the book "that [Ben] was still a voice in the wilderness. Where are they, all those young activists, the new greens, who were going to step into his shoes and give funeral directing a hard time?"
I think we may be slightly more optimistic. The novel describes restrictive practices, notably the prevention by threats of a coffin manufacturer and carriagemaster from dealing direct with the public. Today, a good many coffin suppliers deal direct with the public, as does James Hardcastle with his self-drive hearse.
Running alongside the story there are lots of good anecdotes in RIP Off!, many of them funny, some touching, some instructive. There's an exhumation. There's a glimpse inside a path lab. There are the messages people leave on graves for their dead ones, including one beginning with the words 'We have moved…' There's a Last Supper coffin whose depiction of Christ and his disciples the audience mistakes for a depiction of Showaddywaddy. And here's a thing: did you know that the corpses of alcoholics burn faster and fiercer?
The humour throughout is, come to think of it, dark shading into black. And Ken can be extremely funny. Roger's ancient bearers occasionally let him down by dropping dead. "This was a double-edged sword; he lost a bearer but he gained a funeral." There is no sex in the book, but it concludes with an exhortation to readers to have more.
RIP Off! isn't just an account of the birth pangs of natural burial. Its broader theme is the British way of death and there's no mistaking where Ken's heart lies. It is with simple, down-to-earth funerals organised by empowered people whose farewells are heartfelt and whose understanding is that our dead bodies must be returned to the earth whence they came in such a way that they can give the most back.
RIP Off! offers the general reader a fascinating and demystifying insight into the secretive world, both exotic and banal, of death and funerals. It will likely encourage the brave and the self-confident to take matters more into their own hands. It won't stop people using undertakers, but it will likely alter their relationship with them.
Those who work in the funerals business will agree that the book holds up a mirror of some sort to what actually goes on. It is unquestionably informative and very funny. Whether Ken's mirror distorts truth, and if so how much, is a matter for hot debate.
Buy your copy in time for Christmas here.
Category: funeral directors , Good books , natural burial
Masses banned at the crem December 12, 2013
Graveyard snappers: the finalists December 13, 2013
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
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Nate Houser is a retired American soccer player who coaches the Baker University men's and women's soccer teams. He played professionally in the A-League, National Professional Soccer League and second Major Indoor Soccer League.
Player
In 1990, Houser graduated from Poway High School. He attended Baker University, playing on the men's soccer team from 1990 to 1993. He graduated with a bachelor's degree in history and political science. In 2007, Baker University inducted Houser into its Athletic Hall of Fame. In 1993, the Wichita Wings drafted Houser in the territorial round of the National Professional Soccer League draft, but traded him to the Kansas City Attack. He went on to play eleven seasons with the Attack. In 1997, Kansas City won the NPSL championship. In addition to playing the winter indoor season with Kansas City, Houser also played outdoors with the Hampton Roads Mariners during the 1996 A-League season and the Rochester Rhinos during the 1997 A-League season. On March 7, 2000, Houser signed with the Milwaukee Rampage. On November 1, 2004, Houser joined the St. Louis Steamers. On March 19, 2005, the Steamers traded Houser and Mike Apple to the Baltimore Blast for Carlos Farias. In October 2010, he signed a one-year contract with the Missouri Comets.
Coach
In 2003, Baker University hired Houser to coach its women's soccer team. In 2008, he also became the head coach of the men's soccer team.
In 2010, he led the women to their first NAIA National Tournament appearance. They made it all the way to the Fab Four. In 2011 the women returned to the national tournament making it to the quarterfinals.
In 2008 the boys made their first NAIA sweet 16 appearance and in 2011 the boys made it to the Fab-Four.
References
Living people
1972 births
American Professional Soccer League players
American soccer coaches
American soccer players
Baltimore Blast (2001–2008 MISL) players
Virginia Beach Mariners players
Kansas City Attack players
Kansas City Comets (2001–2005 MISL) players
Major Indoor Soccer League (2001–2008) players
Milwaukee Rampage players
National Professional Soccer League (1984–2001) players
Rochester New York FC players
St. Louis Steamers (1998–2006) players
People from Poway, California
Sportspeople from California
Baker Wildcats men's soccer players
Association football forwards
Association football midfielders
Baker Wildcats men's soccer coaches
Baker Wildcats women's soccer coaches
Sportspeople from San Diego County, California
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\section{Introduction}
In this work we use the term ``Birkhoff-Hopf Theorem'' to refer to a number of results of different authors that overall show that a large class of cone-preserving linear operators behaves as contraction mappings with respect to the Hilbert projective metric. The original versions of this classical result were independently proved by Birkhoff \cite{birkhoff1} and Hopf \cite{hopf1}. Various authors have contributed afterwards to extend, generalize and sharpen the original theorems. A very partial list of contributors include Eveson and Nussmaum \cite{BHNB}, Liverani and Wojtkowski \cite{liverani1994generalization}, Lim \cite{lim2003birkhoff}. For a review, we refer to the monograph by Lemmens and Nussbaum \cite{NB} and, in particular, Appendix A therein.
The Birkhoff-Hopf theorem and the ideas behind it arise and play an important role in a wide variety of problems. For example, this result can be used to prove so-called linear and nonlinear
ergodic theorems in population dynamics \cite{cohen1979ergodic}, it has applications in control theory and concerning ordinary and partial differential equations, particularly filtering theory \cite{budhiraja1998robustness,nussbaum1994finsler}, it is an important tool in problems concerned with rescaling matrices or non-negative integral kernels, so-called $DAD$ theorems and Sinkhorn-Knopp algorithms \cite{borwein1994entropy,brualdi1974dad,knight2008sinkhorn}, it has been used to provide tight lower bounds for the logarithmic Sobolev constant of Markov chains~\cite{pmpaper}, and, in particular, the ideas behind the theorem play a central role in the Perron-Frobenius theory for linear and nonlinear mappings that leave a closed cone invariant \cite{babaei2018stochastic,Gaubert,multiPF,liverani1995decay,NB,rugh2010cones}.
In this work we extend the Birkhoff-Hopf theorem to multilinear mappings acting on finite products of cones in Banach spaces. This extension allows us to prove a new Perron-Frobenius theorem, based on a Hilbert cone-metric and the concept of Lipschitz matrix. Due to the Banach fixed point theorem, the latter result provides new conditions for the existence and uniqueness of a solution for systems of nonlinear equations of the type $f_i(x_1,\dots,x_\nu)=\lambda_i x_i$, $i=1,\dots,\nu$, with $x_i$ being an element of the Banach space $V_i$, and $f_i$ being a nonlinear cone-preserving mapping.
The paper is structured as follows: In the next section we recall the most general formulation of the Birkhoff-Hopf theorem we are aware of. In Section \ref{sec:multilinear_BH} we introduce multilinear and weakly multilinear maps and extend the Birkhof-Hopf theorem to these mappings. Then, in Section \ref{sec:multilinear_PF} we use that theorem to prove a new Perron-Frobenius theorem for cone-preserving multilinear maps. As for the linear setting, our new results have a wide range of applications. In particular, in Section \ref{sec:applications} we consider a class of nonlinear integral operators and provide an explicit formula for the contraction ratio of this type of mappings. This formula is particularly useful to provide conditions on the existence, uniqueness and computability of a solution to various systems of functional equations that arise in a number of diverse contexts. Examples include the integral equations considered in \cite{Bus73,bushell1986cayley}, the generalized Schr\"{o}dinger equation discussed in \cite{ruschendorf1998closedness}, the optimization of Kullback-Leibler divergence in optimal transport \cite{benamou2015iterative}, the matching problem for hypergraphs \cite{nguyen2017efficient}, various eigenvalue and rank-one approximation problems for tensors \cite{friedland2014number,tensorPF}, the optimization of multivariate polynomials \cite{zhou2012nonnegative} and the analysis of central components in complex networks \cite{arrigo2019multi,tudisco2017node}.
\section{Cone theoretic background}\label{Hilbsection}
We start by recalling few useful and standard definitions and properties of cones. See e.g.\ \cite{BHNB,Nussb} for further details.
Let $V$ be a real vector space and let $C\subseteq V$. We say that $C$ is a (convex and pointed) cone
if $C$ is closed and convex set such that $\alpha x\in C$ for any $x\in C$ and any $\alpha \geq 0$, $C\cap (-C)=\{0\}$.
Any such a cone $C\subseteq V$ induces a partial ordering on $V$ defined as
$$x \preceq_C y \quad \text{if and only if}\quad y-x\in C.$$
If additionally $(V,\norm{\cdot})$ is a Banach space, and there exists a constant $\gamma>0$ such that $\norm{x}\leq \gamma\norm{y}$ whenever $0\preceq_C x \preceq_C y$, we say that $C$ is a normal cone in $(V,\norm{\cdot})$.
For a lighter notation, in what follows we write $x\preceq y$ in place of $x\preceq_C y$ when there is no danger of confusion.
Given $x\in C$ and $y\in V$, we say that $x$ dominates $y$ if there exist $\alpha,\beta \in \mathbb{R}$ such that
$\alpha x\preceq y \preceq \beta x$.
If $x$ dominates $y$ and $x\neq 0$, then one can consider the quantity
\begin{align*}
M(x/y;C) = \inf\{\beta \in \mathbb{R} \colon x \preceq \beta y\}\,
\end{align*}
For $x,y\in C \setminus\{0\}$, we say that $x$ is comparable to $y$, and write $x\sim_C y$, if $x$ dominates $y$ and $y$ dominates $x$. This defines an equivalence relation on $C$ and its equivalence classes are called the components of $C$. In particular, for $u\in C\setminus\{0\}$, we denote by $C_u$ the equivalence class
\begin{equation}\label{defCu}
C_u= \{x\in C \colon x \sim_C u\}.
\end{equation}
Note that $C_u$ is itself a cone and, as $0$ only dominates itself, we have $C_0=\{0\}$.
\begin{definition}[Infimum]\label{def:inf}
Let $\Omega\subseteq C$ be a bounded subset of $C$. We say that $u\in \Omega$ is the infimum of $\Omega$, in symbols $u=\inf \Omega$, if $u$ is the largest lower bound of $\Omega$, that is $u\preceq x$ for all $x\in \Omega$ and if $v\preceq x$ for all $x\in \Omega$, then $v\preceq u$.
\end{definition}
\begin{definition}[Hilbert projective metric]
Let $x,y\in C$ be such that $x\sim_C y$. The Hilbert projective distance $d_C(x,y)$ between $x$ and $y$ is defined as follows: Either $x=y=0$ and we set $d_C(0,0)=0$, or $x,y\neq 0$ and
$$d_C(x,y)=\log\Big( M(x/y;C)\, M(y/x;C)\Big).$$
\end{definition}
It is well-known that, for any $u\in C$, $(C_u,d_C)$ is a pseudo-metric space. In particular, for every $x,y\in C_u$, it holds
\begin{equation*}\label{projprop}
d_C(\alpha\,x,\beta\, y) = d(x,y)\ \text{ for all }\ \alpha,\beta>0.
\end{equation*}
In other words, $d_C$ is a metric on the space of rays in $C_u$.
There is a rich literature on the completeness of $d_C$, we recall below a result that is particularly useful for us (see \cite{NB}, for example).
\begin{lemma
\label{NBcomplete}
Let $C$ be a normal closed cone in a Banach space. For $u \in C \setminus\{0\}$, suppose that $\varphi\colon C_u \to (0,\infty)$ is continuous in the norm topology and homogeneous (i.e.\ $\varphi(\alpha x)=\alpha \varphi(x)$ for all $\alpha\geq 0$), and let $S_\varphi= \{x\in C_u\colon \varphi(x)=1\}$. Then $(S_\varphi,d_C)$ is a complete metric space.
\end{lemma}
Next, we recall the definition of projective diameter.
\begin{definition}[Projective diameter]
Let $V$ be a real vector space and $C\subseteq V$ a cone. For $S\subseteq C$, the projective diameter of $S$ with respect to $d_C$ is defined as
$$\operatorname{diam}(S;C)=\sup\{d_C(x,y)\colon x,y\in S\text{ and }x\sim_Cy\}.$$
\end{definition}
The projective diameter is the key of the Birkhoff-Hopf theorem. In fact, the latter result shows that the best Lipschitz constant of a linear mapping between cones can be expressed in terms of the projective diameter of the image of the mapping and thus allows for a formula that characterizes the contraction ratio of linear maps. We recall the theorem below:
\begin{theorem}[Birkhoff-Hopf]\label{thm:linear_BH}
Let $C$ be a cone in a real vector space $V$, $\mathit \Gamma$ be a cone in a real vector space $W$ and $f\colon V\to W$ a linear map with $f(C)\subseteq \mathit \Gamma$. Let $\kappa(f;C,\mathit \Gamma)$ be the smallest Lipschitz constant of $f\colon (C,d_C)\to (\mathit \Gamma,d_\mathit \Gamma)$, i.e.
\begin{align*}
\kappa(f;C,\mathit \Gamma)=\inf\big\{\lambda \geq 0 \ \big| & \ d_\mathit \Gamma(f(x),f(y))\leq \lambda\, d_C(x,y), \\
&\forall x,y \in C \text{ such that } x\sim_C y\text{ and } f(x) \sim_\mathit \Gamma f(y)\big\}.
\end{align*}
Then
$\kappa(f;C,\mathit \Gamma)= \tanh\big(\tfrac{1}{4}\operatorname{diam}(f(C);\mathit \Gamma)\big)$,
with the convention $\tanh(\infty)=1$.
\end{theorem}
Different proofs of the above theorem are known, see for instance \cite{birkhoff1,cavazos2003alternative,BHNB}. The quantity $\kappa(f;C,\mathit \Gamma)$ is usually referred to as the Birkhoff contraction ratio and in the following we shall write $\kappa(f)$ in place of $\kappa(f;C,\mathit \Gamma)$ when there is no danger of confusion.
\begin{remark}\label{rmk:positive_linear_map}
An important example of cone is $C=\mathbb{R}^n_+$, consisting of all nonnegative vectors in $V=\mathbb{R}^n$, with interior being the set of positive vectors $\mathbb{R}^n_{++}$. For this cone we have
$d_{\mathbb{R}^n_+}(x,y) = \log\big( \max_i(x_i/y_i)\max_j(y_j/x_j)\big)$, for any $x,y\in \mathbb{R}^n_{++}$. Moreover, if $f:\mathbb{R}^n\to\mathbb{R}^n$ is linear and positive, that is $f(\mathbb{R}^n_+\setminus\{0\})\subseteq \mathbb{R}^n_{++}$, then it holds (see \cite[Thm. A.6.2]{NB} e.g.)
\begin{equation}\label{matrixBHformula}
\operatorname{diam}(f(\mathbb{R}^n_{+});\mathbb{R}^n_{+})=\max_{i,j,k,l}\log\left(\frac{\ps{e_i}{f(e_j)}\ps{e_k}{f(e_l)}}{\ps{e_i}{f(e_l)}\ps{e_k}{f(e_j)}}\right)\, ,
\end{equation}
where $e_1,\dots,e_n$ is the canonical basis of $\mathbb{R}^n$ and $\ps{\cdot}{\cdot}$ the Euclidean scalar product. Therefore $\operatorname{diam}(f(\mathbb{R}^n_{+});\mathbb{R}^n_{+})$ is bounded and thus $\kappa(f)<1$, by Theorem \ref{thm:linear_BH}. In other words, any positive linear map $f\colon\mathbb{R}^n\to \mathbb{R}^n$ acts as a strict contraction with respect to the Hilbert metric.
\end{remark}
\section{Birkhoff-Hopf theorem for weakly multilinear maps}\label{sec:multilinear_BH}
We are interested in the case of maps defined on product of cones $\Co = C_1\times \cdots \times C_\nu$.
As the product of cones is a cone itself, the Birkhoff-Hopf theorem can be applied to linear mappings acting on $\Co$ with not much difficulties. However, by exploiting the particular product structure of $\Co$ we can obtain a tighter contraction ratio given in terms of what we call the \textit{mode-$i$ Birkhoff contraction ratio} of the mapping. Moreover, this allows us to generalize the theorem from linear to multilinear mappings.
\subsection{The contraction ratio of multilinear mappings}
Let $\nu$ be a positive integer. Let $V_1,\ldots,V_\nu$ and $W$ be real vectors spaces and define $\mathcal{V}} \newcommand{\G}{\mathcal{G} = V_1\times \ldots \times V_\nu$, the Cartesian product of the $V_i$. For $x\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$ and $i=1,\ldots,\nu$, we denote by $x_i$ the projection of $x$ onto $V_i$ so that $x=(x_1,\ldots,x_\nu)$ with $x_j\in V_j$ for all $j$.
\begin{definition}[Multilinear map]\label{def:multilinear_map}
Let $\mathcal{V}} \newcommand{\G}{\mathcal{G}$ be as above. A mapping $f\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to W$ is multilinear if for each $i=1,\dots,\nu$ and every $z\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$, the mapping $f|_{z}^i\colon V_i\to W$
\begin{equation}\label{deffi}
f|_{z}^i(x_i)=f(z_1,\ldots,z_{i-1},x_i,z_{i+1},\ldots,z_\nu)
\end{equation}
is linear.
\end{definition}
We aim at extending the Birkhoff-Hopf theorem to multilinear mappings. However, in order to facilitate its application, we introduce a wider class of maps, which we call \textit{weakly multilinear}, and prove the theorem for this larger class.
\begin{definition}[Weak multilinearity]
Let $f\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to W$. We say that $f$ is weakly multilinear, if there exist positive integers $s$ and $1\leq i_1<\ldots<i_s\leq \nu$ and a multilinear mapping $\widetilde f\colon V_{i_1}\times\ldots\times V_{i_s}\to W$ such that $f(x)=\widetilde f(x_{i_1},\ldots,x_{i_s})$ for every $x\in\mathcal{V}} \newcommand{\G}{\mathcal{G}$.
\end{definition}
A simple example of mapping which is weakly multilinear but not multilinear is $f\colon V_1\times V_2\to W$ defined as $f(x)=g(x_1)$ where $g\colon V_1 \to W$ is a linear mapping.
Let $C_1 \subseteq V_1,\ldots,C_\nu\subseteq V_{\nu}$ and $\mathit \Gamma\subseteq W$ be cones and let $\Co = C_1\times \ldots \times C_\nu$. Let $f\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to W$ be a weakly multilinear mapping such that $f(\Co)\subseteq \mathit \Gamma$. As for each fixed $z\in\Co$ and $i=1,\ldots,\nu$, the mapping $f|_z^i$ defined as in \eqref{deffi} is either linear or constant, $f|_z^i(C_i)$ is either a cone or a singleton. In both cases, $f|_z^i(C_i)$ is a subset of the cone $\mathit \Gamma$ and so we may consider its diameter with respect to $d_\mathit \Gamma$. This observation allows us to define the mode-$i$ Birkhoff contraction ratio of a weakly multilinear mappings as follows:
\begin{definition}[Mode-$i$ Birkhoff contraction ratio]\label{defKi}
Let $f\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to W$ be a weakly multilinear map such that $f(\Co)\subseteq \mathit \Gamma$. The mode-$i$ Birkhoff contraction ratio of $f$ is defined as
\begin{equation*}
\kappa_{i}(f; \Co,\mathit \Gamma) =\sup_{z\in \Co} \tanh\big(\tfrac{1}{4}\operatorname{diam}(f|_z^i(C_i);\mathit \Gamma)\big).
\end{equation*}
For brevity, we write $\kappa_i(f)$ in place of $\kappa_{i}(f; \Co,\mathit \Gamma)$, when there is no danger of confusion.
\end{definition}
Note that if $f|_z^i$ is constant, then $f|_z^i(C_i)$ is a singleton and so~{$\operatorname{diam}(f|_z^i(C_i);\mathit \Gamma)=0$}, which implies that $\kappa_{i}(f)=0$.
Now, we state our Birkhoff-Hopf theorem for weakly multilinear mappings.
\begin{theorem}[Multilinear Birkhoff-Hopf]\label{mainres}
Let $f\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to W$ be weakly multilinear and suppose that $f(\Co)\subseteq \mathit \Gamma$. Let $\kappa_{i}(f)$ be the mode-$i$ Birkhoff contraction ratio of $f$. Then it holds
$$
(\kappa_1(f),\dots, \kappa_\nu(f)) = \inf\Big\{\textstyle{\lambda \in \mathbb{R}^\nu_+ : d_\mathit \Gamma(f(x),f(y))\leq \sum_{i=1}^\nu \lambda_i\, d_{C_i}(x_i,y_i), \, \forall x,y\in\Co}\Big\}
$$
where the infimum is understood in the sense of Definition \ref{def:inf}.
\end{theorem}
\begin{proof}
Set $\Co = C_1\times\ldots\times C_\nu$ and let $x,y\in \Co$ be such that $x\sim_{\Co}y$.
First, suppose that $f$ is multilinear.
Define $z[1],\ldots,z[\nu+1]\in \Co$ as $z[1]=x$, $z[\nu+1]=y$ and $z[i]=(y_1,\ldots,y_{i-1},x_{i},\ldots,x_\nu)$ for every $1<i\leq \nu$. By the triangle inequality, we~have
\begin{align*}\label{trieqpf}
d_{\mathit \Gamma}\big(f(x),f(y)\big)
\leq\sum_{i=1}^\nu d_\mathit \Gamma\big(f(z[i]),f( z[i+1])\big)=\sum_{i=1}^\nu d_\mathit \Gamma\big(f|^i_{z[i]}(x_i),f|^i_{z[i+1]}(y_i)\big).
\end{align*}
Since for any $i$ we have $f|^i_{z[i]}=f|^i_{z[i+1]}$, by
the Birkhoff-Hopf theorem \ref{thm:linear_BH} we deduce that
\begin{align*
d_{\mathit \Gamma}\big(f|^i_{z[i]}(x_i),f|^{i}_{z[i+1]}(y_i)\big)&\leq\tanh\big(\tfrac{1}{4}\operatorname{diam}(f|_{z[i]}^i(C_i);\mathit \Gamma)\big)\,d_{C_i}(x_i,y_i)\\
&\leq\kappa_{i}(f)\,d_{C_i}(x_i,y_i).
\end{align*}
Combining the above inequalities proves the claim.
Now, if $f$ is weakly multilinear, then there exist integers $1\leq i_1<\ldots<i_s\leq \nu$ and a multilinear mapping $\widetilde f\colon V_{i_1}\times\ldots\times V_{i_s}\to W$ such that $f(v)=\widetilde f(v_{i_1},\ldots,v_{i_{s}})$ for all $v\in\Co$. In particular, we then have
$d_\mathit \Gamma(f(x),f(y))=d_\mathit \Gamma(\widetilde f(x_{i_1},\ldots,x_{i_{s}}),\widetilde f(y_{i_1},\ldots,y_{i_{s}}))$. Hence, the above argument implies that
\begin{equation}\label{tildeeq}
d_\mathit \Gamma(f(x),f(y))\leq \sum_{j=1}^s \kappa_{j}(\widetilde f)\, d_{C_{i_j}}(x_{i_j},y_{i_j}).\end{equation}
Now, let $z\in\Co$.
As $f$ is weakly multilinear, $f|_z^i$ is either constant or linear. Let $i\in\{1,\ldots,\nu\}$ and suppose that there is $k$ such that $i=i_k$.
Then, with $\widetilde z=(z_{i_1},\ldots,z_{i_s})$, it holds
%
\begin{align*}
f|_z^i(C_i)&=f(z_{1},\ldots,z_{i-1},C_i,z_{i+1},\ldots,z_\nu)\\
&=\widetilde f(z_{i_1},\ldots,z_{i_{k-1}},C_i,z_{i_{k+1}},\ldots,z_{i_s})=\widetilde f|_{\widetilde z}^i(C_i).
\end{align*}
As the projection $z\mapsto \widetilde z$ is surjective, it follows that $\kappa_{i_k}(f)=\kappa_{k}(\widetilde f)$. Now, if $i\notin \{i_1,\ldots,i_s\}$, then it holds $\kappa_i(f)=0$. It follows that
$$ \sum_{j=1}^s \kappa_{j}(\widetilde f)\, d_{C_{i_j}}(x_{i_j},y_{i_j})=\sum_{j=1}^s \kappa_{i_j}(f)\, d_{C_{i_j}}(x_{i_j},y_{i_j})=\sum_{i=1}^\nu \kappa_{i}(f)\, d_{C_{i}}(x_{i},y_{i}),$$
and, with \eqref{tildeeq}, this shows that $(\kappa_1(f),\dots,\kappa_\nu(f))$ belongs to $\Omega = \{\lambda \in \mathbb{R}^\nu_+ : d_\mathit \Gamma(f(x),f(y))\leq \sum_{i=1}^\nu \lambda_i\, d_{C_i}(x_i,y_i), \, \forall x,y\in\Co\}$.
Finally note that, for any $\lambda \in \Omega$, any $z\in \Co$ and any $\varepsilon>0$, by Theorem \ref{thm:linear_BH}, there exist $x^{\varepsilon}_i,y^{\varepsilon}_i\in C_i$ with $x^{\varepsilon}_i\neq y^{\varepsilon}_i$ such that $$\tanh\big(\tfrac{1}{4}\operatorname{diam}(f|_z^i(C_i);\Gamma)\big)\leq\frac{d_{\Gamma}(f|_z^i(x^{\varepsilon}_i),f|_z^i(y^{\varepsilon}_i))}{d_{C_i}(x^{\varepsilon}_i,y^{\varepsilon}_i)}+\varepsilon\leq \lambda_i + \varepsilon\, .$$
It follows that
$\kappa_i(f) \leq \lambda_i+\varepsilon$ and, as $\varepsilon>0$ is arbitrary, we have $\kappa_i(f)\leq \lambda_i$. Hence, $(\kappa_1(f),\dots,\kappa_\nu(f))$ is a lower bound of $\Omega$. As $(\kappa_1(f),\dots,\kappa_\nu(f))\in\Omega$, it follows that $(\kappa_1(f),\dots,\kappa_\nu(f))$ is the infimum of $\Omega$ which concludes the proof.
\end{proof}
In the next section, we show how to exploit Theorem \ref{mainres} in order to obtain a Perron-Frobenius theorem for multilinear self-mappings on~{$\Co = C_1\times\cdots\times C_\nu$}.
\section{Multilinear Perron-Frobenius theorem}\label{sec:multilinear_PF}
As before, let $\mathcal{V}} \newcommand{\G}{\mathcal{G}=V_1\times\cdots\times V_\nu$ be the product of Banach spaces and let $f_i:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to V_i$, $i=1,\dots,\nu$ be such that $f_i(\Co)\subseteq C_i$, for normal cones $C_1,\dots,C_\nu$ and $\Co = C_1\times\cdots\times C_\nu\subseteq \mathcal{V}} \newcommand{\G}{\mathcal{G}$. Our main goal in this section is to provide conditions under which the system of functional equations
\begin{equation}\label{eq:system_spectral_equations}
\left\{
\begin{array}{l}
f_1(x_1,\dots,x_\nu) = \lambda_1 x_1 \\
\,\,\vdots \\
f_\nu(x_1,\dots,x_\nu) = \lambda_\nu x_\nu
\end{array}
\right. \quad \lambda_1,\dots,\lambda_\nu \geq 0
\end{equation}
has a unique solution, which can be efficiently computed.
To this end, we need a preliminary fixed point result which we present in the setting of general metric spaces, as it does not depend on the choice of the metric.
\subsection{A Banach fixed point theorem on product of metric spaces}\label{fpsec}
Let $(M_1,\mu_1),\ldots,(M_\nu,\mu_\nu)$ be metric spaces and set $\mathcal{M}=M_1\times \dots \times M_{\nu}$. As above, if $x\in\mathcal{M}$, then we denote by $x_i$ the projection of $x$ onto $M_i$. Furthermore, consider the cone-metric $\delta:\mathcal{M}\times\mathcal{M}\to\mathbb{R}_+^\nu$ defined by
$$
(x,y)\mapsto \delta(x,y) = (\mu_1(x_1,y_1), \dots, \mu_\nu(x_\nu,y_\nu))\, .
$$
Note that the system of equations \eqref{eq:system_spectral_equations} can be compactly written as $f(x) = (\lambda_1x_1, \dots,\lambda_\nu x_\nu)$, where $f$ is the self-map $f=(f_1,\dots,f_\nu):\mathcal{V}} \newcommand{\G}{\mathcal{G}\to\mathcal{V}} \newcommand{\G}{\mathcal{G}$. This suggests that existence of a solution to \eqref{eq:system_spectral_equations} can be addressed by means of a fixed point argument. Moreover, if $f$ is a contraction, then the solution must be unique. In what follows we observe how the contractivity of $f$ can be related to the concept of Lipschitz matrix.
\begin{definition}
Let $(M_1,\mu_1),\ldots,(M_\nu,\mu_\nu)$ be metric spaces and let $\mathcal{M}=M_1\times \dots \times M_{\nu}$.
We say that an entry-wise nonnegative matrix $A$ is a Lipschitz matrix for $f:\mathcal{M}\to\mathcal{M}$ if
\begin{equation}\label{eq:lip-matrix}
\delta(f(x),f(y))\preceq A\, \delta(x,y)
\end{equation}
for all
$x,y\in \mathcal{M}$ and where the inequality is understood coordinate-wise, i.e.\ with respect to the partial ordering induced by $\mathbb{R}_+^\nu$.
\end{definition}
A Lipschitz matrix for $f:\mathcal{M}\to\mathcal{M}$ gives an estimate on the variation of $f$ on each subspace $(M_i,\mu_i)$. However, the next theorem shows that the spectral radius of such matrix provides an estimate on the variation of $f$ on the whole space $\mathcal{M}$. Since the seminal work of Perov \cite{perov1964}, several authors have developed new fixed point results for vector valued and cone metric spaces (see for example \cite{cvetkovic2014quasi,radenovic2017some,vetro2018some} and the review \cite{aleksic2018new}) and our next result contributes to this active line of research.
In particular, note that such result extends the Banach fixed point theorem for cone-metrics (see e.g.\ \cite[Thm.\ 4.1]{aleksic2018new}) to the setting where a Lipschitz matrix exists, rather than just a Lipschitz constant with respect to some fixed metric product.
\begin{theorem}\label{thm:fixed-point}
Let $(M_i,\mu_i)$ be complete metric spaces and let $\mathcal{M} = M_1\times\dots\times\mathcal{M}_\nu$. Let $f:\mathcal{M}\to\mathcal{M}$ be a mapping with Lipschitz matrix $A$. If $\rho(A)<1$, then $f$ has a unique fixed point $x^\star \in \mathcal{M}$ and $\lim_{n\to\infty}f^n(x) = x^\star$, for any $x\in \mathcal{M}$. Moreover, it holds
$$
\delta\big(f^n(x), x^\star\big) \preceq (I-A)^{-1}A^n \delta\big(f(x),x\big)
$$
for any $x\in \mathcal{M}$ and any integer $n\geq 0$.
\end{theorem}
\begin{proof}
Let $x\in\mathcal{M}$, we have
\delta\big(f^2(x),f(x)\big)\preceq A\delta\big(f(x),x\big).
$
Adding $\delta(f(x),x)$ on both sides of such inequality we get
\begin{equation*}
\delta\big(f^2(x),f(x)\big)+\delta(f(x),x)\preceq A\delta\big(f(x),x\big)+\delta(f(x),x),
\end{equation*}
which can be rearranged into
\begin{equation*}
(I-A)\delta(f(x),x)\preceq \delta(f(x),x)-\delta\big(f^2(x),f(x)\big).
\end{equation*}
It follows from $\rho(A)<1$ that $I-A$ is invertible and that $(I-A)^{-1}$ is component-wise nonnegative. Therefore
\begin{equation*}
\delta(f(x),x)\preceq (I-A)^{-1}\Big( \delta(f(x),x)-\delta\big(f^2(x),f(x)\big)\Big).
\end{equation*}
Then, by the triangle inequality, for every $m\geq n>0$ we have
\begin{align}\label{mainineqthm1}
\delta\big(f^{m+1}(x),f^{n}(x)\big)&\preceq \sum_{i=n}^m\delta\big(f^{i+1}(x),f^{i}(x)\big)\notag \\
&\preceq (I-A)^{-1}\sum_{i=n}^m \delta\big(f^{i+1}(x)-f^i(x)\big)-\delta\big(f^{i+2}(x),f^{i+1}(x)\big)\notag \\
&= (I-A)^{-1} \Big( \delta\big(f^{n+1}(x),f^n(x)\big) - \delta\big(f^{m+2}(x),f^{m+1}(x)\big) \Big)
\end{align}
In particular, if we set $n=1$ and let $m\to\infty$, we get
\begin{equation}\label{eq:ser}
\sum_{i=1}^{\infty}\delta\big(f^i(x),f^{i+1}(x)\big) \preceq (I-A)^{-1}\delta\big(f^2(x),f(x)\big).
\end{equation}
Now, let $\|\cdot\|$ be any monotonic norm on $\mathbb{R}^\nu_+$, i.e.\ such that $a\preceq b$ implies $\|a\|\leq \|b\|$. Then $\vartheta(x,y) = \|\delta(x,y)\|$ is a metric on $\mathcal{M}$ and the topology induced by $\vartheta$ is the product topology. Thus, as $(M_i, \mu_i)$ are complete, $(\mathcal{M},\vartheta)$ is complete too.
It follows from \eqref{eq:ser} that $\sum_{i=1}^\infty\vartheta(f^i(x),f^{i+1}(x))<\infty$ and so $\{f^{n}(x)\}_{n}$ is a Cauchy sequence. Thus, by completeness, $f^n(x)$ converges to some $x^\star\in \mathcal{M}$. As $f$ is continuous this implies $x^\star = \lim_n f^{n+1}(x) = f(\lim_n f^n(x))=f(x^\star)$, i.e. $x^\star$ is a fixed point of $f$. Moreover, $x^\star$ is the unique fixed point. In fact, if $y$ is such that $f(y)=y$, then
$$
0 \leq \vartheta(x^\star,y) = \vartheta( f^n(x^\star), f^n(y)) \leq \|A^n\|\, \vartheta(x^\star,y)
$$
and letting $n\to\infty$ we have $x^\star = y$. Eventually, combined with \eqref{mainineqthm1}, we have
\begin{align*}
\lim_{m\to\infty}\delta(f^n(x),f^{m+1}(x))=\delta\big(f^n(x),x^\star\big) &\preceq (I-A)^{-1}\delta\big(f^{n+1}(x),f^n(x)\big)\\
&\preceq (I-A)^{-1}A^n \delta(f(x),x)\, ,
\end{align*}
which concludes the proof.
\end{proof}
\begin{remark}\label{rem:multi-homogeneous}
Multi-homogeneous mappings, introduced in \cite{multiPF}, are an example of maps having a well-defined non-trivial Lipschitz matrix. Recall that, given a product of cones $\Co=C_1\times\cdots\times C_\nu$, a map $f:\Co\to \Co$ is said to be multi-homogeneous if there exist coefficients $B_{ij}\geq 0$ such that $f(x_1,\dots,\lambda x_j,\dots, x_\nu)_i = \lambda^{B_{ij}} f(x_1,\dots,x_\nu)_i$, for any nonnegative number $\lambda\geq 0$. The matrix $B$ is called \textit{homogeneity matrix} of $f$. When a multi-homogeneous map is order-preserving, i.e.\ when $x\preceq_{\Co} y$ implies $f(x)\preceq_{\Co} f(y)$, then its homogeneity matrix is also a Lipshitz matrix. In fact, as
$x = (x_1,\dots,x_\nu)\preceq_\Co (M(x_1/y_1;C_1)y_1,\dots,M(x_\nu/y_\nu;C_\nu)y_\nu) =: G(x/y)$ for any $x,y\in \Co$, we have
\begin{align*}
d_{C_i}(f(x)_i,f(y)_i) &= \log\{M(f(x)_i/f(y)_i;C_i)\, M(f(y)_i/f(x)_i;C_i)\}\\
&\leq \log\{M(f(G(x/y))_i/f(y)_i; C_i)\, M(f(G(y/x))_i/f(x)_i; C_i)\}\\
&=\textstyle{\sum_{j=1}^\nu}B_{ij}\, d_{C_j}(x_j,y_j)\, .
\end{align*}
Several examples of multi-homogeneous mappings can be found in \cite{multiPF}. In particular, note that any multilinear map $f=(f_1,\dots,f_\nu):\Co\to\Co$ is multi-homogeneous, with Lipschitz matrix $B_{ij}=1$, for all $i,j$. However, Theorem \ref{mainres} shows that, for multilinear mappings, $A_{ij}=\kappa_j(f_i)$ is a Lipschitz matrix too and, since $\kappa_j(f_i)\leq 1$, it always holds $\rho(A)\leq \rho(B)$.
\end{remark}
In the next section we combine Theorems \ref{mainres} and \ref{thm:fixed-point} to obtain a Perron-Frobenius theorem for multilinear mappings.
\subsection{Perron-Frobenius theorem}\label{subsec:multilinear_PF}
Let $V_1, \ldots,V_\nu$ be Banach spaces, and let $C_1\subseteq V_1,\ldots,C_{\nu}\subseteq V_\nu$ be cones all different from $\{0\}$. Set $\Co=C_1\times \ldots \times C_{\nu}$ and let $u=(u_1,\ldots,u_\nu)$ with $u_i\in C_i\setminus\{0\} $ for all $i$. Define $\Co_u$ as $\Co_u=(C_1)_{u_1}\times \ldots \times (C_{\nu})_{u_{\nu}}$ where $(C_i)_{u_i}$ is the component of $u_i$ in $C_i$ defined in \eqref{defCu}. Finally, let $\varphi_i:(C_i)_{u_i}\to (0,\infty)$ be continuous and homogeneous, and consider the product of unit slices $\So(\Co_u)=S_{\varphi_1}\times \ldots \times S_{\varphi_\nu}$ where $S_{\varphi_i} =\{x_i\in (C_i)_{u_i} : \varphi_i({x_i})=1\}$ for every~$i \in \{1,\dots,\nu\}$.
Throughout this section we assume that each $C_i$ is normal and closed. Therefore, by Lemma \ref{NBcomplete}, we have that $(S_{\varphi_i}, d_{C_i})$ is a complete metric space for every $i=1,\dots,\nu$, with $d_{C_i}$ being the Hilbert metric on $C_i$. Thus, when a cone-preserving map has a Lipshitz matrix $A$ with respect to the Hilbert metric and $\rho(A)<1$, the following Perron-Frobenius type theorem follows from Theorem~\ref{thm:fixed-point}
\begin{theorem}\label{mainPF}
Let $u\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$ be such that $u_i\in C_i\setminus \{0\}$ for all $i$ and let $f\colon \Co_u\to \Co_u$ be such that $f(\Co_u)\subseteq \Co_u$. Let $A$ be an entry-wise nonnegative matrix such that
\begin{equation*
d_{C_i}(f(x)_i,f(y)_i)\leq \sum_{j=1}^\nu A_{ij}\,d_{C_j}(x_j,y_j)\qquad\quad \forall x,y\in\mathcal{M}\, ,
\end{equation*}
for all $i=1,\dots,\nu$. If $\rho(A)<1$, then there exists a unique $x^\star\in \So(\Co_u)$ and unique positive coefficients $\lambda_1,\ldots,\lambda_\nu>0$ such that $f(x^\star)_i=\lambda_i\,x^\star_i$, for all $i=1,\dots,\nu$. Moreover, the sequence
\begin{equation}\label{pmdef}
x^{({n+1})} = \left(\textstyle{\dfrac{f(x^{(n)})_1}{\varphi_1\big(f(x^{(n)})_1\big)},\ldots,\dfrac{f(x^{(n)})_\nu}{\varphi_\nu\big(f(x^{(n)})_\nu\big)}}\right)
\end{equation}
converges to $x^\star$, as $n\to\infty$, for every $x^{(0)}\in \So(\Co_u)$ and, for every nonnegative $w$ such that $wA=\rho(A)w$, there exists $\gamma>0$ such that
\begin{equation}\label{eq:conv-bound}
w_i \, d_{C_i}\big(x^{(n+1)}_i,x^\star_i\big) \leq \gamma \, \rho(A)^n
\end{equation}
for all $i=1,\dots,\nu$ and any integer $n\geq 0$.
\end{theorem}
\begin{proof}
Consider the map $g:\So(\Co_u)\to\So(\Co_u)$ defined by $g(x)_i = f(x)_i/\varphi_i(f(x)_i)$, for $i=1,\dots, \nu$. As $d_{C_i}$ is projective for every $i$, then $A$ is a Lipshitz matrix for $g$ and, by Theorem \ref{thm:fixed-point}, the sequence $x^{(n)}$ converges to the unique $x^\star \in \So(\Co_u)$ such that $g(x^\star)=x^\star$, for any $x^{(0)}\in\So(\Co_u)$. Moreover, there exist unique coefficients $\lambda_i>0$ such that $f(x^\star)_i = \lambda_i x_i^\star$, for all $i=1,\dots,\nu$. Finally, if $\delta:\So(\Co_u)\times \So(\Co_u)\to \mathbb{R}^\nu_+$ is the cone-metric $\delta(x,y) = \big(d_{C_1}(x_1,y_1),\dots,d_{C_\nu}(x_\nu,y_\nu)\big)$, from Theorem \ref{thm:fixed-point} we have
\begin{align*}
w\,\delta(x^{(n+1)},x^\star) &\leq w A^n(I-A)^{-1}\delta(x^{(1)},x^{(0)})\\
&= \rho(A)^n (1-\rho(A))^{-1} \big(w\,\delta(x^{(1)},x^{(0)})\big)
\end{align*}
which, with $\gamma = (1-\rho(A))^{-1}\sum_i w_i d_{C_i}(x^{(1)}_i,x^{(0)}_i)$, implies the final convergence bound.
\end{proof}
\begin{remark}
Note that when $w_i=0$ for some $i$, in the theorem above, then \eqref{eq:conv-bound} does not give information on the convergence rate of $d_{C_i}(x_i^{(n+1)},x^\star_i)$. In fact, the bound \eqref{eq:conv-bound} does not hold in general when $A$ has no positive left-eigenvector $w$ and a weaker upper-bound holds in this case:
Combining Young's theorem \cite{young1980norm} with Theorem \ref{thm:fixed-point} one easily deduces that there exists $\widetilde \gamma>0$ such that
$$d_{C_i}(x_i^{(n+1)},x^\star_i)\leq \widetilde \gamma\, \binom{n}{\nu-1}\rho(A)^{n-\nu+1}$$
for all $i=1,\dots,\nu$ and all $n\geq \nu$.
\end{remark}
A direct application of Theorems \ref{mainres} and \ref{mainPF} eventually leads to the following
\begin{theorem}[Multilinear Perron-Frobenius]\label{thm:multilinear_PF}
Let $u\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$ be such that $u_i\in C_i\setminus \{0\}$ for all $i$ and let $f=(f_1,\dots,f_\nu)\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to \mathcal{V}} \newcommand{\G}{\mathcal{G}$ be such that $f(\Co_u)\subseteq \Co_u$ and such that, for every $i=1,\ldots,\nu$, the mapping $f_i\colon \mathcal{V}} \newcommand{\G}{\mathcal{G}\to V_i$ is weakly multilinear. Then Theorem \ref{mainPF} holds for $f$, with $A_{ij}$ bein
$$A_{ij}= \kappa_j(f_i) \qquad \forall i,j=1,\ldots,\nu\, ,$$
where $\kappa_j(f_i) = \kappa_j(f_i;\, \Co_u, (C_i)_{u_i})$ is the mode-$j$ Birkhoff contraction ratio of $f_i$. In particular, if $\rho(A)<1$, then the system of nonlinear equations \eqref{eq:system_spectral_equations} has a unique solution in $\So(\Co_u)$ which can be computed with the power sequence \eqref{pmdef}.
\end{theorem}
\begin{proof}
As $\Co_u$ and $(C_i)_{u_i}$ are normal cones and $(S_{\varphi_i},d_{C_i})$ are complete metric spaces by Lemma \ref{NBcomplete}, the result follows by applying Theorems \ref{mainres} and \ref{mainPF} to $f_i$ for every $i=1,\ldots,\nu$.
\end{proof}
\begin{remark}\label{rmk:contractivity_of_h}
The theorem above together with Theorem \ref{mainres} extend the Birkhoff-Hopf and the Perron-Frobeius theorems to multilinear maps and obviously reduce to those classical results when $f:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to \mathcal{V}} \newcommand{\G}{\mathcal{G}$ is linear and $\nu=1$. However, even for linear mappings, when $\nu>1$ our theorems improve the contraction bound given by the standard Birkhoff-Hopf theorem. This is shown by the following simple example:
Consider the finite dimensional setting of Remark \ref{rmk:positive_linear_map}: $C=\mathbb{R}^n_+$, $\mathring C=\mathbb{R}_{++}^n$, $V=\mathbb{R}^n$, $\Co=C\times C$ and $\mathcal{V}} \newcommand{\G}{\mathcal{G} = \mathbb{R}^n\times \mathbb{R}^n$. Let $f:V\to V$ be a positive linear map, i.e. $f(\mathbb{R}^n_+\setminus\{0\})\subseteq \mathbb{R}_{++}$. We know from the Birkhoff-Hopf theorem that $f$ acts as a contraction on $C$, i.e.\ $\kappa(f;C,C)=\kappa(f) < 1$ (see also Remark \ref{rmk:positive_linear_map}). Now, define $h:\mathcal{V}} \newcommand{\G}{\mathcal{G} \to \mathcal{V}} \newcommand{\G}{\mathcal{G}$ as $h(x_1,x_2) = (f(x_2),f(x_1))$. Then $h$ is still linear and $h(\Co)\subseteq \Co$. Moreover,
$$
A = \begin{pmatrix}
0 & \kappa_2(h_1)\\
\kappa_1(h_2) & 0
\end{pmatrix} = \begin{pmatrix}
0 & \kappa(f)\\
\kappa(f) & 0
\end{pmatrix}
$$
is a Lipschitz matrix for $h$.
Noting that $\rho(A) = \kappa(f)$, we deduce from Theorem \ref{thm:multilinear_PF} that $h:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to\mathcal{V}} \newcommand{\G}{\mathcal{G}$ acts as a contraction on $\Co$. However, it is known that $\kappa(h; \Co, \Co)=1$ (see for instance \cite[Thm.~3.10]{Seneta1981}) and therefore the classical Birkhoff-Hopf result does not reveal any contractivity of $h$.
\end{remark}
\section{Application to nonlinear integral operators}\label{sec:applications}
In this section we consider a class of mappings $f_i$ defined as particular nonlinear integral operators acting on cones of continuous and nonnegative functions via a positive continuous kernel function $K$. This setting generalizes the case of positive linear integral operators $f$, originally considered by Hopf, and extends the formula for $\kappa(f)$ known in that case \cite{BHNB,hopf1}.
In particular, for this kind of maps we obtain an explicit formula that gives an upper bound on $\kappa_j(f_i)$, the mode-$j$ contraction ratio of $f_i$, in terms of the kernel function. Due to Theorem \ref{thm:main_integral_op}, this formula is useful to address existence, uniqueness and computability of a solution to various systems of equations including for instance the integral equations considered in \cite{Bus73} and \cite{bushell1986cayley}, the generalized Schr\"{o}dinger equation discussed in \cite{ruschendorf1998closedness} and various eigenvalue equations for hypermatrices (or tensors) \cite{friedland2014number,tensorPF} which are connected, for example, with optimal transport, hypergraph matching, network science and multivariate polynomial optimization \cite{benamou2015iterative,nguyen2017efficient,tudisco2017node,zhou2012nonnegative}.
Note that our goal is not to have the most general assumptions possible, but to illustrate how to apply our results to this particular kind of mappings. For instance, few careful adjustments should be enough to transfer the results to spaces of integrable but possibly discontinuous functions.
\def\cont{ \mathscr C }
\subsection{Systems of positive integral equations}\label{sec:integrals}
Let $X_1,\dots,X_\nu$ be compact Hausdorff spaces and let $\eta_1,\dots,\eta_\nu$ be regular Borel measures on $X_1,\dots,X_\nu$, respectively, i.e.\ such that $\eta_i(U_i)>0$ for any nonempty open subset $U_i\subseteq X_i$. For $i=1,\ldots,\nu$, let $V_i =\cont(X_i, \mathbb{R})$ be the Banach space of continuous and real valued functions on~$X_i$.
For $i=1,\dots,\nu$, let $C_i\subseteq V_i$ be the cone
$$C_i = \{x_i\in V_i :x_i(\xi_i)\geq 0\,, \forall \xi_i\in X_i\} \, $$
and consider $\varphi_i:\mathring C_i\to(0,\infty)$ continuous and homogeneous. Note that the interior $\mathring{C}_i$ is the set of positive valued functions $\mathring C_i=\{x_i\in C_i : x_i(\xi_i)>0\}$. Moreover note that each $x_i\in V_i$ attains its maximum and its minimum, since each $X_i$ is compact and any $x_i\in V_i$ is continuous. It follows that every $x_i\in \mathring C_i$ is comparable with the constant function $\mathbf 1(\xi_i)=1$ and we have $\mathring C_i = (C_i)_{\mathbf 1}$, i.e.\ $\mathring C_i$ is the component of $C_i$ containing $\mathbf 1$. Thus, by Lemma \ref{NBcomplete}, we deduce that $(S_{\varphi_i},d_{C_i})$ is a complete metric space, with $S_{\varphi_i} = \{x_i\in \mathring C_i : \varphi_i(x_i)=1\}$.
Finally, set $\mathcal{V}} \newcommand{\G}{\mathcal{G}=V_1\times \cdots \times V_{\nu}$, $\Co = C_1\times \cdots \times C_\nu$, $\mathring \Co = \mathring C_1\times \cdots \times \mathring C_\nu$ and $\So(\mathring \Co)=S_{\varphi_1}\times \cdots \times S_{\varphi_\nu}$.
Now, for any $i$, let
$\Omega_i = X_1\times \dots \times X_{i-1}\times X_{i+1}\times \dots \times X_{\nu}$
and consider a positive continuous kernel $K:X_1\times\cdots\times X_\nu\to (0,\infty)$. Given real numbers $\alpha_{ij}\in \mathbb{R}$, $i,j\in \{1,\dots,\nu\}$, define the integral operator $f_i:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to V_i$ as
\begin{equation}\label{eq:integral_operator}
f_i(x)(\xi_i)= \int_{\Omega_i} K(\xi_1,\ldots,\xi_\nu)\prod_{\substack{j=1, j \neq i}}^{\nu}x_j(\xi_j)^{\alpha_{ij}}\,\, d\, \eta_j(\xi_j)\, ,
\end{equation}
for every $\xi_i\in X_i$.
In the next Theorem \ref{thm:main_integral_op} we specialize Theorems \ref{mainres} and \ref{mainPF} to this setting and, in particular, we derive an upper bound for the mode-$j$ contraction ratio of such $f_i$, in terms of $K$ and the coefficients $\alpha_{ij}$. In practice, this formula can be used to derive conditions for the existence and uniqueness of a solution to the following system of nonlinear integral equation
\begin{equation}\label{integraleq}
f_i(x) =\lambda_i \, x_i ^{\,\gamma_i} \qquad \forall i =1,\ldots,\nu\, ,
\end{equation}
where $\gamma_1,\dots,\gamma_\nu$ are nonzero real exponents. Particular cases of this system of equations include for example the integral equations considered in \cite{Bus73} and \cite{bushell1986cayley}, when $\gamma_i=\alpha_{ij}=1$ for all $i,j$ and the generalized Schr\"{o}dinger equation \cite{ruschendorf1998closedness}, when $\gamma_i=-1$ and $\alpha_{ij}=1$ for all $i,j$. When the spaces $X_i$ are discrete, other examples include for instance the higher-oder Kullback-Leibler divergence problem \cite{benamou2015iterative}, the $(\sigma,p)$ tensor eigenvalue problem \cite{tensorPF}, the optimization of multivariate polynomials \cite{zhou2012nonnegative} and the best rank-one approximation of tensors \cite{friedland2014number}. Moreover, we will briefly discuss an example discrete problem in Example \ref{ex:discrete}.
For $j = 1,\dots,\nu$, consider the following kernel cross-ratio
\begin{equation}\label{eq:contraction_integral_kernel}
\triangle_j(K)=\max_{\substack{\xi_1\in X_1,\dots, \xi_\nu\in X_\nu\\ \xi_1'\in X_1,\dots, \xi_\nu'\in X_\nu}} \frac{K(\xi_1,\dots,\xi_\nu)\, K(\xi_1',\dots,\xi_\nu')}{K(\xi_1,\dots,\xi_j', \dots,\xi_\nu)\, K(\xi_1',\dots,\xi_j,\dots,\xi_\nu')} \, .
\end{equation}
Note that, since $K$ is continuous, the maximum is attained. Moreover, since $K$ is positive valued, it holds $f_i(C_i\setminus\{0\})\subseteq \mathring C_i$ for any $i=1,\dots,\nu$. We have
\begin{lemma}\label{lem:formula_for_integral_operators}
Let $f_i:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to V_i$ be defined as in \eqref{eq:integral_operator} with $\alpha_{ij}=1$, for all $i,j=1,\dots,\nu$. Then $f_i$ is weakly multilinear and for any $j=1,\dots,\nu$, $j\neq i$, it holds
$$
\kappa_i(f_i)=0 \qquad \text{and} \qquad \kappa_j(f_i) \leq \tanh\Big(\frac 1 4 \log \triangle_{j}(K) \Big)\,
$$
with the convention that $\tanh(\infty)=1$.
\end{lemma}
\begin{proof}
For a fixed $z\in\Co$, consider the map $f_i|_z^j:V_j\to V_i$ defined, as in \eqref{deffi}.
From \eqref{eq:integral_operator} we see that $f_i|_z^i$ is constant, which implies $\kappa_i(f_i)=0$. Now, if $j\neq i$, for any $x_j\in C_j$ we have
$$
d_{C_i}(f_i|_z^j(x_j),f_i|_z^j(y_j)) = \log\Big( M(f_i|_z^j(x_j)/f_i|_z^j(y_j); C_i) \cdot M(f_i|_z^j(y_j)/f_i|_z^j(x_j); C_i) \Big)\, .
$$
Moreover, since $f_i|_z^j$ is continuous on the compact domain $X_i$, we have
$$
e^{(d_{C_i}(f_i|_z^j(x_j),f_i|_z^j(y_j)))} = \max_{\xi_i,\xi_i'\in X_i}\frac{f_i|_z^j(x_j)(\xi_i) \, f_i|_z^j(y_j)(\xi_i')}{f_i|_z^j(y_j)(\xi_i)\, f_i|_z^j(x_j)(\xi_i')} =: \max_{\xi_i,\xi_i'\in X_i}R(x_j,y_j)(\xi_i,\xi_i')\, .
$$
Thus, if we let $\xi=(\xi_1,\dots,\xi_\nu)$ and $\xi'=(\xi_1',\dots,\xi_\nu')$, by definition we get
\begin{align*}
R(x_j,y_j)(\xi_i,\xi_i') &=\frac {\int_{\Omega_i\times\Omega_i} K(\xi)x_j(\xi_j)\prod_{l\neq i,j} z_l(\xi_l)K(\xi')y_j(\xi_j')\prod_{l\neq i,j} z_l(\xi_l') \, d\eta_i^\times d\eta_i^\times} {\int_{\Omega_i\times\Omega_i} K(\xi)y_j(\xi_j)\prod_{l\neq i,j} z_l(\xi_l)K(\xi')x_j(\xi_j')\prod_{l\neq i,j} z_l(\xi_l') \, d\eta_i^\times d\eta_i^\times} \\
&\leq \max_{\substack{\xi_k\in X_k, k\neq i\\\xi_k'\in X_k, k\neq i}} \frac { K(\xi_1,\dots,\xi_\nu)x_j(\xi_j)\, K(\xi_1',\dots,\xi_\nu')y_j(\xi_j')} { K(\xi_1,\dots,\xi_\nu)y_j(\xi_j)\, K(\xi_1',\dots,\xi_\nu')x_j(\xi_j')}\\
&= \max_{\substack{\xi_k\in X_k, k\neq i\\\xi_k'\in X_k, k\neq i}} \frac{K(\xi_1,\dots,\xi_\nu)\, K(\xi_1',\dots,\xi_\nu')}{K(\xi_1,\dots,\xi_j', \dots,\xi_\nu)\, K(\xi_1',\dots,\xi_j,\dots,\xi_\nu')}
\end{align*}
Putting all together we obtain $ d_{C_i}(f_i|_z^j(x_j),f_i|_z^j(y_j)) \leq \log \triangle_j(K)$, for any $x_j,y_j\in C_j$. Thus $\operatorname{diam}(f_i|_z^j(C_j);C_i)\leq \log \triangle_{j}(K)$ for any $z\in \Co$, and this concludes the proof.
\end{proof}
Note that, since $K$ is positive valued, if the coefficients $\alpha_{ij}$ are all nonnegative, then the map $f=(f_1,\dots,f_\nu):\Co\to\Co$, with $f_i$ as in \eqref{eq:integral_operator}, is order-preserving and multi-homogeneous, with homogeneity matrix $B_{ij}=\alpha_{ij}$, $i,j=1,\dots,\nu$. As observed in Remark \ref{rem:multi-homogeneous}, this implies that $B$ is a Lipschitz matrix for $f$. However, similarly to the multilinear case, next Theorem \ref{thm:main_integral_op} exhibits another Lipschitz matrix $A$ for $f$, with $\rho(A)\leq \rho(B)$.
As before, let $\mathring \Co = \mathring C_1\times \cdots\times \mathring C_\nu$. We have
\begin{theorem}\label{thm:main_integral_op}
Let $f_i$ be defined in terms of the kernel $K$ as in \eqref{eq:integral_operator} and consider the map $f=(f_1,\dots,f_\nu):\mathcal{V}} \newcommand{\G}{\mathcal{G}\to\mathcal{V}} \newcommand{\G}{\mathcal{G}$.
Then Theorem \ref{mainPF} holds for $f$, with $A_{ij}$ being
$$
A_{ii}=0, \qquad A_{ij} = |\alpha_{ij}| \cdot \tanh\Big(\frac 1 4 \log \triangle_{j}(K) \Big), \qquad \forall i,j=1,\dots,\nu\, .
$$
Moreover, if $\gamma_i\neq 0$ for all $i=1,\dots,\nu$, let $B$ be the matrix with coefficients $B_{ij}=A_{ij}/|\gamma_i|$. Then, if $\rho(B)<1$, the system of nonlinear integral equations \eqref{integraleq} has a unique solution in $\So(\mathring \Co)$ which can be computed with the power sequence \eqref{pmdef}, applied to the scaled mappings $\widetilde f(x)_i = f(x)_i^{1/\gamma_i}$, $i=1,\dots,\nu$.
\end{theorem}
\begin{proof}
For $i\in\{1,\dots,\nu\}$ consider the map $g_i:\mathcal{V}} \newcommand{\G}{\mathcal{G}\to\mathcal{V}} \newcommand{\G}{\mathcal{G}$ defined by $g_i(x)_j(\xi_j) = x_j(\xi_j)^{\alpha_{ij}}$, for all $\xi_j\in X_j$ and all $j=1,\dots,\nu$. Note that $g_i(\mathring \Co)\subseteq \mathring \Co$ and that $f_i = \widetilde f_i\circ g_i $, where $\widetilde f_i$ is the weakly multilinear mapping defined as in \eqref{eq:integral_operator} but with $\alpha_{ij}=1$, for all $j=1,\dots,\nu$. Then, combining Lemma \ref{lem:formula_for_integral_operators} with Theorem \ref{mainres}, for any $x,y\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$ we have
\begin{align*}
d_{C_i}(f_i(x),f_i(y)) &= d_{C_i}(\widetilde f_i\circ g_i (x), \widetilde f_i\circ g_i(y)) \leq \sum_{j=1}^\nu \kappa_j(\widetilde f_i)d_{C_j}(g_i(x)_j, g_i(y)_j)\\
&=\sum_{j=1}^\nu |\alpha_{ij}|\kappa_j(\widetilde f_i) \, d_{C_j}(x_j,y_j) \leq \sum_{j=1}^\nu A_{ij}\, d_{C_j}(x_j,y_j)\, ,
\end{align*}
which shows that the assumptions of Theorem \ref{mainPF} hold for $f$ and $A_{ij}$. Moreover, for any $x,y\in \mathcal{V}} \newcommand{\G}{\mathcal{G}$ we have
$d_{C_i}(f_i(x)^{1/\gamma_i},f_i(y)^{1/\gamma_i})\leq \sum_{j=1}^\nu B_{ij}\, d_{C_j}(x_j,y_j)$.
By taking the $1/\gamma_i$ power on both sides of \eqref{integraleq}, such inequality, together with Theorem \ref{mainPF}, implies the thesis.
\end{proof}
Our final result shows that, for the particular type of integral operator we are considering and a large range of choices of the real parameters $\alpha_{ij}$, the system of nonlinear equations \eqref{integraleq} admits a solution with a global scaling coefficient, i.e.\ $\lambda=\lambda_i$, for all $i=1,\dots,\nu$. This is shown in the following
\begin{corollary}
Let $f$ and $B$ be defined as in Theorem \ref{thm:main_integral_op} and assume that $\alpha_{ij} = \alpha_{j}$, $\gamma_j\neq 0$ and $\alpha_j+\gamma_j\neq 0$, for all $i,j=1,\dots,\nu$. If $\rho(B)<1$, then there exist a unique $\lambda >0$ and a unique $u\in \mathring \Co$ with $\int_{X_i}u_i^{\alpha_i+\gamma_i}\, d\eta_i=1$ such that $f_i(u)=\lambda\, u_i^{\gamma_i}$ holds for any $i=1,\dots,\nu$.
\end{corollary}
\begin{proof}
Since $\alpha_i+\gamma_i \neq 0$ by assumption, we can consider the continuous and homogeneous map $\varphi_i(x_i) = (\int_{X_i}x_i^{\alpha_i+\gamma_i}d\eta_i)^{\frac 1 {\alpha_i+\gamma_i}}$.~Then, by Theorem \ref{thm:main_integral_op}, there exists a unique $u\in \So(\mathring \Co)$ such that $f_i(u)(\xi_i)=\lambda_i u_i(\xi_i)^{\gamma_i}$ for all $\xi_i\in X_i$ and $i=1,\dots,\nu$. Multiplying by $u_i(\xi_i)^{\alpha_i}$ and integrating over $X_i$ both sides of such equations, we~get
\begin{equation}\label{eq:lambdas}
\int_{X_i}f_i(u)(\xi_i)u_i^{\alpha_i}(\xi_i)\, d\eta_i(\xi_i) = \lambda_i \int_{X_i}u_i(\xi_i)^{\alpha_i+\gamma_i}\, d\eta_i(\xi_i)= \lambda_i\, ,
\end{equation}
where the rightmost identity holds because $u_i\in S_{\varphi_i} = \{x_i:\varphi_i(x_i)=1\}$. Noting that, by the assumption on the coefficients $\alpha_{ij}$, the left hand side of \eqref{eq:lambdas} does not depend on $i$ and is positive, we conclude.
\end{proof}
We conclude with an example application of Theorem \ref{thm:main_integral_op} to the problem of computing the norm of the Hilbert tensor.
\begin{example}\label{ex:discrete}
We consider here an example operator of the type \eqref{eq:integral_operator}, corresponding to the discrete kernel known as Hilbert tensor. In this example the $X_i$ are discrete finite spaces and, for simplicity, we further assume here $X_1=\dots=X_\nu = \{1, \dots, n\}$. The general case can be analyzed in an analogous way. In this setting we have $V_1 = \dots = V_\nu = \mathbb{R}^{n}$, $C_1=\dots =C_\nu = \mathbb{R}^{n}_+$ and the interior $\mathring C_i=\mathbb{R}^{n}_{++}$ is the set of vectors with $n$ positive components. The Hilbert tensor is defined by
$$
H(i_1, \dots, i_\nu) = \frac{1}{i_1+\dots+i_\nu -\nu +1}
$$
for $i_1, \dots, i_\nu \in \{1, \dots, n\}$. In \cite{song2014infinite}, the following Hilbert--type inequality has been proved for $H$
$$
\sum_{i_1,\dots,i_\nu} \frac{|x(i_1)|\cdots|x(i_\nu)|}{i_1+\dots+i_\nu-\nu+1}\leq n^{\nu/2} \sin(\pi/n) \Big(\sum_{i=1}^n x(i)^2\Big)^{\nu/2} \, ,
$$
which boils down to the famous Hilbert inequality for linear operators when $\nu=2$ (see e.g.\ \cite{frazer1946note}). It is interesting to observe that such inequality provides an upper bound on the tensor norm
$$
\|H\|_{p_1, \dots, p_\nu} = \max\Big\{\, \big|\!\!\!\sum_{i_1,\dots, i_\nu} H(i_1,\dots,i_\nu)x_{1}(i_1)\cdots x_\nu(i_\nu)\big| \, : \|x_1\|_{p_1}=\cdots =\|x_\nu\|_{p_\nu} =1\Big\}
$$
where $p_1, \dots, p_\nu \geq 1$. In fact, since $H$ is symmetric, when $p_1=\dots = p_\nu = 2$ the following tight inequality holds for all $x\in \mathbb{R}^n$ (see e.g.\ \cite{tensorPF})
$$
\sum_{i_1,\dots, i_\nu} H(i_1,\dots,i_\nu)x(i_1)\cdots x(i_\nu) \leq \|H\|_{2,\dots,2} \, \, \|x\|_2^\nu \, .
$$
However, unlike the matrix case, a good approximation of $\|H\|_{2,\dots,2}$ is not always computable. New conditions that allow us to compute $\|H\|_{2,\dots,2}$ follow as a consequence of Theorem \ref{thm:main_integral_op}. In fact, if we look at the critical point conditions for $\|H\|_{p_1, \dots, p_\nu}$ we observe that a maximizer has to be a solution of the system of equations $f_i(x) = \lambda_i x_i$, $i=1, \dots, \nu$, where $f_i$ is of the form \eqref{eq:integral_operator}, with $K=H$ and $\alpha_{ij}=\frac{1}{p_i-1}$. Moreover, since $H$ is positive, any maximizer $x$ must be nonnegative, as otherwise we could replace $x$ with its absolute value $|x|$ and further increase the value of the objective function. As Theorem \ref{thm:main_integral_op} gives us conditions on the existence of a unique positive solution, this must be the global maximizer i.e.\ the one realizing the norm $\|H\|_{p_1,\dots,p_\nu}$ In addition, the particular structure of the Hilbert kernel $H$ allows us to compute the cross-ratios \eqref{eq:contraction_integral_kernel} exactly. In fact, as $H$ is symmetric, we have $\triangle_1(H)=\dots=\triangle_\nu(H)=\triangle(H)$ and
$$
\triangle(H) = \frac{n^2 (\nu-1) + n(2-\nu)}{n\nu -\nu + 1} \, .
$$
This shows that, for example, when $p_1=\dots=p_\nu=2$, the spectral radius of the matrix $B$ in Theorem \ref{thm:main_integral_op} is smaller than one when $\nu=4$ and $n\leq 11$ or $\nu=3$ and $n\leq 13$. Thus, for these choices of $\nu$ and $n$, using the power sequence \eqref{pmdef}, we are guaranteed we can compute $\|H\|_{2,\dots,2}$ to an arbitrary precision. Figure \ref{fig:norms} compares the actual value of $\|H\|_{2,\dots,2}$ with the Hilbert--type bound $n^{\nu/2}\sin(\pi/n)$, for $\nu =2,3,4$, showing that the quality of the bound degrades when the order $\nu$ increases.
\begin{figure}[t]
\includegraphics[width=.9\textwidth]{Bound_norm_comparison_with_xaxis_label}
\caption{This figure compares $\|H\|_{2,\dots,2}$ with its upper bound $n^{\nu/2}\sin(\pi/n)$ and shows that, while the bound is relatively tight in the linear case $\nu=2$, its precision degrades when $\nu$ increases.}\label{fig:norms}
\end{figure}
\end{example}
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| null | null |
ELYON
teddekker.com
**DEK** **K** **ER FANTASY**
BOOKS OF HISTORY CHRONICLES
THE LOST BOOKS
_Chosen_
_Infidel_
_Renegade_
_Chaos_
_Lunatic_
_Elyon_
THE CIRCLE SERIES
_Black_
_Red_
_White_
_Green_ (SEPTEMBER 2009)
THE PARADISE BOOKS
_Showdown_
_Saint_
_Sinner_
_Skin_
_House_ (with FRANK PERETTI)
**DEK** **K** **ER MYSTERY**
_Kiss_ (WITH ERIN HEALY)
_Blink of an Eye_
MARTYR'S SONG SERIES
_Heaven's Wager_
_Heaven's Wager_
_When Heaven Weeps_
_Thunder of Heaven_
_The Martyr's Song_
THE CALEB BOOKS
_Blessed Child_
_A Man Called Blessed_
**DEK** **K** **ER THRILLER**
_THR3E_
_Obsessed_
_Adam_
© 2009 by Ted Dekker
All rights reserved. No portion of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, scanning, or other—except for brief quotations in critical reviews or articles, without the prior written permission of the publisher.
Published in Nashville, Tennessee, by Thomas Nelson. Thomas Nelson is a registered trademark of Thomas Nelson, Inc.
Published in association with Thomas Nelson and Creative Trust, Inc., 5141 Virginia Way, Suite 320, Brentwood, TN 37027.
Thomas Nelson books may be purchased in bulk for educational, business, fund-raising, or sales promotional use. For information, please e-mail SpecialMarkets@ThomasNelson.com.
Publisher's Note: This novel is a work of fiction. Names, characters, places, and incidents are either products of the author's imagination or used fictitiously. All characters are fictional, and any similarity to people living or dead is purely coincidental.
Page design by Casey Hooper
Map design by Chris Ward
**Library of Congress Cataloging-in-Publication Data**
Dekker, Ted, 1962-
Elyon / Ted Dekker and Kaci Hill.
p. cm. -- (Lost books ; bk. 7)
"A Lost Book."
Summary: The Chosen Ones need Elyon's grace to face their greatest threat yet, but Darsal is torn between her new mission, trying to love the Horde as Elyon asked her to, and her original one, especially now that Johnis and Silvie no longer seem to be on her side.
ISBN 978-1-59554-374-5 (hardcover)
[1. Fantasy. 2. Christian life--Fiction.] I. Hill, Kaci. II. Title.
PZ7.D3684Ely 2009
[Fic]--dc22
2009007891a
Printed in the United States of America
09 10 11 12 13 QW 6 5 4 3 2 1
CONTENTS
beginnings
one
two
three
four
five
six
seven
eight
nine
ten
eleven
twelve
thirteen
fourteen
fifteen
sixteen
seventeen
eighteen
nineteen
twenty
twenty - one
twenty - two
twenty - three
twenty - four
twenty - five
twenty - six
twenty - seven
twenty - eight
twenty - nine
thirty
thirty - one
thirty - two
thirty - three
thirty - four
thirty - five
thirty - six
thirty - seven
thirty - eight
beginnings
**o** ur story begins in a world totally like our own, yet completely different. What once happened seems to be repeating itself two thousand years later.
Twenty years have passed since the lush, colored forests were turned into desert by Teeleh, enemy of Elyon and vilest of all creatures. Evil now rules the land and shows itself as a painful, scaly disease that covers the flesh of the Horde.
The powerful green waters, once precious to Elyon, vanished from the earth. Those few who chose to follow the ways of Elyon bathed once daily in those waters to cleanse their skin of the scabbing disease. For thirteen years, the number of their sworn enemy, the Horde, grew, and the Forest Guard was severely diminished by war, forcing Thomas, supreme commander, to lower the army's recruitment age to sixteen. A thousand young recruits showed themselves worthy and served in the Forest Guard.
From among the thousand, four young fighters—Johnis, Silvie, Billos, and Darsal—were handpicked by Thomas to lead.
Unbeknownst to Thomas, the four heroes were also chosen by the legendary white Roush, guardians of all that is good, for a far greater mission, and were forbidden to tell a soul. Braving terrible battles, crushing defeat, capture, death, and betrayal, they pursued their quest to find the seven original Books of History, a mission that took them from one reality into another.
From their world to the histories, two thousand years into their past, into a city known as Las Vegas, their journey ended deep in the mountains of Romania. On the day after their great victory, having secured all seven books—thereby foiling the plans of the Dark One, who would use the books to destroy humankind—they left our world to return to Thomas and the Forest Guard, two thousand years from now.
But five years have passed since they left their home in the distant future. The world they once knew has changed in favor of their sworn enemy, the Horde. Qurong now rules the city. He has a new high priest—Sucrow, a ruthless servant of Teeleh—to replace Ciphus, who killed Witch. He also has a new general by the name of Marak, sworn to kill every albino on the face of the earth.
Forced to flee the city, Darsal, Johnis, and Silvie have become separated. Worse, Elyon's water, once green, is now red and has apparently lost its healing properties. Johnis and Silvie are soon consumed by the scabbing disease.
To further complicate matters, the Shataiki have mated with some of the Horde, creating a strange race of predatory creatures known as the Leedhan. Insanely jealous of the Leedhan's half-human appearance, Teeleh banished them to the far side of a great river. Outcast and despised, the Leedhan are thought to be gone forever.
But one of them, their embittered queen, named Shaeda, has returned. She has come to seize control of the Horde, and to overthrow Teeleh himself. To do so she needs a human, and she has chosen none other than Johnis as her agent for revenge.
Shaeda seduced Johnis and has fully possessed him. Completely deceived, both Johnis and Silvie have made an alliance with the priest Sucrow with promises of destroying Thomas Hunter and the Circle in three days. But to do so they must acquire a legendary amulet that gives its owner control over the Shataiki.
Meanwhile, Darsal has encountered a different fate. She's discovered the secret of the new red waters—that drowning in its depths heals one of the scabbing disease. Having drowned in the red waters, Darsal has accepted a mission from Elyon: to return to the Horde . . . and love them.
Now our three fallen heroes—Darsal, Johnis, and Silvie—find themselves pitted against each other while the world awaits its fate.
one
**M** arak of Southern, Qurong's general over all the Horde army, paced inside one of the bunk rooms reserved for the officers. Two narrow beds stacked on top of each other jutted out of each wall. No windows. Just a torch stand and the candles on his desk. Behind him was a narrow shelf of books.
His captain and best friend, Cassak, was taking too long to bring in the prisoners. He had said he would be here by now. Marak's patience was running out.
"Where is he?" Marak grumbled to himself, storming over to the two open books on the desk. One had once belonged to the long-gone general Martyn, who'd trained him; and the other, to his dead betrothed, Rona.
How, in Teeleh's name, had everything gone wrong in a week? He was a general, for goodness' sake, respected and trusted and feared. He'd been a good man with a loyal brother and a soon-to-be wife.
And now . . .
General Marak had sequestered himself in the officers' hall at the north end of Middle, with fifty warriors standing guard. For two days they had roasted in the hot sun, choosing loyalty to their general over the orders of the Dark Priest. And for two days all of Middle remained tense, caught in the battle lines drawn between High Priest Sucrow and Marak.
Marak took a long swig of his drink and continued his trek around the room. The meal his slave had brought him earlier sat untouched on the table. He couldn't eat; his stomach felt as if it were full of knives.
He went to the door and swung it open. "Is Darsal here yet?"
"No, sir," the warrior replied, falling into his salute. "We've not yet seen—"
"Find her."
"My lord—"
"Find her!" Marak shut the door and went back to his inner tirade. This was a mistake. All of it. He'd had everything under control a week ago. At least, as much as the mess left by his predecessor allowed.
In less than a week, the priest had undone everything Marak had built, all in a bizarre sense of revenge and power play. Marak hadn't wanted to defy Qurong—and technically he hadn't. He had no reason to. But a series of events had led him to defy the Dark Priest and sequester himself in the officers' quarters. Now Qurong, the supreme commander, must hear him out on the absurd notion of a general taking orders from a priest. He had to.
Knotting his fist and glowering at the cold plate of food, he reviewed this plunge into dishonor.
First, upon gaining rank over Marak, Sucrow had ordered him to execute his own family—all albinos. Marak had stalled as long as possible, but Sucrow was powermongering.
Marak's jaw tensed at that thought. It'd been some time since he'd given the order and stood by as Cassak administered the hideous potion—Marak's albino-killing concoction called the Desecration—to his family. His brother.
He whirled around to the door and thrust his head out again. "Why are you still standing there?" he barked at the guard. "Did you find her?"
"The albino is still out on your previous orders, General," the guard replied cautiously. "I've sent a scout for her."
"Good." Again Marak turned back to his predicament. Where was he . . . ? Oh, right. His second problem. Sucrow had struck a deal with this Josef character from the backside of the desert, who claimed to have a better, faster way of killing off the albinos: a magic amulet made of Leedhan magic—whatever that was—that would give control over the mythical Shataiki and command them to wipe out the blight that is the albinos.
Marak had dismissed the idea. Sucrow had not.
Which led him to his third problem: Sucrow had taken Josef and Arya and had gone after the amulet without him. Immediately upon learning this, Marak sent his captain, Cassak, after them. If Sucrow was so convinced and so willing to risk his life for this amulet, there had to be some merit to its power.
Acting upon Marak's order, Cassak had captured Josef and Arya and taken the amulet from them. The move had infuriated Sucrow, so Marak had moved into the officers' quarters, barred the windows, and set guards around the sundial for his and his prisoners' protection.
So here he was. For two days Sucrow had made no move, but that would not last.
So be it. Marak had the amulet and the two prisoners, Josef and Arya, in his custody. His slave, Darsal, knew them as Johnis of Middle and Silvie of Southern, but he did not. Whatever their reasons were, he would not yet let them know he had that information. A knock at the door snapped him out of his silent rant.
"Who is it?" he growled.
"Darsal. Let me in."
Darsal, his albino slave, had been in the cells the same night his family was executed and had spoken with them before their deaths. She wore his brother's Circle pendant around her neck, his gift to her. Marak wasn't sure why he'd spared her, but he had. Twice. Once that night, when she vowed to be his slave. The second time in a glen, shortly after Sucrow had ordered him to kill her and, to his horror, he found he could not.
This at least partly explained his rationale to sequester himself here in the officers' quarters. Qurong might not yet know Darsal was still alive despite Sucrow's orders. And Sucrow couldn't use her in his sadistic rites—or worse yet, kill her—if Marak still had her.
"Marak, are you going to let me in?" The knob was rattling. He quickly crossed the room to unhook the latch and swing the door open.
There she was. This albino slave, this woman . . . Darsal of the Far Northern Forest, who claimed to have crossed time and space through worn leather portals called the Books of History. She stood before him, arms crossed. Morst covered her exposed skin, and a blue veil wrapped around her head, covering her nose and mouth. Rich brown eyes watched him, noticeably frustrated.
"Thank you," she said. "You summoned me?" Their eyes met.
If he wasn't mistaken, he was falling in love with her. With an albino. This was most definitely a mistake.
He forgot what he'd summoned her for. He released a breath and worked the knot of frustration and anxiety back down into his belly.
"General." Darsal spoke softly, pulling him out of his thoughts. The citrus scent she wore drifted through the room.
Oh. Right. He was a general with a thousand problems to take care of. Unwilling to be caught in her warm gaze again, Marak stormed down the dark hall to the war room.
"Has Cassak arrived yet?" he asked her as he shoved the door open, not missing a step.
"Not yet," Darsal said, straightening the blue veil. She watched his irritated pacing, characteristic of the last several hours. He circled around the eight-foot oval table made of cherrywood. A green runner draped the width of the table, laid squarely beneath three copper candelabra. White pillars of wax flickered as curls of smoke drifted through the war room.
"He'll be here," Darsal said.
He tugged at the collar of his rust-colored tunic, sweaty and itchy, and turned toward the east-facing window he'd had Cassak's men bar and cover with a heavy crimson drape so no one could see in. Every window in the building had received the same treatment. The room was dark, but he couldn't very well light the torches without suffocating them all. Why Darsal would unnecessarily coat herself in morst, then drape a veil over her head in here, was beyond him.
Her fruity scent mingled with that of the candles.
"Relax, Marak. He'll be here."
_Focus._
"He's certainly taking his time about it. Read the message again," he ordered, turning back to her.
"It hasn't changed, my _general_." Darsal quirked a brow, completely exasperated with him. Her veil slipped, revealing dark brown braids. "He'll be here with your amulet and your prisoners."
"Just read it. I don't have the patience for your obstinacy. Not today. Not when we're at the brink of a civil war and Sucrow is halfway to Qurong by now. If your so-called friends hadn't been so stupid—"
"It was the Throaters' fault, and you know it. Cassak said so himself."
"They were only out there because they're a bunch of superstitious religious idiots who convinced the priest one of his own myths might be true," he argued.
"Jordan believed Shataiki exist," Darsal pushed. Marak tensed. "And the Roush. And Elyon. Was your brother a fool, Marak?"
Marak scowled at her. "Jordan was mistaken on many things. That didn't make him a fool."
"Yet you call drowning foolish."
"Your persistence is aggravating."
She studied him. "You're missing the point of all of this, my general."
"What's that?" He almost regretted the question. He knew her answer.
"This is about—"
"Elyon. You keep saying that."
"More than that, Marak. I mean, yes. But you're still missing it. Elyon doesn't just love the Circle. He loves the Horde too. You. This is all about you and Elyon. That's why I'm here." She opened her arms wide, indicating the room. "All of this."
Marak started to protest but was interrupted by a knock at the door. Secretly he appreciated the diversion from her nonsense about being Elyon's emissary. "We don't have time for this. Who is it?" he growled, unwilling to open the door on a whim.
"A messenger from the captain, General!" a familiar voice called through the door. Cassak's favored scout.
Marak nodded at Darsal, who let the scout in. She'd taken to staying by the door, even so far as to sleep in front of the threshold at night. A curious thing.
The small warrior saluted and went to one knee. Marak bid him stand, then bellowed, "He's late."
"He was avoiding the Throaters," the scout explained. "He's bringing the prisoners from the southeast to avoid further confrontation with the rebels."
Marak queried him on Eram, the half-breed rebel, then came to his real question. "When will Cassak be here?"
"Shortly, sir. He's making sure the prisoners and the amulet are secure. He's already sent messages to the commanders so they can respond to the rebels accordingly."
"Tell me something," he asked the scout. "Were you there?"
"Yes, sir."
"Exactly what did you see?"
"Well, sir, it was just like the captain's report said."
"And no one would obey the captain?"
"Oh, _we_ did, sir. We didn't kill any of them. Warryn and his men did the killing."
Marak bit back a comment. "What else? Cassak kept talking about black trees and clouds."
The scout didn't answer. He kept looking at Darsal. Staring. What was this scout looking at Darsal for?
"You have a problem, soldier?" Marak growled. He resisted the urge to jump between Darsal and the stupid scout and slice his head off.
The scout backed up. "No sir."
"Then answer the question." From what Marak had already gleaned from his scouts and an irritating message from Cassak, Josef wanted Sucrow's assistance—which meant Marak needed information. There was no way he was letting the priest race off with Marak's prisoners, much less in secrecy, with delusions of glory and self-aggrandizement in his head.
"Well, sir, it's just that no one's really sure what we saw."
Marak threw Darsal an over-the-shoulder glance.
"Were they furry?" Darsal interrupted, startling both Marak and the scout. She appeared beside him, so close he was drowning in her scent. A flash of heat shot up his arm where hers brushed his. "Black fur, leathery wings, red eyes. Do you remember that?"
"Albino," Marak warned, snapping his head around. But that was his mistake. Their eyes met . . .
He broke the gaze first.
_Never again._
"Bring some water." Marak kept his voice even. Tried to calm it just a little.
She raised a brow. "It's . . . _water_ you want?"
What business did she have bringing up the red lakes with Cassak's scout in the room? He answered slowly. "Not that water."
Darsal left without answering. Marak finished business with the scout and dismissed him. For the next few minutes he was alone. "Jordan," he muttered. "What I wouldn't give to fight this out with you right now."
"Marak." Darsal's voice startled him. He turned, and she offered him a bottle of water and a small scroll with Qurong's seal on it. "This just came."
"Read it." He drank greedily as she opened the message and scanned it.
"It's a summons to the palace. Qurong wants to know what happened out there."
"He should ask his bloody priest. My hands are tied."
"So get them untied."
Marak eyed Darsal as she took a swig of water.
"I'm just saying," she explained, "in less than a week, Sucrow started what you've spent a year and a half preventing." She read on, her voice suddenly tense. "It's about the expedition."
Marak didn't answer.
"I'm not Jordan, but I'll fight it out with you."
"You weren't supposed to hear that."
Darsal raised her gaze to him. Sighed. "Follow your heart, Marak."
His eyes narrowed. Now, that was a strange thing to say. "My heart?"
"That's what Thomas always said. Elyon speaks through the heart. Love." She touched his chest.
Marak frowned. Bit his tongue. Would his heart have killed his family or saved them? His heart was a black-riddled coward.
"Elyon's who got us into this mess."
A short commotion caught his attention. The pair listened, both reaching for blades on instinct, even though Darsal didn't have one. He then realized she had reached for one of his.
"Must be Cassak, finally," Marak growled.
"Try making an ally rather than an enemy of him," Darsal said. Marak eyed her. "Johnis, I mean."
Great. Now Darsal was playing games too.
"Why? Planning on drowning them as well?"
"I might be."
"I think not. You'll wait in the hall."
SUCROW SAT IN THE SHADOWS, MASKED BY CURLING SMOKE. Incense filled his nostrils. He knelt down on a silk cushion before the winged-serpent image of Teeleh and prayed for the success of the coming expedition, that their destruction of the albinos would find favor with him and be a fragrant offering to the Great One.
At last he lifted his forehead from the ground and sat straight on his knees, gazing up at the icon.
"My lord," one of his servants spoke from behind. Sucrow scowled. "Qurong sends for you and the general."
He paused. "Very well. Be gone."
Footsteps carried the informer away. Sucrow turned back to Teeleh and repeated his petition. Breathing deeply, he entered his trance and embraced the vision that came to him. He stood before the altar and drank in the depths of what he knew to be his master's lair. As the room chilled, a low growl and acidic breath came over his shoulder. Sucrow didn't turn. A taloned claw traced his throat, cold and hard. Sinewy fingers touched his skin.
His master. The Great One. Teeleh.
"I do not care to be petitioned so that my servants might complain of their own failures, priest," his master warned. "And now this is what you will do: bring me the blood of the one long ago chosen, and ensure the medallion falls into your hands. I will not tolerate the vampiress any longer. The Leedhan must face penalty for her insolence."
Sucrow lifted his face, further exposing his throat to his master. "Lord?"
"Do not allow them to cross the river."
Confusion overtook him. But before he could ask, the chill seeped from the room, along with the presence.
"My lord . . . Warryn has returned."
Warryn, the foolish chieftain who had embarrassed him. A pebble in the shoe to be dealt with.
"Bring him in."
Warryn soon stood before Sucrow, who looked his wayward chieftain over, scrutinizing him. The chief serpent warrior had been tainted. Penalties were required. "An eye for an eye," wasn't that how the saying went? Sucrow would give Warryn's position to another, but he would also take Warryn's eye. A more formidable ally with a sense of duty and honor. If Marak could not be persuaded . . . his captain likely could.
The thought of an entire army of serpent warriors, all led by a chieftain and general who served the Great One with faithfulness . . .
"My lord . . ."
"Summon the officers," Sucrow ordered. "And you, Warryn, will at last be humiliated before your favorite captain." He sneered.
Warryn remained stoic. He bowed and left to retrieve the officers.
Sucrow looked through his library, seeking his book of incantations. Relighting the incense, he spoke a prayer to his master and bowed prostrate before Teeleh's image six times.
What Teeleh's intentions were, he didn't know. But that was not his place. Marak had the amulet, the young chosen one, and his arrogance. Soon all would be Sucrow's. Soon. Josef wouldn't even know what to do with such power.
"If Marak cannot be bought or intimidated, another must take his place," he said to himself.
Sucrow took a bird from its cage and put the tiny creature on the altar. Using a sharp blade with a heavily jeweled handle, he pierced the bird in its heart. Blood seeped out and around the small fowl, forming a pool on the altar. Sucrow slid the knife down the bird's chest, exposing its twitching organs. He withdrew a vial and mixed its contents into the bird's blood, mingling with the entrails, and read from the book the proper spell.
"Who shall succeed you, most foolish of generals, so lofty, so proud? From such great heights you have fallen, O infidel!"
Fog and haze slithered over the room like so many snakes. He breathed deep the pungent aroma and shut his eyes a moment . . . then opened them. Sucrow lifted his staff over the concoction and stirred the empty air until a greenish-red light appeared.
He used a bone to mix the blood and entrails, careful not to let the substance touch his skin. Sucrow's mantra continued. Teeleh's eyes formed in the shadows, glaring at him. He dipped his head.
"Tell me, my seeing eye, my great wonder from the sky, who shall succeed our general who must die?"
The eyes swelled, growing together into a single, enormous orb that opened into a reddish mirror, a pool's reflection in midair. Soon a face appeared, one in desert tans and browns who stood at his general's side.
"Ah, Captain, so you are the next in line." Sucrow chuckled, watching in the mirror as Cassak led the prisoners to their captor.
He stirred the entrails again.
A stream of greenish-yellow light drifted from the end of his staff. It formed a spiral, coming ever closer to the captain's image.
The light snaked around and grew brighter. It burst into a thousand stars, blinding him for a moment. Then a glittering blue star appeared in his palm, resting on a short cord.
Of course, the good captain would never willingly fall in league with his general's enemy. But Sucrow had already compromised him once during the ordeal regarding Jordan and Rona. Still, he could not afford for anything to go wrong.
Sucrow raised his staff and spun it, reciting another incantation, ignoring the pain that always came with transformation. His body screamed as it twisted, bent, and stretched into the form he desired.
He took a deep breath and waited. It was finished. He walked to the ornate mirror, framed by wooden snakes, and looked into the glass. A young scout greeted his reflection. Good.
He changed his clothes and stuffed them in a bag over his shoulder. His staff became a sword. This would not take long. He would have plenty of time to change back before the meeting with Qurong and Marak.
One last look in the mirror. His own mother wouldn't recognize him—much less Cassak.
two
**T** he march back into Middle was quiet. No fanfare, no fuss—the way Cassak preferred it. He barked at the gatekeeper, who let him through, then took his prisoners down the main road, past vendors and merchants, toward the officers' hall where Marak had barricaded himself. The lake came up on their left, and the palace was ahead on the right.
He mopped sweat, morst, and grime from his forehead and silently maligned the priest, his Throaters, the rebels, and finally Marak for the indecision that had forced his hand, for being so bullheaded with all of this.
The entire mess was simple, but Sucrow, Marak, Qurong, and Eram seemed bent on complicating things. Hang them all. It was only midmorning, and he'd already ridden all over Middle and a good portion of desert.
"Captain, a word," Josef said.
"What is it, runt?"
Josef kept his eyes up the road. The young man was strange, his skin shimmery white against his black horse, and his gray-white eyes tinted with that strange purple hue. "I know how those three albinos got in and out of the attic in the palace. Interested?"
Cassak frowned. "How is that?"
"That's for me to know." Josef gave a wicked grin. Now his eyes almost glowed. His skin was nigh translucent. Unnerving. "You've heard of albino magic, haven't you?"
Cassak considered this. He wasn't sure what he thought about the albino sorcery, but this nobody had the attentions of the general, the priest, and now Qurong himself. He waited.
"They have books in which they've written their spells and incantations," Josef continued. "It's where things such as the amulet come from."
Curious. Marak might find the information useful.
Cassak's eyes narrowed. "And?"
"I have one of their books," Josef explained. He withdrew a leather book bound with red twine from beneath his tunic and showed him the worn, bloodstained cover. "They were after the rest of them, left inside the palace. Without them they cannot complete a ritual that they must—within the next week."
"How do you know these things?"
"I was slave to them for a time. Did you search the attic?"
"Of course."
"Search it again. Look everywhere, inside everything. Bring them to me. Then you will see."
Of course he would. Marak would be irritated if the priest found them first. In fact, the priest was likely the reason the books were missing. But he didn't want this youth knowing his interest.
Cassak pushed away from Josef. "I have things to do."
"Just go look, Captain."
The captain mulled it over. Finally, "If you're lying, I'm telling Marak to slit your throat."
"That won't be necessary."
"We will see."
Cassak rode ahead. Idly he scratched at a spot on his arm. The sunlight grew hazy and strange, making it difficult to see. He shielded his eyes and pressed on. Soon footsteps drew his attention. He squinted to see, one hand on his sword.
A young scout approached and dropped to his knee. Cassak stopped his horse and nodded. Relaxed.
Something sweet wafted in the air. For some reason Cassak felt disembodied, dizzy. He shook off the numbing sensation. His eyes fixed on those of the scout. Curious, this was.
His eyes narrowed. The scout rose, offering a small blue star. Cassak inspected it. "What is this?"
"A gift," the scout replied. "From my son."
Cassak continued to stare at the little star. His skin prickled.
He should send the scout away, tell him to take his silly trinket and leave. But as he watched, the star shifted, turning into the eye of a serpent before melting into his palm and becoming part of his skin. Then it disappeared.
He rubbed his palm, unnerved and riveted by the sight.
"What does it do?" Cassak's own voice sounded distant, constricted. He looked again at his palm. Cold to the touch.
The scout's lip curled into a strange smile. Cassak found it difficult to breathe and more difficult to break eye contact with this scout, whom he suddenly realized he didn't recognize.
"Allows your eyes to see."
Cassak shook his head, trying to clear it.
When he looked up, the scout was gone.
_What in the world just happened?_
They were coming up on the officers' hall, surrounded by fifty men, windows sealed with iron bars. No one could see in or even get close enough to try. Cassak caught himself staring at his hand.
Josef was watching him.
"What?" Cassak barked.
"Just wondering who that was."
"A scout."
"Well, yes, but could it have—"
"I've had enough of your mouth." They approached the guard. "In."
CASSAK'S WARRIORS PRODDED JOHNIS AND SILVIE THROUGH the halls and into a dark war room where Marak stood waiting. The haze intensified. A salty, copper taste flooded Johnis's mouth. He needed to further the mission. Further their revenge.
With the end of the Circle came the end of the Horde.
With the conquer of the Horde came the end of Teeleh. The end of Teeleh and the beginning of something new.
"Kneel." A rough hand shoved Johnis to his knees. Silvie thumped to the ground next to him. Cassak brushed past him and gave Marak the amulet.
The general turned it over in his hand. Studied the small thing that had caused so much trouble. Looked perturbed.
"You two have caused me a lot of grief," he said.
"It's not my fault the rebels attacked."
"It's your fault the priest went on this cursed fool's hunt."
Johnis bristled. Shaeda didn't like this. Neither did he.
With Shaeda's heightened senses, he became aware of every-thing: The long, oval table surrounded by chairs. Pillar candles casting eerie shadows. Torches on six-foot stands, unlit. The place made him think of a Shataiki lair, made him edgy. Or was that Shaeda?
He could set the place ablaze, storm into the thrall, and demand Sucrow comply. He could end this now. He could . . .
His eyes fixed on the amulet. Shaeda's focus soaked into his flesh, rushing over his body like a waterfall, a broken dam spilling into the ocean and sweeping him away in the riptide.
Marak held the medallion. _He hinders the mission._
No. Offer a truce first. Waste not, want not. Shaeda couldn't argue with that.
Johnis looked Marak straight in the eye. The man found honesty impressive. So Johnis would give him impressive. They had no time to waste with all this.
"I'm the reason they were there, then. Drawing attention to your men."
"Josef," Silvie whispered.
His mind shifted. Silvie was the key to subverting Shaeda, to harnessing the Leedhan's power on his own. And he was almost positive he knew how.
Marak studied him. He dragged a chair with his foot and shoved it in front of Johnis. "Sit. Your girl can take the other."
There were only two chairs.
Johnis scowled. He helped Silvie stand, then let her have the chair. A second one was dragged from the table, and only then did he sit.
"Why is Sucrow interested in this medallion?"
Johnis laughed. A husky laugh that came from Shaeda. "General, that amulet is the key to your trouble. Think of it."
Marak eyed him. For a moment his eyes went to his captain. Then back to Johnis. He didn't look convinced. "This amulet."
Shaeda took over. Johnis could feel her magic course through him. Her eyes, it was all about her eyes . . .
"Yes. That amulet. Come on, Marak. Surely a general knows appearances are deceptive."
Marak's expression became unreadable. What was she doing to the general?
_"Press the matter."_
"Release us. Make alliance with myself and Arya. Once the priest has outworn his uses, we'll be rid of him."
Marak's gray eyes searched both of them. "And why should I be interested in an alliance?"
"Because you can do it my way, in the time frame Qurong wants," he said. Shaeda said. Was there a difference anymore?
Silvie touched his arm. Shaeda bristled.
"You already made your bed," Marak reminded.
"Warryn and his men were uninvited guests. Sucrow turned me down, and I came alone. The Throaters decided to tag along anyway."
"I'm not interested. You change loyalties too quickly."
For some reason that stung. He shoved it aside. "Come now, General, we both know that isn't true. You don't like the priest, and you won't let him have the credit for getting rid of the albinos, either."
Marak fell quiet.
Alliance or death. _"Which will it be, General?"_
Shaeda chuckled in Johnis's head. Her power of influence had no limitation, save that of a human conductor.
"You have a plan, then."
"I always have a plan, General." He and Silvie had discussed this, and Shaeda's foresight had let him see all the way to a place called Ba'al Bek, from whence they would unleash the Shataiki on the albinos.
Marak's eyes narrowed. "I don't require you to use it."
"You assume you have all the pieces. Would I have asked for the priest's help if I didn't have to?" The general seemed not to remember the harach fruit. Johnis didn't intend to remind him of it until he'd secured him as an ally.
Marak still didn't seem quite convinced. He hadn't forgotten that Johnis had gone to the priest first. He stood. "Cassak, keep these two under guard."
Johnis jumped up. "General, if you keep us in custody, we remain a liability. If you release us, we can help you defend this place against the Throaters."
Marak glared at him. Shaeda was working, but he was so stubborn.
"Do you want the amulet that close to Sucrow?" Johnis watched. Could Marak be manipulated? "I can't help you if I'm tied up. And Sucrow is likely to intercept that medallion the second you walk out of there."
Marak still didn't look ready to play ball. A muscle in his jaw twitched. "When I return."
"Trust begins somewhere, General. And neither of us has any sentiments toward the priest. He took your family, I heard."
Marak's fist curled into a hard knot.
"We could do something about that, you and I." It was out before Johnis really had time to think about it, but now he was glad Shaeda's foresight had come through.
The general passed the amulet to Cassak. The shackles fell from Johnis's wrists. He resisted the impulse to rub them. Bit back a pleased smile. So Shaeda had uses beyond physical strength as well. Surely he already knew that.
"Don't lose sight of the amulet, General."
Shaeda's vision overpowered Johnis, turning his focus toward the desert, toward Ba'al Bek. He required blood and sacrifice . . . Blood so full of iron he could taste the metal in his mouth. The Circle and the Horde would die by this plague, and a new era would begin. One of power and might. One where all bowed to—
"Josef," Silvie interrupted.
He blinked. Marak was waiting for an answer to a question Johnis hadn't heard. Shaeda was in a hurry; she was always in a hurry. The slower her movements appeared, the more haste she required.
"We don't have time to waste. The window of opportunity grows short. The amulet's guardian will come for his trophy."
"Guardian," Marak repeated.
"I highly doubt you wish to be the one holding that amulet when the queen, Derias, comes for it."
The general's eyes narrowed, as if considering whether or not that was a threat. He turned to leave. "Don't do anything foolish."
DARSAL WAS ALONE IN THE GENERAL'S CHAMBER. SHE HAD eavesdropped a few minutes before hearing more than she cared to, and now wished to consider her options in private. She studied the room. A bedroll. A table. Two journals, side by side—one Martyn's war journal, one Rona's. They were the two sides of her Scab general. One cunning and tactical, stoic and cold. One warm and full of barely restrained passion.
She fingered Jordan's necklace.
Everything began to sink in. So much to reclaim. So much lost. Romania and the Black Forest and old Middle Forest haunted her, whispering specters in the back of her mind.
"Where are our vows now?" she grumbled, her eyes narrowed. The shock of hearing Johnis talk like that had worn off, and now the summer's heat of anger stirred up inside her.
_Follow your heart_ , Thomas, then Johnis, had always said.
"My heart wants to beat some sense into him."
Frustrated, she groaned. Part of her remembered she was a slave and would be summoned at any moment. But for now she was free to rage.
A gentle laugh tittered through the room. Darsal whirled, landed in a crouch. Marak had extra knives in a small trunk. How to get to them?
Her eyes widened.
A furry white bat with round, green eyes was laughing at her. It took her a second to realize who and what it was.
Darsal's arms fell to her sides. "Gabil?"
"Well, yes, I believe that is my name. I trust you haven't forgotten me."
"Forgotten—Where have you _been_?" she snapped at him.
"That isn't important, and it isn't why I'm here." He hopped toward her, wings slapping the air.
"Do you know the half of what's been going on over here? Johnis and Silvie, and—"
"Oh, yes." Gabil turned serious for half a second. "Yes, I'm afraid it's been a dreadful time."
"You didn't bother warning us. Didn't bother to tell us we all had to drown!"
Gabil waited until she was looking at him again. "No, I suppose we didn't."
"Johnis and Silvie are rotten through because no one told us we had to—" She stopped.
"Well, Darsal, you knew you had to find water, didn't you?"
"But not to drown. No one would just decide to do that."
"You did, didn't you?"
She scoffed. "I had Jordan."
"So why do you assume it's all a loss?"
She didn't answer.
"What did Elyon tell you, Darsal?"
"'Return to the Horde, and love them for me. For Johnis.'"
"Yes, for Johnis. Ultimately, though, Darsal, it isn't about you. It's about Elyon. This saving the Circle—most of whom you've never met—learning to love a Scab . . ."
"Elyon." She let the name spread over her tongue and fill her mouth. Her fury subsided. Whatever happened, Elyon was here, and Gabil was in front of her, destined to drive her crazy.
She dropped down and hugged her old friend. Ran her fingers through his fur.
Gabil laughed. "That's a much better welcome, if I do say so myself. And that tickles."
Darsal sat down. Pulled one knee up and propped her chin on it. "Well, it's been awful. Where's Thomas, the Forest Guard—I mean, Circle? Why is the Horde in Middle?" The flood of questions continued. She couldn't help it, now that someone with answers was right in front of her. "We lost the books, Gabil. We had to leave them in the attic. I don't know how we'll get them back. All that trouble for nothing."
The Roush shook his head. "Maybe the books weren't meant for you, child. Did you consider that?"
No, she hadn't.
Darsal let that thought sink in. Then, "So what do I do? Why here, now? How does loving the Horde—Marak—save the Circle?"
"That is a mystery. I suppose you keep doing what you've been doing."
"Fight with Marak, and pray Johnis and Silvie come to their senses? Yes, that's helping so much." She started thinking out loud. "They're Horde. They've turned their backs on everything, Gabil. Everything. Johnis went to the priest. To Sucrow. I swear, he's possessed."
Gabil became very, very quiet. Unnervingly so. "So he is."
"What's wrong with him? His eyes and skin are all wrong. And please don't tell me it's the scabbing disease. It's beyond that."
A long pause.
"Gabil, please."
"Patience. I'm trying to decide what I can tell you. Yes, in a sense Johnis is possessed, by a Leedhan. She calls herself an entity . . ." His expression was unreadable. "Half-Shataiki, half-Horde."
Darsal furrowed her brow.
"Her name is Shaeda."
"The Leedhan."
He nodded. "She wishes to conquer the Horde and the Circle as part of a plot to exact revenge on Teeleh. A spiteful, evil creature."
Darsal's eyes narrowed. "That won't happen."
The Roush tensed. Hesitated. "I would focus on what you can do, not what you can't, Darsal."
"You aren't helping, Gabil."
"Well, keep talking. We'll come up with something, I'm sure of it. Certainly a plan will take form. I have all confidence."
She was back to wanting to smack the oversized white bat.
"Well, go on," he urged.
Darsal took a long, deep breath. "If I help Johnis and Marak, the Circle dies. If I take out the priest, it'll fall on Johnis, Marak, or both."
"Or you."
"I'm beside the point!" she snapped. "If my death serves the mission, so be it."
"Now you sound like Johnis."
Darsal ground her teeth. "I need an immediate solution."
Even as she said it, she knew what she would do. She was Elyon's emissary, sent to bring him the hearts of Scabs. Marak was one. Now there were two more.
"I need to see Johnis."
Gabil eyed her but offered no indication on her course of action. "Well, whatever you decide, hurry, as I believe your general is returning. And he's in a foul mood, I might add."
Darsal fingered her pendant, eyes narrow. "We'll see."
three
**S** ucrow retreated to his chambers and completed the ritual to undo his facade of the young scout. Then he started for the palace to meet Marak and Qurong. As he neared the palace, he spotted Cassak up the road, taking orders from Marak. He sneered, pleased at the obvious rift in their friendship. The captain turned to summon the commanders. Anxious. And foolish to think that he could keep Teeleh's priest out of the officers' hall with a simple barricade.
How easily the loyal dog of the general was enticed.
Sucrow cackled. "Ambitious little captain, is he not?" He watched Cassak until the captain broke away from the others. Warryn was in place for his next assignment.
Now for the next item of business. What was that old saying? "That which bends not, break shall." Marak would bow before Lord Teeleh—one way or another.
"Let us see what can be done for the captain's ambition," Sucrow muttered to himself. "Surely he has better thoughts of glory than his brazen general."
Cassak broke off from the commanders outside Marak's quarters and started back up the street as the others went inside.
Sucrow followed, slowly catching up. At last he was abreast of the man. Cassak glanced over, a scowl on his face.
"What do you want?" the captain snapped.
So angry, this one was. Pleased, Sucrow withdrew a sidna and took a bite. He twisted his staff. A strange light seeped out—noticeable only to those with eyes to see.
"Warryn maintains you provoked the Eramites," Sucrow said, still looking ahead. He chewed slowly and swallowed, watched Cassak tense as the spell took root. Oh, yes, already the little charm was doing its work, crawling beneath the skin into the captain's heart. "But we both know my chieftain has a tendency to exaggerate, don't we?"
Cassak's scowl hardened. His eyes briefly landed on his own palm. Most excellent. Sucrow could barely contain the excitement, the thrill of the hunt, the rush of adrenaline involved whenever his spell fell over a new victim.
"Of course, I will have to inform Qurong." Sucrow raised a brow. "What say you?"
The captain remained edgy. Tendrils of shadow swirled around his throat and constricted. The others never seemed to notice. Curious. Blind, all of them.
"What's your game, Priest?"
"It is not for holy men to engage in petty games, Captain. Rather, we strive to bring instruction and exhortation, to train the sons of men." Mentally Sucrow recited an incantation, a mantra opening the captain's mind further to suggestion. Treacherous thoughts that could drive a wedge between Marak and Cassak. A wedge not even an albino wench could remove.
Marak of Southern wasn't really all he seemed, was he? Loyalty, integrity, and honor, he'd taught. And yet his loyalty betrayed his family to his supreme commander, then his supreme commander—and his own people—to an albino. What did that say of loyalty, of integrity? And what did his arrogance say of honor?
Self-imposed honor, perhaps. Naught else.
Cassak's gaze fell again to his hand. Of course, by now the little star had migrated to his throat, the jugular. "And what might your teaching to a warrior be, Priest?"
Sucrow retrieved a fruit from his robes. "Would you care for a sidna, Captain? They are quite delicious." A simple fruit, nothing more. The true magic was in what he had already done. The fruit was merely a personal joke, a private symbolism. Marak would have understood it, oddly.
Cassak, however, did not. Dumb ox.
"A sidna?"
"It is from the north forest." He extended the fruit in his hand. For a second the captain looked offended at the offer, then seemed to think better of his own offense. He accepted the sidna.
Sucrow watched Cassak bite, turning his staff in his hand, keeping the end level with Cassak. The captain's eyes changed, and he tugged the collar of his tunic. "Is your general displeased with you?"
"I grow weary of your questions, Priest. Don't you have a reckoning with Qurong?"
Bitter fool, wasn't he? How terribly disappointing to catch a smaller fish because the larger one refuses to be caught. But still, the smaller could be set to catch the larger.
Cassak's pupils shrank to needle points. His eyes took on the same greenish-yellow cast as Sucrow's other serpent warriors, a cast they themselves could not see. Yes, this captain would become a great general, one who heeded the servants of Teeleh rather than his own foolhardy ambitions.
_There we are, my fool._
"I was merely curious," Sucrow said. "You manage to prevent a war, and yet the general finds no cause to promote you? Many less experienced have already surpassed you."
Cassak's face hardened. Ah, the great captain's underbelly. He'd done so much for Marak, only to be left behind while Marak climbed the ranks.
"That is not your concern. It is you who almost caused it."
_Incompetent serpent warrior_ , Sucrow thought. "All of Middle is my concern. We all serve the Great One, no?"
More hesitation. Sucrow knew most of Marak's men didn't directly serve Teeleh, but all feared him, even more than their general.
"Think on it, Captain. I must be gone now. I have a high position available, one more suited to you, and I have favor with Qurong. Come and see me should you reconsider."
THIN LIGHT STREAMED FROM A CRACKLING TORCH. THEY were in an office converted into a bedroom. No windows, only a single torch stand. Two cots and a trunk made up the whole of the furnishings.
"Ba'al Bek," Johnis said to Silvie. She leaned against the wall, arms folded. Marak had ordered a servant to give them clean clothes and allow them weapons. A show of good faith, so it seemed.
And now Shaeda disclosed the next stage. Her patience was running thin. Her thoughts opened, and he saw barren desert and the high place she called Ba'al Bek and a throng of Shataiki led by Derias . . .
"We need to go to Ba'al Bek."
"Why?" Silvie shifted forward. "That takes longer, Johnis."
She lifted a brow. "We need a plan, love. We aren't pretending to do her will if we never work to undermine her."
He hesitated.
"Is she listening?" Silvie asked.
"I . . . can't tell. She's not strangling me right now."
"What's your heart say?"
Johnis swallowed. "She's likely always in my head, and occasionally allows me enough rope to hang myself if she so chooses. She's manipulative."
Silvie scoffed, but didn't comment. They couldn't plan an escape if Shaeda was always listening. He had but two advantages: Silvie alone could command his attentions over Shaeda's. And Shaeda's wishes were always open to interpretation.
"But you can't stop trying. And she can't possibly be everywhere at once."
"I don't think she has to be, anymore than I do." His focus shifted. "We're going to Ba'al Bek because it's one of Teeleh's holy places, which is why Shaeda feels compelled to desecrate it. She hates him, Silvie. Despises him. You've never felt anything like it." Johnis paused. "We just have to assume her power before . . ."
Shaeda cinched her grip on him. Silvie's eyes narrowed. For a long minute the Leedhan glowered at Silvie through Johnis, and Silvie returned the glare.
"Johnis. Silvie."
Johnis's hand went for the sword that one of Marak's men had given him. He and Silvie exchanged glances—no one here knew them by those names. An albino entered—Marak's slave. She wore a scarf over her head and face. Clanking metal. A length of chain ran between her ankles. Dark eyes searched their faces.
_Darsal_.
Darsal was an albino. An enemy. She would try to stop Shaeda's plans. Johnis's plans.
No, that wasn't true. Darsal wasn't the enemy.
The talons clawed at him. Yes, yes, she will do all to thwart them, should she know . . .
Silvie scowled, hands falling to her knives. "What do you want?"
Darsal pushed back her hood, revealing smooth skin painted white with morst. Long, dark hair, braided in Horde fashion.
"To see you," she said. Her gaze swept over Silvie, then Johnis. "What . . . happened?"
"You little leech." Silvie looked like a viper. "You left us for the Horde."
Darsal caught her breath. "I was captured, Silvie," she said simply. She was working hard not to stare at Johnis. "What is going on?"
Johnis scowled. His lip curled into a snarl. Shaeda saw albino meat—an enemy that must die.
Darsal took a step back. "I heard you have a Leedhan. An entity. Very self-indulgent term, if you ask me."
"And why would you care?" Silvie demanded.
Darsal stared Johnis in the face. All he could see was her smooth albino skin covered in white paste, and her rich, dark eyes enhanced by a single scar. She would bleed red.
Johnis didn't want Darsal dead. Not now. But she hindered the mission.
"I saw Gabil," Darsal said. "And Elyon."
Shaeda hissed. Johnis hissed. "You're lying."
"I swear on the books," Darsal said.
The books. He wondered if Cassak had located the others yet. Odd that Darsal would make such a vow now.
Johnis scowled. "You betrayed us."
"Johnis . . . trust me."
He recoiled. "Why would we listen to a treacherous Shataiki-lover like you?"
"Because you _forgave_ me! Don't you remember, Johnis? You saved me."
Footsteps echoed in the hall, cutting her short. She glanced over her shoulder. "Remember, Johnis. Elyon—it's all about Elyon."
He bristled at the name.
Angry shouts and a skirmish in the hall echoed through the door. They all jumped. Johnis and Silvie drew their blades. Darsal hid behind the door.
The knob turned. Men with tan robes and drawn, crimson-stained swords poured into the room, aiming straight for Johnis. He heard Darsal drop one, unconscious, behind him. Silvie's knife pinned the next assailant to the wall. A second flashed out. Johnis swung his own blade. Metal grated against metal.
His attacker sliced into his shoulder. Johnis blocked the next blow and slashed a diagonal arc with enough force to sever the man's torso.
Another was on him. Johnis almost lost his balance but used the momentum to spin sideways and catch the man between the ribs.
Darsal had found someone's knife and drew an opponent out into the hall. Johnis heard a yelp and a crash and nothing more.
A blow from behind knocked him flat. He rolled. The assailant struck him in the head. He saw a flashing light and tried not to pass out. Thrust with his sword. It clattered across the hard floor. Johnis kicked.
His arms were pinned. A knee drove between his shoulder blades. Johnis wrestled loose. _Shaeda!_ He tried to invoke her power.
Silvie shouted. Someone struck her, and she fell. Silence. Hellish silence. Where had the Leedhan gone . . . ?
Johnis swept his attacker's feet from under him and slashed down with his sword. An intruder dove into the hall with an unconscious Silvie over his shoulder. More shouting.
What should he do?
The priest. It had to be the priest. Johnis grabbed an iron poker and rammed it between the bars on the window and the wood surrounding. He ripped away the barrier and jumped through the window. Ran around the side of the building and darted down an alleyway. They wouldn't risk taking Silvie down the main road. He wouldn't bother trying to catch up and overpower that many men.
Instead he raced for the temple.
Shaeda had not given him her strength. As they ran closer, her thoughts grew erratic, senses heightened. She was . . . nervous? Invisible talons drove into him. Raked over his body. Johnis bit his lip so he wouldn't cry out.
Just as before, his loyalty, his love for Silvie, overpowered Shaeda's stranglehold. Her grip slipped. He pressed on.
Johnis caught up to the Throaters and raced up the temple steps to meet them at the top. He drew his sword, but suddenly Shaeda overwhelmed him, forced his knees to buckle.
_No! They have Silvie! I must save her from the priest!_
Shaeda growled in his head. The Throaters came at him. Johnis struggled, but the Leedhan was too strong. Everything grew hazy and purple, then faded . . .
four
**M** y general and my priest," Qurong mocked. "What's a ruler to do when he grants his priest authority over his general, only to have the priest prove less competent than the general?" The supreme commander had spent the better part of an hour upbraiding both Marak and Sucrow, and Marak was more than ready to move on.
"My lord—" Marak began, even though at the moment Qurong was raging against Sucrow.
His leader continued his rant. "No! You saw an opportunity to show off, and you failed miserably, Priest! Now, give me one reason I shouldn't just execute the both of you and start over with this newcomer who claims he can do both your jobs!"
"Respectfully, my lord, he cannot," Marak interjected.
Qurong swerved and demanded a report. Marak told him everything—beginning with the arrival of the mysterious couple, Josef and Arya, and ending with his reasons for refusing to turn over the amulet and the prisoners.
"A Leedhan." Qurong bristled.
"Yes, my lord," Sucrow answered. "The boy's account fits the legends."
The supreme commander glared at Marak. "Where is the amulet the priest wished in his possession?"
_Tread lightly_ , Jordan would have told him. _Don't be hasty,_ _brother. Don't accept power when you don't trust the source._
"It is in safe keeping, my lord, secured along with the two prisoners."
"And so you've defied my orders to report to the priest?" Qurong demanded. "Have you gone the way of the rebels?"
"No, my lord. I have not. And I—"
"And the wench Sucrow wanted is now dead?"
Marak tensed.
This pleased the priest. Sucrow was smirking at him, staff in hand. Marak felt light-headed and angry. Jordan's chiding voice echoed in his mind.
Marak cleared his throat. "My lord," he spoke in a very low voice. "Those albinos were executed days ago."
"You finally proved man enough to do it, then," Qurong sneered. He glanced at the slave near his general, saw the little pendant she was wearing, and scowled.
Jordan would tell him not to go through with this.
_Don't accept evil to further good_ , he would say.
_Why not?_
_Marak, you bullheaded idiot. What good comes of wiping out an_ _entire race of people?_
Marak was barely listening to Qurong and Sucrow, even as Sucrow went on about the Leedhan's capabilities. He should be paying attention, but he couldn't with this strange feeling nagging at him.
He threw the priest a glare. Sucrow seemed uninterested. No, he was . . . manipulating them?
"My lord," Marak interrupted, "If this expedition mounts and proves successful, all of the albinos, including Thomas of Hunter, will be dead in a matter of days. And I prefer to conduct my own interrogations since the priest's serpent warriors seem to have a fascination with cutting out prisoners' tongues before they've a chance to talk."
Qurong threw the priest a dirty look. "Is that so?"
"A rare occurrence, my lord," the priest assured, his staff turning in his hand. "It's the mongrel he last gave me he's so irritable about. But she was worth nothing."
Marak's attention snapped back. His hand curled around his hilt.
"Now, on to this albino and Shataiki business," Qurong growled. "Speak, General. Don't allow a priest to outdo you."
Marak remained unwilling to give his superior the satisfaction of a reaction.
"Oh," Qurong taunted. "The general doesn't like my assessment." He chuckled. "Of course, if that whelp succeeds, he'll have made fools of you both. You are supposed to be my best. Frankly, I'm disappointed."
"He found a harach, my lord," Sucrow interjected. "He has no idea what to do with it on his own."
"So you are holding out on me," Marak growled.
"Maybe you aren't as perceptive as you used to be, General," Sucrow sneered. "Your vision seems blurry these days. Losing your edge, perhaps? Your captain certainly thinks so."
_Cassak_.
Marak knew better, though. Or did he? What was Sucrow up to? His eyes narrowed. He forced a direct gaze, sizing up the man with the staff. Sucrow had never, to his knowledge, performed any sorcery on him.
But this strange sense of unease . . . Was Sucrow threatening or taunting him?
Finally Marak answered, choosing to pretend nothing was suspicious. "Keep it up, Priest."
He could have sworn Sucrow blinked.
_Unaccustomed to being suspected so early, aren't you, Priest?_
The priest broke eye contact. The constricted, numbing sensation left. "You wouldn't dare."
"Try me." Marak's hand remained on his sword.
"Stand down, General," Qurong warned. "Priest, speak."
A dark look crossed the priest's face. What was he plotting now? Would Sucrow have Cassak killed just to demoralize Marak?
Cold fingers slid up his back. It would work, too.
"I fail to see where the medallion comes in." Qurong glared. "Get to the point."
"The point, my lord," Sucrow replied, "is that while little is known of these things, the legends themselves exist."
Marak narrowed his eyes. He had no desire to run all over the desert chasing a legend. But he'd given Josef and Arya his word. And they were convinced they could finish off the Circle in three days. Sucrow wanted in, and that was all the convincing Marak needed.
He would do whatever it took to get Qurong off his back and put the priest in his place. Most curious was that not even Qurong had heard of the Leedhan.
Qurong spoke, his eyes wide with conspiracy, as if some ancient favor had come to him from the sky. "So there really is an amulet that controls these . . . things."
Sucrow handed Qurong his book. "The kind of tree that produced the wood it's made from supposedly no longer exists. He showed us the harach earlier, and I thought, perhaps if it does exist, we can be rid of the vermin more quickly." The priest sneered. "Be rid of our general's hesitation."
Marak white-knuckled his belt, fighting the urge to bash in the priest's head. "Why involve a human?" he asked.
Sucrow laughed hard and loud. "We are catalysts. We live in two worlds, Marak. Haven't you realized that?"
Marak didn't comment.
"An expedition may well be worthwhile, to rid ourselves of them once and for all. It is quite simple. We gain control of this Shataiki amulet guardian, invoke a ceremony on Ba'al Bek, and unleash the Shataiki on the albinos."
Qurong was so lost in thought he didn't seem to hear them anymore. He turned to go. "I will do this: you will both go, with equal authority and equal standing. You will mount this expedition, and—provided you don't kill each other—both return with the Shataiki on a leash and a solution for your stupidity with the rebels. If either of those directives fail, I will hold you both responsible. You have two days. Am I clear?"
"My lord—" Sucrow started.
"Begone."
MARAK HAD BARELY LEFT THE PALACE BEFORE CASSAK CAME galloping back up the road for him, Marak's mount in tow. He swung up, knife in hand. His face was flushed, eyes wide, pupils tiny.
"There's been a breach, General," Cassak announced. "The whole building's coming—"
"Who is it?" Marak snapped, suddenly frustrated. Sucrow snickered from behind. A chill swept over him. Marak checked his pocket for the amulet as he raced back with Cassak.
"Don't know yet, sir. No insignias. We're assuming Eram."
Eram. Cassak had no business making assumptions.
Marak grumbled. "Who's on the roof?"
"Six archers. My men are gone; Reyan's are divided. We don't know how they breached the blockade."
Bloody Eram. He never should have trusted that half-breed Horde trickster and his bunch of ex–Forest Guard in the first place.
He and Cassak reached the hall, where men were beating each other down with swords.
"They're ransacking everything," a fighter said.
"Take a hostage," Marak growled. He swung off his horse and rushed into the hall. Ran an invader through and rolled him over. Cassak was right—no identifying insignia. But why would Eram go through the trouble to mask his men's identity?
Unless it wasn't Eram after all . . .
The general whipped around and let fly one of his knives into someone's temple. He cut down a third.
Someone was going to pay for this.
five
**S** triking the cold, hard floor, Johnis woke. He heard Silvie yelp and tried to sit up.
"Let me go!" she demanded.
Shaeda was quiet, too quiet. Everything was foggy, dreamlike. Another kind of darkness lingered here.
The Throaters dragged Johnis to his knees and pushed him forward onto his palms. The bag was ripped from his head, yanking strands of hair with it.
Johnis squinted in the dim candlelight. He'd needed the images that Shaeda's gift of foresight could offer. Why had she allowed the Throaters to take him? But that was it, wasn't it? To prove he needed her, not the other way around. He had to find a way to keep her power but get her claws out of him.
"Bloody priest," Silvie spat. She was on his left. Her face was tense, lips pressed together, eyes narrowed. A deep, fresh gash oozed blood just over her brow. A red trickle made its way down the side of her pallid cheek and off her jaw to her shoulder and the ground.
Her knuckles were raw. Her limbs pulled as tightly against her restraints as she could manage. Even on all fours, her snakelike eyes had fixed on someone in front of her and refused to be distracted.
The door locked behind them. Johnis raised his head to see the object of Silvie's killing gaze: a skinny, black-hooded Scab with white skin flaking to the point of disfigurement, dripping in gaudy jewelry. His hawkish expression leered at them.
Sucrow.
This time he did not need Shaeda's influence. Nor did he want it.
Johnis rose to his knees and rolled his shoulders back. His muscles tightened. The invisible claws tore at his back, but he fought through the pain. Shaeda's talons and Sucrow's magic pulled him in opposite directions.
A small metallic sound rang from behind and to the left of Johnis. An apprentice had a silver knife at Silvie's throat. The only change in her expression was that she looked much angrier.
Sucrow wanted to play with them. Pungent incense wafted from a bowl on the far side of the room, next to what looked like another shrine and hundreds of feathered serpents that represented Teeleh. Just off center was Sucrow's altar, much like the one they recently encountered in the Black Forest. Narrow grooves were carved out of the rim to catch blood and guide it into a small silver tray below.
Johnis tried not to shudder as Shaeda's fear and hatred of the Shataiki overtook him. A purple-and-blue haze fell on him. He could feel every ounce of her disgust at the winged-serpent image. At the Dark Priest.
"What do you want, Priest?"
"Respect," the priest said. "Your loyalty."
Johnis growled. "I give respect where it is due, Priest."
A fist struck him from behind. Johnis buckled under the blow and saw yellow and blue flashes of light. He righted himself and shook it off.
Shaeda's thoughts turned dark, knocking the wind out of him. She was strangling him. _Shaeda_ , he managed. _You're killing me . . ._
She loosed her grip a little, still tense. Her talons still cut into him, so great was her hatred of all things Teeleh.
_Release me!_ he protested.
The talons dug harder, pinching him. " _Put aside these thoughts_ _of freedom. Freedom for you shall come with death."_
Sucrow laughed. "Still struggling with glorious delusions, Chosen One?"
"I don't know what you mean."
_"Does Sucrow know? How?"_
The priest forced Johnis's head sideways and traced his crescent-shaped birthmark—the one behind his ear—with his fingernails. Chuckled.
"Oh yes, Witch spoke of you, before Ciphus killed him," Sucrow taunted. "And then I killed Ciphus. And now, you, Chosen One."
Sorcerors, to the last of them. Johnis's skin crawled under the touch. He fought the impulse to recoil out of sheer revulsion. In the end pride quelled his horror.
"Drop dead," Silvie snapped.
"Arya," Johnis scolded, refusing to confirm what Sucrow already gathered.
"Pity that wench who bore you had to die."
Johnis ground his teeth. Sucrow chuckled, still stroking along Johnis's neck, sending the tingling down his arms and legs. He scrutinized his prey. Reached for the ring on Johnis's hand. His mother's ring.
Johnis curled his hand into a fist. The Dark Priest sneered. He pressed into Johnis's skin, digging at his flesh until he made a ragged cut. Johnis winced.
"You've caused me enough trouble." Sucrow grabbed Johnis by the hair and jerked his head up. "I want to make something perfectly clear so that you understand your place. Agreeable, don't you think?"
A Throater shoved Silvie to her feet, knife still at her throat, and forced her to the edge of the altar. Her movements were stiff, as if under some spell. She was made to climb on top and lie down on her back.
He chained her to the wood.
Silvie craned her neck and shot Johnis a desperate look. "Jo . . . sef . . ."
She had almost used his real name.
Blood pounded in his temple; his hate rose. He channeled both into a rage and lunged against his shackles. Surely Shaeda would give him strength. Strength to tear off these shackles and destroy the priest who dared touch Silvie.
"She stays with me!"
Nothing. He was helpless.
_Shaeda._
Sucrow cackled. "You understand, then. Insurance."
MARAK WAS COVERED IN BLOOD. HE FOUGHT HIS WAY DOWN the hall toward Josef and Arya's room in time to see Darsal knife-fighting with an enemy. She sliced into his upper arm and ducked low to keep from tripping. Why didn't she kill the man?
"Darsal!"
Another intruder. Marak fought him off, took a graze to the ear. He heard a crash and Darsal's yelp cut short. Marak whirled and saw her motionless on the floor.
His heart lurched.
Marak was on the man before he knew what he was doing. Her opponent slammed into the wall. Marak's sword fell toward him. Their blades clanged together. Marak blocked a blow. Feinted and sliced a diagonal arc.
The intruder blocked with such force it rattled Marak's arms. Marak dodged another and slashed against the man's abdomen, disarmed him, then slashed off his head.
Marak burst into the room that served Josef and Arya and spun around in time to block an attack. He pivoted sideways, unwilling to be trapped by a wall.
A hard hit slammed him to his knees. Blood oozed from his shoulder. Marak blocked again. The sword rose up. Fell.
Then his attacker fell. Marak rammed his knife into the man's throat.
Darsal kicked the dead man aside and wiped her stolen sword on his tunic. "My general."
She extended her hand. He jumped up and knocked the blade from her hand. Instantly Darsal punched him in the chest, then went into a defensive stance.
"Darsal," he growled. She was alive. He could kiss her. Slap her.
_Settle down, idiot. She's alive. Thank Teeleh, she's alive._
She straightened. "You're welcome," she snapped.
Cassak came into the room with several warriors. He tried not to gawk at the albino with blood all over her. What was he staring at, anyway? He'd seen a female albino before. Especially this one.
"They're gone," she said.
Thank Teeleh he still had the medallion. Yes, Cassak had barely stopped a war with the Eramites. But his messages had been growing increasingly inappropriate. His interference had cost Marak his entire family, and Qurong's trust.
Sucrow's mockery echoed in his head.
The surge of frustration continued, though Marak wasn't entirely sure why he was so angry with his captain, his lifelong friend.
Of course, Cassak had stood there and watched the priest torture Jordan and Rona. Cassak had carried out Marak's order to kill them while Marak watched. Cassak had suggested the use of the Desecration on them. Cassak wanted Darsal to die just as badly as the priest.
Cassak had been in command of this stronghold. Only he had access. Only he could have caused the breach.
Sucrow was right about one thing.
"General, they're—"
Marak exploded.
"Did the entire watch fall asleep at the same time?" he screamed in Cassak's face. "Was the only person awake in the whole building an albino slave?"
"We're looking into—"
"Get the scouts on the move now! And when I find out who was asleep on the watch, they're going to wish they were dead!"
"Gen—"
"Find them, fool!" Marak struck his captain with the flat side of his blade. Ignoring the stammering compliance, he grabbed Cassak by the scruff. "Now!"
"Marak." Darsal's voice cut through the purple haze in his mind.
He drew a hard breath at Darsal's gentle rebuke and let go. "Was it rebels? Or someone else?" he asked. He turned over a body. Inspected it. Recognized it as one of Eram's men.
"We're interrogating a hostage now," Cassak assured him, slightly stunned at being the brunt of his best friend's wrath. The thought crossed Marak's mind that he should apologize. But what could he say to explain the outburst?
Cassak slowly composed himself, finished his thought. "One of our men thinks he saw Warryn. Of course, if it was, the hostage won't admit it."
Sucrow.
He slammed his fist against the wall. "Sucrow, you bloody bat lover . . . !" He spun back around and got in Cassak's face, the fool captain who'd caused this mess and nearly got Darsal killed.
"Marak, we'll—"
"Get out of my sight, and get me answers," Marak growled. He shoved Cassak toward the door. "We're moving out. Now."
He swerved back around and surveyed the damage.
Darsal remained. She eyed his sword. "You want my help?"
Marak drew a breath, simmering. "I want you to pack up."
"Marak, don't be stubborn. Not now."
He sheathed his sword and started for the door.
"They're _my_ friends, my general," she growled.
"You'll get yourself killed. Wait here."
"Mar—"
"I said wait here, Rona!"
Awkward silence slashed through the room.
"My name is Darsal."
His jaw tightened.
"What are you going to do?" Darsal snapped. "Storm Sucrow's temple? At least if they kill me, it's no big—"
"I need someone here," he barked. "Wait for the messenger; then find Cassak and tell him I'm going to kill that priest."
"Good riddance." Darsal followed him out the door and snaked her hand around his waist, toward his knife.
He grabbed her wrist. For a second they both stood still. All the fury drained out of him and turned to . . .
Something else. He pulled the knife toward himself, both their hands still wrapped around it. Darsal was almost touching his chest.
"Let me go with you."
Marak uncurled her fingers from the weapon and slid it into a sheath, then turned for the door. "That priest _will_ kill you."
Darsal started after him again. He turned sharply, and she ran into him. He held her at arm's length. "Don't follow me."
"I have to. Elyon's orders."
Hating himself, Marak shoved her into the room and forced the door shut before she could yank it open again, then locked it.
"Post a guard," he barked at the warrior coming to his aid. "She doesn't leave. Secure the premises, and prepare to move out. And fetch me a scout."
six
**D** arsal waited until Marak was long gone. She stewed and tried not to think about what might be happening to Johnis and Silvie. Or what could possibly have caused such a fight between general and captain. This whole mess was taxing on everyone. Marak had clearly lost his mind.
Serve the mission. She loved the Horde, and she loved Marak. How loving them could help anything, how that would serve Elyon's purposes, she wasn't sure. Yet.
But Elyon made the Horde, and he loved them, wanted them, as badly as the albinos.
Finally, she could wait no longer. "You have another thing coming if you think I'm staying in here, my general."
She studied the room and took in the contents. Since the building had never been intended for a barrack, there was little to work with.
Marak's men had sealed the windows when Johnis and Silvie were quartered here. And aside from a long candle stand or a torch, there was little in the way of weapons. And the guard wouldn't likely fall for a trick.
Darsal eyed the window, considered breaking out the bars. No, too much time.
The torches were still unlit, though. If she used one, the place would go up in flames too quickly. Instead Darsal scooted the candle stand right next to the curtains over the window, lit it, stood back, and watched them smoke.
The flame caught.
She ran for the door. "Fire!"
"LET HER ALONE," JOHNIS SNARLED. EVERYTHING WAS A HAZE. He drew a ragged breath. Silvie couldn't die. _Shaeda, help me._ _Together we can kill him now!_
_"Entice me not,"_ the entity growled in his ear.
"More important, you will do as I tell you, or I guarantee she won't outlive the hour." Sucrow took the knife from his servant and traced the tip along Silvie's throat. She didn't move.
Johnis saw no way out. Not with Silvie one flick of the wrist from death.
She caught his eyes and gave a slight nod, meaning for him to let her die. Let her go. Save himself, take revenge later. They could not kill the priest yet. Shaeda didn't trust herself to not kill him if she unleashed.
Johnis sagged and let out a soft groan. "Will you let her live if I promise not to defy you?" He spoke the words out loud. Of course, he still had his private thoughts of unlocking the keys to her power and keeping them—apart from her.
Darkness and fog descended, a thunderstorm on the torrent of fire. Johnis felt the abyss of failing Shaeda—her punishment, her whipping—conquer his inner rebellion.
"Josef," Silvie warned, her eyes half-closed.
Shaeda's punishment grew more insistent: Finish the mission. Regardless of cost. Even at the cost of Silvie.
Even if it meant an alliance with the priest.
_"The mission holds greater weight. We require the priest's_ _knowledge."_
So she could restrain her passions, when she chose. Her hate she held at bay, knowing the result of the mission would bring far greater satisfaction than killing him now to save Silvie.
"Only as long as you do as you're told." Sucrow played with the blade resting against Silvie's neck. Revulsion snaked down Johnis's spine, twisting his face in disgust. Of course the priest would think Johnis was talking to him.
"Be careful what you wish for," Silvie whispered, pulling away from the priest, her voice low and devoid of emotion.
The door burst open. Darsal stood on the threshold, wielding a long silver candle stand, her cowl once more over her face.
Sucrow curled his lip. "Stay out of this, albino."
She came between Johnis and Sucrow, inching toward the altar. Johnis took advantage of the slave's entrance and managed to stagger to his feet with his arms at his sides.
The albino joined Sucrow at the altar. She hesitated with her makeshift club.
"Put that down," Sucrow ordered the slave. His hand opened, palm stretched out toward her, fingers curled. Darsal was suddenly flung against the wall. Her weapon clattered to the ground. She didn't move.
A guard went for her.
_Shaeda, we have to get out of here. Now._
Johnis drew a sharp breath. "I will take you there, and I will do what you will. But if you kill her, I will come after you." He met Sucrow's eyes. "And then I will kill you."
"You're hardly in a position to make threats."
Sucrow nicked Silvie's throat to make his point. Her blood oozed along her soft skin and onto the altar. The priest collected the crimson liquid onto his fingers and dipped them into a bowl of water.
"It's always more fun through the throat."
Sucrow poured the bowl's contents onto the wound. Smoke curled, sizzling. Silvie yelped and tried to jerk away but had nowhere to go.
The priest kept pouring. Silvie's skin turned from white to yellow- green to gray.
Johnis lunged, but the guards held him back by the wrists. "Leave her alone!"
"It won't kill her. At least, it isn't supposed to." Sucrow cackled.
A flash of movement. Darsal lifted the candle stand and went for the priest. Swung. Sucrow barely dodged the blow and dropped his bowl, reeling backward. Darsal jumped between Silvie and the priest.
Sucrow stood. He opened his palm and unleashed a stream of fire. Darsal dodged as the flame grazed her shoulder and scorched the stone floor. Her body slapped against the rock, her head bouncing.
Sucrow glided to Silvie's side, amused at the whole situation. "Or perhaps I could do worse." He dug his nails into her cheek. Silvie growled but could do nothing. The bloodstain taunted Johnis.
The priest kissed his fingers.
Johnis's chest constricted. His muscles curled into knots. Shaeda—or he—snarled.
As Darsal groaned and picked herself up off the floor, Sucrow threw his knife at her. But another knife whizzed through the air and struck the priest's midflight. The weapons ricocheted off each other and skittered across the hard floor. A blast of sound. Darsal slammed back against the wall, away from Johnis. Sucrow's sorcery.
The room went still.
General Marak of Southern stood on the threshold, another knife ready. His gray-white eyes homed in on the priest.
"I'm pleased you could join us, General," Sucrow scoffed, turning.
Johnis could feel the changes as Shaeda's power finally began to flow into him. His heart pounded. They would end this, ally with the priest, get the general and the albino out of the way. His fists knotted. He could snap the metal chains like twigs.
"You're well out of line, Priest," Marak growled.
"She's just an albino."
"Arya is not. Release them now. We're getting this cursed expedition over with."
Johnis lunged for Silvie, but Marak caught him by the collar. Shaeda—through Johnis—lifted her hand and raised it toward Sucrow. She began to recite in a language Johnis didn't know. His heart rate spiked.
"Save it," the general snapped. "The next time, Priest, I will kill you."
Sucrow cackled. "I half expected you to go running for Qurong."
Marak's eyes narrowed. "More proof I am not a priest. Let the girl up. We don't have time for this."
Inside him, Shaeda stirred, acknowledged the shift in focus. She lowered her talon and stopped mid-incantation. Marak was not in defiance of the priest; neither would he allow the priest access to the amulet. They were working together. He felt her power ebb. There would be no snapping of the chains.
_Shaeda, please!_
Johnis tugged his shackles. Didn't Shaeda care?
No, not as long as he was not in danger. Marak was now the mediator between this entity inside and the priest. As long as it furthered the mission, she would not interfere. He must endure a little longer.
"And if I choose not to?" Sucrow sneered.
"Then Josef and I make the expedition without you." The general's expression darkened.
_No! Silvie!_
Johnis dove for one of Marak's knives. Marak drew back and slapped him to the ground, hard. Johnis started up, but Marak's sword point threatened to run him through.
"Enough," Marak snarled. "What are your terms, Priest?"
Sucrow considered his options. "I keep the girl until this is over."
"Fine. If she dies, the agreement is breached."
"Agreed. And you kill the albino. She attacked me."
The two stared each other down.
Marak pulled Johnis up and let him stand, but kept a knife pressed against his ribs. "Come," he ordered Johnis and Darsal. "We have preparations to make."
seven
**S** ucrow left his servants to clean up the mess and load the girl into a small cart with a built-in cage for transport. She would be ready along with his other provisions. He went to take a final look at the old legends, at the ceremony. It had been there all along, right under his nose. He chided himself for not seeing these things before.
But soon enough he would no longer require these fools.
Perhaps by then Marak would be in line. If not . . . more drastic measures might be required. But what more could you do to a man once you'd stripped him of everything?
Well, not everything. Marak still had his position and his very prominent ego.
And his life. And his best friend, Cassak.
But his beloved captain would soon be leaving him. The mere thought made Sucrow laugh. Already the potion was doing its work. Loyalties could be bought, coerced, and traded for improved honor.
"My lord?"
Sucrow glanced up, scowling. A servant stood at the door. Upon his bidding the wretch approached and bowed low.
"What could possibly lead you to bother me at this hour?"
"Marak's captain is here."
_Like a faithful dog._ Sucrow chuckled.
"Bring him in."
Sounds of commotion filtered in from the hallway as the captain stalked in, sword half-slung. His face was tight, shoulders back. Sucrow couldn't quite read his expression.
"Reconsidered so soon, Captain?" Sucrow asked.
Cassak's eyes turned icy. "What is it you want of me?"
Sucrow sat forward and laced his fingers beneath his chin. So the fish had taken the bait, had he? He concentrated, summoning the power of his lord and master to his aid. The captain scratched a spot on his neck, uncomfortable. He could not see the little serpent with its red, pulsing, star-shaped eye at his own throat.
So simple, this ability to control the heart and mind and body of a man.
"Nothing too difficult," Sucrow assured. "You executed Jordan of Southern along with the other two, correct?"
The captain answered slowly. "I did."
Technically true. Cassak carried out Marak's order. It didn't really matter. Marak was there; Marak gave the order. Sucrow just needed the general to remember who let fly the arrow.
"I would like a copy of your report, as well as Marak's notations and Martyn's war journals." At Cassak's hesitation, Sucrow reminded, "Qurong gave the general and me equal standing. He did not relinquish my rights to oversee executions. Besides, my understanding is the general made copies. I merely wish to see one of them."
"Why do you want it now?"
"Merely review." Sucrow managed something close to a pleased look. He took his staff in hand. "There is no need to tell Marak. I also want the amulet."
"That doesn't answer my question."
"Patience, Captain. Tell me something: do you enjoy being a captain? I will put in a word to Qurong that your services have not yet been rewarded. What do you think?"
The little snake bit the captain on the jaw, entrancing him.
Cassak didn't answer, but his eyes said he was interested.
"Together we will remind Marak of his duties."
MARAK STOOD IN THE CLEARING SOUTH OF MIDDLE, JUST beyond the gates. His commanders flocked around him. Everyone was accounted for save Sucrow, Darsal, and Josef. He half listened to his commanders, who all parroted things he already knew.
Teeleh's breath, since when had he become so irritable with his own men?
Darsal had slipped away. He didn't like the albino being where he couldn't see her. Where had she gone?
"General, the priest and his men are unaware—"
"A warrior is prepared to break camp and run in under five minutes," Marak said. Sucrow would show up, just as planned. If the old priest moved too slow and had to catch up, so be it. "We're leaving as soon as the scouts report."
He reviewed the checklist in silence. Cassak was supposed to meet up with him in the desert and signal his men to follow . . . provided he didn't make any more mistakes. He'd become intolerable since his return, since the Eramite skirmish.
And spending so much time on his own . . .
"General, are you certain this is wise?"
"Are you afraid of a superstitious old man, Commander?" Pause.
"No, sir. It's only—"
Marak passed his checklist to the commanders to mark off. "What makes a warrior, Reyan?"
The man snapped to attention. "Loyalty, integrity, honesty, sir."
"Shall I think less of my officers, Commander Reyan?"
"No, sir."
At his look the men scattered to their final preparations. Marak turned on his heel, scanning the shoreline. The priest would come. It was only a matter of time. He bit back a mocking laugh.
He didn't wait much longer before Warryn, chief of the Throaters, came riding hard through the forest. Warryn swung down. Marak noticed he wore an eye patch now.
So the Throater's blunder had cost him his eye; Sucrow was a harsh master.
"The priest wants to know why you're leaving without him."
Marak shrugged. "I'm ready to leave. Or do priests not move as swiftly as warriors?"
"He's on his way," Warryn persisted. A smug look crossed his face, as if he knew something Marak didn't. "He's sent me ahead to ensure you do not leave."
"We don't have the time for games."
Warryn's expression sobered. "It has to do with the expedition, General. I'm sure he has his reasons."
"He is aware we're on a schedule, is he not?"
One blank, cold eye drilled him, then shifted to Darsal, who had just appeared through the clearing. Darsal glared back at him, then turned her attention to Marak. She touched the Circle pendant around her neck.
Warryn made a sound in the back of his throat. "The priest wishes also to know when you plan to kill the slave."
"Excuse me?"
"Are you doing it yourself, or will you have another perform the execution?"
Marak snapped his head up. His hand brushed his hilt. This Throater would never touch Darsal. A fleeting thought crossed his mind, that Cassak had asked the same question. He dismissed it.
"Concern yourself with the present, not the future, Throater. I'll kill her when I'm done punishing her."
The gloat on Warryn's face shriveled to a blank, wide-eyed stare. Then his eye narrowed and darkened.
"Respectfully, General, the future and the present are not so distant from one another. What occurs in one will affect the other by design."
Someone cleared his throat. Reyan. His ranking commander rubbed a spot on his ear, not quite shaking his head, and made brief eye contact.
"Tell Sucrow we need to move out quickly," Reyan said to the Throater. "There's no time to waste."
Warryn's face tightened.
"Now."
The Throater gave one look at Marak, who nodded, and took his leave.
Reyan waited.
Marak relaxed his fist.
Reyan nodded pointedly toward the trees. "We brought in a dozen albinos, General."
More albinos? They were getting harder to find by the day. "Where?"
"More of Jordan of Southern's brood. Apparently the Eramites drove them out. We await your command to execute them."
A test. Only Cassak would be so bold as to test Marak by forcing him to order an execution just to see if he would do it. He must have set this up so Reyan would have to ask. The captain was making a point to the men. And to his general. Since when did Cassak question Marak's abilities?
Something was wrong. He'd never been so angry with his friend in his life, and never had Cassak had cause or desire to doubt him. It all started with Jordan and Rona, didn't it?
Or . . . did it?
Reyan cleared his throat. "General?"
On instinct he checked his pocket for the medallion. It was . . . gone.
Marak snarled. "Execute them."
He stalked off without waiting for a reply, grabbing Darsal by the scruff on the way and dragging her off into the trees.
eight
**E** _lyon, why is he manhandling me? The fire?_
Marak glanced over his shoulder. He loomed over her. Close. So close . . .
"Where's the amulet? Are you trying to ruin me?" He straightened and turned toward her, his eyes drilling her. He wanted her to say it. To admit it.
Darsal couldn't help but feel startled. Marak fully expected nothing but the truth from her. An albino. Had she made so much progress?
She crossed her arms and looked Marak in the eye. She didn't know what Marak was talking about. For all she knew this was a ruse so he could say he'd already interrogated her before conducting his real search. Her sense of vengeance flared over the con demned albinos, equally met with the utter despair of his deception and the shocking revelation of his trust.
Her mind caught up. She couldn't save the albinos. She could keep this thread of trust. "You want the truth."
Marak's arms folded over his chest. Her heart skipped a beat. Did he really trust her so much? The general was so close. And now—now everything seemed to hinge on her answer.
She drew a breath. Let his newfound trust in her sink in. "I didn't take the amulet, my general."
His fist curled. "Someone did."
"It wasn't me. Ask your captain."
"Cassak is my best friend," he said. But his eyes betrayed doubt. Marak considered his albino slave more trustworthy than his Scab captain now?
Darsal backed off. Marak was irrational when it came to those close to him. Irrational enough to accuse his best friend of stealing from him. "It still wasn't me."
"And the fire?"
"I just needed out of the room. I wasn't trying to burn the place to the ground."
And for that she thought he might either break down or explode.
"Neither Josef nor Sucrow has it?"
Marak cleared his throat. "Both claim innocence. My guess is the bloody priest, but he's got someone else holding it."
"You want me to steal it from him?"
He didn't answer immediately. For a full minute she stared at his back. She started to reach for his arm, but he turned back around.
"In the lair, if something were to happen, you wouldn't be able to run."
Her brow furrowed. Surely he didn't think her a coward. She studied his eyes. No, no, it was something else. "Now, there's a change of subject."
"I can handle the priest," he said.
He had not answered her question. Silent affirmation? Denial?
Marak withdrew something small and silver from his pocket, then stooped and reached for her leg. Darsal jerked. Kicked, out of habit. Marak stilled, and something in his expression twisted. With an uneven breath, Darsal willed herself to relax.
"What are you doing?" she demanded.
Her general lifted her foot to his knee and unlocked the shackle. He then did the same with the other. For a moment he stayed there, kneeling with her sandaled foot on his knee, key and open shackle in his hands. Darsal suddenly felt silly.
Marak was . . . releasing her?
He straightened and set her foot on the ground.
And then she was alone.
Marak's voice bellowed across the clearing at his men. A few horses whinnied. The breeze sent a chill through her, despite the warm sun.
Her feet felt so light after wearing the heavy chain. Now . . . now all was weightless and surreal. Even the ground beneath her barely seemed to touch her. Dare she think she had Marak's heart?
Dare she think she could keep it?
Tree branches swayed gently, leaves rustling. Instinctively she looked up, hoping for a flicker of white wings.
"What will you do?"
Darsal swung around, dropped to a crouch.
Gabil was in front of her. "You could leave, you know. He would understand."
"I don't know what you mean." That idea stung her. It wasn't part of her mission. Elyon's mission.
"Yes, you do."
Darsal straightened her shoulders. "I can't leave without Johnis and Silvie. Without Marak."
"They've chosen their paths."
"They're in pain."
"Yes. They are. They are deceived."
"You would have me leave them like this?" She didn't believe what she was hearing. Gabil wanted her to scrap the mission?
"You cannot save them all, Darsal."
Indignation filled her. The Horde was as worth saving as the Circle, and save them she would. Or die trying.
"I only want to save three. Why do you want me to run to safety? If I leave, I condemn them. I condemn the Circle."
"That is true."
Darsal didn't answer. _Gabil isn't telling me to leave them. He's_ _showing me why I have to stay._
"Love him for Elyon, Darsal. For Johnis."
She balked. The hair on the back of her neck rose. It was a thread of hope, but it hinged on her ability to love a Scab general.
And on his returning that love.
"Darsal!" Marak's voice bellowed from the clearing, through the grove of trees. They were ready to leave.
Gabil flapped off.
"Darsal?" Marak came through the trees, sighted her. Stopped.
She raised her chin. Stood in front of him just as she had that day in the dungeon. Looking at him, the fight left her. In its place was deep sorrow and love.
"I'm here."
Marak looked at her gravely with an expression she'd never seen. And she knew: he'd expected her to leave.
For a moment they stared at each other. And then it was over.
Marak turned back into the stoic warrior and started back for the others. "It's time to leave."
NIGHT FELL OVER THE EXPEDITION PARTY. SERVANTS CARRYING long torches surrounded their masters, creating a ring of fire against the starlit night. The desert cooled with the rising moon. Johnis rode ahead, Sucrow and Marak behind and to either side of him. Out on the wings, two commanders. He'd noticed some strange activity between Cassak and Sucrow but thought little of it. Cassak was a mediating figure—it was likely all usual. Marak either didn't notice or wasn't disturbed by his captain's movements.
Behind them all, servants . . . followed by the Throaters. They cut south through the canyons, past Natalga Gap, and into the endless sand.
Silvie should be riding next to him, not held captive by an evil priest and caged at the tail of the procession. He had to think of a way to free Silvie. He had to . . .
The siren song swelled, overpowered his vision so he could no longer think of Silvie. Johnis felt his senses sharpen and his focus narrow. He could think only of the mission.
Shaeda.
_You are beautiful,_ he thought. _Tell me more. You are a queen, with_ _a mate, yet the Leedhan were not born until after the Desecration._
She gave a low, seductive laugh. _"You are correct, my fair one, I_ _am the eldest of our kind, at eighteen. Does such please you, that one_ _so young might wield such power?"_
He didn't have time to answer.
"I see nothing," Sucrow growled. He clutched his staff. A strange, heady sensation fell over them.
The moon rose high into the east now, and Johnis turned his horse to confront the broad length of shadow, moon at his back.
"Patience, Priest," Marak snapped. His irises were enormous, or his pupils had shrunk strangely.
"I think we've shown more than enough patience for the time being, General."
"How far until we turn west?" Marak demanded. His mood had gone from irritable to completely foul. Now he seemed to struggle with something, but Johnis couldn't pinpoint it.
The siren song distracted him. Shaeda's mind was open to Johnis once more. She gave him instruction as they traveled. The further they went, the more he saw through multicolored Leedhan eyes.
"Not much farther. Another hour or so, I think."
Marak humphed his answer. "We'll need to make camp, then."
"Camp?"
"You didn't expect to ride through the night, did you?"
"It's a long way. I thought you were all in a hurry."
Shaeda's song spurred him along. She was fantasizing as much as she was planning their next move, seeing farther ahead than anyone could have realized.
These miserable fools made of clay had no idea what was coming for them.
Marak had been taking stock of the area. Shaeda's gaze lingered on the general for a long moment. Johnis could make nothing of her assessment. Her thoughts were growing more guarded, more cautious.
"Here's as good a place as any," Marak said.
_"Continue on . . ."_
"We should continue," Shaeda said. Johnis said.
"There is nothing." Johnis said, his voice hard and clipped. "Not until we reach the canyon. We should keep going."
Marak dismounted. "Ten minutes." Silvie refused Sucrow's assistance down and nearly fell off the horse, trying to dismount.
Silvie had refused to look at Johnis as she was forced into a cage. Johnis considered how to rescue her while Marak, the officers, and Sucrow went to discuss whatever it was that Marak wanted to discuss.
_Silvie . . ._
Shaeda clamped down, her rival now out of the way.
Johnis stumbled off his horse and sank to the ground, elbows on his knees. He rubbed his temples. Against Shaeda's wishes, the caravan had stopped.
_"We must not linger, my pet._ " Her claws cut into him.
"I can't control him," he protested under his breath. "I can't. There's no telling the blasted general what to do. Patience, please."
He was punished every time someone else slowed her down. Shaeda's invisible grip tightened.
"Let me go," he whispered. He couldn't see. He couldn't think.
She was crushing him, squeezing the life out of him. Her will, her mind, her heart, her thoughts—her loves and hates—all his. And his were hers. _Silvie . . ._
Shaeda suddenly relented. She chuckled. _You are correct, my_ _pet, my little human . . . Leave such obstacles to me._
Johnis struggled for air. He opened his eyes and sat up. Brushed dust off his arms.
"Johnis?"
Johnis's head shot up. Darsal stood beneath a desert tree, an overgrown piece of white bark and shriveled branches that thrived with cacti growing from it. He tensed. Darsal came closer. He could smell her raw, pungent skin even through the citrusy fragrance she was wearing. He curled his lip and showed her his back.
"What should we do?" he whispered. He watched the others, waiting for Shaeda's insight to overtake him.
"Elyon, Johnis."
Shaeda bared their teeth and growled. "Elyon abandoned us, wench!" He spun, close enough to smell her sickly sweet breath.
And then he saw Marak wasn't making camp. Instead he was preparing to speak with his officers and Sucrow. If he could get to Silvie . . .
_"Patience, Johnis. She shall be returned. But she is needed to convince_ _the albino to stand down."_
_What do you mean?_ It was Darsal, after all . . .
And then, for the moment, Shaeda was gone. At least, he didn't sense her. That could change.
"Why don't you focus on killing Sucrow, not the Circle?"
"Sucrow." The name drew bile from deep within. He glanced over at the priest's caravan, where Silvie was.
Darsal's eyes followed his. "We don't have long, Johnis. Back out. Silvie needs you to drown."
"What?" He withdrew from her. Was she mad?
Darsal started over. "No, listen. The red pools—You need to drown in them. It's the only way. It's—"
"The heat's gotten to you."
She grabbed his arm.
Johnis pulled free. Drown. Murderous albino wench. His lip curled. "Leave me."
Her brow arched. "Is that you or the entity talking?"
The Leedhan's eyes homed in on Darsal. Darsal could drop dead.
"Distract the guard," the albino said. "We can save Silvie from the priest." Her eyes flicked to the officers and Sucrow.
His eyes narrowed. "Why should I trust an albino?"
"Because the albino is the only other person who cares about Silvie." Darsal crossed her arms. "And because I think your answer will help you determine where your heart's going. But decide. I don't have all night."
Johnis struggled for control. His heart . . . He was following his heart, wasn't he? Or . . . was he?
His heart was with Silvie. As long as he didn't thwart the mission . . .
_Shaeda, Shaeda, don't tell me one woman can thwart the mission._ _Just give me this._
The Leedhan didn't like the idea. No, she wouldn't. Silvie had his heart, which meant his entity did not.
_If Darsal dies, it doesn't hinder the mission. What's the harm?_
"I need an answer, Johnis. They'll move out any minute."
Shaeda finally relented. As long as this didn't interfere. The priest and the general must remain allies, must continue this fool's quest.
They were so naive . . .
Johnis gave Darsal a sharp nod. "Let's go."
nine
**D** arsal left Johnis and stole through groups of Throaters and warriors who waited while their leaders convened. A waning moon gave her just enough light to see by. Guards skirted the perimeter of the band of Horde while the officers and Sucrow spoke in private. The light from a few torches broke through the shadows.
She could still barely wrap her mind around the fact that Johnis was being controlled by a Leedhan. And she felt guilty about the ruse of going after Silvie—she didn't need Johnis's help, and chances were slim she'd be able to aid Silvie. But if she could get Johnis to think, maybe, just maybe . . . he'd forgive her in the end, once he saw she'd only meant to steer his attention away from the Leedhan.
Silvie would be more than willing to be rid of the priest and to help Johnis with the amulet. Still . . . that did nothing for the nagging in the back of Darsal's mind. She passed by the outcropping of rock where Marak and the others were still meeting. They were mildly secluded, yet still in the open. Darsal dodged a couple of servants. Marak's voice sounded strained, furious about something. But he didn't yell. He kept his voice low—a soft, chilling sound.
Darsal inched toward the canvas-covered cage on wheels, where Silvie was being held, then caught herself. She hugged the shadows. Two Throaters stood guard. One could be Warryn.
She waited for Johnis, who said something to the guard to draw his attention away. The guard hesitated. Johnis grew persistent. At last the guard grumbled and followed Johnis.
Good. The scrapper was still there, inside his flaking shell—somewhere.
Darsal looked both ways, climbed up, and ducked inside. Incense filled her nose and mouth. She coughed and stumbled over something.
A muffled voice. Far corner. Darsal's heart nearly stopped. _Silvie_.
Hating herself, Darsal inched around and started a sweep for the medallion. If Sucrow had left it, she could get it. She'd rather Silvie not know she was here.
Darsal heard a low groan. Silvie was hurting. Time was running out. She heard voices. Rummaged faster.
_Love them, Darsal. Love them._
"Stay away from me," Silvie groaned.
Darsal froze. Silvie was looking straight at her. Darsal started to speak, then thought better of it. What could she say? She climbed over Sucrow's meager supplies, trying not to gag on the smell of the incense.
She saw a bag, reached for it. Started to dig. "What happened, Silvie?"
Icy silence.
Reaching deep into the bag, Darsal felt something cool and round. The medallion. So the rat _had_ managed to somehow get it from Marak. Interesting. Who took it? Warryn, perhaps?
Or was Sucrow working some magic? If that were the case, he could have made Marak give it to him himself, and Marak wouldn't necessarily remember a thing.
Frustrated, she shoved it in her pocket and stood. Glanced at Silvie. Her hands and ankles were tied, and she was lying on her stomach on the wood. She was bruised and had a nasty gash on her neck. She glared, then turned her head away.
"Sil—"
Movement. When she turned to the door, two Throaters stood there, torches in one hand, swords in the other. One wore an eye patch.
Warryn.
"Looking for something?" the Throater sneered.
Where was Johnis?
Darsal scanned the tent for a weapon. "Orders," she snapped.
"Really? Marak's?" Warryn spat.
"It isn't your concern." She raised a brow. "What should be your concern is what will happen when Marak discovers you holding me at sword point."
A gentle, invisible tug reprimanded her. Love Warryn too? He was Horde, wasn't he? No. Not Warryn. Marak was one thing, but this monster . . .
Warryn snorted. "What does Marak care about an albino?"
Darsal chose her answer carefully. "I should ask him for you." She raised a brow. "You want me to ask him?"
The Throater didn't quite know what to do with that. She got a good look at him. Sucrow had taken his eye. Now the quiet sorrow poured in. Elyon, they were all so deceived . . .
No time.
"Let me pass." She started forward.
Warryn caught her at the door. Yanked her back by the hair. His sword touched her throat. "What did you take?"
"Kill me and find out." Darsal lifted her chin. Her heart pounded. Elyon might not want her to harm this Scab, but she was about to have no alternative. "I'm under orders not to talk.
What do you make of that?"
"Whose orders?"
"Are you deaf? Let me pass, or I'll take your other eye out."
Warryn hesitated.
Darsal ducked free of the blade. He barely missed her neck. She somersaulted, landed on her feet, and ran for the other tents. Servants scattered. She grabbed one and flung him in Warryn's direction.
Several more Throaters came after her.
She ran for open desert, slid down the far side of a dune, letting the sand cover her. Darsal held her breath.
"DARSAL! SILVIE!" JOHNIS'S HUSHED WHISPER ECHOED OVER the dunes. Shaeda overpowered him, made him stagger like a drunk.
_"The albino betrayed you,"_ Shaeda kept insisting. _"Seek her_ _not . . . Your mate is yet within the priest's claws; resist no further."_
"Her name is _Silvie_ , you bloody vampire!" Johnis continued his search. Darsal would have hidden out here someplace, away from the chaos their ruse had created.
She'd used him. The bloody albino had used him. He'd find her and—
Darsal, covered in sand, came out of hiding to face him. He drew his sword, ready for the kill, but Shaeda was there . . .
He was vaguely aware of Darsal speaking to him, saying his name. But before his eyes she became Shaeda. Slender fingers with clawlike nails tipped his chin up. He shuddered at the rush of power the contact sent roaring through his veins.
Tasty, like copper and salt.
"Johnis." He knew Darsal was talking to him. Knew she'd come out of the sand dunes and stood in front of him. But he _saw_ the Leedhan.
Her long, white-gold hair spilled over her shoulders like a wedding veil. Perfectly smooth skin, so delicate a scratch might break through to the veins. A seductive smile spread across her face. Her haunting gaze drank him in.
"Johnis, I had to do it," Darsal was saying. "I had to get the amulet back from Sucrow. I wasn't trying to cheat you, I promise."
_"Look upon me, my pet."_ Shaeda's fingertips traced his throat, his jaw, his lips.
He found his voice. "You have more than enough power to free her."
"Power?" Darsal scoffed. "I am a slave, Johnis." Her eyes widened as she realized he hadn't meant her. The Leedhan had him in her grasp. "Let him be."
_"All in time. I will not abandon you."_ Shaeda stroked his cheek. The heavy, oppressive darkness bore down on his mind. His body tensed. Senses heightened.
Shaeda and he were one.
"She means no harm," Johnis said. Shaeda said. Did he really believe that? Did it matter? "She guides and protects me. She loves me."
"She'll use and kill you," Darsal warned.
Shaeda embraced him. Her iron grip held him fast. Her scent and gaze overwhelmed him. She kissed him. Hard and long. Needlelike teeth pinched his lip. She . . . bit him. Blood trickled from the small puncture.
"Silvie loves you, Johnis. So does Elyon. Even I do, when you aren't being foolish." Darsal, not Shaeda.
The Leedhan nipped him again. Johnis tried to turn his head and pull out of her kiss, but her slender arms and lithe body held him fast. When she finally drew back, a small drop of his blood glittered on her eerie white skin. Johnis licked his lips and tasted salt and iron.
Her mind opened to him once more.
"Johnis!" Darsal slapped him, hard, and grabbed him by the tunic. Her dark eyes met his. "Listen to me."
Shaeda couldn't be kissing him, could she? It was just another mirage, another illusion to control him . . .
His lip curled. Shaeda hissed. "Give me the amulet!"
Darsal drew back, scowling. Shaeda grabbed at her. Darsal slashed Johnis's arm with her fingernails and darted free. Shaeda's power poured into him. He would kill her.
No, he didn't want to kill Darsal, did he?
"Grab me like that again," Darsal warned, "and I'll give the amulet right back to the priest."
Shaeda snarled. She—Johnis—lunged for Darsal again. The albino grabbed Johnis's wrist and slammed him into the sand.
"Johnis, stop it!"
He was on his feet in a second and dove for Darsal's throat. She dodged. Shaeda pounced.
Johnis struggled hard. He was mad at her, but he didn't want to kill her, did he? Shaeda squeezed him, breathing threats. His vision went black.
A white wing soared past their heads. Shaeda shrieked and jumped back. Johnis's gaze shot skyward. A Roush!
She feared Roush as well? His entity slammed the door shut on all thought.
Darsal snatched the amulet from where it had fallen. She turned and ran toward the officers before the Leedhan could recover.
_"You fool!"_ Shaeda snapped.
Embracing Shaeda's wrath, Johnis bared his teeth. Silvie was still with the priest. He'd kill that albino.
ten
**G** abil, thank Elyon," Darsal whispered as she ran. The Roush darted around her shoulders, soundlessly following her. Torchlight settled over rock and sand, turning both orange and yellow. Smoke drifted around the warriors. Marak and his men were still meeting. She crept forward.
"Try not to do anything foolish," Gabil whispered back, worried. "There is no sense in you getting killed, although you might have assisted Silvie while you were at it. I daresay you'd be best off destroying that thing."
"There wasn't time. And I don't have a choice. Marak will be in a world of trouble if something happens." Gabil didn't answer. "Besides, I can't love him if I'm dead."
"You've a point."
Sucrow said something she couldn't hear. He sounded low and dark, a serpent on the hunt. Darsal's skin prickled.
"Leave her out of this," Marak barked back. "My private life is not your concern."
Sucrow laughed. Spoke clearly. "You're still in love with a dead albino, aren't you?"
Metal sang from a scabbard.
"Put that away, General."
"If I can execute my brother, Priest," Marak said evenly, "what do you think I can do to you?" Technicality. Marak gave the order. Cassak carried it out. Marak, true to his word, had stood watch. But giving the order was the same thing as doing it, really.
Seconds ticked by. Then Sucrow stormed away, seething.
Darsal ducked behind him. She pressed her hands along the rock. Gabil flapped off before anyone could spot him. Marak still stood with his sword half-drawn.
The general let it slide back into its scabbard when he saw her. "What did you do? Warryn came barging over here and—"
Darsal reached into her pocket. "I stole something." She held the medallion where he could see it.
His scowl deepened. Brow furrowed. His foul mood from the meeting with Sucrow was souring fast. "Priest and his magic," he grumbled. "Where was it?" he asked Darsal.
"Sucrow's things. He lied to you."
"Sucrow's . . ." He glared. Reached for the medallion.
His big, calloused fingers brushed hers. Warm and rough.
Electrifying.
He paused there, with the medallion half in his hand, half in hers. He was glowering at her, but behind the anger was something else . . .
The spell broke. He took the amulet. "I told you to stay out of this," he snapped.
"It was worth the risk, don't you think?" She raised a brow. "Or don't you want that? You know, maybe I should have given it back to Josef. He'd like that." She reached for the medallion. He pulled it out of her reach.
"That was careless." Marak shut his eyes and took several breaths.
"He'd like Arya back too. Or would you rob him of his lover as the priest did you?"
The general grew still for a long moment. Then tried to brush past her. She was pushing. Too far and she would run counter to her own mission.
"Move."
"Marak." Darsal put her hand on his wrist and drew closer. "Josef won't rest until Arya is as far away from Sucrow as possible. I would think you of all people would know what the priest can do."
"My duty is to Qurong, Darsal." He tried to go around her again, but she planted herself in front of him. "What makes you think Sucrow will hurt Josef's girl?"
"What makes you think he won't?" She wound her hands around each of his wrists. "Why are you being so bullheaded?"
Marak stared at her, half-irritated, half-relenting. He didn't trust the priest, and they both knew it. "She was part of the deal."
She threw him a dirty look.
He drew a heavy breath and pulled his arms out of her grasp.
"Dars—" He'd started to yell, but caught himself. "I'll handle the priest."
"Thank you. Josef and I would appreciate that."
He gave her a long look. "Do you really think I want that girl hurt?"
"I think your sense of duty overpowers your common sense." Darsal quirked a brow. "I think Jordan likely thought the same."
"Why do you keep bringing him up?"
She glanced over her shoulder and lowered her voice. "Because sometimes I think that's the only way I can get through to you."
Marak slid past her and went back to the expedition party. Darsal watched him, panged with guilt. Elyon wouldn't like her being this way with him, losing the ground she'd already gained. Even losing his heart. She drew a breath, knew she had to . . .
"Well, that didn't go well."
She turned. Gabil was perched on the rock.
"You're going to let him leave like that?"
"I was on my way." She glared at him. "I swear he's going to be the death of me."
Gabil fell quiet a second. "Hopefully not. He's deceived, though. You have to remember that."
"Deceived, not stupid." Darsal crossed her arms.
"He's killed his brother and his lover, and he isn't allowed to even mourn them, daughter."
She softened. "So what do I do? Now he and Johnis are both mad at me."
"Surely you didn't need Johnis to steal the amulet from Sucrow."
A pang of guilt. "It was easier. And I thought . . . I thought it would help him see things properly."
"Did you?"
Darsal looked to the side. No, she hadn't. She just knew she had to get the amulet from Sucrow, and Johnis would help her get it if Silvie were involved.
"Love comes naturally for humans. Stop making it difficult."
Her general called out to her.
She glanced back, conceded the Roush's point. "When will I see you again?"
Gabil smiled. "When Elyon pleases."
She grabbed the torch and hurried back, caught Marak's tunic before he'd gone far. He stopped, but didn't turn.
"Marak, I'm . . . I'm sorry." Darsal came around in front of him, still holding the torch. The light caught his eyes, and suddenly she wondered what color they would be. What color his skin would be.
He looked so haggard, so worn by all of this. The general was exhausted, physically, emotionally, mentally. Her heart ached for him.
Marak gave her a long look, eyes softening. He started to answer; then his gaze shot over her shoulder. Darsal looked. Cassak was coming. She could almost feel the captain and general turning cold.
Something had definitely happened.
"General," Cassak said with a curt nod. His eyes looked strange. Darsal studied him. Funny, she thought she saw the snake tattoo on his neck, with a star-shaped eye.
"Eyes to see," Gabil whispered from somewhere.
Her eyes widened. Elyon was showing her something. Someone had gotten to the captain—and changed him.
Marak folded his arms. "Captain. The priest somehow got ahold of the amulet. I'd like to know how."
Cassak's eyes narrowed. He responded slowly. "I'll find out.
The commanders are ready to move out when you are."
"I'm ready now."
Cassak saluted and turned to leave. Marak grabbed Cassak's forearm and brought his face close to the side of his captain's head.
"Provided nothing else goes missing."
The captain's expression hardened. "I'll see to it, General." Marak let him go, and Cassak was dismissed.
Darsal studied Marak, who was staring after his childhood friend. "You think he took it?"
Marak answered slowly. "I think I put nothing past the priest."
"The priest, no . . . but . . ." She barely knew the man and could barely fathom the thought. Still, she saw what she saw, and her heart ached all the more for her general.
"Nothing is for certain, Darsal. Nothing." Marak's voice was cool. "Let's go."
A THOUSAND POSSIBILITIES FOR RESCUING SILVIE PRESENTED themselves, and Shaeda denied him every one. Her presence settled hard over Johnis, the blue-purple haze tinting the torches held by the warriors' servants.
The commanders rode and ordered the questing party to fall in line. Once more a ring of torches surrounded the main party. Beyond, Cassak and his hundred men guarded them from Eramites, jackals, albinos, and anything else they might encounter.
Marak loped back to the head alongside Johnis. "Ride."
Johnis glowered, prepared to invoke Shaeda. Then he saw Sucrow sneering at him, and his blood ran cold. Silvie . . .
He scanned the group. He glimpsed Silvie by one of the horses, bound, face bloody and whiter than usual. Something clear oozed between the cracks in her skin.
"What did you do to Arya?"
Shaeda's talons dug into him.
"That's for me to know." Sucrow leered and licked his lips.
Shaeda, through Johnis, stared down Sucrow.
"Priest." Marak's harsh voice interrupted, an edge in it not present before. "Enough."
He couldn't get Silvie's attention . . . or she wasn't going to look at him. Shaeda's mind opened to him, honing his focus on baiting the Shataiki guardian queen. This was the final stretch.
A stray thought: _Why are they called "queens"? There's no gender_ _with Shataiki. It's confusing._
Shaeda turned coy. _"Shataiki thrive on confusion, my pet."_
"Josef?" Darsal spoke to him from his right. Why couldn't she just let him be? She probed him with deceptively warm brown eyes.
"Mind your own business." Johnis tried to mount.
She grabbed the reins.
Johnis pushed past her. "We finish the mission."
A long stare. "Sucrow doesn't care either." She let him go and went to catch up to the general before Johnis could shove her in the dirt.
Johnis took his place at the head of the group, Shaeda guiding them with him as mediator.
_Never in a million years will I be like that inhuman priest._
eleven
**D** awn broke over the horizon, turning the desert pink and orange. On and on south they rode, past carrion birds and cacti. She'd heard jackals through the night, but thankfully, never saw them.
Darsal couldn't stop twisting around in her saddle and swinging her legs like a child as Johnis—Josef—turned their course west. She would be lucky to accomplish anything more than a free trip to the nuthouse at this rate. Her thoughts centered on what to do next, how to stop the tide.
She sagged forward in her saddle and rode on, separated from the others by every means possible. Thirty minutes passed, then an hour.
Half-consciously, Darsal spurred her horse and rode out to circle and look for any sign of danger. She drove her horse on, eleven seeing nothing but the occasional flicker that could have been Cassak's men, Eram's men, or a bat of either variety.
Marak called after her, but she wasn't ready to acknowledge him yet, unprepared to again face persuasion or death. Marak could wait. She needed Elyon.
Darsal went into a full gallop over the dunes, streaking over sand for almost a mile before remembering to circle back to catch up to the others.
She wasn't given the chance. Marak appeared out of nowhere and grabbed her horse by the reins. The animal squealed and reared. Darsal hit the ground hard. He jumped down after her and grabbed both arms. Darsal lashed at him, tried to get up, but Marak's grip held fast.
"What are you thinking? If you were going to run away, you should have done it long before now!"
"I wasn't running! I was watching for Eram's men. I used to be Guard. It's habit."
Marak tensed, searched her face, then exhaled and plopped beside her, one arm across her in a defensive posture.
"Dars—" He took a ragged breath. "Oh, Darsal, what did you go do that for?"
"I . . . wasn't thinking."
Without warning, Marak leaned over and held her against his chest. She was too stunned to react. "No, you weren't." The growl had left his voice.
He lifted her carefully and rocked her for a few moments before letting her sit. Her mind reeled, desperate to catch up. Marak pushed back her headscarf and brushed away strands of hair that had fallen loose of her braids.
_Elyon, is he . . . ?_
"I'm sorry. You went into a gallop, and we all thought . . . Well, it was me go after you or my men."
He wiped her face with the edge of his cloak. Darsal caught his wrist and rose up on her knees, wincing at the pain in her ribs.
His expression went flat. He put her headscarf back up and drew it across her face. And she felt it. In the depth of her being was the cruel emotion she hadn't known from the time Billos had thrown his arms around her and saved them all, to the day Marak tried to kill her but turned his back forever on that door.
And now she knew it again, a thousand times stronger.
Marak had frozen. He shook his head at her, even though he looked just as stunned as she felt.
"It isn't possible, Darsal. It would never work."
"But you do care for me. Don't you?"
"We don't have feelings for albinos, Darsal. Nor do they for us."
"Forget us and them!" She knotted her fists and leaned toward him.
He cared. He had to.
His hands were on her arms, but not in the rough fashion she was accustomed to. Marak didn't quite make eye contact. When he looked away, her emotions boiled over.
"I like you, woman. I trust you. Isn't that enough?"
Darsal squeezed her eyes shut. The volcano was erupting, and she could do nothing about it, nothing about the pain in her heart and the forbidden words gnawing at the tip of her tongue.
"Marak, the truth is I . . . I love you. Don't you understand? I've stayed for you!"
"You can't!"
He hadn't moved. The man was like ice. He'd have to kill her now. He didn't have a choice, not after this. And that infuriated her.
"Why not? Who says I can't love you? You're human, right? Or is the truth that I'm not human enough for you? Is that it?"
"Darsal—"
"I love you, Marak, and I want you to love me, too, and see Elyon loves you, and drown with him and become like me!"
"Darsal."
"But if that doesn't happen, then I really am doing all this for nothing, and I really am a complete fool like you say! It's—"
Marak snatched her off balance, one arm around her. His lips brushed her neck, her scarred cheek. "I doubted."
Darsal looked up at his face. Marak tipped her head back and cupped the base of her chin in his warm fingers.
"General."
The greeting sliced between them. Marak threw her back. Darsal scrambled away, and they both found their feet. She yanked her cowl over her face, pulse spiking. Caught. Caught and dead.
Cassak sat on horseback before them. He dropped down and threw the reins at Darsal. The general and the captain sized each other up.
Cassak saluted Marak, expression grim. "The Eramites have been following us."
Marak remained silent.
That cold sensation slithered along, the same she had felt from Sucrow before.
"I sent some messengers to remind them this was not a war party nor a band of spies. We do not wish a fight; we are at peace and intend to stay that way. It is only a temporary solution, however."
Darsal peeked up at her general. He traded another look with Cassak, then gave a nod, but it was a full minute before he spoke, choosing his words carefully.
"That will suffice. Peace is best for all at this stage. Tell them to keep their fires far from our expedition. We go only as far as the canyon."
Cassak looked at Darsal, staring until she could no longer stand it. "The road is muddy." His eyes drifted back to her general. "Perhaps we should heed the warning."
Marak looked angry. "What will you do?"
The captain hesitated. "I will watch. There is no need, as of yet, to report the matter to Qurong. I haven't decided what, if anything, to say to Sucrow."
Darsal's head shot up. They were not talking about the rebel general, the half-breed Eram. Cassak was warning Marak about falling in love with an albino.
"Some treasures are best left hidden." Marak bowed his head. "Thank you, Captain. I'll see you promoted."
Cassak frowned. "It would not be wise at this time." He came closer to Darsal and inspected her, grimaced at the smell of her skin.
The captain was making a pronouncement. Judgment on their sin.
Marak mounted Cassak's horse. His and Darsal's had run off. Cassak bound Darsal's wrists and tossed the other end of the chain to Marak.
Cassak leaned close to Darsal's ear and whispered. "Another stunt like that, and I _will_ go to Qurong. After today it is over. Understood?"
Renounce her love and save Marak's life.
Darsal's heart sank to her heels. She couldn't let him go. Elyon had changed her heart for these Scabs, for Marak, and he wouldn't release her. So she couldn't release Marak.
Cassak released her and gave his horse a thump. "Good."
To Marak, Cassak said, "I'll find your horses. The canyon is just over that rise." He pointed. "Welcome to the Teardrop."
twelve
**M** arak towed Darsal up the rise. Cassak followed at a distance, then disappeared once more into the dunes. Of all the foolish things he could have done! He'd let his guard down for one moment. For one second tasted the forbidden.
At the same second Cassak came looking for his missing general.
"You executed your own family on principle," he could imagine the captain saying. "You round up albinos and kill them on orders, out of loyalty. And now you throw your principles out the window for what—a rotting corpse of a woman? Why don't you just make love to the dead!"
Maybe Cassak was right to steal the amulet and take it to the priest. Marak was getting too close to this. Either Sucrow had used his magic on Cassak, or Cassak really did throw loyalty and friendship to the wind. Which?
At the top of the rise, Marak stopped his horse and stared down over the teardrop-shaped gash in the desert floor. The north end made the bulge, the south the point.
As if Elyon himself were crying.
Now, that was a silly thought. As silly as taking an albino woman in his arms and kissing her. As silly as wishing he'd gone ahead and given in to the impulse completely.
Darsal stood near the horse's head, stroking its neck. The chain that now bound her to his horse clattered. "I've never seen one this big."
"Seen what? A canyon?" He furrowed his brow.
The canyon was barren from what he could see, save a narrow path that wandered around the rim before starting down. The rest of their number had already approached but hadn't started down.
"A Black Forest."
"Cassak's watching our backs. What are you worried about?" He started down, wondering if his old friend at his back still meant anything to him. Darsal submitted to the pull of her tether.
"I'm worried about what happens when Josef uses that medallion."
He paused and looked down at her. "Why are you always so insistent that you're in the right? This reasoning is what has Cassak trying to decide if he's going to inform Qurong as to what I've done."
She closed her mouth.
"That wasn't fair. You may take your own life lightly, Darsal, but why must you expect the same of me? Isn't it enough that I—"
He still couldn't say it, and hated the question that would follow.
Darsal's brow creased.
_Forget it._
Marak spurred the horse fast enough to make Darsal run and unable to ask any more questions. Not enough to drag her.
Run Darsal did, easier than he'd expected.
Marak pressed on. Sucrow, Josef and Arya, his three commanders, and the two Throaters waited at the edge of the canyon, their eyes fixed on him and his rebellious albino slave. Marak slowed to a walk. He didn't look at her.
"I see you've caught her," Sucrow sneered, turning his staff. "That should remind you not to trust the wench."
"Who said I did?"
He glimpsed the rim of the canyon, splashed orange and red with sunlight. Purple and rust streaked along the upper portion. Stunning. A bridge spanned the length of the teardrop, and, just as Cassak said, a path led around the edge of the canyon and down into its basin.
He looked instead at Josef, whose appearance had changed. The younger man's skin was pale, almost transparent. His body looked harder, more muscular. Skin and hair almost aglow. And his eyes. A purple cast.
"Show us the way."
"We'll have to leave the horses partway down. The brush gets too thick toward the south end." Josef reached inside his shirt. "It's steep."
"There's more than brush down there." Darsal's voice carried a strange edge to it.
"No one asked your opinion," Sucrow snapped. Marak didn't take the time to correct him.
"Patience," Josef said. "She is correct. Yet such is why we possess the amulet. Withdraw such."
Marak eyed him, curious at the strange speech. He took the medallion out of his pocket.
A loud shriek crashed in from overhead, accompanied by a whoosh of leathery wings. Marak ducked, arm raised, and looked up.
His mind revolted against what his eyes saw. Shadows fell over their faces, as if there had been an eclipse. A black, furry bat the size of a human child with beady, red eyes flew at them again, claws extended, fangs bared.
The entire expedition fell into shock.
Josef snatched the amulet from Marak, held up his hand, and shouted. The beast dove over their heads, circled high, and swooped down into the canyon.
The bat disappeared into a black gash in the ground. Trees with black bark and wood sprang out of the canyon several hundred feet and blotted out the sun. The muddy road ran around the edge of the canyon before heading straight down, beneath the bridge, completely lost to the cold woods.
He heard Sucrow unleash a tirade at him for stealing the amulet back.
"Now do you believe me?" Josef and Darsal spoke at once, then silenced when they realized it. "The amulet shall protect us from such," Josef finished.
Believe them? Marak's heart lodged in his throat. Josef's eyes hardened. Alien, inhuman.
There was a black forest. _Darsal was right. She was right all_ _along._ A chill wound around his spine. _What else is she right about?_
He shook it off and rode high in the saddle, offered a hand to Darsal. "Get up." She obeyed without hesitation, content to lean against his back.
_Boneheaded fool_. . . Marak could almost see his brother's narrowed eyes, his crossed arms, his exasperation.
_Not now. You mean not ever. And didn't you make a promise to_ _Darsal?_ He'd forgotten. It was insignificant. But Darsal was right; he never should have let Sucrow take the girl.
_That's more like it._
_Would you get out of my head?_
_I'm dead, brother._
Marak grunted, then turned his attention to the priest. "Sucrow, release Arya. Arya, ride with Josef, and the two of you take us down."
"But she—"
"I said let her go!" Marak snapped.
A Shataiki had just attacked them and vanished into its lair. They were walking into hell. And the priest was still on his quest for power.
Sucrow untied Arya and allowed her to swing off the horse. Arya marched over to Josef and jumped up behind him. The priest growled and remounted. Marak ordered his commanders and the two Throaters to wait for them to return.
He gave Josef the word, and the three horses started down.
Josef took them around to a ledge with more slope to it and picked his way toward the creek. The lower they descended, the darker the forest became. Bat wings slapped around them, and the occasional pair of beady eyes glared through the trees. Sucrow began to chant softly, in words Marak didn't understand.
Darsal slid her arm around his waist.
He took her hand and, in the darkness that now surrounded them all, kissed it lightly.
thirteen
**J** ohnis led them downward in a spiral trajectory, like going down a drain or a whirlpool. Ever downward, into a pit. Into sewage and waste. Pitch-black trees with rotten, black leaves that curled. Even the grass and dirt were black. The canyon was perilous, and everything was obscenely still.
Deeper they went, the droplet shape narrowing with time, walls caving in around them. Darsal heard a dripping somewhere. A black waterfall.
"Elyon, save us," she whispered.
A bat screeched overhead, underscoring her plea.
_"Were you ever really alone, Darsal? Really?"_ Elyon asked gently.
_I'm alone now._
But that wasn't true either.
Marak was here. Johnis and Silvie were alive. The rest of the Circle was alive somewhere.
As long as Johnis's plan didn't play out, they would stay that way. And right now she had no means of stopping him.
Except Elyon's charge of love.
Would that be enough . . . ?
The forest taunted her. It closed in around her and groped at her, crushed her lungs. Sucrow was chanting somewhere, an incantation that sounded familiar to her, though she couldn't remember where she'd heard such a hideous thing.
Thoughts of the last lair she'd crawled into clawed at her, mocked her.
They reached the bottom and followed a murky, stale stream until the path narrowed too much for the horses. Darsal didn't want to leave the animals, but Marak had her tether all three, and they pressed on.
"You're sure you know where you're going?" she asked Johnis.
"I'm sure, albino," he snapped.
"There are things stronger than amulets," Darsal whispered back, ignoring his jibe. "Stronger than Leedhan and bats."
Johnis didn't respond. He led them on foot through thorny brush and thick, black mud, traveling along a streambed. Even Sucrow held his silence. All remained pensive and still. The stream rushed into a waterfall, and Johnis led them around the dark, bubbling water.
A shaman once had told Darsal that bodies of water were living things. They laughed and played along the shore. This water was different though. This water cackled like a villain about to take his prey as it spilled over a hillside and splashed into a cauldron below.
A shallow clearing opened up, creating a kind of bowl. Headstones rose up out of the water, wrapped in mist. In the middle of the small lake was a platform.
An eerie, purplish haze enveloped them. Darsal pressed against Marak, then remembered Cassak's warning and shifted away. All around them the trees were weighed down by black bats with glowing red eyes and sharp claws and teeth.
Memories haunted her mind. She had to work to push them aside.
Johnis looked at Silvie, then Sucrow. "I need some water. And the rest. You've brought it?"
Sucrow nodded. He withdrew from his bag a silver bowl that Silvie took from him. She waded into the water. Next came a clay bowl and a small leather pouch. The priest began to chant.
Johnis took a silver knife from Sucrow; then they both followed Silvie out to the platform, their supplies held over their heads.
Darsal and Marak waited on the bank. Johnis couldn't hear her. Darsal sank into a crouch and put her chin on her fists, elbows on her knees.
_Bloody Leedhan._
Johnis stood sentinel, his face white, while Sucrow and Silvie made preparations. Silvie filled the silver bowl with water and placed it in the center. Sucrow took what looked like a makeshift altar and set it out. Incense soon wafted through the air and flooded their nostrils.
A nauseating stench. Where had she smelled that? The priest's invocation continued, witnessed by hundreds of red-eyed Shataiki with visions of carnage in their heads.
What was Johnis doing? It was supposed to be a simple incantation.
Darsal could barely watch. So Johnis had needed Sucrow after all. Sucrow withdrew a bird with bound wings from a small cage she hadn't seen earlier and killed it, pouring its blood over the altar. The bats swarming around them began to thrum.
Johnis placed the medallion around his neck in open view and waited for a signal from Sucrow. By his expression, something like terror had overtaken him, but was it his or the Leedhan's?
Silvie took the knife from Sucrow. She would never relinquish it, Darsal knew. The slender, lithe woman looked more serpentine than ever and kept eying Sucrow as if judging the distance for a successful death throw.
Sucrow stopped chanting. He held aloft something silver and round in his right hand for the bats to see.
Johnis found his confidence and stood to one side of the altar. He puffed out his chest, raised his chin high, and spoke clipped words in a language Darsal didn't recognize. He reached into his robe and withdrew a yellow, rotted, maggoty fruit that was bigger than his palm and held it at arm's length in both hands.
The bats fell quiet.
"I come seeking audience with your guardian!" Johnis demanded of the Shataiki. "I come with a gift, should he desire such! Or is Derias a coward?"
Dissention and arguing rustled through the ranks.
A Shataiki twice the size of the others flapped overhead, circled, and swooped down onto the platform, landing directly across from Johnis before the altar, his wings partly folded.
"Who comes to my home?" the beast asked. His eyes didn't leave the fruit. He ran his long, pink tongue over his black lips and sneered. "So you survived. And returned."
Johnis raised his chin. He started to change. To turn completely transparent. His eyes took on the purple gaze. Lips curled into a wicked sneer. Animallike.
_The Leedhan._
Even Silvie looked unnerved by his behavior. Derias made a coughing sound that was probably a laugh. His eyes narrowed and brightened. "Then you understand the danger."
"I concern myself not with such risks." Johnis tightened his jaw. "I present to you a means of restoring that which has so long been denied you. The glory of the sons of our Great One, our lord Teeleh, shall at last be made complete again. These trappings which now bind you shall no longer hinder. What say you, mighty guardian?"
Johnis would know better. The entity had to be lying. Shataiki could never regain "glory," assuming they'd ever had any.
The bat drooled over the fruit. He wanted it, badly, but something was holding him back. Only one choice would allow them to find out. Was it base to ask Elyon to bestow wisdom upon a Shataiki?
"You think me so easily swayed?" Derias stroked his chin with a claw. His gaze flicked from the fruit to the sacrificed bird to Johnis. "Begone!"
"We have an agreement." Johnis's voice was husky. Seductive.
"I am not persuaded."
"Such is for you and you alone, my prince. Taste and see." Johnis opened his free hand toward Silvie. She passed him the knife. He cut the fruit open, returned the knife to her, and smelled half of the fruit.
Darsal's stomach churned.
Johnis said something so soft she couldn't even hear his voice. She only saw his mouth move.
But the bat heard. Silence lingered.
Then Derias turned to Sucrow and took the bird from his outstretched hand. Johnis watched, blank faced, while the Shataiki tore its prey to pieces and fed. Darsal imagined Johnis was the bird, his soul ripped apart by cruel talons.
Silvie whispered to Johnis, and the bat replied.
"Such is not within reach forever," Johnis warned.
The throng of Shataiki fluttered in the trees. Darsal grabbed for one of Marak's knives. He pulled her hand away.
"Take and eat, most excellent of beasts." Johnis offered the fruit to the bat one last time, his words lost in the air that clung to them.
_No, Johnis, no._
Derias shrieked and took off into the air, circled high beyond the trees, and dove back down, wings folded, straight for Johnis.
Darsal grabbed Marak's knife and whipped her arm back to throw. Marak grabbed her, pinned her down, and took the knife away.
The bat let out another roar and whooshed past Johnis's head, knocking him down. His talons closed around the fruit, and he swerved upward again. The other Shataiki took flight, and hundreds upon hundreds joined their queen in the sky. They screeched and dove over the humans' heads.
Marak threw himself over Darsal.
"Did he eat it?" Darsal screamed. "Did he eat it?"
"I don't know!"
Darsal fought at first, then remembered the general wasn't going to hurt her. He scooped her up and ran with her in a dark, hot cocoon.
"Josef!" Marak yelled. "Get down from the—"
Johnis shouted over the din. Water splashed when he jumped in and started swimming.
"What's happening?" Darsal demanded. "What's going on? Did they take it?"
"Yes," Marak snarled. "They're following us out. Josef ordered them to meet us in the sky but not to attack."
"Then put me down!"
"They aren't all obeying the command! I don't want you to—"
He grunted and fell flat on his face on top of her. He fought off the Shataiki clawing them. Another bat assaulted the first, and the pair rolled away. Marak picked Darsal back up and continued his retreat.
"Sucrow! Forget that! Come on!"
"Marak!" She threw her arms around his neck.
"Hold on!" He lost his footing, and they both went flying.
Darsal fell, her head smashing against rock, with Marak's weight slamming into her. Red and yellow stars, then darkness.
fourteen
**J** ohnis raced with the others back through the forest, with two million Shataiki at their heels. Shaeda dug into him, riding him like a horse to steer clear of the bats. Derias had relayed the order not to attack the humans, but the ranks were unstable, and the beasts kept breaking the line to harass them. The queen had taken the bait.
And he was enraged.
The bats roared around them, their wings like thunderclaps, darkening the sky further. Silvie scrambled ahead of Johnis and the others and went for the horses. She yelled.
Shaeda's power surged through him, charging his muscles and shoving blood through his body with enough force to mow down a Horde army.
Johnis and Marak, still carrying Darsal, were only seconds behind. Sucrow straggled. Johnis tripped over something solid and fumbled. He rolled sideways and jumped back up, looked down.
A horse's leg bone. Grimacing, Johnis darted around the corpse. All three horses were completely torn to shreds and stripped of flesh.
Marak's knife was in his hand. He shifted his wriggling bundle over one shoulder. Disgusting, Johnis thought, holding an albino like that.
"They did this?"
"Better the horses than us. Can't she walk?"
With a snarl, Marak started back up the path, seething over the dead horses. Johnis hurried after him with Silvie and Sucrow.
On and on they fled, breathless and fumbling in the unnatural night. Shaeda made Johnis swift and surefooted, skirting up the sides of the rock faces and canyon with ease. Twice the general stumbled with his burden, and twice Johnis caught him and helped him regain his footing.
"Just leave her!" Johnis said the second time. They were halfway up, and the wench was only slowing them down. "Leave her already! How do you stand the smell of the worm?"
Marak glowered at him. "She'll die at the appointed time!"
"So now you favor the albino," Johnis snapped, appalled at the thought. Shaeda bared her teeth in scorn. "Will you be joining Eram's ranks?"
Marak struck him with his free hand. "Mind your tongue, boy. Bats or no, I'll have your head and—"
"You think you can destroy me?" Johnis rose from the ground. Shaeda bristled, terrified of the Shataiki and ready to engage any lesser being. This general was now simply a nuisance. Johnis's hands curled like talons.
Marak turned his back. "You can kill her with the others."
He marched on, heedless of the rest. Johnis started after him, compelled to tear the general's heart out and feed it to Derias.
Silvie grasped his shoulder. Shaeda tensed. "Enough," Silvie said. "Deal with the albinos first. Then the general."
fifteen
**D** arsal regained consciousness while she was still slung over the general's shoulder. She grunted as her teeth snapped together, chin bouncing off Marak. He took the final steps up the side of the canyon and set Darsal on her own two feet. With Shataiki still swarming in the cauldron, they hadn't dared slow. Her head throbbed where she'd hit it. Blood caked the back of her neck.
The blow she'd taken seemed to jar her general more than anything else.
"Can you walk?" He had an edge to his voice. Who knew it would take a swarm of blood-lusty Shataiki to unnerve a general?
Darsal staggered, wincing. "Of course I can walk."
Her general's gaze lingered on her.
His touch was astonishingly light. Those big hands that could crush held her steady with all the care one would give a newborn. His eyes were wild from the chase, lit with terror at the implications of the carnage these beasts could create.
The Throaters were quiet, faces ashen and set like flint in an attempt to conceal their obvious fear. Good. Nothing like a trip to hell to put the fear of Elyon in a cutthroat.
Sucrow stood gaping, awestruck by the sight of his master's servants. The Dark Priest fell to his knees and uttered a prayer to his god, thanking him for their success thus far. Darsal frowned.
"I'll be surprised if he doesn't sacrifice to Teeleh," she scoffed.
Johnis had won this round. Assuming any deal made with a Shataiki could be considered a win. Johnis had the power and the medallion that controlled the bats. And Marak's ear.
_"She is using him, daughter."_
She bristled at that. _What will she do?_
Elyon's silence made her skin crawl.
Desert greeted them. Stark, silent desert that vanished beneath a shadowy, writhing curtain. Marak ordered the torches lit. The bats howled and shrieked, keeping their distance from the flames.
"We have four days," Johnis warned Marak in that deep, husky voice that had to belong to the entity Gabil spoke of. "We've no time to waste. You've brought fresh horses as instructed?"
In answer, horses and riders pounded toward them, kicking up a dust storm. From out of the sands came Cassak and some of his men, leading horses. Ignoring the surprise of the rest of the group, Cassak brought a stallion to Marak and Darsal.
Captain and general traded long, cold looks. What had become of these two, once friends?
Without a word, Marak helped Darsal astride, then leaped behind her.
Shataiki filled the canyon and poured out of it into the sky, a giant black tornado, a whirlwind of leather, fur, fangs, and claws mottled with red, beady eyes.
Johnis, Silvie, and Sucrow mounted their new horses. Johnis held his accursed medallion in one hand and looked to the blackened sky, enthralled, terrified, his eyes stained purple. He was speaking in the foreign language again.
Johnis afraid of the Shataiki?
No, the thing inside of him was.
At this moment Darsal feared him more than Sucrow. Johnis knew no boundaries beyond the thoughts of his heart. Right now he either wasn't listening to his heart or his heart had turned as black as the hurricane gathering above them.
"Are you ready?" Marak whispered into her shoulder.
Had it really only been a few days since Johnis asked her the same question?
"I'm ready to die, Marak. But this? Never. This is mindless slaughter." Darsal straightened in the saddle. The acid ball in her stomach knotted further at her epiphany.
Johnis was still reciting whatever wicked spell pleased him as Sucrow lifted his clawlike hands to the sky. Silvie pricked her finger with the silver ceremonial dagger, for reasons Darsal didn't know. But then, the girl seemed to have developed a fetish for those knives. Cassak kept a baleful watch, ordering his men not to panic, to keep the line.
None of them had ever seen so much as one Shataiki—much less this swarm of two million.
Derias, the Shataiki queen, erupted from the throng of beasts and circled Johnis, shrieking over his head. He spiraled back into the cloud, roaring against his entrapment. His long, cold shadow eased by.
"Have you heard of the mountain called Ba'al Bek?" Johnis asked, his voice still the strange sound of one possessed by a Leedhan.
_Ba'al Bek._ Darsal's eyes narrowed. Why did that sound familiar? Certainly she hadn't learned it from this earth.
"No." Marak tensed. The certainty in his voice had dissipated. Sucrow was not the only one capable of sorcery.
The Leedhan . . .
"I will show you the way. We have four days to reach it. But first we require the blood of the ruler of this world."
Marak's eyes narrowed. "Qurong's blood."
Johnis gave a sharp nod. "Only a little."
"Why?"
Marak glared at Johnis. Darsal watched him. Her general's eyes fixed onto Johnis's purplish-blue ones and seemed half-drugged. Johnis's mouth curled into a wicked, coy grin.
"I must perform a ceremony preceding the incantation," Sucrow said. "It can only be done at Ba'al Bek."
The general didn't seem to notice. He was seeing something else entirely.
"General Marak." Darsal cleared her throat, unwilling to touch him in front of the priest. The trance broke.
"You know where this place is?" Marak snapped at Sucrow and Johnis.
"We must make haste," Johnis said in Shaeda's voice. "Such is two days beyond Middle, and a day and a half must pass before we reach the esteemed leader."
sixteen
**T** he eclipsing clouds of Shataiki merged together, blotting out the sun entirely. No moon, no stars, nothing but millions of red dots marking the beasts' faces. Their unblinking eyes stared down at the band of humans below. Overhead the Shataiki queen raged and thrashed, darting in and out of the throng, barely restrained. Derias snarled and howled against his imprisonment.
The hours passed, and evening came, further pitching the blackness. The cold night air strangled Darsal. How the others still knew where they were going, she had no idea. They were lost out here. At the mercy of savage monsters.
Her unease returned. Marak's outbursts of affection had ebbed. Another half hour passed. She couldn't abide both his silence and the Shataiki's wrath.
"Tell me about Jordan," she said. His mind had refused to make the connection between his family and the albinos, between not serving Elyon and serving Teeleh. Maybe in drawing the two brothers together she could make him see . . .
The general didn't respond for a minute. Then he clicked his tongue at the horse and rode forward, a short distance away from the others. Away from Sucrow.
"He was my brother."
Stubborn Scab. "And . . . ?"
"He'd be a captain by now if the disease hadn't taken him."
The general looked ahead, his voice quiet. For a minute he looked like his brother, hidden beneath a shell.
"I wish I'd known him better."
"Me too." A half smile crossed Marak's face. "Stubborn fool."
THE EXPEDITION PARTY RODE ON TO THE STEADY THRUM OF rushing bat wings, punctuated by Derias's snarls. Johnis, Silvie, and Sucrow argued occasionally, but even they were mostly silent. Silvie wouldn't relinquish Sucrow's dagger. The priest, understandably, wanted it back.
"What was it like?" Marak's voice rumbled through Darsal's bones and roused her. She sat up straighter and looked around. He'd ridden out again, separating them from prying ears.
"Drowning. I never asked Jordan. You told me how it happened. But . . . there's always more with you."
She summoned the memory back. "Terrifying. Exhilarating. The water's cold as ice. And deep, impossibly deep. The deeper you go, the warmer the water becomes. Darker. And soon you realize Elyon's in the water with you."
She went on, explaining how her lungs burned and how, finally, she'd breathed in the water. Like a fish.
The general listened, emotionless. "Was Jordan out of his mind?" he breathed.
Darsal kept her voice even before speaking of his family's deaths. That wound was still ragged and festering, hot with blood. "Were you out of your mind when you tried to save them and stay loyal to Qurong? You didn't have to do that, Marak. Elyon knows it'd have been easier if you hadn't."
For a full minute they merely stared at each other. Marak was listening now. And he was so close she could feel his body heat. But in five minutes he might consider killing her again.
Her jaw set. Idly, she fingered Jordan's pendant, but she didn't notice until she saw the general staring at it.
"I'm not afraid for myself, Marak." She didn't look. Didn't want to see his reaction to that. He could take it however he liked.
_Elyon . . ._
Seconds ticked by.
"People die whether albino or not, Darsal."
She drew a breath. "Then I have already failed."
TORCHLIGHT DID LITTLE MORE THAN ILLUMINATE THEIR faces in this unnatural darkness. Cassak spoke from horseback to his four scouts, who were flanked by servants carrying the flames. Sucrow was right—Marak no longer considered him a friend, not since Jordan and Rona's arrests. He hadn't seen it before, but now, with the growing rift following their executions, he could see plainly.
And now Marak was falling for an albino. Worse, Marak knew Cassak had stolen the amulet right from under his nose and taken it to the priest. He'd taken the copies of the journals, too, but thus far the general hadn't noticed. More of the priest's skills.
"Keep the torches in rotation," he said to the scouts. "And relay from beyond the cloud. Try not to agitate the beasts." Cassak glimpsed the priest riding up. "You're dismissed."
He narrowed his eyes at Sucrow's approach, staff in hand. He still detested the priest and his cutthroats, and he had no intention of watching Marak send himself down a hole. Maybe this would wake him up and snap him back into the real world, where albinos were the enemy to be destroyed, and loyalty to Qurong was to be held above all else.
Loyalty, integrity, honor. Where were Marak's in all of this?
"What do you want now?" Cassak snapped. That strange sensation swept over him again, the numbing one that left him dizzy and wondering what he'd just done.
"Patience," Sucrow answered. Cassak circled him, both irritated and unable to simply leave. He had to do this, had to make Marak see the truth.
"Do you have the copies?"
The war journal. Marak had made a copy and put it in his captain's care shortly after discovering it. Upon learning their former general's information, the Desecration hadn't taken long to concoct. Cassak had helped develop it.
He nodded and gave Sucrow the book, along with his report on Jordan's death. "Don't expect anything else."
Dark humor crossed the priest's face. "Of course not, Captain." His staff turned in his hand. Cassak's throat tickled, making him cough.
"You're still prepared for the other, are you not?"
Josef and Arya. Sucrow wanted Josef and Arya dead, the entity gone. Why, Cassak could only speculate, but there were reasonable explanations.
"Now it is you who requires patience," Cassak warned. "The men will be ready. But beyond that I wash my hands of this."
Sucrow chuckled. His hand moved in a circular motion.
Cassak scratched his neck.
"Still believe yourself loyal to the general, do you?"
"That is not your concern." Or was it? Lately the priest was making more sense than the general, though Cassak hardly dared admit it.
"Well, understand this then, Captain: the general's loyalties no longer lie with Qurong. I suggest you make up your mind."
seventeen
**T** ime was running out to get back to Qurong and on to Ba'al Bek, wherever that was. As far as Darsal could tell, only the Leedhan actually knew.
Darsal couldn't stand the sight of those beady, red eyes staring at her from all sides any longer. Skirmishes among the bats disrupted the stillness, but all was otherwise well. In a matter of hours, she would be dead. She had not won Marak. She had not stopped Johnis.
Ill at ease, she shifted in the saddle. This place was full of devilry.
The Shataiki ranks began to rustle, the throngs shifting into formation. They were hungry, Johnis had said, ravenous for a kill, their nostrils riddled with the scent of their favored prey.
Marak grated his teeth, irritated at being pulled in two directions.
"Josef, one bat gets out of hand and I'll have your head. I'll keep the head and give the body to the bats. Understood?"
Johnis didn't answer right away; instead he looked up at the swarm he controlled. "Understood."
They were exhausted but pressed on into the night. Soon all was quiet. Not one wing fluttered. Darsal heard nothing except the blood surging through her veins and her throbbing, pulsing heart.
As one, the Shataiki surrounding them roared and took flight. Screams shook the night. Darsal jumped and strained to see, but all was black. Then the shrieks were overpowered by the sound of Shataiki feeding on flesh. Living or dead, she did not know.
The expedition party fell into a panic. The Scabs rushed around, trying to find the source of the slaughter, shouting in the midst of Shataiki whipping about them. The bats clawed and bit, wings open wide.
Darsal leaped from the saddle and ran, searching for a weapon. A bat caught her by the shoulders and ripped into her back with its claws. She screeched and kicked it in the gut, refusing to fall to a beast almost as big as she was. It knocked her down.
She grabbed a rock and smashed it into the head of one. She glimpsed a green eye among the red but didn't have time to respond. Two now fell on her, fighting over her body. One had her by the leg, another by the wrist. They ripped at her flesh and clung to her. Blood seeped from her wounds. She smashed a claw into the hard-packed sand.
Bloodlust sent the rest of the bats into a frenzy. The entire mass began to swarm and rage, boiling in a kind of cauldron.
Metal rang out and slashed through the meat of one of the bats on top of her with a sick, sucking sound. The beast roared as it died. The second turned on her rescuer and left her in the dust. Darsal rolled away and jumped to all fours, still in search of a weapon. The Scabs were fighting now, torches lit and swords in hand. Johnis and Silvie were in there . . . somewhere . . . shouting to one another.
A powerful arm snatched her around the waist and ran, fighting Shataiki with one arm. Darsal was pinned against his side, dangling like a toy and being further battered by the melee.
Gruff utterances against the fates. Marak. The general dumped her on her feet as he barked another order. Darsal snatched a knife from his thigh sheath as he passed her and went back to back with him. Minutes passed. Minutes filled with the sounds of men and Shataiki in battle.
Then it was over.
All was pensive and riddled with nervous, quivering bodies. Darsal turned, eyes drawn to the commotion behind her. The warriors and Throaters had formed a circle around Marak. Torchlight cast odd shadows over their faces. Her eyes followed their gaze until she saw Marak. He stood holding Johnis by his throat, his feet dangling above the ground. Johnis's arms were wrapped around Marak's wrist, his face twisted in pain. A standoff.
Cassak held Silvie by the arms, restraining her. But why did Marak have Johnis?
Johnis's skin and eyes took on their recent unnatural look. His face twisted into a hard snarl. "Release me," he warned.
"You ordered them to attack," Marak growled. He flung Johnis down, realized Darsal had his knife, and swiped it back. The weapon sang into its sheath.
Johnis landed in a crouch. Wild-eyed. "You doubt me?" His voice had turned low and inhuman. Shaeda.
Had she persuaded him to set the Shataiki on them? If so, why? Or had they come after Shaeda?
Marak's sword ran red, dripping on the ground. Now he raised the weapon. "Is this the best the great Josef has to offer?"
Johnis still looked possessed. As though he might spring at Marak and slit his throat without hesitation. "Your men interfered with their hunt."
The anger radiated off Marak's body.
"She is lying." Darsal heard Gabil and glanced around. The Roush's wing vanished behind a rock. She tensed. If the amulet could reveal the Shataiki, it could reveal a Roush.
"I did not break our agreement," Johnis insisted.
The general's sword came to rest at Johnis's throat. "Do you prefer to die kneeling or standing?"
Silvie grumbled from behind Johnis. He turned to look at her, and the two traded a look Darsal didn't understand.
The look Cassak gave Marak, though, was clear. One wrong move now, one mistake, and the captain's hand would be forced. Cassak would declare Marak a traitor. Marak would die.
But Marak had also given his word, and he would not break it.
Would she lose both Marak and Johnis in one foolish moment?
"I prefer not to die at all." Johnis sneered and fingered his medallion. His eyes—Shaeda's eyes—were ruthless.
If Shaeda attacked . . .
Lose Marak or Johnis or both.
"Wait, General!" All eyes fell on Darsal. "This was a mistake." She stepped up beside him, then between Johnis and Marak. "General, don't kill him. This was . . . an accident."
Marak turned, obviously angry. "An accident?"
"A Shataiki thought I was attacking Josef. It wouldn't do for their master to perish."
Darsal waited. He wouldn't buy it. Marak would know this was all an act. That she was lying. And she knew it was absurd to claim the bats were protecting Johnis from an alleged attack by a desperate albino. But the Scabs might not know that. Not even Sucrow had seen this before. And Johnis didn't want to die.
"General," Cassak said finally. "We need your decision."
Marak looked at Johnis. "Is this true?"
Hesitation. Was Shaeda considering making him do something foolish?
Johnis regained control of himself. "Yes."
Marak sheathed his weapon and stormed off into the desert.
"The next to cause an _accident_ dies."
eighteen
**D** arsal rode with Marak, lying still so he would think her asleep. So close to dawn, and yet the eclipse blacked out the sky. They rode ahead, with Sucrow somewhere behind, reciting a chant that sounded eerily familiar. Johnis and Silvie had also dropped back, whispering about something.
"Let it alone, Cassak. It was nothing." Marak's voice startled her. She shifted in the saddle. "She has her uses. I would like to keep her as long as is reasonable."
"Be fair. I'm not a fool." Cassak was impatient, his tone irreverent toward his general. But they were friends, which alone explained his casual behavior.
"You don't intend to execute her at all."
Unfortunately Cassak was more observant than the others.
"She'll die soon enough." Marak was still bristling. The edge in his voice was unmistakable.
"She should already be dead."
Marak grumbled something under his breath.
"So now you're doing her favors?" Cassak sounded scandalized. Why was he so bent on her being dead? He'd been patient enough with Marak's family. She dared a peek. Once more she saw the strange, starry-eyed serpent on the captain's throat.
What did it mean?
"I'm doing myself a favor."
"Jordan and Rona."
Another low, angry remark from the general. The silence lingered.
If pushed, what would Marak do?
A white wing caught her attention. Gabil, hiding in the shadows. His green eyes shone in the dark, then vanished. "Pay attention," she heard him whisper.
So this was about more than killing one lone albino. Everything came back to the Circle. To Thomas. To Elyon. She'd distracted herself from that truth. Hopefully not to the point of no return.
"Aren't you the one who said, 'Loyalty comes before and above all else'?" the captain was asking. Something was in his tone, a strained sound.
"Cassak . . ."
"Loyalty. Integrity. Honor. Those are the first things you taught me, and you learned everything from Martyn himself."
"I'm not betraying you, Cassak."
"I can't keep quiet forever." The two men fell silent. The unease was catching. It spread like poison. "She's like Rona." The captain paused. "Isn't she?"
Marak didn't answer.
"You need to execute her, Marak." Worry spilled into Cassak's voice. Worry or fear? Darsal leaned in. No, something was wrong. Cassak was acting. She wasn't entirely sure how she knew, but Cassak was no longer Cassak.
"You need to do it tonight. Don't throw away your career and your life for an albino wench."
"Don't call her that!"
"Why not? She _is_!"
"Because I—" Marak caught himself.
"You what?" the captain demanded. He snorted. "I don't believe this. You love an albino."
"I do not—"
"She's using you, Marak. Can't you see that?"
"There's nothing to see."
"I'm sorry, General." That part Darsal wanted to believe. Cassak's voice was strained, conflicted. "I can't protect you this time." He rode away.
Darsal waited until Cassak was gone before shifting. Marak rode farther ahead.
"We have no time. It's over, Darsal. Cassak will have me marked a traitor shortly after the business with the Circle is done."
Darsal let that sink in and didn't like the implications. She wanted so much more and knew it would never happen. Marak was resolute.
Adrenaline pounded through her, making her dizzy. His hand lingered a second before releasing her, always too soon.
Darsal grabbed the reins. "Come on."
"Middle is the other—"
"We need water, Marak. We need to—"
He went rigid and spun her toward him. "I've been far too lenient if you truly think that after so little time I would be swayed."
He knew she wanted him to drown. Of course he did.
"I save your life and you ask me to kill myself?" He let go of her. "Isn't my love enough?"
A flash of heat made its way up Darsal's spine. She forced herself to inhale, forced her mind to catch up. He still didn't understand.
"Love is deeper than this, Marak. So much—"
"I spared your friends at your request. I let you lie for them. I spared your life when I should have sentenced you on the spot. All of this, Darsal, and still you want my life?"
"I gave you mine." Darsal breathed deep. "That wasn't fair." She backed down, trying to reclaim whatever was left of this mad relationship. With Elyon's gentle prompting as her guide, she softened.
"You love Elyon, don't you, Marak?"
He didn't answer.
No, he wouldn't admit that much. But just maybe . . .
"Don't do it for me. Do it for Elyon. Don't you wonder where he went? Why he's silent? Haven't you wondered why all of these things are happening and still Elyon says nothing?"
Marak let out a low, raspy breath, irritated because he didn't want to answer.
"Do you really believe I came from another world, Marak? That I did not bathe for ten years?"
"I believe you. But what does that have to do with—"
"Jordan watched my skin turn in the dungeon, my general. They watched me rot in a cell for three days before Jordan helped me escape. I didn't believe him either."
That stopped him.
"I didn't believe him until the water went into my lungs and I stopped breathing air and started breathing water. I just wanted Elyon more than I wanted to live."
_"Patience, daughter, patience,"_ she heard Elyon chastise.
Marak thrust a finger in her face. "I am not having this conversation again. There will be no more talk of drowning."
"Marak—"
"No more, Darsal. No more."
nineteen
**Y** ou're sure you control the bats?" Silvie argued. She glared at him, commanding his attention with her voice. They rode a little ahead of the others, alone able to see inside this throng of shadows.
"Yes," Johnis snapped. He didn't mean to, but everything was purple haze, and Shaeda was anxious, so anxious. "She's terrified," he managed. "She's half-human; she can't fight this many . . ."
Shaeda tore into his thoughts. Blue and purple sparked across his mind, raking over his eyes. She didn't like him exposing her weaknesses, and the weakness was that she was only half-Shataiki. Powerful but mortal.
Her alluring gaze, her siren song . . .
Everything in him screamed to gallop ahead to Middle and get out from beneath this swarm of Shataiki, to lead the guardian queen where he willed, to silence that horrific sound of Derias lusty for a kill.
"Josef," Silvie said. His mind shifted, focusing on her. Shadows drifted over him, Shaeda's night vision retreating with her thoughts. "Why did the bats attack?"
"Because . . ."
The overpowering foresight took hold. He saw red desert fanning before him, giving way to canyons and a glorious mountain range full of desert trees and shrubs. The treacherous peaks were all angles and drop-offs, narrow cliffs and passes.
Beyond that, more desert, the land growing increasingly desolate. Jackals fought over dried bones, and carrion birds sought elsewhere for food, preying instead on the packs of hounds that fed off each other.
_"Forget not, my pet . . . The human of my choosing was you. Yet_ _such can alter . . . alter at a moment's breath . . ."_
He smelled sulfur and felt as if his face were basking in the steam of hot springs, soothing his skin of the flaking, rotting cracks and the stiffening pain that overwhelmed him.
Twice divinely forsaken, by both Elyon and Teeleh, and thrice by the sons of men. And yet over the rise, beyond the cliffs, down the sharp ravine where craggy rocks grew from the earth like teeth, were the springs, near the mighty rushing river which the great tree spanned. A red river no human dared cross, for none could survive its falls. This river girded the earth as a belt and guarded the world of purebloods from the world of half-breeds.
From the far side of the world was no return . . .
_How did you cross, then?_
"Johnis!" Silvie dared use his real name. The vision retreated. He looked at her. "Why did the Shataiki attack us?"
Understanding washed over him. Shaeda looked upon her and raised his chin. "Take comfort, little female . . . Such will not occur again."
Silvie scowled. "Shaeda. It was you they wanted."
The Leedhan's thoughts darkened. Johnis's night vision returned. His gaze fell ahead. He kicked the horse and broke into a gallop, desperate for Middle, for home. Visions of blue forests and sweet, tangy badaiis swept over him.
He barely heard the general call after him. Let them keep pace.
twenty
**T** he expedition party marched down the main road of Middle toward Qurong's white palace, now eclipsed by the shadow of Shataiki.
People ran out of their homes in panic, but Marak's men were ready. He rode at the head of the procession with Sucrow on his left. At his right, Cassak and Reyan. Warryn and the Throaters rode at Sucrow's far side.
Next came Johnis and Silvie. Behind them were the servants. Cassak had split his men to form a rear guard and two flanks to keep the streets clear of spectators.
Bats screeched and flapped, soaring through the city. Horns sounded the return of the priest and the general, announcing to all of Middle their success and the prize they brought Qurong.
The sun was already settling into the western sky, and they still hadn't acquired Qurong's blood for the ritual.
Johnis and Shaeda mentally rehearsed their plans. And very carefully, Johnis considered his personal interpretations of her instructions—interpretations that allowed him to manipulate her words so he could undermine her wishes on technicalities.
Only with Silvie did he have an opportunity for success. He could throw Shaeda off, but he couldn't plan anything without her knowing, could he?
"Do you remember what we talked about?" Johnis asked Silvie. Silvie had to do the bulk of the work; otherwise they would be discovered. He couldn't guard his thoughts from the entity inside him.
_"Tread lightly, my Chosen One,"_ Shaeda warned.
Silvie watched him, an eyebrow quirked. She pursed her lips. "I'll handle the priest," she said. "You watch the general."
Shaeda wanted to control the pair, not destroy them. But if controlling them meant they were dead, far easier. A permanent control.
Johnis sneered. Yes, as soon as he used the amulet, he would call on the Shataiki to circle. But what constituted a circle, anyway? Technicalities.
Shaeda came over him, heightening his perceptions. Silvie's eyes narrowed. Had the Leedhan heard him?
"We'll deal with the other later," Silvie scoffed. Her voice briefly cleared his head.
_"Your attentions, my pet . . ."_
They dismounted at the broad, white steps and came up the stairs. First Marak and Sucrow, then Johnis and Silvie. Darsal passed Johnis and came alongside Marak's flank. Warryn, Cassak, and Reyan followed, swords ready.
As they passed through the atrium to be admitted into Qurong's throne room, Johnis's hand brushed a leather cover in his back pocket. The remaining book of history.
_I'm forgetting something._
That unnamed something nibbled at the back of his mind, even as he pushed through the crowd. Shaeda tried to pull him back, but the impulse to see this through was momentarily stronger.
A fleeting image of Thomas in the desert flashed across his mind.
_"Such is madness, my Johnisss . . ."_
He grabbed Cassak by the arm. "Those magic books in the attic. Did you ever find them?"
The man stared hard at him and yanked free. "I sent a man to look. The attic was cleared."
Johnis stiffened. Silvie's head snapped toward him. From seven to one in so short a space? "They were in a crate."
_"We have not time for such indulgences, my pet . . ."_ Shaeda was getting impatient. She had absolutely no patience for anything not directly related to her purposes, her goals. Still, she was hiding something from him. Many somethings.
Silvie touched his shoulder, snapping him out of his trance.
Cassak shook his head. "I double-checked myself once I got around to it. The entire room was empty. Sorry."
Heart racing, Johnis followed the captain around the corner. He was confident, but Shaeda's anxiety grew as they neared the throne room. Her memories surfaced, memories of things the Shataiki—Derias—had done. Shaeda's terror wound around his heart and chilled him to the core.
"What was that about?" Silvie asked.
Johnis blinked. Shaeda cut off the connection. Her cold, tangible fear, though, lingered.
"Josef." Silvie pressed her fingers on his chest. "You are going to be rid of her? Her power, remember?"
Was he? Did he still desire to?
Life without Shaeda . . .
A low, menacing laugh sounded in his head.
Johnis froze. Then managed to clear his throat. "Not now." He changed the subject, hoping to throw Shaeda off, and possibly distract her fear. "What did Sucrow do to you?"
_I can't do this with you strangling me,_ he protested. Her grip relaxed slightly.
Silvie didn't answer immediately. "He tortured me."
The priest and the general stopped abruptly and saluted four Scabs armed with spears who stood before the broad, white double doors that led into Qurong's throne room. The warriors saluted Marak and stepped to the side.
The doors swung open with a solid crash like thunder against the walls. Qurong's hall echoed, first with the sound of the doors, then again as the guards slammed their spear butts down in unison. Three times the sound pealed through the hall and rattled the fixtures, even Teeleh's winged-serpent image.
Shaeda braced herself. She recoiled at the sight of the idol. Johnis took a long, ragged breath and crossed the threshold.
DARSAL GAPED AT THE FAN-SHAPED ROOM THAT SPRAWLED before them. Red-robed warriors armed with swords and spears lined the wall. A chandelier with six rings, the widest easily eight feet across, hung full of dripping candles from the ceiling twelve feet above them. Hibiscus and broad-leafed gold hyling plants splashed orange, red, green, gold, and purple around the room and gave off a sweet scent that almost masked the stink of the Horde.
A long, purple carpet lined the center of the white stone floor and circled around and over a six-foot platform that served Qurong's throne. The high-backed chair was made of a reddish wood and covered in what looked like rich purple silk. Torch stands stood proud on either side.
And there sat Qurong, robed in blue and tan, with a gold necklace at his throat and his sword at his side. Long braids spilled down his back and over his shoulders. He sat tall and regal, every inch the great Horde leader. His cloak was off one shoulder and bared his right arm. A steward attended him. Qurong displayed only power and anger. If the Shataiki swarm unnerved him, Darsal couldn't tell. He was a mean snake, and the bats had only seemed to make him meaner.
The Scabs bowed upon their approach. When Darsal did not, Marak gave her a look. She shook her head. He motioned her to stand out of sight.
Qurong scowled at his priest and his general, his expression mocking. "I see you've managed not to kill each other." He shifted forward, leaning as if to rebuke wayward children.
He said nothing of the Shataiki outside.
"Respectfully, lord," Marak said, his voice stiff. "Our mission is not complete."
"Oh, really?" The supreme commander leaned farther forward. A sneer split the morst on his face. "Then why are you here?"
Darsal glanced at Johnis, expecting him to answer. But his eyes had that purple cast to them, and he seemed pale.
Who was really in control?
Marak spoke. "We've four days to kill the albinos before the amulet's powers reverse. A day and a half has already passed."
"I repeat my original question then." Qurong scowled.
"My lord," Sucrow said, "we must journey to a high place in the northwest desert, in the mountains. The journey will take the majority of what little time remains. However, there is—"
"Then what are you still here for? Ride through the night if you must, but get rid of those albinos once and for all," Qurong snapped. He stood.
"Lord, there is one other thing . . ." Sucrow continued.
Qurong snarled. "What?"
"The ritual requires a small amount of blood. That is why we are here rather than continuing on our way—"
"My lord,"—Marak tensed—"it's your blood he and Josef insist they need. That is why he's dancing around like a child on an anthill."
Sucrow scowled at Marak.
"Excuse me?" Qurong roared.
"The ritual calls for the ruler of men to spill a portion of his blood," Sucrow explained. "It need not be more than a drop or two."
The Horde leader's eyes narrowed. He considered this for a long minute, then growled. "Very well. But do not try my patience again. When next I see your faces, the albinos had better be dead, down to the last squalling infant. You will leave immediately."
twenty- one
**D** arsal went with Marak to a guest room while Sucrow drew Qurong's blood, again with more pomp and ceremony than truly needed, thus turning five minutes into an hour. As though they had more time to lose. Let them lose time.
Perhaps it would spare the Circle. It would certainly give her more time.
She swept the room. Linen blankets, reed mats, more bright colors. A scribe's desk sat to the side, with Marak's original Desecration plans strewn over it. Martyn's war journal. Marak was keeping his plans as backup in case Johnis failed.
Marak stripped off his cloak and crossed the room to dig in his pack for morst. He stripped off his tunic, exposing rotting, flaking white flesh. A fresh gust of rotten-egg smell hit Darsal.
She grimaced at the sight of his back and looked away. She'd thought she was used to the sight of Scab skin but had never seen the full extent of the general's scabbing disease. An absolute beast. She tried hard not to gag.
He rubbed the white paste over his chest, arms, and neck, then as much of his back as he could reach. Watching him was painful.
And she remembered it wasn't only his skin that was diseased. His coarseness, his decision to kill the Circle, his execution of his family—all part of the Great Deception that ate away at his mind, soul, and body.
She cleared her throat. "Has Cassak gone to Qurong?"
No answer. Her general pulled his tunic back over his skin and drew his cloak over his shoulders. He put away the morst.
"Marak."
He didn't turn toward her, instead staring at the wall for a long minute. "Soon enough it won't matter."
Darsal furrowed her brow. "You don't mean that."
"Get me some water."
"It's right there on the table," she protested.
"I don't want that water." He went to his desk and studied something. He wouldn't look at her, and it was maddening.
Darsal knotted her fists. Marak was just being boneheaded, deflecting emotion by pulling rank, but now it was getting to her. "It's all the water there is, unless you feel like taking a side trip to a red lake."
"Darsal," he scoffed. "It's over. Don't you understand that?"
_Deceived,_ she reminded herself. _He's deceived._
"As soon as Sucrow reaches the high place, it's over for the Circle."
Elyon's love had no place in this hellhole, no seat of honor among snakes. Darsal slammed her fist on the wood. "Is this a game to you?" Marak's papers and notebook rattled. The tumbler sloshed over, and a thick, black mark streaked across the top page.
He jumped back. "Are you insane?"
She was going mad, acting like this. But they were out of time, and she was sick of dealing with him.
Marak raised his arms, glaring at the table. "What's wrong with you?"
"What do you think is wrong with me?"
His mouth clamped shut, and he took several long, heavy breaths, nostrils flaring. He finally broke his death glare and turned his back to her.
Darsal's anger exploded. The general's precious papers were all over the table. She gripped the edge and flipped the table. Everything went flying. "Don't turn your back on me!"
He didn't turn. He just stood there with his back to her, gawking at the mess without a word, cold and lifeless. A hacksaw tore its way through her body.
"Marak, you don't have to do this."
Elyon's gentle prodding suggested she relent. She wouldn't. Couldn't.
"Yes, I do need to do this, Darsal." Her general's voice deepened. "We're going to execute the albinos. All of them."
"Marak, _I'm_ an albino!"
"I _know_!" He refused to look at her, instead surveying the strategies and plans strewn all over the floor, months of work that, if Johnis's plan worked, would amount to nothing.
The Desecration. He'd sold Jordan for that.
Darsal's heart sank into her shoes at his pronouncement. This ruthless Scab in front of her would never back down, even for love, because Elyon was not with him.
_I'm sorry, Elyon. I can't do this anymore. I can't._
Marak righted the table, then the chair. His own temper was flaring, and he was doing his best to control it. She could tell by his slow, deliberate movements. It sobered her, shamed her, that he succeeded where she had failed.
"The thought of anyone living in that kind of pain drives me mad. I can't force anyone to live like that. That's why. And their minds . . . Darsal, I can't let that go on. I cannot."
His words grated at her. Darsal's fists knotted at her sides. Could she really give up on him?
Elyon wouldn't.
Heaven help them.
"That includes me."
Marak continued to clean up her mess. The man was ice. The comment hung in the air, thick and oppressive, just like the mass of bloodthirsty Shataiki outside.
"You're different," Marak whispered.
Darsal tried to rein in her temper. She reached out to put her hand on his shoulder. _Deceived. He is deceived, rotten to the core._ _He doesn't know . . ._
"I'm going to do my job." His voice sounded like piano strings pulled too tight. He wouldn't even look up, wouldn't turn and show her his face.
She withdrew her hand.
The general separated several wet pages and returned them to their proper places. Each movement was stiff, unnatural.
A thought crept into her mind, a desperate card she had no right to play. Darsal removed Jordan's pendant from her throat and placed it on top of the journal he was holding.
Marak was on his feet and in her face before she knew he'd turned around. "Leave my brother out of this! The lakes are poison, my people are getting sick and dying, and the albinos are to blame! And in under three days we'll have purged the world of their plague!"
"You really think your brother was a plague?"
The morst around his face had cracked. "I would rather you die than be an albino!"
"Then kill me!" Darsal grabbed one of Marak's writing journals and tore it at the spine. She ripped at the pages and scattered them across the room. Then she flung the ruined leather cover against the wall.
The cover splayed upside down, title showing.
A chilly noose tightened around Darsal's throat.
They both stared at the book, frozen in place for a minute.
Rona's journal.
She had destroyed it.
Darsal's hand went to her mouth.
Marak started around the room. He found each page of the journal, smoothed the creases out, and stacked them in order. He sank down and stared awhile longer, uncertain what to do with his recovered treasure.
Finally, he flipped over the remaining pages of the book, still bound, and tucked the shorn ones in the back. He placed the cover back in position and bound the whole mess together with twine. Then he set the book down and traced the leather with calloused fingers.
It was all he had left of Rona.
And Darsal had taken it from him.
"Marak."
He didn't respond. He'd forgotten she was in the room.
"I lost my temper. I'm sorry. I . . . I didn't mean . . ."
He did not blink. He did not move.
She stole forward, all her rage evaporated in an instant. Her eyes fell to the book's cover.
_To Marak, with all my love._
Marak's hand spread over the writing. He looked up at her, eyes cold, gray, expressionless. Not even hate. Numbness overtook her.
_Elyon, what have I done?_
Someone knocked. "General, it's Cassak."
Marak didn't answer. Darsal stepped away from him, toward the door. "Enter, Captain." Her voice was dry, her throat parched.
The captain came in, saluted Marak, and surveyed the room. Jordan's Circle necklace was beneath Marak's foot. Cassak's eyes narrowed. "What happened in here?"
Still Marak didn't speak. Cassak's hawkish gaze turned on Darsal, accusing.
"Is Sucrow ready to leave?" Darsal asked sharply.
The captain's scowl deepened. He gave a short nod. "Sucrow sealed the blood in a vial. Qurong's given us leave to go. It's almost sundown."
Now Darsal and Cassak both stood waiting for Marak to say something.
Finally the captain said, "Go ready his horse."
Darsal blinked, then ran out the door, face hot. Marak didn't even yell after her.
twenty- two
**N** ight fell over Middle, made darker by the swarming cloud above them. Sucrow looked up, fascinated and terrified all at once. Such a glorious sight, the silent shroud of Shataiki slowly drawing up over Middle, coming to cover them beneath black wings.
Sucrow's elite surrounded him, each Throater's robes glistening in the torchlight borne by his acolytes. Neither stars nor moon, merely the ruby-red eyes of his master's servants.
Soon, soon all would see the truth, even obstinate Marak.
"You've the book of rites?" Sucrow whispered as Warryn rode up alongside him. The tall serpent warrior gave a single nod. "Keep it close." His eyes narrowed in the direction of Marak and Josef. "I don't want it in the hands of infidels. And give the blood to one of the others. I'll not have any more tricks. Get the captain in place."
An hour out the scouts ahead slowed. Marak clucked to his horse and rode forward. His albino slave rode close, holding a torch for him to see. Her dark eyes fixed on Sucrow.
Sucrow cackled. "Lost already?"
"I'm not lost, General," the scout protested, making his appeal to Marak instead of Sucrow. "The bats block out the sky."
"Why don't you have a torch?" Sucrow demanded. "Am I surrounded by imbeciles?"
"A torch will not show me the stars," the scout snapped. "I'm trying to ride beyond the swarm, but they're fast. I sent three ahead and told them to loop back."
"What's wrong?" Josef rode up, brooding.
"Our illustrious priest doesn't seem able to comprehend the concept of scouting," Marak quipped. Sucrow bristled. To the scout Marak said, "Try to stay ahead of the swarm. And take another torch. What happened to yours?"
"I got caught in some mud and nearly fell into one of those foul red pools," the scout said.
Marak didn't comment.
"Well, get on with it," Josef scoffed. "There is no reason to stop."
That drew Marak's attention. "Blame the priest."
"It's your scout, I might remind you," Sucrow warned evenly. He scowled. This Josef would have to be done away with. The Master would not be pleased that such an unbeliever held his servants hostage. And Marak was in the way.
"And it's Josef's directions and your bloody ritual," Marak snapped. He sent the scout off. "We're wasting time."
Sucrow waited until Josef and Marak broke off. He called Warryn to him. "Wait until tomorrow," he said. "Then invoke the Law of Naroush."
A knowing look crossed the chief serpent warrior's face. The Law of Naroush was the cry for blood on behalf of a petitioner.
Josef had started them on this path. Surely he would not mind using his own blood to petition Teeleh's blessing.
ONCE MORE JOHNIS SAT ASTRIDE A HORSE, THIS TIME NORTH-bound on the west side of Middle. Once more into the unknown. If he looked back, he couldn't even see the city anymore; it was so consumed with the black cloud of Shataiki. The boiling cauldron was quiet. Johnis dropped back to Silvie.
Shaeda's cold talons dug into him. This many Shataiki so close made her nervous, despite her control over the swarm. She lingered in a hazy place between gloating and panicking. This, on top of Johnis's own apprehension, didn't help matters.
"You fear them more than I do," he whispered.
_"Silence,"_ she hissed. But her mind was open, thoughts set on her goal. They had conned the Shataiki amulet guardian and bound him. They would destroy the Horde and return victorious, and then she would be powerful enough to undermine Teeleh, to usurp his power and take it for her own.
Johnis blinked. Where had that come from?
"What was that all about?" Silvie's face was impossible to read.
"Sucrow being Sucrow."
Shaeda turned her focus to her missing mate, away from her plans for glory. She understood now. Silvie was to him as Rasmuth was to her.
Johnis's eyes flicked toward the enraged Derias. He'd taken Shaeda's mate, but Shaeda wouldn't explain everything about such.
How aware of the Leedhan's movements was Teeleh?
Sucrow, of course. Teeleh could guess through his priest.
So what would he do when . . .
Shaeda took his mind from those troubling thoughts.
Johnis fingered the amulet. So close, so close. And soon he would conquer the Horde and rule Middle with Silvie as his queen.
They reached a series of canyons and spread out to cross what otherwise was too narrow a path for the horses to pass through. A loud, snarling roar went up, spooking the horses.
"What's that?" one of the warriors asked.
Johnis's head whipped around. Shaeda completely balked. His nostrils flared. "Derias," he said, fingering the amulet around his neck. "He hasn't forgiven us for his imprisonment."
A flickering of fear snaked through him.
_"We shall have accomplished our mission, yet upon its end what_ _shall befall? The Guardian shall be full of wrath once he is released."_
Johnis stiffened. "Shaeda, what do you mean?" he whispered.
Silvie looked at him. "What's wrong?"
He shook his head. What _would_ Derias do once the amulet's powers were spent? They couldn't hold him forever—even Shaeda knew that.
_"Have no fear,"_ Shaeda soothed, as much to herself as to him. _"We will order his own termination ere this ends."_
The ritual that unlocked the amulet's power required Sucrow's presence. He alone knew the incantation. Only a priest of Teeleh could deliver the offering and approach the high place.
"Do you hear that?" Johnis whispered to Silvie. She eyed him. "Derias will kill us if we lose control of him before our mission is complete."
He grew uneasy. His entity was not telling him everything. Her dark presence came over him like a hot, thick blanket. He wasn't supposed to tell Silvie of his private conversations with the Leedhan monarch.
With Shaeda's night vision he could see Silvie fingering her knife. "Yes."
"Whatever happens, we cannot let the priest have the amulet."
Silvie was quiet a moment. Then, "So what do you want to do?"
"We need to plan."
THE SCOUTS REPORTED BACK TO MARAK CLOSE TO MIDnight. At least, that was his best estimation. The foursome traded off riding ahead and doubling back, a system that took them beyond the eclipse and beneath the stars.
"Past the canyons is a stretch of open desert," the lead scout told him, thumbing northwest. "If we turn west now, we'll bypass the foothills, then make north again along the rim. That'll take us to the peak."
"How long?" Marak snapped.
_Easy, brother,_ he imagined Jordan saying, half-amused that Marak had let a girl get to him, and half-frustrated with Marak's tyrannical behavior since the fight with Darsal. _What did that_ _scout do to you?_
_Nothing, you bonehead._
But it didn't matter. It just didn't matter.
He caught himself fingering Jordan's Circle pendant.
"A few hours, General," the scout was saying. "The delay will be inconsequential. It would take longer to go through than around."
"You're certain."
The scout hesitated. "General—"
"We're ready to get this done. Tell the captain to follow your lead." The scout saluted him and galloped off.
"You kept it." Darsal's voice surprised and agitated him. They had barely spoken since she'd destroyed Rona's journal.
Marak's hand closed around the pendant. He put the necklace away. Thoughts of the pool mingled with those of the high place. He had the strange urge to break away from the others and ride until the horse dropped dead to the high place, to not wait for the priest or the others . . .
_Focus, man._
"Sucrow has his hands in too deep," he said, changing the subject. "And what do you care?" Of course, he knew the answer as quickly as he asked it.
Darsal raised her torch higher and glimpsed in the direction of the enraged Shataiki queen. "I shouldn't have done that, General." General. In front of the men he was just "General." Behind their backs he was _her_ general. Her Marak.
He snorted. "The albino admits she's wrong." Teeleh's breath, she destroyed everything, and now she was trying to dig in again.
She pursed her lips and waited for the apparent frustration to pass. "I was a fool."
He'd had some time to think about this. In some strange way the ripped journal knotted a loose thread, let him say good-bye. Tore the last of the barbs out of his heart.
Her horse drew abreast of his. Their knees brushed briefly. Heat shot up his leg. Marak threw her a look, eyes narrow. Darsal seemed not to notice. The torchlight gave her skin a strange cast, made it glow orange red.
His mind drifted again, just for a minute, just long enough to consider they could reach the high place so much faster with fewer men . . .
"Green for Elyon's lake," she said under her breath, just loud enough for his ears alone. Her voice brought him out of the wanderings. "Black for the Black Forest and the Great Deception. Red for the blood mingled with water."
He softened. "Jordan told you that."
"He did."
"And the white center?"
"Yet to come." Darsal moved a step ahead of him, looked up at the Shataiki swarm. "Sooner or later."
"Albino." The word came out more sharply than Marak had intended. He caught up to her. She glanced over, then turned her eyes forward again. Marak hesitated. He wanted to keep it. Now it really was all he had left.
"Get out of my blind spot," she corrected quietly. It was one of the first things he'd said to her when he'd taken her to his home as a slave.
Marak drew a breath, then offered it to her. "It means more to you than me."
She managed a half smile. "I think he'd want you to keep it."
"He gave it to you."
"But not to keep." Darsal spurred her horse and rode well ahead of everyone but the scouts.
Sucrow shouted after her. "Marak, get ahold of your bloody albino!"
Marak pocketed his brother's necklace before anyone could notice. "She's on orders, Priest. Let her alone."
The priest fumed and threatened, but Marak's attentions were lost. A sense of dread washed over him. With every step toward the high place, it increased. After an hour with no sight of Darsal and the gnawing still in his gut, Marak called Cassak to him.
They studied each other, remnants of a friendship scarcely there. Cassak rubbed a spot on his neck, a strange habit he'd picked up over the last few days.
"The Eramites relocated," the captain reported. "They reached the base of the foothills, turned around, and went back south."
"Did something spook them?" Marak's stomach knotted. Cassak had stolen from him once; what else might he do?
"Nothing that we've seen. But we did find a few stripped skeletons, both horse and human." Suspicion clouded the captain's eyes. Marak could tell there was a lingering question his old friend wanted to ask but wouldn't. Probably about Darsal's running off. She'd likely left to let Marak think. As for Cassak, he had always used indirect methods to communicate and came to his point at his own leisure.
But that Cassak Marak no longer knew.
"Jackals?" he asked.
Cassak's expression turned dark. "Marak, I don't think a jackal could do this."
His first impulse was to look skyward, but he resisted. Knew already. Instead Marak looked long at the priest, then in the direction Darsal had gone. Something was wrong. Darsal was missing, Cassak was behaving strangely, and Marak could not shake his foul mood. He felt like a Throater.
"Find out."
Unease settled in. A slow draw toward the high place, a desire to hurry, seeped over him. He needed to get to the high place. He needed to keep an eye on the priest.
"General." Marak blinked. Cassak was still standing there, waiting.
"Well, go," Marak snapped.
twenty- three
**T** he sky ahead was gradually turning from gray to purple, just barely hinting at the dawn of morning. Behind them, abysmal black dotted with red engulfed everything in its path. The Shataiki cauldron boiled hot, its queen raging from somewhere within the throng. Faster they flew, blotting out those last wisps of light from beyond. The mere sight made Shaeda's—Johnis's—skin crawl.
The scouts led the expedition party out of the canyons and west across open desert. Not exactly according to plan, but not hindering either. This way they would have less climbing this afternoon.
Shaeda's anticipation mounted. She hadn't punished his thoughts of keeping her powers, and he began to think she'd forgotten, not heard, or forgiven him.
Yes, that was right.
Wasn't it?
Her prompting led him to the front of the pack, along the left flank, away from the others. Of course he would go. Why would he not? Idly he fingered the amulet in their hands. He licked his lips. Oh, yes, the time was nigh. He had overpowered and enslaved this queen, and now he would do Shaeda's will. Teeleh would be pleased, very pleased.
"Joh . . . sef." Silvie rode up beside him, her pale eyes narrow. "Where are you going?"
Johnis's mind snapped into focus. He glanced at her. Silvie had found a piece of flint and now sharpened her daggers to thin, lethal edges. She remained skeptical. "You're too far ahead."
Irksome female. Why did she have to nag at him like that? Johnis's brow furrowed. "The scout reported carrion. I was looking into it."
Silvie's expression indicated she didn't believe him. She scanned the desert floor. The Shataiki hive was overhead now, and once more they could see little. Johnis rode forward.
"And you saw nothing?" she asked.
"Still looking. My concern was feeding bats."
"Marak and the priest will be angry."
He studied Silvie. Shaeda's talons stroked his neck, tickling his skin. He'd allowed her presence to dominate his since the slip. But she was getting stronger. With all his senses on such high alert and firing in his body, he felt like a madman. He saw her eyes, her beautiful, intoxicating eyes . . .
Shaeda came over him. Her strength became his.
Her will . . . her mind . . .
Johnis's back—Shaeda's back—arched. Prepared to strike.
"Johnis?" The brief silhouette rode toward them.
Darsal approached, her torch high. Sweat glistened on her face, streaking morst and exposing smooth, dark skin.
Johnis scowled. Shaeda bristled. His vision turned hazy. They were done with this albino. Shaeda wanted her blood.
But Johnis restrained the impulse first. Not now, not when in a matter of hours it wouldn't matter who killed the wench.
"What do you want?" Silvie demanded.
The albino's gaze swept from Silvie to Johnis.
"Help. We're almost out of time. You really want to kill the Guard? Make an alliance with a Shataiki?"
Silvie's jaw hardened. "What do you know?"
Johnis narrowed his eyes.
"More than you think." Darsal's voice was strained. Desperate. Of course she was desperate. As soon as Sucrow performed the ceremony and Johnis gave the order, she was dead. Johnis would make sure of that.
"Johnis, do you know what the Circle is?"
He snorted, fingered his ring. "My name is Josef."
"Josef is bound to a Leedhan. You are Johnis. You are Johnis who forgave me. Remember that."
He saw only a swarm of bats and blood mingling in water.
Shaeda showed her teeth.
Darsal jabbed her finger in his face. "Your mother would not tolerate you killing hundreds of our own people because she was murdered. I didn't know her long, but I know that much!"
"You know nothing!" Johnis rose up in the saddle. "You don't talk about her. You don't even speak her name."
"The Circle is your mother. It is me. You and Silvie."
A surge of heat billowed deep in his gut and worked its way up through his chest and down his arms. "You have no business talking to me this way," he growled. Darsal was in the way of the mission. She'd served her purpose.
Shaeda wanted to kill the albino. Here. Now. Johnis craved Darsal's blood.
_No!_
"You are a doomed slave, and I am the next ruler of Middle."
Darsal drew her horse close and put her hand on his leg. "You can defeat Sucrow without the amulet, without Shaeda. You've never needed magic or anything but the brain Elyon gave you."
She'd grabbed him like that before.
_That_ Darsal.
He kicked, then swung his sword at her, broadside. She hit the ground and rolled sideways, limbs sprawled, groaning from her injuries. The horse squealed and barely avoided crushing her.
"Go back to your precious Scab. You're already dead."
Darsal struggled to rise. "Silvie, tell him! You know it's absurd to think that siding with Sucrow or the bats is a good idea."
"Leave her out of this," Johnis snapped. Shaeda was going to pounce. He was going to tear Darsal to shreds.
"She's already in it." Darsal made it to her feet.
"It is my kisses he prefers," Shaeda said through Johnis's mouth. Her laughter overtook him.
"Excuse me?" Silvie snapped.
Johnis fought for control. What was she doing, telling the girls that?
But he had liked Shaeda's kisses, hadn't he?
Shaeda chuckled.
"She kissed you?" Darsal turned on him, completely stunned. She grabbed Silvie's reins. "Since when have you let anyone but Silvie kiss you?"
"You're just trying to divide us. I love Silvie, and that's final."
"Final as using black magic to overpower the Shataiki and destroy everything we all bled and died and sacrificed for. Is it that final, Johnis?"
He threw Silvie a look. She jumped off the horse and on top of Darsal, then pinned her, arm behind her back. Darsal wrestled free and struck Silvie broadside. She hit the ground, unconscious.
Johnis snarled.
"You're as certain as my death that those bats are completely under your control? That they will not and cannot betray you?"
"They are bound to the medallion. I could have a throng of them kill you now, right here."
"Tell me something, O mighty Chosen One. What makes you think that after you destroy the Circle and destroy everyone you hate, they'll leave the Scabs alone? They'll do what you command, Johnis, and more, just like last night. They defied the boundaries once; they'll do it again. And you and Silvie will wind up bat food, like the rest of us."
Shaeda poured into him. He knew he was transforming. Again. He was becoming Leedhan.
"You're wrong."
"I pray to Elyon I am. Remember him? Teeleh hates him. Teeleh hates you too. Tried to kill you once. Open your eyes, Johnis. You're going to destroy what you love the most."
She had a point, didn't she? They were going to use Shaeda's power to turn tables on the Leedhan, to somehow turn the bats on the Horde . . .
_"The albino poisons you,"_ Shaeda rebuked. The transformation completed. _"She wishes your destruction. She will destroy our true_ _mission . . ."_
"Johnis, you stubborn fool, listen to me!"
Shaeda exploded. They sprang at Darsal and slammed her against the ground. Tore at the albino's throat. Darsal thrashed from under Johnis, rammed into the horse. She knocked his pack off. Water and food splattered across the desert sand.
"Johnis!" Darsal went into a crouch and sought a weapon. Her eyes found the horse.
Shaeda—inside Johnis—pounced on the albino. Darsal barely dodged her, rolled. Johnis caught her by the shoulder. Darsal clawed at his hand and struck him hard in the face, wrenched loose. She tore the reins from one of the bridles and snapped them like a whip.
Their blood mingled with the water, stained the desert sand.
"Shaeda," Darsal snapped, "let him go!"
Shaeda hissed. Johnis's lip curled.
_"Kill her."_
"Kill her now and we lose Marak," Johnis growled. He gasped for breath. Shaeda's energy taxed him. Darsal had torn a hunk of flesh out of him.
Silvie stirred from the ground. In the end Shaeda would kill Silvie, wouldn't she? Darsal was right. He was destroying the very thing he loved.
Did his heart really desire to kill the Circle?
Kill Silvie and Darsal?
Shaeda was not rational when she gave way to her hate. Her talons dug into him, punishing his contradiction. And now she knew her pet would never be wholly hers.
Darsal didn't lower the leather rein serving as her whip. "Let him go," she repeated.
Hoofbeats pounded toward them from the foothills.
Throaters. Hair on end, Johnis turned. Five of them. His blood ran cold. Why hadn't he foreseen this? Why hadn't Shaeda—
Talons tore into him. Leedhan fury bore down on his shoulders, almost knocked him off balance. "Shaeda, what are you—"
"Let him go!" Darsal screeched.
"I do not tolerate weakness," Shaeda warned between Johnis's teeth. His knees buckled.
_I am not weak!_
_"You have not given me your heart."_
Darsal turned and met the Throaters head-on. Warryn caught her across the throat with a spear shaft and sent her flying. She hit with a disgusting thud.
_"Foolish albino."_
Silvie was throwing a fit. Johnis found his sword and invoked Shaeda's power. Nothing. The Throaters fell on Silvie and struck her hard across the skull. Johnis lunged, then hit the ground and rolled, medallion in his fist.
_Shaeda!_
He crossed blades with the Throater. The Leedhan hissed in his ear, all her strength, all her power pouring out of him. As she left, the full weight of everything she had sustained him through bore down on him. He had neither eaten nor slept. He'd ridden for days on end. He'd fought, he'd run, he'd—
Johnis went down, sword clattering. Desperate, groping for the medallion. A heavy boot stomped on his hand and took it from him. The Throater sneered. Someone flipped him on his belly and bound his wrists and ankles.
Shaeda wanted his heart and could not have it. Now she would let the priest have him. Johnis's mind began to swim.
Heavy fog surrounded him, blurred his vision.
The Throaters were talking, but Johnis could barely under stand them, even as they dragged him up and slung him across the back of a horse as if he were a deer carcass.
"We'll deal with it," said Warryn. "Let the general handle his slave."
twenty- four
**D** arsal woke to the end of a spear shaft probing her. She groaned and rolled away from the intrusion. Where . . . ?
Eyes opening, she saw reddish-brown desert and warm blood drying on a rock. Everything came crashing back: Johnis, Shaeda, Silvie, the Throaters, Warryn . . .
She jumped into a crouch and spun.
"Easy, albino." Cassak had dismounted and glared at her, still holding his spear. Behind him his horse stamped and shied, nervous. He spat. "I should have talked the general into executing you."
"Talked him into it?" How dare he talk about Marak like that. Darsal raised a brow, scanned the ground, heart pounding. This wasn't the Cassak loyal to Marak—who would spare her for his friend's sake.
The starry-eyed serpent at his throat seemed to come alive.
"We could find out what he thinks of that." Her blood and Johnis's had already soaked into the dirt. The horses were gone. The Throaters, Johnis, and Silvie were all gone. Were they dead? Had Warryn taken them somewhere?
"He knows what I meant." The captain seemed pensive, though, as if he hadn't intended it the way it sounded after all. What was Sucrow using him for?
"I really don't have time to argue."
Behind Cassak the rest of the expedition party was coming, a black shroud of Shataiki in the lead. All was gray and black, riddled with beady, glowing red.
What had Warryn done to them?
Elyon's words nibbled at the back of her mind. She felt her heart straining in two. Darsal was being spiteful, and she knew it. At the moment she wasn't sure she cared. But she loved them, didn't she? Even Marak's captain.
She forced herself to soften. _Love the Horde._
"I think you do. What's happened here?" the captain demanded. He traded his spear for his sword. Darsal kept her palms extended. She'd taken Johnis's knife, but the Throaters must have taken it away from her, thought her dead. Why didn't Cassak just run her through?
Because Marak wouldn't want him to. That knowledge would work to her advantage. Part of the captain still struggled against the enchantment. Her mind raced for an answer.
"I was looking for water," she snapped. "Is that a crime?"
_Easy, Darsal._
Why should she be? This man would kill her were it not for Marak's orders, and Marak had every intention of allowing the priest to kill all of them.
_Return to the Horde and love them for me. For Johnis._
She pushed back the gentle reminder.
"There was a fight," he said.
"The priest's Throaters are a pack of jackals." Darsal's brow went up again. She crossed her arms, then remembered this captain had hated the priest at one point. She wondered how much he hated Warryn, chief of the Throaters. Maybe if she could get to the bottom of Cassak's enchantment, she could give Marak his best friend and most trusted officer back.
She had never lied to Marak, and he was impressed by that. Impressed that he could trust her, a sworn enemy. And Cassak and Marak were made of the same cloth.
So she told the truth.
"Warryn attacked us. Sucrow's making a power play." She frowned. "Marak doesn't know about it. Did you?"
Cassak tensed. He rubbed his neck. "Where are Josef and Arya?"
"Tied to a cactus, for all I know. I need to find them before Warryn kills them. Remember Warryn, the one who made you watch him torture your best friend's family?" Her heart was in her throat _. I'm sorry, Marak. I don't have a choice._ Darsal thrust out a hand. "Lend me a knife, in case the Throaters come back. I'll return it."
The captain's eyes narrowed.
"I swear by Elyon." _And on the books._ "And I won't tell anyone where I got it, either."
"General would know."
Darsal stared at him. The man was split in two. One side showed her concern out of loyalty to Marak. The other seemed to despise everything he and Marak once held in common.
"What's Sucrow done, Captain? Are you really going to punish your best friend for what never was? Turn your back on him to serve a man you despise? That's what Josef's done. And it's killing him."
He hesitated. Darsal snatched his knife and ran. Cassak grabbed her collar. "Get back here, you little—"
"So you won't get in trouble." She punched him in the face, swung onto his horse, and galloped off.
JOHNIS BUCKLED IN PAIN. THE WORLD SEEMED TO SWIM, and everything was fuzzy. He tried to open his eyes but couldn't see more than a blur. Tried to move, but his cold, stiff muscles wouldn't cooperate. Sand kissed his cheek.
_"Such a weakling you've proven, Chosen One. Such a pity . . ."_
"Bloody fool," said a familiar voice that Johnis couldn't place.
Another kick to his already broken ribs. His head rose up against his will. A potent drink that smelled like Rhambutan and eggs slid down his throat. Bitter, hot liquid flooded his mouth.
Johnis gagged and tried to spit it up.
"None of that, now," said his tormentor. The rebuke came with a sharp blow to the side of his throbbing skull.
He swallowed. Shaeda . . . Where was Shaeda?
She'd left him. Abandoned him to the priest she despised. Had she planned this all along? Johnis rolled his head back and let out a groan.
_"Foolish son of Ramosss . . . Did you truly believe I would remain_ _with one so powerless? Nay, my pet . . . there are much larger trophies_ _than you in poor Middle."_
"Silvie . . . Silvie, where are you?" His voice echoed.
More voices.
_"'Silvie, Silvie!'"_ Shaeda taunted. _"That leech has passed into the_ _nether realm. Since you will not fully aid me, I will not allow her to_ _live. Nor you, my unchosen one."_
A whip lashed across his bared, flaking skin. Johnis opened his mouth to scream, but no sound came out. He struggled, but his limbs rebelled against his will.
A cord wound around his neck and pulled taut, strangling him.
He sputtered and coughed, writhed on the ground. It felt like someone was dragging him over a bed of nails or hot coals. Johnis screamed this time. Laughter answered him.
_"Pitiful son of Ramosss . . . Thomas would be so displeased . . . So_ _disappointed that his best was far too weak . . ."_
Johnis lost consciousness and dreamed, dreamed he was underwater, hunted by a creature and devoured alive. The beast gave one last gulp, and Johnis slid into the hot, acidic blackness.
"Wake up!"
Johnis groaned and rolled over, startled to realize he could. His body felt torn to shreds. And maybe it was. The hand shook him. "I said wake up!"
Someone helped him sit up and tried to give him water. He turned his head to the side, but they grabbed his jaw and forced him to drink it. Warm, muddy water mixed with some kind of citrus slid down his throat.
"You're worse than your wench." His captor cackled.
_Why are you doing this?_
_"I have spoken, my Johnisss . . . I require a more formidable ally,_ _one whose loyalties are wholly mine . . . Farewell . . ."_ Shaeda laughed.
Johnis's head cleared a little, enough to know his arms were bound behind his back and his ankles secured painfully against each other. A bloody gash oozed on the side of his head, and needle pricks of pain drilled into his arms and legs. His rib cage felt crushed.
"I'm not sure who screams louder, you or the wench," the taunt continued. "She broke easily enough. We'll see about you."
He struggled to breathe, and on top of the rotten egg, citrus, and Rhambutan juice, he smelled a sickly sweet substance that dominated his senses above all else.
Johnis shook his head and opened his eyes. He was in the desert, surrounded by Throaters. Warryn was the speaker. Sucrow had the medallion. Silvie . . . Where was Silvie?
_Shaeda . . . Shaeda, wait! You gave your word!_
Warryn snickered. "So you haven't died yet. Pity."
Johnis pursed his bloodied lips. He scanned the ground. Before him was a pit, a yawning gash in the ground, just deep enough that if he were thrown in, he wouldn't be able to climb out. But Silvie . . .
The Throater struck him across the side of the head, then cackled. "Such a pretty thing, the girl was."
Johnis snarled and lunged, then realized his wrists were over his head. "If you've touched Silvie . . ."
"I really don't care." Warryn raked his nails over Johnis's face and drew blood. Johnis swallowed the coppery-tasting liquid and too-salty saliva.
"Where is Silvie?"
Warryn leered. "Regrettably, she didn't last very long."
"I want to see her!" Johnis pushed up with his elbows but couldn't find any leverage. Someone kicked him down. His shoulder popped. Johnis grimaced.
"There's really nothing there you'll want to see."
"I want to see her." Johnis's stomach rebelled on him. He couldn't make himself believe that Silvie was dead. The Throater was lying; he had to be.
"What did you do to her?"
Warryn dragged Johnis up by the chain that tethered his arms together and laughed in his face. "I'll leave her fate to your imagination."
Johnis started to protest, but Warryn flung him into the pit. The chain went taut and snapped his shoulders out of place. All his weight was suspended on his joints. He nearly passed out from the pain.
Johnis glared up at the Throater, looked for any source of leverage. He tried to grab the chain but couldn't.
Warryn left him, still gloating, no doubt. Johnis forced himself to breathe. He was in a hole . . . in the ground. A grave.
twenty- five
**w** here are they?" Marak was in Sucrow's face. He hadn't taken Sucrow's divulgence well. Josef and Arya were dead; Marak's precious albino had abandoned him.
The general really needed to mind his priorities.
Sucrow sneered, amused at the general's outrage. He had considered lying to Marak, but in some ways this was better. Sucrow twisted the staff in his hand and fingered the amulet beneath his tunic. Warryn had done better than Sucrow anticipated, which pleased him. At the moment his chief serpent warrior was likely making up his grievance with the Eramites the previous week.
Now, how would Marak respond to his captain's betrayal?
"Are you more concerned about the loss of extra baggage, General," Sucrow cackled, "or the loss of your albino and the amulet?" Dark tendrils sifted from his staff to Marak's neck, constricting. Marak rubbed the spot unwittingly.
Sucrow extended his hand to his servant and accepted the second jar of blood. The Chosen One's blood.
Marak's white eyes sized Sucrow up, no doubt considering tearing him apart. Morst cracked across his face and dripped down his cheeks and neck.
The general fingered his sword.
Sucrow laughed. "Do you really believe that sword will be of any use against me, Marak? I am Teeleh's high priest, and the amulet is back where it rightfully belongs. I have had power beyond comprehension for longer than you have been alive, and this is the greatest charm I have ever known. So you tell me how you think you will fare with two million of my lord's faithful at my back."
As if in answer, Derias gave out an agitated roar as the edge of the eclipse passed over them. Sucrow chanced a glimpse, still awed at the presence of so great a beast. _Soon,_ he thought. _Soon you will_ _be released from your prison._
Marak snarled a minute longer, hand still on his sword. "Ride," he snapped, quickening the pace.
Sucrow spurred his own mount, still considering the amulet. "As soon as this is over, General," he promised, "Teeleh's servants will feast on you as well."
MARAK GALLOPED AHEAD OF THE OTHERS, NO LONGER willing to run alongside the priest but compelled to ride out to this high place as swiftly as possible and be done with the matter. The black horde above prodded him on.
Beneath his tunic, Jordan's pendant bounced against his chest. Why he was wearing it, he'd never explain to the others. But why shouldn't he wear his brother's necklace?
Forget it. And Darsal. Above all, forget Darsal. A knot formed in his stomach.
"General!" A figure on foot waved. As his mount's pounding hooves carried him closer, Marak saw his captain, blood and dirt smeared over him. No knife. Cassak fumed.
Marak drew up on the reins, circled his captain. "Where's your horse?" He pulled up and glanced back. The dark shadow was already over them, and Sucrow would be only minutes behind.
"Your albino," Cassak snapped. "She knocked me out and took my knife and my horse and rode off to Teeleh knows where. Cursed wench."
Marak bristled at the slur and felt the knot in his gut tighten.
"She left," the captain accused. "She ran like a bloody coward."
Marak didn't respond.
Cassak snatched the reins and jerked the horse's head around. "I told you this would happen. I sent men after her. If she fouls this up, Marak—"
Marak snatched the reins free of his captain. "She can't foul it up, Cassak. Josef and Arya are dead. Sucrow has the amulet. I have the army. Why don't you tell me how one unarmed woman knocks you out and takes your knife right out of your belt?"
One of the scouts raced back to him and saluted. "General, we've located the Ba'al Bek. Also, Eram's search parties—"
"Give the captain a fresh horse," Marak barked at him. He scowled at Cassak, awareness of their breaking—already broken—friendship settling on his shoulders.
The scout dismounted and offered his reins to the captain. "I run fast enough, sir." Normally the gesture would have been immediately rewarded, but Marak was too frustrated to bother responding to it.
To Cassak, Marak ordered, "Take ten and clear out the rebels. Don't tell them anything."
The brusque charge stunned Cassak, and for a moment he just stared. Then he gave a crisp salute and swung onto the scout's horse. He shouted at the beast and was gone.
The eclipse now completely overshadowed them. Derias's howl drowned out everything. Marak glanced back and saw the priest signaling him. He let Sucrow catch up.
"General, there is—"
"Last leg. Try to keep pace." Marak slapped the reins, knocking foam off horseflesh.
twenty- six
**D** arsal rode through the desert, praying to Elyon she would find Johnis and Silvie alive. She kept her course toward the high place, guessing that Warryn would plan to rejoin Sucrow and the other Throaters once he'd finished with his prisoners.
Two million Shataiki blacked out the sky and made time impossible to determine. She searched for Cassak's water bottle and drank from it, then grimaced. Horde water was anything but clean.
Somewhere beneath the canopy, one hundred warriors, twenty Throaters, Marak, and the priest were headed for the high place.
A cold, numb sensation swept over her. Darsal shook it off. On this path around the foothills, Warryn could find plenty of places to dump bodies and still reach his master quickly, she surmised.
_Don't think that._
Still, the gnawing understanding that Johnis and Silvie were most likely dead, combined with the knowledge that she'd probably ruined any chance of winning Marak's love, wouldn't leave her. She felt the coarse, grating pain down to her bone and marrow.
Her mission had failed, and they were all dead.
Several hours passed, and still no sign. Her torch burned out, leaving her in the unnatural darkness. Darsal stayed her course, headed now into the foothills where the race was on. Marak and Sucrow would follow the scouts' advice and go around along the easier trail. But Darsal would cut through, and she was alone.
Assuming she was still heading north.
"Follow the bats," she grumbled to no one.
The horse startled. Darsal shouted and yanked his head down, pulled him in a tight circle. "Easy," she snapped. "Two million Shataiki and now you decide to—"
"Didn't mean to spook him," said a familiar voice. Darsal whipped her head toward Gabil, who slapped the air with his wings and lighted in front of her in the saddle. His green eyes stared up at her. "But you're going the wrong way."
"I'm going north," Darsal fired back. She heard the Shataiki queen's snarl from above, but when she looked up, she could see nothing but a black sea of the swarming beasts.
"Well, yes. But Marak's ahead of you now."
Darsal cracked the reins and got the horse moving again. The motion unsettled Gabil and made his wings flutter as he rebalanced himself.
"How far?"
"Half a mile or so. Not too far. But that isn't what I meant. You see—"
"Where are Johnis and Silvie?"
Gabil cocked his head. "I thought your mission was Marak."
"My mission is the Horde. To woo and win their love for Elyon. And I failed. My only choice is to try to find Johnis and get out of this mess." It sounded foolish when she said it, though. "I can't take on two million Shataiki, Gabil. Even you can't do that."
The Roush was slow to answer. "Well, true, but who told you to take on two million Shataiki, Darsal?"
"I can run a blade through their priest easily enough," she snarled. "If I reach them in time." Yes, that was a good plan, now that she thought about it. "Just tell me where Johnis and Silvie are, and point me through the mountains."
"You know I can only do so much, child."
He sounded more like Michal just then, and that unnerved her.
"How do you plan to drown them?" he asked at last.
"I'll figure it out."
"And Marak?"
"I broke his heart. It's over."
Gabil glanced up at the Shataiki swarm, then back at Darsal. "So that's it?"
"Human love only goes so far. Johnis, Gabil. Johnis."
"But Johnis isn't—"
"I am not going to talk about Marak." She fought the urge to knock him clean off the horse. But that would be foolish. Gabil was trying to tell her something, and she didn't like where he was going.
"I'm out of time with him," she insisted.
"Well, I don't know where they've taken Johnis and Silvie," Gabil admitted. "However, I don't think you'll succeed unless you first love the Horde."
"Love them." Darsal scoffed. "I tried. I've been patient."
Gabil chuckled. "Patient for you, yes."
She started to argue, then thought better. "You have a point. But that isn't helping me." Darsal studied him. A memory surfaced. She drew up short. "That's why you're here. I said all along the Shataiki will kill them all, Horde and Circle. It's true, isn't it?"
Gabil listened.
"I'm not going to find Johnis out here, am I?"
"You might. You might not."
She scowled.
"But you can find Marak."
Darsal tensed.
Gabil continued. "But the question remains: will you be patient a little longer, or do you wash your hands of him?" A pause. "You think you love him more than Elyon?"
She started to protest, but instead accepted his gentle rebuke.
"You think you love Johnis and Silvie more than Elyon? Or do you wash your hands of them as well? You're all quite stiff-necked."
Darsal glanced up at the sky, which was no longer visible. Thunder pealed with the sharp crack of lightning. "I need a pool, Gabil. I can't find one in the dark." Even as she said it, she knew what she was going to do.
She still loved Marak, and Marak couldn't die a Scab.
A screech overhead. Shataiki wings slapped the air and circled over the peaks. The scouts.
Marak the Scab would never change his mind. But Marak the albino might.
_Elyon save us._
The Roush laughed softly. "You'll always find water when you need it, Darsal. Trust that much. Elyon didn't bring you out here to die."
Another memory surfaced, and with it came understanding. Darsal drew a breath. Marak would be back with the rest of the expedition, headed north. She'd gone east a ways, looking for Johnis and Silvie, before turning north. Now she'd have to turn back west a bit to intercept the general.
No, Gabil said they'd passed her. Fine. Even more easily done.
But if Sucrow was making a power play, what would he do to Marak?
She'd find out . . .
"I leave them and find Marak, then. So be it." With those words came an ache.
A loud rush of leather wings and Shataiki roars split the air. The swarm circled twice in formation, endless rows and columns of glowing red eyes.
Gabil nodded. He flapped twice and was airborne. "Now, if you'll excuse me . . ."
"Wait, you're leaving again?"
"Two million Shataiki, Darsal. Neither of us is doing this alone. I would keep north, if I were you."
"WE WILL CUT THROUGH THE PASS," SUCROW SAID TO Marak's commander. "Spread the word." He gestured at two of his serpent warriors, who rode up on either side of the officer.
"Marak will be expecting us to follow the scout's advice," Reyan argued. "He'll be waiting."
"Is your general here?" Sucrow snapped. The commander tensed. "Inform your men that Marak has deserted to the rebels, and I am in command."
Reyan scowled. His hand fell to his scabbard, but Sucrow held up his hand. He twisted his fingers around his staff and silently invoked Teeleh's powers, already at hand. The commander's expression tensed. Tendrils of crimson slithered around Reyan's throat. Not that the commander would notice.
Sucrow flashed a wicked grin. If only this fool knew what was coming. "Come, now, Commander. Marak led you into the desert, only to desert in the final hours. I have equal rank with the general, if not higher, and it is to me you will look."
The commander's jaw tightened. "Marak's angry. Nothing more."
A fighter, then. As formidable as Cassak was, though the captain was more stubborn. So be it. If Reyan's will would not bend, it would break.
"Are you so certain?" Bile rose in Sucrow's throat. The general's mantra of loyalty, integrity, and honor had poisoned the entire army. A disgusting parasite he would soon rid them of. Sucrow dipped his staff.
Confusion drifted across the commander's face, just as surely as Sucrow's enchantment did its work. Reyan started to reply.
A rider in full gallop rushed straight for them. The scout raced straight across, heading for the front of the line. Their horses reared. The rider swerved in with a whoop, trying to knock them all off course.
Sucrow swung his staff. The rider grabbed the end and swung it level across his throat. Sucrow fell off the horse and landed on his back with the assailant on him. The smell hit him—an albino.
"Kill her, you fools!" he screamed, clawing at the albino. Three swords rang out. A hot knife blade dug into his throat, a thin trickle of blood forming below it.
"I'll kill him first! Where is Marak, Priest?" the general's slave growled. "What did you do with him? He's supposed to be here!"
Sucrow sneered. "What do you care?"
She leaned in close and whispered. "Three seconds, Priest. They can't kill me before I slit your throat."
"He deserted," Reyan snapped. "He left."
"Where, you half-brained dimwit?"
"North," Sucrow sneered. "Not that any of this will save you."
"It isn't about me." She grabbed him and swung back onto her horse, Sucrow slung across like a carcass. "Follow me and he dies! Ya!" The albino whipped the horse into a gallop and raced away from them.
Sucrow struck at her. She beat him over the head. "The medallion," she snapped. "Where is it?"
He snarled. "You're mistaken if you think I'd tell you."
"I could just search your clothes after you're dead."
Sucrow mentally began an incantation.
The albino turned the horse, taking a zigzag pattern to throw him off. The sky was almost too dark to see. The albino searched his clothes. Sucrow's hand clamped down around the amulet.
She tried to wrestle it from him. Sucrow sliced his sharp nails into her flesh. She fought with him. They both fell off the horse and hit hard. Sucrow snarled and raised his hands, clawlike.
"Your magic will not aid you," she snapped.
Sucrow didn't answer. He'd nearly killed her with a well-placed invocation before. He summoned Teeleh's power into his hands. An orb formed.
She dodged the blast and swung back onto the horse, then galloped into the mountains, presumably after her arrogant general.
The fools could both die out there. The Shataiki would have both of them.
The commander caught up to him, bringing the priest's horse and his staff. He mounted.
"She escaped."
"She won't escape for long." Sucrow motioned to his serpent warriors. The nearest ran his spear through Reyan and knocked him off his horse. Sucrow watched idly. "Never betray your master, Commander." He sneered. "Tragically, the albino killed you."
To his men, "Summon the captain. Inform him his general has deserted and his commander is dead. We must make haste to the high place before the albino does something foolish."
twenty- seven
**M** arak guided his horse into the pass, following the scout's advice. From here he could see the precipice, the mountain where everything would end. He'd had enough of the priest, no desire to see him again before the ceremony, and certainly not after.
_Idiot, why did you leave?_ he imagined Jordan demanding. _You_ _left the priest unattended. Do you realize what he can do while you're_ _gone? He already killed Josef. He has the medallion, brother._
He knew, and his reason told him he needed to turn back, to stop following this insane compulsion to reach the peak ahead of Sucrow. Something was there, something he needed to get to before Sucrow. As important as the amulet itself.
A loud roar erupted from the mountain, underscored by the lightning storm that had started a half hour or so ago. When the light flashed again, Marak glimpsed the massive amulet guardian circling the high place, raging against his enslavement. A mere mortal had tricked him; no wonder he was so angry.
Marak shook his head, not sure how he knew such things or why he speculated them. The horse faltered, and he carefully set the animal's course on better footing.
"How in Teeleh's name is this faster?" he grumbled. The scout had to be mad.
"Marak!" A voice echoed over the wind. "Marak! Wait!"
_Darsal?_
He balked, looked over his shoulder. She was back?
Impulse took over. She'd ripped his heart out. Marak turned his back and kept going at a steady pace. Darsal called out again, making her way toward him as fast as the narrow drop-off allowed. Shataiki screeched and boiled above them, frothing at the mouth, Derias howling louder than all. Marak's senses were at their end, worn ragged by the chase.
His emotions twisted at the sound of her voice, at the smell of albino caught in the wind. Impulse drove him forward while his heart said to wait, to pull back, to let her catch him, to sweep her off her mount and hold her.
Darsal caught up to him. She rode up the side of the ravine and back down in front of him. Her hand lashed around his mount's reins. "Come with me!"
For a second he could only stare at her. Marak jerked on the leather. "I thought you left."
"Sucrow tried to kill us," she said. "I went after Warryn, but I didn't find him! We have to leave now!" She pulled the reins free of his hands and hurried the horses.
"Darsal!"
"Hurry!"
The bats were screaming above the mountains.
Darsal got them through the pass and into a narrow valley. Ignoring the fretting horses, she whipped them into a run. The sky grew darker. The bulk of the Shataiki swarm was almost over them. Darsal smashed into a winged serpent shrine and sent the idol and the incense altar clattering down the hillside.
Marak finally quit trying to get the reins from her and hung onto the saddle horn. "Darsal, if you'd stop for just a—"
The sand turned to mud and worn rocks. Darsal barely avoided a tree, then darted around two more. On they fled, zigzagging through the treacherous terrain.
Darsal stopped and dismounted. Marak jumped down and grabbed her shoulder. Her skin was hot and slick. "What's going on?"
"I know you're mad at me, Marak," she panted. "And you're going to—going to hate me for this, but I—I have no choice!"
"No choice but—"
Darsal whipped out a dagger and cracked him across the skull.
DARSAL CAUGHT MARAK AROUND THE CHEST AND UNDER HIS arms. She half carried, half dragged him over the sand. Her arms were killing her. Sweat poured down her skin. Marak's dead weight slowed her down. Darsal dragged him by the armpits to the red pool and plopped him next to it. She sank down alongside him.
He wouldn't be out long.
She caught her breath, then tugged Marak's head so that he hung over the edge of the pool. Darsal grabbed a tuft of hair and shoved his whole head facedown into the pool and held him under. She yanked him back out, then under again.
Marak started to sputter and struggle. Darsal knocked him out and jumped on his back. She straddled his shoulders and baptized him again.
Again.
Darsal plunged him back under, clinging to his scalp. She jerked his head out and shoved him all the way into the pool. Her stomach churned. She pulled herself over the edge and yanked his head above the surface by the hair. He was barely breathing.
Blood oozed out his nose and ran down his face.
She pushed him under again. "Drown already! For the love of Elyon, drown, you fool Scab! Drown already!" Again and again she forced him under.
Until he . . . went limp . . . in her grasp.
She dragged him out of the pool and rolled him over. A flash of light splashed over his skin. Her heart froze. Marak's flesh was still flaky. Scab.
Darsal's eyes widened. Her stomach curdled.
"No! Why are you still Scab? You drowned; you can't be—" She cut herself off as the revelation dawned.
It wasn't just drowning. Marak hadn't believed. And she'd drowned him.
Darsal ripped off his shirt and pounded on his chest.
"Wake up! Wake up! By Elyon, wake up!"
She slapped his face and struck him hard with both fists, slamming into his heart with all her strength.
"Marak, I love you. I didn't mean to hurt you!"
Darsal's fists struck the unconscious general's chest one more time. She raised her fists up, then let them drop. She knew it was over. Darsal fell across him, bawling like an infant, her arms around his neck.
"Elyon, Elyon, please . . ."
His heart. She couldn't hear his heart.
She sat over him. Stroked the scaly flesh and let her fingers hover along his torso a minute. She touched his cheek and wiped away her tears that fell on his face.
Once more. Just once more.
Darsal put her mouth to his and breathed into him, then pumped his chest. She breathed air into his lungs, then pumped again.
A third time she blew air into his lungs and prayed to Elyon they would fill and he would take in life.
Nothing.
Furious, she slapped him hard.
"Oh, come on, you stubborn, bullheaded Scab! If you won't live for me, won't you live to spite Sucrow, at least? Please, Marak, I need you. Why didn't you believe?"
A desperate thought passed through her crazed mind. It was stupid and foolish, and there was absolutely nothing in it. Something from another time, another world altogether, when a man had begged the Maker for the life of a boy.
Even so, Darsal put his arms on either side of him and straightened his legs. She lay directly on top of him, forehead to forehead. She kissed him on the lips. Begged Marak and Elyon one last time for some form of cooperation.
How long would it take for them to kill everyone? Days? Hours? Minutes?
_This whole mission was doomed from the day I walked back into_ _the dungeon. It's worse than the books, a thousand times worse. I'm_ _sorry, Johnis. I couldn't stop either of you._
Darsal rolled away from Marak and curled into a ball.
"Marak," she wept. "Marak. My general. My friend. My love. I failed you. I'm so sorry. I'm sorry. By Elyon, I'm sorry . . ."
Darsal lay still in the darkness, the impossible hope that her general might rise from the dead forcing her to linger.
She didn't have the energy anymore. Twice she'd lost a lover, twice a man had brushed her cheek with a kiss, only to perish.
She didn't want this fight. Elyon had made her do it. The general had been so close, and then she'd ruined it.
Now she'd killed him.
"Elyon, why can't you just let me die? Take me, not him."
Mud stained her face, caking her eyes shut. She didn't care.
Marak was gone. Gone.
twenty- eight
**d** arsal folded up on herself, limp. Minutes passed. And then, silently, languidly, a mist began to curl up from the ground, winding around her like so many octopus tentacles. Darsal twisted around, looking toward the pool where Marak's body lay. Already the mist was so heavy she couldn't see man or pool. The haze turned a purple-red hue.
Darsal got up on her knees and felt for any of Marak's daggers, even her own, stolen from Cassak.
Either the mist was too thick or she was too frantic to search. Helpless, worthless, useless, alone. She had nothing.
"Peace, Darsal." A musical voice floated from the trees.
Out stepped a delicate, willowy woman, almost glowing. She had flawless, white, translucent skin and wore a long, thin, green gown. White-gold hair fell to her calves. Her wide eyes burned in the darkness and cut through the haze.
The entity. Johnis's Leedhan.
Shaeda.
Darsal drew back at the woman's approach. Her mouth ran dry. The woman crouched in front of her and pressed her slender hand against Darsal's chest. Darsal's heart thrummed faster at the contact.
She couldn't pull her gaze from the woman's eyes. Her steady, penetrating gaze that probed the soul and soothed the mind.
That could seize control of body, mind, and soul.
"Peace." Shaeda blew a gentle puff of air in Darsal's face, an unnervingly sweet aroma. "I have need of you, albino . . ."
Darsal's body relaxed of its own accord. Her eyes drooped. "Who are you . . . ?"
Shaeda cupped Darsal's face and gave her something to drink from a stone bowl. "Take such."
She hesitated.
"Such is not fruit," Shaeda said. "Such will not yield you to me. I desire not to grant you my power, nor gain control over you. Accept my restraint."
Darsal wanted to resist, but found she couldn't. She obeyed, and the Leedhan removed the bowl. The drink smelled like Rhambutan and citrus.
"Shaeda . . . you tricked Johnis . . ."
"Men hear what they will."
"Marak . . ." Darsal's thoughts were scattering, petals breaking off of flowers and drifting away in the wind. "Johnis . . . Thomas . . ."
"Remain with me, daughter of men. The potion is strong, but will take time to work its course. Then such will enable you to resist me. Concern yourself not with this man. He is beyond your skill. Drink again."
The stone bowl returned to Darsal's mouth. She drank her fill while Shaeda talked.
"Johnis . . ."
"Teeleh's priest has the amulet, yet he must not keep such.
The Shataiki must be thwarted, lest they kill every human in this world . . . and naught shall prevent such foul creatures from passing to the other side of the river. I shall reveal to you the way in which you must go. Comprehend you such? Daughter of men, awake."
Shaeda traced her sharp half claw of a nail over the scar on Darsal's cheek and down the side of her throat. She kissed her on the forehead and both cheeks. "Do not slumber now. We have need of you yet."
Darsal tensed, head clearing in the fog. "Johnis."
Shaeda nodded once. "He is shattered to pieces. The priest will unleash the Shataiki on your Circle. Your kind and the Horde shall perish. The priest will prevail unless Johnis dies. Do you comprehend?"
Darsal struggled to keep up. Shaeda spoke slowly but covered many subjects in the time it took most to process the first sentence. Time seemed almost irrelevant.
"Johnis . . . lives?"
Darsal's mind was reeling. Shaeda didn't want the priest to have control of the Shataiki. The Leedhan wanted Johnis and Silvie to drown. Needed them to drown.
_My enemy's enemy . . ._
"You want him to drown," Darsal said.
Pause. "You must make haste, daughter of men. Upon Johnis's death the amulet's power shall break. Retrieve the medallion and take such to the river. There you may cross but once."
Darsal bit her lip. "Why? What have you done to them?"
The maddening Leedhan simply could not answer quickly. "Johnis must drown that another might gain control. The son of Ramos refused me his whole heart; thus our ways have parted."
"You used him." Darsal scoffed. "You used him and left him for dead." But now her mind was catching up. Shaeda was not telling her to drown them out of the goodness of her heart. She was asking her because she was an albino.
Shaeda would use the very albino she wished to destroy to make sure Johnis was dead and her own plans furthered.
Whether or not Johnis returned to life as an albino destined to die was none of her concern.
Wench. Vampiress.
Darsal bristled. "How much time do I have?"
Shaeda answered in her own time. "The Dark Priest shall reach the summit at sunrise." She gave Darsal directions to Johnis's prison. "But a mile from Ba'al Bek lies one of the red lakes, a narrow oasis. Make haste and go there."
Darsal nodded. Shaeda helped her stand.
"But Marak . . ."
The Leedhan's brow creased. "Go now and be swift, daughter of men."
Shaeda took a step back, spread wide her arms, and threw her head skyward. She sang out a single note just barely audible. The sound permeated the ravine and shook the ground. Thunder clapped.
The pool bubbled. Fog swarmed around them. Shaeda bowed her head to her chest. And the mist was gone. As was Shaeda.
Darsal needed to leave. Her legs remained riveted, drawn instead to the Leedhan's presence. A rustling sound.
"Darsal?" The fluttering landed just beyond her. She blinked. All was dark save a pair of glowing green eyes illuminating white fur. Gabil.
The spell lifted. She shook her head, looked from Gabil to Marak's body lying by the pool. Darsal's jaw clenched as she fought the emotions welling up inside her.
The Roush hopped forward. "I don't imagine Elyon's through with you."
"How do I stop Sucrow, Gabil?" Her voice was flat. She rolled her shoulders back and knotted her fists.
"Sucrow? I thought perhaps you'd go after Johnis and Silvie."
"You told me to—"
"I told you nothing, daughter."
She tensed. "Can I trust her?"
"Trust her?" Gabil's eyes narrowed. "She is as determined as you to keep that accursed charm from the priest."
"And Marak?"
The Roush hesitated. "You've run out of time, child."
Elyon help them.
Darsal glanced up at the sky. "I need to move now."
"Yes, you do. You should already be gone. But a moment . . ." Gabil motioned her to him. She went down on one knee. The Roush touched his wing tips to her eyelids.
Darsal's vision shifted. She could see greens and reds and blues just as easily as the day. The colors were rich and dark, but she could see quite well. Her eyes widened.
Gabil nodded. Now that she could see him, he looked as if he'd been in a fight already. "There's your light." He smiled. "Remember, north."
Darsal hugged the Roush and jumped up. "Will I see you again?"
"Elyon knows. Now go!"
She ran.
twenty- nine
**J** ohnis hung helpless in his prison. The pit was deep and provided no comfort. He listened to Shataiki screaming into the night. Empty. Bitter ashes and stale vinegar. Johnis tried to vomit but had nothing in his stomach. In some ways he was glad Silvie was already dead.
Laughter.
_"Your little female was a nuisance, a pebble in my shoe,"_ Shaeda taunted. Her physical presence was gone, but she could still communicate over a great distance, and now she mocked him. Constantly.
_"The priest is but a pawn in this. Still, he has pleased me more_ _than you, my pet, who have shown weakness rather than strength."_
Sucrow. The conniving, shrewd, lying jackal! If he had the strength to stand, he would climb out, run back, and tear the priest limb from limb. As it was . . . he couldn't ever remember if he was dreaming or if he really was trapped in a pit awaiting death.
Let them come. Silvie was dead. Middle was gone.
Sucrow had won.
_"Do you truly wish to know truth, my pet?"_
"Leave me," he growled.
The entity laughed. More infuriating, he still felt the pull of her eyes, the tug of her siren song in his head. He would do anything for her, even now.
Her purplish-red haze came over him. Johnis saw Ba'al Bek and the priest, saw the Horde conquered and the Circle destroyed. He saw the Shataiki enslaved to Shaeda, who stood on the precipice with her fists raised, amulet high.
Icy, invisible fingers slithered up his spine.
A scuffle came from above, shouts and flesh striking flesh. "How quaint," Warryn's voice taunted the intruder.
"Scared, Cyclops?" a semifamiliar female voice snarled. Metal rang out, and Johnis listened to the pair fight. Clumps of dirt fell on Johnis's head. He looked down.
The skirmish ended. A body thumped hard against the earth. Someone sent it flying down the shaft. Johnis turned his head away.
Warryn's one eye gaped up at him. Blood poured out his head and torso.
_"As you shall be . . . "_
Moments later the rope around his wrists tugged tight. A soft grunt. Johnis was pulled upward. His back and legs scraped along the side of the pit. He bent his head forward to keep from banging it around.
He submitted to the dragging and felt the final jerk of the line as he went over the lip. Then he was on his back. His tormenter hoisted him over one shoulder, rotten stench overwhelming.
_Albino?_
More deep, husky laughter. _"Such is at my disposal, my pet . . ."_
He refused to look, refused to let the albino see his face. The stale smell of overripe fruit struck him full force. Johnis gagged. Warm, smooth fingers touched his bared shoulder. He recoiled.
A cloth bag went over his head. The albino secured it and slung him sideways over a horse. He was tied across the horse's back and left alone.
They broke into a gallop, two sets of maddening horses' hooves bent on rattling him to death.
SHAEDA KNELT OVER THE GENERAL A LITTLE LONGER, stroking his face with her half talons. All was not lost, not yet. The albino girl was so overwrought with passion that she could not see the life slowly seeping back into her precious general.
Yet Shaeda had seen the slight flush of life return to his cheek. Poor wretches, both of them. It was best if the albino didn't know her magic had succeeded.
Piteous albino, to fall so easily.
All of these children of clay fell readily into her arms. She smiled, amused at her own scheming. Her pets never did learn. Pity the last had to perish.
But Shaeda needed this one, this mighty general, just as wretched a mortal as the smooth-skinned worm who destroyed him. Ah, Marak. So strong, so broken. Such was piteous, to lose so mighty a son of man as this. She half smiled and licked her fingers.
Overhead the cauldron lingered, and Derias's screams intensified. Such was to his peril. Such his reward for the abduction of her mate. Such the price the amulet guardian must pay for more glorious designs, designs such as hers.
An even costlier price would the great usurper Teeleh pay for banishing her and the other Leedhan across the river.
Soon they would all feel her wrath. Her calculations were impeccable, from the ensorcelled captain Cassak to the enticement of the female Darsal.
Such was pleasing.
And yet the tingling in her spine reminded her she dared not linger. Soon enough she would glory; she would triumph. When she brought on Teeleh's demise, all would be as they ought. She would rule with her mate, and rule well.
She took a lingering look at the general. Once she took her pet and entered him, she would know all of his thoughts at all times.
Shaeda leaned across Marak's still form and kissed him full on the mouth. A hunger overcame her. She clung tight and tasted his skin. Her needlelike fangs split his lip, and his blood tinged her tongue.
Reluctantly she pulled away, tracing her half claw across his lips, smiling. "An excellent lover would you have made, my general . . ."
Another of Derias's roars.
A hint of fear threatened her. Shaeda shoved this emotion back. He could not harm her, not yet. Not as long as the amulet's power held.
She rose up on her knee, slid Marak's daggers back into their thigh sheaths. Another thing the girl, in her foolishness, had missed. Shaeda then arranged his cloak and stood.
"Fear not, Guardian Derias," she said, half-smiling. "Your demise comes, and from there the demise of your master and all your kind." Shaeda withdrew a badaii and ate it, taking pleasure from the sweet nectar. "Arise, my new pet, my mighty Chosen One . . ."
thirty
**J** ohnis waited in the silence broken only by the occasional whisper of a voice and the _bad-dum_ , _bad-dum_ , _bad-dum_ of pounding hooves. He tried not to let his imagination run away with him.
The nightmares came anyway, as surely as the rising and falling slopes and the horse's steady, never-ending gait. The horse squealed and reared up.
Shaeda's eyes haunted him, her scent, her skin . . . her kisses.
Invisible talons stroked through his hair. _"Our time together_ _was never more than a vapor, my pet . . ."_
_I don't understand. Shaeda . . ._
Someone screamed. The horse jerked back down, backed up quivering, readying for some great feat. Then it jumped—it seemed forever passed—and hit the other side of whatever obstacle it tried to clear, back leg catching the rim. Yellow, blue, and red stars sparked across his mind's eye.
Johnis cried out. The beast jerked, hopped, and fumbled forward. All grew still. Someone rushed over and checked the horse's leg. Another whisper. More rustling.
They were moving again, slower. The horse limped for a few minutes, then regained its confidence and strength. Its gait became steady, now slow enough that Johnis could feel its heaving, panting sides and hear its heart deep within its barrel torso. Foam oozed against Johnis's exposed skin. The beast was done. Its body quivered with fatigue, begging for rest.
Farther and farther from Shaeda, from his lovely, his entity, Johnis still felt the pain of separation, as though he were being torn in half by two powers. She'd used him, hadn't she?
And yet he wanted her. Needed her. _Shaeda, come. Come and_ _save me! Come, and together we will . . ._
She _tsk_ ed him like a child. _"No, my Johnisss, you shall indeed further_ _my mission. You have accomplished my desires and brought the_ _amulet to me. You have taken the Horde to the high place, taken control_ _of the Shataiki . . . These you have done at my bidding. And now,_ _now, my Chosen One, you must die. I have told you such, have I not?"_
_You said nothing of dying!_
_"Your sacrifice shall not be forgotten, my pet. Yet your heart was_ _never fully mine, therefore required I another, one stronger, one whose_ _heart beats as one with mine . . ."_
The stagnant breath of the desert gave way to cool, crisp air that smelled almost sweet. Not the sickly sweet smell of an albino, but a pleasant, spicy sweet he couldn't quite place. Like fruit trees or an intoxicatingly fragrant flower.
Crisp grass crushed beneath the horse's weary feet. A bird twittered, answered by what sounded like an owl. Soft wings and the faint sound of cicadas filled the silence.
_I do not wish to die! Shaeda, no, don't do this! I promise I will not_ _leave you!_
She chuckled. _"Oh, but you must, my Johnis. My general cannot_ _possess the amulet's power until the current possessor dies. And, thus,_ _you must drown."_
His skin crawled. Twigs and leaves crunched beneath the horse's feet. They passed through a shadow. Water lapped against a shore close by. A few toads croaked in warning.
Rough, strong hands untied him from the beast and hauled him down over powerful shoulders. Citrus. Albino and citrus.
_"I thought perhaps 'twas fitting you died at the hands of one of_ _your former comrades in arms. She is going to drown you, my pet, and_ _willingly. Her delusions are but misguided lies."_
He was placed on the ground. The chain at his wrists snapped in half.
_"What occurs when blood touches the water, my pet? Do you_ _know?"_ Shaeda's dark laughter filled his head, making him dizzy. _"Such is defiled. And you have defiled that which is sacred."_
Someone sat on him and hammered a stake into the earth, pinning his chain through a link. Whoever it was jumped over him and staked his other arm the same way. The same treatment was given to his ankles.
His captor left him.
"Shaeda," Johnis groaned, writhing in agony from the cold separation. "Shaeda, my entity, my love . . . I gave you everything. Shaeda, don't leave."
More hammering, but several feet away.
A soft voice spoke in soothing tones to someone who thrashed. The brief conflict ended to the satisfaction of the first voice.
_"Truly you are a fool, my pet, should you ever have entertained_ _the thought I would share power. Nay, little Chosen One, entities_ _do not share power. Yet I did enjoy your kisses and your embrace._ _Now comes my executioner, and she shall wish you to die. Fail me_ _not, my pet."_
Footsteps.
_"L_ _INGER_ _, G_ _ENERAL_ _. . ."_ A VOICE. A WOMAN. MARAK SHIFTED. A firm, slender hand pushed him back down. _"Yield . . . Fear_ _me not . . ."_
He couldn't breathe. Someone was on top of him, lips pressed against his, breathing life back into him. Marak sputtered. Turned sideways. She held him.
Citrus. He smelled citrus. Darsal? No, the crazy albino had tried to kill him.
A purple haze flooded his mind. Marak sank back into the dark dreams, hypnotized by a siren song he couldn't place. He was dying, dead. Maybe he would see Rona again . . .
Darkness.
_"Awaken . . . mighty warrior."_
A firm hand shook him awake. He reached for a knife. His eyes opened to mist, to a lithe woman with long, white-gold hair, who wore the fog as a robe. Her gown was green and bared her shoulders, scooped low. Her skin was translucent white and flawless, so pale he could see vibrant blue veins beneath. So perfect, so alluring . . .
His gaze met hers. She had one purple eye and one blue, both with thin, bloodred slivers. Marak's eyes widened. He started, but rose slowly, hypnotized by the all-consuming eyes that drank him like water. The knife slid from his fingers.
_"Peace, mighty general."_ Her musical voice drew him to her. No, she hadn't spoken, not yet, not out loud. Her thoughts came directly into his mind.
They were in a ravine less than a mile from Ba'al Bek, next to a small pool. All was barren wasteland, brambles, and briars. Nothing survived this far into the desert—not here.
Marak drew a breath.
_"Gaze upon me, O valiant one; think not of your darkened_ _troubles. Rather, listen to me, and know that I am she who aids_ _you . . ."_
The woman ran her fingers across his chest, up his neck, along his jaw. Her hand closed around the Circle pendant at his throat. For a moment she simply looked at it, a strange smile on her face.
Then she let it rest against his chest.
"Who are you?" Marak stiffened. His hand touched the fallen knife, but he made no attempt to use it. He eased the weapon back into its sheath.
She smiled and withdrew a silver bowl he hadn't seen a minute ago. _"My name is Shaeda, mighty general of Qurong. Such I am who_ _has brought you back from death's halls and to the realm of the living._ _Be at peace . . ."_
Josef's Leedhan. He never would have guessed such a strange creature could be so intoxicating.
_Focus, brother._ But the voice seemed weak, distant.
Shaeda's eyes seemed to grow larger, to swallow him up. They grew, and then he could see Sucrow on the mountain, preparing his sacrifice, preparing to use the amulet on the albinos. He could sense the Shataiki's fury, feel their rage and torment . . .
_"Indeed, General Marak of Southern, of Middle, I am the_ _Leedhan monarch of whom the Chosen One has spoken. Regrettably,_ _his sacrifice was a necessary one. And now, now it is you who are chosen_ _for appointed tasks . . . Drink, man of valor, for you are weak_ _from your trials and from thirst, from this woman who twice now has_ _sought your life."_
His throat was parched, wasn't it? And how did Shaeda know Darsal had tried to kill him? What else had she seen?
He narrowed his eyes. "What do you want?"
She seemed hurt and spoke out loud for the first time. "Mighty warrior, I have returned your life to you. Assuredly, my desire is for your welfare. Shall you spurn a maid who rescues you, or disbelieve what your eyes behold?"
Darsal had said something similar. So had Jordan, so long ago. Shataiki, Roush, Teeleh . . . Why not a Leedhan? She had been trying to help them wipe out the albinos, hadn't she?
This was Shaeda's plan they were unfolding.
"Taste and see, mighty general." Musical laughter flooded his mind. _"You see, such is not so difficult . . . Taste and see for yourself,_ _my handsome warrior king."_
He hesitated a moment longer, then accepted the water and drank. His head spun as the citrusy, spicy liquid flooded his mouth and burned down his throat. Greedily he drank to the bottom.
"What is that?" he asked.
Shaeda took back the bowl, which vanished. She smiled. Fog swirled around Marak's shoulders. She tickled his skin. "Such is eluweiss, made from herbs, teas, and the juice of the badaii. But drink is not all you require, magnificent one."
She then retrieved a purple fruit with translucent, almost glowing, skin. She took a small bite with needlelike teeth, then offered it to him.
He studied the fruit, heart racing.
"The priest has killed your commander and ensorcelled your captain," Shaeda said. Her voice was low, husky. She palmed the fruit. "He has crouched at the door of your victory, and his desire is for your blood."
Marak had partially extended his hand to take the fruit, but now he hesitated. Shaeda offered more than a mere fruit, more than food to sate his hunger.
"I offer you alliance," she said. "The Dark Priest has both the power of the amulet and the power of the Great One, whose name is Teeleh. I give you my own powers, my own craft. You shall have my mind, my eyes, and my strength coursing through your veins. Together we shall put an end to this one who would dare rise up against the lord Qurong and unseat his mighty general."
He stood slowly and took a step back. "You think me weak."
"This battle is not won by mortal strength, man of valor. You are strong and full of courage, and for this I come to you. Come, take the amulet from the priest and wield such against the earth's bane, this Circle. Then ride victorious to Qurong and be rewarded."
The gnawing in his stomach grew, along with the desire to destroy Sucrow. He heard Derias's howl. They were out of time.
Marak accepted the fruit and bit into the tender flesh. So sweet the taste, so forbidden . . . He held it there a moment, let the flavor burst over his tongue. His skin tingled; his head buzzed. His senses heightened, and Shaeda's power, her mind, her will, poured into him.
The smell of bats and humans, dust and Leedhan, assaulted his nostrils. The smell of rotten eggs mingled with the paste. He heard each individual roar, each flap of Shataiki wing, each nervous stamping of his warriors' horses. His clothes brushed against his flaking, morst-crusted skin.
He swallowed that one bite and felt it surge through him.
Shaeda's thoughts opened to him. He saw now how delicately she had orchestrated the entire scheme. Long had she considered such a plot, now coming to fruition. She had arranged Jordan's death; Johnis, Silvie, and Darsal separated . . . She'd left Johnis, who attempted to defy her, and now came to Marak, all with one purpose in mind.
Stop Sucrow and acquire the amulet from the guardian Derias.
_"He cannot be allowed to wield such himself,"_ Shaeda told him. _"We must retrieve the amulet, or else the son of Ramos's sacrifice is_ _for naught."_
Anything to pay back that priest. He drew a sharp breath and devoured the remainder of the fruit. The fog surrounded them. Shaeda stepped closer, her mesmerizing gaze fixed on him. She traced his cheek and slid into his embrace, smiled. Her needlelike fingers tickled his skin. The heady sensation set him aflame.
_"We have not time for the pleasantry of acquaintance, my pet."_
Shaeda kissed him full on the mouth, bit his lip. Her grip tightened around him—so much strength in so delicate a creature. She wanted him, and he wanted her.
_"My will is your will, my strength your strength,"_ she thought to him. _"Relinquish all to me, my mighty warrior-king."_
Resistance was not an option. Not that he wanted it. He could eat and drink of her and never want again. One purpose, one mind . . .
Marak surrendered his will.
_"Grant me your heart."_
Shaeda's full might poured into him. His skin turned translucent: shimmering white and purple seeped from his eyes. Now he could see in the dark, invigorated by her sight. Rich, dark hues tinged purple.
All was not lost. This was only the beginning . . .
Marak sped up the side of the rock face and was over the lip before he realized he had moved. The wind against his face was breathtaking, exhilarating. He rushed northward, deeper under the wings of the Shataiki toward the plateau. Shaeda's mind kept him riveted solely on getting the amulet from Sucrow before he could use it, taking all power away from the priest . . .
_Ba'al Bek . . . Ba'al Bek . . ._
He had to reach Ba'al Bek, and he had to do it now. What he wouldn't give for a horse—although what horse could possibly run this fast?
_Make haste, make haste . . ._
His mind struggled to catch up. Shaeda was running at a maddening pace. She was driving him like cattle. Despite the shadows, Marak could see plainly everything before him. He could even make out individual bats amid the swarm.
_"See and understand, General . . . Be at peace; go to Ba'al Bek and_ _win back the amulet. Come with me, General. Fly to the high place_ _. . . Make haste . . ."_
"Why?" he asked.
_"We shall overcome."_
Shaeda spurred him on. They came down the next rise and into the canyon, then across open wilderness. There he saw a hundred warriors—Cassak's men—circled around the base of a high-rising plateau that fanned wide like a yawning mouth. The jagged piece of rock was easily over a mile wide. Their torches made a ring of fire darkened by heavy, curling black smoke. Oil and incense and burning wood filled the air.
The entity grew anxious beneath the Shataiki swarm. Cold fear trickled through Marak's body. Furious at her own weakness, Shaeda pushed him on. They had to get the amulet from Sucrow, and now.
No, not from Sucrow. They needed Josef to die first for the guardian to retake the amulet. Then Marak would take the medallion from the beast's claw and have favor. He drew a heavy breath.
Atop the plateau was another ring of torches, and from above he could hear Sucrow, savoring this moment and taking pause to worship his god before making his final invocation and calling down the Shataiki guardian queen on the albinos.
"High priest of the Great One am I, and upon my shoulders falls so excellent a task that I might be found worthy to speak words before the Throne and uplift my voice on high. O mighty Teeleh, hear my prayer and the invocation I speak this hour!"
Those words still made Marak's skin crawl, even though he must have heard Sucrow's daily prayers for years. Jordan's voice nagged at him.
_"Tread lightly, brother . . ."_
He pressed on. The men heard him coming and turned to look. Of course, they couldn't see him. Not from where he stood.
But the Shataiki could . . .
"Move!" Shaeda screamed through him. She lifted Marak's hand in clawlike fashion. The men fell away. "Stand aside!"
"Let the spirit of the Great One fall on me, for I have found favor in his hand!" Sucrow's voice continued to bellow across the desert. "Call down blessing and boon upon your servants; from the hands of Teeleh most almighty, the great one whom we serve, let goodness and favor fall. Rain upon us, O master of all!"
Marak plunged ahead, shouting for the warriors to get out of his way. He scaled the side of the plateau, Sucrow's opening rite growing louder with every footstep. A lightning storm broke out overhead.
He reached the top and stood behind a semicircle of serpent warriors in time to see a ball of light consume the Dark Priest. He was surrounded by two half-moons of serpent warriors, staff held high, and for a moment he glowed, his skin, hair, and clothing radiant.
Shaeda drove him into a crouch, bidding him linger still. The priest stood in the center of a craggy, rugged hole easily a mile wide. There in his black and purple robes, tight fists gripping the white staff of power, Sucrow truly did look every inch Teeleh's high priest and not a superstitious old wizard.
The opening orations continued—how long was the priest going to go on? Couldn't he just kill the bloody Circle and be done with them?
But that would work in their favor, wouldn't it?
In the back of his mind, a prickling sensation raised his neck hairs, and Jordan's faint voice drew his hand to his throat, touching the pendant. But Shaeda's siren song silenced his brother, directed his attention back to the priest.
"And may the accursed albinos fall, and with them whoever dares attempt to thwart us. Let their flesh shrivel and fall aside and their intestines rot and burst forth . . ."
The serpent warriors' spear butts struck the rock in unison and began pulsing like war drums.
Marak lunged for the priest, but Shaeda held him back. _"Patience, my general, patience . . ."_
But why? The priest had to die. The priest had to die before the ceremony ended and the invocation rang out. If they waited much longer, they would be too late.
_"The Chosen One has not yet died. Yet, when he does, you shall_ _attend the priest and claim the amulet for us."_
_You will kill him to further your own purposes?_ Marak felt a tingling in his spine. If she would turn her back on Josef, could she not do the same to him?
Shaeda's soothing hand caressed his skin. _"Have no fear, my pet._ _Such was necessary and regrettable. You, however, are required to live_ _and rule with me . . ."_
Sucrow lowered his staff. "Bring the sacrifice and the blood." He took a silver dagger and readied himself while the serpent warriors prepared an offering on the rock, spilling the blood of the Chosen One and of Qurong over grain and wine and the innards of a jackal.
The priest began to speak over those present. "A boon to him who hears my words, who this day comes to the mountain to glory in the work of the Great One, our lord and master Teeleh. Glorious and valiant is he who overcomes such evils and this day becomes participant in the destruction of his master's enemies! For long have we waged war against the diseased among us, those who would spill out our blood as drink offerings. Against such evil we have long toiled, and now, now, my fellows, my brethren in arms and in faith, comes the fruition of our labors . . ."
The Chosen One . . . The Chosen One was Josef . . . Johnis, onetime friend of Darsal, so long ago overdrawn and destroyed. Shaeda's mind opened, and he saw her with Johnis and Silvie in the desert, feasting with them as they succumbed to her power.
Shaeda's power, the mind-bending combination of speed, strength, sensation, and foresight that made her impossible to resist and so intimately desirable.
Johnis had to die, and once he was dead, they would take the amulet from Sucrow. But hadn't Sucrow killed him already?
No, not yet. Not yet, not yet, but why . . . ?
Not Sucrow, Derias. He hated Derias.
Shaeda's presence slithered around his throat and clamped down tight. Marak ached to be at the priest's throat, but the Leedhan's talons drove hard into his back and shoulders, pinning him in place.
Above him the Shataiki hosts roiled, lusty for blood. They screeched above the thunder, beady red eyes glinting in the blinding flashes of lightning.
Derias, queen guardian of the amulet, swooped low over their heads, his massive leathery wings so close the tip nigh brushed Marak's ear. Shaeda tensed. Her fear trickled down his spine as melting ice. They both sucked a breath.
Marak's hand slid to his knife. Shaeda's intoxicating presence reprimanded him; his mind's eye saw the Leedhan's shape—her long, willowy body; her silky, white-gold hair; her perfect skin; and above all, her eyes.
And he also saw Sucrow in all his glory, bathed in a purple haze. Marak licked his lips as the startled priest resumed his ceremony.
A Throater placed a bloodstained knife on the stone before Sucrow. A row of seven Eramites, shackled hand and foot, was dragged before them. Forced to their knees, the rebel half-breeds were stripped, their flesh already torn and bloodied.
A sacrifice, as part of the ceremony leading up to the command to attack the albinos. The fool.
The Shataiki quivered and bristled with anticipation, all snapping their fangs and hissing at the victims. Sucrow stroked the amulet around his neck.
Marak drew his knife and started to rise. Shaeda forced him back down, shoved his blade back into its sheath. Sucrow was so close . . .
Not yet.
First the Chosen One had to die. Marak licked his lips. Then the end would come.
thirty- one
**J** ohnis tensed and squeezed his eyes shut. Someone knelt beside him—a horrible-smelling beast with a seductive voice. She untied the canvas sack around his head, then ripped it off.
_"Are you prepared to die, my pet?"_ Shaeda's voice still taunted him.
He blinked, wrinkling his face while his eyes adjusted. Darkness lingered, with two million Shataiki overhead. Thin shafts of light flickered between black leather wings.
The same rough hand pushed his head and shoulders up a few inches and pressed a water bottle to his lips. Johnis turned his head, determined to resist.
"Johnis, don't fight me anymore."
Soft chuckling in his head. _"No, my little Chosen One, no longer_ _shall you resist. You must lay down your life for me and die."_
He squinted and blinked a few more times, then turned his head to look at the woman beside him. His eyes widened, then narrowed. The voice.
Johnis growled. "Traitor."
"No, Johnis. Look at me. Open your eyes, my friend."
He obeyed.
"Darsal?" His throat was dry and parched. "D-Darsal . . . ?"
Her brown eyes were bright, brow creased with worry. Her tanned, smooth skin shone in the dusky light.
_"Die, Johnis. You must die."_
_No, Shaeda, don't do this._ Part of him still wanted his entity, his Leedhan. Her power, her strength . . .
Her will dug into him. Johnis squirmed. She really intended to kill him. And Darsal was helping.
Darsal smiled. "Yes, Johnis. Here, drink. I know you're thirsty.
Look, Silvie's already had some."
Silvie.
His head cleared, heart ached.
_You said she was dead!_
_"She shall be . . . just as you shall be, my Johnisss. She shall have_ _part in your death. In this she shall serve me, she who would not give_ _me your heart."_
Darsal scooted aside so Johnis could see the second figure, much smaller, slimmer, and paler, also staked to the ground about four feet away. Just beyond arm's reach.
Silvie had turned her head to watch them.
"S-Silvie?" Johnis licked his lips, but his tongue was too dry to wet them. "I thought . . . They told me . . ."
Now he saw her tearstained cheeks. "I saw everything, Johnis. Everything. They made me watch."
Darsal pressed her water bottle to his mouth again. This time he accepted and drank greedily. Then he let his chin strike his chest. Darsal laid him back down. He tugged the chains.
"Where are . . . ?"
"An oasis in the northwest desert, a mile south of the high place. A particular Leedhan told me its existence."
"Shaeda." Johnis struggled, trying to clear his head as much as free himself. His blood grew chilly. The Leedhan was serious. She and Darsal and Silvie were all going to kill him. "So you believe me now."
"I believed you before. And I see how intoxicating she can be." Darsal's smile faded a little, mournful.
"What do you want with us?" He pulled at the chain. "They're going to set off the attack. The Shataiki, they're—"
"They've reached Ba'al Bek. It won't be long now." Darsal brushed mud and grime off his face and washed it with her head-scarf. Pain shone on her face.
"They'll find you too."
"Yes. They will . . . Sucrow meant to kill you, Johnis. If I wanted to betray you, I would have left you with him. Is that not right?"
She had a point.
"Shaeda told me how to find you, how to bring you here. And she told me there was only one way to keep Sucrow from using the amulet. I saw Gabil. He said she was telling the truth."
A cold feeling crept up Johnis's legs, then up to his midsection.
Yes, he knew that too. Whoever took the amulet from the Shataiki guardian . . .
"You die."
Darsal offered him more water, then squeezed fruit on his wounds. The burning made him flinch.
"What are you—?"
"The only thing I can do, Johnis. It's a healing fruit. There's a whole grove here. Don't struggle. Now, listen. I'm trying to help you. So I need you to listen, and listen fast."
"Help us? We're staked to the ground in the middle of—"
"Just listen. Do you know why there is an oasis in the northwest desert, Johnis? Look to your right. Just look. What do you see?"
He turned his head and strained to see, knowing there was a body of water behind him.
A lake. A moderate-sized lake surrounded by trees with leaves as wide as Johnis's head, and long vines drooping down. Heavy mist lingered in the air, dissipating fast in the light of the rising orange-gold sun.
A red lake. The crazy albino slave had taken them to a red lake.
"By the Maker . . . you're going to drown us."
"Don't panic, Johnis. I haven't the time to calm you down. But listen to me. I've thought about this." Darsal spoke quickly. "Johnis, Shaeda used you."
Johnis winced and tried to scratch an itch he couldn't reach. The grass made it worse. He twitched, desperate to make it stop. Shaeda chuckled in his head, voice low and intoxicating.
_"My foolish little pet, heed my voice once more . . ."_
Cold and darkness swarmed over him. Shaeda needed him free, free to kill Sucrow, free to take back the amulet and use it for his own designs. He needed her powers. Needed . . .
_"No, my pet . . . die . . . Even your Elyon wishes such . . ."_
"Let us go, and stop this nonsense. Sucrow—We have to get to Sucrow."
Darsal found the spot on his side and scratched it, scowling as she understood Johnis wasn't talking to her. When she withdrew her hand, it was covered with flakes of skin.
"Yes, we do." She brushed her fingers off and gave him more water. "Which is why you have to drown. Think about it, Johnis. Shaeda is half-Shataiki. She wanted you to kill the Circle _and_ the Horde. She used you. Her power is a drug. And the amulet's power lasts four days or until the one who took the amulet dies."
The cold water cleared his head.
Darsal helped Silvie drink. She rubbed an itch on Silvie's arm for her.
"We can stop Sucrow. But first you have to drown. Both of you."
His mind reeled, desperate to keep up. Darsal was talking fast, and she couldn't seem to stop moving. Johnis scowled.
"Drown."
MARAK WATCHED THE DARK PRIEST FORCE EACH OF THE seven Eramites to their knees with Derias raging overhead. He struggled with Shaeda, tried reasoning with her. _Take it, take it_ _now! Before Josef and his lover come back! Before Sucrow takes the_ _amulet's power for himself!_
Shaeda wrapped herself around him like a robe and drew him into her seductive embrace. Her eyes drank him in, showed him what would befall. _"A little longer, my pet, a little longer. We must_ _wait until the other dies. Only then, only then . . ."_
Understanding flowed from her mind into his, her answer to his barely conjured question. They could not take the amulet from the priest. Marak felt a cold chill at the next revelation: they would have to take it from the Shataiki guardian. From Derias.
His name brought bile into Shaeda's mouth.
She cut off the flow of thought and directed him once more to the crazed priest, drunk on his own asserted victory. Sucrow had not even noticed Marak here in the darkness, covered by whatever spell Shaeda cast over him.
From the shadows came a figure Marak hadn't noticed earlier but recognized now as Cassak, sword in hand.
Cassak was with the priest? _Focus._ Marak gripped his knife. Shaeda spilled over him. So his favored captain thought him a traitor and sought ambition over friendship. Marak's jaw tensed. How long had they been in league together?
Everything started to make sense now. Sucrow had enchanted him. Cassak had changed sides.
_"My general, unfortunately his eagerness to attend your family was_ _not for your benefit. He used them, used your pain, for his own glory._ _Such was he who determined they would never be released. Qurong_ _would have relented . . . for he as well lost a child to the albinos."_
He felt an invisible knife tear into his gut. Cassak had him convinced he'd had no choice. But why had Cassak lied? He'd killed them on principle. He'd taken Jordan and Rona and Grandfather out into the desert and slaughtered them like . . .
The memory came back to him, stark and vivid as the day he'd gone with Cassak to do it. Thus far Marak had managed to silence it with Darsal, but now . . .
He drew his knife and started after the priest and his treacherous captain.
Shaeda's talons dragged him back. He snarled. _Let me go!_
Not yet, she insisted, not yet. Marak knew what was coming now, now that Sucrow took blood and sereken and poisons from deep within the desert's bowels and mixed them in a stone bowl, chanting.
Shaeda distracted him, setting his mind to Martyn's journal, so similar to this—minus the key component. Martyn had been thorough. From various hints and implications—either overlooked or ignored in favor of war—Marak had been able to glean what poisons would react with an albino's skin, what they would be susceptible to that a non-albino would not.
He'd read it in Martyn's journal, set his men to work making three copies of notes regarding the Desecration of the albinos. And he had watched as his family was eaten alive: their skin eroded away and stripped, their flesh boiled off their bones, their brittle gray skeletons turned to ash.
Nothing could spare them now.
_Pay attention!_
Shaeda tightened her grip on him. Marak watched as Cassak executed the Eramites. His stomach curdled. For some reason his mind drifted to his last execution. Jordan's screaming slammed into his head.
No. He never was, nor would he ever be, like his brother.
He was general to Qurong, trained by Martyn. And soon he would be greater than his lord.
Again the Leedhan cut off his thoughts, bound his emotions to hers. The albinos would die by Shataiki swarm, their bodies torn to shreds, leaving them to rot on the desert floor.
At last the final Eramite thumped lifeless to the ground.
_"Have no fear, general mine, for the end shall not be the same for_ _you. You will be great among men, for you shall take such and wield_ _against all who oppose you. The time grows nigh . . ."_
His attention centered on the priest, now surrounded by seven corpses along with his men. Sucrow took his knife and slit his own arm and mingled his blood into the mix of sacrificial elements.
"Blood of the Chosen One," Sucrow began. "Blood of the First and of the Ruler of men. Blood of the enemy, twicefold to die. Blood of the righteous, whose souls upward fly. Wine of the gods, elixir divine, grain of the earth, bound by mortal swine. Elements of air and water and fire; elements of earth, the living immortal mire."
Marak's hair rose, tickling his neck. His back and shoulders tensed. Once more his hand went for his knife. This was it. He had to act now. Already Derias was swooping, circling, lost in reverie and the anticipation of freedom.
_"Not yet!"_ Shaeda screamed in his head. The sound echoed, deafening him. He missed the rest of Sucrow's opening, his final invocation. Shataiki wings thrummed. The end was in sight. Even Shaeda coiled up in anticipation, ready to spring at the last possible second. Sucrow continued his dark blessing.
The wind picked up, and the flames from the torches swelled, burning so hot and bright that no one could look at them. Sucrow shouted over the din, his voice escalating. Below them the earth began to rumble. A few Throaters lost their balance. Shaeda held Marak fast.
Sucrow's staff was high overhead, gripped between both rotting hands, knuckles white. His face shone in self-made glory, as though he'd seen a vision of Teeleh himself. Marak's heart thrummed.
The spears began to pound against the earth. Below a shout went up, a chant from the warriors led by one of the commanders. "Death to the albinos! Slay them all! Find them from the four corners of the earth and cut them down! Let the sons of Tanis fall down dead, let them all be torn to shreds!"
Marak fought for breath. Was that him or Shaeda?
She cut off her thoughts and dug hard into his back with invisible claws. His nostrils flared. Time was growing short. So close, so close . . . Would Johnis die in time, or would she miss her final stroke?
_Kill them. Kill them all._
Marak rushed forward and cut down two Throaters before Shaeda could stop him. He let out a scream that Shaeda cut short. The other Throaters turned, shocked to see him alive. He felt Shaeda dominating him, knew Sucrow was deliberately ignoring him, saw Cassak go for his sword . . .
_"Patience!"_
Sucrow's final rite began. Still Shaeda held Marak back, her hypnotic gaze his only restraint. Derias circled once and landed to the side. Cassak and the Throaters shrank back from the sight. The Shataiki queen stood waiting, wings unfurled, talons curled.
"And now, O guardian queen, blessed servant of the Great One, hear our emboldened request. For blood this day shall be spilled. A thousand years from now this day shall be remembered as the albinos' final hour, when the Shataiki came unleashed, and in their blessed fury rid us of this bane! Come, come to me, and ready yourselves; come to the high priest of man and beast, and let forth your blood-driven fangs!"
Marak and Shaeda both bristled.
_Come on! Die already!_
Shaeda's lip curled. Marak's curled. They both gave a low snarl. Marak could feel the end coming, the rush.
_How will we know Johnis is dead?_
Shaeda growled, frustrated with his questions. _"Such will not_ _be questionable. Take heed and behold!"_ Her grip tightened, as if checking the reins of a restless warhorse.
Their clothes flapped around their bodies; the great Shataiki throng hissed and snapped, whipped into a hurricane around them, their beating wings a deafening roar, adding to the thunder and lightning.
Sucrow chanted louder. Marak's pulse spiked. The priest put the amulet on the end of his staff and raised it high above his head. The roar above and below swelled.
And still Shaeda waited.
thirty- two
**S** he really is trying to kill us." Silvie groaned.
"No, no, listen to me! So little time, so much to—" Darsal pulled at her hair and gave an exasperated cry. She drew a ragged breath and faced them, circling both of them. "Okay, you tried to bathe, didn't you?"
Lake water scalding his flesh, burning it off. He tried not to think about that. Besides, these waters were red, not green.
"It's been polluted," Silvie said. "It doesn't work. If you put us in there, we'll die."
"In the green lakes you had to bathe once a day, and the scabbing disease always came back if you didn't, right?"
"Darsal, don't make me go in the water." Johnis stared at her.
She couldn't be serious. She couldn't really mean to drown them. She couldn't really be conspiring with Shaeda to kill him.
"You've been with the Horde too long."
The pained look crossed her face again. "Maybe I have. It doesn't matter anymore."
"The gen—"
"Don't talk to me about the general! Don't talk to me about Marak."
Shaeda clamped down on him again, the moment of clarity lost. Her hypnotic eyes he could drown in . . . He had to die, for Shaeda. Could he do that? Did he want to?
He should leave the Leedhan to wallow in her own failure. Silvie was right—she was a self-absorbed seductress, and she'd used him.
No, that wasn't true. Shaeda loved him, wanted him.
And he wanted her.
"Now listen to me," Darsal said. "What if Elyon decided to make it so we didn't have to keep bathing? What if he decided to change something? What if the water changed so that instead of just coating our skins with water, we drown ourselves in it? Do you see?"
"I don't. Why would Elyon change the rules? And I am not touching that water. Nor am I going to die."
Shaeda . . .
"But you will, Johnis. The Shataiki can't be trusted. As soon as Sucrow uses them to kill the Guard, Derias will turn on him and kill the Horde too. You remember watching them feed off the bodies after battle."
Johnis was having difficulty breathing. He felt numb. Darsal was making sense. He just couldn't fathom the thought of getting in that water and inhaling it until the bubbles stopped.
"You're trying to kill us."
"Maybe." Darsal dropped to her knees between them. "Or maybe I think the only way for you to stop Sucrow is to drown. I drowned, Johnis. Do I look dead?"
Johnis didn't answer.
"Listen to me, Johnis. If nothing else, what's your heart telling you? Here."
His heart. Johnis groaned. He didn't know anymore. He wanted Shaeda, needed her. Hated her. Elyon help him, he wanted his entity back. The same one now determined to kill him at an albino's hand.
Fitting.
"This is about the heart." Darsal planted her index finger hard against the center of his chest. It hurt horribly. "This is about Elyon loving a Scab. He sent me to the Horde so I would love a Scab and love you." Pause. "Sucrow will kill you. And I might drown you." Her voice caught.
Johnis wondered what had happened with Marak.
"Johnis, Middle is dying. Sucrow is killing the Circle. Killing our families. Killing Thomas. Killing every human in this world.
Decide."
"I'll do it." Silvie startled him. She pulled on her restraints. "For Elyon's sake, let me up! I'll do what you want. Just let me get up!"
Darsal hurried to comply. Silvie rubbed her wrists.
"Sil—"
"I would rather drown myself than let Sucrow near me!"
And Silvie dove in.
Shaeda laughed at a joke only she seemed to grasp.
"Silvie!" Johnis fought his chains. "Don't let her die, Darsal! Don't let her—"
"Trust me, Johnis. Trust Elyon." Darsal stood by the water's edge. Her breath was shallow, and she didn't move.
"I don't want to trust Elyon. I want Silvie to live! Let me up!"
"If I let you up, will you drown?"
"No! I'm going to jump in there and pull Silvie—"
"That lake's bigger and deeper than you think, Johnis. It's no pool, and you won't find Silvie. You'll find something, but it won't be Silvie. But you'll see her when you come out, I think."
Something. Something in the water.
Shaeda's eyes . . . beckoning him as she'd done before . . .
"You think!" Johnis started to weep. "Darsal, don't kill her. Don't kill Silvie. I'm sorry for everything. Just don't kill her."
"I'm not killing her, Johnis." Darsal released him from the stakes. He was on his feet before she grabbed him by the collar.
_"Oh yes, my pet, go to your little female . . . and drown with her."_
"Now, listen to me. You jump in there, you won't see Silvie. You have to trust Elyon or you _will drown_ down there. You understand?"
He stared down into the water that still rippled from Silvie's plunge. The seconds ticked by. The impulse grew. Shaeda's will wrenched at his throat.
She was winning. Again. He couldn't find his heart when all three of them were ripping it apart.
Sweat collected on his forehead and down his neck and spine. Johnis tried to move forward, but Darsal had a vise grip on him and wouldn't relent. Seconds turned to minutes. Silvie hadn't yet surfaced. She was not going to die.
"All right, all right. You win."
Darsal stared at him, searching his eyes for a trick. He pushed her hand away and pulled off his shirt.
"You win."
thirty- three
**J** ohnis plunged into the cold water after Silvie and swam deep beneath the surface, looking for her. The red water was clear, but he saw nothing. He swam in a large circle, hoping for a glimpse.
Was she already dead? Would her body sink or float if she was?
Deeper still.
More chuckling. Shaeda's laugh ran his blood cold. _"Perhaps_ _. . ."_ His Leedhan's haunting melody trickled through. _"Perhaps she_ _is deceased, as you shall be. My foolish, troubled pet, so arrogant, so_ _weak . . . If you must know the truth, then yes . . . I have planned_ _such from the beginning, and you have all played your parts so well."_
_You will not kill Silvie,_ he insisted within. That only amused Shaeda further.
If Silvie was down here, he would find her, even if he had to drag her up from the bottom. The farther beneath the surface he went, the warmer the water became. Johnis swam faster, listening for any sign of struggle, any gasping for air indicating she was caught.
_"Shall I tell you what I will do, my pet? I have indeed taken_ _another for my own, a new lover . . . one whose heart is fully devoted_ _to my will, unlike you . . . you who always found me second to your_ _troublesome female . . ."_
The minutes ticked by. He was out of air in the bowels of the lake. He turned for the surface, but couldn't find his direction. He continued to swim, certain he was being pulled down, not up. And he couldn't find Silvie. Maybe the same suction had forced her under as well.
His lungs burned. Johnis kicked and thrashed, resisting the impulse to inhale. No, no! He would not die!
_"Trust me, Johnis. Trust me."_
He froze. That voice was not Shaeda. It was masculine, and didn't match that of the Leedhan at all.
And yet her laughter now came on the new voice's heels. _"Such_ _will not be long now . . ."_ Shaeda dragged him down, forcing him with the pull of her mesmerizing gaze, the lethal, bottomless eyes.
The surface was nowhere to be found. Yellow and red overtook his vision. He knew he was dying, thrashing in the lake like a fish caught in a net. The more he fought, the worse it became.
_"Johnis . . ."_ came the new voice again.
The outline of a hand appeared, a large, calloused palm with worn and bleeding fingers, cracked from years of hard work. The hand extended toward him.
Instinctively he reached. Their hands touched. _"Breathe,_ _Johnis. You need to breathe,"_ the new voice commanded.
A sharp jerk pulled him down. Johnis gasped. Water poured into his lungs. He curled into a ball and started to sputter. Not like this. Anything but this. More water flooded his lungs.
_"Breathe, Johnis!"_ the male voice shouted in his head. _"Trust_ _in me!"_
The faster the stranger pulled him, the more water gushed into his body. His mouth opened wide against his will. Johnis pulled back.
_"And now, my pet,"_ Shaeda taunted. _"Your life is forfeit._ _Farewell, son of Ramos. Now, die."_
_"Breathe!"_ the new voice commanded once more.
And he did.
Wide-eyed and terrified, with absolutely no way out and this hand pulling him deep, deep into the heart of the lake, Johnis stopped fighting and drew in a greedy mouthful of water.
The pain completely racked him. Johnis screamed and allowed himself to go limp, allowed this person to carry him where he willed. Everything went dark, and all he knew was the rushing water all around him.
His body was dead, he knew. And he knew whose hand he held. Through the darkness he went, boyish laughter all around.
_Elyon?_
The giggle swelled.
_"Hello, Johnis. Swim with me."_
Blackness gave way to green light, and green to red and gold. Elyon's laughter turned to screaming, and Johnis's whole body almost exploded at the sound of it, coming apart at the seams.
And then it ended, and they swam.
Johnis continued to breathe, taking in water in the same manner as a fish. They swam along the bottom and skimmed the mud with their fingers. Johnis quivered at the rush.
_"There are still a few things for you to do, Johnis. Are you ready?"_
They started for the surface.
Johnis felt the water cool, and in moments his head broke through. He flung droplets from his hair and swam to the ledge, then hoisted himself over, still shaking.
He vomited water.
A fair-skinned, slender body tackled him to the ground and rolled along the grass with him, arms locked around his neck.
"Johnis!" Silvie kissed him over and over.
Johnis returned the embrace and the kiss, savoring his reunion with his beloved. Then he stood, brushing himself off. He stared at his hands. His smooth, tanned hands. Even his injuries from the torture were gone.
"I thought you were . . . I thought . . ."
Silvie draped her arms around him and kissed his temple. Johnis looked up and saw Darsal watching them.
"Stubborn little scrapper," Darsal said.
The humor faded quickly. With one mind they glanced up at the shadow above.
Johnis glanced at Darsal. "How much time do we have?"
"Not much. Sucrow has already gone up. It won't be long. Now's a perfect time to put that brain of yours to use."
He ground his teeth and fell quiet for a second.
"I'm sorry for—"
"All's forgiven between us, scrapper. But we need to move."
Johnis studied the two women and looked once more at the brewing storm cloud of bats. Something else came to mind. In those last seconds Shaeda had said something about the general, about Marak.
He had to know. "Marak . . . ?"
"Don't ask me about Marak." Darsal looked away from him.
Like Billos. She didn't like to talk about it. And as far as Johnis knew, she still blamed herself and always would. A knot formed.
"Oh, Darsal. You loved him."
Silence. It was worse than the expected reaction.
"That's how I knew I couldn't force you to drown."
His eyes snapped open. But he said nothing. Instead, he settled his nerves and focused on the task. So Shaeda had lied. Marak was dead. It was only a taunt blowing in the wind.
"What of the amulet?" Silvie took the second horse. Johnis swung up behind her.
Darsal mounted. "Its power is broken."
MARAK STRUGGLED AGAINST SHAEDA, ANXIOUS TO KILL Sucrow and take the amulet, to kill the albinos and be done with it. She held him fast, invisible talons cutting into his marrow. He watched the priest raise staff and amulet high over his head, and a crack of lightning sounded behind him. From within the ring of fire, bats readied to fly, and Sucrow began to speak.
"And now, guardian of the Shataiki and all your brood, prepare to take flight! May your wrath take full vent upon our greatest enemy! Let all behold and be terror-struck, and all the—"
A sharp gale of wind snuffed out the torches, and a loud thunderclap shook the ground. The force of the gale was deafening. Sucrow, the Throaters, Cassak, and Marak were thrown hard off their feet. Marak landed on his shoulder and winced.
All went perfectly still. A tingling sensation took hold of him. For a full minute there was no sound, not even the rustling of wings.
They stood quietly, gaping. Marak saw the amulet lying on the ground, inches from Sucrow's hand. The priest rose and held it up, shaken but undeterred.
Marak's skin tingled. Purple haze washed over him. Shaeda's siren song turned to musical laughter. Her strength began to pour into him. His mind sharpened, homed in on the priest.
"And now," Sucrow said, his voice echoing in the strange quiet. "Now, go ye forth; hunt down and feast upon every last albino that has breath, from the eldest among them to the smallest squalling babe! And—"
A black blur swooped down over Sucrow's head with a deafening roar. Derias's talons slashed through the air and tore the amulet from the priest. The sound of snapping bone split the air. Sucrow screamed in pain, grabbing his arm, blood spilling from where the priest's hand used to be.
The Shataiki swooped again and threw the Dark Priest across the depression, then circled around, landing a short distance away with the amulet, Sucrow's bloody, ring-studded hand still attached, dangling from his claw.
Derias started to laugh, a low, dark sound. His wings opened wide. The monstrous Shataiki turned to Sucrow, who hadn't quite recovered from his fall. His large talon opened to finish off the priest.
Shaeda's restraining hand released Marak. Her power burst into him. Marak felt his skin and eyes fill with her unnatural light. He unslung his sword. Derias turned. Shaeda slashed off part of the Shataiki's claw and swept the medallion into Marak's hand before it could fall.
Derias bellowed, shaking the rocks. His huge wings pounded the air. Marak palmed the amulet and looked up. Once more the bats came alive, awaiting their new master. Sucrow shouted indignations and tied off his wrist. Marak vaguely heard the priest's healing incantation.
Shaeda's mind opened. She drove down on him. _"Now, my pet!_ _Hesitate not!"_
Marak caught up. He bristled. Everything now hinged upon him, not the priest. But how . . . ?
_"Johnis is dead; concern yourself not with him! All the power now_ _lies with you, for you have taken the amulet from the Shataiki_ _guardian. Use such!"_
Killing the albinos meant killing Darsal. He couldn't—
"Well, what are you waiting for?" The priest snarled. He stood, still bloody. All eyes were on Marak, expecting him to give the incantation and command.
But . . .
Shaeda grilled him. Fog, purple haze, and searing anguish drove down on him, demanding he give in to such. One sentence and it would all be over. One sentence and it would be done.
Marak grimaced, buckling under the weight of her might. Teeleh's breath, she was strong. Her mesmerizing gaze took hold. Once the albinos were dead, he could kill the priest and take full control of the Horde, of the Shataiki.
Forever.
_"Yield to me, my mighty one. Yield . . . Speak this command, and_ _all shall be well; I wish not to harm you. But the incantation you_ _must give . . ."_
"No," he breathed, barely standing. He glimpsed Sucrow staggering for him. The bats had formed a ring around Marak so that no one could harm him. The cloud started to boil. Thunder struck the sky.
And in that same moment he understood the depths of Shaeda's cunning. She had missed no detail. A chill wound around him.
She had persuaded Josef to kill himself. Suicide.
"I can't kill my own—"
Her claws ripped into his back. Marak bellowed in pain, his voice ricocheting over the desert. _I will not fail!_
Marak ground his teeth. "I cannot—"
But he could, couldn't he? Destroy them all, purge this world of the beasts, these so-called men who destroyed everything he loved. Destroy the albinos with their filthy, diseased skin and their tyrant god. Destroy the priest and treacherous Cassak, those who plotted against and killed his family. Those who sought his ruin would perish with the very enemy they detested.
He could almost hear Jordan in his head, almost hear his brother telling him he deserved death, that justice demanded anyone who set themselves against the master should die.
This pleased Shaeda. Only Jordan would never want this.
Marak straightened and raised the amulet overhead before he realized what he was doing. One mind, one heart, one will, one strength.
"You have a new master now," he said slowly, savoring the moment. The priest would die first, of that he was certain. Marak sneered. "And now, hear and obey, dark servants of the Great One, of him who rules the brilliant side of the river. Listen and heed me, my puppets, my pets, for you in all your glory are about to face the ultimate defeat. Indeed . . . upon the destruction of these mortals of clay you shall fall from favor, and I shall rise—"
"Marak!"
thirty- four
**A** male voice shouted over the throng, a rider rushing up the side of the plateau. No, three riders. Marak whipped his head around. He recognized Josef's voice but wouldn't have recognized his face if he hadn't called out. No, not Josef, the Scab, but Darsal's old friend . . . Johnis, she had called him. He had tanned, smooth albino skin and light brown hair and eyes. With one hand he held the reins; with the other he had a sword at chest level.
Arya charged behind him. Only this was Silvie—Marak's mind was still making the adjustment—with short, blonde hair and icy-blue eyes, two knives at each thigh and another ready in her hand.
And bringing up the rear—
His heart lodged in his throat. Darsal. Dear Teeleh, Darsal.
She brought her horse to a halt and for a moment just stared. Johnis and Silvie kept coming.
_"Finish such and all is complete!"_
"I thought you said they were dead!" he bellowed at her.
_"They drowned."_
Marak barely had time for that to sink in. The Leedhan's claws tore into his spine. A tingling sensation went up. Shaeda continued to grind against him. " _Recite the incantation; make haste and_ _unleash these Shataiki upon the foe."_
"Marak, don't use the amulet!" Johnis shouted, reaching him. He circled on his mount, staying just out of reach. "You don't want to kill Darsal!"
His lip curled into a snarl.
The three albinos rushed across the high place. Darsal was catching up to Johnis, her face looking as stunned as he felt. Darsal had come back. She hadn't left. She hadn't—
_"She attempted to slay you, my pet, my Chosen One. You are_ _alive because I breathed life into your body and revived a lifeless_ _corpse."_
But the look on her face . . .
No. She'd left him for dead. He remembered the water filling his lungs, the searing pain as Darsal held him down . . .
Marak's grip tightened on the amulet.
"How are you alive?" Sucrow growled. A Throater had bandaged his arm. He went for his staff. "Get them!"
"You can't touch him!" Johnis snapped at the priest. To Marak, "The more you rely on her power, the more control she has! Do you want to be her puppet forever?"
Marak bristled. "I am no one's puppet," he warned.
_"He lies. Come now, brother, will you still not see your own illness?"_
Realization hit. Shaeda had watched Darsal drown him.
"Ride with us." Silvie's blonde hair whipped against her face as she pulled her horse around. The nervous mount reared. She yanked the reins and steadied the animal, twirled her dagger.
"Look at yourself," Johnis argued. "Your skin turns colors, your eyes glow, and you aren't following your heart."
Follow his heart. He never had answered his own question: would his heart have killed his family, or died trying to save them?
A gentle nagging tugged at the back corner of his mind.
Shaeda tightened her grip.
Marak's eyes narrowed. Of course they would try to save their own skins. Shaeda curled his lip into a sneer and gave a low, dark growl.
"Marak." Darsal spoke for the first time. Immediately his mind refocused on her. She rode a sweat-slicked warhorse, armed and streaked with dirt and scratches.
"You—" He tensed. Shaeda clamped down, twisting his face into a scowl, forcing a dark haze over his eyes. The amulet. He had to use the amulet. "I should kill you all right here."
"You don't mean that," Darsal fired back. "You love me, Marak. And you always will."
Sharp talons drove into his skull, demanding his submission. Shaeda's song overwhelmed him. He had more reason to use it than to not. Marak ground his teeth.
"It's Shaeda," Johnis said, his voice stern. "Marak, it's Shaeda, not you."
"Joh—" Darsal started to speak, but Johnis raised his hand and cut her off.
He circled Marak again. "You've been deceived far longer than I, Marak. I know well how difficult she is to resist—and it's worse for you because you've been deceived longer. But she can't touch your heart, Marak, and she never will."
Shaeda's presence flooded his mind.
"Yes, I drowned!" Johnis snapped. "You cannot control Shaeda! She will use you and leave you for dead, just like she did me. We're alive because of Darsal, because Elyon sent her and we found him in the water, you understand?"
Marak could see nothing but the Leedhan's penetrating gaze, riddled purple-red, and the amulet in his palm.
"Marak, my love." Darsal jumped down in front of him. She reached out and touched Jordan's Circle pendant, still around his neck. He'd forgotten it. His mind centered on the sound of Darsal's voice, on her face, her eyes.
"Your mind is deceived, but you have my love," she said.
_What does your heart tell you . . . ?_
There was a commotion from behind, but Johnis and Silvie quickly put it down. Derias let out another roar, jerking against his invisible leash. Shaeda used the distraction to settle her mind and will into his.
Darsal ignored them, instead pressing her hand flat against Marak's chest. A dizzying sensation shot through him. Shaeda screamed in his head, but Darsal had him riveted.
"This is what I meant, Marak. This is what I meant." She kept eye contact. "Your mind is telling you to follow the Leedhan, to destroy everyone, to give in. But where is your heart, my general? I love you."
Shaeda snarled in his head. She would kill this albino harlot first. The Leedhan slammed full-force into him, sucker punching.
Marak's fist curled. He bent and fell away from Darsal, amulet still safe in his fist. He jerked back around, knife in hand.
Darsal swung onto her horse. "Come with me to the river, Marak!" She threw out her hand. "Come with me!"
His heart was not Shaeda's. His mind cleared, heart racing. The Throaters suddenly moved, swords drawn. Johnis shouted, back to back with Silvie. They pushed the Throaters back.
He could not kill Darsal.
"Get them!" Sucrow screeched.
They would die up here. Marak grabbed Darsal's hand and swung up behind her. Darsal kicked the heaving beast and sped across the top of the plateau after Johnis and Silvie, knocking aside the priest.
They jumped over the ledge and raced down the side of the plateau, past the mass of warriors led by Cassak. At the sound of attacking Throaters, the battlecry went up. Cassak screamed from above. Marak glanced back and saw his captain jump astride his horse and barrel after them.
Darsal threw Marak the reins and sprang from the saddle onto another mount, knocking off its rider. She slapped leather against flesh and raced on. "Come on, Marak, ride with me!"
_"Loyalty, integrity, and honor,"_ Shaeda hounded. _"Are these not_ _your own words?"_
Darsal snatched his wrist.
Shaeda—Marak—grabbed at Darsal's throat with claw-like hands.
Johnis caught Marak by the tunic and yanked his face close. "We _are_ completing the mission! Our mission is to put a stop to this, to keep the Circle alive. I swear on the books, I'm getting the amulet to the river and away from Sucrow—with or without your help! You are a general, Marak—a general under Qurong, the greatest of them all, in league with Martyn! Now, stop fighting the Leedhan with your mind and start thinking with your heart!"
Then Johnis was gone, Silvie and Darsal following.
Marak bellowed at the horse and spurred him after the albinos. Shaeda screamed in his head, the pull of her voice irresistible. He started to slow.
Darsal circled back. "To the river!"
He put the amulet around his neck next to Jordan's pendant and followed.
thirty- five
**T** eeleh guided Sucrow's feet for three days as they crossed into the northeast and through a series of plateaus and mesas. The terrain was changing again, turning to quicksand and becoming a bold, fiery red.
Throaters and warriors sped over the rise and down the sharp ravine. Sucrow stood in his saddle with his staff raised high over his head. _Bloody fools they are, thinking they could lose anyone with_ _two million Shataiki in their wake!_ He felt Teeleh's power funnel through the staff and into him. A shaft of lightning broke out.
His senses sharpened. He could smell the Leedhan, smell the humans over the edge of the black, ashen ravine. The wind picked up. His skin prickled with excitement.
Cassak kept pace, his torch high. The wretched fire blazed between them, turned the ground the color of blood. Cassak signaled the men. The warriors split and fanned out into a broad semicircle. Sucrow rode ahead with his Throaters. Gradually they surrounded Marak and his albino pets, bent on trapping them.
The chase took them northeast, well beyond anything they'd charted. The ravine grew increasingly desolate, naught but a vacant wasteland. Here only the dead seemed to thrive—even cacti perished beneath the brazen sun swallowed by a Shataiki storm.
The air grew stagnant, repulsive. Sulfur filled their nostrils, mingled with blood and mire. Rotting flesh curled Sucrow's nose. The horses squealed and reared, balking at the stink of death. Sucrow urged the beasts on.
"Hold fast," he bellowed at the men.
Nervous horseflesh quivered beneath him. Sucrow licked his lips. All was silent and dark. The animals were desperate to stop, to turn back, stumbling with fatigue and soaking in their own foam. The ravaged beasts wouldn't survive the trip back.
Good. That meant no one could tuck tail and run.
Tens and twenties of men surrounded the ravine. Sucrow took the point position and rushed through the narrow valley. Hard-packed dirt thumped beneath their mounts' hooves. At this point not even the vultures circled.
They reached the plateau in time to see the blonde albino dart over it. They were gaining now. It was only a matter of time.
He sneered. Marak and the albinos would be dead within the hour.
thirty- six
**T** he throng of bats seethed above. Hot, red sun vanished behind two million Shataiki. The bright torches from Sucrow's posse behind them looked like so many fallen stars beneath the canopy of black bodies and beady, red eyes. Darsal felt the horses pound against the hard-packed earth, already weary from their previous run, northbound over rugged, untouched wilderness Shaeda knew well.
All the while Marak had struggled with Shaeda, with the amulet. They fought and reasoned with him endlessly during the three-day chase. Barely avoided Cassak's three-pronged attack by using directions Gabil gave them to navigate a series of tunnels in a sprawling cave.
Darsal's night vision gave guidance through the tunnels and back out under the stark cloud that was the Shataiki swarm. Derias swooped down and circled Marak the moment he stepped out of the cave. There the Shataiki spilled into a canyon fed by a black stream and overrun with briars and tumbleweed. Sucrow and Cassak came from opposite sides of the gap. Darsal led them in a sprint out of a winding, snakelike canyon into billowy dunes.
On they fled, Sucrow and his Throaters at their heels. All three albinos and Marak were starting to slump in the saddle.
The horses were exhausted and not going to make it much longer. Darsal felt her mount try to slow despite her urging. The poor beast had run from Middle to the Teardrop Canyon; back from the Teardrop to Ba'al Bek, which was well beyond Middle; and now to Elyon knows where.
"They've topped the ledge," Silvie announced. "Faster!"
Darsal's muscles momentarily went rigid. The long shadow of Shataiki drifted over their heads. All was dark and bleak, pain and death. The Shataiki queen, Derias, was up there somewhere. A chill snaked around Darsal like a noose and pulled tight.
A hot rain started to fall. Darsal smelled brimstone and ash. Death ruled this place.
Marak shook on the back of the horse in front of her, torn between two wills. His skin carried a glossy sheen and peeled away easily in the desert heat. His face was set, and he said very little. Every muscle in his body curled into tight knots.
"I gave you my love, Marak," she said as she rode alongside him, for probably the hundredth time since Ba'al Bek. "I give it to you still. And so does Elyon."
They headed through another canyon, trudging through sand that was gradually turning from red to deep purple. Crossing beneath another overhang, they left the canyon and rode and rode on. The river had to be close, in fact if she stilled her breathing she thought she might hear the sound of water even now.
Darsal glanced over her shoulder and saw the dust rising from the army behind. It all came down to this, she thought. They could go no faster and Sucrow was gaining. The end would come now. Dear Elyon, deliver us to safety. Bring us the river!
Then the river was there, looming suddenly as they raced around a bend. A red river. Darsal gazed at the other side and caught her breath.
There appeared to be no sun across the river. A dark, forboding landscape that looked like it might be hell itself! They'd come for this? Dear Elyon, help!
She spun back. Any minute Sucrow would catch them. They were trapped between the river and the Scabs.
"Hurry!" Johnis slid off his mount and dropped to the ground. His stiff legs collapsed, and he struggled back to his feet and brushed himself off.
Marak halted alongside and jumped down with Darsal. Silvie followed suit. The foursome stumbled forward and stopped at the water's edge.
The river was about fifty feet wide where they approached but widened both up- and downstream of them, stretching as far as the eye could see. The water was crimson from height to depth, bank to bank, length to length.
"Well . . ." Johnis stared at the water. "This is it. We have to cross."
Marak quivered, staring across the river. "Impossible. I'd rather fight here and die."
Dark, barren wasteland. A place for the dead. The mighty river was nothing more than a craggy red line that separated them from sulfur springs and the stink of rotten fish. Not even the carrion birds came this way. It was the back side of hell.
Sucrow was almost to them. All eyes went to Marak.
Darsal stepped closer to Marak. "Marak, please, for the love of Elyon . . ."
Marak stared at the water as if it were a thing from which to flee, as though to merely touch it might kill him.
"You have to drown," Johnis said. "It's the only way across and the only way to stop Sucrow."
Darsal tried to put her arms around him, but he withdrew. _I_ _can't lose you, Marak._ "I can't do this again."
Johnis shed his cloak. He was going, of course. Going, and no one could stop him. Or maybe he was hoping Marak would jump in after him.
"We're out of time for arguing."
Marak wasn't answering. He stood trembling, grasping the medallion in his fist. His eyes were purple, his skin transluscent white, so thin Darsal could see his blue veins.
The Shataiki cloud had reached them above and formed a semicircle on this side of the river, spread all the way around the humans, boxing them in. She could see Derias now, crossing back and forth above them. The whole hive writhed in fury. Not one of them flew across the river, even the queen.
The bats were probably the only ones with any energy left in this chase.
Sucrow's Throaters pounded around the bend with Marak's warriors, now led by Cassak. They fanned out on either side and came to a stomping halt on worn mounts. Teeleh's priest trotted up the center, gloating in his victory already. Everything grew quiet as Sucrow savored his moment. He had them, could kill them at will.
Johnis, Darsal, and Silvie traded looks and stood facing the Throaters, backs to the river.
"Marak," Darsal said, loud.
Marak's expression changed. His face became dark, angry, full of something she'd seen only after the execution of his family.
"Remain, Priest," he growled. His eyes had gone fully purple, his voice husky and surreal. Shaeda. His eyes narrowed. He palmed the amulet.
A mirage of Shaeda appeared, white-gold hair streaming down. Mist surrounded her like a robe. "Toy not," she warned. The Throaters and warriors stepped back. She raised her hands over her head and let out the highest note Darsal had ever heard. The river surged, the ground quaked, and the horses spooked.
Darsal drew her sword and stepped to her general's right. Sucrow extended his remaining hand. "So that's how you want it." A starry-eyed serpent slithered around his neck, unnoticed by the priest. Darsal's eyes widened. She glanced at the others. Johnis and Silvie both saw.
The Shataiki queen suddenly swooped overhead. Derias came in low, straight for Shaeda. His talons slashed Shaeda's face. She remained silent.
Wounds opened on Marak's face, mimicking Shaeda's. She was still inside him, merely projecting an apparition. A flaming orb appeared in Sucrow's palm, and he hurled it at Marak. It slammed to the ground at his feet and turned to ash.
Shaeda chuckled. "Amusing," she taunted, gently wiping blood off her cheek. "The Great One sends his servant to deal with me."
"Marak," Darsal whispered. The Throaters tightened their circle on them, each armed with a curved silver sword.
"Contend, then, Dark Priest of the Usurper," Shaeda hissed.
Sucrow growled at her, snatching up his staff. His eyes turned dark and cold as he began his chant.
A low hum began, a thrumming sound that made the earth vibrate beneath their feet. Sucrow's sneer grew as the thrumming gave way to a chant in a tongue Darsal had never heard. She gripped her sword. _Come what may_.
In return, Shaeda began to sing, a beautiful, mournful siren's song that echoed through the air. It rose up, higher than the human ear could detect.
Sucrow countered with a low, snarling note. The sky grew darker, and the Shataiki above began to shriek and writhe in flight. A thick bolt of lightning split the air. The river began to boil.
Darsal's eyes darted back and forth from Sucrow invoking some sorcery to Marak trembling on the bank. She couldn't attack Shaeda for fear of hurting Marak. The pain in her head rang.
Sucrow's chant grew louder. To hear the priest actually pray was worse than hearing any of his other utterances. A death knell. His voice grated against her skin, raising the hairs on her body.
Marak snarled like a man possessed and flung himself at Shaeda.
HE KNEW IT WAS FOOLISH, BUT MARAK COULDN'T STAND himself a moment longer. He lunged, felt her presence bear down like a heavy rock inside his chest, and fell to his knees. Her laughter cackled through the air.
"Fear not, my pet. It will soon end."
He swayed, barely staying conscious. Everything crashed back on him, his family's deaths, Darsal, Cassak's betrayal . . .
They were all going to die here, by Shaeda's hand or by Sucrow's.
The water. The water could save them.
Sucrow laughed. "And what's in the heart of a man who tortured his own brother to death? Give it to me, Marak. You'll have total amnesty, and all will be over. We'll forget this . . . this lunacy in the desert."
The apparition of Shaeda stood in front of Marak, blocking him from the priest. Marak sucked a breath, set his jaw, and stood.
MAN AND BEAST WAITED ON THE BANKS, ANXIOUS TO SEE what the general would do. Darsal felt her body weaken.
Marak held the amulet in his fist and kissed it. For Elyon's sake, what was he waiting for? She groaned. Shaeda melted back into the general.
Marak was going to die.
"Servants of Teeleh," the general said softly. There was a quality about his voice that silenced the sky. The Shataiki grew still, and the color drained from Sucrow's face.
"Guardian of evil in this world," Marak continued, his voice stronger. Resolve clipped each word. "I hold in my hand the power of command and loyalty and servitude."
Darsal's heart sank. The general had made his choice. He chose Deception over Romance, Teeleh over Elyon. Knowing all that had happened, he spurned her still.
Oh, Elyon, how she had failed . . .
"And now, Derias, queen of Teeleh, listen to these words I say," Marak cried. "You . . . are under . . . my command! For what is done cannot be undone, that which is bent cannot be made straight. And after today the world will change."
It was true, Marak still had the amulet.
The general fell quiet a moment. He looked up, and his eyes met Sucrow's. "Kill the Dark Priest and his Throaters."
The air went still, perfectly silent.
Then Marak was moving. He grabbed Darsal in his arms, flung the amulet into the current, and dove straight off the sharp bank, plunging both of them into the depths of the river. The red water swallowed them both.
thirty- seven
**T** he water was so frigid it knocked the breath out of Marak.
The Leedhan in him searched frantically for the medallion, propelling him downward, hand outstretched. He lost hold of Darsal in Shaeda's haste.
But not even she could bring it back. The amulet was gone, forever lost to the river. He'd lost everything.
Darsal swept past him and caught his wrist. She dove for the bottom, pulling him with her.
_"No!"_ Shaeda screamed, tearing at his mind. _"No, no, no!"_
Darsal could not have had time to take a breath of air as he had. But she was pulling him deeper.
He shuddered, swam deeper. This was madness, all of it. Deeper, deeper he swam, unnerved by the sudden quiet.
_"Perish, then! But know this: you can never return to the land of_ _the purebloods . . ."_
Shaeda let go. She vanished.
Darsal gave a tug, drawing him into the deeper, warmer water. Marak pulled back, lurching for the surface, desperate to breathe. He was trying to help her, not drown!
She was . . . breathing the water. Her chest rose and fell rhythmically. Demonstrating, she took a lusty gulp and swallowed. Her face showed no trace of longing, uncertainty, or desperation.
_"Hello, Marak,"_ whispered a soft voice. His eyes flew open. Who was that?
The seconds ticked by. Darsal treaded water, trying to stay with him, begging with her eyes. Her face grew uneven, rippling. Dark. The brown eyes widened. Darsal tugged at him.
His mind reeled. _Elyon?_
Darsal squeezed his hand. Marak felt his world going dark. Knew he was about to drown one way or another.
He steeled himself and sucked in a huge, greedy breath of water. His ribs and lungs and throat screeched in jagged, raw pain. Still, Marak continued.
All fell still and quiet. Blackness . . .
And Marak of Southern drowned.
But no sooner had the darkness swallowed him whole than a light blossomed in his mind, and he gasped with new life. His heart began to beat.
And his body shook with a new pleasure.
Life. Pure, living, breathing life.
_"Swim with me,"_ the voice whispered _._
JOHNIS WATCHED IT ALL HAPPEN IN STUNNED SILENCE: First Marak's trembling opposition to Shaeda deep inside his mind, which Johnis knew all too well. Then Marak's order to Derias while the guardian queen was still under his control. Then Marak and Darsal diving into the river. The cold splash drove everything silent. Johnis couldn't breathe. For half a second no one moved.
A shadow fell across him. Johnis looked up. Derias whooshed over his head and landed to his left, so close Johnis could have reached out and touched his half-furled wing. A low chuckle rumbled from deep inside the Shataiki queen's chest. A chill swept through him.
Sucrow had his eyes firmly planted on the river, but he now turned and saw what they all saw. He went white with fear.
Derias licked his thin, pink lips. The priest stepped backward and caught his heel, but maintained his balance. He was ready to flee. But before he could even turn, Derias snarled. Then he was on Sucrow, ripping into his throat and tearing the priest limb from limb. Blood covered the Shataiki and pooled on the ground. Derias ripped Sucrow's back with his claws. Bones and cartilage snapped like twigs.
And it wasn't only Derias who had this thirst for blood. The Shataiki swarm suddenly descended on the Throaters, invigorated by their release.
"Silvie!" Johnis grabbed Silvie's hand and scrambled for the river.
Together they dove over the side of the steep bank into the cold, red water.
thirty- eight
**D** arsal and Marak swam through the river, relishing the water as it rushed through their battered bodies. Marak's skin had become smooth and dark, healed by the power of Elyon's water. At last they reached the far bank and pulled themselves, dripping, from the water. For a moment neither was able to speak.
Everything had changed. The darkness was gone. It wasn't hell, it wasn't hell at all. Beyond the bank, trees filled a magical-looking forest, surrounded by color.
Then Darsal broke the silence, spitting up water. "You see?" Cough, chuckle. "What did I tell you? The Great Romance, as they say."
Marak stared at the forest like a boy struck by the wonder of a magic trick. He slowly faced her and his eyes softened, and he stepped closer. "I do see. I certainly do see," he said and kissed her gently on her lips. "The Great Romance."
The battle sounds raged behind them, but Darsal did not care. She understood more clearly now, her own love for Marak really was symbolic of the Great Romance. Of Elyon's love for them all.
Freed of any lingering restraint, she threw her arms around him, and suddenly they were falling into the shallows with a mighty splash. Laughing, they clambered to their feet and ran from the water onto the bank. Marak's black skin was clean and smooth, gleaming in the strange light that reflected off the water still clinging to him. Purplish-blue sand covered them.
The screams from the far side grew, and they turned to face the battle. Together they watched, breathless as the Shataiki queen tore the Dark Priest Sucrow to shreds and devoured him, licking his blood.
Johnis and Silvie . . . no sign. Did the Shataiki get them?
Cassak cut loose a shout across the river. "Run!"
An angry, dark cloud of Shataiki attacked the Horde who thundered back toward the relative safety of the valleys behind. Derias, covered in blood, roared.
Johnis and Silvie suddenly broke the surface of the water not ten feet from Darsal and Marak and splashed up onto the bank. "Thank Elyon . . ."
The battle across the river moved into the hills and vanished from sight. But the fate of most could not be in doubt. The distant shrieks slowly faded.
The four stood dripping, looking at each other like dumbfounded but quite happy children.
"Now what?" Silvie finally asked, glancing across the river. "We can't go back, can we?"
Marak gazed at the bloody carnage across the river. "Not now. Even if we could, not now."
"You will never return," a husky voice said from behind. As one they spun. Shaeda stood, watching them, her purple and blue eyes narrowed. She wore heavy mist as a robe. Blood dripped from Derias's claw mark. She was lucky not to have lost her whole head.
Darsal stood frozen, unable to break away from that siren's gaze. At first she wondered why the Leedhan didn't just tear into them and kill them. But then she knew why. The creature faced Elyon's power in them now. She couldn't climb into any of their minds unwelcomed, not as long as they had Elyon's water in them.
"For now, my pets, you prevail," Shaeda said. "For now." Then she turned, glided into the trees, and was gone.
CROSSING THE RIVER HAD OPENED THEIR EYES. FOR THE first time Darsal, Marak, Johnis, and Silvie took a long look at their new home. From the opposite shore everything had looked lifeless and evil.
But now a bright blue sun warmed them. The rich smell of citrus flooded Darsal's nostrils. No longer muddled with Horde scent, she could smell pine and ash, luna flowers and fruit. And other scents she couldn't name.
She stared at the wood into which Shaeda had disappeared. Rich blue grass and blue-black wood covered the hillside. Strange purple, pear-shaped fruits so translucent they almost glowed, dangled from a tree with broad, pale blue leaves. A thousand new smells and sights caught their senses. An insect made a whirring sound like a cicada, but not quite. Hundreds of small bugs flickered wisps of light. Green fireflies? No, they were shaped more like pixies, no bigger than Darsal's palm from head to toe. Nothing less than amazing in every way.
"Now what?" Silvie asked again.
Darsal turned back to the group and settled her gaze on Johnis. "So . . . let me get this straight. Shaeda takes advantage of your weakened state to control you. She gets you to retrieve the amulet. But she knew you would die and lose power over the amulet. She'd planned to enter Marak all along, as soon as you died."
"She couldn't have known for certain I would drown."
Darsal fell quiet. "She saw me try to drown Marak. She knew I wouldn't stop."
Her general squeezed her shoulder. They fell quiet a minute. From deep within the wood came a high voice singing, a siren's song of sorts.
"The world of the half-breeds," Johnis mused.
"Badaii," Silvie said, glancing at Johnis. He didn't respond.
"Badaii?"
"The fruit," Silvie explained.
Darsal scanned the edge of the blue forest. A cool wind tickled her skin.
"It's what Shaeda gave us," Johnis said finally.
Darsal searched their faces. "So what was her real purpose?"
"Shaeda wanted to take over Teeleh's half of the world," Johnis told her. "She's the eldest of all Leedhan—it's been eighteen years since Shataiki first mated with Horde to create the race of half-breeds. Teeleh kicked them out because they were half-human and he was jealous. Now she's back to exact her revenge."
"She needed a human to help her do it." Silvie's expression darkened a minute.
"She failed," Marak said stiffly.
"So be it," Johnis said. A strange look came over him, as if he were considering something new and grave. "So how did you two . . . ?"
Marak stiffened, but shook his head and threaded his fingers through Darsal's. She traced Jordan's pendant at Marak's throat. "I was captured and thrown into the dungeon, where I met Marak's brother, Jordan, an albino. He helped me escape and told me I had to drown, explained it all to me. When I came back for him, he was already gone. And Marak came in. Elyon told me to love the Horde. 'Return to the Horde and love them, Darsal. For me. For Johnis.' So I did. I asked Marak to make me his slave. Later he released me." Darsal glanced up at Marak.
"So Jordan was . . ."
"Jordan is with Elyon," Darsal said softly. Marak looked away.
"Oh."
For a moment there was nothing more to say on the matter. Johnis withdrew his single book of history and studied it. "We lost the other six," he said, stroking the soggy leather. "I kept it so that all seven couldn't be used to unlock the rules of history. With any luck, the other six will remain hidden until we can figure out how to get them back, but at least we have the one."
"Good." Darsal thought a minute. "Gabil said the books weren't meant for us. We were only meant to find them."
They all eyed her.
Darsal composed her thoughts carefully, trying to grasp the meaning that nibbled at her mind. "I just mean Elyon has different paths for all of us."
Johnis continued to study the book. "I'd really like to have seen Thomas again. He's safe, for now anyway. That's what counts." Pause. "You're right. We each have our own battles. Elyon didn't lead us to this side of the river by accident."
Johnis tucked the book back into his waistband. He faced the forest, eyes brightening with adventure. The old Johnis was back. "So . . ."
They stared at the magical blue forest with him. "So," Silvie replied.
"You ready to go?"
"What about Shaeda? The other Leedhan?"
A bird sang out from the trees. Music played deep within the forest, a sweet, light melody. Darsal glanced up. The forest really was gorgeous, a whole world of unexplored, untouched, and untamed territory ripe for the taking.
"We're protected by Elyon," Marak said, stepping forward. "I've never felt so full of power in my life." He stopped and faced them. "What's a few Leedhan now?"
Johnis grinned. "So, the end of one adventure . . ."
"And the beginning of a new one," Darsal said, winking at Marak. He returned it.
"The Lost Books are still lost, but we are now found," Johnis said. "I think that was the whole point, don't you?"
"To be found by Elyon," Silvie said.
As if on cue, the distant sound of a child's laughter whispered through the trees. Or was it just a bird?
"So then . . ." Johnis looked at each of them. "Now that Elyon's found us, let's see what he has in mind."
"Yes. Let's see," Silvie said. She put her hand in Johnis's. Darsal took Marak's, and together all four walked into the blue forest.
TED DEKKER is the _New_ _York Times_ best-selling author of more than twenty novels. He is known for stories that combine adrenaline-laced plots with incredible confrontations between good and evil. He lives in Texas with his wife and children.
_Lunatic_ and _Elyon_ , co-written with Ted Dekker, are Kaci Hill's first novels. Between substitute teaching and grading and editing papers, she is a moderator for The Circle, Ted's internet forum.
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{
"redpajama_set_name": "RedPajamaBook"
}
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Self-contained Breathing Apparatus With Nanocylinders
16,000 breathing apparatus with graphene nanotube-enhanced cylinders adopted by firefighter services globally.
Self-contained breathing apparatus with nanocylinders show wide adoption by fire services in the Middle East, Europe, and Southeast Asia.
Equipped with a lighter cylinder, firefighters benefit from reduced fatigue, increased agility, and a longer duration of air supply if using a twinning option.
Ultralight weight and non-limited life performance of fully composite cylinders become possible thanks to their enhancement with graphene nanotubes.
Fire and emergency services work in extreme environments, where the weight of equipment is critical. Dräger, an international leader in manufacturing medical and safety technology products, has commercialized a firefighting breathing apparatus with the world's lightest type 4 composite cylinders, enhanced with graphene nanotubes to minimize weight. Fire services in Saudi Arabia, Turkey, the UK, Germany, Indonesia, Qatar, and many other countries have already recognized the efficiency of the innovative breathing system.
"Reduced weight and a non-limited life performance are the key features of the developed compressed air breathing cylinders. The combination of lightweight sturdy cylinder material, which was achieved with the use of OCSiAl's graphene nanotubes, with impact-resistant caps ensures the high durability and solid robustness of nanocylinders. They are 75% lighter than steel cylinders and 30% lighter than aluminum ones," said Piotr Saferna, R&D leader of Techplast, an innovative company which developed the nanocylinders.
In 2021, Dräger received exclusive rights to use these nanocylinders in its self-contained breathing apparatus. "Thanks to a shell weight of only 2.8 kg and 6.8 l of air, the Dräger NANO Type 4 reduces fatigue and increases firefighter agility. Since 2021, we have provided fire service companies in more than twenty countries worldwide with self-contained breathing apparatus equipped with nanocylinders fully compliant with EN12245:2009," said Mike George, Product Manager for PM Emergency and Rescue Services, Draeger Safety UK Ltd.
Now airport and industrial fire brigades, marine firefighters, and mine rescue teams have the opportunity to increase safety via a longer duration of air consumption and air supply if using a twinning option.
Headquartered in Luxembourg, OCSiAl is the world's largest manufacturer of graphene nanotubes, also known as single wall carbon nanotubes. It employs more than 450 people worldwide in locations including the United States, Europe, and Asia.
Websites: ocsial.com, tuball.com
Dräger is an international leader in the fields of medical and safety technology. Its products protect, support, and save lives. Founded in 1889, Dräger generated revenues of around € 3.3 billion in 2021. The Dräger Group is currently present in over 190 countries and has more than 15,000 employees worldwide.
Website: draeger.com
Techplast was founded in 2002 and based in Poland. It focusses on developing and production of composite cylinders with reduced weight and higher safety and durability. Techplast cooperates with many companies on the European and worldwide market.
Website: safercylinders.net
The post Self-contained Breathing Apparatus With Nanocylinders appeared first on Industry Today.
Click-And-Mortar: How Citizens Bank is Balancing Digital and In-Person Banking
SPOTLIGHT ON SMALL BUSINESS: El Valle es Grande in Sherwood
businesegoal May 5, 2022
Hilton To Retain, Expand Virginia Global Headquarters
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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import com.twilio.Twilio;
import com.twilio.rest.taskrouter.v1.workspace.Worker;
public class Example {
private static final String ACCOUNT_SID = System.getenv("TWILIO_ACCOUNT_SID");
private static final String AUTH_TOKEN = System.getenv("TWILIO_AUTH_TOKEN");
private static final String WORKSPACE_SID = "WSXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";
private static final String WORKER_SID = "WKXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX";
public static void main(String[] args) {
Twilio.init(ACCOUNT_SID, AUTH_TOKEN);
Worker worker = Worker
.updater(WORKSPACE_SID, WORKER_SID)
.setAttributes("{\"type\":\"support\"}")
.update();
System.out.println(worker.getAttributes());
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,088
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{
"redpajama_set_name": "RedPajamaC4"
}
| 9,035
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{% extends "base.html" %}
{% block title %}Contact MyFLsite{% endblock %}
{% block content %}
<h1>Contact us</h1>
<p> Thank you for your message </p>
{% endblock %}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,065
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Find list of Indian Railway trains between stations on Cleartrip. Also, check out the train schedule, timings, routes, number & originating, passing & ending station. Mail/Express/Superfast Train Names with Details. Train Number, Train Name, Train Source Stn, Source Dep. Time, Train Destination Stn, Dest. Arr. Time. Train Schedule. Please enter few characters of Train Name OR few digits of Train Number. e.g. To get the train schedule for Himachal Express i.e. Train No.
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List of All Mail/Express Trains in Indian Railways (Page 1 of 73) Number, Train Name, Starting Station, Terminating Station. · LTT SWV SPL. Want to Know the Train Info in Detail? Native Planet Provides you train list that helps you find trains Names,Train between each stations, train number & railway . Indian railway is popularly known as Lifeline of India. However, understanding the train name and number of Indian Railway has always been a bit complicated . Finding a list of Indian Railway trains running between two stations is easier with this search tool. You may search for trains by using either it's number or any. Train. Table. No. station station. Name. No. T. AG Train Number Index. / Balaghat. Jabalpur. Satpura. / Mumbai CST. Madgaon.
25 Jul Schedule For Rajdhani express. Train Number, Train Name, Source Stn, Source Dep. Time, Train Destination Stn, Dest. Arr. Time, Dep Days. On December 20, , IR switched to a system of 5-digit numbers that are Interestingly, the East Indian Railway decided to name trains towards its base. Spot Your Train through Live Running Train Status of IRCTC Train. Get Real Time In column 1, add the name of the train or number of the train. 4. In column 2. Get here train between two stations by just entering departure and arrival station name or code. Find here full information like Train Number, Name, Train Route.
10 May "Where is my Train" is a unique train app that gets live train status and up-to-date schedules from Indian Railways offline without needing. In accordance with a Indian Ministry of Railways decision, Indian Railways switched from its The first digit of the train number indicates the type of train. Train Enquiry, Route, Time Table, Seats Aavailablity, Running Status, Fare. Step 1: Put the train name or train number in the search box. Step 2: Click on ' Find. jerrydononeal.com Provides Train Running Related and Real-Time Status Queries for all Wanting to go via train, don't know train number or train name or prepares.
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{
"redpajama_set_name": "RedPajamaC4"
}
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The Finish
Also by Mark Bowden
Doctor Dealer
Bringing the Heat
Black Hawk Down
Killing Pablo
Finders Keepers
Road Work
Guests of the Ayatollah
The Best Game Ever
Worm
The Finish
The Killing of
Osama bin Laden
Mark Bowden
Atlantic Monthly Press
NewYork
Copyright © 2012 by Mark Bowden
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means,
including information storage and retrieval systems,
without permission in writing from the publisher,
except by a reviewer, who may quote brief passages in
a review. Scanning, uploading, and electronic distribution of this book or the facilitation of such without the permission of the publisher is prohibited. Please purchase only authorized electronic editions, and do not participate in or encourage electronic piracy of copyrighted materials. Your support of the author's rights is appreciated. Any member of educational institutions wishing to photocopy part or all of the work for classroom use, or anthology, should send inquiries to Grove/Atlantic, Inc.,
841 Broadway, New York, NY 10003 or
permissions@groveatlantic.com.
Published simultaneously in Canada
Printed in the United States of America
ISBN-13: 978-0-8021-9410-7
Atlantic Monthly Press
an imprint of Grove/Atlantic, Inc.
841 Broadway
New York, NY 10003
Distributed by Publishers Group West
www.groveatlantic.com
For Clara and Audrey
Human groupings have one main purpose: to assert everyone's right to be different, to be special, to think, to feel and live in his or her own way. People join together in order to win or defend this right. But this is where a terrible, fateful error is born: the belief that these groupings in the name of a race, a God, a party, or a state are the very purpose of life and not simply a means to an end. No! The only true and lasting meaning of the struggle for life lies in the individual, in his modest peculiarities and in his right to these peculiarities.
—Vasily Grossman, Life and Fate
The properties of a movement are spontaneity, impulsiveness, dynamic expansiveness—and a short life. The properties of a structure are inertia, resilience, and an amazing, almost instinctive, ability to survive.
—Ryszard Kapus´cin´ski, Shah of Shahs
Contents
Prologue
1: A Definition of Evil
2: The Path of Jihad
3: Taking Up Arms
4: The Targeting Engine
[5: "Please Make Sure to Keep the Children and
All of the Families Away from the Areas
That Are Being Photographed and Bombed"](Epub4153_Epub-14.html#x5--Please-Make-Sure)
6: Disguised Uncertainty
7: "Adhering to These Precautions"
8: The Finish
9: Glitter
Acknowledgments and Notes
Prologue
2007–2008
One fall night in western Iraq, as a unit from the U.S. Joint Special Operations Command (JSOC) was executing one of its nightly raids on suspected al Qaeda terrorists, this one a suspected regional commander who called himself "Muthanna," the raiders inadvertently discovered the mother lode.
In another war in a different time, the "mother lode" might have been a huge cache of valuable weapons or a collection of battlefield maps showing enemy troop movements and positions. In the twenty-first century, the raiders of JSOC had discovered something of equivalent value: a Rolodex.
Muthanna was killed in the raid. It was clear from material seized at his residence that he was responsible for coordinating the movement of foreign al Qaeda fighters and potential suicide bombers across the nearby border with Syria and into Iraq, where American and Iraqi forces, and Iraqi civilians, were enduring a mounting campaign of mass slaughter. What they found was not an actual Rolodex; it was something better: a collection of names and numbers that referenced computer files containing names, photos, travel documents, expense reports for phone cards, clothing, vehicles, fuel, money transfers, and many other detailed documents for about five hundred current al Qaeda recruits—just about every mujahidin who had made the trek in recent years through Syria and into Iraq.
For centuries, the basic tactics of infantry warfare were "fire and maneuver." A skilled officer could defeat a larger force by mastering the art of moving his men and effectively focusing their firepower. Those kinds of skills are still essential on a conventional battlefield, but the battles being fought today rarely boil down to armies maneuvering on the ground. "Information and intelligence is the fire and maneuver of the twenty-first century," says Lt. Gen. Michael Flynn, who now heads the U.S. Defense Intelligence Agency.
What does he mean?
The mother lode of documents seized in what became known as the Sinjar raid illustrates the point nicely. It played a big part in decapitating al Qaeda in Iraq. In the six years after the 9/11 attacks, the U.S. military and intelligence communities, representing a wide variety of agencies large and small, those notorious and those secret, had been collaborating on an unprecedented capability for crushing furtive terrorist networks. In addition to the skills of JSOC's talented special operators, the effort used supercomputers and custom software, the forward deployment of skilled analysts, and the ability to turn just about every kind of intel into searchable data, whether tips or documents from old-fashioned human spy networks, transcripts of detainee interrogations, logs of electronic surveillance monitoring communications between cell phones and computers, or the images and sensory readings gathered by drones hovering high and silent over potential targets for days, weeks, months, and even years. With an enormous database consisting of these fragments, few of them clearly related, computers are capable of finding links that would previously remain hidden—a bank account shared by a Hezbollah official and an al Qaeda recruit, a street address in Najaf visited by two known suicide bombers on two separate occasions, a snapshot from the wallet of a slain American soldier on the hard drive of a suspected terrorist paymaster. The computer instantly draws bloody threads between data points that would otherwise remain random and disconnected. Webs are drawn from these bloody threads, illuminating secret networks. Once such connections are made, the special operators know where and whom to hit next.
In the case of the Sinjar haul, JSOC Commander Stanley McChrystal took the surprising step of declassifying all of the material and turning it over to West Point's Combating Terrorism Center, so that analysts from a variety of disciplines could take a crack at it. And what did they uncover? For one thing, the data exploded the propaganda claim that al Qaeda in Iraq was a homegrown resistance movement. The recruits in the Sinjar data came from Libya, Morocco, Syria, Algeria, Oman, Yemen, Tunisia, Egypt, Jordan, Saudi Arabia, Belgium, France, and the UK. American Treasury agents mapping the data's financial transactions were able to identify the entire Syrian-based leadership of al Qaeda in Iraq's foreign-support network, all of it under the direction of a man who called himself Abu Ghadiya. His real name was Badran Turki Hashim al-Mazidih.
Just over one year after the Sinjar raid, the entire senior leadership of this Syrian-based support network for al Qaeda had been destroyed. A single October 2008 raid inside Syria killed Abu Ghadiya, one of his brothers, and two cousins, all members of the top leadership. The database would also provide a road map for JSOC operations throughout Iraq, tracking down and capturing or killing those foreign recruits who had not already sacrificed themselves in suicide attacks.
By the end of 2008, the overall level of violence in Iraq had declined by 80 percent, according to the U.S. Department of Defense. This sharp trend has continued through the withdrawal of U.S. forces from that country in 2011, and remains lower today than at any time since before the American invasion in 2003.
There are multiple reasons for this striking turnabout. The Sunni Awakening in 2008 turned many Iraqi insurgents against al Qaeda—abetted at least to some extent by the Sinjar data analysis, reported in the summer of 2008, which revealed the foreign-born nature of the organization. The dramatic shift in strategy orchestrated by Gen. David Petraeus toward counterinsurgency tactics during the same period deserves much of the credit. But a large part of Petraeus's own approach included ramping up the pressure on "irreconcilable" elements. As he put it, "I like to go to bed every night with more friends and with fewer enemies."
JSOC provided the "fewer enemies," and McChrystal has cited the Sinjar raid as one of his unit's most important breakthroughs.
Prevailing in war often demands new tactics, methods, and tools. The attacks on America on September 11, 2001, challenged a long-standing premise of its national defense. Osama bin Laden and his extremist movement, al Qaeda, posed a new kind of threat, a global network of well-funded, clever, suicidal killers with no fixed address. The nation's vast arsenal, its nuclear stockpiles, its incomparable air force, its army and navy, even its bureaucratic structure for global surveillance, spying, and intel analysis, was designed primarily to deter attack. Who would dare when the response would be swift, fatal, and unstoppable?
But what if attacks came from nowhere? What then?
This was the problem posed by 9/11. The answer was information. Finding the enemy has long been one of the most basic challenges of war. All al Qaeda did was up the level of difficulty. They lived and worked scattered all over the world, using global telecommunications to stay linked. Given the complexity and international nature of those links, the use of pseudonyms and all the tricks of spy craft, how was this new enemy ever to be found?
The seizure of the Sinjar Rolodex and the subsequent takedown shows how. Six years after the 9/11 attacks, deep into two wars, still haunted by the defiant image of a free Osama bin Laden, the United States of America had one strong consolation.
It had figured out exactly how to fight back.
The Finish
1
A Definition of Evil
September 11, 2001
Just before eight o'clock on a brilliant sunny Chicago morning, Barack Obama was driving up Lake Shore Drive when the music on his radio was interrupted by a news bulletin. A plane had crashed into one of the World Trade Center towers in New York City. He thought little of it. He assumed it meant some poor Cessna pilot had screwed up badly.
The Loop was a familiar fifteen-minute commute from Illinois State Senator Obama's house in Hyde Park. To his right stretched the flat expanse of Lake Michigan and ahead, on his left, was the soaring skyline, anchored by the black monolith of the Sears Tower, spiked with antennae. Surrounded by so much lake and Illinois sky, the drive can feel like free falling into a world of blue.
Obama was bound for the Thompson Center, the city's seventeen-story government building, a monumental shiny structure of curved reflective glass that looks like a grounded spaceship. The setting was remarkable but the business he had there was strictly routine, a hearing of the Joint Committee on Administrative Rules. Today's agenda promised hours of bureaucratic minutiae—rules changes for thirty-nine separate boards, programs, commissions, and departments.
Obama represented District 13 at the northern edge of the South Side. He had two other jobs, one practicing law for a prominent Chicago firm and another as a senior lecturer in constitutional law at Chicago University's Law School. He was a moderately prominent man in his adoptive city, seen locally as a young man of great promise, but for all that his career seemed stalled. He had been soundly beaten in a run for Congress two years earlier—a rebuke, really. He had lost by a margin of two-to-one. His intellect was obvious, maybe too obvious, given his Harvard Law degree and his tenure as the first African-American president of that school's prestigious Law Review. Ivy credentials play well in big city politics only when they come with a smothering dose of street, which Obama did not have. He looked and sounded like a law professor. What he did have was "cool," a word people applied to him in both a good and a bad way. He was cool in that he had style and presence; he was tall and lean, poised and charming. But he was cool in the other way, too. He often seemed distant, aloof, even superior. He had turned forty a month before, too old to be considered a prodigy. His black Jeep Cherokee was the car of a family man. He and his wife, Michelle, had two daughters: infant Sasha, and Malia, who was three.
He parked, ascended in one of the exposed shafts inside the center's vast atrium, and was in his chair listening to a witness read a prepared statement when digital phones began chirping and dinging from every corner of the room. Obama looked down to see messages stacking up on his BlackBerry. Murmuring quickly overtook the testimony. The witness plowed on but soon no one was paying attention to him. The news from lower Manhattan flowed in from a thousand points at once. The second tower had been hit. Both planes were commercial airliners. The towers were on fire. This was no accident. This was a coordinated attack.
At that point the Thompson Center was evacuated and Obama left with everyone else. On the sidewalk outside with the thousands of other Chicagoans evacuated from tall buildings in the Loop, his eyes moved involuntarily up to the Sears Tower. Suddenly the city's landmark skyscraper appeared in a different light. It was no longer just a symbol of the lakeside city's identity. It loomed now like a giant target.
In Sarasota, Michael Morell wondered if a plane was bearing down on him. He was President George W. Bush's CIA briefer and was part of the president's entourage that morning. The visit was big news in the west Florida city. Anyone targeting Bush would know right where to find him, and a commercial airliner would do the job nicely.
Morell had been in the backseat of a van in the president's motorcade when the first plane hit. They were racing down Gulf of Mexico Drive on Longboat Key when Ari Fleischer, Bush's press secretary, took a call and then turned to him.
"Michael, do you know anything about a plane hitting the World Trade Center?"
As the in-house intelligence officer, Morell was the man they looked to for the scoop when something startling happened. The plane had hit while they were en route, so he had heard nothing. He was thinking it was probably a small plane that had gotten disoriented in bad weather, something like that, but he called headquarters in Langley, Virginia. The CIA operations center told him that a crash had occurred, the building was the North Tower, and that it wasn't a small plane but a commercial jet.
The veteran CIA analyst had been up before dawn that day, as he usually was, and had spent some time alone in his hotel room prepping for his regular morning session with the president. Each day at eight o'clock, Morell delivered the President's Daily Briefing (PDB), a summary of the most current intelligence reports from around the world. He had flown south on Air Force One the previous afternoon, the start of a weeklong cross-country trip to promote Bush's education initiatives. They had stopped first in Jacksonville, for a round-table discussion, and then driven down to Sarasota, where they had spent the night at the Colony Beach and Tennis Resort, on the barrier island that parallels the city shoreline.
Morell's presence had nothing to do with the week's education theme. Like the military officer who carried the president's "football"—the coding device needed to authorize a nuclear attack—the CIA briefer went wherever Bush went. America had not been directly attacked in any significant way since Pearl Harbor, so the morning briefing usually concerned things more abstract: "national security concerns" was more like it. There were always terror threats, but there had been nothing in the brief that morning about anything specific or imminent.
Bush was not given to poring over written reports. He preferred for Morell to "tee up" highlights in the morning briefing, and would then read the most pertinent parts and ask questions. For Morell this made the morning half hour something of a daily command performance. The president enjoyed it. He would later call it "one of the most fascinating parts of my day." It was a heady role, albeit a virtually invisible one. Morell is a slight, precise man with glasses and neatly combed sandy brown hair, a man who seems ordinary by design. His suit is often rumpled and he moves in a distinctly civilian, loose-limbed slouch; he is the kind of man who tends to fold up on a chair, all knees and elbows. That and his indoor pallor made him look almost frail alongside the president's robust security detail and phalanx of ruddy military advisers. In conversation, Morell was intense. He spoke with a crisp Ohio accent, and bore down on ideas bodily, frowning, chin first. For most of his career at the spy agency he had been an Asian specialist.
By the time the president saw him that morning, Bush had already taken a few minutes to read from his Bible, had jogged in the darkness around the Colony golf course, and had dressed and eaten his breakfast. That day's briefing had mostly concerned China. The briefing is still classified, but months earlier a U.S. Navy EP-3, a propeller-driven intelligence-gathering aircraft, had collided with a Chinese jet fighter off the island of Hainan, killing the fighter pilot and triggering a small international crisis, the first of the Bush presidency. Morell also had fresh intel from Russia, again still classified, but fallout there from the then recent Robert Hanssen spy scandal had prompted both countries to expel some of each other's diplomats. Morell then presented new information about the ongoing Palestinian uprising, an increasingly violent affair at the center of the world's news. One item on the agenda prompted the president to call his national security adviser, Condoleezza Rice, who had stayed behind at the White House, but in later years no one would remember what the call was about. In light of what was coming—all four of the doomed commercial airliners were already in the air—the items on that day's agenda would soon seem small.
When the briefing was done, Bush left for his scheduled visit to Emma E. Booker Elementary School, where at nine a.m. he was supposed to visit a second grade classroom before an array of television cameras and reporters. They were at the school when news of the second plane came. Morell was waiting with the rest of the president's staff in a classroom next door. It had a TV set, which was soon showing video of the crash into the South Tower. Both towers were now aflame.
Andrew Card, Bush's chief of staff, went next door to whisper the news to the president, who was seated in a chair before the classroom, listening to the students read a book about a pet goat.
"A second plane hit the second tower," said Card. "America is under attack."
Cameras caught the stunned look on the president's face. Some would later ridicule him for it, but what is the correct facial expression for news like that? Bush resolved to stay calm. He remained before the class until the story was finished, but his demeanor had dramatically changed. He had been cheerful, enjoying the children's performance. Now he was grim, his mind clearly elsewhere. When the story was done he complimented the class and then walked briskly into the adjacent classroom. On the TV was video of United Airlines Flight 175 plowing straight into the South Tower in slow motion and erupting into a fireball. Fleischer consulted with the president, who hastily scribbled remarks in longhand before walking back into the crowded classroom to face the cameras and reporters again.
"Ladies and gentlemen, this is a difficult moment for America," he began.
Planes were falling from the sky, suicide hijackers guiding them into the nation's iconic public buildings, incinerating themselves and the planes' passengers and killing thousands. And no one knew how many airplanes there were.
Morell thought they ought to move Bush immediately. He started toward a Secret Service agent, but saw that the protection detail was ahead of him. They pointed him out of the building toward the motorcade. When the president's short statement was finished they were off at once to the airport.
Bad news kept on coming. A third plane, American Airlines Flight 77, hit the Pentagon while they were still speeding north on Route 41. Suddenly every tall building, every monument, every American landmark seemed in jeopardy. Where would the next one hit? There was nothing fanciful about the breadth of alarm in those first hours. But along with the fear, the attacks provoked something primal and self-protective. Just seventy-one minutes after the North Tower was hit, hundreds of miles west of New York City and high over Pennsylvania, the passengers aboard United Airlines Flight 93 hastily organized and attacked the men who had hijacked their plane. It crashed in a field just east of Pittsburgh, in Shanksville, Pennsylvania.
The reaction was sudden and national. The military scrambled fighters and secured its bases. Airports were closed, streets blocked, buildings vacated.
In Chicago, when Obama realized that no one was going back into the Thompson Center anytime soon he walked to his car and made the short drive to his law office. The firm of Davis, Miner, Barnhill, and Galland was housed in a brick town house. They had a small conference room in the basement with a TV where the office staff gathered to watch the unfolding tragedy. Along with millions around the world, they saw men and women stranded on the upper floors of the Twin Towers, still alive, crowding at windowsills with flames behind them, waving desperately for help that could not reach them, trying to figure out what to do, some of them jumping to their deaths. Obama watched with the others as the towers fell, imagining the thousands trapped inside. They saw the smoke and flames rising from a demolished wall of the Pentagon.
In San Diego, Bill McRaven watched from a hospital bed in his home, where it was still very early in the morning. Even flat on his back, the Navy SEAL captain had a distinct military bearing. His tall body was lean and muscular. His buzz cut drew defiant attention to his jug ears, and the upper and lower halves of his face were slightly askew, which set his long jaw at a slight jutting angle that asserted resolve. Lately, Captain McRaven hadn't been doing much of anything beyond easing himself from hospital bed to wheelchair and back again. It was a humbling debility for someone so physical. He had been a track star at his high school in San Antonio, Texas, and had then joined the military. Like anyone in an elite special ops unit, he had spent his life pushing himself mentally and physically . . . which catches up to most people. Two months earlier he'd had a terrifying parachute accident, free-falling 10,000 feet before colliding with the opened chute of another jumper. Violently spinning and only half-conscious, he had managed to pull his rip cord, saving his life, but with one leg tangled in the chute's cords and the other in its risers, the force of the opening chute had nearly torn him in two, cracking his pelvis, breaking his back, and tearing away muscle from his stomach wall. There weren't going to be any daring missions in his near future, and even if he managed to rehab out of the chair he would always be held together by plates and pins.
He'd escaped the hospital by having his bed moved to his home, so that's where he watched the attacks unfold that morning. He wasn't bitter. McRaven accepted the rough sorting of his profession. He figured that if he'd actually been good enough to free-fall with a SEAL team into combat, he would never have had the accident. He had been dealt out. He wasn't concerned about losing the chance to advance in rank. If he had been ambitious for rank, he would never have joined a SEAL team. It was the same in the army; special ops were a path to small-team action, not command, which traditionally involved assuming responsibility for more and more men. The regular force saw the "irregulars," the special ops teams, as . . . well, irregular. You went that direction to jump out of airplanes and blow things up and maybe get to test yourself on a real mission even when the nation wasn't officially at war. He was forty-five years old and had served most recently as commodore of the Naval Special Warfare Group in Coronado, which he figured was the best job he would ever have. What he was going to miss was the action.
McRaven had fought in the Persian Gulf War, and had trained for daring missions his entire adult life. There was no way to know exactly how the United States would respond to these attacks, but it was clear that the country was at war and the war was going to pass him by.
Whoever did this, it was not likely to be a nation-state. It was probably a small group of dedicated fanatics working out of a variety of places that were hard to find and hard to reach. War always poses new challenges. A nation, stirred to action by a novel threat, has to feel its way in, has to invent the strategy and tactics that will prevail. It would take time—in this case most of a decade—but McRaven was uniquely positioned to see where it would end. He had made a study of Special Operations. He was already convinced—the first inklings were beginning to appear on TV—that this had been the work of a small terrorist group that called itself al Qaeda. Men like McRaven had heard a lot more about al Qaeda than most of the country. If not that group, then one like it. How would you fight a stealthy, stateless organization that plotted sneak attacks? You fought it with intelligence and with highly trained special units like his SEALs, men who could strike with speed and precision anywhere in the world. He could see it clearly. His squadron would be going to war without him.
But better than most, he also knew this war was going to take time. With time he would heal. With time there might just be a way for him to work himself back into it.
In Washington, Michèle Flournoy saw the smoke rising from the Pentagon across the Potomac River. She had a lot of friends who worked there.
A Harvard- and Oxford-educated scholar, she was, at forty, an influential thinker in defense circles, and one of the few women in Washington who had made national security her career. Everyone who knew her knew that it was only a matter of time before she would assume another top-level position at the Pentagon, but for now, as with many who owed their government jobs to the ascendance of one political party or the other, her background as a senior Pentagon planner during the Clinton administration meant that she was one of many policy experts who were effectively in exile during the first White House term of a Republican administration.
Flournoy was known for advocating an internationalist approach to national defense, one based more on partnerships and pragmatism than ideology. President Bush had filled many of the defense-related posts in his administration with those more inclined to use American military power unilaterally, to seek international partners but not to be bound by them. With the nation at peace, these philosophical differences were primarily of interest to subject matter experts and played out in forums related to military planning and development. Earlier that morning Flournoy had been interviewed on National Public Radio about some of the initiatives planned by Defense Secretary Donald Rumsfeld. She was working for the Center for Strategic and International Studies (CSIS), a bipartisan think tank, and was a professor at the National Defense University, helping the Pentagon prepare its Quadrennial Defense Review, a broad strategic plan for the massive department that afforded the most practical outline for national defense priorities. When the planes started to hit, she was attending a defense forecasts international briefing in a building across the street from the White House.
All of the buildings in the vicinity were evacuated. As she stood on Pennsylvania Avenue eyeing the ominous smoke column from across the river, she knew whatever they had been discussing at that briefing was suddenly moot, as if someone had taken an eraser to the whole board. America's defense priorities were being radically and violently reset.
She walked a few blocks to the CSIS's offices, called home to check on her children, and then began trying to get through to friends at the Pentagon on the phone, without success. So she took some calls from colleagues and from reporters, including the reporter from NPR she had just spoken with hours earlier. She shared the growing suspicion that the attacks were the work of al Qaeda, but at that point it was just a hypothesis.
Another Democrat in exile, Thomas Donilon, was also in downtown D.C., undergoing his annual physical in a suite on M Street. He was forty-six, an age when years of long hours sitting behind a desk begin to take their toll, especially for a big man like him. A lawyer with a long background in government, he was known for doing the work of three and had the slackening frame to show for it. In a world capital of the work-addicted, he was considered exceptional. Donilon had been the youngest aide on the staff of President Jimmy Carter in 1977 and had served as chief of staff for the State Department during the Clinton administration. He had joined the Clinton campaign in 1992 as a stand-in for President G. H. W. Bush and for Ross Perot in debate preparation. Hours of prep armed him with telling facts and examples. He was tenacious: unfailingly pleasant but tough. He had a way of displaying his teeth as he spoke, top and bottom, so that the words seemed chewed. Clinton liked to spar with him verbally before a big match. Now, less than a year into the new Republican administration, he was getting used to life as an outlier, putting his law degree and experience inside government to work as a lobbyist for Fannie Mae.
When his doctor was finished with him, he drove his car from the garage under the building and into gridlock. Office buildings throughout the District had emptied. It seemed as if the entire government workforce was making its way home. Donilon tried to call his wife, but cell phone service was so overwhelmed that his call could not go through. He turned on the radio and listened in horror as he inched his way northeast toward home. The drive took a long time. When he got there he found that his wife had also come home from work, after picking up their daughter early from her Bethesda preschool. They turned on the TV and watched with the rest of the country.
Michael Vickers was just a few blocks away at his own small think tank offices, the Center for Strategic and Budgetary Assessments. He had founded it after leaving intelligence and military work. Twenty years earlier, as a brainy CIA officer, he had put together the clandestine U.S. mission to help a loosely connected group of tribal leaders and Islamist extremists fight the Soviet Union in Afghanistan, an effort that was considered the largest covert mission in the intelligence agency's history. The former army special forces officer was legendary in his own world. He was an expert in the Near East, had extensive contacts in that region, and with a career that had straddled intelligence and special ops would prove to be uniquely credentialed for this new war. The next day he would be back at work at the Pentagon as a consultant, summoned by Rumsfeld to help figure out how the United States should respond.
In Bosnia, Brigadier General David Petraeus was at a Nordic-Polish brigade headquarters in the early evening when the news came. A small and wiry man who walked with a slight stoop from his own jump accident years earlier, he sat with a group of international officers watching as the towers collapsed and realized that his mission, and that of every American soldier, was about to change. His suspicions immediately fell to al Qaeda and its founder, a man named Osama bin Laden.
This was no wild guess. Petraeus had been executive officer for the Joint Chiefs of Staff at the Pentagon from 1997–1999, during the period when the Clinton administration frequently debated whether and how to go after the radical Islamist leader. The decisions then had been to launch cruise missiles at al Qaeda targets in the Sudan and Afghanistan, a noisy gesture that hadn't accomplished much. Bin Laden was slippery. The response now would be a lot bigger—world changing. One of Petraeus's jobs in Bosnia was commanding a clandestine joint task force, one made up of elite representatives from all the service branches, that had been finding and targeting fugitive Serbian and Croatian war criminals, gathering intelligence, and then swooping in on targets swiftly, often from helicopters at night.
Before he left to fly back to his own headquarters, Petraeus was already thinking about adapting his mission.
In New York, graduate student Ben Rhodes saw the tragedy unfold from Brooklyn. He was working toward a master's degree in creative writing at NYU but he also dabbled in hometown politics and, that day, had been pressed into service handing out flyers for City Council candidate Diana Reyna—it was an election day in New York. Rhodes had been pushed into political work after confronting borderline socialists at his upper west side prep school and then Texas-style Republicans at Rice University. He feared doing nothing would concede the field to dogmatism. So now he was on the Brooklyn Heights waterfront handing out flyers.
The flames and smoke rising from the North Tower were shocking enough. Rhodes assumed there had been a bad accident. Seventeen minutes later, across the East River he saw a bright flash high on the South Tower, and then both were aflame high up, sending two great black plumes across the Manhattan skyline. He couldn't believe his eyes. The radio of a cop standing near him squawked with a call for all hands to respond, and the air erupted with sirens. Rhodes turned to see the Brooklyn-Queens Expressway below him filled with flashing ambulances and police cars racing north toward the Brooklyn Bridge and across to Manhattan.
The flames and the smoke trails did not diminish. The magnitude of the event was hard to comprehend. He was still watching when the South Tower fell. No sound reached him across the river. No rumble or crash. The skyscraper just abruptly pancaked down, folding in on itself as if it were something it had been designed to do, vanishing into a great white billowing cloud of debris.
He started walking. It seemed clear that the North Tower was also doomed, and he was not eager to see it. The towers had been landmarks of his childhood in New York. There was nothing in his twenty-three-year-old worldview to accommodate what he had just seen. Rhodes admired Ernest Hemingway—he had carried a paperback copy of The Sun Also Rises in his back pocket for years as an undergrad. At his core, Hemingway believed in facing hard truths head on. Rhodes the would-be novelist walked away from fiction that day, too. Whatever this was he had just seen, it was a thing that needed to be met head on. Like many Americans who witnessed those events, his life would never be the same.
President Bush was airborne when the towers fell. He and his inner circle watched from the staff room at the front of Air Force One, where they could pick up local TV feeds from below. The signals faded in and out. It alarmed Bush that the plane had no satellite TV feed—something he would correct. One commentator said that responsibility for the attacks had been claimed by the Democratic Front for the Liberation of Palestine.
This made no sense to Morell. That organization was an old splinter group of the Palestine Liberation Organization and all but defunct.
"What do you know about this group?" Bush asked him.
"They don't have the capacity to carry out an attack like this," Morell answered.
Within minutes the report was retracted.
The transition to war footing was striking. When the motorcade had reached the tarmac at Sarasota Bradenton International Airport, Air Force One had been ringed with Secret Service armed with automatic rifles. No one had seen an attack like this before, so no one knew what to expect next, who was behind it, or how extensive it would prove to be. Everything and everyone was under suspicion. Agents checked every bag before the president's traveling party climbed the stairs to the plane, including Card's and Morell's, including even those of the military officer carrying the nuclear codes.
As the CIA man stepped on the plane, he had asked one of the agents, "Where are we going?"
"We're just going to be flying around," he said.
With the sky raining planes, perhaps the safest place for the president would just be . . . up.
They flew to Barksdale Air Force Base in Louisiana, to refuel and take on supplies. The taxiway was lined with bombers. Reports of further attacks kept coming in: bombs, more aircraft-turned-missiles, a threat on Air Force One, a report of an attack aimed at Bush's ranch in Crawford, Texas. All would prove false, but in light of how audacious and terrible the known attacks were, every new alarm sounded plausible.
When the president got off the plane to tape a message to the American people, Morell stayed in his seat with most of the staff. The plane's crew hastily loaded water and food; no one was certain how long the president would continue flying around. When a military aide came down the aisle with a flight manifest, selectively ordering people off, the CIA man asked what was going on.
"We're having a bunch of people deplane here," he said.
"What about me?" Morell inquired.
"Andy Card says you stay."
They took off with the load lightened, bound for a Strategic Air Command base in Omaha, Nebraska. When they were back in the air, Morell was summoned once more to Bush's cabin.
"Who do you think did this?" the president asked him.
Morell had been on the phone to Langley, but so far no one had been able to give him a definite answer.
"There are two terror states capable, Iran and Iraq," Morell told the president, "but both have everything to lose and nothing to gain. If I had to guess I'd put a lot of money on the table that it was al Qaeda."
"So, when will we know?" Bush asked.
Morell couldn't say. He explained how long it had taken the agency to affix blame with certainty in earlier attacks—the Khobar Towers bombing in 1996 in Saudi Arabia, the U.S. embassy bombings in Tanzania and Kenya in 1998, the bombing of the USS Cole in waters off Yemen in 2000. In the first case it had taken ten days; in the latter ones, a few months.
"We could know it soon, or it could take a while," he said.
In fact, the news came fast. An analyst at Langley had checked the flight manifests of the doomed aircrafts and linked some of the hijackers directly to al Qaeda. The information had been known for about an hour, but it had not been passed to Morell. Instead, Bush got the news by videophone from CIA Director George Tenet after they had landed in Omaha. The president at that point overruled his own security team, directing them to fly him back to Washington. He was going to address the nation that night, and he wanted to do it from the White House.
On the way back to Washington, Morell briefed Bush again, this time on a foreign intelligence report that there were sleeper cells in the United States prepared to launch a second wave of attacks. One of Morell's briefings had warned Bush in August about al Qaeda's desire to attack, but it had been very low key. No special sense of urgency was felt or had been conveyed, despite the alarming title of the actual report: "Bin Laden Determined to Strike in the U.S." Certainly nothing on the scale of what had just happened. With much of the workforce vacationing, Morell had often scrambled for material to present to the president in August. He called them "summer doldrums pieces." They tended to be broadly strategic, discussions of potential threats with more of a shelf life than most items on the morning agenda, looming problems about which the agency was concerned, but with few details. Bin Laden had been talking about doing something big in the United States, something he said that his followers would "rejoice about," but this was from a man who had been making such threats for years. The report had noted that the FBI had "seventy full field investigations" under way on bin Laden–related threats. The thrust of the report was that al Qaeda was planning something and that the U.S. government had no idea what, but was nevertheless doing all it could to prevent it.
Air Force One descended to Andrews Air Force Base at dusk. Many of the people aboard were dozing, having worked a long and difficult day already and knowing that there was a long night ahead. Morell roused himself to look out the window. Two F-16s had maneuvered to escort them down, flying in precise formation off each wingtip so close that on his side he could see the pilot's face inside the cockpit. In the distance he could see smoke still rising from the Pentagon.
He was at home later that night to watch the president address the nation on TV. Before Morell went to bed, he checked in on his children, sleeping in piles of stuffed animals. He thought: The world they live in has completely changed, and they have no idea.
That night, President Bush spoke from the Oval Office.
"Today our fellow citizens, our way of life, our very freedom, came under attack in a series of deliberate and deadly terrorist acts," he said. He described the events of the day in detail and lauded those who had responded, at great peril, to the emergencies. He vowed "to find those responsible and bring them to justice."
The man ultimately responsible, Osama bin Laden, had not been well known outside national security circles prior to that day, but he would soon be the most famous terrorist in the world. In the coming weeks and months he would acknowledge responsibility for the attacks, praise the murderous hijackers as martyrs to his cause, and be caught on videotape chuckling with delight and praising Allah for their success.
"There is America, hit by God in one of its softest spots," he would say in a videotape released a few weeks later, wearing a camouflage coat, seated alongside the AK-47 he still carried from his days of jihad against the Soviet Union, his long beard showing streaks of gray. "Its great buildings were destroyed, thank God for that. There is America, full of fear from its north to its south, from its west to its east. Thank God for that. What America tastes now is something insignificant compared to what we have tasted for scores of years. Our Nation [he meant Muslims everywhere] has tasted this humiliation and this degradation for more than eighty years [since the demise of the Ottoman Empire during World War I]."
From 9/11 onward, every day that bin Laden eluded America's grasp was a victory for him. It would be hard to overstate the significance of that. No matter what else the country did to avenge 9/11, no matter how many regimes it overturned, no matter how much it hammered and crippled al Qaeda, every day that man remained at large was an affront. It meant he had done this and gotten away with it, and might well do something like it again.
The two men who would lead the United States in the next decade of warfare had markedly different immediate responses to the attacks. Bush would record his feelings in his book Decision Points. Obama would describe his in speeches and writings in coming years, and he spoke to me about it in the Oval Office.
Bush felt outrage and an urgent desire for revenge. "Someone had dared attack America," he wrote. "They were going to pay."
When they had landed at Barksdale Air Force Base that day, the row upon row of parked bombers had reminded Bush of the frightening power at his command. Another man witnessing this display might have reflected on the pointlessness of a Cold War–era arsenal against a stateless enemy with no fixed address, but Bush would later write, "I knew it was only a matter of time before I put that power to use against whoever ordered this attack."
In his remarks on the night of the attacks he expanded the range of this anticipated retribution: "We will make no distinction between those who committed these acts and those who harbor them." The president's eagerness to hit back would continue to pick up speed. It would result in the mobilization of vast armies, the invasion and occupation of two nations, and the launching of smaller military and intelligence missions all over the globe. These missions would consume the next seven and a half years of Bush's presidency, kill and maim untold thousands, and do more than anything else to shape America's first decade of the twenty-first century. The war in Afghanistan, the first country attacked, would prove to be the longest in American history. In Iraq, an even bloodier and costlier war would be launched in the mistaken belief that dictator Saddam Hussein bore some tangential responsibility for the attacks and was harboring weapons that could do worse. However misguided much of this would prove to be, Bush's response accurately reflected the public mood, and satisfied, to some extent, the nation's need to flex its muscles and lash back at its enemies.
If Bush's response on 9/11 was to start looking for somebody to bomb, Barack Obama sounded ready to launch some kind of global antipoverty campaign.
Few people were all that interested in the thoughts of the Illinois state senator, but in the days after the attacks his local newspaper, the Hyde Park Herald, solicited his reaction along with that of other local representatives. Obama gave an answer you might expect from a former community organizer with a distinctly international background—his father was Kenyan, and Obama had spent the early years of his childhood living with his mother in Indonesia (he could still speak some Bahasa Indonesia, a language he learned as a child). At Columbia University, living in uptown Manhattan, he had devoted much of his studies to international relations, and he had traveled widely. Certainly more so than any previous president, Obama had grown up globally, a fact that, along with his mixed race and African name, would fuel stubborn suspicions that he was not authentically American. He had firsthand experience with the resentment and anger directed at the United States by many of those living in less fortunate parts of the world, as well as by many blacks growing up in this country. Anti-Americanism was not just an abstraction for him. He had consciously wrestled throughout his life with his own multicultural, multiracial identity, a process he had described movingly in his 1995 memoir, Dreams from My Father. In his response for the Hyde Park Herald, he called for an examination of the root causes of terrorism. "It grows from a climate of poverty and ignorance, helplessness and despair," he said. He called for America "to devote far more attention to the monumental task of raising the hopes and prospects of embittered children across the globe—children not just in the Middle East, but also in Africa, Asia, Latin America, Eastern Europe, and within our own shores." It read like left-wing boilerplate and, right or wrong, was clearly out of step with the nation's anger.
In fairness, the might of America's armed forces was not yet his to command, and he was not yet responsible for protecting the nation. Nor were his political instincts that good. Obama had a hard time fitting in politically anywhere. In that run for Congress, he was trounced by former sixties activist Bobby Rush, who had cofounded the Black Panther party in Chicago and had once served six months in prison on a firearms charge. Rush's First Congressional District was one of the few in America where a résumé like his would lead to Congress. It was home to Louis Farrakhan's Nation of Islam. Obama's mixed race and international background, along with his Harvard credentials, had worked against him. In the coming years, his message would broaden with his horizons. He had already begun aggressively laying the foundation for his next campaign, a successful effort to unseat Republican Senator Peter Fitzgerald in 2005. But for the moment his response to 9/11 was strictly mundane.
It was from a template that went back to Vietnam. Most liberal Democrats, and many black Americans, had never gotten over that conflict. A quarter century later they still tended to be antiwar and even antimilitary—another of Rush's curious countercredentials was that he had gone AWOL from the army. But the broad political pattern set in the 1960s and early 1970s—hawkish Republicans vs. dovish Democrats—had begun to show cracks. The old hawk vs. dove dynamic had grown a lot more complex, with liberals pushing for humanitarian interventions in Somalia, Bosnia, and elsewhere over the objections of conservatives, who inveighed against the folly of "nation building," and "becoming the world's policeman," and cooperating with the UN.
Obama is a cautious man, and in the days after the attacks his caution showed. He seemed more interested than provoked. He said he hoped America would "draw some measure of wisdom from this tragedy." He sounded more inclined to study the attack than to avenge it. Here was a man whose blood had a higher boiling point than most. He saw himself as someone skilled at navigating between implacable extremes, be they cultural or, as with his work with the Harvard Law Review, intellectual. But in this instance, the forces he imagined had shaped the 9/11 attackers, ignorance and poverty, did not apply. The suicidal killers would turn out to be neither embittered sons of poverty nor especially hopeless or ignorant. Most were well-to-do young Saudis whose families had shipped them overseas for expensive college educations. They were religious fanatics, led by a man who had inherited a fortune. Their grievances were not economic—they were political and religious.
Obama did call for some martial response, but even in that he was careful. "We must be resolute in identifying the perpetrators of these heinous acts and dismantling their organizations of destruction," he said. Not "find them and arrest or kill them," but dismantle their organizations. If Bush's response to the attacks started big and would keep getting bigger, his eventual successor's response was at the opposite end of the spectrum. Any thoughts about war for Obama were deeply couched in restraint. He would eventually wage war fiercely, but the restraint would remain. He was not a pacifist. He saw violence as a necessary resort, albeit a last one. But as long as he was not bearing the responsibility of defending the nation, he could afford to let the shocking events of the day sink in more slowly.
The events were unprecedented. America has had its share of bloodshed, invasion, and surprise attack. Pearl Harbor was a living memory for millions. But because of television, nothing in American history compared with the impact of 9/11. Pearl Harbor was over two thousand miles from the mainland, at a time when the Hawaiian islands were just an American territory. Reports of the Japanese attack arrived via radio and newspaper stories. The attacks on 9/11 happened on live TV and were broadcast worldwide, the key moments replayed in slow motion and in a constant loop. There was nothing indirect about this. Here was heedless slaughter of fellow citizens right before our eyes.
The debates over conflicts in Obama's lifetime—Panama, El Salvador, Kuwait, Somalia, Rwanda, Bosnia, etc.—had all involved abstract questions about the use of American power. What was the country's moral obligation? How broadly should "national interest" be defined? What were the costs of intervention? Would it make things better or worse? How would the rest of the world perceive the decision? There was nothing abstract about 9/11.
Some persistent critics of the United States would argue that the country had brought this on itself. They would blame, among other things, self-serving Middle East policies, attitudes of cultural supremacy, and a steadfast disregard for growing global disparities in wealth and opportunity. Obama's own statements hinted at this. But it was apparent to most that the attacks were rooted in something darker. Washington's global strategies, intrigues, and alliances stirred anger in many parts of the world, particularly the Middle East. Anti-Americanism was real and dangerous. But this . . . this went to some deep well of hatred. The death of innocents has always been a tragic consequence of war, but this was random murder as strategy. It was something new, or, perhaps, something very old.
Obama sat up late on the night of 9/11 watching TV while he cared for infant Sasha, changing her and then giving her a bottle. By then the links with al Qaeda were being widely reported, and screens flashed pictures of bin Laden, a tall, thin, lordly man with a prophet's beard and flowing robes. His picture conjured up wrathful images of the fanatical abolitionist John Brown, or even Jehovah. Obama already knew more about this Saudi Arabian renegade and his extremist movement than did most Americans. The explosions at U.S. embassies in Kenya and Tanzania in 1998 had killed 223 people, mostly Africans. Thousands more had been wounded. Obama had family in Kenya. He had visited that Nairobi embassy. His tendency to search for answers through mutual understanding would be sorely tested here.
It would end up mattering a great deal how the events of this day affected Barack Obama. Few of us are asked to make life and death decisions, or to order someone killed. It is doubtful that Obama, on that night, imagined that he ever would. His personal and intellectual inclination was to bridge the gaps between people, to empathize. He tended to see conflict as something that arose exclusively out of injustice and misunderstanding. He was the son of a Luo tribesman from Kenya and a white girl from Kansas. He was different wherever he went, as a boy making the transition to life and school in Jakarta, as a young interracial man with black skin in a primarily white world. Even internally, negotiating differences was his life story. As he would tell biographer David Maraniss years later, "The only way my life makes sense is if, regardless of culture, race, religion, tribe, there is this commonality, precepts that are universal. And that we can reach out beyond our differences. If that is not the case, then it is pretty hard for me to make sense of my life. So that's the core of who I am." Empathy was his milieu. It's a generous worldview, and often the correct one.
But on September 11 he confronted something that challenged that hopeful insight. Search as he might for some logic to justify or mitigate these attacks, no reach of empathy or reason got him there. Bin Laden's hateful beliefs could not be reconciled. Despite the soft tone of his remarks to the Hyde Park newspaper, Obama also spoke of "a fundamental absence of empathy on the part of the attackers: an inability to imagine, or connect with, the humanity and suffering of others."
There is little evidence that George W. Bush was given to this sort of reflection, at least not openly, about himself or his responsibility. He had been born into a family that wielded power as if it were part of its birthright, and when the attacks came he was more than ready to play his role. Obama came from an opposite place. His roots were among the powerless. But even in his wide experience there was no way to comprehend Osama bin Laden.
Four years after the attacks, after his election to the U.S. Senate sparked a wave of electoral enthusiasm that would eventually carry him to the White House, Obama wrote a new prologue to his memoir. In it, he returned briefly to 9/11: "It's beyond my skill as a writer to capture that day and the days that would follow. The planes like specters vanishing into steel and glass, the slow-motion cascade of towers crumbling into themselves. The ash-covered figures wandering the streets. The anguish and fear. Nor do I pretend to understand the stark nihilism that drove terrorists that day and drives their brethren still. My powers of empathy, my ability to reach into another's heart cannot penetrate the blank stares of those who would murder innocents with abstract, serene satisfaction."
He noted that the murderous swath of al Qaeda in the previous decade hewed oddly close to his own life path—Nairobi, Bali, Manhattan. He spoke more harshly of the attackers than he had years earlier. He condemned anyone "who would seek under whatever flag or slogan or sacred text, a certainty and simplification that justifies cruelty toward those not like us."
Obama had spent a lifetime, no matter where he looked, being not like others. The attacks had crystallized something for him.
When Sasha emptied her bottle that night in 2001 he lifted her to his shoulder and patted her back gently. The terrible images of the day replayed before him on the screen. He wondered what the future would hold for her and her older sister Malia. He felt the attacks personally, as a civilized man, as an American, and as a father. He was working his way toward a personal definition of evil.
2
The Path of Jihad
Summer 2010
In hiding, his hair and beard had grown white. The Sheik, as he liked to be called, was just fifty-three years old, but the long white whiskers made him look like an old man. In a sense, he had been playing an elder his entire adult life, having been severe and serenely self-important since he was old enough to sprout a beard. Wealthy, well connected, and male in a culture that excessively prized those things, he had known deference and esteem from those closest to him all his life.
Despite the hammering his movement had taken in recent years, bin Laden kept an upbeat tone in his letters. His faith did not allow for doubt, or even questions. His perambulations around the Middle and Near East aside, bin Laden's world was exceedingly narrow. If the man in the White House, Barack Obama, the man charged with defending the United States of America, was a surprising confluence of race and nationality, a man of international upbringing and broad liberal education, bin Laden was his opposite. The Sheik had walked a relatively narrow path in life. He had found the truth at a young age and ever since had labored to resist any challenge or contradiction. Even before he became the world's most wanted fugitive, his daily habits and those he imposed on his family were calculated to reduce traffic with those outside his small circle of belief. The rituals he observed—the fasting, the avoidance of women other than his wives, the extra sessions of daily prayer—all of it was designed to stave off outside influence. It was designed to strengthen his devotion to the cause and his faith in ultimate victory.
He saw hopeful signs everywhere.
"Anyone who looks at the enemies in NATO, especially America, will know that they are in big trouble," he wrote. "This year has been the worst for them in Afghanistan since they invaded it. The number of their dead has never been this high, according to their own reports. Their financial crisis continues. Britain has lowered its defense budget and America is reducing the budget at the Pentagon. Anyone who knows the world and who understands politics realizes that it is impossible for them to continue with the war. There is no difference between them and the Soviet Union before it withdrew from Afghanistan."
At heart, the Sheik was a fantasist, and here was the nub of his fantasy. He had left home at age twenty-two to join a seemingly hopeless cause, a pan-Muslim jihad to drive the Soviet Union from Afghanistan. The mujahidin who took up this fight were little more than an untrained, poorly armed rabble going up against one of the richest, best-trained and -equipped, and most powerful military forces in the world. In later years bin Laden would be described as a murderous nihilist, someone who believed in nothing. He was murderous all right, but the opposite of a nihilist. He was a true believer. He had a complete vision of the world as he wanted it to be—indeed, as he was convinced it would be, as he was convinced God Almighty intended it to be. He believed in miracles and signs. He collected them throughout his life as proof of God's favor. His determination to join the jihad in Afghanistan was an act of faith, and the defeat of the Soviets vindicated his commitment. It was the first great miracle on this path, the one that convinced him more than anything else that he was right.
As a boy, growing up one of fifty-four children of a Saudi billionaire construction magnate, bin Laden had gone mostly to Islamist schools, and in religion he found an antidote to the worldliness of his family. He was one of the few bin Laden children who received all of his education in Saudi Arabia. The schools he had attended as a boy included religious studies, but also taught mathematics, science, history, geography, and English. He learned as a boy to speak passable English. Growing up in the 1960s he was among the best educated of his Saudi generation. He had also worked for his father, first as a simple laborer. The bin Laden company was renowned for building roads and parts of the mosques in Mecca and Medina. Young Osama worked his way up to foreman of a labor gang, and finally headed up construction projects himself. One of his specialties was tunneling. This kind of work put him shoulder to shoulder with Muslim workers from all over the region and the world: Egyptians, Yemenis, Moroccans, and even Malaysians. So his ideas about the Muslim world expanded well beyond those of most sheltered young Saudis, who viewed their own Wahhabi brand of the faith as superior to all others. At the same time, bin Laden became exceedingly devout, shunning all contact with women other than his wives (the first of whom, Najwa, he had married at age seventeen). He renounced the affluent lifestyles of his vast family and discovered the work of Egyptian scholar Sayyid Qutb, a small, mean, sickly man with a Hitler mustache who had been hanged by authorities in Egypt in 1966. In death, Qutb's angry words gained fiery eloquence for those who thought as he did.
Qutb had railed against the rapid Westernization of traditional Arab societies. He championed divine revelation in a fallen modern world, penning biting critiques of both capitalist democracy and communism. A fervent Jew hater, he saw secret Zionist plots behind most of what he disliked, embracing every cockeyed forgery and myth in the canon of anti-Semitism. The Koran, he argued, was the one true path. All the wisdom mankind needed was in that book, which he spent a lifetime interpreting and explaining to suit his own vision. Muslims held the truth, the only truth, and had a duty to confront unbelievers, violently if necessary. Regimes and states that stood in the way of religious rule were jahiliyya—ignorant pre-Islamic societies—and as such were legitimate targets for violence. The forces of God must combat the forces of Satan, beginning with the secular regimes of modern Arab states. Qutb urged the faithful to carve out one country in which to base a pure society founded on shariah, Islamist law, a foothold for the faithful in a fallen world, and from that base radiate righteousness outward, by the sword if necessary. The new caliphate thus created would bend all of civilization to God's will. At a time when well-to-do Arabs were becoming increasingly secular and Western, sending their children to Europe and the United States for advanced degrees and adopting lifestyles antithetical to Arab tradition, Qutb urged them to go in the opposite direction.
He had lived for a time in the United States—briefly in Colorado and in California—and seemingly everything he saw clarified his hatred not just for America, but also for the humanism that formed the intellectual undergirding of the Western world. A fastidious man who never married and seemed repelled by sex, Qutb denounced the licentiousness, materialism, and personal freedom of capitalist democracy. He saw clearly that for all its so-called respect for religion, Western society had become primarily secular, that faith, which for him was the dynamic principle of life, had been reduced in capitalist societies to something more akin to a commodity, as though there were different flavors of divine truth arrayed like items on a supermarket shelf for shoppers to pick through. What could it possibly matter to God what sort of truth a man preferred? There was only one truth, and man's job was to accept it reverently and try to live in accordance with it. The very idea of tolerance, of respect for a variety of beliefs, was anathema. One either embraced the truth or was lost. As for Marxism, the Western world's great rival notion, he saw it as simple idolatry, elevating human reason—"Rational Idealism"—above revelation. Lurking behind both Marxism and capitalism, he argued, was world Jewry.
"Islam is a system given by God and it aims to establish a fundamental principle of God's sovereignty and people's servitude to Him alone," Qutb wrote. "As such, Islam has the right to remove all obstacles from its way and address people freely without any impediments such as a political system or social customs and traditions . . . it is the right of Islam to take the initiative. It is not the creed of a particular people or the system of a particular country. It is a system given by God for the entire world. As such, it has the right to take action to remove all obstacles that fetter man's freedom of choice. It is a faith that does not force itself on any individual, it only attacks situations and regimes in order to free individuals from deviant influences that corrupt human nature and restrict man's freedom."
Young Osama bin Laden was not the first youth to be swept up by a pure, simple ideology that promised to create freedom of choice by abolishing everything that disagreed with it. The Koran stood like a rock in the shifting waters of human history. Progress for human beings meant one thing: living more closely to the teachings of the book.
"The Islamic concept of Divinity is utterly distinct from man's . . . and therefore it does not need to develop or change," Qutb wrote. "The One who established this concept can envision without limits of time or space. His knowledge is immune to the obstacles of ignorance and deficiency; and He chooses without being influenced by passion or emotion. Therefore, He has established for the entirety of humanity, in all places and at all times, a firm principle within the framework of which human life freely advances and develops."
Accused of participating in a Muslim Brotherhood plot to assassinate Egyptian strongman Gamal Abdel Nasser, Qutb went to the gallows with his beliefs unshaken. "The Muslim Brotherhood is not a party of preachers and missionaries but rather of divine enforcers," he wrote. "Its mission is to blot out, by force if necessary, oppression, moral anarchy, social disorder, and exploitation so as to finish the so-called divine role of self-styled gods and replace evil with good. 'Fight them,' the Koran says, 'until there is no more oppression, and all submission is made to God alone.'"
Bin Laden became a "divine enforcer." As a young man, he was not a scholar or much of a thinker, and he lacked Qutb's eloquence. Those who knew him found him tongue-tied and unimpressive. But he was ambitious, and rich. His billionaire father was killed in a plane crash in 1967, leaving behind enough of a fortune to make all of his offspring at least multimillionaires. Bin Laden's inheritance at age ten was estimated in the tens of millions. He had no interest in using his wealth to build a fine home or adopt a luxurious lifestyle, though, as many of his siblings did. His inclinations ran the opposite way. He had been educated in a private secular school, but by the time he attended King Abdulazzi University, where he studied economics and business management, he was already preaching simplicity and seemed primarily interested in religion and charitable work. He continued to pursue these interests until the Soviet Union invaded Afghanistan and launched him on the path toward his life's work.
Huthaifa Azzam was just fourteen years old when he answered a bell on the gate outside his father's house in Jordan. He found a very tall, very thin, swarthy and bearded young man wearing Arab robes and a simple white turban, not the typical red-and-white-checked headdress, or shemagh, worn by most Saudi men. The visitor asked, shyly, "Is this the house of Dr. Abdullah Azzam?"
Azzam was a prominent Palestinian Islamist and scholar whose fatwa, "Defense of the Muslim Lands: The First Obligation After Faith," had caused a stir in the Arab world, summoning the faithful to Afghanistan to resist the infidel Soviets. Azzam had done more than preach. He had relocated to Pakistan to take part in the holy war himself. Based in Peshawar, close to the Afghan border, he had established what he called the "Services Office," to recruit and train young Arab volunteers to join the fight. Magazines, photos, and videos prepared by the office spread news of the heroic religious resistance throughout the Arab world . . . and had found their way to young bin Laden. Azzam was taking a short holiday break with his family in Jordan when the young Saudi made the four-hour trip to ring his bell. This volunteer was different from most, of course, because of his fortune. Azzam must have been delighted. The two men spoke for hours that day, and by evening bin Laden was a recruit. He pledged himself to the cause. He was still enough of a loyal Saudi subject, however, that he delayed traveling back with Azzam in order to seek permission from King Fahd. He arrived in Peshawar several weeks later.
At that point, bin Laden's money was more valuable to the cause than his leadership or even his life, and so during those first years with Azzam he stayed safely behind the lines, working at the Services Office and helping to attract other young fighters to the cause. This was not destined to last. Bin Laden was a romantic, and a zealot, and he had not made his jihad to live safely behind the lines. He grew apart from Azzam, increasingly falling in with Ayman al-Zawahiri, the radical Egyptian physician who had left his home country after serving three years in prison. Zawahiri worked at a Red Crescent hospital in Peshawar. Although only six years older than bin Laden, he was a man of wider experience and education, and had been deeply embittered by the torture he had undergone at the hands of Egyptian police. His angry radicalism stirred bin Laden to play a more active role in the holy war—to become a full-fledged mujahid himself.
Bin Laden's growing extremism began to trouble his Palestinian mentor. Azzam, a college professor, balked at bin Laden's refusal to send his children to school. The younger man wanted Arab recruits to form separate, religiously pure fighting units, while Azzam believed the Arabs would be better employed if mixed with the savvier, more experienced Afghan militia. He also resisted his protégé's growing carelessness about human life. Bin Laden had embraced a broad definition of "infidel." Until that point, the enemy had been understood to be Russian soldiers and Afghans who fought with them. They were at war, after all. Bin Laden had expanded the definition. It now applied to any Russian, even any non-Muslim. He was fighting a bigger war than the one being promoted by Azzam. The older man's wife, Samira, remembers her husband arguing with bin Laden about the younger man's plan to place a bomb on a bus full of Russians visiting Pakistan.
"You entered Pakistan on a visa," Azzam reminded him. "The visa is a contract. You signed when you obtained the visa that you would not be a troublemaker nor break the laws. A Muslim should not break a contract."
"Pakistan is a Muslim country," bin Laden told him, by which he meant that non-Muslims had no business coming there.
It was one thing, Azzam argued, to kill Russians who invaded Afghanistan and held it by force, quite another to target innocent civilians on a holiday to a country that welcomed them.
"So what will happen if Russia loses a bus full of people?" bin Laden said dismissively. "It is not going to matter."
He had moved beyond the conflict in Afghanistan. His faith empowered him. God had touched him. This gave him the right to decide, to kill.
Bin Laden also felt that jihad demanded that he actually fight as well, not just take part in recruiting, training, and paying others to do so. The older man argued with him for months, no doubt convinced that a multimillionaire Saudi was worth more to the cause alive than dead. But bin Laden had made up his mind. He was going to cross the border and join the battle. In 1987, he split with Azzam. He recruited his own band of about two dozen Arab fighters, creating the kind of fighting unit he preferred—a pure, all-Arab force of men who fought for religious reasons alone, not just for the principle of Afghan nationalism. Equipped with weapons and bulldozers, they drove ten miles or so into Afghanistan, joined up with some like-minded Afghan fighters, and set about building a mountain outpost near the village of Jaji. Bin Laden fortified a series of ridges and began building roads and other structures—he said a school and a hospital—that advertised their presence. It was in easternmost Afghanistan, in rugged country, and was not a strategically important spot, at least not in any conventional sense. Bin Laden called it al-Masada, the Lion's Den. It was near a much larger Soviet garrison and its primary purpose was to provoke an attack. To a practical man like Azzam (who would be assassinated two years later) this probably appeared foolhardy, but bin Laden lived in a world of romantic fantasy, and in that realm, al-Masada made perfect sense. The battle was not just for Afghanistan, but for the whole world. It was the beginning of a new caliphate, the dawn of a new Muslim age. He was a holy warrior, and warriors did not win battles by writing checks and making videos and leading from the rear. In his view, the idea wasn't to defeat the Soviets in battle, or even to survive, but to display such heroism and resolve that it would inflame the fighting spirit of the greater Muslim Nation.
"God willing, we want the Lion's Den to be the first thing that the enemy faces," bin Laden told a Syrian journalist. "Its place as the first camp visible to the enemy means that they will focus their bombardments on us in an extreme manner."
And the Soviets obliged, dropping napalm and so many tons of conventional explosives that the outpost and the area around it were denuded of trees and vegetation. Then they attacked directly, encircling the outpost. The siege lasted for twenty-two days, with a heavy toll on both sides. Some of bin Laden's men were more skilled fighters than he was. Abu Hafs (Mohammed Atef, an Egyptian policeman who would be killed in 2001) and Abu Ubaidah (Ali Amin al-Rashidi, also a former Egyptian policeman, killed in 1996) led punishing counterattacks. The Soviets eventually gave up and retreated, handing the Arab fighters an inspirational victory. It had unfolded for bin Laden miraculously, a clear sign from heaven.
He would later tell the Syrian journalist, "At seven on the twenty-seventh morning of Ramadan 1407 [April of 1987], most of the people were sleeping in the camp because it was Ramadan. Then I saw things that, by God, I have never seen before. A Soviet airplane, a MIG, I believe, passed by in front of us, when a group of our Afghan mujahidin brothers grouped together [and attacked]. The plane then broke into pieces and fell right in front of our eyes. This battle is what gave me the strong will to continue with this war."
By all accounts bin Laden fought bravely, exposing himself to danger and the extremes of deprivation and cold like everyone else in the camp. He was injured during the fighting and, at one point, he later told an interviewer, he lay unconscious and bleeding in a trench, surrounded by his dead comrades. He was ultimately rescued, but only after losing a lot of blood, an incident that he would later say had given him chronically low blood pressure. Bin Laden's willingness to place himself at risk greatly enlarged his reputation. It mattered little in the end that the battle had been meaningless in practical terms. The Battle of Jaji was proclaimed a great victory, and bin Laden, having conceived it, was its hero. Reporters trekked out to al-Masada to meet this Saudi multimillionaire who fought with suicidal conviction. One of them, Ahmad Zaidan, a Pakistani newspaper reporter working for a group of Arab newspapers, found an extraordinarily pious young man in complete command, who had supplanted the role once played by the far more famous Azzam, and who was surrounded by devoted followers. Bin Laden had transformed himself from a rich-kid backer on the sidelines into a frontline mujahidin leader.
It brought him more than new recruits. It affirmed his sense of destiny. By then he had become the Sheik. He was thirty years old, tall and thin, with long full features and a long dark beard that further elongated his face. He preferred traditional Arab robes and cultivated a lofty, saintly mien, affecting abject humility. He was theatrically holy. From time to time he would receive audiences of reporters, and after each question he would sit silently for a few moments, mouthing prayers, as if waiting for the Almighty to formulate the response for him, and only then would he speak, in a voice so soft that everyone had to lean close to hear him. He fasted once or twice a week and rejected the simple comforts and conveniences of modern life that he could easily afford. He shunned electricity, doing without air-conditioning and refrigeration in even the warmest climates, as when he and his family lived in the Sudan. All the better to harden himself and his family for the privation of war, for life as a fugitive. Followers were now drawn to his renown, to his sincerity, to his daring and his conviction, but also to his money. His fortune was still key. For those who had experienced the heady days of jihad in Afghanistan and preferred to make a career of it, bin Laden could provide the means, and possessed the reckless vision. For most Arabs the caliphate was ancient history, but to the Sheik it was destiny. God had chosen him. Surviving the bitter Russian siege at Jaji reinforced those beliefs. Qutb had called for a pure Muslim state, a base from which to spread the cause. Afghanistan seemed to be the place. It had been called Khorasan when it was converted to Islam in the seventh century and had stood as one of the great pillars of the caliphate for centuries. Defeating the Soviets there would have deep resonance among believers. It was, perhaps, the right place. And in bin Laden's mind, it had started at al-Masada, where the pure of heart, outnumbered and outgunned, had righteously defied Soviet MIGs and bombs and weeks of determined assault.
Then the impossible happened. Just as they had backed away from al-Masada, in 1989 Russian armies retreated in frustration from Afghanistan. Within three years, the Soviet empire itself collapsed, closely followed by the regime it had left behind in Kabul. Bin Laden returned to Saudi Arabia with an outsized reputation as author of this titanic accomplishment, and he gained even more disciples. He and the men who had fought with him at Jaji saw themselves as the fulcrum of this triumph and named themselves "the Base," or al Qaeda. They were the soul of what bin Laden saw as the emerging caliphate, a true Muslim Nation.
It was, of course, absurd. If anything, the source of the mujahidin's triumph had been the billions of dollars of U.S. aid and arms that Michael Vickers had helped steer to Afghanistan after the Soviet invasion. But bin Laden was less interested in the truth than in appearances, and in the latter, he and his followers excelled. Their style spoke volumes. Their long beards and hair and prayer caps and robes made them seem like men from an ancient, holier time. They adopted bin Laden's asceticism. They embraced struggle and death, bragging that their desire for martyrdom trumped their attachment to life itself. They pitted themselves against power. They were natural men, real men. Their very shabbiness advertised their authenticity. They were pious. They believed that happiness and justice were not things civilization was evolving toward, but things that had been lost.
The fall of the Soviet Union had many causes, of course, and the drawn-out humiliation in Afghanistan was certainly among them, but for the devout there was only one cause: the hand of God had once more moved clearly in human history, just as it had in the legends of old. No serious scholar would credit bin Laden with a critical role in the effort, much less a role in the collapse of the Soviet state, but in the Sheik's mind that was how it had gone. It made for a great story, the powerless but pure of heart overcoming impossible odds. The Sheik loved stories like these. He was a poet himself, a fantastical one, given to cosmic sweep and romantic cliché. He celebrated violence and death in the struggle to defend the faith, with centuries-old imagery of swords and steeds, soaring mountains, and fearless warriors.
He hunches forth,
Staining the blades of lances red.
May God not let my eye stray
From the most eminent humans,
Should they fall.
As the stallion bears my witness
That I hold them back,
My stabbing is like the cinders of fire
That explode into flame.
He used his poems to explain, excite, and recruit in parts of the world where traditions were still tribal and oral, but the poems were also an expression of how he saw himself, how he believed the world to be. As a younger man he had composed and recited his poems at weddings and other occasions. He was stitching his own life and his modern struggle into images of a glorious past. The Sheik often enclosed verses in his letters, and instructed that they be read on important occasions—published or broadcast. The Afghanistan victory brought the ages of heroes and mighty deeds to life in modern times. In his poetry, he was arguing that we, too, live in an age of miracles.
After the collapse of the Soviet state, even the wildest reach of his ambition seemed possible. When Saddam Hussein invaded Kuwait, the Sheik, then living in his home country, wrote a series of letters to King Fahd demanding that American forces not be allowed to enter Saudi Arabia and offering to put together a force of mujahidin to expel the Iraqi forces himself. His pleas were ignored. Huthaifa Azzam, who had remained friends with bin Laden for years after the Afghan conflict, remembers this as the only time he ever saw the studiously mild-mannered Sheik ever lose his temper. Bin Laden's outrage and sense of betrayal were complete. He was considered dangerous enough in his home country that he was placed under house arrest.
After the kingdom's refusal to adopt his plan for a renewed holy war, instead opting for the more practical option of inviting the United States and other apostate countries to assemble military forces to confront Saddam, bin Laden's brothers used their influence to get his passport back, and he left Saudi Arabia permanently, first traveling to Pakistan, then to Afghanistan, then the Sudan, and then back to Afghanistan.
The younger Azzam was attending a conference in the Sudan in 1995 when he dropped in to see bin Laden. During his visit, he recalls, he met Khalid Sheik Mohammed, who had brought his notorious nephew, Ramzi Yousef, a Sunni extremist who was at that time a fugitive sought by the United States for the first attack on the World Trade Center, two years earlier. Azzam described Yousef as a scrawny man whose bearded face had been scarred in a bomb-making accident. Both he and his uncle would later be characterized in The 9/11 Commission Report as "rootless but experienced operatives." Yousef would be captured in Pakistan later that year. According to Azzam, the Sheik listened as Yousef outlined a plan to attack targets in the United States again, including the World Trade Center towers, this time by hijacking commercial airliners and flying them into buildings. He wanted al Qaeda to help with recruiting martyrs and raise money for them to travel to the United States for flight training. As Azzam recalls it, the Sheik said, "We have nothing to do with the United States, why should we attack them?"
This may have been for Azzam's benefit, since bin Laden had been preaching a duty to attack America for years. Ever since he had broken with Azzam's father, the Sheik had steered a far more radical course. Huthaifa Azzam was not the radical bin Laden had become, and would have been seen as suspect, perhaps even as a spy. It might explain why bin Laden would have made a show of rejecting Yousef's idea in this meeting. Already al Qaeda had been implicated in attacks and plots on Americans, including sending military advisers to Somalia in 1993 to help tribal militiamen target American helicopters, and a car bomb explosion in Saudi Arabia that killed five American and two Indian soldiers. If the account is true, the meeting Azzam described is significant because it would be the first known mention of what became the 9/11 plot to bin Laden. The idea for the attacks is customarily attributed to Khalid Sheik Mohammed, but Yousef's fixation on the towers is well documented. He later confessed that he had hopes that the 1993 bombing would collapse the towers and kill 250,000 people. Whatever bin Laden said at this session, al Qaeda would endorse the plan soon enough.
Bin Laden left the Sudan when terrorists linked to al Qaeda and the Egyptian group Islamic Jihad were linked to an attempted assassination of the Egyptian President Hosni Mubarak. Pressure mounted on the Sudanese government after that, and the Sheik was expelled. He had other reasons to go. There had been one known attempt on his life there, and Saudi authorities had cut off payments to the al Qaeda leader from his family inheritance. With funding for his ambitious projects in the Sudan dried up, he left for Afghanistan in May 1996.
Three months later, back in the dusty, rugged homeland of the first great miracle, the Sheik held a press conference to declare war on "the head of the snake." He cited a list of grievances against America and demanded that its forces be withdrawn from "the land of the two Holy Places"—Saudi Arabia. It was time for the next great struggle, he preached, which would topple the world's other superpower, the United States. That would mean the end of Israel, America's client state, and the dawn of a new Islamist age. There was nothing stealthy about his plan, just as there had been no disguising his intentions when he built al-Masada near the Soviet garrison at Jaji. The whole idea was to confront the enemy openly, to make a show of inspired defiance. Indeed, making the show was more important than succeeding. Audacity was the point.
In 1998, he told ABC News correspondent John Miller, to whom he gave an interview in order to directly reach American audiences: "I'm declaring war on the United States. I am going to attack your country."
Few Americans took the threat seriously. Some crackpot Arab in the middle of nowhere had declared war on the United States. The country had more important things on its mind . . . like sex. Former White House intern Monica Lewinsky said it had transpired between her and President Clinton, and he was still denying it. Hillary Clinton was conjuring up "a vast right-wing conspiracy." House Speaker Newt Gingrich, who was then secretly carrying on his own extramarital affair with a staffer twenty-three years his junior, was leading the charge to impeach the president. Basketball star Michael Jordan clinched the Chicago Bulls' sixth NBA title with a fade-away jumper in the final seconds of his last game with the team. Bin Laden was of interest to those whose job it was to protect the United States from foreign threats but, as we have seen, even in those circles he did not merit urgent concern.
But the Sheik had big plans, and the means to carry them out. The bombings of American embassies in Nairobi and Dar es Salaam in 1998 and the attack on the USS Cole two years later, got America's attention, but al Qaeda was still considered by most in the intelligence and military communities to be a nuisance—a deadly and growing nuisance, perhaps, but a nuisance. Bin Laden's own life grew more difficult, as the Clinton administration devoted more effort to finding and killing him. Two of bin Laden's wives left him during this period, choosing to abandon the path of jihad. But the Sheik persevered through the next decade, training recruits, plotting, and laying the groundwork for the next miracle.
The fall of the World Trade Center towers was his vindication. What greater proof of God's purpose could the world wish to see? Bin Laden placed great stock in signs. He had long sought to deliver a decapitating strike, hitting the American centers of finance, government, and military. It had seemed an impossible goal. One had to be crazy, or inspired, to think he could pull it off.
The collapse of the World Trade Center had been the second great miracle in his life. The fall of the iconic towers in Manhattan, symbols of the wealth and power of the world's remaining infidel superpower, seemed to presage the imminent collapse of America, too. It was further proof that the path he followed was divinely inspired.
In his wildest hopes he had not imagined that the planes might bring down the towers completely. God's hand had surely been in it. The physical force of the colliding planes, the exploding fuel, and the resulting infernos were themselves, he believed, inadequate to explain it. On a video found by American soldiers in Kandahar weeks after the attacks, bin Laden is seen conversing happily with a group of sympathetic Saudi visitors, alternately praising God and celebrating the remarkable outcome, painting the attacks in magical terms. It was a practice familiar in religious communities. You decorated the truth with dreams and portents, weaving magic into the facts, coloring them with divine favor.
In the footage, bin Laden knelt on a large pillow, wearing his military-style camouflage jacket, his head wrapped in a white turban, speaking so softly that his words were barely audible. When he spoke, the others in the room would fall silent. Bin Laden seemed stiff, perhaps because he knew he was being videotaped, and he elevated his long slender left hand and two fingers like Christ or a saint in an old icon. In older photographs, before he became so notorious, he appears more relaxed and human, even graceful, his long, thin features animated with a frequent smile. Now he was important. He assumed the pose of the important. He said he had received notice about the precise day of the attacks the week before, so he had been ready for the news. In Jalalabad it had been early evening. He described how he and his fellow mujahidin had gathered around a radio to listen to the BBC's Arabic-language radio broadcast.
"We calculated in advance the number of casualties from the enemy who would be killed based on the position of the tower," he explained. "We calculated that the floors that would be hit would [be at most] three or four floors. I was the most optimistic of them all due to my experience in this field [construction]. I was thinking that the fire from the gas in the plane would melt the iron structure of the building and collapse the area where the plane hit and all the floors above it only. This was all that we had hoped for."
When the others began celebrating after the first plane hit, bin Laden said he told them, "Be patient." There was more news to come. The difference between the first and second plane hitting the towers was twenty minutes, and the difference between the first plane and the plane that hit the Pentagon was one hour.
As much as the first miracle, this one seemed to mark a profound milestone in his struggle. But he was cautious at first about claiming credit.
He sought out Hamid Mir, a well-known Pakistani journalist who had met and interviewed him years earlier. As Mir explained it, he was in his Islamabad office when the 9/11 attacks occurred. Within hours a messenger came to him with a written statement from the Sheik. Mir recognized the messenger. He had seen him when he had first met with bin Laden years earlier in Kandahar. The statement read, "I praise all those who conducted that operation. But I am not directly involved."
Mir told the messenger: "You contacted me immediately after the attacks and you reached my office within a few hours and that means that you were not in Afghanistan at that time. That means that bin Laden gave you this statement before the attacks. And that means that you people were aware of the attacks."
The messenger pleaded ignorance.
"The Sheik just gave me this letter. He said, 'You will contact Mr. Mir at six o'clock and you will reach his office at seven o'clock and then you will come back.' So that was my job and I have done my job, okay? Bye."
The messenger left.
Mir's own reporting reputation in Pakistan is controversial. He has often angered the government there, and he has been accused of being sympathetic to extremists, but his reports have been recognized worldwide as credible and often extraordinary. His many run-ins with Pakistani officialdom had burnished his reputation for independence among Western reporters, so in the days immediately after the attacks he was interviewed by many who were searching for some insight into al Qaeda. After he appeared on Larry King's interview program on CNN, Mir was again contacted by one of bin Laden's messengers, who said the Sheik wanted to talk to him. So Mir traveled to Jalalabad in November of 2001 in search of the scoop of a lifetime. Bin Laden was now the most wanted fugitive in the world.
He said that when he arrived in Jalalabad he waited a full day before being contacted by a group of low-level al Qaeda figures, who said they knew nothing of bin Laden's summons.
"We are not aware of why you are here or who wanted you here," one said. "We are not aware, just wait."
More hours passed. Eventually, Mir was contacted and instructed to travel to Kabul. He spent several days in the Afghan capital, being shuttled first to one safe house, then another. It was now weeks into the American invasion, and just days before the Taliban fell. The capital was braced for tumultuous change. He could hear bombs falling on the city day and night, explosions that shook the earth. The Islamist kingdom under construction was coming apart all around him. Mir feared he would never get out alive. If an American bomb didn't kill him, these al Qaeda fighters would. On the morning of November 8, six days before the Taliban fled the city, he was escorted into the presence of bin Laden and al-Zawahiri. Both men said they had come to Kabul to attend funeral services for a comrade.
Bin Laden seemed serenely untroubled by the unfolding disaster around him, and in high spirits. Sitting with the two most wanted men in the world, surrounded by other members of their group, Mir began nervously. He asked, "Are you responsible for 9/11?"
Bin Laden reached over with one long finger and shut off Mir's tape recorder.
He asked, "Can you ask this question to George W. Bush: Are you responsible for the killing of many Muslims in Palestine and Iraq?"
"No, I cannot ask him this question because I'll not get any chance to interview him," said Mir.
"Okay, but if you do get a chance and if you ask this question, will he answer?"
"No," said Mir.
"Then why are you asking this question of me?"
"Because he is a politician and you are a fighter," said Mir, thinking fast, and then, falling back on any journalist's most trusted tactic, he resorted to flattery. "You said that you are a mujahid, so there must be a difference between a politician and a mujahid. Mujahid always speak the truth. You have to answer my question."
"Off the record, yes," said bin Laden. Then he turned the recorder back on. "I cannot answer your question because my answer will create problems for the Taliban."
Clearly the Taliban had problems enough. Bombs were exploding outside so close that the journalist was shaken. His fright amused bin Laden.
"Oh, Mr. Mir, maybe today you will be killed with me at this place," he said, lightly mocking him. "You are here to interview me and maybe you will not be able to report that interview back to your newspaper. What will happen with you?"
Bin Laden and the others laughed. They spoke for hours. Mir worked through a list of questions he had prepared. They discussed the various attempts that had been made on bin Laden's life, and after shutting off Mir's recorder again the Sheik spoke at length about his disdain for Iraqi dictator Saddam Hussein and Libyan strongman Muammar Gaddafi, neither of whom had joined the struggle against the Soviet Union years before. Mir asked him about widespread reports that he suffered a kidney disease and needed dialysis treatments. Again, the Sheik laughed. He promised to address the question in more detail when they had finished the interview. So when Mir finished asking his questions, breakfast was brought in for them—olives, cheese, bread and butter, beef. Bin Laden began eating vigorously.
"A kidney patient cannot eat a lot," he told Mir. "You see this is beef? I am eating beef. You see this is cheese? I am eating cheese."
Mir looked to al-Zawahiri, who agreed. "Yes, I am a doctor, I can confirm, kidney patients cannot eat a lot."
"I can ride my horse seventy kilometers without any stop," said bin Laden.
He kept Mir far longer than the reporter had expected, or desired. The Pakistani, having asked his questions, was eager to leave and get out of the city. He knew that bin Laden might well be a target for the Americans. After this exchange about the Sheik's health, Mir asked, "Can I leave now?"
"No," said his host. "You spend some more time with us and have some tea and you can ask some other questions, off the record questions."
Bin Laden told Mir that the day after the attacks in America, his youngest wife had given birth to a daughter, whom he named Safiyah.
"Why Safiyah?" Mir asked.
Bin Laden explained that Safiyah had been an aunt of the Prophet and an early convert to Islam. She had given up all her possessions to join the faith, and had taken part in battles and slain unbelievers in defense of the faith.
"Are you now planning to involve the females of your family in your fight against the Americans?" Mir asked, mindful of the Sheik's strictly traditional views on the role of women. Bin Laden laughed.
"Maybe Safiyah will follow the footsteps of her father," he said, and resisted when Mir seemed to be taking the comment too seriously.
"Just forget, forget," he said.
"No, no, it's very important for me."
"Okay, rest assured Safiyah will not become a mujahid, don't worry," bin Laden said, and laughed again. And at last he said, "Okay, now you can go back."
Despite the relentless American attacks and the imminent defeat of the Taliban, the Sheik was filled with confidence from the impact of 9/11. All was unfolding as he foretold.
He did not see any of his attacks as wanton terror, as his horrified enemies did. They were retribution. They were not simply just, but divinely inspired. They were his duty.
"We kill civilian infidels in exchange for those of our children they kill," he told an interviewer from Al Jazeera five months after the 9/11 attacks, citing an estimate he often used, that a "million children" had died in Iraq owing to UN–imposed sanctions on that country, a number most serious analysts considered absurdly inflated. Asked about the children killed who had been attending a school inside the World Trade Center, he reasoned: "[Retribution] is permissible in law and intellectually. The men that God helped [on September 11] did not intend to kill babies, they intended to destroy the strongest military power in the world, to attack the Pentagon that houses more than 64,000 employees, a military center that houses military intelligence. The twin towers are an economic power and not a children's school."
It is worth noting here, and for most it goes without saying, that Osama bin Laden's ideas were neither new nor compelling outside his relatively small circle of followers. They belonged to an ugly cul-de-sac of history, an era where witches and heretics were burned in town squares. They were adolescent ideas, in that they remained willfully ignorant of all that had come before. There are many who choose to believe that certain ancient texts are literally the word of one God or the other, but not many who would go so far as to regard as a sacred duty the slaughter of those who disagree with them, or to kill in order to advance their aims. This was a philosophy that would never appeal to more than a few dedicated fanatics. But one of the peculiarities of the modern world is that, because of telecommunications, small groups of like-minded people, even if widely scattered, can form a community of belief. They can feed off of each other, and can come to wield influence far beyond their actual numbers or appeal. Bin Laden's was the first to use these tools to build his network into a deadly force. The idea of turning fully fueled commercial airliners into guided bombs effectively gave al Qaeda the destructive power of a small air force or small arsenal of missiles. The suicide attackers who pulled it off had been recruited and trained internationally, financed by global money transfers, and steered by telephone and e-mail. The attacks themselves were designed to create a horrible spectacle for the entire world, television providing the audience, complete with replays and analyses for those who came late. It was a backward-looking movement with forward-looking tactics.
3
Taking Up Arms
Late Summer 2010
"Mr. President, Leon and the guys at Langley think they may have come up with something."
Tom Donilon brought this up at the end of President Obama's morning briefing one day in August. Instead of being briefed on sensitive national security issues by a CIA analyst, as President Bush had been, Obama preferred to be briefed by Donilon, his deputy national security adviser. Donilon would continue this practice even after he stepped into the top National Security Council job a few months later. It was that time of year when not much was going on in Washington. Heat and humidity drove everyone from the capital except the most determined tourists and those who had to stay.
"Something related to bin Laden," Donilon said. "We don't know yet what this is, but I think you need to have them in here for a briefing."
Donilon had been with Obama ever since the final stages of the 2008 campaign, when he was summoned to reprise a role he had played for President Clinton, coaching the candidate for a series of formal debates with his Republican rival. The Bush years had been a long break from government service for Donilon, who had continued with his work as a lobbyist for Fannie Mae for several years and had then moved on to become a partner in the D.C. law firm O'Melveny & Myers. But his heart was still in politics and governance, and when he was invited to help prep Obama for his face-off against Republican candidate Senator John McCain he leapt at it. He believed in the importance of presidential debates. They not only gave the public a better sense of the candidates, but they forced those running to examine the weaknesses in their own thinking and policy prescriptions, and to confront them, before an audience of millions. One of the first recommendations he made to Obama, which was adopted, was that he debate McCain on foreign policy issues first, precisely because it was an arena in which the veteran senator and war hero was thought to have a strong advantage. McCain's storied military service in Vietnam, where he was held prisoner for five years after his A-4E Skyhawk was shot down over Hanoi, and his twenty-six years in Congress, weighed impressively against Obama, who, twenty-five years younger than McCain, had never served in the military and had yet to complete his first Senate term. On paper, McCain had stronger qualifications for the job. But presidents were not hired, they were elected, and even the most distinguished résumé counted for little next to the impression the candidates made on the public. Donilon felt that if Obama could be seen on national television holding his own in a national security debate with McCain, voters could better begin to imagine him as their president. And better for that to happen sooner than later. He believed this is what Obama accomplished.
His role in prepping the candidate meant confronting him with the cracks in his thinking before he stepped onstage. In that sense, Donilon was one of the only people around Obama whose job it was to kick him, so to speak—to ruffle the candidate's famous cool. He worked at tripping Obama, poking holes in his reasoning, challenging his facts, pushing him beyond his stump-tested applause lines and polished talking points.
"All right, that's what you say on the campaign trail," he would say, "but if you are pressed on it, what do you really mean?"
Or, "I've heard you say that, but are you willing to live with it as president?"
Or, sniffing disagreeably at one of the candidate's typically long-winded responses, "And how do you explain that in ninety seconds?"
The candidate must have liked this sort of thing, because he had kept his tormentor close ever since. Donilon found him to possess a fine mind and a deep knowledge of American history and the law. It was hard to get the better of him in argument. To engage him fully meant being fully prepared; otherwise you were likely to come away humiliated. A physically expressive man, Obama had a way of shooing away an ill-founded argument with an amused smile or a more subtle expression like a raised eyebrow and dismissive tilt of his head. Donilon worked hard to avoid that look. He was rarely seen outside the corridors of the White House, a rumpled creature of the cramped warren of offices occupied by the National Security Council leadership downstairs. He was rarely interviewed by the press and seemed egoless. Obama drove his inner staff hard, but Donilon, if anything, drove himself harder. He graded his performance every day—high or low. After the election, Obama asked him to chair his State Department transition team, and had then placed him under General James Jones on the NSC staff. Jones, a former Marine Corps commandant, had been recruited in part as a bridge to the U.S. military, with which Obama had virtually no firsthand experience, and he had agreed from the start to stay in the job for only a year or two. From the beginning of the term Donilon was seen as Jones's likely successor.
It particularly pleased him to have something new for the president about bin Laden. There had been no scent of the world's most infamous terrorist for more than seven years, ever since he had slipped away from the mountain outpost of Tora Bora during a botched siege by allied troops. The Bush administration had said for years that he was somewhere in the mountainous regions of northwest Pakistan but, in truth, they had no idea. There had not been a lead or a sighting in years. Obama had taken office determined to resurrect the hunt.
On May 26, 2009, four months into his presidency, he had ended a routine national security briefing in the Situation Room by pointing to Donilon, Leon Panetta, his newly appointed CIA director, Mike Leiter, director of the National Counter Terrorism Center, and Rahm Emanuel, his chief of staff.
"You, you, you, and you," he said. "Come upstairs. I want to talk to you guys about something."
The four followed Obama up a short flight of stairs and through the warren of narrow West Wing hallways to the Oval Office. Afternoon sun poured through the windows from the Rose Garden. They didn't sit down. This was something quick that the president had been thinking about and wanted to impress on them personally. They had been on the job now long enough to have taken hold of America's vast intelligence apparatus . . . time enough to have eased fully into their new roles.
As Donilon would tell me, Obama said: "Here's the deal. I want this hunt for Osama bin Laden and al-Zawahiri to come to the front of the line. I worry that the trail has gone cold. This has to be our top priority and it needs leadership in the tops of your organizations. You need to ensure that we have expended every effort to take down the top leadership of al Qaeda, especially these two individuals. And I want regular reports on this to me, and I want them starting in thirty days."
Donilon followed up and drove the point home with a memo, which the president signed. He sent it to each of those present. It read: "In order to ensure that we have extended every effort—directly provide to me a detailed operational plan for locating and bringing to justice Osama bin Laden."
That brief huddle in the Oval Office had not been scheduled, as virtually every minute of the president's day was, and Obama had not discussed it beforehand with Donilon. The president had plenty of other things to think about. He was beginning to withdraw U.S. troops from Iraq and was reevaluating the future of the ongoing conflict in Afghanistan. He had authorized a covert cyberwar on Iran's efforts to enrich uranium to weapons grade, and he was trying to assemble a coalition to apply economic pressure on that country to end its pursuit of nuclear weapons. He had vigorously expanded the secret program to target al Qaeda leaders inside Pakistan and other countries with drones, putting unrelenting daily pressure on the organization. He was trying to counter a Chinese military buildup by reorienting the nation's military forces toward the Pacific Rim. So there was plenty on the agenda every time his national security team sat down with him. But as the president would later tell me, he wasn't hearing enough about bin Laden to convince him that everything was being done, that every effort was being made. He wanted to make sure the right people knew what a big priority this was for him. And in the months that had followed, in between those monthly reports, he brought the matter up again and again. It was one of several things he raised at nearly every security meeting. He would always ask about cybersecurity efforts and he would always ask about Osama bin Laden.
Obama's leadership style was to enumerate clear, consistent priorities, and stay focused on them until they were accomplished. About twice a year he would meet with the national security team for several hours with nothing else on the agenda. He would bring in a legal pad on which he had listed his priorities in handwriting so small and meticulous that from across the room it looked like type.
"Hey guys, these are the three most important things we're working on right now," he'd say. "And this is where I want your efforts."
He'd go through his list item by item and they would discuss and critique their performance: where they had made progress and where they had not. Often he would move things up or down on his list or add things, but when he was done everyone had a clear understanding of where they should be spending their time and resources. Always, from the first such session, finding bin Laden had been at the top of that list.
As far as Obama was concerned, getting him was more than just symbolic. He had long been critical of Bush's "War on Terror." The way he saw it, America was not at war with something amorphous, like a concept or a tactic. It was at war with specific individuals who had attacked the country and continued to threaten it. When he took office in 2009 al Qaeda and its affiliate organizations remained the first clear and present danger, even after two long, bloody wars and the unceasing efforts of America's intelligence and special ops soldiers.
Obama had been sternly warned about this by Bruce Riedel, a former CIA analyst and Brookings Institution scholar whom he had called at home just days after the inauguration and asked to conduct a sixty-day review of American policy in Afghanistan and Pakistan. Eight days before he had pulled his intelligence chiefs into the Oval Office, Riedel had briefed him on his findings in a long meeting aboard Air Force One. He had told Obama that, in his estimation, al Qaeda was more dangerous today than it had been on September 11.
As Bob Woodward would report in his 2010 book, Obama's Wars, Riedel said, "Some al Qaeda watchers would argue that bin Laden, hiding in Pakistan, is irrelevant. He's stuck in a cave somewhere, and yes, he puts out these audiotapes once in a while, but he's more of a symbol than the commander of a global jihad. What I learned is that's just not true. He communicates with his underlings and is in touch with his foot soldiers. His troops believe they are getting his orders, and we know from good intelligence that they are . . . These guys are serious. They are clever, and they are relentless. Until we kill them, they're going to keep trying to kill us."
As Obama saw it, there was no way to defeat al Qaeda so long as its founder and spiritual leader remained at large. He was the soul of the organization. The president believed that bin Laden wasn't just evil, he was charismatically evil.
"He understood that with technology and modern media, the potential impact of a big event can magnify and leverage the power of even a small group," the president told me. "In that sense, although the notions of terrorism hadn't obviously developed or started with him, I think he had an understanding of the West and where our potential vulnerable points were that made him a singular figure, somebody who was uniquely capable of doing great damage to us."
Despite the simple life he preferred and his romantic notions of the past, bin Laden understood modern media and exploited it, Obama said. It gave him an influence far beyond the reach of his actual following. The September 11 attacks had shaken the world.
President Bush had felt the same way. Unable to squelch his Texas swagger early on, he had said he wanted bin Laden "dead or alive." But in the view of the Obama administration, the two wars Bush had launched gradually became usurping priorities. There is, as Donilon would put it, "limited bandwidth" in the White House. In the final years of the Bush administration, even though the man at the top still badly wanted bin Laden, the effort to find him was publicly downplayed in the way Riedel explained. It was said that bin Laden was out of touch. That he had been effectively sidelined and, so far as operations were concerned, rendered irrelevant. Unable to find him, the Bush administration had de-emphasized the importance of finding him.
The way Obama saw it, this was a mistake. America's war-making bureaucracy was vast, and without determined pressure from the White House, without an enumerated list of priorities that kept coming back and coming back until each item was crossed off, even urgent concerns got lost. Just keeping track of all the missions under way on any given day was more than a full-time job. There were U.S. troops on the ground in more than 150 countries around the world. When those missions turned hot, as they had in Afghanistan and Iraq, they devoured not just men and resources but the time and attention of the decision makers atop the chain of command. The essence of leading any very large enterprise was maintaining priorities, and while bin Laden had never slipped from the top during the Bush years, the list itself had become very crowded. The bottom line, as Obama put it to Panetta and Leiter, was that bin Laden's trail had gone cold. The president wanted it warm again.
Now, more than a year later, the agency finally had something to report. It had found an unusual compound just outside Abbottabad while looking for an al Qaeda figure who went by the name Abu Ahmed al-Kuwaiti, "Ahmed the Kuwaiti," a man known to have been a trusted aide and courier for bin Laden. Along with family, known associates, financial webs, and other networks, couriers had long been seen as potential cracks in the walls around the fugitive Sheik. Too wary to use cell phones or Internet links, bin Laden relied on couriers to distribute by hand his letters, poems, and occasional video and audio pronouncements. Reversing the paths to media outlets taken by these tapes or thumb drives always ended one or two steps short of their origin. The Kuwaiti might be one of those final links, perhaps even the courier who dealt with the Sheik directly. The search for him had lasted eight years. It had taken the CIA five just to learn his real name, which was Ibrahim Saeed Ahmed. And then the trail had led them to this very curious residence.
Panetta brought two of the agency's bin Laden team leaders with him to the Oval Office. The lead analyst, who would become known as "John" (his middle name), was a tall former college basketball player, now middle-aged, who had devoted himself to the hunt for most of the previous ten years. He had a broad chin and a big-featured face and looked more like an athlete than someone who spent most of his time before a computer monitor. At Langley, he reported to Michael Morell, who had risen to deputy director in the years since he had been briefing Bush.
The agency men handed around classified pictures and maps and analytical material, and walked the president and Donilon through their thinking in great detail—the reverse engineering that had helped them identify "Ahmed the Kuwaiti" and the suspicious nature of the compound itself. Panetta compared Abbottabad to a well-to-do northern Virginia suburb. The compound was eight times larger than any of the surrounding residences. Unlike most, it did not have any Internet or phone connections. The walls that surrounded it were built unusually high, topped by two feet of barbed wire. There were even walls around a patio at the back of the third floor. There was no way to see inside the house itself, from the ground or above. The windows were made of reflective glass or had been coated to achieve the same effect. The agency first learned that not only Ahmed and his family lived there, but also his brother Abrar and his family. They went by assumed names in the neighborhood, Ibrahim called himself Arshad Khan and his brother went by the name Tareq Khan. Both had been born in Kuwait, but ethnically they were tall, fair-skinned, bearded Pakistani Pashtuns. They had never been wealthy, but their compound appeared extremely pricey. And in addition to the high walls, it seemed the brothers observed extraordinarily strict security measures. They even burned all of their trash on-site. Other than to attend the local religious school or to visit a doctor, none of their children left the compound. In telephone calls to other far-flung family members, always made from locations distant from the compound itself, they lied about where they were living. The CIA had been known to misinterpret many things, but one thing it knew inside out was high operational security.
The agency had been investigating the compound quietly, snapping pictures from above and spying on it with agents on the ground—who couldn't see inside but who asked casual questions of those living nearby, always careful not to appear too curious. Who lives in that big place? I wonder what the people who live there do? That and telephone intercepts had produced two discoveries in recent weeks that the agency considered greatly significant, and persuaded Panetta that he ought to bring the discovery to the president.
The first was that living inside the compound on the upper two floors of the big house was a third family. No member of that family ever left the grounds. Its children did not even leave to attend school with the others. Neighbors in Abbottabad who knew of the Khan brothers and their families were not aware of this third one. And there were signs that the brothers, who ostensibly owned the place, served this hidden family. One or the other brother was always present, so the third family was never left alone. Ibrahim Ahmed and his family occupied the guesthouse on the grounds, and his brother Abrar and his family lived on the first floor of the main house.
The second discovery was that Ibrahim Ahmed was apparently still working for al Qaeda. Though he was known to have been close to bin Laden years earlier, the agency had no proof that he had retained the connection. Some of the detainees interviewed about him over the years had said that he had left the organization, in which case he might now be working for anyone with a need to lie low: An organized crime figure? A rich man with political enemies? A Saudi millionaire with a mistress or hidden second family? But in a telephone conversation with an old friend that summer, a call that the United States monitored, Ahmed was peppered with the standard questions—"What are you doing now? What are you up to?" At first he didn't answer. He dodged the questions. But his friend was insistent, and so he finally gave in, albeit cryptically. "I'm with the same ones as before," he said. His friend seemed to know immediately what that meant and, after uttering "May Allah be with you," dropped the subject. That suggested that whomever Ahmed and his brother were minding in Abbottabad belonged to al Qaeda.
These were the details presented to the president.
"This is the best lead we've had on bin Laden since Tora Bora," said "John."
Obama was familiar enough with bin Laden's background to have long ago stopped picturing him crouched in a cave or living in some sparse mountaintop camp. But to find him in a sprawling compound in an affluent neighborhood known for golf courses and cool summer breezes—they were all surprised by that. Still, the president wasn't especially hopeful. He knew he had been leaning hard on the CIA to come up with something, and demanding updates, so he had to expect they would bring him every scrap. This was a scrap. He found the information intriguing, but only in a general way. The connection to bin Laden was tenuous at best. He encouraged Panetta to press on. He wanted the identity of the hidden family nailed down. He also wanted a "close hold" on the lead, meaning it was not to leave his office. No one else in the military or intelligence chain was to be brought in yet. And they were not to seek help from Pakistan or tip their interest in the compound there . . . yet. The president left open the option of going to his purported Pakistani allies for help once they knew more. In the meantime, he wanted regular progress reports.
"Just emotionally," Obama told me, "I was not particularly optimistic about it. I mean, I think my general view was, okay, these guys are carrying out my orders to pursue every lead. Did I think at that stage that we had the goods? I think I was pretty guarded about not letting myself get overly excited about the prospects."
At that point, the president had been ordering drone hits and special operations raids to kill al Qaeda leaders for nearly twenty months. The skills of America's intelligence and military, honed over nine years of war, had given him tools no president had ever had. National Security Council meetings in this presidency were not just policy discussions. They regularly concerned matters of life and death for specific individuals. The capability developed over the previous decade armed the president with immediate choices about these prospective targets—people who had been found and identified and were now in the nation's crosshairs. They could be killed on his orders without placing a single American in jeopardy. There had been fifty-three drone strikes in Pakistan alone in the first year of his term. In 2010 there had been more than twice that number: 117. The numbers of strikes in Yemen, while fewer, had been steadily increasing every year, from two in 2009 to four in 2010. There would be ten the following year. Nearly every day the president faced immediate, deadly choices. Should this specific person be killed? Would killing him possibly involve killing others—others less culpable, perhaps others completely innocent?
Decisions like this had always come with the office, and sometimes had concerned questions of life and death for thousands, or even hundreds of thousands—one thinks of President Harry S. Truman making the decision to drop the atom bomb. But how many of these decisions concerned taking a single life? It gave the commander in chief a strangely direct role in the war. There were precedents. During World War II, American forces decrypted a Japanese message revealing that Admiral Isoroku Yamamoto, commander of the Japanese fleet, would be making an inspection tour of the Solomon Islands. His plane was intercepted and shot down, and he was killed. President Kennedy had notoriously plotted to assassinate Fidel Castro during the early 1960s. But these incidents were rare, and were undertaken at great risk. Toward the end of his second term, President Bush, and now Obama, had what was, in essence, a sniper rifle pointed at men regarded as significant terrorists. Obama was routinely presented with a brief on the target: who he was, how important he was, how dangerous he was, how much it might matter to be rid of him, and who else might die as a result. He had only to decide to pull the trigger. This was something new.
This war had demanded something new. After the 9/11 attacks, the two most obvious ways of fighting back had both been defensive: prevent the most dangerous kinds of attacks and prepare to cope better with smaller ones when they occurred. So the United States had spent billions on efforts to block known or obvious avenues of attack, and to improve emergency response. This is what the Department of Homeland Security and the Transportation Safety Administration had been all about. Another step was to secure materials worldwide, such as plutonium, surface-to-air missiles, and toxic biochemicals, that could be used to create especially powerful weapons. This approach is what had led, in part, to President Bush's invasion of Iraq—to secure Saddam's supposed arsenal of weapons of mass destruction.
As for offensive strategy—going after al Qaeda itself—this became immeasurably more difficult once the organization had scattered from its safe havens in Afghanistan. In solving this problem, the United States would bring to bear enormous resources of talent, wealth, and technology. The story of the previous ten years of war, viewed in this broad sense, had been the story of developing the right tools to destroy a terror network. It was still a work in progress in 2010, but it had come a long way. With the military's typical disdain for ordinary English, it had slapped an acronym on this capability. It was called "F3EAD" (Find, Fix, Finish, Exploit, Analyze, Disseminate). It stood for a remarkable fusion of instant global telecommunications, drones, computer-data storage, cutting-edge software, experienced analysts, stealth helicopters, precision munitions, and the operational skills of pilots and shooters who could execute strikes with great surprise and skill virtually anywhere in the world.
When Obama took office he inherited this unprecedented and still-evolving capability. The tool—particularly the use of drones—was proving to be lethal to al Qaeda. As much as it troubled those concerned about potential abuses—pinpointing and killing people by remote control was a scary futuristic concept—it was also, paradoxically, a fundamental advance in the humane pursuit of war. The three basic principles of lawful warfare had long been necessity (violence as a last resort), distinction (targeting the right people), and proportionality (not killing the wrong people). Very few would argue that the nation was not justified in using force to protect itself from Osama bin Laden and his movement, bent on suicidal acts of mass murder. Drones uniquely enhanced compliance with distinction and proportionality. The ability to soundlessly observe a target for days, weeks, or months before deciding to attack greatly improved the odds of hitting appropriate targets and avoiding inappropriate ones. There was no comparison with ground combat or even very precise bombs and missiles. If it was necessary to fight, then drones killed far fewer civilians than any previous war-fighting method, and they did so without placing American fighters at risk.
Obama had kept this capability on a tight leash. In most cases, he alone made the final decision to kill. In some cases, the decision was made by the CIA director. They would review the case against the targets and decide whether to shoot. Obama had directed the Justice Department and the CIA's legal staff to draw up secret guidelines that would mark the first step toward institutionalizing those controls, so that whoever succeeded him in office would inherit clear rules, clear precedent, and clear constraints. The administration had not made these guidelines public, which troubled many who were concerned about the growing use of drones. There was no doubt that within those strictures, whatever they were, Obama had proven himself willing to pull the trigger regularly.
This surprised many. Bush had brought to the White House a light dusting of military experience—he had served as a pilot in the Air National Guard during the Vietnam War period—but he was nevertheless seen by the military as one of them, a president who openly admired the armed forces and who was, to a fault, quick to authorize their deployment. He spoke their can-do vocabulary with a Texas drawl. His father had been a war hero and had served as the CIA director—the headquarters building at Langley was even named after George Herbert Walker Bush. Obama, on the other hand, was strictly civilian. His father was Kenyan. He was a liberal Democrat with an international upbringing—an academic and an intellectual. He had been an early, consistent, and outspoken critic of invading Iraq, which he had called a "dumb war." Indeed, he had initially geared his campaign for the Democratic nomination in 2008 as an antiwar candidate, attacking his foes in the primaries, Hillary Clinton in particular, for her early support of the conflict. Obama had also criticized the more controversial tools of the war—coercive interrogation methods, extraordinary rendition, military commissions, and indefinite detention—arguing that the nation's security should never trump its values. He talked a lot about the need for negotiating with enemies and the virtues of mutual understanding—not the kind of talk that rouses the troops. Much of what most Americans heard from him during his scant twenty months in the Senate concerned hastening America's withdrawal from Iraq and spelling out his desire for a clearly defined exit strategy from Afghanistan. They had expected an all but pacifist president.
But the number of drone strikes in his first two years would be more than four times the total in Bush's two terms in the White House. And Obama's appreciation and enthusiasm for the Special Operations Command was clearly genuine. He seemed to fully embrace General Petraeus's line about going to bed each night with more friends and fewer enemies—with particular emphasis on the "fewer enemies."
Those who had been paying close attention to Obama were not surprised. He had been spelling out for years, in increasing detail, his willingness to wage war in general, and, in particular, his intent to wage war on al Qaeda. Just over a year after the September 11 attacks, as President Bush was gearing up to invade Iraq, Obama, still largely unknown outside of his Chicago district, was invited to speak at an antiwar rally in Chicago. He was one of the lesser speakers, and his talk wouldn't even get a line in the account in the next morning's Chicago Tribune. It was received with lukewarm applause. In his book The Bridge, David Remnick captures Obama's discomfort at the overall tenor of the rally, listening to the plaintive strains of John Lennon's "Give Peace a Chance" and leaning to one of the event organizers, Bettylu Saltzman, to ask, "Can't they play something else?" Giving a rousing speech that would excite the gaggle of tired lefties in Federal Plaza might make for a feel-good moment and some admiring local press, but it could also hurt his chances statewide. He had conferred with the consultants helping him prepare for his Senate run, trying to hone a message that, as Remnick wrote, "would express his opposition to an invasion of Iraq without making him seem disqualifyingly weak on terror." His advisers wanted him to speak—any African-American seeking statewide office in Illinois would need the Chicago vote. But he also had to transcend that audience.
So Obama's speech was very carefully thought out. It was an early effort at speechmaking and shows it. The speech was overly dramatic and derivative, echoing the famous "I Have a Dream" speech of Martin Luther King Jr. It showed careful political calculation but, given what we would see years later, it also expressed conviction. It also showed how far his thinking on the subject had evolved since his comments to the Hyde Park Herald the year before. His first words were: "Let me begin by saying that although this has been billed as an antiwar rally, I stand before you as someone who is not opposed to war in all circumstances."
Obama took note of the Civil War, "one of the bloodiest in history," which had driven "the scourge of slavery" from America. "I don't oppose all wars," he said. He noted his grandfather's service in World War II. "He fought in the name of a larger freedom, part of that arsenal of democracy that triumphed over evil, and he did not fight in vain," he said, and then repeated, "I don't oppose all wars."
He would continue to repeat that line as a refrain, imitating King's famous and stirring repetition of the line "I have a dream." It took cheek to borrow the most famous rhetorical device ever employed by King, the great practitioner of nonviolence, to proclaim his belief in the necessity of war.
"After September 11, after witnessing the carnage and destruction, the dust and the tears, I supported this administration's pledge to hunt down and root out those who would slaughter innocents in the name of intolerance, and I would willingly take up arms myself to prevent such a tragedy from happening again. I don't oppose all wars."
He went on to denounce the pending invasion of Iraq as a "dumb war," and a "rash war," but what those listening that day most remembered was his affirmation of war as just and necessary. His belief that some wars were worth fighting. The one against al Qaeda was one of them. It was a doubly bold speech for someone contemplating a run for the U.S. Senate, because it not only ran counter to the blanket antiwar sensibilities of his immediate audience but also bucked the decidedly pro–Iraq War sentiment of Illinois voters, most of whom were far to the right of the small group of protesters in downtown Chicago. Where the Iraq invasion was concerned, Obama was once more out of step with the nation, but where al Qaeda was concerned, he was no longer calling for some sort of global-welfare campaign. He was ready to "take up arms" himself in that war. In a more direct manner than he could have imagined, he would get his chance.
Three years later, after his victory in the 2004 Senate race and rapid ascent to national prominence, Obama was running for president. In August of 2007, he was still struggling. There had been excitement for him when he announced his candidacy in February, but things had quickly leveled off. He was running well behind Hillary Clinton, considered by many to be a shoo-in for the Democratic nomination, and also behind John Edwards, who was thought to be next in line in the unlikely event that Clinton stumbled.
At the time, the strongest thing Obama had going for him seemed to be that 2002 speech. Here was an attractive, smart, antiwar candidate at a time when America's patience for its adventure in Iraq was at an all-time low. Every Democrat in the race was opposed to continuing the war. They vied now only over who was more emphatically opposed to it. Obama had not been in the Senate when votes were cast to authorize the war so, unlike Clinton and Edwards, he could claim ideological purity on the issue. And the Chicago speech put him on record as having spoken out against it from the start. He was the premier antiwar candidate, and that's how he presented himself. The simple thrust of his attack on Clinton, in particular, was that she had gone along with Bush on the war, while he had taken the unpopular, principled stand and had been proved right. Over the course of the campaign Obama would be forced to spell out his thinking in more detail, and the picture would become more complex.
His rise was so meteoric that many felt it had come too fast. His opponents were both baffled and annoyed by the messianic luster that he and his campaign encouraged. The best way to push back was to convince voters that he was in too big a hurry. At age forty-five, with only half of his Senate term behind him . . . well, even if he was destined to be America's first black president, he wasn't ready for the job yet. He was one of the youngest men to ever seek the presidency.
So experience was the hammer, and Clinton lowered it whenever Obama gave her a chance. He gave her one after a CNN/YouTube debate on July 23, when he was asked if he would consider meeting with America's enemies without preconditions. The questioner, whose face was projected on a big screen, approvingly cited Egypt's President Anwar Sadat's courageous (and ultimately fatal) decision, in 1977, to initiate peace negotiations with Israel, and asked if any of the candidates would be willing, in the first year of their tenure, to meet without preconditions the leaders of Iran, Syria, Venezuela, Cuba, and North Korea in an effort to "bridge the gap that divides our countries."
It was an easy question to dodge: Negotiation is terribly important . . . I wouldn't rule it out . . . we have a history with these countries that didn't begin yesterday . . . But Obama didn't dodge it. Up on the glitzy stage before glowing red, white, and blue screens, behind a spare, modernist podium of steel and plastic, he was the first of the eight candidates asked to respond.
"I would," he said.
A gasp rose from the studio audience, no doubt partly because of the directness of his answer. They were used to more maneuvering.
"My reason is this," he explained. "The notion that, somehow, not talking to countries is punishment to them, which has been the guiding diplomatic principle of this [George W. Bush] administration, is ridiculous . . . We may not trust them, they may pose an extraordinary danger to our country, but we have the obligation to find the areas where we may potentially move forward, and I think that it is a disgrace that we have not spoken to them."
Clinton, who answered next, promptly said that she would not. She explained that a lot of groundwork went into negotiations with unfriendly nations; that one did not rush into them. But, perhaps startled like everyone else, she didn't hit Obama too hard onstage. On reflection, however, and no doubt after her campaign strategists weighed in, she returned more harshly to the point the next day in interviews, labeling Obama's answer "irresponsible and frankly naive."
This was strictly politics. The United States had a long bipartisan tradition of negotiating with even its worst enemies, from John Kennedy—"Let us never negotiate out of fear. But let us never fear to negotiate"—to Richard Nixon's opening with China, to Ronald Reagan's famous "walk in the woods" with Mikhail Gorbachev. Obama's position was firmly in line with longstanding diplomatic practice. George W. Bush's post–9/11 policy—"You are either for us or against us"—was the exception, and a bad one. It removed subtlety from international affairs. It made no sense whatsoever for a savvy internationalist like Clinton to ignore the opportunity every newly elected president has to reset relations with hostile nations. Still, conventional wisdom held that you didn't admit such things. It made you sound soft. And naive was a word that worked against Obama.
It worked because many believed he lacked substance. He had yet to really define himself in detail on foreign policy or anything else. He had given a foreign policy address in April in line with his antiwar image, primarily calling for renewed internationalism, a greater willingness to seek consensus, and cooperation from other countries in pursuit of our national security goals. His remark about negotiating with enemies without preconditions made it easy for his critics to paint him as a complete pushover. It also suggested that Obama was a man who did not think things through carefully.
The "naive" label was troublesome. Soon enough the word had attached itself to him. TV pundits seemed unable to mention him without repeating it. Over the next few weeks his standing in the polls continued to fall as Clinton's rose.
Obama's staff fretted. Some wanted him to back off from his position, but he refused. "The thing is that I am right about this," he insisted in a meeting with his advisers Denis McDonough and Robert Gibbs. "Why would we not want to get into any negotiation that we could?" He asked them to schedule a national TV interview to reiterate his position, to underline it. It was, he felt, precisely the kind of message he wanted to send. He was offering to break with the past, to look at these foreign policy issues in a new way.
And he was just getting started. Obama was not about to let others substitute their analysis for his own. His approach to a problem was to look for a new solution, an original one. He believed much of the way America thought about defense issues was cast in archaic molds—the old divisions of left vs. right, conservatives vs. liberals, hawks vs. doves that had been set by the debate over Vietnam. He had been thirteen years old when that war ended. Much of the voting-age population of the country had not even been born. Nothing had shaken up that old dynamic as much as 9/11. Young people in particular were hard to classify in this regard. They tended to be far more liberal than their parents on most social issues—hence more likely to support Obama—but were also strongly supportive of robust military and intelligence efforts. As the candidate saw it, he was as hawkish as any American about defeating al Qaeda, but some of the tools traditionally associated with doves—tools such as negotiation and international cooperation—weren't just means of appeasing an enemy. They were essential to defeating this one.
A few weeks earlier, according to John Heilemann and Mark Halperin in Game Change, Obama had brought one of his close friends and old law professors, Chris Edley, to Chicago to lambaste his inner campaign circle for failing to let him do things his way. They were not giving Obama time and space in his frenetic campaign schedule to lay out his ideas in more detail.
"This is a guy who likes to think, he likes to write, he likes to talk with experts," said Edley, whose work on past Democratic campaigns and in White House service lent authority to his words. "You folks have got to recognize what he's in this for. He's in this because he wants to make contributions in terms of public policy ideas, and you've got to make time for him to do that . . . With all due respect to all you here, you should just get over yourselves and do what the candidate wants."
So in the days after the fallout from his negotiate without preconditions promise, it was decided that Obama would give another major national security speech. He did so at the Woodrow Wilson International Center, in Washington, D.C., on August 1, outlining his thinking on national security in some detail and in the process correcting the impression that he was "naive" or, worse, "soft" on national defense.
A National Intelligence Estimate that spring suggested al Qaeda had actually grown stronger in the previous six years. It noted that Pakistan had become the new safe haven for the terror group after the fall of the Taliban. All Democratic candidates had pledged change, but beyond promising to pull the plug on Iraq and end some of the more controversial intelligence-gathering methods (most of which had ended already), none had clearly articulated an approach to national security that differed significantly from Bush's.
Former Congressman Lee Hamilton introduced Obama at the Wilson Center gathering before an audience of a few hundred, many of them journalists. The speech had engaged all of Obama's foreign policy advisers, and every word in it had been weighed carefully. Tapped with the task of drafting it was Ben Rhodes, the former NYU graduate student who had watched from the Brooklyn waterfront as the World Trade Center towers collapsed. He was now a top-level campaign worker with prematurely thinning black hair and a perpetual five o'clock shadow. Instead of setting to work on a first novel, he had joined Hamilton's staff just as the congressman was named cochair of the 9/11 Commission. Rhodes had helped draft policy proposals for the Commission Report and helped write the chapter entitled "What to Do?" One of the subheads in that chapter had been "Attack Terrorists and Their Organizations," and its first proscription was "No Sanctuaries." Of all the most likely places in the world to play host to terrorist groups, first on the list was Pakistan. Rhodes eventually helped Hamilton and his cochair, former New Jersey Governor Tom Kean, write a book about the commission's work. After serving Hamilton on the Iraq Study Group, which the congressman also cochaired, Rhodes joined Obama's Senate staff as a foreign policy adviser and speechwriter. He had helped draft some of Obama's talks about Iraq in the Senate, and had then signed on as a speechwriter in Obama's Chicago office. This was the first campaign speech he had been asked to draft, and it was a big one. It also returned him to a familiar theme.
In a telephone conference with Rhodes, McDonough, Samantha Power, and various other national security aides, Obama outlined seven points he wanted to make in the speech. These were distilled to five by Rhodes and Power. One of them concerned efforts to destroy al Qaeda. As for the issue of safe havens, Rhodes would remember Obama telling him, "Let's come up with the most forward-leaning formulation to make it clear that we are going to go after these guys, because that's the whole argument."
Before the crowd at the Wilson Center, Obama began by relating his own experiences on 9/11—hearing the first report on his drive into Chicago, standing on the sidewalk in the Loop eyeing the Sears Tower, watching the towers fall on TV. In the six years since then, the stirring sense of national unity and purpose engendered by the attacks had been squandered, he said. The Bush administration had started well, toppling the Taliban and chasing al Qaeda, the real enemy, from its bases in Afghanistan. But then it had dropped the ball. Instead of going after the architects of 9/11, who were on the ropes and on the run, the Bush administration had decided to invade Iraq and topple Saddam Hussein, a move that had quickly absorbed the nation's primary military and intelligence resources. The move had been "rubber-stamped" by Congress, he said, sideswiping his Democratic primary opponents. It was, he said, "A misguided invasion of a Muslim country that sparks new insurgencies, ties down our military, busts our budgets, increases the pool of terrorist recruits, alienates America, gives democracy a bad name, and prompts the American people to question our engagement in the world." Obama pointed to the new Intelligence Estimate as proof that al Qaeda had only changed its home address.
Once again, he pledged to end the Iraq War, not out of any pacifist conviction, but in order to refocus on the real enemy. His focus, he promised, would be on crushing al Qaeda. This was the mission 9/11 had compelled, a national priority that trumped peaceable relations with Pakistan or any other country. The enemy had been too broadly defined by the Bush administration, he said, a failing that not only had diminished the impact of our response but had fed into al Qaeda propaganda that America was at war with the entire Muslim world. The necessary war called for a much smaller focus: to find, target, and destroy the terror organization. To underscore his determination, Obama said he would respect no sanctuary and zeroed in specifically on Pakistan.
"Al Qaeda terrorists train, travel, and maintain global communications in this safe haven," he said. "The Taliban pursues a hit-and-run strategy, striking in Afghanistan, then skulking across the border to safety. This is the wild frontier of our globalized world. There are wind-swept deserts and cave-dotted mountains. There are tribes that see borders as nothing more than lines on a map, and governments as forces that come and go. There are blood ties deeper than alliances of convenience, and pockets of extremism that follow religion to violence. It's a tough place. But that is no excuse. There must be no safe haven for terrorists who threaten America. We cannot fail to act because action is hard. As president, I would make the hundreds of millions of dollars in U.S. military aid to Pakistan conditional, and I would make our conditions clear: Pakistan must make substantial progress in closing down the training camps, evicting foreign fighters, and preventing the Taliban from using Pakistan as a staging area for attacks in Afghanistan. I understand that President Musharraf has his own challenges. But let me make this clear, there are terrorists holed up in those mountains who murdered three thousand Americans. They are plotting to strike again. It was a terrible mistake to fail to act when we had a chance to take out an al Qaeda leadership meeting in 2005. If we have actionable intelligence about high-value terrorist targets and President Musharraf won't act, we will."
That final line was the very last one inserted in the speech. Much deliberation preceded it. Rhodes had originally written, "If we have targets [in Pakistan] and President Musharraf won't act, we will." It was in keeping with the candidate's instruction to be as "forward leaning" as possible. But the issue of Pakistan was delicate. That unstable nation was critical to the war effort in Afghanistan. It was a nuclear power in one of the world's most volatile regions, and yet elements of its government, particularly its powerful intelligence agency, the Inter-Services Intelligence (ISI), were known to be in bed with all manner of Islamist radicals. Pakistan's President Pervez Musharraf had been walking a narrow line with the Bush administration, providing enough cooperation to avoid being branded an enemy but falling well short of routing extremists holed up in Pakistan's lawless northwest. Threatening to go after "targets" without Pakistan's cooperation made Obama's national security team nervous.
Nobody had been happy with the line in a pre-speech review at Obama's Washington headquarters. Present were Robert Gibbs, Susan Rice, Jeh Johnson, Rand Beers, and Richard Clarke, the campaign's premier consultant on security matters.
"Look, that is not how you talk about these things," said Clarke. He explained the importance of working with the tribes in Pakistan's northwest territories.
But the candidate was resolute. He wanted the line in. It said exactly what he thought, and what he planned to do as president. I do not oppose all wars. He was going to go after the real threat. So the discussion focused on the wording. Two caveats were added: "If we have actionable intelligence" and "high-value targets." This was to make it clear that Obama was talking about acting only in an exceptional circumstance, and only in a specific, limited way.
No matter. The careful phrasing was ignored. Obama had covered a lot of ground in the speech, reiterating his plan to get troops out of Iraq, pledging to reinvest in the effort against the Taliban in Afghanistan, and promising to give a major speech somewhere in the Middle East, within his first hundred days as president, to redefine the U.S. mission for that region. He also promised to close the prison at Guantánamo and to end Bush-era programs that "tracked" American citizens. But the line about going after targets in Pakistan got nearly all of the press. There was heat from every quarter.
Jeff Zeleny of the New York Times reported that Obama had "vowed to dispatch American soldiers to eradicate terrorist camps" in Pakistan.
The subhead on the story in the Los Angeles Times said, "He says he'd reserve the right to invade," and reporter Paul Richter wrote, "Senator Barack Obama said Wednesday that the United States should reserve the right to invade the territory of its Pakistani allies and withdraw U.S. financial aid if it believed Pakistani President Pervez Musharraf was failing to do enough to stop terrorists."
Liberals accused Obama of embracing the Bush administration's cowboy mentality. Conservatives faulted Obama for a supposed lack of sophistication: Didn't he understand the delicacy of our relationship with Pakistan? Even if that was his plan, didn't he understand that you don't talk about things like this?
Liberal blogger Jerome Armstrong was disappointed. "For progressive Democrats who want a more peaceful leadership in the world . . . [Obama's speech] fails the threshold of getting us out of picking fights in the Mideast, and discarding the Bush doctrine of preemptive attacks."
Conservative columnist William Kristol wrote that Obama was "frantically suggesting that he would invade Pakistan" in order to shore up his tough-guy credentials against Hillary Clinton.
On his radio show, Rush Limbaugh mocked Obama. He noted that Osama bin Laden had been exhorting his followers to overthrow Musharraf, and now Obama—"I get these guys confused," he said—had threatened to "invade Pakistan." Limbaugh added, "Poor Musharraf is going to get it on both ends if Obama is elected."
"It's a very irresponsible statement, that's all I can say," said Pakistan's foreign minister Khurshid Kasuri. "As the election campaign in America is heating up we would not like American candidates to fight their elections and contest elections at our expense." Kasuri said that President Bush had called to privately reassure Musharraf, terming Obama's comments "unsavory" and prompted by political considerations "in an environment of electioneering."
"I do not concur in the words of Barack Obama in a plan to attack an ally of ours," said former Massachusetts Governor Mitt Romney, who was then a front-runner for the Republican presidential nomination. "I don't think those kinds of comments help in this effort to draw more friends to our effort." He said, U.S. troops "shouldn't be sent all over the world," and called the comments "ill-timed" and "ill-considered."
Again, some in Obama's camp wanted the candidate to issue an explanation, but once again he refused. He had meant what he said. Obama told his staff that their public posture on the comment should be to shoot down any talk of an "invasion," but to stand behind his willingness to act unilaterally in Pakistan if the right occasion presented itself.
"I am not going to be lectured about foreign policy by the same people who were responsible for this catastrophic war in Iraq," he maintained, in response to some of the criticism. It illustrated, he said, his willingness to "think outside the box." The campaign released a memo by Power, reiterating the candidate's promise: "Conventional wisdom would have us defer to Musharraf in perpetuity. Barack Obama wants to turn the page. If Musharraf is willing to go after the terrorists and stop the Taliban from using Pakistan as a base of operations, Obama would give him all of the support he needs. But Obama made clear that as president, if he had actionable intelligence about the whereabouts of al Qaeda leaders in Pakistan—and the Pakistanis continued to refuse to act against terrorists known to be behind attacks on American civilians—then he will use highly targeted force to do so."
Despite this effort to explain, the supposed call to "invade" Pakistan quickly entered campaign lore . . . and evolved. Obama's eventual Republican opponent, Senator John McCain, would claim that Obama had threatened to "bomb" Pakistan.
"The best idea is to not broadcast what you're going to do," McCain said the following February. "That's naive. The first thing that you do is you make your plans and you carry out your operations as necessary for America's national security interest. You don't broadcast that you are going to bomb a country that is a sovereign nation and where you are dependent on the goodwill of the people of that country to help you in the war—in the struggle against the Taliban and the sanctuaries which they hold."
So in 2007 and early 2008, on the question of going after Osama bin Laden, Obama's call for direct, unilateral action was roundly condemned. It remained his plan, however, and as soon as he was elected he acted on it. As Obama settled into the job, his determination to pursue al Qaeda's leadership was plain. If bin Laden had empowered himself, or had felt chosen by God, Obama had been elected. He had sought and had been chosen by the people of the United States to make these life-and-death decisions.
The new president immediately began shifting resources from Iraq, where he was determined to systematically draw down U.S. involvement, to Afghanistan and Pakistan. Large numbers of drones began leaving Iraq and flying missions over the steep mountains of eastern Afghanistan and the lawless regions of northwest Pakistan. The Joint Special Operations Command, which had been operating out of Balad Air Base, in Iraq, relocated in the summer of 2009 to Jalalabad, Afghanistan, beefing up bandwidth at the new encampment to retain links between intelligence computers and analysts in Washington. And as we have seen, the number of drone attacks spiked. America's relationship with Pakistan grew more troubled.
When he was awarded the Nobel Peace Prize in October of 2009, just as he was deciding to send thirty thousand more American troops to Afghanistan, Obama had a chance to fully articulate once more his thinking about war.
Again Rhodes was pressed into service. This time Obama presented him with a handwritten first draft, which had three quotes from Reinhold Niebuhr, the American theologian who argued strongly for the necessity of war and who rejected pacifism as a sure prescription for tyranny. The emergence of fascism in Germany and Japan, and communism in Russia, had prompted Niebuhr to famously renounce his lifelong pacifism. That movement had enjoyed a resurgence after World War I, with its seemingly senseless slaughter of millions. Now, with the world teetering on the brink of an even larger catastrophe, pacifists, who included a good many Christian thinkers in Europe and America, argued that if enough people refused to serve in armies, states would be unable to wage war ever again. Niebuhr did not believe it. The passages Obama quoted were from Niebuhr's 1939 essay, "Why the Christian Church Is Not Pacifist," in which the theologian argues, "If we believe that if Britain had only been fortunate enough to have produced 30 percent instead of 2 percent of conscientious objectors to military service, Hitler's heart would have been softened and he would not have dared to attack Poland, we hold a faith, which no historical reality justifies." Niebuhr believed that just as men were imperfect, so, too, were states, and just as men must struggle to defeat evil in themselves, they must also struggle to defeat evil at large.
Obama had pronounced his willingness to "take up arms" years earlier. Now, armed with more military power than anyone in any other country, he was not just prepared to use it, he felt morally obligated to do so. Just as he had done before the antiwar audience in Chicago seven years earlier, he would use this pacifist platform to argue his belief in the moral use of violence. The Nobel Peace Prize itself had grown out of the same pacifist movement Niebuhr turned against in 1939. It was one of the award categories established by Alfred Nobel at the behest of his friend Bertha von Suttner, a well-known nineteenth-century Austrian novelist, pacifist, and eventual peace prize recipient. So it is not surprising that Obama looked back to Niebuhr's arguments as he prepared to accept the prize himself in Oslo.
His speech there was a brief lecture on the necessity of war, and a tribute to the use of force—American force above all—as the only practical means of achieving the peace prize committee's high ideals. He saluted two of the twentieth century's most famous practitioners of nonviolence, Dr. King and Mahatma Gandhi, but said, "I face the world as it is, and cannot stand idle in the face of threats to the American people. For make no mistake, evil does exist in the world. A nonviolent movement could not have stopped Hitler's armies. To say that force is sometimes necessary is not a call to cynicism—it is a recognition of history, the imperfections of man and the limits of reason."
Evil does exist in the world. As president, Barack Obama had been given an opportunity to take up arms against the enemies of the United States in a more direct way than had any previous holder of that office. He welcomed it. He did everything he could to push the matter. The CIA had long called whoever was in the White House the "First Customer," and on this issue there was no confusion about what the customer most wanted.
High in his seventh-floor office at Langley, overlooking the Potomac, Michael Morell had felt the same way for a long time. In his climb to the post of deputy director, he had run the agency's analysis division, and he knew that, despite their lack of success, they had never lost the sense of urgency. He still remembered flying around with President Bush on 9/11, the uncertainty and fear in the country, the way he had felt looking in on his daughters sleeping when he finally returned home. Even with two wars to fight, there had never been a want of manpower or of resources for finding bin Laden.
Still, he felt, Obama's push might have some effect. Morell's new boss, Panetta, for one, was now demanding those regular progress reports: at least one a month. In any large organization a demand for progress reports has an effect. No one wants to file a progress report showing no progress.
4
The Targeting Engine
There had been times, off and on, when the United States government knew where Osama bin Laden was. The CIA had been interested in him since 1991, after he moved from Afghanistan to the Sudan. Almost everywhere the agency looked in the expanding Sunni extremist world, his name came up. Not as a commander but as the go-to person for false documents, money, training, weapons, or chemicals that could be made into bombs. In December 1995, the agency created a small bin Laden unit, headed by Michael Scheuer.
A burly, confident man with a full beard and glasses who speaks with a flat Midwestern accent, Scheuer was less inclined than many in the CIA hierarchy to swallow his own opinions. He had not been a typical CIA recruit. A Buffalo native, he had worked as a rigger for Union Carbide while earning two master's degrees and then a PhD at the University of Manitoba, in Canada. He believed his bin Laden unit was the first ever established to hunt down an individual, and as the effort matured—as he learned more and more about bin Laden—he grew increasingly convinced of the danger al Qaeda posed for the United States. In time, his assessment of that danger outpaced his superiors'. His small group worked out of an office in a business center just a short drive from the main CIA campus at Langley. Scheuer named the office after his son Alec: "ALEC Station."
The best weapon they had for gathering intelligence at that point was rendition, the practice of arresting a suspect and turning him over to authorities in another country for interrogation. The practice enabled the agency to at least technically abide by rules against torture. The CIA obtained assurances that captives would not be abused, which some foreign governments likely honored more diligently than others. At that point the agency did not have the option of killing suspected senior terrorists: they had to be arrested and held somewhere. Rendition enabled the Clinton administration to avoid the legal difficulties of placing them in U.S. custody. As Scheuer would remember it, this was not so much a matter of explicit policy as it was policy by default. He would seek guidance from the White House about what to do with a target, and the answer would come back, "That's your problem." The problem was solved by willing governments in East Africa, the Balkans, and the Middle East.
Rendition did not, as it happens, produce the first big breakthrough for ALEC Station. That came in September 1996, when a Sudanese militant named Jamal al-Fadl, a former close associate of bin Laden's, turned up at the U.S. embassy in Eritrea offering to tell everything he knew about al Qaeda. He was flown to the United States and placed in the federal witness-protection program. He provided the first trove of fresh information about bin Laden and his organization—about its personalities, structure, and planned operations. His revelations ratcheted up interest in the group, which was clearly willing and able to launch major terror attacks.
By 1999, ALEC Station employed twenty-seven people, many of them women. They ran an unorthodox CIA office, very informal. People dressed casually. Because it maintained informants and contacts worldwide, the office was open twenty-four hours a day. Everyone worked long hours so few formalities of office life took hold. Scheuer would nap every afternoon in his office. As their sense of the threat posed by al Qaeda grew, so did their sense of mission. Some in the office, like Scheuer, passed up offers for promotions in order to stay with the work. Marriages broke up. The place had a cultish feel. Because Scheuer presided over so many dedicated women officers, some started calling his group "the Manson family."
They couldn't get bin Laden arrested in the Sudan, so they came up with a plan to harass him. He had a number of large projects under way there—road building, agricultural programs, and businesses. He was also actively underwriting terror attacks throughout the region. So ALEC Station proposed sabotaging his construction equipment. They wanted to spike engines with slurry that would force them to seize up. When the Senate Select Committee on Intelligence was briefed on the plan, one member objected: "If you do that, won't you be putting some Sudanese farmer out of work?" The project was scrapped.
Not long afterward, when the attempted assassination of the Egyptian President Hosni Mubarak was linked to al Qaeda, the Sudan was pressured by states in the region to expel bin Laden. He relocated to Afghanistan, where he declared his war on the United States. This move pleased ALEC Station, because the NSA could now listen in on phone conversations in Afghanistan; there was also an enormous archive of overhead imagery left over from the mujahidin–Soviet wars, and the CIA had many friendly contacts in that country. In 1997, Mullah Omar, the Taliban leader, invited bin Laden to live in Kandahar, at an experimental agricultural station called Tarnak Farms, south of the city. This was an area where the agency had an especially rich network of spies, a group it called "Tripoints."
For once they could watch bin Laden closely and listen to him and his people. Lacking the authority to kill him, Scheuer's group laid plans to kidnap him—that would have been in May or June of 1998, several months before the embassy bombings in East Africa. They intended to hold him in a remote mountainous area for interrogation and then fly him to an Arab state for imprisonment (unless the United States decided to prosecute him directly). They fleshed out a raid in detail, a snatch-and-grab mission inside Afghanistan employing a special ops team delivered by helicopter. But when the plan was run up the chain it was vetoed as too risky. American forces might get killed, and because bin Laden lived with his wives and children, some of the children might be harmed. Scheuer recalled being mystified by the decision. He asked, "How much more of a threat do you need before you finally do something?"
When Director George Tenet paid a visit to ALEC Station not long afterward, one of the women on Scheuer's staff confronted him angrily: "You and the White House are going to get thousands of Americans killed."
Tenet told them that he understood their anger, but that it would subside. By now the group's growing sense of urgency, coupled with its cultish image and high number of female staffers, had begun to work against it. They were seen as overly emotional and alarmist. Tenet's response reflected this subtle prejudice and rankled ALEC Station still further.
"You will all think clearer in a couple of days," he said.
In August, after the embassy bombings, Scheuer recalls being asked if the plan to kidnap bin Laden could still be pursued. The answer was no. Bin Laden knew that the chances of America taking action would grow after those attacks. He had gone into hiding. They had missed the chance.
By now, the United States was willing to use lethal force on bin Laden. President Clinton authorized two cruise missile strikes soon after the embassy bombings, one targeting Al-Shifa, a pharmaceutical plant in Khartoum thought to be developing chemical weapons, and the other targeting a bin Laden camp near Khowst. The missiles hit on August 20, fired from ships in the Arabian Sea. The CIA would estimate that twenty to thirty people were killed—but not bin Laden, who had reportedly left the Khowst camp a few hours earlier.
After that, the project for ALEC Station became pinpointing bin Laden long enough in advance to be targeted. They presented the White House with eight such opportunities, Scheuer recalled, and each time the strike was called off, primarily over concerns about collateral damage. The CIA man had always been prickly and eccentric. He was so much more willing to accept collateral casualties than his superiors—was so convinced that the threat posed by bin Laden warranted drastic, immediate action—that he had begun to be regarded with suspicion. He seemed obsessed.
In 1998, on the Sunday before Christmas, ALEC Station learned that bin Laden was staying in the Haji Habash house, part of the governor's palace in Kandahar. The CIA had a local spy who knew which wing of the building bin Laden was in, and even which room, because he had escorted him there. It was first-rate, firsthand intelligence, and a target that could easily be reached by Tomahawk missiles launched from ships in the Arabian Sea.
"Hit him tonight—we may not get another chance," advised Gary Schroen, ALEC Station's field officer.
Scheuer took it directly to the White House, along with Director Tenet and John Gordon, the deputy director. It was snowing. The three men drove from Langley into D.C. together, but inside the White House only Tenet was allowed into the meeting, which the Clinton administration's principals joined by teleconference. Scheuer and Gordon waited outside for hours. The missile strike was not authorized. According to The 9/11 Commission Report, there was concern that as many as three hundred people might be killed or injured, and that there was thought to be too great a chance of bin Laden moving at the last minute, as he had before. There was also a mosque nearby that might have been damaged. The CIA men drove back up the George Washington Parkway, disappointed yet again. Scheuer was particularly upset by the administration's worry about damaging a mosque.
The next day, with the opportunity gone, Scheuer wrote to his field officer, Schroen, that he had not been able to sleep. "I'm sure we'll regret not acting last night."
"We should have done it last night," Schroen wrote back. "We may well come to regret the decision not to go ahead."
Scheuer's frustration got the better of him. In 1999 he drafted a memo to the heads of the CIA, complaining about the risks being run to collect timely information, the hours of hard work that went into each targeting opportunity, and the unwillingness of the government to take action.
"[It seemed wrong to] me, to some extent, the idea of continually sending your officers into harm's way to gather information that is credible and usable and to find the government not willing to use it to defend American people for reasons that [exist only in] their own minds," he explained years later in an interview for this book. "You know, how racist is it to think that 1.4 billion Muslims are going to rise up and attack the United States because some shrapnel hits a stone mosque in Kandahar? You have to have zero respect for the humanity or the common sense of the Muslim world to expect something like that to happen. And yet, that's the excuse these brilliant Harvard-trained people come up with."
He was relieved of responsibility for ALEC Station. As he recalled later, he was told, "We want you to tell your people that you are burned out and don't worry, we're going to give you a medal and a monetary award."
Scheuer said he told them, "Stick it in your ass."
Everything changed after 9/11, of course. Then the questions all became, Why hadn't the United States acted against bin Laden more aggressively when it could? "Obsessives" like Scheuer and his "cult" at ALEC Station looked prophetic, not overly emotional. The United States had missed its chance to get bin Laden before his biggest plan bore fruit.
After the invasion of Afghanistan there were battlefield leads that pointed American forces toward a rugged redoubt in Tora Bora, which translates to "Black Cave." It was in the far easternmost part of the country, near the border with Pakistan, and was reputed to have a byzantine maze of caves, natural and man-made. It was also reputed to be bin Laden's hideout. When American forces and Afghan militiamen took it in 2001, over a five-day siege, they found lots of small caves and some bunkers, but nothing like the fortress they had imagined. It turned out to be another place the Sheik had recently left.
The best reports said he had fled over the White Mountains into Pakistan, probably before the assault even began. After that . . . nothing.
No, not nothing.
Start with thousands of small bits of information. Names, lots and lots of names. Sightings. Rumors. Interrogation transcripts. Phone numbers. Phone calls. Dates. Addresses. Geographic coordinates. Aerial photographs. Ground surveillance photos. Videos. Faces. Iris images. Gaits. Maps. Fingerprints. Old diaries. E-mails. Web sites. Social media. Text messages. Tweets. Old-fashioned letters. Blogs. News reports. Broadcasts. Bills. Payment schedules. Traffic tickets. Rent payments. Credit card numbers. Charges. Bank account numbers. Deposits. Withdrawals. Transfers. License numbers. Passport numbers. Police reports. Arrests. Travel itineraries. Everything and anything that can be transformed into data. When you're looking for one person in a world of seven billion, and when that one person does not wish to be found, you cast a wide net.
After 9/11, and after bin Laden escaped Tora Bora, it is safe to say that the United States government was fully engaged in hunting him down. Engaged to a degree that makes the uphill battles of little ALEC Station seem like a basement hobby. The Obama administration might invoke "limited bandwidth" and competing priorities to explain why these efforts fell short, but the truth is that every agency and branch of the vast U.S. military-industrial complex was now fully invested. What did that mean? It meant that finding and eliminating bin Laden was not just a preoccupation of a small group working in a storefront near Langley. It was a central goal. No one would be left waiting in the hall at the White House ever again for permission to strike. But finding bin Laden had also become exponentially more difficult. Tools and networks and units had to be developed to find, fix, and finish al Qaeda and other terror networks like it. What would evolve—this thing they called F3EAD—is worth examining in more detail.
You begin with scraps. Anything that can be transformed into data, those names and numbers and other types of information partially enumerated above. All of that and more, intel from every pipeline: detainee interrogations, HUMINT (human intelligence), SIGINT (signals intelligence), GEOINT (geospatial intelligence), and even something called MASINT (measurement and signature intelligence, which converted into searchable data highly technical things like radar or chemical or sound). Each bit is a potentially useful dot in a vast matrix. Collection flowed from a blizzard of agencies, large and small—CIA, FBI, NSA, NGA, and many more. The SEAL and Delta Force warriors ransacked the hideouts they raided for everything that might contain a lead—they called it "pocket litter." Who knew which stray fact might lead to bin Laden? Or if any of them ever would? At times the CIA had dozens of analysts working on bin Laden full time, but the sheer number and variety of leads was daunting. There was always a good chance, perhaps a better than even chance, that the Sheik would live out his days in hiding and die peacefully in bed, surrounded by his wives and his many children and the devoted members of his intimate circle, perhaps after leveling one last broadside at the "Head of International Unbelief"—thumbing his nose as he entered paradise. For those who believed in such things, evading the grasp of American justice would lend credence to his claim of divine guidance.
In the end, finding bin Laden would illustrate the most banal of truths about intelligence work. More than genius or courage, it is about effort and patience and will. It is also, of course, about money and time—but when we are talking about a goal assigned top priority by not one but two presidents of the United States, and where time and resources are, in effect, bottomless, it boils down, ultimately, to a steady application of will. President Bush famously kept a chart of wanted terrorists in a desk drawer and would personally X out those who were captured or killed. Bin Laden was always "Number One." At his regular daily briefings, Bush would routinely ask, "How're we doing?" and everyone knew what he was talking about. It was the same with Obama. After that impromptu meeting in his office with his new intelligence chiefs in 2009, he would bring it up at nearly every security briefing.
"Are we any closer?"
"What have we learned?"
An intelligence network like America's is not one but multiple bureaucracies, each with its own specialty—listening, observing, photographing, sensing, probing, analyzing. The strength of such an overlapping structure is that things get looked at more than once, and from every conceivable angle. And the strength of bureaucracy—everyone knows about the weaknesses of bureaucracy but rarely do we consider its strength—is in its limitless capacity for work. Steady, unceasing work, like the trickle of the river that ever so slowly carves a gorge. Hour after hour, day after day, year after year, here was an effort that would consume large chunks of the careers of analysts—analysts replaced at intervals with fresher eyes and ears and minds who would eagerly set off down stale trails with new vigor.
Now add supercomputers. Convert those millions of bits of intel gathered from all over the world over years of effort into bytes, and suddenly the impossible, finding the needle in a million haystacks, becomes at least a little more probable.
So when we trace the trail to Abbottabad, this is what we are talking about—a sophisticated targeting engine. Viewed backward, from bin Laden's hideout to the scraps of intel that led to it, the trail seems obvious. Tracing it from end to beginning obscures the level of difficulty: the years of frustration and patient effort, the technological innovation, the lives lost, the mistakes made, the money spent. Just the special ops piece of the story unfolded over a quarter of a century of trial and error, beginning with the improvised mission to rescue American hostages in Iran in 1980.
After Iranian students seized the U.S. embassy in Tehran in November 1979, President Jimmy Carter undertook months of fruitless diplomatic efforts to free the more than fifty Americans held hostage there. During that time, the army's newly formed counterterrorism unit, Delta Force, cobbled together a daring effort to rescue them. They borrowed helicopters from the navy used for minesweeping, and marine pilots unused to the kind of flying required. The mission called for the choppers to fly to a rendezvous point in the desert outside Tehran, called Desert One, refuel the choppers from large fixed-wing aircraft flown in by air force pilots, and then proceed to a hiding place near the city. The following evening Delta Force would emerge from hiding, raid the embassy compound and free the hostages, then assemble in a soccer stadium across the street from the embassy in central Tehran, where they would be picked up by the helicopters and flown to an airport that was to have been seized by U.S. Army Rangers. From there, the rescuers and hostages would be flown out of the country.
This extraordinary bold and complicated mission never made it past the rendezvous point in the desert. Sandstorms damaged choppers and forced several pilots to turn back. With too few helicopters to proceed, the mission was aborted.
As the aircraft maneuvered to fly quietly out of Iran, one of the choppers collided with a plane on the ground, and both exploded, killing eight American servicemen. The disaster ruined hopes of keeping the aborted rescue effort secret. The subsequent embarrassment condemned the hostages to many more months of captivity, handed Iran a large propaganda coup, (they claimed an American "invasion" had been thwarted by God), and likely destroyed Carter's hopes of being elected to a second term.
That episode would bear a striking similarity to the one that killed bin Laden, and it would illustrate how far the talents and tools of the special ops community had come. That 1980 disaster, in effect, created the Joint Special Operations Command, by demonstrating cruelly what this nation could not do. Progress can be further traced back to the heroic and bloody firefight in Mogadishu in 1993, the battle documented in Black Hawk Down, which resulted when another special ops raid spun off track. Thousands of missions, successful and unsuccessful, large and small, honed the men and machines and tactics that would target the Sheik.
That raid could not be launched until bin Laden was found. Finding him meant reconstituting human spy networks dismantled in the complacent years after the Cold War, when spying was considered unseemly and unlawful and a threat to personal liberties and human rights. After 9/11, the public rediscovered the value of spies on the ground and of eyes and ears overhead. It would speed the development of unblinking aerial platforms and telecommunications networks that would allow constant, real-time surveillance unheard of in the past.
Four months after the attacks, former Admiral John Poindexter was appointed to head a new initiative he had helped devise called Total Information Awareness, which sought to use supercomputers to amass unimaginably huge databases in order to, in essence, collect, as its name suggested, everything. With the right software, you could mine that data in order to identify and locate potential terrorists. The admiral's history of lying to Congress during the Iran-Contra episode did not engender confidence, nor did the inherently scary, Orwellian notion of the government compiling vast pools of data about American citizens. In that sense, the name, Total Information Awareness, was a fatal public relations blunder. The bald, white-mustachioed Poindexter was called the "Pentagon's Big Brother," and worse. Congress scotched the program as originally conceived. Poindexter found employment back in the private sector, and the remnants of the project, which was barred from collecting information on American citizens, was tactfully renamed Terrorism Information Awareness.
As wrong a choice as Poindexter was to lead this project, and as tone deaf as he may have been in its presentation, he had the right idea. He had been thinking about it for decades. One of the computer's great contributions—this ability to store and manipulate vast amounts of data—seemed mundane but was in practice so revolutionary that it was transforming modern life, whether performing a Google search, stocking the shelves at a Walmart from an international supply chain, shipping packages anywhere in the world overnight, or mapping the human genome. So why not put that capacity to work tracing a terrorist network—recognizing clues in what would appear, even to teams of skilled analysts, to be random events?
Poindexter's concept did more than survive. It would come to undergird the entire war effort: storing every scrap of intel about al Qaeda and related groups gathered by the nation's very active military and spy agencies, transforming them into data, and then plumbing that data for leads. The hunt for bin Laden and others eventually drew on an unfathomably rich database, accessible to anyone in the world with the proper security clearance, whether a marine officer at an outpost in Afghanistan or a team of analysts working in Langley. Sifting through it required software capable of ranging deep and fast and with keen discernment—a problem the government itself proved less effective at solving than were teams of young software engineers in Silicon Valley. A start-up called Palantir, for instance, came up with a program that elegantly accomplished what TIA had set out to do. Founded in 2004 by Alex Karp and Peter Thiel—the latter is the billionaire cocreator of Paypal and an early Facebook investor—Palantir developed a product that actually deserves the popular designation Killer App. Newly minted software engineers from the best computer schools in the country were put up in a seven-thousand-square-foot workspace in Palo Alto. It was stocked with junk food and video games and nicknamed "the Shire," the home of the Hobbits in Tolkien's Lord of the Rings. (The company itself is named after a magical stone in the Tolkien saga that confers special powers of sight and communication.) The software produced from this very unlikely source would help turn America's special forces into deadly effective hunters. Palantir is now worth billions, and has contracts with, among others, the CIA, the NSA, the Defense Department, the Defense Intelligence Agency, the FBI, the National Counterterrorism Center, and the Department of Homeland Security.
The pace and urgency of war have always accelerated the development of technology and encouraged novel uses of devices that already exist. After rapid initial success toppling the regime of Saddam Hussein in Iraq, American forces found themselves under increasing attack by Sunni extremist groups, the most violent of which was a new branch of al Qaeda, under the direction of an innovative killer named Abu Musab al-Zarqawi. His group mounted a campaign of roadside bombs and brutal suicide attacks, many of them designed to kill Iraqi civilians indiscriminately—the sort of attacks that bin Laden, in hiding, considered mistakes. Indeed, the mass killings eventually helped turn the Sunni majority in Iraq against the insurgency, marking the turning point in the war. But at the same time, under the direction of General Stanley McChrystal, JSOC was hammering away on insurgent cells of the local al Qaeda killers with increasing effectiveness, mounting mission after mission in rapid succession, capturing and killing at a pace that such operations had never before been able to sustain. They found Saddam Hussein hiding in a hole in the ground in late 2003. Zarqawi himself was killed by an American bomb in 2005. McChrystal's success, considered to be one of the major military accomplishments of modern times, was something he called "collaborative operations," by which he meant the fusion of "special operators"—teams of elite shooters from every branch of the service—with this new computational ability, which amassed data from all of the other inputs. The task force built a massive database at Camp Victory in Iraq, and then another at Bagram in Afghanistan, blending the big picture with the small. It meant bringing a different kind of warrior to the front, one more accustomed to clicking a mouse than pulling the trigger.
Guy Filippelli was one of them. A young army captain, a West Point graduate with a master's degree from Oxford, in 2005 he was asked by his commander in Afghanistan to visit the walled-off facilities of the task force—the special ops unit—and show them what he could do with his computer. Filippelli calls himself a geek. He had started writing computer programs as a high school student before heading to West Point's growing computer science department. He was helping the command staff at Bagram design systems to better control "information flow," plugging intel collected from the sites of raids in the field and from the interrogations of detainees into a growing national terror database. He arrived inside the cloistered walls of the task force full of enthusiasm for his work, certain his lecture would excite these frontline troops. The shooters and their staff could not have been less impressed. Filippelli's subject matter was highly technical and abstract, cutting edge, and very cool to him, but he was talking to a roomful of soldiers whose adrenaline rush came from . . . free falling from high altitudes or getting shot at. Their world was the extreme opposite of virtual. So the next time the young captain got a chance, this time with a smaller group of soldiers, he tried a different tack.
"Listen, I know you guys are a thousand times better at this stuff than I am and are probably already doing all this, but let me show you what I'm doing and I'll be out of your hair in ten minutes."
At first it was something easy. The task force was used to simply locking up suspects in the detainment facility as they awaited questioning. Filippelli had built a database for detainees, and had also mapped the facility's population by tribal affiliation, background, kinship, and other factors. Putting a detainee in the wrong place, for instance, with a group from his own village, meant that his comrades would rapidly coach him. Filippelli could show how those poorly placed were significantly less useful afterward in interrogation. So where you put them in the facility was important.
"Look," he said. "You've picked up this guy. Why did you put him with these guys? You could have done this . . ."
And with that, he closed his laptop and started for the door.
"Thanks for your time," he said. "Let me know if there's anything else I can do for you."
"Wait," the men protested. "Tell us a little more about this."
Gradually, he found himself working more and more with the task force, showing them how crunching data could vastly improve their efficiency. The applications went way beyond storing detainees. The name of the game in warfare is to learn faster and act faster than the enemy. So, as Filippelli and others doing the same kind of work came to see it, the contest had to do with time cycles. If it's a detainee who could be held for, say, only twenty-four hours, how do I use that time most efficiently? What questions should he be asked? What do I need to learn in order to ask him the best questions in the time allotted? And that was just one piece of the puzzle. Looking at the larger mission, the special ops teams needed to get inside the information cycle of their enemy. In the past, after a successful night raid where a member of an insurgent cell was killed or arrested, by morning, or even within a few hours, every critical member of that group would know about it and would have taken evasive action. Information spread quickly. Cell phones would be ditched, computer discs destroyed, bomb-making facilities moved—the bad guys would scatter. But if you could get inside that response time—if you could beat their information cycle and learn enough from the first raid through either interrogation or, say, scrutinizing a seized cell phone or hard drive—you might be able to launch a new raid or even multiple raids before word of the first one had gotten out.
The databases enabled local scraps to be instantly cross-checked with the larger data pool. Warrior geeks like Filippelli would examine the pocket litter, and plug that into the national collection; it was like jumping from the middle of the woods to a panoramic view of the forest. The warrior geeks helped connect the dots for the shooters, lifting order from disorder. Soon enough, the teams were doing it for themselves. Armed with such rapid intel, the teams got very fast indeed, going out on multiple missions every night, easily lapping the enemy's information cycle. They had, in strategic terms, "seized the initiative." This capability turned terrorist hunting from a passive endeavor, characterized by long periods of intel collection and analysis and preparation, punctuated by occasional raids, into an aggressive endeavor. To stay alive, the bad guys had to stay in constant communication with each other and keep moving—two activities that actually made them easier to find. In Iraq, under McChrystal in 2007 and 2008, JSOC teams began dismantling networks at an ever increasing pace, taking them down before they knew what hit them.
McChrystal would be handed the entire Afghan command soon after Obama's election, turning over JSOC to Vice Admiral William McRaven, who signed a secret agreement in early 2009 with the new CIA director, Leon Panetta, spelling out guidelines for expanded cooperation. So at the same time Obama was pushing the CIA to find bin Laden, JSOC was deepening its relationship with the spy agency worldwide.
The right weapon had evolved. Just nine years earlier, President Bill Clinton had complained to General Hugh Shelton, then chairman of the Joint Chiefs, about his lack of options in going after Osama bin Laden. "You know, it would scare the shit out of al Qaeda if suddenly a bunch of black ninjas rappelled out of a helicopter into the middle of their camp," he said. It was the wish of a man who had more experience with the military in movies than real life. In order to rappel into an enemy's camp, you first had to know where it was and who exactly was there. From time to time, as we have seen, the United States had obtained reasonably current intel about bin Laden's location, but the ability to act swiftly and effectively on that knowledge, at acceptable levels of risk, did not yet exist.
Now it did. No matter how one felt about the wisdom of invading Iraq, or the seemingly unending conflict in Afghanistan, a near decade of combat had matured a generation of warriors and tools, battle tested and custom-made for finding and killing terrorists. This is what author Bob Woodward had hinted at when he caused a stir in a 2008 interview with 60 Minutes by referring to a "secret operational capability." It briefly inspired wild speculation about a crash military research program like the Manhattan Project in World War II that produced the atom bomb. Some imagined a "terrifying radar cannon" or a "thermal signature" device that could effectively fingerprint a target from twenty thousand feet. But there was no one secret weapon. The new tool was everything: reconstituted human spy networks, supercomputers, state-of-the-art software, global surveillance, and elite commando units.
There was, however, one more critical piece, one of the most dramatic developments in the history of modern warfare. One that began not at some secret lab with cutting-edge scientists, but on an airstrip in Hungary, with an air force colonel they called Snake.
James Clark had planned on a career in politics when he graduated from Catholic University in 1973. He had it all mapped out: law school, legal practice, then a run for Congress . . . But he had accepted an ROTC scholarship to help pay for school, and when he graduated the air force invited him to fly fighter jets. It was a thrill he found hard to leave behind, so his four-year commitment turned into ten, and then ten turned into a career. His call sign was "Snake." He was based in Taszár, Hungary, in 1995 when he got the chance to play with something then called the Gnat. It illustrated how a good idea doesn't always require a blinding stab into the unknown, because the Gnat was basically a glider with an Austrian skimobile engine. It would improve, of course: its surveillance tools would become state-of-the art and its engine virtually silent. Its hover time would greatly lengthen and its optics would become astonishing. It would eventually carry its own missiles. Called the Predator, it rapidly became the most sought-after weapon in the air force's multibillion-dollar arsenal.
The drone, or, as the air force prefers, the UAV (unmanned aerial vehicle), was not new. Radio-controlled aircraft were used during World War II. President John F. Kennedy's older brother, Joe, was killed on a secret mission when his specially engineered B-24, designed to fly itself to a German target after Kennedy had bailed out, exploded prematurely. Drones had been used in Vietnam, and the Israelis had used them to good effect over Lebanon's Bekaa Valley in 1982. Several of the Israeli models were purchased by the CIA, which turned them over to the San Diego defense contractor General Atomics for further development. Clark got four of them in Hungary during this experimental phase. He housed them in small tents out on the runway at Taszár. They were an immediate hit. Soldiers had long sought the ability to see over the next hill and the Gnat gave them a sixty-mile panorama from a platform that could stay airborne more or less permanently, flown in twelve-hour shifts. Manned aircraft could stay aloft for only as long as a pilot could stand it, or until his fuel ran out. Satellites provided a nice view when they happened to be passing overhead, and were in great demand, but they were expensive and few, and not always overhead. Once Clark's Gnats started flying missions over Kosovo they never stopped. Demand for them grew and grew. They have been in continual action ever since.
As the air force saw it, the problem during the Cold War had not been finding the enemy; they were, for the most part, in plain sight—tanks, missile silos, armies, and so on. The problem was how to attack them. The war that began in earnest after 9/11 posed the opposite problem. Al Qaeda terrorists made easy targets, if you could find them. At most they were holed up in compounds with a few armed guards. So a capability that allowed you to silently watch a target from fairly close range over days, months, and even years, in real time, was suddenly as valuable, if not more valuable, than a multimillion-dollar piece of hardware in orbit around the Earth.
General James Poss, working with Clark, commanded the first Predator mission over Iraq early in 2001, when the UN was policing a no-fly zone. The Iraqis would occasionally shoot at American planes patrolling the no-fly zones, aided by a large, clumsy Russian Cold War–era portable radar device called "Spoon Rest." It was mounted on a large van with twelve giant antennae shaped like coat hangers on top. In other words, they were hard to miss. Except that after nine months of trying, the air force could not find any of them. How could something so big and distinctive remain invisible? Whenever an American plane detected it was being tracked by radar, the force would direct an AWACS—Airborne Warning and Control System—to fly over and scan for a Spoon Rest van. None was ever seen. Could the Iraqis be dismantling them after each use? The old Soviet manuals said a unit could not be taken apart in less than twenty minutes, and the AWACS would get overhead a lot faster than that. The air force tried spotting them with a U-2, which also turned up nothing. Poss tried everything he could imagine. He had every large building in the vicinity surveyed. He tried pattern recognition analyses to try to predict where they were likely to show up. Nothing.
The Predator found the answer on the first try. Able to silently watch an Iraqi town where a Spoon Rest van was known to operate, it saw the Iraqis drive the distinctive van through the central market and park it under a bridge. All of the Spoon Rest vans were quickly located and destroyed.
There were other uses for drones. Before the U.S. bombing campaign began over Baghdad in 2003, Poss and Clark flew an old Predator they had planned to retire low and slow over the capital, prompting the Iraqis to fire up the radar at all their antiaircraft installations. This enabled the air force to map the city's defense system. When the Predator ran out of fuel they plunked it in the Tigris River, prompting the Iraqis to claim they had shot down an American fighter. They never recovered the aircraft. The next day, Poss and Clark did the same thing, but they miscalculated the fuel levels. Instead of splashing it into a lake on the outskirts of the city, the drone made it only to the water's edge. Alerted again by claims that an American jet had been shot down, film crews the next day recorded the recovery of an old drone painted with graffiti, without a bullet hole in it.
These first experimental models could only transmit TV signals along a line of sight, but before long Predators were bouncing their feed off communications satellites, which meant the view from above could be monitored and analyzed from anywhere, in real time. This was the real breakthrough. Drones provided not just a view from above—balloons had been floated over Civil War battlefields to accomplish that. The revolutionary change came when drone surveillance was tied into the existing global telecommunications system. This allowed the U.S. military to mount "caps," or permanent stable observation platforms, over whole cities. Tie that capability into supercomputers, with software capable of recognizing the "signature" of a specific target—say, a red pickup truck with a dent on its right rear fender—and you had the ability to track a target night and day.
By 2010, fleets of UAVs—which today include Predators, Reapers, Global Hawks, and a growing variety of others—were part of a worldwide integrated network that enabled remote operators at bases in the United States to fly missions almost anywhere in the world, funneling imagery and sensory data for analysis back to computers at Beale Air Force Base in California and CIA headquarters in Langley. The number of drones was well into the thousands, enough to sustain as many as sixty-five caps at once. For a selected target, the unblinking eye could establish things as simple as: How many people live in a compound? When do they wake up in the morning? When do they go to bed at night? What kind of weapons do they have? The air force was now using drones in teams, producing a system it called Gorgon Stare, that could cover an area four kilometers square—an area the size of Fairfax, Virginia. The image would not have to be monitored continually by human beings; it could be monitored by computers, which never get bored or distracted and are serenely undaunted by complexity. If, say, a vehicle belonging to a suspected terrorist was recognized by the computer—because it had some distinguishing feature that enabled the computer to track it—then the movements of that vehicle could be followed over a small city for months, or even years, permitting a detailed map of the suspect's travels. Combine that map with cell phone tracking, with human intelligence, and you can begin to assemble a detailed and accurate chart of your target's connections, or his network. Improvements in optics had enabled such observations from a great distance, so that the UAVs themselves would not have to be directly over a target. They could "stand off," well outside the restricted airspace over a country such as, say . . . Pakistan.
The trail to Abbottabad that seemed so clear in retrospect represented a triumph of dot connecting. In this case, it began with a name. It was not even a real name, and the reference was to someone reported, falsely, to be dead.
The name Abu Ahmed al-Kuwaiti was first mentioned to authorities in Mauritania by an al Qaeda operative, Mohamedou Ould Slahi, who went by the nom de guerre "Abu Musab." Slahi was a veteran mujahid, having fought twice in Afghanistan: first against the Russians and then against the regime left in place when the Russians departed. He had sworn allegiance to bin Laden and was living in Germany in late 1999, pursuing a degree in electrical engineering, when he befriended two of the young Arabs who would become 9/11 hijackers: Ramzi bin al-Shibh and Marwan al-Shehhi. The two were looking to join the jihad in Chechnya, but Slahi advised them first to travel to Afghanistan for training. Joined by Mohammed Atta, who would become the leader of the 9/11 group, the young Mauritanian helped them make travel arrangements to Karachi, launching them on the road that would take them to the United States and flight training. Performing this service placed Slahi at the origins of the 9/11 plot, and he was thus a highly wanted man after the attacks. In just ten days he was located living in his home country and was brought in for questioning by Mauritanian authorities. He was arrested in November 2001 and underwent extensive questioning in Mauritania and then in Jordan, where he claims he was tortured, and probably was. He has been imprisoned at Guantánamo Bay since 2002.
In telling the story of his travels and battles with the mujahidin, one of the names Slahi mentioned—one among many—was this Abu Ahmed al-Kuwaiti, whom he said had been killed. It was obviously a pseudonym. The name meant "the Father of Ahmed from Kuwait." It was just one name among thousands that were daily being entered into what would become the Terrorism Information Awareness database.
The same pseudonym, and person, would be fleshed out in more detail more than a year later by a true believer named Mohammed al-Qahtani, a baby-faced young Saudi who had pledged himself to al Qaeda and had planned to join the 9/11 hijackers as "muscle"—one of the enforcers trained to seize the plane and keep the passengers under control on the way to impact. He had arrived in Orlando about a month before the attacks—Mohammed Atta was waiting there to pick him up—but was turned away by an immigration officer, whose suspicions, even in that relatively unwary time, were aroused by the fact that Qahtani had a one-way ticket and could not speak English. When Qahtani grew indignant, he earned himself a return flight to Afghanistan. Denied martyrdom, he rejoined bin Laden and fought in the battle of Tora Bora. Fleeing that encounter, he was arrested crossing the border into Pakistan with other mujahidin in December of 2001. Qahtani claimed he had been in Afghanistan to learn the art of falconry. He was turned over to American authorities, who eventually matched his fingerprints with the young Saudi who had been denied entry to the United States in Orlando the previous August. This made him a subject of great interest.
Qahtani was interrogated relentlessly at Guantánamo from early November of 2002 until January of 2003. A daily log of his ordeal reveals a grinding effort to break down the young man's resistance. He displayed heroic defiance. There were repeated hunger strikes and attacks on his guards and interrogators—he frequently spat at them, head-butted one, and threw himself bodily at others. When doctors tried to administer IV fluids he tore out the needle, and when his hands were strapped to his chair he got the IV line in his mouth and bit it in two.
The Obama administration has claimed that torture played no role in tracking down bin Laden, but here, in the first two important steps down the trail, that claim crumbles. At best it demands a very narrow definition of the word. Slahi's prosecutor refused to pursue charges against him before a military commission because he found they were based on statements made under torture. And in Qahtani's case the coercive methods employed are clearly documented and public, and would be described as torture by any disinterested person. Indeed, it was his case that prompted the Department of Defense to draw up guidelines to curb interrogation excesses.
In time Qahtani succumbed to this pressure, however it is defined, and dropped his falconry story and began describing his work with al Qaeda in detail. One of the many names he mentioned as part of bin Laden's inner circle was this same Abu Ahmed al-Kuwaiti. He did not know the man's real name, but said he was not only alive and well but had worked closely with Khalid Sheik Mohammed, al Qaeda's Number Three, and had given Qahtani some preliminary computer instruction at an Internet café in Karachi, showing him how to communicate with the group's leaders once he was in America. As Peter Bergen reported in his excellent account, Manhunt, Qahtani was taught to compose a letter on an e-mail account, and then store it as a draft instead of sending it. His colleagues, armed with a password to the same account, could then log in and retrieve the draft e-mail without it ever having been sent, presumably avoiding America's watchful eye. Qahtani would also describe Ahmed the Kuwaiti as a "courier."
So now the name had come up twice, from two different men in two different countries, separated by more than a year. No one was yet paying attention to it. Many of the early detainee interrogations were not widely distributed, even within the agency—the importance of the single, enormous database would rise only when the software to exploit it appeared in a few years. In the early years of the hunt, even with dozens of analysts working full time, even with President Bush's list in the drawer of his desk in the Oval Office and his constant prods of "How are we doing?," and even with the help of the computers, it was nearly impossible to keep up with the flood of tips and "Elvis sightings." There was a $25 million reward offered by the State Department for information leading to bin Laden, and an additional $2 million put up by an airline trade association and the pilots union, so passing along a tip was like buying a lottery ticket: you can't win if you don't play. Tall, slender, olive-skinned Arab men were seen on every continent. The analysts did not have high expectations for any of these leads, but given the national priority assigned to the task, every single one had to be taken seriously. It was a powerful time suck.
In that context, a detail offered up under duress by Qahtani, one that would later prove key, was years away from being recognized as significant. Qahtani himself was not that big a deal. He was a foot soldier, one of thousands rounded up in Afghanistan as they fled across the border. All of them were questioned, and their answers were all swept into the growing database. Qahtani merited more attention than most, though. He was an Arab fighter, after all, and, unlike most detainees, he had been a member of al Qaeda. He had fought at Tora Bora and had tried to enter the United States shortly before the attacks, and if he had not been turned away he might have played a role in them himself. But he was still just muscle, a foot soldier. There was no reason to believe he could point out the location of Osama bin Laden. His mention of this Ahmed the Kuwaiti was noted. The supposed "courier" had helped prepare Qahtani for the 9/11 mission and apparently had worked closely with Khalid Sheik Mohammed, so he was potentially significant. But it was still just a fake name. Whoever the Kuwaiti was, by 2003 his pseudonym remained just another drop of intel in what was fast becoming an ocean of data.
Then Khalid Sheik Mohammed himself was arrested in Pakistan just a few months after Qahtani started talking. This dark, burly, hairy man was easily the most important al Qaeda figure ever apprehended—the terror group's Number Three, its operations director and the primary architect of 9/11. His arrest stirred a great deal of excitement. Here was someone who could provide a map of the entire organization, possibly cough up the hideouts of bin Laden and al-Zawahiri, or at least lead them closer, and perhaps reveal ongoing plots before they matured into new incidents of mass murder. Khalid Sheik Mohammed got the full treatment. He was interrogated aggressively by both Pakistani and American forces. In between 183 waterboardings at a secret CIA interrogation center in Poland, he was asked about many, many names. One among the many was Ahmed the Kuwaiti. And in addition to the volumes of information Khalid Sheik Mohammed provided—some of it true, some of it false—he acknowledged that such a character existed, but said the man was unimportant and had retired from al Qaeda years earlier.
So it was not as if the teams of analysts at the CIA were now, in 2003, looking at this fellow called "the Kuwaiti" as an important lead. But having been thrice acknowledged, albeit thrice acknowledged under torture, the prospect of his being fiction—someone made up by a detainee spinning stories—became less likely. He existed, or had existed. He may have been dead but was probably still alive. He may even have been, or might be, a member of bin Laden's inner circle—perhaps even a courier. Even so, the name wasn't a real name, and it was one of a multitude. It was not yet a lead, because to know so little doesn't lead or point anywhere.
The teams looking into the matter were smart, dedicated, and possessed the agency's studied, nondescript style. They were members of a kind of university of analysis, working under the direction of Michael Morell. When the effort settled into a routine, there were more than twenty analysts, men and women. There were more women than usual for this kind of job, partly because the CIA had undertaken to achieve a better balance of gender, but also partly because women were considered especially good at this kind of patient detail work and had a reputation for being sensitive to subtleties that eluded many men—the same insight that had guided Scheuer's staffing of ALEC Station. The teams tended to be on the youthful side of middle age, and the analysts had the look of people who commute to a job in a cubicle and spend long working hours before a computer screen or in meetings. They got a chuckle out of the depiction of CIA agents in books and movies—jumping from airplanes, leaping from rooftops, speeding through European capitals in sports cars under fire. They were mostly bookish sorts, but seemed less like academics than like accountants or junior business executives. Indeed, that's probably what they would tell you they did for a living if you asked. Ego and eccentricity were suppressed, sublimated by the clandestine nature of the job.
The Elvis sightings had slowed and then pretty much stopped by 2004. Bin Laden seemed lost. The teams turned more attention to sorting through the accumulated data—sorting it, devising ways to improve how they attacked it. There was his family, his huge family, with a dizzying number of kin and in-laws, any one of whom might become a conduit for a message to his mother (bin Laden had always been very close to her, a point of potential weakness). As the head of al Qaeda, he was known to be sending and receiving messages constantly. People were supplying him with food, medicine, and information . . . what methods did he use? And those video and audio statements? Who in his inner circle was known to make such recordings? The recordings were scrutinized with great care. What kind of wallpaper is that behind him? What sort of plants are in the room? What is he wearing? Analysts were far more interested in the trappings of bin Laden's statements than in anything he had to say. Why, if he was living in a cave in the wilds, were his robes so clean? There was a "media" team that focused on clues like that. And who delivered these offerings to Al Jazeera and other outlets? That was the job of the courier team. The agency got to where it could track the chain of couriers back to Number Three—it was Khalid Sheik Mohammed and then his replacement, a Libyan, Mustafa al-'Uzayti, who went by the nickname Abu Faraj al-Libi—but there the trail always went cold.
In January 2004, Kurdish police arrested Hassan Ghul, a known al Qaeda figure, trying to enter Iraq with money and bomb-making schematics. He was carrying a letter from bin Laden to Abu Musab al-Zarqawi, the murderous leader of al Qaeda in Iraq, the local franchise that was just beginning its bloody campaign against Americans and the Iraqi citizenry. During Ghul's interrogation the name Abu Ahmed al-Kuwaiti surfaced once more; Ghul described him as an important courier, one of the Sheik's most trusted aides. There were now four mentions of this mystery man, who was looking more and more real. But who was he? What sort of person would he be? The most valuable sort in such a role, if bin Laden were hiding in Pakistan, would be someone fluent in both Pashto and Arabic. Did the Kuwaiti fit that profile? If so, how do you track a nickname?
The public line offered during the remainder of the Bush years was that bin Laden was probably living in a cave somewhere in Waziristan. The CIA teams had stopped believing that in 2002. There were no sightings or even rumors of his presence in the northwest Pakistani territories—not a single report. There were also many stories suggesting that he had a serious kidney disease, and these, too, were discounted early on—these were the stories bin Laden himself had attempted to disprove by feasting before the Pakistani journalist Mir. The CIA rejected them because the logistics of dialysis would have been too difficult to sustain, and the Sheik appeared hardy enough in his videos.
When the analysts weren't slugging away on their computers, they were in meetings, proposing theories and arguing about theories. Detailed profiles were worked up. How would bin Laden be living? Who was likely with him? How big was his household? Where would it be? What might it look like?
The four most promising avenues seemed to be family, organization, finances, and couriers. The agency had committees focusing on each. And each of these avenues was generating its own collection of data—names, numbers, photos, interviews, etc. . . . all of it swelling the database, the great pool of potential leads. The work ground on, day after day, week after week, year after year. And nothing seemed especially promising.
The arrest of Abu Faraj al-Libi in May 2005, in Pakistan, raised hopes once again for a breakthrough. The second al Qaeda Number Three to be captured, it was known that he had been in direct communication with bin Laden in the years since the 9/11 attacks. But while he provided a lot of information after his capture, he offered nothing that directly helped the bin Laden teams. He did, indirectly, provide some help, however. Among the many people al-Libi was asked about was the Kuwaiti. Al-Libi said he had never heard of him.
That was interesting. Five different detainees had been asked about him now. Four said they knew of him. Three placed him close to bin Laden (although one of those three said he was dead), and one, Khalid Sheik Mohammed, said he had left al Qaeda. Now al-Libi, who had been with al Qaeda for more than twenty years, said he had never even heard of the man. How could he know nothing about someone Khalid Sheik Mohammed had readily acknowledged? The organization was not that big. Here's what the analysts gathered: their two most important captives either minimized the importance of the Kuwaiti or denied his existence altogether. This might mean that Ahmed the Kuwaiti was very important indeed. Bin Laden was the crown jewel. If the most important captives would protect anything, it would be information that might lead to him. That was one possible explanation. Add the fact that the Kuwaiti had dropped off the map . . . just like bin Laden. For the first time the CIA teams began to consider that the Kuwaiti was with the Sheik even now—his primary conduit with the rest of the world.
So among the various avenues still being explored intensely, the Kuwaiti became more important. Again, the name was just one of many and was just an alias. It would be five years before they managed to connect it with a real person. In 2007, the agency learned that the Kuwaiti's real name was Ibrahim Saeed Ahmed. It will not say how the connection was made. It might have been as simple as an informant, perhaps someone detained and being interrogated in another country, or it might have emerged from the wizardry of its supercomputers—from the Terrorism Information Awareness database—after some conversation on a cell phone somewhere in the world triggered the right connection. One senior official said that the information came from a "third country." Morell would tell me later, "You could write a book about how we figured it out." It is a book he is not ready to see written.
However the connection was made, by 2007, in light of the increasing usefulness of human intel networks and the enormous TIA database, a real name was a huge step forward. A real man had a history. Ahmed came from a large Pakistani family that had moved to Kuwait. He and his brothers had grown up speaking Pashto and Arabic. One of his brothers had been killed fighting against the Soviets in Afghanistan. A man with a large family had relatives who had telephones and mail delivery and computers with Internet connections. A man like Ahmed had a network that could be mapped and monitored. With the ability to pore rapidly over every scrap of data and find links in terabytes of intel, one might, say, notice a suspicious cell phone number that made calls home to Kuwait from Pakistan, and then locate the cell towers where the signal originated and comb through the reams of numbers that pinged that tower, looking for telltale patterns of usage. You could also begin routinely recording the conversations on that cell phone, although there is no evidence that anyone was interested enough to listen in just yet.
There still wasn't that much excitement over Ahmed the Kuwaiti. Again, he was just one of a great number of potential leads, many, many of which looked a lot more promising. Most of the analytical effort focused on finding the new al Qaeda Number Three or other key operational players, which had the added benefit of possibly thwarting ongoing plots. The Kuwaiti was peripheral. Much of what they had heard about him over the years suggested that he had dropped out of the organization altogether. His past associations would have been enough to explain why he kept out of sight. Perhaps it was the renewed pressure generated by President Obama in 2009, or perhaps just a decision by the teams to crank up the courier angle. It might have been that there was no change at all, that the patient collection of information and the growing sophistication of the software used to explore the TIA database finally delivered a key. But in June of 2010, because of either some change in his cell phone or its service package or some improvement in their own capability, the United States was able to pinpoint the phone's location when it was in use. This meant they could find the Kuwaiti, and watch him.
What they found, and what immediately provoked even more curiosity at Langley, was that Ibrahim and his brother Abrar were extremely careful. They would use their phones only in the car. Ahmed drove a white Suzuki Jimny with a spare tire mounted on the back, which could be watched from above. It turned out that before even turning on his phone he would drive for at least an hour from what turned out to be that very curious compound in Abbottabad. Ibrahim and his brother were using assumed names, Arshad and Tareq Khan. That was interesting, but there could be many explanations for it. Ibrahim's past associations alone might account for it. It was possible they were involved in some sort of illegal enterprise. Drug smuggling was big business in the Afghan-Pakistan border areas. Or maybe they were still working for al Qaeda.
These insights were sufficient to ramp up interest. If Ahmed the Kuwaiti was still a courier, perhaps he could lead them to where bin Laden was hiding.
The brothers' recorded phone calls now got close attention. Neither gave away anything in conversation about what they were doing but, significantly, there was that business about telling lies even to close family members about where they were living. And in one of Ibrahim Ahmed's calls came the brief exchange that appeared to confirm that he was still working with al Qaeda.
"I'm with the same ones as before."
Now his compound in Abbottabad had the agency's full attention.
5
"Please Make Sure to Keep the Children and All of the Families Away from the Areas That Are Being Photographed and Bombed"
Fall, 2010
Nine years after his most spectacular success, things were not going as Osama bin Laden had foreseen. He was cut off from his followers, frustrated, and his organization was fraying. The 9/11 attacks had been both his greatest achievement and his undoing. Toppling the World Trade Center towers and crashing a commercial jet into the Pentagon had not, as he supposed, sent the United States into a spiral of fear, retreat, and ruin. It had instead set al Qaeda and himself on the run from a patient, determined, and deadly pursuer. The movement had been fragmented physically and conceptually. It had become less his organization than a franchise, a banner waved by men who did not share his precise, divine insight, and who sullied its name with acts that killed, maimed, and alienated those he sought to defend and convert. The holy cause had gone off the rails. In isolation, he could no longer steer it himself. But the Sheik had not given up. The divinely inspired don't.
So he wrote letters, windy letters that filled many pages, a steady stream of them that were passed along a chain of couriers to the men he recognized as his deputies. Despite the oppressive reality, his letters offered consistently hopeful assessments of al Qaeda's opportunities. They contained detailed instructions promoting men to positions made vacant by virtue of an arrest or drone attack, bestowed or withheld his official blessing on start-up organizations in other countries, requested more detailed updates and information, mourned the dead, and critiqued, guided, and motivated his increasingly far-flung troops. He himself had little else to do. He would either tap away on the keyboard with his long, delicate fingers or dictate to one of his wives. He paced.
"In the name of God most merciful," he began one letter in October, 2010 to "Sheik Mahmoud" Atiyah Abd al-Rahman, one of his most faithful, long-serving soldiers, "may God protect him. I hope that this letter finds you and your family are in good health. I offer my condolences to you for the death of our beloved brothers. May God have mercy on their souls and consider them among the martyrs."
A Libyan, al-Rahman had sought out the Sheik in Afghanistan more than twenty years earlier, when he was a teenager determined to fight the great Soviet military machine. Even today he had a youthful, permanently unkempt look, with pale skin and a beard so sparse that it grew only in wisps on his jaws before thickening under his chin. Until recently, al-Rahman had been living in relative safety in Iran, serving as bin Laden's emissary to that country's mullahs, with whom bin Laden had an uneasy relationship. One of the Sheik's three wives and some of his twenty-two living children had been in Iran for years, either imprisoned or living under "protective custody." It was a matter of interpretation. Al-Rahman had helped broker their release, and was now back in the tribal regions of western Pakistan, somewhere in North or South Waziristan, ready to assume an operational role.
As it happened, there was an opening. The Sheik must have been grateful to have al-Rahman back. Drone attacks on al Qaeda forces in Waziristan had so thinned its ranks that the group was finding it hard to retain anyone in the critical Number Three position —operations commander, beneath only the Sheik himself and al-Zawahiri. Anyone pledged to al Qaeda was now a marked man, but this was especially true for its Number Three. The job required suicidal commitment. Unlike the organization's most infamous leaders, the operations commander had to be in constant touch with the group's rank and file, plotting actions, moving money, and training recruits, and the more active you were the more likely it was that the American satellites, drones, or raiders would find you. Number Threes did not last long. There had been 9/11 planner Khalid Sheik Mohammed, who was found and arrested in Pakistan in 2003. His successor, Abu Faraj al-Libi, was arrested in 2005, and al-Libi's successor, Hamza Rabia, was killed later that year by a drone strike. Next up, Sheik Saeed al-Masri, had been killed in May of 2010. The Americans were getting better. The rain of death was accelerating. Al-Rahman, stepping in for the late al-Masri, would die within the year, less than a month before his successor, Abu Hafs al Shahri, would likewise be killed in a Predator strike. And his successor, Abu Yahya al-Libi, would be killed in June 2012.
By now, every letter the Sheik composed from his cramped third-floor office in Abbottabad began with prayers for the martyrs and lists of condolences.
"This is the path of jihad," he intoned stoically in another letter to Atiyah Abd al-Rahman, his new Number Three. "God said, 'You will sacrifice your money and yourself for His sake.' They strike us and we will strike them back."
The limitations of this movement were more apparent. And while bin Laden politely asked his followers to launch more attacks on the United States, there was no longer any way for al Qaeda to make such ambitious arrangements. The 9/11 attacks had taken years to prepare, and had involved substantial international travel, long months of training, money, and close coordination. When the plan had been set in motion, the group was a peripheral concern for the United States and the Western world. Michael Sheehan, the U.S. ambassador for counterterrorism in the waning years of the Clinton administration, had felt like he was butting his head against a wall trying to get people to take bin Laden and his group seriously in the late 1990s. Michael Scheuer and "the Manson Family" of analysts at ALEC Station were regarded as alarmist, and wore themselves out with frustration.
This was no longer the case. America had spread an invisible web of surveillance that registered seemingly everything that stirred. Death rained continually. It was dangerous for the organization's leaders to move from one house to another, much less put another international plot in motion. And yet here was the Sheik still dreaming his big dream. His own men, even those who shared his vision, were discovering that their revered leader lived in a fantasy. He was still urging them to "hunch forth and stain the blade of lances red." Bin Laden had become the crazy officer waving his sword and rallying depleted troops to run headlong into withering fire—before him, mind you, not behind him. He sent them broad strategic analyses and called for specific missions that were wildly unrealistic, even screwy.
"I asked Sheik Sa'id, Allah have mercy on his soul, to task brother Ilyas to prepare two groups—one in Pakistan and the other in the Bagram area of Afghanistan—with the mission of anticipating and spotting the visits of Obama or Petraeus to Afghanistan or Pakistan to target the aircraft of either one of them," he wrote. "They are not to target visits by U.S. Vice President Biden, Secretary of Defense [Robert] Gates, Joint Chiefs of Staff (Chairman) [Michael] Mullen, or the Special Envoy to Pakistan and Afghanistan [Richard] Holbrooke. The groups will remain on the lookout for Obama or Petraeus. The reason for concentrating on them is that Obama is the head of infidelity and killing him will automatically make Biden take over the presidency for the remainder of the term, as it is the norm over there. Biden is totally unprepared for that post, which will lead the United States into a crisis. As for Petraeus, he is the man of the hour in this last year of the war, and killing him would alter the war's path. So please ask brother Ilyas to send to me the steps he has taken into that work."
Bin Laden diagnosed their primary problem not as the deadly American pursuit, which it was primarily, but their own lack of focus. And he had become a scold.
"After the war expanded and the mujahidin spread out into many regions, some of the brothers became totally absorbed in fighting our local enemies, and more mistakes have been made due to miscalculations by the brothers planning the operations."
Too many operations against Americans had inadvertently killed Muslims. He criticized two specific efforts, both by local jihadists affiliated with al Qaeda: the first being the unsuccessful attempt on the life of Afghanistan regional commander General Abdul Rashid Dostum in January 2005. The suicide bomber in that case had blown himself up outside the Ghocha Park mosque in Dostum's hometown of Sheberghan, where the general and his retinue had been praying during the annual Eid al-Adha festival. About twenty people had been injured. The other was an attempt to kill Pakistani General Muhammad Yusef Khan, in June 2004, again setting off a bomb at a mosque. Both had killed many Muslims, and both, bin Laden wrote, "bear extreme negative impact on the partisans of the jihad . . . It is extremely sad for an individual to fall into the same mistake more than once."
The campaign of terror led by al Qaeda's franchise in Iraq had killed eight times more Muslims than non-Muslims, according to a 2009 study. Bin Laden saw this kind of information reported on satellite TV. The bloodshed was thought to have caused many Sunni groups opposed to the U.S. invasion to turn on al Qaeda. This had been a clear tactical error, and a moral one. The rule was that one did not kill Muslims unless there was no other way to get at legitimate targets.
"[This] has resulted in the killing of Muslims (we ask God to have mercy on them and forgive them, and compensate their families)."
Bin Laden was now not so sure that the rule allowing even this exception to killing brother Muslims was valid. He wanted such rationales "revisited based on the modern-day context, and clear boundaries established for all the brothers, so that no Muslims fall victim except when it is absolutely essential . . . Here is an important issue that we should pay attention to: carrying out several attacks without exercising caution, which impacted the sympathy of the Nation's crowds toward the mujahidin. It would lead us to winning several battles while losing the war at the end. It requires an accurate criterion for the ramifications of any attack prior to carrying it out; also weighing the advantages and disadvantages, to then determine what would be the best attack to carry out."
Even successes troubled him. During a siege in Khobar, Saudi Arabia, in May 2004, a large group of terrorists took hostages from two oil company installations and killed nineteen foreigners. The attackers were part of the "al Qaeda in the Arabian Peninsula" branch, based in Yemen. They had asked each of the hostages if they were Muslims, and slit the throats of those who were not. Most of the attackers were killed in a rescue operation, and the incident helped provoke a brutal Saudi crackdown on extremists.
The Sheik now cautioned against mounting attacks like these and others inside Arab countries.
"The regime shall have a huge reaction toward the mujahidin; this would lead to defending themselves and avenging the regime," he wrote. "The brothers and the regime would then engage in a war that we did not begin against it, because the power of the brothers is not ready for it." The right strategy was to defer conflict with local Arab states, such as Yemen and Iraq and Saudi Arabia, "to avoid wasting our energy with these regimes at this stage [and] . . . losing the sympathy of the Muslims toward us . . . We are the ones defending the Muslims and fighting their biggest enemy, the Crusader-Zionist alliance."
It was now enough that the "general public" considered the victims Muslims, even if bin Laden, with his purer standards, did not. Killing those who fell into this category, while morally defensible, was a strategic error. Better that future attacks should come in places far removed from the Middle or Near East, he said. He mentioned South Korea in particular.
"Among the opportunities to be exploited in targeting the Americans is the state of security laxity found in countries where we have not carried out any attacks."
The Sheik often lectured in these letters, trying to steer his organization back to its central goals. He worried not only that local al Qaeda franchises had drifted away from his guidance, but that its mission was being diluted on targets and concerns he regarded as peripheral.
"By God's grace, jihad is under way on several fronts [Iraq and Afghanistan and, to some extent, Pakistan], and these are sufficient, by His will and His glory, as well as by the steadfastness of the mujahidin there, to perform the functions of bleeding the head of the infidels, America, such that it is defeated, God willing. Then the Islamic Nation will be able to expel that which has stricken it with weakness, servility, and degradation. The plague that exists in the nations of Muslims has two causes: the first is the presence of American hegemony and the second is the presence of rulers who have abandoned Islamic law and who identify with the hegemony, serving its interests in exchange for securing their own interests. The only way for us to establish the religion and alleviate the plague . . . is to remove the hegemony. . . . After this phase comes the phase in which the second cause—rulers who have abandoned Islamic law—are toppled, and this will be the phase in which God's religion is established and Islamic law rules."
Proceeding too hastily in local regions like Yemen undermined the movement's long-term goals, he argued. He saw the Taliban as a cautionary tale in this regard.
"A man might measure the results of establishing a Muslim state before toppling its enemies against the . . . fall of the Islamic emirate in Afghanistan, which we pray to God does not happen again."
In this October letter to al-Rahman, and in several others composed around the same time, the Sheik offered a sweeping assessment of the cause, his organization, and the world. He remained stubbornly optimistic, despite his circumstances. If America was the greater enemy, he considered Pakistan the one closer at hand, and he saw the natural disasters and political strife that year as a hopeful sign.
"As for the local enemy, as you know, they are in big trouble and the government is in danger of falling, especially after the floods [of the previous July] and the increase of the numbers of those who are suffering from the financial crisis." The floods, he wrote, were "God's punishment" on Pakistan for "its sins," but he urged al-Rahman that no one from al Qaeda should say this publicly, "because of the case of the Jewish man with the sick child, whom the Prophet invited to Islam, but did not tell him that his son was sick because he was not a believer." Best not to insult Pakistan.
He relished the conflicts between his two enemies: Pakistan and the American-led NATO coalition in Afghanistan. In recent months Pakistan had closed the border to Afghanistan, shutting down main supply lines for American forces there.
"Through the generosity of God, the situation is moving in the direction of the mujahidin. You should be patient and strong and God will reward us."
Given the persistent American pounding, it was time for all but the most disciplined "brothers" to leave Waziristan. He recommended that the others begin moving back into Afghanistan, urging al-Rahman to instruct them to leave their cars behind, because the Americans might otherwise start targeting houses, and that would "increase casualties among women and children." Bin Laden was very particular about protecting the lives of innocent Muslims. He urged his followers to move on "cloudy days, so that their flight would not be readily detected from above." He sent instructions concerning his grown children, the ones who were not in hiding with him, detailing precautions they should take when traveling, and where he wanted them to go. He had lost two of his elder sons, Saad and Mohammed, to the cause already. The Sheik considered himself an expert on security, especially on avoiding overhead surveillance, advising that travelers be moved from car to car inside tunnels, and that the brothers plant large trees around their bases of operation to provide cover from overhead cameras. He warned that tracking and eavesdropping devices might be "so small that they can be put inside a medical syringe."
Gone from these letters, full of condolences and the need for vigilant security, is the bravado of his younger years. Now and then the Sheik would digress for a moment to fondly recall that glory. He reminisced to al-Rahman, his current Number Three, about that moment in their shared story.
"[The attacks] filled Muslims with sympathy toward their fellow mujahidin, as it became perfectly clear that they are in the vanguard and are the standard-bearers of the Islamic community in fighting the Crusader-Zionist alliance that has caused the people to endure various forms of pain and degradation. One indication of that is the wide-scale spread of jihadist ideology, especially on the Internet, and the tremendous number of young people who frequent the jihadist Web sites—a major achievement for jihad, through the grace of God, despite our enemies and their efforts."
But those enemies and those efforts had kept him on the run or in hiding. He had been disowned by his large extended family. Most of his closest associates were either dead or in prison. He had been certain that America would not dare to directly confront him and the Taliban in Afghanistan. He had boasted to a Pakistani journalist, "I want the Americans to proceed toward Afghanistan, where all of their misconceptions and illusions will be removed. I am sure, however, that the Americans will not come, because they are cowards. They attack only the unarmed and weaker people."
The United States did come to Afghanistan, and they had defeated the Taliban. Despite the costs they were still coming. In addition, the United States had done something the Sheik could never have imagined. They had elected a black man president, a man with the name Barack Hussein Obama. It sounded like a Muslim name. And for almost two years now, Obama's words and policies had helped weaken the anti-Americanism that fueled al Qaeda's cause, while his drones killed off its membership.
Worse still, the indiscriminate brutal tactics of al Qaeda and its self-anointed affiliates had alienated millions of Muslims, those bin Laden meant when he referred to "the people" or "the Nation." This was the hardest thing for him to swallow. All this had happened, he believed, because he had lost control. His isolation had made it impossible for him to shape the group's image and message, and because al Qaeda had failed to make further dramatic strikes inside America, its significance waned. The attacks he had rejoiced over, that had seemed the start of something glorious, had instead set him back further than he had been when he had started. His world now consisted of two upstairs floors of a house in Pakistan that he and his family never dared to leave.
The house stood inside a large triangular-shaped compound at the end of a dirt road about a half hour drive north of Islamabad, the capital of Pakistan, in a neighborhood called Bilal Town. Abbottabad was in a basin surrounded on all sides by the rugged Sarban Hills. The drive from the capital was uphill, and Abbottabad's relatively cool air made it an escape for well-to-do residents of the big city during the brutally hot summer months. There were several golf courses nearby. One mile away was Pakistan's large military academy at Kakul.
The compound was new, and even though Bilal Town was an affluent neighborhood, at thirty-eight thousand square feet it was many times larger than any of the surrounding ones. Its walls were built of cinder block that had been plastered in the front. They were as high as eighteen feet in some spots, topped with barbed wire. The main house was a large white three-layer box, with a third floor that appeared to have been an afterthought, which was only two-thirds as tall as the first and second. This truncated floor was odd. It had windows on only the north wall: a large one at the center filled with glass coated with an opaque reflective material, and four small rectangular ones just under the overhanging roof, similarly coated. Most of the house was painted white, and the windows on the second story were shaded with simple white awnings. The Sheik and his large family lived on the upper floors. Bin Laden himself was rarely seen even by the other two families who shared the compound and who ostensibly owned it—the brothers who called themselves Arshad and Tareq Khan.
Locked away and losing control, bin Laden had not given up, nor had he retreated from life. Two of his first four wives were still with him, and he had taken one more. His most recent, Amal, a Yemeni a quarter century younger than him, shared a mattress with him on the cramped third floor. The two older ones—Khairiah and Siham—waited their turns with him downstairs. There was not, as later events would show, perfect harmony in these domestic arrangements. There was a container of Avena syrup on his kitchen shelf, an oat-based folk remedy that promised arousal to the sexually depleted male. It might even have done him some good, because the cramped hallways of his upstairs cloister were crowded with twelve children, the youngest, Hussein, just two years old. The Sheik's own father had taken twenty-two wives, so by comparison the son was a restrained polygamist who, by most accounts, labored to meet his responsibilities to each wife, even to those who had left him. He had acquiesced in the desires of Najwa and Khadijah to divorce him. He knew the difficulties of his chosen path and did not push it on them or his children. But he personally never wavered in his commitment to the cause. He was soft-spoken, but hardly an easy person to live with. Marriage was no equal partnership for the Sheik. His faith stressed strict patriarchy, and bin Laden was its obedient servant. He ruled his family. He not only made all the decisions, he liked to instruct, and like most men who possess the ultimate truth he liked to hold forth. He gave frequent in-house lectures to his wives about the correct way to raise and discipline children. And there was a daily religious homily.
There was no stoop yet to his tall, lean frame, and daily pacing sessions behind the high walls of his compound gave him at least a modicum of exercise. He walked beneath a tarp suspended over the compound's vegetable garden that deflected direct sunlight and shielded him from prying eyes. The Sheik had been athletic in his youth, playing soccer and volleyball. He was vain about his appearance. The whitening of his hair and beard bothered him. The most wanted man in the world worried less about being recognized than not being recognized. On TV, that is. He had been in such deep hiding that few outside his immediate family had seen him in person for years. But his self-made videos and the periodic pronouncements smuggled out by couriers were seen everywhere. It would not do for him to appear old. Given fundamentalist Islam's ban on depicting the human form, there were only a few images of the Prophet Muhammad, but no one better appreciated the power of pictures than the Sheik, and those of the Prophet that did exist generally showed him young and virile, with flowing robes and a dark beard. He had mimicked those images all his life. So now he dyed his hair and beard black for his taping sessions, with results that were predictably amateurish. The color was too uniform and dark. He looked like a caricature of himself: Osama bin Laden with a cheap dye job.
He had plenty of time to think. He could picture what must be done but could no longer make it happen. Al Qaeda's name had been so usurped and muddied by younger, less careful warriors in Iraq, Yemen, and elsewhere—men less constrained, as he was, by the strict dictates of faith—that bin Laden apparently thought of changing his group's name. Among his papers were long lists of possible alternatives, most of them amusingly clumsy in their English translation, but all attempted to identify the group closer to his religious ambitions. Increasingly, affiliates were fighting local wars over local problems, and ignoring the Sheik's overarching vision. This was no small matter. The path he saw was immutable, and perfect, and straying from it meant nothing less than failure. He weighed al Qaeda's every act and public comment with mounting dismay.
Take the case of Faisal Shahzad, the young man coached by bin Laden's followers in Waziristan to explode a car bomb in Times Square. No doubt Shahzad's attempt was an example of bin Laden's men trying to follow his instructions—he repeatedly urged renewed attacks in the United States at iconic, well-populated locations. Times Square fit the prescription perfectly, as did Shahzad. He was the son of a wealthy and prominent Pakistani air force officer. He had been raised in luxury and given the best of international educations. After marrying an American woman of Pakistani descent, settling in Connecticut, and fathering two children, he applied for and completed a program to become an American citizen. Then he'd traveled to Pakistan and received training on how to set off the bomb. A young volunteer with an American passport must have seemed a godsend to the besieged plotters in Waziristan. But alert Times Square sidewalk vendors had thwarted Shahzad's mission and the would-be bomber was arrested. Just before he was sentenced to life in prison, a judge had asked Shahzad about the oath of allegiance he had sworn to the United States when he was made a citizen.
"I sweared," he said, "but I didn't mean it."
This bin Laden found offensive, despite the fact that years earlier he had taken the opposite viewpoint about breaking an oath in an argument with his mentor Abdullah Azzam, who had opposed bin Laden's plan to bomb a bus full of tourists in Pakistan.
"[Shahzad] was asked about the oath that he took when he obtained American citizenship," he wrote to al-Rahman. "And he responded by saying that he lied. You should know that it is not permissible in Islam to betray trust and break a covenant. Perhaps the brother was not aware of this. Please ask the brothers in Taliban Pakistan to explain this point to their members. In one of the pictures, brother Faisal Shahzad was with commander Mehsud [Hakimullah Mehsud, who would be killed by a drone strike in 2012]; please find out if Mehsud knows that getting the American citizenship requires taking an oath to not harm America. This is a very important matter because we do not want mujahidin to be accused of breaking a covenant."
The Sheik seemed to have little appreciation for the murderous pressure on his followers in the field. He wanted more attacks on America, but he had no new ideas. Instead, with quaint courtesy and diligent thrift, he pushed for a duplication of the 2001 attacks. He wrote: "It would be nice if you would pick a number of the brothers, not to exceed ten, and send them to their countries individually, without any of them knowing the others, to study aviation. It would be better if they are from the Gulf states, as study there is at the government's expense. They have to be picked with the utmost care and with very accurate specifications, one of which is that they are willing to conduct suicide actions and are prepared to do daring, important, and precise missions that we may ask of them in the future. So please pay top attention to this matter due to its utmost importance. Establish a mechanism to monitor and follow up on the brothers going to study aviation so that we reduce the chances of them slackening from conducting jihad. . . . It would be nice if you would ask the brothers in all regions if they have a brother distinguished by good manners, integrity, courage, and secretiveness, who can operate in the United States. He should be able to live there, or it should be easy for him to travel there. They should tell us this without taking any action and also tell us whether or not he is willing to conduct a suicide operation."
He concluded his letter of October 21 to Rahman by inquiring after the growing lists of "widows and orphans."
"Please make sure to keep the children and all of the families away from the areas that are being photographed and bombed. I pray to God Almighty to protect you and all the brothers around you. May He grant you success. May God's peace, mercy, and blessings be upon you."
He signed with an old nickname, "Your brother Zamray."
At the time he was writing this, after all those years in hiding, after his rigorous routines of self-protection had become rote, after not a whisper of suspicion that anyone outside his inner circle knew of his whereabouts, the Sheik had every reason to feel secure.
Except he wasn't.
6
Disguised Uncertainty
Winter 2010–2011
At the White House in the fall of 2010, Ben Rhodes noticed a growing number of meetings to which he was not invited. As with the Nobel Prize acceptance speech, Rhodes had become Obama's go-to writer for speeches and statements explaining his decisions as commander in chief. Rhodes's official title was "Deputy National Security Adviser for Strategic Communications and Speechwriting." His hair had thinned on top, he rarely did anything but work, and he dressed every day in a suit and tie, but at thirty-two he had a job that anyone with his interests would envy. There were not many high-level national security discussions from which he was barred.
His desk was deep in the warren of small offices in the West Wing, just downstairs from the Oval Office and the primary corridors of power. Windowless and closet-like, his and the other offices of the national security staff were as humble as the jobs were important. Rhodes's space was just big enough for his desk and chair, a waist-high bookshelf, and one more chair opposite the desk. It was as spare as an intern's quarters at most law firms. Rhodes helped the president craft speeches, shape security policy, and decide how to frame critical issues for the public. He knew that John Brennan, the president's chief counterterrorism adviser, had been holding frequent meetings now for months, and that Donilon, the president's national security adviser, often sat in. The mystery sessions were simply called "John Brennan's group." Ordinarily there were cameras that monitored the conference rooms so that staffers and secretaries could keep track of where people were, but for John Brennan's group the monitors went black. Rhodes wondered about that. Was the country about to be attacked again? Was it something serious related to nuclear weapons? There was a very short list of things that would engender that level of secrecy within the basement offices of the White House. One of the thoughts that occurred to him was that maybe they had found bin Laden.
After getting briefed in late summer on the compound in Abbottabad, Obama had left his intelligence chiefs with instructions to nail down who was living in it and report back. These regular reports documented heroic efforts to scrutinize the residence from afar. Using a variety of tools, including agents on the ground and surveillance platforms that were far enough away to avoid any possibility of notice, the agency was now able to flesh out life in the compound in far more detail. Other than occasional visits to the mosque, or taking their own children to the madrassa, the religious school attached to it, the "Khan" brothers kept to themselves. No one except a local handyman was ever invited inside the compound walls. Among the most religious people in Bilal Town—and the Khan brothers were clearly that—it was not uncommon to hide women away behind high walls and locked doors. Longer observation confirmed that the children of the hidden family, the ones who did not attend the madrassa, were seen to leave the compound only when one of the brothers took them to the doctor for a routine visit or treatment for some minor ailment or scrape. This would give the CIA an idea.
There was no way to catch a glimpse of the hidden family upstairs. The walls were high, the windows opaque. Only one member of the family could be seen regularly, a tall man in traditional Pashtun dress and prayer cap who took daily walks inside the compound walls. He walked in brisk small circles around the vegetable garden, part of which had a tarp stretched overhead to shield the patch of ground from direct sunlight—or, perhaps, one could imagine, to shield the walker from eyes in the sky. Overhead cameras were able to get images of him anyway, but they were not very good. The agency did not want to risk putting a drone or observation aircraft directly overhead for fear of tipping off the residents—or the Pakistani government, which it feared would amount to the same thing. The angle or altitude of the standoff cameras made it impossible to get a clear look at the walker's face. He appeared to be tall and thin. Efforts were made to more accurately gauge the man's height by measuring his stride and the shadow he cast, but the calculations were only precise enough to confirm what they could see for themselves: he was tall.
Brennan, for some reason he cannot fully explain, and that may have been no more than wishful thinking, felt in his bones that this was bin Laden. They called the man "the Pacer." Perhaps Brennan was inclined to believe it already, given the extraordinary lengths taken to hide this man, but as soon as he saw an image of the Pacer . . . he knew. We recognize people by many things other than their facial features and hair color, or their size and shape. We sometimes recognize someone we have seen before at just a glance, a glimpse out of the corner of the eye, something in the way they carry themselves or stoop or tilt their head or swing their arms. Brennan is a big wide man, imposing and stern, a former CIA officer who had been involved in efforts to go after the al Qaeda leader all the way back to when ALEC Station was up and running. He had been based in Saudi Arabia at the time, butting heads with Scheuer over how much or how little the Saudis' help could be trusted. He had worked closely with the Saudis after the 1998 East Africa embassy bombings. And he had seen Predator images of the Sheik taken from overhead in Afghanistan during that period, a tall man in robes surrounded by security, striding confidently. This was a different setting, Abbottabad, and the clothes were different, but here was the same man, the same walk. There wasn't hard evidence he could show to convince anyone else, but Brennan felt he recognized the Pacer.
Panetta briefed the president periodically through that fall, and in December his deputy Morell, "John," the head of the CIA's bin Laden team, and several others met with Donilon and Brennan at the White House. There was no breakthrough to report. The images of the Pacer were not clear enough to remove all doubt. None of their efforts had managed to pierce the compound's walls. An agency team was now living in a house in Bilal Town. They noted everything they could see, but they couldn't see much. They watched the comings and goings of the Ahmed brothers. They counted the laundry that was hung out to dry. They had determined that the hidden family was large: three wives, a young man, and ten or more children, several of them teenagers or young adults. The number of wives and children corresponded with their theorizing about who might surround bin Laden on the run. He had always kept most of his family with him. The analysts still could not prove that the mystery man was bin Laden but, then again, there wasn't a single scrap of information that ran counter to that theory, either. Sometimes when you are looking hard enough at something, when you are ready for anything that might shoot down your hypothesis, and nothing comes . . . lack of disproof begins to feel like proof.
"We think we have the best intelligence case for the location of bin Laden since Tora Bora," Morell told Donilon.
So, on December 14, just before Obama left for his annual holiday trip with his family to Hawaii, Panetta visited him in the Oval Office.
Obama listened and weighed the evidence. He was impressed. Now that there were actually "eyes on" the compound the whole prospect seemed more real, and all the new intel fit the puzzle neatly. Obama was struck, just as the others had been, by actually being able to see the mystery man. You couldn't tell exactly who it was, but something about actually seeing the target moving inside the high walls, hiding from the world, registered with him.
"At this point, you're saying to yourself, this is all circumstantial, but it's hard to figure out what the explanation would be for that particular pattern," said Obama. "And so at that point I think there's a part of me that's thinking this might be for real."
Still, the president was cautious. He told Panetta, "For all we know this could be some sheik hiding from one of his wives."
He wanted more. He instructed Panetta to get creative, to figure out a way to nail it down. He said to continue keeping a tight lid on it. And he also instructed Panetta to start preparing options for action.
As closely as the secret was held, Bill McRaven had gotten wind of it back in November. Those monitors might have been blacked out for meetings inside the NSC's offices, and McRaven was now spending most of his time in Afghanistan, but it was hard to keep the JSOC commander completely out of the loop.
He had worked in the White House himself. It was when he was just beginning to work his way back from his severe jump injuries, his body adjusting to the plates and pins that now held his pelvis together. He'd gotten a surprise phone call in October 2001, from Wayne Downing, a former four-star general who had led the Special Operations Command. The two men had gotten to know each other during the years before Downing's retirement. The general had just been asked by President Bush to unretire and take up a position in the White House as a kind of counterterrorism czar—an ill-defined special assistant role designed to bring some measure of coordination to the multiple agencies and services involved in the new war. Before he even officially accepted the job, Downing called to ask McRaven if he would come to Washington to help.
"You bet," said the SEAL captain.
A few weeks later, Downing caught up to the still hobbled SEAL as he was driving across the country from San Diego to his new desk job in Norfolk, Virginia.
"Hey, I've taken the job," Downing said. "Can you be here on Monday?" That was just four days away.
"Yeah, I think so," said McRaven.
When he showed up at the White House in his wheelchair, Downing told him simply, "Figure out what you're going to be."
It was a terrific opportunity for any military officer, especially one who had years earlier abandoned the idea of advancement in order to stay in the field, jumping out of planes and working deep underwater. The chance was not lost on McRaven. It seemed clear from the beginning that, in the long term, finding and taking down a furtive terror organization would require the kind of creative, cross-disciplinary skills long practiced by special ops. If every new war demanded that the military rethink how it fights, McRaven was already a few steps ahead. He had written a book on the subject while attending the Naval Postgraduate School in Monterey, California, entitled Spec Ops: Case Studies in Special Operations Warfare: Theory and Practice. It was a rare military graduate thesis to be picked up by a commercial publisher—the Presidio Press, which published it in 1995. In the book, McRaven had studied eight special operations missions, from the German attack on the fortress of Eban Emael in 1940, prior to the blitzkrieg of Belgium, to the Israeli raid at Entebbe, Uganda, in 1976, the raid that prompted President Carter to request creation of a similar counterterrorism unit for the U.S. military. McRaven had visited the sites of these raids, interviewed many key participants, and pieced together his own understanding of why they had succeeded or failed. As he did so, he crafted a way of thinking about such specialized missions. Now he would have a seat at the table, a chance to apply those ideas to America's newest military challenge.
The very idea of "special ops" had long been regarded critically by the conventional military. The elite, secret units that conducted these operations sucked up enormous resources and key personnel for occasional acts of amazing derring-do. When such missions worked they seemed almost magical, as in the Entebbe raid, where Israeli commandos flew 2,500 miles to Uganda, surprised a much larger force, and rescued 102 hostages, killing all of the Palestinian hijackers who had seized a commercial French airliner. When they failed, as in the rescue mission to Iran in 1980, they nearly always seemed harebrained in retrospect. They were daring by definition. The idea was to attempt something bolder than the enemy could reasonably anticipate. The men involved accepted great personal risk, and those in command gambled their reputations and careers on the outcome. And it was in the nature of the work that failures made a huge splash while successes, except in rare instance like Entebbe, were often, by design, unadvertised and unnoticed.
The debacle in the Iranian desert had prompted the creation of JSOC, which is based at Fort Bragg, North Carolina. Much blame for the failure fell on the clumsiness of efforts to borrow from various service branches unused to working together. So the mission had navy helicopters flown by marine pilots carrying army special operators deep into Iran to link up with air force piloted planes and crews. This motley force had left behind a desert staging area littered with destroyed aircraft and incinerated American bodies. Though one of the most spectacular failures in American military annals, the effect was not to kill special ops but to expand it. JSOC was created to integrate elite units from every branch into a smooth fighting force, and to equip them with the kind of vehicles and weapons needed for small, unorthodox missions. It brought together the army's Delta Force and 75th Ranger Regiment, the air force's Special Tactics Squadron, and Navy SEAL teams. Since the Iran mission had broken down trying to deliver the force to the target, the Night Stalkers, the 160th Special Operations Aviation Regiment, was stood up at Fort Campbell, Kentucky, where special choppers were designed and tested, and where the military's best helicopter pilots trained specifically for special ops missions.
McRaven's thesis, which would become part of the curriculum at the Naval Postgraduate School, set out the core concept of special ops: that a small, well-trained force can deliver a decisive blow against a much larger, well-defended one. He defined such a mission as one "conducted by forces specially trained, equipped, and supported for a specific target whose destruction, elimination, or rescue (in the case of hostages), is a political or military imperative." Refining the key elements to success for such missions, he prescribed, in a nutshell, "A simple plan, carefully concealed, repeatedly and realistically rehearsed, and executed with surprise, speed, and purpose."
President Bush's two large wars, each requiring hundreds of thousands of conventional soldiers, gradually proved the point that special ops was the most useful tool against al Qaeda. The tremendous effort and innovation that went into finding and fixing a target relied on men capable of executing the third F in the acronym F3EAD, the finish. The model McRaven had developed in his thesis primarily dealt with assaults on larger, well-entrenched enemy positions, but the principles of the lightning raid—simple, secret, and well rehearsed, executed with surprise, speed, and purpose—would prove devastatingly effective against an enemy that hid itself in a civilian population, in large part because pinpoint raids, as opposed to aerial attacks or direct assaults by conventional forces, avoided killing and injuring innocent bystanders. It also allowed for onsite collection of intelligence, which was essentially for feeding the target engine. Over the next decade, McRaven would get a chance to refine his strategies and put his theories into practice at a pace he had never imagined.
His two years in Washington before returning to a field command enabled him to combine necessary physical rehab with some high-level career rehab, developing the kind of relationships that are necessary to achieve flag rank. Rank was not something McRaven actively sought—indeed, years earlier, even before his accident, he regarded himself as the last person in the navy likely to become an admiral. But in just a few years he was back on his feet, serving in Iraq as deputy to JSOC commander General McChrystal, admiring the fusion of rapid intel and shooters his commander had implemented, and occasionally accompanying his men on night raids—the kind where you could drive or walk to the target. No more jumping out of planes, roping out of helicopters, or long marches in full pack for McRaven. During those years, first under McChrystal and then commanding JSOC himself, the admiral would help forge this new capability into the nation's premier war-fighting instrument. The JSOC force itself doubled in size, to nearly four thousand men and women. It became, in effect, a fifth branch of the U.S. military, an army within an army. It was global, operating in secret in more than a dozen countries, and had been freed from strict mission-by-mission oversight from Washington. The need for speed trumped the desire for close control, so commanders like McChrystal and McRaven were given the authority to launch at least routine strikes without seeking approval all the way up the chain.
Through the first decade of the century, McRaven and his men had carried out more special ops missions than any such unit in history. He estimated that by the time he was summoned to Langley in January 2011 to be officially briefed on the Abbottabad discovery, he had been personally involved, commanding either remotely or on the ground, in thousands of them.
By early 2011, the CIA had its own small armies in the field. After 9/11, the nation had recovered quickly from its misgivings about spying and covert action. Agency operators, most of them former military, had worked ever more closely with JSOC throughout the wars in Iraq and Afghanistan. When Panetta and Morell returned from the White House meeting with Obama in December, the one where he directed them to start thinking about taking action, the first units they considered were their own.
The two broad options were to bomb the compound or to send a raiding party in. The latter would be far more complicated. It would require planning and rehearsal, and involve a variety of special talents, so the instinct was to develop that option in-house. This had the advantage of keeping the now four-month-old secret contained. Outside the agency, those who knew about the compound, or who were supposed to know, could still be counted on two hands. There was the president, of course, and a few top members of his foreign policy staff, including Brennan and Donilon. The director of National Intelligence, James Clapper, had been told. At the Department of Defense there were only four people, Secretary Robert Gates, Chairman of the Joint Chiefs Michael Mullen, Vice Chairman General James "Hoss" Cartwright, and Undersecretary of Defense for Intelligence Michael Vickers.
The CIA teams were excited about the mission and were ready to do it themselves . . . soon. But Panetta and Morell had time. The president had also told them to work harder on identifying the mystery man. Before committing themselves to using their own operators, they wanted to at least consult with McRaven.
All the JSOC commander knew before getting the call was that the CIA had a new lead on bin Laden. He had heard that before over the years, and in each case the lead had failed to pan out. Early in the war in Afghanistan his men had spent a lot of time chasing bin Laden's ghost. This time he was told that the lead seemed better than most, but McRaven didn't think much of it until he was summoned to Langley. That had not happened with any of the previous leads. At the conference table in the deputy director's office, McRaven and one of his top aides met with Panetta, Morell, and the heads of the CIA's own strike force. He was shown pictures of the compound. No one had glimpsed the inside of the buildings. Everything was heavily couched in maybes. Morell made it clear that they were not certain that bin Laden was really there, and they weren't sure yet what course the president would decide to take, if any. But on that qualified basis, they launched into a tactical discussion. If you were going to hit that target, how would you do it?
The CIA men had had a head start. They sketched five different options. That fact alone was telling. McRaven could see at a glance that there was really only one way to do it. He had ruled out a bombing option immediately. Whatever the advantages in simplicity and reduced American risk, his educated guess was that it would take upwards of fifty thousand pounds of ordinance to destroy a compound of that size and make sure bin Laden, if he was there, wouldn't survive. You had to consider the possibility of tunnels or an underground bunker—like the one where Saddam had been hiding. That explosive power would kill everyone inside the compound and quite a few people nearby.
A ground raid, on the other hand, posed relatively few problems. His men had been hitting compounds like this every night for years, often a dozen or more a night. This one was unremarkable. It had a three-story residence, a smaller outbuilding, and high stone walls all around it. The layout and location of the compound clearly indicated to him the right way to assault—a small helicopter-borne force.
He kept this thinking to himself as the CIA unit commanders described the options they had worked up. When it was his turn to comment, McRaven congratulated Panetta and Morell on developing such a strong lead and proceeded to walk them through how JSOC would do it. You would need a team big enough to secure the compound once you were inside. The primary challenge was its location. Abbottabad was in a "denied" space 150 miles from friendly territory, which meant that delivering the force to the target and safely extracting it without triggering a shooting war with Pakistan would be the biggest problem. It was, as the admiral was fond of saying, "sporty," but doable. It would increase the complexity of the mission, and complexity multiplied the number of things that could go wrong. But those problems aside, how to actually raid the compound and the buildings were old hat. The tactics McRaven's teams had developed were built on years of trial and error, missions that had worked and those that didn't. A lot of good men had died perfecting these skills. He ran through for the CIA men how his team would proceed, and why. He even suggested the right man for the mission, his SEAL Team Six commander, who had earned a legendary reputation—he had led the mission that had killed three Somali pirates in 2009, rescuing an American freighter captain. McRaven explained that the most valuable thing his team would bring to the mission was experience. No matter how well the operation in Abbottabad was planned, long experience taught that something would go wrong. Something always went wrong. What you needed were men who could think on their feet and make good decisions under pressure, men who had seen all manner of snafus and survived. No one in the world could rival JSOC's seasoning. The SEAL team he had in mind had just rotated back to the United States and could get to work on the mission right away.
Morell and Panetta were impressed. Their guys were good, but McRaven's men were the pros.
"If the president decides to do this on the ground," Panetta told Morell, "then JSOC are the guys to do it."
Panetta pushed the agency to come up with creative ways to get a better look inside the compound, without much luck. The agency team spent hours kicking around possibilities. No idea, no matter how outlandish, was rejected without serious discussion. Was there some way to flush the residents out of the compound? A fire? A stink bomb? A summons to emergency prayer? Panetta kept a chart, and every suggestion was logged on to it. A suggestion was not crossed off until it was either tried or seriously discussed.
Was there a way to position a camera closer, say on a tree that could peer down over the walls? What about one farther away on high ground but with better optics? How about sewage lines: could a listening device or a camera be threaded in that way? There was a tree inside the compound. Could they put a small camera or listening device up in it somehow? Some of these ideas were tried but yielded nothing of value. The tree inside the compound was chopped down before anyone could figure out a way to get at it—spooky, because it was as if someone inside the compound had seen the director's chart. One by one, the schemes either fizzled or were discarded. They were extremely careful not to tip their hand. The compound had clearly been designed to hide the family inside, and designed well. It would not take much to spook them. Any hint that they were under surveillance would blow everything. Morell lived in fear of waking up one morning to discover that, overnight, the compound had emptied.
One creative idea may have grown out of the observation that the only time any member of the hidden family emerged from the compound was when a child was taken to the doctor. The agency got the idea of opening a free hepatitis B vaccination clinic for children nearby. Maybe they could draw some of the hidden children out that way. They found a Pakistani doctor, Shakil Afridi, whose passion was setting up such clinics all over the country. He would go door-to-door notifying residents and persuading them to bring their children in for shots. Agents approached Afridi and offered him a substantial sum—something in six figures worth of American dollars—enough to sustain his program for some time. All he would have to do in return was give them the needles he used. They never told him why they wanted the needles, but the plan was to recover DNA from them and analyze it. The CIA had DNA samples from close relatives of bin Laden. If genetic material from one of the hidden children closely resembled it, it would come very close to proof positive that the Sheik was the father. The clinic would be real, the inoculations completely legit. The children of Abbottabad would emerge healthier and the agency might get the confirmation it needed. The agents did not hide their affiliation from Afridi; he was told that the CIA was funding the program.
Over the next few months, as planning proceeded at Langley and in the White House, Afridi set up the clinic. He went door-to-door, inviting everyone to bring in children. He inoculated many. But when he knocked on the door to the big compound in Bilal Town, no one answered.
No one would ever answer.
Planning for either an air or a ground assault on the compound proceeded through February. Despite Panetta's push for an answer, the CIA was no closer to the identity of the Pacer. McRaven's man was drawing up detailed plans in an unmarked office on the first floor of the agency's printing plant, and the air force was plotting out a B-2 mission to obliterate the compound in one blinding strike. All of this required enlarging the circle of knowledge. Michèle Flournoy, the undersecretary of defense for policy, was read in by her boss Mike Vickers, and she began working closely with General Cartwright. The various deputies were now meeting every week, usually at the White House but sometimes at the CIA, getting updates on the intelligence-collection efforts and discussing every possible permutation of a raid. These "deputies" meetings were usually attended by Cartwright, Morell, Vickers, Robert Cadillo, the deputy director of National Intelligence, and sometimes John Brennan and deputy National Security Adviser Denis McDonough. Toward the end of the month, McRaven sat in on a few of these sessions, prepping for a March 14 principals meeting with Obama, where they would formally present the president with recommendations.
As usual, the national security agenda was full. An earthquake and tsunami three days earlier had caused widespread death, destruction, and dislocation in Japan, and the U.S. military was mobilizing to deliver humanitarian assistance. There were sweeping popular protests in Egypt, as the "Arab Spring" spread across the Middle East—an inspiring but potentially treacherous period of change in a region whose stability had long been vital to U.S. interests. In mid-February, Obama had called for Egypt's longtime president Hosni Mubarak to step down, and was now weighing options for some kind of limited intervention in Libya, where dictator Muammar Gaddafi's long-standing regime was being pressured by increasingly violent protests. And in Pakistan itself, a CIA contractor working out of the Lahore consulate, Raymond Allen Davis, had shot and killed two armed men on the street when he said they had tried to rob him. He was under arrest and facing murder charges, and the United States was having the devil of a time trying to extract him. Local frustration over American policies in Pakistan had warped the incident into a standoff, with demonstrators and some prosecutors demanding that the CIA contractor be prosecuted and punished. So at the same time options were being prepared for various ways of violating Pakistani sovereignty with a raid on Abbottabad, the White House and State Department were engaged in delicate discussions over Davis.
It was in this context that Obama met with the National Security Council to formally consider the CIA's case. It was time to start making the important decisions. Obama was acutely aware that the longer he delayed, the more people were read in on the secret—and greater became the likelihood that it would leak, or that something critical would change. The group met in the White House Situation Room, where much of the drama over the next two months would unfold.
The Situation Room is a few steps down from the ground floor of the West Wing, the largest in a complex of small meeting rooms, and is hardly what a set designer would imagine as the decision center for the world's only superpower. Long ago nicknamed "the Woodshed," it was installed by President Kennedy after the Cuban Missile Crisis to create a secure command center fully wired for global telecommunications. It is windowless and cramped, much smaller than the dining room in most grand residences. Much of the mahogany paneling that gave the room its nickname was removed in a 2007 renovation to make it easier for electronic technicians to get at the cables and wiring. Now its beige walls are hung with flat video screens. The ceiling is low and lined with harsh recessed fluorescent lights. The room is all but filled by a long mahogany table at its center, polished to a high gloss. Around it are thirteen high-backed black leather chairs. The blue carpet beneath has a yellow border around the edges, on which are lined smaller black leather chairs for deputies and staff members. The president sits at the north end of the table beneath the circular presidential seal. There is no chair at the opposite end, which is open to afford a clear view of a video screen that reaches from tabletop to ceiling. There are leather desk pads at each place around the table for the secretaries of defense and state, the national security adviser, the vice president, the director of National Intelligence, the chairman of the Joint Chiefs, the president, and, for nearly all of these sessions, the CIA director and his deputy and various others. Until his work in the field took him away, Admiral McRaven was present.
Above all, one is struck by how intimate the space is. When full, as it was for many of these meetings, the top leadership of the nation can be said, without exaggeration, to be huddled.
By early March the agency had determined that the Abbottabad compound held a "high value target," and that it was most likely Osama bin Laden. "John," the team leader at the CIA and the most veteran analyst on the trail, was close to convinced. He put his confidence level at 95 percent.
The president surveyed confidence levels around the room. Brennan felt about the same as "John," but others were less certain—some far less certain. The opinion had already been "red-teamed" three times—worked over by agency analysts assigned to poke holes in it: at the Counterterrorism Center, by Brennan's staff, and by a group within the CIA. Four senior leaders at the Directorate of National Intelligence had reviewed the case and written out their own opinions. Most seemed to place their confidence level at about 80 percent. Some were as low as 40 or even 30 percent. Obama then asked Morell, who was seated in a chair against the wall behind him, under the presidential seal.
Morell had come to admire Obama's decision-making skills. He had worked with President Bush up close almost every day, and he had admired him, too, but the two men were very different. Morell and others who worked closely with Bush believed he was widely underestimated. He was plenty smart. He was not as eager as Obama to ingest written reports, but he did read them, and he was a good listener. He grasped the nut of an issue quickly, asked sharp questions, encouraged lively debate, and then, unhesitatingly, often on the spot, made a decision. Obama, on the other hand, had a level of study and contemplation that he kept private. He liked to pore over written reports and, after initiating a discussion of opposing views, would generally retire before coming back with a decision.
One thing in particular impressed Morell about Obama. Morell had given and sat through thousands of presidential briefings by now, enough to know the in-house tactics of policy makers. Advisers had a way of narrowing the choice to option A or option B, and then steering the president to the one they preferred. It was all in how the issue was framed. This method didn't have a chance with Obama. He would listen to A and B, ask a lot of good questions, and more often than not propose an entirely different course, option C, which seemed to emerge wholly formed from his head. He had done this just a few days earlier in a widely reported instance concerning Libya. It came during a prolonged policy discussion over what the United States should do about Gaddafi's apparent intent to slaughter rebels and civilians who were contesting his regime. In that case, option A was just to stand back and not get involved. The consequences would be awful but U.S. military intervention in a third country (Iraq and Afghanistan still being very much live wars) would be hugely unpopular domestically and might, in Libya, where there was no clear idea what would emerge after Gaddafi, end up making things worse. Option B was to intervene militarily on the side of the rebels, essentially do whatever had to be done to prevent them from being systematically slaughtered by the regime. There were strong views on both sides, but the first option was clearly the one favored by most of the staff. Obama then proposed an option C, the course he would eventually pursue. This called for the United States to spearhead air attacks on Gaddafi's forces for a few days, and then let a coalition of European and Arab countries take over. U.S. forces would step back from most combat missions after the initial thrusts but, through NATO, continue providing critical air support and patrol a no-fly zone. Morell thought it was brilliant.
He now placed his own certainty that the Pacer was bin Laden at 60 percent.
"Okay, this is a probability thing," said Obama. "Leon, talk to me about this."
The director explained that ever since the agency's erroneous call, a decade earlier, that Saddam Hussein was hiding weapons of mass destruction, a finding that had kicked off a long and very costly war, the CIA had instituted an almost comically elaborate process for weighing certainty. It was like trying to contrive a mathematical formula for good judgment. Analysts up and down the chain were now asked not only for their opinion, but to assign it a confidence level—high, medium, or low. Then they had to explain why they had assigned that level. What you ended up with, as the president was finding, and as he would later explain it to me, was not more certainty but more confusion.
Obama said as much, and then turned in his chair and looked at the deputy director.
"Michael, what do you think?"
Morell had thought a lot about it. He had been personally involved in the finding about Saddam's supposed weapons of mass destruction, and had felt more certain about that than he felt about this.
"People don't have differences because they have different intel," he said. "We are all looking at the same things. I think it depends more on your past experience." He explained that counterterrorism analysts at work on al Qaeda over the past five years had enjoyed a remarkable string of successes. They had been crushing the terror group inside Pakistan, and they had directly or indirectly prevented further terrorist attacks inside the United States So they were very confident. Those who had been at work longer, like him, had known failure. They knew the fragility of even the soundest-seeming analysis. The WMD story had been a bracing lesson. He bore responsibility for it.
"Mr. President, if we had a human source who had told us directly that bin Laden was living in that compound, I still wouldn't be above 60 percent." He said he had spent a lot of time on both questions—WMDs and Abbottabad. He had seen no fewer than thirteen analytical drafts on the former question, and at least as many on the latter.
"And I'm telling you, the case for WMDs wasn't just stronger, it was much stronger," he said.
This kicked off more discussion about percentage levels of confidence. The president listened, but he had already pretty much made up his mind.
"One of the things you learn as president is you're always dealing with probabilities," he told me. "No issue comes to my desk that is perfectly solvable. No issue comes to my desk where there's one hundred percent confidence that this is the right thing to do. Because if people were absolutely certain then it would have been decided by somebody else. And that's true in dealing with the economic crisis. That's true in an order to take a shot at a pirate. That's true about most of the decisions I make during the course of the day. So I'm accustomed to people offering me probabilities. In this situation, what you started getting was probabilities that disguised uncertainty as opposed to actually providing you with more useful information."
Obama had no trouble admitting it to himself. If he acted on this, he was going to be taking a gamble, pure and simple. A big gamble.
If they were successful, and if the Pacer was bin Laden, then killing or capturing him would mark a clear and central victory in the war al Qaeda had started almost ten years ago. It would deliver on the promise Obama had made campaigning four years earlier, the one where he said he would take a shot unilaterally in Pakistan if he got a good chance, the promise that nearly everyone had criticized, including some, such as Hillary Clinton and Joe Biden, who were now in the room helping him to decide. That promise in some ways had defined his national security strategy. So success would be a demonstration of justice achieved at great cost and sacrifice, and with tremendous skill. It would be a satisfying achievement for America and the world, an emotional turning point, but more, it would vindicate the determination and skill of everyone who had given of themselves—in some cases all of themselves—to the struggle. On a practical level, it would be the single greatest blow yet to an organization still scheming to take American lives.
If he tried and failed, however—and they had not yet begun to calculate all the spectacular ways it might fail—then some brave American warriors might lose their lives attempting something that might turn out to be a major national embarrassment. Failure would likely be as prestige-enhancing for al Qaeda as Desert One had been for Iran's mullahs in 1980. Bin Laden's stature, which had waned considerably since 2001, would get a new boost, the kind that translated into more money, more recruits, and more attacks. Success might bump up Obama's political standing at home for a few weeks, but failure could brand him as an ineffectual commander in chief, and doom his chances for a second term as surely as Desert One had doomed Carter's.
Either way, success or failure, there would be an outraged Pakistan to deal with. American relations with that difficult, nuclear-armed nation were already strained nearly to breaking. Whatever he decided, Obama later told me, was going to be a judgment call based on circumstantial evidence, piecing together patterns. There was still a possibility that this was some warlord from Afghanistan who had set up shop, or that this was a drug dealer from the Gulf who valued his privacy or had a mistress or a second family. There were other stories that might have explained the pattern. The calculation the president had to make was whether it was probable enough that bin Laden was there to justify the risks, given the importance to America's national security.
So as the conversation around him about levels of certainty wore on, the president, who usually did more listening than speaking in these meetings, interrupted.
"This is fifty-fifty," he said. That silenced everyone. "Look guys, this is a flip of the coin. I can't base this decision on the notion that we have any greater certainty than that."
So, if he decided to act, what were his options? Obama was presented with two. The simplest, and the one that posed the least risk to American forces, was to reduce the compound to dust, along with everyone and everything in and around it. To do the job right, the air force had calculated that would mean raining as many as thirty or more precision bombs from a high-flying B-2, or launching a comparable number of missiles. This would be enough to guarantee that anything breathing on, in, or near that plot of earth would be killed. It would vaporize everything above ground and pulverize anything below. There would be minimal worry about encountering Pakistani air defenses—a lone high-flying B-2 Stealth bomber would be long gone before the country knew it had been hit. With no ground forces there was no chance of mixing it up with that nation's army or police. It would be a mighty, sudden stroke from a dark sky that would leave nothing but a big smoking hole in the middle of Abbottabad—which, wasn't going to sell very well. Collateral damage would make the Pakistani fury all the more righteous. But it would get the job done.
Obama asked how many people were living at the compound and was informed that there were four adult males, five women, and nearly twenty children. He asked about the houses that were close to the compound in the neighborhood. Those, too, would be completely destroyed, along with every resident man, woman, and child. This really gave the president pause. America was not going to obliterate them on a fifty-fifty chance of also killing Osama bin Laden.
So the president scrapped that plan immediately. He said the only way he would even consider attacking the compound from the air was if the volume and precision of munitions was such that the blast area would be drastically reduced.
Then McRaven explained the ground option for the first time. His team had not yet fleshed out the mission completely. The one thing he could tell the president for sure was that if his team could be delivered to the compound, they could clear it and kill or capture bin Laden with minimal loss of life. The admiral delivered this opinion with the kind of confidence that can come only with long experience. He wasn't trying to sell it. He had been in these meetings back in the early years after 9/11, and he had seen how various factions or branches or agencies had worked to sell their approach to the president. This was not like that. He was surprised, given the importance of this mission and the risks it entailed, that the discussions were not more rancorous. Panetta and Brennan had set the tone from the beginning. In every meeting he had attended, options were laid on the table and discussed, pro and con. McRaven had told his aide on the project: "We may end up doing this thing, we may not. In the end we're going to do what's best for the country. If it's dropping one bomb on the compound, then that's what we're going to do." So he presented the still-sketchy ground operation as a simple statement of fact. Without bringing any more people into the planning loop, he said, "I can tell you that we can succeed on the raid. What I can't tell you yet is how I get in and how I get out. To do that requires detailed planning by air planners who do this for a living and assess the air defense capabilities of that country and who can plot and route how we would get in and how we would get out and what obstacles we would face getting in and getting out.
"So I am not recommending a raid," he told the president. "I am telling you that if I could get in, we could execute a raid. Getting out might be a little sporty. I can't recommend a raid until I do the homework."
Even if he had done the homework, the admiral felt no need to push for the raid. He believed everyone in the room would come to that conclusion on his or her own. The facts would steer them to it. He also believed the president would not let this opportunity slip. The bombing option was too loud and messy, too many innocents would be killed, and in the end you would not have any way to prove you had killed bin Laden. After a strike like that, with the big smoking hole in Abbottabad, Pakistan would be understandably furious. There would be no chance that an American team would get the chance to sift patiently through the rubble looking for DNA. Actually getting bin Laden was the only thing that would make the blowback from Pakistan worth it. But you would have to be able to show that's what you had done. Nothing would accomplish that short of having his corpse or living person in custody. Only that would eliminate any mystery about why you had done it. The risks were greater whenever you sent men in on the ground, but his men were more than capable, and he knew Obama knew it. He had also learned that this president was not unduly risk averse. He had been favorably impressed over the previous two years. Obama had made the final call on almost every major mission JSOC had undertaken in that time, and he was not timid. He would always listen without tipping his thoughts to discussions of the military and political risks, then he would retreat for a time, a few hours or until the next morning, and would generally come back to say, "I gotta go do it." The only time he said no was when the risks were prohibitively high. Understanding that the president had a broader range of responsibilities than he had as a military commander, McRaven had come to trust Obama's judgment. The president counted the real risks for the men on the ground more heavily than the political risks, which is what any military officer wants from the commander in chief. In a few cases where even McRaven's superiors had advised waiting—had said, "It's a little too risky"—it was the president who had come back to say, "No, okay, let's go do it." So the admiral did not voice his own thoughts about which way to go. There was no need.
Panetta had another thought about the raid option. If bin Laden was not in the compound, the SEALs might be able to depart without creating a major disturbance. The people living there and the neighbors would have a story to tell, for sure, but because the mission was conceived as CIA covert action, the United States could simply deny it. Such a denial would hardly fool the Pakistani government, but it would make the thing less of a poke in the eye. Deniability pushed the mission into the gray area that had sustained secret American operations in Waziristan for years.
When the meeting ended, Obama asked the air force to work on developing a more surgical strike, and also some "targeted stand-off options," which meant missiles or, more likely, drones. But the president also wanted a fuller picture of what a ground raid would look like. Could they deliver the force without setting off alarms? Could they get in and out without the need for going to war with Pakistan's air defenses?
"Sir, it's just me and one other guy right now and this concept that we've got to come up with," said McRaven. "I can't tell you whether or not this will work. I can't tell you until I pull the team together and we do the rehearsals, and then I can get back to you."
So McRaven was sent off to do his homework.
This meant running what he called "all the trap lines." There were a lot of variables. The Abbottabad compound was relatively large at thirty-eight thousand square feet. Bigger meant more people. On a normal-sized compound in Afghanistan, McRaven was used to sending in seventy men. You had to be able to strongpoint the perimeter and every door and window. There was a three-story house and an outbuilding. So you had to get the right force there. You had to get them there without being detected. It was a long way in and a long way out, so you had to be able to refuel before flying back, which meant a staging area somewhere outside the city where you could set down larger choppers carrying fuel and a quick reaction force. The helicopters all had their specifications, depending on altitude and temperature and other factors, so you had to figure out how many men they could carry. At the end of the day it was all about load. Pounds cut into airtime. The more choppers you used, the larger your presence and the greater the likelihood of being discovered, or of mechanical or pilot malfunction—ghosts of Desert One. He wouldn't have the final calculations until they started rehearsing, but he could tell right away that they were going to have to go in heavier and with fewer men than he would like.
Two weeks later, at the end of March, he was back in the Situation Room with a full plan. McRaven now told the president that he was completely confident that his men could execute the raid. His air planners had worked out entering Pakistan's airspace without being seen by means of two stealth Black Hawks, secret aircraft specially designed to fly silently and avoid radar detection, followed by two big MH-47E Chinooks carrying fuel and a backup force, which would set down in Kala Dhaka, fifty miles northwest of Abbottabad. The Black Hawks would deliver the "operators" to the compound and, when they had finished taking it down, fly them out to the Chinooks and refuel before flying back to Afghanistan. He said it was likely they could do this without tripping any alarms. McRaven said that if his men could get on and off the compound within thirty minutes, there was a good chance that they would encounter no organized Pakistani defense. There was always a possibility that a small armed police unit—a couple of guys armed with AK-47s—might stumble on them. It was even possible that the compound had its own nearby defenders. But forces that small would not pose a serious threat to his men.
If it happened this way, then the obstacles were minimal. But what if the Pakistanis were more alert than they imagined? What if something significantly delayed them at the compound? The admiral was grilled hard at this second meeting. Many in the room were skeptical of the response time he projected for the Pakistanis. Didn't he realize how close the compound was to the military academy? Less than a mile. That there was an army facility and an Inter-Services Intelligence compound nearby? McRaven was aware. He explained that proximity in this case did not guarantee a speedy reaction. Even if some low-level soldier or cop or agent was awakened or alerted to something fishy going on at the compound, it would still take time for any kind of coordinated response. The Pakistani forces adhered to a rigid command structure, with lower-ranking men rarely acting without permission. It was a command philosophy the U.S. military discouraged but was typical of many militaries around the world. Most young officers would prefer to get in trouble for doing nothing than for doing something wrong. That calculation was built into the thirty-minute estimate. That was about as fast as they could do it, the admiral said. But what if he was wrong? What if the Pakistani forces responded faster than he imagined they could? What if something happened on the compound that slowed his men down?
McRaven explained that if a significant Pakistani force showed up before his men could get out, then there was going to be a gunfight. He didn't want to get into that gunfight. His men would win it, but in the process lose the war. That scenario would give the Pakistanis the high moral ground. There were big political ramifications whenever American forces killed a single Pakistani soldier or policeman. They didn't know for sure that bin Laden was there, after all. As soon as the admiral had brought more of his planning team in, he had told them that rule one was they were going to do everything conceivable to avoid killing Pakistanis. It had been a priority at every point in the planning. If they got in and out fast, there would be no problem, but he could readily imagine a scenario that might delay them. If they got on target and were not able to find bin Laden, but they thought he was there hiding from them, behind a false door or false wall—something they had encountered often—then what would they do? Did they just hop on the helicopters and leave? Suppose they had his wives and other key people who confirmed that bin Laden was there somewhere? The answer was no, they would not leave. They had come too far and were too close at that point to give up. At that point, they had to be prepared to strongpoint the compound and start tearing things apart until they found him. Which would mean overstaying their limit. There was a strong potential for that, perhaps even a likelihood, and every extra minute upped the chances of a confrontation with Pakistani troops.
"So at what point in time do you stop trying to find him?" McRaven asked hypothetically. "And now you are surrounded by Pakistanis, what do you do?"
The admiral's answer was surprising. He recommended that if it came to that, his men would just hunker in and wait for Washington to work things out with Pakistan's leaders.
"You go to them and say, 'Okay, guys, this was the one we've been telling you about for umpteen years, that if he was there we were coming. Well he's here. We haven't killed anybody. We're holed up. Let's talk about this.'"
That, McRaven thought, might buy them thirty more minutes. After that, he wouldn't be dealing with a local response, but with the entire Pakistani chain of command.
Here's where the thinking of an admiral differed from the thinking of a president. As far as McRaven was concerned, his men could fight their way out of anything. There was a Quick Reaction Force nearby in case things got unexpectedly hairy. So they could fight their way off the compound. But then you had the rendezvous in Kala Dhaka, and then four American choppers flying out of Pakistani airspace, which was patrolled by F-16 fighters. Protecting the helicopters would now involve facing down the Pakistani air force. Again, this was something the U.S. Air Force could handle, with its superior fighters and air-to-ground capability, but . . . well, the fight would now be very sporty, indeed. The admiral thought this was a scenario to be avoided at all cost. After two years in Afghanistan, where the bulk of his force had moved from Iraq, he was acutely sensitive to the delicacy of the Pakistani relationship. It would not likely withstand a trail of dead Pakistanis and downed fighters and burning ground-to-air stations. So at the point where the raiding force inside the compound found itself surrounded, he suggested they should decline the fight. They would strongpoint the compound, hole up, and wait for Washington to work things out with Islamabad. They were, after all, American soldiers on a mission that Pakistan, ostensibly, supported . . . apprehending the world's most wanted terrorist. Someone in the White House or at the State Department would then get on the phone with General Ashfaq Kayani, the Pakistani army chief of staff, or President Asif Zardari, and explain the situation. Ask, How do we extract ourselves from this without killing a lot of people? We don't want dead guys; you don't want dead guys. This is how McRaven imagined the conversation might proceed. The very fact that they preferred standing down to getting into a gunfight demonstrated that they intended no harm to Pakistanis and posed no threat to that nation.
The president saw it differently than the admiral. He was not going to have any such conversation with Pakistani authorities. Counterterrorism adviser Nick Rasmussen would later describe the president's response to McRaven's suggestion as "visceral."
"I thought the possibilities of them being held, being subject to politics inside of Pakistan, were going to be very, very difficult," the president explained to me. "I did not want to put them in a position of that kind of vulnerability."
If he were going to deal with an outraged Pakistan, which he would have to do in almost any event, he would do it without a force of brave Americans in the middle.
Just days earlier, Obama had finally brought to a close the difficult wrangling over CIA contractor Davis, who had been released only after the United States agreed to pay $2.4 million to the families of the men he had killed. The incident had stirred up a small furor in Pakistan, where much of the public and the leadership was already fed up with American intrusions on their sovereignty—publicly, at least. Unofficially, the country's top leadership was a lot more flexible, but there was only so far you could push them.
Where this mission was concerned, Obama wasn't going to count on Pakistani goodwill, because there appeared to be little to spare. Like many countries in that part of the world, Pakistan's leadership was less a coherent hierarchy than a collage of overlapping interests. Part of the art of managing that relationship was in balancing those interests. It was an important relationship. Most of the supplies and fuel for the American war effort in Afghanistan flowed across Pakistan's border. Even though al Qaeda terrorists had taken refuge in the country's northwestern territories and had the tacit sympathy of powerful factions in its leadership, the United States depended upon the government's silent support to continue its drone campaign. And Pakistan was a nuclear power, a thing never to be forgotten. Its stability was vital to the security of not just the region but the world. With tempers in Islamabad already hot, imagine handing the Pakistanis a small force of elite American soldiers. Imagine trying to negotiate their exit with them trapped inside a compound with hostages or dead bodies, one of them quite possibly Osama bin Laden. The SEALs could all end up dead or held hostage. It wasn't hard to imagine.
"And I also had confidence, based on my subsequent conversations with McRaven, that they could get out of there without engaging the Pakistani military," the president explained. "There was a good enough chance of them being able to get in and get out, even if something went wrong, even if it wasn't bin Laden, that they could hold off the Pakistani military, which we anticipated couldn't respond faster than a certain period of time, so that the likelihood of a firefight erupting between the United States and Pakistani military was very slim. And in that situation, I just wanted to get them out of there, and then we would deal with the fallout knowing that those guys were back here safe."
So Obama told McRaven that if his SEALs went in, they were coming out. Bin Laden was an imperative that outweighed the relationship. If the Pakistanis sounded an alarm and responded faster than they anticipated, so be it. There would have to be a confrontation. He told the admiral to be fully prepared to fight his way out.
But the president had not decided on the raid yet. The air force came back with a plan for smaller bombs and smaller blast circles. They could hit the compound without harming people living in homes outside its walls, but the lesser assault meant that they could not guarantee taking out anything underground. There would still be a lot of bodies, women and children included, and no way to tell if one of the dead was bin Laden.
But there was another air option, one that appealed especially to Cartwright, one of Obama's favorite generals. It had been Cartwright who had come up with a middle path the year before when Obama was caught between launching a large counterinsurgency campaign in Afghanistan and essentially pulling the plug on the American mission. Cartwright had proposed sending a much smaller force than the Pentagon was requesting, one capable of conducting counterterror operations, but not large enough for the nation-building exercise contemplated.
Cartwright's new proposal for Abbottabad was to target the Pacer alone. Wait for the tall man dressed in shalwar kameez and prayer cap to emerge for his daily exercise around the vegetable garden and shoot him down with a small missile fired from a drone. It would require great precision, but the air force could do it with the equivalent of a sniper drone. There would be no smoking hole in the center of Abbottabad, no dead wives and children, little collateral damage, if any, and there would be no potential dead or wounded SEALs, no chance of a sticky standoff against Pakistan's armed forces at the compound.
It felt too good to be true. The guys who operated these things felt pretty good, but there was a strong whiff of testing stage about it. And what if it worked and you dropped the Pacer in his tracks? What then? How would you know that you had killed Osama bin Laden? And what if you hadn't? What if you had dropped some cheating sheik from Dubai? How would you know? It meant that the uncertainty that surrounded this mission would live on, and that in some sense bin Laden would live on, even if it had been him. And it was strictly a one-shot deal. If you missed, the Pacer and his entourage would vanish.
There was one strong clue that Obama had already made up his mind. McRaven had said that his team would be ready to conduct the raid by the first week of May, when the moon would vanish for a few days over Abbottabad and the nights would be black—the way JSOC liked them. No one said anything, but that window seemed to impose a hard deadline. The drone option had no urgency. It was a daylight opportunity, and the Pacer walked every day. You could take the shot whenever you wished. So why did everyone feel that the moon's cycle was so important?
Obama told McRaven to start full-dress rehearsals and to be ready to go when the nights turned black. He also told Cartwright to get ready to attempt the drone strike. He wanted both options kept alive until he made a decision.
But to those who knew him, there was little doubt which way he was leaning.
7
"Adhering to These Precautions"
April 2011
In what would prove to be the final weeks of his life, events had overtaken the Sheik. There were popular uprisings throughout the Middle East. The tectonic shifts of what would be called the Arab Spring were remaking his world, country by country, but the revolutions bore little resemblance to his visions or his methods. The insignificance of al Qaeda in these events was widely noted. This worried him.
He had much to worry him that April, and he spelled it all out in another of his long letters, dated April 26 but likely begun well before then, again to "Mahmoud," Atiyah Abd al-Rahman. The letter would never be sent. This was his sixth spring confined in Abbottabad. His caliphate had shrunk to the confines of his high compound walls, to the cramped and crowded space of the house's upper two floors. On the upper floor, when he stood with his prayer cap on, his head was just inches from the ceiling. His days and nights followed very familiar routines, rarely broken: meals, his seven daily prayer sessions, his readings, his brisk daily walk around the vegetable garden, teaching poetry to his children and grandchildren, and the regular sermons and lectures to his three wives.
Much of the rest of the day, he was in front of his TV, absorbing the startling news by satellite from all over the world. Tyrants had been overthrown or were besieged in Egypt, Tunisia, Libya, Yemen, and Syria. There were rumblings elsewhere. It was a groundswell of Arab pride, Islamic fervor, and passion for democracy that no one had foreseen, and that certainly he had not foreseen. Bin Laden felt sidelined, felt it like some kind of punishment, and was troubled. The great awakening he had longed for and predicted was happening without him.
"I protest to God so much about my isolation and being alone," he had written in a different letter, "that I worry people will tire of me and [my ideas] will become old and worn out to them! But I protest only to God."
He worried. His vision for the Middle East was a return to a model many centuries old, the ancient caliphate, where all true believers would be united in a single holy nation, a strict Islamist state run according to principles of the Koran as interpreted by Qutb, by himself, and by other like-minded religious scholars. His methods, the suicide attacks on infidels designed to spread fear and confusion, had been superseded by popular, mostly nonviolent, mass movements, crowds of joyous, angry, brave protesters singing and chanting defiantly, demanding freedom and change. He had a lot to say about all of this, tapping at his computer keyboard with his long, thin fingers in his tiny third-floor office alongside a crude wooden bookshelf, or pacing and dictating. He had recently dyed his beard and donned more elegant robes to record a new video statement that would go out with this packet of letters. In one to al-Rahman he raced to catch up with the Arab Spring, to interpret the events in light of his own immutable beliefs, and to instruct his followers on how to think about the changes and what posture to take toward them. He saw the revolutions as a partial fulfillment of his prophesies—he dubbed them "half solutions"—but potentially hazardous to the ultimate goal, insofar as much of the popular support came from young Arabs "tainted" with softer notions of Islam, or, even worse, Western secular views of tolerance, human rights, and democracy. He still spoke of "the Nation" as his vision of a unified Muslim empire.
"To start, I want to talk about this most important point in our modern history, the launching of the Nation's revolution against the tyrants, which I ask Allah to make the impetus for a revival of the dignity of the religion and its glory. What we are witnessing in these days of consecutive revolutions is a great and glorious event, and it is most probable, according to reality and history, that it will encompass the majority of the Islamic world . . ."
The influence and control of the United States was being cast out.
"And the Americans worry about that, which is great; the secretary of state indicated in her visit to Yemen that, 'We worry that the region will fall into the hands of the armed Islamists.' . . . the fall of the remaining tyrants in the region became certain, with the will of Allah, and it was the beginning of a new era for the whole nation. These events are the most important events that the Nation has witnessed for centuries . . . and it is known that comprehensive popular movements inevitably change conditions, so if we redouble the efforts to direct and educate the Muslim people and caution them from half solutions, while taking care in providing good advice to them, the oncoming stage will be for Islam, Allah willing."
The rise of the Muslim Brotherhood in Egypt, for instance, troubled him, because the organization was not, as he saw it, purely devoted to his brand of strict and violent jihad. He was hopeful that the group was coming around, noting news reports of growing militancy within it, especially among the young. "So the return of the Brotherhood and those like them to the true Islam is a matter of time, with the will of Allah. The more attention paid to explaining Islamic understanding, the sooner their return is, so preserving the Muslim movements today and adjusting their direction requires effort and attention, keeping in mind the necessity of being kindly to the sons of the Nation who fell under misguidance for long decades."
The role of al Qaeda now, he explained, would be "the duty of guidance and advice, which is connected to the fate of the Nation."
The Sheik complained that his recommendation years earlier to establish "a number of scholars and wise men" to guide the emergence of the caliphate had been ignored, and that this now helped explain why the Arab Spring was progressing along improper paths. Now, at this "pivotal moment," he wrote, "it is incumbent on us, the mujahidin, to fulfill that duty and to plug that gap as much as we can, which became one of the utmost duties after faith, so that the Nation is liberated with the will of Allah and the religion regains its glory. There is no doubt that the duties of the mujahidin are numerous, except that this great duty should take the main share of our efforts so that we do not shortchange it, and expose the Nation's shake-up today to what the revolutions against Western occupation got exposed to in the past."
In the past, such revolutions had been co-opted by corrupt, Westernized, secularized dictators like Saddam Hussein and Muammar Gaddafi, or had, as in Afghanistan, been toppled by Western intervention. Bin Laden argued that he and his followers were the ones with the right vision, with the God-inspired vision to lead the changes. Contrary to interpretations of the Arab Spring that claimed al Qaeda was irrelevant, the Sheik argued that it had been his efforts that prepared the way. It was al Qaeda that had "bled down the head of international apostasy"—that is, America—"and emboldened their Muslim brothers to rise up against the regimes it had propped up for much of the last century. The most important thing for now was to end conflict between Islamist factions, at least temporarily, and for every Muslim to join this great rising tide.
"So we have to get into expanding the programmed and directed media, and our efforts in directing the Nation's research and deciding on a specific plan that we all discuss, as the oncoming stage is important and very dangerous and does not tolerate the apparent differences in our directions," he wrote. "Initially, I would see that one of the most important steps of the oncoming stage is inciting the people who have not revolted yet, and encouraging them against the rulers and their methods, indicating that it is a religious duty and a logical necessity, so the arrows are concentrated on toppling the rulers without discussing the differences in issues, while paying maximum attention to spreading awareness and correcting the understanding. We should tell the brothers in all the regions to pay attention to spreading the book Misunderstandings About Islam by Sheik Muhammad Qutb. Please inform Sheik Yahya [Abu Yahya al-Libi, who would be killed in a drone strike in little more than a year] and the other brothers who have expressive abilities . . . and inform me of their opinions without missing any of them, as every voice that can contribute in this stage should not be excluded."
Bin Laden now set down a list of "general points," asking that a video statement he had recorded on a thumb drive about the Arab Spring, and which he would enclose, be given to Al Jazeera for broadcast, and seeking advice about an essay he had written on the same subject. As for the al Qaeda brothers in various countries undergoing dramatic change, he wrote, "It would be nice to remind [them] to be patient and deliberate, and warn them of entering into confrontations" with other Islamist factions. He foresaw, correctly, that the newly elected governments in most states would "belong to the Islamic parties and groups, like the Brotherhood and the like, and our duty at this stage is to pay attention to the call among Muslims and win over supporters and spread the correct understanding, as the current conditions have brought on unprecedented opportunities . . . The more time that passes and as the call increases, the more the supporters will be of the people [who agree with al Qaeda's goals], and the more widespread will be the correct understanding among the coming generations of Islamic groups."
The Sheik had a lot to say in this letter. He moved from sweeping political commentary and advice to a host of detailed instructions for the far-flung branches of his organization. He had read or heard that some members of al Qaeda in Yemen were experimenting with the use of poison gases, which worried him. He advised that they proceed only with great care, alluding to his concern about tactics that killed Muslims as well as infidels. He expressed worry over "the political and media reaction against the mujahidin and their image in the eyes of the public." He wondered why he had not heard anything from "the brothers in Iraq" and instructed those touting an al Qaeda affiliation in Somalia (whom he had opposed granting official status) to release a female hostage and some of the others they held, and then wait to kill the remainder until after the revolution in Libya had resolved itself, and until after national elections were held in France. He wanted the "brothers in Somalia" to concentrate more on economic development in that ravaged country, and to temper strict enforcement of the harsher measures prescribed by shariah law. Citing the Prophet, he said, "Use doubts to fend off the punishments."
The letter went on and on, offering guidance for safely moving specific members of the organization from country to country, about the travel of his twenty-year-old son, Hamza, and other things.
And in this same letter the Sheik found time to hammer home some advice about staying hidden. After more than nine successful years on the run, he considered himself to be an expert on the subject.
"It is proven that the American technology and its modern systems cannot arrest a mujahid if he does not commit a security error that leads them to him," he wrote. "So adherence to security precautions makes their advanced technology a loss and a disappointment to them."
As troubled as he was by world developments, he personally felt safe, very confident in his security methods. But he knew that not everyone was capable of his discipline. There were those who could stay hidden and those who could not.
"There is a percentage of people who cannot do that, and those need to be handled in a different manner than the others, and it may be better to provide them with an opportunity in the field," he wrote. In other words, these people were disposable. "As for those whom you have observed as being disciplined and capable, you arrange homes for them on the outskirts of the city . . . and they will be with trusted companions, and the companions will have some work as cover, as if they lived from it, especially for those who live close by and have observing neighbors."
He was describing his own situation, his compound just outside Abbottabad, and his trusted followers the Ahmed brothers, who, under their assumed names, Arshad and Tareq Khan, said they worked in the transportation business. To evade the Americans, it was best to live exactly as he lived. There was, however, one constant problem. Children.
"One of the most important security issues in the cities is controlling children, by not getting out of the house except for extreme necessity like medical care, and teaching them the local language; and that they do not get to the yard of the house without an adult who will control the volume of their voices, and we with the grace of Allah have been adhering to these precautions for nine years . . ."
Nine years since 9/11.
He had five more days to live.
As the Sheik was writing this letter, his last, as he was boasting of his security prowess, adhering to his precautions—albeit with the problem posed by children and grandchildren—he was in the crosshairs of the United States. In the terms used by the American military, he had been "found and fixed."
For the finish, President Obama had ordered the two remaining options to be more fully developed and wanted both to be ready by the first week of May. The ground option was time sensitive. In addition to there being no moon in the first few days of May, it was also mid-spring, which meant nighttime temperatures at four thousand feet were still cool enough to avoid overheating the choppers. The Black Hawks would have to maneuver and hover over the target after having flown low and fast for an hour and a half en route from Jalalabad. They would arrive hot and heavy.
Four choppers would make the trip into Pakistan: the two Black Hawks to deliver the twenty-four-man raiding party directly to Abbottabad and two much bigger MH-47E Chinooks to haul fuel bladders and a twenty-four-man Quick Reaction Force to a remote spot outside of the city. A fifth chopper carried a larger reserve force, Plan C, in case the forward troops needed more help—this force was even larger now that the president had ordered McRaven to be prepared to fight his way out. It would remain just inside the Afghan border ready to launch if needed. All of the choppers were outfitted with stealth and sound-damping technology. The loads had been finely calibrated to get the most performance at Abbottabad's altitude and expected air temperature. Waiting a month would push the mission into early summer and warmer weather, which would up the stress on the aircraft and probably require changes—more choppers or fewer men. McRaven had moved this force into position in Jalalabad, and they would be ready to go on Obama's command.
The other alternative was called the "air option," and it had been reduced to Cartwright's advocacy of a one-shot try—a single shot from a drone. That could be done whenever the Pacer showed himself and the order was given.
It would be hard to overestimate the importance of this mission, not just to America—getting Osama bin Laden would be like closing an open wound—but to Obama's presidency. He would formally announce his run for a second term in early April, and it was by no means a sure thing. A stubbornly sluggish economy had steadily eroded his popularity. His relationship with Congress, never good, had been at an impasse ever since the November elections had erased the Democratic majority in the House and substantially reduced it in the Senate. He had been labeled a big-spending, old-fashioned liberal, even a socialist, at a time when the United States had accumulated massive debts and Republicans were signing oaths to oppose any tax increases, promising to finally end the era of "big government." Obama the bridge builder—what he'd said he hoped to be on taking office—had become a deeply polarizing figure.
Much of the negative assessment was still grounded in the notion that he was somehow inauthentic. He was not really an American. For some, the suspicion was quite literal. They argued that his Hawaiian birth certificate had been faked. Or that he was not a Christian, as he professed and that his twenty years of churchgoing affirmed. No, he was secretly a Muslim. Most people didn't buy these stories; there was overwhelming evidence they were false. But such beliefs colored or swayed the perceptions of even sensible voters, who suspected subtler shades of inauthenticity—who suspected that Obama, with his lefty, Harvard elitist, internationalist, interracial background, was not fully committed to bedrock national principles. He was less a believer in personal liberty than government power. That he was not a true believer in the American experiment, in the Constitution, but was more in the mold of European social democrats, who preferred a society and economy managed by government, by smart people like him. The president's famously "cool" personal style still hurt him, too. His attempts to halt the 2008 financial collapse had unloosed a flood of federal spending, and although that approach had simply continued the policies of his Republican predecessor, and were believed by most experts to have at least partly worked, the economic recovery was slow, people were discouraged, and budget deficits were scarily large, with the president seemingly bent on making them larger still. His biggest legislative triumph, national health care, had seemed to hurt him politically more than it helped him. It had cemented the perception of Obama as a closet socialist, or at least a traditional big government, big spending, big taxing liberal. National health care added a whole new social program to the roster of those already bankrupting the country, his critics claimed. It was denounced as unconstitutional, proof of Obama's secret, un-American agenda. His shrillest political opponents had created so much doubt over his unusual ancestry and upbringing that the president had found it necessary to release the complete 1961 file from the Kapi'olani Maternity and Gynecological Hospital in Honolulu in order to prove that he possessed the most basic qualification for the White House, citizenship by birth. It satisfied all but fringe critics that he was truly American, but it didn't persuade many that he wasn't engaged in a plot to turn America into a European-style state.
Perhaps the most effective counter to this suspicion of inauthenticity was his performance as commander in chief. Obama had effectively and aggressively defended America. During the campaign he had skillfully associated his rise with that of another young, charismatic, tough-minded Democrat a half century earlier. He had cultivated the family of John F. Kennedy, winning the endorsement of Senator Ted Kennedy in the months before Kennedy's death, even orchestrating a powerful endorsement from Caroline Kennedy, who compared him with her father. But now Obama was in danger of being too much in the model of JFK, a spellbinding orator and stylish young leader with only a callow grasp of national leadership. It had been President Lyndon Johnson, after all, who had come along after the assassination to shore up Camelot's legacy; it had taken his hardheaded mastery of power, of Congress, to enact the signature legislation Kennedy himself had been unable to achieve. Killing bin Laden would be one accomplishment that even Obama's worst critics would acknowledge. Here was the one arena where a president could decide and act without outside political interference, especially given the covert nature of the enterprise. Within that arena differences of opinion were strictly subject to his judgment and decision. The most significant criticism of his performance as commander in chief had come from his own former supporters. After promising to close the military detention center at Guantánamo Bay, a symbol of the Bush administration's presumed abuses of power, Obama had failed to overcome congressional opposition to transferring detainees to prisons in the United States. On the big issues he had kept his campaign promises. He had ramped down and would soon end America's involvement in Iraq, and in this he had broad public support. While initially boosting American forces in Afghanistan by 30,000 troops, he had concluded that efforts to build a functioning central government there were unlikely ever to succeed and had quietly reversed direction. He was determined to end America's large-scale military commitment there, too. He had been criticized for not decisively jumping into the Libyan revolution, and then for not doing so more directly, but the NATO–led intervention on behalf of the rebels—what Obama's critics had termed "leading from behind"—was already starting to look like a smart strategy. In a country weary of two long wars, there was little or no opposition to Obama's minimalist, pragmatic approach to using America's military power. Even the Republican candidates already battling for the chance to unseat him in 2012, who missed no chance to fault Obama, rarely spoke of national security concerns.
Getting bin Laden would be the capstone. It would be a milestone emotionally and strategically.
"I thought it would be cathartic for the American people to know that we stay with something," the president told me. "We don't let it slip. I thought that was important. Once I got into office, we were making significant progress against high-value targets in al Qaeda below bin Laden—the lieutenants, the captains, the field generals, we were taking them out pretty systematically—so there was a sense that we understood that the organization was getting hollowed out, and that if we could get the guy at the top, then we might be in a position to strategically defeat the organization. As long as bin Laden was still out there, though, even if we were making a whole bunch of progress at the lower levels, their capacity to reconstitute itself, I thought, would still be pretty significant."
It would inevitably have political benefits, too. No one involved with Obama's handling of the bin Laden effort saw the slightest hint that politics shaped his thinking, but there's no question that success would help, and that a public failure would hurt. It was the thing that President Bush, for all his bluster, had been unable to do. Obama was a skilled politician. There was not a move he made that did not include a measure of calculation, even if only in understanding the stakes. No one understood the stakes better. Killing or capturing the author of 9/11 would register with every American, of every political stripe. It would be a thing that transcended politics in an age where very little else could. There were very few things he might accomplish as president that would compare. Getting bin Laden would not completely destroy al Qaeda or end the threat of terror attacks, but it would be a huge step in that direction. It would slam shut the door on a painful national trauma. It would feel . . . perfect. He had argued from the beginning that it was the correct military response. It was the thing he had promised to do if he got the chance. So while Obama had not yet officially made up his mind about the compound in Abbottabad, and had tipped his hand to no one, those close to him believed he would go for it. He was leaning that way, and because of his confidence in McRaven he was leaning toward doing it on the ground.
Raiding the compound was the riskiest option. It posed a slew of hard questions that the air option did not. One of the most interesting was what to do if bin Laden was not killed but captured. The success of Obama's drone war had meant that very few high-value targets ever found themselves in American custody any more. It had prompted speculation that this president was less interested in capturing al Qaeda figures than in killing them, or even that JSOC was under orders to avoid taking prisoners.
"Our basic attitude was that, given his dedication to his cause, the likelihood of surrender was very low," the president explained. "We also knew that there would always be the possibility of him strapping on explosives and trying to take out a team with him. So I think people's general attitude was, if he's going to surrender, he better be naked and on the ground. Had that occurred, then we would have arrested him and held him. I won't go into all the details of what those various steps would have been, but ultimately, we would have brought him to justice. We would have brought him back here."
This, too, had to be thought through. Did they want a captured bin Laden? If they had him, what would they do with him?
What to do with high-profile terrorists had been a hot political issue for years. Congress had done nothing to resolve the problem. Bush had locked most of them away—like Khalid Sheik Mohammed and Abu Zubaydah—at Guantánamo, and talked about military tribunals somewhere down the line. But some, like the shoe bomber Richard Reid and the would-be Times Square bomber Faisal Shahzad—the latter of whom had betrayed his citizenship oath, an idea that troubled the Sheik—had been arrested and tried in federal courts and were now serving life sentences. Attorney General Eric Holder's announced intention to put Khalid Sheik Mohammed on trial at the federal courthouse in lower Manhattan had generated so much political protest that the administration had been forced that very month to back down and announce that he would instead face a military tribunal at Guantánamo.
In the unlikely event that bin Laden surrendered, Obama saw an opportunity to resurrect the idea of a criminal trial.
"We worked through the sort of legal and political issues that would have been involved, and Congress and the desire to send him to Guantánamo, and to not try him, and Article Three," the president told me. "I mean, we had worked through a whole bunch of those scenarios. But, frankly, my belief was if we had captured him, that I would be in a pretty strong position, politically, here, to argue that displaying due process and rule of law would be our best weapon against al Qaeda, in preventing him from appearing as a martyr."
Bin Laden in custody might give him the political capital he had lacked with Khalid Sheik Mohammed. It might be the very thing to end all the confusion over what to do with top-level terrorist detainees, and to end it in the right way. Obama believed that placing these terrorists before a judge and jury in a criminal court, affording them the full rights of criminal defendants, would showcase America's commitment to justice for even the worst of the worst. It would present bin Laden to the world not as a heroic holy warrior but as the ill-informed fanatic and mass murderer he was. The president had to do more than just imagine these scenarios. It was one more outcome that needed to be thought through completely and planned for.
Obama added, "I think it's important to emphasize, having made those plans, our expectation was that if, in fact, he was there, that he would go down fighting."
McRaven's men did their first rehearsal on April 7. They worked on an isolated acre deep inside the sprawling wooded grounds of Fort Bragg, where a faithful mock-up of the three-story Abbottabad house had been built. Chairman Mullen and Michael Vickers were among those who came down from the Pentagon and CIA to watch.
For the first practice session, the SEALs rehearsed the critical piece of the mission: hitting the compound and target house at night. They approached aboard two Stealth Black Hawks. One unit roped down to the roof of the building and assaulted it from the top down. The other roped into the compound and assaulted from the ground floor up. This part of the operation took only about ninety seconds to complete. The delivery choppers moved off while the men did their work, and then swooped back in to pick them up. The speed and coordination were impressive. They did this twice.
In part, McRaven was putting his men through this demonstration in order to impress. They had done this sort of thing so many times they could almost do it blindfolded. McRaven had handpicked shooters from SEAL Team Six. It was a Dream Team: men who, in the thousands of raids he had overseen, had shown they did not rattle, had shown they could handle themselves coolly and intelligently not just when things went according to plan, but when things went wrong. Those situations required quickly assessing the significance of the error or malfunction or whatever unexpected event had occurred, and then making the necessary adjustments to complete the mission. The core talent required was the ability to adapt, to think for yourself and make smart decisions. These were men who had proved it over and over in combat. They did not really need to rehearse, but rehearsals have other uses. McRaven wanted the assembled brass to see how good they were, how fast, how certain. He wanted them to witness the speed and coordination firsthand, to hear the sounds of the rotor blades and of the flash-bang explosions and of the weapons being fired, and to be able to imagine themselves on the receiving end of it. He wanted them to meet the men, touch their equipment and weapons, talk to them, get a sense of how professional, how experienced, and how confident they were, and then to carry that experience back to the White House—"Mr. President, they just did a rehearsal that will knock your socks off!"
SEAL Team Six had rotated home not long before. The men on these elite special operations teams went to war in shifts. For most of the last ten years they had been regularly deploying to Iraq or Afghanistan for three to four months, where they maintained a very high tempo, going out on missions every night, sometimes two or three times a night. Each unit had its own embedded combat support, administrative staff, and logistical teams that traveled together, every one of them handpicked. When deployed they lived for the most part sequestered from conventional troops, either at their own forward operating bases or on a portion of a larger base that was sealed off. The work was deadly serious. The men would spend the day getting their rest, cleaning their weapons, working out, and getting ready to go back out. They had their own TV and Internet access, but under rules that were far more restrictive than for most soldiers. Their pace and discipline were severe. They would blow off steam for a few months at home and then go back. When they were deployed, it was all business.
It was a demanding but extremely satisfying way of life. The men who achieved membership in these units tended to stay. Many found it hard to adjust to doing anything else. The skills required were not readily applicable to other kinds of work. And when you have been part of life-and-death operations for years—adrenaline-pumping missions where you risked your life, shot to kill, and where some of your good friends gave their lives—and when you believe that your work is vital to the security of your country, it is hard to find anything else that compares. When you work every day with people who are the very best at what they do, and when you enjoy the silent admiration of everyone you meet, even if they had only a vague idea of what you do—well, there is nothing quite like it.
On average, the operators were a decade or more older than most soldiers. Most were in their early thirties, veterans of several tours in regular units or "vanilla" special forces teams, as opposed to "black ops." Some were in their forties, which skewed the average age to thirty-four. Some of the men in these units would joke that their biggest worry wasn't so much getting shot by the enemy as it was throwing their back out. They excelled at a lot of things, but particularly at doing exactly what would be called for in Abbottabad: hitting a target fast and hard, making correct split-second decisions about whether to shoot or not to shoot, and distinguishing between friend and foe, combatant and noncombatant. They usually did their work in the dark, wearing night-vision devices, but had in recent years been mixing it up with day raids, partly to vary the pattern and partly just because of the demand to move quickly on fresh intelligence—staying inside the information cycle of the enemy.
Being called in like this to begin rehearsals after just rotating home was enough to tip them off that the mission was special. When they were told that they were going after bin Laden, the men cheered.
They reassembled for a second week of rehearsals in Nevada, where the heat and altitude—about four thousand feet—were similar to Abbottabad's. Again chairman Mullen and Vickers and the others came out to watch. This time the rehearsals were designed to duplicate the conditions they would be flying in. On the real mission the helicopters would have to fly ninety minutes before arriving over Abbottabad. They would be flying very low and very fast to avoid Pakistani radar. Mission planners had to test precisely what the choppers could do at that altitude and in the anticipated air temperatures. How much of a load could the choppers carry and still perform? Originally they had thought they might be able to make it there and back without refueling, but the margins were too close. The choppers would have been coming back on fumes. So the refueling area was necessary. In Nevada they went through the entire scenario. The mock-up of the compound was much cruder. They had already practiced storming it again and again at Fort Bragg. This time the buildings were just Conex containers, and instead of stone walls around the compound there was a chain-link fence. The purpose of this rehearsal was not to duplicate the storming of the compound. The purpose here was to simulate the stresses on the choppers. It came off smoothly. The Black Hawks handled the job well.
Again, McRaven wanted Mullen and Vickers and the others to be impressed, because he wanted his own confidence in his men and the mission to be fully conveyed to the president. The best way to do that was not just to tell him about it. He understood that confidence was key if the SEALs were going to get the job.
Because the alternative, the drone strike, was tempting. It was so much less risky. The air option offered a kind of magic bullet, in the form of a small guided munition that could be fired from a tiny drone. No one involved with planning the mission would discuss its particulars, but the weapon sounded very much like a newly designed Raytheon GPS-guided missile about the length and width of a strong man's forearm. General Cartwright was its chief advocate in the White House. Designed to help reduce the collateral damage that had always been an inevitable consequence of air strikes, the missile could strike an individual or a single vehicle without damaging anything nearby. Called simply an STM (small tactical munition), it weighed just thirteen pounds, carried a five-pound warhead, and was fired from under the wing of a drone that itself was no larger than a model airplane, small enough to escape the notice of any country's air defenses. It was a "fire-and-forget" missile, which meant you could not guide it once it was released. It would find and explode on the precise coordinates it had been given. Since the Pacer tended to walk in the same place every day, Cartwright believed the missile would kill him, and likely him alone. It placed no American forces at risk. If the missile missed, or if the Pacer turned out not to be bin Laden, well, then it would just be an unexplained explosion in Abbottabad. No one need be the wiser. And if the missile did kill bin Laden, any Pakistani anger over an unauthorized U.S. drone strike would likely be offset by the embarrassment of revealing that the world's most wanted terrorist had been living safely not just in Pakistan, but only a short drive from Islamabad and less than a mile away from its national military academy.
The weapon had yet to be used in combat, although the technologies involved—drones and missiles—were hardly new. The only difference with this one was its size. Still . . . did you want to hinge such a critical opportunity on one shot, with a missile that had never been fired in anger? The drone option also robbed the strike of certainty. To his followers and to those who thought as he did, bin Laden still had tremendous influence, even though he had not been seen in years. If there was no proof he was dead, the organization could theoretically keep issuing statements and pronouncements to the faithful, raising contributions, urging and planning future attacks as if he were alive. And Obama would become the third U.S. president to have let him slip through his fingers. Arguments in favor of the drone kept coming back to these two things. What if the missile missed? And, if it killed bin Laden, how would you know for sure?
It was clear that the only way to know for sure was to send in a team of operators and bring him out, dead or alive.
But there were so many things that could go wrong. Recent history was littered with examples of how badly things could turn out. The failure of Desert One was an obvious caution. With its long insertion, desert refueling rendezvous point, and the target inside an urban area surrounded by potential enemies the situation was so similar it was eerie. The Iran disaster had shaken the military to its core, embarrassed the nation, and ended a presidency. And the long firefight that had followed the shooting down of two helicopters in Mogadishu on October 3, 1993, had so rattled the Clinton administration that it had shied away from using military force for years afterward, with some disastrous consequences such as the slaughter of hundreds of thousands in Rwanda in 1994. In Iran, the mission had been an abject public failure; in Mogadishu, the mission had actually been a success but had prompted a bloody eighteen-hour firefight that effectively pulled the plug on the American mission to Somalia. One or the other of these missions, or both, had come up at nearly every meeting to discuss options.
There was only one "ground option" scenario that wouldn't cause trouble. If bin Laden was not there, the SEALs might be able to exit without hurting anyone and without setting off any alarms. No one would be the wiser. All the other outcomes had a big downside. Even perfect success—killing or capturing bin Laden without mixing it up with Pakistani forces—would exact a price: it would certainly trigger outrage and poison relations between the two countries for the foreseeable future. The list of worse outcomes was scary: dead SEALs, dead Pakistanis, embarrassment, a propaganda triumph for bin Laden and al Qaeda, a blow to the reputation of the U.S. military and the CIA.
So confidence was the key. If the president decided to go with McRaven, it would be because the admiral's confidence was contagious.
The final meeting was held in the Situation Room on the afternoon of Thursday, April 28. Popular accounts of this decisive session have portrayed Obama facing down a wall of opposition and doubt among his top advisers. In fact, there was overwhelming support for launching the raid.
Filling the black leather chairs around the table were Obama, Vice President Joe Biden, Secretary of Defense Robert Gates, Secretary of State Hillary Clinton, Chairman of the Joint Chiefs Michael Mullen, Vice Chairman James "Hoss" Cartwright, John Brennan, Thomas Donilon, DNI James Clapper, CIA Director Leon Panetta, and Panetta's deputy, Michael Morell. McRaven did not participate. He and the SEAL team had relocated to JSOC's base in Jalalabad, to be ready to launch in two days. Throughout this series of meetings, the rule was that if you were not in town, you were not involved. Hooking up a satellite link for videoconferencing opened up the discussion to too many people. Technicians that could listen in would be involved on both ends, which compromised secrecy. Most of the president's national security team—including Ben Rhodes, who had been informed weeks earlier—started considering how to announce the mission to the world. Top staffers of the principals ringed the room on the smaller leather chairs.
All sensed that the secret had held about as long as it could. As the planning had progressed over the previous four months, the circle of knowledge had grown. There were now hundreds of people in on it. No secret survived numbers like that for long. It was inevitable that at least one of those hundreds would screw up, let something slip. Somebody was bound to confide in someone else untrustworthy, or might decide for their own reasons to leak it. If they missed the new moon this weekend, they would have to wait a month for another. So for the raid option it was time to decide.
The week had been full for the Pentagon and the CIA. The day before Obama had announced, pending congressional review, that General David Petraeus, who had been commanding allied forces in Afghanistan since the previous July, would leave the army after thirty-seven years to head the CIA, and that Panetta, who had spearheaded this effort to find bin Laden, would become the new secretary of defense, replacing Bob Gates, who had announced months earlier that he would be stepping down. Petraeus had been read in on the bin Laden secret only recently, because the beefed-up rescue force Obama demanded required air and ground forces from his command. Weeks earlier—in fact the day before McRaven's team performed its first rehearsal at Fort Bragg—the president had awarded the admiral his fourth star and promoted him to lead the Special Operations Command.
The president was juggling the usual array of responsibilities. The U.S. military was still helping with massive relief operations in Japan, enforcing a no-fly zone over Libya in cooperation with European allies, and monitoring various stages of revolution or protest in Egypt, Yemen, Syria, Bahrain, and Jordan. That week the president had unsuccessfully lobbied India to award an $11 billion contract for fighter planes to American firms. An outbreak of tornadoes in the Midwest had torn through Kentucky, Alabama, Louisiana, and Tennessee, requiring federal disaster assistance. On the day before this meeting, the president had held a press conference to deal with what he called the "silliness" over the place of his birth, releasing that "long form" birth certificate.
In the week before this session, Brennan had asked the Counterterrorism Center director, Mike Leiter, to assemble a team to perform one last "red teaming" of the intelligence on Abbottabad. So the final meeting began with Leiter's findings, which were deflating. Leiter told the president that his group could arrive at only 40 percent certainty that bin Laden was in the compound. One of those on that red team, an experienced analyst, had estimated the chances at only 10 percent, a number so far below any they had heard, and coming so late in the game, that it drew nervous laughter in the crowded room. "I think you guys are telling yourselves something you want to hear," was that analyst's opinion. Still, 40 percent, the team's estimate, was "thirty-eight percent better than we've been for ten years," said Leiter. This was hardly confidence boosting. Obama asked if the estimate was based on anything new or different. It was not. This team had looked at the same information as everyone else. The president asked Leiter to explain the disparity. Why was their confidence so much lower than, say, that of "John," the leader of the CIA's bin Laden team, whose confidence had been 95 percent all along? Leiter could not explain to the president's satisfaction, and so this new assessment was effectively dismissed. As far as Obama was concerned, the level of certainty was the same as it had been all along, fifty-fifty. So other than dampening the mood, this last red teaming had little influence on the final deliberations.
One by one, the principals around the room were asked to choose one of the three options: the raid, the missile strike, or doing nothing—and then to defend their choice. The president said that he would not make a decision himself at the meeting, but he wanted to hear everyone's final judgment. Nearly everyone present favored the raid.
The only major dissenters were Biden and Gates and, by the next morning, Gates had changed his mind.
Biden was characteristically blunt. "Mr. President, my suggestion is, don't go," he said. "We have to do more things to see if he's there."
The vice president was never shy about political calculations. He believed that if the president decided to choose either the air or the ground option, and if the effort failed in any of the many ways it could, Obama would lose his chance for a second term. Biden felt strongly about it, and never hesitated to disagree at meetings like this, something the president had encouraged him to do. In this case he even disagreed with his top adviser on such matters, Tony Blinken, who was not asked for an opinion at this meeting but who had earlier made it clear to the president that he strongly favored the raid.
Gates spoke with quiet authority against it. He favored taking the shot from the drone. He acknowledged that it was a difficult call, and that striking from the air would leave them not knowing whether they had killed bin Laden, but he had been working at the CIA as an analyst in 1980 when the Desert One mission failed. He had, in fact, been in this very Situation Room when the chopper collided with the C-130 at the staging area in the desert and turned that effort into a gigantic fireball. It was an experience he did not want to revisit. He had visibly blanched the first time he had heard that McRaven was planning a helicopter-refueling stop in a remote area outside Abbottabad, similar to the one inside Tehran in 1980. The contours of this mission looked so much like the earlier failure that it rattled him. He had more of a personal sense for what another disaster like it would mean. He also mentioned the Black Hawk Down episode. He remembered how painful the loss of life and loss of face had been for the previous presidents Carter and Clinton, and he smelled the same potential here. As defense secretary, he also had a deeper appreciation than anyone else in the room for logistics, for the importance of sustaining the huge daily flow of fuel and matériel from Pakistan necessary to the ongoing war in Afghanistan. Blowing up the always dicey relationship with Pakistan would likely short-circuit that vital artery. There was so much to lose, he said, and the intelligence indicating bin Laden's presence in the compound was still so flimsy—strictly circumstantial. Leiter's presentation had driven that home for him. A raid gone wrong would have a huge downside: loss of the SEAL team or a potential hostage situation, a complete break with Pakistan, attacks on the U.S. embassy in Islamabad . . . So he told the president that he would choose the drone. If bin Laden was the Pacer, then they stood a very good chance of killing him. If not, if they missed or they were wrong, it would be disappointing, but the cost would not be so great. That was his advice, and it hung heavily in the room. It carried the weight of long experience and Gates's own formidable reputation.
Cartwright agreed with Gates, but that was expected. He had put the drone option on the table, and after further testing he was more confident than ever that the small missile would do the job. It was the simplest and least risky way to go. The missile also won the endorsement of Leiter. He had expressed relatively low confidence that the Pacer was bin Laden but endorsed taking a killing shot at the fellow anyway.
Everyone else favored sending in the SEALs. At first it didn't seem like Clinton would. She had famously faulted Obama years earlier for asserting that he would take a shot in Pakistan unilaterally if there was a good chance of getting bin Laden, and now, as secretary of state, she would bear the brunt of the diplomatic fallout if he did. Presenting a detailed assessment of pros and cons, she outlined the likely dire consequences for the U.S.-Pakistan relationship but wound up concluding that, because it was built more on mutual dependence than friendship and trust, it would likely survive. Someone pointed out that if going after bin Laden was enough to destroy the relationship, it was probably doomed anyway. Suspense built as Clinton worked her way around to her surprising bottom line. They could not ignore a chance to get Osama bin Laden. It was too important to the country. It outweighed the risks. Send in the SEALs.
Admiral Mullen, the president's top military adviser, gave a detailed PowerPoint presentation before delivering his verdict. McRaven's rehearsals for him and the others had achieved the desired effect. Mullen said he had such high confidence in the SEAL team that he advocated launching the raid.
Brennan, Donilon, Clapper, Panetta, and Morell all agreed. Brennan had long believed in his bones that it was bin Laden hiding in the compound, and if they indeed had found him, he argued, they had to go after him. The CIA director felt particularly strongly about it, which was not unexpected. This had been his project all along, and the analysts who worked for him were so eager to go in that they would have felt betrayed by their boss if he hadn't supported them. The former congressman told Obama that he ought to ask himself, "What would the average American say if he knew we had the best chance of getting bin Laden since Tora Bora and we didn't take a shot?" And going in on the ground would give them the proof they needed to make the mission worthwhile, or, possibly, gave them a chance of slipping out if bin Laden was not there.
Not all of the advisers present were asked for their opinions during this meeting, but they had all made their feelings clear in the previous weeks. To a man and woman they favored the raid. And soon the man who had made the most convincing argument against the raid would reverse himself.
At the Pentagon, when Gates's undersecretaries Michael Vickers and Michèle Flournoy learned what he had recommended, they were distressed. No one knew yet what the president would decide, but they had every reason to believe that their boss's opinion would weigh heavily. They briefly debated confronting him with how they felt, wondering if they would be overstepping, whether it would anger him, and they both decided it was their duty. So they went into his office first thing Friday morning, sat with him at a conference table, and went to work on him for a full hour.
"Boss, we think you're wrong," said Flournoy.
Like most of the other principals, she explained, he had been brought into the loop fairly late. She and Vickers had spent a lot more time working through the questions about the mission than he had. They believed he didn't fully understand how well thought through McRaven's plan was. They again outlined for him the raid's plan, the backup plan, and the plan that backed up the backup plan, to demonstrate how carefully the mission had been designed. They sang McRaven's praises. They had dealt with generals and admirals who rightly saw themselves as experts in their field, and who tended to bristle when a civilian bureaucrat second-guessed them, or expressed doubts about their well-laid plans. McRaven had approached this effort utterly without ego or emotion. He had understood from the start that the significance of this mission meant that he would have a lot of people at the Pentagon and White House and CIA looking over his shoulder asking questions, looking for flaws. Flournoy admired a quality in McRaven that was not always evident in the top brass: a willingness to admit that he didn't know everything. He would sometimes respond to a good question with, "You know, I haven't thought about that but I need to. Let me get back to you about it." And he would. He was unusually open to suggestion, and had made substantial revisions to his plan based on the president's concerns and those of everyone else involved. Flournoy and Vickers had also seen how carefully McRaven picked the members of his team, choosing men coming off fresh deployments who had honed their skills night after night for months. Gates had not, as Vickers had at the rehearsals, met those men and talked to them and obtained a sense of their maturity and experience. Gates had not been as close to any of this as they had, so he did not have their level of confidence.
They also argued that he had not adequately considered the downsides of the drone strike, the alternative he advocated. They questioned the idea that this was a clean, virtually risk-free alternative. First of all, neither Flournoy nor Vickers bought Cartwright's optimism about the small missile hitting the target. The target, after all, was moving. The missile could not be guided. It had never been fired anywhere but on a testing range. You get one shot, they reminded Gates, and if you miss, that's it. Bin Laden escapes again. Imagine the criticism that would follow: You got the chance of a lifetime and you blew it with something untried?
At the end of the hour, Gates phoned Donilon at the White House and asked him to tell the president that he had changed his mind. Obama would not learn of Gates's change of heart until after he had made the decision—but when he did hear, it strengthened his resolve. In the end every one of the president's top advisers except Biden was in favor of taking immediate action. Two—Cartwright and Leiter—wanted to use the drone. Everyone else backed McRaven.
The Thursday meeting ended early in the evening, and with the opinions of the vice president, the secretary of defense, and the vice chairman of the Joint Chiefs still weighing heavily against those calling for the raid, the president's choice seemed anything but certain.
"You'll have my decision in the morning," Obama said.
In truth, as the president told me, he had all but made up his mind when he left the Thursday meeting. He had been thinking about it for months. The advantages of the raid were obvious and, to his way of thinking, outweighed the risks. A missile might go astray and, unlike taking a shot from a drone, the raid offered certainty. If bin Laden was there, they would know it and they would bring him out, dead or alive. Getting him without being able to prove it—worse, without knowing it—would forfeit a big part of the accomplishment. Here was a chance to bring closure to the great tragedy of 9/11 and strike a mortal blow to al Qaeda. Add to that Obama's trust in McRaven, and the near-unanimous support of his advisers, and the decision was clear.
There was another compelling reason to send in the SEAL team. If this had been bin Laden's hideout for years, it might hold a trove of valuable information, perhaps the kind that would enable the United States to further dismantle al Qaeda. Obama knew the logic behind F3EAD. The only way to exploit bin Laden's personal data was to send in men who could collect it.
No matter how compelling it was to attempt the raid, the risks were great for the men he ordered in, for the alliance with Pakistan, for the reputation of the U.S. military and intelligence communities, and for his own presidency.
He reviewed the process over and over again in his mind Thursday night into Friday morning. Just as had been the case ten years ago, when he was a state senator in Illinois, his habit was to stay up much later than Michelle and his girls. They had turned in at ten o'clock. He was up another three hours pacing and thinking in the Treaty Room, the upstairs room that functioned as the family's living room and also the president's private office. The room displays Henry Ulke's portrait of Ulysses S. Grant, Théobald Chartran's large painting of William McKinley signing a peace treaty with Spain, and George P. A. Healy's depiction of Abraham Lincoln conferring with his military advisers near the end of the Civil War. History bears down on you in a room like that.
"It was a matter of taking one last breath and just making sure, asking is there something that I haven't thought of?" Obama explained to me. "Is there something that we need to do?"
The questions stayed with him even as he tried to sleep that night. He believed that waiting longer would not accomplish anything, and might risk everything. They were not likely to get better intelligence, that had been clear. In the end, it boiled down to his confidence in McRaven. He had met him first in 2008 when touring Iraq with several other members of the Senate Foreign Relations Committee. David Petraeus had hosted a dinner in Baghdad and had invited the JSOC commander. He had dealt with him a lot more as president, particularly in these last four months.
"I just felt as if I'd gotten to know McRaven," Obama said. "I had gotten to know the SEALs. I had obviously been monitoring their capacity to carry out night raids consistently in Iraq and Afghanistan. We had mocked up the compound. We had experimented with it. They had run it . . . McRaven—he inspires confidence. And I had pressed him hard. And at that point my estimation was that we weren't going to be able to do it better a month or two months or three months from now. We weren't going to have better certainty about whether bin Laden was there, and so it was just a matter of pulling the trigger."
On Friday morning, before getting the phone call from Gates, before he walked out to the South Lawn to board a helicopter on a trip to the southern states to view tornado damage, he sent an e-mail to Donilon asking him to meet him in the Diplomatic Room at eight o'clock.
Donilon, McDonough, and Chief of Staff Bill Daley were waiting in the large formal room when Obama entered, wearing a dark blue Windbreaker. The view from the room is one of the most dramatic in the White House, over the sloping back lawn, with the Washington Monument in the distance. They could see the waiting presidential helicopter.
"It's a go," said Obama. "We're going to do the raid. Prepare the directives."
8
The Finish
May 1–2, 2011
McRaven's men were in Jalalabad, poised. After the president's order was conveyed Friday afternoon—Afghanistan is eight and a half hours ahead of Washington—they knew the earliest they would go would be early the following evening, Saturday, April 30.
Most of the twenty-four handpicked team were members of Red Squadron of SEAL Team Six. In the more than a year that has elapsed, only one of the men has spoken publicly about it. None were interviewed by me. My account of the raid is based on interviews with the president; senior officials at CIA; sources at JSOC, the White House, and the Pentagon; on interviews with SEAL team members who did not participate directly, and on the account published by the former SEAL under the pseudonym "Mark Owen."
The SEALs were selected primarily because their commander was available, and the corresponding commander of the army's Delta Force was not. With its expanding numbers, JSOC had been divvied up three years earlier by McRaven, with Delta assigned to continue operating in Iraq and the SEALs working from Forward Operating Bases (FOBs) throughout the most contentious regions of Afghanistan. Part of the reasoning for choosing the SEAL team, according to several top Pentagon officials, was that in recent years it had successfully conducted about a dozen secret missions inside Pakistan. They were used to conducting these raids with high-level commanders looking over their shoulders, linked by live audio and video—the men called it "General TV." Sometimes their remote commanders got carried away, steering them around like figures in a video game—"Turn left! Turn right!"
The actual commander, the man they would follow into the target compound, was a short, thickly built, brown-haired naval officer in his late thirties who had chiseled features—if Hollywood were looking for someone to play the role they would be hard-pressed to improve on the original. He had become something of a legend even in these elite ranks, with ten years of experience leading them into combat. It had become so routine for him that he spoke about the job the way an experienced foreman might talk about a construction project. He had a strictly deadpan way of talking; when he cracked a joke, which didn't happen often, there was usually a delay before anyone noticed. Some of the men he commanded were older than him, but not many. Going in with them would be a Pashto translator and a highly trained dog—a Belgian Malinois named Cairo. The translator, a middle-aged man who had to learn how to rope out of a chopper for this mission, and the dog would help keep the curious away from the compound while the SEALs did their work. As they did before every mission, the men spent time readying their gear and weapons, oiling and cleaning and testing laser sights and night-vision devices, and adjusting straps on harnesses and helmets. The barracks at Jalalabad were familiar to all of them; it had been home away from home for years.
The one thing that was not often in their conversation but always in their thoughts was danger. There were small FOBs all over Afghanistan named after team members who had been killed on raids, friends of these men who had gone about their work with the same skill and care but who had been sent home in an aluminum box. Inside the FOBs there were memorials posted on walls or bulletin boards, displaying photos of the dead, and special operators were disproportionately represented. Their photos contrasted with the faces of the other fallen, the eighteen-, nineteen-, and twenty-year-old regulars who had been killed by roadside bombs or in mortar attacks or on routine patrols. The special operators were older, and in the pictures they were often bearded and dressed in local civilian attire. Either that or they appeared in official portraits wearing uniforms decked with ribbons and stripes and medals. They were war-fighting professionals. For most it was their chosen career and, unlike younger men who tended to find reasons why this or that soldier had been hit and they had not—a poor decision, a perceived weakness, a fatal lapse in quickness . . . —these men knew better. You trained and practiced and then you performed with a team made up of men every bit as good as you were, and sometimes in spite of all of this you got killed. This mission, targeting Osama bin Laden, was one nearly everyone in the force had imagined being on since 9/11. It was the raid all of these men believed would someday come, and that they had hoped would include them.
Behind this initial force were the men and choppers and planes that McRaven hoped he would not need. There were three MH-47E Chinooks, big as tractor trailers with flat rotors front and back. Also on alert were the fighters and combat-control aircraft that might be needed to fend off Pakistani fighters and ground-to-air defenses. If it came to that, command of the operation would shift from McRaven's Joint Operating Center in Jalalabad to the theater command center in Kabul, where General Petraeus presided.
Petraeus himself hadn't known about the mission until just weeks earlier, when he had been informed about it in general terms by General Cartwright and by the CENTCOM commander. His resources would not be used at all unless the mission went badly, so he had not been fully briefed by McRaven until a few days earlier. No one on his staff knew about the raid. His history with bin Laden went back a dozen years, to when Petraeus had stood on the tarmac at Pope Air Force Base as the bodies of American servicemen killed in al Qaeda's attack on the USS Cole were flown home. He had been in on the earlier discussions during the Clinton administration when it had decided to launch the cruise missiles at targets in the Sudan and Afghanistan. He would have a ringside seat for this raid, but if all went well he would have nothing to do but watch.
On Saturday afternoon, McRaven took a call from the president. Obama told the admiral that his confidence in him and his men could not be higher.
"Godspeed to you and your forces," Obama said. "Please pass on to them my personal thanks for their service."
He added something that went without saying.
"I will personally be following this mission very closely."
Hours later, on Saturday afternoon Washington time, Ben Rhodes sat down in his small White House office before his keyboard . . . and froze. At some point, the president was going to have to speak to the United States and the world about what had happened, or was happening, inside Pakistan. Rhodes's job would be to have draft remarks ready for success or failure.
George Little, a CIA press officer, had just spent a few hours with the president's staff reviewing every outcome the agency could imagine. They had gone through the various press guides and public-messaging guides for each contingency—which heads of states needed to be informed and in what order, how statements should be made. They roughed them all out. There was one for a clean in-and-out, the best case. If they went in and bin Laden wasn't there and they got out without setting off any big alarms, then they planned to just deny it. It was to remain a covert operation: that is, officially it would not have happened. But what if things got messy? There were a number of those possibilities: messy with bin Laden dead, messy with bin Laden captured, messy but no bin Laden. They went through pages and pages of public-messaging options.
After all that, his head spinning with possibilities, Rhodes sat down to begin drafting something. He planned to start with the best-case scenario, and got as far as the first line, but then stopped. I can't, he thought. I might jinx this. If he wrote a speech about them getting bin Laden, and they didn't, that was going to be an awful document. If he wrote one about not getting bin Laden . . . well, his heart wasn't in it. If he had to do it, he would, but he wasn't going to do it unless he had to. So he didn't write anything. He gave up and got ready to attend the correspondents dinner.
There had been some conversation the evening before about the timing. The dinner was the major black-tie social gala of the year in Washington: televised, and attended by celebrities from Hollywood and the sports world, and by all of the most prominent government leaders and journalists. The main attraction was always the president of the United States, who typically delivered a stand-up comedy routine poking fun at himself and the press. If Obama chose the raid, it would likely take place at the same time as the dinner. How would it look for the president to be making jokes at a podium while the men were risking their lives? And what if something went wrong and everyone had to suddenly leave the party? Every journalist in Washington would realize something major was up. Then again, if they all decided simply not to go, it would alert every news organization in the world that something big was happening.
When someone floated the idea of asking McRaven to postpone the mission for a day, Clinton had heard enough.
"We are not going to let a White House correspondents' dinner drive an operational decision," she said.
That ended it. Obama told Donilon, "Tom, if it turns out that's when we decide to go, you'll just tell them I have a stomachache and I have to bow out."
The question of what to do about the dinner became moot when McRaven's weather experts predicted fog in the Abbottabad area for Saturday night. He decided to push the mission back one day. They would launch on Sunday night.
So in this tense moment, the most suspenseful of Obama's presidency, he and his staff dressed for a formal party.
Rhodes was so nervous that at first he decided not to go, but then he changed his mind. He figured if he stayed home he would just pace and obsess. The dinner would be a distraction. But it was strange. There were maybe a dozen people among the many hundreds in attendance who shared the secret. They were all throwing themselves into the party in an effort to forget the strain for a few hours, and succeeding somewhat, except when they would see someone else who knew. When Michael Morell spotted Rhodes in the crowd he gave him a slight pained smile that made him laugh.
Obama lived up to his reputation for cool. If he was anxious about the next day's mission, he didn't show it, garnering laughs as he poked fun at the long-running dispute over his origins and his own sometimes messianic public image, offering a supposedly never-before-seen video of his live birth, which, he said, he himself had never seen. It turned out to be a clip from the Disney movie, The Lion King, showing the birth of the future king on the plains of Africa—the clouds part and a shaft of heavenly light beams down on the uplifted cub. "Back to square one," Obama joked. Then he took pains to explain to the "Fox TV table" that the video was a joke, a "children's cartoon," he said. "If you don't believe me, you can check with Disney, where they have the long-form version." He skewered New York real estate magnate, publicity hound, reality TV star, and sometime presidential candidate Donald Trump, who for weeks had been loudly demanding proof of Obama's citizenship. The president then gratuitously suggested that Representative Michele Bachmann, a vocal critic and Republican presidential aspirant, might have actually been born in Canada.
There was laughter.
"Yes, Michele," he said. "This is how it starts."
Great care was taken to preserve the appearance of normalcy on Sunday. President Obama left for his weekly golf outing at Andrews Air Force Base, but this time he would play only nine holes. Arrival times at the White House for all of the top staffers and cabinet members were staggered. The principals were instructed to keep their security details at a distance—a thick herd of black SUVs arriving at the gates always attracted attention. They were told not to park in their usual spaces. The West Wing tours normally booked for Sunday had been canceled, which raised the suspicion of ABC TV's George Stephanopoulos, who understood the rhythms of White House life from his years on President Clinton's staff. He got wind of the cancellations and asked Chief of Staff Bill Daley what was going on. He was told there was a "plumbing issue." The Sunday tours were popular with the executive department staffers, who had a chance to show off their access by escorting family members and friends through the White House. Out-of-town guests sometimes planned visits around such perks, so the cancellations caused some disappointment. Obama's personal secretary had planned one for that day, intending to show around the cast members of the hit movie The Hangover, who had come to town for the previous night's gala. Rhodes got a phone call from her that morning.
"Can I just come in as an exception with these guys?" she asked.
"No," said Rhodes. No exceptions.
The National Security Council staff convened at eight o'clock that morning. The deputies met at nine.
Halfway around the world, it was already late in the afternoon in Jalalabad. McRaven had timed the strike to hit the target in Abbottabad at one o'clock in the morning, Pakistani time, looking for the moment when things would be quietest at the compound and in Bilal Town, and when his men would have the longest stretch of darkness possible to finish up the work, fly north to Kala Dhaka for refueling, and get out of the country. That meant they would depart from the base in Afghanistan at about eleven o'clock at night, local time—the force would pick up a half hour on the clock flying east into Pakistan, so they would fly for an hour and a half and arrive at the targeted time. That meant the mission would launch at two-thirty p.m. Washington time and hit the compound at about four in the afternoon. McRaven kept an iPad in front of him throughout the night displaying multiple time zones just to help keep things straight.
So as the assault force readied, the White House pulled itself together. Some key Obama staffers were being called in and informed of the mission for the first time. Jay Carney, the president's press secretary, was on an outing with his children and didn't notice the e-mail on his phone from Rhodes until an hour after it was sent. He forwarded the note to Dan Pfeiffer, the communications director.
"Do you know what this is about?" he asked.
Pfeiffer said that he had received the same summons, and, no, he didn't know what was happening, either.
In the Situation Room and the complex of small meeting rooms around it, staffers worked on setting up the videoconferencing. Panetta, who would officially command the mission from his conference room at Langley, would be up on the big screen relaying the running commentary of McRaven, who would be at his post in Jalalabad. High over Abbottabad, much too high and too small to attract attention, was an RQ-170 Sentinel, a stealthy drone with a high-powered lens, which would provide a live video feed of the assault. In his blue uniform, Air Force General Marshall "Brad" Webb, a broad-faced man with a crew cut and a chest full of ribbons, was testing the video links to it and to Admiral McRaven in one of the small conference rooms. When Donilon learned that he planned to move himself and the feeds into the Situation Room, he put a stop to it. Donilon did not like the prospect of Obama communicating directly with McRaven and watching the mission live. It might appear that he was micromanaging the raid. Webb would have to confine these direct links to the smaller conference room.
The principals convened at noon for a final review of the plans and the president dropped in briefly, wearing his white golf shirt and blue Windbreaker. Each of the principals was given the plans for four possible outcomes, and each was tasked with making certain phone calls, depending on what happened.
Anticipating a long day and night, the table in one of the smaller side conference rooms was covered and topped with a heaping Costco plate of sandwiches, chips, and baby carrots and a tub of sodas and bottled water on ice. The NSC staff spent most of the early afternoon reviewing their "playbook," a large three-ring binder developed for an even broader range of possibilities. If something goes awry, who calls whom? How much of the intelligence case should be laid out after the fact, to explain why the action was taken? If trouble developed, which countries would they contact for support? Who would be the best person to reach out to, which Pakistani leader? Who had the best personal relationship? For instance, Admiral Mullen had a very good relationship with General Kayani. Who were the right people to leverage if the men on the raid found themselves in a bad spot? Did they want to put the president on the phone with the leader of a foreign country if this went badly? Whatever happened, there would be a lot of explaining to do with Pakistan: Here's why we took the extraordinary step of not sharing this information with you. Here's why we didn't work with you.
Success scenarios were easier. There were many more pages devoted to failure.
The president returned at two-thirty p.m., still wearing the white golf shirt and blue Windbreaker.
In Kabul, General Petraeus paid a surprise visit to the JSOC situational awareness room.
"Do you know what's going on?" he asked Colonel Bill Ostlund, who was JSOC's liaison there.
"Yeah, we've got nine operations going on right now and a few more that I think will happen tonight," said Ostlund. His center monitored operations being run out of task force headquarters in Jalalabad, in case problems developed that needed the attention of higher command—typically a helicopter accident or an issue involving civilian casualties. The activity he described was the normal nightly pace.
The colonel knew nothing about the bin Laden raid but had suspected for a few days that something big was in the offing. McRaven had come up from Jalalabad for a short visit and before stopping in to see the commanding general had asked the colonel when Petraeus's office had last been swept for listening devices.
"Sir, I don't know if it has ever been swept," said Ostlund, and joked about the relative openness of the conventional army's habits compared to their own. "General Petraeus will probably have his window open and an Afghani right outside the window."
McRaven laughed and told Ostlund that he wanted him to stay outside while he met with the commander. This was unusual, since Ostlund had been in on every meeting with the admiral up until that point, even the most sensitive ones with the CIA station chief and Petraeus. So he knew something especially interesting was afoot, and since Petraeus rarely stopped by his ops center, he figured tonight must be the night.
"Why don't you ask the rest of your folks to leave?" the general asked Ostlund. "And then we can talk."
As the others filed out, Petraeus said, "They don't need to come back for a while."
When the others were gone, and they were sitting alone, Petraeus asked, "So, what do you think is going on?"
Ostlund guessed that either they were going to do a raid to try to free Bowe Bergdahl, an American soldier taken captive by the Taliban almost two years earlier, or they were going after bin Laden. He wanted to add Ayman al-Zawahiri, al Qaeda's Number Two, but he couldn't remember how to pronounce the name.
"Yeah, it's the latter," said Petraeus.
They sat side by side in the large windowless room, at the head of a U-shaped table lined with now-empty computer stations, facing a wall with eight different plasma screens. They received no video feed from the bin Laden raid because the CIA was running it, but both men could monitor the live chat from JSOC headquarters, the CIA, and the White House.
Petraeus commandeered Ostlund's keyboard and began tapping out questions to the various principals. At one point he directed a question to Admiral McRaven, calling him "Bill," which alarmed Ostlund. Petraeus's comments were being conveyed on the colonel's line, and he was not used to addressing his commanders by their first names.
He asked, "Sir, could you let them know that this is coming from you?"
With a final order from Panetta—"Go in there and get bin Laden; and if he isn't in there, get the hell out!"—McRaven launched the raid.
The two Stealth Black Hawks lifted off from the airfield at Jalalabad precisely at eleven p.m. local time. They were blacked out and both carried a full, minutely calculated load. Each of the SEALs was in full kit: desert camouflage, helmet, night-vision goggles, gloves (for fast roping), and hard knee pads (better for dropping to a knee for shooting). Each carried a booklet with photos of the people they expected to find in the compound. They were armed with various pistols and short-barreled automatic rifles outfitted with silencers. They carried only light arms because the compound was not heavily defended. While they might encounter armed men once on the ground, there would not be many. Attacking loud and fast in darkness, with finely choreographed moves, able to operate in the night as if it were day, the SEALs would have an overwhelming advantage.
About ten minutes into the flight the choppers rose above a series of rugged peaks and crossed into Pakistan. As soon as they did, the three big Chinooks lifted off from Jalalabad. One would set down just inside the border on the Afghan side. The other two would proceed to the staging area north of Abbottabad by a different route. The Black Hawks eased down into the wide Mardan Valley, flying well north of Peshawar, moving fast and hugging the terrain.
The special operators of JSOC like to see themselves as "the point of the spear," and these two helicopters racing east in darkness were unquestionably that. Here was the final thrust of an enormous effort that stretched back over nine and a half years—further if you considered the whole modern history of special ops. The post–9/11 effort to find Osama bin Laden and his small band of zealous killers had engaged two presidential administrations and many thousands of people in America's military and intelligence communities: the analysts working in shifts, the CIA officers rebuilding human spy networks, and the combined satellite and aerial and electronic surveillance efforts of an alphabetical jumble of agencies and branches, developing drones and secure live telecommunication links, creating computer software, and honing strategy and tactics. If a nation must learn how to fight each war anew, borrowing from its existing arsenal, adapting, and innovating to meet the threat, then the SEALs on these Black Hawks were, in effect, America's response to the challenge of 9/11, closing in at last on the war's ultimate target.
McRaven sat in a large rectangular windowless room with plywood walls, surrounded by manned computer stations and looking up at a wall of video monitors. One monitor would show video of the raid itself—the Sentinel feed—but there was nothing to watch there yet. Another had a graphic display showing the location of the choppers. There was some tension as the two smaller choppers crossed into Pakistan, followed about fifteen minutes later by the two Chinooks, but none of them tripped alarms at that country's air defenses. With the full array of national security assets at his disposal, McRaven was able to monitor exactly what the Pakistanis were doing . . . and as the minutes went by it became clear that they were doing nothing. The task force had entered Pakistani airspace before, on covert missions into the tribal areas, so they had been confident they could slip in unnoticed, but it was nevertheless a relief when it had been done. The admiral had precalculated a point where, even if the Pakistanis woke up, the mission would proceed. Soon enough they had passed even that point. Now, as the blacked-out choppers moved toward Abbottabad, there was nothing to do for about an hour but wait.
At that point, McRaven knew he would have decisions to make only if something went wrong.
Up on the big screen in the White House Situation Room, Panetta read out occasional updates on the choppers' progress. One of Obama's aides said, "Mr. President, this is going to take a while, you might not want to sit here and watch the whole thing unfold."
"No, I think I'm going to go ahead and watch," said Obama. In Chicago, nine and a half years earlier he had watched 9/11 unfold in a crowded basement room, now he would watch the final act of that drama from another.
Biden was typically restless, moving in and out of the room, and when he noticed that the live feed of McRaven and the Sentinel were up in the side room, he went in and sat down to watch there. Webb was hunched over his laptop at the head of the table.
In Jalalabad, McRaven's sergeant major was sitting alongside the admiral, communicating on a chat line with Webb and others in the command loop. He looked up.
"Hey, sir," he said. "General says the vice president just walked in."
Secretary of Defense Gates was not far behind.
McRaven knew that the drumming chop of the approaching Black Hawks would be faintly audible about two minutes before they reached the target. The helicopters were stealthy, designed to avoid being spotted by radar, and quieter than standard models, but they still created racket when they were directly overhead. Approaching the compound from the northwest, the Black Hawks were now visible in the grainy overhead feed from the Sentinel.
After that, things happened very fast.
Everyone watched with shock as the first chopper, instead of hovering over the compound to drop the SEAL team from ropes and then moving off, as planned, abruptly wheeled, clipping the compound wall with its tail and hitting the ground. This clearly wasn't good.
The Night Stalker pilot had tried to bring his Black Hawk to a hover, but the chopper wouldn't perform the maneuver. It "mushed," or began to skid uncontrollably. An after-action analysis would conclude that because the compound was encircled by stone walls, whereas the mock target in Nevada had only had a chain-link fence, the air beneath the hardworking Black Hawk warmed more rapidly than anticipated. That meant the air density was insufficient for the precisely calculated weight of the aircraft. The chopper could stay airborne only if it kept moving, so when the pilot halted its forward progress it fell.
The pilots of the 160th train for frantic moments like these. The pilot of the faltering Black Hawk moved with practiced speed. He found a plot of flat ground to execute a hard, controlled crash. It was in the compound's western corner near an animal pen. He swung the craft's tail in that direction and deliberately used it to clip the top of the western wall. This pitched the chopper forward and into the ground. The landing was hard, but upright, which was key. In those seconds the pilot's maneuver had prevented the Black Hawk from pitching over on its side, which is a disastrous way for a helicopter to crash. If its still-spinning rotors strike the ground, the body of the chopper could be thrown or violently rolled. Instead, the nose was in the dirt. The SEALs were strapped in and were on seats designed to absorb a hard landing like this. One second the craft was skidding, and the next it was still, tilted at a forty-five-degree angle, its tail rotor hung up on the top of the wall.
No one watching the small screen in the White House, viewing the scene from far overhead, could see exactly what had happened, or even tell that the chopper was pitched forward with its tail hung up on the wall. They could see only that it was down inside the compound. They knew that was not the plan.
Excruciating moments passed as McRaven sought word from the scene. Every discussion of what could go wrong on this mission had referenced the helicopter that clipped the plane and exploded in the Iranian desert in 1980, and the helicopters that had crashed in crowded Mogadishu in 1993. Here in the first seconds of the mission, they had a Black Hawk down.
Obama had been following Donilon's advice up to this point, receiving mission updates secondhand, talking with Panetta via the video hookup in the Situation Room, and letting others monitor the video feed and chat lines in the side room, but when the chopper went down he abruptly got up and crossed the hall.
Clinton, standing over the food tray in the adjacent room with Ben Rhodes, watched him go.
"Ben, do you think it's a good idea for the president to watch this?" she asked.
"He's not going to be directing anything," Rhodes said. "It's just a feed."
Sitting at the head of the small conference table, Webb stood up to surrender his seat when he noticed Obama enter. The president waved him back down.
"I'll just take this chair here," he said, sliding into the corner. "I need to watch this."
The president's entrance was noted by Webb on the chat line.
In Jalalabad, McRaven's sergeant major said, "Sir, the president just walked into the room."
Clinton followed and took one of the remaining chairs at the table. Other staffers began crowding into the small room to see what would happen next.
In Jalalabad, McRaven was understandably preoccupied. He didn't have time to worry or watch the screen, or to explain things to Washington. He quickly ascertained that no one on the chopper had been hurt. They were already preparing to assault the target house from their downed position. All of these men had long ago proved their talent for adapting quickly to setbacks. This is why they had been picked. Setbacks were commonplace. It was the rare plan that survived even the first minutes of an assault. McRaven had lost helicopters before, and he had options at his fingertips.
Watching on the screen at Langley with Panetta and the other top CIA officials and bin Laden team members, Michael Morell felt a moment of panic when the chopper went down but was immediately reassured, as was everyone watching, by McRaven's manner. The admiral did not seem ruffled or even particularly surprised.
"Mr. Director, as you can see, we have a helicopter down in the courtyard," he said to Panetta. "My men are prepared for this contingency and will deal with it."
At the White House there was still no explanation of what was going on. Obama's face was etched with worry. A White House photographer snapped a picture of the now-crowded side room that would become famous: Webb at the center in his blue uniform, head down, intently monitoring the video feed and chat line on his laptop screen, trying to figure out what had happened; Obama seated in the corner with furrowed brow; Donilon standing behind Webb with his arms crossed, flanked by Admiral Mullen and Bill Daley; Clinton with her hand to her mouth; Gates and Biden looking glum; staffers lining the walls—all fixated on the screen off-camera.
Obama was as nervous as he had ever been. He knew the stakes were huge, mostly for the men in that chopper, but also for the country, for his administration . . . for him. He had persuaded himself that he was willing to accept failure, but to be staring at it in real time on the screen . . . he would later say that these were the longest minutes of his life, with the possible exception of waiting for word from doctors when his youngest daughter was hospitalized with meningitis.
When the first chopper went down, the second Black Hawk diverted from its planned course and landed outside the compound walls in a newly planted field. The mission had called for it to hover briefly outside to drop the translator, the dog, and four SEALs, and then move directly over the three-story house to drop the rest of the team on its roof. It seemed to the viewers that the entire assault plan had gone awry.
Then, abruptly, SEALs began streaming out of both choppers, inside the compound and out. The assault was on. The downed chopper had caused only a momentary delay. To their relief, those watching in Washington concluded that whatever had happened the mission was proceeding. In his flat Texas twang, McRaven ordered one of the two Chinooks waiting on the riverbed at Kala Dhaka to move up.
The team from the crashed chopper moved quickly along the inside wall of the compound, pausing only to blow open a metal door that led to the house. The team from the chopper outside the wall blasted in through another entrance. There were flashes of light on the screen. The men were moving on the house itself now, and then were inside.
Upstairs in that house, according to accounts given by bin Laden's family, the household had been startled awake by a loud crash. One of bin Laden's adult daughters ran up from the second floor to the third and was told to go back down. Bin Laden instructed his wife Amal to leave the lights off. They would not have been able to turn them on anyway, because CIA operatives had cut off electricity to the entire neighborhood in advance of the assault—darkness favored the SEALs. The Sheik waited upstairs with Amal in the dark.
One group of SEALs entered the garage area of the guesthouse. Teams like this had hit houses that were wired to explode, and had encountered people wearing explosives. When they encountered men, they were inclined to shoot on sight. There was a single brief spray of gunfire as they approached, but it was wild and ineffective. It had most likely come from the courier Ibrahim Saeed Ahmed—Ahmed the Kuwaiti. The SEALs returned fire, killing Ahmed and wounding his wife in the shoulder.
Another part of the team moved on the main house, clearing it methodically. Abrar Ahmed, the courier's brother, was in a first-floor bedroom with his wife Bushra. Both were shot dead.
They cleared the first floor room by room, encountering no further gunfire. They passed through two large storage rooms and a kitchen. No one knew the layout of the interior. When they encountered a locked metal door in the rear sealing off a stairway to the upper floors, they slapped on a small C-4 charge, blew it off its hinges, and moved up the stairs. Bin Laden's twenty-three-year-old son, Khalid, a slender bearded man wearing a white T-shirt, was shot dead at the top. There were wailing women and children on this floor, none of whom posed a threat. The team didn't know it yet, but there was only one adult male left in the compound, and he was in the third-floor bedroom.
Originally, half the assaulting SEALs were to have come down through the balcony into the third floor, in which case bin Laden would have been encountered immediately, at about the same time the Ahmed brothers were being shot downstairs. Instead, the Sheik had about fifteen long minutes to wait in the darkness as the SEALs methodically approached. Their rifles had silencers, and if none of the victims had fired he would not have heard the blast of gunfire by Ahmed and then shouting and crying and the sound of the metal doors being blown open. He might also have heard the muted pop of the SEALs' silenced weapons. The only windows on his secure third floor looked north, out over the compound walls. The downed chopper was in the western corner of the compound and the other had landed to the south, so he could only have surmised who was coming for him. He might have thought it was a Pakistani force. The assaulters blew off the door barring the third floor and he would have heard men ascending, coming for him.
Three SEALs came up those stairs, scanning different angles, searching while protecting each other. According to one of the SEALs,* the first man up spotted a tall, bearded, swarthy man in a prayer cap wearing traditional flowing Pakistani clothes, the knee-length shirt worn over pajama-like bottoms. One or more of the SEALs fired at him. The man retreated quickly into a bedroom, and the SEALs followed. In the bedroom they found two women leaning over a fatally wounded bin Laden, who had been shot in the head. The first SEAL violently moved the women out of the way and the other two stood over him and fired several more shots into his chest.
* An account of this killing scene by one of the three SEALs, calling himself "Mark Owen" was published after the first edition of The Finish went to press. He was the first of the raiding party to offer his version of the shooting, and as of this writing is the only member of the team to have done so. It differed in several details from the one I had pieced together in interviews with sources at JSOC. My original account had bin Laden being chased from the top of the stairs into a bedroom, where he was first shot in the chest, and then, once his wife Amal was pushed aside, shot in the head by a SEAL standing over him. The version in the above text is based on the "Owen" account, which, given the source, I assume to be more correct. I had been in discussions with "Mark Owen" early in the reporting of this book, but he opted not to tell me his story and instead pursued a contract to coauthor his own account, called No Easy Day.
The engagement was over in seconds. Amal had been shot in the leg. Bin Laden had weapons on a shelf in his bedroom but had not picked them up. His identity was unmistakable, even with the grotesque hole through his right forehead. The architect of 9/11 had become the most infamous face in the world.
McRaven heard "for God and Country, pass Geronimo. Geronimo. Geronimo." The word "Geronimo" was part of a coded "mission execution checklist." It meant the critical milestone of the raid had been passed successfully, securing bin Laden. McRaven conveyed the report immediately to Panetta, and it began to spread waves of excitement through the CIA and White House, and in Kabul where Petraeus and Ostlund were listening in. Petraeus pumped his fist with satisfaction.
In the White House, in the corner of the small crowded conference room, Obama heard "Geronimo ID'd."
The president knew the ID was still tentative, so he didn't let himself fully believe it. To whatever extent he felt relief or excitement or satisfaction . . . he fought those feelings down. To him it meant the SEALs could now start extricating themselves, which meant they might soon be fighting their way out. There had been a chopper crash and explosions at the compound. If the United States was going to have to defend the raiders on their way out—and there were fighters ready—it meant the worst part might still be ahead. Hearing the report, the president thought, Get the hell out of there now!
But after McRaven had passed that along, it occurred to him that he had not asked specifically whether bin Laden had been killed or captured.
So he asked, "Find out whether it's Geronimo EKIA [Enemy Killed In Action]."
The answer came back, "Roger, Geronimo EKIA." So McRaven passed that on to Panetta and the White House.
"Looks like we got him," said Obama, only half believing it.
The delay between these two reports would cause some confusion in later accounts, which suggested that the SEALs had first found bin Laden, chased him, and then, a few minutes later, killed him. The finding and the shooting had happened in the time it took the three SEALs to crash into his room. Eighteen minutes had elapsed since the choppers had arrived.
McRaven told Panetta: "Look, I've got a Geronimo call, but I need to tell you it's a first call. This is not a confirmation. Please keep your expectations managed a little here." He explained that the adrenaline of operators was sky high on these raids. They were looking at everything through night-vision goggles. They were professionals, but . . . "Let's not count on anything until they get back and we have some evidence." Echoing the president's thoughts, McRaven reminded Panetta, and everyone else watching, "We've still got SEALs on the ground without a ride."
The video on the screen now showed SEALs emerging from the house, herding the uninjured women and children to one corner of the compound, away from the downed chopper. Some of the men came out carrying a body bag—bin Laden's body had been dragged feet-first down the stairs, leaving a bloody trail. One of his daughters would later say that she remembered her father's head banging each step on the way down. The SEALs eventually zipped it into a nylon bag. The assaulters moved deliberately, and Obama felt they were taking too long. Everyone was waiting for the Pakistani response at this point. The president just wanted them in the air.
But the commotion at the compound had, in fact, attracted little interest in the neighborhood, or the country. The translator, wearing a Kevlar vest under his traditional long Pakistani shirt, shooed away the few residents who came out for a look. His training to fast rope was for naught, since his helicopter had instead landed outside the compound. The dog Cairo was enough to convince most to back off. The translator told them sternly in Pashto to go back to their houses, that a "security operation" was under way. People obliged. Monitoring the Pakistani defense forces carefully, McRaven saw no sign that the country's defenses had been aroused.
There was much to do yet at the compound, inside and out. Upstairs, SEALs were hastily bagging bin Laden's papers and computer, discs, flash drives, anything that might contain useful intelligence—the site's pocket litter. Bin Laden's youngest wife, Amal, wounded, was helped down the stairs and outside, haranguing the Americans in Arabic. All four of the men who had lived in the compound, along with one woman, were dead. The surviving women and children were flex-cuffed. The women assumed they were going to be taken away. Questioned by an Arabic-speaking SEAL, the women confirmed that they had killed "The Sheik." One of the children confirmed that it was Osama bin Laden.
The Chinook summoned by McRaven now landed noisily outside the compound walls. Men were working on planting explosives on the downed Black Hawk and destroying its secret avionics with a hammer. A medic from the Chinook unzipped bin Laden's body bag, took swabs of blood, and inserted needles to extract bone marrow for DNA testing. Twenty more minutes elapsed before the body bag was carried out to the Black Hawk. One of the bone marrow samples was placed on the Chinook. The intelligence haul was likewise distributed between the two choppers.
Finally, the White House audience saw the downed Black Hawk explode with the set charges. The demolition team scurried to the Chinook and the choppers lifted off, leaving behind a huge blaze, a stunned collection of cuffed women and children, and four bodies. A photo purporting to be the bloody corpse of Khalid bin Laden would turn up on the Internet in the coming days.
Even with the choppers airborne, the tension didn't lift. They first flew north to Kala Dhaka to rendezvous with the second Chinook and to refuel the Black Hawk. Twenty-five minutes later they took off for the flight back to Jalalabad. All of it without any Pakistani response. When that country's air force did scramble two F-16s into action, the raiding party was safely across the border.
The choppers landed back in Jalalabad at three a.m. local time. None of the men who went on the raid had been hurt. They had lost a helicopter but they had avoided Pakistan's defenses completely. And they had killed Osama bin Laden.
The SEALs were certain of it, but the White House and the world would demand more proof. McRaven signed off on his narration for about twenty minutes to go out and meet the men on the tarmac as they lowered the body bag from the chopper. It was unzipped, and photos were taken and transmitted immediately to Washington and Langley. The man had been dead for an hour and forty minutes, and he had taken a shot to the head, so the face was swollen and distorted.
McRaven called Langley with a question for the bin Laden team.
"How tall is this guy?" he asked.
He was told, "Between six-four and six-five."
The dead man was certainly tall, but no one had a tape measure, so one of the SEALs who was exactly six feet four lay down next to it. The body was roughly the same height.
The president had gone back upstairs while the choppers were in flight and asked to be summoned when they landed. Early Sunday evening in Washington, he surveyed the first photos with other members of the team.
When Rhodes saw the picture he recognized bin Laden immediately, even with the wound. Here was the man who had called a press conference to declare war on the United States fifteen years ago, and who had inspired a trail of blood ever since. Rhodes thought, this is either bin Laden or a six-foot, four-inch, slender, dark-skinned man with a long beard who looked exactly like him, and who had been living in hiding surrounded by bin Laden's family, protected by a known al Qaeda intimate. It was bin Laden.
When McRaven returned to his command center, Obama asked him, "What do you think?"
"Well, without DNA I can't tell you I'm a hundred percent sure," the admiral said. "But I'm pretty damn sure." He said that the men were just beginning to be debriefed, but that there was some indication from the women interviewed at the compound that they had killed the right man. He reiterated, "Mr. President, I have fairly high confidence that we have killed bin Laden here."
Still, the president was inclined to be cautious. What would be worse than to announce that you had killed the founder and leader of al Qaeda only to be proved wrong? When Panetta, Morell, and "John," the bin Laden team leader, arrived at the White House, Morell walked the president through the details of the agency's facial analysis, which had concluded with 95 percent certainty that the dead man was bin Laden. The president asked about DNA analysis, which would be even more conclusive, but Morell told him that the earliest they would get those results would be Monday morning.
Wouldn't it be best then to wait? Why take chances? It was now early Sunday evening. From his command seat in the Situation Room, Obama asked if they should announce bin Laden's death that evening or wait for the DNA results. Would the secret hold? Everyone agreed that the secret would not hold, not with Twitter and e-mail and the Internet and cable TV, not with the mini-conflagration and dead bodies at the compound in Abbottabad, with bin Laden's wives and children in Pakistani custody, and with word now spreading happily from Jalalabad to Kabul and outward. If the White House said nothing, then who knew what version of the story would come out or what kind of conspiracy theories would take root.
"It won't really be true until we say it's true," said Obama. "So I'm not worried about it leaking out. We should confirm it when we are in a position to confirm it, but not feel pressured to do so."
No matter when the White House chose to make an announcement, it had to contact Pakistan and explain. No one knew how that country would react. The raid had been a clear violation of its sovereignty, and the fact that the United States, an ally, had not sought its help or consulted with it beforehand was deeply insulting. Still, as Obama explained to me later, "It would be easier for them to manage the fallout if it was definitive that it was bin Laden, as opposed to there being ambiguity out there for two or three days, in which case the whole issue of Pakistani sovereignty would be magnified."
So Admiral Mullen called General Kayani. The Pakistani army chief by then knew, of course, that there was a downed American helicopter in Abbottabad, but in those early hours of the morning in Islamabad, no one had yet sorted out what had happened. Mullen told him that the United States had conducted a mission and had killed Osama bin Laden.
"Congratulations," said Kayani.
The conversation went downhill from there. There was going to be trouble ahead between the two countries, for sure, but the general immediately helped resolve the question over when to make the announcement.
"Look, I've got a problem," he said. "There are all these stories about American helicopters and a raid inside Pakistan, all without a good explanation. It would be very helpful if you would stand up and say what happened."
That decided the matter. They would make the statement that night. Rhodes went to work drafting the comments he had not been able to bring himself to write the day before. Other principals picked up the playbook for a successful raid, each assigned to telephone a different world leader. Obama got on the phone to inform former presidents Bush and Clinton, who had hunted bin Laden during their terms, and British Prime Minister David Cameron, whose country had been America's staunchest ally during the effort.
Jay Carney went to work assembling the White House press corps for a special announcement. He and his staff started contacting reporters, mostly by e-mail. He told them, one after another, "Look, you'll want to be here, but I can't tell you why." Most guessed that Muammar Gaddafi had been killed—one of the Libyan dictator's sons had been killed the day before. No one guessed bin Laden.
But the news did break out. Twitter users from Abbottabad had been buzzing for hours about helicopters and strange explosions. A Pakistani computer technician named Sohaib Athar filed a report just as the SEAL choppers arrived over the compound, writing "Helicopter is hovering over Abbottabad at 1 a.m. (is a rare event)." Minutes later he reported a loud bang that shook the windows where he was staying nearby. There were other reports like this, but no one knew exactly what had happened until Keith Urbahn, a former chief of staff to Bush Defense Secretary Donald Rumsfeld, tweeted: "So I'm told by a reputable person they have killed Osama bin Laden. Hot damn." Urbahn quickly followed with, "Don't know if it's true, but let's pray it is." This was an hour before Obama appeared in the East Room to make the announcement, and the news was quickly everywhere.
In the White House, Carney was alerted to ESPN's Sunday Night Baseball broadcast of a game between the Phillies and the Mets in Philadelphia's Citizens Bank Park. The sellout crowd was chanting, "USA! USA! USA!" It was 10:45 p.m. The game announcers interrupted to deliver the news that there were reports that bin Laden had been killed.
Still, as Obama had predicted, it would not be true until the United States confirmed it. So he sat behind his desk in the Oval Office making last-minute changes to the speech Rhodes had drafted, and then he walked over to the East Room to give it. There were already crowds across the street in Lafayette Square celebrating and chanting "USA! USA! USA!"
It was 11:35 p.m. when the president appeared on television striding up the red carpet toward a podium, and began: "Good evening. Tonight, I can report to the American people and to the world that the United States has conducted an operation that killed Osama bin Laden, the leader of al Qaeda, and a terrorist who is responsible for the murder of thousands of innocent men, women, and children."
He spoke about the attacks on 9/11, which were, he said, "the worst attack on the American people in our history," and which were "seared into our national memory." He spoke of how long bin Laden had eluded American forces. The president felt proud of his own contribution to the effort, citing his instruction to Panetta soon after taking office to move the priority of the top al Qaeda leaders "to the front of the line." He mentioned the national effort to oust the Taliban, but did not mention Iraq. He believed part of his own contribution had been to alter the misguided priorities of President Bush.
"Then, last August, after years of painstaking work by our intelligence community, I was briefed on a possible lead to bin Laden," he said. "It was far from certain, and it took many months to run this thread to ground. I met repeatedly with my national security team as we developed more information about the possibility that we had located bin Laden hiding within a compound deep inside of Pakistan. And finally, last week, I determined that we had enough intelligence to take action, and authorized an operation to get Osama bin Laden and bring him to justice.
"Today, at my direction, the United States launched a targeted operation against that compound in Abbottabad, Pakistan. A small team of Americans carried out the operation with extraordinary courage and capability. No Americans were harmed. They took care to avoid civilian casualties. After a firefight, they killed Osama bin Laden and took custody of his body."
He noted that the threat of attacks from this group had not ended, and pledged a continued effort against them, and he emphasized once more that the United States was not at war with Islam, pointing out that President Bush had also labored to make that clear. He accused bin Laden of the very thing the Sheik had worried about, his unwanted legacy: "Bin Laden was not a Muslim leader; he was a mass murderer of Muslims. Indeed, al Qaeda has slaughtered scores of Muslims in many countries, including our own. So his demise should be welcomed by all who believe in peace and human dignity."
The president thanked "the countless intelligence and counterterrorism professionals who have worked tirelessly to achieve this outcome. The American people do not see their work, nor know their names. But tonight, they feel the satisfaction of their work and the result of their pursuit of justice.
"We give thanks for the men who carried out this operation, for they exemplify the professionalism, patriotism, and unparalleled courage of those who serve our country. And they are part of a generation that has borne the heaviest share of the burden since that September day."
The president closed by invoking the spirit of unity that the nation experienced after the 9/11 attacks, and was reexperiencing briefly that night.
"Let us remember that we can do these things not just because of wealth or power, but because of who we are: one nation, under God, indivisible, with liberty and justice for all. Thank you. May God bless you. And may God bless the United States of America."
The night was not over for the White House. In Carney's West Wing office, Michael Morell, Mike Vickers, and John Brennan held a group telephone conference with reporters. Morell, who had been with President Bush on the day of the attacks and at the center of efforts to catch bin Laden ever since, now declined to answer most of the detailed questions about the hunt, but he did offer a convoluted summary off the top of his head about finding Ahmed the Kuwaiti.
"It was multiple detainees debriefed over a number of years," he said. "And then it was a composite picture of the courier network and this particular courier that we were interested in—that led us to this compound, and that came out of a composite picture and then was developed further through other intelligence means."
Morell saluted the cooperation between CIA and the military.
"You know, this CIA-U.S. military operation was obviously a major success, and it's a sign of the tremendous partnership that has existed between the intelligence community and the military in the years since 9/11. And it is a testament that the CIA is immensely grateful to those in the military who participated in this operation . . . We understand that the fight against al Qaeda continues, and that fight continues even as we mark the death of Osama bin Laden."
It was very early in the morning when they were done. Morell left the White House at about half past midnight. He heard the large crowd across the street chanting "USA! USA! USA!" and then heard something that this lifelong agency man never thought he would hear. The crowd began chanting, "CIA! CIA! CIA!" He walked out to his car for the drive home to his family. For the last two months he had been working sixteen-hour days and he hadn't been able to tell his wife why. Just that afternoon their daughter, who he had peeked in on at the end of that long day nine years earlier, had been in the last choral concert of her high school career. When he had left at six that Sunday morning, his wife had asked if he could make it.
"I can't come," he'd told her.
"It's her last," she said.
"I just can't," he'd replied, unable to explain why. She had not been happy about it.
Earlier that evening, when the president decided to make the announcement, he had phoned her at home, the concert long over.
"Turn on the TV," he'd told her. "You'll understand why you haven't seen me in the last two months."
Now he was eager to get home.
Carney and Rhodes didn't leave the White House until after two in the morning. The press secretary had some beers in the refrigerator in his office, and they had celebrated by drinking them. They heard the chants across the street, still going at that hour, and were surprised to learn that the crowds had grown so large that White House security at first would not let them drive out. So Rhodes walked home.
It felt like New Year's Eve. There were crowds of people dancing and chanting and singing. The streets were full of honking cars. Young women were standing up in the sunroofs waving their arms and cheering. It brought back all of his memories of 9/11, watching in horror from the Brooklyn waterfront as the towers fell. Most of the people celebrating on this night were of college age, in their late teens or early twenties, likely students from nearby Georgetown or George Washington University, which meant they had been children on the day of the attacks.
Rhodes himself was now thirty-two. Al Qaeda and bin Laden had been a dark shadow over all their lives. Now the shadow was lifted. In his own way, he had been involved in that fight from the start. He was not a soldier. He had not risked his life in the battle as so many in his generation had. He was not a shooter like the brave SEALs who had executed the raid, but he had brought his own talents fully to the effort. He had redirected his life, from deciding to work for Lee Hamilton instead of writing fiction, to helping to write the 9/11 Commission Report, to going to work for Obama—working to shape and articulate his thinking about the war, about who was the right enemy, and why fighting them was not only critical to the nation's safety but just and honorable. From that day in Brooklyn, to sketching out the president's remarks that night about bin Laden's death, the killing of bin Laden formed a full circle for Rhodes. It was the story of his own young life. And that night, walking home, he felt like he had won.
9
Glitter
Spring 2011
Finding and killing Osama bin Laden was an extraordinary accomplishment. President Obama had ample reason to be proud. But whose accomplishment was it? In his speech that night, Obama credited the "countless intelligence and counterterrorism professionals" who had labored over the past decade and more, spanning three presidential administrations. He also thanked the SEALs who had risked their lives in the raid, and who had pulled it off seamlessly. He also thanked allies who had cooperated for years in hunting down and interrogating al Qaeda figures, including, even with its violated sovereignty and the insult of not having been consulted, Pakistan. But the president reserved a large share of the credit for the accomplishment for himself.
"And so, shortly after taking office, I directed Leon Panetta . . .
"I was briefed . . . I met repeatedly with my national security team as we developed . . .
"I determined . . . and authorized . . .
"Today, at my direction . . ."
And all of this was true. Obama did deserve credit for making the search for bin Laden a top priority of his administration, for cautiously laying the groundwork for a raid that avoided killing outright innocents and minimized disruption in Abbottabad, and for shouldering a big risk, not just to the men who carried out the mission, but to his own presidency and legacy. Perhaps it is only fair that having accepted the very large potential downside of a raid gone wrong, Obama should now fully reap the rewards for it having gone right.
But his White House team soon began hyping and spinning a story that really did not need to be spun. They did what political professionals exist to do; they began working the story to their own benefit.
Small falsities began to accrue around the story like splashes of glitter. It started almost immediately. Sitting on the couch in Carney's office after the president's remarks, John Brennan told reporters, "The American team engaged in a firefight . . . Osama bin Laden did resist." He went on to say that the men in the compound "certainly had used women as human shields." The next day he went further, saying that bin Laden himself had used his wife as a shield, as part of an effort to paint the al Qaeda leader as cowardly and hypocritical—"Here is Osama, living in a million-dollar compound, hiding behind women who were put in front of him as a shield. It speaks to just how false his narrative has been over the years . . . he's putting other people out there to wage jihad while he is secure in his luxury compound."
In future interviews, Obama's oft-voiced conviction that al Qaeda was the appropriate enemy and his direction to his intelligence chiefs to move finding bin Laden to the "top of the list" would be portrayed as the impetus that led to finding him, after the previous years of futility. In conversations with me, a number of top administration officials used the expression "limited bandwidth" to describe how even high priorities within administrations can be pushed aside or even forgotten—specifically, how Bush's two wars had crowded out the bin Laden hunt. Obama had made similar comments in his speeches, particularly as a candidate in 2007 and 2008, when he argued that President Bush had "taken his eye off the ball."
Early on in the planning, Obama had insisted that the SEAL team be prepared to fight its way out of Pakistan rather than defend the compound and wait for the United States to negotiate its exit. This was a risky call, made for the right reasons. The president was placing the safety of American soldiers above concerns for preserving diplomatic ties with Pakistan. Approaching the mission this way, which had not been Admiral McRaven's suggestion, might have meant leaving in its wake dead Pakistani soldiers and police and downed Pakistani fighters. Making that decision had altered the planning for the mission, requiring the addition of more backup forces and other options. Members of Obama's staff, after the fact, would point to this decision as critical to rescuing the mission after the first Black Hawk crashed. Only because the president had insisted on a beefed-up backup plan, they argued, did McRaven have the ready recourse of a Chinook loaded with a Quick Reaction Force.
In the weeks after the raid, analysis of the documents seized at the compound revealed, as CIA and administration officials presented it, that bin Laden had not been the isolated, irrelevant figure some said he had become, but, rather, had been actively steering his organization from his hiding place, hatching assassination plots against Obama and Petraeus, for example, and setting in motion further attacks on the U.S. homeland.
Then there was Vice President Biden, with his special gift for the self-aggrandizing overstatement, now in the service of his boss, who would call the raid "the most audacious plan in five hundred years." Biden said that Obama had made this gutsy call after being roundly advised not to, suggesting that only Leon Panetta had been clearly in favor of it. He said Obama had "a backbone like a ramrod."
Versions of all this appeared in accounts of the raid and its aftermath. It was not a coordinated effort, just a cumulative one. Pulling all of it together, the official glitterized version of the tale could be summarized thusly. A bold new president resorted national defense priorities to go after bin Laden. At his direction, the moribund hunt was revitalized, and a new lead to the al Qaeda leader was found and developed. It discovered bin Laden living not in a mountain cave but, rather, like a millionaire in a "luxury" compound in a polite Pakistani suburb. Steered by the president in strict secrecy, the military was emboldened and directed to alter its plan to, in effect, surrender to Pakistani authorities if discovered, and instead to prepare sufficient backup forces to confront any resistance head-on—to be ready to fight its way out. It was this advice that saved the mission, because when a Black Hawk crashed, a backup helicopter was at hand. Surrounded by advisers who either were opposed to launching the raid or expressed deep misgivings, the president overrode them to order one of the boldest military actions in human history. The brave SEALs then killed Osama bin Laden in a firefight inside the compound, despite his effort to shield himself behind his wife. Documents seized at the compound revealed that bin Laden had been a hands-on leader of the terror organization, not just a sidelined recluse.
There is some truth to this version, but only some.
Start with Obama's direction to Panetta and Mike Leiter in May 2009, summoning them to that impromptu huddle in the Oval Office. The newly elected president did make it clear that he regarded the hunt for bin Laden and Ayman al-Zawahiri as the top national security priority of his administration. But did that really change anything? One senior intelligence official told me that it did not.
"This did not represent a big change," he said. "We were already doing everything we could, and had been for years."
Obama's urgency did have an effect, he said, forcing the various bin Laden team leaders to prepare regular progress reports. He also said that having Director Panetta so actively interested "tends to focus people . . . I think that requiring regular updates pushed our guys even harder, but I doubt that was the reason for the breakthrough. The resources available didn't change at all. Our focus on AQ senior leaders never suffered from a lack of resources, certainly not the hunt."
Viewed dispassionately, it appears that the trail to Abbottabad resulted not from redirection but from a slow grind. Each of the critical "breaks," such as learning the pseudonym "Ahmed the Kuwaiti" from several sources, finding out his true identity in 2007, locating him in 2010, and tracking him to Abbottabad, came as the result of steady, patient, unremarkable effort over many years. None of the breaks was even recognized as significant until the compound started raising eyebrows. Until then, Ahmed the Kuwaiti was just one of many, many thousands of possible leads, stored in a growing catchall database. The more remarkable achievement was connecting these disparate facts, and even then the sum of them led only to the residence of a man suspected of once acting as a courier and aide to bin Laden. It was because the CIA had been following every lead for nine years that the compound was found, and because its analysts had been thinking long and hard about how bin Laden might be living—without heavy security, surrounded by his wives and family, with only one or two trusted aides—that they found the configuration of the compound so compelling. So the argument that it was Obama's redirection of effort in 2009 that led to bin Laden is true only insofar as every step on the road to success turns out to have been the right one. It was a factor. Obama deserves credit for it. The larger truth is that finding bin Laden was a triumph of bureaucratic intelligence gathering and analysis, an effort that began under President Clinton and improved markedly after 9/11 under President Bush. The effort was going to continue for as long as it took. It took just under ten years. It is hard to find one man in the wide world when he is smart about not being found.
It should also be noted this effort did involve torture, or at the very least coercive interrogation methods. The first two mentions of Ahmed the Kuwaiti were made by Mohamedou Ould Slahi and Mohammed al-Qahtani in coercive interrogation sessions. The third, the misleading characterization of the Kuwaiti as retired by Khalid Sheik Mohammed, came during one of his many waterboarding sessions. Hassan Ghul verified the Kuwaiti's central role during secret interrogation sessions at an undisclosed CIA detention center. It is not known what methods were used on Ghul, but the agency did seek permission from the Justice Department to employ coercion. There is no simplistic narrative of a hard-pressed detainee coughing up a critical lead, but there is also no way of knowing if these disclosures would have come without resorting to harsh methods. In the case of Qahtani, in particular, given his long and stubborn resistance, it seems unlikely. Torture may not have been decisive, or even necessary, but it was clearly part of the story.
Efforts to characterize bin Laden as living a cushy life in a "luxury" compound were not just false—they missed a far more telling point. The compound in Abbottabad was large for the neighborhood, but it housed four adult couples and nearly twenty children. By all indications, bin Laden's lifestyle, by choice, was a far sight below an American middle-class citizen. There are prisons in the United States with better accommodations—although none allow cohabitation with three wives. Far more revealing was his need to hide from everyone, even his own family and closest neighbors. Colombian drug kingpin Pablo Escobar, the most notorious criminal of his time during the 1980s and early 1990s and a fugitive from his own country and U.S. special forces, lived and moved openly for most of that time in his home city of Medellin, where he was revered by many. There are men the United States considers terrorists living right now in regions of Pakistan and Afghanistan who are revered in their own tribes and regions, and who live openly in them. Bin Laden had no place in the world where many revered him. Al Qaeda was not a popular movement in his home country of Saudi Arabia or anywhere else in the Arab world or the Middle East. It had its adherents, enough to turn out an angry crowd when provoked by, say, the publication of a cartoon depicting the Prophet, or a public demonstration of Koran burning by a buffoonish Florida pastor, but compared to the millions of Arabs who took to the streets to demand the vote in the spring of 2011, al Qaeda was nothing more than a small and violent cult. Bin Laden's "Nation" of like-minded Muslims was pure fantasy. If he had dared show his face in Pakistan, a Muslim country, someone would have turned him in, if not because it was the right thing to do then for the $25 million reward. It is possible that someone did, since the CIA has not told the whole story and will not say whether anyone has collected the reward.
Obama's decision to beef up the assault force, to plan for the possibility that the SEAL team would have to fight its way out of the country, did not save the raid. No JSOC mission like this one would proceed without a Quick Reaction Force close by. McRaven would have brought two Chinooks into Pakistan for backup and fuel anyway. The larger force commissioned by Obama, the soldiers and aircraft that would have been summoned if there were a significant response by Pakistani forces, stayed parked in Afghanistan throughout. They were not needed.
The president's decision to equip the force with enough backup strength to fight its way out of Pakistan, if necessary, said a lot about the deteriorating state of relations with that country. As one of the principals pointed out at the April 28 decision meeting, if the ties were so weak that this raid would break them, then they were not going to last long anyway. Coming off bitter negotiations to free CIA contractor Raymond Davis, Obama clearly did not relish the idea of negotiating for the release of two dozen SEALs—or, as he put it to me, "I thought the possibilities of them being held, being subject to politics inside of Pakistan, were going to be very, very difficult." McRaven had been running occasional raids into North and South Waziristan for years, raids that were officially forbidden but privately winked at by Islamabad, so he had every reason to believe that if his men were discovered in Abbottabad and confronted, something could be worked out. In weighing the repercussions of a mission gone bad, he made the entirely reasonable decision that dead Pakistanis would be more harmful to America's interests than a team of SEALs discovered to be someplace they didn't belong. The president felt differently. As it happens, the skill of the raiding force made such considerations moot.
When Obama decided to launch the raid, he was not acting against the advice of his top-level advisers. There was near unanimity for taking action at the April 28 decision meeting, with only Biden urging the president to wait, and with Cartwright and Leiter preferring to strike bin Laden with a small missile fired from a drone. Gates preferred the drone option at the meeting but had reversed himself by the following morning. All of the other top aides and advisers, principals, deputies, and staffers, particularly those closest to the analysis and planning process, unequivocally supported the raid. And as for Biden's "five hundred year" boast, it says less about the audacity of the mission than it does about the vice president's appreciation of military history.
It is worth noting one far more daring effort, thirty-one years earlier, if only because it is rarely appreciated as such. When President Carter rolled the dice on a long-shot mission to free more than fifty American hostages in Iran, even the men who went gave themselves only a 20 percent chance of success. The consequences of its failure—eight dead, another nine months of captivity for the hostages, Carter's loss of a second term—painfully illustrate how much of a gamble it was. Nevertheless, a year after the bin Laden raid, Mitt Romney, Obama's Republican opponent in the 2012 election, would take a gratuitous slap at Carter in diminishing the significance of Obama's decision, arguing that "anyone in the Oval Office would have made the same call, even Jimmy Carter." A stronger argument could be made that Romney himself would not have ordered the raid, since he had criticized Obama in 2007 for even considering to do such a thing.
Of all the exaggerations that followed the raid, perhaps the most interesting was Brennan's initial insistence that bin Laden had been killed in a "firefight" and had used women as "shields." The White House subsequently backed off these statements, and the most obvious explanation for them appears to be a combination of three things: genuine confusion in the first hours, a completely unnecessary desire to boost the heroism of the SEALs, and the eagerness of an old warrior to paint his longtime enemy in an unfavorable light. Brennan had been on bin Laden's case for almost fifteen years, ever since he had worked as a CIA officer in the Middle East in the 1990s, and the success of the raid was as much of a personal triumph for him as anyone. So he gloated a little, before a worldwide audience. His comments proved to be an embarrassment.
Contrary to initial reports, there was no firefight at the compound. Based on my own reporting and the published account of one of the SEALs, it appears that after an initial burst of inaccurate rounds from Saeed, all of the shooting was done by the SEALs. It is important to note that the SEALs were fired upon initially, even if only briefly and ineffectually. The gunfire confirmed that at least some occupants of the compound were armed and resisting. Having taken this fire, the team had to expect to be fired upon again until the entire compound was secured. None of the other five adults shot in the raid—four killed and two injured—were armed. The raiders were discerning. None of the children were harmed, and only one of the three women shot was killed. It is difficult to second-guess men risking their lives in the rapid takedown of a residence harboring implacable enemies who had fired on them, in the dark, but available evidence suggests that if the SEALs had wanted to take bin Laden alive, they could have.
The Sheik had been upstairs for nearly fifteen minutes as the men approached. If the house had been rigged with explosives for a final suicide blast—and the presence of children argued against it—there would have been ample time for him to detonate before he was confronted in the upstairs bedroom. Amal's wounding and the need to move her away from the fallen bin Laden apparently prompted the claims of a human shield. According to published accounts and my sources, bin Laden was killed by several shots, one to his head, which knocked him down, and the others to his chest as he lay on the floor, apparently dying. Bin Laden was not actively surrendering, but he was not actively resisting either. It is reasonable to argue, under the circumstances, that if the SEALs' first priority had been to take him alive, he would be in U.S. custody today, and Obama would have his "political capital" for the criminal prosecution of the 9/11 ringleaders.
What is more likely is that the SEALs had no intention of taking bin Laden alive, even though no one in the White House or chain of command issued such an order. Indeed, it would have taken a strong directive to capture him to forgo the chance to shoot him dead. The men who conducted the raid were veterans of many raids, hardened to violence and death. Their inclination would have been to shoot bin Laden on sight, just as they shot the other men they encountered in the compound.
It is worth imagining, however, the alternative scenario. Bin Laden at the defendant's table before a judge and jury might have been considerably less inspiring to his followers than bin Laden the martyr. He might have proved implacable in interrogation, but often the more powerful, elder figures in an illicit organization are more amenable to compromise than their underlings. If he chose to talk to his interrogators, he possessed more information than anyone about al Qaeda, its organization and finances, its personnel and methods, its history and ideology, its ongoing projects. Having him in custody would have posed legal and political challenges, but as the president explained to me, he felt such a coup might have worked to his benefit. So as satisfying as it was for millions of Americans to learn that the world's most notorious terrorist was dead, and that his last sight on Earth was of a Navy SEAL leveling an automatic rifle, a live de-mythologized bin Laden might well have been a better outcome.
The documents seized at the compound revealed bin Laden to be a determined and hectoring correspondent, still dreaming of mass murder in America, but also clearly isolated, frustrated, and out of touch with his group's remaining capabilities. The currents of history had left him behind; he just hadn't accepted it yet.
All in all, these efforts to massage the facts about the killing of bin Laden were nothing on the order of President Bush's showboat landing on the aircraft carrier USS Abraham Lincoln in 2003, and his speech beneath the giant mission accomplished banner, which set a standard for presidential hotdogging that will long stand and will no doubt embarrass Bush until his dying day. In that case the mission—the U.S. invasion of Iraq—was still decidedly unaccomplished, and would remain so for another long and bloody eight years. In his memoir Decision Points, Bush suggests that the message conveyed by that event was not the one intended, but nevertheless concludes: "It was a big mistake."
There was nothing on that scale from the Obama White House. Nevertheless, its handling of success illustrates the folly of straining to take credit. Harry Truman said, "It is amazing what you can accomplish if you don't care who gets the credit." The flip side of that observation ought to be: "It is amazing how much credit flows to the deserving who don't claim it."
Obama has apparently received lasting credit from the American people. His poll numbers jumped almost 10 percentage points after his Sunday evening announcement, and a year later had leveled off to a point slightly higher than where they were before. Killing bin Laden did diminish the perception of Obama as inauthentic, despite the efforts of his Republican opponents. The president's popularity remained high even among those who were disappointed in his policies. It also took away any hopes they had of portraying him as a pacifist. Having ended America's military involvement in Iraq and begun the withdrawal from Afghanistan, he might have been vulnerable to charges of "softness" on national security. Killing bin Laden placed Obama's commander in chief credentials on secure footing. It boldly underscored his punishing pursuit of al Qaeda's leadership. Even as this effort spread to Yemen, the number of terror attacks attributed to al Qaeda's various franchises has declined steadily. By 2012 the United States was increasingly targeting midlevel fighters, and the overall number of U.S. drone strikes steadily fell. There is no way to know for sure, but the numbers suggest a dwindling number of targets. U.S. intelligence capabilities have not themselves diminished.
Three days after the raid, in an interview on 60 Minutes, the president said, "It was certainly one of the most satisfying weeks not only for my presidency, but I think for the United States since I've been president. Obviously bin Laden had been not only a symbol of terrorism, but a mass murderer who had eluded justice for so long, and so many families who had been affected I think had given up hope. And for us to be able to definitively say, 'We've got the man who caused thousands of deaths here in the United States and who has been the rallying point for a violent extremist jihad around the world,' was something that I think all of us were profoundly grateful to be a part of."
Killing bin Laden was not a feat of leadership comparable to launching armies across the English Channel or staring down Nikita Khrushchev at the height of the Cold War, but it was a clear military victory in an age that produces few of them. For Americans, it supplied the right hard ending to the story of 9/11, and will likely mark the symbolic end of al Qaeda, if not the real one. The organization itself was already reeling when its founder died, as much from the unfolding revolutions in the Arab world as the constant pounding of American drones and special operators, which is why bin Laden's death, or martyrdom, did not act as a spur to recruitment. Whatever romantic appeal his cause once had, and it never had that much, has been superseded. The popular election of Islamist governments in Egypt and Tunisia may worry the West, but the ability to effect change through legitimate means has undercut the pull of violent extremism. Bin Laden himself was wrestling with this problem in the weeks before his death. The group's methods had already alienated it from even like-minded Muslims. Ayman al-Zawahiri, the group's new leader, was still at large in mid-2012, but he exhibits little of the talent to inspire or organize.
Almost a year later, the president told me, "I think, internationally, it reminded the world that the American military is head and shoulders above anybody else, and that we can do things really well that nobody else can do. I think it reminded the American people that there are at least aspects of our government that can do things really well, and that when we put our mind to something we can pull together and fulfill our commitments.
"When I went up to New York for that small ceremony after bin Laden was killed, to talk to those guys at the fire station who had lost half their unit, and to meet with the children of those who had been killed in 9/11, and the widows and the widowers, and to just understand how fully they appreciated that America hadn't forgotten about them and what happened, the feelings were profound. The mission created some difficulties for us. I think it strained our relations with Pakistan, and we already had strained relations there, and so laid bare this tension, the fact that there are still safe havens inside the country. And so managing that has been a challenge over the last year. But this is one of those times where you make a decision, you're not sure that it's going to work out and, in retrospect, you can say that it did work out."
America's troubled relationship with Pakistan badly worsened for a time, and then worsened still more after a "friendly fire" incident in November 2011 killed twenty-four Pakistani soldiers. But the relationship, which, as Hillary Clinton noted, has long been based more on mutual need than on friendship and trust, has endured. In return for many U.S. dollars, Pakistan reopened supply routes to U.S. forces in Afghanistan in July 2012, and American drone strikes in Waziristan continued.
Pakistan held bin Laden's wives, children, and grandchildren for nearly a year and then deported them to Saudi Arabia. Under interrogation by intelligence agents there and by the CIA, the women revealed that bin Laden had been living in Pakistan for seven or eight years. He had moved four times before settling into the Abbottabad compound, and had fathered four children. If accounts from Pakistani authorities are to be believed, the al Qaeda founder's domestic arrangements were less than blissful. The eldest of the three wives with him, Khairiah, especially resented the youngest wife, Amal—so much so that she was accused by Siham, the third wife at Abbottabad, of betraying their husband to the CIA. If so, I found no evidence to support it. None apparently had any useful information to disclose about al Qaeda's surviving leadership. The compound was destroyed in February 2012.
The Pakistani doctor who worked with the CIA in an effort to obtain a DNA sample from the bin Laden children, Shakil Afridi, was arrested and tried for treason. He is serving a thirty-three-year sentence. Pakistan claims the conviction was for charges unrelated to assisting the CIA, but the doctor's imprisonment was roundly condemned by the United States and American authorities continue to work for his release.
"This is the man's passion, keeping children healthy," said one senior U.S. intelligence official. "He sets up clinics throughout Pakistan to inoculate children. We offered him money to set up an inoculation clinic in Abbottabad, not a fake one, but a real inoculation clinic. The money we paid him was put back into his program. He had no idea why we were interested."
A Senate panel voted to cut $33 million in aid to Pakistan in retaliation, a million for every year of the doctor's sentence. Senator John McCain called his work for the CIA "the furthest thing from treason."
On the Friday after the raid, Obama flew to Fort Campbell, Kentucky, to meet with the SEAL team and chopper pilots. Initially, the president asked to meet with the SEALs, and McRaven suggested that if he traveled to Campbell he could also thank the Night Stalker pilots based there, whose unit had not received the same recognition as the mission's shooters.
"We can bring all the players to Fort Campbell," the admiral told Donilon, and suggested that in addition the president could then also meet with the 101st Airborne Division, which had just returned from a deployment to Afghanistan. So Obama attended four events there that day, ending it with a speech to more than two thousand soldiers.
The first event was with the SEAL team and pilots from the actual mission. They assembled in a drab classroom on the base. Obama was struck by how "ordinary" the group was. With only one or two exceptions, the men did not resemble the bulked-up heroes of Hollywood action films, but a group of fit-looking men who ranged in age from their late twenties to early forties. There were some with gray hair. Dressed differently, he thought, they could have been bankers or lawyers. It wasn't their physical skills that distinguished them, he realized, it was their hard-earned experience and wisdom.
In the front of the classroom was a model of the compound. McRaven had said they would walk the president through the mission in detail. They would tell him everything, except which of them had shot bin Laden. That secret would stay with the team. The president did not ask, and the team did not offer.
Then the helicopter pilot who had so skillfully crashed his Black Hawk inside the compound stood up to speak. He was a tall, thin man with dark hair, who appeared unused to speaking before a group, especially one that included the president of the United States. He described exactly what had happened with his chopper, and how deliberate his crash had been. He explained that once he realized it was going down he maneuvered it to catch the tail on the wall so that it would land upright.
"Was the weather a factor?" Obama asked.
"Yes," the pilot said. The air had been warmer and less dense than the mission plan had anticipated, and then he explained in detail the aerodynamics that brought the Black Hawk down.
When he was finished the SEAL team commander spoke. He was dead serious and perfectly at ease addressing the group. He began by thanking the chopper pilot. "I am here today," he said, "because of the amazing work that this guy did." He then gave a long account of exactly how their successful mission had been "ten years in the making." The capability he and the other men in the classroom represented had been honed over all those years of combat, he said. Their skills and tactics had been purchased with the lives of many men who had served with them. He mentioned the operating bases in Afghanistan that were named in honor of these men. Every one of them, along with everyone else they had served with over the years, was, in effect, a member of the team. Then he explained how the raid's success had depended on every member of the team present in the room, and gave examples. He cited the skill of the pilot setting the falling chopper down upright. He cited the middle-aged translator who was able to turn away the curious people outside the compound.
"I don't know what we would have done if all those people had just started rushing the compound," he said.
He cited others. He even mentioned Cairo, the dog.
"You had a dog?" the president asked, surprised.
"Yes, sir, we always have a dog with us," the commander said.
"Well," said Obama, "I would like to meet that dog."
"Well, Mr. President, then I would advise you to bring treats," said the commander sternly.
The men in the room laughed.
The commander then walked the president through details of the raid. When he made reference to some of the errors and controversy in the press about the details, Obama dismissed them.
"Don't worry about it," said the president. "That's just Washington, that's just media, that's just noise."
Again, the men laughed.
The commander described how going through the house and encountering bin Laden had happened quickly and without complication, from his perspective. He said he and the men had been surprised by how much potentially valuable material was upstairs, and how they had just begun rapidly stuffing it into bags. Perhaps the most complicated part of the mission, he said, had been herding the wives and children to a far corner of the compound while the downed chopper was rigged with explosives, making sure that no one was hurt when they blew it up.
When the commander finished, the president stood and thanked them. He described how, among his advisers, there had been a wide range of estimates about whether bin Laden was in the compound.
"But early on in this process I came to terms with the fact that there was always going to be a fifty-fifty case on the intelligence side," he said. "I made the decision I did because I had one hundred percent confidence in your capability." He called them "the finest small fighting force in the history of the world."
Rhodes looked around the room and thought that the claim, while extreme, might actually be true. Here was the cream of JSOC, handpicked for this mission. Given the previous ten years of constant fighting, it was not likely there had ever been such a group of experienced assaulters, at least not in modern times. The president had earlier presented McRaven with a gift, a gold-plated tape measure, because he had not had one the night he tried to measure bin Laden's body. Now he presented the team with a Presidential Unit Citation, the highest honor the nation bestows on an entire military group. He then shook every hand in the room. He was startled and moved when the team presented him with a gift, a flag they had taken on the mission and had framed, signed on the back by all the team members. He hung it in his residence on the second floor of the White House.
When I spoke with the president in the Oval Office, he reflected on how drones represented the most remarkable new tool he had in fighting al Qaeda, and how the nature of drone warfare posed unique dangers for someone in his position.
"I think creating a legal structure, processes, with oversight checks on how we use unmanned weapons is going to be a challenge for me and for my successors for some time to come—partly because that technology may evolve fairly rapidly for other countries as well, and there's a remoteness to it that makes it tempting to think that somehow we can, without any mess on our hands, solve vexing security problems."
But nearly as remarkable, he said, was the evolution of small, highly skilled teams of warriors like those SEALs.
"I think with Special Forces, the dangers [of using them too liberally] are smaller because the human element is still there. Those are still somebody's dad, somebody's husband, somebody's son. When you send them in, you know they may not come back. And for me at least, as commander in chief, I don't think about that any more casually than I do when I'm sending some green kid off to Kandahar. I think there's just a solemnity and caution that that instills in me that probably won't go away. I do think that just from a broader military strategy perspective, that we can't overstate what Special Forces can do. Special Forces are well designed to deal with very specific targets in difficult terrain and oftentimes can prevent us from making the bigger strategic mistakes of sending forces in, with big footprints and so forth. And so when you're talking about dealing with terrorist networks in failed states, or states that don't have capacity, you can see that as actually being less intrusive, less dangerous, less problematic for the country involved.
"But ultimately, none of this stuff works if we're not partnering effectively with other countries, if we're not engaging in smart diplomacy, if we're not trying to change our image in the Muslim world to reduce recruits [to extremism]. It's not an end-all, be-all. I'm sure glad we have it, though."
Taken together, these capabilities, this weapon forged to fight the latest kind of war, has all but done the job. I asked what the impact of bin Laden's death had been on al Qaeda.
"It was what we anticipated," he said. "They are without focus, without effective leadership. And when you combine that with the degradation of their operational personnel, they're on the way to strategic defeat. But again, you can't overstate the importance of these other elements of American power, because even before bin Laden was killed, we had already seen the operational capacity of al Qaeda shift to AQAP [al Qaeda in the Arabian Peninsula] and Yemen. We had already seen al Qaeda metastasize into al Qaeda in Maghreb. And so the need for vigilance and stick-to-it-ness is critical.
"And what we've also seen is the capacity of lone-wolf terrorists to do damage—not the kind of damage we saw on 9/11, but damage that is still obviously painful, and we've got to do something about. So it [killing bin Laden] didn't solve all our problems, and we didn't expect it to. But it was a big piece of business. And I'll always be grateful for both the intelligence and the military personnel who were involved in it. They deserve all the credit."
In the days after the raid, an album of photographs was delivered to the White House, a series of shots of the dead bin Laden. There would be much discussion that week about whether these photos should be made public, as proof of death, but the president had firmly decided that they would not. The decision was made easier because no one disputed the fact of bin Laden's death. America was not, the president said, going to "spike the football."
As the White House had worked that Sunday night to get the message out, stumbling on the presentation but basking in the country's exhilarated response, Admiral McRaven's men were, in the early hours of Monday morning, at work preparing for the disposal of the Sheik's body.
After much discussion and advice, it had been decided that the best option would be burial at sea. That way there would be no shrine for the martyr's misguided followers. So the body was washed, photographed from every conceivable angle, and then flown on a V-22 Osprey to the aircraft carrier USS Carl Vinson cruising in the North Arabian Sea.
As a formality, the State Department contacted Saudi Arabia's government and offered to deliver the body to his home country, but bin Laden was as unwanted there in death as he had been in life. Told that the alternative was burial at sea, the Saudi official said, "We like your plan."
Procedures for a simple Muslim burial were performed on the carrier. The body was wrapped in a white shroud with weights to sink it.
The last sequence of color photos in the death album were not grotesque. They were strangely moving. A navy photographer recorded the burial in full sunlight Monday morning, May 2. One frame shows the body wrapped in the weighted white shroud. The next shows it diagonal on a flat board, feet overboard. In the next frame the body is hitting the water with a small splash. In the next it is visible just below the surface, a ghostly torpedo descending. In the next shot there are only circular ripples on the blue surface. In the final frame the waters are calm.
The mortal remains of Osama bin Laden were gone for good.
Acknowledgments
and Notes
On the theory that Osama bin Laden's command of his native language was comparable to the average English speaker's mastery of his native tongue, I have taken the liberty of here and there smoothing out the clumsy phrases in the translation of bin Laden's documents by the CIA. The official translations can be found at the Web site of West Point's Combating Terrorism Center: www.ctc.usma.edu.
It has been my practice to compile detailed source notes for my books, but in this case the number of those who did not wish to have specific information attributed to them directly, even when the source seems obvious, would have made the exercise more frustrating than helpful.
This work has been informed by two excellent articles, Nicholas Schmidle's "Getting Bin Laden" (The New Yorker, 8/8/2011), and (in portions of Chapter Four) Shane Harris's "Killer App" (The Washingtonian, 1/31/2012). Anyone who writes about Osama bin Laden is indebted to Lawrence Wright's The Looming Tower (Knopf, 2006), and to the superb reporting of Peter Bergen, who over the last ten years made himself the foremost journalistic authority on the man. This book was particularly informed by Bergen's oral history, The Osama bin Laden I Know (Free Press, 2006), and by his Manhunt (Crown Publishers, 2011). In the latter book, Bergen recounts some of the same scenes I have described here, but those passages in this book, like the rest of it, are based entirely on my own reporting and interviewing—in some cases with the same participants.
I would like to especially thank my son Aaron, my cousin David Keane, and their company, Wild Eyes Productions, for help interviewing. I would also like to particularly thank Ben Rhodes, Jay Carney, Dave Moniz, and Preston Golson for helping me set up interviews, and also those at the CIA and in the JSOC who agreed to be interviewed but asked not to be named.
The others I can thank are listed below:
Samira Abdullah Mouhey el-Dein Azzam, Huthaifa Azzam, Tony Blinken, John Brennan, James Clark, Faheem Dashty, Thomas Donilon, Michèle Flournoy, Larry James, Peter Jouvenal, Habibullah Khan, Hamid Mir, Michael Morell, Asad Munir, Barack Obama, William Ostlund, David Petraeus, Samantha Power, Stephen Preston, Matt Flavin, Guy Filippelli, James Poss, Denis McDonough, Nick Rasmussen, Michael Scheuer, Gary Schroen, Kalev Sepp, Michael Sheehan, Michael Vickers, Jamal Ismail, and Ahmad Zaidan.
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 9,020
|
\section{Introduction}
A univariate polynomial with real coefficients is called {\em real-rooted} if
all of its roots are real. Multivariate generalizations of this concept, known
as {\em hyperbolic} and {\em real stable} polynomials, were defined in the 50's
and in the 80's in the context of Partial Differential Equations and Control
Theory, respectively\footnote{See \cite{pemantle} for a more detailed history.}, and have
since made contact with several areas of mathematics.
In particular, a polynomial $p\in \mathbb{R}[x_1,\ldots,x_n]$ is called {\em real stable} if it
has no zeros with all coordinates in the open upper half of the complex plane.
These polynomials have played a central role in several
recent advances in theoretical computer science and combinatorics --- for
instance, \cite{ao, if2, if1, tsp, bbl}. Each of these works relies in a
critical way on (1) understanding which polynomials are real stable (2)
understanding which linear operators {\em preserve} real-rootedness and real
stability. Motivated by (1) and (2), this paper studies the following two
fundamental algorithmic problems:
\begin{quote}{\bf Problem 1.} Given a bivariate polynomial\footnote{We use
$\mathbb R_n[x_1,\ldots,x_k]$ to denote the vector space of real polynomials in $x_1,\ldots,x_k$ of degree at most $n$ in each
variable. } $p\in \mathbb R_n[x,y]$, is $p$ real stable?\end{quote}
\begin{quote}{\bf Problem 2.} Given a linear operator $T:\mathbb R_n[x]\rightarrow
\mathbb R_m[x]$, does $T$ preserve real-rootedness?\end{quote}
Problem 1 was solved in the univariate case by C. Sturm in 1835 \cite{sturm},
who described a now well-known method that can be turned into a strongly
polynomial quadratic time algorithm given the coefficients of $p$
\cite{basu}. However, we are unaware of any algorithm (polynomial time or not)
for the bivariate case, or for Problem 2.
The main result of this paper is a strongly polynomial time algorithm that
solves Problem 1.
\begin{theorem}[Main]\label{thm:main} Given the coefficients of a bivariate polynomial $p\in
\mathbb R_n[x,y]$, there is a deterministic algorithm which decides whether or
not $p$ is real stable in at most ${O}(n^5)$ arithmetic operations, assuming exact
arithmetic. \end{theorem}
Part of the motivation for solving Problem 1 is the following theorem of Borcea
and Branden, which shows that Problem 2 can be reduced to Problem 1.
\begin{theorem}[Borcea-Branden \cite{bb1}] For every linear transformation
$T:\mathbb R_n[x]\rightarrow \mathbb R_m[x]$, there is a bivariate polynomial $p\in
\mathbb R_{\max(n,m)}[x,y]$ such that $T$ preserves real-rootedness if and only if $p$ is
real stable. Moreover, the coefficients of $p$ can be computed from the
matrix of $T$ in linear time.\end{theorem}
Thus, our main theorem immediately implies a solution to Problem 2 as well.
To give the reader a feel for the objects at hand, we remark that the set of
real stable polynomials in any number of variables is a {nonconvex} set with
nonempty interior \cite{nuij}. In the univariate case, the interior of the set
of real-rooted polynomials simply corresponds to polynomials with distinct
roots, and its boundary contains polynomials which have roots with multiplicity
greater than one. With regards to Problem 2, the prototypical example of an
operator which preserves real rootedness is differentiation. Recent applications
such as \cite{if4} rely on finding more elaborate differential operators with
this property.
We now describe the main ideas in our algorithm. It turns out that testing
bivariate real stability is equivalent to testing whether a certain {\em two
parameter} family of polynomials is real rooted. It is not clear how to check
this continuum of real-rootedness statements in polynomial, or even in
exponential time. To circumvent this, we use a deep convexity result from the
theory of hyperbolic polynomials to reduce the two parameter family to a one
parameter family of degree $n$ polynomials, whose coefficients are themselves
polynomials of degree $n$ in the parameter. We then use a characterization of
real-rootedness as postive semidefiniteness of certain moment matrices to
further reduce this to checking that a finite number of univariate polynomials are {\em
nonnegative} an interval. Finally, we solve each instance of the nonnegativity
problem using Sturm sequences and a bit of algebra.
The set of polynomials nonnegative on an interval forms a closed convex cone,
so the last step of our algorithm may be viewed as a strongly polynomial time membership
oracle for this cone. We would not be surprised if such a result is
already known (at least as folklore) but we were unable to find a concrete
reference in the literature, so this component of our method may be of independent interest.
We see this result as being both mathematically fundamental, as well as useful
for researchers who work with stable polyomials, particularly since many of
their known applications so far (e.g.\cite{if2}) put special emphasis on properties
of bivariate restrictions. More speculatively, it is possible that being able to
test membership in the set of real stable polynomials is a step towards being
able to optimize over them.
\subsection{Related Work}
The paper \cite{henrion} studied the problem of testing whether a bivariate polynomial is {\em real zero} (a special case of real stability). It reduced that problem to testing PSDness of a one-parameter family of matrices which it then suggested could be solved using semidefinite programming, but without quite proving a theorem to that effect. This work is partly inspired by ideas in \cite{henrion}.
The paper \cite{kummer} gives semidefinite programming based algorithms that can test whether certain restricted classes of {\em multiaffine} polynomials are real stable (in more than $2$ variables).
The problem of certifying that a univariate polynomial is nonnegative is typically stated (for instance, in lecture notes) as being the solution to a semidefinite program. If one were able to work out the appropriate error to which the SDP has to be solved, this could give a weakly polynomial time algorithm for nonnegativity, which we suspect must be known as folklore. The paper \cite{mac2} analyzes a semidefinite programming based algorithm in the special case when the polynomial is nondegenerate in an appropriate sense.
\subsection{Acknowledgments}
We thank Eric Hallman, Jonathan Leake, and Bernd Sturmfels for valuable discussions. We also thank Didier Henrion for valuable correspondence regarding other algorthimic approaches to these problems.
\section{Real Stable and Hyperbolic Polynomials}
We recall below the definition of a real stable polynomial in an arbitrary number of variables.
\begin{definition}
A polynomial $p\in \mathbb R[x_1,\ldots,x_n]$ is called {\em real stable} if it is identically zero\footnote{Some works (e.g. \cite{bb1}) consider
only nonzero polynomials to be stable, while others \cite{wagner} include the zero polynomial. We find the latter convention more convenient.} or if $p(z_1,\ldots,z_n)\neq 0$ whenever
$\Im(z_i)>0$ for all $i=1,\ldots,n$. Equivalently, $p$ is real stable if and only if the univariate restrictions
$$ t \mapsto p(te_1+x_1,te_2+x_2,\ldots,te_n+x_n)$$
are real rooted whenever $e_1,\ldots,e_n>0$ and $x_1,\ldots,x_n\in\mathbb R$.\end{definition}
The equivalence between the two formulations above is an easy exercise. Note that a univariate polynomial is
real stable if and only if it is real rooted. Note that we consider the
zero polynomial to be real-rooted.
We will frequently use the elementary fact that a limit of real-rooted polynomials is real-rooted, which follows from Hurwitz's theorem (see, e.g. \cite[Sec. 2]{wagner}), or from the argument principle.
Real Stable polynomials are closely related to the following more general class of polynomials.
\begin{definition} A homogeneous polynomial $p\in \mathbb R[x_1,\ldots,x_n]$ is called {\em hyperbolic} with respect to
a point $e=(e_1,\ldots,e_n)\in\mathbb R^n$ if $p(e)>0$ and the univariate restrictions
$$t\mapsto p(te+x)$$
are real rooted for all $x\in\mathbb R^n$. The connected component of $\{x\in\mathbb R^n:p(x)\neq 0\}$ containing $e$ is called the {\em hyperbolicity cone} of $p$ with respect to $e$, and will be denoted $K(p,e)$.
\end{definition}
Perhaps the most familiar example of a hyperbolic polynomial is the determinant of a symmetric matrix:
$$ X\mapsto \det(X)$$
for real symmetric $X$, which is hyperbolic with respect to the identity matrix since the characteristic polynomial of a symmetric matrix is always real rooted. The corresponding hyperbolicity cone is the cone of positive semidefinite matrices.
The most important theorem regarding hyperbolic polynomials says that hyperbolicity cones are {\em always} convex, and that hyperbolicity at one point in the cone implies hyperbolicity at every other point. Thus, hyperbolic polynomials and hyperbolicity cones may be viewed as generalizing determinants and PSD cones.
\begin{theorem}[Garding \cite{garding}]\label{thm:garding} If $p\in \mathbb R[x_1,\ldots,x_n]$ is hyperbolic with respect to $e\in\mathbb R^n$ then:
\begin{enumerate}
\item $K(p,e)$ is an open convex cone.
\item $p$ is hyperbolic with respect to every point $y\in K(p,e)$.
\end{enumerate}
\end{theorem}
The reason hyperbolic polynomials are relevant in this work is that real stable polynomials are essentially a special case of them.
\begin{theorem}[Borcea-Branden \cite{bb1}] \label{thm:hyperbolic} A nonzero bivariate polynomial $p(x,y)$ of total degree at most $m$ is real stable if and only if its homogenization
$$ p_H(x,y,z) := z^mp(x/z,y/z)$$
is hyperbolic with respect to every point in
$$ \mathbb R_{>0}^2\times \{0\} = \{(e_1,e_2,0):e_1,e_2>0\}.$$
\end{theorem}
Thus, real stable polynomials enjoy the strong structural properties guaranteed
by \prettyref{thm:garding} as well, and we exploit these in our algorithm.
\section{Parameter Reduction via Hyperbolicity}
In this section we use the properties of hyperbolic polynomials to reduce real stability of a bivariate polynomial to testing real rootedness of a one parameter family of polynomials.
\begin{theorem}[Reduction to One-Parameter Family]\label{thm:hypred} A nonzero bivarite polynomial $p\in \mathbb R_n[x,y]$ ofis real stable if and only if following two conditions hold:
\begin{enumerate}
\item The one-parameter family of univariate polynomials $q_\gamma \in \mathbb R[t]$ given by,
\[ q_\gamma(t) = p(\gamma +t,t) \in \mathbb R[t] \]
are real rooted for all $\gamma \in \mathbb R$.
\item The univariate polynomial
\[ t\mapsto p_{H}(t,1-t,0) \]
is strictly positive on the interval $
(0,1)$,
\end{enumerate}
\end{theorem}
\begin{proof}
({\it real-stability of $p$} $\implies$ (1) \& (2))
By \prettyref{thm:hyperbolic}, $p_{H}$ is hyperbolic with respect to the positive orthant $\mathbb R^2_{> 0} \times \{ 0 \}$.
Since $(1,1,0) \in \mathbb R^2_{>0} \times \{0\}$, this implies that for all $(x,y,z) \in \mathbb R^3$,
\[ q(t) = p_H(x+t,y+t,z) \]
is real-rooted. Setting $x = \gamma$, $y = 0$ and $z = 1$ we get that $q_{\gamma}(t) = p_{H}(\gamma+t,t,1) = p(\gamma+t,t)$ is real-rooted for all $\gamma \in \mathbb R$ which is condition (1).
Finally, since
\[ \{(t, 1-t, 0) | t \in (0,1)\} \subset \mathbb R^2_{>0} \times \{0\} \,,\]
and $p_H$ is hyperbolic with respect to $\mathbb R^2_{> 0} \times \{0\}$, it follows that $p_H(t,1-t,0) > 0$ for all $t \in (0,1)$.
((1) \& (2) $\implies$ {\it real-stability of $p$})
First, we claim that the polynomial $p_H$ is hyperbolic with respect to $(1,1,0)$. By (2) we have $p_H(1/2,1/2,0)>0$ so homogeneity implies that $p_H(1,1,0)>0$. It remains to show that $q_{x,y,z}(t) = p_H(x+t,y+t,z)$ is real-rooted for all $(x,y,z) \in \mathbb R^3$. First, consider the case of $(x,y,z) \in \mathbb R^3$ with $z \neq 0$.
\begin{align*}
& \forall (x,y,z) \in \mathbb R^3 \text{ with } z \neq 0, p_{H}(x+t,y+t,z) \text{ is real-rooted} \\
& \iff \forall (x,y,z) \in \mathbb R^3 \text{ with } z \neq 0, p_{H}(\frac{x}{z}+\frac{t}{z},\frac{y}{z}+\frac{t}{z},1) \text{ is real-rooted} \\
& \iff \forall (x,y,z) \in \mathbb R^3 \text{ with } z \neq 0, p_{H}(\frac{x}{z}+t,\frac{y}{z}+t,1) \text{ is real-rooted (replacing $t/z$ with $t$)} \\
& \iff \forall (x,y) \in \mathbb R^2, p_{H}(x+t,y+t,1) \text{ is real-rooted} \\
& \iff \forall (x,y) \in \mathbb R^2, p_{H}(x+t,t,1) \text{ is real-rooted (replacing $t$ with $t-y$)} \\
& \iff \forall \gamma \in \mathbb R, p(\gamma+t,t) \text{ is real-rooted} \\
\end{align*}
By Hurwitz's theorem, the limit of any sequence of real-rooted polynomials is real-rooted. Therefore, if $q_{x,y,z}(t)$ is real-rooted for all $(x,y,z) \in \mathbb R^3$ with $z \neq 0$ then $q_{x,y,z}(t)$ is real-rooted for all $(x,y,z) \in \mathbb R^3$.
Given that $p_H$ is hyperbolic with respect to $e = (\frac{1}{2},\frac{1}{2},0)$, its hyperbolicity cone $K(p_H,e)$ is a convex cone containing $(1,1,0)$. Condition (2) implies that the connected component of $\{x| p(x) \neq 0\}$ containing $(1,1,0)$ contains the open line segment from $(1,0,0)$ to $(0,1,0)$. Together, this implies that the positive quadrant $\mathbb R^2 \times \{0\} \subseteq K(p_H,e)$. By \prettyref{thm:hyperbolic}, this implies that $p$ is real-stable.
\end{proof}
Thus, our algorithmic goal is reduced to testing whether a one-parameter family
is real-rooted, and whether a given univariate polynomial is positive on an
interval. We solve these problems in the sequel.
\section{Real-rootedness of one-parameter families}
In this section we present two algorithms for testing real-rootedness of a one-parameter family of
polynomials. Both algorithms reduce this problem to verifying nonnegativity of a finite number of polynomials
on the real line. The first algorithm produces $n$ polynomials of degree roughly
$O(n^3)$, and has the advantage of being very simple, relying only on elementary techniques and standard
algorithms such as fast matrix multiplication and the discrete Fourier transform.
The second algorithm produces $n$ polynomials of degree roughly $O(n^2)$ and
runs significantly faster, but uses somewhat more specialized (but nonetheless classical) machinery from the theory of resultants.
\subsection{A Simple $O(n^{3+\omega})$ Algorithm}
The first algorithm is based on the observation that real-rootedness of a single polynomial is equivalent to
testing positive semidefiniteness of its moment matrix, which in turn is equivalent to testing nonnegativity of the elementary symmetric polynomials of that matrix. In the more general case of a one-parameter family, the latter polynomials turn out to be polynomials of bounded degree in the parameter, and it therefore suffices to verify that these are nonnegative everywhere.
We begin by recalling the Newton Identities, which express the moments of a polynomial in terms of its coefficients.
\begin{lemma}[Newton Identities]\label{lem:newton} If
$$p(x)=\sum_{k=0}^n (-1)^kx^{n-k}c_k = c_0\prod_{i=1}^n(x-x_i)\in \mathbb R[x]$$
with $c_0\neq 0$ is a univariate polynomial with roots $x_1,\ldots,x_n$, then the
moments
$$ m_k:=\sum_{i=1}^n x_i^k$$
satisfy the recurrence:
$$ m_k = (-1)^{k-1}\frac{c_k}{c_0} +
\sum_{i=1}^{k-1}(-1)^{k-1+i}\frac{c_{k-i}}{c_0}m_i\qquad {0\le k\le n},$$
$$ m_k = \sum_{k-n}^{k-1}(-1)^{k-1+i}\frac{c_{k-i}}{c_0}m_i\qquad {k>n},$$
$$ m_0=n.$$
\end{lemma}
The following consequences of \prettyref{lem:newton} will be relevant to analyzing our algorithm.
\begin{corollary}\label{cor:newton}
\begin{enumerate}
\item The moments $m_0,\ldots,m_{2n-2}$ of a degree $n$ polynomial can be computed from its
coefficients in $O(n^2)$ arithmetic operations.
\item Suppose $p(x) = \sum_{k=0}^n (-1)^kx^{n-k}c_k(\gamma)$ is a polynomial whose
coefficients are polynomials $c_0(\gamma),\ldots,c_n(\gamma)\in \mathbb R_d[\gamma]$ in
a parameter $\gamma$. Then the moments of $p$ are given by $$m_k(\gamma)=r_k(\gamma)/c_0(\gamma)^k,$$ for some polynomials
$r_k\in\mathbb R_{dk}[\gamma]$.\end{enumerate}
\end{corollary}
\begin{proof} The first claim follows because each application of the recurrence
requires at most $n$ arithmetic operations. For the second claim, observe that
each ratio $c_{k-i}(\gamma)/c_0(\gamma)$ is a rational function with a numerator
of degree at most $d$ and denominator $c_0(\gamma)$. Thus, each application of the recurrence
increases the degree of the numerator by at most $d$ and introduces an
additional $c_0$ in the denominator.
\end{proof}
As a subroutine, we will also need the following standard result in linear algebra.
\begin{theorem}[Keller-Gehrig \cite{keller1985fast}] \label{thm:keller} Given an $n\times n$ complex matrix $A$, there is an algorithm which computes the characteristic polynomial of $A$ in time $O(n^\omega \log n)$.\end{theorem}
We now specify the algorithm and prove its correctness.
\begin{theorem} A polynomial $p_\gamma(x)=\sum_{k=0}^n (-1)^k
x^{n-k}c_k(\gamma)$ is real-rooted for all
$\gamma\in \mathbb R$ if and only if the polynomials $q_0,\ldots,q_n$ output by {\bf SimpleRR} are nonnegative on $\mathbb R$. Moreover, {\bf SimpleRR} runs in time $\tilde{O}(dn^{2+\omega}+d^2n^3)$.
\end{theorem}
\begin{proof} We first show correctness. Let $m_k(p)$ denote the $k^{th}$ moment
of the roots of a polynomial. By Sylvester's theorem \cite[Theorem 4.58]{basu}, a real polynomial
$$p_\gamma(x)=\sum_{k=0}^n (-1)^k x^{n-k}c_k(\gamma)$$
is real-rooted if and only if the corresponding moment matrix
$$ M(\gamma)_{k,l} := m_{k+l-2}(p_\gamma)$$
is positive semidefinite. Since $\nu$ is even and $c_0$ has real coefficients, we have for every $\gamma\in\mathbb R$ that is not a root of $c_0$:
$$ M(\gamma)\succeq 0 \iff c_0(\gamma)^\nu M(\gamma) = H(\gamma) \succeq 0.$$
Since $c_0$ has only finitely many roots and a limit of PSD matrices is PSD, we conclude that
$$ M(\gamma)\succeq 0 \quad\forall \gamma\in\mathbb R \iff H(\gamma)\succeq 0 \forall \gamma\in \mathbb R.$$
Note that by \prettyref{cor:newton} the entries of $H(\gamma)$ are polynomials of degree at most
$d(\nu+2n-2)$ in $\gamma$.
We now recall a well-known\footnote{Here is a short
proof: $A$ is PSD iff $\det(zI-A)$ has only nonnegative roots. Since $A$
is symmetric we know the roots are real. We now observe that a
real-rooted polynomial has nonnegative roots if and only if its
coefficients alternate in sign.} (e.g., \cite{hj}) characterization of positive
semidefiniteness as a semialgebraic condition: an $n\times n$ real symmetric matrix $A$ is PSD if and only if
$e_k(A)\ge 0$ for all $k=1,\ldots, n$, where
$$e_k(A)=\sum_{|S|=k}\det(A_{S,S})$$
is the sum of all $k\times k$ principal minors of $A$. Thus, $p_\gamma$ is
real-rooted for all $\gamma\in\mathbb R$ if and only if the polynomials
$$q_k(\gamma):= e_k(H(\gamma))$$
for $k=1,\ldots,n$ are nonnegative on $\mathbb R$.
Since each $q_k$ is a sum of determinants of order at most $n$ in $H(\gamma)$ it has degree at
most $n$ in the entries of $H(\gamma)$, and we conclude that $q_1,\ldots,q_n\in \mathbb R_N[\gamma]$. Thus,
the $q_k$ can be recovered by interpolating them at the $N^{th}$ roots
of unity. Since the $k^{th}$ elementary symmetric function of a matrix is the
coefficient of $z^{n-k}$ in its characteristic polynomial, this is precisely
what is achieved in Step 2.
For the complexity analysis, it is clear that Step 1 takes $O(dn^2)$ time.
Constructing each Hankel matrix $H(s_i)$ takes time $O(dn+n^2)$ by
\prettyref{cor:newton}, and computing its elementary symmetric functions via the
characteristic polynomial takes time $O(n^\omega\log n)$, according to \prettyref{thm:keller}.
Thus, the total time for each iteration is $O(n^\omega\log n+dn)$, so the time
for all iterations is $O(dn^{2+\omega}\log n+d^2n^3).$ The final step requires
$O(N\log N)$ time for each $e_k$ using fast polynomial interpolation via the
discrete Fourier transform, for a
total of $O(dn^3\log n)$. Thus, the total running time is
$\tilde{O}(dn^{2+\omega}+d^2n^3),$ suppressing logarithmic factors.
\end{proof}
\begin{center}
\fbox{\begin{minipage}{\textwidth}
\noindent {\bf Algorithm SimpleRR}\\
\textit{Input:} $(n+1)$ univariate polynomials $c_0,\ldots,c_n\in \mathbb R_d[\gamma]$ with $c_0\not\equiv 0$.\\
\textit{Output:} $n$ univariate polynomials $q_1,\ldots,q_n\in \mathbb R_{3n^2d}[\gamma]$\\
\begin{enumerate}
\item Let $\nu$ be the first even integer greater than or equal to $n$
and let $N=nd(2n-2+\nu)=O(dn^2)$.
Let $s_1,\ldots,s_N\in \mathbb C$ be the $N^{th}$ roots of unity.
\item For each $i=1,\ldots N$:
\begin{itemize}
\item Compute the
$n\times n$ Hankel matrix $H(s_i)$ with
entries
$$H(s_i)_{k,l} := c_0(s_i)^\nu m_{k+l-2}(p_{s_i}),$$
by applying the Newton identities (\prettyref{lem:newton}).
\item Compute the characteristic polynomial
$$ \det(zI-H(s_i)) = \sum_{k=0}^n
(-1)^kz^{n-k}e_k(H(s_i))$$
using the Keller-Gehrig algorithm (\prettyref{thm:keller}).
\end{itemize}
\item For each $k=1,\ldots, n$: Use the points
$e_k(H(s_1)),\ldots,e_k(H(s_N))$ to interpolate the coefficients
of the polynomial $$q_k(\gamma):=e_k(H(\gamma)).$$
\end{enumerate}
Output $q_1,\ldots,q_n$.\\
\end{minipage}}
\end{center}
\subsection{A Faster $O(n^4)$ Algorithm Using Subresultants}
The algorithm of the previous section is based on the generic fact that a matrix
is PSD if and only if its elementary symmetric polynomials are
nonnegative. In this section we exploit the fact that our matrices have a
special structure -- namely, they are moment matrices -- to find a different
finite set of polynomials whose nonnegativity suffices to certify their PSDness.
These polynomials are called {\em subdiscriminants}, and turn out to be related to
another class of polynomials called {\em subresultants}, for which there are
known fast symbolic algorithms.
Let $M_p$ denote the $n\times n$ moment matrix corresponding to a polynomial $p$
of degree $n$. Recall that $M_p = VV^T$ where $V$ is the Vandermonde matrix formed
by the roots of $p$. Let $(M_p)_i$ denote
the leading principal $i\times i$ minor of $M_p$. We define
subdiscriminants of a polynomial, and then show their relation to the leading
principal minors of the moment matrix. For the remainder of this section it will
be more convenient to use the notation
$$p(x) = \sum_{k=0}^n a_k x^k$$
for the coefficients of a polynomial,
with roots $x_1, \ldots, x_n$ and $a_n \neq 0$.
\begin{definition} The $k^{th}$ {\em subdiscriminant} of a polynomial $p$ is defined
as
$$\mathtt{sDisc}_k(p) = a_n^{2k - 2}\sum_{S \subset \{1, \ldots, n\}, |S| = k} \prod_{\{i,j\} \subset S} (x_i - x_j)^2$$
\end{definition}
\begin{lemma} The leading principal minors of the moment matrix are multiples of the subdiscriminants,
$$(M_p)_i = a_n^{2-2k} \mathtt{sDisc}_k(p) = \sum_{S \subset \{1, \ldots, n\}, |S| = k} \prod_{\{i,j\} \subset S} (x_i - x_j)^2$$
\end{lemma}
\begin{proof}
Let $$V_i = \begin{bmatrix} 1 & \ldots & 1 \\ x_1 & \ldots & x_n \\ \vdots &
\vdots & \vdots \\ x^{i-1}_1 & \ldots & x^{i-1}_n \\ \end{bmatrix}.$$
Then $(M_p)_i = \det(V_i V_i^T)$. By Cauchy-Binet, this determinant is
the sum over the determinants of all submatrices of size $i \times i$. These
submatrices are exactly the Vandermonde matrices formed by subsets of the roots
of size $i$. Then the identity follows from the formula for the determinant of a
Vandermonde matrix.
\end{proof}
Equipped with this we can provide an alternative characterization of real
rootedness. Define the sign of a number, denoted $\mathtt{sgn}$ to be $+1$ if it is
positive, $-1$ if it is negative, and $0$ otherwise.
\begin{lemma} \label{lem:discsign}
$p$ is real-rooted if and only if the sequence $\mathtt{sgn}(\mathtt{sDisc}_1(p)),
\ldots, \mathtt{sgn}(\mathtt{sDisc}_n(p))$ is first $1$'s and then $0$'s.
\end{lemma}
\begin{proof}
Note that since $a_n\neq 0$ we have $\mathtt{sgn}(Disc_k) = \mathtt{sgn}(a_n^{2(1-k)}Disc_k) = \mathtt{sgn}((M_p)_i) $.
It is clear from the definition of the subdiscriminants that if $p$ is real-rooted with $k$ distinct roots then $\mathtt{sDisc}_i$ is positive if $i \leq k$ and $\mathtt{sDisc}_i = 0$ if $i > k$.
Conversely, given a polynomial $p$ with $k$ distinct roots, then if $i > k$ we have all the minors of size $i$ in $V_i^T$ contain two identical rows, and hence $V_i^T$ does not have full rank, so $V_i V_i^T$ is singular.
Let $x_1, x_2, \ldots, x_j$ be the real distinct roots of $p$ and $y_1, \bar{y_1}, \ldots, y_l, \bar{y_l}$ be the distinct complex conjugate pairs of $p$ where $j + l = k$. Suppose the multiplicities of $x_i$ are $n_i$ and $y_i$ are $m_i$.
Then the top left $k \times k$ submatrix of $M_p$ is
$$ = \sum_i n_i \begin{bmatrix} 1 \\ x_i \\ \vdots \\ x_i^{k-1} \end{bmatrix} \begin{bmatrix} 1 & x_i & \cdots & x_i^{k-1} \end{bmatrix} + \sum_i m_i\begin{bmatrix} 1 \\ y_i \\ \vdots \\ y_i^{k-1} \end{bmatrix} \begin{bmatrix} 1 & y_i & \cdots & y_i^{k-1} \end{bmatrix} + \begin{bmatrix} 1 \\ \bar{y_i} \\ \vdots \\ \bar{y_i}^{k-1} \end{bmatrix} \begin{bmatrix} 1 & \bar{y_i} & \cdots & \bar{y_i}^{k-1} \end{bmatrix}$$
$$ = \sum_i n_i \begin{bmatrix} 1 \\ x_i \\ \vdots \\ x_i^{k-1} \end{bmatrix} \begin{bmatrix} 1 & x_i & \cdots & x_i^{k-1} \end{bmatrix} + \sum_i m_i \begin{bmatrix} 1 & 1 \\ \Re(y_i) & \Im(y_i) \\ \vdots & \vdots \\ \Re(y_i^{k-1}) & \Im(y_i^{k-1}) \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & -1 \\ \end{bmatrix} \begin{bmatrix} 1 & 1 \\ \Re(y_i) & \Im(y_i) \\ \vdots & \vdots \\ \Re(y_i^{k-1}) & \Im(y_i^{k-1}) \end{bmatrix}^T$$
This shows that this submatrix is positive definite if and only if the distinct
roots are all real. Note that by Sylvester's criterion
this submatrix is positive definite if and only if all the leading principal minors of size $\leq k$ are positive.
\end{proof}
We now obtain a formula for the subdiscriminants of a polynomial in terms of its
coefficients. The connection is provided by another family of polynomials called the {\em
subresultants}.
\begin{definition}
Let $p = \sum_{k=0}^n a_k x^k$ where $a_n \neq 0$. The {\em $k$th
subresultant} of $p$, denoted $\mathtt{sRes}_k(p,p')$ is the determinant of the submatrix obtained from the first $2 n - 1 - 2 k$ columns of the following $(2n - 1 - 2 k) \times (2n - 1 - k)$ matrix:
$$\begin{bmatrix} a_n & \cdots & \cdots & \cdots & \cdots & a_0 & 0 & 0 \\ 0 & \ddots & & & & & \ddots & 0 \\
\vdots & \ddots & a_n & \cdots & \cdots & \cdots & \cdots & a_0 \\ \vdots & & 0 & n a_{n} & \cdots & \cdots & \cdots & a_1 \\
\vdots & \iddots & \iddots & & & & \iddots & 0 \\
0 & \iddots & & & & \iddots & \iddots & \vdots \\
n a_{n} & \cdots & \cdots & \cdots & a_1 & 0 & \cdots & 0 \\
\end{bmatrix}$$
\end{definition}
We will use two properties of subresultants. The first is a good bound on their
degree as a consequence of the determinantal formula above. The second is quick algorithm to compute
them. We refer the reader to \cite{basu} for a more detailed discussion of
subresultants.
In this paper we will only be interested in subresultants of a polynomial with its derivative
We are interested in this because of its relation to our leading principal minors:
\begin{lemma}[\cite{basu} Proposition 4.27]
Let $p(x) = \sum_{k=0}^n a_k x^k$ where $a_n \neq 0$
$$\mathtt{sRes}_k(p,p') = a_n \mathtt{sDisc}_{n-k}(p) $$
\end{lemma}
\begin{corollary}
Since the first column of the determinant used to define the subresultant is divisible by $a_n$, we get $\mathtt{sDisc}_k(p)$ is a polynomial in our coefficients $a_n, \ldots, a_0$ of degree at most $2n$.
\end{corollary}
The benefit of studying the principal minors instead of the coefficients of the
characteristic polynomial for our moment matrix is that we can use an algorithm
from subresultant theory to quickly calculate all the minors at once.
\begin{theorem}[\cite{basu} Algorithm 8.21]
\label{thm:subbres}
There exists an algorithm which, given a polynomial $p$ of degree $n$ returns a
list of all of its subresultants $\mathtt{sRes}_k(p,p')$ for $k=1,\ldots,n$ in $O(n^2)$ time.
\end{theorem}
\begin{remark}
Many computer algebra systems (e.g., Mathematica, Macaulay2) have built-in efficient algorithms to compute subresultants.
\end{remark}
We now combine the above facts to obtain a crisp condition for real-rootedness
of a one-parameter family.
Recall that by \prettyref{thm:hypred}, we are interested in testing when a
family of polynomials $p_\gamma(x)$ are real-rooted for all $\gamma\in \mathbb R$,
where $$p_\gamma(x) = \sum_{k=0}^n a_k(\gamma) x^k$$
with $c_k\in\mathbb R_n[\gamma]$. Let $c_m(\gamma)$ be the highest coefficient that is
not identically zero. We are only interested in the case when $m \geq 2$.
\begin{proposition}
If $p_\gamma(x)=\sum_{k=0}^n x^kc_k(\gamma)$ with $c_k\in\mathbb R_d[\gamma]$,
then $\mathtt{sDisc}_k(p_\gamma)$ is a polynomial in $\gamma$ of degree at most
$2dn$.
\end{proposition}
\begin{proof}
From our previous lemma, we know that $\mathtt{sDisc}_k$ is a polynomial in the
coefficients of $p$ of degree at most $2n$. Since each of these coefficients
$c_k(\gamma)$ is a polynomial in $\gamma$ of degree at most $d$, our result follows.
\end{proof}
We now extend our characterization of real-rootedness in terms of the signs of
the principal minors of a fixed polynomial to a characterization for
coefficients which are polynomials in $\gamma$.
\begin{theorem}
$p_\gamma(x)$ is real-rooted for all $\gamma\in\mathbb R$ if and only if there exists a
$k$ such that $\mathtt{sDisc}_i(p_\gamma)$ is a nonnegative polynomial which is not identically
zero for all $i \leq k$ and $\mathtt{sDisc}_i(p_\gamma)$ is identically zero for $i > k$.
\end{theorem}
\begin{proof}
First suppose that $p_\gamma(x)$ is real rooted for all $\gamma\in\mathbb R$. Observe
that $c_m(\gamma)$ vanishes for at most finitely many points $Z_1$. Moreover,
the degree $m$ discriminant of $p_\gamma$ is a polynomial in $\gamma$, and is zero for at most
finitely many points --- call them $Z_2$. Thus, for
$\gamma\notin Z_1\cup Z_2$, we know that $p_\gamma$ has exactly $m$ distinct real
roots, so by \prettyref{lem:discsign} $\mathtt{sDisc}_i(p_\gamma)$ is strictly positive
for $i\le m$ and zero for $i>m$ on this set. By
continuity this implies that $\mathtt{sDisc}_i(p_\gamma)$ is nonnegative and not
identically zero on $\mathbb R$ for $i\le m$, and $\mathtt{sDisc}_i(p_\gamma)$ is identically zero for
$i>m$, as desired.
To prove the converse, note that for $i \leq k$, $\mathtt{sDisc}_i(p_\gamma(t))$ is not
identically zero, and hence there are finitely many $\gamma$ away from which
$\mathtt{sDisc}_i(p_\gamma)$ is positive for all $i \leq k$, and then all zero. By
\prettyref{lem:discsign} we get that $p_\gamma(x)$ is real rooted for all these
$\gamma$. Since real-rootedness is preserved by taking limits (by Hurwitz's
theorem), we conclude that $p_\gamma(x)$ is real rooted for all $\gamma\in\mathbb R$.
\end{proof}
Combining these observations, and using the $O(n^2)$ time algorithm to compute
the subdiscriminants, we arrive at the following $O(n^4)$ time algorithm for computing all the subdiscriminants.
\begin{center}
\fbox{\begin{minipage}{\textwidth}
\noindent {\bf Algorithm FastRR}\\
\textit{Input:} $(n+1)$ univariate polynomials $c_0,\ldots,c_n\in \mathbb R_d[\gamma]$ with $c_0\not\equiv 0$.\\
\textit{Output:} $n$ univariate polynomials $q_1,\ldots,q_n\in \mathbb R_{2dn}[\gamma]$\\
\begin{enumerate}
\item Find distinct points $\gamma_1, \ldots, \gamma_{2dn}\in$ such that
$c_m(\gamma_i)\neq 0$.
\item For each $\gamma_i$ use the subresultant algorithm (\prettyref{thm:subbres}) to compute all of the
$\mathtt{sRes}_k(p_{\gamma_i})$, with $k=1,\ldots,n$. \\
\item Use the above values to compute $2dn$ different values
$q_k(\gamma_1),\ldots,q_k(\gamma_{2dn})$ for
each of the polynomials
$$q_k(\gamma):= \mathtt{sDisc}_k(p_\gamma) = c_m(\gamma)^{-1}
\mathtt{sRes}_{m-k}(p_\gamma)),$$
$k=1,\ldots,n$.
\item Use fast interpolation to compute the coefficients of
$q_1,\ldots,q_n$.
\end{enumerate}
Output $q_1,\ldots,q_n$.
\end{minipage}}
\end{center}
\begin{theorem}\label{thm:fastrr} {\bf FastRR} runs in $O(n^4)$ time.
\end{theorem}
\begin{proof}
Since $c_n(\gamma)$ is of degree at most $d$ we can test $2dn + d$ points to
find $2dn$ points on which $c_n(\gamma)$ doesnt vanish. Each evaluation takes
$O(d)$ times, so total this takes $O(d^2n)$ time. To compute
$\mathtt{sRes}_k(p_{\gamma_i})$ for each $0 \leq k \leq n-1$ and $1 \leq i \leq 2dn$
takes $O(dn^3)$ time by \prettyref{thm:subbres}. Then to scale all the subresultants,
since we have $O(dn^2)$ data points and have already computed $c_n(\gamma_i)$
takes $O(dn^2)$ time. Finally, since the degrees of the $q_k$ are at most $2dn$,
the total time to interpolate all of them is $O(dn^2\log n)$.
\end{proof}
\section{Univariate Nonnegativity Testing}
In this section, we describe an algorithm to test non-negativity of a
univariate polynomial over the real line.
Let $p \in \mathbb R[x]$ denote a univariate polynomial of degree $d$. The goal of the algorithm is to
test if $p(x) \geq 0$ for all $x \in \mathbb R$. A canonical approach for the problem
would be to use a Sum-of-Squares semidefinite program to express $p$ as a sum of
squares of low-degree polynomials. Unfortunately, the resulting algorithm is
not a symbolic algorithm, i.e., its runtime is not strongly polynomial in the
degree $d$, since semidefinite programming is not known to be strongly
polynomial.
We will now describe a strongly polynomial time algorithm to test non-negativity of the polynomial $p$. Our starting point is an algorithm to count the number of real roots of a polynomial using Sturm sequences. We refer the reader to Basu et al.\xspace \cite{basu} for a detailed presentation of Sturm sequences and algorithms to compute them. For our purposes, we will need the following lemma.
\begin{lemma} \label{lem:sturm}
Given a univariate polynomial $p \in \mathbb R[x]$, the algorithm based on computing Sturm sequences uses $O(\deg(p)^2)$ arithmetic operations to determine the number of real roots of $p$.
\end{lemma}
The polynomial $p$ is positive, i.e., $p(x) > 0$ for all $x \in \mathbb R$, if and only if it has no real roots. Therefore, \prettyref{lem:sturm} yields an algorithm to test positivity using in $O(d^2)$ arithmetic operations. To test non-negativity, the only additional complication stems from the roots of the polynomial $p$. We begin with a simple observation.
\begin{fact} \label{fact:oddmultiplicity}
If $p\in\mathbb R[x]$ is monic then $p(x)\ge 0$ for all $x \in \mathbb R$ if and only if $p$ has no real roots of odd multiplicity.
\end{fact}
\begin{definition}
A square-free decomposition of a polynomial $p \in \mathbb R[x]$ of degree
$d$, is a set of polynomials $\{a_1,\ldots,a_d\} \in \mathbb R[x]$ such that
\[ p(x) = \prod_{i=1}^d a_i(x)^{i} \ ,\]
and each $a_i$ has no roots with multiplicity greater than one. Alternately, for each $i \in [d]$, $a_i(x)^i$ consists of all roots of
$p$ with multiplicity exactly $i$.
\end{definition}
Square-free decompositions can be computed efficiently using gcd
computations. Yun \cite{Yun76} carries out a detailed analysis of
square-free decomposition algorithms. In particular, he shows that an
algorithm due to Musser can be used to compute square-free
decompositions at the cost of constantly many gcd computations.
Now, we are ready to describe an algorithm to test non-negativity.
\begin{center}
\fbox{\begin{minipage}{\textwidth}
{\bf Algorithm Nonnegative}\\
\textit{Input} A monic polynomial $p \in \mathbb R[x]$, $\deg(p) =
d$\\
\textit{Goal} Test if $p(x) \geq 0$ for all $x \in \mathbb R$.
\begin{enumerate}
\item Using Musser's algorithm, compute the square-free decomposition of $p$ given by,
\[ p = \prod_{i \in [d]} a_i^i\]
where $a_i \in \mathbb R[x]$ has no roots with
multiplicity greater than $1$.
\item For each $i \in [\lceil \frac{d}{2} \rceil] $
\begin{itemize}
\item Using Sturm sequences, test if $a_{2i -
1}$ has real roots. If $a_{2i-1}$ has
real roots $p$ is NOT non-negative.
\end{itemize}
\end{enumerate}
\end{minipage}}
\end{center}
\paragraph{Runtime} Let $T_{gcd}(d)$ denote the time-complexity of
computing the gcd of two univariate polynomials of degree $d$.
The runtime of Musser's square-free decomposition
algorithm is within constant factors of $T_{gcd}(d)$.
Let $S_{real}(\ell)$ denote the time-complexity of determining if a degree
$\ell$ polynomial has no real roots.
Observe that
\[ \sum_{i} \deg(a_i) \leq \deg(p) = d\]
Since $S_{real}(\ell)$ is super-linear in $\ell$, we have
$\sum_{i \in [d]} S_{real}(a_i) \leq S_{real}(d) \,.$
The run-time of the algorithm is given by $O(T_{gcd}(d) +
S_{real}(d))$. Using Sturm sequences, $S_{real}(d) = O(d^2)$
elementary operations on real numbers (see \cite{basu}).
Using Euclid's algorithm, $T_{gcd}(d) = O(d^2)$ elemenetary operations
on real numbers. This yields an algorithm for non-negativity that
incurs at most $O(d^2)$ elementary operations.
\section{Conclusion and Discussion}
Finally, we combine the ingredients from sections 3, 4, and 5 to obtain the
proof of our main theorem.
\begin{proof}[Proof of \prettyref{thm:main}] Given the coefficients of $p$, we can
compute the coefficients of the one-parameter family in (1) of
\prettyref{thm:hypred} in time at most $O(n^3)$. By
\prettyref{thm:fastrr}, {\bf FastRR} produces the polynomials
$q_1,\ldots,q_n$ in time $O(n^4)$. We check that some final segment of these polynomials are identically zero by evaluating each one at $O(n^2)$ points. These polynomials have degree
$O(n^2)$, so {\bf Nonnegative} requires time $O(n^4)$ to check
nonnegativity of each remaining one, for a total running time of $O(n^5)$.
For part (2) of \prettyref{thm:hypred}, we simply use a Sturm sequence to ensure that there are no roots in $(0,1)$, and then evaluate the polynomial at a single point to check that the sign is positive.
\end{proof}
The algorithm in this paper offers a starting point in the area of polynomial time algorithms
for real stability. In addition to the obvious possibility of improving the running time to say $O(n^4)$ or below,
several natural open questions remain:
\begin{itemize}
\item Can the algorithm be generalized to $3$ or more variables? The bottleneck to doing this is that we do not know how to check real rootedness of $2$-parameter families, or equivalently, nonnegativity of bivariate polynomials.
\item Is there an algorithm for testing whether a given polynomial is hyperbolic with respect to {\em some} direction, without giving the direction as part of the input?
\item Is there an algorithm for testing stability of bivariate polynomials with {\em complex} coefficients?
\end{itemize}
Perhaps leaving the realm of strongly polynomial time algorithms, the major open question in this area is the following: a famous theorem of Helton and Vinnikov \cite{hv} asserts that every bivariate real stable polynomial can be written as
$$ p(x,y)=\det(xA+yB+C)$$
for some positive semidefinite matrices $A,B$ and real symmetric $C$. Unfortunately, their proof does not give
an efficient algorithm for finding these matrices. Can the ideas in this paper, perhaps via using SDPs to find sum-of-squares representations of certain nonnegative polynomials derived from $p$, be used to obtain such an algorithm?
\addreferencesection
\bibliographystyle{amsalpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/www.nature.com\/articles\/35079275?error=cookies_not_supported&code=5625b84c-8192-4e6b-8611-6c56138ed096","text":"Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.\n\nA change of climate for big oil\n\nAs European environmentalists launch a boycott of US oil firms, other energy companies are winning praise for their efforts to tackle climate change. Mark Schrope examines the oil giants' divergent strategies.\n\nFuture investment: in 1997, BP's chief executive John Browne (top) acknowledged the role of greenhouse gases in global warming. Since then, the company has invested in renewable energy such as this solar-powered lighting rig (top right) used at the Sydney Olympics. Credit: AP\/BP SOLAR\/A. & H. FRIEDER MICHLER\/SPL\n\nIt is rare indeed to find an oil executive who has the respect of environmentalists \u2014 but in May 1997, John Browne, group chief executive of the London-based oil company BP, became just that. Speaking at Stanford University in California, Browne was the first senior executive of an oil company to acknowledge that carbon dioxide and other greenhouse gases probably caused global warming, and to recommend that action be taken.\n\nIt was a brave statement. Both BP's manufacturing processes and its products generate CO2, and by explicitly linking emissions of the gas to global warming, Browne was associating his company with perhaps the biggest environmental threat to our planet. \u201cA lot of people viewed BP as a traitor to the industry,\u201d says Eileen Claussen, director of the Pew Center on Global Climate Change in Washington, a non-profit organization that promotes market-based approaches to tackling climate change.\n\nFour years on, climate-change initiatives taken by BP and the Anglo\u2013Dutch oil company Royal Dutch\/Shell have split the industry and earned the two firms praise from environmental lobbyists. But US companies, most notably ExxonMobil (known as Esso outside the United States), face a summer of protests in Europe. Environmental groups accuse these companies of influencing President George W. Bush's decision to reject the Kyoto Protocol \u2014 the international treaty that aims to limit emissions of greenhouse gases \u2014 and hope to mobilize a consumer backlash against the firms.\n\nDespite the differences in environmental policy, profits are the ultimate measure of success for all the companies. Each oil giant is facing a dilemma \u2014 should it gamble on investments that may prepare it for the future, when concerns about global warming have severely restricted the burning of fossil fuels, or reap maximum short-term rewards while the oil business lasts in its present form?\n\nAll the big oil companies now accept that greenhouse-gas emissions pose a potential threat. All have invested in technologies to reduce such emissions, from techniques for capturing CO2 before it is released into the atmosphere, to alternative methods for producing energy, such as solar power.\n\nBut behind the companies' environmental rhetoric, their approaches are very different. Only BP and Shell have made firm commitments to reducing their emissions of greenhouse gases and backed them up with targets and deadlines. They are also making the heaviest investments in alternative sources of energy.\n\nCentral to BP's efforts is a commitment to knock 10% off its 1990 level of greenhouse-gas emissions by 2010. Working with the New York- based organization Environmental Defense, the company has set rigid yearly emissions targets for each of its business units, from drilling operations to chemical plants.\n\nKey to the scheme is the idea that the reductions do not have to be spread evenly around the business. Instead, cuts in emissions are treated as commodities that can be bought and sold. Under the plan, CO2 emissions are priced at $8 per tonne. If a particular unit finds that the cost of cutting its emissions is less than this, it can aim to beat the 10% target and sell any excess 'carbon credits' on an internal market hosted on the company's intranet. Units that find the cost of cutting their CO2 emissions is greater than$8 per tonne can choose to buy carbon credits, which count towards their 10% target. If it suits them, units can buy their way out of making any cuts. Credit is also given for lowering emissions of other greenhouse gases, based on their warming potential relative to CO2.\n\nJeff Morgheim, BP's climate-change manager, handed out the reduction targets across all units uniformly, regardless of how hard reductions would be for a given group. The process did not endear him to the group leaders. \u201cThat's why I wear shades and a trench coat,\u201d he jokes.\n\nBut the group leaders have now come round, Morgheim argues. The company is already halfway towards meeting its targets, and estimates that it should reach its goal ahead of schedule, probably by 2003. Perhaps more importantly, the overall cost of the programme has been kept down by units finding reductions that stem from efficiency improvements. Morgheim points out that the second phase will be more expensive, as units made the easiest and cheapest savings first, but he is confident that the scheme will succeed.\n\nThe element of profit in the system has also sparked some innovative ideas. Morgheim cites a recent call from a refinery manager who was considering using the heat generated by his refinery to heat water for a nearby community, and wanted to know if he would receive emission credits for the energy saved by the community. \u201cWhen I hung up the phone I knew we had made the right decision,\u201d Morgheim says.\n\nShell, also in conjunction with Environmental Defense, has set itself an even more ambitious target of a 10% cut in 1990 emissions levels by 2002. Again, it is using a system of internal emissions trading, and looks set to meet its target. According to the Pew Center, BP's cut will take longer to achieve as more time is needed to incorporate some of its newly acquired subsidiaries into the programme.\n\nBoth schemes will be watched closely by negotiators seeking to salvage the Kyoto Protocol. If the accord is ever ratified, a similar system for 'emissions trading' will have to be implemented on an international scale. Arguments over the details of such a scheme contributed to the breakdown of the last set of international climate talks. \u201cOne of the reasons why we set up an internal emissions trading system ourselves was to see whether those systems can work in practice,\u201d says Robert Kleiburg, a climate-change analyst with Shell.\n\nShell has also developed an impressive roster of alternative energy projects through a US$500 million investment in its subsidiary Shell Renewables. Last year, together with a consortium of electricity generating and engineering companies, Shell Renewables opened a two-turbine wind farm off the coast of northeast England. The 4 megawatt (MW) farm is supplying electricity to 3,000 households. The company is now considering plans for a bigger project in the Irish Sea. Working with Swedish energy company Sala-Heby Energi, Shell Renewables is also developing environmentally friendly combined heat and power (CHP) plants. Usually powered by gas, CHP plants are highly efficient and can provide both heat and electricity for anything up to a small town. Last August, Shell Renewables unveiled a CHP plant powered by wood chips left over from timber businesses which can provide 10 MW of electricity and 22 MW of heat. Hydrogen-powered fuel cells, batteries that many believe will run the electrical cars of the future, have also attracted investment from both BP and Shell. Other smaller oil companies are investigating carbon sequestration (see \u201cThe North Sea bubble\u201d, overleaf). Despite these projects, alternative energy sources provide only a small fraction of the world's total energy needs. BP Solar, now the largest solar power company in the world, sold 40 MW of new capacity last year. This is a reasonable slice of the 250-MW global total, but with some individual fossil-fuel power stations generating thousands of megawatts, it is clear solar power still has some way to go. Other oil companies seem to have turned their backs on renewables. ExxonMobil, for example, invested US$500 million in alternative energy before deciding that the practical and economic challenges of turning renewables into profitable energy sources were too great to warrant further funding.\n\nFuel for debate: Greenpeace's Steve Sawyer (right) welcomes the strategies employed by BP and Shell but backs the boycott on the anti-Kyoto US companies such as Exxon\/Esso. Credit: M. NICOLAOU\/GREENPEACE\/BELTRA\/GREENPEACE\n\nAlternative sources may have a long way to go, but environmentalists are giving cautious praise to the efforts of BP and Shell. \u201cI think they are way ahead of the rest,\u201d says Claussen. Steve Sawyer, an Amsterdam-based climate campaigner with Greenpeace International, wishes both companies would pursue alternative strategies more aggressively, but he backs their current efforts. \u201cIt's more than just greenwash,\u201d he says.\n\nSuch approval would have been out of the question in the early 1990s. As awareness of climate-change issues was starting to grow, many oil companies, including Shell and BP, funded lobbying groups such as the Global Climate Coalition (GCC). The GCC disputed the emerging scientific evidence for global warming and portrayed attempts to limit emissions as harmful to the world economy. BP and Shell have since withdrawn from the GCC, saying that they are now convinced that the science points to a warming world.\n\nBut ExxonMobil continues to speak out against the Kyoto Protocol and questions the degree to which the Intergovernmental Panel on Climate Change (IPCC), the group of scientists that advises governments on climate-change issues, represents a true consensus.\n\nThe latest IPCC report, issued earlier this year, stated that global temperatures were rising faster than previously thought and that there was strong evidence that greenhouse gases were the cause (see Nature 409, 445; 2001). But Frank Sprow, vice-president of safety, health and the environment at ExxonMobil, says that most of the evidence linking greenhouse gases to global warming comes from climate models, rather than empirical data. \u201cI think the layman and even some scientists don't understand that the question of attribution has to rely on models,\u201d Sprow says. He also claims that the report's executive summary played down substantial uncertainties within the document.\n\nJoyce Penner, an atmospheric modeller at the University of Michigan in Ann Arbor, denies this. \u201cThe summary for policy- makers does tell the story,\u201d she says. Penner was a lead author on the IPCC report chapter dealing with atmospheric aerosols, one of the largest sources of uncertainty in understanding climate change. \u201cIf you choose to ignore some of the things said there then you will get a skewed view,\u201d she says.\n\nPouring oil on troubled waters\n\nSprow does not deny that the build up of greenhouse gases poses long-term risks, but he argues that the Kyoto Protocol is not the way to deal with them. Instead, ExxonMobil advocates a three-tiered voluntary response to climate change. The initial focus is on energy conservation, followed by advances in technologies that reduce CO2 emissions, and finally breakthroughs in areas such as carbon sequestration, which aims to lock emitted CO2 away so that it cannot enhance the greenhouse effect.\n\nSawyer says such a strategy is unacceptable: \u201cAll it means is delay and taking actions which are of no conceivable cost to them at some undefined point in the future.\u201d\n\nSteve Cochran, a spokesman for Environmental Defense, agrees. \u201cExxon has been extraordinarily difficult,\u201d he says. \u201cIt has funded efforts such as the GCC, which has worked very hard to undermine legitimate scientific understanding.\u201d\n\nGreenpeace and other environmental groups have reacted by launching a European boycott of ExxonMobil and other American oil companies such as Texaco and Chevron. Sawyer says the goal is to provide encouragement for companies that do support Kyoto. In the long term, they hope to convince the United States to reconsider its decision.\n\nIf the boycott works, it may force ExxonMobil to factor consumer demand for environmentally friendly products into its long-term plans. Balancing environmental demands from the public and governments with the need to maintain profits will be a key challenge in the future for the oil industry.\n\nReturning to Stanford earlier this year to give an update on BP's work on climate change, Browne described how the job of providing energy can feel like a trade-off between economic growth and a healthy environment. \u201cI believe there is a huge commercial prize for those who can offer better choices which transcend the trade-off,\u201d he said.\n\nThe divergent climate-change policies of the oil giants are, in effect, speculations that reflect different views about that prize. Shell and BP are trying to position themselves as the main providers of the energy sources that may succeed fossil fuels. \u201cThey want to be there first,\u201d observes Claussen. ExxonMobil, on the other hand, appears to have decided that it can make more money by continuing under the present system for as long as possible \u2014 and catching up on alternative energy technologies at a later date.\n\nPipe dreams: US companies seem reluctant to invest in renewable sources to replace fossil fuels. Credit: ROBERT VALARCHER\/STILL PICTURES\n\nGordon Edge, an analyst with FT Energy in London, says ExxonMobil's decision will help profits in ving cautious praise the short term, but will cause problems as renewables become more important. \u201cAdjusting to renewables involves a major culture change. Exxon could take a decade to catch up,\u201d says Edge.\n\nThe long-term payoffs of all the companies' strategies are difficult to judge. But what is clear is that the outcome will affect us all: in gambling on their business futures, the oil giants are staking the Earth's climate.\n\nAuthor information\n\nAuthor notes\n\n1. Mark Schrope is a freelance writer in Melbourne, Florida.\n\n\u2022 Mark Schrope\nAuthors\n\nRights and permissions\n\nReprints and Permissions\n\nSchrope, M. A change of climate for big oil. Nature 411, 516\u2013518 (2001). https:\/\/doi.org\/10.1038\/35079275","date":"2021-10-27 06:21:27","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.22429290413856506, \"perplexity\": 3799.671081220297}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323588102.27\/warc\/CC-MAIN-20211027053727-20211027083727-00616.warc.gz\"}"}
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[Illustration: East View of West Point from the Hudson River]
West Point
An Intimate Picture of the National
Military Academy and of the
Life of the Cadet
By
Robert Charlwood Richardson, Jr.
Captain, 2nd Cavalry, U. S. Army
Late Assistant Professor of English, U. S. M. A.
Foreword by
Major-General Hugh L. Scott
Chief of Staff, U. S. Army
G. P. Putnam's Sons
New York and London
The Knickerbocker Press
1917
COPYRIGHT, 1917
BY
ROBERT CHARLWOOD RICHARDSON, JR.
Second Impression
The Knickerbocker Press, New York
To
THE CORPS OF CADETS
REPRESENTATIVE OF THE BEST AMERICAN MANHOOD, HEIRS TO
A CENTURY OF UNSURPASSED ACHIEVEMENT AND HONORABLE
TRADITION--THE MOST HIGHMINDED, LOYAL, AND
DISCIPLINED BODY OF STUDENT OFFICERS IN
THE WORLD--I AFFECTIONATELY
DEDICATE THIS VOLUME
FOREWORD
West Point played a great part in the gaining of American independence.
It was strongly fortified as the key of the Hudson, and as long as it
was held by the patriots of the Revolution the New England colonies
could not be cut off from the others and conquered one at a time.
The lack of educated officers was greatly felt by the Generals of the
Revolution, and this lack was but feebly supplied by trained officers
from abroad.
It was mainly through the foresight and patriotism of Washington,
Hamilton, and Knox that the Military Academy at West Point was founded,
and their memory is still enshrined there.
The Academy had its inception in very small beginnings, first by the
assignment of students to an Engineer regiment until the organic act of
1802 created an Academy with ten cadets. A firm establishment was not
made, however, until the detail of Colonel Sylvanus Thayer in command
in 1817, who laid down the fundamental principles which govern the
Academy to this day.
The early graduates of the Academy suffered much from the jealousy of
the old veterans of the Revolution who had no use for the educated
soldier. These graduates were too few to make themselves felt in the
War of 1812, and it was not until General Winfield Scott eulogized
their services in the Mexican War that they began to be appreciated by
the nation.
Their services in the Civil War were inestimable and are known to all
who read history. After the Spanish-American War of 1898, the then
Secretary of War, Mr. Elihu Root, reported that the services of the
graduates of the Military Academy in that war alone had far more than
repaid the cost of the Academy since its foundation in 1802.
For many years the Military Academy was what its name implies, an
Academy, but it has expanded from time to time until it is a military
university, giving instruction for all branches of the service except
the Medical Corps, and securing for each graduate a broad foundation
which enables him to specialize in any direction by means of the
various special schools for each branch. The glory of West Point,
however, is in the West Point character, now well known in every
civilized country in the world, with its reputation for fidelity,
efficiency, discipline, and general uprightness. The standing army of
the United States has always been too small for the tasks that have
been laid upon it, and at every crisis it has had to train large forces
of citizen soldiers summoned from civil life for the emergency. These
citizen-soldiers, as well as the Regular Army itself, rely upon the
scientific education and high character of the West Point graduate to
keep the art of war abreast, if not a little ahead, of the times, and
for the initiative and informing leaven to permeate the mass and to
cause the firm progress of discipline and uprightness throughout the
whole.
Shortly after the Mexican War a verse was added to the old West Point
song of Benny Havens:
"Their [graduates] blood has watered western plains
And northern wilds of snow,
Has dyed deep red the Everglades,
And walls of Mexico."
Since that time they have shed it copiously in Cuba, China, and the
Philippines, and they are now about to take their places with comrades
from civil life fighting for liberty and democracy on the battlefields
of France.
HUGH L. SCOTT.
WASHINGTON, D. C.,
_May, 1917_.
PREFACE
This book is intended to give, aside from a brief historical sketch
of West Point, something of the feelings of the cadet from the moment
that he reports for duty until he graduates four years later. Perhaps
some of my fellow West Pointers will disagree with me in regard to my
interpretation of their feelings, but what I have written thereon is
drawn from my own experience and from many conversations with cadets
of to-day. The customs, traditions, methods of training of the Academy
are, I believe, unique, and they make an unforgettable impression upon
the cadet. Especially does he become imbued with an almost indefinable
influence that we of the Academy call the Spirit of West Point, and in
the pages that follow I have tried to seize and translate into words
this spirit of the institution. I have greatly enjoyed writing these
pages about West Point, a subject very dear to my heart, and I offer
this book to the public in the hope that my fellow countrymen may
become better acquainted with the aims and ideals of their National
Military Academy.
It gives me the greatest pleasure to acknowledge here my appreciation
and thanks to Lieutenant Colonel L. H. Holt, U. S. A., Professor of
English and History U. S. M. A., not only for his helpful suggestions
and criticisms, but for his encouragement and unselfish interest in the
preparation of this book.
I also wish to acknowledge the courtesy of the Reverend Herbert Shipman
of New York, formerly Chaplain at the Military Academy, in allowing me
to use his poem _The Corps_, with which I close the volume.
Since this book has gone to press, Colonel John Biddle, the
Superintendent, has been promoted to the grade of Brigadier-General
and relieved from the command of West Point. He has been succeeded by
Colonel Samuel E. Tillman, Retired, who until 1910 was the Professor
of Chemistry and Electricity at the Military Academy. Colonel Tillman
perhaps more than any officer in the Army is better qualified for
this important position. He is a graduate of West Point, to whose
advancement he has devoted most of his life and he has made an
exhaustive study of its needs. His appointment by the President
seems to be particularly felicitous for he possesses a most intimate
knowledge of the Military Academy. All West Pointers rejoice that West
Point is in such good hands.
ROBERT CHARLWOOD RICHARDSON, JR.
WEST POINT, N. Y.,
_May, 1917_.
CONTENTS
CHAPTER PAGE
I.--IN THE DAYS OF THE REVOLUTION 1
II.--THE FIRST HUNDRED YEARS 19
III.--THE REALIZATION OF AN ARCHITECT'S DREAM 37
IV.--THE POWERS THAT BE 75
V.--"BEAST BARRACKS"--BLESSED ARE THE MEEK FOR THEY SHALL
INHERIT THE EARTH 101
VI.--BENDING THE TWIG 127
VII.--THE DISCIPLINE OF THE MIND 163
VIII.--GROWING MUSCLES 194
IX.--LESSONS FROM MARS 213
X.--HENCE, LOATHED MELANCHOLY! 244
XI.--STRENGTHENING THE MORAL FIBER 276
XII.--SPIRITUAL INFLUENCES 291
XIII.--THE SPIRIT OF WEST POINT 300
APPENDIX 305
ILLUSTRATIONS
PAGE
EAST VIEW OF WEST POINT FROM THE HUDSON
RIVER _Frontispiece_
THE SPIRIT OF WEST POINT 2
ARTILLERY TARGET PRACTICE 6
MAJOR SYLVANUS THAYER, "THE FATHER OF
THE MILITARY ACADEMY" 24
From the Painting by Thomas Sully, Library,
U.S.M.A.
CLASS FORMATION IN THE AREA OF BARRACKS 38
THE ADMINISTRATION BUILDING 40
THE ADMINISTRATION BUILDING AND RIDING HALL 42
COLONEL JONATHAN WILLIAMS, CORPS OF FIRST SUPERINTENDENT
OF THEMILITARY ACADEMY 44
From the Painting by Thomas Sully, Library,
U.S.M.A.
COLONEL JOSEPH G. SWIFT, FIRST GRADUATE
OF THE MILITARY ACADEMY 46
From the Painting by Thomas Sully, Library,
U.S.M.A.
CADETS AT EQUITATION IN THE WORLD'S
LARGEST RIDING HALL (600 FT. × 150 FT.) 48
THE CARVED MANTEL IN THE HALL OF THE
ACADEMIC BOARD 50
The Nine Great Warriors of the World. Sculptor,
Laurie
THE NORTH CADET BARRACKS 52
THE CHAPEL 56
THE INTERIOR OF THE CHAPEL 58
VIEW UP THE HUDSON RIVER FROM TROPHY POINT 66
"SPOONING" ON FLIRTATION WALK 68
THE SUPERINTENDENT'S QUARTERS 78
Built in 1820
COLONEL JOHN BIDDLE, CORPS OF ENGINEERS, SUPERINTENDENT 80
"BEAST BARRACKS"--DRAWING MATTRESSES 102
REPORTING FOR DUTY 104
TWO HOURS AFTER REPORTING 108
THE INTERIOR OF A CADET'S ROOM IN BARRACKS 114
MOVING FROM BARRACKS TO CAMP 118
A FIRST LESSON IN SALUTING 122
MARCHING TO BARRACKS FROM DINNER 154
The Academic Buildings
THE EXTERIOR OF THE GYMNASIUM 196
GYMNASTIC EXERCISES 200
THE ATHLETIC FIELD 208
SETTING UP DRILL ON THE PLAIN 210
PARADE ON THE PLAIN 230
AT TARGET PRACTICE ON THE FLATS 236
AT P. M. E. DRILL 240
Building a Pontoon Bridge
A REVIEW FOR THE CHIEF OF THE STAFF OF
THE ARMY 288
GRADUATION--PRESIDENT WILSON ADDRESSING
THE GRADUATING CLASS 302
"We'll bid farewell to Cadet gray and don the
Army blue"
[Illustration: The Spirit of West Point]
WEST POINT
CHAPTER I
IN THE DAYS OF THE REVOLUTION
Despite the successful attempts of the architect to give to the
magnificent new buildings at West Point a mediæval character, there
is nothing about them to suggest a feeling of oldness, a feeling that
they are linked with the history of the place. Not until one wanders
among the ruins of old Fort Putnam, explores the crumbling works of
the chain of Redoubts on the surrounding hills, or rambles over the
débris of Fort Constitution on Constitution Island, does he feel the
flavor of age, the romance of West Point of the past. It is only then
that the imagination races back over the years to the days of the
Revolution where it pauses to rebuild the stirring events that filled
the daily lives of our ancestors in their desperate struggle for our
independence. Looking backward through the vista of more than a century
the most commonplace happenings seem powdered with the golden dust of
romance. Interwoven with each event are the names of the men who helped
to make possible these free United States: Washington, Hamilton, Knox;
and of him who was almost successful in thwarting their efforts, the
traitor Benedict Arnold.
As far back as the time of the French and Indian Wars both the
Americans and British recognized the great value of the control of the
Hudson River. It would seem, therefore, that when the Revolution broke
out both sides would take every means to seize and fortify the most
strategic points along its banks. Strange to say, the Americans were as
indifferent about its control as the British, so that the Revolution
was in progress for three years before West Point, the natural key to
the river's defense, was fortified.
During the Revolution the British were operating from Manhattan on the
south and Canada on the north as bases. Had they controlled the Hudson,
they could have separated the eastern from the middle colonies, which
division would have prevented the patriots from military combination
and from interchanging the necessary commodities for both sections.
Immediately after the battles of Concord and Lexington, the Congress
of New York, acting upon a suggestion from the Continental Congress,
sent a commission to the Highlands to select "the most proper place
for erecting one or more fortifications." Constitution Island, and
the sites where Forts Montgomery and Clinton[1] were afterwards built,
were chosen. Nothing much was accomplished, however, in the way of
fortifications despite the appointment of another commission that
recommended the absolute necessity for works at West Point opposite
Constitution Island.
Washington, accompanied by General Heath, finally sailed up the river
in 1776, and General Heath tells us that "a glance at West Point
without going on shore evinced that this post was not to be neglected."
Meanwhile the Revolution dragged on into its third year, 1778, but
still no fortifications at West Point. Due to Washington's persistence,
work was begun there early in January, 1778. General Parsons with his
brigade arrived at West Point on the 20th of January and began the
erection of defenses. The weather was extremely cold, provisions were
scarce, the men inadequately clothed, and the troops poorly supplied
with the proper implements to carry on their labor. Altogether, a very
depressing and discouraging situation confronted Parsons's men as
they debouched upon the Plain and surveyed their surroundings. If any
thought could have given them courage it must have been the reflection
that at least they were somewhat better off than their comrades in
arms down at Valley Forge, who, despite their wretched condition, were
bravely keeping alive the patriotic fires of the Revolution.
What a contrast was that first sight of West Point to Parsons's troops
to that offered today! Instead of the beautiful level parade ground
surrounded by fine granite buildings they found an undulating plain
covered by a growth of yellow pines ten or fifteen feet high, without
house or habitation. The only point of similarity was the snow, waist
high. After strenuous efforts to get logs from the neighboring hills,
a few rude huts were hastily thrown together, and then, at the end
of three weeks, the soldiers fell to work with a will, building Fort
Clinton under the direction of a splendid young French engineer by the
name of de la Radière. The cold was most intense, but the men went
up the river, cut the timber for the Fort, and assembled it so that
when the river was open, it might be floated down to the Point. Their
hard daily toil was not relieved by any diversions in the evening, for
West Point was a veritable wilderness. General Parsons, in writing
to Colonel Wadsworth, said of West Point, "to a contemplative mind
that delights in a lonely retreat from the world 'tis as beautiful as
Sharon, but affords to the man who loves the society of the world a
prospect nearly allied to the shades of death.... News arrives here
by accident only." The poor soldiers had to repair night after night
to their little log huts and get what pleasure they could from one
another's society.
The rigors of the winter and the hardships to which the Revolutionary
soldiers were accustomed overwhelmed the delicate constitution of
the brilliant young de la Radière. Unhappily, he contracted a severe
cold that culminated in consumption from which he died the following
mid-summer. Another European, attracted by the justice of the
Revolutionary cause, succeeded de la Radière. Thaddeus Kosciusko, a
Pole of education and culture, joined Parsons's officers, with whom he
became a great favorite, not only on account of his engineering ability
but by reason of his charming manners, soft and conciliating, and by
the elevation of his mind. One officer wrote that he took much pleasure
in accompanying Kosciusko with his theodolite measuring the heights of
the surrounding mountains.
Today Kosciusko's name is more familiar to West Pointers than de la
Radière's, for an enchanting little garden, a tiny retreat hanging on
to the cliff near the river, bears his name, and a monument, in the
northeast corner of the Plain near Port Clinton that he helped build,
commemorates his devotion to the Revolutionary cause.
Kosciusko's presence and energy put new life into the work of
construction. Shortly afterwards, when orders came from Washington to
expedite the completion of all of the forts, Parsons and Kosciusko,
under the direction of Colonel Rufus Putnam, immediately commenced
excavations for Fort Putnam.[2] The men now daily trudged up the small
hill back of the Plain and began making clearings for the fort's
foundation. It was hard laborious work, extremely fatiguing, and, to
add to the men's discomfiture, they were greatly annoyed by large
rattlesnakes with which the hill top seemed to swarm.
While the land defenses were being so well prepared, steps were taken
to prevent enemy ships from passing up the Hudson. The topography of
West Point and the adjacent country lent itself most admirably to the
plan of obstructing the river.
The Hudson, as it comes down from Newburgh a straight course of nine
miles, strikes West Point, where it is deflected eastward for a quarter
of a mile, flowing between Constitution Island and the steep cliffs
of the Point before again turning south. Any British sailing vessel
coming up the river from New York would, upon rounding Gee's Point,
lose a great deal of its speed on account of the swift current, and
if stopped by some obstruction could be held under the fire of the
batteries on both shores. General Putnam, therefore, through his
Quartermaster-General, contracted with the Sterling Iron Works of
Noble, Townsend and Co., for an iron chain 500 feet long, each link
about two feet long, to be made of the best Sterling iron 2¼ inches
square, with a swivel to every hundred feet and a clevis to every
thousand feet, for which the government was to pay $440 for every ton
weight of chain and anchors.[3]
[Illustration: Artillery Target Practice
_Photo White Studio_]
The chain was to obstruct the navigation of the river. It was stretched
across the narrowest part on April 30, 1778, and fastened at West Point
in the second small cove west of Gee's Point, and on Constitution
Island where the present small boathouse and landing-place stand. Very
large logs, sixteen or more feet long, a little pointed at the ends to
lessen opposition to the force of the water on flood and ebb, were used
to buoy up the great weight of the obstruction. During the winter it
was taken up, because the ice in the river was an effective blockade,
but when spring came the work of 280 men was needed to lay it across
the stream.
Meanwhile, Kosciusko labored strenuously on the forts, so that by June,
1778, the work on the fort in the northeast corner of the Plain begun
by de la Radière in the January past, was completed and given the
name of Fort Arnold. Later, when Benedict Arnold turned traitor, its
name became Fort Clinton. A small portion of the wall stands today.
Washington, on a visit to West Point in September, 1778, paid Kosciusko
a great compliment, stating to General Duportail, his chief engineer,
that he need have no uneasiness as to Kosciusko's ability.
Additional troops were at this time sent to West Point because
Washington feared an attack by the British. In the spring of 1779,
General McDougall was at West Point with three brigades; there was
one on Constitution Island, and the main body of the Army was near
Haverstraw under General Putnam. Washington, ever watchful, viewed with
great concern the presence of the British in the strong position of
Stony Point because he considered this post a serious menace to West
Point. Wishing to be rid of them he sent for Anthony Wayne, gave him a
corps of light infantry, and directed him to capture the British fort.
A better man than Wayne could not have been selected for the job. On
the 15th of July, Wayne paraded his troops for a minute inspection,
after which, instead of dismissing them, he marched upon Stony Point,
which at midnight he successfully assaulted with the bayonet. The news
of his brilliant exploit was conveyed to Washington in the following
refreshing message:
WEST POINT, 16 July 1779.
2 o'clock a. m.
DEAR GEN'L:
The fort and garrison with Colonel Johnston are ours. Our officers and
men behaved like men who are determined to be free.
Yours most sincerely,
ANT'Y WAYNE.
To supervise better the defenses of the Hudson River, Washington moved
his headquarters to West Point, in July, 1779, where he remained
until November of that year, occupying "Moore's House," a structure
that stood in Washington valley near the shore of the Hudson, a short
distance from the northeast corner of the present cemetery. It was
built by John Moore prior to 1749, and called by all the people in the
vicinity "Moore's Folly" on account of its pretentiousness.
General Clinton tried to draw Washington out into the open country for
a campaign, but the American Commander was too astute and Clinton dared
not attack the Revolutionary forces at bay at West Point because of the
dangers of a campaign in the Highlands.
Spurred on by Washington's presence and by his orders, Kosciusko and
the troops completed Fort Putnam and Redoubts Webb and Wyllys in the
summer. This work necessitated for fatigue duty each day 2500 men, a
large percentage of the garrison. Even at this early period, West Point
was the Mecca for distinguished Americans and foreigners. Nearly every
Revolutionary commander visited the Post at one time or another during
the war, and while Washington was here, Count de Luzerne, the French
minister, was his guest.
Before Washington left the Post in late November, the troops in the
Highlands were distributed to their winter stations. Little money was
available to equip properly the soldiers but they struggled on bearing
their burdens and hardships that we of today might be free. That they
were not fighting for the present alone, without a thought as to those
who would come after them, is revealed to us by an entry in a diary of
General Heath who was then in command of all the troops and Posts on
the Hudson:
25th Nov. 1779. The troops were moving to their different places
of cantonment; many of the soldiers (as fine men as ever stood in
shoes) were marched barefooted over the hard frozen ground, and
with an astonishing patience.
_Remember these things, ye Americans in future times!_
In the spring of 1780, Washington sent Baron Steuben to West Point
to drill the troops, for he feared an attack by the British. This
accomplished officer, a Major-General in the American Army, had seen
seven campaigns in the service of Frederick the Great, so that he
brought to his task a ripe experience. With Prussian thoroughness he
commenced drilling both the old soldiers and recruits of the command,
with the result that by summer he was able to write to Washington that
he had formed a corps of light infantry "that I dare flatter myself
will be the admiration of our allies as much as the terror of our
enemies."
Notwithstanding the patriotic work of the officers and men of the
Army, Washington was aware that America as well as Great Britain was
getting tired of the war. "There never has been a stage of the war," he
said, "in which dissatisfaction has been so general and so alarming."
Governor Reed of Pennsylvania said in August, 1780: "It is obvious that
the bulk of the people are weary of the war."
The stage was therefore set for the most dramatic event of the
Revolution, the treason of Benedict Arnold. Had Arnold succeeded at
this period of the Revolution, the hour of darkness and depression, in
selling West Point to the British, we would probably still be English
colonies. The loss of the Post would have shaken the morale of the
American commanders, not to speak of the paralysis of any movement upon
which Washington's army might have been engaged at that particular time.
For more than a year previous to his assumption of the command of
West Point, Arnold had been hatching nefarious schemes to betray the
Americans. He needed money badly, due to his extravagances while in
Philadelphia. His conduct had not been entirely satisfactory while
in that city and open resentment was expressed on account of his
preference for the British faction, but because of his military
capacity he was held in high esteem by Washington. His abilities led
Washington to offer him the command of the left wing of the army then
in the field, but he pleaded that he was unfit for field duty by
reason of the wound that he had received at Saratoga, and requested
the command of West Point. His desires were respected and on August
5, 1780, he assumed command of his new post with headquarters at the
Robinson House.[4]
Once at West Point, Arnold saw his chance to gain rank and pay from the
British. He immediately entered into a lively correspondence with Major
André, the Adjutant-General of the British forces in America, who was
addressed as "Mr. John Anderson, Merchant." Arnold's communications
were all signed "Gustavus." When negotiations for the betrayal of West
Point had reached a crisis, Arnold requested a personal interview with
a representative of the British. General Clinton then sent Major André
up the river on the sloop _Vulture_ which anchored near Haverstraw.
An agent of Arnold's, one Joshua Hett Smith, returned at midnight,
September 21, with Major André in full uniform, a landing being
made a short distance north of the West Shore Railroad tunnel south
of Haverstraw. Arnold and André then went to Smith's house in West
Haverstraw. They were challenged by an American sentinel and it was
here that André entered the American lines.
While the two officers were in consultation, the American commander
across the river brought a four-pounder within range of the _Vulture_,
and opened a heavy fire upon her, causing her commander to shift his
anchorage downstream. Great was André's dismay at seeing his vessel
forced away, for now he was in the American lines and far from New
York. He had been assured of a safe return to his own lines, and
disliked the idea of traveling alone by land to New York. Moreover,
he was very reluctant to take off his uniform but at Arnold's advice
he changed into civilian clothing, thereby foolishly placing himself
in the light of a spy, if caught within the American lines. Arnold
also gave André important papers regarding the strength of West Point
defenses.
It is not difficult to imagine the state of André's mind at finding
himself in a false position and at the same time disobeying General
Clinton's orders, which were not to change his uniform under any
circumstances nor receive any papers from Arnold. Under the guidance of
Joshua Smith, he crossed the river at King's Ferry (near Stony Point of
today) and proceeded south toward New York.
Although furnished with a pass by Arnold, he was detained by three
American patriots near Tarrytown, searched, and turned over to Colonel
Jameson at North Castle.
Meanwhile, Arnold was at his Headquarters at the Robinson House
awaiting events, and Washington was on his way from Hartford to West
Point. Had Arnold succeeded it is probable that Washington would have
fallen into the enemy's hands at this time, an accident that would
have ruined the Revolution. When Washington was opposite West Point he
sent two aides to inform Arnold of his arrival. They proceeded to the
Robinson House and were enjoying Arnold's hospitality at breakfast when
Jameson's messenger arrived with a note announcing André's capture. The
news must have fallen upon Arnold like a thunderbolt, but with perfect
_sangfroid_ he excused himself, rushed upstairs to tell his wife of
the danger, ordered his horse, sent for the coxswain of his barge, and
then calmly returned to his guests whom he told it was necessary for
him to cross to West Point to prepare for the reception of General
Washington. Instead, he rapidly made his way down the river and boarded
the _Vulture_ which took him to New York.
Major André was tried by court-martial, found guilty of being a spy,
and sentenced to be hanged. Numerous letters were written to Washington
begging that André's life be spared. Arnold himself addressed to his
former chief a long communication exonerating André and taking upon
himself the blame for André's presence in disguise within the American
lines. Even Hamilton was touched, saying: "Never perhaps did any man
suffer death with more justice or deserve it less."
André accepted his fate like a brave soldier but he revolted from the
ignominy of being hanged. When all efforts to change the mode of his
death failed, he personally appealed to Washington in the following
splendid letter:
_From Maj. André to General Washington, 1780._
TAPPAN.
The 1st. of Oct., 1780.
SIR:
Buoy'd above the terror of death by the consciousness of a life devoted
to honorable pursuits and stained with no action that can give me
remorse, I trust that the request that I make to your Excellency, at
this serious period and which is to soften my last moments will not be
rejected.
Sympathy toward a soldier will surely induce your Excellency and
a military tribunal to adapt the mode of my death to the feelings
of a man of honor. Let me hope, Sir, that if aught in my character
impresses you with esteem towards me, if aught in my misfortune marks
me the victim of policy and not of resentment, I shall experience the
operation of those feelings in your breast by being informed that I am
not to die on a gibbet.
I have the honor to be your Excellency's most obedient and most humble
servant,
JOHN ANDRÉ,
Adj. General to the British Army.
His request, however, was not granted and in the early afternoon of
October 2, 1780, arrayed in full dress uniform he paid the penalty on
the scaffold. His body was buried beneath his gibbet but removed to
England in 1831 where it rests in Westminster Abbey.
West Point and the Revolutionary cause was saved to the Americans!
The shock of Arnold's traitorous act with its narrowly averted
consequences caused Washington to take even more stringent measures
for West Point's defense. Orders were issued to continue work on all
of the fortifications and during 1781 and 1782, the garrison labored
faithfully and uncomplainingly notwithstanding the great sufferings
of the men from lack of provisions. At times the stores on hand were
numbered by a few barrels of salt pork and a little flour.
Major-General Knox now assumed command of the Post. After the cessation
of hostilities he was very busy mustering out troops and putting the
garrison in shape.
Despite the poverty that prevailed at West Point, Washington ordered a
celebration to be held in honor of the birth of the Dauphin of France,
Louis Joseph, the son of Louis XVI., born October, 1781. A magnificent
fête was arranged in which all of the troops stationed in the Highlands
participated. Upon the Plain at West Point, Major Villefranche erected
a curious edifice, an improvised temple with a grand colonnade of 118
pillars made of the trunks of trees. The entire building was festooned
with American and French flags, with designs and emblems, muskets and
bayonets fancifully arranged. Washington, with a party of five hundred
distinguished guests, assembled in the colonnade for a banquet. A
series of thirteen toasts were drunk, each one accompanied by a salute
of thirteen cannon. During the evening there was a grand display of
fireworks for the troops and a ball for the officers and their guests.
This dance, led by General Washington, was the first real West Point
hop.
The various details left over from the Revolution were now disposed
of by General Knox and his successor, Lieut.-Col. Rochefontaine. The
genesis of the Military Academy was foreshadowed by the presence of the
Invalid Corps which by act of Congress, 1777, was, among other things,
"to serve as a military school for young gentlemen previous to their
being appointed to marching regiments."
The dark days of the Revolution were over and the troops could now rest
from their strenuous labors. There were important matters, however,
to occupy the leaders, not the least of which was the establishment
of an institution for training officers for the Army. No lesson of
the war was so well learned as the need for such educated leaders,
and immediately the Revolution was over, Washington, Hamilton, and
Knox began urging Congress to establish a National Military Academy.
Although Washington never lived to see his recommendations carried out,
he would have rejoiced, I am sure, to know that Congress three years
after his death founded the United States Military Academy, at his
favorite Post, West Point.
CHAPTER II
THE FIRST HUNDRED YEARS
When at last the colonies found themselves free, and realized that they
were in no immediate danger from any foe, the thoughts of the people,
so long occupied with war, eagerly turned toward the establishment of
their new government. It was only natural that the Army, weary of the
long struggle for independence, should gladly welcome their release
from service, and resume once again the peaceful pursuits of civil
life. For seven long years their days had been filled with arduous
marches through heat and through snow, with tedious vigils on outposts,
or with bloody encounters with the British, and the great mass of the
people joyfully hailed the piping times of peace, and without ado
they turned their battle-axes into billhooks, and their helmets into
beehives.
It could not be expected that during the reaction that followed the
Revolution much attention would be given to the subject of military
education. As a matter of fact, for seven years this question was
allowed to sleep; but Washington, ever on the alert for the welfare
of the new country, suggested in his annual message of 1790 to the
Congress the establishment of a National Military Academy. In spite of
the great prestige that he enjoyed both as President and as the man who
had successfully waged the Revolution, his words were not heeded by
Congress until some years afterwards.
The Congress of those days apparently was like our own and needed to
have a matter brought to its attention many times before any definite
action was taken. Washington undoubtedly appreciated this condition
for we find that on numerous occasions he spoke of his plan, telling
Congress that "it is an inquiry that cannot be too strongly pursued."
His efforts were not without reward, for in 1794 the grade of Cadet
was created, and a military school was established at West Point. This
school was composed of the cadets who were by law attached to the
Engineer and Artillery Corps of the garrison. In each company there
were two of these young men styled "cadets of the Service," whom the
Government aimed to train to become commissioned officers of the Army.
There was, however, no organization to the school, nor scientific
system of instruction, so that the cadets did about as they pleased,
pursuing their studies in a desultory manner.
It was not until the 16th of March, 1802, that the United States
Military Academy was definitely established by law. Congress then
authorized the President to organize the Corps of Engineers whose
cadre contained, in addition to the officers, ten cadets. West Point
was designated as the station of the Corps which was to constitute the
Military Academy. The next year forty cadets, to be appointed from the
artillery troops of the Army, were added and in 1808, 156 additional
men.
During the first ten years of its existence the Military Academy was
in a most chaotic condition. It was in reality "a foundling barely
existing among the mountains, out of sight of, and almost unknown to,
its legitimate parents." It is greatly to be wondered at that the
Academy ever survived the terrible throes of its birth. Almost no
provisions for its existence were made by Congress. The cadets were
lodged in an old barrack of the Revolution, called the "Long Barrack,"
that occupied the site of the present hotel, and their instruction
was given in a wooden building called the "Academy" that stood on the
spot of the present Superintendent's quarters. They were allowed to
board around promiscuously, really living from hand to mouth. Among
the student body there was very little discipline, but a great deal of
idleness and dissipation.
In 1812, a new law placed the school on a firm basis and furnished
the principles upon which the institution has been conducted to
this moment. Two hundred and fifty cadets were authorized and the
respectable sum of twenty-five thousand dollars appropriated for
buildings. To offset this good fortune, the Academy had to fight
against the hostility of Madison's Secretary of War, Eustis, who tried
his utmost to strangle the new-born institution. But happily the
exigencies of the War of 1812 frustrated his hostile designs.
Despite insuperable difficulties, the Academy began to grow, not
scientifically, but in a muddling sort of way. Where the Superintendent
had heretofore been a rover up and down the Hudson Posts, he now
became permanently located at West Point. The professors began to work
together with more harmony, going so far as to recommend a broadly
planned course that included most of the subjects studied today. By
the Regulations of 1815, the cadets were required to mess at a common
table, instead of boarding at private houses, their age limit was fixed
at fourteen to twenty, and their uniform was definitely prescribed.
A little order was being brought out of chaos. Annual vacations were
granted, to commence immediately after the examination in July and to
end on the first day of August. Notwithstanding the excellence of the
above features, the general condition of this infant school was far
from satisfactory. A picture of its inner life is revealed in a letter
written in 1815 by Andrew Ellicott, the Professor of Mathematics, to
the Secretary of War, in which he states:
Until I came here the Academy was abandoned by the Professors and
a great part of the students from the first of December until, the
first of April following every year. This practice I immediately
put a stop to, and kept the Academy open two winters, not even
excluding Sundays, without the aid of any other Professor or
regular assistant. The winter before last, I kept together more
than twenty students, 16 of whom were commissioned last July, and
last winter more than 80, some of whom would do credit to any
country or nation, and will be found among our future rulers. These
extra services are not ideal--they are substantial.
Although Professor Ellicott rather emphasizes his assiduity in his
application for extra compensation we must be grateful, at least, for
the glimpse he gives us of the state of affairs in 1815.
Better days, however, were in store for West Point. That the War
Department was not entirely insensible to the handicap under which
those at West Point were working, is proven by the circumstance
that at this particular time there was in Europe an officer, Major
Sylvanus Thayer, who had been sent abroad "to prosecute inquiries and
examinations calculated for his improvement in the military art." He
was given five thousand dollars for the collection of books, maps,
and instruments for the Military Academy. Shortly after his return,
he was made Superintendent, relieving Captain Alden Partridge whose
administration had not been popular nor very successful. Although
Captain Partridge was much criticized by the professors and cadets his
farewell address to the "Gentlemen Cadets of the Military Academy" was
so high-minded that I am tempted to quote it in full:
Before I take my leave of you, gentlemen, permit me to impress anew
upon your minds some precepts to which I have frequently before
this called your attention. Be attentive to your studies, and
correct and gentlemanly in your deportment. Pursue with undeviating
course the paths of virtue and true honor; and rest assured that
although the vicious and the vain may affect to ridicule and
despise, they will inwardly respect you, and that you will thereby
ensure the applause of the good and the great, and, which is of
more importance, the approbation of your consciences and of your
God.
With the advent of Major Thayer began the golden age of the Academy.
This officer was a veteran of the War of 1812 in which he had served
with great distinction; he had studied the military schools of France,
and had profited by his unusual opportunities to acquire a profound
knowledge concerning the conduct of an institution such as the military
school over which he was chief.
The great talents that Major Thayer possessed were well employed. For
sixteen years he shaped the destiny of the Academy, and with such
wisdom and foresight that the broad fundamental principles which he
laid down for the school's guidance, govern the institution today.
[Illustration: Major Sylvanus Thayer
"The Father of the Military Academy"
From the Painting by Thomas Sully, Library U.S.M.A.]
To him, more than to any one man, is due the elevation of the Military
Academy to its high rank among schools of learning both in this country
and abroad.
Upon taking over the command, he immediately drew upon his genius for
organization, with the result that the cadets were organized into a
battalion of two companies, a "Commandant of Cadets" was created, the
classes were for study purposes divided into sections, transfers were
made between sections, and weekly reports, showing daily progress in
studies, were rendered. Moreover, the system and scale of daily marks,
the publication of the _Annual Register_, the introduction of the
Board of Visitors, the check-book system, the preponderating influence
of the blackboard, and the essential part of the modern Regulations
are proofs of his untiring efforts as an executive. The above changes
that he effected, and the reforms that he introduced, are a part of
the modern organization of West Point. Perhaps no one method has so
much influenced the quality of the instruction of the cadets as the
blackboard recitations. Major Thayer insisted on this form, although
old records show that it was introduced at West Point by Mr. George
Baron, a civilian teacher, who in the autumn of 1801 gave to Cadet
Swift "a specimen of his mode of teaching at the blackboard." Today it
is the prominent feature in Academic instruction.
Major Thayer's success in giving West Point an upward impetus had
attracted general attention and observation throughout the country so
that appointments were now sought after with avidity. The politicians
rejoiced at the Academy's increased importance and the consequent
patronage that the appointments offered. Although the present law
did not obtain, whereby Congressmen appointed cadets, still it had
been the custom for the President to appoint men to West Point upon
the recommendation of a Representative. In 1843, a law was passed
that allowed one cadet for each congressional district. Major Thayer
was at his own request relieved as Superintendent, after a brilliant
administration whose results were so beneficial to the institution as
to gain for him from posterity the title of "Father of the Military
Academy."
Could Major Thayer have only peered into the future he would have seen
Fame, years later, crowning three of his raw young cadets. One of the
lads at West Point under Major Thayer was Edgar Allan Poe, America's
foremost literary genius. He entered West Point July 1, 1830, but
after a troublous stay of a little over eight months was dismissed
for repeated misconduct. Not a great deal is known of his brief cadet
days, but his classmates have stated that he was irritable and morose,
and addicted to excessive drinking. He would steal out of barracks
sometimes, long after taps, and "run it out" to "Old Benny Havens," a
tavern kept by Benny Havens on the banks of the Hudson about a mile
below West Point. Benny Havens' name is preserved in song and story at
West Point, and tales that surrounded the cadet reunions in ye olden
days at "Benny's" are flavored with all the romance of a mythical
legend. Old Benny died in 1877 at the ripe age of eighty-nine years,
but his name survives in a stirring West Point song that I quote in
part:
Come fill your glasses, fellows, and stand up in a row,
For singing sentimentally we are going for to go,
In the Army there's sobriety, promotion's very slow,
So we'll sing our reminiscences of Benny Havens, Oh!
* * * * *
To our comrades who have fallen, one cup before we go;
They poured their life-blood freely out _pro bono publico_.
No marble points the stranger to where they rest below!
They lie neglected far away from Benny Havens, Oh!
* * * * *
When you and I and Benny and all the others too,
Are called before the "final Board," our course of life to view,
May we never "fess"[5] on any point, but straight be told to go
And join the Army of the blest at Benny Havens, Oh!
Poe, however, was only one of many who disobeyed the regulations, but
he did not care for military life and made no effort to conceal his
offenses. Finally he was tried by court-martial. For two weeks prior
to his trial he neglected almost all of his studies as a cadet. Two
of the specifications against him were for absences from parades and
roll calls and two for disobedience of orders, but at the trial, he
deliberately pleaded guilty to the latter and not guilty to the former,
the most patent and obvious of his offenses. Whether or not he did this
from a sense of humor, is not known, but his action was not calculated
to help him in the eyes of his superiors. He was dismissed March 6,
1831. Four days later he wrote Major Thayer the following letter:
_Letter of Edgar Allan Poe, Lately Cadet, U. S. M. A., to the
Superintendent: 1831._
(_Original in the library U. S. M. A._)
NEW YORK,
Mar. 10, 1831.
SIR:
Having no longer any ties to bind me to my country--no prospects--nor
friends--I intend by the first opportunity to proceed to Paris with
the view of obtaining through the interest of the Marquis De La
Fayette, an appointment (if possible) in the Polish Army. In the event
of the interference of France in behalf of Poland this may easily be
effected--in all events it will be my only feasible plan of procedure.
The object of this letter is respectfully to request that you will
give me such assistance as may be in your power in the furtherance of
my views.
A certificate of standing in my class is all that I may have a right to
expect.
Anything further--a letter to a friend in Paris--or to the
Marquis--would be a kindness which I would never forget.
Most respectfully,
Yr. obt. st.
EDGAR ALLAN POE.
Poe, however, abandoned the plan and little more was heard of his
whereabouts by his friends at West Point.
The two other cadets under Major Thayer, were Jefferson Davis and
Robert E. Lee, but their history is too well known to bear repetition
here. Suffice to say that Jefferson Davis was mischievous and human
enough as a cadet to be court-martialed for an escapade.
The prosperity of the Academy continued in spite of its opponents in
Congress who, just prior to the Mexican War, came near accomplishing
its overthrow, but the brilliant achievements of its graduates in that
conflict silenced for a while their mutterings. Many young officers
who served with distinction in this war were later to win greater
fame in the titanic Civil War. Grant (class of '43); Sherman ('40);
Hancock ('44); Thomas ('40); Meade ('35); Hooker ('30); Sedgwick ('37)
participated in the campaigns against the Mexicans.
The nation was given ample proof of the wisdom of Washington, Hamilton,
and Knox in their efforts to establish a Military Academy wherein
officers might be educated and trained to organize and discipline
citizen soldiers, and lead them to victory. At West Point today there
are bronze cannon, tattered flags, and mutilated flagstaffs, trophies
of the Mexican War that were presented to the Academy by General
Winfield Scott, the Commanding General of the Army, who stated, "as
under Providence it is mainly to the Military Academy that the United
States became indebted for those brilliant achievements and other
memorable victories in the same war, I have a lively pleasuring in
tendering the seven trophies (semi-national) to the mother of so many
accomplished soldiers and patriots."
The close of the Mexican War found the Military Academy the pet
and idol of the National Legislature. All of its requirements were
solicitously studied and plenty of funds were forthcoming to supply its
wants. As time went on, however, and no foe appeared at our door, the
usual indifference on the part of some toward military affairs, and the
open hostilities of others, were manifested. As before in its history,
the Academy became the object of numerous attacks, but it ignored them,
continuing unobtrusively the preparation of her cadets for their future
work, little realizing how important this work was soon to be.
In 1852, Brevet-Colonel R. E. Lee, Corps of Engineers, class of 1829,
was appointed Superintendent. Under his administration the course
was extended to include five years, embracing more English studies
and Military Law. A new riding hall was completed in 1855 which
greatly increased the opportunity for cavalry exercises. Colonel Lee,
having transferred to the Cavalry arm of the Service, was relieved as
Superintendent, April, 1855, because according to law at that time,
only Engineer officers could serve as Superintendent.
The year before Lee's administration began, there entered West Point
in July, 1851, a cadet, James Abbott McNeill Whistler, aged sixteen
years and eleven months, destined to become one of America's greatest
artists. Whistler remained three years at West Point when he was
discharged for deficiency in chemistry. In speaking in after years of
his experiences with this study, he said, "Had silicon been a gas, I
would have been a Major-General." He was called up for examination in
the subject of chemistry, which also covered the studies of mineralogy
and geology, and given silicon to discuss. When called upon to recite,
he stated: "I am required to discuss the subject of silicon. Silicon
is a gas." "That will do, Mr. Whistler," said the Professor, and the
artist soldier retired quickly to private life.
Another story was told of him in an examination in history. "What!"
said an officer who was his instructor, "you do not know the date of
the Battle of Buena Vista? Suppose you were to go out to dinner and
the company began to talk of the Mexican War, and you, a West Point
man, were asked the date of the battle. What would you do?"
"Do," said Whistler, "why, I should refuse to associate with people who
would talk of such things at dinner."
Although Whistler was not a success in defining silicon or remembering
dates, he excelled in drawing, standing at the head of his class.
The Professor of Drawing at the time was Robert W. Weir, an artist
of no mean ability himself and of generally recognized standing. For
Whistler, Professor Weir always had a high esteem on account of the
unusual talent he displayed in the drawing classes. Specimens of his
work as a cadet are still preserved at West Point.
* * * * *
In 1860, the rumblings of trouble over the slave question began to
be heard even in the secluded Highlands of the Hudson. At first the
Southern and Northern cadets ardently advocated the views of their
respective States, arguing with all of the warmth and enthusiasm of
their young natures but without any particular bitterness. Soon,
however, the gathering of the war clouds and the noise of the storm
that was brewing brought the Southern cadets face to face with a
problem that of its nature was most difficult to solve. Each one had
sworn allegiance to the Government and taken an oath to defend it
against all enemies. What should they do? To remain and support the
Federal Government meant to fight against their own flesh and blood,
yet to resign was to break one's sworn word. As a Southerner myself, I
have often reflected upon the mental suffering that those fellow cadets
of "the long grey line" must have experienced, trying to decide upon
their duty. General Schaff, in _The Spirit of Old West Point_, gives us
a vivid picture of those days at the Academy. So much has been written
about the cadets who left West Point to fight with the Southern forces
that the following data may prove interesting.
At the outbreak of the Civil War there were from the Southern States
eighty-six cadets. Of this number sixty-three resigned, from various
causes connected with the war, leaving twenty-one who remained loyal
to the Government. In the Army, it is a remarkable fact that of the
officers of Southern blood appointed from civil life, one half went
with the Confederacy, whereas only one fifth of the West Pointers went
South. One hundred and sixty-two Southern graduates withstood the
terrible strain of fighting their own people, and remained true to the
flag.
Although up to the time of the Civil War no graduates of West Point
had been appointed to the rank of general officer, the war had not
been in progress a year before the country eagerly turned to men from
the Academy to lead its armies. In September, 1861, six of the eleven
generals in the Regular Army were graduates. At the conclusion of the
war sixteen of the seventeen Regular general officers of the line were
graduates. Sixty-six graduates rose during the war to the grade of
major-general and 112 to that of brigadier-general of volunteers, which
means that more than one third of the graduates engaged in the war rose
to the grade of general officer. Nine received the thanks of Congress
for conspicuous gallantry.
Turning to the Confederate forces, we find a similar state of affairs.
Of the West Pointers in the Confederate service, eighteen were made
full generals, fifteen lieutenant-generals, forty major-generals, and
eighty-eight brigadier-generals. In command of all was Jefferson Davis,
President of the Confederacy, and a West Pointer.
The most famous West Pointer on the Union side was Ulysses S. Grant,
class of 1843, but scarcely less noted were Sheridan ('53), and Sherman
('45). Other graduates whose services were most conspicuous follow:
George H. Thomas ('40), Meade ('35), Hooker ('35), Sedgwick ('37),
McClellan ('46), Halleck ('39), McPherson ('53), Rosecrans ('42),
Warren ('50), Pleasanton ('44), and Gregg ('55).
On the Confederate side we find Lee ('29), Early ('37), Jackson ('46),
A. S. Johnston ('26), A. P. Hill ('47), Daniel H. Hill ('42), and
Longstreet ('42), Ewell ('40), and Stuart ('54).
At the conclusion of the Civil War, a struggle between three million
combatants, all of the armies in the field on both sides were
commanded by graduates; nearly all of the corps; a large majority
of the divisions; the staff corps or organization of supply of both
forces, and many of the brigades. Every important battle of the war was
commanded on one or both sides by a graduate--generally both. This was
the verdict of the end of the great conflict after a test to which no
other institution of learning has ever been put.
After the Civil War the Academy began to drop out of public notice
because the people were more interested in the commercial development
of the country. Apathy on the part of the public has never, however,
affected West Point's attitude toward its duty, so that year after year
graduates were sent forth to fight the Indians upon the Plains where
they underwent great hardships of which the country was ignorant.
Then came the Spanish War to test again the product of the Academy, but
the work of the graduates in Cuba and the Philippines gave ample proof
that the metal was still good and well stamped.
With the advent of Colonel A. L. Mills as Superintendent, the Academy
received a fresh impetus and many important changes were effected.
The Corps in 1900 was increased by one hundred cadets, hazing in all
of its forms was practically abolished after a long bitter fight, and
elaborate plans were inaugurated for the enlargement and rebuilding
of West Point. In this connection the late Colonel Charles W. Larned,
Professor of Drawing, distinguished himself. It is largely due to his
indefatigable efforts and to the foresight and ability of the late
General Mills, and to the Secretary of War, Elihu Root, that West Point
has its magnificent new buildings. Their construction extended over
a long period, from 1904 to 1911, during which time the courses were
expanded and improved to meet the needs of our new Army.
Once again the country is at war, this time with the most powerful and
resourceful enemy that our citizens have been called upon to face.
The graduates of West Point will prove as true to their traditions in
this struggle as they have in the past, and West Point knows that they
will return in triumph to their Alma Mater who ever stands ready to
press the cup of greeting to the lips of all honorable and loyal sons.
CHAPTER III
THE REALIZATION OF AN ARCHITECT'S DREAM
When the springtime rolls around and the Hudson River is at its best,
the annual influx of visitors begins to arrive at West Point. Trains
and boats disgorge official visitors, tourists, boy scouts, delegations
of various brotherhoods and sisterhoods, and picknickers galore. Little
groups of them appear in all corners of the Post, in the area of
Barracks, on the Plain, in the Public Buildings, and along the famous
Flirtation Walk. Their chief interest, of course, is to catch a glimpse
of the cadets, either _en masse_ or individually. When the Corps starts
either to meals or to dress parade, they gather along the sidewalks,
or at the visitors' seats to watch the marching. Some openly express
their enthusiasm and pleasure, genuinely delighted at everything they
see, while others remain silent and phlegmatic apparently taking only a
languid interest in their surroundings.
As I watch my fellow-countrymen strolling about the grounds of the
Academy, I often wonder what are their impressions of this institution.
To many, of course, the historic traditions of West Point, as well
as its functions and purposes, are thoroughly familiar, but to a vast
majority West Point is a closed book. They see the cadets, the drills,
the buildings, perhaps parade, but they never have an opportunity to
acquaint themselves with the intimate life of the Academy. They do
not derive the full benefit from their visit, because they are in the
position of regarding the institution from the outside. In many cases,
the spirit of investigation is restrained by a feeling of timidity upon
their part, a feeling of awe in the face of military surroundings.
The Army is so little known to the people in the United States, that,
to the average civilian, there seems to be some sort of mystery
surrounding military life, and the presence of a man in uniform, with
a waist belt and pistol, doing plain police duty, appears to act
as a check on every natural impulse. The pleasure of his visit is
consequently marred to some extent and he feels somewhat ill-at-ease.
He wants to investigate with greater freedom, but he shrinks from being
told that his projects are "Verboten." Upon his departure he must
of necessity have but a superficial idea of the great work done at
the Academy, unless he has been fortunate enough to have some friend
stationed at West Point who dissipates the apparently cold atmosphere
of military life.
I have often regretted, as I watched the crowds swarming around, that
each individual might not carry away a real appreciation of West
Point, instead of leaving with only the most superficial impressions.
Unless one has graduated from the Academy it is impossible to seize
fully the spirit of the institution, or have a clear idea of its
intimate life. My long familiarity with West Point, both as a cadet
and as an officer, prompts me to portray for the American people the
history, aims, ideals, and spirit of their National Military Academy.
[Illustration: Class Formation in the Area of Barracks]
West Point seen for the first time from the river, whether in sunshine
or through the mists, is a sight not soon forgotten. The monumental
Riding Hall that rises out of the cliff of which it seems to form a
part, first fixes the eye, but as one's glance wanders a little higher
it drinks in the towering pile of Post Headquarters; higher yet, the
eye rests for a moment on the crenelated border of the roof of the
Academic Building, and then, higher still, it pauses to contemplate
the beauty of West Point's crowning architectural achievement, the
Cadet Chapel. For a moment the beholder seems withdrawn from the sordid
material world, and filled with a multitude of noble impressions. He
experiences a spiritual uplift as he admires the majestic simplicity
and grandeur of the buildings, an architectural triumph worthy to have
inspired Ruskin's beautiful thought, "frozen music."
When the Government determined to rebuild West Point, nearly fifteen
years ago, the presence of two fine buildings of Gothic design--the
Library and the Cadet Barracks--decided the style of architecture.
These two buildings ranked as perhaps the most successful examples
of the Collegiate Gothic that was much in vogue for educational
institutions in the country half a century ago. A limited competition
was held for designs and all architects who had distinguished
themselves in Gothic work were invited to participate. Several
beautiful designs for a Renaissance treatment were offered, but one
group of architects, Cram, Goodhue, and Ferguson, submitted drawings
for so admirable a Gothic treatment that they received the unanimous
approval of a board of judges composed of eminent architects. The
construction of the new buildings lasted over a period of about
seven years, during which time the work was under the direction of
Colonel John M. Carson, Jr., Quartermaster, who was representing
the Government. In writing a book on West Point, any mention of the
buildings involves the name of Colonel Carson who performed his
difficult work with an unusual amount of zeal and intelligence. The
result is that the new buildings are splendidly constructed, and
because the architects had an eye for harmony these structures seem to
grow out of the rocks upon which they stand, emphasizing rather than
detracting from West Point's natural beauty.
[Illustration: The Administration Building]
The north road from the station passes first, on the river side, the
Power House built of granite from local quarries. It is designed to
supply the entire institution with electricity for light and power,
and the central buildings with heat from exhaust steam. In a building
of this nature, a factory-like look would be taken for granted and
pardoned, but, on the contrary, its design is not only adapted for its
function, but the building forms an important link in the architectural
whole. It assumes its place quite naturally and modestly, almost
unobtrusively in the natural landscape, tying the buildings in the
upper terrace with the base. The tall smoke-stack is cleverly concealed
within the walls of an imposing granite tower.
On a slightly higher level, and paralleling the river, is the Riding
Hall splendidly impressive with its broad flat buttresses. The latter
seem almost akin to the classic order, and serve in a very large
measure to reconcile the classicism of the neighboring Cullum Memorial
Hall,--an exotic among its surroundings--with the dominant Gothic of
the place. The present Riding Hall occupies the site of not only the
old hall, but also of the old Cavalry stables, and barracks. The old
hall was built in 1855 and, for the number of cadets at West Point
during the ensuing fifty years, it was sufficiently large. With the
increase of the Corps of Cadets, and the quickened interest throughout
the Service in equitation, however, more spacious accommodations for
instruction were required. Usually when a building has served a useful
and honorable purpose for many years, its demolition is generally
viewed with regret. There was, however, no sentimental attachment for
the Riding Hall. Many a painful hour had cadets spent within its walls
learning to ride on the bare back of a raw-boned horse, or floundering
around in the spongy tanbark.
In the little plaza at the junction of the Power House and Riding
Hall, the road winds and passes under the mediæval arch of the Post
Headquarters, or Administration Building. At this point, the bulk and
dignity of the buildings are stupendous, and admiringly we stand,
imprisoned, it would seem, in a quadrangle of Middle Age fortresses,
whose sternness and solemnity seem symbolic of discipline and strength.
The main entrance to the Riding Hall branches from the road a few paces
beyond the arch, the lower level of the galleries being reached by a
flight of steps that cling to the steep retaining wall of the road. The
great arena is 150 by 600 feet and is covered by a cantilever roof,
so that when the eye first encounters this interior, a sensation of
its vastness holds the spectator in its grip. The roof is mostly of
glass so as to afford a maximum of light, and the floor is covered
with tanbark to make more endurable any sudden and unexpected descent
from the back of a capricious beast. The building is steam-heated and
electric lighted, for during the winter months, equitation drills
extend into the late afternoon. The hall can be divided by curtains
into three smaller halls, a scheme that permits three classes to
undergo instruction at the same time. In one portion of the hall are
stalls for one hundred mounts, but the majority of the horses are
kept at the cavalry barracks. The hall is so large that during the
winter months the U. S. M. A. Battery of Artillery uses it for a drill
ground, thereby keeping the horses in good condition and the men well
instructed. Moreover, the officers and cadets are enabled to keep
up their practice in polo. Every Wednesday and Saturday afternoon,
teams of cadets play each other, or try their skill against civilian
opponents. Along the full length of the west wall, and the north and
south end, are balconies for the accommodation of visitors who are
welcome whenever the hall is open.
[Illustration:
Administration
Building
Riding
Hall]
Passing once more under the arch, we admire again for a moment the
graceful Herculean proportions of the Administration Building whose
imposing square tower, tipped with four smaller towers at the corners,
rises precipitately one hundred and sixty feet. It is an interesting
fact in these days of steel construction that this tower is built of
solid masonry. At the southeast angle of the building, on a level with
the base of the main floor, is an enormous eagle carved in granite,
its head high, its wings outstretched and flattened back proudly
against the two sides of the edifice, as if proclaiming to the world
its mission of protection over the Academy whose administrative heart
is enclosed in this structure. As we ascend the stairway, alongside
the basement at the left, we pass a large Gothic window which affords
light to a vaulted hall used for courts-martial. The interior of this
hall is in keeping with the mediæval donjon appearance of the whole
building, and of such a chill and forbidding aspect as to inspire in
the accused a feeling of guilt, _nolens volens_. The flight of stairs
mounts to the level of the Post proper where an eastern view of the
building is disclosed. A large sally-port leads into the court around
which the building is constructed.
The exterior walls are ornamented with shields representing the
coats-of-arms of various states, territories, and foreign possessions
prepared from the official seals, and expressed according to the
laws of Heraldry. The only coat-of-arms of an individual is that of
George Washington, at the top of the east elevation of the courtyard.
The obverse and reverse of the great seal of the United States will
be found above the east and west entrances, respectively, of the
sally-port. Flanking the obverse of the great seal are the seal of the
War Department and the device of the Corps of Engineers. In addition
to the shields, the devices of the various staff departments, usually
associated with a headquarters, have been placed in the sally-port. Two
of them, the Adjutant-General's Department, and the Quartermaster's
Department, are on shields on the north side of the sally-port, and
the Subsistence Department, Signal Corps, Pay Department, Ordnance
Department, Inspector-General's Department, Judge-Advocate-General's
Department, Medical Department, and Chaplain's Corps, are on corbels at
the bases of the ribs of the arch.
[Illustration: Colonel Jonathan Williams, Corps of Engineers
First Superintendent of the Military Academy
From the Painting by Thomas Sully, Library U.S.M.A.]
In the courtyard the names that are carved in the granite were selected
for the following reasons:
WILLIAMS Colonel Jonathan Williams, first Superintendent
of the Military Academy.
SWIFT Colonel Joseph G. Swift, first graduate
of the Military Academy.
TOTTEN General Joseph G. Totten, the tenth
graduate and _ex-officio_ the first
inspector of the Military Academy
while serving as Chief of Engineers
from 1838-1864.
THAYER Major Sylvanus Thayer, Father of
the Military Academy.
DELAFIELD Colonel Richard Delafield, Superintendent
from 1856 to 1861, under
whose administration much construction
was completed.
JEFFERSON Thomas Jefferson, third President
of the United States, during whose
administration, 1801 to 1809, the
Military Academy was founded.
MONROE James Monroe, fifth President of
the United States, 1817 to 1825,
under whose administration the Military
Academy developed and was
encouraged.
Upon the second floor is the Academic Board room, a Gothic hall
illuminated with stained glass windows containing emblems of the
various arts and sciences. The most striking feature of the room is the
massive stone mantel, modeled by Laurie and ornamented with statuettes
of the world's greatest warriors.
The description of the statuettes and the reasons for selecting the
subject are given in a letter to Dr. Holden, late librarian, dated
November 23, 1906. An Advisory Board of officers recommended:
That the character of the figures on the mantlepiece be of a
general military type--historical or legendary--best suited to
harmonize with the architectural treatment and selected by the
architects themselves from the three lists in this letter of
November 23, 1906.
The heads appearing at the top of the mantel--in the crenelations--have
no relation to the statuettes underneath. The small shields immediately
below the statuettes are, however, indicative of the subjects as
follows:
JOSHUA. Sun and Moon--taken from the Biblical legend describing the
distinctly miraculous standing still of the Sun on the occasion of a
certain battle.
HECTOR OF TROY. Mycenæan Scroll--a sort of triangular fylfot, which
stands for Mycenæan civilization. This device would apply equally to
that of Troy of which Hector was the greatest figure.
[Illustration: Colonel Joseph G. Swift
First Graduate of the Military Academy
From the Painting by Thomas Sully, Library U.S.M.A.]
DAVID. King of all Israel, warrior and psalmist--the harp--selected by
the architects instead of a little sling, especially since the head of
Goliath is under the foot of the figure above.
ALEXANDER THE GREAT. A conventionalized Gordian knot severed.
JULIUS CÆSAR. The standard carried by the famous Roman Legions.
CHARLEMAGNE. King of the Franks--The imperial iron crown.
KING ARTHUR OF ENGLAND. The Holy Grail, symbolizing the whole purpose
of his career.
GODFREY DE BOUILLON. Heraldic cross of Jerusalem of which city he was
king and which forms a part of his own coat-of-arms.
JUDAS MACCABEUS. The hammer--which is the actual meaning of the name
"Maccabeus."
In the mantel, the figures are arranged chronologically and
historically. Three of them, _i. e._, Hector, Alexander, and Cæsar,
were Heathen; three were Christians, viz.: Charlemagne, King Arthur,
and Godfrey; and three were Jews, viz.: Joshua, David, and Judas.
The choice of subjects was suggested to the architects by Caxton's
preface to the first volume of Sir Thomas Malory's _Morte d'Arthur_,
from which the following quotation covering the choice of the figures
is taken:
For it is notorly known through the universal world, that there be
nine worthy and the best that ever were, that is to wit, three
Paynims, three Jews, and three Christian men. As for the Paynims,
they were to-fore the Incarnation of Christ, which were named,
the first Hector of Troy, of whom the history is comen both in
ballad and in prose, the second Alexander the Great, and the third
Julius Cæsar, Emperor of Rome, of whom the histories be well known
and had. And as for the three Jews, which were also to-fore the
Incarnation of our Lord, of whom the first was Duke Joshua which
brought the children of Israel into the land of behest, the second
David, King of Jerusalem, and the third Judas Maccabeus, of these
three the Bible rehearseth all their noble histories and acts. And
since the said Incarnation have been three noble Christian men,
stalled and admitted through the universal world into the number of
the nine best and worthy. Of whom was first the noble Arthur. The
second was Charlemain, or Charles the Great, of whom the history is
had in many places, both in French and English. And the third and
last was Godfrey of Boloine.
[Illustration: Cadets at Equitation in the World's Largest Riding Hall
(600 ft. × 150 ft.)]
Upon the same floor as the Academic Board room are the three offices
of the Superintendent, the Adjutant, and the clerks. The Headquarters
building houses, moreover, the offices of the Treasurer, the
Quartermaster, the printing shops, the Post Office, and the Ordnance
Museum, the entrance to which is at the left of the sally-port. Begun
in 1854, the Museum has throughout the years gathered some valuable
trophies of war, interesting relics, and models of the arms of all
nations. Visitors are well repaid by a visit to this interesting
spot. Historic relics abound in the rooms. I might mention among them a
portion of the flagstaff that was at Fort Sumter in 1861; presentation
swords belonging to distinguished American generals; General Grant's
uniform and horse equipment; mementoes of the Philippine insurrection
and of the war with Spain, not to speak of a rare and beautiful
collection of weapons of all kinds. Not the least interesting part
of the exhibit are the trophies of the Revolution. In glass cases
are preserved five flags captured by the American army during the
Revolution, two of which were British royal colors, and three taken
from the German mercenaries sent over by King George. The former were
taken at Yorktown. All these flags were originally the property of
General Washington by whom they were bequeathed to George Washington
Parke Custis, the son of his adopted son, and grandson of Mrs.
Washington. He in turn bequeathed them to the War Department, which
came into possession of them in 1858. The same year Secretary Floyd
presented them to the Academy.
Across the road from the Administration Building is the Cadet Mess. It
is one of the oldest buildings, the main part dating from 1850. The
architecture conforms in a general way to that of the new buildings.
With its broad pavement in front, it sets well back from the road,
possessing not only the dignity of its more imposing neighbors, but in
addition a certain quaint charm.
The large central doors give access to the main hall whose walls are
hung with portraits of distinguished graduates, chiefly the former
Superintendents of the Academy. Perhaps the most interesting painting
is that of General Robert E. Lee, who was Superintendent in 1852.
Frequently I have heard visitors express surprise that General Lee's
portrait should hang in the halls of the National Military Academy,
notwithstanding he was a graduate and afterwards a Superintendent. The
fact that he fought against the Union, they argue, should preclude the
bestowal of the honor. West Point, however, considers that since we are
a united people once more, his record should be recognized by his Alma
Mater from whom he learned the lessons that brought him his fame and
his glory.
Symmetrically arranged in the hall are the mess tables. They are made
to accommodate ten cadets, but occasionally, here and there, two
tables are shoved together for economy of floor space. At these tables
are twenty cadets. It is a pleasure to enter the Mess Hall prior to
any meal. Every table is immaculate with its snowy clean cloth, its
polished cutlery, and shining crockery. The cadets are not seated by
classes but by companies, each company having a certain number of
tables in the section of the hall assigned its battalion. As a rule,
the ten messmates are made up of three first classmen, two second
classmen, two third classmen, and three fourth classmen. The latter
are given, by custom of the Corps, various duties to perform at mess
such as carving the meat, procuring the coffee and milk.
[Illustration: The Carved Mantel in the Hall of the Academic Board
_Sculptor--Laurie_
The Nine Great Warriors of the World
_Note: There are also two figures on the sides, not visible_]
Three long passageways lead from the main dining-hall to the kitchen.
At first glance the super-cleanliness of the surroundings strikes the
observer, but his attention is soon attracted to the numerous clever
devices for cooking, and for saving time and labor. The preparation
of the food for cooking occurs outside of the kitchen proper. Each
department prepares its kind, whereupon it is carried to the chef to
be cooked and served. The labor of preparation is greatly reduced by
the liberal use of machinery. A clever electrical machine rapidly
peels the potatoes, a whole bushel of them, in a few minutes; other
contrivances make and cut the bread, sterilize the milk, freeze the
ice-cream; and wash and dry the innumerable dishes. Without the aid of
these labor-saving devices it would be impossible to maintain such an
excellent mess for the cadets. Even now the capacity of the plant is
tested almost to its limit, and with the increase in the Corps to 1200
cadets, it will be necessary either to enlarge the present Cadet Mess
or to build a new hall. The disappearance of the present Mess, Grant
Hall, will be viewed with great regret by many graduates who dined for
four long years within its really historic walls.
South of the Cadet Mess is the Hospital for cadets, a large granite
building perched on a terrace, well back from the road. It consists
of a central portion of three stories and basement, with two wings
of two stories each and basement. The older portions date from
1875, but the wings are of more recent construction. The wings are
practically detached from the main portion of the building for the
possible isolation of cases. The equipment is, of course, modern in
every respect. Each wing contains two wards, making four in all, named
respectively Cuyler, McElderry, McParlin, and Wheaton in honor of
former distinguished military surgeons on duty at West Point. I do not
suppose that there is a building on the Post which arouses in cadets so
many different kinds of feeling. To some it is a place to be avoided,
but to a large number, especially to those who succeed in entering for
minor ailments, it is viewed as a haven of rest. It is the one place
where the cadets are free from the irksome routine, where there is no
reveille, and where the convalescents revel in what appears to them
epicurean feasts. Vatel, the famous French chef, never enjoyed more
renown than does the cook at the hospital.
Almost every cadet has a secret longing to be in the hospital at least
for a short period during his course, and those who "break in" for
slight ailments are regarded with a special esteem by their fellows.
One of the first adages that a plebe learns at West Point is "faint
heart never broke into the hospital." The surgeons, however, are
pretty clever men and they size up the situation very clearly in each
case.
[Illustration: The North Cadet Barracks]
I remember that upon one occasion when I was a cadet, a group of
convalescents were, one winter day, holding a mutual congratulatory
meeting in one of the wards, the burden of the conversation being their
luck and also their skill in remaining so long in this abode of rest.
Arthur C----, who was the most successful of the disciples of the "rest
cure," was perched upon a bed explaining to an admiring line of heads
in little snow-white cots, the strategy necessary to remain in the
ward, finishing his discourse oratorically; "Some may come and some may
go but _I_ stay on forever!" when the door opened and in walked the
surgeon. Cadet C---- was next day returned to duty.
The officer in charge of the hospital is the Post Surgeon, who is
assisted by three or four captains of the Medical Corps, and by several
Dental Surgeons. These officers are also in charge of the Soldiers'
Hospital, a separate building for the enlisted men of the garrison, and
are responsible for the general health of the command.
The chief buildings of the Academy occupy relatively a small area
of ground. Just north of the Cadet Mess and flanking the main road
are the two Academic buildings, known as the East and West Academic.
The East building is new, having been completed in 1913, one of the
last provided for in the rebuilding of West Point. The West Academic
building, which was completed in 1895, is built of Massachusetts
granite and cost about five hundred thousand dollars. In this building
are located the Departments of Civil and Military Engineering,
Mathematics, Law, Drawing, Ordnance and Gunnery, and English and
History; in the East building the Departments of Modern Languages,
Chemistry and Electricity, Natural and Experimental Philosophy. The
latter building is provided with the most modern lecture rooms,
electrical and chemical laboratories, besides a mineralogical and
geological museum. The major portion of both buildings contain the
section rooms for recitation purposes. Visitors are admitted if
accompanied by an officer.
The architecture of both of these buildings is Gothic, but that of
the new or East building is of a more exquisite beauty. Splendidly
situated, it gives the impression of bulk and mass, much the same
feeling that one has in regarding a dreadnought for the first time,
but this impression soon gives way to an appreciation of a certain
delicacy of treatment, a simple dignity that pleases. One of the best
impressions of its beauty is obtained about dusk when the evening mists
dim its outlines and its surface is bathed in shadows relieved only by
the glimmering of the mediæval lanterns on either side of the main door.
Immediately facing the center of the East Academic Building and
across the road, is a large opening known as a sally-port through
which the sections of cadets must march to recitations in the East
Academic building. This passageway connects the main road with the
area of barracks, a space of ground that derives its name from the
brown-stone buildings that bound a portion of its perimeter. Along one
side is a cement walk on which the cadets form to be marched to their
recitations, and a sidewalk borders the barracks. With the exception
of a small plot of grass near the Academic building the area is devoid
of verdure, but is covered with a fine gravel that gives a clean and
well-groomed appearance to the ground. The word "Area" has great
connoting power. To a large number of cadets, it vividly brings to
mind the punishment tours that they wearily trudged on Wednesday and
Saturday afternoons across its surface. To the majority, however, it is
the "hub" of cadet life, the assembly place for recitations, sometimes
for meals; the scene of many an inspection or a guard mount, and most
important of all, it contains a small insignificant building with a
clock tower where dwell the Commandant of Cadets and his assistants,
the Tactical officers.
The building on the north and west of the area is the South Cadet
Barracks, built in 1848. This edifice, of 360 feet frontage, is
constructed of native granite, with crenelations and cornices of red
sandstone, and the Elizabethan style of its architecture harmonizes
perfectly with the Gothic of the new buildings. In fact, the old
Cadet Barracks is one of West Point's handsomest buildings. There
are two hundred rooms in the building, 14 × 22 feet, each planned to
accommodate two cadets. It is completely supplied with modern plumbing,
heating, and electric lights. The barracks are divided into divisions,
each containing sixteen rooms. There is no lateral communication
between the divisions, but a certain number of them are assigned to a
company, according to its strength. At present the 1st Bn. Cos. A, B,
C, and D are quartered here.
I have often stood in the Area of Barracks and looked through the
north sally-port to enjoy the fine vista that it framed. A section of
the Plain fills half the picture, a beautiful foreground, either when
resignedly spread out to the heat of the Highland summer, or shivering
under its fleecy blanket of snow, over which the winter winds angrily
blow. In the upper half against the far-away background of the Highland
hills is the slender flagstaff, sometimes swathed in the folds of
our national emblem, sometimes resisting with all its strength the
fluttering of its precious charge which seems to implore its release to
join the flight of the breeze.
As we leave the north sally-port and turn toward the angle between the
two sets of barracks, high on the hill the monumental Cadet Chapel,
West Point's spiritual fortress, looms above with extraordinary
effectiveness. It has a fine site on a commanding spur just above
the old Cadet Barracks on the west, from which point it dominates the
Post. It lies in the shadow of old Fort Putnam of Revolutionary fame,
and, built of stone quarried from its own hill, it seems a part of its
naturally beautiful surroundings.
[Illustration: The Chapel]
This edifice is in reality a large church with a seating capacity of
fourteen hundred persons. In plan it is a crucifix, surmounted by a
large central tower whose parapet is 130 feet above the pavement of the
interior and 420 feet above the level of the river. The tower contains
two stories: the bell-ringer's story and the belfry above. There are
as yet no chimes, but on national holidays, Christmas morning, and
Easter, the band mounts to the bell-ringer's story, and the airs
appropriate for the day float out through the louver windows in a weird
and mysterious manner, as if some invisible symphony was playing in the
clouds.
Just above the stately clerestory windows, and around the cornice of
the building, is a row of carved figures, little bosses, representing
the quest of the Holy Grail. Over the door of the main entrance is a
great two-handed sword, Excalibur.
One should pause for a moment on the terrace in front of the main
entrance to enjoy the magnificent panorama. In the distance, flows the
Hudson winding among the Highland hills, and skirting the great Plain
along whose edge stand the Bachelor Building, Cullum Hall, and the
Officers' Mess. Directly below, in the shelter of the chapel hill,
are grouped all of the main buildings pertaining to the cadets, the
most conspicuous of which are the barracks. Viewed from this height
the arrangement of the buildings resembles a regular nest, _le nid des
cadets_.
A winding road back of the barracks leads to the Chapel. The interior
of the Chapel is 200 feet long, and across the transepts, 72 feet
wide. The nave contains fourteen large Gothic windows, now filled with
temporary glass but which will later be replaced with memorial windows.
The jewel of the interior is the great chancel window, with its noble
inscription:
Erected to the glory of the God of Battles and in faithful memory
of the departed graduates of the United States Military Academy,
West Point, by the living alumni.
The deep shades of purple and red give the window an extraordinary
richness. The best lights from the glass are obtained in the early
afternoon about four o'clock. It is of rare richness and beauty, and
for subject, color, and arrangement it is thought to be unexcelled in
our country. There are twenty-seven panels, each of which contains an
almost life-size figure representing one of the chief militant figures
in the Bible. Services are held in the Chapel every Sunday morning at a
quarter before eleven and are attended by cadets, officers, enlisted
men, their families, and a large number of visitors. In addition to the
regular service in the Chapel, where the cadet choir of one hundred
and five voices is a feature, a series of organ recitals, free to the
public, is given each year.
[Illustration: The Interior of the Chapel]
The organ is of unusually fine quality and is surprisingly effective
for an instrument of three manuals, or keyboards. But it is still
incomplete, being both undersized for this cathedral-like building and
inadequate to the proper performance of the finest music. The addition
of a fourth manual, with its pipes located in the gallery opposite the
present organ, now eloquently vacant, is needed to bring the musical
part of the service and the recitals up to the highest efficiency.
Upon the completion of the improvements contemplated the organ
will become one of the art glories of the country, and with the
Chapel,--perfect in architecture, surroundings, and acoustics--would
create an atmosphere of rare idealism. The acquisition of every new
stop given is indicated by a bronze tablet placed upon the console,
or key desk, of the organ. The significance of such tablets would
make this organ and console unique, not only in establishing historic
traditions but also in affording substantial encouragement to the
volunteer organist and to the choir.
The opportunity here presented is most worthy for anyone desirous of
establishing a memorial to a graduate of the Academy, for a graduate
wishing to honor the memory of one of his immediate family, for a class
gift, or for anyone interested in furthering an artistic influence over
the lives of the future officers of the Army of our country.
To assist in the completion of the organ, a fund, known as the "Organ
Fund" has been started, which is kept alive by recital offerings,
private subscriptions, and proceeds from sale of "The Corps," a popular
West Point song.
In the transepts are galleries but they are not at present equipped
with seats. Along the nave also are covered galleries, almost hidden
from view by the suspended flags.
A request made to the sexton will enable the visitor to see the crypt,
a vaulted room beneath the Chapel that is designed to be the final
resting place of West Point's illustrious military dead.
To care for the spiritual welfare of the cadets and other residents of
the Post, there is a Chaplain who is appointed by the President. His
term of office is for four years, but he is usually re-appointed.
The location of the Chapel makes it visible from many places on
the Post. In walking around the grounds, every once in a while an
extraordinarily effective view of the fine building strikes the
beholder. Each glimpse seems more beautiful than the previous one,
and a general impression remains that the Chapel holds a spiritual
dominion over the institution. Every corner of the main part of West
Point seems under its influence. This feeling is particularly strong
as we stand on the sidewalk between the old and new Cadet Barracks and
gaze at this monumental pile of ethereal beauty that seems to lose
itself in the sky. I never view the Chapel from this point without
thinking of one of Maxfield Parrish's imaginative paintings of the
Arabian Nights.
In the southwest angle of the Plain, from where I like to view the
Chapel, is a white granite statue of Major Sylvanus Thayer, class of
1808. The funds for this modest but beautiful monument, which was
unveiled June 11, 1883, were contributed by loyal graduates of the
Academy and by loving friends. General Thayer was Superintendent of
the Academy from 1817 to 1833. He was the first to establish a real
curriculum, and so valuable were his services that he has since been
called "the Father of the Academy." The body of the distinguished
officer was brought from South Braintree, Mass., and reinterred in the
Post cemetery on November 8, 1877. The sculptor of the monument was
Carl Conrad.
On the west side of the Plain is the North Cadet Barracks, one of the
new buildings completed in 1908. The Gothic style employed in the
treatment of this building, while resembling somewhat that of the old
barracks, has more dignity, beauty, and grace. Not enough difference
exists between the two to cause any lack of harmony. Chief among the
changes made in the new barracks are the windows which are triple
instead of single. As far as the interior is concerned the arrangement
is identical. Modern plumbing has been installed in the old barracks to
conform to its new neighbor, so that the cadets of today are no longer
obliged to run down to the area to draw their water from the hydrant.
The very mention of this ancient and picturesque custom brings back
many memories, chiefly centered around reveille on a bitterly cold
morning. Immediately upon the dismissal of the ranks, hordes of cadets
(it seemed to me), clustered around one poor little hydrant from which
a thin stream of icy water trickled into the _papier maché_ buckets.
Now, upon each floor of barracks are faucets with hot and cold water! I
wish that I were a cadet again!
No one would judge the building to be a military barracks. Rather, a
study of its lines would suggest that it was the home of some religious
order. It has an undeniable ecclesiastical character that impresses one
immediately. I have always derived great pleasure in contemplating its
beauty and my imagination at these times fancies it as the refuge, the
shelter, the sanctuary of a body of men separated from the material
affairs of the world. It seems made to house only the best and noblest
in nature, to be the environment from which high ideals receive their
greatest inspiration. A group of happy smiling cadets coming out
of their rooms at this moment tells me that my imagination has been
dwelling upon reality and not wandering into fantastic fields. This
building is indeed the home of a splendid Order, the inspiring order of
young manhood, clean-minded and honorable, trained in a school where
they are taught the most scrupulous regard for the truth, and where
they are given a _mens sana in corpore sano_.
In the quadrangle the light brick facing gives, in all sorts of
weather, a bright cheerful aspect, a sunny appearance, that contrasts
in a most welcome manner with the gloom of the quadrangle of the old
barracks.
Set well back from the Plain, and to the north of the new barracks,
is the Gymnasium. It is not built of granite like its neighbor, the
new barracks, but has received from the hands of the architect an
artistic and interesting treatment of brick and limestone. The broad
wall-like surface of the front is broken by six flat buttresses, whose
terminals are richly decorated. Viewing the building from the southeast
corner these buttresses appear like giant sentinels, fine specimens
of the building's physical development. Far across the parade ground
the Bachelor Officers' quarters, of similar design, serves with the
Gymnasium to link in one harmonious whole the old and new buildings
surrounding the Plain.
The second story is devoted to the gymnasium proper. It is lighted by
large skylights, and equipped with every possible device for physical
development. The remainder of the building houses a fine natatorium, 77
feet wide and 92 feet long, with a swimming-pool 40 feet wide and 80
feet long; a fencing-room, a boxing-room, a wrestling-room, besides the
necessary dressing-rooms for both cadets and officers. In the basement
is a shooting gallery for indoor rifle and pistol practice.
North of the Gymnasium and fronting the Plain, are the quarters of the
Superintendent of the Academy, an interesting old house that dates
from 1820. Surrounding the house is a quaint old ironwork porch of
later date, but old enough to be a curiosity today. A well-proportioned
central hall gives access to charming suites of spacious rooms on both
sides of the quarters, but the suite on the left is the more beautiful
for it offers a fascinating vista of three large rooms terminating in a
conservatory filled with exotic plants. Delightful hospitality has been
dispensed in these rooms to some of the most noted people in the world.
Royalty, distinguished foreigners, civilians, and soldiers, noted
American men and women are constantly visiting West Point to inspect
the school and are always entertained by the Superintendent. If the
walls of these quarters could speak they would relate some interesting
incidents of the official life of West Point. The beauty of the rooms
is today enhanced by a number of fine family portraits, painted by
Thomas Sully, and the property of the present Superintendent, Colonel
John Biddle, Corps of Engineers.
At any official function the guests usually crowd the fascinating old
porch to watch the evolutions of the cadets upon the Plain opposite, or
sometimes they indulgently stand on the front stone steps to pose for
the breathlessly impatient movie men and photographers. The quarters
are surrounded by beautiful, well-kept lawns and tall graceful elm
trees.
A traveler may go far before he will behold so majestic a view as that
of the Hudson River from Trophy Point and Battle Monument. For pure
beauty it is unsurpassed. In the distance lies the city of Newburg,
against a dim background of the Shawangunk Mountains, and in the
foreground the little village of Coldspring nestles close to the side
of rugged Breakneck. On the opposite side Cro's Nest descends abruptly
to the water. At this spot the Hudson seems to be surrounded on all
sides by land so that the beholder might well imagine himself in Europe
among the Italian Lakes.
Upon this spot are a number of trophies, among the most interesting
of which is a portion of the old chain that, during the Revolutionary
War, was stretched across the river from just above Gee's Point to
Constitution Island to prevent the passage of the British ships.
On a wooden carriage is a large Armstrong gun, captured at Fort Fisher
during the Civil War, and nearby are many other guns taken in the
Mexican and Spanish Wars. The Swartzkopf torpedo inclosed in an iron
railing was captured from the Spanish cruiser _Viscaya_ in the war with
Spain, and the twenty-pound stone ball was brought from Smyrna, Turkey.
The polished monolith of granite nearby upon whose tip stands winged
"Fame," poised with trumpet and outstretched wreath, is Battle
Monument. The names which may be read upon its rolls are the victims of
the Regular Army of 1861, to whose memory their comrades in arms have
created this beautiful memorial.
IN MEMORY
OF THE
OFFICERS AND MEN
OF THE
REGULAR ARMY OF THE UNITED STATES
WHO FELL IN BATTLE DURING THE
WAR OF THE REBELLION
THIS MONUMENT IS ERECTED BY THEIR
SURVIVING COMRADES
In the words of the late Colonel Larned, "this memorial was not built
by a grateful country, but by voluntary offerings from the hard-won
pay of comrades in the field within hearing of the roar of battle,
and in sight of the dead whose memory it preserves.... It is but right
to add that the designer, Stanford White, and the sculptor, Frederick
MacMonnies, have given a generous and enthusiastic labor to the work,
far beyond the money recompense received, and in the true spirit of the
artist and patriotic citizen."
[Illustration: View up the Hudson River from Trophy Point]
Toward the east is an equestrian bronze statue of the Father of our
Country, seated upon his charger and with hand raised toward the
Academy buildings as if in benediction of the institution that he
labored so hard to establish. In these days of materialism, it is
interesting to note that this magnificent gift was recently made to
the Academy by someone who refused to disclose his name. The base of
the pedestal bears the simple inscription "Presented by a Patriotic
Citizen."
The hotel, just in the rear of the Washington Monument, was built in
1829, and with the exception of a wing that was added in 1850, it
has remained practically unchanged. It is not difficult to imagine,
therefore, that its appointments fail to satisfy the luxurious tastes
of present-day Americans, so that many complaints are heard, and not a
few jokes passed at its expense. One humorist remarked that Washington
was raising his hand not in benediction of the Academy, but in a
warning to the guests to keep away from the hotel.
From the hotel, a steep little graveled path entices the visitor into
a most enchanting walk that skirts the steep precipice along the river.
For three-quarters of a mile, Flirtation Walk pursues its way with its
windings and abrupt turnings, its ascents and descents, past the site
of the old chain Battery, and farther on past old Lantern Battery on
Gee's Point, past the Bachelor Officers' quarters, until at the base of
Cullum Hall it ends in Kosciusko's Garden. The latter is a cool little
sheltered plateau, said to have been a favorite of the Pole. When the
trees are in bloom, to stroll along the Walk is to feel the delicacy of
nature, to behold the quintessence of her refinement. The foliage seems
like maiden-hair fern through which charming little vistas of the river
and the opposite bank are framed. On summer days it is a favorite for
the cadets and their girls, who wander along its graveled path whiling
away the time, or who seek out the choice nooks and screen themselves
from profane eyes with a gaily parasol.
Near the end of Flirtation Walk alongside of old Battery Knox, a
Revolutionary relic, stands the Bachelor Officers' quarters. This
building of brick and limestone, serves to tie the new buildings with
the classic Cullum Memorial Hall and the Officers' Mess. Its color is
darker than the pink granite of Cullum Hall, to approach more closely
the dark brown of the Library and the gray of the Academic, while its
flat buttresses harmonize with the straight lines of Memorial Hall.
[Illustration:
_Photo White Studio_
"Spooning" on Flirtation Walk]
In this building there are forty suites of three rooms and a bath
each, besides rooms in the basement for the janitor and for officers'
servants.
Adjoining the Bachelor Officers' quarters is the beautiful Cullum
Memorial Hall, built of Milford pink marble and resembling somewhat
in style, the Erechtheum, on the Acropolis at Athens. Just under the
cornice and above the four Ionic columns is carved: "To the Officers
and Graduates of the Military Academy." To the left of the main hall is
a small assembly room, whose walls contain bronze tablets to graduates
who have been killed in action. The flags are guidons, carried by our
Cavalry, both regular and volunteer, during our wars, chiefly during
the Spanish War.
In the lower halls are tablets to Superintendents and to the deceased
Professors of the Academy, besides fitting bronze memorial shields,
recounting the battles of the Civil War in which graduates of the
Academy participated.
Bronze trophy cannon are freely used in the adornment of the walls,
both in the lower hall and in the hall on the second floor. They are
chiefly Mexican and Confederate trophies, but a few were captured from
the British at Stony Point (south of West Point) in July, 1779.
Among the most interesting perhaps of the cannon are the two large
bronze ones in front of the main entrance. Both were made at Douay,
France, in 1755, under the supervision of J. Béranger, royal
commissioner of foundaries. The one on the right (as one enters the
building) is inscribed "Le Fâcheux," and the one on the left "Le
Conquérant." Both were taken from the Punta Blanca Battery in the
harbor of Santiago de Cuba. These cannon are almost the exact duplicate
of the five cannon at the United States Naval Academy, Annapolis, Md.,
and very similar to two cannon at the Virginia Military Institute,
Lexington, Va. The latter guns, cast about eighty years before the
others, are part of several cannon purchased from France by Virginia
in 1778 for use in the Revolutionary War. It is surprising that the
Spanish should have been using them in Cuba, since the Spaniards
manufactured guns of equally high quality.
The four inverted bronze mortars that surmount the corners of the
piazza were made, two at Sevilla and two at Barcelona, in Spain, and
were surrendered by the Mexicans to the American forces, April 22,
1847. These mortars were known as stone mortars, and they were employed
in siege operations to precipitate large masses of stone upon the heads
of the enemy in the advanced trenches, or in like manner to clear the
trench of its defenders preparatory to an assault.
The second floor is called Thayer Hall, a large, beautifully
proportioned room used for public functions, officers' and cadets'
dances. At one end there is a small stage and a few scenic fixtures.
In this hall are the portraits of graduates who have not only gained
the rank of general officer, but have commanded _in time of war_ units
commensurate with their rank.
The building south of Memorial Hall is the Officers' Mess, where the
bachelor officers obtain their meals. The building was constructed
and partially furnished from Government funds, but it is kept up and
managed by personal funds of officers on duty at West Point. In design
it conforms closely to Cullum Hall, although plainer and more modest.
It was so built as to be inconspicuous and not detract from the classic
beauty of its stately neighbor.
The interior of the Mess is quite beautiful, especially the main
dining-hall and reading-room, whose principal features are mantels
ornamented with small replicas of the figures of Day and Night, Morning
and Evening, that adorn the tomb of the Medicis in Florence. Both
Cullum Hall and the Mess were designed by the late Stanford White and
completed, the former in 1899 and the latter in 1903. The Mess is an
organized body incorporated under the laws of the State of New York as
the West Point Army Mess. It was started in 1841 by General McClellan.
There is no Mess in our Army that has had a continued existence for so
long a term as this Mess, and I have heard it stated that few English
or continental Messes are as old in the above sense.
The trip around the buildings brings us to the Library for which we all
entertain a genuine affection. The quiet and repose of its fine rooms
have an attraction for both officers and cadets that no other building
offers, so that it is usually filled with lovers of books, especially
on winter afternoons. Cadets, officers, enlisted men, women, and
children frequent the various rooms whenever an opportunity presents
itself. There is no greater pleasure, I believe, at West Point than to
draw a big leather armchair over in one corner of the library and there
forget the world in a good book.
Like so many of the buildings at West Point it was built of native
granite, and in the Gothic style of architecture. The present
building was erected in 1841 on the site of the old gun shed and
cost approximately $50,000. It was, however, entirely remodeled in
1900-1901. The Library was originally designed by a board of Army
officers and the style of architecture determined upon was used seven
years later in the present South Cadet Barracks. The dominant note
that these two buildings gave to the character of the structures at
West Point, determined the style of architecture in the comprehensive
rebuilding of the Academy that began in 1904.
The library proper was founded in 1812, and with the years has grown
until at the present time it contains 99,148 books. I am informed that
the 100,000 mark will be celebrated by the purchase of a memorable
volume. The Library may be said to be the oldest inhabitant of the
neighborhood, for all its former associates, the old Riding Hall, the
Cavalry Barracks, and the old Cadet Chapel are gone.
The latter building, however, has not permanently disappeared.
Sentiment against its demolition was so strong that an appropriation
was obtained to remove it to the cemetery to be used as a mortuary
chapel. Consequently in 1911 it was taken down, each stone marked,
and so carefully reconstructed that it is impossible to detect the
slightest change in its appearance. The tablets, and the painting of
"Peace and War" by the late Professor Weir have been preserved, but the
British flags have been removed to the Ordnance Museum.
The cemetery is a beautiful, peaceful spot set aside for the repose of
West Point's dead. In the northeast angle is the cadet monument erected
in 1818, to Cadet Vincent M. Lowe of New York, by his fellow-cadets. On
New Year's day, 1817, Cadet Lowe was killed by the premature discharge
of a cannon while he was firing a salute. The pedestal is covered with
the names of other cadets who died later on. Among the illustrious dead
buried in the cemetery are Major Sylvanus Thayer, General Winfield
Scott, Robert Anderson, and George A. Custer.
Along the main roads both north and south of the Plain are modest
dwellings furnished for the officers on duty at West Point. The
south end terminates in a broad plain used for the Cavalry and Field
Artillery drill of the cadets.
In order that thorough instruction in both of these arms may be
imparted to the cadets, detachments of Cavalry and Field Artillery are
stationed at the Academy. Their barracks and stables form part of the
new buildings, and are fine examples of what intelligence and taste can
do for comfort and convenience. Along the west side of the drill field
are the stables and, directly above, gracefully placed on the hillside,
are the barracks provided with the best and most modern equipment. The
presence of these two detachments of enlisted men, as well as that of
the detachment of Engineers, is absolutely essential to the efficient
instruction of the cadets.
An understanding of the uses of the buildings and some description
of the prominent landmarks is necessary to a correct appreciation of
the cadet's life and activities. The survey that I have given in this
chapter will show that West Point is indeed fortunate in many ways. Few
places have been so endowed by Nature with such wonderful beauty and
picturesqueness, and, in addition, a generous Congress has adorned the
place with magnificent buildings equipped with the finest that money
can buy for the training of the future United States officers.
CHAPTER IV
THE POWERS THAT BE
In a spacious room in the southeast corner of the massive Post
Headquarters building dwells officially the man who orders all of the
comings and goings of the residents of West Point: cadets, officers,
and enlisted men and their families. He is detailed by the President to
the immediate government and military command of the Academy and Post
of West Point for a period of four years, and given the official title
of Superintendent of the Military Academy, which carries with it the
rank, pay, and allowances of a colonel.
The duties of the office are varied and complex. The Superintendent
is directly responsible for the actual state of the discipline,
instruction, police administration, fiscal affairs, and other concerns
of the Academy. The necessary work is organized and under the control
of various officers, his assistants, who constitute his staff. The
office of Superintendent is regarded as one of the most desirable
and most honored that the Government has to offer to an officer of
the Army, and justly so, for the position carries with it a great
responsibility, fascinating work, large powers, and enormous prestige.
The President is in no way limited in his selection for the office. He
may appoint an officer of any rank whatsoever, from second lieutenant
to general officer, but the policy always pursued has been to intrust
the important duties of the position to an officer of character,
ability, and experience. The selection of the Superintendents of the
Military Academy was confined to the Corps of Engineers from the
establishment of the institution, March 16, 1802, till the passage
of the law of July 13, 1866, which opened it to the entire Army. It
is not an easy task to find just the man with all of the necessary
requirements for this office. In addition to the officer's military
ability, grasp of affairs, and experience, it is desirable that his
scholarly attainments be of a distinctly high order, for, since he is
_ex-officio_ the President of the Academic Board, he will find occasion
to use his scholarship for the permanent benefit of the curriculum.
In general, the military demands upon the average officer's time
preclude the pursuit, on his part, of cultural and academic studies to
any great degree, so that, while an officer may be of the highest moral
character, have great experience, and on the whole make an admirable
administrative chief, yet he might lack scholarship, which deficiency
would lessen his value to the Academy as Superintendent.
Besides, the Superintendent should be a good judge of human nature,
and in particular of young men. To be able to throw oneself back in
memory to the age of twenty, re-grasp the fresh and immature viewpoint
of youth, and then make the proper allowances for youth's inability
to see life as a whole, is a gift not given to many men. Some of us
could do it if we would exert our minds, but many are incapable. Where
sympathy and understanding of young men are lacking on the part of the
commanding officer there is too often a tendency to judge a cadet by
the standard held by his superiors which they have gained only through
years of experience. Moreover, a broad man in command dissipates with
a word all of the trivialities of military life that seem big for the
moment, and relieves his subordinates of the haunting fear of an excess
of participation in their affairs.
During the one hundred and fifteen years of its existence West Point
has had but twenty-six Superintendents, each of whom has left a
permanent influence for good at the Academy. The present incumbent,
appointed in June, 1916, is Colonel John Biddle, Corps of Engineers, a
graduate of West Point, Class of 1881.
The military staff of the Superintendent consists of the Adjutant, the
Quartermaster, the Treasurer, and the Surgeon, all officers of the Army
detailed to perform the duties of their respective offices.
The Adjutant is the Superintendent's right-hand man. He is in fact
his chief spokesman and representative in all official and social
matters. He is, moreover, charged with all of the records and papers
of the Academy except those relating to disbursements. Ordinarily,
this officer is the personal choice of the Superintendent, for it is
essential that perfect trust and harmony exist between these officers.
It may be of interest to the layman to know that an Army Post is very
much like a large family, or perhaps a patriarchal tribe would better
describe the relations of the residents. The Superintendent is the
head, and the Adjutant his executive officer.
In the olden days when troops were stationed on isolated frontier
posts, the officers' families were entirely thrown upon one another
for society. Although the necessity for these posts has long since
disappeared, Congress has never authorized their abandonment, because
their presence near some city or small town means a financial benefit
to the towns people. The influence of the Representative of that
district is sufficient to retain it, and consequently, as of yore,
officers' families must live together as one tribe.
This condition does not exist to the same extent at West Point as at
other posts. The Adjutant is the peacemaker, diplomat, aide, buffer for
the Superintendent in his administration of military and social duties.
As may be imagined, he must be a man of great tact, good judgment, and
possessed of Machiavelian diplomacy. He is always being called upon
to make decisions, and since every decision affects somebody adversely,
he has great need of a feeling for humanity. His official decision is
tantamount to that of the Superintendent in whose name he is always
supposed to act.
[Illustration: The Superintendent's Quarters
Built in 1820]
All official letters to the Superintendent, or between officers, must
pass over the Adjutant's desk, so that in a sense he is the central
operator, making connections of the invisible ties for the time being,
between the various departments and persons on the Post. He also acts
as a shield to the Superintendent, saving him from the annoyance of the
minor routine details.
In addition, he is regarded as the hub of the Post's social wheel. He
initiates the public entertainments and authorizes the general social
events of the officers and cadets. Naturally, he has nothing to do
with functions of a private character, but for hops, dances, or other
forms of distraction where one of the public buildings is used, he
gives the authorization of the Superintendent. He makes it his duty to
mingle freely with the officers of the command; at the dances he sees
that visitors are introduced; when _very_ distinguished guests arrive
at the Post, he puts on his full-dress uniform and goes to the station
to meet them. If the guests are merely distinguished, he details some
officer to act in his stead, and if they are plain sightseers with
letters of introduction, a young subaltern gets the job. He is Adjutant
of the Military Academy and of the Post of West Point. The duties
of the former office pertain solely to cadets, their discipline and
instruction, whereas the duties of the latter concern the officers,
enlisted men, and other residents of the Post.
A sort of Damon and Pythias are the Adjutant and Quartermaster: a
mention of one suggests the other. The Quartermaster is in charge of
the public lands and buildings; of the material for the erection of
buildings, and for the repairs and improvements, and for all other
public property for which no other person is especially responsible.
Under the direction of the Superintendent, he enters into contracts and
makes purchases for the Academy and prepares all accounts, returns,
and rolls relative to the public property under his charge. He is also
in control of the workmen employed in the erection or repairs of the
public buildings, or in the improvement of the grounds.
A Quartermaster is in reality a supply officer. Everything necessary
for the up-keep of the Post and the command, come from his storehouses.
Clothes, trucks, wagons, frying-pans, rakes, road-rollers, twine,
furniture, garden hose are a few of the diverse articles that he must
keep on hand. In his work at West Point he is assisted by several
officers, among whom he distributes the various duties pertaining to
the care of the property, purchase of supplies, pay of officers and
enlisted men. The supply of the cadets, however, is not under his
jurisdiction.
[Illustration: Colonel John Biddle, Corps of Engineers
Superintendent]
The Quartermaster's office is not entirely free from the official
cumbersome machinery and red tape that clogs all Government branches.
So efficiently does it check up upon all of its property, even to the
most minute screw, that it has inspired great respect for its routine
into those who borrow from its storehouse. Some years ago, one of the
officers' wives discovered the chimney of her house on fire. As she
lived near the Hospital her first thought was to borrow one of the fire
extinguishers. She rushed to the telephone:
"Hello! Hello! send over right away a fire extinguisher to Lieut. K's
quarters!"
"I'm sorry, madam," replied the attendant, "I have no authority to let
the fire extinguisher leave the Hospital."
"But my house is on fire!" shrieked the angered lady! "What shall I do?"
"You had better telephone the Quartermaster, madam, and get his
permission, for the Hospital holds the fire extinguisher on memorandum
receipt."
All matters that relate to the clothing, equipment, and subsistence
of the cadets, including the purveying and supervision of the Cadet
Mess, are under an officer of the Army detailed as Quartermaster and
Commissary for the Corps of Cadets and Treasurer of the United States
Military Academy.
The Government allows each cadet $600 per year and one ration per day,
or commutation thereof, 40 cents per day, making a total of $746.00,
but the cadet never receives in cash nor manages, his pay. The amount
due him is turned over to the Treasurer, who keeps an account with each
cadet in which he credits him with his monthly pay and charges him
with the cost of his maintenance on a pro-rata basis plus what he has
spent for clothing and supplies. The Treasurer furnishes each cadet
an itemized statement of his account at the close of each settlement
period so that he knows just how much money he has saved, or owes. The
pay provided is ample. Cadets who are economical and take good care
of their clothes, who lose no government property for which they are
responsible, are able to accumulate a nice balance that is paid to them
upon graduation.
In order, however, to insure that all cadets shall leave the Academy
without debts, and with their initial equipment paid for, the Treasurer
deposits fourteen dollars per month from the pay of each cadet. This
fund is known as the Equipment Fund and totals $704 during the four
years. Before graduation each cadet is required to submit a certificate
to the effect, if such be the case, that all articles of an officer's
uniform ordered and received by him have been paid for; that, in case
the complete outfit has not been received and paid for, he has in his
possession $475 or that amount less whatever has been paid out for this
purpose, which sum will be held and applied promptly to the payment
of such articles of his uniform and equipment as have not yet been
received and paid for; and that he has no unpaid debts contracted
during the time he has been a cadet.
This provision is a very wise and beneficial one to the cadet, for he
enters the Service free from the terrifying load of debt. Formerly the
Equipment Fund was turned over to the graduating cadet, without any
restrictions whatsoever. The consequence was that the largest part of
it was spent in New York a few days after graduation, and the young
officer was in debt for his uniform for many months thereafter. He
started his career with a millstone around his neck, to which weight
a few added that of a wife. As one experienced officer remarked, "The
ladies are all right, but do not marry until you are out of debt, else
every time you take a drink in the Club, you will feel as if you are
swallowing the baby's socks."
One of the most important and difficult duties of the Treasurer is
catering to eight hundred ravenous young appetites. To be a successful
Mess officer for this large number requires much study, especially in
this age of the high cost of supplies. The food provided is excellent
in quality and well prepared. In general it is plain and wholesome,
just what one would expect at a Military School, but the menu is
sufficiently varied so as to please even the fastidious. Southern
palates are not forced to long for fried chicken nor Eastern palates
for oysters. To make the New Englander feel quite at home periodic
boiled dinners gladden their gastronomic lives. Then, too, ice-cream,
since the installation of an electric freezer, has become as common as
the proteids.
The monthly cost of the mess per cadet is about twenty dollars. The
Treasurer charges against the cadet not only the cost of his board,
but also his laundry, his uniforms, his clothing, his room equipment,
mattress, pillows, sheets, towels, and all other necessary articles.
Moreover, the salaries of the policemen who clean the halls of the
barracks, the bootblacks, the cost of the cadet hops, athletics,
and text-books, in fact, the cadet's entire maintenance is charged
against his pay. The Government, however, provides for the up-keep
of the buildings, the heating, lighting, and repairs, from separate
appropriations.
The fourth member of the military staff is the Surgeon, who with his
four assistants, medical officers of the Army, watch over the health of
the command. Under his charge is the hospital for cadets, and that for
enlisted men.
The Surgeon has authority to excuse an officer or cadet from any
duty whatsoever on account of illness. In the eyes of the cadets he
stands as the guardian of the Gates of Paradise. When the body is
fatigued, or one's head is choked up and eyes running from a bad cold,
illnesses that in reality do not incapacitate one for duty, to have a
nice sympathetic Dr. St. Peter jingle his keys and take you into the
hospital for a brief rest is like the first whiff of a jasmine scented
spring. The cadets soon learn to estimate the sympathetic qualities
of a new Surgeon, and quickly pass around the word whether there has
commenced the reign of an adamantine or tender Æsculapius.
The officers and cadets are required to undergo an annual physical
examination, of which accurate records are kept. In case of illness,
the nature is noted on special cards and filed with his record in
Washington. The health, therefore, of officers, cadets, and enlisted
men is constantly under the Surgeon's eyes, so that really serious
illnesses are rare. In case of persistent or long illness, the officer
or cadet may be granted a sick leave upon the Surgeon's recommendation.
The conduct of the business methods and military departments of the
Military Academy, by the Superintendent and his staff, is annually
inspected by the Inspector-General of the Army, who comes on from
Washington for the purpose, or by officers recommended by him acting
under specific instructions from the War Department. In addition to the
above inspection, a Board of Visitors annually visits the institution.
Formerly, the President appointed to this Board distinguished citizens
from all parts of the country, who arrived at West Point the first
of June and remained until graduation, about ten days later. They
were shown the workings of the school, and had explained to them the
necessities for changes and improvements, whereupon they made to the
President a written report containing comments and recommendations that
seemed desirable. The Board performed its duties well, but Congress
thought that all information, upon which appropriations are based,
should be more direct. A law was passed therefore decreeing that:
The Board of Visitors to the United States Military Academy shall
consist of five members of the Committee on Military Affairs
of the Senate, and seven members of the Committee on Military
Affairs of the House of Representatives, to be appointed by the
respective chairmen thereof, who shall annually visit the said
Military Academy, together or separately as the said committee may
elect, during the session of Congress; ... It shall be the duty
of the Board of Visitors to inquire into the actual state of the
discipline, instruction, police administration, fiscal affairs, and
other concerns of the Academy.
With the passing of the visits in June of the former Board, some of the
picturesqueness and flavor of the social life of June week has gone.
At this season of the year the beautiful natural scenery of West Point
formed a superb setting for the thrilling artillery drills, the cavalry
charges, the infantry manœuvres, the bridge building, the concerts, the
dances arranged in their honor. The cadets were at their best for they
had just completed their spring training and there were no recruits
in ranks to spoil the smoothness and precision of these manœuvres. It
therefore seemed the best time for an Inspection Board to view and
report upon the work.
Accompanying the Board of Visitors were always the wives and daughters
of the members, who added to the social charm of the Board's visit. The
cadets privately referred to the young ladies attached to the Board as
"splinters." I remember, upon entrance, hearing one cadet ask another
if he would "drag a splinter" for him. I later found out that this
expression meant that he would be pleased if his comrade would escort
one of the young ladies to a dance. The present Board usually pays its
visit in mid-winter when the cadets are busiest with their studies, so
that the equally charming Congressional "splinters" have little chance
to win young hearts.
In the work of the institution the Superintendent is aided by a large
number of subordinates. The number of officers and others in prominent
positions on duty at the Academy is shown in the following list:
Superintendent and staff 5
Professors, permanent 7
Professors, by detail from Army 4
Professors, Associate, detailed 2
Professors, Assistant, detailed 12
Commandant of Cadets and Tactical officers 15
Master of the Sword, Instructor of Military Gymnastics
and Physical Culture 1
Instructors and other officers 68
Medical Corps 4
Dental Surgeons 2
Medical Corps, Instructors in Military Hygiene (August 28 to
October 10) 4
Chaplain 1
Librarian 1
Civilian Instructors of Languages 3
Civilian Instructors of Fencing and Military Gymnastics 3
Teacher of Music 1
Organist and Choirmaster 1
Pay Clerk 1
----
Total 135
The majority of the officers are detailed from the Army-at-large for
varying periods of time, but seven of the professors are permanent. The
Superintendent, the heads of all Departments of Instruction, including
the detailed heads, compose the Academic Board, which controls the
program and methods of instruction. It is non-military in character,
its duties pertaining almost solely to the various branches of
learning. More especially, its duties are to examine cadets, decide
upon their merits and proficiency, grant diplomas, and recommend for
commission in the Army. It reports, through the Superintendent, to the
War Department, on the course of studies and methods of instruction.
It also recommends the text-books to be used by the cadets in each
department. Each member has one vote, including the Superintendent.
The work of the Board is largely done by committees, both General
Committees and Class Committees. The latter are composed of the heads
of those departments whose studies any one class are pursuing.
At the close of every examination the Academic Board reports to the
War Department the names of all cadets who are deficient in studies or
conduct and who are recommended by the Board for discharge or transfer
to a lower class.
The seven professors permanently attached to the Academy are: the
Professor of Civil and Military Engineering, Natural and Experimental
Philosophy, Chemistry and Electricity, Modern Languages, Mathematics,
Drawing, and English and History. These members are appointed by the
President and usually selected from officers of the Army, graduates of
the Academy, who have specialized along the lines of their department.
The President usually appoints an officer recommended by the other
members of the Board, but he is not restricted in his choice and
may select whom he pleases for the position. All of the permanent
Professors at present are graduates except the Professor of English and
History who is a graduate of Yale. When the Department of English was
created in 1910, it was felt that the head of it should be a man who
had specialized in English Literature.
Without reflecting on the graduates of the Academy, no one officer
appeared upon the horizon with the requisite qualifications, a fact
not to be wondered at, for few officers are ever in a position to
pursue English courses that would equip them for this position. Upon
the creation of the Department of English, History was transferred to
this Department from the Department of Law with which it had long been
associated.
In addition to the permanent members of the Board, the detailed ones
are the Surgeon, who as the head of the Department of Hygiene, is
entitled to a seat; the Professor of Practical Military Engineering,
the Professor of Law, the Professor of Ordnance and Gunnery, and the
Commandant of Cadets, all four of whom are detailed by the Secretary of
War from the officers of the Army for a period of four years.
In the Department of Mathematics and Modern Languages the Professor
has an associate professor and an assistant professor whose duty is to
assist in the administrative work as well as the instruction. The other
departments have only assistant professors, officers detailed from the
Army who might be said to act as an Adjutant for the Professor. In
common with the remaining officers, they perform administrative routine
duties, relieving the Professor of the necessity of attending to minor
questions. The Professor's time is very much occupied in the solution
of problems that affect the Academy as a whole, in addition to the
development of their respective courses, so that it is essential that
his time be not employed with the unavoidable trivialities that arise
in the conduct of his Department.
The great mass of officers on duty at the Academy are, of course,
the instructors. These men are all officers of the Army, graduates of
the Academy, who are detailed for duty in the various departments.
Formerly, the tour of duty was for four years, but since the passage
of a law by Congress, the Detached Service Law, familiarly called the
"Manchu Law," the time that an instructor can remain on duty at West
Point, is dependent upon the amount of duty that he has had with troops
during the preceding six years. No officer can remain on detached
service, such as that at West Point, for more than four years.
It is apparent, therefore, that the corps of instructors is constantly
changing, resulting in the introduction into the work of new blood
and fresh viewpoints. This changing of instructors maintains a high
standard of enthusiasm for teaching, so often lacking in institutions
of learning where a subordinate teacher goes over, year in and year
out, the same ground.
Moreover, the system of officer instructors is employed on account of
the disciplinary value of their presence over the cadets. West Point is
first and foremost a Military Academy, and it is of primary importance
that the cadets shall absorb by example the spirit of discipline, and
military deportment. Not the least of the advantages of having officers
teach cadets is the contact that their presence maintains between West
Point and the Army.
Officers are selected for duty at the Academy by the Heads of
Departments who make every effort to secure men especially qualified
for the work. For example, the instructors in the Department of
Engineering are all Engineer officers; in Ordnance and Gunnery,
mostly Ordnance officers; in Chemistry and Electricity, usually Coast
Artillery officers; in Mathematics, officers of the staff and line
who excelled in this study as cadets; in English and History, line
officers with recognized literary tendencies; in Languages, officers
whose advantages have enabled them to acquire a good speaking knowledge
of either French or Spanish. Until the outbreak of the European War,
officers on duty in the Department of Languages were ordered to spend
the summer in study in either France or Spain. They thereby were
able to perfect their knowledge to an extent that rendered them most
efficient instructors. Detailed to this Department are two native
Spaniards and two Frenchmen, whose services are employed to carry along
the instruction of the officer instructors as well as that of the
cadets, so that every opportunity is offered to the cadet to progress
as far as his ability will permit him in the time allotted these
studies.
The time of the officer is well employed while on duty at the Academy.
In those departments whose period of recitation is an hour and a half,
he has two sections daily, but if the period is one hour, he instructs
three sections. He averages, therefore, from fifteen to eighteen
hours of actual teaching per week. To this amount must be added the
conferences of the instructors, conducted either by the Professor or
one of his assistants. These conferences are held, usually daily, and
vary from one to two hours and cover the material in the lesson or in
advance work. By means of these conferences, the Professor is able
to standardize the teaching without restricting the personality or
individuality of his officers.
The routine work, that is, the keeping of records, weekly reports,
the correcting of exercises, problems, and compositions, all demand a
greater or less amount of time, and then what is most important, the
instructor must spend many hours in preparation. I have known many
instructors to work every night until midnight after the routine work
of the day.
In the demand upon an officer's time, consideration is given the fact
that with him teaching is an incident in his career, and he must
therefore have at his disposal, whether he uses it or not, at least a
couple of hours per day for professional work and study. When absent
from troops an officer becomes more or less rusty upon the duties of
his arm, and he should, consequently, by reading, the solution of
problems, writing or what not, keep up with the progress made in his
branch of the Service.
General Orders of the Army prescribe also that at least one hour per
day must be employed in bodily exercise, riding, walking, tennis,
golf, swimming, polo, etc., and the officer is required to submit a
certificate stating that he has taken the prescribed amount.
I give in somewhat tedious detail the employment of the officer's time,
because so frequently I hear, expressed by the layman, the opinion that
officers of the Army have practically nothing to do. It is ordinarily
difficult to disabuse their mind of this idea, chiefly because it is
already made up. A visitor arrives at West Point to spend the day and
seeing a few officers playing golf in the morning he assumes that
_all_ officers have nothing to do. He perhaps little realizes that the
same golfers, or tennis players, are trying to get their exercise at
a time that will not interfere with their academic duties that begin
for each department at varying hours. That same officer, who plays a
game of golf at 9:30 A.M., will in all probability spend a part of the
forenoon and afternoon with the cadets, and all evening in preparation.
Appearances are often very deceptive. This is particularly true in
the Army, which has been, until the war came upon us, subject to more
unjust criticism than any other professional body.
In order to facilitate the instruction, the cadets are arranged in
four distinct classes, corresponding with the four years of study. The
cadets in the first year's course constitute the Fourth Class, those in
the second year's course, the Third Class, those in the third year's
course the Second Class, and those in the fourth year's course the
First Class. The designation of senior, junior, sophomore, and freshman
is not used at West Point as in colleges and universities, but the
terms "Yearling" and "Plebe" are familiarly applied to cadets of the
third and fourth classes respectively. The advancement of the cadets
from one class to another is based upon proficiency in their studies,
the details of which will be found in the chapter on "The Discipline of
the Mind."
In order to distinguish the classes one from another, the device of
putting bands of braid on the sleeve of the uniform has been adopted.
These lengths of mohair are called service stripes and are issued one
for each year of service, so that the "plebe" sleeve is bare, the
"yearling" has a single stripe, the second classmen, two stripes, the
first classmen, three stripes. This insignia is of black braid for all
gray uniforms except the full dress coat, on which gold braid is used.
The chevrons, although primarily a designation of rank, also serve to
distinguish some members of the classes. The cadet officers and the
sergeants are members of the First Class and the corporals are of the
Second Class. To many people, chevrons, or insignia or rank, means
nothing. Girls especially have so little idea of their significance
that they readily swallow anything a cadet tells them. It is the same
today as of yore. I was at a hop not long ago when I overheard a young
miss say to her cadet escort, who had just lost his chevrons, been
"busted" as the cadets say:
"Why don't you wear some of those lovely gold stripes on your arm?"
"Well--er--you see," replied the 'buck,' "why that's a sort of private
matter with me now."
_O Tempora! O Mores! Tempora Mutantur_, but not at West Point.
Until 1816, the cadets had no regular uniform, but were permitted to
wear pretty much what they desired. Poor chaps, I scarcely blame them,
because from the records it appears that for the large part of the
time they were in rags. In winter especially, they hardly had enough
clothes to keep them warm. In 1814, a uniform was prescribed, but
little attention was paid to the prescribed dress, everything being
worn according to fancy up to a major-general's uniform. General R. G.
Ramsey (Cullum Register, Vol. III.) states that "during the winters
of 1814 and 1815 cadets were greatly exposed to cold; great coats had
not become the fashion for boys and such comfort was a specialty. My
wardrobe had been carefully prepared, but the inventory did not include
the great coat." This is the first mention of the cadet overcoat.
In 1816, however, an order from the Adjutant-General changed the
uniform of 1814, and with few modifications made from time to time,
this uniform is worn today. The gray color is said to have been adopted
out of compliment to General Scott and his troops who, clothed in gray
(due to the inability of the government to furnish them with blue),
had, on July 4, 1814, won a victory over the British at Chippewa.
Today the cadets have a few more uniforms, but the general appearance
and the pattern have been only slightly changed since 1816. The present
list includes a full-dress coat, a single-breasted coat of blue gray
cloth, with three rows of gilt bell buttons in front, and button-holes
of black silk cord in herring-bone form with a festoon turned at back
end. The standing collar hooks in front and is ornamented with a blind
hole of cord formed like that of the breast with a button on each side.
The coat is cut off in front just below the waist line, but has in rear
a skirt, ornamented with three buttons and cord holes. The full-dress
coat is a garment of rare beauty and taste. I have never seen a more
military uniform, one that expresses so well the purpose for which
it is intended. It accentuates the good carriage of the cadets and
at the same time clothes him with an air of elegance. It seems to me
that anyone could look smart and well set-up in a cadet full-dress
coat. When seen in full dress without his accoutrements, the cadet,
with his slim waist, his well-developed shoulders, and chest proudly
displaying those shiny buttons, and the little tail hanging down
stiffly and conservatively, appears for all the world like proud young
cock-robin going a-courting Jenny Wren. The full-dress coat is worn for
ceremonies, church, official receptions, hops, and for social calls,
dining out, and entertainments.
For habitual wear, a dress coat, or a blouse (as it is more familiarly
called) is prescribed. The garment was first worn, June 15, 1889. It
is of the same style as the officers' blouse, being of gray cloth and
bound around the edges, the cuffs, and up the seams in the back with
black mohair braid, having a collar of the same material, of height
suited to the wearer.
The trousers are of gray cloth with a black stripe up the side, one
and one-half inch wide. In summer, white is worn, either full white,
blouse, trousers, and cap, or a combination of the gray coat and the
white trousers. This mixed uniform is the most effective, especially
_en masse_, at a ceremony when the white belt and cross belts are worn.
For certain drills a gray flannel shirt is issued, and suitable
breeches are provided for riding. The various combinations of the
uniform are published in a table and designated by letter, so that the
cadet consults the table for, we will say, "Full Dress A," where he
finds in detail all articles of uniform to be worn for a ceremony.
The uniform is admirable in color, appearance, and utility. It is
regrettable that the gray color is not used in the Regular Army instead
of the lifeless ugly olive drab. It is equally as invisible, more
attractive in appearance, no easier soiled, and easier to clean when
soiled.
The only article of cadet uniform that seems out of harmony with the
rest, is the cadet cap. This headgear has no distinction and should be
abolished. It replaced, some years ago, a forage cap patterned after
those worn in the Civil War, but I do not think that the change was any
improvement. The visor is too drooping, and the crown, too narrow and
rigid, is clumsily fashioned. The majority of the cadets look as if
they had put on by mistake, their small brother's hat, giving them a
vaudeville appearance, in some cases as ludicrous as Weber and Fields.
The day's work of the Powers that Be, however, includes so many more
important things than the appearance of a cadet cap that the style of
the cap passes by unnoticed. The great aim of the Academy is to mold
a man's character and train him to think. The Superintendent must
constantly keep his finger on the Academy's pulse to see that these
aims are being successfully carried out. To the cadets he is as far
removed from their life as were the gods of Olympus from the common
mortals. Not that the Superintendent wishes it so, but because of
circumstances. The big problems of the Academy occupy so much of his
time that he comes into comparatively little personal contact with the
cadets. Like Henry IV., by being seldom seen, he is, when he appears,
like a comet wondered at by them who tell each other:
"That is he, the 'Supt.'"
To be summoned before his presence makes a cadet anticipate the feeling
when he will appear before the final bar of justice. He dons his
full-dress uniform, pulls on a pair of white lisle thread gloves,
puts a visiting card in his hat band to have it ready for Woods, the
Superintendent's messenger, and sallies forth, his heart a-tremble at
the thought of appearing before Olympus.
He quickly reviews his past, wondering what he has done, for he thinks
of course that he has unwittingly committed some offense. It is only
when he finds himself standing before the Superintendent's desk
saluting and saying:
"Sir, Cadet Ducrot reports as ordered," that he realizes that he is in
the presence of a very human person like himself.
The wonderful prestige that the Superintendent has with the cadets is
due, not so much to his rank, but to the fact that he too was once
a cadet, and passed through experiences similar to their own. They
appreciate the success that he has made in their chosen profession, and
his example affords inspiration to many, for they argue that once upon
a time, long ago, he too was a new cadet in "Beast Barracks."
CHAPTER V
"BEAST BARRACKS"
Blessed are the meek for they shall inherit the earth.
"You man, there, slouching across the Area! What's your name?"
The person addressed, a short fat chap, looks up over his big round
tortoise-shell glasses, with unfeigned interest, but stands mute,
apparently fascinated by the immaculate white trousers and the military
bearing of the speaker.
"Do you hear me talking to you? What's your name? Take your slimy eyes
off me and look to the front!" sternly commands young Mars, coming a
few steps nearer. The new arrival looks blank and tries to digest all
of the orders at once.
"You other man in the green necktie, come here!" shouts this cadet
officer as he catches sight of a tall lanky civilian in a Hart,
Schaffner, Marx suit, long flat tan shoes, and a flaming green necktie,
who has just sauntered through the sally-port.
"You man, there, do you hear me talking to you? Step out!"
The Green Necktie smilingly approaches the cadet officer, deposits his
dress suitcase on the ground, and mops his brow.
"How do you do?" he cordially remarks, "my name is Jinks. "
The cadet officer glares.
"Your name is _Mr._ Jinks, SIR," he shouts. "_Mr._ Jinks, you get that!"
"And you too, Mr. Dumbguard," turning to the chap with the Harvard
spectacles, "don't you forget to put a _Sir_ on the end of your name.
Who do you think you are around here? Stand up, both of you. Turn down
the cuffs on your trousers, button up your coats, take off all of those
badges and scarfpins and stick them in your pocket. What do you think
this place is? a school for dudes? Put your hats on straight!"
Command follows command with machine-gun rapidity. The green necktie
is almost smothered from view as the candidate buttons his coat, and
reluctantly the cuffs on the trousers are turned down.
"Pick up those suitcases and follow me."
"And so this is an introduction to West Point," ruminates the Harvard
spectacles, "strikes me this chap is somewhat brusque. I wonder where
all the other fellows are!"
Meanwhile over in front of the Administration Building is a large
group of candidates just reporting. Some are laughing and joking,
others remain silent, plunged in thought, wondering why they feel
so strangely. About the same impression fills each one's mind.
Underneath those parti- striped shirts each heart is thumping
just a little faster than usual. The delay in reporting seems
interminable. With thoughts of all sorts racing through their heads,
they await their reception, or their "breaking in" with fearful
interest.
[Illustration:
_Photo White Studio_
"Beast Barracks"--Drawing Mattresses]
Some few have been to West Point before, but the large majority have
never been so fortunate. They know it only by _Cadet Days_, General
King's entertaining book of cadet life, or by _The Spirit of Old West
Point_, General Morris Schaff's charming reminiscent book of life in
the Corps, about the time of the Civil War, or by romantic stories
gathered here and there.
No words that I know of seem as magical as "West Point." To the
candidate it conjures a vision of all that he hopes to be. The honor
of being a cadet, the privilege of wearing the uniform, the immense
possibilities of physical and mental achievement, the soul-satisfying
fear of an ambition about to be realized, the glamour of military life,
and, it must be admitted, a secret feeling of righteous superiority
over his boy friends at home,--all these thoughts crowd his imagination
so that for once he sees frozen the vague ideal that he always has had
of himself.
I am sure that Gawain's first impressions of King Arthur's court were
dim in comparison with the dazzling visions of West Point that fill
the candidate's mind. For months, in some cases for years, he has
striven for an appointment. All of his interests and hopes have been
centered upon becoming a cadet. He has read all the literature about
the place, he has gone to sleep many a night living over in imagination
his career. At last the day comes when he sets forth on the road of
his great ambition. He can hardly believe that he is actually on the
way to West Point! What enchanting pictures crowd his imagination and
beguile the journey! In his mind's eye he is arriving; he sees himself
in uniform, he wonders how he will like the life: one moment he is
troubled by the probability of failure, the next, he spans the years in
thought and is back home again on furlough, and he thrills with pride
and pleasure at the prospect of greeting his old comrades after an
absence of two years. How delightful it is to build castles in Spain!
His imagination runs on and on; he promises himself to study hard, he
wants his family to be proud of his record; he hopes to be a cadet
officer. In his reverie he graduates and joins the Army, his ambition
realized. All a-tingle with excitement he eagerly awaits the arrival at
West Point.
When, however, the great gray buildings loom up as the day-line boat
approaches the wharf, his buoyancy begins to ebb, his exhilaration
cools under a mental Texas Norther, and the joy of anticipation so
recently experienced receives a chill that causes him to gaze around
uneasily and forlornly. He feels a little sad and melancholy. Thoughts
of home sweep over him.
[Illustration:
_Photo White Studio_
Reporting for Duty]
There is, however, about certain fellow passengers, lean lank
youths like himself, something responsive, something about their
hats, something about the unnatural droop of the shoulders, the new
suitcases, the same fearful look that draws him to their side. "Are
you a candidate, too?" he asks hopefully. An answer is unnecessary.
Instinct again has won, and the flood-gates of friendship are
unreservedly opened to the newly made companion about to enter the Land
of Egypt and the House of Bondage. We are timid creatures all of us,
and even the strongest suffer a twinge of timidity, a queer feeling in
the seat of compassion, when about to penetrate the mystery surrounding
an unknown life. At such a moment we all want to be little children,
to have someone take us under shelter. We would like to run away from
ugly, grim Reality that relentlessly blocks our way and with whom we
must battle before we can go forward.
A sort of vague terror pervades the candidate as he climbs the hill
from the station to the Adjutant's office where he must report, but he
grasps his suitcase and sets forth for the Headquarters Building where
his directions tell him to report upon his arrival. If he is ahead
of time he goes to the hotel where he finds a great many candidates,
some of whom have been at the Point several days trying to absorb some
impressions before reporting. Here friends are quickly made. On the
day that they are all ordered to report, when they feel that they are
about to bid farewell to their civilian freedom, they reluctantly set
out for Headquarters. Unwilling though they may be to report, few ever
in after life regret having entered the Academy.
The Rubicon once passed, however, no time is lost in the administrative
routine of receiving the raw material. After reporting to the Adjutant,
the new cadet is turned over to an orderly who directs him to the
office of the Treasurer. No general officer in full uniform, one month
later, could create in the candidate's mind the same impression of the
finished military product as does this first sight of a _simple soldat_
at the Treasurer's. The new cadet is directed to deposit all the money
that he has in his possession. Each new cadet is supposed to deposit
one hundred and sixty dollars upon entrance to cover an initial cost of
equipment, which amount is credited to the cadet's account, together
with any surplus change that he has at the time of admission. Although
the Regulations require this initial deposit of one hundred and sixty
dollars, the requirement is not absolutely obligatory, so that if any
boy receives an appointment he should not be deterred from accepting
on account of the financial stipulation. He should come at all events.
The first equipment will be issued, and with economy he can later on
wipe out the debt. If a boy's parents are poor, it would be foolish for
them to make a great effort to raise this money. Let the boy come and
assume the responsibility of the debt, and let the onus of it rest upon
his more youthful shoulders which will very soon broaden to bear it.
One by one the men pass the little wicket window of the Treasurer and
deposit all their money. Pockets are emptied of all cash and checks,
which are credited to the cadet's account. When eight, ten, or twelve
candidates have been admitted, the young officer present forms them
into a pseudo squad, or rather group, then calls an orderly of the
Regular Army.
"Show these young gentlemen over to the Area of Barracks to the office
of the Officer in Charge of New Cadets."
The orderly comes briskly to attention, his smart salute captivating
the assorted collection of "Prides of Congressional Districts."
They promptly follow his leadership, out of the postern gate of
Headquarters, across the road to the Area of Barracks, reveling in the
clouds of glory that, in their eyes, he trails behind him. They are now
quite happy, fully launched upon their military careers.
The feeling of elation at being at last within the sacred halls of the
Academy begins to intoxicate the new cadet, when, upon the way over
to the barracks, he notices a few stray passersby stop, look at the
queer squad, and then smile slowly, almost insinuatingly, as if amused.
It is an irritating smile. He sees the orderly smile too. Something
has surely gone wrong. His heart goes down, down, down, and he soon
feels as if someone had thrown about him a cloak of lead. But on the
squad goes. He tries to shake off his heavy feeling, but it is no use.
Many days elapse before the heavy mantle is cast aside. He is sure
that something dreadful is about to happen. But stay, what is all this
disturbance in the Area? Running back and forth between a sally-port
and a barracks are a lot of bareheaded individuals, some in military
shirt and cit trousers, others in lovely pink striped shirts and gray
cadet trousers. They appear very uncomfortable. Several well set-up
young cadets are at their heels giving them instructions in stern tones.
"Say, soldier, who are those men?" inquires one bold candidate.
"Those men are your new classmates," explains the orderly.
Just then a lieutenant comes forward; the orderly turns over his
charges and the men of the squad take their places in line with many
other candidates who are awaiting their turn to report to the Officer
in Charge. No sooner have they placed their grips on the ground,
and begun to take life easy while waiting, than a flock of yearling
corporals emerge from the Guardhouse.
"Stand up all along this line!" commands one.
"Hold up your heads, and drag in your chins," shouts another, as he
goes down the line giving each new cadet a little personal attention.
"Mr. Dumbguard, put that hat on straight."
[Illustration:
_Photo White Studio_
Two Hours after Reporting]
All hats are at once adjusted. The whole line assumes an extraordinary
appearance of rigidity. The heat becomes more intense. Large drops,
globules of perspiration, roll off the crimson faces whose features
have assumed a permanent set, depicting grief. Slowly the line
advances. More cadet officers appear, giving each candidate the number
of his room in barracks.
"Mr. Ducrot, your room is 1223, step out and find it, put your baggage
there and report back here immediately."
Mr. Ducrot, whose intellect has become somewhat clouded by all of the
events and instructions that he has received in the last ten minutes,
hurries off in the direction of the twelfth division.
* * * * *
The instruction of new cadets is under an officer of the Tactical
Department. In his work he has both officer and cadet assistants.
In order that the cadets themselves might have experience in breaking
in new men, cadets of the First (or senior) class are detailed as
assistant instructors. They drill the new cadets in the school of the
soldier and of the squad. They give him individual instruction in the
care of his room, his correspondence, and in the use and care of his
equipment and his personal hygiene. It is highly desirable that the
new cadet should feel the influence of the older cadet. I shall never
forget my first impressions of my cadet instructors. I thought that I
had never seen such immaculate human beings in my life. With their
straight backs, their lean faces, piercing eyes that stared coldly
almost contemptuously at me, I was sure that they were all English
generals imported direct from the Boer War. I didn't know that white
duck trousers could be so white, nor brass buckles so shiny. I was then
sure that I had an incapacity for military life, that I would never
attain such a degree of excellence, and I inwardly withered before
their glory.
* * * * *
Meanwhile, Mr. Ducrot and his fellow candidates, having found their
rooms in barracks, are approaching the Guardhouse at a dead run upon
the insistence of a cadet corporal. Once again they stand in front of
their instructors who glare at them like Men of Wrath.
"Fall in," commands the fiercest looking one.
A shuffling of feet, indefinite movements as if to do something, a few
emphatic remarks by a corporal, and a semblance of a line is formed.
Two Messrs. Ducrot ignore the suggestion of the Wrathful One, until a
fresh-faced lieutenant almost pulls them into line.
The squad is now herded over to the Cadet Store to have issued the
initial uniform, consisting of a gray shirt, campaign hat, cap, and
gray flannel trousers.
In less than half an hour a complete metamorphosis takes place. The
heterogeneous crowd of candidates that entered the store has lost the
appearance of a bargain counter on sale day. By no means, however,
have they gained a military aspect: all that can be said is that they
are harmoniously clothed. It takes time to learn to wear a uniform
properly, and nothing is funnier than a new cadet in his first outfit.
These garments have been made up in stock sizes so that an issue can
be made at once. The fit is fairly good, except the blouses. A plebe,
however, soon appreciates a loose blouse. When the cadet instructors
command:
"Mr. Dumbguard, get those shoulders back. More yet! More yet!" a number
of wrinkles appear in the back of the blouse. The looser therefore
it is, the less effort is necessary to produce many wrinkles, and
therefore, the task of appeasing the Man of Wrath easier.
The first day's work goes on rapidly. As soon as the new uniforms are
donned, once again to the Cadet Store go the new cadets to draw their
room equipment.
"New cadets, turn out promptly!" command the cadet instructors in the
lower hall of each division. Down the iron steps hurriedly come running
the novitiates, and line up in the Area. At the Cadet Store, each man
is issued his mattress, pillows, and bedding. A long procession of
young Atlases, sweating like horses, stagger through the sally-port,
bearing aloft everything necessary for sleeping, except the bed. A few
zealous ones add to the burden a bucket, perhaps a dipper rattling
inside, and a broom that sways recklessly on the top of the mattress.
Concealed somewhere in the mass is a bottle of indelible ink that is
sure to drop before the room is reached. Standing in the Area are a few
of the Wrathful tribe ever on the alert to see that no loitering occurs.
"Take up a double time, Mr. Ducrot, step out!"
Poor Mr. Ducrot, this time about five feet four inches tall, whose view
has been obscured by the side of a mattress, attempts to be more of a
hustler, stubs his toe, and down come pillows, mattress, bucket, and
all.
"Well, Mr. Ducrot, you're a pretty mess, you're about the grossest
plebe I ever saw!" consoles one sarcastic Arch-Fiend.
"What do you think you're trying to celebrate out here, Mr. Dumbguard,"
cuts in another, "do you think you're going to take a nap?"
The senior cadet officer comes forward:
"What's the trouble?" he inquires.
Mr. Ducrot (after remembering to raise his hand in imitation of a
salute) speaks up from the midst of his debâcle:
"I was ..."
"Sir! Sir!" commands the officer.
"Sir," recommences Mr. Ducrot, "I was coming through the sally-port
when----"
Further details of this domestic tragedy are cut short by the roll of a
drum.
"Pick up that stuff and get ready for dinner."
"Step out! Step out!" orders the cadet officer.
Dinner! Dinner! Beloved dinner! the thought fills Mr. Ducrot with
ecstasy. Here it is twelve-thirty and he has been at it since 5:30. It
seems three years.
At dinner formation, "Mr. Ducrot, Mr. Dumbguard and Co." learn how to
"brace," a term used to denote the position of the shoulders well down
and back, with the head erect and chin in, hands close to the side. The
companies are marched, after a fashion, to the Mess Hall. The cadet
instructors accompany the new cadets continually commanding:
"Mr. Duflickit, drag in that chin!" "Hold your head up, No. 2, 1st
squad!"
Once in the Mess Hall, the new cadet is allowed to eat all he wishes
without interference. At the meal, however, he must comply with the
instructions for the position of a cadet at table in the Mess Hall.
This position shall be wholly without constraint. While eating the
body shall be erect on the hips, inclining slightly forward, elbows
off the table. When not eating he will sit at ease in his chair,
erect or leaning back as he desires. His forearms may be kept in
his lap, or his hand or hands may rest easily upon the table. At no
time in the Mess Hall shall he tilt his chair back or elevate his
feet, or turn his chair away from the table. Whenever a cadet is
spoken to in the Mess Hall, he will look at the person speaking to
him.
But who cares, this first meal, about the position at table? Nothing
matters except to satisfy that ravenous appetite!
Dinner over, the tragedy of the afternoon is enacted. West Point pays
no attention to the style of hair cutting preferred by the aspirant
for military honors. All cadets must be shorn alike. The new cadets
are consequently marched to the barber shop wherefrom a long line of
shaggy headed plebes protrudes like some serpent caught in a noose.
What a sight is that barber shop! Hair everywhere: black hair, red
hair, yellow hair, and some that resembles sun-burnt vanilla. Thick
wavy locks, the despair of some distant damsel, drop dejectedly one by
one. The hair must be kept short at all times so that it is impossible
to distinguish at West Point cadets with histrionic leanings, or those
poetically and musically inclined.
No rest yet in sight, this busiest of days. First the rooms must be
arranged strictly according to the Regulations--a place for everything
and everything in its place. Dozens of times are the belts piled,
only to be pulled down and thrown on the floor by the Wrathful Tribe
detailed to see that the task is correctly done. The bedding suffers
the same ignominious treatment, for the slightest irregularity
in arrangement is met with severe punishment. It seems hard and
discouraging, but, later on, the reason for such strict compliance with
orders appears. Only by constant repetition do new cadets learn to
do a thing thoroughly.
[Illustration: The Interior of a Cadet's Room in Barracks]
Tired out in body and brain, Mr. Ducrot sits on the edge of his bed for
a moment's rest, when:
"New cadets turn out promptly!" echoes through the hall of the
Division. Not a moment is lost in complying with this command.
He rushes down the stairs in a bewildered sort of way wondering what
calamity is about to befall.
"Hurry up, Mr. Dumbguard, what do you mean by coming out here late?"
greets his appearance upon the stoop of the barracks. From all the
divisions new cadets are scampering to their places in ranks along the
cement walk.
But who are the grave-looking officials in blue uniforms? The question
is not long unanswered. The new cadets are lined up along three sides
of a square. The National colors and the Corps colors are brought to
the center. The Notary Public, in the presence of the Superintendent
and his staff, reads the oath of allegiance to the assembled new body,
who with right hands raised toward Heaven, swear their fealty to the
United States. The ceremony is simple, but to the plebe tremendously
impressive. When he agrees to give four years' service to the
Government after graduation, he feels as if he is signing away his life.
There is no cloud without its silver lining. To Mr. Ducrot's great joy,
the chief Man of Wrath commands:
"New cadets will immediately take a bath."
For the first time since reporting he enjoys a little relaxation,
splashing around under the showers, where occur stolen confidences when
the instructors are busy elsewhere. A refreshed feeling creeps over Mr.
Ducrot and he double times back to his room to await the inspection of
his shoes and feet. Pretty soon, in pops the officer in charge with
tapes and foot sticks for taking the measure of shoes. Alas, no pointed
toes or English lasts are allowed:--all cadets must wear a sensible
military shoe. Regularly, are Mr. Ducrot's feet inspected during his
first few weeks to remedy ill-fitting shoes and prevent cases of
soreness.
Years ago in the days of hazing, a vastly different sort of inspection
of feet occurred. This was an unofficial inspection of the plebe's feet
by upper-classmen. In the middle of the night when the tired plebe was
snoring away, dreaming of being late to a formation and pursued by
raging demons, he was suddenly awakened by a hollow voice in his tent,
commanding:
"Inspec-shun! Feet," the "feet" said crisply and emphatically.
Without delay Mr. Ducrot sticks his bare feet out for the inspection
of the midnight prowler. He then, by order, opens his toes into the
intervals of which the gloating upper-classman poured melted candle
grease, thereby ending the inspection.
At eight-thirty in the evening, Mr. Ducrot, wearily but joyfully, makes
down his bed that has remained folded all day long. At last, he is to
have a rest, blessed sleep is in sight.
At nine o'clock the orderly in front of the Guardhouse beats three taps
on his drum and simultaneously the cry:
"Lights out!" echoes through the halls of the divisions. Immediately
the barracks are plunged into darkness and silence. Only the tread of
the cadet officer doing his half-hour patrol in the Area, disturbs the
stillness of the night.
Mr. Ducrot sinks back upon his pillow, dead tired, almost too tired
to sleep, and strives to bring a little order out of the chaos of his
mind. The oft-repeated names Ducrot, Dumbjohn, Duflicket, Dumbguard
float through his head, indescribably confused with mattresses,
pillows, stern-looking cadet officers, vicious yearling corporals, rows
of red-faced plebes, chins drawn way in, and the perspiration streaming
down their faces. The events of the day are hopelessly jumbled in his
mind. A feeling almost of failure creeps over him, and in the solitude
of the night a yearning for his home seizes him. All through his breast
spasmodic sharp pains play hide and seek. The great loneliness to which
men are prey, fills him with sadness and melancholy until a pleasing
drowsiness drifts along and smothers Mr. Ducrot into unconsciousness.
This period of training of the new cadet is familiarly called "Beast
Barracks." It lasts for about three weeks, at the end of which these
new men are sent to camp to join the Battalions. It is necessary to
segregate them for at least this length of time: otherwise they would
be so wooden that they would be sticking their front rank files in the
head with a bayonet.
It is not difficult to discern the origin of the name "Beast Barracks."
In the cadets' mind, their breaking in is only comparable to the
taming of some wild animals. The training is undeniably severe for a
tenderfoot, but its "beastly" character is an imaginary creation. To
the new man, however, it seems awfully real. I well remember my own
feelings. When I was standing in the fierce sun, "bracing" in ranks
along the cement walk of the Area, occasionally a white dog upon the
hill opposite would come lazily snooping around the ash cans: I envied
him his freedom. It seemed to me that I envied everyone except my
classmates in misery. In my imagination I saw in flaming letters above
every door I entered: "Abandon all hope ye who enter here."
As I was re-christened Mr. Ducrot, I began to think I was someone else,
I felt as if I must have died and that this was my second tour on
earth, a punishment for a wicked first life.
"There must be some way of getting out of this," I reflected, but then,
I thought that if the officers and cadets in charge of me had gone
through with this training I could also. And I did,--Alleluiah!
[Illustration: Moving from Barracks to Camp]
It was a long time, too, before I found out how all of us came to be
addressed as Mr. Ducrot. During the academic year when I began to study
French I made his acquaintance. He appeared in Keetel's French Grammar,
in the exercises of which the older cadets had uncovered a mysterious
scandal concerning his private life. All plebes were at once required
to relate to the upper-classmen the following bit of gossip, known
as the famous Ducrot scandal. 1. Monsieur Ducrot a un fils et _une
fille_. 2. Madame Ducrot a un fils et _deux filles_. _Scandal._ The
name became traditional in the Corps and was, with many others, applied
indiscriminately to all plebes.
Early the next morning, Mr. Ducrot, whom we left sleeping, attends
his first reveille. Although the drums do not begin to play until
five-twenty, he steals out of bed long before and conscientiously
sweeps, dusts, shaves, and dresses, for fear of not being on time for
the formation. Boom! sounds the morning gun! Down the iron steps all
the Mr. Ducrots noisily clatter, bolt out to the cement walk where they
remain rigidly at attention for ten minutes until the cadet officers
emerge half awake and disagreeable. Woe unto the sleepy-headed plebe
who is late! As he peeks his head out of the Division door a couple
of the Wrathful meet him and convoy him at top speed to his place in
ranks. I was once late: I shall never forget the experience. When my
"Boer War Generals" were chasing me I was seized with the same terror
that a child has in dreaming of being pursued by a burly policeman and
unable to run.
At 5:50 the cadet instructors make a cursory inspection of the rooms to
see that they are in order before breakfast. Before entering they knock
sharply on the door, an authoritative knock, but one flavored with a
little bravado. Two immovable, gray-clad figures, with eyes glassily
fixed on the wall in front of them, chins caressing their Adam's apple,
shoulders way back, stand near the fireplace, looking for all the world
like a couple of spoiled children about to cry, while the inspector
rubs his white gloves over the tables and chairs.
Upon the second day commences the instruction of the new cadet in the
elementary drills.
During the first few weeks the following schedule is carried out:
Infantry Instruction 7:15-7:45 a. m.
Physical Exercises 8:15-9:00 a. m.
Infantry Instruction 9:30-10:15 a. m.
10:45-11:30 a. m.
3:00-3:40 p. m.
4:15-5:00 p. m.
Each day the course of instruction is definitely prescribed by the
officer in charge. At the first drill the new cadets are taught the
school of the soldier, the marchings, haltings, facings, and saluting.
These exercises are given without rifles. Usually the second drill
is given under arms. As the service rifle weighs nine pounds, it is
desirable to accustom gradually these young lads to its weight. To
one unaccustomed to carrying a rifle, it seems, after a short while,
to bore into your shoulder. Any officer who has ever been a cadet
will never require an enlisted man to carry his rifle too long, until
fatigued. His own experience in "Beast Barracks" remains too vivid.
The instruction is progressive, so that the cadets are gradually
assembled into squads, the squads into platoons, the platoons into
companies. Naturally, some men improve faster than others. Those whose
intellects seem befogged by the complexities of the drills are formed
into what is known as the "Awkward Squad" whence, as they progress,
they are transferred. Last year one bright cadet instructor thought
of a practical joke to inspire the new cadets to do their very best.
It seems that the schedule of drills included a "sightseeing tour"
around the Post, in order to familiarize the new cadets with their
surroundings. The plebes were told that only the most efficient would
go on this tour. Consequently great efforts were made by members of the
awkward squad to increase their military efficiency. As the instructors
knew and the plebes later discovered the "sightseeing trip" was
anything but a treat. It was made on a broiling hot summer's afternoon
at a rapid walk, and not after the fashion of the Metropolitan
rubberneck wagons. Objects of interest were pointed out in the most
military manner: 1. Eyes Right; 2. Hudson River; 3. Front, or, 1. Eyes
Left; 2. Battle Monument; 3. Front!
Sandwiched between the infantry morning drill are the physical
exercises. This name will make the plebes laugh, for all drills are
physical exercises, but I intend it as a distinguishing name for a
drill where the essence of exercise is dispensed. This drill is now
given in the Gymnasium and consists of every known form of setting-up
exercises that can be devised. For forty-five minutes the cadet
executes them, both at halt and while marching. He is given frequent
short rests of half a minute or a minute, after every different
exercise, but nevertheless it seems to the naturally fatigued new
cadet, as if every muscle, every sinew, and every bone was being
relentlessly punished.
These setting-up exercises are a potent influence in the new cadets'
physical development, and when the fresh young body has become
accustomed to them, they act as a tonic, an elixir. To a visitor the
drill is always interesting as it is rather spectacular, due to the
numbers acting in unison and with perfect cadence.
The early afternoon is devoted to the nomenclature and cleaning of
the rifle. Scattered in groups in the shade of the old gymnasium or
the Cadet Store, perspiring plebes take their rifles apart and, after
cleaning them, try their utmost to put them together again.
[Illustration:
_Photo White Studio_
A First Lesson in Saluting]
Infantry drills fill the remainder of the afternoon until 5:00 P.M.,
when there comes a chance to wash away the grime before retreat.
Immediately after the lowering of the flag each afternoon is an
inspection in ranks, for which all plebes must be carefully groomed.
Each man must appear with immaculate linen and with his blouse and cap,
and shoes carefully brushed. Mr. Ducrot dreads the inspection more
than any other duty. Despite his care in dressing, the inspectors are
sure to espy a tiny wisp from the clothes brush clinging to his cap or
blouse, whereupon His Highness says:
"What do you mean by falling into ranks covered with straw?" Perhaps
Mr. Ducrot is just seventeen years old with only a soupçon of hair on
his face.
"Why, what's this," inquires a sharp-eyed inspector. "Mr. Ducrot, why
didn't you shave today? I see three hairs sticking out of your chin.
Drag in your chin."
Mr. Ducrot's sense of humor overcomes him even in his miserable state
of mind and the corners of his mouth begin to twitch.
"Wipe that smile off your face!" commands the cadet officer.
Up goes the hand: the offending emotion is erased.
"Now, Mr. Ducrot, throw it upon the ground and stamp upon it. Don't
you ever again smile in ranks." Mr. Ducrot begins to feel that the
Wrathful Ones are quite human after all and he feels cheered up for
the remainder of the day. Up and down the line walk the cadet officers
inspecting and "bracing" the plebes, commanding:
"Get your shoulders back! More yet! More yet!"
"Hold your head up; drag in your chin!"
"Suck up your stomach! Lean forward on your hips!" and so on.
For three weeks the new cadets are put through this severe course of
instruction before they are deemed fit to be put in the ranks of the
older cadets without ruining the appearance of the Battalions.
It is astonishing to behold the progress made in elementary training in
this short period. It is true that the days are crammed full, and the
instruction is of the most intensive kind, but even so the results far
exceed what might be expected under the most rigorous of systems.
In the first place, the men lose all appearance of slovenliness
and begin to acquire a distinct military bearing. The unevenness
of gait is replaced by a measured tread, the hanging of heads and
drooping of shoulders gives way to an erect smart carriage, and the
excessive swinging of arms disappears. The group of very crude-looking
individuals of the first few days has been changed into a harmonious
appearing military body. Little by little the new men have begun to
adjust themselves to their uniforms.
No less marked is the change of the mental attitude of the new cadet at
the end of "Beast Barracks." All sense of his own importance, if he
ever had any, has oozed away rapidly. Like Bob Acres, it sneaked out of
the ends of his fingers the first few days, and he realizes what a very
small fish he is in this new pond. He rapidly acquires a most receptive
mood in which he absorbs the most important lesson that a soldier must
learn,--OBEDIENCE. The officers and cadets in charge of him demand
unhesitating and instant compliance with their orders. To this end the
new cadets are made to execute every order at a run, not to harass them
as they sometimes think, but to form the habit of immediate obedience.
This trait is the foundation of discipline, toward the inculcation
of which in the new cadet, an excellent beginning is made in "Beast
Barracks."
At the end of three weeks the "Beasts" are moved from Barracks to
join the rest of the Corps in camp. You ought to see them move.
Carrying their Lares and Penates in striped laundry bags, or on canvas
stretchers, they come and go all morning across the Plain in parallel
rows, resembling for all the world a colony of ants building its new
home. Upon arrival in camp, they join the companies to which they have
been assigned, and from the state of "Beast" they are raised to the
dignity of a plebe, the next lowest grade in the cadet hierarchy.
"Beast Barracks" is over, but its memory remains fresher than any other
at West Point. In spite of the new and more interesting training
of camp life, Mr. Ducrot is forever haunted by recollections of
perspiration and indelible ink.
CHAPTER VI
BENDING THE TWIG
Only when the three hundred odd new cadets have been transferred to
camp and joined the Battalion, do they begin to feel that they are
members of the Corps. They are, however, ill-formed, crude, ungainly
members, and from the moment they pass the hedge that screens the
camp from the visitors' seats, the Tactical gardeners begin the
work of bending these natural twigs, so recently transplanted from
the individualistic soil of civilian life to the orthodox ground of
military training.
Realizing how difficult it is for a young man to adapt himself to the
changed conditions that he meets at West Point, the authorities require
the new cadet to report in June, just as the academic year has closed,
in order that he may receive the benefit of the summer-camp training
before taking up his studies. The physical fatigue that the new plebe
experiences is really so great, that he would not be able to plunge
into the academic course before his body has become accustomed to the
demands made upon it. The aching muscles, the drooping eyes, that
awful heaviness of fatigue must all be given time to pass away so that
the mind may be free to pursue its development. To this end, he goes
into camp after his first few weeks in "Beast Barracks."
The camp is prettily situated in the northeast corner of the Plain
along the bluff overlooking the Hudson. In form it is rectangular, laid
out for six companies whose streets are centrally cut by an avenue
known as the general parade. The streets are parallel to the parade
ground proper, from which they are separated and screened by a hedge.
Nor is the cadet camp lacking in the features that make every permanent
camp comfortable and convenient for the soldier. For these creature
comforts, the cadets have been at times criticised on the ground that
soldiers in the field should be content with the bare necessities of
life. The cadet camp, however, is intended as a camp of instruction
only. In military life there are two kinds of camps, the permanent camp
and the temporary camp. In the latter, soldiers live close to nature
dispensing with the hundred and one little conveniences that all of
us today consider necessary to our physical well-being, but in the
former, such as the cadet encampment, the soldier is provided with a
maximum of comfort--and why not? The illustrated magazines that help
to bring us closer to the Great War in Europe give visual proof that
when men remain for any length of time in one place, even in the zone
of danger, they build and adorn abodes. It may be that an enemy shell
will destroy these shelters the next moment, but the domestic instinct
remains unimpaired. Some of the bomb-proof dugouts on the western front
are miniature triumphs of architecture and comfort. The occupation year
after year of the cadet camp has had the same effect. We therefore see
today a camp with graveled company streets that are illuminated at
night by electricity. The tents, instead of being pegged, are supported
by galvanized iron rails. The dim candle of olden times is replaced by
the brilliant electric bulb, and the cadet, instead of reposing his
weary bones on the hard wooden floor, slumbers luxuriously on a Gold
Medal cot.
A large central tent, like a mother hen watching over her brood, is
reserved for the Commandant of Cadets. The tents of the cadet officers
are on the opposite edge of the space in front of the Tactical
officers' tents, the next indication of hierarchical authority. Then
come the tents of the non-commissioned officers and the privates.
To have a neat-looking camp, strict regulations govern the arrangement
of the tents. Twice a day they are aligned. Due to changes in the
temperature, the supporting cords lengthen or shorten, so that the
front tent-pole gets out of alignment. Then an authoritative voice
rings out:
"Turn out, 'B' company, and straighten your tent-poles!" Whereupon
cadets in all conditions of dress and undress tumble out of the
little brown canvas homes. When it rains the cords must be loosened
at the first pitter-patter of the raindrops on the tent-fly. The new
plebe sitting in his underwear in his tent, probably polishing his
breastplate for the twenty-fifth time that day, does not realize that
this duty must be performed until a dozen or more yearlings command
from the recesses of the canvas bungalows:
"Turn out, you plebes, and loosen those tent-cords!" Out they jump into
the "catacombs" (the space between the tents), bumping their heads
against the rails, and at once commence tugging at the obstinate,
water-soaked tent-cords, while the summer downpour soaks them to the
skin.
* * * * *
To each tent two cadets are assigned, one of whom performs for a week
at a time the duty of tent orderly. Whenever the cadet detailed for
orderly is absent on account of duty or sickness, his tent-mate becomes
responsible. In order that the Tactical officer in charge of any
company may know which cadet is responsible, there is fastened on the
front tent-pole, a revolving octagonal disk of wood, about three inches
in diameter. Both cadets' names, as well as the words "Guard" "Sick,"
are printed on the face of the disk, along one of the sides, and the
disk revolved to indicate the name of the orderly, or the cause of the
occupant's absence. The orderly is also supposed to keep the water
bucket filled, but the occupants of each tent usually have some private
treaty whose provisions prescribe which one shall "drag" the water
from the hydrant.
Generally speaking the orderly is responsible for the cleanliness
and police of the tent, and of the ground adjacent and in front, as
far as the middle of the company street where the rubbish is swept
into a pile to be removed by the policemen. These men are civilian
employees, many of whom have been at the Academy so long that they are
intimately identified with the Corps. In time, some of them will fade
into legendary characters much the same as Benny Havens. Promptly at
police call at five o'clock, the wheelbarrow squad commanded by "Mike,"
"Frank," or "Tony," moves ceremoniously down the street collecting the
sweepings. At this hour the camp presents an animated scene. Cadets are
busily dragging the ground around their tents with a broom to give it a
"spoony" appearance for inspection, and every few minutes some one man
will dart out to the center of the street with a stray match or piece
of paper and throw it in the passing wheelbarrow.
The interior of the tent contains a wooden clothes-press and usually
a canvas stretcher suspended from the ridge pole. Each cadet has a
certain section for his clothes. All articles, belts, gloves, socks
must be folded and arranged in a prescribed manner. The cots are folded
and kept out of sight during the day. Gray, painted wooden lockers for
storing cleaning material and clothing border one side of the tent
floor. Many cadets, however, secrete food, known as "Boodle" in these
convenient places, and I am sure that an unexpected inspection would
reveal many tins of saltines, bottles of olives, and jars of peanut
butter. During my cadet days, the officer in charge of my company
never, for some reason, looked into the lockers. My tent-mate and I
therefore grew more and more bold about filling them with vast supplies
of "Boodle," and we began to think that the "Tac" was inspired by a
sort of _noblesse oblige_ where the lockers were concerned, a sort
of sympathetic remembrance of his own cadet-gnawing appetite. One
Saturday, however, just as he was leaving and I was offering a silent
prayer of thanksgiving, he ordered the lockers opened. A gallon jar in
which some fifty olives lay submerged and a slovenly looking pineapple
cheese met my humiliated gaze. A reprimand that as a cadet officer I
should set an example to the rest of the company, and five demerits,
were awarded to me forthwith.
When the tents are not prepared for inspection, however, cadets may
make down the cots and rest. How wonderfully refreshing it is to rest!
to throw oneself down on the blankets and forget the heat, the weary
march, the grime, the dust, and abandon oneself to the delights of
the imagination, dreaming of the sweetness of the past or building
vast plans for the future! How precious to the cadet is each moment of
repose snatched from the busy day! But it is in the morning that the
real longing for sleep becomes most acute.
Every morning at 5:20, the solitary boom of the reveille gun is echoed
throughout the hills, rudely dissipating the fog of unconsciousness
that envelops the sleeping cadets. Little by little the deathlike
slumber of the camp is broken. Indistinct sounds, a sigh, a yawn, float
gently out upon the air; drugged forms twist and roll uncertainly
beneath the mosquito bars, as if struggling in a bewildered sort of way
to preserve the pleasing heaviness that charms their bodies.
Suddenly the air is torn by the shrill garrulous fifes and the lusty
rub-a-dub-dub of the drums. The reveille march has begun. Around the
camp the "Hell Cats" march, up one street, down another like demons
possessed. The shrieking sounds of the fifes and the deep rolling
noise of the drums brusquely rout the stillness of the dawn, while the
semi-conscious forms toy with danger, beguiling themselves that there
is plenty of time until the assembly. Presently from near the general
parade the familiar warning notes of _Yankee Doodle_ change the camp to
a place of intense animation. Up go mosquito bars and in a twinkling,
almost as if by magic, tents disgorge their sleepy occupants, hastily
and feverishly buttoning their uniforms as they run to their places in
ranks to the fading rolls of the drum corps.
After reveille it takes but a few minutes to police the tents and
perform the necessary ablutions before breakfast. The drills commence
within a half-hour after the morning meal and continue until noon.
They are of various kinds, the majority of which will be described
in the chapter entitled "Lessons from Mars," but I will speak of the
plebe's work in his first camp, since it is somewhat different.
The physical exercises given to the new cadet in "Beast Barracks"
are continued in camp. In addition, he is sent to the Gymnasium for
swimming, where a professional instructor is present to see that no
one drowns, and to teach the various strokes. As many of the cadets
are adept swimmers upon entrance, they are tested, and those found
qualified are excused from further attendance. The men who cannot swim,
the real "land lubbers," attend daily until they are proficient.
The most diverting instruction, however, in plebe camp is the dancing
lesson. A civilian professor spends the summer at West Point to
instruct the fourth classmen in the Terpsichorean art. Every morning
at hour intervals, squads of cadets carrying their pumps march across
the parade to Cullum Hall. Here they remove their coats, put on their
pumps, and line themselves along the wall. The waltz step is first
taught as the basis of all dancing, then later the two-step, and,
since the new dances have come upon us, the fox-trot and one-step
are rehearsed toward the end of the course. The dancing lesson is
not open to visitors. Once upon a time it was, but long cadets,
short cadets, fat cadets, lean cadets, awkward and graceful ones,
all tiptoeing, "one- and two- and threeing" around the room like a
lot of coy young hippopotami with compass bearings lost, became a
famous sight for tourists, who wanted to enjoy a good laugh. How could
anyone learn to dance in the presence of a giggling crowd! But the
crowd wasn't to blame! Here in one corner was a little slender chap
delicate as a reed, perspiring in his efforts to steer his six-foot
partner, a regular steam roller, through the mazes of Professor Vesay's
old-fashioned waltz. Again, all over the room, self-conscious boys in
white shirt-sleeves were in a bewildered state trying to execute the
Professor's directions:
"Right foot in second position--glide and cut!" Nowadays an officer
excludes all sightseers during the lesson.
The instruction of the plebe in infantry drill continues
uninterruptedly, for it is essential that he should not spoil the
appearance of the rest of the battalion. Together with swimming,
dancing, and infantry drill, his morning is completely occupied. After
the midday dinner, he is assembled in squad for instruction in hygiene
and guard duty, or he may be required to spend his time working upon
his equipment, his brasses, his bayonet, and rifle.
Very little social diversion is permitted to the plebe, because he is
usually awkward in appearance and unfamiliar with military customs and
deportment. Consequently he considers that his life is excessively
hard, to him unnecessarily so; but as I have observed cadets for
thirteen years I am convinced of the wisdom of holding them in a
distinct class for one year. Then they emerge from the cocoon of
plebedom as dazzling yearling butterflies.
To afford instruction in guard duty the camp is surrounded by
sentinels. A quota of cadets from each company marches on guard
immediately after parade in the evening. There are three reliefs for
each of the ten posts: three corporals, a sergeant, and two officers of
the guard, and an officer of the day. The guard is under the control
and supervision of the officer in charge, who is one of the Tactical
officers. Each sentinel walks two hours and rests four, so that during
the twenty-four hours the cadet walks eight hours. The effect of this
duty upon the cadet is lasting, for it teaches him the fatigue a
sentinel experiences and prevents him, when an officer, from demanding
too much of his men. The borders of the camp are divided into posts,
numbered from 1 to 10.
The first important duty demanded of the plebe is guard. With what
quivering sensations this youthful soldier approaches his first real
test! Before he goes on guard he is instructed in his orders, both
general and special, but few feel as if they knew them well enough
to stand the ordeal of an inspection by a yearling corporal. No
opportunity is lost, therefore, before the hour to march on post to
perfect his knowledge, so that after supper little groups of excited
and nervous plebes study diligently these orders under the pale and
insect-infested lamp-posts near the guard tent. In the obscure light
these slim gray forms, some seated and some standing, seem shadowy and
motionless except for their gloves, little dabs of white that move
restlessly to and fro, attacking the ubiquitous mosquitoes.
The nearby guard tents under the elms are dark except the main one
where sit the officers of the guard, who keep the record of a stream
of gay upper-classmen, signing out for the hops and concerts. How far
off they are to the plebe! It seems to each one, as he watches them
from the shadows, that there is an impassable gulf between them, and
he wonders as he listens to their hurried voices calling, "Ducrot, hop
with," or "Dumbguard, hop with, extended" if ever his year of plebedom
will roll by. What are those unintelligible remarks? It is some time
before he understands that the above expressions mean that Cadet
Ducrot is taking a young lady to the hop, and that Cadet Dumbguard
also, except that the latter's girl lives at some distance so that
he is allowed ten minutes more after the conclusion of the dance to
escort the young lady to her home. Today, as I stroll by the camp in
the evening and see the same scenes reënacted, I re-live the first
impressions of my own plebe days.
Often while I was waiting my turn to go on post, I sat fascinated
as I watched the scene at the guard tents in the twilight of the
summer evenings. From the obscurity of the camp, stalwart figures
were constantly coming. Their gray coats and the evening mists merged
into one so completely, it seemed as if only animated pairs of white
trousers were flitting across the parade, all converging toward Post
No. 1. Little by little, as they approached the light of the guard
tent, the rays that were stabbing the darkness illumined the bell
buttons of the gray coats, and for a brief moment gleaming forms with
happy laughing faces filled the picture and then into the darkness of
the Plain quickly disappeared.
Such reveries, however, are usually interrupted by a sharp voice
calling:
"Turn out the second relief!" "Hurry up, you plebes," and away the
novitiates scamper to perform their first guard tour. As the relief
marches around the graveled paths under the command of a very military
corporal, the plebe has, in spite of his feeling of uncertainty, a
sensation of pride in being entrusted with the guard of a part of the
camp. Each time that the corporal commands "Relief Halt No. 2!" and
the rifles hit the ground in unison, a pleasurable thrill pervades
his being, a consciousness of a certain importance. Before very much
pride can swell his breast, he is brought back to reality by the
stern corporal exclaiming, "Wake up, Mr. Dumbguard, and come to port
arms!" or "Drag in your chin!" In goes the chin, and the shoulders
instinctively draw to the rear. Glory was brief; humiliation reigns
anew.
Then commences in earnest the lonely two hours of marching up and down,
back and forth, at the end of which time the nine pounds of the rifle
has tripled at least. The arms ache, and legs feel as if they would
bore holes in the body.
The early part of the tour is filled with interest. The animation
in some company streets in contrast to the silence in others, the
occasional tinkling of mandolins, the cries from one tent to another,
the laughter over a surreptitious bucket of lemonade, the Y. M. C.
A. phonograph, the confusion over the wash lists, scampering cadets
noisily returning from hops and concerts--all keep a sentinel from
thinking of himself. It is not until the three taps of the drum,
when the camp is magically plunged into obscurity and silence, that
the plebe begins to feel the monotony of his duty and, while walking
mechanically back and forth on his post, to become introspective.
The stillness of the camp only accentuates his slow nonchalant step on
the path. In his imagination the air seems to be filled with invisible
spirits--the spirits of the night that have come forth. First he is
conscious of only a few timid ones here and there, but as the hours
wear on they seem to grow bolder and bolder, filling the surrounding
atmosphere and whispering in his ear their ghostly messages. Each
nerve becomes more alert as he listens for the crunch, crunch, crunch
of some official step on the gravel. How vivid and eerie seem his
surroundings! The lonesome hours of the night strike a sympathetic
chord in his sensitive nature and the balmy stillness calls forth
his starry fancies. At this hour when his comrades lie in their
tents bewitched by sleep, the most beguiling of enchantments, he is
conscious that another mysterious world is awakening all around him
in the solitude and silence. The air is filled with fairies holding
their imperceptible revels. He hears the rustling of the leaves, the
intermittent chattering of the crickets, the soughing of the breeze in
the branches, as if the trees in great distress were calling mournfully
to each other. Should this be the first time that he is alone at night
on post, he is a little afraid, and starts at the faintest sound. It
seems that when man reposes, the _Things_ come forth to their daily
tasks, performed in a world unknown to us.
Never will he forget, however, the ineffable beauty of the scene, so
beautiful that he is filled with a little sadness. The buildings across
the Plain, stern and melancholy even in the darkness, seemed to be
companion sentinels ever watchful over their traditions, and guarding
the sleeping hills dimly discernible through their misty blankets.
Occasionally a graceful river steamer, like some huge Jack-o'-Lantern
ruffling the smooth waters of the Hudson, glides softly by under the
cliff, her throbbing engines seeming to send forth a certain warmth
that dispels the chill of the early morning.
It is at this hour especially that his thoughts wander to his "ain
Folk" and reveal to his senses the full aroma of his days at home.
The clanking of a sword in the darkness calls him back to earth and to
the realization that the dreaded inspection is at hand.
"Halt! Who goes there?" he quickly challenges.
"Corporal of the Guard," answers a sepulchral voice from the shadows.
"Advance, Corporal of the Guard, with the countersign," uncertainly
commands the plebe. When within whispering distance, the corporal
faintly breathes the countersign, "Saratoga," or "Burgoyne" (or maybe
Tannhäuser or Dumbguard, to test the sentinel), whereupon the corporal
is allowed to pass by the sentinel's order:
"Advance, Corporal of the Guard."
In the eyes of the yearling corporal, a plebe is habitually wrong,
so that for a few trying minutes the benighted sentinel endeavors to
"take charge of his post and all government property in view," while
his preceptor picks him to pieces, his bearing, his accoutrements, his
knowledge, admonishing him at intervals, to "Drag in his chin--way
in." But soon, the solitude of the night begins to work even upon the
yearling corporal constraining him to indulge in a partial intimacy
with the plebe, adding in softened tones:
"Mister, where are you from?"
"South Carolina, sir," proudly responds the sentinel, touched by the
upper-classman's near-cordiality.
With a gruff "Pretty fine State, mister," the corporal virtuously
departs to interrogate his next victim.
How welcome now is the first faint tread of the relief as it makes its
bi-hourly round to take the sleepy sentinel back to the guard tent
where a bed of camp stools awaits his aching muscles.
* * * * *
The tour of guard of a new cadet is sometimes made uncomfortable by the
pranks of the upper-classmen, although since the abolition of hazing
at West Point, this form of diversion has greatly diminished. The
regulations against hazing have been made so stringent that few cadets
indulge in the practice. As a matter of fact hazing no longer exists at
the Military Academy. A few heedless chaps from time to time, forgetful
of the future, unconscious of the heartburns that they will suffer
later on, indulge in hazing the plebes, but they pay the price for
their fun. Formerly, hazing was tolerated among the cadets because some
of its features were not harmful or objectionable, but, as in all cases
where a little liberty is granted to lads of immature judgment, license
followed. The practice was carried too far and moderation ceased to
exist. In 1901, at the instance of a former cadet's parents, Congress
ordered an investigation of hazing conditions, with the result that the
Superintendent was directed to abolish all semblance of mistreatment of
plebes by upper-classmen.
The more vicious practices disappeared at once, but from time to time
investigation revealed isolated cases of the innocent kind. In the days
of hazing, the favorite and most injurious punishment meted out to a
plebe, if he were at all fresh, or "B. J." as the cadets say, was a
series of exercises known as "eagles." The new man would be taken in
a tent, stripped to the waist, and compelled to execute a setting-up
exercise, "Full bend knees." The knees are separated and bent as
much as possible; point of knees forced forward and downward, heels
together; trunk and head erect; but instead of placing the hands on
the hips, he was required to raise the arms laterally. It is not the
exercise itself that was injurious, but the duration of the punishment.
Some men were required to "eagle" 100 or 150 times without a rest, and
if they had committed a particularly heinous offense, this physical
rebuke was administered under the broiling sun in the "catacombs."
Another form of punishment consisted in making plebes, stripped to the
waist, hold pieces of matches or tissue paper, between their shoulder
blades for half an hour or more, while their tormentors stood around
insisting that they flatten their chins to their necks.
But this punishment was not viewed by the plebes with as much dismay
as was the servitude to "Tabasco Sauce." The prowling yearlings would
descend into the Fourth Class sink, line up the plebes, and order them
to stick out their tongues, upon which they dashed a flop or two of the
burning liquid and fled. Sometimes, at the Mess Hall, as much as half
a teaspoonful was meted out for some unconscious transgression by the
plebe of the upper-classmen's wishes. Fortunately the above practices
have long since disappeared.
On the other hand, the greater part of the hazing consisted of what
is known at college as "fagging," such as dragging water, sweeping
tents, making beds, cleaning brasses and rifles, making lemonade,
running errands, sewing buttons on white trousers, etc. Each
upper-classman selected a plebe for his "special duty man" to perform
the aforementioned tasks. Most of the plebes did the duty cheerfully,
buoyed up by the thought that next year their turn to have a plebe
would arrive. A large part of the hazing, moreover, was the so-called
"deviling" the plebes, a generic term applied to all kinds of humorous
and mischievous pranks. Any cadet, for example, who possessed any
peculiarity of size, appearance, or temperament was given a "tech"
or technical name, to be used always in lieu of his own. One of my
classmates, whose tent was in a part of the camp called "Paradise
Alley," was given in consequence of his auburn hair the following
"tech" with strict instructions to use it no matter who asked him his
name. In reply, therefore, to the same inquiry, "Who are you?" many
times daily, he scrupulously replied:
"I am a too-loo-loo bird, sir! Peep-y-ty-peep, sir! Poop-y-ty-poop! Ah!
... there. I'm the sunshine of Paradise Alley, sir; I am a queen, sir.
My hair is sky-blue pink with a heavenly border, sir! Don't you think
I'm handsome, sir? I don't give a damn, sir!"
This "tech" became famous, the peep-y-ty-peep part fastening itself
upon him as a nickname. Of course, all of these pranks were carried
on _sub rosa_ and presumedly without the sanction or knowledge of the
authorities. One night, however, the cadet was detailed for guard for
the first time. It happened that his tour of duty was from 2 A.M. to 4
A.M., those awful hours of the night. "Peep-y-ty-peep" was patrolling
his post ready to charge anything that came along. Suddenly the huge
shadow of a cavalry Tactical officer with a rattling saber and jingling
spurs loomed out of the darkness. Frantically "Peep-y-ty-peep" charged
down the post screaming, "Halt! Halt! who's thar?" (in good old Alabama
English), until most of the sleeping cadets in the vicinity of the post
were awakened. After a few minutes of backing and filling the massive
cavalry officer arrived in front of the now thoroughly bewildered
"sunshine of Paradise Alley," and began to ask him his orders. Poor
old "Peep-y-ty-peep" forgot them all, general and special. After vain,
fruitless efforts to obtain an expression of opinion of some sort
from the sentinel, this officer said in desperation: "Who are you,
anyway?" Whereupon perfectly seriously the rooky sentinel cried at the
top of his voice, while the nearby tents shook with laughter, "I'm a
too-loo-loo bird, sir! Peep-y-ty-peep, sir! Poop-y-ty-poop, sir! Ah...!
there. I'm the sunshine of Paradise Alley, sir! I'm--" The Tactical
officer hurriedly disappeared.
Such incidents as the above kept the plebes from becoming too
depressed. The fun of the upper-classmen found many other outlets. On
days when watermelons were served in the Mess Hall, the plebes were
required at the conclusion of the meal to fill their mouths with seeds,
and thus loaded to the gunwales to march back to camp. The wriggling,
squirming, slippery little black particles fought with one another to
burst open the encircling mouth _en cul de poule_ and leap to freedom,
and occasionally their efforts were successful, on the march back to
camp, to the detriment of the blouse of the plebe's front rank file.
More frequently, however, upon arrival at camp, the plebes of A Co.
were lined up at six paces from those of B Co., and at a given signal
the human machine guns belched forth their glossy black bullets. One
upper-classman ordered me to gather a handful from the battlefield and
plant them around his tent. To my dismay and chagrin they sprouted,
whereupon I was instructed to care for them, keep them in health or
sickness, and train the growing vines on slender cords.
The plebes were hardly allowed a moment to themselves. Every spare
moment was employed in cleaning guns, brasses and other equipment,
chiefly of upper-classmen for whom one happened to be a "special duty
man." If some unoffending sparrows alighted in the company streets,
half a dozen yearling voices rang out, "Turn out, you plebes, and
chase those eagles!" Lads in all sorts and conditions of undress fell
precipitately out of their tents, bayonets in hand, to drive away the
innocent feathered marauders. If an upper-classman wished to know the
time, he would yell, "_Quelle heure est-il?_" a whole chorus replied,
"Two o'clock, sir!" Again, every plebe was required upon inquiry to
give his P. C. S., or previous condition of servitude. Those who
had none, never having worked in their lives, were made to answer
"schoolgirl," as a mark of immaturity and unworldliness. Never was a
plebe permitted to say: "I don't know." "Say something, Mr. Dumbguard,"
was the admonishment followed by: "If you cannot think of anything, say
'steamboat'! Never say that you don't know!"
I once stood behind a man in ranks who weighed, he said, 190 pounds.
I weighed but 120. It became my daily duty to weigh and report to him
how much of his frail body I, as his near rank file, left uncovered and
exposed to the elements. When a plebe was on guard at night, some of
the yearlings would appear on his post covered with sheets which they
fluttered at a great rate.
"Halt! Who goes there?" cries the sentinel.
"A flock of angels," was the reply, and before the sentinel could get
the corporal of the guard, the flock had flown.
* * * * *
The _pièce de résistance_ of the camp was, however, a rat funeral
for which elaborate preparations were made. Efforts for days were
exerted to catch a rat or a mouse, but if neither could be beguiled
into the trap, a grasshopper served the purpose. In a plebe's tent an
imposing catafalque, equal to that prepared for any crowned head, was
constructed of wooden lockers covered with black rubber ponchos. Upon
the top of this bier surrounded by candles was Mr. Rat.
During the night preceding the obsequies a guard of honor of the
plebes, fantastically dressed, kept a running watch over the
fast-stiffening rodent. Next day, after drill, came the funeral. Orders
were issued by the upper-classmen for all plebes to attend and for
those having musical instruments to appear with them. One plebe was
detailed to act as chaplain and prepare the funeral oration, another
as leader of the band, another as chief mourner. The remainder of the
plebes were the afflicted relatives whose weeds were the most bizarre
and fantastic costumes that they could create. In the procession,
therefore, were plebes in underdrawers and dress coats buttoned in the
rear, hats reversed, breeches with no shoes, shoes without breeches,
ponchos over nature only, and sometimes _in puris naturalibus_. Each
mourner, moreover, came with a galvanized bucket to catch his tears.
First appeared the band composed of mandolins and guitars, a stray
violin, and perhaps a lonely cornet, followed by the deceased borne
upon a canvas stretcher strewn with dandelions. To the tune of
Chopin's funeral march, the grotesquely arrayed mourners followed
the bier, chanting from time to time a parody written for the music
and entitled "Somebody Hit Me with a Codfish Ball!" At a signal from
the chief mourner the cortège halted to allow the plebes to deliver
themselves with abandon to their grief. By order, they raised the
galvanized buckets to catch the "tears that stopped the flood-gates
of their eyes," while they filled the air with agonized mournings and
lamentations. If the sobbing and blubbering appeared too faint, the
upper-classmen who lined the route increased the wailings by yelling,
"Weep louder, you plebes!"
At the grave, somewhere in the rear of the camp, the "chaplain,"
"Daddy" Singles, spoke feelingly of the departed one's nobility of
soul. The gnawing grief of the multitude gave way once more to despair
(and usually to laughter) as they lowered into the ground poor old Mr.
Rat, whose rigid whiskers gave him an amused expression, as if he were
enjoying his honorable end.
* * * * *
After two months' training in camp, the cadets return to barracks to
begin their academic duties. At once, all nonsense ceases, and the new
cadet is in no wise interfered with, even in fun. The routine changes
completely and the day becomes fuller. Reveille is a half hour later,
but the work increases and there are fewer leisure moments.
It is to the more serious and inexorable side of his training that the
cadet must now turn. Life in barracks is more sedate, more formal, more
cold than the free existence of camp where he and his comrades were
living close to Nature. The time has arrived to renounce the pleasure
of sleeping in the open, of breathing the fragrant out-of-doors,
of living in the midst of scenery that appeals to every æsthetic
faculty. It is in the rooms of barracks that the next nine months
must be passed, the severe unadorned rooms whose bareness, however,
is forgotten in the ineffable sweetness of the friendship of one's
roommate. At no place, perhaps, are closer friendships formed than at
West Point. They are not of the whirlwind kind so common elsewhere
today, that sweep one off his feet for the time being. Nor are they
like some great roaring wind that shakes one's nature to its depths
and then leaves him bruised and torn, but wide awake at last, to spend
its force in other directions. Rather are they friendships of slower
growth, but deep and sincere, belonging more to a mature age than to
the irresponsible years of a cadet when his enthusiasm, his likes and
dislikes, seem to be the only things necessary to foster.
The difficulties of his studies, the homesickness, the fatigue of
the drills, the irksomeness of the routine, are all lightened by the
intimacy with his chum, by the smile of sympathy, or the word of
encouragement that greets him at all times. It is a great privilege
to live in close contact with a human being and be allowed a glimpse
into his soul. It compensates for all the stony paths of life, for all
hardships, and sends one forth to his duties with a feeling of joy and
gladness, strong in heart and thankful to God.
In every room in barracks dwell two chums, each the "wife" of the
other. The increased number of cadets and the negligence of Congress to
provide extra barracks have caused the introduction of Mormonism, for
in some rooms are three chums, each with _two_ "wives."
The most striking feature about the rooms is their plainness. Here
the cadet is "allowed not more than nature needs," or scarcely more,
for an inventory of the furniture discloses two iron cots, one iron
washstand, two plain wooden tables, two wooden chairs, and two steel
clothespresses. The walls and floors are bare, for the Regulations
prohibit rugs, carpets, pictures, placards, banners, or any other
adornment. Upon the plain black iron mantel in the middle is a mirror,
flanked by black tin frames containing the hours of instruction and a
time schedule designed to indicate at all times the whereabouts of the
occupants of the room. Not to have the hours of instruction correctly
posted is a military offense. No matter where the cadet is, at
recitation, barber shop, church, lecture, hospital, library, his card
must so indicate. In addition, a small inexpensive clock may be kept on
the mantel.
To give each occupant of the room a little privacy, a wooden partition
juts out half way into the room dividing this space into two alcoves,
in which are placed the cots. During the day the mattresses are folded
and upon them the bedding is piled. Only during release from quarters,
and after 9:00 P.M., are the beds allowed to be made down and used.
Along the sides of each alcove are hooks for the clothing, which must
be hung in a prescribed manner; for example, 1st hook, raincoat; 2d
hook, overcoats; 3d, sweater coat, and so on. The shoes are aligned
toes out, along the side of the bed, in a definite order, the high
overshoes as right guide, then the low overshoes, and other shoes
according to height.
Upon the top of the clothespress are the books, arranged according to
height, newspapers, periodicals, stationery, cameras, and tobacco.
In the shelf section each of the various articles of clothing has a
prescribed place, and in the coat section the uniforms are hung in a
regular order. Only on the top shelf of the clothespress may the cadet
keep a photograph.
In front of and against the alcove partition is the washstand with its
two wash bowls. The water, hot and cold, is drawn from a hydrant in the
hall. This arrangement is a great luxury in comparison with the old
days when, to heat water for shaving, we poured it over a joint in the
radiator.
In barracks as in camp there is a room orderly who is responsible for
the condition, cleanliness, and general police of all parts of the
room. The cadets sweep their own rooms and make their own beds. The
halls are swept by the civilian policemen, who also scrub periodically
the floors of both rooms and halls. By Regulations, cadets are not
allowed valets, nor are they permitted to own an automobile, horse, or
dog.
The cadets are in uniform, of course, at all times. Every detail of
their clothing is prescribed. The collars, for example, must project
above the coat collar just one eighth of an inch, and a like display of
cuff is required. Only certain kinds of shoes may be worn, and certain
kinds of gloves both for drills and hops. Although not prescribed by
Regulations, a custom of long standing among the cadets prohibits the
plebes from wearing their overcoats with the end of the capes thrown
back over the shoulder, nor may they wear lisle thread gloves to
chapel, but must content themselves with the thick, coarse Berlin gun
glove. The lowered capes of the plebes give them an air of humility
alongside of the upper-classmen, and the gun gloves accentuate the
crudity of the poor plebe's military appearance.
The day is filled with duties. From the return of the Battalion from
breakfast until 8:00 A.M., is a study period. From 8:00 A.M. until
12:35 P.M., the different classes attend recitations in the prescribed
courses, or perhaps have instruction in gymnastic exercises or in
riding. Dinner comes at 12:40 P.M., after which recitations are held
until 3:50 P.M. In the fall and spring drills commence at 4:00 P.M.,
followed by parade at 5:30 P.M., and retreat and supper at 6:30 P.M.
Cadets do not proceed individually to their classrooms, but are formed
in the area of barracks in sections, under the command of a section
marcher, who, after reporting to the officer of the day any absentees,
marches his men to their section rooms.
In like manner there is a meal formation. The Battalions are formed
in front of barracks and marched by the two senior captains to the
Mess Hall. Just as much observance to step, alignment, and bearing is
required as though marching to parade.
Upon entering the hall, "at ease" is commanded, whereupon the cadets
proceed quietly to their places at table and remain standing back of
their chairs until the cadet captain commands: "A Co., take seats." The
food is always ready so there is no delay. Thirty minutes are allowed
for breakfast and supper, and forty for dinner.
As soon as seated, cadets begin to talk and laugh. The only
restriction upon them is that they must conduct themselves at mess
like young gentlemen. No throwing of food or waste is tolerated. One
first-classman, known as the table commandant, is in charge of each
table and is held responsible for all breaches of regulations upon the
part of the cadets thereat.
Civilian waiters bring the food from the kitchen and place it upon
the table. The cadets are then required to help themselves. Custom
makes the three or four plebes at each table perform the most onerous
duties. One plebe, known as the "water corporal" pours the water and
milk. Another, the "meat corporal," carves the "bone," and another, the
"gunner," pours the coffee, and exercises a general supervision over
the supply. Their duties keep them very busy, for the upper-classmen
constantly demand food.
[Illustration: Marching to Barracks from Dinner
The Academic Buildings]
The life at the Mess Hall is replete with customs, and the vocabulary
of the cadets filled with terms unintelligible to the uninitiated. Some
of their customs would not be approved in polite society but would be,
perhaps, by modern efficiency. If, for example, a man at the end of
the table wishes more water or milk, bang! goes his glass on the table
preliminary to its flight through the air to the outstretched nervous
hands of the "water corporal." The plebe eats in spasms, so to speak,
one eye on his food, and the other on the alert for aërial glasses.
"How's the cow?" yells an upper-classman, meaning how much milk is in
the pitcher.
"Almost dry, sir!" replies the plebe.
"Milk her again!" is commanded as the glass comes speeding down.
Every morning the "gunner" who sits at the end of the table, in
capacity of hostess, so to speak, "sounds off" the number of days
until June. Instead of grace, he commences the meal, "282 days until
June, sir!" On the 300th, 200th, 100th day before June, the plebes
write speeches in which they are allowed great latitude in satirizing
the upper-classmen. The yearling who has been particularly annoying
during the year sees all of his faults held up to ridicule, but he must
swallow his medicine at the hands of the plebe.
It is a real treat to see the men at mess. No melancholy stillness
pervades the Mess Hall. One can hardly hear himself in the din of
rattling dishes, knives, forks, the peals of laughter, the roar of
eight hundred voices all talking at once, punctuated by the plebes
repeatedly shrieking, "Bread! please!" or whatever they want. In
beholding them, one realizes vividly the meaning of the expression
"teeming with life."
Occasionally, orders are read in the Mess Hall by the Adjutant. It
would seem impossible to get the attention of the cadets, but when he
commands:
"Bát-tál-yón ... at-ten-tion!" the roar almost instantly subsides,
like a balloon suddenly pierced. A wave of silence engulfs the hall,
accentuated at times by the fall of a fork or spoon on the tiled floor.
Quietly the cadets sit, as the Adjutant reads his order, on "skins"
(delinquencies). There are no soft notes in his tone. They are all
fortissimo and run together until they become "monotonous," like the
hum of a factory. Some mischievous cadet, unable to bear the enforced
inactivity, enlivens a small group around him by stealthily firing a
bread ball at an unobserving neighbor.
Each cadet has a silver napkin ring with his name and class inscribed
thereon. At graduation all of the rings are melted into a loving cup
which is given to the member of the class who has the first son. This
child is known as the "Class boy."
Just before the conclusion of the meal the first captain makes an
inspection, calls the Mess Hall to attention, and commands: "1st
Battalion, rise." The cadets file out quietly, form in front of the
Mess Hall, and return to their barracks.
* * * * *
The rooms are subjected to a continual series of inspections. First,
there is a rather superficial inspection by the subdivision inspectors,
cadets of the First Class, twenty minutes after reveille. They give the
rooms a _coup d'œil_ chiefly to see that the floors have been swept and
the bedding folded and piled. During the forenoon, the Tactical officer
in charge of the company makes a careful survey of everything. This is
known as the "Tac" inspection, and may occur any time from 8:00 A.M.
to 11:00 A.M. Until the "Tac" makes his morning visit the cadets are
required to wear their uniforms buttoned. The majority of the cadets
sit around in their sweater coats until they hear the authoritative
knock of the "Tac" on the doors of the first-floor rooms. They then
quickly don their blouses until after he leaves, when sweaters are
again brought forth. This time is a study period and it is almost
impossible to concentrate on problems that make you feel like tearing
your hair, when dressed in a tight-fitting uniform.
When roommates attend morning recitations at different periods, the
first-hour men are notified of the inspection by their comrades who
leave the mirror turned to the wall as a signal, or, sometimes, just a
sign--"He has." Once a Tactical officer with a sense of humor traced in
the dust across the face of a cadet's mirror, during his absence, "He
has."
Upon the return from first-hour recitations the divisions ring with
shouts, "Has he?" "Has he?" mingled with the cries to the plebe mail
carrier of, "Mr. Dumbguard, has the mail?"
After dinner the officer of the day inspects to see that the cadets
are not visiting and that the rooms are in order. During the evening
study periods, from about 7:30 to 9:30 P.M., the cadet sentinels posted
in the halls of barracks inspect three times. They open the doors of
each room, inquiring, "All right, sir?" whereupon the occupants reply,
"All right, sir!" or "Cadet Ducrot is absent." The reply "All right"
signifies that all occupants are present, or if any are absent that
their absence is authorized. Any cadet who intentionally makes an
incorrect report is dismissed from the Academy.
The day ends, as it begins, with an inspection of the subdivision
inspectors. At the three taps of the drum in the Area, cries of "Lights
out!" fill the air. The buildings are plunged into darkness except for
a dim hall light, and the inspectors, armed with bull's-eye lanterns,
flit through the halls like nervous fireflies. Each door is hurriedly
opened; a beam of light seeks first one bed then the next, while the
dark form on the threshold calls out sharply, "All in?" "All in, sir!"
replies the room orderly from the depths of the alcove. Bang! goes the
door and the shadow disappears. From all the divisions the fireflies
swarm into the Area and align themselves like a string of shining beads
in front of the officer of the day to whom they report.
* * * * *
For all breaches of regulations the cadets are reported, "skinned"
in their parlance. The list of delinquencies is read out at retreat,
and the next morning the cadet must submit a written explanation of
the offense. The majority of the reports are for minor offenses, such
as lates, absences, inattention, buttons off uniform, and so on.
Ordinarily, no explanation for these offenses is requested, although
the cadet has a right to offer one if he so desires. The more serious
offenses, however, must be explained.
In their explanations cadets must confine their statements to plain
facts. No criticism or argumentation is allowed. Occasionally some
wit transcends the limit and amuses himself for the moment at the
expense of his conduct grade. Once a report was entered against a
cadet for having worn his night-shirt to the Drawing Academy. It seems
that, lacking a plain white shirt, he hastily donned a night-shirt,
stuffing the flowing tails in his trousers. He was betrayed, however,
by the blue embroidery down the front. An instructor, seeing the queer
garment, reported the cadet. Since he had been obliged to attend a
number of lectures in drawing, at which he invariably fell asleep, he
submitted the following facetious explanation to the Commandant of
Cadets:
* * * * *
SIR:
In explanation of the report "wearing a night-shirt to the Drawing
Academy on the 10th inst." I have the honor to state that I heard
that there was to be a lecture in drawing; consequently, I wore my
night-shirt.
* * * * *
I need not add that he walked a number of punishment tours for his wit.
The punishments that may be awarded a cadet are:
(_a_) Confinements; that is, restriction to room
during release from quarters.
Restriction of limits.
Deprivation of privileges.
Punishment tours.
Reprimands.
Reduction of officers or non-commissioned
officers to the grade of private.
Loss of furlough.
(_b_) Suspension.
Dismissal.
Punishment tours are of one-hour duration, during which time the cadet
walks an assigned beat. On Wednesday and Saturday afternoons the Area
is filled with cadets walking to and fro, like pendulums, each tracing
in the gravel a little path. They resemble in their animation the
goings and comings of a colony of ants. No cadet enjoys walking tours.
It is viewed as a particularly disagreeable punishment, much worse
than serving a confinement in one's room, where he may "bone fiction,"
chasing away the gloom of imprisonment with some interesting book. In
the winter months the chill and snow fill their thoughts and hearts as
they pace to and fro, beating their hands together for warmth. But it
is in the autumn and spring when the athletic contests with outside
teams take place that the misery of walking tours becomes terribly
acute. The cheering of the fortunate cadets witnessing the games is
like some magnet which draws and draws. The longing must be resisted
and stifled while they continue upon their monotonous walk, chained to
an inexorable task.
The work demanded of a cadet is hard, but without the restrictions,
obstacles, the petty annoyances, the young plebe that comes to West
Point so plastic and yielding would never grow and develop. At first
the limitations that surround him baffle and bewilder him for a time,
but as the days pass by and he begins to be imbued with the spirit of
the Corps, and to feel the traditions and atmosphere of West Point, he
insensibly rises superior to every annoying restriction. He may indulge
in occasional grumbling and ill-humor but what of that? He knows now
that a reason exists for every obstacle, and he sees in the hardships a
way that leads to the development of his higher self. His moral force
is gradually crystallized and he gains the spirit of willingness to do
his duty toward the Academy and his little bit in keeping strong the
spirit of West Point.
The main idea of West Point after all is to develop the mind and
character of the cadet, to instill into him the proper ideas of
discipline. It does not aim for a discipline where a man's spirit or
will is broken, so that he obeys through fear, but a discipline of the
soul, wherein a cadet performs his duty for the deed's sake. Without
this high moral spirit, no army can be successful, despite the most
brilliant galaxy of officers.
CHAPTER VII
THE DISCIPLINE OF THE MIND
The longer a cadet remains at West Point, the clearer and finer becomes
his point of view. During the first few months of his career, a glimpse
of which we had in the previous chapter, he is so busy learning the
mechanism of the drills, the care of his person and equipment, and
familiarizing himself with all of the strange names and unusual customs
of military life that his point of view is more or less clouded.
Little by little, during the summer encampment, as soon as the newness
of his surroundings begins to wear away, he finds himself undergoing a
change of heart; he experiences a new feeling and appreciation of his
work and a sort of exhilaration of discovering the progress that he is
making in his daily tasks. For example, instead of going out to parade
in a dazed and mechanical manner, he marches forth filled with pride
that he is really a member of so _élite_ a Corps. He strives to do his
bit with all his might. He lends a close attention to all commands so
that no act of his will mar the appearance of his company, and does his
utmost to assume the correct position of a soldier that is incessantly
dinned into his ears by the ever alert file closers. He feels that he
is changing, but does not understand just how. In reality his point
of view is swinging around, it is clearing up, and the new cadet is
beginning to be animated with the spirit of West Point.
The scales seem to drop from his eyes. He is no longer concerned so
completely with his troubles and difficulties, with his inability
to get into his white trousers without mussing them badly, with his
capacity for doing "wooden" things, or with all of the thousand and one
little heartburns for things done and left undone.
On the contrary, the incidents of his surroundings that are unrelated
to himself begin to interest him. With quiet amusement he watches
the antics of the yearlings, envying them their careless nonchalant
air. His heart goes out in sympathy to some fellow plebe who has just
incurred the displeasure of an upper-classman. He secretly admires the
military bearing of the cadet officers, the fit of their blouses, their
erect and graceful carriage. To him they represent the ideal in the
flesh toward which he is striving. There is a certain something about
the manner in which they perform their duties that inspires the plebe
to extra efforts. In the hope of receiving a word of praise from the
cadet captain at inspection before parade, an extra rub is given to the
rifle or breastplate, and more care is taken in climbing into those
stiff white trousers. He listens with the greatest interest to the
chatter about the approaching Academic term and accepts with gratitude
the counsels sometimes offered him by the cadet captain.
As the camp draws to a close, not only the captain but all of the
upper-classmen give the plebe gratuitous advice about the coming
Academic year. At every formation while awaiting the sounding of the
assembly, little groups gather in the company streets and interrogate
the plebes as to their previous mental training. A note of restlessness
begins to pervade the camp as the month of September draws nigh. Once
again the books must be taken down from the shelves and hours of study
devoted to the solution of problems.
The plebe views the close of the camp with a sigh of relief mingled
with not a little anxiety. It is true that he is glad to get into
barracks where he will have a little more personal liberty, and be free
from the incessant drilling, drilling. On the other hand, the opening
of the Academic year fills him with some misgivings about his ability
to master the studies and fulfill his ambition to become an officer.
Before he is really aware of the flight of the days, September the
first has arrived. He leaves the life of camp where almost the entire
day has been devoted to military exercises of one sort or another and
plunges into the Academic work. A new sort of life begins and the
routine of the day is readjusted. With determination he sets out to
climb the stony path of knowledge that alone will lead him to his
commission. The branch of the service that he will eventually select is
as yet unknown to him, but as he proceeds in his career at the Academy
he will have a taste of the duties of each arm, and he will later on be
able to choose his branch with intelligence.
The beauty about the West Point system of training officers is that
it educates them for all branches of the Army, for the line and for
the staff. When a man graduates, he is assigned either to the Corps of
Engineers, the Ordnance, Artillery, Cavalry, or Infantry according to
his choice based on his class standing. The highest men usually select
the Corps of Engineers, although it is not unusual for a man who is
recommended for the Engineers by the Academic Board to choose some
branch of the mobile Army.
The curriculum to which our young cadet must devote nine months of the
year is highly scientific and technical. The corner-stone of the course
is mathematics, and the great mass of the structure is made up of the
exact sciences. Primarily, the curriculum is designed to give the
cadet a liberal education and to turn out a man with sharpened mental
processes. It does not lay the greatest emphasis upon the training of
cadets in the practical duties that pertain to any particular arm or
corps. The reasons for this are very sound.
It is the belief of all officers who have given the question of
military education any thoughtful study that the first requisite of
any army is a corps of officers trained in the essentials of their
profession. What really does this mean? It simply means that officers
of the Army should be well educated men, not only those who are to go
into the technical branches such as the Engineers and the Ordnance, but
the line officers as well. The authorities at West Point have therefore
developed a broad scientific course, fully convinced that the mental
discipline, powers of investigation, and accurate reasoning necessary
in solving problems in the exact sciences are the same mental qualities
that are needed whether in planning a great campaign, building a Panama
Canal, or fighting the savage Moro in the distant Philippines.
The advisability of giving all cadets, those destined for the line as
well as for the staff, the same education has been questioned more than
once. As long ago as 1843, a Board of Officers, of which General Scott
was president, made certain criticisms of the course of instruction. It
is interesting to quote the answer made by the Academic Board, for the
ideas set forth therein express in general the opinions held today:
The Academic Board believes that one of the most important objects
of the Academy is to subject each cadet, previous to his promotion
to a higher grade in the Army, to a thorough course of mental as
well as military discipline to teach him to reason readily and
accurately to apply right principles to cases of daily occurrence
in the life of a soldier. They are satisfied that a strict course
of mathematical and philosophical study, with applications to the
various branches of military science, is by far the best calculated
to bring about this end, and that the present scientific course at
the Academy, the result of the experience of many years, is in its
main feature such a course.
They are aware that many of the cadets, as is the case with most
of those who pursue a scientific course at other institutions,
will have little occasion to make practical applications of the
many mathematical problems that they meet, and that they may have
passed over certain problems without thoroughly understanding
their meaning in all their points. Still, if the course has been
thoroughly taught, the reasoning faculties will have been strongly
exercised and disciplined and a system of habit and thought
acquired which is invaluable in the pursuit of any profession,
and as desirable for the infantry or dragoon officer as for any
other officer in the service. The officer whose mind has thus been
disciplined and who is not forgetful of the duty he owes to the
government that has furnished him with opportunities so valuable,
will acquire facts and information in whatever station the
interests of the service may place him. This discipline and system
he will learn at an early age only, and nowhere so well as during
his term of service at the Academy.
In recent years, strong influences have been brought to bear on the
Academy to change the course so as to make it more practical. The
advocates of this change ignore the ends toward which West Point's
course works, heretofore successfully, and desire to see cadets
leave West Point with what they call a practical knowledge of the
different arms. This means that they wish the graduated cadet to join
his regiment well versed in the routine work of the Army, and would
have West Point take precious time from mental training to teach a
more complete knowledge of the mechanism of the drills. If West Point
followed this advice, the graduated cadet would have a difficult road
in solving the big problems that will arise in his career. If in the
West Point course emphasis were laid upon the practical work rather
than upon the intellectual training, then the cadet would simply be
storing up knowledge instead of learning how to think. When therefore
any situation would arise, the tendency would be to make a requisition
upon the storehouse for a solution. If there is no similar situation
tucked away on the shelves of memory, that will serve as a guide, he
will in many cases be at a loss how to proceed. Not so, however, if his
mind has been trained correctly. He will work out his own solution.
Many people believe that the whole science of the military profession
is embraced in a book of drill regulations whose practical
demonstration on the drill and parade grounds constitutes all that
is necessary to make a successful officer. They do not realize that
battles are won first with the brain and then with the sword. They
rather regard the work of officers much the same as manual labor that
anyone can do, and they do not admit that any great amount of mental
training for the officers is necessary.
I do not wish to give the impression that there is no practical
training at the Academy--far from it. But I am glad to say that it
has been allotted its proper place in the course. Once the theory is
mastered, the practical is quickly learned afterwards. Any cadet with
a trained mind can readily learn the practical duties that may be
demanded of him as an officer.
It is an astonishing fact that I have heard West Point methods
criticised in the Army because a young graduate upon joining his
regiment did not know how to make out a _morning report_! Why should
he? The fact that any boy of average intelligence can learn to make one
out in fifteen minutes should be a complete answer to all demands that
cadets should be taught these trivialities at the Academy.
The criticism leveled at West Point by officers of the Army is unjust.
Older officers expect too much of the graduated cadet. I have noticed
that they demand of these young men, immediately upon joining, the same
mature conception and efficient execution of certain duties as they
themselves are able to display only after years of experience.
Upon graduation from West Point, I dare say that there is no more
highminded, well-trained, and efficient body of young men in the
world. The graduates join their commands brimming over with youth,
intelligence, enthusiasm, and energy and ruled by intense loyalty. They
want to do what is right. They want to go forward in their profession.
They make every effort to perform well their duties. All that they need
are leaders among their superiors who will develop their aspirations.
Sometimes they encounter a distinct air of hostility, occasionally a
petty attitude on the part of some older officers whose one ambition is
to "put them in their place," and, too frequently, simply indifference.
The result is that the young officers quickly become a prey to the
red tape, the dull routine, the narrowness of post life, or to the
mental inertia of prolonged duty upon the border where almost every
stimulating influence is absent. If only there were enough good leaders
to take this wonderful material that the Academy sends forth annually
and develop it, there is no telling to what heights these young
officers would rise.
But to return to our plebe who makes his début in Academic work
September the first. The evening before has been spent in earnest
preparation for the lesson in mathematics, and he sets forth on this
early autumn day to grapple with the hardest study of his course.
First call for recitation is sounded at seven minutes before eight
o'clock. The trumpeter, an enlisted man of the Army, blows "school
call" first in the area of barracks, then outside of the north
sally-port, on the Plain side of the buildings. The call is repeated
several times, and as its notes float out on the air, the barracks
begin to disgorge the cadets, sometimes singly, but more often in
groups of twos and threes. The more prompt ones pile out on the cement
walk, standing near their places in the ranks to await the assembly.
The majority are laughing and talking or discussing the lesson, while
others, thirsting for knowledge until the last, keep their noses
in their books. Their comrades sometimes tease them, calling them
"tenth-boners" in good-natured derision, or steal up behind them and
shut their books for them saying, "Oh, come off spec-ing tenths," which
means to desist from studying at the last moments to better the mark.
At one minute before assembly the cadet officer of the day, a straight
young man in a red sash and red crossbelt (bound up, as Patsy O'Hara of
1904 wittily remarked, in his official red tape), takes his post in the
center of the area and commands: "Form your sections!"
Instantly books are slammed, all noises, talking, laughing, skylarking,
cease, and the scattered gray figures seem to magically form themselves
into compact little squads under the direction of their section
marchers who stand out in front counting them. The door of the
Guardhouse opens and the O. C. (officer in charge) appears upon the
"poop deck," stern, implacable, almost sphinx-like, and surveys coldly
the formation. For the brief space of a few seconds all is quiet except
for the occasional shuffling of a section that has misjudged its proper
space. Then the trumpeter sounds the assembly. A few belated men are
tearing to their places in ranks, running a race with the fading notes
of the trumpet and landing bang! into the rear rank just in time to
keep from being reported absent. The kind-hearted trumpeter often takes
a deeper breath (especially in winter when he sees the belated ones
recklessly dashing across the icy walks), and holds on to those last
notes of assembly in a way that was never intended by the composer. God
bless him!
Meanwhile the instructors are in the section rooms awaiting the arrival
of their classes. Here and there in the windows of the rooms facing the
area is an instructor gazing upon this class formation that is the same
today as it was years ago, and that awakens in him a flood of memories
of his own cadet days when he too set out to recite to an instructor
who never seemed quite human. As he looks at the cadets forming, he
realizes how distinctly the institution creates its types, and he is
able to pick out certain individuals and say to himself:
"There goes so and so of my class!"
The great charm of West Point is that so many things never change. Some
of the cadets, sons of graduates, are doing exactly as their fathers
did at their age, and again a few cadets are reacting the youth of
their grandfathers.
While the instructor is watching the cadets in the area, the section
marcher reports to the officer of the day all absentees in his section
which he then marches off to the Academic Building. On the sections
come in military formation straight to the classroom door. The halls of
the building resound to the tramping of many feet as the cadets march
along with muffled tread, thanks to O'Sullivan rubber heels that are
fitted to every pair of shoes. When opposite the classroom door the
section marcher commands:
"Section halt! Fall out!"
The cadets hang up their caps in the hall, file into the room, and
stand rigidly at attention behind their desks. The section marcher
enters, closes the door, takes his position in the center of the room
facing the instructor, salutes, and reports:
"Sir, all are present," or "Cadet Ducrot is absent."
Mr. Ducrot now makes his acquaintance with Mathematics, the study that
determines more than any other his standing at West Point. From the
day that he commences his studies he feels that he must devote the
greater amount of time to this subject, and with reason. A perusal of
the tables of instruction shows that the greater proportion of time
and weight is allotted to the mathematical studies. The total amount
of time provided for in the course of instruction, including riding
and gymnasium, is 192,900 minutes. If gymnasium and riding are deducted
(11,205 and 10,860 minutes, respectively) there are left 170,835
minutes devoted to Academic work. Of this amount the pure mathematical
subjects are allotted 76,555 minutes, and the non-mathematical
subjects, 94,280 minutes.
These figures represent the time that is actually spent in the
recitation work. To give an accurate idea of the draught of these
subjects upon the cadet's time, however, we should estimate the amount
of time required for preparation plus the time spent in the section
room. The lessons are so assigned that these preparations take the
average cadet twice the time allotted to the recitation. Thus, in
subjects having an hour and twenty-five minute recitations, the average
cadet is expected to spend two hours and fifty minutes in preparation;
and in subjects having one hour periods, two hours of preparation.
Practical Surveying and Drawing are subjects for which no preparation
is required.
Adding the preparation time to the recitation time we find the total
relative amounts of time as follows:
_Mathematical Subjects._ _Non-Mathematical Subjects._
76,555 94,280
136,940 145,440
-------- --------
213,495 239,720
The time devoted to mathematical subjects is divided among only five
departments, whereas the time divided among non-mathematical subjects
is divided among nine departments. Again, each subject is weighted
and the five mathematical subjects have almost as many units as the
nine non-mathematical subjects. Out of the 2325 units required for
graduation (leaving out of account the 200 allotted to conduct) the
five mathematical departments have 1065 and the nine other departments
have 1260. It is no wonder that Mr. Ducrot wishes to make an auspicious
beginning in a study that is so important to his future career. The
conduct of the recitation that he attends for the first time is about
the same in every department. In Mathematics, which is an exact
science, the system is perhaps a little more rigid than in some of the
non-mathematical departments.
As soon as the cadets have taken their seats the instructor asks:
"Are there any questions on the lesson?"
The cadets are then at liberty to ask for an explanation of any part of
the lesson that they have not been able to comprehend. The officer uses
his judgment as to the amount of time to be thus consumed. Sometimes
he will take up half the recitation period to clear up the obscurities
of the lesson, but if he has one of the lower sections he sometimes
has to be on his guard, for the cadets on the days of hard lessons
astutely ask many questions in order to consume the recitation period.
I know one officer who always outwitted these youthful diplomats when
they attempted to stave off the recitation. He would begin speaking so
rapidly that no one could interrupt:
"Any questions-pages-one-two-three-four-too-late-close-your-books. Mr.
Ducrot-take-the-first-front-board."
Each cadet is sent to the blackboard with an enunciation, that is,
some phase of the lesson to discuss, or perhaps the instructor may
question a few men. The cadet writes his name on the board in the upper
right-hand corner and proceeds to place upon the slate enough data to
assist him in his recitation. In Mathematics, he solves his problem; in
other subjects the topic that he will develop orally.
As soon as the cadet is ready to recite he takes a pointer in his hand
and faces the instructor and stands at attention until called upon. In
order to test thoroughly the cadet's reasoning powers the instructor
will sometimes lead him on along a false path, practically making the
recitation himself, saying:
"Is not that so?" and again, "Is that not so?"
To which the lad, if not thoroughly sure of himself, will be betrayed
into replying:
"Yes, sir!" "Yes, sir!"
Finally when the deduction has been rendered ridiculous, the officer
will sharply say:
"That is perfectly absurd." The cadet receives a lesson that he does
not forget. Once or twice as a cadet I was in this position and I know
the feeling.
After each cadet is heard, he is given other problems with which to
wrestle while the other cadets are reciting. When a principle of
particular importance is to be demonstrated, all of the cadets are
required to face about and give their close attention in order that
they may all benefit from the instruction.
During a recitation a visit may be expected at any time from the
Professor or Head of the Department. Upon his entrance, the cadets all
rise and stand at attention until they are told to proceed with their
work.
The Professor either listens to the cadets recite or conducts the
recitation himself. The recitation continues until the bugler blows
the "Recall" in the area. What a welcome sound is this to those few
who have spent the hour at the board, without reciting, vainly staring
at the blank slate in the hope of drawing some inspiration from its
cold surface! They have been "bugling," waiting for the bugle to sound
"Recall." They quickly drop chalk, eraser, pointer, and joyfully file
out of the room exchanging with their co-conspirators sympathetic
smiles, and surreptitiously "rubbing their bellies," as a sign of
excessive joy.
The instructor at West Point has one great advantage over his
fellow instructors in the colleges. His time is not occupied with
trifling on the part of the students. The cadets are so thoroughly
disciplined by the Tactical Department that their deportment in class
is irreproachable. It is very rare that the recitation is interrupted
to make corrections other than academic. The cadets are held to a high
standard of discipline all the time. In class they are not permitted to
communicate with one another, but they talk freely with the instructor
about points in the lesson.
So much for the actual recitation, the conduct of which seems so
smooth and simple. In the background, however, there is an admirable
organization that strives for a maximum of efficiency in the
instruction.
Every department consists of the Professor or Head of the Department,
an assistant professor, and the requisite number of instructors which
varies with the size of the classes. In the Departments of Mathematics
and Modern Languages, each of which instructs two classes, the
Professor is aided by an associate professor, besides the assistants.
The Professor is in complete control of his entire department. He
prepares the courses of instruction, recommends the adoption of new
text-books, or abolition of those in use, apportions the work among
his instructors, conducts and supervises the conferences of his
instructors, prepares and supervises the examination of the classes
pursuing his course, is responsible for all property belonging to his
department, and is the channel through which must pass all reports and
official communications relating to departmental affairs.
In nearly all of the departments the Professor is able to standardize
the instruction of the cadets by means of conferences with his
instructors. These meetings are informal, partaking more of the nature
of a _conversazione_ in which the Professor outlines his wishes to his
officers, emphasizing the points of the lesson that he wishes brought
out. The conferences also offer to the instructors the opportunity
to make suggestions to the Head of the Department in regard to the
section-room work, pointing out the success or failure of certain
features of the previous lesson.
The conferences are comparatively recent in the scheme of instruction
at the Academy, but they are of great value to the officers. The
result is that the instructor enters the section room with a feeling
of confidence and a knowledge that his methods are approved in advance
by his immediate chief. Moreover, the Professor is able to go from
one section room to another and find that the teaching of the lesson
is progressing uniformly. I have always considered the conference
feature the greatest aid in my work as an instructor, for besides the
profit derived from the Professor's talk, there is always a constant
interchange of ideas, of impressions, or perhaps a heated argument
between the officers, all of which stimulate the mind and the
imagination, and sharpen the wits. Furthermore, these meetings tend to
produce harmony by drawing the officers together in a common cause. The
introduction of conferences has markedly changed the former attitude
of the instructor toward his work, so that instead of merely hearing
the lesson and marking the cadet, as prevailed too frequently in years
gone by, the officer is inspired to impart a maximum of knowledge and
help to his student. I feel sure that the average of the teaching is
rising year by year, due in large measure to the intelligent conduct of
conferences by the various professors with their officer assistants.
In addition to their work in the preparation and teaching of the daily
lessons, instructors are required to keep the record of the cadets'
marks. For this purpose, pasteboard cards properly ruled for the days
of the week, averages, and proportional parts are provided, one for
each cadet. After the conclusion of the day's recitation the mark is
entered by the instructor on the cadet's card, and at the end of the
week, all of the marks are transferred to a weekly report that each
instructor submits for the cadets under his charge. These reports, or
"tenth sheets" as the cadets call them, are publicly posted in glass
frames in the sally-port, where they remain for one week, during
which time the cadets are at liberty to inspect them. In this manner,
a cadet can always tell exactly what progress he is making, whether
deficient or proficient. There is never any attempt at secrecy, but,
on the contrary, every facility is afforded the cadet to ascertain
his standing. The pasteboard cards form the permanent record and are
carefully filed in the department.
The weekly reports are usually posted every Saturday while the
battalions are at inspection. Immediately upon breaking ranks, what
a scramble ensues to get a peep at the result of the week's work!
Struggling cadets elbow and crowd one another to get close to the
frames, each heart beating in anticipation of the figures that mean
for some success and for others failure. The difference of perhaps one
tenth in the total will sometimes fill the lad with dejection for the
rest of the afternoon.
No one is deprived of the privilege of consulting his marks. Even those
cadets serving punishment, such as confinement to rooms, can obtain
permission to inspect the reports. More often, however, they send some
plebe to copy the marks for them. The publicity of the marking has an
excellent effect upon the cadet, for he knows what each man in his
section accomplished during the week and sees that no partiality is
shown nor injustice done by the instructor.
The scale of marking that is used at West Point was introduced when
Major Sylvanus Thayer was Superintendent in 1837. Upon this scale a
perfect recitation receives a mark of 3.0; good is represented by 2.5;
indifferent by 2.0; bad, 1.5; imperfect, 1.0; and complete failure
0.0. The instructor may mark as close as a tenth giving a 2.8 or a 2.1
or a 1.4 as the recitation merits.
Since the marks determine a cadet's graduation standing and affect his
whole career as an officer, they naturally are given by him no little
consideration. Sometimes I think that the cadets give entirely too much
thought to attaining a good grade rather than to the thorough mastering
of the subject; that is, they have a tendency to develop the memory
at the expense of the thinking functions. As I have explained before
West Point methods are strictly opposed to such a system, and the
departments discourage verbatim recitations. The marking offers many
difficulties at an institution such as West Point because a difference
of a few hundredths between two cadets' standing will alter their
choice of a branch or Corps and affect their relative promotion by
years. At colleges and universities this condition does not exist, for
a man's standing has little connection with his future career.
The cadet is not allowed to select his own course, or follow his own
inclinations in regard to the curriculum. The mental diet is prescribed
and no deviation therefrom is permitted. The three broad fundamentals
governing the Academic course are: first, that every cadet shall take
every subject; second, that before advancement every cadet shall be
proficient in every subject; and third, that every cadet must recite
every day.
As regards the above principles there is, of course a little
qualification in each, sufficient to admit of some flexibility in
application. While no cadet is permitted to elect whether or no he will
take a subject, but is required to take all of them, still, some of
the more advanced cadets go further in the subjects. In nearly every
department the higher men have advanced or special courses.
As for the second principle, a cadet who is deficient in any one
subject is usually dismissed. Occasionally, however, where a man stands
especially well in all of his studies but fails in one, he may be
conditioned by the Academic Board, or in some cases turned back to join
the next class. Among the cadets, he becomes known as a "turnback," a
name that usually sticks to him, but conveys no reproach or stigma.
Again, the cadet must recite every day. Owing to the small section of
ten or twelve cadets the instructor is ordinarily able to hear every
man, so that the studies must be prepared. There is no such thing
at West Point as a "cut." Sometimes, due to the lack of time, the
instructor may not hear a few of the cadets, but this is rare. In such
a case the cadet does not get a mark but is given what is colloquially
known as "stay-back," that is, a blank. The certainty that he must
recite every day and that no failure can be hidden obliges each cadet
to prepare his lesson with great thoroughness. The effect of this
system on moral character is immediate. It inculcates attention to
duty, habits of study and thought, and pride in achievement.
At West Point good intellectual performance is a duty just as much as
guard, parade, or inspection, so that an unsatisfactory recitation
due to the cadet's negligence not only begets a bad mark, but not
infrequently a punishment. Moreover, since the cadets realize that
their final standing at graduation permits them to choose their branch
of the service, they are keen to do their very best to beat the other
fellows. This spirit of competition is fostered by transfers of cadets
from one section to another either up or down, according to their
weekly marks.
Cadets receive individual instruction in every subject. No man can
therefore hide his lack of preparation because he is always called upon
to develop some phase of the lesson. At the beginning of the term, the
Fourth Classmen or plebes are arranged alphabetically into sections in
which they remain for about six weeks. Then there is a general transfer
or rearrangement of sections according to the marks made during this
period. The top man in each section is the section marcher. Thereafter
cadets rise and fall in the sections, either weekly or monthly as the
Professor wishes. The transfers from one section to another are a great
stimulant to the cadet. He gets the reward for his labor. Sometimes,
however, in spite of determined efforts, some cadets lose sections, due
perhaps to a lack of preparation prior to entrance; others go down
through laziness or negligence.
The cadets that land in the last section are known as "The Goats" (in
olden days, "The Immortals"), usually a carefree lot who never worry
until the examinations roll around. They are a great contrast to the
first section men who "bone tenths" with Prussian thrift. But whether
"Goats" or first section men each one receives individual instruction.
Nor are the cadets who are low in their studies deprived of extra
instruction. When Major-General Thomas H. Barry was Superintendent,
he introduced a system permitting cadets to receive, during their
recreation hours, extra instruction upon any back lesson. The cadets
can therefore overcome the obstacles that prevent them from going
forward in any particular study. Due to this system, many a cadet has
been saved who otherwise would have been "found," simply because he was
slow and had not had time to digest his lesson.
It is in the lower sections chiefly that humorous incidents occur to
lighten the tension of the atmosphere. As an instructor in French, I
had many a chuckle over the struggles of some of the Goats to master
the tongue of _la douce France_. On one occasion a cadet was attempting
to translate a passage in the reader. His efforts were futile. Few of
the words meant anything to him. All at once he came to the proper name
"Léopold, Duc d'Autriche." With a triumphant gleam at me who had been
humiliating him with embarrassing questions, he proudly translated the
phrase: "The leopard, the duck, and the ostrich."
On another occasion there was in the section a foreign cadet from
Venezuela whose acquaintance with English was chiefly limited to swear
words. While translating a passage in French in the presence of the
Professor, he came across the sentence: _Mon Dieu, j'ai laissé tomber
le vase._ Immediately he began:
"My God----"
"Oh no, Mr. Honduras," gently interposed the Professor.
"Oh Hell," he began once more.
"Dear no, Mr. Honduras, not so strong!" exclaimed the thoroughly
shocked Professor. But Honduras understanding (maliciously I thought)
that a stronger translation was wanted, ventured once more:
"----! ----! ----!"
Had Honduras been a little American boy, I am sure that the Professor
would have made him wash out his mouth with soap.
The success of the West Point system is largely due to several unique
reasons. In the first place the authorities control the time of the
cadets so completely that it can be utilized to the greatest advantage.
Again, West Point's remoteness from any large city and the strict
regulations that govern the privileges of the cadet remove the many
temptations that consume the college man's time. To the same extent,
the mind of the cadet is not diverted. Every effort is made to get the
maximum mental results from the cadet's labor. He has regular hours of
study, plenty of exercise, a judicious amount of recreation, and good
wholesome food. In addition, the cadet is in a studious atmosphere. No
opportunity is lost to impress upon him correct habits of study.
I dare say that at no other institution of learning is there such
serious preparation of the lessons. The cadet's academic day contains
but half an hour of leisure from 6:00 A.M. to 10:00 A.M. except during
the extreme cold weather when drills are suspended the cadets have
two hours in the afternoon. All during the day therefore when not at
recitations, riding, or gymnasium, the cadets are studying, and the
long study period is from 7:00 to 9:30 P.M. Although prohibited by
Regulations, many men study after taps, especially those low in the
class. To conceal the light they hang a leg of their trousers over the
electric light, lowering the cord until it almost touches the table.
Just a little circle of light shines upon the book, and not enough to
be detected from without.
West Point is not indifferent to the performance of its students. It
cannot afford to be less exacting, but it has a powerful leverage over
other institutions for it dangles before the cadet's view the prize of
a commission in the Regular Army, a career in an honorable profession.
The course of instruction at the Military Academy develops in the
cadet certain traits of character that are invaluable to him in a
profession where, as an officer, he is constantly being called upon
to meet all sorts of contingencies, to exercise his judgment, and to
make decisions. His studies and duties broaden his mind, make him
self-reliant, and teach him self-control. It is astounding to see
the results obtained by the system. As a proof of the intellectual
product of the Academy, I shall quote the following table, giving the
occupations of the graduates who have gone into civil life where they
have measured their strength with the graduates of other institutions
of learning:
President of the United States 1
President of the Confederate States 1
Presidential candidates 3
Vice-Presidential candidates 2
Members of the Cabinet 4
Ambassador 1
Ministers from the United States to foreign courts 14
Chargés d'affaires to foreign courts 2
United States consuls-general and consuls 12
Members of the U. S. Senate and House of Representatives 24
United States civil officers of various kinds 171
Presidential electors 8
Governors of States and Territories 16
Bishop 1
Lieutenant-governors of States 2
Judges 14
Members of State Legislatures 77
Presiding officers of State Senates and Houses of Representatives 8
Members of conventions to form state constitutions 13
State officers of various grades 81
Adjutants, inspectors, and quartermasters-general of States and
Territories 29
Officers of State militia 158
Mayors of cities 17
City officers 57
Presidents of universities and colleges 46
Principals of schools and academies 32
Regents and chancellors of educational institutions 14
Professors and teachers 136
Superintendent of Coast Survey 1
Surveyors-general of States and Territories 11
Chief engineers of States 14
Presidents of railroads and other corporations 87
Chief engineers of railroads and other public works 63
Superintendents of railroads and other public works 62
Treasurers of railroads and other corporations 24
Civil engineers 228
Electrical engineers 5
Attorneys and counsellors at Law 200
Superior general of clerical order 1
Clergymen 20
Physicians 14
Merchants 122
Manufacturers 77
Artists 3
Architects 7
Farmers and planters 230
Bankers 18
Bank presidents 8
Bank officers 23
Editors 30
Authors 179
-----
Total 2371
The above list should be convincing that if methods of training which
are primarily intended to develop officers can produce such signal and
distinguished successes in every walk of civil life, no fault can be
found with their soundness.
The Academic year is divided into two terms that end in the fall
and the spring. A month prior to the conclusion of each term, each
Department conducts a general review of the subjects studied that
semester. Cadets who make a proficient average upon this review, which
is generally written, are exempt from the examinations. These reviews
are very thorough and searching. The questions are framed to test the
cadet's real knowledge of the subject. In order to avoid all personal
element entering into the marks, the papers are graded by all of the
instructors, each marking one question. In this manner the marks are
uniform and fair as possible, and no one instructor has any great
influence in assigning to a man his class standing.
Following the reviews come the examinations for those who failed
upon the review. These tests are also quite rigid, and in order to
be declared proficient a man must make two thirds of the mark, .66
per cent. The examination papers are likewise marked by all of the
instructors and by the Professor. In the event that a cadet fails he
is reported to the Academic Board for their action. In general, if
deficient in any one subject, the cadet is dismissed.
I feel how weak are any words that I might use to attempt to describe
the despair into which a discharged cadet is plunged. For days he lives
in an excruciating suspense awaiting the result of the examinations.
The thought of wasted opportunity, the regret for lack of early
preparation perhaps, and worse than all, the sense of failure torment
him. It is bitter to renounce the camaraderie and friendship of his
fellows and to see himself involuntarily separated from surroundings
that he has come to love. At last the dread news comes. The Adjutant
rises from his seat in the Mess Hall and calls the Battalion to
attention. Immediately a deathlike stillness pervades the cadet body.
The gravity and dignity of the Adjutant's demeanor unconsciously
inform the Corps that distressing news is about to be communicated.
Slowly and distinctly the names are read out, one by one, and as they
fall upon the straining ears of the cadets, they sound like so many
death sentences for the unfortunate lads who are "found." A gloom of
sorrow settles over the Corps and the companies file out of the hall
in sympathetic silence. But the reality must be faced. Suitcases and
trunks are packed, accounts are quickly settled, affectionate and
emotional good-byes are said, and sadly the discharged cadets drop out
of the ranks of the Corps. The long gray line closes up and once again
marches forward to do battle with the Academic obstacles that block the
road to graduation.
CHAPTER VIII
GROWING MUSCLES
Whenever the cadets leave the seclusion of West Point and appear in
public in uniform, their erect carriage, their smart tight-fitting
dress coats that show off their broad muscular shoulders and slender
waists never fail to excite favorable comment and praise. It most
generally finds expression from a group of giggling maidens who evince
a great curiosity about the cadets' slender waists, either openly
remarking that they are artificial or more specifically assuring
themselves, when advantage can be taken of a cadet, by poking the gray
bound torso around the middle line, timidly asking him if he wears
corsets, a remark that usually serves as an introduction to a harmless
flirtation.
The splendid set-up of the cadets is not, however, due to stays,
whalebones in the dress coats, Dr. Quack's abdominal bandages, or to
any other mechanical appliances. It is the result of a very highly
intelligent system of physical training, to which the supple young body
of the cadet is submitted for four years. Naturally, little by little
his muscles, through exercise, attain their proper development, and
since no one set of muscles is neglected, the body gradually assumes
a well-rounded, finished appearance. The material for instruction is
good and healthy, because all of the cadets have been submitted to a
rigid physical examination before entrance. They are not, however,
all perfect specimens, for many possess minor defects and blemishes,
unimportant as far as affecting their military value to the Government,
but which can be eradicated by proper physical training.
The instructor of physical training is greatly aided in his actual
work, by the kind of life the cadet leads, so that he has not to
struggle with a crowd of men who after having received physical
training daily, indulge themselves to their heart's content. He has,
on the contrary, a set of young men who live under the strictest and
simplest conditions in a healthy environment, and whose diet is most
wholesome. No late suppers, no beer, no rich food are at work to keep
up the rotundity of the stomach, the _coram nobis_ of the Romans, or
to produce a lot of flabby fat, but good cereals, nourishing meats and
vegetables, even the despised "slum," are indirect factors in keeping
healthy the cadet's body.
West Point believes that for a man to do the best mental work,
his body must be in the best condition. The Academy was the first
educational institution in the country to recognize that hand in hand
with the student's mental training must go the proper development
of his physical powers. As long ago as 1817, Captain Partridge, the
Superintendent of the Military Academy, incorporated in the curriculum
bodily exercises. Since that time the importance of physical training
in the cadet's course has been given recognition, but frankly there
was no real system of physical training until 1846. A gymnasium was
then prepared and instruction given by First Lieut. H. C. Wayne, First
Artillery. This was a beginning, but the authorities were hampered
by lack of equipment, and also by no very great knowledge of how to
proceed. The science of physical training was in its infancy, it must
be remembered, but crude as was the instruction it was the genesis of
the splendid course that now exists.
For a long period after the Civil War, 1865-1882, cadets attended the
gymnasium as they saw fit, a system that was no system. The original
course from which the present course has developed was inaugurated in
February, 1885.
The daily routine at the Academy is extremely exacting and hard, and
I doubt very much if a large number of men could stand the strain and
daily grind of the Academic year, if they were not physically prepared
to meet its requirements. Since all Academic duties are suspended
during part of June, July, and August, in order to devote these
months to practical military instruction, the new cadets are directed
to report in June. Two months are then at the disposal of the
authorities to strengthen the new arrivals' bodies, both by prescribed
physical exercises and by the exercise incident to the drills and
maneuvers, before the studies begin in September.
[Illustration: The Exterior of the Gymnasium]
During the first three weeks of the new cadet's training, setting-up
exercises begin his day's work. After his breakfast has had time
to digest, he and his fellows are marched over to the main room of
the gymnasium for forty-five minutes' physical drill. Although the
setting-up exercises may be given outdoors, and have always been
heretofore, the gymnasium is now used to eliminate the distraction of
the cadet's attention by passersby whose amusement at the efforts of
the stiff and awkward "beasts" reacted upon the new cadets.
The recruit instruction begins with the most simple exercises. The
cadet is taught first the position of attention; that his heels must
be together, his feet turned out just so much, his knees devoid of
stiffness, in a word, what he shall do with his hips, arms, and hands,
keeping his head erect, his chin drawn in, and his eyes straight to the
front. Simple as is the position of attention, many men take a long
time to learn it. Some never can comply with all the requirements, for
how can the bow-legged man and the knock-kneed chap keep their legs
"straight without stiffness"?
Then follow breathing exercises to increase the wind capacity, to
permit longer and more extended drills, and to lead up to the simple
movements designed to develop the muscles upon which the position of
attention is dependent.
The cadets line up on the gymnasium floor. The instructor commands:
"Count off!"
"One--two--three--four!" "One--two--three--four!" in weak voices and
strong voices, diminuendo and crescendo, is repeated all down the line,
each man snapping his head to the front as he calls his number. The
inequality of tone of voice is gradually eliminated so that after a few
drills the count off is uniform in pitch.
"Take distance. March!" commands the drill master followed by "Company,
halt!" when the men have become sufficiently separated to perform the
exercises without interfering with one another.
Various exercises are then taught, the simple ones first, followed by
the more complex movements to develop a coördination of all muscles
and a feeling of control over one's body. The set of exercises used
at the Academy are simple in the extreme and executed by even simpler
commands. It is astonishing how in a few minutes a perfectly green
squad can be taught to execute movements not only in unison, but even
with precision and smartness. The great value of the commands lies in
the fact that no elaborate explanations are necessary. All the recruit
has to do is to watch the instructor. Let me illustrate by an example.
The instructor commands:
"1. Arms forward. 2. Raise."
The cadet raises his arm in front of him to height of shoulders,
holding them in this position while the instructor says:
"Swing arms down at 1 and up at 2. Ready! exercise! One! Two! ... One!
Halt!"
All movements cease with arms in raised position.
"Arms down." All drop their arms smartly.
Of course, to the simple movements are added various combinations,
and all exercises are executed both at a halt and while marching. The
walking with measured step gives poise and grace of carriage. The
recruits are also practiced in the run and double time, the latter a
military step to gain ground rapidly, but with a minimum inroad upon
the wind and endurance of the soldier. Setting-up exercises are the
most valuable preliminary training for any body of men entering the
military service. For the first week the body is sore and aches to the
point of great fatigue, but after the preliminary soreness disappears,
a feeling of control supplants it, and the general health of the body
is better. No brown pills are necessary; no headaches from biliousness
exist. A good forty-five minute setting-up drill every morning, plenty
of wholesome food, and eight hours' sleep contribute to the cadet's
good health. The Mess Hall, not to be outdone by other departments,
lends its aid by serving judicious plates of prunes. These preliminary
setting-up drills, given during the first few weeks, are discontinued
for a short period in camp when the cadets are busy learning other
drills.
Swimming now replaces the setting-up exercises until the battalions
return to barracks in September. The new cadets must be able to swim at
least ten minutes without changing their stroke, which standard each
cadet must measure before he is excused from attendance at the swimming
drills. These drills are never a bore, however, but anticipated with
great pleasure by nearly all of the men. Nothing is so refreshing on a
hot summer's day, after a tedious drill upon the dusty Plain, than the
march over to the "Gym" for a swim in the deliciously cool clean water
of the tank. Instruction is also given in resuscitating men who are
apparently drowned.
When September comes and the studies are commenced, the Fourth Class
resumes its setting-up exercises, to which are added gymnastic work.
In the fall each cadet is given a thorough examination at which all
of his measurements are accurately taken, and various strength tests
are made. This information is entered on a card and filed for future
reference, because later on the cadets are again measured and tested in
order that the improvement may be noted.
Measurements are made of the height, chest, waist, arms, legs; and
strength tests are made of the arms, hands, back, and legs. These
methods quickly reveal wherein the cadet is deficient, and allow
the instructor, like a doctor, to prescribe for each individual
the necessary exercises. For example, those whose chests are
under-developed are assigned to the chest weights until the deficiency
is made up, and where the smaller muscles of the arms and shoulders
need attention practice is given with the Indian clubs and medicine
balls.
[Illustration: Gymnastic Exercises]
To develop in all of them power, vigor, and endurance, the groups of
large muscles of the back, chest, abdomen, and legs are improved by
setting-up exercises, dumb-bells, and wands, jumping, climbing, and
lastly by apparatus work. This class of exercises is reserved until
the muscles have been more or less controlled and respond to the will,
for the execution depends not so much upon muscular effort as it does
upon agility. It would never do to start in green men on the apparatus
work, because there would soon result broken legs and arms. This work
is hard enough for those lacking "muscle sense," even after many months
of preliminary exercises.
Included in the schedule for the first year's work is instruction
in the saber and the foils, but as the amount of time that can be
devoted to these branches of instruction is limited, only the most
elementary features of the arts can be taught. An opportunity, however,
is afforded cadets to perfect themselves in the use of both the saber
and the foil after regular hours. During the winter months, when
the vigorous weather requires a suspension of outdoor drilling, the
fencing master gives individual lessons to those who desire to take
them. The volunteers are formed into a squad known as the Fencing
Squad, from which are organized, for each weapon, class teams. The
interests at West Point are so many and varied that it is impossible
for each cadet to be an accomplished fencer, boxer, wrestler, gymnast,
or swimmer, but each one is given instruction in the fundamentals. The
cadets usually select the art that appeals to them most and perfect
themselves along the chosen line. The saber is popular, and many
cadets acquire great dexterity in its manipulation. It is distinctly
a soldierly exercise, so that it exercises a fascination for the men,
especially for those who intend to choose the cavalry.
Instruction in the use of the foils is given to the entire class
assembled by sections, and consists of preliminary instruction in the
single rank without weapon, in the single rank with foils, and in the
double rank with foils. As with the saber, the men whose sport by
predilection is fencing with foils take individual lessons from the
fencing master every afternoon from November until March. The interest
in fencing at one time was exceedingly great, and the sport was
regarded as one of the major activities of cadet life. This interest
was due to the participation of cadet teams in the Intercollegiate
Fencing Meet, but five years ago the Academy authorities prohibited
cadet teams from attending these competitions. This action killed the
interest in fencing for several years, but at present the former
popularity of this excellent sport is returning, and a visitor may now
see the thirteen double mats, accommodating fifty-two men, constantly
filled.
When President Roosevelt, in 1905, ordered that all cadets should
attend gymnasium daily, assistants were detailed to assist the officer
in charge of physical training. For the fencing, the Academy secured
the services of a _maître d'armes_ under whose careful and scientific
training, the fencing teams of the Academy continued their brilliant
achievements begun in 1902. Beginning with that year until 1910, West
Point sent to the annual intercollegiate championship meets, teams
that contested with Harvard, Yale, Cornell, Pennsylvania, Columbia,
and the Navy. Out of the nine meets, West Point won six, and obtained
second place in the other three, yielding their supremacy to their
great rivals, the Navy. This remarkable record was accomplished by the
untiring efforts of the team and of their much-liked instructor, M.
Vauthier, whose skill excited their admiration and inspired in them a
splendid spirit of emulation.
More attention is now paid to the bayonet fencing due to the extended
use of that weapon in the present European War, but as with the other
arts, the limited time permits the teaching of only the fundamentals.
The cadet learns enough in each branch to build upon afterwards and
make himself a competent instructor.
Not less popular than the fencing are the boxing and wrestling
exercises. The first year men are assembled in classes and given
instruction in boxing in the guard, footwork, parries, simple direct
leads and counters. Similarly in wrestling, the simple holds, resultant
falls, and the breaks for the simple holds are all taught.
It is not, however, to the regular class work that one must go to
judge of the grip that these manly sports have upon the cadets. In the
afternoon, after recitations, embryo Jeffries and Fitzsimmonses gather
in the boxing room to receive the holy instruction from the master, Mr.
Jenkins, or "Tom," as he is affectionately called among themselves.
There he teaches the aspirant pugilist how to land a blow and how to
avoid one, and occasionally to make the lesson more realistic he treats
his young charge to the experience of receiving one. Some experiences
in a man's life grow dim, but never this one.
When the preliminary bouts are being fought, large numbers flock to the
boxing room to cheer for the weaker fellow even though he be of another
class than one's own. Boxing develops fine qualities among the men. It
teaches them to give and take, to receive punishment without flinching,
and to respect the skill of a good opponent. Besides it gives a man
confidence in his powers, making him think quickly and move quickly,
all excellent qualities for an officer of the army.
Boxing, however, shares the popular appeal with wrestling. This manly
sport that we have inherited from our ancestors of the stone age
fascinates men chiefly by virtue of its brute strength and to a lesser
degree by its skill. It is a game for men of all sizes, provided they
possess the necessary qualities of courage and strength.
The boxing room on winter afternoons presents a warm and pleasing
contrast to the cold and snow outside. The mats are covered with agile
forms in black jersey tights wriggling and squirming, the perspiration
rolling off the wrestlers as they endeavor to grind the shoulders of
their opponents to the mat. All men receive instruction in wrestling
in class, but like the other sports, its devotees must repair for
extra instruction to Mr. Jenkins during recreation hours. It is in
this time that men practice for their class teams, one for each of
the following weights: unlimited, heavy, light heavy, middle, welter,
light, and feather. The four class teams meet each other successively
to wrestle for the class championship. There is besides a contest for
the individual championship, the final bouts which take place publicly
at the Annual Indoor Meet.
Prior to the resumption of the afternoon military drills in March, the
cadets hold their annual gymnastic event called the Indoor Meet. The
contests, which are held with great ceremony in the Gymnasium, include
races, pole climbing, work on horizontal bars and parallel bars, long
and short horse, rings both stationary and flying, and the tug of war
between the classes.
Each class enters so many men for each event, and for the awards of
first, second, or third, the contestant receives a designated number
of points. The class receiving the greatest total wins the meet. This
athletic event is a very fitting way to end the winter course, for it
offers an opportunity to those men who have labored faithfully during
the winter afternoons to reap the reward of their efforts. It also is
an incentive for better work because of the spirit of competition. The
Athletic Association upon this occasion, presents sabers, both to the
captain of the football team and to that member of the First Class who
during his cadet career has done the most for athletics. It is a very
proud night for these young men as they walk forward to receive the
coveted saber, the first part of their officer's equipment.
There is great rivalry among the classes during the events. The four
corners of the room are filled with the members of each class, who
yell like demons to encourage their representatives. Almost every
minute the air is filled with shrieks and yells of excited cadets whose
"Zis-boom-ahs!" "Rah! Rah! Rahs!" "1917! 1918!!..." are hurled at one
another to the delight and amusement of the spectators, young and old,
hanging over the iron railing of the gallery.
The courses in gymnastics, wrestling, and boxing, increase in
difficulty according to the class, so that the Third and Second
Classmen pursue a more advanced course than the plebes. When, however,
the cadets become First Classmen, emphasis is laid upon the theories of
physical training with the object of preparing these "near officers"
for their duties as instructors in the service. The needs of the Army
are carefully considered in the training of the last year in order to
send out from West Point men who can at once take hold of a group of
recruits and whip them into good physical shape, according to the most
intelligent methods.
Unfortunately, the setting-up exercises in the Army are only
spasmodically taught. There is very little uniformity in the method,
despite the excellent manual with which the troops are provided.
West Point is at present making an effort to influence the Service to
a better appreciation of the results to be derived from regular drill
in setting-up exercises. To this end, the First Classmen are taught to
act as instructors, and are grounded not only in actual practice but in
theory. Every year extra classes are held to develop good instructors
for the coming summer camps, and for future service in the Army. It
is to be hoped that commanding officers will make good use of these
enthusiastic young teachers.
Although the control of athletics at the Academy is not under the
gymnasium authorities, still it is fitting to speak of the sports in
this chapter. The Academy has its football, baseball, basketball,
and hockey teams, and in addition the cadets play golf, polo, and
tennis. There is little in the training or conduct of these teams that
differs from other educational institutions, except the question of
time allowed for preparation. It has always been the rule at West Point
that no inroads shall be permitted upon the Academic course to aid the
development of any athletic team. Consequently, what practice the teams
get must be during recreation hours. The only concessions made are
supper a half-hour later for the football men, and exemptions twice a
week from parade for the baseball men. Athletics receive, however, the
greatest support and encouragement from the authorities, whose aim is,
however, not to develop a few good men or an excellent team in any one
sport, but to seek a good average.
Every cadet is urged to join in some form of athletics instead of
remaining in his dress coat along the side lines as an interested
spectator. The efforts made in this direction have received a warm
response from the cadet body, so that during recreation hours the Plain
presents a busy scene of cadet activities. The green parade ground is
dotted with the golfers in gray shirts and white trousers; the tennis
courts are filled with animated figures; groups of happy cadets ride by
on horseback for a gallop in the woods, while others prefer the more
sedate hiking in the surrounding hills. It is a great temptation after
the recitations and drills to be lazy, hang around one's room, or
"bone fiction" which means reading novels, but in recent years the men
have become more and more sensible of the many advantages offered them
during their cadet days, and a new spirit of _carpe diem_ has come over
the Corps.
[Illustration: The Athletic Field
_Photo by White_]
But to return to my subject of physical training proper. No opportunity
is lost to impress upon each man the practical use to which he will
put his knowledge of physical training when he becomes an officer. He
is urged to prepare himself to the best of his ability to become a
proficient instructor for the enlisted men whom he will later command.
In this connection, the cadets learn in their course of Military
Hygiene that the object of all physical training is to develop the
human body in its entirety in order that there shall result a perfect
equilibrium between all its functions. Many recruits join the Army
without the slightest coördination of their body. Although well
formed they are awkward, clumsy, stoop shouldered, without ability
to make their different members act in unison with their minds. If
an officer does not know what to do with these men he will never
succeed in getting good work out of them. His first duty therefore is
to develop the recruit's body, especially the functions of control,
the coördination between eye and hand, because the success of line
troops is largely dependent upon physical aptitude. The modern war
makes greater demands than ever upon the soldier's physique. I heard
an observer, recently returned from the European War, state that the
infantryman is now so loaded down with packs, steel helmets, hand
grenades, and rifle that he finds it difficult to advance faster than a
walk. The strain upon the physique of the infantryman carrying his pack
is greater than upon soldiers of other arms, and since graduates in
time of war will be concerned largely with the training of infantry, it
is of paramount importance that cadets should understand the building
up and care of the bodies of their men. A soldier must possess more
than the average muscular strength, endurance, and organic vigor.
I see before me daily the fine results of the system of physical
training at the Academy. Ungainly plebes gradually assume a
well-rounded appearance, an erect carriage with head up and an elastic
walk. I sometimes have to rub my eyes when I behold a cadet whom I once
remembered as an unformed plebe, as loose jointed as a big Newfoundland
puppy, but who now appears before my astonished vision as a smart
soldierly First Classman. When the cadets have completed their four
years course they have a decided physical stamp, showing that each one
has been trained by the same system.
At the end of the year in June, when the Post is thronged with
visitors, relatives, and friends of cadets who are present for the
graduation exercises, an outdoor demonstration of the setting-up
exercises is given on the Plain. The precision and uniformity with
which the movements are executed arouse great interest as eight hundred
supple young bodies respond as one to the sonorous commands of the
instructor perched on a solid wooden table.
[Illustration: Setting up Drill on the Plain]
This drill is usually followed by the Outdoor Meet, the annual athletic
event corresponding to the Indoor Meet. Each class has its best
representatives entered to win a victory in the dashes, hurdle races,
long distance races, hammer throwing, jumping, and pole vaulting. Back
of the roped lines surge the cadets of the various classes, cheering
themselves hoarse for their own representatives. Mothers, sisters,
sweethearts, friends, friends' friends, in the fluffiest and gayest
summer dresses devouringly trail their "Kaydet," and give excited
and exaggerated opinions about things of which they are totally
ignorant,--but bless their hearts! their presence is an inspiration to
the young gods at their Olympian games.
On the June morning of the Outdoor Meet, West Point usually offers one
of her incomparably beautiful days as a fitting setting for the display
of her cadets' physical prowess. And when the Meet ends, the cadets
all feel that one more year's progress been made in their physical
development. The First Classmen who on the morrow will go forth into
the Army, leaving the protecting walls of West Point, reflect with
emotion and gratitude upon all that West Point's training has done to
strengthen their bodies to endure whatever hardships that might arise
in their new lives as officers.
CHAPTER IX
LESSONS FROM MARS
In the Area of the South Barracks, directly opposite the sally-port,
is a little brick building with a clock tower. It is small and
insignificant looking to the ordinary observer, but not so to the
cadet. Here dwell the "Tacs," the officers of the Tactical Department,
who are charged with the discipline and purely military instruction of
the Corps. More especially, it is the Headquarters of the Commandant,
his assistants, the cadet Officer of the Day, the officers of the
guard, and the orderlies. The mail, the precious mail, is assorted
twice daily within its old walls, and its creaky wooden floor is worn
thin by the lively tread of hurrying cadets feverishly crowding around
the bulletin boards.
In the second-floor room of the Tower is the Officer in Charge, the
monarch of all he surveys. True, his reign is but twenty-four hours,
but he returns to the throne about once a week. During his tour he is
the Corps monitor. From the quaint little porch off his room, the "poop
deck," as the cadets think of it, he coldly and inscrutably regards
all formations in the Area. When the punishment squad is walking tours,
the door of the "poop deck" opens unobtrusively, and for a moment he
stands casting a glance over the oscillating gray figures, walking
their narrow paths back and forth. As quietly as he comes forth he
fades from view. The "Area Birds" breathe more freely as he disappears,
but soon again he reappears like an accusing conscience. His presence
hovers over the daily life of the cadets. To them he is the "O. C."
and source of all information. His decisions have the sacredness and
authority of the Delphian oracle. If the weather is threatening,
it is he who decides whether raincoats shall be worn to meals. If
visitors arrive during study hours, his permission must be obtained
to speak with them for half an hour. If knotty problems of interior
administration bother the Officer of the Day, his advice is immediately
sought. He is amazingly omniscient.
Each day brings a new "O. C." until the roster of the Tactical officers
has been exhausted, whereupon the cycle begins anew. There are various
species of "O. C.'s," and it is astonishing how the personality of each
one will influence the day of the cadet. There is the cheerful "O.
C." with a kind manner and a cordial tone in his voice. Between him
and his young charges there seems to be a bond of mutual confidence
and affection. They feel that his reserve is assumed "By order," and
that if they only knew him, he would be their friend. They feel his
human side, his understanding of their difficulties, and they have no
resentment when he reports them because they know that in doing so, he
feels a sympathetic pang. When he enters the Mess Hall, his presence is
welcomed, as much as cadets can welcome the presence of any officer.
Somehow the laughter seems gayer and the day altogether brighter during
his tour. There is no unconscious load to carry in addition to the
actual burdens of the day. At parade, a little more effort is made to
execute smartly the manual when he gives the commands.
Then there is the gloomy "O. C.," the stand-off kind that looks daggers
upon the approach of any cadet. He appears to circle over the Corps
like some hungry bird ready to pounce any moment upon his prey. When he
has occasion to question a cadet, a barrier of ice immediately rises
between them and their viewpoints drift miles and miles apart. He seems
to them never to have been a young man himself, so little of the power
of understanding does he possess. They look him up in the Army Register
and discover that he too was a cadet not so many years ago, but to
believe it strains their credulity to the breaking point. When things
go wrong, instead of pointing out the error in a natural manner, there
are anger and resentment in the voice. All of his "skins" seem flavored
with malice. Apparently, he goes out of his way to be disagreeable,
as if to be so was to be military. His tour is regarded with dread
especially by the First Classmen detailed that day for guard.
But the influence of either type of Officer in Charge is transient. It
passeth from day to day. If the Gloomy One is on duty, there is the
consolation that the Cheerful One will succeed him like sunshine after
rain. It is the Commandant of Cadets, the chief of all the "Tacs," who
exercises the great permanent influence over the Corps. Ever since the
creation of his office in 1825, he has been "the Com" to the embryo
officers under him. He prescribes all of their drills and casts the
mold for the discipline of their bodies and souls. He is the tribunal
that grants or withholds their privileges and that punishes them for
their premeditated or thoughtless misdeeds. Whereas a few years ago he
exercised his power for the seclusion of his office, at a distance from
the cadets, today he meets and talks with them daily, ascertains their
viewpoint, giving to his work the new spirit of the personal touch that
has crept into the instruction at West Point. To be successful in his
important work, he must never look bored. He must take an interest in
the cadets rather than in the Regulations. He must be human. To gain
the admiration of his men he must be above all efficient, fairly good
to look upon, military in appearance, and well dressed, and to gain
their liking and respect he must be smart, strict, and impartial. There
are two faults in an officer that a cadet finds hard to forgive: lack
of neatness and "being wooden."
In his work, the Commandant is assisted by the "Tacs," Infantry,
Cavalry, Field, and Coast Artillery officers. Officers of every branch
of the Service are represented because at West Point, the duties of all
arms are taught. It is with these officers more than any others that
the cadet comes into the most direct contact.
For purposes of administration, each company is commanded by a Tactical
officer. He passes upon all permits, requests, requisitions for
clothing and for ordnance. He inspects the rooms of his command to see
that they are clean and in order. He examines the rifles and equipment
for dirt and rust. He supervises one or more of the drills. He is
really the presiding genius over the company, in whose welfare he takes
unselfish interest. It is the duty of him and his brother "Tacs" to
uphold the discipline of the Corps, which means that when a man has to
deal with eight hundred young wills, American nurtured, he must utilize
something stronger than mere words to see that the eight hundred
conform to the set standards of the institution. His chief weapon to
emphasize to the cadet the importance of the Regulations is the report
or "skin," which carries with it a certain number of demerits, and
sometimes punishment tours.
The cadet consequently looks upon the "Tac" as his arch enemy. One
cannot help having a little resentment toward a person who is always
present to check up his misdoings, no matter how just and well deserved
the punishment may be. The feeling is only human and the military
atmosphere rather augments it. It is especially difficult, I think, for
Americans to feel continually the heavy hand of authority, because each
one of us is so individualistic. Unconsciously, the cadet cannot get
away from the presence of the "Tac." Life in barracks seems to revolve
around this individual. From the early morning inspection, until the
evening study period when he again comes around, knocking sharply on
each door and interrupting the train of thought, his spectre, if not
himself, is haunting the surroundings. The cadets know that he is just
across the way in the Guard House, and that they will meet him at drill
in the afternoon. He is the important factor that must be considered in
their daily comings and goings. He is a sort of irritating yoke.
It is not to be wondered at then, that he is the subject of unlimited
discussion, despite regulations to the contrary, and that every
peculiarity of manner, dress, or speech is noticed and criticized. His
entire personality is usually summed up in some nickname that comes
like an inspiration and hits the nail upon the head. Occasionally
the name is complimentary, in unconscious recognition of an innate
nobility which marks him out as of finer clay, but more often it is
uncomplimentary and droll.
Nothing pleases a cadet quite so much as to see a "Tac" do something
wooden. They say that he is gross, which has nothing whatsoever to
do with being fat, but simply means that his mind is somewhat dense.
Immediately the blunder spreads like wild-fire from lip to lip, growing
as it goes and repeated with a joy that approaches delirium. There
was at one time an officer on duty whose idiosyncrasies were told and
retold. He furnished many a good story for the delight of the Corps,
and his departure threatened the existence of _The Howitzer_, the
cadets' annual publication, and of the _Hundredth Night_, the annual
play in which the officers may be satirized. His mind seemed to work
by rule and regulation. One night when he was making his inspection of
barracks, he came to a room where only one cadet was studying at the
center table. He entered, looked around, and then inquired:
"Cadet, where is your roommate?"
"In bed, sir!" was the reply.
"Is he asleep?" asked the officer.
"I don't know, sir," answered the cadet.
"Well, find out," ordered the "Tac."
The man then turned to his roommate who was plainly visible in bed, and
asked:
"Jim, are you asleep?"
"Yes" sounded off a voice from the depths of the comforters.
"He says he's asleep, sir."
"Very good, cadet," replied the "Tac," and quite satisfied, left the
room, just in time to escape the outburst of laughter that followed
this highly intellectual conversation.
To be always under the observation of so many pairs of keen
young critical eyes is sufficient to make any officer somewhat
self-conscious, and to give a certain kink and twist to his actions.
The cadets, like all youth, are merciless in their judgment, sometimes
almost cruel. They are ever on the alert for any slip that the "Tac"
may make and intolerantly condemn him. But so responsive are the cadets
that it would take but a smile, or a word or so bordering on intimacy,
to remove all critical feelings and bring about "glad confident
morning." I wonder sometimes why that so seldom happens. I suppose it
is because we are all artificial.
Although the Tactical officer is very much occupied with the interior
discipline and economy of his company, the greater portion of his time
is given over to the military instruction of the cadets. The purpose of
this instruction is to familiarize the cadet with the duties and needs
of a private in the ranks by practical experience, to impress upon his
character the habit of obedience, and to train him in the function of
command by repeated exercise.
In order best to accomplish this purpose, the cadets are organized
into two battalions of four companies each. This is the present
organization, but as soon as the Corps has been increased to the full
strength recently organized by Congress, the Commandant intends to
make a regiment. Although the Tactical officers command the companies
in the sense that they are the supervisors of the discipline and
administration, the actual commanding of the companies on the drill
ground is entrusted to the cadets. Selected men perform all of the
duties of the officers and non-commissioned officers. They are chosen
for this honor on account of their good conduct and studious habits,
and the soldier-like performance of their duties. They are as strict
and conscientious in upholding the Regulations as are the officers
themselves. As a matter of truth they are more severe because they
seldom take it upon themselves to put any interpretation upon the
motive underlying the act. A thing is right or it is wrong. There is
no middle line. Whenever any cadet is on duty, he insists that all
under him obey implicitly his orders, and should any man be so rash
as to disregard his authority, he instantly enters a report against
the offender. It would seem that such an action would arouse the
resentment of his fellow cadets, but this does not occur, due to the
honor system at West Point. Cadets generally recognize that their
attitude toward their work must be different from the student at the
average educational institution because their duties are all in serious
preparation for their future careers.
Of course, there are some men who carry their authority too far when
they find themselves in command of their fellows. Sometimes they lack
judgment and consequently deserve sympathy; sometimes there are a few
men who deliberately try to make an impression upon their superiors
at the expense of the men in the ranks. These men who allow their
desire for probable advancement to lead them astray are quickly sized
up by the Corps, and dubbed "quilloids." They are usually disliked
and made to feel the displeasure of their comrades. In nearly every
class there are some of these men who do not see clearly, and who
persist, throughout their whole course, in placing false values upon
trivialities.
Since the cadets are organized into Infantry battalions, the greatest
amount of time is devoted to the work of this arm. There are many
reasons why this should be so. The Infantry is the largest branch of
the Army, and to it is assigned the greatest percentage of graduates.
Infantry drill is the basis of all drills and is the best for
inculcating discipline and cohesion among the men. Besides, the Great
War in Europe has proven that Infantry is still the Queen of Battle,
and that all of the other branches, the Artillery, the Cavalry, the
Engineers, the Aviation Corps are but her minions. It is the Infantry
that decides the fight.
The practical military instruction of the cadets, although carried
on throughout the year, varies in intensity at different periods.
In the depth of winter it is impossible to drill out of doors. The
Infantry instruction is then suspended, except for the daily class and
meal formations. When, however, March 15th rolls around, the Ides of
March remember, and the snow leaves the ground, the Corps begins its
annual training. Immediately after the dismissal of the sections from
recitations at four o'clock, the battalions form in front of barracks
for the afternoon drill. Despite the raw March winds that blow across
the Plain, chilling one to the marrow, the battalion designated for
Infantry drill sets about overcoming the inequalities of marching, the
lack of precision in the execution of the manual, raggedness of the
movements that have been produced by the long inactivity of the winter.
It is at this period that the most scrupulous attention must be paid to
the manner of executing the various movements. Every little dereliction
is criticized, every mistake is corrected, and every movement repeated
until it can be faultlessly performed.
First the companies are drilled alone and then later assembled for a
short battalion drill before going back to barracks. Up and down the
Plain the companies march, now in column, now in line. The right guides
of each company seem to be carrying the burden of the drill as with
tense faces they fixedly regard the two points upon which they are
directing the march of the company. Meanwhile they are measuring their
step by a silent count of "one-two-three-four." The officers and file
closers are attentive and alert, giving a word of caution here and
one of reprimand there, as the line crowds in on the left, or, like
an accordion, opens out on the right. The plebes in the rear rank are
striving to the utmost to keep in step and on the line, and at the same
time carry their rifles straight and drag in their chins. The detail
and care with which every command must be executed begins to produce a
feeling of monotony, and stolen glances seek the clock in the tower.
Fifteen more minutes! The hour seems interminable and the wind more and
more disagreeable. Finally the hands of the clock roll around to five
and the musician appears in the sally-port and sounds the recall.
The next afternoon the second battalion attends close order drill and
the first takes its place at extended order. A lighter gayer crowd
march forth to this exercise. Here they will have a little chance
for individual leadership, the command of a platoon perhaps, or of a
squad, or they will enjoy the comparative freedom and independence of
the skirmisher. In the early part of the spring course the mechanism
of the drill must be rehearsed upon the Plain. The parade ground is
therefore dotted with prone and kneeling groups of platoon columns and
of squad columns. The blast of the officer's whistle, the simultaneous
outstretching of the squad and platoon leaders' arms as a signal, and
the columns magically deploy into one long line of skirmishers. Once
again the blast of the whistle sounds; more signals; bayonets are fixed
and squads begin their rushes forward to the delight of the small boys
and visitors who line the surrounding walks. Then follows the assembly
and the companies do it all over again.
As soon as the mechanism is well learned, the battalion is taken up
into the hills and maneuvered over all sorts of ground. Combat problems
involving advance guard and outposts are worked out under the direction
of the Tactical officer. In these exercises the actual command of the
companies is in the hands of the cadets, but the Tactical officer,
assisted by other officers, directs the drill. The cadets detailed
for this drill called Field Training are assembled in front of the
old gymnasium where the officer outlines the problem and gives the
men a talk on the principles that are involved. Each man is made to
understand just what he must do before he starts out and must know the
general principles to be applied in cases that arise. A situation is
assumed where the cadets are a force in the country of the enemy. They
are to form, we will say, the advance guard of their regiment. The
instructor gives to the cadets who are to command all information that
he has of his own forces and of those of the enemy and he points out to
the young commanders what is to be accomplished. The cadet officers are
then called upon to communicate to the men under them the instructions
that, in their opinion, are necessary to accomplish the mission. The
officer stands near to make suggestions and corrections, or to point
out errors of judgment. As soon as all understand what they are to do
the command moves out to work out the problem.
It is in the Field Training of the Infantry that the cadet acquires a
real knowledge of command. He must be able to size up situations and
quickly form a decision. He must then issue orders, clear and definite,
to cover the case. It is in these drills that he learns something of
the art of handling troops and what is the feeling of responsibility.
The cadets who actually exercise command are the First Classmen. They
are detailed by roster, irrespective of whether they are privates or
cadet officers, so that every man has many opportunities to command
a company before he graduates. It is highly important that the cadet
should be given practice in appearing before a body of men and in
giving them instructions. Nothing helps so much to give him confidence
in himself. It is of great value to him when he joins his regiment
in the Service. Cadets of the First Class are therefore detailed for
every kind of duty. They are company commanders, acting adjutants,
lieutenants, officers of the day and of the guard. Whenever there is a
chance to place responsibility upon the cadet, advantage is taken of it
by the Commandant.
The Infantry instruction is progressive. The First Classmen are trained
in more advanced work by means of tactical walks. These exercises are
similar to those prescribed for officers in the Service and are in line
with their future work as subalterns. An officer takes four or five
men with him to some neighboring terrain well adapted to a particular
problem. All of the different phases of the problem are considered and
the cadets required to size up each situation and issue their orders as
if in actual warfare. They are provided with maps which they must be
able to read with facility. At the close of the exercise the officer
holds a critique.
Nor is target practice, that important branch of Infantry instruction,
neglected. In summer when the cadets are in camp, the complete course
of firing as prescribed for Infantry and Cavalry troops is given the
First Class. It is held down on the flats near the river in the shelter
of Cro's Nest where a fair range parallels the Hudson. Every clear
morning at seven the detachments march down to the range. At this hour
the air is cool and crisp and so crystalline that every feature of
the landscape stands out sharply defined. West Point is incomparably
beautiful at this season and time of the day. But as the sun mounts
higher in the Heavens the coolness is replaced by a steadily increasing
heat. From the arrival at the range until noon, Washington Valley
echoes with the crack! crack! of the Springfields. Little groups of
cadets are stretched out in the blazing sun trying to find the bull's
eye and hoping to pile up a big enough score to win the coveted medal
of Expert Rifleman or Sharpshooter. Meanwhile another portion of the
men is down behind the butts, taking its turn in shifting the targets.
All morning long they monotonously pull the frames up and down, pasting
on the target, now a white paster, now a black one, or mechanically
waving the red flag back and forth. Intermittently the telephone rings:
"Ting-a-ling-a-ling-a-ling."
"Re-mark No. 8!" sings out the operator.
Careful search is made on No. 8 for the third time and up goes the red
flag, the sight of which fills the hopeful cadet back at the firing
point with a feeling of disappointment and disgust. And so the morning
passes, the men firing so interested that they are oblivious of its
flight, and the men in the butts thinking less of pasters and red flags
than of the cool shower that waits them in camp, and blessed dinner.
If one wishes, however, to see the finished results of the discipline
and cohesion produced by Infantry training he must attend either a
review and inspection by the Corps, or a parade.
Every Saturday, shortly after the return of the cadets from dinner,
there is an inspection on the Plain, preceded by a review, at which
the appearance, clothing, and equipment of the cadet are minutely
examined by his Tactical officer. I know of no finer sight at West
Point than this ceremony, especially in the summer and early fall when
the Plain is green and the cadets wear the excellent combination of
the gray coats and white trousers. As the companies maneuver on the
Plain preparatory to taking their places on the line, the perfection of
their marching, their impeccable appearance, the white cross-belts, the
glittering breastplates, and bell buttons of coat, the foreign-looking
dress hat with its rigid little pompon, the splendid bearing of the
men, betray the beholder into believing that he is watching the
evolutions of some legendary _corps d'élite_. The scene seems foreign
and yet again very American. The most characteristic feature is the
thoroughness with which every detail of dress, equipment, and marching
has been worked out. When the Corps turns the bend near Sedgwick
monument and comes swinging down past the reviewing officer, the most
callous spectator could not fail to have his emotions stirred. His
pride is flattered. He is watching a ceremony whose perfection of
execution and beauty is symbolic of an institution that in a sense
belongs to him, to the man next to him, and to all the spectators along
the line. It is the product of America. No wonder he reverently removes
his hat as the colors march by.
No less beautiful although not so elaborate is the ceremony of parade.
During the spring and fall, daily parades are given by the battalion
that has attended infantry drill on that day. The drummers sound the
first call in the sally-port. The Area of Barracks is practically
deserted, but within the rooms cadets are feverishly adjusting their
belts, wiping off their guns, struggling into their coats, or looking
for mislaid breastplates. Out of the doors all at once begin to dart
the plebes, first one then another, and still others. They hastily
proceed to their places on the walk and mark the rear rank. The hands
of the clock slowly creeping around to the hour for the assembly are
watched intently by the Officer of the Day who stands in the sally-port
ready to give the signal.
From all the doors of the barracks are now pouring the upper-classmen
immaculately dressed in stiffly starched and evenly creased white
trousers, gleaming white belts, and shining buckles. Their faces
are so obscured by the chin strap of their high dress hat that all
personalities are lost, and each man appears to be the duplicate of
his fellow. The picturesqueness of the uniforms and the background of
the severe stone barracks recall the days of Frederick the Great. The
assembly sounds. At once the companies are formed and inspected. They
proceed to their places in the sally-ports and between the neighboring
buildings preparatory to debouching on the Plain. At the termination
of the Adjutant's call the band begins its march. One company emerges
unexpectedly from the north sally-port, another from the south, another
from near the Academic building, still one more from the shadow of the
old gymnasium. More of them keep coming and move out on the Plain. The
fresh green grass offers a charming contrast to the white of the
uniforms as the companies perform their evolutions before advancing to
the line. The Plain is dotted with companies in column, companies in
line, companies in columns of platoons, marching in perfect cadence as
if animated by machinery.
[Illustration: Parade on the Plain]
The line is now formed stretching from the flag pole to the trees in
front of barracks. A few minutes of silence reign over the parade
while the Adjutant moves smartly and rapidly to his place in front
of the Battalion, and by command, brings the Corps to "parade rest."
The golden sun sinking in the west plays its dying rays on the long
gray line, causing the men in ranks to blink and blink on account of
its brilliancy, and illuminating the bell buttons of the dress coats
until they sparkle like so many gems. Meanwhile, the band has marched
in front of the Corps and resumed its place on the right. The retreat
sounds. Then a hush falls over the visitors' seats as the spectators
rise to do honor to the flag, while the neighboring hills reverberate
with the strains of the _Star Spangled Banner_. The exercise in the
manual of arms being terminated, the band once again crashes forth
and the thin gray line of cadet officers, with their feathered plumes
fluttering and the knots of their red ashes swinging back and forth,
sweeps forward to the officer reviewing the parade. Smart salutes are
exchanged, the cadet officers face about and return to their companies
to march them in review and back to barracks.
Hand in hand with the Infantry instruction goes that of the Cavalry
to which is allotted the next greatest amount of time in the schedule
of training. Cadets are taught the fundamentals of every branch
of the Service, and all cadets receive instruction in riding and
in Cavalry tactics whether or not they are destined for that arm.
Infantry officers must know how to ride as well as those of the mounted
branches. Frequently their duties require them to be mounted, and when
they arrive at the grade of field officer, major, and above, they
are obliged to command their troops from the back of a horse. It is
only during their first year at the Academy that cadets do not attend
cavalry instruction. When they become Third Classmen their acquaintance
with the horse begins. Cadets must be taught to ride before they
can be advanced to the tactics of the cavalry, and as a matter of
fact, learning to ride well takes so much of the allotted time that
comparatively little is left for the cavalry problems. The cadets
who join this branch of the service will learn their cavalry tactics
chiefly in the Army.
Beginning with the Yearlings, therefore, lessons are given in
equitation, outdoors in good weather and in the magnificent Riding
Hall during the winter. At first life in the Riding Hall is hard for
those men who have never before ridden, but once they learn the art of
"sticking on" they enjoy the exercise that riding affords. The first
few weeks are particularly trying. When the Yearlings march in upon
the spongy tanbark, they find themselves face to face with a whole row
of bareback horses lined up along one side of the hall. The animals are
champing their bits and wagging their heads apparently in sheer joy
of the anticipation of "policing" a few victims. Little chills run up
and down the spines of the Yearlings and their bodies are covered with
goose flesh as they read the challenge in the eyes of the beasts.
"Fall out!" orders the instructor. Ranks are broken and the men
run over to the grinning horses, scrutinizing them with breathless
impatience, first one, then the other, hoping to catch a sight of a
kind and gentle glance.
"1. Prepare to mount! 2. Moun-n-n-n-t!" commands the instructor in a
sepulchral voice. Then follow frantic efforts to climb the slippery
hides--ineffectual jumps succeeded by sudden descents. Finally they get
aboard and all goes well until the heartless instructor intones:
"Slow trot. March-h-h-h-h-h!"
Such efforts at balancing never before were seen! One man on a
razorback tries every spot from the mane to the croup in an attempt to
find one little piece of hide whereon he might sit in peace and quiet;
another on an imitation Percheron wabbles most dangerously and falls
off going around the curve; another is firmly grasping the mane, or
tugging at the iron mouth of some malicious brute that insists upon
holding its head high, with both ears bent back to enjoy the muttered
curses of the rider. The galleries are lined with the daily visitors
who smile gleefully upon the embryo cavalrymen, but the distressed
Yearling's gaze turns reproachfully toward the spot where the young
girls of the Post may be seen bunched together and giggling.
As the days pass by the Yearling finds that his seat becomes more and
more secure and by the time that he has arrived at the dignity of a
Second Classman he feels that he is able to cope with the wildest of
the equine breed. During the first year the drill was more or less
drudgery, but after twelve months of practice he enjoys the lessons. He
feels the pleasure that comes from the ability to make one's muscles
obey the will, to feel the horse yielding to the slightest touch of leg
or rein. The thrill of the leap over the ditch and of the jump over the
wall are sensations that he loves. Later on when he goes out to the
cavalry drill ground for instruction in tactics, it is the gallop and
the charge _en masse_ that give a new meaning to the word "drill." It
is no longer a task but a pleasure.
His progress in handling his horse enables him to proceed to mounted
pistol practice and to enjoy the privilege of riding on the road,
and of polo. By the time that he has become a First Classman he is
ready to devote his time not so much to equitation as to real Cavalry
instruction. He learns how to reconnoiter, how to patrol. As in his
Infantry instruction, he must solve problems innumerable: the forming
of the advance and rear guards, the establishing of outposts, making
and breaking camp, the proper conduct of the march, how to care for his
horse the same as though he were an enlisted man. He must groom him,
feed him, and water him. He is called upon to perform every duty that
is required of enlisted men in the Cavalry so that when he shall become
an officer, he will know just how much to expect of his men. He will
so understand the fatigue of grooming, the difficulty of managing some
horses, and the impossibility of always being alert and attentive that
he will be patient and sympathetic, judging his men by their limited
advantages and not by the standard that he has attained through a
training _par excellence_.
Portions of the Cavalry instruction are devoted to hippology and to
packing. In hippology the cadets study a text-book upon which they
recite, but in addition they are frequently taken to the stables where
all types of horses are trotted out for their inspection and criticism.
They must be able to tell all of the horse's good and bad points and
must be conversant with the remedies for the ordinary diseases. The
packing is entirely practical. A pack train is kept at West Point for
the use of the cadets, and they are drilled in putting up an aparejo
and packing the mules. They must be experts in throwing the diamond
hitch.
The branch of the Service, however, that is more closely allied to the
Infantry than the Cavalry is the Field Artillery. They are indeed
brother arms. In the fight the Artillery must prepare the way for
the Infantry, using its powerful explosive shells to demoralize and
decimate the enemy so that the Infantry's task, hard enough at best,
may be made easier. Among the cadets the Field Artillery is a popular
branch of the training almost rivaling the Cavalry. The course of
instruction is splendidly progressive. During Fourth-Class year, the
plebes learn all about the instruments, how to set the sights, to
read the scales, the use of the quadrant, and to perform the duties
of cannoneer. By the time that they go into their Yearling camp each
individual is sufficiently trained to be a good gunner, so that the
class is ready to receive instruction both in the squad acting alone,
and as part of a battery. During the fall and drill periods of the
Third-Class year, the Yearlings are called upon to perform the duties
of driver, sometimes wheel driver and again lead driver. As in the
Cavalry instruction, the cadets must learn all of the duties of
enlisted men. Their experience as drivers will teach them how hard
it is to bring horses and carriage to a stop at a designated place,
how difficult it is to estimate the ground correctly, and how a man's
patience can be tried by fractious and unruly beasts.
The members of the Second Class are taught in the fall the technique
of the mountain battery, and in the spring they act as officers at the
drill of the field battery while the First Classmen who have already
passed through this stage of the training are detailed to command the
organization. The First Classmen also spend a great deal of their time
upon the theory of artillery fire, and practice accumulating firing
data. During the First-Class camp they conduct regular target practice
with the battery.
[Illustration:
_Photo White Studio_
At Target Practice on the Flats]
The course in Field Artillery has been vastly improved in recent
years. All of the instruction is given by Field Artillery officers,
and non-commissioned officers who are specialists along certain lines,
instead of as in former days by a stray Infantry, Cavalry, or Coast
Artillery Tactical officer. All the plebe drill period at that time
seemed to be consumed in jumping up on the caisson and off again. I
always felt like a squirrel in a cage going round and round without
getting anywhere. Sometimes, too, the instructions that the officer
gave us were a little mixed to say the least. I remember once an
instructor to whom Field Artillery was an alien art giving us at drill
the following order much to the merriment of the plebes:
"The cadets will now be divided into three squads: those that have
fired, those that have not fired, and those that have done neither."
There are other drills in the cadet's military calendar besides those
of the three main branches of the mobile army. No little attention
is given to Practical Military Engineering. In camp one third of the
class spends four hours of the day practicing the various methods
of signaling, how to make knots and lashes, how to construct gabions
and fascines, how to use tackle, and how to construct bridges. The
First Class make position and road sketches, they lay out field
fortifications, and dig trenches. They learn the use of explosives,
the placing of mines, and the dynamiting of trees, buildings, and
railroads. During the Academic year the Department of Practical
Military Engineering gives the Fourth Class a thorough course in
surveying that embraces both theory and practical work with the
instruments in the field.
The Tactical Department is charged with the instruction of the Coast
Artillery. Several modern batteries, both rifles and mortars, are
installed at West Point so that the cadets may have every facility
for learning the technique of this arm. The Yearlings act as gunners,
performing the same duties that are required of privates in the Regular
Army. The Second Classmen act as gun pointers, range and azimuth
setters, do the plotting and observing, or, in other words, perform the
duties of non-commissioned officers in the Regular Service. The First
Classmen act as battery officers or as range officers, so that upon
graduation they may join their commands fully acquainted with their
prospective duties.
After the Corps has been given the maximum of military training for any
one year, a week's practice march is held as a climax to the intensive
work of the summer camp. With band playing and with all the panoply
of war the cadets march down to the ferry to cross to the other side
of the Hudson. For the next six days they march and maneuver through
the beautiful country in the neighborhood of West Point. Every day
camp is established at a new point and a problem worked out on the
march from one place to the other. All branches of the Service are
represented. The main body of the Corps go as Infantry, but the First
Class make up the Cavalry and Field Artillery. The "hike" is a valuable
experience for the cadets. They learn what it means to be a "doughboy"
and carry a pack on one's back through the sweltering heat and the dust
of the road. They appreciate how tired the Cavalryman and the Field
Artilleryman are when they throw themselves down in their pup tents
after the labors of the day. Their understanding of real soldiering
is broadened and their sympathy for the duties that enlisted men have
to perform, awakened. They return to the Post, footsore and weary,
prepared to take up their studies in barracks and continue their
military training in the limited time after recitations.
During the entire year all military instruction ceases at six o'clock
in the evening. Military methods are, however, inextricably woven into
every part of the cadet life in addition to what might be called purely
military training. All during the evening study period, for example,
a certain number of cadets are on guard in the hall of the divisions
to prevent the cadets from visiting in each other's rooms, and to
preserve the utmost silence in the barracks. The only noise that can be
heard is the tread of the sentinel who walks back and forth wrapped in
his own thoughts that occasionally are interrupted by the Corporal of
the Guard sticking his head in at the door and saying:
"All right on your post?"
"All right, sir," answers the sentinel, who as soon as his superior
disappears replunges into his reverie until time for his relief.
At twenty minutes past nine a preliminary tapping of the drums is heard
on the Plain near the Commandant's quarters. A few minutes of silence
ensue. Then the music of the fifes and drums startles the night as the
drum corps commences its march to barracks to sound tattoo. The notes
of the fifes float out over the darkened Plain in the weirdest possible
manner, as if the spirits of the night were trying to be gay but could
not suppress a certain plaintiveness in spite of their joy. They are
like a little boy going upstairs in the dark who keeps saying out loud,
"I'm not afraid, I'm not afraid." On they come, the music growing
louder and louder, until they reach the sally-port where their racket
is a signal to the cadets to cease work and make down their beds. Some
of the men are already asleep, but the vast majority are still sitting
at tables, supporting their heads on their hands as they try to absorb
the meaning of the printed words that dance before their eyes. The
Drum Corps has ceased to play and stands near the Guard House waiting
for half-past nine. The silence of the Area is broken only by the tramp
of the third relief marching around the stoop of barracks from one
division to another.
[Illustration:
_Photo White Studio_
At P. M. E. Drill
Building a Pontoon Bridge]
"No. 1. Off!" commands the Corporal.
The sentinel joins his leader and passes on to relieve the other
sentinels. Meanwhile the hands of the clock indicate nine-thirty. The
"Hell Cats" sound the tattoo. For the next half-hour the barracks
are animated with cadets running up and down stairs to the showers,
with the noise of beds being made down and water drawn. Gradually ten
o'clock draws near. The Officer of the Day standing in the Area turns
to the musicians:
"Sound taps!" he commands.
THUMP! THUMP! THUMP! goes the drum in measured beat.
"Li-i-i-i-i-ghts out!" call the subdivision inspectors. The windows of
the barracks seem to blink for a moment and then darkness envelops all
of the rooms.
And so ends the day that has been continually under the eyes of the
Tactical Department. The next day will be the same and the next and
the next. Next year, too, the mills of the Gods will be grinding away
bending, twisting, shaping Mr. Ducrot for his future work. No act of
his is passed unnoticed or unrecorded. Every time that he performs
a duty the "Tacs" give him a mark that goes toward determining his
standing in military efficiency and deportment. This is as it should be
because the attitude toward duty that he displays as a cadet is a good
indication of his future attitude as an officer, and to deny to merit,
talents, and acquirements their just rewards would be to check the
emulation which brings genius into action and qualifies the industrious
student to become an ornament to his country.
The object of the Tactical Department is to make the cadets loyal,
obedient, and disciplined young soldiers. It requires them to perform
all of the duties of the enlisted men of the Army as a method of
understanding what an officer can demand of his men. They can then go
to their regiments with a sympathetic understanding of the trials and
thorns in the path of the men for whose lives they are responsible.
Moreover the "Tacs" aim to give the cadet a good training in the
fundamental principles of the tactics of each arm so that he leaves
the Academy prepared to take up the duties of a subaltern. He is not
supposed to leave West Point with the knowledge of a colonel as some
seem to think.
In our present war with Germany, West Point will continue to send
forth her product as heretofore to help train the immense number of
recruits for the new Army. They will be called upon to train also the
new officers that are needed for the large force that we will raise,
and to this task they must bring not only a practical knowledge of
certain drills, but a mind capable of thinking straight. They will lend
all of the aid that is possible but they realize also that in training
officers, drill and mechanical maneuvers, however useful they may be,
are subordinate to the more rare and difficult acquirements that alone
can produce accomplished and scientific officers. What is chiefly
needed in an officer is acuteness of intellect, either the result of
genius or habits of reasoning on scientific subjects. To this of course
must be added tactical knowledge, the foundation of which is securely
laid at West Point.
In the immense army that will soon be ours, the graduates of West Point
will indeed be a small leaven, but I am confident they will bring to
this mass of raw soldier material the ideals and the spirit of their
Alma Mater. They will not forget the lessons learned at her knee, but
will justify to the nation that has given them their education the
soundness of West Point's methods of training officers.
CHAPTER X
HENCE, LOATHED MELANCHOLY!
For days and days groups of Army Service Corps men going around the
Post clipping the trees, mowing the grass on the Plain, and daubing
with black paint the cannon on Trophy Point have been heralding the
approach of June. The odors of the fresh grass and of the tar in the
gutters are exhilarating smells for every cadet in the Corps. There are
buoyancy and hope in their manner and a decided note of anticipation
in the air. This feeling of anticipation is the greatest charm of a
cadet's life. It really begins with the candidate before he enters
the Academy. He anticipates his entrance; then as a plebe, he looks
forward with even greater pleasure to the day of his "recognition" when
he shall become an upper-classman. Words are too weak to express the
eagerness with which, as a Yearling, he sees the spring slip by and
June arrive bringing with it his long desired furlough. And then he has
before his eyes the seeming El Dorado of graduation.
Our plebe, Mr. Ducrot, is especially on the _qui vive_ for the passage
of the days. Ever since the snow left the Plain and the surrounding
hills, and the first little blades of grass began to peep through
the boggy spring earth, his attitude toward life has somehow seemed
different. For the past ten months he has led the life of an obscure
being, like the silk worm in his cocoon spinning his silk. He has
almost completed his work of the plebe year and is about to emerge
from his shell. For a few weeks he is seized with the languor of
spring. The drills while not irksome seem unduly long; the lessons
harder to prepare. But as the days of May fly by he feels his wings
growing stronger and stronger and the spring fever is forgotten in the
anticipation of being a Yearling.
At last the first of June arrives! At reveille even, everyone is happy.
He tries his best to answer about a dozen upper-classmen who ask him
all at once, "Mr. Ducrot, how many days until June?"
"_No_ days until June, sir!" he replies in a voice that vibrates with
joy. It is hard for Mr. Ducrot to believe that the day that he has
so long anticipated is here. It has been so long coming. He cannot
be mistaken, however, for all around him are cadets in fresh white
trousers, the first time since the previous summer. He knows that for
years and years it has been the custom for "the Battalion to go into
white" on the first of June, at reveille. Only a few days now remain
before he will put aside his humility and meekness and be received by
the upper-classmen upon terms of equality.
The great metamorphosis or "recognition," as it is called, occurs
upon the day before graduation, immediately after the return of the
Battalion from supper, and just prior to the graduation ball. On this
night, at supper formation and in the Mess Hall, the upper-classmen
are particularly severe. They "brace" and "crawl" the plebes more
than ever before, filling the air with, "Get your shoulders back, Mr.
Ducrot, more yet! more yet!" or, "Draw in that chin!" On this night,
however, the whole affair seems humorous, for the plebes have completed
their year and the upper-classmen are now about to extend to them a
warm handclasp. In order not to let the plebe training fizzle out or
have an inglorious end, the rigor of the "crawling" that for months
has diminished little by little is all at once revived with great
earnestness and enthusiasm. No one minds, however, but regards this
last evening's treatment more as a "grind," or joke.
After supper the battalions form in front of the Mess Hall and march
back to the barracks in the soft June twilight. To the observer at
a distance, a roar seems to arise from the ranks as the corporals,
sergeants, and lieutenants hurl corrections at the plebes. The noise
continues until the Corps wheels into line to listen to the orders of
the first captain standing under the trees in front of the barracks
consulting with the Officer of the Day. The various instructions and
orders having been announced he commands:
"Dismiss your companies!"
At once the upper-classmen in the front ranks turn and cordially grasp
the hands of the plebes and slap them on the back, the first time in
a year since their arrival at West Point. All of the dreariness of
a year's subjection is dissipated by the affectionate and fraternal
welcome in the Corps proper by the upper-classmen, whose strong grips
are to the plebe a sufficient reward for the hardships of the year
just completed. Friendships whose seeds were sown, but prevented from
growing by the great gulf between upper-classmen and plebes, now find
their fullest opportunity for development. The Rubicon is passed,
and our plebe lays aside his sackcloth-and-ashes manner for the more
man-of-the-world one of a Yearling. And richly does he deserve this
recompense for his manliness and grit! Following Kipling's advice in
_If_, he has for a long year (sometimes by _force majeure_) filled
"the unforgiving minute with sixty seconds' worth of distance run," so
that his "recognition" by his fellow cadets means that he is stamped
approved, and that he is entitled to associate with real men.
Mr. Ducrot is now entitled to enjoy all the privileges allowed the
cadets by regulation and by the custom of the Corps. As a plebe,
tradition ordains that he shall not attend the hops, or be allowed
the social recreations of the upper-classman, but now the bars to the
pasture of pleasures are removed and he scampers in like a young colt
to enjoy his new freedom.
The two months of camp life that follow graduation give cadets plenty
of opportunities to enjoy their spare moments. The entire forenoon is
taken up with the various kinds of military instruction, with infantry
drill, practical military engineering, target practice, artillery
drill, equitation, swimming, and what not, but the afternoon is at
their disposal from the return of the Battalion from dinner until
parade at five-thirty. They have many diversions from which to choose.
Close by the camp are five tennis courts for the devotees of the
racquet. Upon the Plain is a good golf course for those who like this
sport and speak its unintelligible language. A selected number of the
First Class defy the afternoon heat playing polo down on the Flats,
while others don their bathing suits and go canoeing upon the river.
The less energetic throw their blankets in the shade of the trees near
the Y. M. C. A. tent and abandon themselves to a siesta, or to the
delights of some good book.
Then, there are the social beings who spend most of their time in the
society of girls. They are the "spoonoids" of the Corps. After dinner
they flock _en masse_ either to the visitors' seats or to the hotel
where mothers, sisters, sweethearts, friends and friends' friends
gather around admiringly. It must not be imagined that all "spoonoids"
are alike. There are the virulent kind who are never in camp during
"release from quarters," who are never seen on the athletic field
except in a dress coat. They are always rushing some girl, first
one, then another, and are of the genus that are never quite on time
for any formation. They come running into camp at the last minute,
breathless and excited, and are peevish if everyone doesn't turn in
and help them into their belts for parade. Then there is the more
moderate "spoonoid," the unobtrusive sort, who, when he goes walking
with a girl, dons his comfortable gray shirt and white trousers, and
sets forth carrying a few deceptive golf sticks. Lastly, there is the
timid kind who sneaks into his dress coat and tries to slip out of camp
without being seen by his fellows. He really wants to go out but he is
a little ashamed of his desire, and he doesn't want the other chaps to
know anything about it. Besides, the chorus of "ahs-s-s-s-s-s!" from
all the tents along the line terrify him.
West Point, however, is indebted to these social beings for the touch
of romance and glamour that they give to the summer life. Their bright
uniforms and the gay dresses of their partners (and the still gayer
parasols) are seen everywhere on Flirtation Walk, on the balcony back
of Cullum Hall, on the Plain, and chiefly at the visitors' seats, and
their youth and enthusiasm add a distinct charm to the social life.
But the real amusements and pleasures of summer camp come after supper.
Thrice weekly small hops are held from eight to ten o'clock and on the
other three nights open-air concerts are given by the band.
The hops are the most popular and enjoyed of all the pleasures. The
Yearlings have an opportunity of showing how much they profited by
their dancing lessons of the previous summer and they flock to Cullum
Hall in droves. On hop nights the camp is practically deserted. Some
few men who do not care for dancing, and another small group who pose
as women haters, remain in the limits visiting one another or reading.
The new plebes, of course, are in their tents, silently working upon
their equipment. Commencing at seven-thirty, however, a stream of
upper-classmen begins passing the guard tents, signing out for the hop,
bound first for the hotel or for some officers' quarters where charming
young partners await them. As soon as darkness falls the couples set
forth for the dance. As they emerge out of the obscurity of the Plain
into the brilliant light that pours out of the main entrance of the
hall they appear for all the world like a lot of summer insects drawn
to a bright electric bulb.
It is a charming picture that the cadets in their uniforms and the
girls in their pretty dresses make as they gather in Cullum Hall for
the dances. It recalls all of the stories of beauty and chivalry that
poets have so often idealized. As I watch them today, their youth
tempts my imagination and it runs away, but as a matter of truth the
reality is not quite so ideal.
The cadets, even the most imaginative, see things more clearly and
recognize that some of the girls that come to the hops were not the
subject of the poet's thought when he wrote his odes to beauty. There
are all sorts of girls. There are young girls, and some not so young;
pretty girls and homely ones; vivacious girls and inanimate ones;
intelligent girls and dull ones; and occasionally some few attend the
dances who are so little favored with feminine charms that for years
the cadets have called them "L. P.'s." These damsels are usually the
friends of friends, or maybe, the friends of friends of friends--very
distant as you see, and the poor cadet is called upon to pay off his
friend's social debt. He does it well, too, for the dances are all by
card so that every girl has her partners arranged beforehand, and she
leaves the ball having experienced the intoxication of a great belle.
The cadets have no little fun over these girls, and if by any chance
they know them ahead of time they make an attempt to ensnare one of
their classmates, saying:
"Say, Jim, there is a peach of a _femme_ coming up for the next dance,
will you 'drag' her for me?"
He elaborates upon her charms with the deceit of an experienced
politician until accommodating Jim accepts.
Most men, however, are wily about these unknown friends' friends, but
occasionally they are caught. I know one cadet who was asked to take
such a girl to a hop. He replied that he would not do so himself but
that he would find some other cadet. With true Irish persuasiveness and
unexampled Blarney he prevailed upon a classmate. When the latter was
making out the card of the supposedly beautiful girl (but in reality a
true L. P.) his first thought was to offer some dances to the promoter
of the young lady. The arch-plotter, however, innocently replied:
"I'm awfully sorry, Joe, but my card is full."
This answer appeared exceedingly strange to Joe, until he beheld
his partner for the dance. Then the base ingratitude of his friend
so enraged him that he at once broke off all diplomatic and social
relations.
So wary have the cadets become lest they be taken in, that when a
fellow cadet comes out into the hall to get one of the stags to dance
with a girl, he is at once the object of suspicion. When he asks his
friend to take a dance because the girl's partner failed to turn up, or
what not, the friend instantly demands:
"Where is she?" "Where is she?"
Some of the more astute cadets then point out the prettiest girl in
sight saying:
"There she is; she's a fiend," meaning she is all that is to be
desired, and lead off their victim apparently in her direction, but
by a well-planned movement, the victim is shunted off so that before
he realizes it he finds himself bowing before Miss L. P. His comrade
has escaped in the crowd, leaving him to "darkness and despair." Here
begins a desultory conversation, not marked by any great intellectual
effort.
L. P.: "Do you like to dance?"
Cadet: "Yes, do you?"
(Long pause--atmosphere strained.)
Polite cadet: "Isn't this a beautiful hall?"
L. P.: "Yes, how many lights are there in the ceiling?"
Cadet: "340."
(Second longer pause--atmosphere at breaking point.)
Usually a chap relieves the situation by suggesting:
"Let's go out on the balcony."
There one can at least console himself with the beauty of the scene,
for unless devoid of all feeling, no person can behold the glory of
the Hudson from the balcony of Cullum Hall, by night, or better, by
moonlight without being greatly stirred.
Two hundred feet immediately below the balcony lies the river,
apparently calm and unruffled, but anyone who knows it well visualizes
the deep current beneath that flows resistlessly toward the sea. On
moonlight nights its surface is agleam from the rays of the full moon
standing almost stock-still over the hills that form the river's
opposite banks. Here and there as far down as Anthony's Nose the
obscurity is dotted with lights mostly yellow, but with an occasional
red or green that tells of the approach of a boat. Peace and beauty
reign over this scene. It is as if one were gazing upon the enchanted
garden of a land of fairies. Occasionally the charm and wonder of the
river are added to by the passage of a night boat that goes churning
by, brilliantly lighted, with its name _Berkshire_ or _Trojan_ outlined
in electric lights, and with its searchlight flashing broad beams
on the banks, first on this spot, then on the other. The operator
plays the beam upon the Riding Hall, then slowly passes it to the
Administration building, bathing the tower in light, then to the
Officers' Mess, or maybe some caprice will seize him and up dances the
beam to the chapel on the hill, descending as captiously to Cullum
Hall. For a few moments the entire balcony is illuminated by the cold
light of the searchlight that reveals other cadets and their girls,
some seated on the broad granite railing, and others strolling up
and down. The beam moves slightly upward, and the beauty of Cullum's
classic lines is outlined against the blackness of the night. Then a
jerky movement of the operator's arm and darkness once more enshrouds
the building. The steamer passes on, darting its beam back and forth
like a spoiled child, until it rounds Gee's Point where it is lost to
view.
The strains of the music draw all of the couples back to the ball room.
A more beautiful hall for a dance could hardly be imagined. Conceived
by the artistic brain of Stanford White, it forms a most exquisite
setting for the gray and white uniforms of the cadets and the rainbow
hues of the gowns. The fine old portraits of West Point's famous
generals, the wall bronzes commemorating their deeds, the battle-torn
flags, the Mexican cannon, the names of the great victories of the
Mexican and Civil wars, are inspiring surroundings for young men and
women. The atmosphere of the hall impels the cadets to be chivalrous
and courteous. It would be impossible not to have good manners in such
a hall. It is no wonder that the cadets enjoy the dances and that the
girls find a certain glamour in the entertainments.
On the nights when there are no hops, the concerts are held, and
although lacking the brilliancy of the dances, they have a delightful
charm of their own. Twice a week the concerts are given in camp, and
once a week in front of the quarters of the Superintendent. Upon these
occasions the visitors' seats are crowded, chiefly with the officers,
their families, and guests. Here and there on the parade ground are
groups of cadets and girls seated on camp stools. The chaperone sits
near by wrapped in a blanket to protect her from the heavy dew of the
evening. Perhaps, another group will be made more comfortable by some
energetic cadets who spread their blankets on the ground for seats and
arrange camp stools on their sides for backs. The band is conspicuously
placed on a concrete stand, whose brilliant lights cause the iron
supports to cast weird shadows over the listening crowd.
On concert nights the camp is much more animated than on hop nights.
Many cadets do not go beyond the hedge or frequent the visitors' seats,
but remain in their tents stretched out lazily upon their blankets,
where they "laugh and joke, and talk and smoke, and turn to boys
again." Here, clad chiefly in their underclothes, they comfortably
enjoy the music, reveling in the freedom from the stiff uniform.
Occasionally, to add to their pleasure, a squad of plebes is
summoned and ordered to prepare for Olympus a delicious "brew." One
upper-classman who takes the rôle of Zeus directs the plebe messengers
of the gods how to brew the libation. Having detailed one plebe to
perform the duties of Ganymede, Zeus orders him to get his own G.
I. (galvanized iron) water bucket, clean it thoroughly, squeeze the
lemons, add the sugar and water, and taste it until pronounced perfect.
To give the brew a proper color and add a little pungency, a bottle
of grape juice is recklessly poured into the delectable drink. With
the strains of the music floating over the camp and dippers full of
"brew" constantly at one's elbow, the upper-classmen reclining at their
feast rival the luxury of the Romans of old. Nor are the "messengers"
forgotten. They are permitted, as a reward for their services, to drink
their fill from the brimming bucket. Of course, there are a few "eats"
too; nothing elaborate, but oh! how good! saltines, peanut butter, and
jam! Words to conjure with!
Or perhaps, a roving crowd of Yearlings, restless and filled with
adventure, go from company street to company street, visiting, playing
pranks and jokes, poking their heads into some plebe's tent, almost
scaring him to death by yelling:
"Mister, what's your name."
"Mr. Ducrot, sir!"
"Who am I?" asks the Yearling.
"I don't know, sir!"
"What!!! don't know who I am? Well, Mr. Ducrot, you're pretty ignorant,
you get that; you 'bone' me up!"
On goes the gang from one tent to another, drawn to some parts of
the camp by a "brew" fight, or to another part by the tinkling of
some mandolins and strumming of some guitars. From the depths of each
street strong voices call out to their comrades in other companies:
"Oh-h-h-h-h! Scott Fulton-n-n!" More often the night is startled by the
frequent call:
"Turn out a plebe!"
Out of the tents bound a dozen plebes to find out the wishes of the
Mighty One.
In the camp there are many sharp contrasts. Strangest of all is to
see some serious-minded cadet seated in his tent calmly reading,
enthralled by the contents of a book, while all around him are
disturbing distractions. Neither the fluttering of the moths and lady
bugs around his electric light, the attentions of the mosquitoes, nor
the laughter and chatter of his comrades, nor the crashing music of
the band seem to draw him from his imaginary world. Not even the cry
of "Yea! Furlo-o-o-o ...!" so oft repeated by the Yearlings, makes any
impression upon him. Whenever a Yearling has a little surplus energy
that he must get rid of, he sticks his head out of the tent and yells:
"Yea! Furlo-o-o-o ...!"
From all parts of the camp, voices echo the call, and for a few seconds
the air vibrates with the sound of hopeful voices.
After a plebe has been recognized and has become a Yearling, the
one engrossing thought of his life is his furlough. This furlough,
coming at the end of his second year, is the only vacation accorded
the cadet in the four years, and is anticipated by him with the
keenest yearnings. For two years he has been living under the severest
discipline and restrictions and separated from the loved ones at home.
The thought of returning again to the family circle and of picking up
all of the old threads of friendship causes a lively feeling of joy
to fill his manly young heart. It is no wonder that "Yea! Furlo-o-o-o
...!" finds a sympathetic response in the hearts of all who have been
cadets.
On Sunday evenings, usually a dull time in camp, the regular concerts
by the Military Academy Band are replaced by a concert given by the
cadets themselves. This entertainment is known as the Color Line
concert. A canvas is made of the plebe class and all of these who
admit any musical talent are ordered to practice. Mandolins, guitars,
violins are all brought out and the whole aggregation, plebes and
upper-classmen, assemble in front of the hedge. For an hour or more
they play and sing for their comrades and friends, who sit around on
blankets or camp stools, and wave burning Chinese joss sticks to drive
away the tormenting mosquitoes. The simplicity of the entertainment
gives to these little Color Line concerts an intimate and charming
atmosphere.
As soon as the concert is over the crowd quickly disperses, the girls
going to the hotel or wherever they happen to be stopping, and the
cadets to their company streets. The quiet of Sunday evening is then
for half an hour broken by the shouts of the men as they litter up the
company streets trying to assort their clothing for the Monday wash.
"Turn out a wash list, you plebes!" "Step out, Mr. Ducrot!" are heard
on all sides.
There grows thereupon before one's eyes small piles of drawers,
undershirts, socks, towels, and white duck uniforms. Each article is
carefully counted and listed because if the laundry discover an error
on the slip, or find the garment of some other cadet in the bag,
a report is entered against the offender for which he receives a
demerit. Furthermore, the name of each cadet must be distinctly marked
upon each article of clothing.
It is not to be supposed that any such fortunate set of circumstances
would escape the attention of the practical jokers among the cadets.
Often the surnames of certain men are identical with the given names
of girls, as for example, Grace, or Bell(e) or Nelly. Naturally, their
garments are all marked in this way. The jokers surreptitiously steal
an article or two from each of the above and slip it in the bag of
the most Y. M. C. A. man in the company. The following day when the
delinquency list is read out the Corps is thrown into gales of laughter
by the following reports:
"Cadet Prude: one pair of drawers in wash marked 'Grace'"; or "Cadet
Helldodger: one undershirt in bag marked 'Nelly.'"
The legitimate amusements of the day are at an end. Taps comes and
plunges the camp into darkness and all turn in for their much needed
rest. It is then that the practical jokers begin to think of their
nefarious plots. They remain quiet for some time until the inspections
are made and the company commander has retired after his half-hour
solitary patrol of the company street. When all the camp is apparently
asleep, dark forms steal forth to their rendezvous and proceed in a
body to the tent of some classmate to "drag" his cot. Cautiously they
approach the tent, grab the ends of the cot with the sleeping form,
and quickly drag it to the center of the street. Just as the occupant
of the cot is rudely awakened, and tries to arise bewildering to defend
his rights, some one of the gang treats him to a cold bath from a
bucket of water provided beforehand. In the days of hazing this form of
amusement was practiced almost exclusively upon the plebes, but today
the men leave the plebes alone and devote their attention to their
classmates and friends.
When one is busy and happy the time flies by rapidly so that before the
cadet is aware of its flight, the summer camp is brought to a close
with a Color Line entertainment. The spare moments of the Corps are
for days beforehand spent in preparation for this event that marks the
end of a happy summer. The Practical Military Engineering squad now
comes into its own. They build roller coasters, triumphal arches, small
theaters with cabarets, Japanese gardens, with the greatest ingenuity
and skill. The company streets are transformed into bits of New York,
Tokio, and Chinatown. Upon the parade is erected a large open-air
dancing platform smothered in the flags of all nations, where the
cadets and their guests dance away the last evening in camp. They make
the most of their opportunity, for the next day they must return to the
barracks and commence the Academic term.
Once the studies have been resumed, the time for diversion of any
sort is limited. The entire day from 6:00 until 10:00 P.M. is employed
with studies, drills, and necessary personal duties, so that there is
nothing for the cadet but work, work, work. There are, however, two
weekly breaks in the severe routine. One of these lulls is on Wednesday
afternoon when there are no drills, an arrangement that gives two hours
of leisure to the cadets.
There are many ways of driving away dull care during these two hours.
The Second and Third Classmen, who have riding privileges, ride on the
roads around West Point where they enjoy, in the autumn, a variety
of scenes of surpassing beauty. Clad in their riding clothes, they
impatiently await in the barracks, usually in the lower hall, the first
note of "release from quarters" that is blown at 3:50 P.M. The moment
the bugler raises his instrument to his lips and sends forth the first
sound of release from quarters the "ridoids," except First Classmen,
burst from the hall and race to the stables in order to secure their
favorite mount. Each First Classman has his mount assigned to him, so
that he can be more leisurely in his movements.
Other men who prefer the society of books spend all of their leisure
at the library where they seek out a quiet corner and a big leather
arm chair and lose themselves in their surroundings. They enjoy the
atmosphere of calm dignity and peace that pervades the reading rooms
in refreshing contrast to the noise of barracks where the men are
constantly running in and out, calling to one another.
The noise in barracks, however, makes no impression on the men who
spend their leisure catching up with sleep. An inspection of the rooms
on Wednesday and Saturday afternoons would disclose many a cadet
"pounding joyously his ear." Grown weary by the routine, he does not
resist the overpowering feeling of fatigue, but abandons himself to a
delicious slumber.
Meanwhile, numbers of his comrades are out on the athletic field
engaged in tennis, golf, or if not playing, encouraging by their
presence the work of the football team. The leisure moments of
a large percentage of the cadets are given over in the fall to
practicing football songs and yells. Usually, some cadet who lacks
self-consciousness and who is popular with his fellows, is selected
as cheer leader. Under his direction the cadets practice their songs
and yells, while the team perfects its play in front of them on the
gridiron. At no institution of learning does there exist among the
students a greater _esprit de corps_ than among the cadets. In the
fall, all sorts of personal wishes and inclinations are stifled in
order to attend the cheering practice, and bring it to a high degree of
perfection for the Saturday afternoon games on the home grounds, and
chiefly for the contest with the Navy. Few of the cadets fail to turn
out for the cheering, because these are accused of lacking in spirit,
and thereby lose prestige with their comrades.
Cadets who elect to devote their time to other forms of athletics,
however, are regarded with no reproach, but men who absent themselves
in order to attend teas or to go "spooning" are looked upon with some
disfavor. Corps spirit ranks everything in the eyes of the cadet, and
he justly demands that it come first.
Such is the way that cadets spend their two hours of leisure on
Wednesday afternoons. After the 1:30 P.M. inspection on Saturday the
cadets are also at liberty for the remainder of the day. They spend
their time as described above, the various diversions changing slightly
with the seasons. Saturday is anticipated with the greatest pleasure,
for in addition to the afternoon leisure, the evening is free to do as
one pleases. How welcome is the relaxation from incessant study! There
are so many things to do. Some men attend the hops that are held twice
a month; others dine out at the officers' quarters; still others go to
the "Movies" which have become a stock entertainment every Saturday
evening in the gymnasium. Advantage is taken of the freedom to visit
one another's rooms in the barracks, to laugh, to talk, to "knock,"
possibly to make some "fudge" on the electric stove that spends the
week days hidden in the recesses of some mattress. Perhaps one of the
men has received some money from home, unknown to the authorities, and
has treated his comrades to unlimited quantities of Huyler's from the
Boodlers, or maybe an invitation has been received to a real "party"
after taps where cold turkey, jams, nuts, sandwiches, smuggled into
quarters, are eaten by an eternally hungry crowd. After such a feast
the condition of the room can better be imagined than described. The
next morning the occupants make the most frantic efforts to remove
the grease spots from the floor and table before the Sunday morning
inspection. All of the previous night's feasters lend a hand in the
scrubbing and polishing; the plebes are called in to wave towels in the
air, or anoint the furniture with bay rum to drive out all odors of
food that hung over the room from the previous evening.
The two weekly breaks of Wednesday and Saturday are increased, however,
when the snows come in November. Drilling out of doors then becomes
impossible so that from 4:00 until 6:00 P.M. daily, the cadets are
at liberty. Most of the men spend these gray afternoon hours in the
gymnasium, or in reading. The Second Class has its riding class during
this period.
After the football season, the diversions of the winter months are
few. The "spoonoids" whose acquaintance we made in camp recommence
their activities, chiefly visiting the quarters of officers. The most
pernicious ones are called by their comrades "Tea Hounds" or "Parlor
Snakes," in a good-natured spirit, of course. The percentage of cadets
who meet the officers' families socially is small. The men who do most
of the visiting upon the Post are army officers' sons who have known
some of the instructors at other Posts.
It is regrettable that so many men go through West Point without
having known any of the officers or their families socially. They meet
the officers only in an official way where the demands of discipline
require formal relations. This has a tendency to remove the officer
too much from this large number of cadets who lack the opportunity of
knowing informally men with whom they will later serve. Many cadets in
consequence form altogether erroneous impressions of their instructors
that they carry with them through their entire service, unless they are
fortunate enough to meet these gentlemen later on. While at West Point
had they conversed informally for a few minutes only over the dinner
table, or at a dance, this impression would have been eradicated.
The great gulf that has always separated the cadet from the officer
is, however, yearly becoming narrower. I have observed lately a
different attitude of the officers toward the cadets. Their manners
are more cordial, more sympathetic, and more informal. They treat the
cadets more like men instead of schoolboys; their manner is more that
of a superior officer toward a junior. The result is that the old
defensive attitude of the cadet toward his instructors is gradually
disappearing, and he now regards his officers as instructor coadjutors
instead of instructor tyrants. This spirit is highly beneficial to both
officer and cadet, because the latter, feeling that his instructor is
ready to aid him, becomes very receptive and consequently calls forth
from the former a natural response unhampered by self-consciousness.
Graduates of the Academy have often expressed their opinion that the
transition from a cadet to an officer is too abrupt, and have regretted
that before graduation a cadet did not acquire more the viewpoint of
an officer. It is not possible for a cadet to gain, simply through
official contact with an officer, ideas regarding the service and
little points concerning the command of enlisted men. Instruction in
these matters is provided, but it must be remembered that time is
limited, and that all recitations, lectures, talks, are in general
marked by formality and a certain degree of restraint.
In order to make a distinction between the First Class and the under
classes, the authorities have established a social organization called
the "First Classmen's Club." Its object is to segregate the First
Class from the remainder of the Corps, entrust to it greater powers of
command over the other cadets, and to put into its hands more fully the
discipline of the rest of the Corps. In other words, its object is to
inculcate in its members a greater feeling of responsibility by giving
them greater powers accompanied by greater privileges. The privileges
that are accorded thereby make them feel that they have passed the
schoolboy period, and prepare them to accept properly the greater
privileges of an officer. Although it is called the "First Classmen's
Club," it is in no sense a club as known in civilian life. Nothing
to drink, or to eat, is permitted, nor are there pool or billiard
tables. The Club has a spacious hall over the north sally-port of the
new barracks; it is supplied with papers, magazines, a phonograph, a
piano, and games such as dominoes and chess, and comfortable lounging
chairs. This meager equipment may appear ludicrous to the college man
who is accustomed to the comforts and luxuries of his fraternities, but
to the West Pointer who knows nothing but Spartan simplicity for the
past three years, it means a great deal. The First Classmen have the
privilege of using the Club at all times during the day, during call
to quarters as well as during release from quarters, but men who are
deficient in their studies are denied its use during study periods. The
affairs of the Club are regulated by a Board of Governors, of which the
first captain is a member ex-officio.
With the exception of the First Classmen's Club the authorities do not
permit any social organizations such as fraternities among the cadets.
In the first place, such bodies are in conflict with the principles
of democracy upon which the institution was founded and which still
characterizes every act of its administration; and in the second
place, the cadet's time is otherwise employed to a greater extent than
that of any other university student in the country. West Pointers have
no time for much else but to study their profession and develop their
bodies. The relaxations provided for their spare moments are simple,
healthful, and democratic.
There is, however, an organization at West Point called the Dialectic
Society. This body was originally organized as a literary club in
1824 for purposes of discussing subjects more or less profound, and
of affording members an opportunity to read their literary efforts.
Today, it is an assembly room open to all upper-classmen who gather
there either to read or chat, or to enjoy the good fellowship of their
comrades. It is also used as a gathering place whenever the Corps
wishes to deliberate upon some weighty question that affects their body
and that calls for a solution by a referendum. Its rooms are now over
the east sally-port of the north barracks. Old graduates will remember
its location as the hall over the north sally-port of the old barracks.
The present room is larger and better adapted for the increased number
of the Corps.
As the fall wears on the principal topic of conversation wherever the
cadets are gathered, whether in the Dialectic Hall or in the First
Classmen's Club, is the approaching Christmas leaves. All thoughts
center on the mid-winter vacation, and efforts are bent to keeping off
the delinquency list. Not all cadets get Christmas leave. Those of
the upper classes are granted leaves from December 23d to 4:00 P.M.,
December 31st, provided that they are not undergoing examinations, or
special punishment, and that their number of demerits for the preceding
year has not been greater than nine per month in barracks and twelve
per month in camp. There are other provisos attached, chief of which
is the condition that a cadet must visit relatives or friends. This
regulation prohibits them from going to New York and staying at the
hotels. This restriction works a great hardship upon cadets from
distant States who have no relatives nearby, or who do not happen to
have made friends in the East; but its promulgation was found necessary
to prevent the cadets from going to the hotels where they borrowed
money and got into debt.
The tendency at West Point is to be more and more liberal about
granting leaves of absence. I personally feel that the new policy
is the correct one. The First Classmen especially should have the
privilege of going to New York occasionally during their last
year. Their close restriction to the Reservation at West Point
where everything is done for them makes them too dependent and not
sufficiently self-reliant. Their appreciation, however, of the vacation
is indeed keen. No more happy faces could be imagined than those of the
cadets going on leave as they descend the hill to the station. Not even
the woe-begone and dejected attitude of their less fortunate comrades
can detract one bit from the exhilaration of their spirits. Those left
behind, either on account of studies or conduct, spend their time
tramping in the woods, or skating, bobbing, riding, reading, or else
"boning" for the dread ordeal of the examination.
The vacation ends on December 31st when the men on leave return to the
Post. That night is held the New Year's hop for which the girls in
shoals come to West Point. It has always remained a mystery to me where
these girls come from. All of a sudden they descend upon the Post like
a swarm of locusts, and the next day as quickly disappear.
The characteristic feature of the New Year's hop occurs at midnight.
A few seconds before twelve o'clock, a musician in the orchestra
sounds the "attention." An impressive stillness falls over the ball
room, while the trumpeter blows "Taps" just as the old year dies. Not
a person in the whole room stirs. At the first stroke of twelve, the
trumpeter blows the "Reveille," a signal that another year has awakened.
The cadets of the upper classes then rush to the center of the ball
room, form into class groups, and give their class yell. The under
classes yell for the First Class which politely responds with a class
yell for each. The First Classmen then end the incident by a yell,
adding three prolonged and joyous cries:
"Never again! Never again! Never again!"
They mean that never again as cadets at West Point will they attend a
New Year's dance. They are announcing to all present the completion of
a definite period, the closing of one chapter of their lives that can
never again be relived. The music starts up, the dancers float off,
and the incident is soon forgotten, but to one standing by who takes
the trouble to reflect a little there is an element of sadness in the
almost debonair manner that these young men renounce a portion of their
lives that has not been lacking in benefits and in happy associations.
After the mid-winter break nothing interrupts the routine of the
cadets' ordinary diversions until the annual play on the 20th of
February. The upper-classmen give the _Hundredth Night Play_. It is
ordinarily a satire upon conditions at the Academy. The setting is
invariably West Point, and the principal characters are the officers
on duty. The other characters satirize the type with which West
Point abounds: the cadet girl, her friend, the chaperone, the cadet
"spoonoid," the professors and instructors. Shouts of laughter greet
the appearance of the impersonations of the officers, and rounds of
applause follow jokes gotten off at their expense. There is nothing
assumed or counterfeit about the genuineness of the cadets' enjoyment.
There is, of course, an officer who censors the play before its
production, for although there is no more polite body of men in the
world than the Corps of Cadets, yet their enthusiasm and eagerness
might lead them to indulge in personalities that would offend. The
Tactical officers who are immediately over the cadets are most
generally impersonated; the exaggeration of their little weaknesses
is not more enjoyed by the cadets than by the officers themselves. In
fact, whenever any one of them is left out he rather regrets it.
The approach of spring leaves but little time for pleasure. Drills
are resumed after study hours, followed by parade and guard mounting,
then more study hours after supper. The Battalions must be whipped
into shape for June week; each class must be given drills to prepare
the individuals for their coming task in June. Many things occupy the
cadets' attention. The First Classmen can think of little else except
graduation. They are busy looking over samples of uniforms, boots,
civilian clothing, or ordering same, or trying on uniforms. Some
few have the added responsibility of planning for their approaching
marriage. Naturally, the interest of First Classmen in cadet activities
begins to wane. The Second Class anticipate their First Class camp
when the reins of power pass to them, the Yearlings dream and dream
and dream of furlough. Every spring evening during the half-hour after
supper they gather upon Battle Monument to sing their furlough songs.
Little snatches float across the Plain, partly unintelligible, but
from which the words "love" and "girl" and "moon," sung with greater
emphasis apparently, can be clearly distinguished. Only the "call to
quarters" drags them back to earth, whereupon with a vociferous "Yea!
Furlo-o-o-o!" they break up the meeting and march back to barracks,
arm in arm, singing of the pleasures to come when they will leave the
Academy for two months and return to the bosom of their families.
Not least of the pleasures at West Point is the camaraderie. There
are always plenty of friends to be had, fine manly fellows with clean
thoughts, affectionate and kind. A cadet rarely fully appreciates what
this comradeship means until he is about to graduate. Then he reflects
upon his four years spent in the society of so many fine men, and he
feels a poignant regret at leaving their midst. The recollections of
the hardships endured and overcome together, of the mutual confidences,
of the sympathy when needed, of little sacrifices made for him, fill
him with tenderness and sadness. He finds it hard to say good-bye to
the truest friends that he will ever have.
The last few months, however, are so filled with duties and obligations
that he has few moments for reflection. Before he knows it June and
graduation are upon him. He then attends his own Graduation Ball. Just
prior to the last dance, once again the First Class assembles in the
center of the room, gives its class yell followed by the three cries:
"Never again! Never again! Never again!"
A little lump comes in his throat as the echo dies away. Never again
will he be a cadet at West Point. A yell that has heretofore been most
musical has all of a sudden become most melancholy.
Never again!
CHAPTER XI
STRENGTHENING THE MORAL FIBER
When a new class of cadets reports at West Point, it is composed of
men as diverse in appearance, in points of view, and in character as
the parts of the country from which they come. But after they have
been at the Academy for a couple of years a marked change occurs, and
by the time they are ready to graduate they have undergone a complete
metamorphosis. In some mysterious manner they seem to have been
leveled to a certain standard, like some scraggly hedge that has been
scrupulously trimmed by its painstaking guardian. The fat ones have
lost their extra pounds; the thin ones have made good their deficit;
the round-shouldered have straightened up, and the hollow-chested have
filled out. Instead of a heterogeneous looking lot of men, they give
the impression of having been made from the same die. And then too
there is a uniformity about their point of view. Whereas at entrance
their whole thought was by the life from which they came and
by what they hoped to be, once enrolled in the Corps, they quickly and
involuntarily have found themselves worshiping identical ideals--the
ideals of Duty, Honor, and Country. They have discovered at West Point
certain standards that have been approved by other men, and they have
gradually adopted them as their own. But the real stamp of West Point
appears in their faces. The imprint is evident wherever a group of the
cadets are gathered together, but it is never so apparent as at the
graduation ceremonies when the cadets individually mount the platform
to receive their diplomas. Then one can see a certain look in the
eye and a certain feeling of strength about the features that is the
same. It is the look of men who have accomplished something and of the
strength that comes from character.
What, you ask, is this leveling influence at the Academy? It comes
from discipline, the discipline of the body, the discipline of the
mind, and the discipline of the soul. It is the one governing factor
in the success of West Point. All three kinds of it begin on the day
that the cadet reports for duty, and continues without interruption
during his entire course. The discipline of the body and the mind is
a comparatively simple affair, especially when there is a willingness
on the part of the subject, but the discipline of the soul is the
influence that is hardest to make cadets appreciate. Some people shy
when the word discipline is mentioned; they think that it means to
break a man's will and to destroy his individuality, but that is not
so. The discipline that I speak of is a process of education whereby a
man's mental attitude is trained to a certain viewpoint; whereby his
actions unconsciously respond to the correct ethical view of his duty.
It is aimed to teach respect for law and order, to teach truthfulness
and honesty, loyalty and obedience. It inculcates respect for
superiors, if not for the man, then for the office that he holds. It
teaches a soldier the sacredness of orders; it is the quality without
which no army is successful.
Under this strong influence of discipline come men from all sections of
our great country and from all classes of society. Viewed exteriorly
they are, upon reporting, as motley a looking lot as could be imagined.
An examination of their interiors would reveal natures and characters
of equal variety. Some come from homes where they have received the
most careful moral nurture; others from environments of vague and lax
standards. Side by side with youths who are models of truth are lads
with uncertain ideas of right and wrong. Among the throng are brilliant
boys and stupid ones; well-educated lads and those whose advantages
have been of the most limited sort; sons of rich men and boys who have
known the meaning of want. From everywhere they come: from the city and
from the farm; from the mountain and from the plain.
It is interesting to dwell for a moment on the following table showing
the sources of the personnel of the cadet body. Herein are listed the
occupations of the parents of the cadets and the number engaged in
each, covering a period of fifty years.
Accountants 3
Agents 62
Architects 5
Artists 4
Auctioneer 1
Auditor 1
Author 1
Baggagemaster 1
Bakers 4
Bankers and bank officers 90
Barbers 4
Bookkeepers 18
Brewers 3
Brokers 40
Builders 2
Butchers 2
Capitalist 1
Chief of police 1
City marshal 1
Clergymen 128
Clerk of House of Representatives 1
Clerks 90
Collectors 4
Commercial travelers 13
Conductors 2
Contractors 38
Cook 1
Cotton buyer 1
County officers 74
Cutlery commissioner 1
Dairyman 2
Dentists 14
Detectives 2
Distiller 1
Dock commissioner 1
Dock master 1
Draftsman 1
Druggists 13
Editors 62
Electroplater 1
Engineers:
Civil 13
Mechanical 10
Locomotive 3
Stationary 1
Enlisted men 4
Express business 2
Farmers and planters 1,149
Fishing master 1
Foreman 1
Gardeners 3
General business 5
Hatter 1
Heads of corporations 10
Hotel keepers 55
Iceman 1
Importer 1
Inspector of buildings 1
Inspectors of factories 2
Inspectors of police 2
Insurance business 38
Inventor 1
Jewelers 3
Journalists 8
Justice of peace 1
Laborers 29
Lawyers and judges 645
Letter carriers 1
Librarians 2
Lithographer 1
Liverymen 15
Lumbermen 20
Manager of brewery 1
Manager of engines and boilers 1
Manager of factory 1
Manager of land company 1
Manufacturers 151
Marble dealer 1
Mechanics 341
Member of city board 1
Member of State Legislature 1
Members of Congress 32
Merchant tailor 1
Merchants 722
Messenger 1
Millers 11
Mining 26
Museum keeper 1
Musician, band leader 1
Musicians 2
Newspaper correspondent 1
Newspaper manager 1
No occupation 191
Nurserymen 6
Officers of the Army 362
Officers of the Navy 59
Officers of volunteers 21
Oil business 2
Overseers 4
Photographers 6
Physicians 367
Pilot 1
Policemen 7
Police justices 2
Politicians 3
Postmasters 5
President of manufacturing company 1
President of steam heating company 1
President of wire mill 1
Presidents of colleges 4
Presidents of insurance companies 3
Printers 12
Professors 27
Proprietor of elevator company 1
Publishers 8
Railroad employees 6
Railroad officers 13
Ranchmen 2
Real estate 37
Restaurant keeper 1
Salesmen 5
Saloonkeeper 1
School teachers 56
Secretaries 14
Ship captains 25
Speculators 10
State officers 27
Steamboatman 1
Steward 1
Stock dealers (cattle) 10
Stock raisers 6
Stocks 1
Superintendent of coal and iron company 1
Superintendent of factory 1
Superintendent of iron work 1
Superintendent of mine 1
Superintendent of prison 1
Superintendent of railroad 1
Superintendents of gas works 2
Superintendents of schools 4
Surveyors 5
Tanners 2
Teacher of garment cutting 1
Teacher of music 1
Teamster 1
Theater manager 1
Undertakers 5
United States civil officers 85
Unknown 39
Wagonmaster 1
Warden of prison 1
It is to the sons of men in this list that West Point applies its
discipline in order to create the type of officer that the Government
desires for its Army. From them must be eliminated the unfit and the
unworthy during the molding process to which they are subjected.
The immediate effect of the application of discipline to this variety
of material is the creation of an ideal democracy. All of the new
arrivals are thrown indiscriminately into the melting pot, and no
attention is paid to any man's antecedents. The boys of rich and
influential parents are not allowed little life-preservers of wealth,
family, and position whereby they might remain on top, but they must
boil away, sometimes on top, sometimes at the bottom of the pot,
rubbing and bumping against boys to whom riches and influence are
strangers. Whether they sink or swim, live or die, survive or perish,
depends on individual effort alone. Men are esteemed at West Point for
what they are and not for what they have. Each man feeling that he has
as good an opportunity to succeed as the other man becomes imbued from
the outset of his cadet career with the spirit of democracy that exists
at the Academy.
From the moment that a cadet enters West Point, his past life,
experiences, advantages, record, disappear into oblivion so far as
the authorities and other cadets are concerned. No reference is ever
made to any cadet's home, to his connections, to his family, unless he
introduces the subject. Once he becomes a cadet, a new clean sheet of
his life is started for him, and whatever is entered thereon depends
solely upon himself. Every man at West Point has the same chance--the
chance of advancement based upon merit and efficiency and upon nothing
else. It makes no difference to the officers in charge or to the
other cadets whether a man's family is wealthy or distinguished. As
a matter of fact this information is rarely known because all of the
cadets report together; they are totally unknown to those in charge so
that there is no possible way to ascertain anything about the cadet's
antecedents. They lose their identity completely, and so much so that
the upper-classmen take months to learn their real names, meanwhile
calling them by the generic names, Ducrot, Dumbguard, and Dumbjohn.
The character of the rooms in barracks illustrates most strikingly
this democratic ideal that discipline fosters. The plain and homely
furnishings of each room are identical in pattern, material, and
quantity, so that no cadet is housed better than his fellow. The walls
are free from pictures, the windows from curtains, the floors from
rugs. There are no soft easy chairs but only an old-fashioned wooden
one for each man, that is as hard for the rich cadet as for the poor
Mr. Ducrot. Nor are there any cliques that occupy particular rooms in
the barracks. Each company has so many rooms for its members, and as
far as possible the men within the company may choose their roommates.
Their selection is made on mutual attraction and congeniality solely.
Whenever two chaps enjoy each other's companionship, that indefinable
mingling of mute spirits, they try to room together.
And then again, the cadets are free from the distinctions and the
social barriers that money creates. They are prohibited from receiving
any money from their homes and are not allowed the handling of the pay
that they receive from the Government. Instead, the authorities supply
all of their wants, their food, their clothing, their books, their
amusements, so that they might have no need of cash. In fact there is
but one store on the reservation where they can spend money, and that
is a place called "The Boodlers," a sort of a general store at the foot
of the hill near the gas tank. Here they may, if out of debt, obtain a
permit for two dollars per month, and only those cadets with permits
are allowed even to enter the store.
In this ideal democracy, among the influences that are considered
prejudicial to good order and military discipline are drinking,
gambling, and cigarette smoking. All alcoholic drinks are consequently
banished from the life of the young embryo officer, for he must keep
a clear brain in order to think straight and master his problems. He
is permitted only the wholesome beverages of milk, tea, and coffee
that are supplied in the greatest abundance. Occasionally there is a
case of drinking among the cadet body, but as a vice, intoxication
does not exist at the Military Academy. One has only to look at
the healthy ruddy complexions of the cadets to be convinced of the
truth of this statement. Any girl might envy them their skins, whose
brilliancy and transparency would soon disappear if late hours and
beer were permitted. Nor is there any gambling in the Corps, unless
the betting of one's ice cream on the result of some football game be
so considered. The cadets are not even allowed the use of cards or of
any games of chance. They may not indulge in so harmless a pastime as
bridge. Their chief solace in their free moments must be their pipes of
briar, for cigarettes are frowned upon and regarded as contraband of
war, liable to seizure by any Tactical officer. The weed is confiscated
and the cadet receives a report. What becomes of those confiscated
cigarettes has always been a matter of great speculation. Tactical
officers are always under suspicion. I remember one case where a cadet
was caught with three hundred cigarettes in his possession and told by
his officer to turn them in at the Guardhouse. This order grieved the
cadet very much because he felt that perhaps someone else would enjoy
those cherished smokes. He therefore bored a hole in each one with a
pin, before complying with his directions. Soon after turning in the
cigarettes, he was reported for having mutilated them and was made to
walk punishment tours on the Area for many days. The inference was that
some disappointed Tactical officer could not make the cigarettes draw.
The ability to maintain a high state of discipline at West Point is
due partially to the wisdom of placing the instruction of the cadets
in the hands of officers who are themselves graduates of the Academy.
The officers have more prestige with the cadets and they understand
better the preparation of these young men for their future duties than
could civilian instructors. They have to a greater degree than most
instructors the prestige of a physical and moral superiority over their
students. They are familiar with the spirit of the institution and are
always on the alert to guard against corrupt influences. They better
understand how to instill the austere virtues that a soldier ought to
have, and how to form a brave and virile heart in their young charges.
In a measure they re-create the man and develop in him the national
soul.
The attitude of the cadets themselves, however, toward their discipline
is the real reason for the success of West Point's efforts to turn
out men who are high-minded and honorable. They are as zealous as the
officers over them in seeing that their associates live up to certain
standards. Honor is their shibboleth, and each new man upon his arrival
is instructed in what is meant by Corps Honor. Upper-classmen give
the plebes lectures wherein they explain the ethics that govern their
body, and leave them no room for doubt regarding the penalties for an
infringement of their code. From the outset of their careers cadets
are taught the hatred of a lie, and are made to understand that only
by the most scrupulous regard for the truth, every detail of it, can
they be considered fit to hold their places as cadets and gentlemen.
Any cadet who is found guilty of making a false statement regarding
even the most trifling circumstance is dismissed. If he is caught in
a dishonorable act, he is reported by his fellows to the authorities,
or told by his classmates that his resignation would be favorably
received. In order to do justice to any man accused of breaking the
code, the cadets have among their body a Vigilance Committee that is
composed of representatives from the three upper classes. These men
investigate all questionable acts that ordinarily would not come to
the eyes of the authorities, and if they are satisfied that the man is
guilty they report him. For example, at the written examinations the
officers never supervise the cadets as regards their moral conduct,
but frequently leave the room for long periods. If any man should
take advantage of these circumstances to cheat, his act, if seen by
a comrade, is at once reported to either the Vigilance Committee or
to the officers. It is apparent therefore that the honor of the Corps
will always remain unsullied so long as it is left in the hands of the
cadets themselves.
[Illustration: A Review for the Chief of the Staff of the Army]
This rigid code of discipline to which the cadet is subjected for four
years and the influence of the honor system in the Corps develop in
him to a high degree the sentiment of duty. At West Point duty comes
first. The idea is that when a cadet is given a task to perform he will
approach it with a strength of purpose that never gets weary or tired.
It teaches him to make his resolve so strong that he can listen to the
murmurings of the ignorant, to their sophistry, receive their insults
and slanders, conscious that the ideals for which he stands will
eventually triumph. It is the sentiment that will sustain him not only
in time of war, for then he has the sympathy of the people, but in time
of peace when the average layman who does not understand the character
of his work condemns it as an activity that produces nothing.
The result of four years' immersion in the atmosphere at West Point
is the molding of the cadet's character. When he entered the Academy
he was just a boy, fresh from the hands of his parents and still
malleable, but when his course has been completed under the painstaking
care of his foster mother, his standards have been crystallized and he
has developed into a man of courage, intellect, and honor. And when
graduation day arrives, and West Point hands each man his diploma, with
it she gives her stamp of approval and acknowledges her willingness
to entrust to his keeping the cherished traditions of the Military
Academy.
CHAPTER XII
SPIRITUAL INFLUENCES
Cadets love to lay aside the restrictions of their everyday routine
life, put on their athletic uniforms and most care-free manners, and
wander among the beautiful hills that are all around West Point. They
like to enjoy the emotions that spring from a close communion with
Nature, both in the winter, when the afternoons are short and the
valleys quickly fill up with purple lights, and in the summer, when the
country is extravagantly clothed in luxuriant foliage. If the day of
the cadet has been warped by all sorts of petty annoyances, all that
he has to do is to climb to Redoubt No. 4 or go to Fort Putnam, and
feast his eyes upon a scene of unsurpassing beauty in order to have
his cramped soul straightened out and to be lifted above his material
surroundings. What greater pleasure does his life afford than to lie
in the warm spring sunshine of Fort Putnam and drink in the panorama
below? All of the cares of his daily existence drop away under the
spell of a mysterious kind of an influence that fills his being and
stirs his innate nobility. He is thankful that he is privileged to
live in such a wonderful and beautiful place. Its effect is like that
of some drug that soothes and calms, that gives him a kindly feeling
toward humanity, and that makes him glad to be alive. On all sides
he is affected by Nature who has done her best to develop all of
his spirituality and to awaken his finer sensibilities. Wherever he
wanders or wherever the eye roves, there is a scene to admire, almost
reverentially. No less appealing than the hills is the river with its
many moods.
And there are the buildings whose beauty likewise exerts a subtle
spiritual influence and acts as a stimulant to the development of the
cadet's æsthetic tastes. His Barracks, his Recitation Halls, his Riding
Academy, his Gymnasium, his Mess Hall, and especially his Chapel, built
as they all are from the natural rock of West Point's hills, seem to
grow right out of their surroundings as if God planted them there as
a part of His natural design. Their presence is ever a reminder to
the cadet that he has consecrated his life to an ideal, for on their
exteriors are carved in conspicuous places the shields of his Alma
Mater and of his country, bearing their motto of duty and honor. The
walls of the interiors are hung with the portraits of famous sons of
the Academy, whose devotion to their country and to an ideal serves
as an inspiration to the cadet and makes him sensible to the value of
moral qualities.
Hovering over both the grounds and the buildings is the influence
of the flag. As a cadet sees it floating from its tall white staff,
somehow it has come to have a different meaning from the days when he
was a care-free civilian. It seems to him to possess a personality of
which he never before was aware. He feels for it a real reverence,
because he is conscious of being in the presence of something big, as
if beholding the whole power of a nation. He sees in it the emblem of
the country's sovereignty and the symbol to which he has pledged his
life's service. Mingled with his feeling of reverence is his personal
affection. Day after day he has watched it silhouetted against the sky
and has felt the thrill of patriotism, when it was being lowered at
retreat to the accompaniment of _The Star Spangled Banner_.
It is not to the beauty of Nature and to the flag alone that the cadet
must turn for his spiritual refreshment. The Chaplain, a man with a
fine grip upon the Corps, gathers together in classes those cadets
who desire to come, and explains to them the word of God. His Bible
classes today are a continuation of the famous classes that were held
at West Point for so many years by Miss Anna Warner. During the summer
encampment, she taught her boys in the old chapel after the morning
services, where for one hour the cadets received from her sainted lips
an interpretation of the Scriptures, and were elevated by contact
with her noble character. I can see her before me now, her quaint
silk dress, her small delicate body, her ethereal face framed in the
neatest and whitest of curls that peeped from out of her charming poke
bonnet. Her whole presence radiated goodness and spirituality. Prior to
the dismissal of the class she would regularly present to each cadet a
fragrant little bouquet of flowers that she had that morning gathered
from her modest garden, and arranged into the daintiest of nosegays.
These few flowers were simple, like the donor, but they brought into
the life of the recipient a spiritual perfume that awakened his
memories and took him back home to rose-scented gardens and neat
graveled paths where another sainted woman was praying for the welfare
of his soul. So he took the little nosegay back to camp with him and
put it carefully in his tumblerful of water alongside of his tent, as
a reminder of what he should be, and as a check on ignoble impulses.
Here and there in his own company streets, he would see his comrades'
bouquets, little dashes of color, the red of the petunia, the blue of
the cornflower, the yellow of the marigold, and as they caught his eye
they seemed to be a part of Miss Warner still exerting her inspiring
influence.
It is regrettable that the cadets of the future will never have the
good fortune to know her, for last year (1916) she passed to her reward
after ninety years in the service of God. Although it is rare that
anyone outside the Academy is buried in the cemetery at West Point, her
body was laid to rest there, near the bluff that overlooks the Hudson
and in sight of her home on Constitution Island across the river, that
a short time before her death she generously gave to the Government. To
the Corps of Cadets that she loved, she willed a magnificent original
portrait of Washington by Gilbert Stuart, that now hangs in the library.
Her Bible class still goes on. Every Sunday when the weather is fair
the Chaplain takes the cadets over to Constitution Island, where, under
the trees that Miss Warner loved so well, he continues her work. If
Miss Warner sees her "boys" studying the word of God in the shadow of
the old Revolutionary House, hallowed by her presence, what pleasure
she must feel!
If, however, neither the beauties of Nature nor the interest of the
Bible class appeal to the cadet, he cannot help having his spiritual
self stirred by the impressive service at the Cadet Chapel. All cadets
are required to attend divine service. The large majority go to the
Cadet Chapel because it is for all denominations, the building never
having been consecrated to any particular faith, but about ten per
cent. of the cadets attend service at the Catholic Chapel.
The service at the Cadet Chapel is so impressive and interesting
that the majority of the cadets look forward with pleasure to Sunday
morning. I suppose that all former cadets will smile upon reading this
statement, when they remember the reluctance with which they donned
their dress coats and belts for the weekly service, at which they
had difficulty in keeping awake while the lessons and sermon were
being read. But times have changed since then, due principally to the
atmosphere of the new Chapel and the music of its splendid organ. Sir
Roger de Coverly would rejoice to behold so model a congregation and to
hear such excellent singing.
The interior of the Chapel is worthy of its beautiful service. "Storied
windows richly dight" rise majestically to the high Gothic roof and
throw upon the gray walls a myriad of delicate lights, pale blues and
pinks, saffrons, and deep purples. Two parallel rows of silk flags, the
scarlet of the artillery, the somber blue of the infantry, and the gold
of the cavalry, hang from the long covered galleries on either side
of the nave. The deep rich shades of the magnificent memorial window
shroud the chancel in a "dim religious light." Nor is the service
lacking in military pomp. Company after company of gray-clad cadets,
their brass buttons shining, file briskly into the Chapel. The tramping
of hundreds of pairs of feet up the aisle and the rattling of their
buttons against the pews as they take their seats reverberate through
the vast hall. The officers, in their uniforms, and their families
assemble in the seats along the sides.
The first note from the organ announces the commencement of the
service. The choir of over a hundred voices, singing the processional
hymn, walk two by two in slow and solemn order up the aisle to their
places in the stalls. A wave of music sweeps through the church as the
procession moves forward. Last of all comes the Chaplain, immaculate in
fresh linen surplice, and conspicuous by his distinguished bearing.
The service proceeds. The Chaplain advances to the reading desk and
reads the lessons for the day. Inspiring hymns are then sung, followed
by an eloquent sermon upon subjects that touch the daily lives of the
cadets. Once again the celebrated organ peals forth, and during the
offertory casts with its music a spell over the devout congregation.
Two stalwart cadet officers then march quickly up the aisle to the
chancel where awaits the Chaplain to receive the offerings. The organ's
music fills the church anew and the hall resounds to hundreds of
strong voices singing "Praise Father, Son, and Holy Ghost," followed
immediately by the patriotic hymn,
My Country 'tis of thee,
Sweet Land of Liberty,
Of thee I sing--
Land where our Fathers died,
Land of the Pilgrims' pride,
From every mountain side
Let Freedom ring!
The Chaplain standing upon the steps of the altar pronounces the solemn
benediction, which is scarcely concluded when the choir begins to sing
the "Amen" to the accompaniment of Holy Grail motif from _Parsifal_.
Faintly at first the singing arises from the stalls, then stronger and
stronger, then diminishing in volume until it dies away with a final
"Amen."
Besides the service at the Chapel there is another service held on
Sundays. It is the Y. M. C. A., a purely religious body among the
cadets and not as in the cities a sort of club house where a swimming
pool, assembly rooms, and gymnasium are the main attractions. These
advantages are already a part of West Point's equipment. The Y. M. C.
A. at the Academy meets every Sunday evening after supper in a hall
over one of the sally-ports, and here after a few prayers, a speaker
makes a short address. On week days the hall is frequented by cadets
only to read the papers or to play the victrola, and in Lent the
Chaplain holds afternoon services. Formerly the Chaplain held these
prayers immediately after breakfast, but once a cadet captain, wishing
to remind the cadets that the services would take place immediately
after the dismissal of the Battalion, mixed up his verbs and announced
very emphatically "cadets are _cautioned_ about the ten-minute service
in the Y. M. C. A."! The Sunday service, however, is the reason for
the existence of the organization. The prayers are not long and the
addresses sometimes most interesting, especially when they relate to
the work that the cadet will have to do as an officer. The meetings are
usually terminated when the bugler blows the evening call to quarters
in the sally-port under the hall. Of all the sounds at West Point,
Sunday evening "call to quarters" is the most doleful and depressing.
It means that after the break of Saturday and Sunday, the cadet must
once more turn to his books and dig out the problems for Monday. When
he hears its melancholy, long-drawn-out notes, he has the Sunday
evening feeling, which is only a degree more cheerful than the blue
Monday feeling, and he reluctantly goes back to his room to begin anew
the weekly cycle.
The cadet is really never quite free from the spiritual influences of
the Academy. Nature, his Chapel, traditions, precept, and example so
arouse and sharpen his insight into things and into himself that his
day gradually assumes a new background. These are the influences that,
when he is an officer, draw him back to his Alma Mater and make him
speak of it always with undisguised affection.
CHAPTER XIII
THE SPIRIT OF WEST POINT
On a fine bright morning about the middle of June, every year, the
Corps of Cadets wakes up to find that Battle Monument and vicinity have
been completely transformed. The Quartermaster's men have canopied a
portion of the monument's platform with beautiful brand-new flags,
and placed under them comfortable wicker chairs for the President,
the Secretary of War, the various generals, and other dignitaries who
usually honor West Point with their presence on this graduation day.
On the front edge of the platform is a rostrum, flag bedecked, for the
speaker of the occasion, and spread over the green lawn are rows and
rows of seats that await the coming of the cadets. Promptly at ten
o'clock, the Corps swings across the parade ground to take its place
for the final ceremonies that mark the separation of another class from
its midst.
This is the day of days in the life of each man of the graduation
class. His four years are at last completed and he is about to be given
the great prize for which he has so ardently striven--a commission
in the Army. As he takes his seat in front of the platform, he is a
little nervous in spite of the joy at having achieved his ambition. He
realizes that he is about to sever the ties that have held him fast for
the last four years and to bid farewell to a portion of his life that
is finished. A little tug comes at his heart-strings but it quickly
vanishes as he listens to the eloquent words of the chief speaker,
oftentimes the President, unfolding to his receptive imagination the
duties and honors that await him in his new life as an officer. And
when the President reminds him of West Point, of her traditions, of the
advantages that he has been lovingly given, and of what is expected
of him in the Army, there comes to his eyes a moisture from pride and
gratitude. Into his mind rapidly crowd a thousand and one recollections
of his associations at the Academy. He knows now that he must leave the
Corps behind, that he must renounce the delightful camaraderie of its
members, and give up the beautiful surroundings wherein he has grown in
body, mind, and soul.
It is true that he can no longer wear the "gray," or take away with
him his friends, or the buildings, but he does take away with him
something that is finer than all of these. One can see it in his face
and in his bearing. He goes forth, his heart armed with the triple
brass of Duty, Honor, Country, and his soul filled with the Spirit
of West Point. All of his nature has been elevated and benefited
by this indefinable essence. It forever connects him with hundreds
of other men in all parts of our country and identifies him with an
institution whose very name, WEST POINT, no matter where seen or heard,
thrills him with pleasure. This name connotes the details of the most
impressionable period of his life. Even the words themselves seem to
have a distinction and personality that no other words possess. They
are flavored with romance and make one think of something fresh and
crisp and clean, something almost hallowed. They are themselves clothed
with the spirit of the place under whose influence and power he will
forever remain.
He leaves the Academy to join the great fraternity of West Pointers in
the Service, animated by the same spirit. With them, he is this year
(1917) called upon by the President to train for war a large army of
his fellow citizens, and prepare them to meet an enemy schooled in the
art of war by disciplined leaders. West Point sends him forth to this
task, rich in knowledge. His Alma Mater is confident that he will train
these men of the new Army in the fundamentals of their profession and
that he will inspire them with his ideals of courage and of honor, and
imbue them with the Spirit of West Point.
[Illustration:
_Photo White Studio_
Graduation--President Wilson Addressing the Graduating Class
"We'll bid farewell to Cadet grey and don the Army blue"]
In the training of the National Army, he will have all sorts of men
under his command, but the spirit of the Academy will make him patient
and kind with the stupid, lend a hand to the weak, give a word of cheer
to the down-hearted (there will be plenty of them), and instill
into all the ideal of duty. The kind of discipline that he himself
received at West Point will be theirs. He will teach them to bear
uncomplainingly their burdens, to be loyal and obedient, to care for
their health, and to march and to fight with a spirit that knows not
weariness or depression. Then when these men shall be sufficiently
trained, he will go with them to France, in the wake of the first
division of Regulars led by a gallant West Pointer, Major-General
John J. Pershing. Here he will appreciate as never before the value
of a great moral force like the spirit of West Point. It will aid
him in overcoming the obstacles in his path and in those of his men,
especially when the heroics of war and the novelty of being abroad have
ceased to interest them, and they find themselves in the trenches in
No Man's Land. They will be drenched by the rain and burnt by the sun;
they will have to endure the vermin, the mud, and the dust. They will
be driven nearly mad by the shrieking and bursting of the shells, they
will see their comrades killed and wounded, and perhaps they too will
suffer the same fate, but they will not flinch; because he who leads
them will have given them something of his spirit--a part of himself
that West Point made. He must be the prop upon which they may lean,
if need be, and his spirit the reservoir upon which they may draw for
refreshment. And should he be called upon to pay the supreme sacrifice,
he will leave them the Spirit of West Point to carry them to victory,
while he goes to join the ghostly assemblage of his fellow West
Pointers, standing bareheaded to salute him, as he has stood many times
in the presence of the living Corps.
The Corps! Bareheaded salute it,
With eyes up, thanking our God
That we of the Corps are treading,
Where they of the Corps have trod--
They are here in ghostly assemblage,
The men of the Corps long dead,
And our hearts are standing attention,
While we wait for their passing tread.
We, sons of today, we salute you,
You sons of its earlier day,
We follow, close order behind you
Where you have pointed the way;
The long gray line of us stretches
Through the years of a century told,
And the last man feels to his marrow
The grip of your far-off hold.
Grip hands with us now, though we see not,
Grip hands with us, strengthen our hearts,
As the long line stiffens and straightens,
With the thrill that your presence imparts.
Grip hands, though it be from the shadows,
While we swear, as you did of yore,
Or living or dying to honor
The Corps, and the Corps, and the Corps.
APPENDIX
(From the Official Register of the United States Military
Academy--1916)
WAR DEPARTMENT
Information Relative to the Appointment and Admission
of Cadets to the United States
Military Academy
(1916 Edition. Revised Annually.)
[Communications relating to matters connected with the Military
Academy should be addressed to The Adjutant General
of the Army, Washington, D. C.]
THE CORPS OF CADETS
The Act of Congress approved May 4, 1916, provides as follows:
"That the Corps of Cadets at the United States Military Academy shall
hereafter consist of two for each Congressional district, two from each
Territory, four from the District of Columbia, two from natives of
Porto Rico, four from each State at large, and eighty from the United
States at large, twenty of whom shall be selected from among the honor
graduates of educational institutions having officers of the Regular
Army detailed as professors of military science and tactics under
existing law or any law hereafter enacted for the detail of officers
of the Regular Army to such institutions, and which institutions are
designated as 'honor schools' upon the determination of their relative
standing at the last preceding annual inspection regularly made by the
War Department. They shall be appointed by the President and shall,
with the exception of the eighty appointed from the United States
at large, be actual residents of the Congressional or Territorial
district, or of the District of Columbia, or of the island of Porto
Rico, or of the States, respectively, from which they purport to be
appointed: _Provided_, That so much of the Act of Congress approved
March fourth, nineteen hundred and fifteen (Thirty-eighth Statutes
at Large, page eleven hundred and twenty-eight), as provides for
the admission of a successor to any cadet who shall have finished
three years of his course at the academy be, and the same is hereby,
repealed: _Provided further_: That the appointment of each member of
the present Corps of Cadets is validated and confirmed.
"Sec. 2. That the President is hereby authorized to appoint cadets to
the United States Military Academy from among enlisted men in number
as nearly equal as practicable of the Regular Army and the National
Guard between the ages of nineteen and twenty-two years who have served
as enlisted men not less than one year, to be selected under such
regulations as the President may prescribe: _Provided_, That the total
number so selected shall not exceed one hundred and eighty at any one
time.
"Sec. 3. That, under such regulations as the President shall prescribe,
the increase in the number of cadets provided for by this Act shall be
divided into four annual increments, which shall be as nearly equal as
practicable and be equitably distributed among the sources from which
appointments are authorized."
=Annual Increments.=--States at large, 21; Congressional districts,
92; Alaska, District of Columbia, Hawaii and Porto Rico, combined, 1
each year to the source longest without an appointment, and, when the
periods are equal, the choice to be by lot; Honor Schools, 5; Regular
Army, 23 in 1916, 22 in 1917, 23 in 1918, and 22 in 1919; National
Guard, 22 in 1916, 23 in 1917, 22 in 1918, and 23 in 1919.
APPOINTMENTS
=How Made.=--The appointments from a Congressional district are made
upon the recommendation of the Representative in Congress from that
district, and those from a State at large upon the recommendations
of the Senators of the State. Similarly, the appointments from
a Territory are made upon the recommendation of the Delegate in
Congress. The appointments from the District of Columbia are made
upon the recommendation of the Commissioners of the District. Each
person appointed must be an actual resident of the State, District, or
Territory from which the appointment is made.
The appointments from the United States at large are made by the
President of the United States upon his own selection. The cadets from
Porto Rico, who must be natives of that island, are appointed by the
President on the recommendation of the Resident Commissioner.
The appointments from among the honor graduates of educational
institutions designated as "honor schools" will be made upon the
recommendation of the heads of the respective schools.
The appointments from among the enlisted men of the National Guard will
be made upon the recommendation of the Governors of the respective
States and Territories.
The appointments from among the enlisted men of the regular army will
be made upon the recommendation of the Commanding Generals of the
Territorial Departments.
The Secretary of War is authorized to permit not exceeding four
Filipinos, to be designated, one for each class, by the Governor
General of the Philippine Islands, to receive instruction at the United
States Military Academy at West Point: _Provided_, That the Filipinos
undergoing instruction, shall receive the same pay, allowances,
and emoluments as are authorized by law for cadets at the Military
Academy appointed from the United States, to be paid out of the same
appropriations: _And provided further_, That said Filipinos undergoing
instruction on graduation shall be eligible only to commissions in
the Philippine Scouts. And the provisions of section 1321, Revised
Statutes, are modified in the case of Filipinos undergoing instruction,
so as to require them to engage to serve for eight years, unless sooner
discharged, in the Philippine Scouts.
=Date of Appointments.=--Appointments are required by law to be made
_one year in advance_ of the date of admission, except in cases where,
by reason of death or other cause, a vacancy occurs which cannot be
provided for by such appointment in advance. These vacancies are filled
in time for the next examination.
=Candidates.=--For each vacancy from a State at large, or Congressional
or Territorial district, _three candidates_ should be nominated, one of
the candidates to be named as _principal_, one as _first alternate_,
and one as _second alternate_. The first alternate, if qualified,
will be admitted in the event of failure of the principal; the second
alternate, if qualified, will be admitted in the event of the failure
of the principal and the first alternate.
For vacancies in the cadetships allotted to the honor graduates of the
"honor schools," _one candidate_ may be nominated each year before
September 1st from each school. In case the total number of candidates
so nominated is not equal to three times the number of vacancies, the
War Department will assign additional appointments among the schools to
complete this total.
For vacancies in the cadetships allotted to the enlisted men of
the National Guard, the candidates will be apportioned as near as
practicable among the States, Districts, and Territories according to
their enlisted strength. With the exception of the candidates from
the District of Columbia, they will be selected by the Governors from
successful competitors in a _preliminary examination_ held between
January 1st and January 15th of each year, such examination to be of
a scope and nature similar to the regular examination for entrance to
the United States Military Academy. The candidates from the National
Guard of the District of Columbia will be similarly selected by the
Commanding General of that organization.
The candidates nominated for the cadetships allotted to the enlisted
men of the regular army shall not exceed three times the number of
existing vacancies and shall be equitably distributed among the
Territorial Departments by the War Department. If the number of
applications in any Department exceed the share allotted to it by the
War Department, the candidates in such Department will be chosen from
the successful competitors in a _preliminary examination_ held between
January 1st and January 15th, such examination to be of a scope and
nature similar to the regular examination for entrance to the United
States Military Academy.[6]
Each candidate designated to take the regular examination for admission
to the United States Military Academy will receive from the War
Department a letter of appointment, and he must appear for examination
at the time and place designated therein.[7]
Fitness for admission will be determined as prescribed in the
Regulations, United States Military Academy.
REGULAR EXAMINATION OF CANDIDATES
Examinations of candidates will be competitive in the following
classes, and will be the regular examination for entrance to the United
States Military Academy:
(1) Candidates from the United States at Large, other than honor
graduates of honor schools.
(2) Candidates from the United States at Large, who are honor graduates
of honor schools.
(3) Candidates from the enlisted men of the National Guard.
(4) Candidates from the enlisted men of the Regular Army.
The Filipino candidates selected for appointment, unless otherwise
notified by the War Department, shall appear for mental and physical
examination on the second Tuesday in January of each year before a
board of Army officers to be convened at such place in the Philippine
Islands as the commanding general of the Philippine Department may
designate.
=Admission by Examinations.=--On the third Tuesday in March of each
year candidates selected for appointment shall appear for mental and
physical examination before boards of Army officers to be convened at
such places as the War Department may designate.
Each candidate must show by examination that he is well versed in
algebra, to include quadratic equations and progressions, and in plane
geometry, English grammar, composition and literature, descriptive and
physical geography, and general and United States history, as explained
in the circular of notification.
=Admission by Certificate.=--The Academic Board will consider and _may
accept_ in lieu of the regular mental examination:
(1) A properly attested certificate (Form I) that the candidate is
a regularly enrolled student in good standing without condition in
a university, college, or technical school accredited by the United
States Military Academy, provided that the entrance requirements of the
course he is pursuing require proficiency in subjects amounting to not
less than 14 units of the list given below.
If attendance at college extends over a semester, a full record of
academic work at the college, giving subjects taken and grades
attained in each, must accompany the certificate; if attendance at
college extends over less than a semester and the candidate was
admitted to college by certificate, a certificate (Form II) from the
preparatory school giving a full record of studies taken and grades
attained must accompany the college certificate. If a scrutiny of
the certificate submitted shows low grades, the certificate will be
rejected.
A certificate indicating enrollment in or admission to an institution
at any other time than that specified in the college register for
regular admission or enrollment will be not accepted.
(2) A properly attested certificate (Form II) that the candidate has
graduated from a preparatory school or public high school accredited by
the United States Military Academy, provided that he has in his school
work shown proficiency in subjects amounting to not less than 14 units
of the list given below.
If a scrutiny of the certificate submitted shows evidence of low grades
or of graduation at an irregular date, the certificate will be rejected.
(3) A properly attested certificate (Form III) from the College
Entrance Examination Board that the candidate has shown proficiency in
the examinations set by the board in subjects amounting to 14 units
from the list given below. If a scrutiny of the certificate submitted
shows low grades, the certificate will be rejected.
* * * * *
The list of subjects and the corresponding weights in units is as
follows:
(_a_) REQUIRED.
_Every certificate must show evidence of proficiency in the following
subjects._
Units.
Mathematics, A1 1
Mathematics, A2 ½
Mathematics, C 1
English, A 2
English, B 1
Units.
History, A }
History, B }
History, C } any two 2
History, D }
-----
7½
(_b_) OPTIONAL.
_The remaining 6½ units may be supplied from among the following
subjects, and no others._
Units.
Mathematics, B ½
Mathematics, D ½
Mathematics, E ½
Mathematics, F ½
History, A } Any not submitted 1
History, B } among 1
History, C } required subjects 1
History, D } 1
Latin, 1 1
Latin, 2 1
Latin, 3 2
Latin, 4 1
Latin, 5 1
Greek, A1 ½
Greek, A2 ½
Greek, B 1
Greek, C 1
Greek, F 1
French, A 2
French, B Either one 1
French, BC but not both 2
German, A 2
German, B Either one 1
German, BC but not both 2
Spanish 2
Physics 1
Chemistry 1
Biology 1
Botany 1
Physiology 1
Physical geography 1
Drawing 1
-----
35
The definition of unit and of the ground covered by the designated
subjects is that of the College Entrance Examination Board. Credits
must correspond to the unit values of the respective subjects. Greater
credit than indicated will not be allowed; less credit will be
understood as evidence that the entire subject has not been completed.
Certificates should be submitted not later than February 15th. A
certificate received between February 15th and the examination will
receive consideration, but in view of the short time left to the
Academic Board to investigate its value, no assurance will be given
that such certificate can be acted on in time to exempt the candidate
from the mental examination.
Candidates who submit certificates on a date which does not allow the
Academic Board sufficient time to investigate its value and notify
them regarding the final action thereon prior to the day set for the
examination, should proceed with the regular examination.
Candidates who are informed that their certificates have been accepted
must present themselves at the regular time and place as herein
prescribed, for physical examination.
A certificate which is accepted as satisfactory for one examination
will be regarded as satisfactory for any other examination which may be
set for entrance with the same class.
Any certificate accepted for one class, and presented for a succeeding
class, should be accompanied with a full statement of the candidate's
educational work in the interim, and both certificate and statement
will be subject to careful scrutiny by the Academic Board. (Par. 65,
Regs., U. S. M. A.)
All necessary papers, =including a set of blank certificate forms=, are
furnished to each duly nominated candidate by The Adjutant General of
the Army.
_Note._--Certificates will be accepted only from candidates appointed
from States at large, Congressional districts, Territories, and the
District of Columbia.
Certificates may be accepted for admission of candidates from the
Regular Army and National Guard in the same manner as they are accepted
for candidates nominated by Congressmen, except that acceptable
certificates entitle the candidate to appointment only in case the
authorized number of vacancies for that year are not filled by the
regular examination.
=Date of Admission.=--Candidates who fully conform to the requirements
set forth in the preceding paragraphs, and who report in person to
the Superintendent before 10:30 A.M. the second day, Sunday excepted,
following the date of regular graduation, shall be admitted as cadets
of the United States Military Academy, and shall receive their warrants
as soon as practicable.
_Engagement to Serve._--Immediately after reporting to the
Superintendent for admission and before receiving their warrants of
appointment candidates are required to sign in the presence of the
Superintendent, or of some officer deputed by him, engagements for
service in the following form:
I, ---- ----, of the State (or Territory) of ----, aged ---- years,
---- months, do hereby engage (with consent of my parent or guardian)
that from the date of my admission as a cadet of the United States
Military Academy I will serve in the Army of the United States for
eight years unless sooner discharged by competent authority.
In the presence of ---- ----.
In the case of the Filipino cadets the engagement shall be made to
serve in the Philippine Scouts. (See Sec. 1321, R. S.)
_Oath of Allegiance._--Each cadet shall, previous to his admission to
the academy, take and subscribe an oath or affirmation in the following
form:
I, ---- ----, do solemnly swear that I will support the Constitution of
the United States and bear true allegiance to the National Government;
that I will maintain and defend the sovereignty of the United States
paramount to any and all allegiance, sovereignty, or fealty I may owe
to any State, county, or country whatsoever, and that I will at all
times obey the legal orders of my superior officers and the rules and
articles governing the Armies of the United States. (Sec. 1320, R. S.)
Sworn to and subscribed at ---- this -- day of ----, nineteen hundred
and --, before me.
=Qualifications.=--No candidate shall be admitted who is under 17 or
over 22 years of age or less than 5 feet 4 inches in height at the age
of 17, or 5 feet 5 inches in height at the age of 18 and upward, or
who is deformed or afflicted with any disease or infirmity which would
render him unfit for the military service or who has, at the time of
presenting himself, any disorder of an infectious or immoral character.
Candidates must be unmarried.
Each candidate must on reporting at West Point present a certificate
showing successful vaccination within one year; or a certificate of two
vaccinations made at least a month apart, within three months.
_Note._--Candidates are eligible for admission from the day they are 17
until the day they become 22 years of age, on which latter day they are
not eligible.
Each candidate designated as principal or alternate for appointment as
cadet at the Military Academy should ascertain as soon as practicable
whether or not he has any physical defect that would disqualify him for
admission to the academy or any that should be corrected by treatment
previous to presenting himself for examination. For this purpose
he should immediately cause himself to be examined by his family
physician, and, if he desires, also by an Army surgeon at the nearest
military post. Such an examination should enable the candidate to
decide whether to devote the time and possible expense which may be
necessary for preparation for the entrance examination or to relinquish
his appointment.
The presentation by a candidate of his letter of conditional
appointment, or the presentation by a _prospective_ candidate of a
letter signed by a Member of Congress stating that the bearer is to be
a candidate for cadet appointment and requesting that he be physically
examined, will be sufficient authority for an Army surgeon at any
military post to make the desired physical examination. Upon completion
of this examination, the Army surgeon will inform the candidate of the
result, and, in case a disability be found, whether such disability
is believed to be permanent and disqualifying for military service or
whether it is believed to be of a temporary or curable nature. The
examination is to be regarded as preliminary only, and in no manner to
affect the decision of the regular medical examining board.
CHARACTER OF EXAMINATIONS
PHYSICAL EXAMINATION
The physical examination is conducted under the following instructions
prepared by the Surgeon General of the Army: Candidates who, upon
reporting, present evidence that they have been excused from the mental
examination under the provisions of the certificate privilege, or as
the result of having qualified mentally at a previous examination, are
usually examined physically as soon as possible after reporting and are
not required to wait until the schedule of mental examinations has been
completed. The physical examination of all candidates taking the mental
examination begins on the fourth day and is continued daily until
completed.
Hearing must be normal in both ears.
Vision as determined by the official test types must not fall below
20/40 in either eye. If below 20/20, it must be correctable to 20/20 by
proper glasses.
In the record of all examinations the acuity of vision without glasses,
and also with glasses when the acuity is less than 20/20, will be given
for each eye separately; in the latter case the correction will also be
noted.
Hyperopia with vision less than 20/20 and myopia or astigmatism,
either hyperopic or myopic, with vision less than 20/40, are causes for
rejection.
Squint uncorrectable by glasses (not prisms) is a cause for rejection.
Color blindness, red, green, or violet, is cause for rejection.
The foregoing requirements apply to eyes from disease, either acute or
chronic. All lesions of the fundus, except those due to simple myopia,
lesions not progressive in character, whether old or of recent origin,
are causes for rejection.
A certificate from a competent oculist may be accepted at the option of
the examining board, as evidence of freedom from lesions of the fundus.
_Teeth._--A candidate must have at least 12 of the 20 double teeth in
serviceable condition, so placed that 6 of them are "opposed" by 6
others. Where not all of the third molars have erupted and there are
none opposed, 8 serviceable double teeth must be present, so placed
that 4 are opposed by 4 others. Where there are two opposed third
molars, the requirements will be at least 6 double teeth opposed by
6 others. Well crowned teeth are considered as good teeth. Teeth
containing large cavities or exposed nerves are considered as cause
for rejection, but a candidate with unsound teeth may be accepted
subject to the condition of having cavities filled and teeth put in
satisfactory shape before the date set for his entrance to West Point.
The following are causes of disqualification if found to exist to such
a degree as would immediately or at no very distant period impair the
efficiency of the candidate:
1. Feeble constitution; unsound health from whatever cause;
indications of former disease, glandular swellings, or other
symptoms of scrofula.
2. Chronic cutaneous affections, especially of the scalp.
3. Severe injuries of the bones of the head; convulsions.
4. Impaired vision, from whatever cause; inflammatory affections
of the eyelids; immobility or irregularity of the iris; fistula
lachrymalis, etc.
5. Deafness; copious discharge from the ears.
6. Impediment of speech.
7. Want of due capacity of the chest, and any other indication of a
liability to a pulmonic disease.
8. Impaired or inadequate efficiency of one or both of the superior
extremities on account of fractures, especially of the clavicle,
contraction of a joint, deformity, etc.
9. An unusual excurvature or incurvature of the spine.
10. Hernia.
11. A varicose state of the veins of the scrotum or spermatic cord
(when large), hydrocele, hemorrhoids, fistulas.
12. Impaired or inadequate efficiency of one or both of the
inferior extremities on account of varicose veins, fractures,
malformation (flat feet, etc.), lameness, contraction, unequal
length, bunions, overlying or supernumerary toes, etc.
13. Ulcers or unsound cicatrices of ulcers likely to break out
afresh.
The requirements of the following tables of physical proportions are
_minimum for growing youths_ and are for the guidance of medical
officers in connection with the other data of the examination, a
consideration of all of which should determine the candidate's physical
eligibility. Mere fulfilment of the requirements of the standard tables
does not determine eligibility, while on the other hand no departure
below the standard should be allowed unless upon the unanimous
recommendation of the medical examining board for excellent reasons
clearly stated in each case.
The physical requirements should be those of the age at the birthday
nearest the time of the examination. Fractions greater than one-half
inch will be considered as an additional inch of height, but candidates
17 years old must be at least 64 inches, and those 18 years and upward
at least 65 inches in height.
TABLE FOR PHYSICAL PROPORTION FOR HEIGHT, WEIGHT, AND CHEST MEASUREMENT
=========+===========+===========+===============+============
_Age._ | _Height_, | _Weight_, |_Chest_ | _Chest_
| _inches_. | _pounds_. |_measurement_--| _mobility_,
| | |_expiration_, | _inches_.
| | |_inches_. |
---------+-----------+-----------+---------------+------------
{| 64 | 110 | 29 | 2
{| 65 | 112 | 29¼ | 2
{| 66 | 114 | 29½ | 2
{| 67 | 116 | 29¾ | 2
17 yrs. {| 68 | 119 | 30 | 2½
{| 69 | 122 | 30¼ | 2½
{| 70 | 125 | 30½ | 2½
{| 71 | 128 | 30¾ | 2½
---------+-----------+-----------+---------------+------------
{| 65 | 117 | 30¼ | 2
{| 66 | 119 | 30½ | 2
{| 67 | 121 | 30¾ | 2
{| 68 | 124 | 31 | 2½
18 yrs. {| 69 | 127 | 31¼ | 2½
{| 70 | 130 | 31½ | 2½
{| 71 | 133 | 31¾ | 2½
{| 72 | 136 | 32 | 3
---------+-----------+-----------+---------------+------------
{| 65 | 121 | 30¾ | 2
{| 66 | 123 | 31 | 2
{| 67 | 125 | 31¼ | 2
{| 68 | 129 | 31½ | 2½
19 yrs. {| 69 | 133 | 31¾ | 2½
{| 70 | 137 | 32 | 2½
{| 71 | 141 | 32¼ | 2½
{| 72 | 145 | 32½ | 3
{| 73 | 149 | 32¾ | 3
---------+-----------+-----------+---------------+------------
{| 65 | 122 | 31 | 2
{| 66 | 124 | 31¼ | 2
{| 67 | 126 | 31½ | 2
{| 68 | 130 | 31¾ | 2½
{| 69 | 134 | 32 | 2½
20 yrs. {| 70 | 138 | 32¼ | 2½
{| 71 | 142 | 32½ | 2½
{| 72 | 146 | 32¾ | 3
{| 73 | 150 | 33 | 3
{| 74 | 154 | 33¼ | 3½
---------+-----------+-----------+---------------+------------
{| 65 | 123 | 31¼ | 2
{| 66 | 125 | 31½ | 2
{| 67 | 127 | 31¾ | 2
{| 68 | 132 | 32 | 2½
{| 69 | 137 | 32¾ | 2½
21 yrs. {| 70 | 142 | 32½ | 2½
{| 71 | 147 | 32¾ | 2½
{| 72 | 152 | 33 | 3
{| 73 | 157 | 33¼ | 3
{| 74 | 162 | 33½ | 3½
{| 75 | 167 | 33¾ | 3½
---------+-----------+-----------+---------------+------------
{| 65 | 125 | 31½ | 2
{| 66 | 127 | 31¾ | 2
{| 67 | 129 | 32 | 2
{| 68 | 134 | 32¼ | 2½
{| 69 | 139 | 32½ | 2½
{| 70 | 144 | 32¾ | 2½
22 yrs. {| 71 | 149 | 33 | 2½
{| 72 | 154 | 33¼ | 3
{| 73 | 159 | 33½ | 3
{| 74 | 164 | 33¾ | 3½
{| 75 | 169 | 34 | 3½
{| 76 | 174 | 34¼ | 4
---------+-----------+-----------+---------------+------------
The following is a list of the Army posts at which the examination is
usually held:
Fort Banks, Mass.
Fort Slocum, N. Y.
Washington Barracks, D. C.
Jackson Barracks, New Orleans, La.
Fort Shafter, Honolulu, Hawaii.
Columbus Barracks, Ohio.
Fort Williams, Maine.
Fort St. Michaels, Alaska.
Fort Sill, Okla.
Fort Leavenworth, Kans.
Jefferson Barracks, Mo.
Fort Ethan Allen, Vt.
Fort Dade, Fla.
Fort Logan H. Roots, Ark.
Fort Logan, Colo.
Fort Sam Houston, Tex.
Presidio of San Francisco, Cal.
Corozal, Canal Zone.
Fort McPherson, Ga.
Fort Snelling, Minn.
Fort Sheridan, Ill.
Vancouver Barracks, Wash.
Fort Bliss, Texas.
Fort Wm. H. Seward, Alaska.
Fort Rosecrans, Cal.
MENTAL EXAMINATION
The examination takes place as follows, viz.:
1st Day.--Blank for personal and school history to be filled out
by all who report for examination, 11 a.m. to 12,
noon, 1 hour.
History, 1 to 5 p.m., 4 hours.
2d Day.--Algebra, 9 a.m. to 1 p.m., 4 hours.
Geography, 2 to 5 p.m., 3 hours.
3d Day.--Geometry, 9 a.m. to 1 p.m., 4 hours.
English Grammar, Composition, and Literature, 1:30 to
5:30 p.m., 4 hours.
Every candidate who reports is required to fill out, in the most
careful manner, the personal and school history sheet and the autograph
and official notification address blanks. The fact that a candidate may
be reporting for the physical examination only, does not by any means
exempt him from accomplishing these blanks, as the information they
contain is vitally necessary for the permanent and statistical records
of the Military Academy.
The candidate is given all assistance needed to insure the proper
filling out of these papers.
* * * * *
=Algebra.=--Candidates will be required to pass a satisfactory
examination in that portion of _algebra_ which includes the following
range of subjects: Definitions and notation; the fundamental laws; the
fundamental operations, viz.: Addition, subtraction, multiplication,
and division; factoring; highest common factor; lowest common multiple;
fractions, simple and complex; simple or linear equations with one
unknown quantity; simultaneous simple or linear equations with two
or more unknown quantities; graphical representation and solution
of linear equations with two unknowns; involution, including the
formation of the squares and cubes of polynomials; binomial theorem
with positive integral exponents; evolution, including the extraction
of the square and cube roots of polynomials and of numbers; theory of
exponents, radicals, including reduction and fundamental operations,
rationalization, equations involving radicals; operations with
imaginary numbers; quadratic equations; equations of quadratic form;
simultaneous quadratic equations; ratio and proportion; arithmetical
and geometrical progressions. Candidates will be required to solve
problems involving any of the principles or methods contained in the
foregoing subjects.
The following questions were used at a recent examination:
1. (_a_) Simplify [(_x_ - _y_)^2 + 6_xy_] - [(_x_^2 + 2_xy_) -
{_x_^2 - [2_xy_ - (4_xy_ - _y_^2)]} - (-_x_^2 - 2_xy_)].
(_b_) Factor (1) _a_^9_b_^9 + 64_c_^6 (2) _x_^2 - _y_^2 - 2_y_ - 1
(3) _x_^3 - 3_x_^2 + 4.
2. Solve [sqrt]((4/_x_^2) + 5) - [sqrt]((4/_x_^2) - 5) = 2. Prove
that your answers are correct.
3. How many terms will there be in the expansion of (_a_^{⅒} +
_b_^{⅕}×15) by the binomial formula?
Write the 6th term in the simplest form. What other term will have
the same coefficient?
Write down this term and simplify it.
4. A number of workmen, who receive the same wages, earn together
a certain sum. Had there been 7 more workmen, and had each one
received 25 cents more, their joint earnings would have increased
by $18.65. Had there been 4 fewer workmen, and had each one
received 15 cents less, their joint earnings would have decreased
by $9.20. How many workmen are there, and how much does each one
receive?
5. (_a_) Find the value of 5_x_^3 + 2_x_^2 - 3_x_ - 1 when _x_ = 1
- [sqrt](-4)
(_b_) Simplify (5×[sqrt](_x_^{4/3})^{-3/2}
6. Two trains run toward each other from A and B, respectively, and
meet at a point which is 15 miles farther from A than it is from B.
After the trains meet, it takes the first train 2⅔ hours to run to
B, and the second 3⅜ hours to run to A. How far is it from A to B?
{ (1/_a_ + 1/_b_)_x_ + (1/_a_ - 1/_b_)_y_ = 4
7. Solve {
{ _x_/(_a_ + _b_) + _y_/(_a_ - _b_) = 2
8. (_a_) Deduce a test for finding when the roots of the equation
_ax_^2 + _bx_ + _c_ = 0 are: 1º real and unequal; 2º real and
equal; 3º imaginary; 4º numerically equal with contrary signs.
(_b_) Apply the tests to find the nature of the roots of the
equations
1º 3_x_^2 + 4_x_ - 10 = 0
2º 5_x_^2 + 6 = 0
9. Given a square whose side is 2. The middle points of its
adjacent sides are joined by straight lines forming a second
square inscribed in the first. In the same manner, a third square
is inscribed in the second, a fourth in the third, and so on
indefinitely. Find the sum of the perimeters of all the squares.
Substitute for any of the above.--A person has $6,500, which he
divides into two portions and lends at different rates of interest,
so that the two portions produce equal returns. If the first
portion had been lent at the second rate of interest, it would have
produced $180; and if the second portion had been lent at the first
rate of interest, it would have produced $245. Find the rates of
interest.
* * * * *
=Plane Geometry.=--Candidates will be required to give accurate
definitions of the terms used in _plane geometry_, to demonstrate any
proposition of plane geometry as given in the ordinary text-books and
to solve simple geometrical problems either by a construction or by an
application of algebra.
The following questions were used at a recent examination:
1. Theorem: The three medians of any triangle intersect in a common
point which is at two-thirds of the distance from each vertex to
the middle of the opposite side.
2. Theorem: If two triangles have their three sides respectively
equal, the triangles are equal in all respects.
3. (_a_) How many circles can be drawn tangent to three given
straight lines? (_b_) Problem: To draw a circle through a given
point and tangent to two given straight lines.
4. Theorem: If two parallel right lines be divided into
corresponding parts, proportional each to each, and straight lines
be drawn through the corresponding points of division, these
straight lines will pass through a common point.
5. Exercise: Find the locus of all points, the sum of the squares
of the distances of any one of which from two fixed points is equal
to a given square.
6. Problem: Given two circles, to construct a third circle
equivalent to their difference.
7. Exercise: If the radius of a circle is 5, find the area of the
segment subtended by the side of a regular hexagon.
8. Theorem: The areas of two triangles which have an angle of
the one equal to an angle of the other, are to each other as the
products of the sides including those angles.
9. Problem: Through a given point on one side of a triangle to draw
a right line which shall divide the triangle into two equivalent
areas.
Substitute for any one of the above.--(_a_) Define _commensurable
quantities_; _incommensurable quantities_. Give example of each.
(_b_) Theorem: In the same circle or equal circles, two angles at
the centre have the same ratio as their intercepted arcs (whether
commensurable or incommensurable).
* * * * *
=English Grammar.=--Candidates must have a good knowledge of _English
grammar_; they must be able to define the terms used therein; to
define the parts of speech; to give inflections, including declension,
conjugation, and comparison; to give the corresponding masculine and
feminine gender nouns; to give and apply the ordinary rules of syntax.
They must be able to parse correctly any ordinary sentence; giving
the subject of each verb, the governing of each objective case, the
word for which each pronoun stands or to which it refers, the words
between which each preposition shows the relation, precisely what each
conjunction and each relative pronoun connects, what each adjective and
adverb qualifies or limits, the construction of each infinitive, and
generally to show a good knowledge of the function of each word in the
sentence.
They must be able to correct in sentences or extracts any ordinary
grammatical errors.
It is not required that any particular textbook shall be followed; but
the definitions, parsing, and corrections must be in accordance with
good usage and common sense.
The following questions indicate the character of the examination:
1. (_a_) He comes, the herald of a noisy world. (_b_) Next anger
rushed, his eyes on fire. (_c_) Get on your nightgown, lest
occasion call us and show us to be watchers. (_d_) Hark! Hark!
the lark at heaven's gate sings. (_e_) Why do you stay so long,
my lords of France? (_f_) Go you before to Gloucester with these
letters. (_g_) Society has been called the happiness of life. (_h_)
The guardsman defended himself bravely. (_i_) They that reverence
too much old times are but a scorn to the new. (_j_) I will bring
you certain news from Shrewsbury.
In the above sentences pick out the following grammatical
constructions. (Indicate the number of the sentence and write the
word or words which answer the question.)
Imperative mood. Abstract noun. Transitive verb. Two relative
pronouns. Noun in apposition. Verb in subjunctive mood. Adverb of
manner. Relative pronoun. Indirect object. Interjection.
2. Write a simple sentence containing a compound subject. Write a
simple sentence containing a compound predicate. Write a complex
sentence containing an adjective clause. Write a complex sentence
containing an adverbial clause of manner. Write a sentence
containing a preposition with a compound object. Write a sentence
containing an adverb clause of time. Write a sentence containing a
noun (or substitute) clause used as the subject of the sentence.
Write a complex sentence containing an adverb clause of place.
Write a sentence containing an adjective phrase, and an adverb
phrase. Write a sentence containing a verb in the passive voice.
3. Write sentences containing the following: The preterite (or
past) tense (active voice) of the verb "choose." The perfect tense
(active voice) of the verb "swim." The pluperfect (or past perfect)
tense (active voice) of the verb "burst." The future perfect tense
(active voice) of the verb "eat." The perfect tense (active voice)
of the verb "know." The present participle of the verb "lie." The
perfect infinite of the verb "study." The perfect participle of
the verb "knock." The future tense, passive voice, of the verb
"defeat." The future perfect tense, passive voice, of the verb
"pay."
4. In the passage below, indicate the gender of all the nouns and
pronouns by the following device: Underscore once those that are
masculine; twice those that are feminine; thrice all those that are
neither.
"The bride kissed the goblet, the knight took it up.
He quaffed off the wine, and he threw down the cup,
She looked down to blush, and she looked up to sigh,
With a smile on her lips and a tear in her eye.
He took her soft hand ere her mother could bar,--
'Now tread we a measure!' said young Lochinvar.
So stately her form and so lovely her face,
That never a hall such a galliard did grace;
While her mother did fret, and her father did fume,
And the bridegroom stood dangling his bonnet and plume;
And the bride-maidens whispered, ''Twere better by far,
To have matched our fair cousin with young Lochinvar.'"
5. Write sentences containing the following: An auxiliary verb.
The comparative of "recent." The superlative of "bad." The plural
of "lily." The masculine of "witch." An intransitive verb. A
collective noun. The comparative of "lazy." The plural of "shelf."
The plural of "ruby."
6. Parse the words in italics in the following sentences: "Some
soils, _like_ the rocky tract _called_ the Estabrooke Country in
_my_ neighbourhood, is so suited to the apple, that it will grow
_faster_ in _them without any_ care, _than_ it _will_ in many
places with any amount of _care_."--Henry D. Thoreau.
7. Correct all errors in the following: The man who committed the
murder was hung. Who can this letter be from? It is me that he
fears. The red rose smells sweetly, but the yellow one does not
smell so good. He asked if either of the men could identify their
own clothing.
8. Punctuate and capitalize the following: it was old dr parr who
said or sighed in his last illness oh if i can only live till
strawberries come the old scholar imagined that if he could weather
it till then the berries would carry him through no doubt he had
turned from the drugs and the nostrums or from the hateful food
to the memory of the pungent penetrating and unspeakably fresh
quality of the strawberry with the deepest longing the strawberry
is always the hope of the invalid and sometimes no doubt his
salvation it is the first and finest relish among the fruits and
well merits dr botelers memorable saying that doubtless god could
have made a better berry but doubtless god never did john burroughs.
* * * * *
=English Composition and English Literature.=--Candidate will be
required:
1. By the writing of short themes on subjects chosen by themselves
within limits set by the examination paper, to prove (_a_) their
ability to spell, capitalize, and punctuate, and (_b_) their mastery of
the elementary principles of composition, including paragraphing and
sentence structure.
2. To give evidence of intelligent acquaintance with three plays of
Shakespeare--one comedy, one history, and one tragedy--_The Merchant of
Venice_, _Henry V_, and _Macbeth_ being especially recommended.
3. To exhibit a fair knowledge of the history of English literature and
of the names of the most prominent authors, and of the names of their
principal works.
The general character and scope of the examination are indicated by the
following:
1. In a few paragraphs (about 250 words) tell the most important
facts about the life and works of any _one_ of the following
authors: Robert Burns, John Milton, John Keats, Edgar Allan Poe,
Alfred Tennyson, Charles Dickens.
2. In a paragraph (about 250 words) discuss the Victorian period in
English literature, paying attention to the following points: (_a_)
the characteristics of the literature, (_b_) the chief writers,
both in prose and poetry.
3. In a few paragraphs (about 250 words) discuss the Puritan period
in English literature, telling what is meant by the term, the
object and results of the Puritan movement, the chief writers with
their works, and the main characteristics of the literature.
4. Elective question (may be chosen in place of either 2 or
3). Write a few paragraphs (250 words) on the characteristics
and importance of the works of the Concord writers, Emerson,
Hawthorne, and Thoreau, mentioning the chief works of each.
5. Write two compositions of about 200 words each selecting your
subjects from the following list: (_a_) The story of the chase.
(Lady of the Lake--Scott.) (_b_) Silas Marner's Early Life. (Silas
Marner--George Eliot.) (_c_) The Story of Jessica. (Merchant of
Venice--Shakespeare.) (_d_) The Character of Brutus. (Julius
Caesar--Shakespeare.) (_e_) The Story of Ida and the Prince. (The
Princess--Tennyson.) (_f_) The Trial of Rebecca. (Ivanhoe--Scott.)
(_g_) The Murder of Duncan. (Macbeth--Shakespeare.) (_h_) Character
Sketch of the Ancient Mariner. (The Ancient Mariner--Coleridge.)
(_i_) Threshing Day on a Western Farm. (_j_) The Village Drug
Store. (_k_) Along the Wharves in a Seaport Town. (_l_) An
Irrigated Farm. (_m_) A Cotton Mill. (_n_) An Accident.
* * * * *
=Geography.=--Candidates will be required to pass a satisfactory
examination in _descriptive geography_ and the elements of _physical
geography_. A preponderance of weight is attached to a knowledge of the
geography of the United States.
In descriptive geography of the United States, candidates should be
thoroughly informed as to its general features and boundaries; adjacent
oceans, seas, bays, gulfs, sounds, straits, and islands; lakes, the
location and extent of mountain ranges; the sources, directions, and
terminations of the important rivers, the names of their principal
tributaries, and at what points, if any, these rivers break through
highlands on their way to the ocean; the water routes of communication
from one part of the country to another; the location and termination
of important railroad lines; the boundaries of the several States and
Territories and their order along the coasts, frontiers, and principal
rivers; the location and boundaries of the island possessions; and the
names and locations of the capitals and other important cities of the
several States, Territories, and island possessions.
In short, the knowledge should be so complete that a clear mental
picture of the whole of the United States is impressed on the mind of
the candidate.
In descriptive geography of other countries, candidates should be
familiar with the continental areas and grand divisions of water; the
earth's surface; the large bodies of water which in part or wholly
surround the grand divisions of the land; the capes, from what part
they project and into what waters; the principal peninsulas, location,
and by what waters embraced; the parts connected by an isthmus; the
principal islands, locations, and surrounding waters; the seas, gulfs,
and bays, the coasts they indent, and the waters to which they are
subordinate; the straits, the lands they separate, and the waters
they connect; the locations of the principal lakes, the locations,
boundaries, capitals and principal cities of the political divisions of
the world.
In physical geography, candidates should be familiar with the relief
of the earth's surface; the principal mountain systems, the river
systems and watersheds; the coastal and lake plains; and the influence
of climate, soil, mineral deposits, and other physical features on
the resources, industries, commercial relations, and development of a
country and its people, especially of the United States.
The following questions indicate the character of the examination:
1. Define. (_a_) Geography, (_b_) Physical Geography, (_c_) strait,
(_d_) isthmus, (_e_) isotherm.
2. In respect of climate, into what zones is the earth's surface
divided? Name the circles separating these zones from one another.
In what zone are the Philippines?
3. (_a_) What and where is the International Date Line? (_b_) In
going from San Francisco to Manila is a day lost or gained? Give
reasons for answer.
4. How many "times" has the United States! What are they?
5. What waters surround the United States?
6. Is it possible to go from Duluth to Detroit by water? If so,
what bodies of water would be passed through?
7. Name the larger islands of the Philippines, and of the Hawaiian
Group, respectively. On what island is Manila? Honolulu? Iloilo?
8. Name two great coal regions of the United States.
9. What is (_a_) the most northern State of the United States?
(_b_) the most southern? (_c_) the most eastern? (_d_) the most
western?
10. Which of the United States has the longest coast line?
11. Where is the Mohawk Valley?
12. Bound--Michigan, Kentucky, Connecticut.
13. Locate accurately the following cities--El Paso, Albany,
Zamboanga, Panama, San Antonio, Kalamazoo.
14. Name the transcontinental railways west of the Mississippi in
order from north to south.
15. Name the countries of Central America. Which one of these
borders on Mexico?
16. Name in order, beginning at the Isthmus of Panama, the
countries of South America that touch on the Caribbean Sea and the
Atlantic Ocean.
17. The meridian through Atlanta, Georgia, intersects what South
American Republics? Is the continent of South America, as a whole,
east or west of the United States?
18. What two countries of South America have no sea coast?
19. A vessel goes from London, England, to San Francisco by the
Suez Canal. Through what waters does it pass?
20. What waters connect the Black Sea with the Mediterranean? The
Gulf of Aden with the Red Sea?
21. Where does the Danube rise? through what countries does it
flow? and where does it empty?
22. What three rivers flow north into the Arctic from Siberia?
23. What mountains lie between France and Spain? Between Tibet and
India?
24. Name in order in a clockwise direction the countries bordering
on the Mediterranean.
25. Where is--Mount Shasta, Popocatepetl, Chimborazo, Everest, Apo,
Fujiyama, Blanc, Mayon.
26. Where and what is--Mukden, Valdivostok, Liberia, Melilla, The
Celebes.
27.--Locate--Elba, Saint Thomas, Cape Race, Hankow, Formosa, Bonin
Islands, Juraez, Zanzibar, Colon, Volga River, Elbe River, Cebu,
Seville, Andalusia, Zaragoza, Macedonia, Nepaul, Bogota, Beirut,
Malta, Macao, Dublin.
28. Name the capitals respectively of--Afghanistan, Portugal,
Nebraska, Vermont, French Indo-China, Philippine Islands,
Montenegro, Georgia, Oregon, Roumania, Persia, Florida, Java.
* * * * *
=History.=--Candidates must be thoroughly familiar with such material
as is contained in good high school textbooks on the subject (_a_) of
the History of the United States, and (_b_) of the History of Europe
from the Fall of Constantinople (1453) to the outbreak of the French
Revolution (1789).
In history of the United States, the examination will include questions
concerning early discoveries and settlements; the forms of government
in the Colonies; the causes, leading events, and results of wars;
important events in the political and economic history of the Nation
since its foundation.
In history of Europe from 1453 to 1789, special emphasis will be laid
upon the political and social development in France, Prussia, and
England.
The following questions indicate the character of the examination:
European History (1453-1789).
1. Describe political conditions during the latter half of the
fifteenth century in what is now Germany.
2. What countries were ruled by Charles V of Spain at the height of
his power?
3. Why was Luther summoned to the Diet of Worms? What was done at
this Diet?
4. Who was Melanchthon? What was the Religious Peace of Augsburg?
What was its importance?
5. What was the Council of Trent? Over how long a period did its
meetings extend? What were the important acts of this Council?
6. What ruler was instrumental in separating England from Roman
Catholic influence? How was this separation accomplished? Describe
two acts of Parliament important in this connection.
7. Outline the causes of Elizabeth's quarrel with Mary Queen of
Scots. State its political importance and its results.
8. Under what circumstances during Elizabeth's reign did England
come into conflict with Spain? What event marked the crisis of this
conflict?
9. State the nature, causes, dates, and leaders of the Puritan
Reformation.
10. Describe the important acts of Parliament passed in the reign
of Charles II to regulate the religious situation.
11. Describe the court and court life in France in the time of
Louis XIV. Name five prominent men connected with Louis XIV's court.
12. What part did Gustavus Adolphus and Richelieu play in the
Thirty Years' War? How may we reconcile Richelieu's political acts
with his religious convictions?
13. What nations were engaged in the War of the Spanish Succession?
What issues were at stake? What were the important provisions of
the Peace of Utrecht (1713)?
14. What was the revolution of 1688 in England? How was it
accomplished?
15. What is meant by the cabinet system of government? Account for
the advance of cabinet government in the reigns of George I and
George II.
16. For what qualities and what acts was the Great Elector
(Frederick William of Prussia) noted?
17. State the cause and the result of the first war between
Frederick the Great and Maria Theresa. Name two famous battles of
the Seven Years' War in which Frederick the Great was victorious.
18. State the results of the Seven Years' War for France according
to the provisions of the Treaty of Paris (1763).
19. Why were Frederick the Great, Catherine II of Russia, and
Joseph II of Austria called "enlightened despots"? Describe the
work of any one of these rulers.
20. Outline two of the fundamental causes for the unrest in France
during the early years of the reign of Louis XVI.
* * * * *
1. State concisely the achievements of--(_a_) De Narvaez; (_b_) De
Soto; (_c_) Hudson; (_d_) La Salle.
2. (_a_) Where and when was the first permanent English settlement
in America made? (_b_) What arrangement was made for the government
of this settlement?
3. (_a_) When and where did the first colonial assembly in America
meet? (_b_) What was Bacon's Rebellion? (_c_) When and where was
the first permanent English settlement in New England established?
4. (_a_) What brought the first settlers to Maryland? (_b_) Who was
their leader?
5. (_a_) What was the immediate cause of the Revolutionary War?
(_b_) What were "writs of assistance"? (_c_) What was the "Mutiny
Act"?
6. (_a_) When and where did the first Continental Congress meet?
(_b_) What was accomplished by this Congress? (_c_) Name the
original thirteen colonies.
7. (_a_) Who were the principal leaders in the two battles of
Saratoga? (_b_) What were the effects on the American people of
these battles? (_c_) What was the Wyoming Massacre?
8. (_a_) What European country was the first to acknowledge the
American independence? (_b_) In what ways did this country aid in
bringing the Revolutionary War to a successful close?
9. State the significance of the following in United States
history: (_a_) Shays' Rebellion; (_b_) Steuben; (_c_) Alien and
sedition laws; (_d_) Kosciusko.
10. (_a_) What were the causes of the war with England in 1812?
(_b_) What treaty ended this struggle? (_c_) Who was President of
the United States during this war?
11. By what means, from whom, and during whose Presidency were
the following territories obtained for the United States? (_a_)
Louisiana, (_b_) Florida, (_c_) Alaska.
12. (_a_) What was the "Spoils System"? (_b_) What was the
Nullification ordinance passed by South Carolina in 1832?
13. Discuss briefly the nature and importance of the following:
(_a_) The Wilmot Proviso. (_b_) The Dred Scott Decision. (_c_) The
Fugitive Slave Law.
14. Name the commanders and the results of the following battles:
(_a_) Vicksburg, (_b_) Fredericksburg, (_c_) Cold Harbor.
15. Name the Presidents of the United States who have had a second
term of office.
16. (_a_) What various causes underlay the declaration of war
against Spain? (_b_) What important battles on land and sea were
fought during the Spanish-American War? (_c_) What treaty ended
this war and what territory was ceded to the United States as a
result of it?
PHYSICAL EXAMINATION
All cadets are examined physically in May of each year, and those
found physically disqualified to continue with the course, or, in case
of the first class, for commission in the Army, are discharged.
VACATIONS AND LEAVES OF ABSENCE
Academic duties are suspended from the completion of the June
examinations until the end of August. During this period cadets live in
camp and are engaged in military duties and exercises and in receiving
practical instruction in military and other subjects. Academic duties
are also suspended from December 24th until January 2d, except for
those undergoing examination. All duties and exercises, as far as
practicable, are suspended on New Year's Day, February 22d, May 30th,
July 4th, Thanksgiving Day, and Christmas Day.
Cadets of the first, second, and third classes not undergoing
examination are allowed short leaves at Christmas, if their conduct
during the preceding year has been satisfactory. Excepting these short
leaves for good conduct, cadets are allowed but one leave of absence
during the four years' course. This leave is granted to those cadets
who have successfully completed the third-class course of study, and
extends from the middle of June to the 28th of August.
PAY OF CADETS
The pay of a cadet is $600 per year and one ration per day, or
commutation therefor at 30 cents per day. The total is $746.00 to
commence with his admission to the academy. The actual and necessary
traveling expenses of candidates from their homes to the Military
Academy are credited to their accounts _after_ their admission as
cadets.
No cadet is permitted to receive money, or any other supplies, from
his parents, or from any person whomsoever, without the sanction of
the Superintendent. A _most rigid_ observance of this regulation is
urged upon all parents and guardians, as its violation would make
distinctions between cadets which it is the especial desire to avoid;
the pay of a cadet is sufficient for his support.
Candidates are authorized to bring with them the following articles:
Hairbrush, nailbrush, toothbrush, shoebrush, comb, 8 drawers (summer),
12 handkerchiefs (white), 4 nightshirts or pajamas, 8 socks (black
cotton), 6 bath towels, 6 face towels, 1 trunk, 8 undershirts (summer),
whisk broom, shaving mug, winter underwear, and athletic uniforms,
shoes, and goods.
Cadets are required to wear the prescribed uniform. All articles of
their uniform are of a designated pattern, and are sold to cadets at
West Point at regulated prices.
DEPOSIT PRIOR TO ADMISSION
Immediately after admission candidates must be provided with an outfit
of uniform, etc., the cost of which is about $160. This sum, or at
least $100 thereof, _must be deposited with the treasurer of the
academy before the candidate is admitted_. It is best for the candidate
to take with him no more money than he needs for traveling expenses and
for his parents to send the required deposit by draft, payable to the
Treasurer, United States Military Academy. The deposit is credited at
once to the cadet's account. Upon graduation a cadet who has exercised
proper economy will have sufficient money to his credit with the
treasurer of the academy to purchase his uniform and equipment as an
officer.
PROMOTION AFTER GRADUATION
The attention of applicants and candidates is called to the following
provisions of an Act of Congress approved May 17, 1886, to regulate the
promotion of graduates of the United States Military Academy:
That when any cadet of the United States Military Academy has gone
through all its classes and received a regular diploma from the
academic staff, he may be promoted and commissioned as a second
lieutenant in any arm or corps of the Army in which there may be a
vacancy and the duties of which he may have been judged competent to
perform; and in case there shall not at the time be a vacancy in such
arm or corps he may, at the discretion of the President, be promoted
and commissioned in it as an additional second lieutenant, with the
usual pay and allowances of a second lieutenant, until a vacancy shall
happen.
ACADEMIC DUTIES
There axe two terms of academic instruction: September 1-December
23, and January 2-June 4. A semiannual examination is held December
26-31, and an annual examination June 5-12. At the December examination
cadets, who are found to be proficient in subjects they have completed
during the preceding term are arranged according to merit in each
subject. At the June examination they are similarly arranged and they
are also assigned general standing in the class as determined by their
standings in the various subjects. When a subject of study is completed
during a term an examination concluding the work in that subject is
sometimes held. Cadets deficient in studies at any examination are
discharged from the academy unless for special reasons the academic
board recommends otherwise. Cadets exceeding at any time the maximum
number of demerits allowed for six months are reported to the academic
board as deficient in conduct.
THE ACADEMIC CALENDAR
First term, September 1-December 23.
Second term, January 2-June 4.
Semiannual examination, December 26-31.
Annual examination, June 5-12.
DEPARTMENT OF TACTICS
ALL CLASSES
New cadets, upon reporting for duty, are given infantry recruit
instruction, with gymnastic and calisthenic exercises, until they join
the battalion.
Practical instruction is given during the summer encampment, and from
September 1st to November 1st, and from March 15th to June 1st, in
infantry, artillery and cavalry drill regulations, in target practice
with the rifle, revolver, mountain gun and field gun, and in military
engineering.
During the summer encampment, cadets of the third and fourth classes
are also taught swimming and dancing, and those of the first
class, the service of seacoast artillery and submarine defense at
fortifications. The first, third, and fourth classes participate in
exercises in minor tactics, practice marches, problems and practical
field work, in which the employment of all arms is exemplified.
Practical instruction in fencing and gymnastic exercises and in boxing
and wrestling is given to the fourth class from October 1st to June
1st, and to the other classes from November 1st to March 15th.
Instruction in riding is given to the first class during the encampment
and from September 1st to June 1st, excepting the month of February;
to the second and third classes, from November 1st to March 15th and
also to the third class during the summer encampment. Instruction with
English pad saddles is given to the first class, and in polo to the
first and second classes.
During the academic season recitations in hippology are held for the
first class and in drill regulations for the second, third, and fourth
classes. Instruction is also given in writing orders and in solving
problems involving the disposition of small forces.
Previous to graduation, lectures are given the first class upon
uniforms and equipments, and upon etiquette and customs of the service.
TEXTBOOKS
Infantry Drill Regulations, U. S. Army.
Field Artillery Regulations, U. S. Army.
Mountain Artillery Drill Regulations, U. S. Army.
Cavalry Drill Regulations, U. S. Army.
Elements of Hippology. Marshall.
Coast Artillery Drill Regulations, U. S. Army.
BOOKS OF REFERENCE
U. S. Army Regulations.
Field Service Regulations, U. S. Army.
Small Arms Firing Manual, U. S. Army.
Drill Regulations for Machine Gun, Infantry.
Drill Regulations for Machine Gun, Cavalry.
Manual of Interior Guard Duty, U. S. Army.
Manual of Physical Training, U. S. Army.
Regulations for Field Maneuvers, U. S. Army.
Manual of Instruction for Pack Transportation.
Regulations, U. S. M. A.
ISSUED TO FIRST CLASS BEFORE GRADUATION
U. S. Army Regulations.
Regulations for the Uniform of the U. S. Army.
Manual of Courts-Martial, U. S. A.
Army Register, U. S.
Engineer Field Manual.
DEPARTMENT OF CIVIL AND MILITARY ENGINEERING
FIRST CLASS
The course in civil and military engineering and the art of war is
confined to the first-class year.
The course in civil engineering begins September 1st and is completed
during the first term, which closes with the Christmas holidays. It
comprises brief treatises on the mechanics of civil engineering, framed
and masonry structures, the materials of engineering, water supply, and
sewerage.
The course in military engineering and the art of war begins on January
2nd and closes on the 3rd of June. Military engineering embraces the
study of field and permanent fortifications and siege works. The art
of war embraces the study of the organization of armies, employment
of the different arms in combination, logistics, and strategy. To
familiarize the students with its principles, lectures are delivered on
military subjects and the principal operations of about twenty selected
campaigns are studied. During this course the students are taken to
the battlefield of Gettysburg to familiarize them with the effects of
topography on the employment of troops in the field.
TEXTBOOKS
Civil Engineering. Fiebeger.
Field Fortifications. Fiebeger.
Permanent Fortifications. Fiebeger.
Elements of Strategy. Fiebeger.
Army Organization. Fiebeger.
Siege Works. Mercur.
Field Service Regulations, U. S.
Campaign of Gettysburg. Fiebeger.
BOOKS OF REFERENCE
Campaigns and Battles. Department.
Story of the Civil War. Ropes. Cambria Steel.
The department has a well selected reference library on civil
engineering, military engineering, and the art of war.
DEPARTMENT OF NATURAL AND EXPERIMENTAL PHILOSOPHY
SECOND CLASS
The course in natural and experimental philosophy begins with and
continues throughout the third academic year. Mechanics is studied
during the first term. The text used is Gordon's _Mechanics_. Many of
the principles are illustrated by apparatus in the lecture and section
rooms, and the students are required to repeat and explain these
experiments. The course aims to be as complete as possible with the
limitation that it can be properly covered in a term of about 90 to 100
days by students having a proficient knowledge of the calculus; the
treatment is sufficiently mathematical to furnish a confident basis for
advanced work in the technical staff after graduation.
During the second term about 120 lessons are allotted to this
department. The first half of this time is devoted to the subjects of
sound and light. The authorized textbook is Gordon's _Sound and Light_.
Astronomy is studied in the remainder of the second term. The text used
are Young's _General Astronomy_ and Michie and Harlow's _Practical
Astronomy_. The principal aim of this course, in addition to its
important value in educational development, is to furnish an ample
basis for the establishment of stations in explorations and surveys.
The class attends daily throughout the year, except eight days, during
which half the class attends daily.
TEXTBOOKS
Sound and Light. Gordon.
Mechanics. Gordon.
General Astronomy. Young.
Practical Astronomy. Michie and Harlow.
Numerous standard works on the general subjects covered by the course
are available for reference.
DEPARTMENT OF MATHEMATICS
THIRD AND FOURTH CLASSES
The course in mathematics begins with the fourth-class year and
continues through the third-class year.
In the fourth-class year, algebra is completed in alternation; first
with geometry, then with trigonometry. Plane analytical geometry is
begun.
In the third-class year, plane and solid analytical geometry and
descriptive geometry are completed in alternation. The calculus and
least squares finish the course.
The course in algebra covers the entire subject as generally taught
in colleges, but the student is expected to have already mastered
elementary algebra to include the progressions and the solution of the
quadratic equation. The course in elementary geometry includes the
books that relate to the plane and those that relate to space, but the
student is expected to have mastered the former. Plane and spherical
trigonometry includes the complete solution of the plane and spherical
triangles. The course in analytical geometry includes the discussion
of the general equation of the second degree in the plane and the
particular forms of the equation of the second degree in space.
Descriptive geometry includes the orthographic projections of the right
line, the plane, ruled surfaces and surfaces of revolution, tangent
planes and intersections of surfaces. It also takes the subjects of
shades and shadows, perspective, isometric projections and spherical
projections.
The course in differential and integral calculus covers the ground of
the usual college textbook, including briefly the subject of ordinary
differential equations.
TEXTBOOKS
Elements of Geometry. Phillips and Fisher.
Advanced Course in Algebra. Wells.
Quadratics and Beyond. Fisher and Schwatt.
Elements of Plane and Spherical Trigonometry. Crockett.
Logarithmic Tables. Newcomb.
Conic Sections, Coördinate Geometry. C. Smith.
Coördinate Geometry. Fine and Thompson.
Elements of Analytical Geometry (Solid). Smith and Gale.
Descriptive Geometry. Church.
Linear Perspective. Pillsbury.
Differential and Integral Calculus. Granville.
Integral Calculus. D. A. Murray.
Differential Equations. D. A. Murray.
Method of Least Squares. Johnson.
DEPARTMENT OF CHEMISTRY, MINERALOGY AND GEOLOGY
SECOND CLASS
This department embraces two branches of physics not included in its
title, namely heat and electricity.
The course begins September 1st of the third academic year and extends
throughout this year; exercises, recitations, laboratory work or
lectures take place on all week days.
Commencing September 1st, general chemistry, alternating with lessons
in heat, occupy the time until the close of the term in December,
recitations or other exercises being had daily.
During this term all members of the class whose progress, as shown
by their recitations, warrants it, are given laboratory practice
in chemistry. This practice begins with chemical manipulations and
proceeds in the usual general order of elementary laboratory work.
The laboratory exercises are one hour and fifty minutes long. It is
generally possible to give all parts of the class some laboratory
experience; the amount of this work, however, varies with the aptitude
of the student from a few hours to forty-five or fifty hours.
This term closes with an examination upon the essential parts of
the entire course, which all cadets who have not shown a required
proficiency in daily work must take.
In chemistry the course is a descriptive general one, based upon
a concise statement of the more essential principles of chemistry,
and includes that class of information deemed most important to
non-specialists, together with an accurate and logical treatment of
many useful applications of chemistry.
The course in heat is short, but it is a comprehensive elementary
course intended to embrace what is most applicable to subsequent work
at the academy and what is most useful in general education.
Beginning January 2d the daily exercises alternate between geology,
mineralogy, and electricity. This term also closes with an examination,
covering the essential parts of the subjects studied during the term,
which all cadets who have not shown a required proficiency in daily
work must take.
The course in geology is a brief but scientific presentation of the
essential elements of this branch of science.
The mineralogy is an eminently practical course consisting of the
descriptive study and the practical determination of the important
minerals. The lithological and palæontological part of geology is
accompanied in study by the continued practical examination of the
objects described.
The course in electricity is a brief exposition of the leading
electrical phenomena and their relations to each other. It includes
a study of the general principles of the subject and of the typical
machines, generators, motors and transformers, together with the more
important uses of electricity. The laboratory exercises give experience
with a number of the machines and in the use of a great variety of
apparatus employed in the numerous forms of electric measurements. In
this term the laboratory work is a part of the electrical course and
all cadets enter the laboratory. All laboratory work is performed under
the immediate supervision of an instructor.
TEXTBOOKS
Elementary Lessons in Heat. Tillman.
Descriptive General Chemistry. Tillman.
Practical Chemistry. (Laboratory Guide.) Clowes.
Elements of Geology. Le Conte.
Important Minerals and Rocks. Tillman.
Elements of Electricity. Robinson.
During all terms standard works on the respective subjects are
available for reference both to cadets and instructors.
DEPARTMENT OF DRAWING
THIRD AND SECOND CLASSES
The course in drawing extends through the third- and second-class
years, attendance on alternate afternoons for a period of two hours
during the full academic year.
The order of instruction is as follows:
_Third Class Year_
1. Use of drawing instruments.
2. Problems in plane geometry.
3. Problems in descriptive geometry.
4. Lettering. Exercises in this subject continue throughout the
course.
5. Building construction drawing.
6. Isometric and oblique projection.
_Second Class Year_
1. Elementary problems in third angle projection.
2. Machine drawing, third angle projection.
3. Assembly and working drawings from models.
4. Topographical sketching and drawing.
Instruction is mainly through a loose-leaf system of printed
instruction sheets covering the various drawings and phases of the
work. These are supplemented by short section-room lectures and
blackboard illustrations when necessary. Personal instruction is given
when needed.
DEPARTMENT OF MODERN LANGUAGES
THIRD, SECOND, AND FIRST CLASSES
The course in modern languages comprises instruction in French and in
Spanish.
FRENCH
THIRD CLASS
Instruction is given in reading, in composition, and in conversation.
The course opens September 1st, and continues until June 4th, some 219
lessons in all.
SPANISH
SECOND AND FIRST CLASSES
Instruction is given in reading, in composition, and in conversation,
to which special attention is paid.
The course opens October 4th, of the second-class year and closes June
4th of the first-class year, 176 lessons all told.
The present textbooks are:
THIRD CLASS
French:--Martin's French Verbs.
Grammar. Essentials of French, François.
Elements of French Pronunciation, Jacobs. Bercy's La Langue
Française.
Introductory French Prose Composition, François. Mérimée's Colomba.
About's Roi des Montagnes.
Marchand's French Idioms. L'Illustration. Lecture pour Tous.
Labiche and Martin's Voyage de M. Perrichon.
Daudet's Lettres de Mon Moulin.
Rostand's Cyrano de Bergerac.
Pattou's Causeries en France.
French Conversation Exercises. Military Reading.
Dupont's En Campagne.
SECOND AND FIRST CLASS
Spanish:--Spanish Grammar, Olmsted and Gordon. A Spanish Reader,
Bramby.
Crawford's Spanish Composition.
A Trip to South America--Waxman.
Por Esos Mundos, monthly, published in Madrid.
"A B C," Spanish Daily Newspaper.
Spanish Conversation and Idioms, Department of Modern Languages, U.
S. M. A.
Scientific and Technical Spanish Reader, Willcox.
Lecturas Modernas--Charles Alfred Downer.
BOOKS OF REFERENCE
French:--Cassell's French Dictionary.
Military Technical Dictionary. Willcox.
Spanish:--New Spanish-English and English-Spanish Dictionary, by
Cuyás. Appleton.
DEPARTMENT OF LAW
FIRST CLASS
The course in law, which is carried throughout the entire first-class
year, embraces the following subjects:
1. Elementary Law.
2. Constitutional Law.
3. International Law.
4. Military Law.
5. The Law of War.
The quiz method of instruction is employed in the section room. The
authorized textbooks are supplemented from time to time by means of
lectures, and important principles are emphasized by requiring an
examination and analysis of a considerable number of leading cases.
Some time is also devoted to library work, with a view to familiarizing
students with the use of a law library in the solution of practical
questions. The purpose in view in the course is to give the student an
elementary knowledge of the fundamental principles of law, with special
emphasis upon those subjects a knowledge of which is essential to the
proper understanding of his obligations and duties as a citizen and as
an officer of the Army.
TEXTBOOKS
Elements of Law. Davis, G. B.
International Law. Davis, G. B.
Constitutional Law. Davis, E. G.
Military Law. Dudley.
BOOKS OF REFERENCE
The department has a law library of about 2,500 volumes, accessible to
cadets.
DEPARTMENT OF PRACTICAL MILITARY ENGINEERING, MILITARY SIGNALING AND
TELEGRAPHY
FOURTH, THIRD, AND FIRST CLASSES
_Fourth Class._--This class is given an elementary course in the theory
and practice of surveying, instruction in this subject alternating
with mathematics during the last 66 recitation days of the academic
year. From May 1st to June 4th the entire morning is devoted to
practical instruction in the methods of surveying and in the use and
adjustment of instruments. During this period cadets apply in the
field the principles and methods taught them in their theoretical
study of the subject. The course includes instruction in the use of
chains and tapes, in profile and differential leveling and in earthwork
computations, in the use of compass, plane table, transit and stadia
with special reference to the employment of these instruments in
military topographic surveying. The slide rule used to facilitate the
work of computation, and the principles upon which it is based are
discussed during the theoretical course.
_Third Class._--During the period of the summer encampment the
cadets of this class receive practical instruction in military field
engineering and military signaling. The course in field engineering
comprises knots and lashings, rowing, construction of floating bridges
with wooden pontoons, canvas pontoons and rafts, and instruction in
military camp expedients. The course in signaling is limited to visual
means only, including the flag, the heliograph, and the acetylene
lantern. The International Morse Code is applied in the transmission of
short messages both plain and cypher.
Simple exercises in topographic and hydrographic surveying are also
given.
_First Class._--During the summer months cadets of the first class are
instructed in military reconnaissance and map making. This work follows
close upon the fundamental instruction in the same subject given in
the Department of Drawing, extends the instruction in sketching to
include road and position sketching, mounted and on foot, individual
and combined. Demonstrations and limited instruction are given in the
various processes of map reproduction.
In the fall instruction is given in all classes of improvised bridges
and stream crossing, the use of cordage and tackle, erection of
derricks, flagpoles, etc., and the use of explosives in military
demolitions.
The spring course is on field fortification work including the
principles of locating, tracing, and profiling field works, the
construction of trenches, revetments, obstacles, head cover, splinter
and bomb proofs. This instruction is arranged in a progressive series
of exercises, resulting finally in the construction of a section of a
simple infantry redoubt.
Military signaling is taught this class in both the fall and spring
periods; the work covers the construction and operation of field-wire
and buzzer lines and the radio-communication equipment.
TEXTBOOKS
Theory and Practice of Surveying (17th Edition).--Johnson--Smith.
BOOKS OF REFERENCE
Plane Surveying. Tracy.
The Engineer Field Manual. Office of the Chief of Engineers, U. S.
A.
Signal Book, U. S. Army. Office of Chief Signal Officer, U. S. A.
The Slide Rule. Alexander. The Slide Rule. Clark.
DEPARTMENT OF ORDNANCE AND GUNNERY
FIRST CLASS
The subject of ordnance and gunnery is studied by the cadets of the
first class throughout the academic year.
The course of instruction covers the principles involved in the
construction and use of war material. It is broadly divided into
three parts: the theoretical, the descriptive, and the practical. The
theoretical part includes the study of the action of explosives, the
study of interior and exterior ballistics, the theories of gun and
carriage construction, and the principles of gunnery. The theoretical
part of the course is not the same for all cadets, those showing the
necessary proficiency taking a special course in the time devoted by
the remainder of the class to review work.
The descriptive part of the course covers the processes of manufacture
of powders, guns, projectiles, and armor; and describes the small
arms, cannon, machine and rapid-fire guns in use in the United States
service, with the carriages, ammunition and accessory appliances
required for their service. The department is well supplied with
models, which are used in conjunction with the text.
The practical part of the course covers the operation of machines and
appliances used in the fabrication of modern ordnance, the latter work
being in effect a short but valuable course in manual training.
In connection with the course, visits are made to Watervliet Arsenal,
where the process of gun construction is observed, and to the Ordnance
Proving Ground at Sandy Hook, where actual firings from the several
classes of guns are observed, including usually one or more shots
against armor, and where the latest developments in war material are
seen.
TEXTBOOKS
Ordnance and Gunnery. Lissak.
Exterior Ballistics. O'Hern.
Stresses in Wire-Wrapped Guns and in Gun Carriages. Ruggles.
BOOKS OF REFERENCE
Ballistic Tables. Ingalls.
Mathematical Tables. Newcomb.
Publications of Ordnance Department. U. S. Army.
DEPARTMENT OF MILITARY HYGIENE
THIRD CLASS
The course in military hygiene begins with the second academic year and
consists of 13 recitations and 6 demonstrations.
The textbook used is Keefer's _Military Hygiene_; the instruction
covers the essentials in the care of troops from the point of view of
the line officer, particular attention being given to personal hygiene,
transmissible diseases, post and camp sanitation, clothing, and the
effects of alcohol and other narcotics.
Practical demonstration in the field is given of the methods of
construction and operation of the various camp sanitary appliances such
as latrines, water sterilizers, incinerators, etc.
Instruction in first-aid is given to cadets in small groups by
practical demonstrations in the treatment of wounds, hemorrhage,
fractures, drowning, poisoning, and other emergencies.
During the summer practice march, practical instruction is given in
camp sanitation.
TEXTBOOKS
A Textbook of Military Hygiene and Sanitation. Keefer.
REFERENCE BOOKS
Military Hygiene. Havard.
Elements of Military Hygiene. Ashburn.
Practical Hygiene. Harrington.
DEPARTMENT OF ENGLISH AND HISTORY
FOURTH CLASS
The course in English and History begins with the fourth class in
September and continues throughout the academic year, the whole class
attending daily except Saturday. The class is divided into two parts,
which alternate in reciting English and History.
In English, the course of instruction is planned to inculcate the
essential principles of rhetoric, both by study of the textbook and
by frequent practice in the various forms of composition (including
practice in personal and official correspondence), to create an
intelligent appreciation of the best in English Literature by the study
of selected literary masterpieces, and to impart a knowledge of the
important facts in the history of English literature and language by
the study of a textbook and by lectures.
In History, the course of instruction is planned to acquaint the
student with the political, social, and economic history of Europe from
the beginning of the French Revolution to the present day, to make him
familiar with the fundamental principles of civil government, with
special reference to the United States, and to give him knowledge of
various typical forms of modern national and municipal governments.
TEXTBOOKS--ENGLISH
English Composition in Theory and Practice (new and revised
edition). Henry S. Canby and others.
Leading English Poets, Ed. by Holt.
Shakespeare's Works.
History of English Literature, by W. J. Long.
The Major Dramas of Sheridan.
Selections from Addison.
Selections from the Prose of Macaulay.
Selections from Stevenson.
TEXTBOOKS--HISTORY
The Development of Modern Europe, Vol. I. By J. H. Robinson and C.
A. Beard.
Europe since 1815. C. D. Hazen.
Introduction to the Study of Government. Holt.
THE LIBRARY
Cadets and officers have free access to the library, which comprises
over 95,000 books, maps, and manuscripts. The collection contains
substantially all standard books on the subjects taught in the Academy
and is especially complete in military subjects. Its card catalogues
(about 338,000 cards) are arranged with the special object of saving
the time of cadets. The library is open on week-days from 8 A.M. to
7:30 P.M.; Saturdays from 8 A.M. to 9:30 P.M.; on Sundays and Holidays
from 2 to 6 P.M.
(A. O., M. A., July, '16.)
SUPERINTENDENTS OF THE UNITED STATES MILITARY ACADEMY
===================================================================================================================
| | | TERM OF SERVICE |
NO.| NAME. | ARMY RANK WHEN APPOINTED. +-------------------+-------------------+ REMARKS.
| | | FROM | TO |
---+------------------------+------------------------------------+-------------------+-------------------+----------
1 | JONATHAN WILLIAMS | Major, Corps of Engineers | April 15, 1802 | [8]June 20, 1803 | Resigned.
2 | JONATHAN WILLIAMS | Lieut. Colonel, Corps of Engineers | [8]April 19, 1805 | July 31, 1812 | Resigned.
3 | JOSEPH G. SWIFT | Colonel, Corps of Engineers | July 31, 1812 | Mar. 24, 1814 | Relieved.
4 | ALDEN PARTRIDGE | Captain, Corps of Engineers | Jan'y 3, 1815 | July 28, 1817 | Relieved.
5 | SYLVANUS THAYER | Captain, Corps of Engineers | July 28, 1817 | July 1, 1833 | Relieved.
6 | RENÉ W. DERUSSY | Major, Corps of Engineers | July 1, 1833 | Sept. 1, 1838 | Relieved.
7 | RICHARD DELAFIELD | Major, Corps of Engineers | Sept. 1, 1838 | Aug. 15, 1845 | Relieved.
8 | HENRY BREWERTON | Captain, Corps of Engineers | Aug. 15, 1845 | Sept. 1, 1852 | Relieved.
9 | ROBERT E. LEE | Captain, Corps of Engineers | Sept. 1, 1852 | Mar. 31, 1855 | Relieved.
10 | JOHN G. BARNARD | Captain, Corps of Engineers | Mar. 31, 1855 | Sept. 8, 1856 | Relieved.
11 | RICHARD DELAFIELD | Major, Corps of Engineers | Sept. 8, 1856 | [9]Jan'y 23, 1861 | Relieved.
12 | PETER G. T. BEAUREGARD | Captain, Corps of Engineers |[9]Jan'y 23, 1861 | Jan'y 28, 1861 | Relieved.
13 | RICHARD DELAFIELD | Major, Corps of Engineers | Jan'y 28, 1861 | Mar. 1, 1861 | Relieved.
14 | ALEXANDER H. BOWMAN | Major, Corps of Engineers | Mar. 1, 1861 | July 8, 1864 | Relieved.
15 | ZEALOUS B. TOWER | Major, Corps of Engineers | July 8, 1864 | Sept. 8, 1864 | Relieved.
16 | GEORGE W. CULLUM | Lieut. Colonel, Corps of Engineers | Sept, 8, 1864 | Aug. 28, 1866 | Relieved.
17 | THOMAS G. PITCHER | Colonel 44th Infantry | Aug. 28, 1866 | Sept. 1, 1871 | Relieved.
18 | THOMAS H. RUGER | Colonel 18th Infantry | Sept. 1, 1871 | Sept. 1, 1876 | Relieved.
19 | JOHN M. SCHOFIELD | Major General, U. S. Army | Sept. 1, 1876 | Jan'y 21, 1881 | Relieved.
20 | OLIVER O. HOWARD | Brigadier General, U. S. Army | Jan'y 21, 1881 | Sept. 1, 1882 | Relieved.
21 | WESLEY MERRITT | Colonel 5th Cavalry | Sept. 1, 1882 | July 1, 1887 | Relieved.
22 | JOHN G. PARKE | Colonel, Corps of Engineers | Aug. 28, 1887 | June 24, 1889 | Relieved.
23 | JOHN M. WILSON | Lieut. Colonel, Corps of Engineers | Aug. 26, 1889 | Mar. 31, 1893 | Relieved.
24 | OSWALD ERNEST | Major, Corps of Engineers | Mar. 31, 1893 | Aug. 21, 1898 | Relieved.
25 | ALBERT L. MILLS | 1st Lieutenant, 1st Cavalry | Aug. 22, 1898 | Aug. 31, 1906 | Relieved.
26 | HUGH L. SCOTT | Major, 14th Cavalry | Aug. 31, 1906 | Aug. 31, 1910 | Relieved.
27 | THOMAS H. BARRY | Major General, U. S. Army | Aug. 31, 1910 | Aug. 31, 1912 | Relieved.
28 | CLARENCE P. TOWNSLEY | Colonel, Coast Artillery Corps | Aug. 31, 1912 | June 30, 1916 | Relieved.
29 | JOHN BIDDLE | Colonel, Corps of Engineers | July 1, 1916 | |
---+------------------------+------------------------------------+-------------------+-------------------+----------
NOTE.--The selection of the Superintendents of the Military Academy
was confined to the Corps of Engineers from the establishment of
the Institution, March 16, 1802, till the passage of the law of
July 13, 1866, which opened it to the entire Army. By the Act of
June 12, 1858, the local rank of Colonel was conferred upon the
Superintendent.
A DICTIONARY OF CADET SLANG
A. B., _n._ Area Bird, term used to designate one who regularly
walks the area.
B. A., _n._ Busted aristocrat. Title given to a cadet officer who
has been deprived of his chevrons.
B-ache, _n._ An official explanation of a report.
B-ache, _v._ To submit an explanation, to talk.
Beast, _n._ Name given to new cadets during their first few weeks
at M. A.
Beast Barracks, _n._ Designation for the period of time a man is a
beast: the first three weeks when he is quartered in barracks.
Bird, _n._ See A. B.
B. J., _a._ Literally means "bold before June"; as applied to a
fourth classman who is impertinent and fresh.
Black Book, _n._ Regulations, U. S. M. A.
Blasé, _a._ Indifferent. Syn. B. J.
Bone, _v._ To study.
---- check book. To be economical.
---- dis. To try to avoid getting demerits.
---- efficiency. To be military for no apparent reason.
---- files. To strive for class standing.
---- make. To strive for chevrons.
---- muck. To endeavor to increase in brawn.
---- tenths. To study hard for a better mark.
Boodle, _n._ General term used to designate all eatables,
contraband.
Boodler's, _n_. The confectioner's.
Bootlick, _v._ To curry favor obsequiously, to praise.
Bootlick, _n._ A "stand in."
Bootlick Alley, _n._ A street passing in front of the officers'
tents in camp (off limits to plebes).
Brace, _n._ Term applied to muscular efforts of fourth classmen to
look military.
Brace, _v._ To assume an excessive military position. Obsolete.
B. S., _n._ Loquaciousness; superfluity of talk.
B. S., _v._ To be loquacious.
Buck, _n._ Cadet in ranks; one who has no chevrons.
Bugle, _v._ To stand at the board all the period to escape
reciting. (Not applicable to first-class year).
Bump, _v._ To deprive cadet officer of chevrons.
Butt, _n._ The remainder of anything, as the butt of a skag; of a
month.
Cit., _n._ A Civilian.
Cits., _n._ Civilian clothing.
Clean Sleeve, _n._ A cadet who has never worn chevrons.
Com., _n._ Commandant of Cadets.
Con., _n._ Confinement.
Corp., _n._ Corporal.
Crawl, _v._ To correct or rebuke someone (especially fourth
classmen) in a severe manner.
Crawling, _n._ A rebuke.
Deadbeat, _n._ An easy job; one who deadbeats.
Deadbeat, _v._ To avoid some distasteful duty.
Dis., _n._ Discipline.
Dissy, _a._ Lacking in demerits.
<DW37>., _n._ A division of barracks.
Doughboys, _n._ The infantry.
Drag, _v._ To escort a lady; to pull a man out of bed; to pull off
a pair of white trousers.
Drag, _n._ A puff of skag.
Femme, _n._ A member of the fair sex.
Fess, _v._ To fail.
Fess, _n._ A failure.
File, _n._ A member of the male sex; one of the successive grades
in military rank.
Find, _v._ To find deficient and discharge.
Flirtation, _n._ Flirtation Walk.
Formation, _n._ Any military function or military gathering.
Fried Egg, _n._ The crest of the U. S. M. A. used on the cap and
full dress hat.
Gig, _v._ To report for a delinquency.
Gig List, _n._ The delinquency list.
Goat, _n._ A low ranking man in any subject.
Grind, _n._ A joke.
West Point Grind, _n._ A practical joke of the kind in which the
victim sees no humor.
Gross, _a._ Lacking in intelligence.
Growley, _n._ Tomato catsup.
Growley, _v._ To blush.
Gum, _v._ To make a mistake.
Gumstick, _n._ One who is in the habit of gumming it.
Hell Cats, _n._ The U. S. M. A. detachment of field music.
Hell Dodgers, _n._ Active members of the Y. M. C. A.
Hive, _v._ To understand; to discover.
Hivey, _a._ Smart, brainy, able to understand things.
Ignorance and Gummery, _n._ Ordnance and Gunnery.
Juliet, _n._ A cadet who enters in July.
Laundry Spike, _n._ An especially long pin used by the laundry; a
girl who works in the laundry.
Limits, _n._ The boundary beyond which a cadet may not go.
L. P., _n._ A person who is undesirable.
L. P., _v._ To give an undesirable task to anyone.
Make, _n._ A cadet officer.
Max, _n._ A perfect mark.
Max, _v._ To finish a job in a perfect manner.
Missouri National, _n._ A tune supposed to bring rain.
Muck, _n._ Muscle.
O. C., _n._ The Officer in Charge.
O. D., _n._ The Officer of the Day.
O. G., _n._ The Officer of the Guard.
--oid. A suffix added to a noun or a verb to denote the agent by
which the action in the noun or verb is accomplished, _i. e._
Ridoid--one who rides; Hopoid--one who attends hops.
P., _n._ A Professor.
P. C. S., _n._ Previous condition of servitude. Occupation before
entering.
P. D., _n._ Pennsylvania Dutchman.
Pipe, _v._ To look forward to anything; to build castles in the air.
Plebe, _n._ A fourth classman.
Plebeskin, _n._ A flannel blouse issued to new cadets. Very badly
fitting.
Plebeskin, _n._ A report for hazing.
P. M. E., n. Practical Military Engineering.
Podunk, _n._ A cadet's home town. A name applied to any small town
to denote its insignificance; a local newspaper.
Police, _v._ To discard; to relegate to the scrap pile; to throw
from a horse's back; to clean up, as to police a room.
Poop, _v._ To memorize verbatim.
Poop, _n._ One who memorizes by heart.
Poop Deck, _n._ The balcony of the south cadet guard house, used by
the officer in charge.
Pred., _n._ Predecessor; a cadet's forerunner in office.
P. S., _v._ To spoon on the post.
Quill, _n._ A person addicted to reporting cadets on every
opportunity; subject matter for a report.
Recognize, _v._ To admit a fourth classman to the upperclass status.
Reverse, _n._ A position of disfavor, as to get a reverse on the
tac.
Run-it-on, _v._ To take advantage of.
Scavenge, _v._ To acquire something that someone else no longer
wants or has thrown away.
Skag, _n._ A cigarette.
Skin, _n._ A report for delinquency.
Skin, _v._ To report a delinquent.
Skin list, _n._ The delinquency list.
Slug, _n._ A disagreeable duty; an award of special punishment for
some major offense.
Soirée, _n._ An unpleasant task or duty.
Soirée, _v._ To cause inconvenience or annoyance.
Speck, _v._ To commit to memory.
Speck, _n._ One who commits to memory.
Slum, _n._ Mess Hall stew (unknown ingredients).
Soundoff, _n._ A voice capable of being heard at long range.
Sound off, _v._ To bellow; to use the voice to the limit of its
capacity.
Spoon, _v._ To court, amuse, entertain, or converse with a femme.
Spoony Up, _v._ To make neat or attractive.
Step Out, _v._ To hurry.
Sub-<DW37>., _n._ A subdivision of barracks: a cadet officer in charge
of a subdivision.
Supe, _n._ The Superintendent.
Tac, _n._ A Tactical Officer.
T. D., _n._ The Department of Tactics.
Tarbucket, _n._ The full dress hat.
Tenth, _n._ The smallest division of the West Point system of
marking.
Tie Up, _v._ To get a thing gloriously mixed up.
Turnback, _n._ A cadet who has been turned back to join the next
succeeding class.
Walri, _n._ One who cannot swim.
Writ, _n._ A written review recitation.
Yearling, _n._ A third classman.
[1] Fort Clinton was originally named Fort Arnold in honor of Benedict
Arnold, but after his defection its name was changed. It stood in
the N. E. corner of the Plain at West Point.
[2] Fort Putnam was named for Colonel Rufus Putnam whose regiment,
the Fifth Massachusetts, commenced it and did much toward putting it
in shape.
[3] The Sterling Iron Works are still in operation at Sterlington,
N. Y., on the Erie R. R., where the remains of the Revolutionary
furnace are still standing.
[4] The Robinson House was situated on the eastern shore of the Hudson
about two miles below West Point. It was built in 1750 by Beverly
Robinson, a man of note and wealth. He had been a personal friend of
Washington until the Revolution separated them, when he went to New
York and raised a regiment known as the "Loyal American" for service
under the British. He assisted Arnold and André in their negotiations.
At the close of the Revolution, Robinson went to England. This house
was destroyed by fire, March 17, 1892.
[5] "Fess" means a complete failure at a recitation. It is an
abbreviation of "confess."
[6] In the Philippine Department the preliminary examination will be
held between December 1st and December 15th.
[7] The board before which a candidate is directed to appear will be
the one convened at the place nearest or most convenient to his home,
or to the school at which he is in regular attendance at the time of
appointment.
[8] Major Williams resigned June 20, 1803, on a point of command, and
pending its settlement until April 19, 1805, when he again returned to
service as Chief Engineer, no permanent Superintendent of the Military
Academy was appointed, the command devolving upon the senior officer of
the Corps of Engineers present for duty.
[9] Bvt. Major P. G. T. Beauregard, Corps of Engineers, by order of
John B. Floyd, Secretary of War, relieved Colonel Delafield, Jan.
23, 1861, from the superintendency of the Military Academy, but was
himself displaced five days later, Jan. 28, 1861, by direction of the
succeeding Secretary of War, Joseph Holt, the command again devolving
upon Colonel Delafield.
[Transcriber's Note:
TOC entry "VIII.—Growing Muscles 174" changed to read "VIII.—Growing
Muscles 194" to match actual page.
Obvious printer errors corrected silently.
Inconsistent spelling and hyphenation are as in the original.]
End of Project Gutenberg's West Point, by Robert Charlwood (Jr.) Richardson
***
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"redpajama_set_name": "RedPajamaBook"
}
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Q: Set permanent first bullet starting point in beamer I'm trying to set a permanent starting point for bullets in my Beamer slides. By default, the bullets are centered in the middle of the page. I have tried using the [t] option, but it places the first bullet at the very top of the page. I would like the bullet to start further down the page. Is there a way to set a specific starting point for the first bullet of every slide in a custom template?
An example of the roadblock I've run into is visible below using [t] in /documentclass[t]{beamer}.
\documentclass[t]{beamer}
\setbeamertemplate{itemize item}[default]
\setbeamertemplate{frametitle}{\vspace{12pt}\color{DBlue}\bfseries\insertframetitle\par\vskip-25pt}
\definecolor{DBlue}{rgb}{.1,.1,.4}
\begin{document}
\pagecolor{white}
\begin{frame}
\frametitle{TITLE FOO}
\begin{itemize}
\item foo1.
\item foo2.
\item foo3.
\item foo4.
\end{itemize}
\end{frame}
\end{document}
The first bullet "foo1" overlaps the title of the page. I'd like the bullet to start below the title. Is there a way to set all first bullets of a document class in a specific location? For example, 10mm down the page?
A: Just adapt your frametitle accordingly. In your MWE you got a negative length causing the subsequent text to start right in the middle of the frametitle.
\documentclass[t]{beamer}
\setbeamertemplate{itemize item}[default]
\setbeamertemplate{frametitle}{\vspace{12pt}\color{DBlue}\bfseries\insertframetitle%
\par}%%gap between frametitle and text ist determined by the last lenght (or par) here
\definecolor{DBlue}{rgb}{.1,.1,.4}
\begin{document}
\pagecolor{white}
\begin{frame}
\frametitle{TITLE FOO}
\begin{itemize}
\item foo1.
\item foo2.
\item foo3.
\item foo4.
\end{itemize}
\end{frame}
\end{document}
Another solution could be obtained with Easy absolute positioning in beamer
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"redpajama_set_name": "RedPajamaStackExchange"
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\section{INTRODUCTION}
Many overcontact binaries are thought to have evolved from initially detached binaries by angular momentum loss (AML) via magnetic torques
from stellar winds and to end with coalescence of both components into single stars (Bradstreet \& Guinan 1994; Pribulla \& Rucinski 2006).
In this scenario, the orbital angular momentum is tidally coupled to the spin angular momentum. In order for the spin-orbit coupling
to work efficiently, the initial orbital periods should be shorter than about 5 days. Circumbinary objects in multiple systems may remove
angular momentum from the central pairs via Kozai oscillation (Kozai 1962; Pribulla \& Rucinski 2006) or a combination of the Kozai cycle
and tidal friction (Fabrycky \& Tremaine 2007) and form the initial tidal-locked detached binaries with a short orbital period.
The statistical study of Pribulla \& Rucinski (2006) suggests that a large percentage of close binares reside in triple or multiple systems.
The presence of a third body orbiting an eclipsing close binary causes a periodic variation of the eclipsing period due to the increasing
and decreasing light-travel times (LTT) to the observer (Irwin 1952, 1959). The LTT effect can be studied by a detailed analysis of
eclipse timing diagram, showing the differences between the observed ($O$) and the calculated ($C$) timings of minimum light {\it versus}
time (e.g., Lee et al. 2009a, 2013). In order to advance this subject, we have been observing short-period eclipsing binaries,
such as overcontact and near-contact systems. In this work, we choose the W UMa-type binary EP And, because the list of eclipse timings
goes back far enough to understand the binary's period behavior.
Since the discovery of its variability by Strohmeier et al. (1955), EP And (TYC 2827-17-1, GSC 2827-17, 2MASS J01422933+4445424;
$V$=+11.90, $B$--$V$=+0.57) has been the topic of several investigations, but its properties are relatively poorly known compared to
other short-period binaries. Most recently, Manzoori (2012) reviewed the observational history of the system and presented the first
comprehensive photometric study. The author analyzed the photometric data from both the AAVSO (American Association of Variable Stars Observers)
International Database\footnote {http://www.aavso.org/} and the WASP (Wide Angle Search for Planets) public archive (Butters et al. 2010),
and concluded that EP And is an A-type (defined observationally by Binnendijk 1970) overcontact binary with a mass ratio of $q$=0.395,
an orbital inclination of $i$=81$^\circ$.5, a temperature difference between the components of $\Delta T$=120 K, and a fill-out factor
of $f$ = 16.6 \%. Here, $q$ is the ratio of the secondary'mass to that of the primay star (eclipsed at the primary minimum) and
$f$=($\Omega_{\rm in}$--$\Omega$)/($\Omega_{\rm in}$--$\Omega_{\rm out}$), where the potentials $\Omega_{\rm in}$ and
$\Omega_{\rm out}$ define the inner and outer critical surfaces in Roche geometry and $\Omega$ is the potential corresponding
to the surface of the overcontact binary. From the analysis of eclipse timings including five epochs determined from the AAVSO data,
he suggested that the orbital period of EP And can be sorted into a secular period decrease caused by mass transfer between
the components, an LTT effect due to the orbit of a third body with a period of 41.2 yr and a minimum mass of 0.15 M$_\odot$, and
the effect of magnetic activity with a cycle length of 11.7 yr.
In order to obtain a unique set of photometric solutions and to examine whether the Manzoori's (2012) suggestion is appropriate
for the orbital period change, we have studied in detail the long-term photometric behavior of EP And from all available data.
Our results from both the light-curve synthesis and the orbital period study show that EP And is probably a multiple system.
This study follows the following structure. In section 2, we present our new photometric observations of EP And.
Absolute dimensions of the eclipsing pair are determined from light-curve modeling in section 3. In section 4, we present
an orbital period study of the eclipse timing diagram and determine two significant periods in the timing measurements.
In the last section we give a discussion highlighting that the two periodic variations are most likely attributed to the presence
of circumbinary companions.
\section{NEW LONG-TERM CCD PHOTOMETRY}
New CCD photometric observations of EP And were obtained between 2007 and 2012, using CCD cameras and a $BVR$ filter set attached
to the 61-cm reflector at Sobaeksan Optical Astronomy Observatory (SOAO) in Korea. The observations of the first two seasons were
carried out to secure complete multiband light curves and the others to collect additional eclipse timings. A summary of
the observations is listed in Table 1, where we present observing interval, numbers of nights, CCD type, and field of view (FOV).
The instruments and reduction methods for the SITe 2K and FLI IMG4301E CCD cameras are the same as those described by
Lee et al. (2007, 2011). The observations of both 2011 and 2012 seasons were obtained with a PIXIS: 2048B CCD camera that offers
cooling down to $-70\rm ^o$ C. The e2v CCD42-40 chip has 2048$\times$2048 pixels and a pixel size of 13.5 $\mu$m.
With the conventional IRAF package, we processed the CCD frames to correct for bias level and pixel-to-pixel inhomogeneities of
quantum efficiency (flat field correction) and applied simple aperture photometry to obtain instrumental magnitudes.
Following the procedure described by Lee et al. (2010), TYC 2827-103-1 ($V\rm_T$=10.99, ($B$--$V$)$\rm_T$=+0.64) and TYC 2827-72-1
($V\rm_T$=10.98, ($B$--$V$)$\rm_T$=+1.16), imaged on the chip at the same time as the variable (V), were chosen as comparison (C)
and check (K) stars, respectively. From the 2007 and 2008 seasons, a total of 3,027 individual observations were obtained in
the three bandpasses (1007 in $B$, 1012 in $V$, and 1008 in $R$) and a sample of them is listed in Table 2. The light curves are
plotted in the top panel of Figure 1 as the (V$-$C) magnitude differences {\it versus} orbital phase, which was computed according
to the quadratic ephemeris for our binary model (Model 2) determined later in this article with the Wilson-Devinney synthesis code
(Wilson \& Devinney 1971, hereafter W-D). The differences ('07-'08) between the two seasons are shown in the middle panel and
the magnitude differences between the check and comparison stars appear in the bottom panel. The 1$\sigma$-values of the dispersion
of the (K$-$C) differences are $\pm$0.016 mag, $\pm$0.012 mag, and $\pm$0.013 mag from $B$ to $R$ bandpasses, respectively,
for the 2007 season and $\pm$0.009 mag, $\pm$0.005 mag, and $\pm$0.005 mag for the 2008 season. Whereas the reference stars were
evidently constant, the light curves display season-to-season light variability, with evident changes in the phase interval
encompassing primary eclipse.
\section{LIGHT-CURVE SYNTHESIS AND ABSOLUTE DIMENSIONS}
As shown in Figure 1, our observations display a typical light curve of an overcontact system and a flat bottom at primary minimum,
indicating that the smaller primary star is totally occulted by the secondary. This would mean that EP And belongs to the W-type
of W UMa stars. On the contrary, Pribulla et al. (2001) and Manzoori (2012) analyzed their $BV$ light curves and both the AAVSO
and WASP datasets, respectively, and classified the binary system as a member of the A-type category with the mass ratios of 0.34
and 0.395. The light curves of 2008 present equal light levels at the quadratures (Max I and Max II) within about 0.002 mag,
while those of 2007 show the O'Connell effect with Max I brighter than Max II by about 0.014, 0.011, and 0.009 mag for
the $B$, $V$, and $R$ bandpasses, respectively. The effect is usually interpreted as spot activity on the component stars and
the seasonal light variations most likely arise from the variability of the spots with time presumably produced by a magnetic dynamo.
In order to obtain a consistent solution of EP And, we simultaneously solved all avaliable light curves using contact mode 3 of
the W-D synthesis code and with a weighting scheme identical to that for the eclipsing binary GW Gem (Lee et al. 2009b). Table 3
lists the light-curve sets for EP And analyzed in this paper and the standard deviations ($\sigma$) of a single observation.
Although the binary parameters have been reported by Pribulla et al. (2001) and Manzoori (2012), their solutions with $q<$1.0
do not correspond to our high-precision observations of 2008, showing a total eclipse at primary minimum and hence implying $q>$1.0.
To resolve this confusion, we analyzed the light curves of EP And in a manner similar to that for the overcontact systems AR Boo
(Lee et al. 2009c) and GW Cep (Lee et al. 2010) using the so-called $q$-search procedure. In the computation of our solutions,
the surface temperature of the larger, and presumably more massive, star was held fixed at 6,360 K from Flower's (1996) table,
according to ($B-V$)=$+$0.57$\pm$0.02 given by Terrell et al. (2012) and $E$($B-V$)=$+$0.09 calculated following
Schlegel et al. (1998). The logarithmic bolometric ($X$, $Y$) and monochromatic ($x$, $y$) limb-darkening coefficients were
interpolated from the values of van Hamme (1993) in concert with the model atmosphere option. Before the light curves are analyzed,
the AAVSO times were transformed from JD into HJD. Further, two LTT effects proposed in the following section were applied to
the observed times of all individual points: HJD$_{\rm new}$=HJD$_{\rm obs}$--($\tau_{3}$+$\tau_{4}$). The quantities shifted by
the two LTTs are 0.00722$\sim$0.00871 d for 2001, 0.00733$\sim$0.00831 d for 2007, and 0.00026$\sim$0.00052 d for 2008.
In this paper, we refer to the primary and secondary stars as those being eclipsed at Min I and Min II, respectively.
Terrell \& Wilson (2005) showed that the mass ratio for a totally-eclipsing overcontact system can be accurately determined from
a light-curve analysis. Thus, we conducted the detailed $q$-search procedures for both all datasets and only the 2008 light curves,
permitting no perturbations such as a third light ($l_3$) or a spot. As displayed in Figure 2, the $q$-search results indicate
a minimum value of the weighted sum of the squared residuals ($\Sigma$) around $q$=2.75. This value corresponds to an occultation
at primary minimum and indicates that EP And is a W-type overcontact binary. To obtain an unperturbed solution (Model 1),
we analyzed all light curves by treating the initial value of $q$ as a free parameter. The results are listed in columns (2)--(3)
of Table 4. Then, we reanalyzed the EP And curves by considering a third light ($l_3$) as an additional adjustable parameter
because it had been suggested by our period study later. New results with the third light source are given as Model 2 in Table 4
and the light residuals from this binary model are plotted in Figure 3. There is a statistically significant difference in
the mass ratios between the two models due to the third light effect. In a formal sense, as shown by the entries on the last line
of the table, the third-light model gives a smaller value of $\Sigma W(O-C)^2$.
As indicated by Figure 3, the model light curves describe the observations of the 2001 and 2008 seasons quite well, but not those
of the 2007 season. The non-modelled light could be explained by a magnetic cool spot on either of the component stars. Model spots
were added to fit the small light variations of 2007 by adjusting only the spot and luminosity parameters among the Model 2 parameters.
Final results are given in Table 5, and the residuals from the cool-spot model on the secondary star are plotted as the plus symbols
in the middle panels of Figure 3. From these displays, we can see that the spot model does fit the asymmetries in the light maxima
acceptably but it is difficult to distinguish between the cool-spot models because there is no $\Sigma$ differences among them.
Our light-curve solutions indicate that EP And is a totally-eclipsing W-type overcontact binary with a fill-out factor of about 28 \%
and with a small temperature difference of 27 K between the components and that $l_3$ contributes 2--3 \% light in all bandpasses.
Absolute dimensions for EP And can be estimated from the photometric solutions (Model 2) in Table 4 and from Harmanec's (1988) relation
between temperature (spectral type) and stellar mass. We assumed the more massive secondary star to be a normal main-sequence one
with a spectral type of about F6 and computed the physical properties for the system listed in Table 6. The luminosity ($L$) and
bolometric magnitudes ($M_{\rm bol}$) were computed by adopting $T_{\rm eff}$$_\odot$=5,780 K and $M_{\rm bol}$$_\odot$=+4.73
for solar values. For the absolute visual magnitudes ($M_{\rm V}$), we used the bolometric corrections (BCs) appropriate for the temperature
of each component from the expression between $\log T_{\rm eff}$ and BC given by Torres (2010). Using an apparent visual magnitude of
$V$=+11.90 (Terrell et al. 2012) at maximum light, the computed light ratio at phase 0.25, and the interstellar absorption of $A_{\rm V}$=0.28,
we calculated an approximate distance to the system of about 470 pc. In the mass-radius, mass-luminosity, and Hertzsprung-Russell diagrams
from Hilditch et al. (1988), the locations of both components of EP And conform to the general pattern of overcontact binaries.
\section{ORBITAL PERIOD STUDY}
From the SOAO observations, 29 new times of minimum light and their errors were determined with the weighted means for the timings
in each filter by using the method of Kwee \& van Woerden (1956). In addition, 61 eclipses were newly derived by us from the WASP data
and five timings from the AAVSO data. The AAVSO times from Manzoori (2012) may be not HJD but JD. For a period study of EP And,
we have collected a total of 414 timings (58 photographic plate, 216 visual, 140 photoelectric and CCD) including our measurements.
All photoelectric and CCD timings are listed in Table 7, wherein the second column gives the HJED (Heliocentric Julian Ephemeris Date)
timings transformed to the terrestrial time scale (Bastian 2000). Because most earlier timings from Kreiner et al. (2001) were published
without error information, we calculated the standard deviations of the scatter bands of the timing residuals to provide mean errors
for the observational methods, as follows: $\pm$0.0101 d for photographic plate, $\pm$0.0076 d for visual, and $\pm$0.0012 d for PE
and CCD minima. Relative weights were then scaled from the inverse squares of these values consistent with the errors and weights
for the PE and CCD timings.
The orbital period of EP And was studied for the first time by Qian \& Yuan (2001). From a quadratic least-squares fit, they reported
a period increase with a rate of $+$1.16$\times$10$^{-7}$ d yr$^{-1}$. Recently, Manzoori (2012) claimed that two periodicities of
41.2 yr and 11.7 yr, superimposed on the upward parabolic variation, exist in the timing residuals. As the first step for
ephemeris computations, we applied a periodogram analysis to the complete dataset using the \texttt{PERIOD04} program (Lenz \& Breger 2005).
As can be seen from Figure 4, two frequencies of $f_1$=0.0000424 cycle d$^{-1}$ and $f_2$=0.00149 cycle d$^{-1}$ were detected
corresponding to 23,585 d (64.6 yr) and 671 d (1.8 yr), respectively. Thus, the two periods were used to provide an initial guess
for the Levenberg-Marquart (LM) fitting procedure (Press et al. 1992). The oscillations were assumed to be due to a combination of
two LTT effects caused by the third and fourth bodies in the system and all times of minimum light were fitted to the following
two-LTT ephemeris:
\begin{eqnarray}
C_1 = T_0 + PE + \tau_3 + \tau_4.
\end{eqnarray}
Here, $\tau_{3}$ and $\tau_{4}$ are the LTT due to two additional companions orbiting the eclipsing pair (Irwin 1952, 1959) and each
includes five parameters ($a_{12}\sin i$, $e$, $\omega$, $n$, $T$). The LM technique was applied to solve for the twelve parameters
of the ephemeris and the results are listed in columns (2)--(3) of Table 8, together with related quantities. Our absolute dimensions
presented in Table 6 have been used for these and subsequent calculations.
The $O$--$C_1$ diagram constructed with the linear terms of the two-LTT ephemeris is plotted in the top panel of Figure 5, where
the solid and dashed curves represent the full contribution and the $\tau_{3}$ orbit, respectively. The middle panel displays
the PE and CCD residuals from the complete ephemeris and the bottom panel represents the $\tau_{4}$ orbit. As displayed in the figure,
all times of minimum light currently agree with the two-LTT ephemeris satisfactorily. The successful fit to the times of minimum light
with the two LTT orbits tempted us to try to discover a secular term which might be hidden in the two periodic variations.
Because EP And is in an overcontact configuration with common convective envelope, a parabolic variation should be produced by
mass transfer between both components and/or by AML due to magnetic stellar wind. Therefore, a more general fit to the times of
minimum light was made by adding a quadratic term to the two-LTT ephemeris:
\begin{eqnarray}
C_2 = T_0 + PE + A E^2 + \tau_3 + \tau_4.
\end{eqnarray}
The calculations using the LM method converged quickly to yield the results given in columns (4)--(5) of Table 8.
The $O$--$C_2$ diagram constructed with the linear light elements are drawn at the top of Figure 6 with the solid curve due to
the sum of the non-linear terms and the dashed parabola due to the quadratic term of equation (2). The second to bottom panels
are plotted in the same sense as in Figure 5. The timing residuals from the full ephemeris appear as $O$--$C_{\rm 2,full}$
in the fifth column of Table 7. Figure 7 shows the PE and CCD residuals phased with the $\tau_{4}$ cycle (1.8340 yr) listed
in Table 8. This ephemeris resulted in a smaller $\chi^2_{\rm red}$=0.981 than the two-LTT ephemeris ($\chi^2_{\rm red}$=1.102).
Its long-term period ($\tau_4$) is short compared to that of the two-LTT ephemeris by about 21 yr, while the short-term periods
($\tau_3$) for the two ephemerides are in excellent agreement with each other.
If it is assumed that the orbits of the two circumbinary objects are coplanar with that of the eclipsing pair of EP And
($i_{3,4}$=83\fdg3), the masses of the third and fourth bodies are $M_3$=0.25 M$_\odot$ and $M_4$=0.90 M$_\odot$, respectively.
If they are main-sequence stars, the radii and temperatures are calculated to be $R_3$=0.26 R$_\odot$ and $T_3$=3039 K, and
$R_4$=0.92 R$_\odot$ and $T_4$=5082 K from the empirical relation of Southworth (2009). The third and fourth bodies would
contribute about 0.1 \% and 11.6 \%, respectively, to the total bolometric luminosity of the quadruple system. Because
our light-curve solutions in Tables 4 and 5 detected only $l_3$ of 2--3 \% in all bandpasses, the putative fourth object
have to be very under-luminous in comparison to the binary components and may be a compact star. Alternatively, it is possible
that the fourth body might be a binary itself. This could reduce the luminosity for the given total mass of 0.90 M$_\odot$
and implies that EP And should be a quintuple system. The semi-amplitude of the expected systemic radial velocity changes of
the eclipsing pair due to the third and fourth components would be about 1.5 km s$^{-1}$ and 11.8 km s$^{-1}$, respectively.
Hence, the M-type third companion is very difficult to reveal because of the low systemic velocity change and
the large orbital period suggested by the LTT model, while the massive circumbinary object might be easily detected with
high-resolution spectroscopy. On the other hand, the eclipse timing variations might be partly caused by the perturbative effect
of the fourth component added to the geometrical LTT effect because its LTT period is very short (Borkovits et al. 2003, 2011).
One such example is IU Aur: \" Ozdemir et al (2003) showed that the third companion with a period of 293.3 d cause the non-negligible,
dynamical contribution to the $O$--$C$ curve. We computed the semi-amplitude of the fourth-body dynamic perturbation on the motion
of the overcontact binary to be 0.000013 d and found that its contribution is not significant.
The positive coefficient of the quadratic term ($A$) listed in Table 8 yields a secular period increase with a rate of
+5.09$\times$10$^{-8}$ d yr$^{-1}$, corresponding to a fractional period change of +1.39$\times$10$^{-10}$. This value agrees
well with the value of $+$1.40$\times$10$^{-10}$ calculated with our W-D binary code, independently of the eclipse timings.
Under the assumption of conservative mass transfer, this gives a continuous mass transfer from the less massive primary to
the secondary component at a modest rate of 3.41$\times$10$^{-8}$ M$_\odot$ yr$^{-1}$. The observed value is small by a factor of
about 50\% compared with the predicted rate of 6.77$\times$10$^{-8}$ M$_\odot$ yr$^{-1}$ calculated by assuming that the primary
transfers its present mass to the secondary on a thermal time scale. Thus, the possible explanation of the parabolic variation
might be some combination of non-conservative mass transfer and AML due to magnetic braking.
\section{DISCUSSION AND CONCLUSIONS}
In this article, we presented and analyzed new long-term CCD observations of EP And, together with historical data collected
from the literature. The light curves display a total eclipse at primary minimum and season-to-season light variability.
The asymmetric light curves in 2007 were modeled by a magnetic cool spot on either of the component stars. Our detailed study
of the light curves and the orbital period represent EP And to be a quadruple (or a quintuple) system with a W-type overcontact binary.
Because the period is increasing and the mass is transferring from the primary star to the more massive secondary, the eclipsing pair
may presently be in an expanding state evolving from a overcontact to a non-contact configuration as it undergoes thermal relaxation
oscillations (Lucy 1976; Lucy \& Wilson 1979).
In principle, the periodic variations in the eclipse timing residuals can be expected because of stellar activity variations
of a magnetically active star, as was initially proposed by Applegate (1992) and later modified by Lanza et al. (1998). With
the modulation periods ($P_{3,4}$) and amplitudes ($K_{3,4}$) listed in columns (4)--(5) of Table 8, the model parameters
for each cycle were calculated from the Applegate formulae and are listed in Table 9, where the rms luminosity changes
($\Delta m_{\rm rms}$) converted to magnitude scale were obtained with equation (4) in the paper of Kim et al. (1997).
In the table, the primary component with 1.2 L$_\odot$ and the secondary with 2.7 L$_\odot$ exhibit
the predicted luminosity variations of 55.4 L$_\odot$ and 34.8 L$_\odot$, respectively, for the short-term cycle. The variations
of the gravitational quadrupole moment ($\Delta Q$) for the long-term cycle are two orders of magnitude smaller than typical values
of $10^{51}-10^{52}$ for close binaries (Lanza \& Rodono 1999). Moreover, it is difficult for the model to produce perfectly
smooth and tilted periodic components in the eclipse timing variation. These suggest that Applegate mechanism cannot explain
the observed period modulations of EP And. On the other hand, a single periodic variation could be attributed to the rotation
of the apsidal line of the binary orbit due to tidal forces between the two binary components. However, our light-curve analysis
suggest that the binary orbit is circular which in turn excludes timing variations from apsidal precession.
As can be seen in Figures 5--7, all times of minimum light agree quite well by interpreting the observed LTT signal as caused
by a third and fourth body surrounding the eclipsing pair. The possible existence of the circumbinary objects is consistent
with the suggestion of Pribulla \& Rucinski (2006) that most W UMa systems exist in multiple systems.
We have carried out a stability study for the orbit parameters in Table 8, under the assumption that the eclipsing pair
can be replaced by a single massive object with mass equal to the combined mass of the two binary components. In general,
our methodology on assessing the orbital stability is similar to the work presented in Hinse et al. (2012) who considers
the stability of a similar system (SZ Herculis) of two circumbinary M-type companions (Lee et al. 2012).
The dynamical stability test suggests that the two proposed companions are on highly unstable orbits. In order to reconcile
the apparent contradiction we are therefore left with two options. Either i) we discard our two-companion interpretation
or ii) our LTT model is in lack of important physics that is not included in the present analysis/model. In light of
the above given arguments we do not favour to discard the two companion interpretation as presented in this work.
Of the possible causes of the periodic variations, the Applegate effect and apsidal motion can be ruled out.
The most reasonable explanation of both cycles is a pair of the LTT effects driven by the presence of circumbinary companions.
In future work we plan a re-analysis of the data with an improved model that formulates the LTT effect in Jacobi coordinates
and includes mutual gravitational interactions. Mutual interactions between the companions is a highly non-linear process and
could result in a significant different orbital architecture consistent with the observed timing data. The two-Kepler assumption
might be inadequate when larger companion masses are involved. This system is an obvious candidate for
future photometric follow-up programs for further characterisation (Pribulla et al. 2012).
Assuming our LTT interpretation is correct, then the outer components may have played an important role in the formation and
evolution of the inner eclipsing pair, which would cause it to evolve into an overcontact configuration by AML via magnetic braking
and ultimately to coalesce into a single rapid-rotating star. High-resolution photometry and spectroscopy will help to identify and
understand the orbital period variation of the binary system and to determine the absolute parameters and evolutionary status of the
multiple system better than is possible with photometry alone.
\acknowledgments{ }
We would like to thank the staff of the Sobaeksan Optical Astronomy Observatory for assistance during our observations.
We appreciate the careful reading and valuable comments of the reviewer Dirk Terrell. This research has made use of
the Simbad database maintained at CDS, Strasbourg, France. We have used data from the AAVSO International Database and
the WASP public archive in this research. The WASP consortium comprises of the University of Cambridge, Keele University,
University of Leicester, The Open University, The Queen's University Belfast, St. Andrews University and the Isaac Newton Group.
Funding for WASP comes from the consortium universities and from the UK's Science and Technology Facilities Council. This work was
supported by the KASI (Korea Astronomy and Space Science Institute) grant 2013-9-400-00. T.C.H. acknowledges financial support from
the Korea Research Council for Fundamental Science and Technology (KRCF) through the Young Research Scientist Fellowship Program.
\newpage
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,691
|
import {Type, ComponentMetadata, DirectiveResolver, DirectiveMetadata} from 'angular2/angular2';
import {stringify} from 'upgrade/src/util';
var COMPONENT_SELECTOR = /^[\w|-]*$/;
var SKEWER_CASE = /-(\w)/g;
var directiveResolver = new DirectiveResolver();
interface Reflect {
getOwnMetadata(name: string, type: Function): any;
defineMetadata(name: string, value: any, cls: Type): void;
}
var Reflect: Reflect = <Reflect>(<any>window).Reflect;
if (!(Reflect && (<any>Reflect)['getOwnMetadata'])) {
throw 'reflect-metadata shim is required when using class decorators';
}
export function getComponentSelector(type: Type): string {
var resolvedMetadata: DirectiveMetadata = directiveResolver.resolve(type);
var selector = resolvedMetadata.selector;
if (!selector.match(COMPONENT_SELECTOR)) {
throw new Error('Only selectors matching element names are supported, got: ' + selector);
}
return selector.replace(SKEWER_CASE, (all, letter: string) => letter.toUpperCase());
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,020
|
Q: Spark master switch because of RECEIVED SIGNAL TERM The Spark master happens switch, it meets the below errors. at 17/12/08 19:17:16
Master: RECEIVED SIGNAL TERM then master dead, worker also receive the SIGNAL TERM, the worker cannot connect the master, then the spark cluster restart, why does this happen?
17/12/06 17:44:31 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60402
java.io.IOException: Connection reset by peer
at sun.nio.ch.FileDispatcherImpl.read0(Native Method)
at sun.nio.ch.SocketDispatcher.read(SocketDispatcher.java:39)
at sun.nio.ch.IOUtil.readIntoNativeBuffer(IOUtil.java:223)
at sun.nio.ch.IOUtil.read(IOUtil.java:192)
at sun.nio.ch.SocketChannelImpl.read(SocketChannelImpl.java:379)
at io.netty.buffer.PooledUnsafeDirectByteBuf.setBytes(PooledUnsafeDirectByteBuf.java:221)
at io.netty.buffer.AbstractByteBuf.writeBytes(AbstractByteBuf.java:899)
at io.netty.channel.socket.nio.NioSocketChannel.doReadBytes(NioSocketChannel.java:275)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:119)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/06 17:44:31 INFO Master: 10.1.13.182:60402 got disassociated, removing it.
17/12/06 17:44:39 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60510
java.io.IOException: Connection reset by peer
at sun.nio.ch.FileDispatcherImpl.read0(Native Method)
at sun.nio.ch.SocketDispatcher.read(SocketDispatcher.java:39)
at sun.nio.ch.IOUtil.readIntoNativeBuffer(IOUtil.java:223)
at sun.nio.ch.IOUtil.read(IOUtil.java:192)
at sun.nio.ch.SocketChannelImpl.read(SocketChannelImpl.java:379)
at io.netty.buffer.PooledUnsafeDirectByteBuf.setBytes(PooledUnsafeDirectByteBuf.java:221)
at io.netty.buffer.AbstractByteBuf.writeBytes(AbstractByteBuf.java:899)
at io.netty.channel.socket.nio.NioSocketChannel.doReadBytes(NioSocketChannel.java:275)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:119)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/06 17:44:39 INFO Master: 10.1.13.182:60510 got disassociated, removing it.
17/12/06 17:44:47 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60559
java.io.IOException: Connection reset by peer
at sun.nio.ch.FileDispatcherImpl.read0(Native Method)
at sun.nio.ch.SocketDispatcher.read(SocketDispatcher.java:39)
at sun.nio.ch.IOUtil.readIntoNativeBuffer(IOUtil.java:223)
at sun.nio.ch.IOUtil.read(IOUtil.java:192)
at sun.nio.ch.SocketChannelImpl.read(SocketChannelImpl.java:379)
at io.netty.buffer.PooledUnsafeDirectByteBuf.setBytes(PooledUnsafeDirectByteBuf.java:221)
at io.netty.buffer.AbstractByteBuf.writeBytes(AbstractByteBuf.java:899)
at io.netty.channel.socket.nio.NioSocketChannel.doReadBytes(NioSocketChannel.java:275)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:119)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/06 17:44:47 INFO Master: 10.1.13.182:60559 got disassociated, removing it.
17/12/06 17:44:47 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60629
java.lang.IllegalArgumentException: Frame length should be positive: -9212956363171296264
at org.spark_project.guava.base.Preconditions.checkArgument(Preconditions.java:119)
at org.apache.spark.network.util.TransportFrameDecoder.decodeNext(TransportFrameDecoder.java:134)
at org.apache.spark.network.util.TransportFrameDecoder.channelRead(TransportFrameDecoder.java:81)
at io.netty.channel.AbstractChannelHandlerContext.invokeChannelRead(AbstractChannelHandlerContext.java:367)
at io.netty.channel.AbstractChannelHandlerContext.invokeChannelRead(AbstractChannelHandlerContext.java:353)
at io.netty.channel.AbstractChannelHandlerContext.fireChannelRead(AbstractChannelHandlerContext.java:346)
at io.netty.channel.DefaultChannelPipeline$HeadContext.channelRead(DefaultChannelPipeline.java:1294)
at io.netty.channel.AbstractChannelHandlerContext.invokeChannelRead(AbstractChannelHandlerContext.java:367)
at io.netty.channel.AbstractChannelHandlerContext.invokeChannelRead(AbstractChannelHandlerContext.java:353)
at io.netty.channel.DefaultChannelPipeline.fireChannelRead(DefaultChannelPipeline.java:911)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:131)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/06 17:44:47 INFO Master: 10.1.13.182:60629 got disassociated, removing it.
17/12/06 17:45:06 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60693
java.io.IOException: Connection reset by peer
at sun.nio.ch.FileDispatcherImpl.read0(Native Method)
at sun.nio.ch.SocketDispatcher.read(SocketDispatcher.java:39)
at sun.nio.ch.IOUtil.readIntoNativeBuffer(IOUtil.java:223)
at sun.nio.ch.IOUtil.read(IOUtil.java:192)
at sun.nio.ch.SocketChannelImpl.read(SocketChannelImpl.java:379)
at io.netty.buffer.PooledUnsafeDirectByteBuf.setBytes(PooledUnsafeDirectByteBuf.java:221)
at io.netty.buffer.AbstractByteBuf.writeBytes(AbstractByteBuf.java:899)
at io.netty.channel.socket.nio.NioSocketChannel.doReadBytes(NioSocketChannel.java:275)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:119)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/06 17:45:06 INFO Master: 10.1.13.182:60693 got disassociated, removing it.
17/12/06 17:45:15 WARN TransportChannelHandler: Exception in connection from /10.1.13.182:60765
java.io.IOException: Connection reset by peer
at sun.nio.ch.FileDispatcherImpl.read0(Native Method)
at sun.nio.ch.SocketDispatcher.read(SocketDispatcher.java:39)
at sun.nio.ch.IOUtil.readIntoNativeBuffer(IOUtil.java:223)
at sun.nio.ch.IOUtil.read(IOUtil.java:192)
at sun.nio.ch.SocketChannelImpl.read(SocketChannelImpl.java:379)
at io.netty.buffer.PooledUnsafeDirectByteBuf.setBytes(PooledUnsafeDirectByteBuf.java:221)
at io.netty.buffer.AbstractByteBuf.writeBytes(AbstractByteBuf.java:899)
at io.netty.channel.socket.nio.NioSocketChannel.doReadBytes(NioSocketChannel.java:275)
at io.netty.channel.nio.AbstractNioByteChannel$NioByteUnsafe.read(AbstractNioByteChannel.java:119)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:652)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
at java.lang.Thread.run(Thread.java:745)
17/12/08 19:17:16 ERROR Master: RECEIVED SIGNAL TERM
The Worker side log:
17/12/08 19:15:40 INFO Worker: Asked to kill executor app-20171208003131-0039/0
17/12/08 19:15:40 INFO ExecutorRunner: Runner thread for executor app-20171208003131-0039/0 interrupted
17/12/08 19:15:40 INFO ExecutorRunner: Killing process!
17/12/08 19:15:41 INFO Worker: Executor app-20171208003131-0039/0 finished with state KILLED exitStatus 143
17/12/08 19:15:41 INFO Worker: Cleaning up local directories for application app-20171208003131-0039
17/12/08 19:15:41 INFO ExternalShuffleBlockResolver: Application app-20171208003131-0039 removed, cleanupLocalDirs = true
17/12/08 19:17:16 ERROR Worker: RECEIVED SIGNAL TERM
17/12/08 19:17:16 INFO ExecutorRunner: Killing process!
17/12/08 19:17:17 INFO Worker: hdh52:7078 Disassociated !
17/12/08 19:17:17 ERROR Worker: Connection to master failed! Waiting for master to reconnect...
17/12/08 19:17:17 INFO Worker: hdh52:7078 Disassociated !
17/12/08 19:17:17 ERROR Worker: Connection to master failed! Waiting for master to reconnect...
17/12/08 19:17:17 INFO Worker: Connecting to master hdh52:7078...
17/12/08 19:17:17 INFO Worker: Not spawning another attempt to register with the master, since there is an attempt scheduled already.
17/12/08 19:17:17 INFO TransportClientFactory: Found inactive connection to hdh52/10.66.71.52:7078, creating a new one.
17/12/08 19:17:17 WARN Worker: Failed to connect to master hdh52:7078
org.apache.spark.SparkException: Exception thrown in awaitResult
at org.apache.spark.rpc.RpcTimeout$$anonfun$1.applyOrElse(RpcTimeout.scala:77)
at org.apache.spark.rpc.RpcTimeout$$anonfun$1.applyOrElse(RpcTimeout.scala:75)
at scala.runtime.AbstractPartialFunction.apply(AbstractPartialFunction.scala:36)
at org.apache.spark.rpc.RpcTimeout$$anonfun$addMessageIfTimeout$1.applyOrElse(RpcTimeout.scala:59)
at org.apache.spark.rpc.RpcTimeout$$anonfun$addMessageIfTimeout$1.applyOrElse(RpcTimeout.scala:59)
at scala.PartialFunction$OrElse.apply(PartialFunction.scala:167)
at org.apache.spark.rpc.RpcTimeout.awaitResult(RpcTimeout.scala:83)
at org.apache.spark.rpc.RpcEnv.setupEndpointRefByURI(RpcEnv.scala:100)
at org.apache.spark.rpc.RpcEnv.setupEndpointRef(RpcEnv.scala:108)
at org.apache.spark.deploy.worker.Worker$$anonfun$org$apache$spark$deploy$worker$Worker$$tryRegisterAllMasters$1$$anon$1.run(Worker.scala:218)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:471)
at java.util.concurrent.FutureTask.run(FutureTask.java:262)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)
at java.lang.Thread.run(Thread.java:745)
Caused by: java.io.IOException: Failed to connect to hdh52/10.66.71.52:7078
at org.apache.spark.network.client.TransportClientFactory.createClient(TransportClientFactory.java:228)
at org.apache.spark.network.client.TransportClientFactory.createClient(TransportClientFactory.java:179)
at org.apache.spark.rpc.netty.NettyRpcEnv.createClient(NettyRpcEnv.scala:197)
at org.apache.spark.rpc.netty.Outbox$$anon$1.call(Outbox.scala:191)
at org.apache.spark.rpc.netty.Outbox$$anon$1.call(Outbox.scala:187)
... 4 more
Caused by: io.netty.channel.AbstractChannel$AnnotatedConnectException: Connection refused: hdh52/10.66.71.52:7078
at sun.nio.ch.SocketChannelImpl.checkConnect(Native Method)
at sun.nio.ch.SocketChannelImpl.finishConnect(SocketChannelImpl.java:739)
at io.netty.channel.socket.nio.NioSocketChannel.doFinishConnect(NioSocketChannel.java:257)
at io.netty.channel.nio.AbstractNioChannel$AbstractNioUnsafe.finishConnect(AbstractNioChannel.java:291)
at io.netty.channel.nio.NioEventLoop.processSelectedKey(NioEventLoop.java:640)
at io.netty.channel.nio.NioEventLoop.processSelectedKeysOptimized(NioEventLoop.java:575)
at io.netty.channel.nio.NioEventLoop.processSelectedKeys(NioEventLoop.java:489)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:451)
at io.netty.util.concurrent.SingleThreadEventExecutor$2.run(SingleThreadEventExecutor.java:140)
at io.netty.util.concurrent.DefaultThreadFactory$DefaultRunnableDecorator.run(DefaultThreadFactory.java:144)
... 1 more
why does the master switch and the spark restart ?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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Rails.application.routes.draw do
# get 'welcome/index'
resources :articles
root 'welcome#index'
# For details on the DSL available within this file, see http://guides.rubyonrails.org/routing.html
end
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{
"redpajama_set_name": "RedPajamaGithub"
}
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El Mal de Köhler es una osteocondrosis que afecta al hueso escafoides del pie. Fue descrita por un radiólogo alemán, Alban Köhler, en 1908. Consiste en una necrosis avascular del escafoides tarsiano (cesa el aporte sanguíneo en el hueso, cuyas células mueren de hipoxia).
Epidemiología y Clínica
La enfermedad afecta mayoritariamente a niños varones jóvenes, de entre 4 y 6 años, aunque también puede afectar a niñas. Los pacientes afectos presentan dolor e inflamación en el dorso del pie, por lo que presentan una cojera. Para reducir este dolor durante la marcha, los pacientes suelen apoyar el peso sobre el borde externo del pie.
Tratamiento
Se basa en el reposo y en evitar el apoyo de pesos sobre el pie afecto. En algunos casos puede indicarse el uso de férulas de descarga.
Pronóstico
La mayor parte de los casos se curan en un plazo de dos años desde el momento del diagnóstico.
Referencias
Enlaces externos
Imágenes e información sobre el mal de Köhler en Fisaude.com
Köhler
Enfermedades del aparato locomotor
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
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Calauag è una municipalità di prima classe delle Filippine, situata nella Provincia di Quezon, nella regione di Calabarzon.
Calauag è formata da 81 baranggay:
Agoho
Anahawan
Anas
Apad Lutao
Apad Quezon
Apad Taisan
Atulayan
Baclaran
Bagong Silang
Balibago
Bangkuruhan
Bantolinao
Barangay I (Pob.)
Barangay II (Pob.)
Barangay III (Pob.)
Barangay IV (Pob.)
Barangay V (Pob.)
Bigaan
Binutas
Biyan
Bukal
Buli
Dapdap
Dominlog
Doña Aurora
Guinosayan
Ipil
Kalibo (Santa Cruz)
Kapaluhan
Katangtang
Kigtan
Kinamaligan
Kinalin Ibaba
Kinalin Ilaya
Kumaludkud
Kunalum
Kuyaoyao
Lagay
Lainglaingan
Lungib
Mabini
Madlangdungan
Maglipad (Rosario)
Maligaya
Mambaling
Manhulugin
Marilag (Punaya)
Mulay
Pandanan
Pansol
Patihan
Pinagbayanan
Pinagkamaligan
Pinagsakahan
Pinagtalleran
Rizal Ibaba
Rizal Ilaya
Sabang I
Sabang II
Salvacion
San Quintin
San Roque Ibaba
San Roque Ilaya
Santa Cecilia
Santa Maria
Santa Milagrosa
Santa Rosa
Santo Angel (Pangahoy)
Santo Domingo
Sinag
Sumilang
Sumulong
Tabansak
Talingting
Tamis
Tikiwan
Tiniguiban
Villa Magsino
Villa San Isidro
Viñas
Yaganak
Note
Altri progetti
Collegamenti esterni
Comuni della provincia di Quezon
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{
"redpajama_set_name": "RedPajamaWikipedia"
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Q: Prove that $M \cap \mathbb{N} \neq\emptyset$, where $M = \{ x-qd \mid q \in \mathbb{Z} \}$ I need to prove that $M \cap \mathbb{N} \neq\emptyset$, where $M = \left \{ x-qd \mid q \in \mathbb{Z} \right \}$, and $x,d \in \mathbb{Z}$, $ d > 0$
My attempt: Choose $x \geq 0$ then for all $qd \leq x$ we have that $(x - qd) \in \mathbb{N}$, and thus $M \cap \mathbb{N} \neq\emptyset$.
But I feel like this is not right, can anyone explain how to prove it?
A: As written, it appears that $x$ cannot be chosen. The statement is nonetheless true, for the following reason: let $x \in \mathbb{Z}$ and $d \in \mathbb{N}$. If $x > 0$ then $x \in \mathbb{N}$ and $x = x-0d \in M\cap \mathbb{N}$. If $x < 0$, we can take $q = 2x$ and so
$$
x - 2xd = x(1-2d) > 0
$$
because $x < 0$ and $1-2d < 0$. Thus, $x-2xd \in M \cap \mathbb{N}$. The remaining case is $x = 0$, for which you can take $q = 1$.
A: To brush away all the obfuscation:
For fixed $x,d\in \mathbb Z; d> 0$ then for any $q \in \mathbb Z$ then $x - qd \in \mathbb Z$. You are simply asked to prove that for some values of $q$ than $x - qd$ might be positive.
$x - qd > 0 \iff x > qd \iff \frac xd > q$.
So that that's it. For any integer $q < \frac xd$ then $x - qd\in M$ and $x - qd \in \mathbb Z$ and $x - qd > 0$ so $x-qd \in \mathbb N$ so $x-qd \in M \cap \mathbb N$ so $M\cap \mathbb N$ is not empty.
..... or .....
let $m = x - \lfloor \frac xd \rfloor d$ then $m > 0$ and $m \in \mathbb Z$ so $m \in \mathbb N$ and $m \in M$. So $m \in M \cap \mathbb N$ and $M \cap \mathbb N\ne \emptyset$.
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{
"redpajama_set_name": "RedPajamaStackExchange"
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\section{Introduction}
\IEEEPARstart{T}{raditionally}, electric power distribution systems have been designed and operated as passive systems to meet the customers' demand. However, with transformation of the grid to a smart grid, the reliability and operational challenges of distribution systems have increased. An operator will need to manage the distribution system more closely in the future, requiring improved visibility of its states~\cite{paudyal_optimal_2011}
which will involve real-time monitoring~\cite{ardakanian_real-time_2014}. Indeed, most solutions to smart grid related challenges at the distribution level assume a knowledge of the states of the system, and therefore essentially rely on Distribution System State Estimation (DSSE), which is a key function of supervisory control that some utilities have already began rolling-out \cite{atanackovic_deployment_2013}.
The state of a power system can be completely defined from the knowledge of all bus voltage magnitudes and angles at time $t$ \cite{monticelli_state_1999}; typically, state estimation is carried out based on measurements of variables such as the voltage magnitudes and angles, available from Phasor Measurement Units (PMUs)
State estimation of power systems is a well understood problem at the transmission level and is traditionally solved using a snapshot-based weighted least square (WLS) method which relies on high quality measurement data from PMUs \cite{monticelli_state_1999}.
However, transmission systems generally have a limited number of buses and are equipped with many measurement devices since it is important to precisely monitor and control the system at all times. On the other hand, distribution systems comprise a large number of buses with little to no measurements available.
While several recent studies have focused on developing low-cost, easy to deploy PMUs \cite{von_meier_micro-synchrophasors_2014, rodrigues_low_2016}, it is not practical to install PMUs at every distribution bus. If PMUs were to be placed at selected buses only, there would be infinitely many solutions to the DSSE problem. In order to reduce the number of possible solutions, pseudo-measurements can be used \cite{fantin_using_2014}, which are load forecasts computed ahead of time to aid DSSE in finding a ``good'' solution. Typically, a pseudo-measurement at a given load bus comprises an estimate of the expected active and reactive power consumptions at the bus. Load forecasting at the distribution level is difficult, hence pseudo-measurements are usually of poor quality. These fundamental differences, and the need for affordable solutions, mean that new state estimation approaches are needed for distribution systems.
Many studies have extended the WLS approach from transmission to distribution systems. A review of literature on the different state estimation techniques and their application to DSSE problems is presented in \cite{primadianto_review_2016}. One of the first applications of the snapshot approach to the DSSE problem was reported in \cite{ghosh_distribution_1997}, where a probabilistic formulation based on pseudo-measurements was used.
In \cite{schenato_bayesian_2014}, the power-flow equations were linearized and a computationally friendly solution method was proposed. The authors also showed that PMUs are needed for accurate state estimation. Compressed sensing theory was used for state estimation with sparse measurements in \cite{alam_distribution_2014}, while \cite{wang_revised_2004} used line-current magnitudes and angles. Finally a semi-definite programming approach was used to solve the DSSE problem in \cite{klauber_distribution_2015}.
Several researchers have used Kalman filters in state estimation problems for transmission systems \cite{filho_forecasting-aided_2009}.
However, in distribution systems, the poor quality of the pseudo-measurements renders such methods ineffective. Therefore, very few Kalman filtering based methods have been developed for DSSE and none improve over the WLS. Huang \textit{et al}. compared the extended Kalman filter to the unscented Kalman filter in \cite{huang_evaluation_2015}. From the reported results it was noted that there was no visible improvement in performance of the Kalman filter based methods over WLS. In \cite{sarri_state_2012} the impact of choice of the model and measurement covariance matrix on the performance of the extended Kalman filter was examined. It was noted from the results that the proposed filtering approach did not result in any performance improvement.
The above discussed Kalman filter based approaches apply the methods directly from the transmission to distribution systems. The problem of poor quality of pseudo-measurements is alleviated by assuming that measurements are available at every bus in real-time or quasi-real-time, usually from synchronized smart-meters, which is not realistic.
In this paper, a past-aware method for DSSE, named PASE (Past-Aware State Estimation), where the estimate at time $t$ depends on anterior estimates and based on the Ensemble Kalman Filter (EnKF) \cite{evensen_ensemble_2003} is presented. Applying the EnKF to this problem is non-trivial, since measurements from sources with different time-scales must be merged. Contrary to WLS and other approaches using different variations of the Kalman filter, PASE does not embed the power flow equations into the estimator, making it a versatile technique. Instead it relies on an external power-flow solver, which is left to the choice of the operator.
In a snapshot-based context where the state at time $t$ is computed independently of the estimates at times anterior to $t$, the WLS objective function provides the best performance possible (excluding ill-conditioned cases)\cite{singh_choice_2009}. Such an estimator is referred to as the State of the Art (SoA) in this paper, for the purpose of comparison.
Specifically, the contributions of the work are threefold: 1) A maiden attempt is made to apply EnKF to a distribution system sparsely monitored by PMUs for state estimation; 2) An analytical framework is developed to evaluate the performance of PASE; 3) The theoretical results are validated via extensive simulations on a 33-bus distribution system and using power consumption traces from real households. The performances of the proposed PASE approach and WLS are compared and engineering insights are provided to understand the impact of each decision variable on the performance of PASE, as well as the trade-offs to make.
Based on the above discussions, the main message of this work is that PASE is the first technique to improve upon the SoA. It does so significantly when the elapsed time between two consecutive state computations is small (less than 15 minutes
, i.e., less PMUs are needed to achieve the same estimation error.
The rest of the paper is organized as follows.
The background and assumptions are presented in Section \ref{system_model}. The SoA method is presented in Section \ref{SoA} and the proposed PASE solution in Section \ref{proposed_solution}. The validation results are reported in Section \ref{validation}. Finally, the conclusions are drawn in Section \ref{conclusion}.
\section{Background and Literature Review}
\section{System and Assumptions}
\label{system_model}
The assumptions are stated in this section. A three-phase balanced distribution system under normal operations is considered. The DSSE problem is solved by the local distribution company (LDC) using an appropriate computational platform. The following information is needed to implement DSSE, both with the SoA method and the proposed PASE method.
\textbf{Computational timescale}: a new state estimate is computed every $\Delta T$. Typically in transmission systems, a time-step of 5 to 15 min is considered. In distribution systems smaller time-steps are needed because of higher load volatility, which can arise for example with high penetration of renewables. The value of $\Delta T$ has an impact on the computational burden. In this work time-steps from 6 seconds to 15 minutes are considered. Altogether, the choice of an appropriate timescale for DSSE problems is still an open question.
\textbf{Topology:} the distribution system has a radial topology and is defined by a set of buses $I$ of cardinality $|I|$ as well as a set of branches $B$ of constant and known impedances, connecting the buses. The substation transformer is modeled as a reference voltage source of magnitude $V_0$.
\textbf{Measurements:} the subset $S \subseteq I$ of buses are equipped with PMUs that monitor every $\Delta T$ both the bus voltage magnitudes ($V_s$) and bus angles ($\delta_s$). The measurements reported by the PMUs are assumed to be unbiased and the variance of the error of the readings is known. These assumptions are commonly made in state estimation works \cite{monticelli_state_1999}. A broadband communication infrastructure is available to transmit the measurements with low latency and high reliability. The PMUs are placed in the distribution system according to a given mapping $\mathscr{S}$.
\textbf{Pseudo-measurements:} these are forecasts that ``measure'' both active and reactive powers. They are available for each bus $i$ in $I$.
Forecasts are made at periodic intervals $\Delta T'$, typically once a day for the next day (day-ahead forecast). At the time of computation, the most recent forecast is used. Clearly, forecasts and PMU measurements are on completely different time-scales ($\Delta T' \gg \Delta T$), hence the non-triviality of the EnKF. Forecasts are made based on historical data. Previous estimation work based on Kalman filters assumed real-time consumption data. This strong requirement is relaxed with forecasts.
\textbf{Data requirements:} both the SoA and PASE approaches require a forecasting method as well as sample power consumption traces (active and reactive) from the system at the level of each distribution transformer, from which the forecasting method can be calibrated. Using the data, error parameters can be obtained offline. Let $e_i(t)$ be the forecast error at bus $i$ and time $t$ (for active power, for example); $e_i(t)$ is assumed to be a stationary random process. Moreover, forecasts are assumed to be unbiased ($\text{E}[e_i(t)] = 0$) and the variance of the errors ($\text{E}[e_i(t)^2]$) to be known. The estimation of the variance of the forecast errors comes from the acquired data. The assumption of an unbiased forecast is a strong hypothesis, although it is almost always used by researchers \cite{schenato_bayesian_2014}.
The proposed PASE method needs two additional information that can be derived from the same sample data: a load evolution model (which will be discussed in Section \ref{evolution_model}) and the forecast error correlation coefficient, evaluated between two (computation) time-steps at a given bus (i.e., $\text{E}[e_i(t) e_i(t-\Delta T)]$). Given that the data samples are needed for both methods, not much work is involved to derive these additional quantities from it.
Finally, the load forecast errors are assumed to be uncorrelated between buses, an assumption often made in the literature \cite{schenato_bayesian_2014}.
\textbf{System state:} it is represented by state vectors; different (equivalent) state representations may be used depending on their ease of use in the problem formulation. For example,
$$\mathbf{y}[t] = [\mathbf{V}[t]^T, \mathbf{\delta}[t]^T]^T$$
is a possible state vector representation, where $\mathbf{V}[t]$ is the vector of voltage magnitudes at each bus, and $\mathbf{\delta}[t]$ the vector of voltage angles. Another way is to define $\mathbf{x}[t] = [\mathbf{P}[t]^T, \mathbf{Q[t]}^T]^T$ where $\mathbf{P}[t]$ and $\mathbf{Q}[t]$ denotes the vectors of active and reactive power injections at each bus, respectively. Note that the power-flow equations link the state-vectors $\mathbf{x}$ and $\mathbf{y}$. A third way, used in theoretical formulations, is $\mathbf{w}[t] = [ \underline{v}_1[t], \hdots, \underline{v}_{|I|}[t]]^T$ where $\underline{v}_i[t]$ is the voltage phasor at bus $i$, time $t$; this can also similarly be related to other representations.
\textbf{Limitations:} In this work, unbalanced system, distributed generation and biased measurements are not considered and are left for future studies.
\section{State-of-the-Art DSSE Method}
\label{SoA}
The SoA method \cite{monticelli_state_1999} used to solve the DSSE problem is a snapshot approach and uses a nonlinear WLS objective function. Given the system characterized by the sets $I, B, S$ and the mapping $\mathscr{S}$, the system state, at a given time, is estimated using an overdetermined set of equations. In the following, the time dependency of the variables is dropped for better readability. The variables to be determined are the $2|I|$ state variables. Each measurement adds one constraint. There are either 2 or 4 measurements per bus (active/reactive power forecast, voltage magnitude, and angle), depending on whether there is a PMU at the bus. The number of constraints is given by $M = 2|I|+2|S|$.
The PMU measurements and the forecasts are stored in a vector $\mathbf{z}$ of length $M$, and are related to the system state as per the following model:
$\mathbf{z} = f(\mathbf{y}) + \eta$
where $f$ is the function that maps the state vector to the measurement vector, and $\eta$ is the vector containing the noise term of each measurement. For example, $f(y) = [\mathbf{V}(y)^T, \delta (y)^T, \mathbf{P}(y)^T, \mathbf{Q}(y)^T]^T$ where $\mathbf{V}(y)$ and $\delta(y)$ are the vectors, respectively, containing the voltage magnitude and angle measurements at the buses with PMUs and $\mathbf{P}(y)$ and $\mathbf{Q}(y)$ are vectors of active and reactive power forecasts of size $|I|$, respectively. Assuming that the measurement errors are uncorrelated and have zero mean, the covariance matrix $\Sigma$ of the error vector $\eta$ is written as, $\Sigma = \text{diag}(\sigma_1^2, ..., \sigma_M^2)$, where $\sigma_m^2$ is the variance of the $m^{th}$ measurement.
The objective function to be minimized at each time-step is given below:
\begin{equation}
J(\mathbf{y}) = (\mathbf{z} - f(\mathbf{y}))^T \Sigma^{-1} (\mathbf{z} - f(\mathbf{y}))
\end{equation}
Several methods exist to minimize the objective function, the simplest being to iteratively linearize $f$ and solve the resulting objective using the normal equations.
\section{Characterization of Load Changes}
\label{load_model}
\section{Proposed Method: PASE}
\label{proposed_solution}
To solve the DSSE problem, PASE, an EnKF-based method, is proposed. Kalman filters are sequential filtering methods. Each iteration is a two steps process: 1) the system state is integrated in time using an evolution model, defining an (\textit{a priori}) state estimate. 2) Available measurements (including pseudo-measurements) are used to correct the estimate and define the updated state. The term \textit{assimilation} is used to refer to the second step. The load evolution model used in this approach is presented in Section \ref{evolution_model}. The idea behind the proposed approach is simple: the additional information provided by the load evolution model and the previously estimated states are used to alleviate the poor quality of pseudo-measurements.
\vspace{-6pt}
\subsection{Load Evolution Model}
\label{evolution_model}
For each distribution transformer bus, an evolution model for the aggregate load is needed, both for the active and reactive power consumptions. Specifically, the load variation between two (computation) time-steps is considered: let $L_i^p(t)$ and $L_i^q(t)$ denote the instantaneous active and reactive aggregated power respectively, at bus $i$ and time $t$. It is assumed that $L_i^p(t)$ and $L_i^q(t)$ are stationary random processes. The load variation (aka load evolution model) for active and reactive powers are defined as the stationary random processes $L_i^p(t) - L_i^p(t- \Delta T)$ and $L_i^q(t) - L_i^q(t- \Delta T)$ respectively, characterized by their probability density functions (pdf). The mean of the processes is zero and the variance of the processes can be computed from the pdf both for active and reactive powers at bus $i$, denoted $(\sigma^p_i)^2$ and $(\sigma^q_i)^2$, respectively. Such an evolution model is simple and fits within the EnKF framework. The pdf can be derived empirically, for example, from the existing required sample traces, discussed in Section \ref{system_model} as will be explained later.
Clearly a given load evolution model is valid only for systems with similar load compositions, and will vary for different geographical areas.
\vspace{-6pt}
\subsection{Ensemble Kalman Filter}
\label{EnKF}
The traditional Kalman filter maintains a covariance matrix associated with the state estimate. The EnKF does not use such a matrix and represents the system state pdf using a set of state vectors called ensemble. Such ensemble at time-step $k$ (i.e., time $k \Delta T$) is named $X^k$. The covariance matrix is replaced by the empirical covariance computed from the ensemble. The estimated system state is simply the mean of the ensemble columns. The size of the ensemble, $L$, will impact performance. A small ensemble size will yield faster computations. However the covariance estimate from the ensemble will be less accurate. Therefore there is a trade-off between computational speed and accuracy and a typical choice is a size of $L = 500$ or $1000$. The covariance estimator $\text{cov}(A, B)$ of two ensembles $A, B$ is defined as \cite{evensen_ensemble_2003}:
\begin{equation}
\text{cov}(A, B) = \frac{1}{N-1}(A - \text{E}[A])(B - \text{E}[B])^T
\end{equation}
where $\text{E}[A]$ is the mean of the column vectors contained in ensemble A. For $\text{cov}(A, A)$ the shorter syntax $\text{cov}(A)$ is used. Each iteration of the EnKF (corresponding to a computation of the state vector at time-step $k$) follows the procedure detailed in Algorithm \ref{alg:EnKF}, each steps of the algorithm are discussed next.
\begin{figure}
\begin{algorithm}[H]
\caption{Estimation of the state at time-step $k$}
\label{alg:EnKF}
\begin{algorithmic}[1]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\REQUIRE $X^{k-1}$, measurements and pseudo-measurements at time-step $k$.
\STATE Compute $X_p^k$: integrate the ensemble in time (Eq. \ref{eq:Xp_integration})
\STATE Compute $X_u^k$: assimilate pseudo-measurements (Eq. \ref{eq:Xu_correlated})
\STATE Compute $X_a^k$: assimilate PMU measurements (Eq. \ref{eq:Xu})
\STATE $X^k \gets X_u^k$
\ENSURE Estimated state $\mathbf{\tilde{x}^k} = E[X^k]$ for time-step $k$.
\end{algorithmic}
\end{algorithm}
\vspace{-15pt}
\end{figure}
\vspace{-6pt}
\subsection{Initial Ensemble}
\label{initial_ensemble}
The state vector $\mathbf{x} = [\mathbf{P}^T, \mathbf{Q}^T]^T$ (of size $2|I|$) is used. It is chosen given that the load evolution model described in Section \ref{evolution_model} is defined in terms of injected power. The pdf of the state vector $\mathbf{x}$ is represented by an ensemble of size $L$: $X^0 = [\mathbf{x}_1^0, \hdots, \mathbf{x}_L^0]$, $X^0$ is a $2|I| \times L$ matrix containing the ensemble members. The initial ensemble is built by choosing a ``best-guess'' estimate $\mathbf{x}^0$ of the state vector, to which perturbations are added to represent the error statistics of the initial guess. The error distribution chosen for the initial ensemble is discussed in Section \ref{validation}.
\vspace{-6pt}
\subsection{Ensemble Integration}
The EnKF is considered at time-step $k$. The prior ensemble $X^k_p$ is obtained by individually integrating forward in time each vector of the ensemble $X^{k-1}$, which was computed at the previous time-step. The integration is such that:
\begin{equation}
X_p^k = X^{k-1} + [\mathbf{n}_1, \hdots, \mathbf{n}_L] \label{eq:Xp_integration}
\end{equation}
where $\mathbf{n}_l$ ($l=1, \hdots, L$) are column vectors of size $2|I|$ containing the stochastic noise which accounts for the uncertainties of the load evolution model. Based on the load evolution model defined in Section \ref{evolution_model}, two variance values $(\sigma^p_i)^2$ and $(\sigma^q_i)^2$ are associated to each bus $i$ ($i=1,\hdots, |I|$), respectively for the active and reactive powers. Their values depend on the empirical pdf derived.
Each $n_{i,l}$ and $n_{|I|+i, l}$ ($i=1, \hdots, |I|$) is respectively drawn from a distribution which represents the empirical pdf of the load evolution model. Note that the EnKF can accept any load evolution model.
\vspace{-6pt}
\subsection{Assimilation of Pseudo-Measurements}
\label{time_correlation_pseudo_measurements}
The assimilation of measurements and pseudo-measurements correspond to the update step of the Kalman filter, described at the beginning of Section \ref{proposed_solution}.
An assumption in Kalman filtering is that the measurement error is white Gaussian noise. Since pseudo-measurements are forecasts and do not depend on the state of the system, they do not satisfy this requirement; instead the forecast error is correlated in time. This problem, which is recurrent in Kalman-based kinematic GPS applications has been solved previously, and a summary of the different existing techniques can be found in \cite{wang_practical_2012}. The solution chosen in this paper is the time-differencing approach described in \cite{petovello_consideration_2009} to remove time-correlated error in the pseudo-measurements. This method was selected for two reasons: 1) it does not require any reinterpretation of the Kalman equations and 2) it does not introduce any latency.
To remove the correlations, the following process is used. Let the transition matrix $\Psi$ of the time-correlated error be defined as:
\begin{equation}
\Psi = \text{diag}(\psi^p_1, \hdots, \psi^p_{|I|}, \psi^q_1, \hdots, \psi^q_{|I|}) \label{eq:psi}
\end{equation}
where $\psi^p_i$ and $\psi^q_i$ ($i=1, \hdots, |I|$) are the forecast error correlation coefficients at bus $i$, respectively for active and reactive powers, introduced in Section \ref{system_model}
$\Psi$ is diagonal since the forecast errors between buses are assumed to be uncorrelated. $Q$ is defined as the model noise covariance matrix, and is given as:
\begin{equation}
Q = \text{diag}((\sigma^p_1)^2, \hdots,(\sigma^p_{|I|})^2, (\sigma^q_{|I|+1})^2, \hdots, (\sigma^q_{2|I|})^2 ) \label{eq:Q}
\end{equation}
$R$ is the covariance matrix of the forecast error, of size $2|I| \times 2|I|$. $R$ is diagonal since the forecast errors are assumed not correlated across buses, and is given as:
\begin{equation}
R = \text{diag}((\sigma_1^{fp})^2, \hdots, (\sigma_{|I|}^{fp})^2, (\sigma_{|I|+1}^{fq})^2, \hdots, (\sigma_{2|I|}^{fq})^2 ) \label{eq:R}
\end{equation}
where $\sigma_i^{fp}$ and $\sigma_i^{fq}$ are the standard deviations of the forecast error at bus $i$, respectively for the active and reactive powers. The pseudo measurements are contained in a vector $\mathbf{d}$ of size $2|I|$. An ensemble $D$ of $L$ perturbed observations is defined such that $D = [\mathbf{d}_1, \hdots, \mathbf{d}_L]$ with each $\mathbf{d}_l = \mathbf{d} + \epsilon_l$ ($l=1, \hdots, L$), where $\epsilon_l$ is a vector drawn from a distribution which models the pseudo-measurement noise. Before establishing the update step, intermediary matrices are defined next, which will be reused for the theoretical derivations.
\begin{align}
& H^* = H - \Psi H, ~~~ C = Q H^T \Psi^T, ~~~ D^* = D -\Psi D \label{eq:Hstar} \\
& R^* = (R - \Psi R \Psi^T) + \Psi H Q H^T \Psi^T \label{eq:Rstar}
\end{align}
The updated observation and measurement matrices ($H^*$ and $D^*$, respectively, are computed in (\ref{eq:Hstar}). The updated measurement error matrix $R^*$ is computed in (\ref{eq:Rstar}); $\Psi$ is used to remove the time correlation of the forecast error between two time-steps. The model noise matrix $Q$ is needed to ensure that the noise introduced by the evolution step is retained. Indeed such noise does not have any time correlation component. In this context, the observation matrix $H$ is the identity matrix (in Section \ref{theoretical_performance} the observation matrix will not be the same). The update equations for the assimilation of pseudo-measurements are given as:
\begin{align}
& E = H^* \text{cov}(X^k_p) H^{*T} + R^* + H^* C + C^T H^{*T} \\
& K = (\text{cov}(X^k_p)H^{*T} + C) E^{-1} \label{eq:K} \\
& X_u^k = X^k_p + K (D^* - H^* X^k_p) \label{eq:Xu_correlated}
\end{align}
\vspace{-6pt}
\subsection{Assimilation of PMU Measurements}
\label{PMU_assimilation}
Similar to the pseudo-measurements, the measurements coming from the PMUs are contained in a vector $\mathbf{z}$ of size $2|S|$. An ensemble $Z$ of $L$ perturbed observation vectors is computed such that $Z = [\mathbf{z}_1, \hdots, \mathbf{z}_L]$, with each $\mathbf{z}_l = \mathbf{z} + \xi_l$ ($l=1, \hdots, L$), where $\xi_k$ is a vector drawn from a distribution which models the measurement noise.
The measurements from the PMUs can be related to the state vector using a function $h$, such that $\mathbf{z}_l = h(\mathbf{x}_l) + \gamma_k$, where $\gamma_k$ is an error vector. The function $h(\cdot)$ takes as input the system state and returns a vector containing the measurements that would have been observed considering that particular system state. Given that $\mathbf{x}$ contains the active and reactive powers injected at each bus, $h(\cdot)$ is the power-flow solution; the EnKF does not need to know the analytical expression of $h(\cdot)$. It is the solution given by the LDC's power-flow solver, for example. This makes the EnKF independent of the way power-flows are computed. The cost of such independence is computational: one need to compute $L$ power-flows at each time-step.
Since $h(\cdot)$ is non-linear, the measurements cannot be obtained directly from the state using a simple multiplication by an observation matrix. Instead, $h(\mathbf{x})$ needs to be computed explicitly. A temporary augmented state $\widehat{\mathbf{x}}$ and augmented ensemble $\widehat{X}_u^k$ are used to perform the assimilation, where:
\begin{equation}
\widehat{\mathbf{x}}_l = [\mathbf{x_l}^T, h^T(\mathbf{x}_l)]^T, ~~~
\widehat{X}_u^k = [\widehat{\mathbf{x}}_1, \hdots, \widehat{\mathbf{x}}_L]
\end{equation}
The updated ensemble $X_a^k$ is then computed:
\begin{align}
& X_a^k = X_u^k + K(Z - \widehat{H} \widehat{X}^k_u) \label{eq:Xu}\\
& K = \text{cov}(X_u^k, \widehat{H} \widehat{X}^k_u) [\text{cov}(\widehat{H} \widehat{X}_u^k) + \text{cov}(Z) ]^{-1}
\end{align}
where $\widehat{H}$ is a selection matrix used to select the rows of the state vector corresponding to the desired measurements.
\vspace{-6pt}
\subsection{Theoretical Estimate of Performance}
\label{theoretical_performance}
In this section, a method to compute a theoretical estimate of the performance and the improvement achieved by the proposed PASE method is developed. It is based on \cite{schenato_bayesian_2014}, where the authors proposed a technique for estimating a priori the performances of the WLS estimator. Their work is extended in this paper to fit the EnKF and compute the relative gain between the two. The derivation is performed under the following assumptions, also made in \cite{schenato_bayesian_2014}. The state vector is represented by $\mathbf{w} = [\underline{v}_1, \hdots, \underline{v}_{|I|}]^T$. The forecast variance, the forecast error time-correlation and load evolution model variance are assumed to be constant and identical for active and reactive powers. They are denoted respectively $(\sigma^f_i)^2$, $\psi_i^f$ and $(\sigma^d_i)^2$. At each bus $i$, the apparent power magnitude $|S_i^f|$ is used to represent the load forecast. In the analysis framework, the shape of the load evolution model is not need to be known, the value of the variance is sufficient.
The theoretical computations are performed by using a linear Kalman filter. The covariance matrices are made time-invariant in order to obtain a steady-state formulation of the filter \cite{anderson1979optimal}. From this formulation, the covariance matrix of the system state can be computed and used to approximate the performance of the non-linear EnKF. The performance of WLS can also be computed since it can be seen as a Kalman filter that is reset for each new estimation. To evaluate the performance of the two state estimators over a period of time $T$, the average root mean square error of the voltage estimate (ARMSEV) is used as metric:
\begin{equation}
\text{ARMSEV} = \sqrt{\frac{1}{T|I|} \sum_{t=0}^{T}\sum_{i=1}^{|I|} \mathbf{E}[|\underline{\hat{v}}_i[t] - \underline{v}_i[t]|^2]}
\end{equation}
where $\underline{v}_i$ is the true voltage at bus $i$ and $\underline{\hat{v}}_i$ the estimated one. A linear version of the power-flow equations is used; it is the first iteration of backward-forward sweep. A vectorized formulation is obtained by using a distribution load flow (DLF) matrix, denoted by $M$, as described in \cite{teng_direct_2003}. The relationship between the injected power at each bus (represented by the vector $\mathbf{s} = [\underline{s}_1, \hdots, \underline{s}_{|I|}]^T$, with $\underline{s}_i$ the injected power at bus $i$) and the state vector is given as:
\begin{equation}
\mathbf{w} = [V_0, \hdots, V_0] + \frac{1}{V_0}M\times \overline{\mathbf{s}}
\end{equation}
where $\overline{\mathbf{s}}$ is the conjugate of $\mathbf{s}$. Several matrices used by the Kalman equations are defined. The load evolution noise covariance matrix $Q$ expressed in terms of the apparent power, and the forecast error covariance matrix $R_S$ are computed as follows:
\begin{equation}
Q = \text{diag}((\sigma^d_1)^2, \hdots, (\sigma^d_{|I|})^2) \label{eq:Qtheoretical}
\end{equation}
\begin{equation}
R_S = \text{diag}((\sigma^f_1 )^2, \hdots, (\sigma^f_{|I|} )^2) \label{eq:RS}
\end{equation}
The PMU measurement error covariance matrix is approximated by assuming that the variance of the voltage error when projected onto the real and imaginary axes is the same and equal to $\sigma_{PMU}^2 V_0^2$, where $\sigma_{PMU}^2$ is the relative variance of the PMU measurements such that $R_{PMU} = 2 \sigma_{PMU}^2 V_0^2 \times I_{|S|}$, where $I_{|S|}$ is the $|S|\times |S|$ identity matrix.
The steady state covariance matrix of the state vector is computed by iterating the Kalman equations. The covariance matrix is denoted by $\Sigma_a^{(\cdot)}$. The iteration number is indicated in the parenthesis $(\cdot)$. Such matrix will converge to a steady state covariance matrix $\Sigma_a^{(ss)}$. For each iteration, two other matrices are used to track the covariance matrix during intermediary steps: $\Sigma_p^{(\cdot)}$ and $\Sigma_u^{(\cdot)}$. They represent respectively the covariance matrix of the prior state and the state after assimilation of PMU measurements. At iteration $0$, the prior covariance matrix of the state is computed such that:
\begin{align}
& \Sigma_p^{(0)} = M \times R_S \times M^H \label{eq:priorCovarianceMatrix}
\end{align}
where $(\cdot)^H$ indicates the Hermitian transpose (transpose conjugate operator). The updated covariance matrix obtained after the assimilation of the PMU measurements is then computed:
\begin{align}
& \Sigma_a^{(0)} = \Sigma_p^{(0)} - K H \Sigma_p^{(0)} \label{eq:sigma_u} \\
& K = \Sigma_p^{(0)} H^T (H \Sigma_p^{(0)} H^T + R )^{-1} \label{eq:K_sigma_i}
\end{align}
where $H$ is the observation matrix for PMU measurements. It is a selection matrix that relates state variables to the measurement vector. One can estimate the ARMSEV performance of WLS based on $\Sigma_a^{(0)}$: $\text{ARMSEV}_{\text{WLS}} = \sqrt{\frac{1}{|I|}\text{trace}(\Sigma_a^{(0)})} \label{eq:ARMSEV_WLS}$.
Any iteration $it$ ($it \neq 0$) is performed in 3 steps: first the prior covariance matrix $\Sigma_p^{(it)}$ is computed based on the previous iteration, then the covariance matrix is updated using the PMU measurement covariance matrix, and finally the pseudo-measurements are assimilated. The first two steps are such that (where $H$ is the same matrix as in (\ref{eq:sigma_u})):
\begin{align}
& \Sigma_p^{(it)} = \Sigma_a^{(it-1)} + M \times Q \times M^H \\
& \Sigma_{a}^{(it)} = \Sigma_p^{(it)} - K H \Sigma_p^{(it)} \\
& K = \Sigma_p^{(it)} H^T (H \Sigma_p^{(it)} H^T + R_{PMU} )^{-1}
\end{align}
The third step differs because of the pseudo-measurement error time correlation (see Section \ref{time_correlation_pseudo_measurements}). The same time-differentiation method is used. The same updated matrices are computed according to (\ref{eq:Hstar})-(\ref{eq:Rstar}) with only a few differences. Now $H$ is the inverse DLF matrix, mapping the state vector to the injected power ($H = M^{-1}$). The forecast error time correlation matrix is such that $\Psi = \text{diag}(\psi_1^f, \hdots, \psi_{|I|}^f)$. Finally, the matrix $R$ used in (\ref{eq:Rstar}) is such that $R = R_S$. The update equations thus become:
\begin{align}
\Sigma_{a}^{(it)} &= \Sigma_{u}^{(it)} - (\Sigma_{u}^{(it)} (H^*)^{T} + C) \times K^T \\
K &= \begin{aligned}
&[\Sigma_{u}^{(it)} * (H^*)^{T} + C] \times [H^* \Sigma_{u}^{(it)} (H^*)^{T} \\
& + R^* + H^*C + C^T (H^*){T}]^{-1}
\end{aligned}
\end{align}
Once the steady state is reached after a few iterations, the theoretical performance of the EnKF can be computed. The ARMSEV error is such that: \newline
$\text{ARMSEV}_{\text{EnKF}} = \sqrt{\frac{1}{|I|}\text{trace}(\Sigma_a^{(ss)})}$.
The relative gain is expressed as: $\text{Gain} = \frac{\text{ARMSEV}_{\text{WLS}} - \text{ARMSEV}_{\text{EnKF}}}{\text{ARMSEV}_{\text{WLS}}}$.
\section{Validation and Results}
\label{validation}
The improvement in performance achieved by the proposed PASE method over WLS is evaluated by considering a 33-bus test distribution feeder \cite{baran_network_1989} under normal operations. The WLS estimation problem is modeled in GAMS environment and solved using the MINOS solver. Attention has been paid to avoid potential numerical issues. The ensemble size is set to $L = 500$ and the power flow solutions obtained from $h(\cdot)$ are computed using the backward/forward sweep method \cite{teng_direct_2003}. The system is simulated over a period of 24 hours. For the theoretical estimation, 50 iterations ($(ss) = 50$) are enough to compute the steady-state of the state covariance matrix.
\subsection{Load Evolution Model}
\label{validation_load_evolution_model}
The (bus) load evolution model was developed using a fine-grained energy consumption dataset from Ontario, Canada. The dataset used to build the model is described in \cite{ardakanian_markovian_2011} and comprises instantaneous active power consumption data from 20 homes, collected over eight months, with a resolution of 6 seconds.
The dataset is split randomly into two subsets, one for deriving the characterization (training set), and one for the validation process (testing set). No distinction is made between the size of the houses nor the time of the year. The resulting dataset is a collection of a few thousands of traces. Although 20 homes may seem to be a limited sample size, considering the daily power traces independently allows to have a large number of unique profiles. Moreover the 20 households cover a wide range of living area sizes and energy consumption patterns which increases the trace diversity.
Let $n$ be the number of households connected to a bus. Using the training set, empirical distributions for load changes were constructed for different values of time-steps $\Delta T$ and aggregation levels $n$. A Laplace distribution described by a scale parameter $b$ (and variance $\sigma^2 = 2b^2$) was found to be a good fit.
The mean value is set to zero since as many positive and negative load changes are expected. This implies that the transition model is the identity, while its uncertainty is characterized by the Laplace distribution.
The influence of $\Delta T$ and $n$ on the distribution variance is illustrated in Fig.~\ref{fig:influence_parameter}. The variance essentially describes the load variation over time, a small value implying little variations. It is noted that as $n$ increases and $\Delta T$ shrinks, the value of $\sigma^2$ diminishes.
It was assumed that load changes are uncorrelated between buses; which can be verified to hold true from the dataset, for any value of $n$ and $\Delta T$ up to 30 minutes.
The values of $\sigma^2$ are derived empirically as a function of $n$ and $\Delta T$. They are used to compute the evolution step of the EnKF. Since no reactive power consumption dataset was available, a similar model is assumed for reactive power changes. However, active and reactive power consumption changes are assumed to be independent, which is a common assumption in DSSE literature. The proposed method is generic and can be applied to any dataset from across the globe.
\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{figures/betas_aggregation_time-step-autumn.eps}
\caption{Influence of aggregation level and time step on the scale parameter $b$. The fit of the Laplace distribution is visually good for all the time-steps and aggregation levels considered here.}
\label{fig:influence_parameter}
\end{figure}
\vspace{-6pt}
\subsection{Test Distribution System}
The 33-bus test feeder data includes active and reactive power loads at each bus; bus-1 is the substation transformer bus, with $V_0$ set to 12.66 kV. The number of houses $n_i$ aggregated at a bus $i$ is selected such that $n_i = n_{11}P_i^{33bus}/P_{11}^{33bus}$ where $n_{11} = 10$ houses and $P_i^{33bus}$ is the static 33-bus active power load at bus $i$.
The corresponding distribution transformer traces are generated from the second half of the dataset, by summing the desired number of profiles, picked randomly. Each trace is then scaled so that the mean of the profile matches the load values. The values given by the empirical function in Section \ref{validation_load_evolution_model} are scaled accordingly. Because no dataset for reactive power consumption is available, active and reactive power profiles are generated independently from the same dataset.
\vspace{-6pt}
\subsection{Measurement Model}
The simulation models used for measurements are described in this section.
\textbf{PMU:} the PMU measurement error is simulated as an additive white Gaussian noise of nominal variance $\sigma^2_{PMU}$, for both voltage magnitudes and angles. The readings $\tilde{V}_s$ and $\tilde{\delta}_s$ provided by the PMU at each bus $s$ ($s \in S \subseteq I$) have an error variance such that $\mathbf{E}[\tilde{a}^2] = \sigma^2_{PMU} * \tilde{a}^2$, where $\tilde{a}$ indicates either the voltage magnitude or angle. The measurement errors are independent across buses, and the voltage magnitude error independent of the angle error. The PMU resolution is set to 1\% ($\sigma_{PMU} = 0.01$); the PMU placement map $\mathscr{S}$ is determined using a greedy method \cite{schenato_bayesian_2014}, i.e., PMUs are sequentially added at the location that provides the most improvement (with 32 load buses, a maximum of 32 PMUs). The placement of PMUs is beyond the scope of this work; many researchers have addressed this issue, see for example \cite{singh_measurement_2009}.
\textbf{Pseudo-measurements}: the forecasts $P^f_i$ and $Q^f_i$ are taken as the mean value of the load profile generated at each distribution transformer $i$, as in \cite{schenato_bayesian_2014}. They are constant over the simulated period. Using the training set, the nominal standard deviation of the forecast was evaluated and set to $\sigma_0 = 30\%$, for both active and reactive powers, irrespective of the aggregation level. Therefore for each bus $i$, $\sigma_i^{fp} = \sigma_0 P_i^f$ and $\sigma_i^{fq} = \sigma_0 Q_i^f$ (\ref{eq:R}). The constant apparent power forecast $|S_i^f|$ is such that $|S_i^f| = |P_i^f + jQ_i^f|$. Finally each $\sigma^f_i$ (\ref{eq:RS}) is computed as $\sigma^f_i = \sigma_0 |S_i^f|$. Pseudo-measurements with a Gaussian distribution are used as ``best-guess'' initial ensemble (Section \ref{initial_ensemble}).
\textbf{Error time-correlation}: $\psi_i^p$ and $\psi_i^q$ are evaluated as follows: since the same data is used for generating the active and reactive power profiles, $\psi_i^p$ and $\psi_i^q$ are equal. They are evaluated on the training set. Given an aggregation level and a time-step length, load profiles are built. The autocorrelation function $R^e_i$ of the difference between the profile and its mean (representing the forecast error) is computed. The value of $\psi_i^p$ and $\psi_i^q$ is given by $R^e_i(\Delta T)$.
\vspace{-6pt}
\subsection{Validation}
\begin{figure*}
\centering
\subfloat[][]{\includegraphics[width=0.28\textwidth]{figures/comparison_performance_6s.eps}\label{fig:validation_6s_performance}}
\subfloat[][]{\includegraphics[width=0.28\textwidth]{figures/performance_gain_6s.eps}\label{fig:validation_6s_gain}}
\subfloat[][]{\includegraphics[width=0.28\textwidth]{figures/average_gain_comparison_5_20_PMUs.eps}\label{fig:validation_5_20_PMUs}}
\caption{\protect\subref{fig:validation_6s_performance} ARMSEV value function of the number of PMUs. The performance of the proposed PASE method is compared with WLS. The theoretical results are also compared against simulation results. A lower value means better performance. \protect\subref{fig:validation_6s_gain} Comparison of the gain from using PASE over WLS on ARMSEV depending on the number of PMUs. The theoretical results are compared to the observed gain in simulation. \protect\subref{fig:validation_5_20_PMUs} Influence of the time-step on the mean performance gain. The theoretical results are compared to the observed gain in simulation. The time-step axis has a logarithmic scale. The error bars represent the variance.}
\end{figure*}
The theoretical and simulation results are presented in Figs.~\ref{fig:validation_6s_performance}-\ref{fig:validation_5_20_PMUs}, obtained by averaging the results of several realizations. A realization is defined as the observed performance of both the WLS and PASE on the 33-bus system. For each realization, new load profiles are generated based on the testing set, while the other parameters stay the same. The performance of the WLS and PASE are plotted alongside with the theoretical ones in Fig.~\ref{fig:validation_6s_performance}, where a time-step of 6 seconds has been used. WLS has been studied in \cite{schenato_bayesian_2014} using synthetic data. Similar trends are observed here with real data. Note that since WLS is snapshot-based, the size of the time-step does not matter. For PASE, the theoretical results are close to the actual performance observed in simulation as the number of PMUs introduced in the system increases, which validates the theoretical approach. Similar trends are observed for different time-steps. The actual gain brought about by PASE is compared with the theoretical one in Fig.~\ref{fig:validation_6s_gain} for a time step of 6 seconds.
Finally the influence of the time-step on the gain is compared in Fig.~\ref{fig:validation_5_20_PMUs} for two PMU configurations (5 PMUs and 20 PMUs). Theory and simulation follow the same trend. The gap between theory and simulation is relative to that observed in Fig.~\ref{fig:validation_6s_gain}. For 5 PMUs, a separation between the curves is observed.
\vspace{-6pt}
\subsection{Comparison Between WLS and Proposed PASE Method}
The results presented in Fig.~\ref{fig:validation_6s_performance} illustrate the improvements achieved by the proposed PASE method. Clearly, using a load evolution model improves the performance of the estimator; given an arbitrary target error of 0.004 p.u., WLS requires more than 10 PMUs while PASE only 4. Even when each bus of the distribution system is monitored by a PMU, the proposed PASE method still brings about an improvement of more than 40\% when using a time-step of 6 seconds. As illustrated in Fig.~\ref{fig:validation_5_20_PMUs}, higher gains are obtained for smaller time-steps. Indeed, for larger time-steps, the load has more chances of changing by a large magnitude between two estimates and thus has less inertia. Even for large time-step (e.g., 10 mins) there is a gain of about 15\%. In practice, the granularity of the time-step depends on the available computational speed. The smallest time-step considered in this work is 6 seconds and represents a lower-bound on what was tried out. In comparison, the DSSE problem was solved at each step in under 1 second.
\vspace{-6pt}
\subsection{Engineering Insights}
\begin{figure}
\centering
\subfloat{\includegraphics[width=0.25\textwidth]{figures/influence_sensor_accuracy.eps}\label{fig:sensor_accuracy}}
\subfloat{\includegraphics[width=0.25\textwidth]{figures/engineering_insight.eps}\label{fig:engineering_insight}}
\caption{\protect\subref{fig:sensor_accuracy} Influence of PMU quality on the (theoretical) gain achieved by PASE over WLS. The PMU accuracy is characterized by its measurement error standard deviation, a lower value means a more accurate PMU. A logarithmic scale is used for the variance axis. \protect\subref{fig:engineering_insight} Minimum number of PMUs required to achieve an average target error of $2.25e-3$ p.u., function of time-step and for two PMU accuracies (computed using the theoretical formulation).}
\end{figure}
In practice, the LDC will need to make trade-offs in the choice of the following parameters: number of PMUs, their accuracy and the time scale. The influence of PMU accuracy on the theoretical gain achieved by PASE is shown in Fig.~\ref{fig:sensor_accuracy}, the three parameters considered are depicted in the plot. The maximum gain is attained for a PMU error variance of about 1\%. Clearly as the PMU measurement standard deviation decreases (i.e., the PMU becomes more and more accurate) the gain achieved by PASE decreases since the load evolution model is not as useful in such circumstances. Similarly, as the standard deviation of the PMU increases, the gain decreases, since the load evolution model has to compensate for both poor forecast accuracy and poor PMU measurement accuracy. This figure also illustrates the role of the time-step, the gain achieved by the filtering technique decreasing as the time-step increases, underlining the limits of the load evolution model.
The trade-off between the three parameters considered is illustrated by Fig.~\ref{fig:engineering_insight}: two PMU accuracies are used to draw the plots. An arbitrary target error is fixed and the minimum number of PMUs required is determined as a function of the time-step. Clearly, the time-step has little influence on a very accurate PMU. However, the more accurate the PMU, the more costly it will be. With the same number of PMUs placed in the system (4), choosing a PMU ten times less accurate will provide the same performance given that a time-step small enough (6 seconds) is chosen.
\section{Conclusions}
\label{conclusion}
A novel PASE method for DSSE and its analysis framework were presented. The PASE method performs the fusion of measurements and pseudo-measurements and requires fewer PMUs than WLS to achieve the same estimation error, for time-steps under 15 minutes. Engineering insights were presented highlighting the major trade-offs in the choice of decision variables for the LDC. Using a smaller time-step allows the LDC to relax the requirements on the PMU quality and their number. There are several remaining challenges, such as the influence of distributed generation and its modeling as well as the impact of an unbalanced system on PASE.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,580
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\section{Introduction}
The cuprate high-$T_c$ superconductors (HTSCs) are an important class of materials for both fundamental science research, as well as novel technological applications. Obviously, a primary reason is the rather high critical temperature $T_c$, which allows to operate such devices with reliable and easy-to-handle cryocooler technology. The well-known applications of almost loss-less energy transport in superconducting cables and the creation of intense magnetic fields by superconducting coils require high critical current densities \cite{CARD03M} that can be achieved for instance by inclusion of nanoparticles \cite{HAUG04} to increase flux pinning. On the other hand, possible applications of HTSCs in superconducting circuits and devices for novel quantum technologies \cite{WORD17M,MOSH10M} do not require high critical currents but instead advanced nanostructuring methods to pattern thin films of HTSCs. However, the anisotropic layered structure and the brittle nature of HTSCs pose severe constraints to conventional micro- and nanopatterning methods.
But it is exactly the complex crystal structure of HTSCs that allow for an intriguing and unconventional nanopatterning method. In the prototypical HTSC YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO), oxygen is situated at several different atomic positions. Whereas the oxygen atoms in the CuO$_2$ planes that carry the supercurrent have a binding energy of about 8.4 eV \cite{TOLP96}, the oxygen atoms in the CuO chains are bound by only about 1 eV \cite{CUI92}. They are also important for superconductivity, because they supply the charge transfer to the CuO$_2$ planes. For this reason, YBCO is rather sensitive to light-ion irradiation during which the oxygen --- and to a lesser extent also the other atoms --- are displaced from their sites. The resulting vacancies and interstitials are point defects in an otherwise still intact crystallographic framework. Due to the $d$-wave symmetry of the superconducting gap in the HTSCs, even minor distortions of the atomic lattice lead to a reduction of $T_c$ \cite{WANG95b}, in particular when the defects concern the CuO$_2$ planes \cite{TOLP96}. The delicate influence of the oxygen positions in the YBCO structure is for instance illustrated by the observations that $T_c$ can be increased again when disordered oxygen is re-ordered by thermal annealing \cite{JORG90} or by optical illumination \cite{STOC98a}. Thus, irradiation with light ions is a convenient tool for a controlled modification of the superconducting properties of YBCO \cite{LANG04,CYBA14a}.
\begin{figure*}[t!]
\centering
\begin{subfigure}[b]{0.52\textwidth}
\centering
\includegraphics[width=\textwidth]{MIBS}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\textwidth}
\centering
\includegraphics[width=\textwidth]{Mask}
\end{subfigure}
\caption{(a) The principle of masked ion beam direct structuring (MIBS), where a collinear ion beam is partially blocked by a stencil mask. Ions reaching the superconductor's surface create columns of point defects that reduce or suppress the critical temperature. (b) Scanning electron microscopy picture of a typical 2 $\mu$m-thick silicon stencil mask used for MIBS. It consists of a rectangular area of $200\,\mu\text{m} \times 80\,\mu\text{m}$ perforated with a square array of holes with $(302 \pm 2)\,$nm pitch. The blow-up shows a detailed view of a few holes with diameters $(180 \pm 5)\,$nm \cite{HAAG14}.}
\label{fig:MIBS}
\end{figure*}
Nanopatterning using stencil-mask lithography has been applied to several materials and has a number of advantages over other structuring techniques \cite{VAZQ15,VILL11a}. In combination with the afore-mentioned specific properties of HTSCs, shadowed ion irradiation can be employed to locally modify the superconducting properties. This provides a route to create small non-superconducting structures in thin YBCO films that can act as commensurate pinning centers for magnetic flux quanta.
Some of the previous experiments have used a variant of the stencil technique by using a pre-patterned layer of photoresist with etched voids \cite{KAHL98,KATZ00,BERG05,SWIE12} or a deposited metal layer that is patterned by ion beam milling \cite{KANG02a,BLAM03} as the ion-blocking material. By irradiating YBCO with 200 keV Ne$^+$ \cite{KATZ00} or 100 keV O$^+$ \cite{BERG05} ions through a 20~nm wide slit in the photoresist the fabrication of Josephson junctions has been demonstrated. However, such procedures lack some of the typical advantages of stencil lithography.
In our approach, a thin Si stencil mask is placed on top of the YBCO film and kept at well-defined distance by a $1.5\text{-}\mu$m-thick spacer layer. By this procedure any contact between the surfaces of the mask and the YBCO film is avoided. This masked ion beam direct structuring method (MIBS), sketched in Fig.~\ref{fig:MIBS}(a), provides a 1:1 projection of the hole pattern inscribed in the mask, since the ion beam from a commercial implanter is highly collinear and can only reach the YBCO surface through the mask holes. Scanning electron microscopy pictures of a typical mask are presented in Fig.~\ref{fig:MIBS}(b). The ion irradiation produces columnar defect-rich regions (CDs) in the sample. A detailed description of MIBS can be found elsewhere \cite{LANG06a,ZECH17a}. Patterns with linewidths down to 67~nm have been demonstrated \cite{PEDA10}.
Ion-irradiation has many advantages for nanopatterning of HTSCs. By adjusting the ion fluence, the $T_c$ of the superconductor can be reduced, it can be converted to a normal conductor, or even to an insulator. With the ion's energy the penetration depth can be tuned according to the thickness of the HTSC film. In contrast to chemical etching or ion milling, the surface of the HTSC remains essentially flat after ion irradiation, which avoids deterioration of the superconducting part of the film by out-diffusion of oxygen through the open side faces. It is a severe stability issue when many small structural features would be prepared by removing material.
Using ion irradiation together with stencil lithography avoids any contact with the sample surface, does not require chemical treatment or etching, is a time-economic parallel method applicable to large areas, and the mask can be reused many times. Another non-contact method has been recently demonstrated employing a focused He$^+$ beam. Josephson junctions in thin YBCO bridges are fabricated by irradiating narrow stripes with the focused 30~keV ion beam of a helium ion microscope that is scanned over the sample surface \cite{CYBA15,CHO18,CHO18a,MULL19}. Since no mask is used this method offers great flexibility and sub-10~nm resolution \cite{MULL19}, but can be only applied to very thin HTSC films due to penetration depth limitations of the available ion energy.
\begin{figure}[t!]
\centering
\includegraphics[width=\columnwidth]{Matching}
\caption{Critical current of a YBCO sample, nanopatterned with a square array of defect columns by MIBS, as a function of the applied magnetic field $B$. Each individual datum was measured after in-field cooling from above $T_c$ to 35~K to achieve the ground state of the vortex arrangement. The inset shows a sketch of the magnetic field profile at the matching field $B_m = 22.6$~mT, corresponding to the $n=1$ peak of the critical current, where every defect column is occupied by one flux quantum $\phi_0$. The current is aligned parallel to the defect rows. Data taken from \cite{ZECH17a}.}
\label{fig:Matching}
\end{figure}
Using MIBS with a 75 keV He$^+$ ion beam with a fluence of $3 \times 10^{15}\ \textrm{cm}^{-2}$, supplied by a commercial ion implanter, a square array of CDs with lattice constant $d = (302 \pm 2)$~nm was patterned into a $(210 \pm 10)$~nm thick YBCO film on a MgO substrate. The thin Si stencil mask (custom fabricated with e-beam lithography by ims-chips, Germany) was perforated with a square array of about $670 \times 270$\ holes with diameters $D = (180 \pm 5)$~nm and covered the entire sample area used for the electrical measurements. Marker holes in the stencil mask were used to align the hole array in an optical microscope parallel to the YBCO bridge with a deviation of less than $0.3^\circ$. Details of the fabrication method have been reported elsewhere \cite{ZECH17a}.
The desired local suppression of $T_c$ in thin YBCO films can be demonstrated by commensurability effects of magnetic flux quanta $\phi_0 = h/(2e)$, where $h$ is the Planck constant and $e$ the electron charge, the so-called fluxons or vortices \cite{HAAG14}. At the matching field $B_m = \phi _0/d^2$ exactly one fluxon is trapped in every CD which leads to a peak in the critical current as shown in Fig.~\ref{fig:Matching}. Besides this $n=1$ peak, it is possible to observe peaks when a larger number $n$ of fluxons are trapped in every CD, or when no magnetic field is present ($n=0$). Since the matching field $B_m$ is solely determined by the density of CDs, the peak in the critical current at $B_m$ provides direct evidence of the commensurate trapping of fluxons in the irradiated areas. Details on the observation of fluxon commensurability effects in the critical current of YBCO films, patterned with artificial defects by MIBS, are reported elsewhere \cite{HAAG14}. In addition, an unconventional critical state \cite{ZECH17a} and a sign change of the Hall effect \cite{ZECH18a} have been observed in such samples.
Although it is well established that fluxons can be trapped by regions in which superconductivity is suppressed, little is known about the 3-dimensional (3D) profile of the local critical temperature $T_c$ in and around CDs fabricated by ion irradiation. The evaluation of the shape of the irradiated columns and the possible blurring with increasing depth is important for an in-depth understanding of the experimental results. In this paper, we present simulations of defect cascades after ion irradiation through a stencil mask and an assessment of the resulting local $T_c$ variation by comparing the calculated defect density to experimental data.
\section{Methods}
The defects caused by the impact of ions onto the surface of the superconductor are calculated with the program ``Transport of Ions in Matter'' (TRIM) \cite{ZIEG85M}, which is part of the package ``The Stopping and Range of Ions in Matter'' (SRIM) \cite{ZIEG10}. It can compute the impact of ions on solids using a binary collision approximation of ion-atom and atom-atom collisions, providing the energy loss and final spatial distribution of ions, and, most importantly, the full collision cascades. It is based on approximations to quantum mechanical screened interaction potentials and a statistical Monte Carlo algorithm to compute nuclear and electronic stopping cross-sections in amorphous targets. However, ion channeling, thermal effects, diffusion and recrystallization are not considered.
Our simulations were performed with the \emph{Monolayer Collision Steps} method to force a calculation of ion-atom interaction and full interatomic collision cascades in each target layer, thus disabling the free-flight-path approximation. To enable comparison with our previous experimental results, the incident ion species is He$^+$ with an energy of 75~keV and a direction orthogonal to the sample surface. The density of the YBCO target layer is set to 6.3~g~cm$^{-3}$ \cite{MARW89a} with the number of compound atoms according to their stoichiometric abundance, but considering the one oxygen site per elementary cell in the CuO chains separately. The displacement energies $E_d$ for the various atom species are: $E_d^{O_c}=1$~eV for the chain oxygen atoms \cite{CUI92}, $E_d^{O_p}=8.4$~eV for the in-plane and apical oxygen atoms \cite{TOLP96}, $E_d^{Cu}=15$~eV for the Cu atoms \cite{LEGR93}, and 35~eV for the Y and Ba atoms. Note that the results are not sensitive to minor deviations from these values. For further evaluations, displacements of all atoms in the YBCO structure are considered as defects, where O atoms represent about 75~\% and Cu atoms about 18~\% of the total defect number.
The output of SRIM has to be further processed to reflect the actual experimental situation. In SRIM, collision cascades are calculated independently for individual ions impacting at the same spot at coordinates $(x,y)=(0,0)$. The number of ions $N$ that correspond to a particular irradiation fluence $\Phi$ of a circular area with diameter $d$ is $N=\Phi {d^2}\pi/4$. For typical experimental values $d=180$~nm and $\Phi=3\times 10^{15}\textrm{~cm}^{-2}$, and hence $N=763,407$. For each incident ion, the impact coordinates $(x_i,y_i)$ are determined by evenly distributed random number pairs with $\sqrt{x_i^2+y_i^2}\leq d/2$ and all output data from SRIM (defects) related to this ion trajectory are then shifted by $(x_i,y_i)$.
\begin{figure}[t!]
\centering
\includegraphics[width=\columnwidth]{fluence}
\caption{Ion fluence profiles at various depths for a YBCO thin film uniformly irradiated with 75~keV He$^+$ ions through a stencil mask hole with 180 nm diameter.}
\label{fig:fluence}
\end{figure}
Since SRIM uses a Monte-Carlo method on an amorphous target structure, details of the elementary cell are not resolved and, thus, the various defects are counted in cells of $2 \times 2 \times 2$~nm$^3$ \--- a size that roughly corresponds to the in-plane Ginzburg-Landau coherence length of YBCO. The results are then converted to commonly used \emph{defects per atom} (dpa) values considering the YBCO's crystal structure. In our samples, the CDs form a square array of CDs (CDA) with 300~nm lattice constant. If an ion trajectory leaves the CDA unit cell and, thus, produces defects in the neighboring CD, it is mapped back to the primary unit cell for proper visualization.
\section{Results and discussion}
\begin{figure*}[t!]
\centering
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{dpa_prof}
\subcaption{Lateral profiles at various depths.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{dpa_cross}
\subcaption{Cross-sectional view.}
\end{subfigure}
\caption{Distribution of the defect density (in dpa) within and around a defect column produced by 75~keV He$^+$ ion irradiation of YBCO with a fluence of $3\times10^{15}\textrm{~cm}^{-2}$.}
\label{fig:dpa}
\end{figure*}
The fluence of He$^+$ ions at various depths of a 200-nm-thick YBCO film is presented in Fig.~\ref{fig:fluence}. With increasing depth, the ions are multiply deflected from their previous trajectories, which leads to a blurring effect and to a change from the homogeneous fluence at the top of the sample to a peaked distribution towards the bottom. At first sight, this straggling of ion trajectories and the resulting reduction of their fluence seems to impede the envisaged applications.
However, for the calculation of the local dpa values not only the ion trajectories but also the full collision cascades resulting from the knock-ons of target atoms have to be considered. The resulting dpa profile is shown in Fig.~\ref{fig:dpa} for various depths and in a cross-sectional view. Surprisingly, the defect density is lowest near the sample surface that is subjected to the ion beam and gradually increases with depth as reported before \cite{CYBA14a}. This is a direct consequence of the increasing number of additional collision cascades originating from knocked-on target atoms. The dpa profile near the bottom of the sample is also somewhat blurred, but as can be seen in Fig.~\ref{fig:dpa}(b) the CD is well formed over the entire depth and its diameter increases by about 20~nm.
Several mechanisms have to be considered for understanding the depth dependence of the dpa values. On the one hand, the dpa increase due to accumulation of recoil cascades. Assuming a constant ion fluence and negligible backscattering of ions and impinged target atoms, the collision cascades originating from primary recoil atoms create a plume of defects around their trajectory, but also trigger secondary collision cascades by hitting other atoms, and so on. Thus, the density of collision cascades increases with depth, in particular at the center of the irradiated area. Additionally, the ions lose energy with depth due to electronic stopping, i.e., target ionization. With reduced energy the nuclear stopping cross-section of ions increases and so does the number of created defects. All these processes cause an increase of dpa with depth.
\begin{figure}
\centering
\includegraphics[width=\columnwidth]{Tc}
\caption{Temperature dependence of the resistivity and superconducting transition of a full-area irradiated YBCO film for several 75~keV He$^+$ ion fluences. At a fluence of $4\times 10^{15}$~cm$^{-2}$, superconductivity is fully suppressed (not shown). The lines and their intersection indicate the evaluation of $T_\text{c-onset}$. Data taken from \cite{LANG04}.}
\label{fig:Tc}
\end{figure}
On the other hand, the ion fluence decreases with depth, as can be seen in Fig.~\ref{fig:fluence}, which counteracts the increase of dpa. In samples with a larger thickness than those studied here, this would eventually lead to the implantation of ions, the reduction of dpa, and finally, limiting the defect creation process at some depth. For most applications this is not acceptable and, hence, the ion energy must be high enough to ensure (almost) full penetration of the sample. By choosing ion energy and fluence the defect profile can be adjusted with the constraints that higher energy requires higher fluence to achieve the same dpa, but in turn provides larger penetration depth.
The main aim of this paper is to estimate the 3-dimensional $T_c$ profile within and around the CDs. To this end the defect density from the SRIM simulation has to be correlated with experimental $T_c$ data. The issue that the simulated dpa values are expected to be higher than those in the real system, since several processes for defect annihilation are not considered in SRIM, can be overcome by mapping the simulation data to experimental $T_\text{c-onset}$ results from our previous work on full-area irradiation of thin YBCO films with 75~keV He$^+$ ions \cite{LANG04} shown in Fig.~\ref{fig:Tc}. $T_\text{c-onset}$ marks the temperature above which the entire sample is in the normal state.
The reduction of $T_c$ with increasing point defect density can be modeled by the pair-breaking theory of Abrikosov and Gor'kov \cite{ABRI60}. Although devised for magnetic impurities, the theory can be also used to describe the situation in HTSCs, where non-magnetic point defects can break up superconducting pairs due to the $d$-wave symmetry of the superconducting gap \cite{LESU90,TOLP96,TOLP96a}. The normalized $T_\text{c-onset}/T_0$, where $T_0=90$~K is the critical temperature of the non-irradiated superconducting film, can be expressed as a function of the pair-breaking scattering time $\tau_p$ \cite{TOLP96}
\begin{equation}
\label{eq:pairbreaking}
\ln\Big(\frac{T_{c\text{-onset}}}{T_0}\Big)=\Psi\Big(\frac{1}{2}\Big) - \Psi\Big(\frac{1}{2}+\frac{C}{4 \pi \tau_p T_{c\text{-onset}}} \Big),
\end{equation}
where $\Psi$ is the digamma function, $C$ a constant of dimension K$\cdot$s and $\tau_p$ is inversely proportional to the defect density expressed in dpa.
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{dpa_Tc}
\caption{Relation between experimentally determined $T_{c-\text{onset}}$ values and simulated defect density in dpa averaged over different cylindrical slices. The symbols indicate different depth zones for computing the mean dpa. The dashed curve is the fit to the data for 10~nm to 22~nm depth. The yellow region marks a possible range for the fit, explained in the text.}
\label{fig:dpa_Tc}
\end{figure}
In Fig.~\ref{fig:dpa_Tc} the relation between the experimentally determined $T_\text{c-onset}$ values and the defect density obtained from the simulations is presented. $T_\text{c-onset}$ is determined by the layer in the sample with the lowest defect density and, thus, the highest local $T_c$. Since the dpa vary with the depth in the sample, as illustrated in Fig.~\ref{fig:dpa}(b), it makes a difference where the dpa value is determined. The previous findings indicate that the dpa is lowest near the surface of the sample, but in the experiments it has also to be considered that a top layer of a few nm thickness is deteriorated by ambient influences. It is therefore reasonable to average the dpa in a slice from 10~nm to 22~nm depth, which corresponds to a thickness of about 10~unit cells of YBCO. As can be noted in Fig.~\ref{fig:dpa_Tc} this choice is not critical, as long as the upper part of the sample is used. The qualitative variation of $T_\text{c-onset}$ with dpa is similar to results obtained with 190~keV He$^+$ irradiation \cite{NEDE89,LESU90}.
\begin{figure*}[t!]
\centering
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{Tc_prof}
\subcaption{Lateral local $T_c$ profiles at various depths.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{Tc_cross}
\subcaption{Cross-sectional view of the local $T_c$ profile.}
\end{subfigure}
\caption{Local $T_c$ profiles within and around a defect column produced by 75~keV He$^+$ ion irradiation of YBCO with a fluence of $3\times10^{15}\textrm{~cm}^{-2}$.}
\label{fig:Tc3D}
\end{figure*}
As found in other studies with different irradiation parameters \cite{TOLP96,LESU90} the dependence of $T_\text{c-onset}$ with defect density roughly follows Eq.~(\ref{eq:pairbreaking}) with minor deviations \textbf{}near $T_\text{c-onset} \rightarrow T_0$ and $T_\text{c-onset} \rightarrow 0$. For this reason and the complexity of the implicit Eq.~(\ref{eq:pairbreaking}) we use a fit to the data for further interpolation, shown as a dashed line in Fig.~\ref{fig:dpa_Tc}, using $T_0=90$~K and the fixed constraint of going through the point (0,\ 90~K). With this function the local $T_c$ can be calculated from the 3D defect profiles in Fig.~\ref{fig:Tc}. The results are shown in Fig.~\ref{fig:Tc3D} as lateral $T_c$ profiles at various depths and as a cross-sectional view. When comparing the profiles of defects and local $T_c$ in the sample, it is remarkable that, even at the bottom of the sample, the region of suppressed superconductivity shows only marginal blurring and reproduces the shape of the incident ion irradiation well. Fig.~\ref{fig:Tc3D}(b) demonstrates that the channel of suppressed $T_c$ has rather sharp fringes and only marginally widens up with depth. Ideally, for experiments YBCO films with a thickness of only about 100~nm should be used or, alternatively the ion energy and consequently their fluence should be increased. These findings confirm the previous experimental results that indeed irradiation of YBCO with moderate-energy He$^+$ ions through a stencil mask allows for the fabrication of well defined 3D landscapes of the superconducting order parameter.
\section{Conclusions}
The 3D profile of the local critical temperature in a cuprate high-$T_c$ superconductor that was nano-patterned by ion irradiation has been examined. The interaction of 75~keV He$^+$ ions with a thin film of YBCO leads to displacements of mainly the oxygen atoms and creates point defects in the material. These defects cause a suppression of superconductivity and are deduced from simulations of the collision cascades with the program package SRIM/TRIM. Using previous experimental results for calibration we obtain a relation between the simulated defect density and the experimental $T_\text{c-onset}$. With these ingredients, the 3D pattern of the local $T_c$ in thin YBCO films can be visualized. It is found that masked ion irradiation through a stencil mask produces well-defined areas of suppressed $T_c$ with a lateral shape corresponding to the mask's holes with a resolution in the order of 10~nm. This structure persists up to 200~nm in depth with surprisingly low blurring. The present results support previous experimental findings of pronounced fluxon trapping effects that are caused by the particular $T_c$ landscape. Since ion irradiation through a stencil mask is a convenient fabrication method, our results support its potential usefulness for future quantum devices based on HTSCs.
\section*{Acknowledgments}
This work was supported by the European Cooperation in Science and Technology via COST Action CA16218 (NANOCOHYBRI).
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{
"redpajama_set_name": "RedPajamaArXiv"
}
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Q: Http-Server weird behavior with .js files I have a super basic website, which has an index.html, and 2 folders, js and css.
app.js only contains a console.log, to show if the file is being loaded properly. If i open the index.html file by double clicking it, the messagge appears in chrome console normaly, when adding it to the html with this line:
However, if I open the webpage by executing http-server -o, that console.log is not printed in screen. In order to make it appear, I have to include script like this:
Can anyone explain why this happens? It just doesn´t make sense to me, but obviously there is an explanation.
Thank you
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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Acid Rap est la deuxième mixtape de Chance The Rapper, diffusée à partir du en téléchargement gratuit.
L'album s'est classé au Top Heatseekers et au Top R&B/Hip-Hop Albums.
Acclamé par la critique, le site Metacritic lui a attribué la note de 86/100. Pitchfork l'a classé à la du « Top 50 des albums de 2013 » et le magazine Rolling Stone à la des « 50 meilleurs albums de 2013 ». Il a également été nommé dans la catégorie « Meilleure mixtape » des BET Hip-Hop Awards 2013.
Liste des titres
Notes et références
Album de hip-hop américain
Album musical sorti en 2013
Album auto-produit
Mixtape
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{
"redpajama_set_name": "RedPajamaWikipedia"
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\section*{Outline of the paper}
A remarkable example of ``non-equilibrium criticality'' is represented by
the phenomenon of aging \cite{agingbook}.
Such ``non-equilibrium criticality'' can be observed in a feromagnetic spin system (an Ising model) prepared in a high-temperature state which after being quenched to a temperature at or below its critical temperature is left to evolve freely. It is observed that the size of the clusters of ordered spins (which form and grow) is time-dependent and scales as time to some power, the inverse of which defines the dynamical exponent. In addition, the 2-point correlation functions in such systems depend on {\it both} time values (and not {\it only} on the their difference, as it is the case in other critical phenomena which do not break time-translation) \cite{agingbook, Henkel:2010ec}.
The essential
physics of aging (which is crucially a non-stationary process) \cite{agingbook} has been
recently discussed in the context of the AdS/CFT duality \cite{michel, Jottar:2010vp}.
In this letter
we clearly distinguish between aging realized as
``dressed'' Schr\"odinger dynamics from pure aging. In particular we explicitly demonstrate this
difference at the level of the 3-point function.
Our {\it novel results} regarding the 3-point function should be of practical importance in both real and numerical experiments involving aging dynamics \cite{agingbook}.
Let us begin by reviewing the current understanding of holographic aging \cite{agingbook, michel, Jottar:2010vp}.
The Schr\"odinger group is the group of symmetries of the free Schr\"odinger equation
$
(2i{\cal M}\partial_t+\nabla^2)\varphi_S(t,\vec x)=0\label{sch1}.
$
The Age (or Aging) group is the same as the Schr\"odinger group, minus the time translation. To break time-translation invariance, but maintain scale invariance,
a simple modification
can be made to
the previous equation by adding a time-dependent potential $v(t)$ \cite{agingbook}, so that
$
(2{\cal M}[i\partial_t-v(t)]+\nabla^2)\varphi_A(t,\vec x)=0\label{age1}.
$
(For a general discussion regarding the breaking of time-translation invariance, consult \cite{agingbook}.)
However, $v(t)$ needs to transform the same way as $\partial_t$ and $\nabla^2$, so $v(t)=k/t$, where $k$ is an arbitrary constant.
The field transformation which maps these two equations into each other is given by
$
\varphi_A(t,\vec x)=\exp(-i\int^t_{t_0} d\tau v(\tau))\varphi_S(t,\vec x)=({t}/{t_0})^{-ik}\varphi_S(t,\vec x).
$
If one considers operators with a certain mass ${\cal M}$, then
$
O_A(t,\vec x)=({t}/{t_0})^{-ik{\cal M}}O_S(t,\vec x)\label{cor1}.
$
This leads straightforwardly to a relationship between the Age and Schr\"odinger $n$-point correlators:
$
G_A^{(n)}(t_i,\vec x_i;{\cal M}_i)=\prod_{i=1}^n t_i^{-ik{\cal M}_i} G_S^{(n)}(t,\vec x_i;{\cal M}_i)
$
where the $t_0$ dependence cancels due to the Bargmann selection rule $\sum_i {\cal M}_i=0$.
The holographic dual of a system which is invariant under the realization of Age algebra
using the above trick (and which takes into account the singularity at $t=0$ in $v(t)=k/t$) was constructed in \cite{Jottar:2010vp}. The relevant Age metric $ds_A^2$ \cite{Jottar:2010vp} reads as:
\be
ds_{A}^2=\frac{R^2}{z^2} \bigg(dz^2+\frac{2\alpha\beta}{z} dz \,dt-\frac{\beta^2}{z^2}\left(1+\frac{\alpha z^2}{\beta t}\right)dt^2-2 dt\,d\xi + d\vec x^2\bigg)\label{agemetric}.
\ee
(This geometry is locally Schr\"odinger, but its global structure is not.)
Then it is easy to check that
$
\Phi_{A}(t,\xi,\vec x, z)=\Phi_S(t,\xi+\frac{\alpha\beta}{2}\ln\frac{\beta t}{z^2},\vec x, z)\label{age map}
$
obeys the equation of motion $\Box \Phi_A=0$ in the Age metric if $\Phi_S$ obeys the equation of motion $\Box \Phi_S=0 $ in the Schr\"odinger background
\be
ds_{S}^2=\frac{R^2}{z^2} \bigg(dz^2-\frac{\beta^2}{z^2}dt^2-2 dt\,d\xi + d\vec x^2\bigg).
\ee
(This can be extended for fields of arbitrary spin.)
In terms of the boundary field values $\bar\Phi_S$, the bulk Schr\"odinger field can be written as
\be
\Phi_S(t,\xi,\vec x,z)=\!\!\!\int_{t',\xi', \vec x'} \!\!\!\!\!{\cal G}_S(t-t',\xi-\xi', \vec x-\vec x',z)\bar \Phi_S(t',\xi',\vec x'),
\ee
which, after applying the above map becomes
\bea
\Phi_{A}(t,\xi-\frac{\alpha\beta}2\ln\frac{\beta t}{z^2},\vec x,z)&=&\!\!\!\int_{t',\xi', \vec x'} \!\!\!\!\!{\cal G}_S(t-t',\xi-\xi', \vec x-\vec x',z) \nn \\
&&\!\!\!\!\!\!\!\times \bar \Phi_{A}(t',\xi'-\frac{\alpha\beta}{2}\ln\frac{\beta t'}{z_{b}^2},\vec x'),
\eea
where $z_b$ is the value of $z$ at the regularized boundary ($z_b\ll 1$). Here ${\cal G}_S(t-t',\xi-\xi', \vec x-\vec x',z)$ denotes the boundary-to-bulk propagator of a field in the Schr\"odinger background.
Fourier-transforming along the $\xi$ direction, we find
\bea
\Phi_{A}(t,\vec x,z; {\cal M})&=&\int_{t', \vec x'} \exp\left(i {\cal M}\frac{\alpha\beta}{2}\left(\ln\frac{\beta t}{z^2}-\ln\frac{\beta t'}{z_b^2}\right)\right) \nn \\
&&\times {\cal G}_S(t-t', \vec x-\vec x', z; {\cal }M)\bar \Phi_{A}(t',\vec x'; {\cal M}). \nn \\
\eea
This enables us to reconstruct, with relative ease, the holographic answer for the correlators of primary operators with respect to the Age algebra from those derived using the Schr\"odinger background holography \cite{bvwa, bvw}. For example, the 3-point function of a scalar operator is
\be
\delta({\cal M}_1+{\cal M}_2+{\cal M}_3)\Lambda\!\!\!\!\prod_{i=1,2,3}(t_i)^{-i{\cal M}\frac{\alpha\beta}{2}}\int_{t,\vec x,z}\!\!\!{\cal G}_S(t-t_i, \vec x-\vec x_i; {\cal M}_i),\label{a 3 point}
\ee
assuming that the scalar source, $\bar\phi({\cal M})$, has a cubic coupling in the bulk: $S_{grav}=\int (\dots+ \frac{1}{3!}\Lambda \phi^3(t,\vec x, z;{\cal M}) +\dots).$ By using the Bargmann superselection rule $\sum_i {\cal M}_i=0$ (which in this holographic context is simply the momentum conservation along the $S^1$ direction parametrized by $\xi$) the 3-point function is reduced to the previous form.
To get the Age correlator one performs a DLCQ projection along $\xi$ followed by a functional differentiation with respect to the boundary fields.
This guarantees that the Age correlators differ from the Schrodinger correlators only by time-dependent phase factors, if the tensor indices are in the $\vec x$ directions, as in the case of scalar operators.
{\it One of the main points of this letter is that this realization of aging does
not capture the most general aging dynamics and that what has been described above is
just a particular realization of the Schr\"odinger dynamics!}
In what follows we clearly distinguish between this special case and the most
general aging dynamics.
For simplicity, let us consider a 1+1-dimensional theory with coordinates $t,r$. We use $\xi$ to denote the Fourier variable conjugate to the mass ${\cal M}$ of a certain primary operator. In the notation of \cite{agingbook, hu}, the Schr\"odinger and Age algebras are respectively spanned by the generators $\{X_{-1}, X_0, X_1, M_0, Y_{\frac{1}{2}}, Y_{-\frac{1}{2}}\}$ and $\{ X_0, X_1, M_0, Y_{\frac{1}{2}}, Y_{-\frac{1}{2}}\}$, which obey the following commutation relations
\bea
&&\!\!\!\!\![X_n, X_{n'}]=(n-n')X_{n+n'}, \;\;[X_n, Y_m]=(\tfrac {n}{2} -m)Y_{n+m}\nn\\
&&\!\!\!\!\![X_n, M_{n'}]=-n' M_{n+n'}, \;\; [Y_m, Y_{m'}]=(m-m')M_{m+m'}.\nn\\
\eea
The most general realization of these generators (which is apparently {\it new}) is
\bea
X_{-1}&=&-\partial_t+\frac{g(t)-\gamma}{t}+\frac{h(t)-\delta}{t} i \partial_\xi\nn\\
X_0&=&-t\partial_t -\tfrac 12 r \partial_r -\tfrac {\Delta}2 + g(t)+h(t) i\partial_\xi\nn\\
X_1&=&-t^2 \partial_t - tr\partial_r - \Delta t + \tfrac i2 r^2 \partial_\xi \nn\\&+& t(g(t)+\gamma)+t(h(t)+\delta)i\partial_\xi\nn\\
Y_{-\frac{1}{2}}&=&-\partial_r, Y_{\frac{1}{2}} = -t\partial_r + ir \partial_\xi, M_0=i\partial_\xi\equiv -{\cal M},
\label{agerealiz}
\eea
where $g(t), h(t)$ are arbitrary time-dependent functions and $\gamma,\delta$ are arbitrary constants. In arriving at (\ref{agerealiz}) we have kept the form of the generators $M_0$ and of the spatial translation $Y_{-\frac{1}{2}}$ and generalized Galilean-invariance $Y_{\frac{1}{2}}$ unchanged. This general realization is central for the new results presented in what follows.
Next we solve the partial differential constraints imposed on the 3-point functions (namely that they are left invariant by the Age generators). The conclusion is that the most general scalar 3-point function is
\bea
&&\!\!\!\!\!\!G_{A}(\{t_i, r_i, \xi_i\})=\bigg(\prod_{i=1}^3 t_i^{\gamma_i}\bigg)
\exp(\sum_{i=1}^3 \int^{t_i} d\tau\frac{g(\tau)}\tau)\nn\\
&&\!\!\!\!\!\!\times
(t_3-t_1)^{-\tfrac 12 \Delta_{31,2}+\gamma_{31,2}} (t_3-t_2)^{-\tfrac 12 \Delta_{32,1}+\gamma_{32,1}}\nn \\
&&\!\!\!\!\!\!\times
(t_2-t_1)^{-\tfrac 12 \Delta_{21,3}+\gamma_{21,3}} \Theta_A(u_1, u_2, u_3, \frac{t_3(t_2-t_1)}{t_2(t_3-t_1)})\label{mostgenage}
\eea
where
$
\gamma_{31,2}=\gamma_3+\gamma_1 -\gamma_2 \;{\rm etc} $ and
$\Delta_{31,2}=\Delta_3+\Delta_1 -\Delta_2 \;{\rm etc}$.
Here $\Theta_A(u_1, u_2, u_3, \frac{t_3(t_2-t_1)}{t_2(t_3-t_1)})$ is some unconstrained function of:
\bea
&&u_1=-2i(\xi_2-\xi_1) + \frac{(r_2-r_1)^2}{t_2-t_1}+2\int_{t_1}^{t_2} d\tau \frac{h(\tau)}{\tau}\nn\\
&& + 2(\delta_2-\delta_1)\ln(t_2-t_1)
+2(\delta_1+\delta_2)\ln\frac{t_3-t_2}{t_3-t_1}\nn\\
&&-2\delta_2\ln t_2+2\delta_1\ln t_1,\nn\\
&& u_2=
-2i(\xi_3-\xi_1) + \frac{(r_3-r_1)^2}{t_3-t_1}+2\int_{t_1}^{t_3} d\tau \frac{h(\tau)}{\tau}\nn\\
&& + 2(\delta_3-\delta_1)\ln(t_3-t_1)+2(\delta_1+\delta_3)\ln\frac{t_3-t_2}{t_2-t_1}\nn\\
&&-2\delta_3\ln t_3+2\delta_1\ln t_1,\nn\\
&&u_3= -2i(\xi_3-\xi_2) + \frac{(r_3-r_2)^2}{t_3-t_2}+2\int_{t_2}^{t_3} d\tau \frac{h(\tau)}{\tau}\nn\\
&& + 2(\delta_3-\delta_2)\ln(t_3-t_2)+2(\delta_2+\delta_3)\ln\frac{t_3-t_1}{t_2-t_1}\nn\\
&&-2\delta_3\ln t_3+2\delta_2\ln t_2.
\eea
For the Schr\"odinger 3-point correlator we find a similar expression, but without the dependence on the additional variable
$\frac{t_3(t_2-t_1)}{t_2(t_3-t_1)}$:
\bea
&&\!\!\!\!\!\!G_{S}(\{t_i, r_i, \xi_i\})=\bigg(\prod_{i=1}^3 t_i^{\gamma_i}\bigg)
\exp(\sum_{i=1}^3 \int^{t_i} d\tau\frac{g(\tau)}\tau)\nn\\
&&\!\!\!\!\!\!\times
(t_3-t_1)^{-\tfrac 12 \Delta_{31,2}+\gamma_{31,2}} (t_3-t_2)^{-\tfrac 12 \Delta_{32,1}+\gamma_{32,1}}\nn \\
&&\!\!\!\!\!\!\times
(t_2-t_1)^{-\tfrac 12 \Delta_{21,3}+\gamma_{21,3}} \Theta_S(u_1, u_2, u_3).\label{mostgensch}
\eea
Note that despite the presence of the time-dependent prefactors this correlator is time-translation invariant.
In fact, it is easy to check that a redefinition of the primary fields of the Schr\"odinger algebra, effected by factoring out appropriate time-dependent functions, gives the correlators of the type (\ref{mostgensch}).
However, this redefinition does not change the fact that $X_{-1}G_S(\{t_i, r_i, \xi_i\})=0$. The fundamental difference between Age and Schr\"odinger 3-point functions lies in the dependence of the former on
$\frac{t_3(t_2-t_1)}{t_2(t_3-t_1)}$.
At this stage we pause to note that the analysis performed at the beginning of this letter regarding the form of the Age correlators was too restrictive.
Since the time-dependent potential is introduced by a simple redefinition of the fields, $\varphi_S(t,\vec x)=\exp(i\int^t d\tau v(\tau)) \varphi_A(t, \vec x)$, the relevant symmetry group is still the full Schr\"odinger and {\it not} the Age group. One of the consequences of this observation is that the holographic realization of Aging (\ref{agemetric}) is equally restrictive, and thus, the most general holographic Age background is yet to be found. This is further evidenced by the fact that the 3-point correlators implied by the holographic Age metric (\ref{agemetric}) are dressed Schr\"odinger correlators (i.e. they are ``fake'' Age correlators), whereas the ones in (\ref{mostgenage}) are not.
For completeness, we also present the 3-point correlators of the scalar fields in terms of their masses:
\bea
&&\!\!\!\!\!\!\!
G_A(\{t_i, r_i, {\cal M}_i\})=2\pi\delta(\sum_{i=1}^3 {\cal M}_i)\bigg(\prod_{i=1}^3
t_i^{-\gamma_i +{\cal M}_i \delta_i}\bigg)\nn\\
&&\!\!\!\!\!\!\times\exp\bigg(\sum_{i=1}^3 \int^{t_i} d\tau\frac{g(\tau)-{\cal M}_ih(\tau)}\tau\bigg)\nn\\
&&\!\!\!\!\!\!\times
(t_3-t_1)^{-\tfrac 12 \Delta_{31,2}+\gamma_{31,2}-({\cal M\delta})_{31,2}}\nn\\
&&\!\!\!\!\!\!\times (t_3-t_2)^{-\tfrac 12 \Delta_{32,1}+\gamma_{32,1}-({\cal M}\delta)_{32,1}}
\nn\\
&&\!\!\!\!\!\!\times
(t_2-t_1)^{-\tfrac 12 \Delta_{21,3}+\gamma_{21,3}-({\cal M}\delta)_{21,3}} \nn \\
&&\!\!\!\!\!\!
\times \exp\bigg(-\frac{{ \cal M}_2 (r_2-r_1)^2}{2(t_2-t_1)}-\frac{{\cal M}_3(r_3-r_1)^2}{2(t_3-t_1)}\bigg)
\nn \\
&&\!\!\!\!\!\!\times
\tilde\Theta_A({\cal M}_2, {\cal M}_3,w,
\frac{t_3(t_2-t_1)}{t_2(t_3-t_1)}). \label{mostgenageM}
\eea
Here
$
({\cal M}\delta)_{31,2}={\cal M}_3\delta_3+{\cal M}_1\delta_1-{\cal M}_2\delta_2,
$
and
$
w=\frac{[(t_3-t_1)(r_2-r_1)-(t_2-t_1)(r_3-r_1)]^2}{(t_3-t_2)(t_2-t_1)(t_3-t_1)}.
$
For the Schr\"odinger 3-point correlators one obtains an expression similar to (\ref{mostgenageM}), but with an unconstrained function $\tilde\Theta_S=\tilde\Theta_S({\cal M}_2, {\cal M}_3,w)$.
We mention in passing that there are extensions of both Age and Schr\"odinger algebras which involve the addition of new generators that ensure the closure of the respective algebras. For example, provided that $\delta=0$ in (\ref{agerealiz}), we may add to both algebras
$
N=-t\partial_t +\xi\partial_\xi + g(t)-\gamma' + [h(t)+\int^t d\tau\frac{h(\tau)}\tau + \delta']i\partial_\xi \label{N}.
$
The non-zero commutators that involve $N$ are $[N,X_{\pm1}]=\mp X_{\pm 1}$, $[N, M_0]=-M_0$,
$[N, Y_{\frac{1}{2}}]=-Y_{\frac{1}{2}}$.
In this case the scalar 3-point function of this extension of Age algebra is given by
\bea
&&\hat G_A(\{t_i, r_i, {\cal M}_i\})=2\pi\delta(\sum_{i=1}^3 {\cal M}_i)\bigg(\prod_{i=1}^3
t_i^{-\gamma_i}\bigg)\nn\\
&&\!\!\!\!\!\!\times\exp\bigg(\sum_{i=1}^3 \int^{t_i} d\tau\frac{g(\tau)-{\cal M}_i h(\tau)}\tau\bigg)
(t_3-t_1)^{-\tfrac 12 \Delta_{31,2}+\gamma_{31,2}}\nn\\
&&\!\!\!\!\!\!\times (t_3-t_2)^{-\tfrac 12 \Delta_{32,1}+\gamma_{32,1}}
(t_2-t_1)^{-\tfrac 12 \Delta_{21,3}+\gamma_{21,3}} \nn \\
&&\!\!\!\!\!\!
\times \exp\bigg(-\frac{{ \cal M}_2 (r_2-r_1)^2}{2(t_2-t_1)}-\frac{{\cal M}_3(r_3-r_1)^2}{2(t_3-t_1)}\bigg)\nn \\
&&\!\!\!\!\!\!\times
w^{-\tfrac 12 (\Delta_1+\Delta_2+\Delta_3)+\gamma_1+\gamma_2+\gamma_3+2}\nn \\
&&\!\!\!\!\!\!\times
\widetilde{\widehat\Theta_A}(w{\cal M}_2 , w{\cal M}_3,
\frac{t_3(t_2-t_1)}{t_2(t_3-t_1)}
).\nn \\
\label{mostgenage1M}
\eea
For the Schrodinger algebra extended by $N$, we encounter again an expression similar to (\ref{mostgenage1M}) but with an unconstrained function $\widetilde{\widehat \Theta_S}=\widetilde{\widehat\Theta_S}(w{\cal M}_2, w{\cal M}_3)$.
Yet another closed subalgebra extension of Age is obtained by adding both $N$ and $V_+$, where
$
V_+ = -2t r\partial_t -2\xi r\partial_{\xi} -(r^2 + 2i\xi t)\partial_r -2 \Delta r+ 2r (g(t)+\gamma)
\label{Vp},
$
and where $h(t)=0, \delta=0$ in (\ref{agerealiz}), and $\delta'=0, \gamma'=\gamma$ in the expression for $N$.
On the other hand, adding both $N$ and $V_+$ to the Schr\"odinger algebra and requiring its closure \footnote{From $[X_{-1}, V_+]=-2i V_-$ it is clear that the Schrodinger algebra does not admit an extension which includes $V_+$ without adding all the other generators of the conformal algebra.}, leads to the full 1+2-dimensional conformal algebra in a space parametrized by $t,r , \xi$ coordinates. The generators take the form given by (\ref{agerealiz}), the expressions for $N$ and $V_{+}$, with $\delta=0, h(t)=0,\gamma'=\gamma,\delta'=0$, supplemented by
$V_-=-\xi\partial_r + ir\partial_t-\frac{ir}{t}(g(t)-\gamma)$ and
\be
W=-\xi^2\partial_\xi -\xi r \partial_r + \tfrac i2 r^2 \partial_t -\Delta\xi+2\gamma\xi
-\frac {ir^2 (g(t)-\gamma)}{2t}.
\ee
The familiar scalar 3-point function is dressed by time-dependent factors which originate in a particular realization of the generators allowing for non-zero $\gamma$ and $g(t)$:
\bea
&&\!\!\!\!\!G_c(\{t_i, r_i, \xi_i\})=\bigg(\prod_{i=1}^3 t_i^{\gamma_i}\bigg)
\exp(\sum_{i=1}^3 \int^{t_i} d\tau\frac{g(\tau)}\tau)\nn\\
&&\!\!\!\!\!\times X_{21}^{-\tfrac 12 \Delta_{21,3}+\gamma_{21,3}}
X_{31}^{-\tfrac 12 \Delta_{31,2}+\gamma_{31,2}}
X_{32}^{-\tfrac 12 \Delta_{32,1}+\gamma_{32,1}}.\label{conf}
\eea
Here $X_{12}$, etc. are the Lorentz invariant intervals
$
X_{12}=-2i(t_2-t_1)(\xi_2-\xi_1)+(r_2-r_1)^2, {\rm etc}.
$
However, we want to stress that the time-dependent factors in (\ref{conf}) once again do not signal any breaking of time-translation invariance, and can be obtained by redefining the primary operators of the type we have encountered earlier in this letter.
Finally, we would like to comment on the holographic realization of the Age algebra in terms of metric isometries of a 1+3-dimensional space. The holographic dual space is parametrized by $x^\mu$ coordinates: $t, r ,\xi$ and the holographic coordinate $z$. The main observation is that once one identifies the Killing vectors $K=K^\mu \frac{\partial}{\partial x^\mu} $ obeying the Age algebra, one can reverse engineer the metric by solving the Killing vector equations for the components of the metric, i.e. $(g_{\rho\nu} \partial_\mu + g_{\rho\mu}\partial_\nu)K^\rho+K^\rho \partial_\rho g_{\mu\nu}=0$. It is natural to assume that $Y_{-\frac{1}{2}}$ and $M_0$ are bulk Killing vectors. If one makes the additional assumption that $Y_{\frac{1}{2}}$, given by (\ref{agerealiz}), is a bulk Killing vector then the problem becomes quite tractable. The bulk forms of the Killing vectors $X_{0}$ and $X_1$ are
$
X_0=-t\partial_t+X_0^\xi \partial_\xi -\tfrac 12 r\partial r
+X_0^z\partial_z
$
and
$
X_1=-t^2\partial_t+X_1^\xi\partial_\xi -tr\partial_r +X_1^z\partial_z,
$
where
$X_0^z=\frac{\partial_t (tg_{rr})}{\partial_z g_{rr}}$,
$X_1^z=\frac{\partial_t(t^2 g_{rr})}{\partial_z g_{rr}}$ and
\bea
&&\!\!\!\!\!\!\! X_0^\xi =\frac{i}{2t\partial_z g_{rr}}\bigg
(-\partial_z(g_{rr} S)-t\partial_t g_{rr} \partial_z S
+t \partial_t S\partial_z g_{rr} \nn\\
&&\;\;\;\;+ 2tT\partial_z g_{rr} + 2tC_1\partial_z g_{rr}\bigg)\nn\\
&&\!\!\!\!\!\!\! X^\xi_1=\frac{i}{2\partial_z g_{rr}}\bigg(-z^2 \partial_z g_{rr}-2 g_{rr}\partial_z S - S\partial_z g_{rr}-t\partial_t g_{rr}\partial_z S \nn\\
&&+ t\partial_t S\partial_z g_{rr}+2tT \partial_z g_{rr} \bigg).
\eea
Here $g_{rr}=g_{rr}(t,z), S=S(t,z), T=T(t)$ and $C_1$ is an arbitrary constant. Solving the Killing vector equations corresponding to $Y_{-\frac{1}{2}}$ and $M_0$ leads to a metric which is $\xi, r$-independent. Furthermore, solving the $Y_{\frac{1}{2}}$ Killing equations brings the metric to a form which coincides with the initial ansatz of \cite{Jottar:2010vp}:
$
ds^2 = g_{tt}(t,z) dt^2 + g_{rr}(t,z) dr^2 + g_{zz}(t,z) dz^2
- 2i g_{rr}(t,z) dt d\xi + 2 g_{tz}(t,z) dt dz.
$
The other components of the metric are determined by the remaning Killing equations:
$g_{zz}=\frac{C_2 (\partial_z g_{rr})^2}{g_{rr}^2} $ and
\bea
&&\!\!\!\!\!\!g_{tz}=\frac{g_{rr}\partial_z S}{2t}+\frac{C_2 \partial_z g_{rr}\partial_t(t^2 g_{rr}) }{t^2 g_{rr}^2} + C_1 \partial_z g_{rr}\nn\\
&&\!\!\!\!\!\!g_{tt}= C_3 g_{rr}^2 + \frac{C_2(\partial_t(t^2 g_{rr}))^2}{t^4g_{rr}^2}\nn\\
&&+
\frac{2C_1\partial_t(t^2 g_{rr})}{t^2}+\frac{g_{rr}(2tT-S+t\partial_tS)}{t^2},
\eea
where $C_2, C_3$ are additional integration constants. We stress that this metric is the {\it most general} solution of the reverse-engineering procedure, given the confines of the initial assumption that $Y_{\frac{1}{2}}$ becomes a bulk Killing vector while remaining unchanged.
However, we cannot claim that we have identified the holographic dual of a general theory possessing the full symmetry of the Age algebra. The reason for this is that we are able to identify one more Killing vector of the metric compatible with the following bulk extension of $X_{-1}$
\bea
&&\!\!\!\!\!\!-X_{-1}=\partial_t
- \frac{\partial_t g_{rr}}{\partial_z g_{rr}}\partial_z\nn\\
&&\!\!\!\!\!\!
+i\bigg(-\frac{2 C_2}{t^2 g_{rr}}+ \frac{S}{2t^2} - \frac{\partial_t S+2T +4C_1}{2t} + \frac{\partial_t g_{rr}\partial_z S}{2t \partial_z g_{rr}
\bigg)\partial_\xi .\nn\\
\eea
Thus the isometries of the above metric generate the full Schr\"{o}dinger algebra, as in \cite{Jottar:2010vp}. Naturally the correlators computed from this metric using holography exhibit the kind of "fake" aging discussed earlier, and are constrained by the full Schr\"odinger algebra.
For the time being we can only trace this feature to the assumption made regarding the bulk realization of $Y_{\frac{1}{2}}$. (This assumption was also made in \cite{Jottar:2010vp}.) Relaxing this condition makes the problem of identifying the holographic metric of Aging much more complicated. We leave this question for our future work.
In conclusion, in this letter we have clearly pointed out the difference between the aging dynamics realized as
``dressed'' Schr\"odinger dynamics from pure aging. In particular we have obtained the 3-point functions for aging which {\it cannot} be obtained by ``dressing'' the 3-point Schr\"odinger correlators. The physical implications of our new results are yet to be understood.
Nevertheless, it is reasonable to expect that these results will have practical importance in
the real and numerical experiments of aging dynamics \cite{agingbook} and that they should be generalizable to the relativistic context, with possible applications to the physics of the quark-gluon plasma. We plan to address these issues in our future work.
{\bf Acknowledgements:}
We thank Rob Leigh, Leo Pando Zayas and Michel Pleimling for insightful discussions and,
in particular, we thank Malte Henkel for generous and incisive comments on this work. {DM}
is supported, in part, by the U.S. Department of Energy
under Grant No. DE-FG05-92ER40677, and
{DV and CW} under Grant No. DEFG02-
97ER41027.
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Humble's Australian Bushfire Relief Bundle Raises Over $1.7 Million
The Best Gaming Podcasts For 2020
Why Video Games Are Delayed So Often
Worth Reading: Trying To Develop A Brand New Drinking Game
Patrick Klepek
Jul 4, 2015, 2:30pm
It's time for Worth Reading, our weekly roundup of the best games writing around. Enjoy!
Hey, You Should Read This
"Mario's Big Brother: Shigeru Miyamoto" by David Sheff
This is not a new interview with Shigeru Miyamoto, so you won't learn anything about the NX or read any tidbits about the next Legend of Zelda. This is from back in 1992, when Nintendo was rolling out the SNES in the United States and Nintendo mania was everywhere. Seriously, there's a line in here about doctors diagnosing children with "Nintendoitis" for playing too many games and Oprah hosting fearful segments about game players becoming "zombies." It's great.
"Interestingly, older, smarter, tougher players may miss some of the hidden magical moments in Miyamoto's games. Young children, or those who explore at a leisurely pace, have a better chance of finding them than do kids or grown-ups who blast through a game, charging toward the goal, trying for the highest score and best time. "The players must be thinking, 'Well, there must not be anything here,' but it can be," says Miyamoto. "Then the player is curious enough to visit that place. When he finds something he never expected, he feels, 'Ah, I did it. I made it.' It's a great satisfaction.''
As the popularity of Miyamoto's games has grown — an astounding 60 million copies of his eight Mario games have been sold since 1985 — Miyamoto has become well known in Japan and beyond. Westerners who have made the pilgrimage to Kyoto to meet him have included Paul McCartney, who said he wanted to see Miyamoto, not Mount Fuji, during a Japanese tour. Yet despite his success, Miyamoto seems to have changed little in the fifteen years since he first came to Nintendo. His hair may be shorter, but he still bikes to work. He dresses in oxford shirts and wool vests; one red tie is dotted with tiny Mickeys."
"I went to a drinking game jam and this is what I did" by Mattie Brice
I'm not much of a drinking game person these days (though no promises for this upcoming holiday weekend), but I love the way Mattie Brice frames the reasons we engage with them in the first place. While it might be about getting wasted for some people, I'd say the majority of us engage in drinking games for other reasons: breaking the ice between new friends, putting us in a state of mind to share more freely, etc. Brice attended a game jam where she helped come up with a drinking game, which also required her to, naturally, test out the drinking game herself.
We started this discussion to get ideas flowing to start our games. First, was a general explanation of what a canonical drinking game is: a game where drinking is the result of some performance test, or is the main act of performance. The main tension that popped up for me was the ambiguity of whether drinking was a punishment or a reward, after all, when playing a drinking game, you mean to drink in the first place and to get comfortable with friends, and being sober around a lot of drunk people is not usually a common goal. Creating a difficult choice between drinking and another action appealed to me, like having to confess an emotion or drink, or some other lose-lose situation. We also noted that most drinking games are designed for skill level to steadily deteriorate once you've started to take some hits and drink, that is, the parts of your brain that is affected by alcohol will be the parts needed to avoid drinking.
There is also the why. Most found that drinking games are more of a reason to facilitate drinking itself; you have friends, you have booze, now here's a reason why you will be drinking it. Some want to get completely wasted, or get at least get to a place in a certain amount of time that they can't unaided. I was fascinated with the less mechanistic reasons we drink, like for getting to know each other. Games like Never Have I Ever also let people get to know each other, typically with things we wouldn't readily admit. And that's an aspect of our culture that I wished to prod, that we often use alcohol in order to be vulnerable, to admit and share things, or to do risky behaviour. What kinds of games could we make around that?
If You Click It, It Will Play
Oh, And This Other Stuff
David Motley analysed how some Christian leaders are responding to video games.
Jamie Madigan examined Mass Effect 3's ending changed perception of the whole series.
Chris Kohler interviewed one of Metroid's chief overseers on feeling like an "outsider."
A reddit thread discussed whether it's sleazy for games to specifically be about addiction.
Raph Koster considered if designers should worry how their games can affect people.
Rowan Kaiser looked back at how Diablo 2 reshaped RPGs.
Hua Hsu considered the impact of Japanese musicians on popular music at large.
Catt Small wrote about how their team developed a black female lead who "mattered".
Peter Moore recounted asking permission from Microsoft to spend a billion dollars.
Win A SEGA Mega Drive Mini, Games And Thousands More With Our Reader Survey
Kotaku Australia 17 Jan 2020 2:15 PM
Who likes free stuff? We've got another reader survey to kick off 2020, and naturally we'd like you to be rewarded for your time, so there's a whole truckload of stuff you could win: several gaming packs from Five Star including a SEGA Mega Drive Mini bundle, vouchers for The Iconic, $300 of food from Deliveroo, and an Ultimate Gamer Pack for all your console gaming courtesy of Turtle Beach.
Alex Walker 17 Jan 2020 1:59 PM
It's pouring buckets in Sydney, which is the perfect time for playing video games.
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JB Hi-Fi's Flogging Off A Ton Of Gamer Laptops, Monitors, Headsets, Mice
Sony's Brilliant Noise Cancelling Earbuds Are On Sale [Update: There's A Better Deal]
EB Games Is Flogging Off A Ton Of Headsets, Mice, Monitors, Games Today
My Quest To Find A Special Tree In The Witcher 3
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Home / News / New York Auto Show
Plug-in Prius Prime, Outlander delay, Bolt EV assembly line, Mirai manga: The Week In Reverse
John Voelcker March 26, 2016 Comment Now!
Which popular and important plug-in hybrid model made its world debut in New York this week?
And, what European brand is returning to North America with an electric car?
This is our look back at the Week In Reverse--right here at Green Car Reports--for the week ending on Friday, March 25, 2016.
Friday is our day for slightly unusual or oddball stories, and our contributor Matthew Klippenstein provided one: a translation of a Japanese manga comic about the Toyota Mirai hydrogen fuel-cell vehicle.
Filled with cautions about the car's usage—only four seats, fueling in Japan must be done by an attendant, and hydrogen stations are still being built—it nonetheless compares the Mirai favorably to not only the Nissan Leaf and BMW i3 electric cars, but even Toyota's own Prius Plug-In Hybrid.
We also wrapped up a week of New York Auto Show news, with more details on the cars that were launched, updated, or shown as close-to-production models.
2017 Toyota Prius Prime, 2016 New York Auto Show
We learned that the 2017 Toyota Prius Prime plug-in hybrid, which made its global debut, has a 22-mile electric range and can operate up to 80 mph on electricity alone, according to the company.
The 2017 MItsubishi Outlander PHEV was shown in almost-ready form for its U.S. debut—but its launch date was delayed once more, this time until November 2016.
The plug-in hybrid Outlander SUV may also get revised lithium-ion cells for its battery pack and more software updates to match it better to U.S. driving conditions and maximize its electric range, the company said.
The 2017 Hyundai Ioniq made its U.S. debut in New York, after a global reveal a few weeks ago at the Geneva Motor Show. All three versions—Ioniq Hybrid, Electric, and Plug-In—were again on display.
Finally, the 2017 Toyota Highlander Hybrid will be offered in four trim levels, with two new and less-expensive versions joining the top-end trims available to date.
2017 Volkswagen Golf Alltrack
Oh, and one more: Volkswagen is pulling a Subaru, with the 2017 VW Golf Alltrack being the same kind of raised, body-cladded, all-wheel-drive wagon that the Subaru Outback proved could attract buyers more than 20 years ago.
In other news, on Tuesday we published a GM video showing the pre-production models of the 2017 Chevrolet Bolt EV on the assembly line. The electric car will debut at the end of this year, more or less.
Monday, we explained how to reserve a Tesla Model 3 online when reservations open this coming Thursday.
Of course, we'll cover the unveiling of Tesla's 200-mile, $35,000 volume car when it happens Thursday night in Hawthorne, California.
Over the weekend, we covered evidence that showed Tesla is ramping up for Model 3 production with increases in its assembly-plant capacity.
Tesla Model 3 teaser image with Model S and Model X, March 2016
All of these weekly roundups seem to contain news on the Volkswagen diesel scandal. This week, all three parties—VW, the EPA, and the California Air Resources Board—asked a judge to postpone his deadline for a settlement until April 21; he agreed.
Finally, the French brand Renault hasn't been seen in North America in decades, but it's making a (very limited) comeback. The Twizy low-speed electric car ix coming to Canada; it will be sold in the province of Quebec.
Those were our main stories this week; we'll see you again next week. Until then, this has been the Green Car Reports Week in Reverse update.
Follow GreenCarReports on Facebook, Twitter, and Google+.
Green New York Auto Show News The Week In Reverse
2023 Mitsubishi Outlander PHEV revealed: With bigger battery, will it top 42-mile RAV4 Prime?
2023 Kia Sportage Plug-In Hybrid priced just under $40,000, goes 34 electric miles
Kia EV9 electric SUV: Production version due in 2023 will be three-row 4WD off-roader
California rule will make EV charging more affordable, reduce load on grid
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Home » Posts tagged with 'Hayabusa'
Malaysia PM Najib Razak takes Shinkansen bullet train to Sendai Japan
JAPAN PRODUCTS | News, Transportation News | 05/26/2015
Najib takes Shinkansen bullet train to Sendai
Source: The Malaysian Insider
Prime Minister Datuk Seri Najib Razak today experienced first-hand the Shinkansen, Japan's renowned bullet train which travels at 320km per hour.
Panasonic batteries to support Hayabusa 2 for 6 years in space
JAPAN PRODUCTS | Reports, Science and Technology Reports | 03/13/2015
Off For a 6-Year Mission. Panasonic Batteries on Board Hayabusa2
Source: Panasonic Corporation
Osaka, Japan – Panasonic's lithium primary batteries have been mounted in the asteroid explorer "Hayabusa2"* launched on December 3, 2014. Three models of graphite fluoride (BR series**) cylindrical-type lithium primary batteries (BR-A, BR-1/2AA, and BR-C) with an extensive shelf life have been mounted this time. The same type of batteries had also previously been mounted in "Hayabusa," which returned to Earth in 2010.
Japan has successfully launched its new asteroid explorer Hayabusa 2
JAPAN PRODUCTS | News, Science and Technology News, Transportation News | 12/03/2014
Launch Success of H-IIA Launch Vehicle No. 26 with "Hayabusa2" Onboard
Source: Japan Aerospace Exploration Agency
Mitsubishi Heavy Industries, Ltd. and the Japan Aerospace Exploration Agency (JAXA) successfully launched the H-IIA Launch Vehicle No. 26 (H-IIA F26) with the Asteroid Explorer "Hayabusa2" onboard at 1:22:04 p.m. on December 3, 2014 (Japan Standard Time, JST) from the Tanegashima Space Center.
Have You Ever Heard of Shinkansen Gran Class? It's Premium Class (total 18 seats) on Hayabusa
JAPAN PRODUCTS | Reports, Vehicles & Transportation | 05/06/2014
Inside the Gran Class
Source: Japan Rail Pass – By Japan Experience
Most of Japan's shinkansen normally have a green class and a standard class, but in recent years, newer models of train have introduced a new class for the ultimate bullet train travel: the Gran Class.
Top 10 Japan's companies list from all industries in 2017
by JAPAN PRODUCTS on 08/25/2017 - 0 Comments
Top 10 Japan's companies list from all industries in 2017 This list comprises the Japan largest public, state-owned, and private businesses by their rankings f...
Top 10 Japanese cosmetics companies in 2018
Top 10 Japan's companies list from cosmetics industries in 2018 Japan is one of the world's largest markets for cosmetics and personal care products, and has...
Top 10 Japan's chemical companies list in 2017
Top 10 Japan's companies list from chemical industries in 2017 In Japan, 860,000 people work in chemical industry field, and shipment value related to chemic...
Two Japanese Researchers Win 2015 Canada Gairdner International Award
Japanese researchers win Gairdner Intl. Award Date: Mar 25, 2015 Source: NHK World Two Japanese researchers have won a prestigious international medical aw...
General Atomics Aeronautical Systems Begins Demonstration Flights of the Guardian Remotely Piloted Aircraft in Iki Island, Nagasaki Prefecture of Japan
GA-ASI Begins Demonstration Flights in Japan Date: May 9, 2018 Source: General Atomics Aeronautical Systems, Inc. TOKYO - General Atomics Aeronautical Syst...
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Summer's tomato bounty brings back memories—or creates new ones.
It's that time of year—possibly my favorite time of year—when backyard gardens and farmers markets are bursting with summer produce. Strawberries may be on their way out, but tomato season is in full swing—and now is the time to get your fill of these plump, just-off-the-vine fruits that are packed with antioxidants, vitamin C and vitamin A.
Roasting is one of my favorite ways to prepare tomatoes, particularly the bruised and slightly older ones because it both concentrates their flavor and camouflages any puckered skins in the process. If you've never had homemade roasted tomato sauce, man, are you in for a treat. Traditional roasted sauces have an amazingly intense flavor but can take hours in the oven. I don't know about you, but I just can't get into the idea of having my oven on for hours on end with the heat of summer at its peak.
Quick roasting smaller tomatoes at a much higher temperature will kick-start the cooking and caramelization process, which means you can turn off your oven sooner and still have a delicious sauce in just under 30 minutes. Adding a can of tomato paste, some sun-dried tomatoes and a little brown sugar helps create the depth of flavor from slow-roasted sauces that will rival even your Italian grandma's marinara.
1. Leave the beefsteak behind. Big, beefy tomatoes will yield a less flavorful quick-roasted sauce because of their higher water content. Look for smaller tomatoes, no bigger than 2 to 2 1/2 inches in diameter, and quarter them, which will help them cook faster. If you feel like experimenting, try cherry or grape tomatoes instead.
2. Look for deals on overly ripe tomatoes. They create greater depth of flavor, and you might be able to score a discount on them at your local farmers market or grocery store.
4. Substitute dry-packed sun-dried tomatoes instead. If you already have dry-packed sun-dried tomatoes on hand, reconstitute them rather than buying the oil-packed variety. While your fresh tomatoes roast, place the sun-dried tomatoes in a heatproof bowl, cover them with 1 cup of boiling water mixed with 1/2 teaspoon salt, and cover the bowl. After 5 to 10 minutes, drain the tomatoes and blot them with a paper towel before adding them to your blender or food processor.
5. Double the recipe and freeze leftovers. Why not cook once and eat twice? This recipe will heartily serve 4–6, but you can save money on in-season tomatoes and your precious time by doubling the recipe. Simply transfer leftovers to a freezer bag and lay it flat to freeze for later use.
Preheat the oven to 500 F (on the convection setting if available), and line a large baking sheet with parchment paper.
Place the garlic on a small piece of foil and drizzle with 1 tablespoon olive oil. Fold the foil to form a sealed packet and place on the baking sheet.
Whisk together the remaining 2 tablespoons olive oil, brown sugar and 1/4 teaspoon kosher salt until the sugar has mostly dissolved. Place quartered tomatoes in a large bowl, drizzle with the olive oil mixture and toss to coat well. Transfer tomatoes skin-side down to the prepared baking sheet, reserving the remaining olive oil mixture left in the bowl. Roast the tomatoes and garlic for 20 minutes. If time allows, remove the garlic from the oven after 20 minutes and continue to roast the tomatoes for an additional 20 minutes.
While the tomatoes and garlic roast, add the tomato paste, basil, sun-dried tomatoes and remaining olive oil mixture to a food processor or high-powered blender. When done roasting, add the tomatoes and garlic to the processor or blender and puree, working in batches if necessary, until the desired consistency is reached. The sauce will be thick but can easily be thinned (preferably with pasta water) if desired.
Season to taste with additional salt and brown sugar, freshly ground black pepper, and/or red pepper flakes if desired.
Serve over pasta, use as a pizza sauce or spoon onto a toasted baguette with a drizzle of olive oil for a delicious roasted-tomato bruschetta.
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\subsubsection*{\bibname}}
\begin{document}
\twocolumn[
\icmltitle{Measure Estimation in the Barycentric Coding Model}
\begin{icmlauthorlist}
\icmlauthor{Matthew Werenski}{CS}
\icmlauthor{Ruijie Jiang}{ECE}
\icmlauthor{Abiy Tasissa}{math}
\icmlauthor{Shuchin Aeron}{ECE}
\icmlauthor{James M. Murphy}{math}
\end{icmlauthorlist}
\icmlaffiliation{CS}{Department of Computer Science, Tufts University }
\icmlaffiliation{math}{Department of Mathematics, Tufts University }
\icmlaffiliation{ECE}{Department of Electrical and Computer Engineering, Tufts University }
\icmlcorrespondingauthor{Matthew Werenski}{matthew.werenski@tufts.edu}
\icmlkeywords{...}
\vskip 0.3in
]
\printAffiliationsAndNotice
\begin{abstract} This paper considers the problem of measure estimation under the \emph{barycentric coding model (BCM)}, in which an unknown measure is assumed to belong to the set of Wasserstein-2 barycenters of a finite set of known measures. Estimating a measure under this model is equivalent to estimating the unknown barycentric coordinates. We provide novel geometrical, statistical, and computational insights for measure estimation under the BCM, consisting of three main results. Our first main result leverages the Riemannian geometry of Wasserstein-2 space to provide a \emph{procedure for recovering the barycentric coordinates as the solution to a quadratic optimization problem} assuming access to the true reference measures. The essential geometric insight is that the parameters of this quadratic problem are determined by inner products between the optimal displacement maps from the given measure to the reference measures defining the BCM. Our second main result then establishes an \emph{algorithm for solving for the coordinates in the BCM when all the measures are observed empirically via i.i.d. samples}. We prove precise \emph{rates of convergence} for this algorithm---determined by the smoothness of the underlying measures and their dimensionality---thereby guaranteeing its statistical consistency. Finally, we demonstrate the utility of the BCM and associated estimation procedures in three application areas: (i) \emph{covariance estimation} for Gaussian measures; (ii) \emph{image processing}; and (iii) \emph{natural language processing}.
\end{abstract}
\section{Introduction}
A number of recent machine learning applications including computer vision \cite{schmitz2018wasserstein, bonneel2016coordinates}, domain adaptation \cite{montesuma2021wasserstein, redko2019optimal}, natural language processing (NLP) \cite{singh2020context, colombo2021automatic, xu2018distilled}, and unsupervised segmentation of multivariate time series data \cite{cheng2021dynamical} have shown the utility of representing and modeling high-dimensional data as probability distributions. The essential insight in these applications is to utilize the Riemannian geometry of the space of probability distributions induced by the Wasserstein-2 metric and the Wasserstein-2 barycenters as alternatives to the Euclidean distance and linear combinations, respectively.
In this context, the methods that use Wasserstein barycenters for data modeling and inference involve solving two core problems which we term the \emph{synthesis problem} and \emph{analysis problem}. To be precise, let $\Pac$ denote the space of absolutely continuous distributions on $\mathbb{R}^d$ with finite second moment. For $\mu, \nu \in \Pac$,
\begin{equation} \label{eq:wass_dist}
W_2^2(\mu,\nu) \triangleq \min_{T\#\mu = \nu} \int_{\mathbb{R}^{d}} ||T(x) - x||_2^2 d\mu(x)
\end{equation}
defines the \emph{Wasserstein-2 metric} where the minimum is over all measurable maps $T:\mathbb{R}^d \rightarrow \mathbb{R}^d$ and the \emph{pushforward} $T\#\mu = \nu$ is such that for all Borel sets $B$ we have $\nu[B] = \mu[T^{-1}(B)]$ \citep{villani2003topics, santambrogio2015optimal}. Under the assumption $\mu,\nu\in\Pac$, unique minimizing $T$ are known to exist and the resulting $W_{2}$ distance is finite \citep{villani2003topics}. We refer to the space $\Pac$ equipped with the metric $W_{2}$ as the \emph{Wasserstein-2 space}, denoted $\mathcal{W}_{2}$.
Let $\Delta^p = \left \{\lambda=(\lambda_{1},\dots,\lambda_{p}) \in \mathbb{R}^p : \lambda_{i} \geq 0, \sum_{i=1}^p \lambda_i = 1 \right \}$ and let $\{\mu_{i}\}_{i=1}^{p}$ be known \emph{reference measures}. The \emph{$W_{2}$ barycenter} for coordinates $\lambda\in\Delta^{p}$ with respect to $\{\mu_{i}\}_{i=1}^{p}$ is defined as
\begin{equation} \label{eq:barycenter}
\nu_{\lambda} \triangleq \argmin_{\nu\in \Pac} \frac{1}{2}\sum_{i=1}^p \lambda_i W_2^2(\nu, \mu_i).
\end{equation}
The measure $\nu_{\lambda}$ is an advection of $\{\mu_i\}_{i=1}^{p}$ and blends their geometric features; it may be thought of as a ``displacement interpolation" \citep{mccann1997convexity, villani2003topics}. In contrast, the linear mixture $\sum_{i=1}^{p} \lambda_i \mu_i$ simply sets $\lambda_{i}$ to be the rate we draw samples from $\mu_i$. Figure \ref{fig:bc_vs_lin} demonstrates the important difference between linear mixture models and Wasserstein barycenters on Gaussian distributions: the linear mixture is a standard Gaussian mixture model \citep{murphy2012machine}, while the Wasserstein barycenter is itself Gaussian. The important takeaway is that Wasserstein barycenters offer a more geometrically meaningful interpolation between measures compared to mixtures, and as indicated above have been successfully leveraged in a number of applications.
Now, let $\bary(\{\mu_i\}_{i=1}^p) \triangleq \left \{ \nu_{\lambda}: \lambda \in \Delta^p \right \}$ denote the set of all of possible barycenters of $\{\mu_i\}_{i=1}^p$. The \emph{synthesis} problem (\ref{eq:barycenter}) seeks to combine the reference measures $\{\mu_{i}\}_{i=1}^{p}$ in a notion of weighted average, with relative contributions determined by $\lambda$. This problem is well-studied \citep{mccann1997convexity, agueh2011barycenters, kroshnin2019complexity} and known to have a unique solution under mild assumptions on the $\{\mu_{i}\}_{i=1}^{p}$. Moreover, there exist fast algorithms for computing or approximating $\nu_{\lambda}$ when samples from the $\{\mu_{i}\}_{i=1}^{p}$ are available \citep{rabin2011wasserstein,cuturi2014fast,bonneel2015sliced, claici2018stochastic, yang2021fast}, which have spurred the application of Wasserstein barycenters to machine learning problems.
In this paper, our focus is on the less well-studied \emph{analysis} problem: given $\mu_0$ and reference measures $\{\mu_{i}\}_{i=1}^{p}$, solve
\begin{equation} \label{eq:analysis}
\argmin_{\lambda\,\in\Delta^{p}} W_2^2\left ( \mu_0, \nu_{\lambda} \right ).
\end{equation}
Instead of \emph{combining} the measures $\{\mu_{i}\}_{i=1}^{p}$ according to the weights $\lambda\in\Delta^{p}$ as in (\ref{eq:barycenter}), the analysis problem (\ref{eq:analysis}) \emph{decomposes} a given measure $\mu_{0}$ into its optimal representation in the set $\bary(\{\mu_{i}\}_{i=1}^{p})$ as parameterized by the learned barycentric coordinates $\lambda\in\Delta^{p}$. If the measure $\mu_0\in\bary(\{\mu_i\}_{i=1}^p)$, then $\min_{\lambda\,\in\Delta^{p}} W_2^2 ( \mu_0, \nu_{\lambda})=0$ and solving (\ref{eq:analysis}) is equivalent to learning the barycentric coordinates $\lambda\in\Delta^{p}$ such that $\nu_{\lambda}=\mu_{0}$. We refer to this general model of parameterizing measures $\mu_0 \in \bary(\{\mu_i\}_{i=1}^p)$ through the associated coordinates $\lambda\in\Delta^{p}$ as the \emph{barycentric coding model} (BCM).
\begin{figure}[t!]
\centering
\includegraphics[width=\linewidth]{figures/bc_vs_lin.pdf}
\caption{\emph{Top four}: reference Gaussians. \emph{Bottom left}: linear mixture with $\lambda=(\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4} )$. \emph{Bottom right}: Wasserstein barycenter with same $\lambda$. (Intensities adjusted to show detail.)}
\label{fig:bc_vs_lin}
\end{figure}
\vspace{10pt}
\textbf{Main Contributions:} This paper addresses the analysis problem (\ref{eq:analysis}) as a measure estimation problem under the BCM. For this general problem, we make the following geometrical, statistical, and computational contributions:
\begin{enumerate}[(1)]
\setlength \itemsep{-3pt}
\item When all the measures are directly observed, Theorem \ref{thm:main} provides a \emph{geometric} characterization of the solution to \eqref{eq:analysis} as corresponding to a solution to a quadratic program. Our analysis leverages the Riemannian geometry of $\mathcal{W}_{2}$ space and establishes that the quadratic program is determined by the angles between the optimal displacement maps between the measures. When specialized to the case of Gaussian measures, Corollary \ref{cor:gaussian} provides a closed-form characterization of the solution to the analysis problem.
\item When the measures are indirectly observed via i.i.d. samples, we provide an algorithm for estimating the barycentric coordinates $\lambda$ of a given measure with respect to the reference measures. Theorem \ref{thm:convergence} gives precise rates of convergence of the angles between the optimal displacement map by a computationally tractable estimator that exploits entropic regularization, thereby establishing the statistical consistency of our approach in Corollary \ref{cor:consistency}.
\item We showcase the utility of the BCM and the proposed algorithm on several data analysis problems: covariance estimation for Gaussian measures; image inpainting and denoising; and document classification from limited labeled data. We show that the BCM provides a simple yet effective approach that outperforms competing methods in the regimes considered.\footnote{Code to reproduce results is available at \url{https://github.com/MattWerenski/BCM}}
\end{enumerate}
\subsection{Related Work}
The synthesis problem (\ref{eq:barycenter}) is well-studied. \citep{agueh2011barycenters} propose $W_{2}$ barycenters for a finite set of reference measures $\{\mu_{i}\}_{i=1}^{p}$ and prove their existence and uniqueness in a very general setting. \citep{le2017existence} extend this to barycenters constructed from infinitely many reference measures. Statistical rates of estimation in the setting of i.i.d. samples from the measures $\{\mu_{i}\}_{i=1}^{p}$ are established in \cite{kroshnin2019complexity}. Building on fundamental advances in estimating transport maps between measures using entropic regularization \cite{cuturi2013sinkhorn}, fast estimation methods for solving the synthesis problem have been developed for entroptically regularized barycenters \cite{cuturi2014fast}. Approaches to computing a barycenter based on alternating direction of multipliers on the dual problem \cite{yang2021fast} and parallelization schemes \cite{claici2018stochastic} have also been considered.
The literature on the analysis problem (\ref{eq:analysis}) is much sparser. To the best of our knowledge, our geometrical characterization of solutions to the analysis problem (Theorem \ref{thm:main}) and sample complexity results for estimating the optimal coordinates $\lambda$ (Theorem \ref{thm:convergence}, Corollary \ref{cor:consistency}) are the first of their kind. Note that our approach extends \citep{bonneel2016coordinates, schmitz2018wasserstein}---which consider measure estimation under the BCM but only for measures with finite support---in three fundamental ways. First, we enable the application of the BCM to absolutely continuous measures. Second, we prove precise theoretical characterizations of the solutions to (\ref{eq:analysis}). Third, we avoid the expensive procedure of differentiating through an iterative algorithm as required in \citep{bonneel2016coordinates} and instead provide the direct Algorithm \ref{alg1} that enjoys statistical consistency (Corollary \ref{cor:consistency}). At the level of technical analysis, our Theorem \ref{thm:main} relies on an alternative characterization of $W_{2}$ barycenters that leverages known conditions under which Karcher means are guaranteed to be $W_{2}$ barycenters \citep{panaretos2020invitation}.
For the special case when all the measures are zero-mean Gaussians, the \emph{synthesis} problem is again well-studied, with a fixed-point algorithm for computing the barycenter given in \citep{alvarez2016fixed} that is shown to have a linear convergence rate in \citep{chewi2020gradient, altschuler2021averaging}. The corresponding \emph{analysis} problem for the specific case of Gaussian measures has only been recently studied in \cite{musolas2021geodesically} but limited to the case when $p=2$. When specialized to this case, our results extend the model considered in \cite{musolas2021geodesically} to the $p \geq 3$ case and characterize solutions to barycenter parameterized covariance estimation.
In Section \ref{sec:emp_res}, we use the proposed BCM framework to model and address several problems in image processing and natural language processing. In this context our work is related to a long lineage of methods in signal processing and machine learning that use coefficients in a basis or a dictionary for data modeling and processing \citep{mallat1999wavelet, donoho2006compressed, tovsic2011dictionary}. Our approach of representing a general measure in terms of its barycentric coordinates with respect to a fixed set of reference measures is a novel approach in this tradition, and our results in Section \ref{sec:emp_res} suggest its utility for data modeled as probability measures.
\section{Convex Optimization for the Analysis Problem}\label{sec:Theory}
To solve the analysis problem (\ref{eq:analysis}), we propose to solve a convex optimization problem based on an alternative characterization of $W_{2}$-barycenters as minimizers of a certain functional. We leverage this alternative characterization to show in Theorem \ref{thm:main} that, under mild assumptions on $\{\mu_{i}\}_{i=1}^{p}$, one can use the optimal value of a convex program to both check if $\mu_{0}\in\bary(\{\mu_{i}\})_{i=1}^{p}$ and if so, recover its barycentric coordinate.
Before proceeding, we must introduce some background on the Riemannian geometry of the $\mathcal{W}_{2}$ space. The geodesic curve from $\nu_0$ to $\nu_1$ in $\mathcal{W}_{2}$ is given by $[\nu_t]_{t=0}^1$ where $\nu_t = (tT + (1-t)\id)\#\nu_0$ where $T$ is the optimal transport map from $\nu_0$ to $\nu_1$ in (\ref{eq:wass_dist}) \cite{santambrogio2015optimal}. These facts together with Brenier's Theorem (see Supplementary Material Section \ref{SM:PreciseStatements}) motivate the definition of the tangent space at $\nu$: \begin{align*}
&T_\nu\Pac \\
\triangleq&\overline{\{\beta (\nabla \varphi - \id): \beta > 0, \varphi \in C_c^\infty(\mathbb{R}^d), \varphi \text{ convex}\}},
\end{align*} where the closure is in $L^{2}(\nu)$ \citep{ambrosio2005gradient}. For $u,v \in T_\nu\Pac$, the inner product is defined by $\langle u, v \rangle_\nu \triangleq \int_{\mathbb{R}^d} \langle u(x), v(x) \rangle d\nu(x),$
which also gives the standard norm of $u \in T_\nu\Pac$, $||u||_\nu \triangleq \sqrt{\langle u, u\rangle_{\nu}}$.
\subsection{Alternative Characterization of Barycenters}
Given the reference measures $\{\mu_i\}_{i=1}^p$ and barycentric coordinates $\lambda \in \Delta^p$, the \emph{variance functional} is $G_{\lambda} : \Pac \rightarrow \mathbb{R}$ defined by $$\displaystyle G_{\lambda}(\nu) \triangleq \sum_{i=1}^p \frac{\lambda_i}{2} W_2^2(\nu, \mu_i),$$ so that the barycenter for $\{\mu_i\}_{i=1}^p$ and $\lambda \in \Delta^p$ is
$$\nu_{\lambda} =\displaystyle\argmin_{\nu \in \Pac} G_{\lambda}(\nu).$$
In many unconstrained optimization problems, the most direct way of checking if a point is optimal is to use first-order optimality conditions: compute the gradient at the point and check if it is zero. Without further assumptions this is a necessary, but not sufficient, condition for optimality. Applying this to a general variance functional, one arrives at the definition of a \emph{Karcher mean} \citep{karcher1977riemannian}.
\begin{definition}
Let $(X,\rho)$ be a metric space furnished with a tangent space at every $x \in X$. For a collection of points $\{x_i\}_{i=1}^p \subset X$ and coordinates $\lambda \in \Delta^p$, a point $y\in X$ is said to be a \emph{Karcher mean} of the set for $\lambda$ if $G_{\lambda} = \sum_{i=1}^p \lambda_i \rho^2(\cdot, x_i)$ is differentiable at $y$ and $||\nabla G_{\lambda}(y)||_y = 0$ where $\nabla G_{\lambda}(y)$ is understood as an element of the tangent space at $y$.
\end{definition}
\begin{figure}
\centering
\includegraphics[width=0.35\textwidth]{figures/tangent_space.pdf}
\caption{Visualization of the tangent space $T_{\nu}\Pac$ and $\nabla G_{\lambda}$. The red arc is the path along which $G_{\lambda}$ is maximized, starting at $\nu$ and the green arrow points in that direction in the tangent space at $\nu$.}
\label{fig:tangent_space}
\end{figure}
Any barycenter $y$ is a global minimizer of $G_{\lambda}$. Using first order optimality conditions, this implies $||\nabla G_{\lambda}(y)||_y = 0$, and therefore $y$ must be a Karcher mean. Special care must be made to ensure that being a Karcher mean is sufficient to be a barycenter. When it is sufficient, it immediately gives an alternative test for $y$ to be a barycenter for $\lambda$: simply check if $||\nabla G_{\lambda}(y)||_y = 0$.
An example of a Karcher mean which is not a barycenter is given in the Supplementary Material Section \ref{sec:karcher_not_bc}. To ensure that being a Karcher mean is sufficient to be a barycenter we require the following assumptions:
\textbf{A1:}\,\,The measures $\{\mu_i\}_{i=0}^p$ are absolutely continuous and supported on either all of $\mathbb{R}^d$ or a bounded open convex subset. Call this shared support set $\Omega$.
\textbf{A2:}\,\,The measures $\{\mu_i\}_{i=0}^p$ have respective densities $\{g_i\}_{i=0}^p$ which are bounded above and $g_1,...,g_p$ are strictly positive on $\Omega$.
\textbf{A3:}\,\,If $\Omega = \mathbb{R}^d$ then $\{g_i\}_{i=0}^p$ are locally H\"older continuous. Otherwise $\{g_i\}_{i=0}^p$ are bounded away from zero on $\Omega$.
Under these assumptions if $\mu_0$ is a Karcher mean with coordinates $\lambda$, then $\mu_0 = \nu_{\lambda}$ \citep{panaretos2020invitation}; see the Supplementary Material Section \ref{SM:PreciseStatements} for a precise statement.
This characterization of barycenters can be much easier to work with and the assumptions required are mild in practice. To accompany the notion of a Karcher mean, the \emph{Fr\'{e}chet derivative} \citep{frechet1948elements} of the variance functional $G_{\lambda}$ is given by
\begin{equation} \label{eq:grad}
\nabla G_{\lambda}(\nu) = -\sum_{i=1}^p \lambda_i \left ( T_i - \id \right ),
\end{equation} where $T_i$ is the optimal transport map from $\nu$ to $\mu_i$ as in (\ref{eq:wass_dist}) \citep{ambrosio2005gradient, panaretos2020invitation}.
We now have all the tools to begin building up to Theorem \ref{thm:main}. The first step is to derive a formula for $||\nabla G_{\lambda}(\mu_0)||_{\mu_0}^2$ in terms of $\lambda$ and show its convexity.
\\
\\
\begin{proposition}\label{prop:Prop1}
Let $\{\mu_i\}_{i=0}^p \subset \Pac$. Then
$||\nabla G_{\lambda}(\mu_0)||_{\mu_0}^2 = \lambda^TA\lambda$ where $A \in \mathbb{R}^{p \times p}$ is given by
\begin{equation} \label{eq:A_ij}
A_{ij} = \int_{\mathbb{R}^d} \langle T_i(x) - \id(x), T_j(x) - \id(x) \rangle d\mu_0(x)
\end{equation}
and $T_i$ is the optimal transport map from $\mu_0$ to $\mu_i$ as in (\ref{eq:wass_dist}). Furthermore, this is a convex function in $\lambda$.
\end{proposition}
The proof is given in the Supplementary Material Section \ref{SM:Prop1Proof}. The expression $T_i(x) - \id(x)$ is the displacement of the point $x$ when being transported from $\mu_0$ to $\mu_i$. Under this interpretation, $\langle T_i(x) - \id, T_j(x) - \id \rangle$ can be thought of as the angle between the displacement associated to the optimal transport map between $\mu_0$ to $\mu_i$ with that of $\mu_0$ to $\mu_j$. Integrating this quantity with respect to $\mu_0$ therefore quantifies the average angle between displacements and if the optimal displacement maps move in similar directions.
We now use this functional form as part of a convex program and show that it can be used to check if a $\mu_0$ is a Karcher mean. Our first main result ties Propositions \ref{prop:Prop1} to the conditions for equivalence between barycenters and Karcher means.
\begin{theorem} \label{thm:main}
Let $\{\mu_{i}\}_{i=0}^{p}$ satisfy \textbf{A1}-\textbf{A3}. Then $\mu_0\in \bary(\{\mu_{i}\}_{i=1}^{p})$ if and only if
\[\min_{\lambda\in\Delta^{p}} \lambda^TA\lambda = 0\]
where $A \in \mathbb{R}^{p \times p}$ is given by (\ref{eq:A_ij}). Furthermore, if the minimum value is 0 and $\lambda_*$ is an optimal argument, then $\mu_0 = \nu_{\lambda_*}$.
\end{theorem}
The proof is given in the Supplementary Material Section \ref{SM:Cor1Proof}. Theorem \ref{thm:main} gives a geometric characterization of the solution to (\ref{eq:analysis}) which relies on the evaluation of inner-products in the tangent space $T_{\mu_0}\Pac$ (noting that $A_{ij} = \langle T_i - \id, T_j - \id \rangle_{\mu_0}$) and solving a constrained quadratic program. Furthermore, this result suggests a method for finding an approximator of the $\mu_0$ in the set of barycenters: simply minimize the objective and use $\lambda_*$, even if the minimum value is not zero.
Note that if $A$ has rank less than $p-1$ there may be multiple minimizers which correspond to redundancies in the set $\bary(\{\mu_i\}_{i=1}^{p})$; see Supplementary Material Section \ref{sec:rank_def}.
\subsection{Theorem \ref{thm:main} For Gaussians}\label{subsec:SpecialCases}
In the Gaussian case there are formulas for both the optimal transport maps and the integration involved in $A_{ij}$. Let $\mathbb{S}_{++}^d$ denote the set of symmetric positive definite $d \times d$ matrices. Let $\mu_i = \mathcal{N}(0, S_i)$ with $S_i \in \mathbb{S}_{++}^d$ for $i=0,\dots,p$. Then the optimal transport map from $\mu_0$ to $\mu_i$ is given by $T_i(x) = C_ix$ where
\begin{equation} \label{eq:map_mat}
C_i = S_0^{-1/2}\left ( S_0^{1/2} S_i S_0^{1/2} \right )^{1/2} S_0^{-1/2}
\end{equation}
\cite{agueh2011barycenters}. Furthermore, \textbf{A1}-\textbf{A3} are satisfied for non-degenerate Gaussians. Combining Theorem \ref{thm:main} with (\ref{eq:map_mat} gives the following.
\begin{corollary}
\label{cor:gaussian}
For $i=1,\dots,p$, let $\mu_i = \mathcal{N}(0,S_i)$ with $S_i\in\mathbb{S}_{++}^d$. Then $\mu_0$ is a barycenter if and only if $\mu_0 = \mathcal{N}(0,S_0)$ for some $S_0\in\mathbb{S}_{++}^d$, and the convex program of Theorem \ref{thm:main} has minimum value 0, where the matrix $A$ is given by $A_{ij} = \Tr\left ( (C_i - I)(C_j - I)S_0 \right ).$
Furthermore, if the minimum value is zero and $\lambda_*$ is a optimal argument, then $\mu_0 = \nu_{\lambda_*}$
\end{corollary}
The proof is deferred to the Supplementary Material Section \ref{SM:Cor1Proof}. We note that in the Gaussian case, one can use $||\nabla G_{\lambda}(\mu_0)||_{\mu_0}$ to upper bound $W_2(\mu_0, \nu_{\lambda})$ \citep{chewi2020gradient, altschuler2021averaging}. This further justifies the choice of optimizing $||\nabla G_{\lambda}(\mu_0)||_{\mu_0}^2$, since it can be seen as a convex, sharp upper bound on the distance to the set of barycenters.
\subsection{Projections of Compatible Measures}
If one imposes extra structure on the set $\{\mu_i\}_{i=0}^p$, then it is possible to substantially strengthen Theorem \ref{thm:main}.
\begin{definition}
A family of measures $\{\mu_{i}\}_{i=0}^{p}$ is said to be \emph{compatible} if for any $i,j,k \in \{0,1,...,p\}$ the optimal transport map $T_i^k$ from $\mu_i$ to $\mu_k$ can can be expressed as
$$T_i^k = T_j^k \circ T_i^j$$
where $T_i^j,T_j^k$ are the optimal transport maps from $\mu_i$ to $\mu_j$ and $\mu_j$ to $\mu_k$ respectively.
\end{definition}
Note that whenever these maps exist, the map $ T_j^k \circ T_i^j$ is a valid map from $\mu_i$ to $\mu_k$, but it need not be optimal. Under the condition of compatibility, we have the following result.
\begin{theorem} \label{thm:projection}
Suppose that $\{\mu_i\}_{i=0}^{p}$ are compatible and let $\lambda_*$ be the minimizer in Theorem \ref{thm:main}. Then
$$\lambda_* = \argmin_{\lambda \in \Delta^p} W_2^2(\mu_0, \nu_\lambda).$$
\end{theorem}
The proof is deferred to the Supplementary Material Section \ref{sec:projection}. In other words, when the measures are compatible one can solve (\ref{eq:analysis}) and find the \emph{exact projection} of $\mu_0$ onto $\bary(\{\mu_i\}_{i=1}^p).$
There are several known conditions under which the family of measures is compatible. These include any set of continuous measures on $\mathbb{R}$, any family of Gaussians with simultaneously diagonalizable covariance matrices, families of radial transformations of a base measure, or families with a "common dependence structure''; see \cite{panaretos2020invitation} Section 2.3 for further details.
\section{Finite Sample Analysis and Rates of Convergence} \label{sec:SampleSetting}
The results of the previous section are all reliant upon having exact knowledge of both the underlying measure $\mu_0$ as well as the optimal transport maps $T_i$. In practice, outside of specific parametric families (e.g., Gaussians), it is rare that one will have either of these available.
Much more common is the setting where the $\mu_i$ are accessed through i.i.d. sampling. In this setting we need to estimate the maps $T_i$, as well as $\mu_0$ and use these estimates to compute an $\hat{A}$ whose entries are $\hat{A}_{ij} = \langle \hat{T}_i - \id, \hat{T}_j - \id \rangle_{\hat{\mu}_0}$,
where $\hat{T}_i$ and $\hat{\mu_0}$ are our estimates of the transport maps and $\mu_0$ respectively. The quality of the estimate $\hat{A}$ will depend on the approximations used above, and ideally these would be accompanied by performance guarantees.
\subsection{The Entropic Map Estimate}
Let $X_1,...,X_n \sim \mu_0$ and $Y_1,...,Y_n \sim \mu_1$ be i.i.d. samples. In \cite{pooladian2021entropic} the authors propose using the \textit{entropic map} to estimate the transport maps. For $\epsilon > 0$, this map is defined by
\begin{equation} \label{eq:entropic_map}
\hat{T}_\epsilon(x) \triangleq \frac{\frac{1}{n}\displaystyle\sum_{i=1}^n Y_i \exp\left (\frac{1}{\epsilon} (g_{\epsilon}(Y_i) - \frac{1}{2}||x - Y_i||_2^2) \right )}{\frac{1}{n}\displaystyle\sum_{i=1}^n \exp\left (\frac{1}{\epsilon} (g_{\epsilon}(Y_i) - \frac{1}{2}||x - Y_i||_2^2) \right )}
\end{equation}
where $g_\epsilon$ is defined to be the optimal variable in the dual entropic optimal transport problem on the samples. See the Supplementary Material \ref{SM:Entropic_Map} for details on $g_\epsilon$ and important properties of $\hat{T}_\epsilon$. Practically, the calculation of $g_\epsilon$ has been well studied and there exists fast algorithms for its computation \cite{peyre2020computational}. The estimate has also been shown to converge (with rates) to the optimal transport map in $L_2(\mu_0)$ under the appropriate technical conditions.
To accompany this we also have the following result, stated informally below. In this result $a \lesssim b$ means that there exists a constant $C > 0$ such that $a \leq Cb$. We allow this constant $C$ to depend on the size of the support of the measures, upper and lower bounds on their densities, and the regularity properties of the optimal transport maps $T_i,T_j$, but it is importantly independent of the sample size $n$.
\begin{theorem}(\textbf{Informal}) \label{thm:convergence}
Let $i,j \in \{1,...,p\}$ and suppose that $\mu_i,\mu_j,\mu_0$ are supported on bounded domains and that the maps $T_i$ and $T_j$ are sufficiently regular. Let $X_1,...,X_{2n} \sim \mu_0, Y_1,...,Y_n \sim \mu_i, Z_1,...,Z_n \sim \mu_j$. For an appropriately chosen $\epsilon$, let $\hat{T}_i$ and $\hat{T}_j$ be the entropic maps computed using $\{X_{i}\}_{i=1}^{n}, \{Y_{i}\}_{i=1}^{n}, \{Z_{i}\}_{i=1}^{n}$. Then we have
\begin{equation}
\begin{split}
& \mathbb{E}\left [ \left | A_{ij} - \frac{1}{n} \sum_{k=n+1}^{2n} \langle \hat{T}_i(X_k) - X_k, \hat{T}_j(X_k) - X_k \rangle \right | \right ] \\
&\hspace{1.5cm} \lesssim \frac{1}{\sqrt{n}} + n^{-\frac{\alpha + 1}{4(d' + \alpha + 1)}}\sqrt{\log n}
\end{split}
\end{equation}
where $d' = 2\lceil d/2 \rceil$, and $\alpha \leq 3$ depends on the regularity of optimal transport maps.
\end{theorem}
A precise statement and proof of this theorem is given in the Supplementary Material Section \ref{SM:Thm2Proof}. Theorem \ref{thm:convergence} tells us that in expectation, by using the entropic map we can accurately approximate the entries of the matrix $A_{ij}$, and do so in a numerically feasible way. We chose the entropic map as it is computationally tractable and has competitive convergence rates when compared to the intractable but optimal estimator of \cite{hutter2021minimax}. We expect similar analysis holds for other recently proposed estimators \cite{deb2021rates, gunsilius_2021, manole2021plugin, muzellec2021near} under different assumptions.
Theorem \ref{thm:convergence} can be combined with a matrix perturbation analysis to demonstrate the consistency of the estimated barycentric coordinates $\hatlambda$ from Algorithm \ref{alg:estimate_lambda} for the true ones $\lambda_{*}$ when $\mu_{0}\in \bary(\{\mu_{i}\}_{i=1}^{p})$, that is when $\lambda_{*}^{T}A\lambda_{*}=0$. This is stated more precisely as follows.
\begin{corollary}\label{cor:consistency} Let $\hatlambda$ be the random estimate obtained from Algorithm \ref{alg:estimate_lambda}. Suppose that $A$ has an eigenvalue of 0 with multiplicity 1 and that $\lambda_{*}\in\Delta^{p}$ realizes $\lambda_{*}^{T}A\lambda_{*}=0$. Then under the assumptions of Theorem \ref{thm:convergence}, \[\E[\|\hatlambda -\lambda_{*}\|_{2}^{2}]\lesssim \frac{1}{\sqrt{n}} + n^{-\frac{\alpha + 1}{4(d' + \alpha + 1)}}\sqrt{\log n}.\]
\end{corollary}
\begin{algorithm}[ht!]
\caption{\label{alg1}Estimate $\lambda$} \label{alg:estimate_lambda}
\begin{algorithmic}
\STATE {\bfseries Input:} i.i.d. samples $\{X_1,...,X_{2n}\} \sim \mu_0, \{\{Y_1^i,...,Y_n^i\} \sim \mu_i: i=1,...,p\},$ regularization parameter $\epsilon > 0$.
\FOR{$i = 1,...,p$}
\STATE Set $M^i \in \mathbb{R}^{n\times n}$ with $M^i_{jk} = \frac{1}{2}||X_j - Y_k^i||_2^2$.
\STATE Solve for $g^i$ as the optimal $g$ in
\begin{equation*} \begin{split}
&\max_{f,g \in \mathbb{R}^n} \frac{1}{n}\sum_{j=1}^n f_j+ \frac{1}{n}\sum_{k=1}^n g_k \\
&\hspace{1.5cm}- \frac{\epsilon}{n^2}\sum_{j,k}^n \exp \left((f_j + g_k - M_{jk}^i)/\epsilon \right).
\end{split}
\end{equation*}
\STATE Define $\hat{T}_i$ through \ref{eq:entropic_map} with $g_\epsilon = g_i$ and $\{Y_1^i,...,Y_n^i\}$.
\ENDFOR
\STATE Set $\hat{A} \in \mathbb{R}^{p \times p}$ to be the matrix with entries
\begin{equation*}
\hat{A}_{ij} = \frac{1}{n}\sum_{k=n+1}^{2n} \langle \hat{T}_i(X_k) - X_k, \hat{T}_j(X_k) - X_k \rangle.
\end{equation*}
\STATE \textbf{Return} $\hat{\lambda}=\displaystyle\argmin_{\lambda \in \Delta^p} \lambda^T\hat{A}\lambda$.
\end{algorithmic}
\end{algorithm}
The proof is deferred to the Supplementary Material Section \ref{SM:Cor2Proof}. Note that the implicit constant in the inequality of Corollary \ref{cor:consistency} depends on $p$ in addition to the dependencies of listed above. Corollary \ref{cor:consistency} ensures that in the large sample limit, the entropic regularization parameter may be chosen to guarantee precise estimation of the true barycentric coordinates. Note that the rate of convergence in Corollary \ref{cor:consistency} depends crucially on the smoothness of the transport maps between the reference measures ($\alpha$) and the dimensionality of the space in which they are supported ($d'$).
In the next section we illustrate the utility of the BCM and propose novel approaches based on Theorem \ref{thm:main} and Algorithm \ref{alg:estimate_lambda} for several applications.
\section{Applications \label{sec:emp_res}}
\subsection{Barycenter Parameterized Covariance Estimation}
Extending the set-up in \cite{musolas2021geodesically}, we first consider the case where $\mu_i = \mathcal{N}(0,S_i), S_i \in \mathbb{S}^d_{++}$ for $i=0,\dots,p$. We will use $S_i$ both as a matrix and to refer to $\mu_i$; similarly, let $S_{\lambda}$ denote $\nu_{\lambda}$. Let $\{x_i\}_{i=1}^n$ be i.i.d. samples with empirical covariance $\hat{S}$. In this setting, we can use the formulas laid out in Corollary \ref{cor:gaussian}.
For comparison, we also consider maximum likelihood estimation (MLE) for the parameter $\lambda$ in the BCM. Let $P_{\lambda}$ denote the probability density function of $S_{\lambda}$. The MLE is $\argmax_{\lambda \in \Delta^p} \prod_{i=1}^n P_{\lambda}(x_i),$ which is equivalent to minimizing the KL-divergence $D_{KL}(\hat{S},S_{\lambda})$. However, this problem may be non-convex and difficult to optimize. We solve it numerically using auto-differentiation \citep{bartholomew2000automatic} and use the coordinates recovered by this method, which may not be the true MLE.
\textbf{Experimental Setup:} We consider the problem of estimating the covariance matrix $S_0$ from i.i.d. samples $\{x_i\}_{i=1}^{n} \sim \mathcal{N}(0,S_0)$ when $S_0$ is known to be a barycenter of $S_1,...,S_p$. To do so we use the following procedure:
\vspace{-5pt}
\begin{enumerate}
\setlength \itemsep{-4pt}
\item \textbf{Choose $\lambda$ and $\{S_i\}_{i=1}^p$:} Select $\lambda \in \Delta^p$ and the reference measures $\{S_{i}\}_{i=1}^{p}$ either by hand or at random.
\item \textbf{Generate $S_{\lambda}$:} Using Algorithm 1 of \citep{chewi2020gradient}, find the true barycenter, $S_{\lambda}$.
\item \textbf{Sample:} Sample $\{x_i\}_{i=1}^n$ i.i.d. from $\mathcal{N}(0,S_{\lambda})$. Compute the empirical covariance
$\hat{S} = \frac{1}{n} \sum_{i=1}^n x_ix_i^T.$
\item \textbf{Estimate $\hat{\lambda}$:} Perform the optimization in Corollary \ref{cor:gaussian}, or use MLE with $S_0 = \hat{S}$ to recover an estimate $\hat{\lambda}$.
\item \textbf{Compute $S_{\hat{\lambda}}$:} Again using Algorithm 1 of \citep{chewi2020gradient} find $S_{\hat{\lambda}}$ and use that as the estimate of $S_{\lambda}$.
\end{enumerate}
The results are in Figure \ref{fig:gaussian}. These show that using our approach (denoted \emph{gradient norm}) we can estimate the underlying covariance matrix much more accurately than the empirical covariance. Our optimization is competitive with the auto-differentiation approach to MLE, while being significantly more stable and much faster. Indeed, computing all the estimates $\hat{\lambda}$ to generate Figure \ref{fig:gaussian} takes our method less than 1 second compared to over 3 hours and 40 minutes for MLE. For reference it takes on average roughly 0.01 seconds to perform empirical covaraiance estimation\footnote{All reported times are obtained using 20 Intel Xeon CPU E5-2660 V4 cores at 2.00 GHz.}. Further details are in the Supplementary Material Section \ref{SM:Covariance}.
\begin{figure}[ht!]
\centering
\includegraphics[width=0.93\linewidth]{figures/gaussian.pdf}
\caption{$W_{2}$ between true covariance and estimates. We set $p = 6, d = 10$, $\lambda \sim \text{Unif}(\Delta^p)$, and $\mu_i \sim \text{Wish}(I_d) + 0.5 I_d$ with results averaged over 250 trials, and 1 standard deviation shaded.}
\label{fig:gaussian}
\end{figure}
We now consider applications where it is necessary to directly estimate the optimal transport map from samples (unlike the previous case where we estimate it via sample-covariance estimators) and between measures with non-uniform weights on the observed support. To that end, we first modify Algorithm \ref{alg:estimate_lambda} for practical purposes.
\subsection{Adapting Algorithm \ref{alg:estimate_lambda} for Applications}
In practice, Algorithm \ref{alg:estimate_lambda} has a few mild requirements: that we use the same number of samples for each reference measure; that the weight on each sample is the same; and access to an extra set of points for evaluating the inner products. Algorithm \ref{alg:estimate_lambda_pc} relaxes these requirements and is in terms of matrix-vector operations, making it suitable for practical implementation. We note that if one uses Algorithm \ref{alg:estimate_lambda_pc} with the same constraints as in Algorithm \ref{alg:estimate_lambda}, then both produce the exact same $\hat{T}_i$ on the samples $X_1,...,X_n$ \cite{pooladian2021entropic}. The main difference between the two approaches is that the dual potentials in Algorithm \ref{alg:estimate_lambda} make an out-of-sample extension possible which may be of its own interest.
\begin{algorithm}
\caption{Estimate $\lambda$ on Point Clouds} \label{alg:estimate_lambda_pc}
\begin{algorithmic}
\STATE {\bfseries Input:} PMFs $p \in \mathbb{R}^{n_0}$, $q^i \in \mathbb{R}^{n_i}$, support matrices $X \in \mathbb{R}^{n_0 \times d}$,$Y^i \in \mathbb{R}^{n_i \times d}$, regularization parameter $\epsilon > 0$.
\FOR{$i = 1,...,p$}
\STATE Set $M^i \in \mathbb{R}^{n_0 \times n_i}$ with $M^i_{jk} = ||X_j - Y_k^i||_2^2$.
\STATE Solve for the entropic assignment matrix $\pi^i$ as the optimal matrix in
\begin{equation*}
\min_{\substack{\pi \in \mathbb{R}^{n_0 \times n_i}_+ \\
\pi\bm{1} = p \\
\pi^T\bm{1} = q^i}} \sum_{j=1}^{n_0}\sum_{k=1}^{n_i} M^i_{jk}\pi_{jk} + \epsilon \pi_{jk}\log \pi_{jk}.
\end{equation*}
\STATE Compute the approximate transport matrix $\hat{T}_i \in \mathbb{R}^{n_0 \times d}$ as
\begin{equation*}
\hat{T}_i = \text{diag}(1/p)\pi^i Y^i.
\end{equation*}
\ENDFOR
\STATE Set $\hat{A} \in \mathbb{R}^{p \times p}$ to be the matrix with entries
\begin{equation*}
\hat{A}_{ij} = \Tr\left(\text{diag}(p)(\hat{T}^i-X)(\hat{T}^j-X)^T \right).
\end{equation*}
\STATE \textbf{Return} $\hat{\lambda}=\displaystyle\argmin_{\lambda \in \Delta^p} \lambda^T\hat{A}\lambda$.
\end{algorithmic}
\end{algorithm}
\subsection{Image Inpainting and Denoising}
We consider the problem of recovering an image in the presence of corruption, interpreting the image as a probability measure. We consider two specific models of corruption: \textbf{a.} additive \emph{noise} and \textbf{b.} \emph{occlusion} of a portion of the image. Our experimental procedure for both of these problems is outlined below taking as experimental data the MNIST dataset of $28\times28$ pixel images of hand-written digits \citep{lecun1998mnist}. Additional details are in Supplementary Material Section \ref{SM:MNIST}. Note that after normalization, these can be treated as measures supported on a $28\times28$ grid.
\textbf{Experimental Setup:}
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{figures/MNIST_in_out.pdf}
\caption{\emph{Left to right}: corrupted image; recovery by linear projection; recovery using $\hat{\lambda}$ from Algorithm \ref{alg:estimate_lambda_pc}; original image. \emph{Top}: white noise added to the image as in \textbf{a.} \emph{Bottom}: occlusion of the image as in \textbf{b.} We see the linear reconstruction fails, while Algorithm \ref{alg:estimate_lambda_pc} recovers well, albeit with some blurring that can be interpreted as a consequence of entropic regularization.}
\label{fig:MNIST_IO}
\end{figure}
\begin{enumerate}
\setlength \itemsep {-3pt}
\item \textbf{Select $\mu_{0}$:} Select a digit $\mu_0$ \textbf{a.} generate a white noise image $\zeta$. Set $\Tilde{\mu}_0$ to be $\Tilde{\mu_0} = (1 - \alpha)\mu_0 + \alpha \zeta$. \textbf{b.} Set $\Tilde{\mu}_0$ to be $\mu_0$ with the central $8 \times 8$ square removed, and renormalized.
\item \textbf{Select $\{\mu_{i}\}_{i=1}^{p}$:} Select a set of images of the same digit as $\mu_0$ to serve as the reference measures. \textbf{a.} Let $\Tilde{\mu}_i = (1 - \alpha)\mu_0 + \alpha \mathbb{E}[\zeta]$. \textbf{b.} Let $\Tilde{\mu}_i$ be $\mu_i$ with the central $8 \times 8$ square removed, and renormalized
\item \textbf{Estimate $A$, $\lambda$:} Use Algorithm \ref{alg:estimate_lambda_pc} to compute the approximate Gram matrix $\hat{A}$ using $\Tilde{\mu}_0, \Tilde{\mu_1}, ... \Tilde{\mu_p}$ and then compute estimated coordinates $\hat{\lambda}$.
\item \textbf{Compute $\hat{\nu_{\lambda}}$:} Output $\hat{\mu}_0 = \nu_{\hat{\lambda}}$, where the barycenter is reconstructed from $\mu_1,...,\mu_p$.
\end{enumerate}
An illustration of the procedure is shown in Figure \ref{fig:MNIST_IO}. We also show for comparison digits reconstructed using a linear method, in which the corrupted image is recovered by computing the Euclidean projection onto the convex hull of the reference measures (see the Supplement \ref{sec:linear_rec} for further details). To recover the barycenter we use the method of \cite{benamou2015iterative}. As a competitive baseline we compare to a well-known existing method for histogram regression \cite{bonneel2016coordinates} in this setting. Our results are summarized in Tables \ref{tab:mnist} and \ref{tab:mnist_comp}. We note that our method is over an order of magnitude faster than \cite{bonneel2016coordinates} on this dataset and achieves competitive results. This is particularly remarkable because \cite{bonneel2016coordinates} is specifically adapted to measures with structured support such as grids and meshes, while our Algorithm \ref{alg:estimate_lambda_pc} is much more general.
\begin{table*}[]
\centering
\begin{tabular}{c|c|c|c|}
\cline{2-4}
& Bon., $\epsilon = 10$ & Alg. 2, $\epsilon = 10$ & Alg. 2, $\epsilon = 0$ \\
\hline
\multicolumn{1}{|c|}{Occlusion} & 2.5101 (2228s) & 2.5488 (3.371s) & 2.5287 (1.062s) \\
\hline
\multicolumn{1}{|c|}{Noise ($\alpha=0.5$)} & 2.4058 (2391s) & 2.6797 (86.32s) & 2.3787 (50.67s) \\
\hline
\end{tabular}
\caption{Average quality of recovery of $\mu_0$ measured in $W_2^2(\mu_0, \hat{\mu}_0)$ when reconstructing 500 random 4's using a barycenter constructed from 10 random 4's, as well as run times of each method. Algorithm \ref{alg:estimate_lambda_pc} affords comparably accurate reconstructions in orders-of-magnitude faster time than the state-of-the-art \cite{bonneel2016coordinates}\label{tab:mnist}.}
\end{table*}
\begin{table*}[]
\centering
\begin{tabular}{c|c|c|c|}
\cline{2-4}
& (Alg. 2, $\epsilon=10$) - (Bon., $\epsilon = 10$) & (Alg. 2, $\epsilon=0$) - (Bon., $\epsilon = 10$) & (Alg. 2, $\epsilon=10$) - (Alg. 2, $\epsilon=0$) \\
\hline
\multicolumn{1}{|c|}{Occlusion} & $0.03872 \pm 0.3103$ & $0.01868 \pm 0.2934$ & $0.02004 \pm 0.2145$ \\
\hline
\multicolumn{1}{|c|}{Additive} & $0.2739 \pm 0.3564$ & $-0.02706 \pm 0.2558$ & $0.3009 \pm 0.2486$ \\
\hline
\end{tabular}
\caption{Average and standard deviation of the pairwise-difference in reconstruction quality measured in $W_2^2(\mu_0, \hat{\mu}_0)$ in the same setting as Table \ref{tab:mnist}. The average pairwise-difference is smaller than the standard deviation in all cases involving \cite{bonneel2016coordinates}, suggesting there is no statistically significant difference. Our approach should thus be preferred to \cite{bonneel2016coordinates}, on the grounds that it is considerably more efficient while achieving essentially the same accuracy.}
\label{tab:mnist_comp}
\end{table*}
\subsection{Document Classification}
Finally, we consider the task of identifying the topic of a document using its word embedding representation as the empirical distribution. We assume that there are $t$ topics and that we have $p$ reference documents about each topic. Each document can be represented as a high-dimensional empirical measure using a combination of a bag-of-words representation and a node2vec \cite{mikolov2013distributed} word-embedding, and is paired with topic label. We use the publicly available dataset provided by \cite{huang2016supervised}. The task is to use a small number of labelled documents from each topic to predict the topic of a test document.
We consider four predictors: \textbf{(1) 1-Nearest Neighbor (1NN)} which classifies using the topic of the $W_2^2$-nearest reference document; \textbf{(2) Minimum Average Distance} which selects the topic with reference documents on average $W_2^2$-closest to the test document; \textbf{(3) Minimum Barycenter Loss} which runs Algorithm \ref{alg:estimate_lambda_pc} using the references from each topic separately and selects the topic with the smallest loss in the quadratic form; \textbf{(4) Maximum Coordinate} which runs Algorithm \ref{alg:estimate_lambda_pc} using all the reference documents and chooses the topic which receives the most mass from $\hatlambda$.
\begin{figure}[t!]
\centering
\includegraphics[width=\linewidth]{figures/bbcsport.pdf}
\includegraphics[width=\linewidth]{figures/news20.pdf}
\caption{Document topic prediction accuracy as a function of number of reference documents in each class. \emph{Top:} BBC Sport dataset (5 classes). \emph{Bottom:} News20 dataset (20 classes).}
\label{fig:NLP}
\end{figure}
Our findings on the BBCSport (5 topics) and News20 (20 topics) datasets are reported in Figure \ref{fig:NLP}. To generate these figures we randomly sample $k$ reference documents per topic and a test set of 100 random documents. We apply the four methods listed above and compute the accuracy on the test set. This procedure is repeated 50 times for each choice of $k$ and the average accuracy is plotted. See Supplementary Material Section \ref{sec:NLP_figs} for details.
We see that even with a very small amount of training data, our BCM approaches perform well. Importantly, the BCM is able to represent unseen documents using these small training sets, giving it a clear advantage over simply classifying based on which document class it is $W_2^2$-nearest (1NN) or $W_2^2$-nearest in an aggregate sense (Min. Avg. Dist.). This suggests that even when $p$ is small, the BCM has high modeling capacity and that the learned barycentric coordinates encode important information.
\section{Conclusion}
We have proposed a new method for computing coordinates under the BCM, together with guarantees on its solution via a convex program (Theorem \ref{thm:main}) with closed-form coordinates in the Gaussian case (Corollary \ref{cor:gaussian}). We further developed an algorithm for estimating the coordinates under the BCM when all measures are accessible only via i.i.d. samples (Algorithm \ref{alg1}) which enjoys a natural smoothness and dimension-dependent rate of convergence to the true parameters (Theorem \ref{thm:convergence}, Corollary \ref{cor:consistency}). The BCM paradigm affords significant gains in runtime and robustness for barycenter parameterized Gaussian measure estimation, and provides an effective approach to image reconstruction and document classification when interpreting these data as measures. The results in this paper suggest the efficiency and effectiveness of the BCM as a broadly viable modelling tool.
\textbf{Future Work and Open Questions:} Section \ref{sec:SampleSetting} provides a consistency analysis for $A$ and $\lambda$ by estimating the transport maps between each measure. But, all that is needed is an \emph{estimate on the inner product} between the displacement maps, which in principle could admit more sample efficient approaches that avoid explicitly estimating the maps.
Section \ref{sec:emp_res} suggests that unseen data can be well-represented in the BCM for randomly chosen reference measures. An interesting theoretical problem is to understand the representational capacity of the BCM using particular reference measures (e.g., random ones, optimally chosen ones, those in certain parametric families). This naturally touches on the question of the smoothness of the synthesis map $\lambda \mapsto \nu_{\lambda}.$
Computationally, all of our real data experiments use randomly chosen reference measures. It is of interest to develop efficient procedures as in \cite{schmitz2018wasserstein} for \emph{learning} reference measures that induce low reconstruction error. Beyond that, one could regularize the analysis problem (\ref{eq:analysis}) to encourage sparse or otherwise structured coordinates as is well-studied in Euclidean settings \cite{aharon2006k}.
\section*{Acknowledgements}
MW is supported by NSF CCF-1553075. RJ is supported by NSF DRL 1931978. SA acknowledges support by NSF CCF-1553075, NSF DRL 1931978, NSF EEC 1937057, and AFOSR FA9550-18-1-0465. JMM acknowledges support from the Dreyfus Foundation and the NSF through grants DMS-1912737, DMS-1924513. All authors acknowledge support through the Tufts TRIPODS Institute, supported by the NSF under grant CCF-1934553. We acknowledge the reviewers for their helpful comments which improved the paper considerably.
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Alm. Néstor Evencio Yee Amador es un marino militar mexicano. Nació el 8 de octubre de 1946 en San José de Comondú, Baja California Sur.
Carrera militar
Ingresó a la Armada de México en la Heroica Escuela Naval Militar el 8 de enero de 1964. Fue oficial de Cargo, Jefe de Máquinas y Segundo Comandante de diversas Unidades de Superficie de la Armada. De igual forma, fue comandante de la ARM Córdova (PC-202), el ARM Seri (ARE-03), el ARM Yaqui (ARE-02), el Guardacostas "OCAMPO", y Buque Salvamento Manzanillo. Fue Comandante de la Sexta Flotilla y Director de Área de Armas Navales, Área de Personal Naval y General de Oceanografía Naval. Fue Jefe de la Sección Primera del Estado Mayor General y Jefe del Estado Mayor de la Tercera Zona y Primera Región Naval. Fue Comandante del Sector Naval de Coatzacoalcos y Agregado Naval en la Embajada de México en Francia. Fue profesor, jefe de estudios y subdirector de la Heroica Escuela Naval Militar. Fue Comandante de la Octava Zona Naval y de la Región Naval Central, la Segunda Región Naval y la Cuarta Región Naval. Es comandante de la Fuerza Naval del Pacífico (México).
Enlaces externos
Ficha en semar.gob.mex
Referencias
Militares de México
Alumnado de la Heroica Escuela Naval Militar
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NEW YORK, Dec 10, 2018 (GLOBE NEWSWIRE via COMTEX) -- NEW YORK, Dec. 10, 2018 (GLOBE NEWSWIRE) -- Attorney Advertising -- Bronstein, Gewirtz & Grossman, LLC reminds investors that a class action lawsuit has been filed against Stitch Fix, Inc. ("Stitch Fix" or the "Company") (NASDAQ: SFIX) and certain of its officers, on behalf of shareholders who purchased or otherwise acquired Stitch Fix securities between June 8, 2018 and October 1, 2018, inclusive (the "Class Period"). Such investors are encouraged to join this case by visiting the firm's site: www.bgandg.com/sfix.
The Complaint alleges that throughout the Class Period, Defendants made materially false and/or misleading statements and/or failed to disclose that: (1) Stitch Fix's sales growth prospects were not as positive as stated because active client growth had dramatically slowed; (2) defendants had ceased running a television advertising campaign for much of the fourth quarter of 2018; and (3) as a result, defendants' statements were materially false and misleading and/or lacked a reasonable basis at all relevant times.
On October 1, 2018, after-market hours, Stitch Fix revealed its fourth-quarter financial results ending July 28, 2018, reporting lower revenue and active client numbers. Following this news, on October 2, 2018, Stitch Fix stock dropped almost $16 per share, or over 35%,on unusually high trading volume.
A class action lawsuit has already been filed. If you wish to review a copy of the Complaint you can visit the firm's site: www.bgandg.com/sfix or you may contact Peretz Bronstein, Esq. or his Investor Relations Analyst, Yael Hurwitz of Bronstein, Gewirtz & Grossman, LLC at 212-697-6484. If you suffered a loss in Stitch Fix you have until December 10, 2018 to request that the Court appoint you as lead plaintiff. Your ability to share in any recovery doesn't require that you serve as a lead plaintiff.
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Алфави́тная за́пись чи́сел — система, в которой буквам (всем или только некоторым) приписываются числовые значения, часто (но не всегда) следующие порядку букв в алфавите. Чаще всего первые девять букв получают значения от 1 до 9, следующие девять — от 10 до 90. Для записи числа составляются буквы, сумма значений которых выражает это число. Для очень больших чисел применяются своего рода диакритические знаки, показывающие, например, что перед нами — не единицы, а тысячи.
Основные системы алфавитной записи чисел
Арабская
Греческая
Примечание 1. В Византийской империи вместо дигаммы (ϝ) значение 6 стала выражать стигма (ϛ), лигатура букв сигма (σ) и тау (τ).
Примечание 2. Архаические буквы коппа (ϟ) и сампи (ϡ) не входят даже в классический 24-буквенный древнегреческий алфавит, но для записи чисел (имея значение 90 и 900, соответственно) изредка применяются до сих пор.
Для записи чисел могли применяться как строчные, так и прописные буквы. Порядок — сотни-десятки-единицы. Числа от слов текста отличались тем, что над ними проводилась черта и (или) после числа ставился штрих («числовой апостроф»). Тысячи, десятки тысяч, сотни тысяч обозначались теми же буквами, что и простые единицы, десятки, сотни, но со штрихом внизу слева ,α σ λ δ' = 1234.
В старопечатных книгах по причине отсутствия литер для коппы и сампи обычно применялись похожие знаки — еврейский ламед (ל) вместо коппы и знак наподобие заглавной русской буквы «Э» вместо сампи. Стигма же ставилась строчная даже в числа, набранные прописными буквами.
Eврейская
В иврите каждой букве соответствует численное значение от 1 до 400 согласно следующей таблице:
Запись — позиционная, сначала (справа) старшие порядки, затем младшие. Например, ל"ג — это 30+3=33, ט"ו — это 9+6=15. Для получения чисел крупнее, чем 499, используется сочетание двух букв: ת"ק имеет значение 500, ת"ש имеет значение 700, а תת"ק — это 400+400+100=900. Тысяча может обозначаться как תת"ר или как 'א; во избежание разночтений тысяча будет обозначаться как תת"ר тогда, когда буква א может быть понята как количество единиц. Для выражения более крупных числительных численное значение букв умножается на нужную степень тысячи; так, число ברכ"ה означает 2000+200+20+5=2225: буква ב, стоящая в числительном перед более высокой по числовому значению буквой ר, должна читаться как «две тысячи», а не как «два».
Эти цифры чаще всего используются для записи дат.
Кириллическая
Кириллическая система буква в букву воспроизводит греческую. В стандартном церковнославянском варианте, используемом и сегодня, она имеет следующий вид:
Для записи чисел используются почти исключительно строчные буквы (даже в составе текста, набранного одними прописными), хотя изредка можно найти и примеры применения прописных. Порядок обычный — сотни-десятки-единицы, но в числах, оканчивающихся на 11, 12, …, 19, последние два знака переставляются согласно славянскому прочтению (один-на-дцать, то есть сперва «один», а потом «дцать» = 10). Тысячи, десятки тысяч и сотни тысяч обозначаются теми же буквами, что и обычные единицы, десятки, сотни, но слева (или слева снизу) ставится особый значок «҂». Для отличия от обычных слов текста над числом ставится особый знак «титло» (над единственной или над предпоследней буквой). Например, ҂асл҃д = 1234.
Примечания:
Числовое значение 5 первоначально несла обычная буква е, так называемая «узкая е», но так как по церковно-славянской орфографии она не могла стоять в начале слова или изолированно, позже стал применяться её другой вариант , так называемая «широкая е» , из которого впоследствии развилась украинская буква «є».
Для числового значения 6 в древности применялась как обычная буква «зело» (ѕ), так и зеркально перевёрнутая.
Буква «і» в числовом употреблении точек не имеет.
По той же причине, что и для 5, для числового значения 70 обычно применяется не обычная буква «о», а её так называемый «широкий» вариант (ѻ, этот символ в Юникоде по недоразумению называется «круглой омегой», ).
Значение 90 в самых древних кириллических текстах выражала не буква «ч», а заимствованный из греческого знак «коппа» (ҁ).
В западнорусских церковнославянских изданиях до последней четверти XIX века (а на Западной Украине и позже) в значении 200 использовалась не обычная буква «с» (очень узкая и мелкая в полууставных шрифтах), а её крупный круглый вариант (более широкий, чем прописная «С», но поменьше по вертикали).
Значение 400 в древности выражала буква ижица (ѵ), позже так называемый «ик» — у-образный знак, используемый только как числовой и в составе диграфа «ук» (ѹ). Использование в числовом значении ика характерно для российских изданий, а ижицы — для старопечатных западнорусских, позднейших южнославянских и румынских.
В значении 800 могла применяться как «голая» омега (ѡ), так и (чаще) составной знак «от» (ѿ); подробнее см. в статье «Омега (кириллица)».
Значение 900 в древности выражалось малым юсом (ѧ), несколько похожим на соответствующую греческую букву «сампи» (Ϡ); позже в этом значении стала применяться буква «ц».
Кроме того, старинные варианты кириллической записи чисел могли отличаться следующим:
до и после числа, а иногда и между «цифрами» ставились точки;
знак титла мог ставиться над каждой буквой, либо же он мог быть длинным и покрывать всё число;
в случае с денежными суммами титло иногда заменяли надстрочной лигатурой «ру», «де» или буквой «а», соответственно символами рубля, денги или алтына;
большие числа (десятки тысяч, сотни тысяч) могли выражаться не как «знак "҂" + буква для десятков или сотен», а как буква для единиц, специальным образом обведённая; разные способы такого обвода соответствовали разным разрядам: сплошной кружок — десяткам тысяч («тьмам»), пунктирный — сотням тысяч («легеонам»), из запятых — миллионам («леодрам»), из крестиков — десяткам миллионов («вранам»); впрочем, для больших чисел эти обозначения были довольно нестабильны;
в старопечатных книгах западнорусского происхождения, более точно воспроизводящих греческую систему обозначений, в конце чисел мог ставиться штрих (иногда выглядящий как ударение над последней буквой).
Церковнославянская изопсефия
Тибетская
В Тибете для нумерации страниц и книг в библиотеках применяется тибетский алфавит. От 1 до 30 — простые буквы, от 31 до 60 — те же буквы с огласовкой гигу, от 61 до 90 — с огласовкой жабкью, от 91 до 120 — дренбу, от 121 до 150 — наро. Подобная система применяется и в тибетской астрологии карци.
Программы
«Creounity Машина Времени» — нумизматический конвертер дат, в том числе по следующим системам алфавитной записи: русская кириллическая, еврейская, грузинская и др.
«Титло» — переводчик чисел из современной записи в запись буквами кириллицы и глаголицы (и обратно) и др.
Литература
Iеромонахъ Алѵпій (Гамановичъ), Грамматика церковно-славянскаго языка, Джорданвилль: Свято-Троицкій монастырь, 1964. [Существуют репринты.]
B. A. van Groningen, Short manual of Greek palaeography, Leiden: A. W. Sijthoff's Uitgeversmaatschappij N. V., 1955.
G. Ifrah, The universal history of numbers, N. Y. etc.: John Wiley & Sons, 2000. ISBN 0-471-39340-1.
Математические обозначения
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After the Galaxy S22, we hope to see these Samsung devices next
By Loretta W. Benjamin on March 6, 2022 Gadget store
The Samsung Galaxy S22 range.
Lisa Eadicicco/CNET
We're not even halfway through 2022, but it's already been a busy year for Samsung. The company began by introducing the Galaxy S21 FE in January just before Galaxy S22 series launched in February. He also published three new tablets and a range of Galaxy Book Laptops before the end of February.
While the Galaxy S line is one of Samsung's most popular devices, Samsung is releasing Galaxy devices in many categories and will likely feature more product reveals throughout the year. We can't say for sure which ones, but several major product lines were left out of Samsung's January and February announcements.
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Here's a look at some of the other Samsung products I hope to see in 2022. Samsung usually has an Unpacked event every August, so it's possible that at least some of these gadgets will arrive then.
The Galaxy Watch 4, which debuted in August, marked a milestone for Samsung's smartwatches. It's the first model to ship with the new version of Google's Wear OS software which was created in partnership with Samsung. Some of the benefits of this partnership are already evident in the Galaxy Watch 4, particularly its compatibility with the wide selection of apps available in the Google Play store.
The Galaxy Watch 4.
Lexy Savvides
But we were hoping to see more Google-inspired features, as my colleague Scott Stein wrote in his Galaxy Watch 4 review. The Galaxy Watch 4 didn't even come with the Google Assistant at launch, although that will change in the coming months. Hopefully the next model will retain the features we already love – like its wide variety of health tracking features and great display – while infusing more of the Google experience into the software. It would also be great to see longer battery life, given that the Galaxy Watch 4 only lasted between one and two days during CNET's testing.
There haven't been any Galaxy Watch 5 leaks or rumors yet, but there's a chance we could hear more as August approaches.
The Samsung Galaxy Buds 2.
New Samsung Galaxy headphones
Samsung has released new headphones in August for the past two years, so there's a chance it could do the same in 2022. The question, though, is whether the company can release a new version of the top of the line. range. Galaxy Buds ProThe standard Galaxy buds 2 or bean-shaped Galaxy Buds Live.
Regardless of the model, a new pair of headphones could be in the works, according to Galaxy Club. The Netherlands-based blog speculated in December that a recent battery entry on the Korean product safety certification website may belong to the charging case of a new pair of Samsung headphones.
We won't know for sure until Samsung makes an announcement. But if Samsung releases a new version of the Galaxy Buds Pro, we'd like to see a design with a tighter fit for better noise cancellation.
Products like Samsung's Galaxy Buds and Galaxy Watch are becoming an increasingly important part of the smartphone experience, which makes me think Samsung will continue to release new headphones on a regular basis. The appeal of a device isn't just about the phone itself, but also how well it works with other products we often use with our phones, like headphones, fitness trackers, and smartwatches.
It's a strategy that has worked well for Apple, which has become a major player in the wearables market thanks to the apple watch and AirPods. I'm sure Samsung will continue to compete in this regard.
The Galaxy Z Flip 3.
Patrick Holland/CNET
Samsung Galaxy ZFlip 3 is the most convenient foldable phone currently available. But it has significant trade-offs compared to Samsung's non-foldable Galaxy phones, especially when it comes to camera and battery life.
If Samsung sticks with its current model, we could see another Z Flip 4 in August that will hopefully fill in those gaps. There aren't many rumors about the Z Flip 4 yet, apart from a report from a Korean media outlet The elect indicating that Samsung's next flip phone will have a slightly larger cover screen.
Such a change would make it even easier to view notifications without opening the device, which was one of the biggest flaws of the original Z Flip. Samsung fixed this on the Z Flip 3 by making the cover screen four times larger. But making the display even slightly larger could go a long way to making the Z Flip's front display even more useful for reading notifications. I also hope Samsung continues to add new software features that take advantage of the Flip's foldable screen, like Flexible mode.
A Samsung patent covered by the tech blog Let's go digital showing a device that looks like the Z Flip, but with a rotating camera located inside the hinge, has also sparked some speculation. But a move like this seems a long way off, especially since Samsung's design changes to the Z Flip have been mostly incremental so far.
Samsung launched the original Galaxy Z Flip in February 2020, while the 5G version came a few months later in August. This too announced the Galaxy Z Flip 3 in August 2021. Samsung's timeline has varied, but the fact that it's already released three versions of this phone in two years makes me believe it could be a regular part of Samsung's annual upgrade cycle.
The Galaxy Z Fold 3.
While the Galaxy Z Flip 3 is designed for people who want to make their phone more compact, the Galaxy Z Fold takes the opposite approach. Open it up and you'll find a 7.6-inch tablet-sized screen inside. the Galaxy Z Fold 3 is the third iteration of Samsung's full-size foldable phone, and it's by far the most refined.
But it still feels awkward to use as a regular phone when closed, which is still its biggest drawback. Samsung has already tried to solve this problem by making the Z Fold 3 thinner and lighter than the Z Fold 2, and I hope it will continue in this direction.
As with the other products on this list, we haven't heard many rumors about the Galaxy Z Fold 4 yet. But based on the improvements between the second and third generations of the Z Fold, I would expect to see a new processor, some design improvements, and hopefully better battery life on the next version. It would also be great to see software improvements that make better use of that large internal display.
This phone would also hopefully benefit from Android 12Lwhich is specially designed for foldable phones, tablets and dual-screen devices.
Samsung launched the Galaxy Z Fold 3 and Galaxy Z Fold 2 in August 2021 and 2020, respectively, while the first Galaxy Z Fold was released in September 2019. This makes it seem like the Z Fold has also become a regular fixture in Samsung's annual product lineup, so there's a luck that we can see a new device closer to the fall.
The Galaxy S21 FE.
Samsung's "Fan Edition" smartphones are a more affordable alternative to the Galaxy S series devices. Galaxy S20 FE launched in 2020 as a cheaper version of the Galaxy S20but the Galaxy S21 FE didn't arrive until early 2022, just before the Galaxy S22's debut.
So it's unclear when Samsung might release the Galaxy S22 FE, if at all. Samsung is essentially positioning the Galaxy S21 FE as its previous-gen option aimed at those who typically buy last year's device to save money, which makes me think it will continue that strategy as it continues the FE line. .
If the Galaxy S22 FE looks like the S21 FE, it will likely have a bigger screen than the regular S22 but smaller than the S22 Plus. It may also have a larger battery than the standard Galaxy S22, as the S21 FE's battery is larger than the regular S21.
If so, I think the Galaxy S22 FE has the potential to be the best choice in Samsung's lineup for those who need an affordable Android phone. Although I generally liked the regular S22, it was slightly too small for my liking and the battery life was lacking. Samsung has the opportunity to address both of these points in a future FE model.
Samsung is perhaps best known for its Galaxy smartphones when it comes to mobile devices. But products like the Galaxy Watch 4 and Galaxy Buds prove that the company is also more focused on smartphone-adjacent devices. As for what's next after smartwatches and headphones, that's a question only Samsung can answer. But I still hope to see a pair of smart glasses one day.
battery life samsung galaxy
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Identifying Anxiety
Types of Anxiety
Four Ways to Support Your Shy Child
Jo Rooks December 4, 2019 10:00 am
anxiety in kidsshyness
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Part of living a full life involves having new experiences. New experiences help us grow and develop as a person, gain confidence, and build self-esteem. Whether it's starting a new job, taking up a new hobby, or meeting new people, most of us are familiar with a feeling of shyness or anxiety that can be stirred up within even the most extroverted personalities.
Sometimes shyness can affect us in all sorts of negative ways. It's important to let our kids know that we all feel this emotion from time to time, and that there are lots of strategies to help us cope with new experiences without being overcome with anxiety.
Shyness is the main theme of Magination Press book Sophie's Shell. Sophie is a happy snail who wants to learn more about the world around her. In fact, she is counting down the days before she can start school. When she gets to school though, that all seems to change. Sophie's shy feeling is so strong that she has to keep popping back into her shell. POP!
Parents may also identify with this. Many have had the experience of taking an excited child to a birthday party, but upon arrival, they could hardly look up, didn't want to play, dance, or join in with the games, and just clung to their leg for the entire time. As a parent, you can feel surprised and frustrated and want to say, "Just go and enjoy yourself!", "Don't be shy!", "Speak up!", but these reactions won't help your child or you.
Don't draw attention to it
In Sophie's Shell, Sophie has many episodes of feeling shy. This is often because people are paying lots of attention to her, even if it's for positive things like admiring her beautiful art. Adults can help children when they are feeling shy by simply carrying on calmly and not drawing attention to it. Discreetly asking other adults to do the same can also help.
Everyone feels shy sometimes, even grown ups
Let your child know that everyone can feel shy in certain situations, and that it's not something to feel ashamed of. Shyness can make us feel uncomfortable: sometimes Sophie has "a wobbly feeling in her tummy." Share with your child times when you have felt shy, how you coped with it, and how the feeling went away.
With all experiences, the more familiar you are with a new situation, the easier it becomes and the less shy you feel. This means being patient and believing that being in new situations will get easier.
Before a new experience, talk to your child about where they are going and how many people might be there.
Suggest a way to make a new friend, such as smiling and saying, "Hi."
Arrive to a party early, so there are fewer people. This can help your child get used to the environment without them feeling they are arriving to lots of new faces.
Bring a conversation piece. Encourage your child to bring something along to the gathering (a gift, a stuffed animal for a young child, etc.) that makes them feel more comfortable and provides something to talk about.
You could also ask to help set up. This will empower your child and focus them on an activity before the event begins.
This will prepare your child a little bit better for the new experience. If they join in and relax, make sure to praise them and tell them how proud you are of them. If they don't join in, try not to make it a big deal of it, and try again next time. Each experience can help to build your child's self-esteem and confidence for next time.
If a child is looking worried, sometimes it's a natural reaction to mirror that worried expression, but smiling can give the reassurance your child needs. When Sophie met Stanley, he let her know that he understood how she was feeling: "Sometimes I feel shy too." Then he helped take her mind off it by asking, "Want to hear a joke?" Don't forget that a hug and laughter are always great ways to refocus your child's attention on something positive.
Most people feel a bit anxious in new social situations. Help your child cope with shyness and build positive experiences by letting them know that we all feel that way sometimes, and sharing strategies to manage their stress.
These tips are from the author of Magination Press book, Sophie's Shell, Jo Rooks.
by Jo Rooks
This Article's Author
Jo Rooks is an award-winning author-illustrator who studied graphic design and illustration at Bath School of Art and Design. She illustrated several award-winning books, including A Box of Butterflies and Hector's Favorite Place. Visit her at Jo Rooks Illustration and Follow her on Facebook: @JoRooksIllustration, Twitter: @JoRooksArt, and Instagram: @JoRooksIllustration.
Related Books from Magination Press
Sophie's Shell
Jo Rooks
Sophie was always ponders big questions, like
Why are raindrops wet?
What are stars made of?
But when Sophie starts school, there's a wobbly feeling in her tummy and she can't help popping back into her shell.
She is left with one big question: Why am I so shy?
When Sophie meets Stanley, she realizes that she's not the only one who feels shy. Can she gain the confidence to help a new friend?
A heart warming tale about a sensitive snail who overcomes her shyness with a little help from her new friends.
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Magination Press Quick Tip: Supporting Your Child with Depression by Fostering Positive Thinking
Magination Press Quick Tip: Supporting Grieving Siblings
Magination Press Quick Tip: Three Ways to Support Teens with Depression
When Memories Start to Fail: Four Ways to Help Children Cope with Dementia in Loved Ones
Five Ways to Teach Kids the Importance of Self-Care
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Q: Editing pages using Telescope Open Source Project I just started playing around with the telescope open source project and I wanted to know how do you edit pages for example the signup page. If I wanted to add an picture to the background or something
A: Swifter, one issue with your question is that the documentation for Telescope outlines how to make small changes to the framework. To make an update like you are suggesting one would need to understand how a "view" loads styles. The documentation has a great walk-through on how to change styles or theme Telescope.
A better question would be, I am coming from an HTML and CSS background. I noticed that Telescope uses SCSS. What is the Telescope/Meteor way to load a custom CSS library into the framework.
A: one can also take this question to mean: "What is the correct way to alter telescope code?"
which would require you to understand meteor packages
(see docs.meteor.com),
and the use of telescope-packages as the "telescope preferred way" to add your own functionality. You see, telescope is an app you base YOUR app upon, and telescope gets updated periodically and if you are using telescope as the basis for YOUR app, you should consider updating telescope periodically also, and the "package way" allows you to keep your custom code separate from the telescope code.
http://www.telescopeapp.org/docs/customizing/customization-basics/
http://www.telescopeapp.org/docs/customizing/creating-packages/
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Zacchaeus Okoth (Nyakach, Quênia, 5 de julho de 1942) é um ministro queniano e arcebispo católico romano emérito de Kisumu.
Em 14 de novembro de 1968, Zaqueu Okoth recebeu o sacramento da ordenação sacerdotal para a diocese de Kisumu.
Em 27 de fevereiro de 1978, o Papa Paulo VI o nomeou ao Bispo de Kisumu. O Arcebispo de Nairobi, cardeal Maurice Michael Otunga, o consagrou em 30 de abril do mesmo ano; Os co-consagradores foram o Pró-Núncio Apostólico no Quênia, Arcebispo Agostino Cacciavillan, e o Bispo de Kakamega, Philip Sulumeti. Em 21 de maio de 1990, João Paulo II o nomeou Arcebispo de Kisumu.
O Papa Francisco aceitou sua aposentadoria em 15 de novembro de 2018.
Ver também
Arcebispos católicos do Quênia
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,929
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Q: Read file and find if all lines are the same length Using python I need to read a file and determine if all lines are the same length or not. If they are I move the file into a "good" folder and if they aren't all the same length I move them into a "bad" folder and write a word doc that says which line was not the same as the rest. Any help or ways to start?
A: You should use all():
with open(filename) as read_file:
length = len(read_file.readline())
if all(len(line) == length for line in read_file):
# Move to good folder
else:
# Move to bad folder
Since all() is short-circuiting, it will stop reading the file at the first non-match.
A: First off, you can read the file, here example.txt and put all lines in a list, content:
with open(filename) as f:
content = f.readlines()
Next you need to trim all the newline characters from the end of a line and put it in another list result:
for line in content:
line = line.strip()
result.append(line)
Now it's not that hard to get the length of every sentence, and since you want lines that are bad, you loop through the list:
for line in result:
lengths.append(len(line))
So the i-th element of result has length [i-th element of lengths]. We can make a counter for what line length occurs the most in the list, it is as simple as one line!
most_occuring = max(set(lengths), key=lengths.count)
Now we can make another for-loop to check which lengths don't correspond with the most-occuring and add those to bad-lines:
for i in range(len(lengths)):
if (lengths[i] != most_occuring):
bad_lines.append([i, result[i]])
The next step is check where the file needs to go, the good folder, or the bad folder:
if len(bad_lines == 0):
#Good file, move it to the good folder, use the os or shutil module
os.rename("path/to/current/file.foo", "path/to/new/desination/for/file.foo")
else:
#Bad file, one or more lines are bad, thus move it to the bad folder
os.rename("path/to/current/file.foo", "path/to/new/desination/for/file.foo")
The last step is writing the bad lines to another file, which is do-able, since we have the bad lines already in a list bad_lines:
with open("bad_lines.txt", "wb") as f:
for bad_line in bad_lines:
f.write("[%3i] %s\n" % (bad_line[0], bad_line[1]))
It's not a doc file, but I think this is a nice start. You can take a look at the docx module if you really want to write to a doc file.
EDIT: Here is an example python script.
with open("example.txt") as f:
content = f.readlines()
result = []
lengths = []
#Strip the file of \n
for line in content:
line = line.strip()
result.append(line)
lengths.append(len(line))
most_occuring = max(set(lengths), key=lengths.count)
bad_lines = []
for i in range(len(lengths)):
if (lengths[i] != most_occuring):
#Append the bad_line to bad_lines
bad_lines.append([i, result[i]])
#Check if it's a good, or a bad file
#if len(bad_lines == 0):
#Good File
#Move file to the good folder...
#else:
#Bad File
with open("bad_lines.txt", "wb") as f:
for bad_line in bad_lines:
f.write("[%3i] %s\n" % (bad_line[0], bad_line[1]))
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,535
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BSC's Quality Assurance Roadmap outlines the approach to quality assurance in the construction process as recommended by Building Science Corporation for new residential construction. Seven process steps are described from the assessment of current construction practice, through design and documentation changes, to training and quality control for on-site personnel. This document is intended to be used in lieu of a formal QA process to support high performance construction in Building America Research Prototype houses.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 251
|
package jp.co.future.uroborosql.mapping.mapper;
import static org.hamcrest.CoreMatchers.*;
import static org.hamcrest.MatcherAssert.*;
import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.Statement;
import java.time.LocalDate;
import java.time.LocalDateTime;
import java.time.LocalTime;
import java.time.OffsetDateTime;
import java.time.OffsetTime;
import java.time.ZoneId;
import java.time.ZonedDateTime;
import java.util.Calendar;
import java.util.Date;
import org.junit.Before;
import org.junit.BeforeClass;
import org.junit.Test;
import jp.co.future.uroborosql.SqlAgent;
import jp.co.future.uroborosql.UroboroSQL;
import jp.co.future.uroborosql.config.SqlConfig;
import jp.co.future.uroborosql.filter.AuditLogSqlFilter;
import jp.co.future.uroborosql.filter.SqlFilterManager;
import jp.co.future.uroborosql.mapping.annotations.Table;
public class DateTimeTest {
private static SqlConfig config;
@BeforeClass
public static void setUpBeforeClass() throws Exception {
String url = "jdbc:h2:mem:DateTimeTest;DB_CLOSE_DELAY=-1";
String user = null;
String password = null;
try (Connection conn = DriverManager.getConnection(url, user, password)) {
conn.setAutoCommit(false);
// テーブル作成
try (Statement stmt = conn.createStatement()) {
stmt.execute(
"drop table if exists test");
stmt.execute(
"create table if not exists test( "
+ "id NUMERIC(4)"
+ ",date_value DATE"
+ ",datetime_value DATETIME"
+ ",time_value TIME"
+ ", primary key(id))");
}
}
config = UroboroSQL.builder(url, user, password).build();
SqlFilterManager sqlFilterManager = config.getSqlFilterManager();
sqlFilterManager.addSqlFilter(new AuditLogSqlFilter());
}
@Before
public void setUpBefore() throws Exception {
try (SqlAgent agent = config.agent()) {
agent.updateWith("delete from test").count();
agent.commit();
}
}
@SuppressWarnings("unused")
@Table(name = "TEST")
public static class LocalTestEntity {
private long id;
private LocalDate dateValue;
private LocalDateTime datetimeValue;
private LocalTime timeValue;
public LocalTestEntity(final long id) {
this.id = id;
this.dateValue = LocalDate.now();
this.datetimeValue = LocalDateTime.now();
this.timeValue = LocalTime.now();
}
public LocalTestEntity() {
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
result = prime * result + (dateValue == null ? 0 : dateValue.hashCode());
result = prime * result + (datetimeValue == null ? 0 : datetimeValue.hashCode());
result = prime * result + (int) (id ^ id >>> 32);
result = prime * result + (timeValue == null ? 0 : timeValue.hashCode());
return result;
}
@Override
public boolean equals(final Object obj) {
if (this == obj) {
return true;
}
if (obj == null) {
return false;
}
if (getClass() != obj.getClass()) {
return false;
}
LocalTestEntity other = (LocalTestEntity) obj;
if (dateValue == null) {
if (other.dateValue != null) {
return false;
}
} else if (!dateValue.equals(other.dateValue)) {
return false;
}
if (datetimeValue == null) {
if (other.datetimeValue != null) {
return false;
}
} else if (!datetimeValue.equals(other.datetimeValue)) {
return false;
}
if (id != other.id) {
return false;
}
if (timeValue == null) {
if (other.timeValue != null) {
return false;
}
} else if (!timeValue.equals(other.timeValue)) {
return false;
}
return true;
}
@Override
public String toString() {
return "LocalTestEntity [id=" + id + ", dateValue=" + dateValue + ", datetimeValue=" + datetimeValue
+ ", timeValue=" + timeValue + "]";
}
}
@SuppressWarnings("unused")
@Table(name = "TEST")
public static class DateTestEntity {
private long id;
private java.sql.Date dateValue;
private java.util.Date datetimeValue;
private java.sql.Time timeValue;
public DateTestEntity(final long id) {
this.id = id;
this.dateValue = java.sql.Date.valueOf(LocalDate.now());
this.datetimeValue = new java.util.Date();
this.timeValue = java.sql.Time.valueOf(LocalTime.now());
}
public DateTestEntity() {
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
result = prime * result + (dateValue == null ? 0 : dateValue.hashCode());
result = prime * result + (datetimeValue == null ? 0 : datetimeValue.hashCode());
result = prime * result + (int) (id ^ id >>> 32);
result = prime * result + (timeValue == null ? 0 : timeValue.hashCode());
return result;
}
@Override
public boolean equals(final Object obj) {
if (this == obj) {
return true;
}
if (obj == null) {
return false;
}
if (getClass() != obj.getClass()) {
return false;
}
DateTestEntity other = (DateTestEntity) obj;
if (dateValue == null) {
if (other.dateValue != null) {
return false;
}
} else if (!dateValue.equals(other.dateValue)) {
return false;
}
if (datetimeValue == null) {
if (other.datetimeValue != null) {
return false;
}
} else if (!datetimeValue.equals(other.datetimeValue)) {
return false;
}
if (id != other.id) {
return false;
}
if (timeValue == null) {
if (other.timeValue != null) {
return false;
}
} else if (!timeValue.equals(other.timeValue)) {
return false;
}
return true;
}
@Override
public String toString() {
return "DateTestEntity [id=" + id + ", dateValue=" + dateValue + ", datetimeValue=" + datetimeValue
+ ", timeValue=" + timeValue + "]";
}
}
@SuppressWarnings("unused")
@Table(name = "TEST")
public static class OffsetTestEntity {
private long id;
private OffsetDateTime datetimeValue;
private OffsetTime timeValue;
public OffsetTestEntity(final long id) {
this.id = id;
this.datetimeValue = OffsetDateTime.now();
this.timeValue = OffsetTime.now();
}
public OffsetTestEntity() {
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
result = prime * result + (datetimeValue == null ? 0 : datetimeValue.hashCode());
result = prime * result + (int) (id ^ id >>> 32);
result = prime * result + (timeValue == null ? 0 : timeValue.hashCode());
return result;
}
@Override
public boolean equals(final Object obj) {
if (this == obj) {
return true;
}
if (obj == null) {
return false;
}
if (getClass() != obj.getClass()) {
return false;
}
OffsetTestEntity other = (OffsetTestEntity) obj;
if (datetimeValue == null) {
if (other.datetimeValue != null) {
return false;
}
} else if (!datetimeValue.equals(other.datetimeValue)) {
return false;
}
if (id != other.id) {
return false;
}
if (timeValue == null) {
if (other.timeValue != null) {
return false;
}
} else if (!timeValue.equals(other.timeValue)) {
return false;
}
return true;
}
@Override
public String toString() {
return "OffsetTestEntity [id=" + id + ", datetimeValue=" + datetimeValue + ", timeValue=" + timeValue + "]";
}
}
@SuppressWarnings("unused")
@Table(name = "TEST")
public static class ZonedTestEntity {
private long id;
private ZonedDateTime datetimeValue;
public ZonedTestEntity(final long id) {
this.id = id;
this.datetimeValue = ZonedDateTime.now();
}
public ZonedTestEntity() {
}
@Override
public int hashCode() {
final int prime = 31;
int result = 1;
result = prime * result + (datetimeValue == null ? 0 : datetimeValue.hashCode());
result = prime * result + (int) (id ^ id >>> 32);
return result;
}
@Override
public boolean equals(final Object obj) {
if (this == obj) {
return true;
}
if (obj == null) {
return false;
}
if (getClass() != obj.getClass()) {
return false;
}
ZonedTestEntity other = (ZonedTestEntity) obj;
if (datetimeValue == null) {
if (other.datetimeValue != null) {
return false;
}
} else if (!datetimeValue.equals(other.datetimeValue)) {
return false;
}
if (id != other.id) {
return false;
}
return true;
}
@Override
public String toString() {
return "ZonedTestEntity [id=" + id + ", datetimeValue=" + datetimeValue + "]";
}
}
@Test
public void testZoned() throws Exception {
try (SqlAgent agent = config.agent()) {
agent.required(() -> {
ZonedTestEntity test1 = new ZonedTestEntity(1);
agent.insert(test1);
ZonedTestEntity zoned = agent.find(ZonedTestEntity.class, 1).orElse(null);
LocalTestEntity local = agent.find(LocalTestEntity.class, 1).orElse(null);
assertThat(zoned.datetimeValue, is(test1.datetimeValue));
assertThat(zoned.datetimeValue.toLocalDateTime(), is(local.datetimeValue));
});
}
}
@Test
public void testOffset() throws Exception {
try (SqlAgent agent = config.agent()) {
agent.required(() -> {
OffsetTestEntity test1 = new OffsetTestEntity(1);
agent.insert(test1);
OffsetTestEntity offset = agent.find(OffsetTestEntity.class, 1).orElse(null);
LocalTestEntity local = agent.find(LocalTestEntity.class, 1).orElse(null);
assertThat(offset.datetimeValue, is(test1.datetimeValue));
assertThat(offset.datetimeValue.toLocalDateTime(), is(local.datetimeValue));
assertThat(offset.timeValue.toLocalTime(), is(local.timeValue));
});
}
}
@Test
public void testDate() throws Exception {
try (SqlAgent agent = config.agent()) {
agent.required(() -> {
DateTestEntity test1 = new DateTestEntity(1);
agent.insert(test1);
DateTestEntity date = agent.find(DateTestEntity.class, 1).orElse(null);
LocalTestEntity local = agent.find(LocalTestEntity.class, 1).orElse(null);
assertThat(date.datetimeValue.getTime(), is(test1.datetimeValue.getTime()));
assertThat(date.dateValue.getTime(), is(test1.dateValue.getTime()));
System.out.println(date.timeValue);
final Calendar c = Calendar.getInstance();
c.setLenient(false);
c.setTime(date.timeValue);
c.set(Calendar.YEAR, 1970);
c.set(Calendar.MONTH, 0);
c.set(Calendar.DAY_OF_MONTH, 1);
Date time = c.getTime();
assertThat(date.timeValue.getTime(), is(time.getTime()));
assertThat(new Date(date.datetimeValue.getTime()).toInstant().atZone(ZoneId.systemDefault())
.toLocalDateTime(),
is(local.datetimeValue));
assertThat(new Date(date.dateValue.getTime()).toInstant().atZone(ZoneId.systemDefault()).toLocalDate(),
is(local.dateValue));
assertThat(new Date(date.timeValue.getTime()).toInstant().atZone(ZoneId.systemDefault()).toLocalTime(),
is(local.timeValue));
});
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,035
|
It focuses on many targets like Groundwater exploration and detection the main subsurface reservoirs, Archaeological investigations and detecting the unrevealed objects, Geotechnical and engineering investigations and determination the subsurface cavities,faults, fractures, voids, and impermeable beds, Environmental Risk Assessment, Mineral Explorations and detecting the location of economic minerals, and Geothermal explorations and detecting the main geothermal reservoirs. Geoelectric and geothermal lab. has the latest geophysical techniques (Electric and Electromagnetic techniques) that can achieve these targets and give accurate results.
It is used for measuring the electrical resistivity Distributions in the subsurface medium by injecting an electric current through a pair of electrodes into the ground and measuring the potential difference through another pair of electrodes to detect the subsurface geological layers, geotechnical problems, and groundwater aquifers.
TEM method detects underground conducting materials by transmitting electrical pulses along loops of cables laid on the ground surface. It is an inductive method, which utilizes a strong direct current passed through a square loop commonly extended on the ground surface. The flow of this current in the surface loop creates a primary magnetic field, which spreads out into the ground. When the applied current is abruptly terminated, the primary magnetic field starts to decay with time. According to Faraday's law, the decay of the primary magnetic field with time induces eddy currents that flow outward and downward in the subsurface conductors. The rate of change of these currents and of their respective secondary magnetic field depends on the size, shape and conductivity of the subsurface conductors.
It is an electromagnetic technique used for high-resolution detection, mapping and imaging of the subsurface soils and rock conditions. It investigates the subsurface conditions by transmitting radio waves into the ground and recording the response at the ground surface. This system has a capability to investigate the subsurface medium at different depth levels according the used antenna. Each antenna is designed to operate over a range of frequencies. The high frequency is related to shallow investigations and the low frequency is corresponding to deeper investigations. It is strongly used for Archaeological Investigations.
VLF method utilizes Very Low Frequency radio communication signals in the range of 15-30 KHz, to determine electrical properties of near surface soils and shallow bedrock. The technique is valuable especially for mapping steeply dipping structures such as faults, fracture zones and areas of mineralization.
Assessment of Geothermal Resources in Farafra Oasis, Egypt.
Geoelectric (VES+ERT) and electromagnetic (TEM+AMT) studies in Abou Ramad area, Red Sea Province for delineating and assessment groundwater aquifer associated with the old delta, to be exploited in agriculture and sustainable development.
Construction of the interactive maps of the archeological ruins in the subsurface of the valley of the Golden Mummies VGM, Bahariya Oasis, Egypt.
Imaging the geometry of the Kharga Basin, New Valley Oasis and its groundwater Capacity.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 248
|
{"url":"https:\/\/en.academic.ru\/dic.nsf\/enwiki\/717449","text":"Cyclic homology\n\nCyclic homology\n\nIn homological algebra, cyclic homology and cyclic cohomology are (co)homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry. They were independently discovered by Boris Tsygan and studied by Connes, Karoubi, Feigin-Tsygan, Loday, Quillen, and others.\n\nThe first definition of the cyclic homology of a ring A over a field of characteristic zero, denoted\n\nHCn(A) or Hn\u03bb(A),\n\nproceeded by the means of an explicit chain complex related to the Hochschild homology complex of A. Connes later found a more categorical approach to cyclic homology using a notion of cyclic object in an abelian category, which is analogous to the notion of simplicial object. In this way, cyclic homology (and cohomology) may be interpreted as a derived functor, which can be explicitly computed by the means of the Connes bicomplex.\n\nOne of the striking features of cyclic homology is the existence of a long exact sequence connecting Hochschild and cyclic homology. This long exact sequence is referred to as the periodicity sequence.\n\nCase of commutative rings\n\nCyclic cohomology of the commutative algebra A of regular functions on an affine algebraic variety over a field k of characteristic zero can be computed in terms of Grothendieck's algebraic de Rham complex. In particular, if the variety V=Spec A is smooth, cyclic cohomology of A are expressed in terms of the de Rham cohomology of V as follows:\n\n$HC_n(A)\\simeq \\Omega^n\\!A\/d\\Omega^{n-1}\\!A\\oplus \\bigoplus_{i\\geq 1}H^{n-2i}_{DR}(V).$\n\nThis formula suggests a way to define de Rham cohomology for a 'noncommutative spectrum' of a noncommutative algebra A, which was extensively developed by Connes.\n\nVariants of cyclic homology\n\nOne motivation of cyclic homology was the need for an approximation of K-theory that be defined, unlike K-theory, as the homology of a chain complex. Cyclic cohomology is in fact endowed with a pairing with K-theory, and one hopes this pairing to be non-degenerate.\n\nThere has been defined a number of variants whose purpose is to fit better with algebras with topology, such as Fr\u00e9chet algebras, C * -algebras, etc. The reason is that K-theory behaves much better on topological algebras such as Banach algebras or C*-algebras than on algebras without additional structure. Since, on the other hand, cyclic homology degenerates on C*-algebras, there came up the need to define modified theories. Among them are entire cyclic homology due to Alain Connes, analytic cyclic homology due to Ralf Meyer or asymptotic and local cyclic homology due to Michael Puschnigg. The last one is very near to K-theory as it is endowed with a bivariant Chern character from KK-theory.\n\nApplications\n\nOne of the applications of cyclic homology is to find new proofs and generalizations of the Atiyah-Singer index theorem. Among these generalizations are index theorems for quantum tori and quantum groups,[1] for D-modules,[2] for deformation quantization [3](Weyl quantization). The index theorem for quantum tori is linked to the quantum Hall effect,[4] and the index theorem for deformation quantization to the study of band energy redistribution in the Born-Oppenheimer approximation in molecular physics.[5]\n\nReferences\n\n\u2022 Alain Connes, Noncommutative differential geometry. Inst. Hautes \u00c9tudes Sci. Publ. Math. No. 62 (1985), 257\u2014360.\n\u2022 Jean-Louis Loday, Cyclic Homology, Grundlehren der mathematischen Wissenschaften Vol. 301, Springer (1998) ISBN 3-540-63074-0\n\nWikimedia Foundation. 2010.\n\n\u0421\u043c. \u0442\u0430\u043a\u0436\u0435 \u0432 \u0434\u0440\u0443\u0433\u0438\u0445 \u0441\u043b\u043e\u0432\u0430\u0440\u044f\u0445:\n\n\u2022 Cyclic category \u2014 In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree 1 maps between them. It was introduced by Connes (1983). Contents 1 Definition 2 Properties 3 Cyclic sets \u2026 \u00a0 Wikipedia\n\n\u2022 Cyclic order \u2014 In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Cyclic (mathematics) \u2014 There are many terms in mathematics that begin with cyclic: Cyclic chain rule, for derivatives, used in thermodynamics Cyclic code, linear codes closed under cyclic permutations Cyclic convolution, a method of combining periodic functions Cycle\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Cyclic nucleotide-gated ion channel \u2014 Cyclic nucleotide gated (CNG) ion channels are ion channels that function in response to the binding of cyclic nucleotides. CNG channels are nonselective cation channels that are found in the membranes of various types of cells. Signal\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Hochschild homology \u2014 In mathematics, Hochschild homology is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Definition of Hochschild homology of algebras Let k be a ring, A an associative k\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Reduced homology \u2014 In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero. This change is required to make statements without some number of exceptional\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 List of mathematics articles (C) \u2014 NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Spectral sequence \u2014 In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a\u2026 \u2026 \u00a0 Wikipedia\n\n\u2022 Group Hopf algebra \u2014 In mathematics, the group Hopf algebra of a given group is a certain construct related to the symmetries of group actions. Deformations of group Hopf algebras are foundational in the theory of quantum groups. DefinitionLet G be an arbitrary group \u2026 \u00a0 Wikipedia\n\n\u2022 Noncommutative geometry \u2014 Not to be confused with Anabelian geometry. Noncommutative geometry (NCG) is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative\u2026 \u2026 \u00a0 Wikipedia\n\n\u041f\u043e\u0434\u0435\u043b\u0438\u0442\u044c\u0441\u044f \u0441\u0441\u044b\u043b\u043a\u043e\u0439 \u043d\u0430 \u0432\u044b\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435\n\n\u041f\u0440\u044f\u043c\u0430\u044f \u0441\u0441\u044b\u043b\u043a\u0430:\n\u041d\u0430\u0436\u043c\u0438\u0442\u0435 \u043f\u0440\u0430\u0432\u043e\u0439 \u043a\u043b\u0430\u0432\u0438\u0448\u0435\u0439 \u043c\u044b\u0448\u0438 \u0438 \u0432\u044b\u0431\u0435\u0440\u0438\u0442\u0435 \u00ab\u041a\u043e\u043f\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u0441\u044b\u043b\u043a\u0443\u00bb","date":"2021-01-21 02:28:34","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\": 0.7976202368736267, \"perplexity\": 890.4289629275015}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703522150.18\/warc\/CC-MAIN-20210121004224-20210121034224-00026.warc.gz\"}"}
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Doing Business | IT & Technologies
Google removes 'view image' button from search results to make pics harder to steal
Google is making a change to image search today that sounds small but will have a big impact: it's removing the "view image" button that appeared when you clicked on a picture, which allowed you to open the image alone.
The button was extremely useful for users, since when you're searching for a picture, there's a very good chance that you want to take it and use it for something. Now, you'll have to take additional steps to save an image.
The change is essentially meant to frustrate users. Google has long been under fire from photographers and publishers who felt that image search allowed people to steal their pictures, and the removal of the view image button is one of many changes being made in response. A deal to show copyright information and improve attribution of Getty photos was announced last week and included these changes.
The intention seems to be either stopping people from taking an image altogether or driving them through to the website where the image is found, so that the website can serve ads and get revenue and so people are more likely to see any associated copyright information. That's great news for publishers, but it's an annoying additional step for someone trying to find a picture. Now you'll have to wait for a website to load and then scroll through it to find the image. Websites sometimes disable the ability to right click, too, which would make it even harder for someone to grab a photo they're looking for.
Fortunately, there's still at least one way around it: if you right click, you can select "open image in new tab" or "view image" (or whatever your browser's equivalent option is), and you'll still open up the full-size picture. It's just a bit less likely that everyone will realize this is an option. And since the "visit" site button is now the most visible button, that's probably what'll end up getting clicked the most.
In addition to removing the "view image" button, Google has also removed the "search by image" button that appeared when you opened up a photo, too. This change isn't quite as big, however. You'll still be able to do a reverse image search by dragging the image to the search bar, and Google will still display related images when you click on a search result. The button may have been used by people to find un-watermarked versions of images they were interested in, which is likely part of why Google pulled it.
While it's good to see Google protecting photographers and driving traffic to websites, it's still hard not to be a little annoyed by the changes. There are plenty of legitimate and legal uses for copyrighted images. And while it's fair to ask users to do their due diligence by making sure they're properly attributing photos, these changes really seem designed to stop images from being grabbed in the first place.
Text by The Verge
Wikipedia, Google Protest Internet Bills
Wikipedia went dark, Google blotted out its logo and other popular websites planned protests on Wednesday to voice concern over legislation in the US Congress intended to crack down on online piracy.
Google's Excellent Plan To Bring Wireless Internet To Developing Countries
The WSJ is reporting that Google GOOG -1.1% is working on various technologies to bring wireless internet access to a number of developing countries.
There's an Android Bot Peeing on an Apple Logo on Google Maps
Sick of all the Apple Watch news today? You're in luck, because we have something completely different for you. An image of an Android mascot, also known as an Android bot or Bugdroid, peeing on an Apple logo has been discovered on Google Maps.
Live 360 YouTube Gets Us One Step Closer to the Matrix
ASK PEOPLE TO DESCRIBE virtual reality and they'll probably say something along the lines of It's like you're there, man. But even when you're courtside at the NBA slam dunk contest, you're "there" after the fact.
Google Leak Unveils New Chromecast, Pixel Smartphone, Home And Daydream VR Details
At the beginning of October, Google is reportedly announcing several highly anticipated devices. Specifically Google will host an event on October 4th where it will reveal new "Pixel" smartphones and a new version of the Chromecast, according to a source with Android Police.
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Q: Merge 2 data frames so that each have same number of columns I have loaded a data set from a csv file as :
data <- read.csv("data.csv", header = FALSE)
I segregated data into sets as follows:
d3 = training_data[785,data[785,] %in% c(3)]
d5 = training_data[785,data[785,] %in% c(5)]
Now the number of rows in d3 are equal to d5 but they in the number of columns. d3 and d5 both have 100 and 200 columns respectively. I want to create equal set for both. So I need a new data frame, let us say d_3_5 where both d3 and d5 have 100 columns each. How could I do this?
A: I was able to merge using a function called cbind. Here is what I did:
data <- read.csv("data.csv", header = FALSE)
d3 = training_data[785,data[785,] %in% c(3)]
d5 = training_data[785,data[785,] %in% c(5)]
d_3_5 = cbind(d3, d5[1:100,])
This created a new data frame with equal share from d3 and d5.
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Diacetone alcohol is an organic compound with the formula CH3C(O)CH2C(OH)(CH3)2, sometimes called DAA. This colorless liquid is a common synthetic intermediate used for the preparation of other compounds, and is also used as a solvent.
Synthesis and reactions
First identified by Heintz, one standard laboratory preparation of DAA entails the Ba(OH)2-catalyzed condensation of two molecules of acetone.
It undergoes dehydration to give the α,β-unsaturated ketone called mesityl oxide. Hydrogenation of diacetone alcohol gives hexylene glycol. Condensation with urea give "diacetone-monourea", i.e. the heterocycle 3,4-dihydro-
4,4,6-trimethyl-2(1H)-pyrimidone.
Uses
Diacetone alcohol is used in cellulose ester lacquers, particularly of the brushing type, where it produces brilliant gloss and hard film and where its lack of odor is desirable. It is used in lacquer thinners, dopes, wood stains, wood preservatives and printing pastes; in coating compositions for paper and textiles; permanent markers; in making artificial silk and leather; in imitation gold leaf; in celluloid cements; as a preservative for animal tissue; in metal cleaning compounds; in the manufacture of photographic film; and in hydraulic brake fluids, where it is usually mixed with an equal volume of castor oil.
Safety
The (oral, rats) is 4 g/kg.
References
Tertiary alcohols
Aldols
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\section{\label{sec:Introduction}Introduction}
In 1996 Kasianowicz $et\:al.\:$ demonstrated the possibility of translocating by electrophoresis single-stranded DNA (ssDNA) and RNA
molecules through nano-sized biological channels~\citep{Kasianowicz1996}. This discovery initiated a surge of proposals for novel DNA
sequencing protocols~\citep{Branton2008, Zwolak2008}. Among the many Zwolak $et\:al.\:$ proposed to sort the nucleobases from each other in a sequence
by measuring the transverse tunneling current across a ssDNA as this is driven through a nanopore~\citep{Zwolak2005}. It was suggested
that single base resolution is in principle achievable, as the differences in the electronic structure among the nucleobases may translate
into distinguishable tunneling current signals. However, as the tunneling process is extremely sensitive to the distance between the
electrodes and the nucleotides, one is left wondering whether the fluctuations in the transverse tunnel current, due to the fluctuations
in the local geometry, may be too large to allow the identification of the various nucleotides. Furthermore additional fluctuations may
arise from the electrostatic gate action introduced by the solvent molecules~\cite{Ivan1,Das2010}. In order to overcome these intrinsic
difficulties it was further suggested to trace the current fluctuations as the ssDNA is translocated across the pore, and to use their
statistical distribution in order to unambiguously recognize the electronic signatures of the various nucleobases~\citep{Lagerqvist2006, Lagerqvist2007,Krems2009}.
Experimentally, Tsutsui $et\:al.\:$ showed that it is possible to identify single nucleotides in solution by two-probe tunneling current measurements
and a thorough statistical analysis of the time-resolved current \citep{Tsutsui2010}. In this case the electrodes could be mechanically moved
to optimize the current through a given nucleotide. As such, although the experiment proves the concept of using electrical currents for
the sequencing, it does not demonstrate a working device.
Prototype sequencing devices with electrodes integrated
in solid-state nanopores and nanofluidic channels have been also proposed\citep{Gierhart2008, Liang2008, Jiang2010,
Spinney2009, Ivanov2010}. These have been realized experimentally by high resolution milling-based methods for a number
of metal electrodes, but it has been speculated that similar techniques could be used for CNTs with possibly higher resolution
\citep{Jiang2010}. On the theoretical front, the transverse tunneling conductance across
nucleobases placed between two gold electrodes has been actively investigated and debated \citep{Zwolak2005, Lagerqvist2006,Zikic2006,
Lagerqvist2007comment, Zikic2007reply, Zhang2006, He2008, He2010}. Interestingly recently some special attention has been dedicated
to exploring graphene nanopore, graphene nanoribbon and carbon nanotubes (CNT) as potential electrodes materials
\citep{Nelson2010,Prasongkit2010,Meunier2008,Nikolic2011}.
Despite these many works a key question still remains largely unanswered, namely how can one enhance the nucleotide-electrode
interaction to a point where the transmigration is still possible, but the geometrical fluctuations are sufficiently suppressed to allow
unambiguous single nucleotide recognition. Possible strategies for achieving this goal are based on functionalizing the electrodes
with various chemical agents (including nucleobases themselves for example), which interact differently with the different nucelobases
\citep{Ohshiro2006, Meunier2008, He2007, He2008}. Yet, the functionalization may be extremely challenging in particular if this
needs to be selective at the length scale of the typical nanopore (a few nm). Here we use a different strategy that does not involve
any chemical functionalization and considers single-walled close-ended (6,6) CNT electrodes placed at an ultra-short distance
[see Fig. \ref{Fig:CNT-Device}~(a)]. An important feature of these electrodes is that the benzene-like six-membered ring at the
closed end cap provides the possibility of $\pi$-$\pi$ coupling with the nucleobases, as ssDNA is transmigrated across. Importantly
the $\pi$-$\pi$ channel forces the nucleotides to align flat with respect to the electrode cap so that conformal fluctuations are
highly suppressed. Our work analyses in detail the electron transport in this favourable condition and propose a protocol for
distinguishing the nucleotides.
In short our computational strategy unfolds as follows. We first overview the general characteristics of the transmission coefficient
as a function of energy for the four nucleotides sandwiched between two such electrodes. Then we search for the optimal molecular
configurations of the nucleotides about the electrodes. For these configurations the electronic coupling is maximized and so is the
low bias current. The electronic structure, the zero-bias transmission coefficients, and the $I$-$V$ curves for all the nucleotides are
analyzed next at the resulting optimal configurations. Finally we calculate the transmission coefficient profiles along the full DNA
translocation path and propose a DNA sequencing protocol combining multiple data analysis. A method and a conclusion section
complete this work.
\section{Method}
\label{sec:Method}
The device proposed here consists of a pair of semi-infinite close-ended CNT (6,6) electrodes aligned along the $z$-axis,
and embedded inside a Si$_{3}$N$_{4}\,$ nanopore [see Fig.~\ref{Fig:CNT-Device}]. The separation between the CNTs' caps is initially
only $6.6$~\AA\ (this will be then optimized as described later). Since the carbon van der Waals radius
is about $1.7$~\AA, one may expect that the small space between the electrodes will only accommodate the planar nucleobases
with their base plane parallel to the plane of CNT end caps, but not the non-planar sugar ring and phosphate groups.
This is indeed confirmed by molecular dynamics (MD) simulations performed with empirical potentials for a ssDNA pulled
through a Si$_{3}$N$_{4}\,$ nanopore [see the snapshot in Fig. \ref{Fig:CNT-Device}(b)], from which we find that in general the
nucleobases pass the gap between the CNTs approximately as indicated Fig. \ref{Fig:CNT-Device}(a). A detailed description of the
MD simulations for the DNA translocation is outside the scope of the present paper and it will be published elsewhere. Here we focus
only on the transport properties of the ideal case. We note that not only does such a setup minimize the structural fluctuations during
translocation, but it also leads to an effective $\pi$-$\pi$ bonding and to a strong electronic coupling between the nucleotides and both
the electrodes. We therefore expect a much larger current than that for systems where the nucleotides are oriented perpendicular to
the electrodes, i.e. for the setup considered in several other studies\citep{He2008, Prasongkit2010, Meunier2008}.
\begin{figure}
\center
\includegraphics*[width=3.25in,clip=true]{./Fig1}
\caption{The device setup considered in this work. In (a) we present the CNT/pXp/CNT (X=A, C, G, and T) junction used to
calculate the electron transport. The left- and right-hand side (6,6) CNT electrodes are semi-infinite and periodic along the transport
direction ($z$-axis). In the scattering region the pXp molecules are sandwiched between the CNTs. A few layers of carbon atoms
of both the CNTs are included in the scattering region allowing the convergence of charge density at the boundaries with the
semi-infinite electrodes. In (b) a typical MD snapshot of the entire device, where the CNT electrodes are embedded into a
Si$_{3}$N$_{4}\,$-based nanopore [sketched by the circle in panel (a)], and an 11-base oligo-deoxyriboguanosine translocates through
the nanopore (grey, cutaway view). The single-stranded DNAs translocate through the nanopore along the $x$-axis. A guanine base
can be seen passing the gap between CNTs. Water and electrolyte ions are not displayed for clarity.}
\label{Fig:CNT-Device}
\end{figure}
The four nucleotides commonly found in DNA are represented by four neutral chemical species, namely, adenosine 3'-phosphate-5'-phosphate
(pAp), cytidine 3'-phosphate-5'-phosphate (pCp), guanosine 3'-phosphate 5'-phosphate (pGp) and thymidine 3'-phosphate-5'-phosphate (pTp).
The two phosphate groups at both sides of each nucleobase are included in order to approximate the nearest
chemical environment. In the initial configurations, each of the pXp (X=A, C, G, and T) molecules is sandwiched between the two
CNT end caps, with their nucleobase mass centers coinciding with the origin. This is defined as the middle point of the electrode
gap and the bonds connecting the sugar ring and the nucleobases aligned along the $y$-axis. We assume that the nucleotides
translocate along the $x$-axis. The unit cell size is set so that the distance between molecules in neighboring cells is at least
$20$~\AA, along both the $x$ and $y$ direction (we use periodic boundary conditions in the direction orthogonal to that of the
transport, namely in the $x$-$y$ plane).
The computation of the transmission coefficients ($T$) and the current-voltage ($I$-$V$) characteristics is performed by using
the \textit{ab initio} electronic transport code {\sc Smeagol}\cite{Rocha2005,Rocha2006,Rungger2008}. {\sc Smeagol} implements
the non-equilibrium Green's function (NEGF) method over density functional theory (DFT), by using the pseudopotential code
{\sc Siesta} \cite{Soler2002} as its electronic structure platform. In {\sc Smeagol} the device under investigation is partitioned into
three regions: the left- and right-hand side semi-infinite current-voltage electrodes, and the scattering region
[see Fig.~\ref{Fig:CNT-Device}(a)]. In our calculations the scattering region comprises 156 and 144 carbon atoms respectively
of left- and right-hand side CNT electrodes, and one of the pXp molecules. The portion of the electrodes included explicitly in
the scattering region is large enough to ensure that the calculated charge density at the outermost layers converges to that of
bulk the CNTs.
Both the electronic structure and the transport properties are calculated with the local density approximation (LDA) of the DFT
exchange and correlation functional. A double-$\zeta$ plus polarization basis sets is used for C($2s2p$), N($2s2p$),
O($2s2p$), P($3s3p$) and H($1s$) throughout. All calculations are carried out with an equivalent real space mesh cutoff
of $300$~Ry and an electronic temperature of $300$~K. In {\sc Smeagol} the charge density is evaluated by separating the
integral over the non-equilibrium Green's function into an equilibrium part, which is performed along a contour in the complex
energy plane, and a non-equilibrium part, which is performed along the real energy axis~\cite{Rocha2006}. For the first we use 16
energy points on the complex semi-circle, 16 points along the line parallel to the real axis and 16 poles. The integral over real energies
necessary at finite bias is evaluated over a mesh, whose energy spacing is not larger than 1~meV~\cite{Rocha2005,Rocha2006}.
\section{\label{sec:Results}Results and discussion}
\subsection{\label{sec:TatFermiLevel}General characteristics of the transmission at zero bias}
We first examine the general transport properties of all the possible four CNT/pXp/CNT (X=A, C, G, and T) junctions by plotting,
in Fig.~\ref{Fig:InitialConfig-Tat0V}, the zero-bias transmission coefficient as function of energy for the initial geometries,
where the nucleobases' center of mass coincides with the middle point of the electrode gap. Electron tunneling between
the CNT electrodes ($6.6$~\AA\, apart in these initial simulations) through vacuum (we denote this configuration as
CNT//CNT) is extremely small ($T\sim1.3\times10^{-12}$) around the Fermi level, $E_\mathrm{F}$. Note that the linear
response (zero-bias) conductance, $G$, is simply $G=G_0\:T({E_\mathrm{F}})$, where $G_0=2e^2/h$ is the quantum
conductance, $e$ is the electronic charge and $h$ the Planck constant, so that a tiny $T({E_\mathrm{F}})$ is equivalent
to a small linear response conductance.
\begin{figure}
\center
\includegraphics*[width=9.0cm,clip=true]{./Fig2}
\caption{Zero-bias transmission coefficient as a function of energy for CNT//CNT and the four CNT/pXp/CNT (X=A, C, G, and T)
junctions. The curves refer to the initial configurations where the nucleobase' center of mass coincides with the middle
point of the electrode gap. The CNT electrodes are $6.6$~\AA\ apart.}
\label{Fig:InitialConfig-Tat0V}
\end{figure}
The inclusion of the pXp molecules in the device results in an increase of the transmission coefficient by over eight orders of magnitude with typical
values of $T(E_\mathrm{F})$ of around 10$^{-4}$--10$^{-3}$. We therefore expect in general a drastic change in the measured current
when a nucleotide passes between the CNT electrodes, regardless of the nucleotide type. As such our device is at least capable
of distinguishing whether or not a molecule is between the two electrodes. Notably the magnitude of the transmission coefficient at
$E_\mathrm{F}$ is found to be orders of magnitude larger than that found by using either functionalized gold
($\sim10^{-6}$)~\cite{He2008} or graphene ($>10^{-10}$)\cite{Prasongkit2010} electrodes (in both cases
the calculations have been carried out with {\sc Smeagol} using similar computational parameters). Clearly our much larger
tunneling current originates from the short electrode-electrode separation and by the fact that the nucleobases lie flat
between the electrodes.
In the various $T(E)$ profiles there are peaks, as the one clearly visible at 0.5~eV, common to all the junctions. All of these are very pronounced and
extremely sharp and they are characteristic of the CNT//CNT device as well (see peaks at $-2.61$~eV, $-1.64$~eV, $-1.48$~eV and $1.95$~eV, with all
the energies taken with respect to the CNT $E_\mathrm{F}$). These are all due to localized surface states
of the close-ended CNTs and therefore are not representative of any feature of the nucleotide electronic structure. Such CNT surface
states can be readily identified by comparing the density of states (DOS) of an infinite CNT with the one of the semi-infinite
close-ended CNT, shown in Fig.~\ref{Fig:InitialConfig-DOS}.
\begin{figure}
\center
\includegraphics*[width=8.5cm,clip=true]{./Fig3}
\caption{Density of states (DOS) of a (6,6) CNT electrode and of both the CNT//CNT and the CNT/pAp/CNT junctions
as function of energy for the initial configurations. CNT/pAp/CNT is chosen as a representative of the CNT/pXp/CNT
junctions.}
\label{Fig:InitialConfig-DOS}
\end{figure}
For all the CNT/pXp/CNT junctions investigated we can identify two distinct transport regimes (Fig.~\ref{Fig:InitialConfig-Tat0V}):
a tunneling regime for energies between $-1.0$~eV and $1.5$~eV, and a resonant transport regime through
the nucleotides' molecular levels for energies outside this range. Around $E_\mathrm{F}$, the transmission curves for all the
nucleotides are very smooth and vary little over energy. Importantly, the relative order of magnitude of the transmission coefficients,
namely $T_\mathrm{pAp}$ $>$ $T_\mathrm{pGp}$ $>$ $T_\mathrm{pCp}$ $>$ $T_\mathrm{pTp}$, is preserved for a rather
large energy range around the Fermi level. This indicates that it is possible to distinguish the nucleotides already in the
low-bias tunneling regime, and that the recognition is relatively robust with respect to fluctuations in the position of $E_\mathrm{F}$.
Furthermore the flatness of the transmission coefficient around $E_\mathrm{F}$ suggests that one
can infer the current for voltages up to about 1~V from the simple relation $I\approx T(E_\mathrm{F})V$. Therefore, in the next
section we will analyze the transport properties at the Fermi energy only, and search for the molecular configurations of
the CNT/pXp/CNT junctions that yield the largest transmission at the Fermi energy. When these configurations are explored by the ssDNA
during the translocation process they will provide the largest contribution to the current.
\subsection{\label{sec:SearchConfigs}Search for the molecular configurations yielding the maximum transmission}
For the device setup investigated here we have identified four possible degrees of freedom, which determine the relative
position of the pXp molecules with respect to the electrodes: (1) the rotation angle of pXp around the $z$-axis [up to $60^\circ$
due to the (6,6) CNT symmetry], (2) a translation of the pXp molecules about the $y$- and (3) the $x$-axis and (4) a variation of the
distance between the two CNT electrodes. Here we assume that the internal structure of the pXp molecules does not deform and
that the nucleobases remain parallel to the CNT end cap planes during the translocation.
In section \ref{sec:ConfigutationEffect} we will discuss in details the effects of these operations on the electron transport; here we first
identify the configurations which maximize the transmission at $E_\mathrm{F}$. To this goal we start from the initial configurations of the
CNT/pXp/CNT junctions, defined in Sec.~\ref{sec:Method}, and perform all the possible independent rotations and translations.
Interestingly and importantly, we find that the molecular configurations having the largest transmission coefficients are generally found
to be close to those which minimize the system energy. This is due to the fact that when the $\pi$-$\pi$ interaction between the nucleotides
and the CNTs is large the total energy is generally minimized and the transmission maximized.
We first determine the optimal distance between the CNTs. The guiding principle for the optimization is that the transmission is expected
to increase for decreasing CNT separation, but the separation needs to be large enough to allow the translocation of the nucleotides.
In any hypothetical fully operational device the CNT electrodes' position is fixed as these are embedded in the nanopore, so that we
have to find a separation which is optimal for all the four nucleotides. In particular the electrodes gap should be wide enough to allow
also the non-planar methyl group on thymine to pass through. In order to determine the optimal distance between the CNT electrodes we then
fix the molecule in the lateral position (in the $x$-$y$ plane) that yields the largest transmission at a CNT separation of 6.6~\AA\ and then change
the separation between the electrodes, always keeping the molecule in the middle of the gap.
\begin{figure}
\center
\includegraphics*[width=8.5cm,clip=true]{./Fig4}
\caption{Total energy as function of the distance between the CNT electrodes, $d_\mathrm{CNT-CNT}$, for the
CNT/pXp/CNT junctions (X=A, C, G, and T). The energy zero is taken at the lowest energy calculated.}
\label{Fig:EvsCNTDistance}
\end{figure}
We examine first the junction total energy as function of the separation between the CNT caps (see Fig.~\ref{Fig:EvsCNTDistance}). The
smallest possible CNT electrodes gaps can be seen to be approximately $5.8$~\AA, since there is a sharp increase of the energy for
closer separations regardless of the nucleotide type. Considering that the optimal distance may be underestimated by DFT calculations
in which the van der Waals interactions (which tends to be repulsive at short distances) are not included, and that we should use a
common distance for all four CNT/pXp/CNT junctions, in all subsequent calculations we assume that the device has been set up with
a distance of $6.4$~\AA\ between the two CNT electrodes. For this electrodes distance the molecular configurations of the four
CNT/pXp/CNT junctions yielding the maximum transmission at $E_\mathrm{F}$\ are summarized in Table~\ref{Tab:PreferredConfig} in terms of
the geometrical offset relative to their initial configurations. We denote these configurations as the {\it optimal configurations}.
\begin{table}
\caption{Optimal molecular configurations, which lead to maximal transmission at $E_\mathrm{F}$,
for the four CNT/pXp/CNT junctions (X=A, C, G, and T), relatively to the initial
configurations. $\theta$ is the right-hand rotation angle of the nucleobases about the
$z$-axis. The distance between the CNTs for optimal configurations is chosen to be commonly $6.4$~\AA.}
\begin{center}
{\small
\begin{tabular}{p{100pt}p{30pt}p{30pt}p{30pt}p{30pt}}\hline
& pAp & pCp & pGp & pTp \\ \hline
$\theta$ & $14.32^\circ$ & $12.28^\circ$ & $14.28^\circ$ & $11.08^\circ$\\
Offset $y$(\AA) & $-0.21$ & $-0.14$ & $-0.09$ & $ 0.03$ \\
Offset $x$(\AA, peak 1)& $-0.05$ & $-2.13$ & $-0.58$ & $-1.88$ \\
Offset $x$(\AA, peak 2)& $--$ & $ 1.01$ & $--$ & $ 1.19$ \\
\hline
\end{tabular}}
\end{center}
\label{Tab:PreferredConfig}
\end{table}
\begin{figure}
\center
\includegraphics*[width=8.5cm,clip=true]{./Fig5}
\caption{Optimal molecular configurations for the CNT/pXp/CNT junctions (X=A, C, G, and T). For pCp and pTp the
two equivalent configurations are both shown.}
\label{Fig:PreferredConfig}
\end{figure}
An interesting result of our search for the optimal configurations is that pCp and pTp turn out to have two configurations where
the transmission coefficient peaks (see figure~\ref{Fig:PreferredConfig} for a graphic representation of all the optimal configurations).
In these the smaller pyrimidine bases of the cytosine and thymine are located at either side of the CNT electrodes along the $x$-axis.
In contrast, pAp and pGp appear to have only one major peak, and the configuration is such that the larger purine bases of adenine
and guanine are located in the center of electrodes gap. This difference between purine and pyrimidine bases results in distinct profiles
of the transmission coefficient along the ssDNA translocation direction (see later in Section~\ref{sec:TalongTranslocation}). In the
calculations that will follow we will consider always the configuration responsible for the first of the transmission peaks for the
CNT/pCp/CNT and CNT/pTp/CNT junctions.
\subsection{\label{sec:ElectronicStructure}Electronic structure and zero-bias transmission at the optimal configurations}
In order to understand the details of the electron transfer across the CNT/pXp/CNT (X=A, C, G and T) junctions, we now analyze the
relation between the transmission and the electronic structure of the devices at their optimal configurations. In
Fig.~\ref{Fig:Preferred-PDOS-Tat0V-pXp} we plot the zero-bias transmission coefficient and the DOS of the pXp molecules
forming the CNT/pXp/CNT junctions. The vertical dashed lines indicate the energies of the eigenvalues of the isolated pXp
nucleotides, i.e. they correspond to the DOS of the isolated molecules. From the figure it is clear that the eigenvalues
of the isolated molecules align well with the peaks in the DOS of the corresponding junction (note that a global shift is applied
in order to align the highest occupied molecular orbital -HOMO- of the molecule in the gas phase to that in the junciton).
This is indicative of the fact that the molecule-electrode interaction does not involve charging, so that the molecule spectrum is
not distorted in any significant way. However the DOS of the junctions reveals a considerable level broadening, suggesting that there
is a substantial overlap between the molecular orbitals of the nucleotides and the extended states of the electrodes.
\begin{figure}
\center
\includegraphics*[width=9cm,clip=true]{./Fig6}
\caption{Zero-bias transmission coefficient as function of energy and corresponding density of states (DOS)
projected onto the pXp molecules for the four CNT/pXp/CNT junctions. In the panels showing the DOS
we also present, as dashed vertical lines, the DOS of the pXp molecules in the gas phase.}
\label{Fig:Preferred-PDOS-Tat0V-pXp}
\end{figure}
This strong overlap is responsible for the high transmission and Fig.~\ref{Fig:Preferred-PDOS-Tat0V-pXp} reveals a one to one
correspondence between the molecule DOS and the peaks in the transmission functions. In particular for all the four junctions the
HOMO and the lowest unoccupied molecular orbital (LUMO), both located on pXp molecules, are far away from the electrodes'
Fermi level. As such the tunneling transmission region around $E_\mathrm{F}$\ corresponds to the molecule HOMO-LUMO gap. A summary
of the energy position of both the HOMO and the LUMO of the four junctions is presented in Table~\ref{Tab:pXp-HOLU}.
\begin{table}
\caption{Energy position of the HOMO and the LUMO of the pXp molecules in their corresponding CNT/pXp/CNT junctions
(X=A, C, G, and T).}
\begin{center}
{\small
\begin{tabular}{p{50pt}p{40pt}p{40pt}p{40pt}p{40pt}}\hline
& pAp & pCp & pGp & pTp \\ \hline
HO (eV) & $-1.86$ & $-1.65$ & $-1.40$ & $ -1.98$ \\
LU (eV) & $ 2.06$ & $ 1.81$ & $ 2.42$ & $ 1.78$ \\ \hline
\hline
\end{tabular}}
\end{center}
\label{Tab:pXp-HOLU}
\end{table}
At the optimal configurations (see Fig.~\ref{Fig:PreferredConfig}) the pXp molecules are strongly coupled to the CNT electrodes,
through the optimal $\pi$-$\pi$ coupling of the nucleobases with the CNT end caps. In order to visualize such a $\pi$-$\pi$
bond, we calculate the real space local density of states (LDOS) associated to the charge density of both the HOMO and the LUMO
of the CNT/pXp/CNT junctions. For the HOMO (LUMO) we integrate the charge density over an energy window $45$~meV ($50$~meV)
wide around the associated peak in the DOS. The results are shown in Fig.~\ref{Fig:Preferred-HOLU}, where the $\pi$-$\pi$ bonds
are clearly visible. The face-to-face $\pi$-$\pi$ stacking of the six-member rings of the CNT end caps with the nucleobases not only
makes the optimal configurations energetically favorable, but also enhances the electron tunneling. Since the $\pi$-$\pi$ interaction
disappears when the nucleobases are outside the central region in between the electrodes, one may expect that the distribution of
transmission coefficients (and hence the currents) should peak when the nucleotides are inside such a region and that the high
transmission configurations should be rather stable.
\begin{figure}
\center
\includegraphics*[width=9cm,clip=true]{./Fig7}
\caption{Local density of state (LDOS) isosurfaces of the HOMO and LUMO of the CNT/pXp/CNT junctions at zero-bias. The
geometries corresponds to the optimal configurations.}
\label{Fig:Preferred-HOLU}
\end{figure}
Importantly the $\pi$-$\pi$ interaction of the pXp (X=A, C, G, and T) molecules with the CNTs involves only the nucleobases.
This means that the sugar ring and two nearest phosphate groups in pXp do not play any significant r\^ole either in the bonding or in the
electron transport. A demonstration of this feature is provided in Fig.~\ref{Fig:Preferred-PDOS-pXp-Components}, where we present the
DOS projected respectively onto the nuclebase, the sugar and the phosphate groups. From the figure it is clear that both the HOMO and the LUMO
are almost entirely associated to the nuclebases, while both the sugar and the phosphate groups contribute only to molecular levels far way from the
Fermi level. This is a rather important aspect of the electronic structure of the DNA/CNT system investigated here, namely the fact that the
non-sequence specific features of the DNA spectrum are away from the electrodes Fermi level and therefore are not expected to
contribute significantly to the transport at least at relatively moderate voltages.
\begin{figure}
\center
\includegraphics*[width=9cm,clip=true]{./Fig8}
\caption{Density of states (DOS) projected onto the base, the sugar and the phosphates of the various pXp molecules in the CNT/pXp/CNT junctions,
calculated at zero-bias at the optimal configurations.}
\label{Fig:Preferred-PDOS-pXp-Components}
\end{figure}
Finally we wish to investigate further which functional part of the nucleotides contributes the most to the $\pi$-$\pi$ bonding by looking at the DOS
projected either on the amine (NH$_2$) or the carbonyl (C=O) group (see Fig.~\ref{Fig:Preferred-PDOS-pXp-NH2CO}). Note that pAp, pCp and pGp
have one primary amine group, pCp and pGp have one carbonyl and finally pTp has two carbonyls. From Fig.~\ref{Fig:Preferred-PDOS-pXp-NH2CO}
we note that for pAp, the primary amine group contributes the most to the HOMO, with a major peak in the DOS at around $-1.86$~eV and minor peaks at around
$-1.66$~eV and $-1.44$~eV. These form because of the coupling to the CNT electrodes. The presence of such minor peaks helps to explain why at zero-bias pAp has the largest
transmission coefficient despite its major HOMO peak lies below those of pCp and pGp (Table~\ref{Tab:pXp-HOLU}). In contrast for pCp, the carbonyl group
contributes more than the primary amine one to the HOMO, while for pGp these two groups contribute similarly to their HOMO. The main peaks of the
carbonyl groups appear to be similar for pGp and pTp (around $-2$~eV) but these are located at higher energies for pCp (around $-1.65$~eV). The
different positioning and strength of the electronic states located on these functional groups are important, since they affect the tunneling signals for the different
nucleobases. Their characteristic signals may be augmented by functionalizing the electrodes with suitable chemical agents in order to amplify the
electronic contrast between the different nucelobases\citep{Ohshiro2006, He2007, He2008}.
\begin{figure}
\center
\includegraphics*[width=3.25in,clip=true]{./Fig9}
\caption{Density of states (DOS) projected onto the amine and carbonyl groups of the various pXp molecules in the CNT/pXp/CNT junctions,
calculated at zero-bias at the optimal configurations.}
\label{Fig:Preferred-PDOS-pXp-NH2CO}
\end{figure}
\subsection{$I$-$V$ characteristics at the optimal configurations}
\label{sec:TransportProperties}
We now investigate the transport properties of the pXp molecules (X=A, C, G, and T) by assuming that these are ideally measured at the optimal configurations.
Fig.~\ref{Fig:Preferred-Tat0V} shows the zero-bias transmission coefficient, $T(E)$, plotted on a logarithmic scale. As noted previously, the peaks in transmission
at around $0.5$~eV are due to localized surface states belonging to the CNT close-ends. These are unaffected by the pXp configuration and
they contribute little to the electron current as bias is applied (for a discussion on the resonant transport properties of surface localized state see reference
[\onlinecite{IvanTMR}]).
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig10}
\caption{Zero-bias transmission coefficient as a function of energy for CNT/pXp/CNT (X=A, C, G, and T) junctions at the optimal configurations.}
\label{Fig:Preferred-Tat0V}
\end{figure}
At the Fermi level the relative order of magnitude of the transmission coefficient is now $T_\mathrm{pAp}$ $>$ $T_\mathrm{pGp}$ $>$ $T_\mathrm{pCp}$ $>$ $T_\mathrm{pTp}$,
i.e. it is the same order that we have found for the initial configurations (see Fig.~\ref{Fig:InitialConfig-Tat0V}). However, if one now looks at energies away from $E_\mathrm{F}$
a few changes are notable. For instance at $-0.77$~eV (energies are always taken from $E_\mathrm{F}$) the transmission coefficient of pGp surpasses that of pAp and the
order becomes $T_\mathrm{pGp}$ $>$ $T_\mathrm{pTp}$ $>$ $T_\mathrm{pAp}$ $>$ $T_\mathrm{pCp}$. In contrast for positive energies $T_\mathrm{pTp}$ and
$T_\mathrm{pCp}$ first surpass $T_\mathrm{pGp}$ at $0.5$~eV and then $T_\mathrm{pAp}$ at $1.07$~eV. In the region $[1.1, 1.8]$~eV, the order is now
$T_\mathrm{pTp}$ $>$ $T_\mathrm{pCp}$ $>$ $T_\mathrm{pAp}$ $>$ $T_\mathrm{pGp}$, which roughly reflects the energy order of the various LUMOs
(Table~\ref{Tab:pXp-HOLU}). Such a rather sensitive energy dependence of the order of the transmission coefficients for the various molecules reflects the fact
that the nucleotides are electronically rather similar. However, we will show that the $I$-$V$ curves offer a reasonable voltage range where the molecules can be
distinguished.
The calculated $I$-$V$ curves in the moderate bias range [-1, 1]~Volt are presented in Fig.\ref{Fig:Preferred-IV-LowBias}. In this particular bias window the transport
is well within the tunneling regime, since there are no peaks in the transmission attributable to any pXp molecular orbitals (see Fig. \ref{Fig:Preferred-Tat0V}). Importantly
in this moderate bias region the order of the currents amplitude is the same as that of the transmission coefficients at the Fermi level, namely
$I_{\textrm{pAp}} > I_{\textrm{pGp}} > I_{\textrm{pCp}} > I_{\textrm{pTp}}$. This is persistent throughout the entire bias values investigated, suggesting that a current
measurement in this range should be able to distinguish between the nucleotides. Furthermore, the current curves in Fig.\ref{Fig:Preferred-IV-LowBias} are well spaced
when the bias is between $0.7$~V and $1$~V, a bias interval which therefore emerges as the ideal probing voltage range. We note that recently Tsutsui $et\:al.\:$ reported a similar trend,
namely $I_{\textrm{G}} > I_{\textrm{C}} > I_{\textrm{T}}$, for the peak currents of single nucleotides measured by two gold nanoelectrodes at a constant dc bias of
$0.75$~V \citep{Tsutsui2010}.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig11}
\caption{$I$-$V$ characteristics for the CNT/pXp/CNT (X=A, C, G and T) junctions at the optimal configurations in the [-1, 1]~Volt bias range.}
\label{Fig:Preferred-IV-LowBias}
\end{figure}
In Fig.~\ref{Fig:Preferred-IV-FullRange} the $I$-$V$ curves for the same configurations are shown over an extended bias window ranging now from $-4$~V to $4$~V.
From the figure we can clearly identify the transition from tunneling to a resonant transport regime at about $\pm 3$~V for all nucleotides. This is the voltage which
coincides with a drastic increase of the current. For voltages larger than $3.5$~V and smaller than $-3.5$~V, the current signals associated to the different nucleotides
have a steady order, namely $I_{\textrm{pGp}} > I_{\textrm{pTp}} > I_{\textrm{pCp}} \sim I_{\textrm{pAp}}$ (Fig.~\ref{Fig:Preferred-IV-FullRange}). Also notable is the
fact that the $I$-$V$ characteristics are approximately symmetric with respect to the bias polarity, since the nucleotides are placed in the middle of the gap between
the CNT electrodes.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig12}
\caption{$I$-$V$ characteristics for the CNT/pXp/CNT (X=A, C, G and T) junctions at the optimal configurations in the [-4, 4]~Volt bias range.}
\label{Fig:Preferred-IV-FullRange}
\end{figure}
\subsection{\label{sec:TalongTranslocation}Transmission profile of nucleotides along the translocation path}
In the discussion presented in the previous section, each of the four nucleotides is placed at the optimal configuration in the corresponding
CNT/pXp/CNT (X=A, C, G, and T) junction. We now examine the evolution of the transport properties of the nucleotides when they translocate through
the gap between the CNT electrodes along the $x$-axis. This is precisely the motion that the nucleotides will undergo in a nanopore experiment
(Fig.~\ref{Fig:CNT-Device}). For simplicity, the pXp molecules, which have limited conformational flexibility near the $6.4$~\AA-wide electrode gap,
are assumed to be rigid. Their positions are measured as the distance between the nucleotide center of mass and the mid-point of CNT electrodes.
Fig.~\ref{Fig:TranslocationX-ACGT-Tat0V} shows the profiles of the transmission coefficient at the Fermi level, $T(E_\mathrm{F})=T_{0}$, along the nucleotides'
translocation paths, with the peaks appearing at the optimal configurations [see Table~\ref{Tab:PreferredConfig}]. As already mentioned in Section~\ref{sec:SearchConfigs},
one can clearly see that the profiles of pCp and pTp are distinguishable from those of pAp and pGp by having one more pronounced transmission peak.
The double peak structure arises from the two nearly degenerate optimal configurations, that both pAp and pGp possess because of their different
symmetry. Since both the cytosine and the thymine base can be flipped before entering the electrode gap, the order and the relative magnitude of these
two peaks can be reversed. In addition we also note that the profile of pGp appears to have a broad shoulder, indicative of a second high transmission configuration
along the translocation path. From Fig.~\ref{Fig:TranslocationX-ACGT-Tat0V} we also observe that the transmission coefficient decays sharply once the nucleotides
is moved outside the electrodes gap. Notably the radius of the (6,6) CNT is about $4.1$~\AA\ while the distance between adjacent nucleotides in a stretched ssDNA
is about $7$~\AA. As the tails of the transmission coefficient curves are quite small when $x<-3.5$~\AA\, or $x>3.5$~\AA~(i.e., when the nucleobase is outside of
electrodes gap), we conclude that having nucleotides in a sequence should not affect much the reading of the tunneling current of a single nucleotide.
We next integrate $T_0$ along the translocation path to obtain the aggregate transmission coefficient (denoted as $AT$). Our results are summarized in
Table~\ref{Tab:TranslocationX-AggregateT}. $AT$ over the path $-3.5<x<3.5$~\AA\ accounts for 99~\%, 94~\%, 92~\% and 96~\% of the $AT$ calculated over the
more extended path $-8<x<8$~\AA, respectively for pAp, pCp, pGp and pTp. This is a further indication that most of the current is collected when the nucleobase
is within the CNT region and that adjacent nucleobases are far enough not to affect the measurement. Similar conclusions have been reached\cite{Zwolak2005}
for Au electrodes at separations smaller than 1~nm.
The aggregate transmission coefficient represents the time-average low-bias conductance over the translocation of each nucleotide, once we assume that the translocation
occurs at a constant velocity. Interestingly, we find a well spaced order in the $AT$, namely $AT_{\textrm{pAp}} > AT_{\textrm{pGp}} > AT_{\textrm{pCp}} > AT_{\textrm{pTp}}$,
both when the $AT$ is calculated within $\pm 3.5$~\AA\ or $\pm 8$~\AA\ from the electrode gap center. Notably the order of the integrated transmission corresponds to the
order found for the transmission at the optimal positions, which indeed dominate the transport during the translocation. More importantly this fact indicates that the
pAp$>$pGp$>$pCp$>$pTp order is recurrent in most of the transport measurements we have described and therefore it is a rather robust result of the geometry
investigated here.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig13}
\caption{Transmission coefficient at the Fermi level along the DNA translocation path.}
\label{Fig:TranslocationX-ACGT-Tat0V}
\end{figure}
\begin{table}
\caption{Aggregate transmission coefficient at the Fermi level along the DNA translocation path centered in the middle plane between the CNT electrodes (unit: $10^{-4}$~\AA).}
\begin{center}
{\small
\begin{tabular}{p{60pt}p{40pt}p{40pt}p{40pt}p{40pt}}\hline
& pAp & pCp & pGp & pTp \\ \hline
$\int_{-3.5}^{3.5} T_{0}\,dx$ & $17.03$ & $14.06$ & $15.81$ & $12.30$ \\
$\int_{-8.0}^{8.0} T_{0}\,dx$ & $17.24$ & $14.93$ & $17.19$ & $12.82$ \\
\hline
\end{tabular}}
\end{center}
\label{Tab:TranslocationX-AggregateT}
\end{table}
\subsection{\label{sec:ConfigutationEffect}Effect of molecular configurations on the transport properties}
In the previous discussion about the transmission profiles, we have assumed that the nucleotides translocate ideally along the $x$ direction without any lateral displacement within
the electrodes gap (along the $y$-axis). We now examine how $T_{0}$ varies when the nucleobases position fluctuates along the $y$ direction, by using the nucleobase center
of mass of the relative optimal configuration as origin, $y=0$. As it can be seen in Fig.~\ref{Fig:Factors-VariationInY}, $T_{0}$ decays quickly when the nucleobases move downwards away
from the electrodes (negative $y$). This is similar to what we have observed in Fig.~\ref{Fig:TranslocationX-ACGT-Tat0V} for a longitudinal displacement. Note that there is not
much room for positive $y$ displacement now as this will need the non-planar sugar ring and phosphate groups to enter the narrow electrodes gap. As such we stop the
calculations at $y=1.5$~\AA, which corresponds to the largest displacement possible along that direction.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig14}
\caption{Transmission coefficient at Fermi level for the CNT/pXp/CNT (X=A, C, G, and T) junctions as the nucleotides move along the $y$-axis.}
\label{Fig:Factors-VariationInY}
\end{figure}
Next we consider the effect of rotations of the pXp molecules about the $z$-axis. As shown in Fig.~\ref{Fig:PreferredConfig}, at the optimal configurations, the six-member ring
of the end cap in each of the CNT electrodes is parallel to the plane of the nucleobases. Moreover, the cap ring tends to align with the pyrimidine rings of the purine bases
(adenine and guanine) so that the corresponding hexagon edges are parallel to each other. In contrast the edges are staggered with the pyrimidine rings of cytosine and thymine so
that one of its vertex atoms faces the center of the pyrimidine. One may then expect that rotations may produce significant change in the low-bias conductance. This is however not
the case. In fact by plotting $T_0$ as a function of the rotation angle, $\theta$, (Fig.~\ref{Fig:Factors-CNT-Rotation}) we find only small changes, and most importantly also that the
order of the amplitudes of the conductance of the various nucleobases does not change. This essentially means that rotations about the optimal configurations will not undermine our
ability to identify the nucleobases.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig15}
\caption{Transmission coefficient calculated at the Fermi level for the CNT/pXp/CNT (X=A, C, G, and T) junctions as a function of the rotation of angle of the pXp molecules about the $z$-axis (vertical).}
\label{Fig:Factors-CNT-Rotation}
\end{figure}
Finally, we investigate the effects that the gap size between the CNT electrodes has on the transport by plotting $T_{0}$ as function of the electrode distance, $d_\mathrm{CNT-CNT}$ (Fig.~\ref{Fig:Factors-CNT-Distance}).
In this case we maintain the position of the plane containing the pXp molecules fixed at the midpoint between the electrodes. As expected from a tunneling process we find that the transmission
coefficient decreases exponentially with increasing $d_\mathrm{CNT-CNT}$. The figure~\ref{Fig:Factors-CNT-Distance} also shows that the exponential decay rate $\alpha$, defined as the slope of the
$\ln T (d)$ curves, is rather similar among the nucleotides. Interestingly $T_0$ for pAp is always well separated from that of the other nucleotides for all the electrode gap distances investigated. In contrast
the relative order between pCp, pGp and pTp depends on $d_\mathrm{CNT-CNT}$. It then emerges that it is absolutely crucial to maintain the electrode separation as stable as possible during
a measurement and also that this should be the smallest possible, so that configurational fluctuations will be highly suppressed.
\begin{figure}
\center
\includegraphics*[width=8cm,clip=true]{./Fig16}
\caption{Transmission coefficient at Fermi level for the CNT/pXp/CNT (X=A, C, G, and T) junctions as a function of the electrode separation, $d_\mathrm{CNT-CNT}$. Note that $T_0$ decays exponentially when $d_\mathrm{CNT-CNT}$
increases.}
\label{Fig:Factors-CNT-Distance}
\end{figure}
\subsection{\label{sec:SequencingProtocol}DNA sequencing protocol}
With all the results of the previous sections in mind we can now formulate a possible protocol for reading the nucleotide sequence. The proposed device functions by translocating ssDNA through a nanopore
and simultaneously by measuring the transverse current between two closely spaced CNT nanotubes [(6,6) close-ended CNTs at 6.4~\AA\ separation in our case]. The DNA strand can be pulled through
the nanopore mechanically by an optical or magnetic tweezer~\cite{Keyser2006, Peng2009} with an approximately constant velocity. Typical velocities for optical tweezers have been
reported~\cite{Keyser2006} at around 30~nm$\cdot$s$^{-1}$. This means that one need a time resolution in the kHz range in order to obtain a spatial resolution of 0.1~\AA, which is certainly enough for
detecting accurately the transmission profiles of the nucleotides shown in Fig.~\ref{Fig:TranslocationX-ACGT-Tat0V}. Note that the currents involved are of the order of 10~nA and we need an amplitude
resolution of the order of 1~nA or less (depending on the bias) for typical resistances of the order of 10~M$\Omega$. These are rather standard demands for conventional electronics.
In contrast if the ssDNA translocation is electrophoretically driven, then the velocity may fluctuate considerably so that the recognition of the current profiles may become difficult.
Furthermore the typical translocation velocities are much larger than those achievable by mechanical manipulations. For instance early studies\cite{Fologea2005} reported speeds of the order of
10$^6$~nm$\cdot$s$^{-1}$, which require GHz time-resolution for a sub-\AA\ spatial resolution. More recently a substantial slowing down has been achieved by gate modulation of the nanopore wall surface
charges, with reported velocities of 55~$\mu$m$\cdot$s$^{-1}$. This translates in a 5~MHz time resolution for 0.1~\AA\ spatial resolution. Clearly GHz frequencies are out of the reach, unless the typical
resistances are in the k$\Omega$ range, while MHz resolution may be possible. In any case we believe that for a usable device setup electrophoretically driven translocation
is not suitable at present, at least if the signal is made of the current profiles during translocation.
Further information however can be extracted by simply taking the integral over time of each current peak and/or successive peaks. These are acquired during the translocation of an entire
nucleobase across the gap between the electrodes. As such the time-resolution required is now about two orders of magnitude larger than that needed for resolving the profiles. This means
operating the device at $\sim$100~kHz frequencies for slow electrophoretically driven translocations.
Finally an alternative quantity to measure is, as proposed first by Zwolak $et\:al.\:$ \citep{Zwolak2005}, the statistical distribution of the current over time. This is a measure probably achievable only
with the tweezers setup and essentially consists in holding the ssDNA at a fixed position and then, after the system has thermally equilibrated inside the nanopore, in measuring the current.
We expect that the details of the current distributions may be device-dependent, but the peak currents of the nucleobases should maintain the order
$I_{\textrm{pAp}} > I_{\textrm{pGp}} > I_{\textrm{pCp}} > I_{\textrm{pTp}}$, at least in the suitable low bias range around $[0.7, 1]$~V.
\begin{figure}
\center
\includegraphics*[width=8.5cm,clip=true]{./Fig17}
\caption{Transmission coefficient at the Fermi level against the interaction energy for the CNT/pXp/CNT (X=A, C, G, and T) junctions along DNA translocation path.}
\label{Fig:TranslocationX-ACGT-TvsE}
\end{figure}
The statistical distributions of the transmission coefficient/current of the CNT/pXp/CNT junctions are yet to be calculated for our device (Fig.~\ref{Fig:CNT-Device}). However,
some insights can be obtained by plotting the $T_0$ together with the interaction energy between the pXp molecules and the CNT electrodes along the
translocation path. The interaction energy is defined as $\Delta E = E_{\textrm{pXp}}+E_{\textrm{CNT}}-E_{\textrm{CNT/pXp/CNT}}$, where $E_\alpha$
is the DFT total energy of the $\alpha$ system ($\alpha=$~pXp, CNT and CNT/pXp/CNT). Our results are shown in Fig.~\ref{Fig:TranslocationX-ACGT-TvsE}. The calculated
interaction energies are one order of magnitude larger than that for typical hydrogen bonding ($0.1-0.4$~eV). This is due to the strong $\pi$-$\pi$ interaction found in our device
at the optimal configurations. Interestingly, we find that the position of the maximum transmission corresponds approximately to the position displaying the largest interaction energy.
As such, one may expect that when a nucleobase passes through the device, it will tend to remain between the electrodes and parallel to the end caps of CNTs. In other words
the same interaction responsible for the relatively large currents and for the suppression of the geometry fluctuations also acts to slow down the DNA translocation
across the nanopore.
\section{\label{sec:Conclusions}Conclusions}
In summary we have proposed a device for high throughput DNA nanopore sequencing, based on reading the transverse current across the nucleobases of ssDNA as it passes between
two closely spaced single-walled close-ended (6,6) CNTs. The device operation has been investigated theoretically with state of the art density functional theory combined with non-equilibrium
quantum transport. In general the electron transport through the various nucleobases can be roughly separated into a tunneling regime at low bias and a resonant transport
one at higher bias. We have identified the optimal position of the various nucleotides yielding the highest zero-bias conductance and used them to analyze the various parameters affecting
the device. In particular we have focussed our attention on the dependence of the electron transmission on the longitudinal position of the nucleotides with respect to the center of the
electrodes, on possible lateral displacements and on the electrode separation.
The current/conductance profiles of the nucleotides along the DNA translocation path reveal that the pyrimidine bases (cytosine and thymine) have a two peaks structure, indicative
of two high transmission geometries. The same is not found for the other two bases. Importantly we have found that the peak tunneling currents of the nucleobases have the following
order $I_{\textrm{pAp}} > I_{\textrm{pGp}} > I_{\textrm{pCp}} > I_{\textrm{pTp}}$ at low bias and that the same order is maintained for the aggregate transmission coefficients.
Furthermore we have demonstrated that at this close electrode separation the current drops drastically as the nucleotides exit the electrodes region, so that well separated
current signals should be detected during the translocation.
Finally we have proposed a measurement protocol for rapid DNA sequencing. This is presently suitable for tweezer driven translocation and consists of three independent measurements.
The first involves the pattern recognition of the current profile during the translocation of the nucleobases. The second relies on the fact that the aggregate transmission coefficient (and hence the
integral of the current) along the translocation path has a well-defined order. Finally the third concerns the time-distribution of the current for mechanically stabilized junctions, where the
nucleotide to measure is held at a fixed position.
\begin{acknowledgments}
XC gratefully acknowledges the European Community's Seventh Framework Programme for financial support (Project: nanoDNAsequencing: NanoTools for Ultra Fast DNA Sequencing;
Grant agreement no.: 214840). Additional financial support has been provided by (CDP and SS) Science Foundation of Ireland (Grant No. 07/IN.1/I945) and (IR, US and SS) by the King Abdullah
University of Science and Technology (ACRAB project). Calculations have been performed on the Shaheen supercomputer at the King Abdullah University of Science and Technology.
Illuminating discussion with Nadjib Baadji are kindly acknowledged.
\end{acknowledgments}
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{"url":"https:\/\/www.physicsforums.com\/threads\/integral-of-a-function-on-a-cylinder.537118\/","text":"# Integral of a function on a cylinder\n\n## Homework Statement\n\nFind the integral of the function x^2 on a cylinder (excluding button and top)\nx^2 + y^2 = a^2,\n0 <= z <= 1\n\n## Homework Equations\n\n$\\int\\int\\int x^{2} dx dy dz$\n$x = a * cos \\Theta$\n$y = a * sin \\Theta$\n$z = z$\n\n## The Attempt at a Solution\n\nI'm not quite sure what to do but I give it a try.\n\nDetermine the Jacobian...\n\n$\\frac{(\\partial(x,y,z))}{(\\partial(a,\\Theta,z))}$ = a\n\nBy change of variables one gets:\n\n$\\int^{1}_{0}\\int^{2\\Pi}_{0}\\int^{a}_{0} a^{3}*cos^{2}(\\Theta) da d\\Theta dz = \\frac{\\Pi}{4}*a^4$\n\nIs this right or am I wrong? I guess I got stuck in the middle between parametrization, divergence, stokes, greens thm and simple integration.\n\nLast edited:\n\nFind the integral of the function x^2 on a cylinder (excluding button and top)\n\nTechnically this quesiton feels incomplete.\n\nSo you are looking for volume with f(x,y,z) = x^2 ?\n\nWhy do you only have on integral with three differentials??\n\nSorry that's all we got. That's the reason why I'm not sure what to do.\n\nOh my fault. Yes it should be three integrals.\n\nIt looks more like a surface integral to me but this means my calculations up there are incorect\n\nLast edited:\nAfter deeper consideration the only reasonable posibility is a surface integral.\nIn that case I do following:\nOne knows that $r^{\\rightarrow}(\\theta,z) = (a*cos(\\theta), a*sin(\\theta), z)$\n\nthen one gets\n\n$\\left\\|\\frac{\\partial r}{\\partial \\theta} \\times \\frac{\\partial r}{\\partial z}\\right\\| = a$\n\nfinally\n\n$\\int_{S}x^{2}dS =\\int^{2\\Pi}_{0}\\int^{1}_{0} a^{3}*cos^{2}(\\theta) dz d\\theta = \\pi a^{3}$","date":"2021-06-22 14:49:33","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\": 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\": 0.6188974380493164, \"perplexity\": 1601.7646661604424}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623488517820.68\/warc\/CC-MAIN-20210622124548-20210622154548-00142.warc.gz\"}"}
| null | null |
Q: Сортировка массива Помогите отсортировать массив.
Нужна сортировка по [count] от наибольшего значения.
Array
(
[response] => Array
(
[0] => Array
(
[pid] => 343215590
[likes] => Array
(
[user_likes] => 0
[count] => 38
)
)
[1] => Array
(
[pid] => 343215587
[likes] => Array
(
[user_likes] => 0
[count] => 60
)
)
)
)
A: usort
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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